diff --git a/Agda.cabal b/Agda.cabal
new file mode 100644
--- /dev/null
+++ b/Agda.cabal
@@ -0,0 +1,883 @@
+cabal-version:   2.4
+name:            Agda
+version:         2.6.4.2
+build-type:      Custom
+license:         MIT
+license-file:    LICENSE
+copyright:       (c) 2005-2024 The Agda Team.
+author:          The Agda Team, see https://agda.readthedocs.io/en/latest/team.html
+maintainer:      The Agda Team
+homepage:        https://wiki.portal.chalmers.se/agda/
+bug-reports:     https://github.com/agda/agda/issues
+category:        Dependent types
+synopsis:        A dependently typed functional programming language and proof assistant
+description:
+    Agda is a dependently typed functional programming language: It has
+    inductive families, which are similar to Haskell's GADTs, but they
+    can be indexed by values and not just types. It also has
+    parameterised modules, mixfix operators, Unicode characters, and an
+    interactive Emacs interface (the type checker can assist in the
+    development of your code).
+    .
+    Agda is also a proof assistant: It is an interactive system for
+    writing and checking proofs. Agda is based on intuitionistic type
+    theory, a foundational system for constructive mathematics developed
+    by the Swedish logician Per Martin-L&#xf6;f. It has many
+    similarities with other proof assistants based on dependent types,
+    such as Coq, Idris, Lean and NuPRL.
+    .
+    This package includes both a command-line program (agda) and an
+    Emacs mode. If you want to use the Emacs mode you can set it up by
+    running @agda-mode setup@ (see the README).
+    .
+    Note that the Agda package does not follow the package versioning
+    policy, because it is not intended to be used by third-party
+    packages.
+
+tested-with:
+    GHC == 9.8.1
+    GHC == 9.6.4
+    GHC == 9.4.8
+    GHC == 9.2.8
+    GHC == 9.0.2
+    GHC == 8.10.7
+    GHC == 8.8.4
+    GHC == 8.6.5
+
+extra-doc-files:
+    CHANGELOG.md
+    README.md
+    doc/user-manual/agda.svg
+    doc/release-notes/2.6.4.1.md
+    doc/release-notes/2.6.4.md
+    doc/release-notes/2.6.3.md
+    doc/release-notes/2.6.2.2.md
+    doc/release-notes/2.6.2.1.md
+    doc/release-notes/2.6.2.md
+    doc/release-notes/2.6.1.3.md
+    doc/release-notes/2.6.1.2.md
+    doc/release-notes/2.6.1.1.md
+    doc/release-notes/2.6.1.md
+    doc/release-notes/2.6.0.1.md
+    doc/release-notes/2.6.0.md
+    doc/release-notes/2.5.4.2.md
+    doc/release-notes/2.5.4.1.md
+    doc/release-notes/2.5.4.md
+    doc/release-notes/2.5.3.md
+    doc/release-notes/2.5.2.md
+    doc/release-notes/2.5.1.2.md
+    doc/release-notes/2.5.1.1.md
+    doc/release-notes/2.5.1.md
+    doc/release-notes/2.4.2.5.md
+    doc/release-notes/2.4.2.4.md
+    doc/release-notes/2.4.2.3.md
+    doc/release-notes/2.4.2.2.md
+    doc/release-notes/2.4.2.1.md
+    doc/release-notes/2.4.2.md
+    doc/release-notes/2.4.0.2.md
+    doc/release-notes/2.4.0.1.md
+    doc/release-notes/2.4.0.md
+    doc/release-notes/2.3.2.2.md
+    doc/release-notes/2.3.2.1.md
+    doc/release-notes/2.3.2.md
+    doc/release-notes/2.3.0.md
+    doc/release-notes/2.2.10.md
+    doc/release-notes/2.2.8.md
+    doc/release-notes/2.2.6.md
+    doc/release-notes/2.2.2.md
+    doc/release-notes/2.2.4.md
+    doc/release-notes/2.2.0.md
+
+extra-source-files:
+    stack-9.8.1.yaml
+    stack-9.6.4.yaml
+    stack-9.4.8.yaml
+    stack-9.2.8.yaml
+    stack-9.0.2.yaml
+    stack-8.10.7.yaml
+    stack-8.8.4.yaml
+    stack-8.6.5.yaml
+
+data-dir:
+    src/data
+
+data-files:
+    emacs-mode/*.el
+    html/Agda.css
+    html/highlight-hover.js
+    JS/agda-rts.js
+    JS/agda-rts.amd.js
+    latex/agda.sty
+    latex/postprocess-latex.pl
+    lib/prim/agda-builtins.agda-lib
+    lib/prim/Agda/Builtin/Bool.agda
+    lib/prim/Agda/Builtin/Char.agda
+    lib/prim/Agda/Builtin/Char/Properties.agda
+    lib/prim/Agda/Builtin/Coinduction.agda
+    lib/prim/Agda/Builtin/Cubical/Path.agda
+    lib/prim/Agda/Builtin/Cubical/Id.agda
+    lib/prim/Agda/Builtin/Cubical/Sub.agda
+    lib/prim/Agda/Builtin/Cubical/Glue.agda
+    lib/prim/Agda/Builtin/Cubical/Equiv.agda
+    lib/prim/Agda/Builtin/Cubical/HCompU.agda
+    lib/prim/Agda/Builtin/Equality.agda
+    lib/prim/Agda/Builtin/Equality/Erase.agda
+    lib/prim/Agda/Builtin/Equality/Rewrite.agda
+    lib/prim/Agda/Builtin/Float.agda
+    lib/prim/Agda/Builtin/Float/Properties.agda
+    lib/prim/Agda/Builtin/FromNat.agda
+    lib/prim/Agda/Builtin/FromNeg.agda
+    lib/prim/Agda/Builtin/FromString.agda
+    lib/prim/Agda/Builtin/IO.agda
+    lib/prim/Agda/Builtin/Int.agda
+    lib/prim/Agda/Builtin/List.agda
+    lib/prim/Agda/Builtin/Maybe.agda
+    lib/prim/Agda/Builtin/Nat.agda
+    lib/prim/Agda/Builtin/Reflection.agda
+    lib/prim/Agda/Builtin/Reflection/External.agda
+    lib/prim/Agda/Builtin/Reflection/Properties.agda
+    lib/prim/Agda/Builtin/Sigma.agda
+    lib/prim/Agda/Builtin/Size.agda
+    lib/prim/Agda/Builtin/Strict.agda
+    lib/prim/Agda/Builtin/String.agda
+    lib/prim/Agda/Builtin/String/Properties.agda
+    lib/prim/Agda/Builtin/TrustMe.agda
+    lib/prim/Agda/Builtin/Unit.agda
+    lib/prim/Agda/Builtin/Word.agda
+    lib/prim/Agda/Builtin/Word/Properties.agda
+    lib/prim/Agda/Primitive.agda
+    lib/prim/Agda/Primitive/Cubical.agda
+    MAlonzo/src/MAlonzo/*.hs
+    MAlonzo/src/MAlonzo/RTE/*.hs
+
+source-repository head
+  type:     git
+  location: https://github.com/agda/agda.git
+
+source-repository this
+  type:     git
+  location: https://github.com/agda/agda.git
+  tag:      v2.6.4.2
+
+-- Build flags
+---------------------------------------------------------------------------
+
+flag debug
+  default: False
+  manual: True
+  description:
+    Enable debug printing. This makes Agda slightly slower, and
+    building Agda slower as well. The --verbose=N option only
+    has an effect when Agda was built with this flag.
+
+flag debug-serialisation
+  default: False
+  manual: True
+  description:
+    Enable debug mode in serialisation. This makes serialisation slower.
+
+flag debug-parsing
+  default: False
+  manual: True
+  description:
+    Enable debug mode in parsing. This makes parsing slower.
+
+flag enable-cluster-counting
+  default: False
+  manual: True
+  description:
+    Enable the --count-clusters flag. (If enable-cluster-counting is
+    False, then the --count-clusters flag triggers an error message.)
+
+flag optimise-heavily
+  default: False
+  manual: True
+  description:
+    Enable some expensive optimisations when compiling Agda.
+
+-- Setup
+---------------------------------------------------------------------------
+
+custom-setup
+  setup-depends:
+    , base      >= 4.12.0.0 && < 4.20
+    , Cabal     >= 2.4.0.1  && < 3.11
+    , directory >= 1.3.3.0  && < 1.4
+    , filepath  >= 1.4.2.1  && < 1.5
+    , process   >= 1.6.3.0  && < 1.7
+
+-- Common stanzas
+---------------------------------------------------------------------------
+
+common language
+
+  if flag(optimise-heavily)
+    cpp-options:
+      -DOPTIMISE_HEAVILY
+    ghc-options:
+      -fexpose-all-unfoldings
+      -fspecialise-aggressively
+
+  ghc-options:
+      -- ASR (2022-05-31). Workaround to Issue #5932.
+      -Wwarn
+      -Wwarn=cpp-undef
+      -Wwarn=deprecated-flags
+      -Wwarn=deriving-typeable
+      -Wwarn=dodgy-exports
+      -Wwarn=dodgy-foreign-imports
+      -Wwarn=dodgy-imports
+      -Wwarn=duplicate-exports
+      -Wwarn=empty-enumerations
+      -Wwarn=identities
+      -Wwarn=inaccessible-code
+      -Wwarn=inline-rule-shadowing
+      -Wwarn=missing-fields
+      -Wwarn=missing-home-modules
+      -Wwarn=missing-methods
+      -Wwarn=missing-pattern-synonym-signatures
+      -Wwarn=missing-signatures
+      -Wwarn=noncanonical-monad-instances
+      -Wwarn=noncanonical-monoid-instances
+      -Wwarn=overflowed-literals
+      -Wwarn=overlapping-patterns
+--      -Wwarn=redundant-constraints
+      -Wwarn=semigroup
+      -Wwarn=simplifiable-class-constraints
+      -Wwarn=star-binder
+      -Wwarn=star-is-type
+      -Wwarn=tabs
+      -Wwarn=typed-holes
+      -Wwarn=unbanged-strict-patterns
+      -Wwarn=unrecognised-pragmas
+      -Wwarn=unrecognised-warning-flags
+      -Wwarn=unticked-promoted-constructors
+      -Wwarn=unused-do-bind
+      -Wwarn=unused-foralls
+      -Wwarn=warnings-deprecations
+      -Wwarn=wrong-do-bind
+
+  -- The following warning is an error in GHC >= 8.10.
+  if impl(ghc < 8.10)
+    ghc-options:
+      -Wwarn=implicit-kind-vars
+      -- #6623: Turn off this (nameless) warning:
+      -- "Pattern match checker exceeded (2000000) iterations in a case alternative."
+      -- See: https://gitlab.haskell.org/ghc/ghc/-/issues/13464
+      -Wno-incomplete-patterns
+      -Wno-overlapping-patterns
+
+  if impl(ghc >= 8.8)
+    ghc-options:
+      -Wwarn=missed-extra-shared-lib
+
+  if impl(ghc >= 8.10)
+    ghc-options:
+      -Wwarn=compat-unqualified-imports
+      -Wwarn=deriving-defaults
+      -Wwarn=redundant-record-wildcards
+      -Wwarn=unused-packages
+      -Wwarn=unused-record-wildcards
+
+  if impl(ghc >= 9.0)
+    ghc-options:
+      -Wwarn=invalid-haddock
+      -- #6137: coverage checker works only sufficiently well from GHC 9.0
+      -Wwarn=incomplete-patterns
+      -Wwarn=incomplete-record-updates
+      -Wwarn=overlapping-patterns
+
+  -- ASR (2022-04-27). This warning was added in GHC 9.0.2, removed
+  -- from 9.2.1 and added back in 9.2.2.
+  if impl(ghc == 9.0.2 || >= 9.2.2)
+    ghc-options:
+      -Wwarn=unicode-bidirectional-format-characters
+
+  if impl(ghc >= 9.2)
+    ghc-options:
+      -Wwarn=operator-whitespace
+      -Wwarn=redundant-bang-patterns
+
+  if impl(ghc >= 9.4)
+    ghc-options:
+      -Wwarn=forall-identifier
+      -Wwarn=type-equality-out-of-scope
+
+  default-language: Haskell2010
+
+  -- NOTE: If adding or removing default extensions, also change:
+  --         .hlint.yaml
+  default-extensions:
+      BangPatterns
+      BlockArguments
+      ConstraintKinds
+      --L-T Chen (2019-07-15):
+      -- Enabling DataKinds only locally makes the compile time
+      -- slightly shorter, see PR #3920.
+      -- DataKinds
+      DefaultSignatures
+      DeriveFoldable
+      DeriveFunctor
+      DeriveGeneric
+      DeriveTraversable
+      DerivingStrategies
+      ExistentialQuantification
+      FlexibleContexts
+      FlexibleInstances
+      FunctionalDependencies
+      GeneralizedNewtypeDeriving
+      InstanceSigs
+      LambdaCase
+      MultiParamTypeClasses
+      MultiWayIf
+      NamedFieldPuns
+      OverloadedStrings
+      PatternSynonyms
+      RankNTypes
+      RecordWildCards
+      ScopedTypeVariables
+      StandaloneDeriving
+      TupleSections
+      TypeFamilies
+      TypeOperators
+      TypeSynonymInstances
+
+  other-extensions:
+      CPP
+      DeriveAnyClass
+      PartialTypeSignatures
+
+
+-- Agda library
+---------------------------------------------------------------------------
+
+library
+  import:           language
+
+  hs-source-dirs:   src/full
+
+  -- Andreas, 2021-03-10:
+  -- All packages we depend upon should be mentioned in an unconditional
+  -- build-depends field, but additional restrictions on their
+  -- version for specific GHCs may be placed in conditionals.
+  --
+  -- The goal is to be able to make (e.g. when a new GHC comes out)
+  -- revisions on hackage, e.g. relaxing upper bounds.  This process
+  -- currently does not support revising conditionals.
+  --
+  -- An exceptions are packages that are only needed for certain configurations,
+  -- like for flags, Windows, etc.
+
+  if flag(debug)
+    cpp-options:    -DDEBUG
+
+  if flag(debug-serialisation)
+    cpp-options:    -DDEBUG_SERIALISATION
+
+  if flag(debug-parsing)
+    cpp-options:    -DDEBUG_PARSING
+
+  if flag(enable-cluster-counting)
+    cpp-options:    -DCOUNT_CLUSTERS
+    build-depends:  text-icu >= 0.7.1.0
+
+  if os(windows)
+    build-depends:  Win32 >= 2.6.1.0 && < 2.15
+
+  -- Agda cannot be built with GHC 8.6.1 due to a compiler bug, see
+  -- Agda Issue #3344.
+  if impl(ghc == 8.6.1)
+    buildable: False
+
+  -- Agda cannot be built with Windows and GHC 8.6.3 due to a compiler
+  -- bug, see Agda Issue #3657.
+  if os(windows) && impl(ghc == 8.6.3)
+    buildable: False
+
+  -- For libraries that come with GHC, we take the shipped version as default lower bound.
+  build-depends:
+    -- Please keep in alphabetical order!
+    , aeson                >= 1.1.2.0   && < 2.3
+    , ansi-terminal        >= 0.9       && < 1.2
+    , array                >= 0.5.2.0   && < 0.6
+    , async                >= 2.2       && < 2.3
+    , base                 >= 4.12.0.0  && < 4.20
+    , binary               >= 0.8.6.0   && < 0.9
+    , blaze-html           >= 0.8       && < 0.10
+    , boxes                >= 0.1.3     && < 0.2
+    , bytestring           >= 0.10.8.2  && < 0.13
+    , case-insensitive     >= 1.2.0.4   && < 1.3
+    , containers           >= 0.6.0.1   && < 0.8
+    , data-hash            >= 0.2.0.0   && < 0.3
+    , deepseq              >= 1.4.4.0   && < 1.6
+    , directory            >= 1.3.3.0   && < 1.4
+    , dlist                >= 0.8       && < 1.1
+    , edit-distance        >= 0.2.1.2   && < 0.3
+    , equivalence          >= 0.3.2     && < 0.5
+    -- exceptions-0.8 instead of 0.10 because of stack
+    , exceptions           >= 0.8       && < 0.11
+    , filepath             >= 1.4.2.1   && < 1.5
+    , ghc-compact          == 0.1.*
+    , gitrev               >= 1.3.1     && < 2
+    -- hashable 1.2.0.10 makes library-test 10x
+    -- slower. The issue was fixed in hashable 1.2.1.0.
+    -- https://github.com/tibbe/hashable/issues/57.
+    , hashable             >= 1.2.1.0   && < 1.5
+    , haskeline            >= 0.7.4.3   && < 0.9
+    -- monad-control-1.0.1.0 is the first to contain liftThrough
+    , monad-control        >= 1.0.1.0   && < 1.1
+    , mtl                  >= 2.2.2     && < 2.4
+    , murmur-hash          >= 0.1       && < 0.2
+    , parallel             >= 3.2.2.0   && < 3.3
+    , peano                >= 0.1.0.1   && < 0.2
+    , pretty               >= 1.1.3.3   && < 1.2
+    , process              >= 1.6.3.0   && < 1.7
+    , regex-tdfa           >= 1.3.1.0   && < 1.4
+    , split                >= 0.2.0.0   && < 0.3
+    , stm                  >= 2.4.4     && < 2.6
+    , STMonadTrans         >= 0.4.3     && < 0.5
+    , strict               >= 0.4.0.1   && < 0.6
+    , text                 >= 1.2.3.1   && < 2.2
+    , time                 >= 1.8.0.2   && < 1.13
+    , time-compat          >= 1.9.2     && < 1.10
+        -- time-compat adds needed functionality missing in time < 1.9
+    , transformers         >= 0.5.5.0   && < 0.7
+    , unordered-containers >= 0.2.9.0   && < 0.3
+        -- unordered-containers < 0.2.9 need base < 4.11
+    , uri-encode           >= 1.5.0.4   && < 1.6
+    , vector               >= 0.12      && < 0.14
+    , vector-hashtables    >= 0.1.1.1   && < 0.2
+    , zlib                 >= 0.6       && < 0.8
+
+  -- We don't write upper bounds for Alex nor Happy because the
+  -- `build-tool-depends` field can not be modified in Hackage.
+  build-tool-depends:
+    , alex:alex   >= 3.2.3
+        -- alex-3.2.3 is packaged with Ubuntu 18.04
+    , happy:happy >= 1.19.8
+        -- happy-1.19.8 is packaged with Ubuntu 18.04
+
+  exposed-modules:
+      Agda.Auto.Auto
+      Agda.Auto.Options
+      Agda.Auto.CaseSplit
+      Agda.Auto.Convert
+      Agda.Auto.NarrowingSearch
+      Agda.Auto.SearchControl
+      Agda.Auto.Syntax
+      Agda.Auto.Typecheck
+      Agda.Benchmarking
+      Agda.Compiler.Backend
+      Agda.Compiler.Builtin
+      Agda.Compiler.CallCompiler
+      Agda.Compiler.Common
+      Agda.Compiler.JS.Compiler
+      Agda.Compiler.JS.Syntax
+      Agda.Compiler.JS.Substitution
+      Agda.Compiler.JS.Pretty
+      Agda.Compiler.MAlonzo.Coerce
+      Agda.Compiler.MAlonzo.Compiler
+      Agda.Compiler.MAlonzo.Encode
+      Agda.Compiler.MAlonzo.HaskellTypes
+      Agda.Compiler.MAlonzo.Misc
+      Agda.Compiler.MAlonzo.Pragmas
+      Agda.Compiler.MAlonzo.Pretty
+      Agda.Compiler.MAlonzo.Primitives
+      Agda.Compiler.MAlonzo.Strict
+      Agda.Compiler.ToTreeless
+      Agda.Compiler.Treeless.AsPatterns
+      Agda.Compiler.Treeless.Builtin
+      Agda.Compiler.Treeless.Compare
+      Agda.Compiler.Treeless.EliminateDefaults
+      Agda.Compiler.Treeless.EliminateLiteralPatterns
+      Agda.Compiler.Treeless.Erase
+      Agda.Compiler.Treeless.GuardsToPrims
+      Agda.Compiler.Treeless.Identity
+      Agda.Compiler.Treeless.NormalizeNames
+      Agda.Compiler.Treeless.Pretty
+      Agda.Compiler.Treeless.Simplify
+      Agda.Compiler.Treeless.Subst
+      Agda.Compiler.Treeless.Uncase
+      Agda.Compiler.Treeless.Unused
+      Agda.ImpossibleTest
+      Agda.Interaction.AgdaTop
+      Agda.Interaction.Base
+      Agda.Interaction.BasicOps
+      Agda.Interaction.SearchAbout
+      Agda.Interaction.CommandLine
+      Agda.Interaction.EmacsCommand
+      Agda.Interaction.EmacsTop
+      Agda.Interaction.ExitCode
+      Agda.Interaction.JSONTop
+      Agda.Interaction.JSON
+      Agda.Interaction.FindFile
+      Agda.Interaction.Highlighting.Common
+      Agda.Interaction.Highlighting.Dot
+      Agda.Interaction.Highlighting.Emacs
+      Agda.Interaction.Highlighting.FromAbstract
+      Agda.Interaction.Highlighting.Generate
+      Agda.Interaction.Highlighting.HTML
+      Agda.Interaction.Highlighting.JSON
+      Agda.Interaction.Highlighting.Precise
+      Agda.Interaction.Highlighting.Range
+      Agda.Interaction.Highlighting.Vim
+      Agda.Interaction.Highlighting.LaTeX
+      Agda.Interaction.Imports
+      Agda.Interaction.InteractionTop
+      Agda.Interaction.Response
+      Agda.Interaction.MakeCase
+      Agda.Interaction.Monad
+      Agda.Interaction.Library
+      Agda.Interaction.Library.Base
+      Agda.Interaction.Library.Parse
+      Agda.Interaction.Options
+      Agda.Interaction.Options.Help
+      Agda.Interaction.Options.Lenses
+      Agda.Interaction.Options.Warnings
+      Agda.Main
+      Agda.Syntax.Abstract.Name
+      Agda.Syntax.Abstract.Pattern
+      Agda.Syntax.Abstract.PatternSynonyms
+      Agda.Syntax.Abstract.Pretty
+      Agda.Syntax.Abstract.UsedNames
+      Agda.Syntax.Abstract.Views
+      Agda.Syntax.Abstract
+      Agda.Syntax.Builtin
+      Agda.Syntax.Common
+      Agda.Syntax.Common.Pretty
+      Agda.Syntax.Common.Aspect
+      Agda.Syntax.Common.Pretty.ANSI
+      Agda.Syntax.Concrete.Attribute
+      Agda.Syntax.Concrete.Definitions
+      Agda.Syntax.Concrete.Definitions.Errors
+      Agda.Syntax.Concrete.Definitions.Monad
+      Agda.Syntax.Concrete.Definitions.Types
+      Agda.Syntax.Concrete.Fixity
+      Agda.Syntax.Concrete.Generic
+      Agda.Syntax.Concrete.Glyph
+      Agda.Syntax.Concrete.Name
+      Agda.Syntax.Concrete.Operators.Parser
+      Agda.Syntax.Concrete.Operators.Parser.Monad
+      Agda.Syntax.Concrete.Operators
+      Agda.Syntax.Concrete.Pattern
+      Agda.Syntax.Concrete.Pretty
+      Agda.Syntax.Concrete
+      Agda.Syntax.DoNotation
+      Agda.Syntax.Fixity
+      Agda.Syntax.IdiomBrackets
+      Agda.Syntax.Info
+      Agda.Syntax.Internal
+      Agda.Syntax.Internal.Blockers
+      Agda.Syntax.Internal.Defs
+      Agda.Syntax.Internal.Elim
+      Agda.Syntax.Internal.Generic
+      Agda.Syntax.Internal.MetaVars
+      Agda.Syntax.Internal.Names
+      Agda.Syntax.Internal.Pattern
+      Agda.Syntax.Internal.SanityCheck
+      Agda.Syntax.Internal.Univ
+      Agda.Syntax.Literal
+      Agda.Syntax.Notation
+      Agda.Syntax.Parser.Alex
+      Agda.Syntax.Parser.Comments
+      Agda.Syntax.Parser.Layout
+      Agda.Syntax.Parser.LexActions
+      Agda.Syntax.Parser.Lexer
+      Agda.Syntax.Parser.Literate
+      Agda.Syntax.Parser.LookAhead
+      Agda.Syntax.Parser.Monad
+      Agda.Syntax.Parser.Parser
+      Agda.Syntax.Parser.StringLiterals
+      Agda.Syntax.Parser.Tokens
+      Agda.Syntax.Parser
+      Agda.Syntax.Position
+      Agda.Syntax.Reflected
+      Agda.Syntax.Scope.Base
+      Agda.Syntax.Scope.Flat
+      Agda.Syntax.Scope.Monad
+      Agda.Syntax.TopLevelModuleName
+      Agda.Syntax.TopLevelModuleName.Boot
+      Agda.Syntax.Translation.AbstractToConcrete
+      Agda.Syntax.Translation.ConcreteToAbstract
+      Agda.Syntax.Translation.InternalToAbstract
+      Agda.Syntax.Translation.ReflectedToAbstract
+      Agda.Syntax.Treeless
+      Agda.Termination.CallGraph
+      Agda.Termination.CallMatrix
+      Agda.Termination.CutOff
+      Agda.Termination.Monad
+      Agda.Termination.Order
+      Agda.Termination.RecCheck
+      Agda.Termination.SparseMatrix
+      Agda.Termination.Semiring
+      Agda.Termination.TermCheck
+      Agda.Termination.Termination
+      Agda.TheTypeChecker
+      Agda.TypeChecking.Abstract
+      Agda.TypeChecking.CheckInternal
+      Agda.TypeChecking.CompiledClause
+      Agda.TypeChecking.CompiledClause.Compile
+      Agda.TypeChecking.CompiledClause.Match
+      Agda.TypeChecking.Constraints
+      Agda.TypeChecking.Conversion
+      Agda.TypeChecking.Conversion.Pure
+      Agda.TypeChecking.Coverage
+      Agda.TypeChecking.Coverage.Match
+      Agda.TypeChecking.Coverage.SplitTree
+      Agda.TypeChecking.Coverage.SplitClause
+      Agda.TypeChecking.Coverage.Cubical
+      Agda.TypeChecking.Datatypes
+      Agda.TypeChecking.DeadCode
+      Agda.TypeChecking.DisplayForm
+      Agda.TypeChecking.DropArgs
+      Agda.TypeChecking.Empty
+      Agda.TypeChecking.EtaContract
+      Agda.TypeChecking.Errors
+      Agda.TypeChecking.Free
+      Agda.TypeChecking.Free.Lazy
+      Agda.TypeChecking.Free.Precompute
+      Agda.TypeChecking.Free.Reduce
+      Agda.TypeChecking.Forcing
+      Agda.TypeChecking.Functions
+      Agda.TypeChecking.Generalize
+      Agda.TypeChecking.IApplyConfluence
+      Agda.TypeChecking.Implicit
+      Agda.TypeChecking.Injectivity
+      Agda.TypeChecking.Inlining
+      Agda.TypeChecking.InstanceArguments
+      Agda.TypeChecking.Irrelevance
+      Agda.TypeChecking.Level
+      Agda.TypeChecking.LevelConstraints
+      Agda.TypeChecking.Lock
+      Agda.TypeChecking.Level.Solve
+      Agda.TypeChecking.MetaVars
+      Agda.TypeChecking.MetaVars.Mention
+      Agda.TypeChecking.MetaVars.Occurs
+      Agda.TypeChecking.Modalities
+      Agda.TypeChecking.Monad.Base
+      Agda.TypeChecking.Monad.Base.Warning
+      Agda.TypeChecking.Monad.Benchmark
+      Agda.TypeChecking.Monad.Builtin
+      Agda.TypeChecking.Monad.Caching
+      Agda.TypeChecking.Monad.Closure
+      Agda.TypeChecking.Monad.Constraints
+      Agda.TypeChecking.Monad.Context
+      Agda.TypeChecking.Monad.Debug
+      Agda.TypeChecking.Monad.Env
+      Agda.TypeChecking.Monad.Imports
+      Agda.TypeChecking.Monad.MetaVars
+      Agda.TypeChecking.Monad.Modality
+      Agda.TypeChecking.Monad.Mutual
+      Agda.TypeChecking.Monad.Open
+      Agda.TypeChecking.Monad.Options
+      Agda.TypeChecking.Monad.Pure
+      Agda.TypeChecking.Monad.Signature
+      Agda.TypeChecking.Monad.SizedTypes
+      Agda.TypeChecking.Monad.State
+      Agda.TypeChecking.Monad.Statistics
+      Agda.TypeChecking.Monad.Trace
+      Agda.TypeChecking.Monad
+      Agda.TypeChecking.Names
+      Agda.TypeChecking.Opacity
+      Agda.TypeChecking.Patterns.Abstract
+      Agda.TypeChecking.Patterns.Internal
+      Agda.TypeChecking.Patterns.Match
+      Agda.TypeChecking.Polarity
+      Agda.TypeChecking.Positivity
+      Agda.TypeChecking.Positivity.Occurrence
+      Agda.TypeChecking.Pretty
+      Agda.TypeChecking.Pretty.Call
+      Agda.TypeChecking.Pretty.Constraint
+      Agda.TypeChecking.Pretty.Warning
+      Agda.TypeChecking.Primitive
+      Agda.TypeChecking.Primitive.Base
+      Agda.TypeChecking.Primitive.Cubical
+      Agda.TypeChecking.Primitive.Cubical.Id
+      Agda.TypeChecking.Primitive.Cubical.Glue
+      Agda.TypeChecking.Primitive.Cubical.Base
+      Agda.TypeChecking.Primitive.Cubical.HCompU
+      Agda.TypeChecking.ProjectionLike
+      Agda.TypeChecking.Quote
+      Agda.TypeChecking.ReconstructParameters
+      Agda.TypeChecking.RecordPatterns
+      Agda.TypeChecking.Records
+      Agda.TypeChecking.Reduce
+      Agda.TypeChecking.Reduce.Fast
+      Agda.TypeChecking.Reduce.Monad
+      Agda.TypeChecking.Rewriting
+      Agda.TypeChecking.Rewriting.Clause
+      Agda.TypeChecking.Rewriting.Confluence
+      Agda.TypeChecking.Rewriting.NonLinMatch
+      Agda.TypeChecking.Rewriting.NonLinPattern
+      Agda.TypeChecking.Rules.Application
+      Agda.TypeChecking.Rules.Builtin
+      Agda.TypeChecking.Rules.Builtin.Coinduction
+      Agda.TypeChecking.Rules.Data
+      Agda.TypeChecking.Rules.Decl
+      Agda.TypeChecking.Rules.Def
+      Agda.TypeChecking.Rules.Display
+      Agda.TypeChecking.Rules.LHS
+      Agda.TypeChecking.Rules.LHS.Implicit
+      Agda.TypeChecking.Rules.LHS.Problem
+      Agda.TypeChecking.Rules.LHS.ProblemRest
+      Agda.TypeChecking.Rules.LHS.Unify
+      Agda.TypeChecking.Rules.LHS.Unify.Types
+      Agda.TypeChecking.Rules.LHS.Unify.LeftInverse
+      Agda.TypeChecking.Rules.Record
+      Agda.TypeChecking.Rules.Term
+      Agda.TypeChecking.Serialise
+      Agda.TypeChecking.Serialise.Base
+      Agda.TypeChecking.Serialise.Instances
+      Agda.TypeChecking.Serialise.Instances.Abstract
+      Agda.TypeChecking.Serialise.Instances.Common
+      Agda.TypeChecking.Serialise.Instances.Compilers
+      Agda.TypeChecking.Serialise.Instances.Highlighting
+      Agda.TypeChecking.Serialise.Instances.Internal
+      Agda.TypeChecking.Serialise.Instances.Errors
+      Agda.TypeChecking.SizedTypes
+      Agda.TypeChecking.SizedTypes.Solve
+      Agda.TypeChecking.SizedTypes.Syntax
+      Agda.TypeChecking.SizedTypes.Utils
+      Agda.TypeChecking.SizedTypes.WarshallSolver
+      Agda.TypeChecking.Sort
+      Agda.TypeChecking.Substitute
+      Agda.TypeChecking.Substitute.Class
+      Agda.TypeChecking.Substitute.DeBruijn
+      Agda.TypeChecking.SyntacticEquality
+      Agda.TypeChecking.Telescope
+      Agda.TypeChecking.Telescope.Path
+      Agda.TypeChecking.Unquote
+      Agda.TypeChecking.Warnings
+      Agda.TypeChecking.With
+      Agda.Utils.AffineHole
+      Agda.Utils.Applicative
+      Agda.Utils.AssocList
+      Agda.Utils.Bag
+      Agda.Utils.Benchmark
+      Agda.Utils.BiMap
+      Agda.Utils.Boolean
+      Agda.Utils.BoolSet
+      Agda.Utils.CallStack
+      Agda.Utils.Char
+      Agda.Utils.Cluster
+      Agda.Utils.Empty
+      Agda.Utils.Environment
+      Agda.Utils.Either
+      Agda.Utils.Fail
+      Agda.Utils.Favorites
+      Agda.Utils.FileName
+      Agda.Utils.Float
+      Agda.Utils.Functor
+      Agda.Utils.Function
+      Agda.Utils.Graph.AdjacencyMap.Unidirectional
+      Agda.Utils.Graph.TopSort
+      Agda.Utils.Hash
+      Agda.Utils.HashTable
+      Agda.Utils.Haskell.Syntax
+      Agda.Utils.Impossible
+      Agda.Utils.IndexedList
+      Agda.Utils.IntSet.Infinite
+      Agda.Utils.IO
+      Agda.Utils.IO.Binary
+      Agda.Utils.IO.Directory
+      Agda.Utils.IO.TempFile
+      Agda.Utils.IO.UTF8
+      Agda.Utils.IORef
+      Agda.Utils.Lens
+      Agda.Utils.Lens.Examples
+      Agda.Utils.List
+      Agda.Utils.List1
+      Agda.Utils.List2
+      Agda.Utils.ListT
+      Agda.Utils.Map
+      Agda.Utils.Maybe
+      Agda.Utils.Maybe.Strict
+      Agda.Utils.Memo
+      Agda.Utils.Monad
+      Agda.Utils.Monoid
+      Agda.Utils.Null
+      Agda.Utils.Parser.MemoisedCPS
+      Agda.Utils.PartialOrd
+      Agda.Utils.Permutation
+      Agda.Utils.Pointer
+      Agda.Utils.POMonoid
+      Agda.Utils.ProfileOptions
+      Agda.Utils.RangeMap
+      Agda.Utils.SemiRing
+      Agda.Utils.Semigroup
+      Agda.Utils.Singleton
+      Agda.Utils.Size
+      Agda.Utils.SmallSet
+      Agda.Utils.String
+      Agda.Utils.Suffix
+      Agda.Utils.Three
+      Agda.Utils.Time
+      Agda.Utils.Trie
+      Agda.Utils.Tuple
+      Agda.Utils.TypeLevel
+      Agda.Utils.TypeLits
+      Agda.Utils.Update
+      Agda.Utils.VarSet
+      Agda.Utils.Warshall
+      Agda.Utils.WithDefault
+      Agda.Utils.Zipper
+      Agda.Version
+      Agda.VersionCommit
+
+  autogen-modules:
+      Paths_Agda
+
+  other-modules:
+      Paths_Agda
+      Agda.Interaction.Highlighting.Dot.Backend
+      Agda.Interaction.Highlighting.Dot.Base
+      Agda.Interaction.Highlighting.HTML.Backend
+      Agda.Interaction.Highlighting.HTML.Base
+      Agda.Interaction.Highlighting.LaTeX.Backend
+      Agda.Interaction.Highlighting.LaTeX.Base
+      Agda.Interaction.Options.Base
+      Agda.Interaction.Options.HasOptions
+      Agda.Utils.CallStack.Base
+      Agda.Utils.CallStack.Pretty
+      Agda.Utils.Unsafe
+
+-- Agda binary
+---------------------------------------------------------------------------
+
+executable agda
+  hs-source-dirs: src/main
+  main-is:        Main.hs
+  build-depends:
+    , Agda
+      -- Nothing is used from the following package,
+      -- except for the Prelude.
+    , base
+  default-language: Haskell2010
+  -- If someone installs Agda with the setuid bit set, then the
+  -- presence of +RTS may be a security problem (see GHC bug #3910).
+  -- However, we sometimes recommend people to use +RTS to control
+  -- Agda's memory usage, so we want this functionality enabled by
+  -- default.
+
+  -- The threaded RTS by default starts a major GC after a program has
+  -- been idle for 0.3 s. This feature turned out to be annoying, so
+  -- the idle GC is now by default turned off (-I0).
+  ghc-options:
+    -threaded
+    -rtsopts
+    -with-rtsopts=-I0
+
+-- agda-mode executable
+---------------------------------------------------------------------------
+
+executable agda-mode
+  hs-source-dirs:   src/agda-mode
+  main-is:          Main.hs
+  autogen-modules:  Paths_Agda
+  other-modules:    Paths_Agda
+  build-depends:
+    , base      >= 4.12.0.0 && < 4.20
+    , directory >= 1.3.3.0  && < 1.4
+    , filepath  >= 1.4.2.1  && < 1.5
+    , process   >= 1.6.3.0  && < 1.7
+  default-language: Haskell2010
diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,47 @@
+Release notes for Agda version 2.6.4.2
+======================================
+
+This is a bug-fix release.  It aims to be API-compatible with 2.6.4.1.
+Agda 2.6.4.2 supports GHC versions 8.6.5 to 9.8.1.
+
+Highlights
+----------
+
+- Fix an inconsistency in Cubical Agda related to catch-all clauses: [Issue #7033](https://github.com/agda/agda/issues/7033)
+- Fix a regression in instance search introduced in 2.6.4.2: [Issue #7113](https://github.com/agda/agda/issues/7113)
+- Fix a bug related to `opaque`:  [Issue #6972](https://github.com/agda/agda/issues/6972)
+- Fix some internal errors:
+  * [Issue #7029](https://github.com/agda/agda/issues/7029)
+  * [Issue #7034](https://github.com/agda/agda/issues/7034)
+  * [Issue #7044](https://github.com/agda/agda/issues/7044)
+- Fix building with cabal flag `-f debug-serialisation`: [Issue #7081](https://github.com/agda/agda/issues/7081)
+
+List of closed issues
+---------------------
+
+For 2.6.4.2, the following issues were
+[closed](https://github.com/agda/agda/issues?q=is%3Aissue+milestone%3A2.6.4.2+is%3Aclosed)
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+- [Issue #6972](https://github.com/agda/agda/issues/6972): Unfolding fails when code is split up into multiple files
+- [Issue #6999](https://github.com/agda/agda/issues/6999): Unification failure for function type with erased argument
+- [Issue #7020](https://github.com/agda/agda/issues/7020): question: haskell backend extraction of `Data.Nat.DivMod.DivMod`?
+- [Issue #7029](https://github.com/agda/agda/issues/7029): Internal error on confluence check when rewriting a defined symbol with a hole
+- [Issue #7033](https://github.com/agda/agda/issues/7033): transpX clauses can be beat out by user-written _ clauses, leading to proof of ⊥
+- [Issue #7034](https://github.com/agda/agda/issues/7034): Internal error with --two-level due to blocking on solved meta
+- [Issue #7044](https://github.com/agda/agda/issues/7044): Serializer crashes on blocked definitions when using --allow-unsolved-metas
+- [Issue #7048](https://github.com/agda/agda/issues/7048): hcomp symbols in interface not hidden under --cubical-compatible
+- [Issue #7059](https://github.com/agda/agda/issues/7059): Don't recompile if --keep-pattern-variables option changes
+- [Issue #7070](https://github.com/agda/agda/issues/7070): Don't set a default maximum heapsize for Agda runs
+- [Issue #7081](https://github.com/agda/agda/issues/7081): Missing `IsString` instance with debug flags enabled
+- [Issue #7095](https://github.com/agda/agda/issues/7095): Agda build flags appear as "automatic", but they are all "manual"
+- [Issue #7104](https://github.com/agda/agda/issues/7104): Warning "there are two interface files" should not be serialized
+- [Issue #7105](https://github.com/agda/agda/issues/7105): Internal error in generate-helper (C-c C-h)
+- [Issue #7113](https://github.com/agda/agda/issues/7113): Instance resolution runs too late, leads to `with`-abstraction failure
+
+These PRs not corresponding to issues were merged:
+
+- [PR #6988](https://github.com/agda/agda/issues/6988): Provide a `.agda-lib` for Agda builtins
+- [PR #7065](https://github.com/agda/agda/issues/7065): Some documentation fixes
+- [PR #7072](https://github.com/agda/agda/issues/7072): Add 'Inference in Agda' to the list of tutorials
+- [PR #7091](https://github.com/agda/agda/issues/7091): Add course to “Courses using Agda”
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,45 @@
+Copyright (c) 2005-2024 remains with the authors.
+Agda 2 was originally written by Ulf Norell,
+partially based on code from Agda 1 by Catarina Coquand and Makoto Takeyama,
+and from Agdalight by Ulf Norell and Andreas Abel.
+Cubical Agda was originally contributed by Andrea Vezzosi.
+
+Agda 2 is currently actively developed mainly by Andreas Abel,
+Guillaume Allais, Liang-Ting Chen, Jesper Cockx, Matthew Daggitt,
+Nils Anders Danielsson, Amélia Liao, Ulf Norell, and
+Andrés Sicard-Ramírez.
+
+Further, Agda 2 has received contributions by, amongst others,
+Arthur Adjedj, Stevan Andjelkovic,
+Marcin Benke, Jean-Philippe Bernardy, Guillaume Brunerie,
+James Chapman, Jonathan Coates,
+Dominique Devriese, Péter Diviánszky, Robert Estelle,
+Olle Fredriksson, Adam Gundry, Daniel Gustafsson, Philipp Hausmann,
+Alan Jeffrey, Phil de Joux,
+Wolfram Kahl, Wen Kokke, John Leo, Fredrik Lindblad,
+Víctor López Juan, Ting-Gan Lua, Francesco Mazzoli, Stefan Monnier,
+Guilhem Moulin, Konstantin Nisht, Fredrik Nordvall Forsberg,
+Josselin Poiret, Nicolas Pouillard, Jonathan Prieto, Christian Sattler,
+Makoto Takeyama, Andrea Vezzosi, Noam Zeilberger, and Tesla Ice Zhang.
+The full list of contributors is available at
+https://github.com/agda/agda/graphs/contributors or from the git
+repository via ``git shortlog -sne``.
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,37 @@
+Agda 2
+======
+
+[![Hackage version](https://img.shields.io/hackage/v/Agda.svg?label=Hackage)](http://hackage.haskell.org/package/Agda)
+[![Stackage version](https://www.stackage.org/package/Agda/badge/lts?label=Stackage)](https://www.stackage.org/package/Agda)
+[![Test](https://github.com/agda/agda/workflows/Build,%20Test,%20and%20Benchmark/badge.svg?branch=master)](https://github.com/agda/agda/actions?query=workflow%3A%22Build%2C+Test%2C+and+Benchmark%22)
+[![Documentation Status](https://readthedocs.org/projects/agda/badge/?version=latest)](http://agda.readthedocs.io/en/latest/?badge=latest)
+[![Agda Zulip](https://img.shields.io/badge/zulip-join_chat-brightgreen.svg)](https://agda.zulipchat.com)
+
+![The official Agda logo](doc/user-manual/agda.svg)
+
+Note that this README is only about Agda, not its standard
+library. See the [Agda Wiki][agdawiki] for information about the
+library.
+
+Documentation
+-------------
+
+* [User manual](http://agda.readthedocs.io)
+  (per-commit pdf can be downloaded from the
+  [github actions](https://github.com/agda/agda/actions/workflows/user_manual.yml) page)
+* [CHANGELOG](https://github.com/agda/agda/blob/master/CHANGELOG.md)
+
+Getting Started
+----------------
+
+* [Installation](https://agda.readthedocs.io/en/latest/getting-started/installation.html)
+* [Quick guide to editing, type checking and compiling Agda
+  code](https://agda.readthedocs.io/en/latest/getting-started/a-taste-of-agda.html)
+
+Contributing to Agda
+--------------------
+
+* Contribution how-to: [`HACKING`](https://github.com/agda/agda/blob/master/HACKING.md)
+* [Haskell style-guide](https://github.com/andreasabel/haskell-style-guide/blob/master/haskell-style.md)
+
+[agdawiki]: http://wiki.portal.chalmers.se/agda/pmwiki.php
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,150 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+import Data.List
+import Data.Maybe
+
+import Distribution.Simple
+import Distribution.Simple.LocalBuildInfo
+import Distribution.Simple.Setup
+import Distribution.Simple.BuildPaths (exeExtension)
+import Distribution.PackageDescription
+import Distribution.System ( buildPlatform )
+
+import System.FilePath
+import System.Directory (makeAbsolute, removeFile)
+import System.Environment (getEnvironment)
+import System.Process
+import System.Exit
+import System.IO
+import System.IO.Error (isDoesNotExistError)
+
+import Control.Monad (forM_, unless)
+import Control.Exception (bracket, catch, throwIO)
+
+main :: IO ()
+main = defaultMainWithHooks userhooks
+
+userhooks :: UserHooks
+userhooks = simpleUserHooks
+  { copyHook  = copyHook'
+  , instHook  = instHook'
+  }
+
+-- Install and copy hooks are default, but amended with .agdai files in data-files.
+instHook' :: PackageDescription -> LocalBuildInfo -> UserHooks -> InstallFlags -> IO ()
+instHook' pd lbi hooks flags = instHook simpleUserHooks pd' lbi hooks flags where
+  pd' = pd { dataFiles = concatMap (expandAgdaExt pd) $ dataFiles pd }
+
+-- Andreas, 2020-04-25, issue #4569: defer 'generateInterface' until after
+-- the library has been copied to a destination where it can be found.
+-- @cabal build@ will likely no longer produce the .agdai files, but @cabal install@ does.
+copyHook' :: PackageDescription -> LocalBuildInfo -> UserHooks -> CopyFlags -> IO ()
+copyHook' pd lbi hooks flags = do
+  -- Copy library and executable etc.
+  copyHook simpleUserHooks pd lbi hooks flags
+  unless (skipInterfaces lbi) $ do
+    -- Generate .agdai files.
+    generateInterfaces pd lbi
+    -- Copy again, now including the .agdai files.
+    copyHook simpleUserHooks pd' lbi hooks flags
+  where
+  pd' = pd
+    { dataFiles = concatMap (expandAgdaExt pd) $ dataFiles pd
+      -- Andreas, 2020-04-25, issue #4569:
+      -- I tried clearing some fields to avoid copying again.
+      -- However, cabal does not like me messing with the PackageDescription.
+      -- Clearing @library@ or @executables@ leads to internal errors.
+      -- Thus, we just copy things again.  Not a terrible problem.
+    -- , library       = Nothing
+    -- , executables   = []
+    -- , subLibraries  = []
+    -- , foreignLibs   = []
+    -- , testSuites    = []
+    -- , benchmarks    = []
+    -- , extraSrcFiles = []
+    -- , extraTmpFiles = []
+    -- , extraDocFiles = []
+    }
+
+-- Used to add .agdai files to data-files
+expandAgdaExt :: PackageDescription -> FilePath -> [FilePath]
+expandAgdaExt pd fp | takeExtension fp == ".agda" = [ fp, toIFile pd fp ]
+                    | otherwise                   = [ fp ]
+
+version :: PackageDescription -> String
+version = intercalate "." . map show . versionNumbers . pkgVersion . package
+
+projectRoot :: PackageDescription -> FilePath
+projectRoot pd = takeDirectory agdaLibFile where
+  [agdaLibFile] = filter ((".agda-lib" ==) . takeExtension) $ dataFiles pd
+
+toIFile :: PackageDescription -> FilePath -> FilePath
+toIFile pd file = buildDir </> fileName where
+  root = projectRoot pd
+  buildDir = root </> "_build" </> version pd </> "agda"
+  fileName = makeRelative root $ replaceExtension file ".agdai"
+
+-- Andreas, 2019-10-21, issue #4151:
+-- skip the generation of interface files with program suffix "-quicker"
+skipInterfaces :: LocalBuildInfo -> Bool
+skipInterfaces lbi = fromPathTemplate (progSuffix lbi) == "-quicker"
+
+generateInterfaces :: PackageDescription -> LocalBuildInfo -> IO ()
+generateInterfaces pd lbi = do
+
+  -- for debugging, these are examples how you can inspect the flags...
+  -- print $ flagAssignment lbi
+  -- print $ fromPathTemplate $ progSuffix lbi
+
+  -- then...
+  let bdir = buildDir lbi
+      agda = bdir </> "agda" </> "agda" <.> agdaExeExtension
+
+  ddir <- makeAbsolute $ "src" </> "data"
+
+  -- assuming we want to type check all .agda files in data-files
+  -- current directory root of the package.
+
+  putStrLn "Generating Agda library interface files..."
+
+  -- The Agda.Primitive* and Agda.Builtin* modules.
+  let builtins = filter ((== ".agda") . takeExtension) (dataFiles pd)
+
+  -- Remove all existing .agdai files.
+  forM_ builtins $ \fp -> do
+    let fullpathi = toIFile pd (ddir </> fp)
+
+        handleExists e | isDoesNotExistError e = return ()
+                       | otherwise             = throwIO e
+
+    removeFile fullpathi `catch` handleExists
+
+  -- Type-check all builtin modules (in a single Agda session to take
+  -- advantage of caching).
+  let loadBuiltinCmds = concat
+        [ [ cmd ("Cmd_load " ++ f ++ " []")
+          , cmd "Cmd_no_metas"
+            -- Fail if any meta-variable is unsolved.
+          ]
+        | b <- builtins
+        , let f     = show (ddir </> b)
+              cmd c = "IOTCM " ++ f ++ " None Indirect (" ++ c ++ ")"
+        ]
+  env <- getEnvironment
+  _output <- readCreateProcess
+      (proc agda
+          [ "--interaction"
+          , "--interaction-exit-on-error"
+          , "-Werror"
+          , "-v0"
+          ])
+        { delegate_ctlc = True
+                          -- Make Agda look for data files in a
+                          -- certain place.
+        , env           = Just (("Agda_datadir", ddir) : env)
+        }
+      (unlines loadBuiltinCmds)
+  return ()
+
+agdaExeExtension :: String
+agdaExeExtension = exeExtension buildPlatform
diff --git a/doc/release-notes/2.2.0.md b/doc/release-notes/2.2.0.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.0.md
@@ -0,0 +1,102 @@
+Release notes for Agda 2 version 2.2.0
+======================================
+
+Important changes since 2.1.2 (which was released 2007-08-16):
+
+Language
+--------
+
+* Exhaustive pattern checking. Agda complains if there are missing
+  clauses in a function definition.
+
+* Coinductive types are supported. This feature is under
+  development/evaluation, and may change.
+
+  http://wiki.portal.chalmers.se/agda/agda.php?n=ReferenceManual.Codatatypes
+
+* Another experimental feature: Sized types, which can make it easier
+  to explain why your code is terminating.
+
+* Improved constraint solving for functions with constructor headed
+  right hand sides.
+
+  http://wiki.portal.chalmers.se/agda/agda.php?n=ReferenceManual.FindingTheValuesOfImplicitArguments
+
+* A simple, well-typed foreign function interface, which allows use of
+  Haskell functions in Agda code.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Docs.FFI
+
+* The tokens `forall`, `->` and `\` can be written as `∀`, `→` and
+  `λ`.
+
+* Absurd lambdas: `λ ()` and `λ {}`.
+
+  http://thread.gmane.org/gmane.comp.lang.agda/440
+
+* Record fields whose values can be inferred can be omitted.
+
+* Agda complains if it spots an unreachable clause, or if a pattern
+  variable "shadows" a hidden constructor of matching type.
+
+  http://thread.gmane.org/gmane.comp.lang.agda/720
+
+Tools
+-----
+
+* Case-split: The user interface can replace a pattern variable with
+  the corresponding constructor patterns. You get one new left-hand
+  side for every possible constructor.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.QuickGuideToEditingTypeCheckingAndCompilingAgdaCode
+
+* The MAlonzo compiler.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Docs.MAlonzo
+
+* A new Emacs input method, which contains bindings for many Unicode
+  symbols, is by default activated in the Emacs mode.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Docs.UnicodeInput
+
+* Highlighted, hyperlinked HTML can be generated from Agda source
+  code.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.HowToGenerateWebPagesFromSourceCode
+
+* The command-line interactive mode (`agda -I`) is no longer
+  supported, but should still work.
+
+  http://thread.gmane.org/gmane.comp.lang.agda/245
+
+* Reload times when working on large projects are now considerably
+  better.
+
+  http://thread.gmane.org/gmane.comp.lang.agda/551
+
+Libraries
+---------
+
+* A standard library is under development.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Libraries.StandardLibrary
+
+Documentation
+-------------
+
+* The Agda wiki is better organised. It should be easier for a
+  newcomer to find relevant information now.
+
+  http://wiki.portal.chalmers.se/agda/
+
+Infrastructure
+--------------
+
+* Easy-to-install packages for Windows and Debian/Ubuntu have been
+  prepared.
+
+  http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.Download
+
+* Agda 2.2.0 is available from Hackage.
+
+  http://hackage.haskell.org/
diff --git a/doc/release-notes/2.2.10.md b/doc/release-notes/2.2.10.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.10.md
@@ -0,0 +1,238 @@
+Release notes for Agda 2 version 2.2.10
+=======================================
+
+Language
+--------
+
+* New flag: `--without-K`.
+
+  This flag makes pattern matching more restricted. If the flag is
+  activated, then Agda only accepts certain case-splits. If the type
+  of the variable to be split is `D pars ixs`, where `D` is a data (or
+  record) type, pars stands for the parameters, and `ixs` the indices,
+  then the following requirements must be satisfied:
+
+  - The indices `ixs` must be applications of constructors to distinct
+    variables.
+
+  - These variables must not be free in pars.
+
+  The intended purpose of `--without-K` is to enable experiments with
+  a propositional equality without the K rule. Let us define
+  propositional equality as follows:
+
+  ```agda
+  data _≡_ {A : Set} : A → A → Set where
+    refl : ∀ x → x ≡ x
+  ```
+
+  Then the obvious implementation of the J rule is accepted:
+
+  ```agda
+  J : {A : Set} (P : {x y : A} → x ≡ y → Set) →
+      (∀ x → P (refl x)) →
+      ∀ {x y} (x≡y : x ≡ y) → P x≡y
+  J P p (refl x) = p x
+  ```
+
+  The same applies to Christine Paulin-Mohring's version of the J rule:
+
+  ```agda
+  J′ : {A : Set} {x : A} (P : {y : A} → x ≡ y → Set) →
+       P (refl x) →
+       ∀ {y} (x≡y : x ≡ y) → P x≡y
+  J′ P p (refl x) = p
+  ```
+
+  On the other hand, the obvious implementation of the K rule is not
+  accepted:
+
+  ```agda
+  K : {A : Set} (P : {x : A} → x ≡ x → Set) →
+      (∀ x → P (refl x)) →
+      ∀ {x} (x≡x : x ≡ x) → P x≡x
+  K P p (refl x) = p x
+  ```
+
+  However, we have *not* proved that activation of `--without-K`
+  ensures that the K rule cannot be proved in some other way.
+
+* Irrelevant declarations.
+
+  Postulates and functions can be marked as irrelevant by prefixing
+  the name with a dot when the name is declared. Example:
+
+  ```agda
+  postulate
+    .irrelevant : {A : Set} → .A → A
+  ```
+
+  Irrelevant names may only be used in irrelevant positions or in
+  definitions of things which have been declared irrelevant.
+
+  The axiom irrelevant above can be used to define a projection from
+  an irrelevant record field:
+
+  ```agda
+  data Subset (A : Set) (P : A → Set) : Set where
+    _#_ : (a : A) → .(P a) → Subset A P
+
+  elem : ∀ {A P} → Subset A P → A
+  elem (a # p) = a
+
+  .certificate : ∀ {A P} (x : Subset A P) → P (elem x)
+  certificate (a # p) = irrelevant p
+  ```
+
+  The right-hand side of certificate is relevant, so we cannot define
+
+  ```agda
+  certificate (a # p) = p
+  ```
+
+  (because `p` is irrelevant). However, certificate is declared to be
+  irrelevant, so it can use the axiom irrelevant. Furthermore the
+  first argument of the axiom is irrelevant, which means that
+  irrelevant `p` is well-formed.
+
+  As shown above the axiom irrelevant justifies irrelevant
+  projections. Previously no projections were generated for irrelevant
+  record fields, such as the field certificate in the following
+  record type:
+
+  ```agda
+  record Subset (A : Set) (P : A → Set) : Set where
+    constructor _#_
+    field
+      elem         : A
+      .certificate : P elem
+  ```
+
+  Now projections are generated automatically for irrelevant fields
+  (unless the flag `--no-irrelevant-projections` is used). Note that
+  irrelevant projections are highly experimental.
+
+* Termination checker recognises projections.
+
+  Projections now preserve sizes, both in patterns and expressions.
+  Example:
+
+  ```agda
+  record Wrap (A : Set) : Set where
+    constructor wrap
+    field
+      unwrap : A
+
+  open Wrap public
+
+  data WNat : Set where
+    zero : WNat
+    suc  : Wrap WNat → WNat
+
+  id : WNat → WNat
+  id zero    = zero
+  id (suc w) = suc (wrap (id (unwrap w)))
+  ```
+
+  In the structural ordering `unwrap w` ≤ `w`. This means that
+
+  ```agda
+    unwrap w ≤ w < suc w,
+  ```
+
+  and hence the recursive call to id is accepted.
+
+  Projections also preserve guardedness.
+
+Tools
+-----
+
+* Hyperlinks for top-level module names now point to the start of the
+  module rather than to the declaration of the module name. This
+  applies both to the Emacs mode and to the output of `agda --html`.
+
+* Most occurrences of record field names are now highlighted as
+  "fields". Previously many occurrences were highlighted as
+  "functions".
+
+* Emacs mode: It is no longer possible to change the behaviour of the
+  `TAB` key by customising `agda2-indentation`.
+
+* Epic compiler backend.
+
+  A new compiler backend is being implemented. This backend makes use
+  of Edwin Brady's language Epic
+  (http://www.cs.st-andrews.ac.uk/~eb/epic.php) and its compiler. The
+  backend should handle most Agda code, but is still at an
+  experimental stage: more testing is needed, and some things written
+  below may not be entirely true.
+
+  The Epic compiler can be invoked from the command line using the
+  flag `--epic`:
+
+  ```
+  agda --epic --epic-flag=<EPIC-FLAG> --compile-dir=<DIR> <FILE>.agda
+  ```
+
+  The `--epic-flag` flag can be given multiple times; each flag is
+  given verbatim to the Epic compiler (in the given order). The
+  resulting executable is named after the main module and placed in
+  the directory specified by the `--compile-dir` flag (default: the
+  project root). Intermediate files are placed in a subdirectory
+  called `Epic`.
+
+  The backend requires that there is a definition named main. This
+  definition should be a value of type `IO Unit`, but at the moment
+  this is not checked (so it is easy to produce a program which
+  segfaults).  Currently the backend represents actions of type `IO A`
+  as functions from `Unit` to `A`, and main is applied to the unit
+  value.
+
+  The Epic compiler compiles via C, not Haskell, so the pragmas
+  related to the Haskell FFI (`IMPORT`, `COMPILED_DATA` and
+  `COMPILED`) are not used by the Epic backend. Instead there is a new
+  pragma `COMPILED_EPIC`. This pragma is used to give Epic code for
+  postulated definitions (Epic code can in turn call C code). The form
+  of the pragma is `{-# COMPILED_EPIC def code #-}`, where `def` is
+  the name of an Agda postulate and `code` is some Epic code which
+  should include the function arguments, return type and function
+  body. As an example the `IO` monad can be defined as follows:
+
+  ```agda
+  postulate
+    IO     : Set → Set
+    return : ∀ {A} → A → IO A
+    _>>=_  : ∀ {A B} → IO A → (A → IO B) → IO B
+
+  {-# COMPILED_EPIC return (u : Unit, a : Any) -> Any =
+                      ioreturn(a) #-}
+  {-# COMPILED_EPIC
+        _>>=_ (u1 : Unit, u2 : Unit, x : Any, f : Any) -> Any =
+          iobind(x,f) #-}
+  ```
+
+  Here `ioreturn` and `iobind` are Epic functions which are defined in
+  the file `AgdaPrelude.e` which is always included.
+
+  By default the backend will remove so-called forced constructor
+  arguments (and case-splitting on forced variables will be
+  rewritten). This optimisation can be disabled by using the flag
+  `--no-forcing`.
+
+  All data types which look like unary natural numbers after forced
+  constructor arguments have been removed (i.e. types with two
+  constructors, one nullary and one with a single recursive argument)
+  will be represented as "BigInts". This applies to the standard `Fin`
+  type, for instance.
+
+  The backend supports Agda's primitive functions and the BUILTIN
+  pragmas. If the BUILTIN pragmas for unary natural numbers are used,
+  then some operations, like addition and multiplication, will use
+  more efficient "BigInt" operations.
+
+  If you want to make use of the Epic backend you need to install some
+  dependencies, see the README.
+
+* The Emacs mode can compile using either the MAlonzo or the Epic
+  backend. The variable `agda2-backend` controls which backend is
+  used.
diff --git a/doc/release-notes/2.2.2.md b/doc/release-notes/2.2.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.2.md
@@ -0,0 +1,22 @@
+Release notes for Agda 2 version 2.2.2
+======================================
+
+Tools
+-----
+
+* The `--malonzodir` option has been renamed to `--malonzo-dir`.
+
+* The output of `agda --html` is by default placed in a directory
+  called `html`.
+
+Infrastructure
+--------------
+
+* The Emacs mode is included in the Agda Cabal package, and installed
+  by `cabal install`. The recommended way to enable the Emacs mode is
+  to include the following code in `.emacs`:
+
+  ```elisp
+  (load-file (let ((coding-system-for-read 'utf-8))
+                  (shell-command-to-string "agda-mode locate")))
+  ```
diff --git a/doc/release-notes/2.2.4.md b/doc/release-notes/2.2.4.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.4.md
@@ -0,0 +1,54 @@
+Release notes for Agda 2 version 2.2.4
+======================================
+
+Important changes since 2.2.2:
+
+* Change to the semantics of `open import` and `open module`. The
+  declaration
+
+  ```agda
+  open import M <using/hiding/renaming>
+  ```
+
+  now translates to
+
+  ```agda
+  import A
+  open A <using/hiding/renaming>
+  ```
+
+  instead of
+
+  ```agda
+  import A <using/hiding/renaming>
+  open A
+  ```
+
+  The same translation is used for `open module M = E …`. Declarations
+  involving the keywords as or public are changed in a corresponding
+  way (`as` always goes with import, and `public` always with open).
+
+  This change means that import directives do not affect the qualified
+  names when open import/module is used. To get the old behaviour you
+  can use the expanded version above.
+
+* Names opened publicly in parameterised modules no longer inherit the
+  module parameters. Example:
+
+  ```agda
+  module A where
+    postulate X : Set
+
+  module B (Y : Set) where
+    open A public
+  ```
+
+  In Agda 2.2.2 `B.X` has type `(Y : Set) → Set`, whereas in
+  Agda 2.2.4 `B.X` has type Set.
+
+* Previously it was not possible to export a given constructor name
+  through two different `open public` statements in the same module.
+  This is now possible.
+
+* Unicode subscript digits are now allowed for the hierarchy of
+  universes (`Set₀`, `Set₁`, …): `Set₁` is equivalent to `Set1`.
diff --git a/doc/release-notes/2.2.6.md b/doc/release-notes/2.2.6.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.6.md
@@ -0,0 +1,290 @@
+Release notes for Agda 2 version 2.2.6
+======================================
+
+Language
+--------
+
+* Universe polymorphism (experimental extension).
+
+  To enable universe polymorphism give the flag
+  `--universe-polymorphism` on the command line or (recommended) as an
+  `OPTIONS` pragma.
+
+  When universe polymorphism is enabled `Set` takes an argument which is
+  the universe level. For instance, the type of universe polymorphic
+  identity is
+
+  ```agda
+  id : {a : Level} {A : Set a} → A → A.
+  ```
+
+  The type Level is isomorphic to the unary natural numbers and should
+  be specified using the BUILTINs `LEVEL`, `LEVELZERO`, and
+  `LEVELSUC`:
+
+  ```agda
+  data Level : Set where
+    zero : Level
+    suc  : Level → Level
+
+  {-# BUILTIN LEVEL     Level #-}
+  {-# BUILTIN LEVELZERO zero  #-}
+  {-# BUILTIN LEVELSUC  suc   #-}
+  ```
+
+  There is an additional BUILTIN `LEVELMAX` for taking the maximum of two
+  levels:
+
+  ```agda
+  max : Level → Level → Level
+  max  zero    m      = m
+  max (suc n)  zero   = suc n
+  max (suc n) (suc m) = suc (max n m)
+
+  {-# BUILTIN LEVELMAX max #-}
+  ```
+
+  The non-polymorphic universe levels `Set`, `Set₁` and so on are
+  sugar for `Set zero`, `Set (suc zero)`, etc.
+
+  At present there is no automatic lifting of types from one level to
+  another. It can still be done (rather clumsily) by defining types
+  like the following one:
+
+  ```agda
+  data Lifted {a} (A : Set a) : Set (suc a) where
+    lift : A → Lifted A
+  ```
+
+  However, it is likely that automatic lifting is introduced at some
+  point in the future.
+
+* Multiple constructors, record fields, postulates or primitives can
+  be declared using a single type signature:
+
+  ```agda
+  data Bool : Set where
+    false true : Bool
+
+  postulate
+    A B : Set
+  ```
+
+* Record fields can be implicit:
+
+  ```agda
+  record R : Set₁ where
+    field
+      {A}         : Set
+      f           : A → A
+      {B C} D {E} : Set
+      g           : B → C → E
+  ```
+
+  By default implicit fields are not printed.
+
+* Record constructors can be defined:
+
+  ```agda
+  record Σ (A : Set) (B : A → Set) : Set where
+    constructor _,_
+    field
+      proj₁ : A
+      proj₂ : B proj₁
+  ```
+
+  In this example `_,_` gets the type
+
+  ```agda
+   (proj₁ : A) → B proj₁ → Σ A B.
+  ```
+
+  For implicit fields the corresponding constructor arguments become
+  implicit.
+
+  Note that the constructor is defined in the *outer* scope, so any
+  fixity declaration has to be given outside the record definition.
+  The constructor is not in scope inside the record module.
+
+  Note also that pattern matching for records has not been implemented
+  yet.
+
+* BUILTIN hooks for equality.
+
+  The data type
+
+  ```agda
+  data _≡_ {A : Set} (x : A) : A → Set where
+    refl : x ≡ x
+  ```
+
+  can be specified as the builtin equality type using the following
+  pragmas:
+
+  ```agda
+  {-# BUILTIN EQUALITY _≡_  #-}
+  {-# BUILTIN REFL     refl #-}
+  ```
+
+  The builtin equality is used for the new rewrite construct and
+  the `primTrustMe` primitive described below.
+
+* New `rewrite` construct.
+
+  If `eqn : a ≡ b`, where `_≡_` is the builtin equality (see above) you
+  can now write
+
+  ```agda
+  f ps rewrite eqn = rhs
+  ```
+
+  instead of
+
+  ```agda
+    f ps with a | eqn
+    ... | ._ | refl = rhs
+  ```
+
+  The `rewrite` construct has the effect of rewriting the goal and the
+  context by the given equation (left to right).
+
+  You can rewrite using several equations (in sequence) by separating
+  them with vertical bars (|):
+
+  ```agda
+  f ps rewrite eqn₁ | eqn₂ | … = rhs
+  ```
+
+  It is also possible to add `with`-clauses after rewriting:
+
+  ```agda
+  f ps rewrite eqns with e
+  ... | p = rhs
+  ```
+
+  Note that pattern matching happens before rewriting—if you want to
+  rewrite and then do pattern matching you can use a with after the
+  rewrite.
+
+  See `test/Succeed/Rewrite.agda` for some examples.
+
+* A new primitive, `primTrustMe`, has been added:
+
+  ```agda
+    primTrustMe : {A : Set} {x y : A} → x ≡ y
+  ```
+
+  Here `_≡_` is the builtin equality (see BUILTIN hooks for equality,
+  above).
+
+  If `x` and `y` are definitionally equal, then
+  `primTrustMe {x = x} {y = y}` reduces to `refl`.
+
+  Note that the compiler replaces all uses of `primTrustMe` with the
+  `REFL` builtin, without any check for definitional
+  equality. Incorrect uses of `primTrustMe` can potentially lead to
+  segfaults or similar problems.
+
+  For an example of the use of `primTrustMe`, see `Data.String` in
+  version 0.3 of the standard library, where it is used to implement
+  decidable equality on strings using the primitive boolean equality.
+
+* Changes to the syntax and semantics of IMPORT pragmas, which are
+  used by the Haskell FFI. Such pragmas must now have the following
+  form:
+
+  ```agda
+  {-# IMPORT <module name> #-}
+  ```
+
+  These pragmas are interpreted as *qualified* imports, so Haskell
+  names need to be given qualified (unless they come from the Haskell
+  prelude).
+
+* The horizontal tab character (U+0009) is no longer treated as white
+  space.
+
+* Line pragmas are no longer supported.
+
+* The `--include-path` flag can no longer be used as a pragma.
+
+* The experimental and incomplete support for proof irrelevance has
+  been disabled.
+
+Tools
+-----
+
+* New `intro` command in the Emacs mode. When there is a canonical way
+  of building something of the goal type (for instance, if the goal
+  type is a pair), the goal can be refined in this way. The command
+  works for the following goal types:
+
+    - A data type where only one of its constructors can be used to
+      construct an element of the goal type. (For instance, if the
+      goal is a non-empty vector, a `cons` will be introduced.)
+
+    - A record type. A record value will be introduced. Implicit
+      fields will not be included unless showing of implicit arguments
+      is switched on.
+
+    - A function type. A lambda binding as many variables as possible
+      will be introduced. The variable names will be chosen from the
+      goal type if its normal form is a dependent function type,
+      otherwise they will be variations on `x`. Implicit lambdas will
+      only be inserted if showing of implicit arguments is switched
+      on.
+
+  This command can be invoked by using the `refine` command
+  (`C-c C-r`) when the goal is empty. (The old behaviour of the refine
+  command in this situation was to ask for an expression using the
+  minibuffer.)
+
+* The Emacs mode displays `Checked` in the mode line if the current
+  file type checked successfully without any warnings.
+
+* If a file `F` is loaded, and this file defines the module `M`, it is
+  an error if `F` is not the file which defines `M` according to the
+  include path.
+
+  Note that the command-line tool and the Emacs mode define the
+  meaning of relative include paths differently: the command-line tool
+  interprets them relative to the current working directory, whereas
+  the Emacs mode interprets them relative to the root directory of the
+  current project. (As an example, if the module `A.B.C` is loaded
+  from the file `<some-path>/A/B/C.agda`, then the root directory is
+  `<some-path>`.)
+
+* It is an error if there are several files on the include path which
+  match a given module name.
+
+* Interface files are relocatable. You can move around source trees as
+  long as the include path is updated in a corresponding way. Note
+  that a module `M` may be re-typechecked if its time stamp is
+  strictly newer than that of the corresponding interface file
+  (`M.agdai`).
+
+* Type-checking is no longer done when an up-to-date interface exists.
+  (Previously the initial module was always type-checked.)
+
+* Syntax highlighting files for Emacs (`.agda.el`) are no longer used.
+  The `--emacs` flag has been removed. (Syntax highlighting
+  information is cached in the interface files.)
+
+* The Agate and Alonzo compilers have been retired. The options
+  `--agate`, `--alonzo` and `--malonzo` have been removed.
+
+* The default directory for MAlonzo output is the project's root
+  directory. The `--malonzo-dir` flag has been renamed to
+  `--compile-dir`.
+
+* Emacs mode: `C-c C-x C-d` no longer resets the type checking state.
+  `C-c C-x C-r` can be used for a more complete reset. `C-c C-x C-s`
+  (which used to reload the syntax highlighting information) has been
+  removed. `C-c C-l` can be used instead.
+
+* The Emacs mode used to define some "abbrevs", unless the user
+  explicitly turned this feature off. The new default is *not* to add
+  any abbrevs. The old default can be obtained by customising
+  `agda2-mode-abbrevs-use-defaults` (a customisation buffer can be
+  obtained by typing `M-x customize-group agda2 RET` after an Agda
+  file has been loaded).
diff --git a/doc/release-notes/2.2.8.md b/doc/release-notes/2.2.8.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.2.8.md
@@ -0,0 +1,626 @@
+Release notes for Agda 2 version 2.2.8
+======================================
+
+Language
+--------
+
+* Record pattern matching.
+
+  It is now possible to pattern match on named record constructors.
+  Example:
+
+  ```agda
+  record Σ (A : Set) (B : A → Set) : Set where
+    constructor _,_
+    field
+      proj₁ : A
+      proj₂ : B proj₁
+
+  map : {A B : Set} {P : A → Set} {Q : B → Set}
+        (f : A → B) → (∀ {x} → P x → Q (f x)) →
+        Σ A P → Σ B Q
+  map f g (x , y) = (f x , g y)
+  ```
+
+  The clause above is internally translated into the following one:
+
+  ```agda
+  map f g p = (f (Σ.proj₁ p) , g (Σ.proj₂ p))
+  ```
+
+  Record patterns containing data type patterns are not translated.
+  Example:
+
+  ```agda
+  add : ℕ × ℕ → ℕ
+  add (zero  , n) = n
+  add (suc m , n) = suc (add (m , n))
+  ```
+
+  Record patterns which do not contain data type patterns, but which
+  do contain dot patterns, are currently rejected. Example:
+
+  ```agda
+  Foo : {A : Set} (p₁ p₂ : A × A) → proj₁ p₁ ≡ proj₁ p₂ → Set₁
+  Foo (x , y) (.x , y′) refl = Set
+  ```
+
+* Proof irrelevant function types.
+
+  Agda now supports irrelevant non-dependent function types:
+
+  ```agda
+  f : .A → B
+  ```
+
+  This type implies that `f` does not depend computationally on its
+  argument. One intended use case is data structures with embedded
+  proofs, like sorted lists:
+
+  ```agda
+  postulate
+    _≤_ : ℕ → ℕ → Set
+    p₁  : 0 ≤ 1
+    p₂  : 0 ≤ 1
+
+  data SList (bound : ℕ) : Set where
+    []    : SList bound
+    scons : (head : ℕ) →
+            .(head ≤ bound) →
+            (tail : SList head) →
+            SList bound
+  ```
+
+  The effect of the irrelevant type in the signature of `scons` is
+  that `scons`'s second argument is never inspected after Agda has
+  ensured that it has the right type. It is even thrown away, leading
+  to smaller term sizes and hopefully some gain in efficiency. The
+  type-checker ignores irrelevant arguments when checking equality, so
+  two lists can be equal even if they contain different proofs:
+
+  ```agda
+  l₁ : SList 1
+  l₁ = scons 0 p₁ []
+
+  l₂ : SList 1
+  l₂ = scons 0 p₂ []
+
+  l₁≡l₂ : l₁ ≡ l₂
+  l₁≡l₂ = refl
+  ```
+
+  Irrelevant arguments can only be used in irrelevant contexts.
+  Consider the following subset type:
+
+  ```agda
+  data Subset (A : Set) (P : A → Set) : Set where
+    _#_ : (elem : A) → .(P elem) → Subset A P
+  ```
+
+  The following two uses are fine:
+
+  ```agda
+  elimSubset : ∀ {A C : Set} {P} →
+               Subset A P → ((a : A) → .(P a) → C) → C
+  elimSubset (a # p) k = k a p
+
+  elem : {A : Set} {P : A → Set} → Subset A P → A
+  elem (x # p) = x
+  ```
+
+  However, if we try to project out the proof component, then Agda
+  complains that `variable p is declared irrelevant, so it cannot be
+  used here`:
+
+  ```agda
+  prjProof : ∀ {A P} (x : Subset A P) → P (elem x)
+  prjProof (a # p) = p
+  ```
+
+  Matching against irrelevant arguments is also forbidden, except in
+  the case of irrefutable matches (record constructor patterns which
+  have been translated away). For instance, the match against the
+  pattern `(p , q)` here is accepted:
+
+  ```agda
+  elim₂ : ∀ {A C : Set} {P Q : A → Set} →
+          Subset A (λ x → Σ (P x) (λ _ → Q x)) →
+          ((a : A) → .(P a) → .(Q a) → C) → C
+  elim₂ (a # (p , q)) k = k a p q
+  ```
+
+  Absurd matches `()` are also allowed.
+
+  Note that record fields can also be irrelevant. Example:
+
+  ```agda
+  record Subset (A : Set) (P : A → Set) : Set where
+    constructor _#_
+    field
+      elem   : A
+      .proof : P elem
+  ```
+
+  Irrelevant fields are never in scope, neither inside nor outside the
+  record. This means that no record field can depend on an irrelevant
+  field, and furthermore projections are not defined for such fields.
+  Irrelevant fields can only be accessed using pattern matching, as in
+  `elimSubset` above.
+
+  Irrelevant function types were added very recently, and have not
+  been subjected to much experimentation yet, so do not be surprised
+  if something is changed before the next release. For instance,
+  dependent irrelevant function spaces (`.(x : A) → B`) might be added
+  in the future.
+
+* Mixfix binders.
+
+  It is now possible to declare user-defined syntax that binds
+  identifiers. Example:
+
+  ```agda
+  postulate
+    State  : Set → Set → Set
+    put    : ∀ {S} → S → State S ⊤
+    get    : ∀ {S} → State S S
+    return : ∀ {A S} → A → State S A
+    bind   : ∀ {A B S} → State S B → (B → State S A) → State S A
+
+  syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂
+
+  increment : State ℕ ⊤
+  increment = x ← get ,
+              put (1 + x)
+  ```
+
+  The syntax declaration for `bind` implies that `x` is in scope in
+  `e₂`, but not in `e₁`.
+
+  You can give fixity declarations along with syntax declarations:
+
+  ```agda
+  infixr 40 bind
+  syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂
+  ```
+
+  The fixity applies to the syntax, not the name; syntax declarations
+  are also restricted to ordinary, non-operator names. The following
+  declaration is disallowed:
+
+  ```agda
+  syntax _==_ x y = x === y
+  ```agda
+
+  Syntax declarations must also be linear; the following declaration
+  is disallowed:
+
+  ```agda
+  syntax wrong x = x + x
+  ```
+
+  Syntax declarations were added very recently, and have not been
+  subjected to much experimentation yet, so do not be surprised if
+  something is changed before the next release.
+
+* `Prop` has been removed from the language.
+
+  The experimental sort `Prop` has been disabled. Any program using
+  `Prop` should typecheck if `Prop` is replaced by `Set₀`. Note that
+  `Prop` is still a keyword.
+
+* Injective type constructors off by default.
+
+  Automatic injectivity of type constructors has been disabled (by
+  default). To enable it, use the flag
+  `--injective-type-constructors`, either on the command line or in an
+  `OPTIONS` pragma. Note that this flag makes Agda anti-classical and
+  possibly inconsistent:
+
+    Agda with excluded middle is inconsistent
+    http://thread.gmane.org/gmane.comp.lang.agda/1367
+
+  See `test/Succeed/InjectiveTypeConstructors.agda` for an example.
+
+* Termination checker can count.
+
+  There is a new flag `--termination-depth=N` accepting values `N >=
+  1` (with `N = 1` being the default) which influences the behavior of
+  the termination checker. So far, the termination checker has only
+  distinguished three cases when comparing the argument of a recursive
+  call with the formal parameter of the callee.
+
+  `<`: the argument is structurally smaller than the parameter
+
+  `=`: they are equal
+
+  `?`: the argument is bigger or unrelated to the parameter
+
+  This behavior, which is still the default (`N = 1`), will not
+  recognise the following functions as terminating.
+
+   ```agda
+   mutual
+
+      f : ℕ → ℕ
+      f zero          = zero
+      f (suc zero)    = zero
+      f (suc (suc n)) = aux n
+
+      aux : ℕ → ℕ
+      aux m = f (suc m)
+  ```
+
+  The call graph
+
+  ```
+  f --(<)--> aux --(?)--> f
+  ```
+
+  yields a recursive call from `f` to `f` via `aux` where the relation
+  of call argument to callee parameter is computed as "unrelated"
+  (composition of `<` and `?`).
+
+  Setting `N >= 2` allows a finer analysis: `n` has two constructors
+  less than `suc (suc n)`, and `suc m` has one more than `m`, so we get the
+  call graph:
+
+  ```
+  f --(-2)--> aux --(+1)--> f
+  ```
+
+  The indirect call `f --> f` is now labeled with `(-1)`, and the
+  termination checker can recognise that the call argument is
+  decreasing on this path.
+
+  Setting the termination depth to `N` means that the termination
+  checker counts decrease up to `N` and increase up to `N-1`. The
+  default, `N=1`, means that no increase is counted, every increase
+  turns to "unrelated".
+
+  In practice, examples like the one above sometimes arise when `with`
+  is used. As an example, the program
+
+  ```agda
+  f : ℕ → ℕ
+  f zero          = zero
+  f (suc zero)    = zero
+  f (suc (suc n)) with zero
+  ... | _ = f (suc n)
+  ```
+
+  is internally represented as
+
+  ```agda
+  mutual
+
+    f : ℕ → ℕ
+    f zero          = zero
+    f (suc zero)    = zero
+    f (suc (suc n)) = aux n zero
+
+    aux : ℕ → ℕ → ℕ
+    aux m k = f (suc m)
+  ```
+
+  Thus, by default, the definition of `f` using `with` is not accepted
+  by the termination checker, even though it looks structural (`suc n`
+  is a subterm of `suc suc n`). Now, the termination checker is
+  satisfied if the option `--termination-depth=2` is used.
+
+  Caveats:
+
+  - This is an experimental feature, hopefully being replaced by
+    something smarter in the near future.
+
+  - Increasing the termination depth will quickly lead to very long
+    termination checking times. So, use with care. Setting termination
+    depth to `100` by habit, just to be on the safe side, is not a good
+    idea!
+
+  - Increasing termination depth only makes sense for linear data
+    types such as `ℕ` and `Size`. For other types, increase cannot be
+    recognised. For instance, consider a similar example with lists.
+
+    ```agda
+    data List : Set where
+      nil  : List
+      cons : ℕ → List → List
+
+    mutual
+      f : List → List
+      f nil                  = nil
+      f (cons x nil)         = nil
+      f (cons x (cons y ys)) = aux y ys
+
+      aux : ℕ → List → List
+      aux z zs = f (cons z zs)
+    ```
+
+    Here the termination checker compares `cons z zs` to `z` and also
+    to `zs`. In both cases, the result will be "unrelated", no matter
+    how high we set the termination depth. This is because when
+    comparing `cons z zs` to `zs`, for instance, `z` is unrelated to
+    `zs`, thus, `cons z zs` is also unrelated to `zs`. We cannot say
+    it is just "one larger" since `z` could be a very large term. Note
+    that this points to a weakness of untyped termination checking.
+
+    To regain the benefit of increased termination depth, we need to
+    index our lists by a linear type such as `ℕ` or `Size`. With
+    termination depth `2`, the above example is accepted for vectors
+    instead of lists.
+
+* The `codata` keyword has been removed. To use coinduction, use the
+  following new builtins: `INFINITY`, `SHARP` and `FLAT`. Example:
+
+  ```agda
+  {-# OPTIONS --universe-polymorphism #-}
+
+  module Coinduction where
+
+  open import Level
+
+  infix 1000 ♯_
+
+  postulate
+    ∞  : ∀ {a} (A : Set a) → Set a
+    ♯_ : ∀ {a} {A : Set a} → A → ∞ A
+    ♭  : ∀ {a} {A : Set a} → ∞ A → A
+
+  {-# BUILTIN INFINITY ∞  #-}
+  {-# BUILTIN SHARP    ♯_ #-}
+  {-# BUILTIN FLAT     ♭  #-}
+  ```
+
+  Note that (non-dependent) pattern matching on `SHARP` is no longer
+  allowed.
+
+  Note also that strange things might happen if you try to combine the
+  pragmas above with `COMPILED_TYPE`, `COMPILED_DATA` or `COMPILED`
+  pragmas, or if the pragmas do not occur right after the postulates.
+
+  The compiler compiles the `INFINITY` builtin to nothing (more or
+  less), so that the use of coinduction does not get in the way of FFI
+  declarations:
+
+  ```agda
+  data Colist (A : Set) : Set where
+    []  : Colist A
+    _∷_ : (x : A) (xs : ∞ (Colist A)) → Colist A
+
+  {-# COMPILED_DATA Colist [] [] (:) #-}
+  ```
+
+* Infinite types.
+
+  If the new flag `--guardedness-preserving-type-constructors` is
+  used, then type constructors are treated as inductive constructors
+  when we check productivity (but only in parameters, and only if they
+  are used strictly positively or not at all). This makes examples
+  such as the following possible:
+
+  ```agda
+  data Rec (A : ∞ Set) : Set where
+    fold : ♭ A → Rec A
+
+  -- Σ cannot be a record type below.
+
+  data Σ (A : Set) (B : A → Set) : Set where
+    _,_ : (x : A) → B x → Σ A B
+
+  syntax Σ A (λ x → B) = Σ[ x ∶ A ] B
+
+  -- Corecursive definition of the W-type.
+
+  W : (A : Set) → (A → Set) → Set
+  W A B = Rec (♯ (Σ[ x ∶ A ] (B x → W A B)))
+
+  syntax W A (λ x → B) = W[ x ∶ A ] B
+
+  sup : {A : Set} {B : A → Set} (x : A) (f : B x → W A B) → W A B
+  sup x f = fold (x , f)
+
+  W-rec : {A : Set} {B : A → Set}
+          (P : W A B → Set) →
+          (∀ {x} {f : B x → W A B} → (∀ y → P (f y)) → P (sup x f)) →
+          ∀ x → P x
+  W-rec P h (fold (x , f)) = h (λ y → W-rec P h (f y))
+
+  -- Induction-recursion encoded as corecursion-recursion.
+
+  data Label : Set where
+    ′0 ′1 ′2 ′σ ′π ′w : Label
+
+  mutual
+
+    U : Set
+    U = Σ Label U′
+
+    U′ : Label → Set
+    U′ ′0 = ⊤
+    U′ ′1 = ⊤
+    U′ ′2 = ⊤
+    U′ ′σ = Rec (♯ (Σ[ a ∶ U ] (El a → U)))
+    U′ ′π = Rec (♯ (Σ[ a ∶ U ] (El a → U)))
+    U′ ′w = Rec (♯ (Σ[ a ∶ U ] (El a → U)))
+
+    El : U → Set
+    El (′0 , _)            = ⊥
+    El (′1 , _)            = ⊤
+    El (′2 , _)            = Bool
+    El (′σ , fold (a , b)) = Σ[ x ∶ El a ]  El (b x)
+    El (′π , fold (a , b)) =   (x : El a) → El (b x)
+    El (′w , fold (a , b)) = W[ x ∶ El a ]  El (b x)
+
+  U-rec : (P : ∀ u → El u → Set) →
+          P (′1 , _) tt →
+          P (′2 , _) true →
+          P (′2 , _) false →
+          (∀ {a b x y} →
+           P a x → P (b x) y → P (′σ , fold (a , b)) (x , y)) →
+          (∀ {a b f} →
+           (∀ x → P (b x) (f x)) → P (′π , fold (a , b)) f) →
+          (∀ {a b x f} →
+           (∀ y → P (′w , fold (a , b)) (f y)) →
+           P (′w , fold (a , b)) (sup x f)) →
+          ∀ u (x : El u) → P u x
+  U-rec P P1 P2t P2f Pσ Pπ Pw = rec
+    where
+    rec : ∀ u (x : El u) → P u x
+    rec (′0 , _)            ()
+    rec (′1 , _)            _              = P1
+    rec (′2 , _)            true           = P2t
+    rec (′2 , _)            false          = P2f
+    rec (′σ , fold (a , b)) (x , y)        = Pσ (rec _ x) (rec _ y)
+    rec (′π , fold (a , b)) f              = Pπ (λ x → rec _ (f x))
+    rec (′w , fold (a , b)) (fold (x , f)) = Pw (λ y → rec _ (f y))
+  ```
+
+  The `--guardedness-preserving-type-constructors` extension is based
+  on a rather operational understanding of `∞`/`♯_`; it's not yet
+  clear if this extension is consistent.
+
+* Qualified constructors.
+
+  Constructors can now be referred to qualified by their data type.
+  For instance, given
+
+  ```agda
+  data Nat : Set where
+    zero : Nat
+    suc  : Nat → Nat
+
+  data Fin : Nat → Set where
+    zero : ∀ {n} → Fin (suc n)
+    suc  : ∀ {n} → Fin n → Fin (suc n)
+  ```
+
+  you can refer to the constructors unambiguously as `Nat.zero`,
+  `Nat.suc`, `Fin.zero`, and `Fin.suc` (`Nat` and `Fin` are modules
+  containing the respective constructors). Example:
+
+  ```agda
+  inj : (n m : Nat) → Nat.suc n ≡ suc m → n ≡ m
+  inj .m m refl = refl
+  ```
+
+  Previously you had to write something like
+
+  ```agda
+  inj : (n m : Nat) → _≡_ {Nat} (suc n) (suc m) → n ≡ m
+  ```
+
+  to make the type checker able to figure out that you wanted the
+  natural number suc in this case.
+
+* Reflection.
+
+  There are two new constructs for reflection:
+
+    - `quoteGoal x in e`
+
+      In `e` the value of `x` will be a representation of the goal type
+      (the type expected of the whole expression) as an element in a
+      datatype of Agda terms (see below). For instance,
+
+      ```agda
+      example : ℕ
+      example = quoteGoal x in {! at this point x = def (quote ℕ) [] !}
+      ```
+
+    - `quote x : Name`
+
+      If `x` is the name of a definition (function, datatype, record,
+      or a constructor), `quote x` gives you the representation of `x`
+      as a value in the primitive type `Name` (see below).
+
+  Quoted terms use the following BUILTINs and primitives (available
+  from the standard library module `Reflection`):
+
+  ```agda
+  -- The type of Agda names.
+
+  postulate Name : Set
+
+  {-# BUILTIN QNAME Name #-}
+
+  primitive primQNameEquality : Name → Name → Bool
+
+  -- Arguments.
+
+  Explicit? = Bool
+
+  data Arg A : Set where
+    arg : Explicit? → A → Arg A
+
+  {-# BUILTIN ARG    Arg #-}
+  {-# BUILTIN ARGARG arg #-}
+
+  -- The type of Agda terms.
+
+  data Term : Set where
+    var     : ℕ → List (Arg Term) → Term
+    con     : Name → List (Arg Term) → Term
+    def     : Name → List (Arg Term) → Term
+    lam     : Explicit? → Term → Term
+    pi      : Arg Term → Term → Term
+    sort    : Term
+    unknown : Term
+
+  {-# BUILTIN AGDATERM            Term    #-}
+  {-# BUILTIN AGDATERMVAR         var     #-}
+  {-# BUILTIN AGDATERMCON         con     #-}
+  {-# BUILTIN AGDATERMDEF         def     #-}
+  {-# BUILTIN AGDATERMLAM         lam     #-}
+  {-# BUILTIN AGDATERMPI          pi      #-}
+  {-# BUILTIN AGDATERMSORT        sort    #-}
+  {-# BUILTIN AGDATERMUNSUPPORTED unknown #-}
+  ```
+
+  Reflection may be useful when working with internal decision
+  procedures, such as the standard library's ring solver.
+
+* Minor record definition improvement.
+
+  The definition of a record type is now available when type checking
+  record module definitions. This means that you can define things
+  like the following:
+
+  ```agda
+  record Cat : Set₁ where
+    field
+      Obj  : Set
+      _=>_ : Obj → Obj → Set
+      -- ...
+
+    -- not possible before:
+    op : Cat
+    op = record { Obj = Obj; _=>_ = λ A B → B => A }
+  ```
+
+Tools
+-----
+
+* The `Goal type and context` command now shows the goal type before
+  the context, and the context is shown in reverse order. The `Goal
+  type, context and inferred type` command has been modified in a
+  similar way.
+
+* Show module contents command.
+
+  Given a module name `M` the Emacs mode can now display all the
+  top-level modules and names inside `M`, along with types for the
+  names. The command is activated using `C-c C-o` or the menus.
+
+* Auto command.
+
+  A command which searches for type inhabitants has been added. The
+  command is invoked by pressing `C-C C-a` (or using the goal menu).
+  There are several flags and parameters, e.g. `-c` which enables
+  case-splitting in the search. For further information, see the Agda
+  wiki:
+
+    http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.Auto
+
+* HTML generation is now possible for a module with unsolved
+  meta-variables, provided that the `--allow-unsolved-metas` flag is
+  used.
diff --git a/doc/release-notes/2.3.0.md b/doc/release-notes/2.3.0.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.3.0.md
@@ -0,0 +1,1124 @@
+Release notes for Agda 2 version 2.3.0
+======================================
+
+Language
+--------
+
+* New more liberal syntax for mutually recursive definitions.
+
+  It is no longer necessary to use the `mutual` keyword to define
+  mutually recursive functions or datatypes. Instead, it is enough to
+  declare things before they are used. Instead of
+
+  ```agda
+  mutual
+    f : A
+    f = a[f, g]
+
+    g : B[f]
+    g = b[f, g]
+  ```
+
+  you can now write
+
+  ```agda
+  f : A
+  g : B[f]
+  f = a[f, g]
+  g = b[f, g].
+  ```
+
+  With the new style you have more freedom in choosing the order in
+  which things are type checked (previously type signatures were
+  always checked before definitions). Furthermore you can mix
+  arbitrary declarations, such as modules and postulates, with
+  mutually recursive definitions.
+
+  For data types and records the following new syntax is used to
+  separate the declaration from the definition:
+
+  ```agda
+  -- Declaration.
+  data Vec (A : Set) : Nat → Set  -- Note the absence of 'where'.
+
+  -- Definition.
+  data Vec A where
+    []   : Vec A zero
+    _::_ : {n : Nat} → A → Vec A n → Vec A (suc n)
+
+  -- Declaration.
+  record Sigma (A : Set) (B : A → Set) : Set
+
+  -- Definition.
+  record Sigma A B where
+    constructor _,_
+    field fst : A
+          snd : B fst
+  ```
+
+  When making separated declarations/definitions private or abstract
+  you should attach the `private` keyword to the declaration and the
+  `abstract` keyword to the definition. For instance, a private,
+  abstract function can be defined as
+
+  ```agda
+  private
+    f : A
+  abstract
+    f = e
+  ```
+
+  Finally it may be worth noting that the old style of mutually
+  recursive definitions is still supported (it basically desugars into
+  the new style).
+
+* Pattern matching lambdas.
+
+  Anonymous pattern matching functions can be defined using the syntax
+
+  ```
+  \ { p11 .. p1n -> e1 ; ... ; pm1 .. pmn -> em }
+  ```
+
+  (where, as usual, `\` and `->` can be replaced by `λ` and
+  `→`). Internally this is translated into a function definition of
+  the following form:
+
+  ```
+  .extlam p11 .. p1n = e1
+  ...
+  .extlam pm1 .. pmn = em
+  ```
+
+  This means that anonymous pattern matching functions are generative.
+  For instance, `refl` will not be accepted as an inhabitant of the type
+
+  ```agda
+  (λ { true → true ; false → false }) ≡
+  (λ { true → true ; false → false }),
+  ```
+
+  because this is equivalent to `extlam1 ≡ extlam2` for some distinct
+  fresh names `extlam1` and `extlam2`.
+
+  Currently the `where` and `with` constructions are not allowed in
+  (the top-level clauses of) anonymous pattern matching functions.
+
+  Examples:
+
+  ```agda
+  and : Bool → Bool → Bool
+  and = λ { true x → x ; false _ → false }
+
+  xor : Bool → Bool → Bool
+  xor = λ { true  true  → false
+          ; false false → false
+          ; _     _     → true
+          }
+
+  fst : {A : Set} {B : A → Set} → Σ A B → A
+  fst = λ { (a , b) → a }
+
+  snd : {A : Set} {B : A → Set} (p : Σ A B) → B (fst p)
+  snd = λ { (a , b) → b }
+  ```
+
+* Record update syntax.
+
+  Assume that we have a record type and a corresponding value:
+
+  ```agda
+  record MyRecord : Set where
+    field
+      a b c : ℕ
+
+  old : MyRecord
+  old = record { a = 1; b = 2; c = 3 }
+  ```
+
+  Then we can update (some of) the record value's fields in the
+  following way:
+
+  ```agda
+  new : MyRecord
+  new = record old { a = 0; c = 5 }
+  ```
+
+  Here new normalises to `record { a = 0; b = 2; c = 5 }`. Any
+  expression yielding a value of type `MyRecord` can be used instead of
+  old.
+
+  Record updating is not allowed to change types: the resulting value
+  must have the same type as the original one, including the record
+  parameters. Thus, the type of a record update can be inferred if the
+  type of the original record can be inferred.
+
+  The record update syntax is expanded before type checking. When the
+  expression
+
+  ```agda
+  record old { upd-fields }
+  ```
+
+  is checked against a record type `R`, it is expanded to
+
+  ```agda
+  let r = old in record { new-fields },
+  ```
+
+  where old is required to have type `R` and new-fields is defined as
+  follows: for each field `x` in `R`,
+
+    - if `x = e` is contained in `upd-fields` then `x = e` is included in
+      `new-fields`, and otherwise
+
+    - if `x` is an explicit field then `x = R.x r` is included in
+      `new-fields`, and
+
+    - if `x` is an implicit or instance field, then it is omitted from
+      `new-fields`.
+
+  (Instance arguments are explained below.) The reason for treating
+  implicit and instance fields specially is to allow code like the
+  following:
+
+  ```agda
+  record R : Set where
+    field
+      {length} : ℕ
+      vec      : Vec ℕ length
+      -- More fields…
+
+  xs : R
+  xs = record { vec = 0 ∷ 1 ∷ 2 ∷ [] }
+
+  ys = record xs { vec = 0 ∷ [] }
+  ```
+
+  Without the special treatment the last expression would need to
+  include a new binding for length (for instance `length = _`).
+
+* Record patterns which do not contain data type patterns, but which
+  do contain dot patterns, are no longer rejected.
+
+* When the `--without-K` flag is used literals are now treated as
+  constructors.
+
+* Under-applied functions can now reduce.
+
+  Consider the following definition:
+
+  ```agda
+  id : {A : Set} → A → A
+  id x = x
+  ```
+
+  Previously the expression `id` would not reduce. This has been
+  changed so that it now reduces to `λ x → x`. Usually this makes
+  little difference, but it can be important in conjunction with
+  `with`. See Issue [#365](https://github.com/agda/agda/issues/365)
+  for an example.
+
+* Unused AgdaLight legacy syntax `(x y : A; z v : B)` for telescopes
+  has been removed.
+
+### Universe polymorphism
+
+* Universe polymorphism is now enabled by default.  Use
+  `--no-universe-polymorphism` to disable it.
+
+* Universe levels are no longer defined as a data type.
+
+  The basic level combinators can be introduced in the following way:
+
+  ```agda
+  postulate
+    Level : Set
+    zero  : Level
+    suc   : Level → Level
+    max   : Level → Level → Level
+
+  {-# BUILTIN LEVEL     Level #-}
+  {-# BUILTIN LEVELZERO zero  #-}
+  {-# BUILTIN LEVELSUC  suc   #-}
+  {-# BUILTIN LEVELMAX  max   #-}
+  ```
+
+* The BUILTIN equality is now required to be universe-polymorphic.
+
+* `trustMe` is now universe-polymorphic.
+
+### Meta-variables and unification
+
+* Unsolved meta-variables are now frozen after every mutual block.
+  This means that they cannot be instantiated by subsequent code. For
+  instance,
+
+  ```agda
+  one : Nat
+  one = _
+
+  bla : one ≡ suc zero
+  bla = refl
+  ```
+
+  leads to an error now, whereas previously it lead to the
+  instantiation of `_` with `suc zero`. If you want to make use of the
+  old behaviour, put the two definitions in a mutual block.
+
+  All meta-variables are unfrozen during interactive editing, so that
+  the user can fill holes interactively. Note that type-checking of
+  interactively given terms is not perfect: Agda sometimes refuses to
+  load a file, even though no complaints were raised during the
+  interactive construction of the file. This is because certain checks
+  (for instance, positivity) are only invoked when a file is loaded.
+
+* Record types can now be inferred.
+
+  If there is a unique known record type with fields matching the
+  fields in a record expression, then the type of the expression will
+  be inferred to be the record type applied to unknown parameters.
+
+  If there is no known record type with the given fields the type
+  checker will give an error instead of producing lots of unsolved
+  meta-variables.
+
+  Note that "known record type" refers to any record type in any
+  imported module, not just types which are in scope.
+
+* The occurrence checker distinguishes rigid and strongly rigid
+  occurrences [Reed, LFMTP 2009; Abel & Pientka, TLCA 2011].
+
+  The completeness checker now accepts the following code:
+
+  ```agda
+  h : (n : Nat) → n ≡ suc n → Nat
+  h n ()
+  ```
+
+  Internally this generates a constraint `_n = suc _n` where the
+  meta-variable `_n` occurs strongly rigidly, i.e. on a constructor
+  path from the root, in its own defining term tree. This is never
+  solvable.
+
+  Weakly rigid recursive occurrences may have a solution [Jason Reed's
+  PhD thesis, page 106]:
+
+  ```agda
+  test : (k : Nat) →
+         let X : (Nat → Nat) → Nat
+             X = _
+         in
+         (f : Nat → Nat) → X f ≡ suc (f (X (λ x → k)))
+  test k f = refl
+  ```
+
+  The constraint `_X k f = suc (f (_X k (λ x → k)))` has the solution
+  `_X k f = suc (f (suc k))`, despite the recursive occurrence of
+  `_X`.  Here `_X` is not strongly rigid, because it occurs under the
+  bound variable `f`. Previously Agda rejected this code; now it instead
+  complains about an unsolved meta-variable.
+
+* Equation constraints involving the same meta-variable in the head
+  now trigger pruning [Pientka, PhD, Sec. 3.1.2; Abel & Pientka, TLCA
+  2011]. Example:
+
+  ```agda
+  same : let X : A → A → A → A × A
+             X = _
+         in {x y z : A} → X x y y ≡ (x , y)
+                        × X x x y ≡ X x y y
+  same = refl , refl
+  ```
+
+  The second equation implies that `X` cannot depend on its second
+  argument. After pruning the first equation is linear and can be
+  solved.
+
+* Instance arguments.
+
+  A new type of hidden function arguments has been added: instance
+  arguments. This new feature is based on influences from Scala's
+  implicits and Agda's existing implicit arguments.
+
+  Plain implicit arguments are marked by single braces: `{…}`. Instance
+  arguments are instead marked by double braces: `{{…}}`. Example:
+
+  ```agda
+  postulate
+    A : Set
+    B : A → Set
+    a : A
+    f : {{a : A}} → B a
+  ```
+
+  Instead of the double braces you can use the symbols `⦃` and `⦄`,
+  but these symbols must in many cases be surrounded by
+  whitespace. (If you are using Emacs and the Agda input method, then
+  you can conjure up the symbols by typing `\{{` and `\}}`,
+  respectively.)
+
+  Instance arguments behave as ordinary implicit arguments, except for
+  one important aspect: resolution of arguments which are not provided
+  explicitly. For instance, consider the following code:
+
+  ```agda
+    test = f
+  ```
+
+  Here Agda will notice that `f`'s instance argument was not provided
+  explicitly, and try to infer it. All definitions in scope at `f`'s
+  call site, as well as all variables in the context, are considered.
+  If exactly one of these names has the required type `A`, then the
+  instance argument will be instantiated to this name.
+
+  This feature can be used as an alternative to Haskell type classes.
+  If we define
+
+  ```agda
+  record Eq (A : Set) : Set where
+    field equal : A → A → Bool,
+  ```
+
+  then we can define the following projection:
+
+  ```agda
+  equal : {A : Set} {{eq : Eq A}} → A → A → Bool
+  equal {{eq}} = Eq.equal eq
+  ```
+
+  Now consider the following expression:
+
+  ```agda
+  equal false false ∨ equal 3 4
+  ```
+
+  If the following `Eq` "instances" for `Bool` and `ℕ` are in scope, and no
+  others, then the expression is accepted:
+
+  ```agda
+  eq-Bool : Eq Bool
+  eq-Bool = record { equal = … }
+
+  eq-ℕ : Eq ℕ
+  eq-ℕ = record { equal = … }
+  ```
+
+  A shorthand notation is provided to avoid the need to define
+  projection functions manually:
+
+  ```agda
+  module Eq-with-implicits = Eq {{...}}
+  ```
+
+  This notation creates a variant of `Eq`'s record module, where the
+  main `Eq` argument is an instance argument instead of an explicit one.
+  It is equivalent to the following definition:
+
+  ```agda
+  module Eq-with-implicits {A : Set} {{eq : Eq A}} = Eq eq
+  ```
+
+  Note that the short-hand notation allows you to avoid naming the
+  "-with-implicits" module:
+
+  ```agda
+  open Eq {{...}}
+  ```
+
+  Instance argument resolution is not recursive. As an example,
+  consider the following "parametrised instance":
+
+  ```agda
+  eq-List : {A : Set} → Eq A → Eq (List A)
+  eq-List {A} eq = record { equal = eq-List-A }
+    where
+    eq-List-A : List A → List A → Bool
+    eq-List-A []       []       = true
+    eq-List-A (a ∷ as) (b ∷ bs) = equal a b ∧ eq-List-A as bs
+    eq-List-A _        _        = false
+  ```
+
+  Assume that the only `Eq` instances in scope are `eq-List` and
+  `eq-ℕ`.  Then the following code does not type-check:
+
+  ```agda
+  test = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ [])
+  ```
+
+  However, we can make the code work by constructing a suitable
+  instance manually:
+
+  ```agda
+  test′ = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ [])
+    where eq-List-ℕ = eq-List eq-ℕ
+  ```
+
+  By restricting the "instance search" to be non-recursive we avoid
+  introducing a new, compile-time-only evaluation model to Agda.
+
+  For more information about instance arguments, see Devriese &
+  Piessens [ICFP 2011]. Some examples are also available in the
+  examples/instance-arguments subdirectory of the Agda distribution.
+
+### Irrelevance
+
+* Dependent irrelevant function types.
+
+  Some examples illustrating the syntax of dependent irrelevant
+  function types:
+
+  ```
+  .(x y : A) → B    .{x y z : A} → B
+  ∀ x .y → B        ∀ x .{y} {z} .v → B
+  ```
+
+  The declaration
+
+  ```
+  f : .(x : A) → B[x]
+  f x = t[x]
+  ```
+
+  requires that `x` is irrelevant both in `t[x]` and in `B[x]`. This
+  is possible if, for instance, `B[x] = B′ x`, with `B′ : .A → Set`.
+
+  Dependent irrelevance allows us to define the eliminator for the
+  `Squash` type:
+
+  ```agda
+  record Squash (A : Set) : Set where
+    constructor squash
+    field
+      .proof : A
+
+  elim-Squash : {A : Set} (P : Squash A → Set)
+                (ih : .(a : A) → P (squash a)) →
+                (a⁻ : Squash A) → P a⁻
+  elim-Squash P ih (squash a) = ih a
+  ```
+
+  Note that this would not type-check with
+
+  ```agda
+  (ih : (a : A) -> P (squash a)).
+  ```
+
+* Records with only irrelevant fields.
+
+  The following now works:
+
+  ```agda
+  record IsEquivalence {A : Set} (_≈_ : A → A → Set) : Set where
+    field
+      .refl  : Reflexive _≈_
+      .sym   : Symmetric _≈_
+      .trans : Transitive _≈_
+
+  record Setoid : Set₁ where
+    infix 4 _≈_
+    field
+      Carrier        : Set
+      _≈_            : Carrier → Carrier → Set
+      .isEquivalence : IsEquivalence _≈_
+
+    open IsEquivalence isEquivalence public
+  ```
+
+  Previously Agda complained about the application
+  `IsEquivalence isEquivalence`, because `isEquivalence` is irrelevant
+  and the `IsEquivalence` module expected a relevant argument. Now,
+  when record modules are generated for records consisting solely of
+  irrelevant arguments, the record parameter is made irrelevant:
+
+   ```agda
+  module IsEquivalence {A : Set} {_≈_ : A → A → Set}
+                       .(r : IsEquivalence {A = A} _≈_) where
+    …
+  ```
+
+* Irrelevant things are no longer erased internally. This means that
+  they are printed as ordinary terms, not as `_` as before.
+
+* The new flag `--experimental-irrelevance` enables irrelevant
+  universe levels and matching on irrelevant data when only one
+  constructor is available. These features are very experimental and
+  likely to change or disappear.
+
+### Reflection
+
+* The reflection API has been extended to mirror features like
+  irrelevance, instance arguments and universe polymorphism, and to
+  give (limited) access to definitions. For completeness all the
+  builtins and primitives are listed below:
+
+  ```agda
+  -- Names.
+
+  postulate Name : Set
+
+  {-# BUILTIN QNAME Name #-}
+
+  primitive
+    -- Equality of names.
+    primQNameEquality : Name → Name → Bool
+
+  -- Is the argument visible (explicit), hidden (implicit), or an
+  -- instance argument?
+
+  data Visibility : Set where
+    visible hidden instance : Visibility
+
+  {-# BUILTIN HIDING   Visibility #-}
+  {-# BUILTIN VISIBLE  visible    #-}
+  {-# BUILTIN HIDDEN   hidden     #-}
+  {-# BUILTIN INSTANCE instance   #-}
+
+  -- Arguments can be relevant or irrelevant.
+
+  data Relevance : Set where
+    relevant irrelevant : Relevance
+
+  {-# BUILTIN RELEVANCE  Relevance  #-}
+  {-# BUILTIN RELEVANT   relevant   #-}
+  {-# BUILTIN IRRELEVANT irrelevant #-}
+
+  -- Arguments.
+
+  data Arg A : Set where
+    arg : (v : Visibility) (r : Relevance) (x : A) → Arg A
+
+  {-# BUILTIN ARG    Arg #-}
+  {-# BUILTIN ARGARG arg #-}
+
+  -- Terms.
+
+  mutual
+    data Term : Set where
+      -- Variable applied to arguments.
+      var     : (x : ℕ) (args : List (Arg Term)) → Term
+      -- Constructor applied to arguments.
+      con     : (c : Name) (args : List (Arg Term)) → Term
+      -- Identifier applied to arguments.
+      def     : (f : Name) (args : List (Arg Term)) → Term
+      -- Different kinds of λ-abstraction.
+      lam     : (v : Visibility) (t : Term) → Term
+      -- Pi-type.
+      pi      : (t₁ : Arg Type) (t₂ : Type) → Term
+      -- A sort.
+      sort    : Sort → Term
+      -- Anything else.
+      unknown : Term
+
+    data Type : Set where
+      el : (s : Sort) (t : Term) → Type
+
+    data Sort : Set where
+      -- A Set of a given (possibly neutral) level.
+      set     : (t : Term) → Sort
+      -- A Set of a given concrete level.
+      lit     : (n : ℕ) → Sort
+      -- Anything else.
+      unknown : Sort
+
+  {-# BUILTIN AGDASORT            Sort    #-}
+  {-# BUILTIN AGDATYPE            Type    #-}
+  {-# BUILTIN AGDATERM            Term    #-}
+  {-# BUILTIN AGDATERMVAR         var     #-}
+  {-# BUILTIN AGDATERMCON         con     #-}
+  {-# BUILTIN AGDATERMDEF         def     #-}
+  {-# BUILTIN AGDATERMLAM         lam     #-}
+  {-# BUILTIN AGDATERMPI          pi      #-}
+  {-# BUILTIN AGDATERMSORT        sort    #-}
+  {-# BUILTIN AGDATERMUNSUPPORTED unknown #-}
+  {-# BUILTIN AGDATYPEEL          el      #-}
+  {-# BUILTIN AGDASORTSET         set     #-}
+  {-# BUILTIN AGDASORTLIT         lit     #-}
+  {-# BUILTIN AGDASORTUNSUPPORTED unknown #-}
+
+  postulate
+    -- Function definition.
+    Function  : Set
+    -- Data type definition.
+    Data-type : Set
+    -- Record type definition.
+    Record    : Set
+
+  {-# BUILTIN AGDAFUNDEF    Function  #-}
+  {-# BUILTIN AGDADATADEF   Data-type #-}
+  {-# BUILTIN AGDARECORDDEF Record    #-}
+
+  -- Definitions.
+
+  data Definition : Set where
+    function     : Function  → Definition
+    data-type    : Data-type → Definition
+    record′      : Record    → Definition
+    constructor′ : Definition
+    axiom        : Definition
+    primitive′   : Definition
+
+  {-# BUILTIN AGDADEFINITION                Definition   #-}
+  {-# BUILTIN AGDADEFINITIONFUNDEF          function     #-}
+  {-# BUILTIN AGDADEFINITIONDATADEF         data-type    #-}
+  {-# BUILTIN AGDADEFINITIONRECORDDEF       record′      #-}
+  {-# BUILTIN AGDADEFINITIONDATACONSTRUCTOR constructor′ #-}
+  {-# BUILTIN AGDADEFINITIONPOSTULATE       axiom        #-}
+  {-# BUILTIN AGDADEFINITIONPRIMITIVE       primitive′   #-}
+
+  primitive
+    -- The type of the thing with the given name.
+    primQNameType        : Name → Type
+    -- The definition of the thing with the given name.
+    primQNameDefinition  : Name → Definition
+    -- The constructors of the given data type.
+    primDataConstructors : Data-type → List Name
+  ```
+
+  As an example the expression
+
+  ```agda
+  primQNameType (quote zero)
+  ```
+
+  is definitionally equal to
+
+  ```agda
+  el (lit 0) (def (quote ℕ) [])
+  ```
+
+  (if `zero` is a constructor of the data type `ℕ`).
+
+* New keyword: `unquote`.
+
+  The construction `unquote t` converts a representation of an Agda term
+  to actual Agda code in the following way:
+
+  1. The argument `t` must have type `Term` (see the reflection API above).
+
+  2. The argument is normalised.
+
+  3. The entire construction is replaced by the normal form, which is
+     treated as syntax written by the user and type-checked in the
+     usual way.
+
+  Examples:
+
+  ```agda
+  test : unquote (def (quote ℕ) []) ≡ ℕ
+  test = refl
+
+  id : (A : Set) → A → A
+  id = unquote (lam visible (lam visible (var 0 [])))
+
+  id-ok : id ≡ (λ A (x : A) → x)
+  id-ok = refl
+  ```
+
+* New keyword: `quoteTerm`.
+
+  The construction `quoteTerm t` is similar to `quote n`, but whereas
+  `quote` is restricted to names `n`, `quoteTerm` accepts terms
+  `t`. The construction is handled in the following way:
+
+  1. The type of `t` is inferred. The term `t` must be type-correct.
+
+  2. The term `t` is normalised.
+
+  3. The construction is replaced by the Term representation (see the
+     reflection API above) of the normal form. Any unsolved metavariables
+     in the term are represented by the `unknown` term constructor.
+
+  Examples:
+
+  ```agda
+  test₁ : quoteTerm (λ {A : Set} (x : A) → x) ≡
+          lam hidden (lam visible (var 0 []))
+  test₁ = refl
+
+  -- Local variables are represented as de Bruijn indices.
+  test₂ : (λ {A : Set} (x : A) → quoteTerm x) ≡ (λ x → var 0 [])
+  test₂ = refl
+
+  -- Terms are normalised before being quoted.
+  test₃ : quoteTerm (0 + 0) ≡ con (quote zero) []
+  test₃ = refl
+  ```
+
+Compiler backends
+-----------------
+
+### MAlonzo
+
+* The MAlonzo backend's FFI now handles universe polymorphism in a
+  better way.
+
+  The translation of Agda types and kinds into Haskell now supports
+  universe-polymorphic postulates. The core changes are that the
+  translation of function types has been changed from
+
+  ```
+  T[[ Pi (x : A) B ]] =
+    if A has a Haskell kind then
+      forall x. () -> T[[ B ]]
+    else if x in fv B then
+      undef
+    else
+      T[[ A ]] -> T[[ B ]]
+  ```
+
+  into
+
+  ```
+  T[[ Pi (x : A) B ]] =
+    if x in fv B then
+      forall x. T[[ A ]] -> T[[ B ]]  -- Note: T[[A]] not Unit.
+    else
+      T[[ A ]] -> T[[ B ]],
+  ```
+
+  and that the translation of constants (postulates, constructors and
+  literals) has been changed from
+
+  ```
+  T[[ k As ]] =
+    if COMPILED_TYPE k T then
+      T T[[ As ]]
+    else
+      undef
+  ```
+
+  into
+
+  ```
+  T[[ k As ]] =
+    if COMPILED_TYPE k T then
+      T T[[ As ]]
+    else if COMPILED k E then
+      ()
+    else
+      undef.
+  ```
+
+  For instance, assuming a Haskell definition
+
+  ```haskell
+    type AgdaIO a b = IO b,
+  ```
+
+  we can set up universe-polymorphic `IO` in the following way:
+
+  ```agda
+  postulate
+    IO     : ∀ {ℓ} → Set ℓ → Set ℓ
+    return : ∀ {a} {A : Set a} → A → IO A
+    _>>=_  : ∀ {a b} {A : Set a} {B : Set b} →
+             IO A → (A → IO B) → IO B
+
+  {-# COMPILED_TYPE IO AgdaIO              #-}
+  {-# COMPILED return  (\_ _ -> return)    #-}
+  {-# COMPILED _>>=_   (\_ _ _ _ -> (>>=)) #-}
+  ```
+
+  This is accepted because (assuming that the universe level type is
+  translated to the Haskell unit type `()`)
+
+  ```haskell
+  (\_ _ -> return)
+    : forall a. () -> forall b. () -> b -> AgdaIO a b
+    = T [[ ∀ {a} {A : Set a} → A → IO A ]]
+  ```
+
+  and
+
+  ```haskell
+  (\_ _ _ _ -> (>>=))
+    : forall a. () -> forall b. () ->
+        forall c. () -> forall d. () ->
+          AgdaIO a c -> (c -> AgdaIO b d) -> AgdaIO b d
+    = T [[ ∀ {a b} {A : Set a} {B : Set b} →
+             IO A → (A → IO B) → IO B ]].
+  ```
+
+### Epic
+
+* New Epic backend pragma: `STATIC`.
+
+  In the Epic backend, functions marked with the `STATIC` pragma will be
+  normalised before compilation. Example usage:
+
+  ```
+  {-# STATIC power #-}
+
+  power : ℕ → ℕ → ℕ
+  power 0       x = 1
+  power 1       x = x
+  power (suc n) x = power n x * x
+  ```
+
+  Occurrences of `power 4 x` will be replaced by `((x * x) * x) * x`.
+
+* Some new optimisations have been implemented in the Epic backend:
+
+  - Removal of unused arguments.
+
+  A worker/wrapper transformation is performed so that unused
+  arguments can be removed by Epic's inliner. For instance, the map
+  function is transformed in the following way:
+
+  ```agda
+  map_wrap : (A B : Set) → (A → B) → List A → List B
+  map_wrap A B f xs = map_work f xs
+
+  map_work f []       = []
+  map_work f (x ∷ xs) = f x ∷ map_work f xs
+  ```
+
+  If `map_wrap` is inlined (which it will be in any saturated call),
+  then `A` and `B` disappear in the generated code.
+
+  Unused arguments are found using abstract interpretation. The bodies
+  of all functions in a module are inspected to decide which variables
+  are used. The behaviour of postulates is approximated based on their
+  types. Consider `return`, for instance:
+
+  ```agda
+  postulate return : {A : Set} → A → IO A
+  ```
+
+  The first argument of `return` can be removed, because it is of type
+  Set and thus cannot affect the outcome of a program at runtime.
+
+  - Injection detection.
+
+  At runtime many functions may turn out to be inefficient variants of
+  the identity function. This is especially true after forcing.
+  Injection detection replaces some of these functions with more
+  efficient versions. Example:
+
+  ```agda
+  inject : {n : ℕ} → Fin n → Fin (1 + n)
+  inject {suc n} zero    = zero
+  inject {suc n} (suc i) = suc (inject {n} i)
+  ```
+
+  Forcing removes the `Fin` constructors' `ℕ` arguments, so this
+  function is an inefficient identity function that can be replaced by
+  the following one:
+
+  ```agda
+  inject {_} x = x
+  ```
+
+  To actually find this function, we make the induction hypothesis
+  that inject is an identity function in its second argument and look
+  at the branches of the function to decide if this holds.
+
+  Injection detection also works over data type barriers. Example:
+
+  ```agda
+  forget : {A : Set} {n : ℕ} → Vec A n → List A
+  forget []       = []
+  forget (x ∷ xs) = x ∷ forget xs
+  ```
+
+  Given that the constructor tags (in the compiled Epic code) for
+  `Vec.[]` and `List.[]` are the same, and that the tags for `Vec._∷_`
+  and `List._∷_` are also the same, this is also an identity
+  function. We can hence replace the definition with the following
+  one:
+
+  ```agda
+  forget {_} xs = xs
+  ```
+
+  To get this to apply as often as possible, constructor tags are
+  chosen *after* injection detection has been run, in a way to make as
+  many functions as possible injections.
+
+  Constructor tags are chosen once per source file, so it may be
+  advantageous to define conversion functions like forget in the same
+  module as one of the data types. For instance, if `Vec.agda` imports
+  `List.agda`, then the forget function should be put in `Vec.agda` to
+  ensure that vectors and lists get the same tags (unless some other
+  injection function, which puts different constraints on the tags, is
+  prioritised).
+
+  - Smashing.
+
+  This optimisation finds types whose values are inferable at runtime:
+
+    * A data type with only one constructor where all fields are
+      inferable is itself inferable.
+
+    * `Set ℓ` is inferable (as it has no runtime representation).
+
+  A function returning an inferable data type can be smashed, which
+  means that it is replaced by a function which simply returns the
+  inferred value.
+
+  An important example of an inferable type is the usual propositional
+  equality type (`_≡_`). Any function returning a propositional
+  equality can simply return the reflexivity constructor directly
+  without computing anything.
+
+  This optimisation makes more arguments unused. It also makes the
+  Epic code size smaller, which in turn speeds up compilation.
+
+### JavaScript
+
+* ECMAScript compiler backend.
+
+  A new compiler backend is being implemented, targetting ECMAScript
+  (also known as JavaScript), with the goal of allowing Agda programs
+  to be run in browsers or other ECMAScript environments.
+
+  The backend is still at an experimental stage: the core language is
+  implemented, but many features are still missing.
+
+  The ECMAScript compiler can be invoked from the command line using
+  the flag `--js`:
+
+  ```
+  agda --js --compile-dir=<DIR> <FILE>.agda
+  ```
+
+  Each source `<FILE>.agda` is compiled into an ECMAScript target
+  `<DIR>/jAgda.<TOP-LEVEL MODULE NAME>.js`. The compiler can also be
+  invoked using the Emacs mode (the variable `agda2-backend` controls
+  which backend is used).
+
+  Note that ECMAScript is a strict rather than lazy language. Since
+  Agda programs are total, this should not impact program semantics,
+  but it may impact their space or time usage.
+
+  ECMAScript does not support algebraic datatypes or pattern-matching.
+  These features are translated to a use of the visitor pattern. For
+  instance, the standard library's `List` data type and `null`
+  function are translated into the following code:
+
+  ```javascript
+  exports["List"] = {};
+  exports["List"]["[]"] = function (x0) {
+      return x0["[]"]();
+    };
+  exports["List"]["_∷_"] = function (x0) {
+      return function (x1) {
+        return function (x2) {
+          return x2["_∷_"](x0, x1);
+        };
+      };
+    };
+
+  exports["null"] = function (x0) {
+      return function (x1) {
+        return function (x2) {
+          return x2({
+            "[]": function () {
+              return jAgda_Data_Bool["Bool"]["true"];
+            },
+            "_∷_": function (x3, x4) {
+              return jAgda_Data_Bool["Bool"]["false"];
+            }
+          });
+        };
+      };
+    };
+  ```
+
+  Agda records are translated to ECMAScript objects, preserving field
+  names.
+
+  Top-level Agda modules are translated to ECMAScript modules,
+  following the `common.js` module specification. A top-level Agda
+  module `Foo.Bar` is translated to an ECMAScript module
+  `jAgda.Foo.Bar`.
+
+  The ECMAScript compiler does not compile to Haskell, so the pragmas
+  related to the Haskell FFI (`IMPORT`, `COMPILED_DATA` and
+  `COMPILED`) are not used by the ECMAScript backend. Instead, there
+  is a `COMPILED_JS` pragma which may be applied to any
+  declaration. For postulates, primitives, functions and values, it
+  gives the ECMAScript code to be emitted by the compiler. For data
+  types, it gives a function which is applied to a value of that type,
+  and a visitor object. For instance, a binding of natural numbers to
+  ECMAScript integers (ignoring overflow errors) is:
+
+  ```agda
+  data ℕ : Set where
+    zero : ℕ
+    suc  : ℕ → ℕ
+
+  {-# COMPILED_JS ℕ function (x,v) {
+      if (x < 1) { return v.zero(); } else { return v.suc(x-1); }
+    } #-}
+  {-# COMPILED_JS zero 0 #-}
+  {-# COMPILED_JS suc function (x) { return x+1; } #-}
+
+  _+_ : ℕ → ℕ → ℕ
+  zero  + n = n
+  suc m + n = suc (m + n)
+
+  {-# COMPILED_JS _+_ function (x) { return function (y) {
+                        return x+y; };
+    } #-}
+  ```
+
+  To allow FFI code to be optimised, the ECMAScript in a `COMPILED_JS`
+  declaration is parsed, using a simple parser that recognises a pure
+  functional subset of ECMAScript, consisting of functions, function
+  applications, return, if-statements, if-expressions,
+  side-effect-free binary operators (no precedence, left associative),
+  side-effect-free prefix operators, objects (where all member names
+  are quoted), field accesses, and string and integer literals.
+  Modules may be imported using the require (`<module-id>`) syntax: any
+  impure code, or code outside the supported fragment, can be placed
+  in a module and imported.
+
+Tools
+-----
+
+* New flag `--safe`, which can be used to type-check untrusted code.
+
+  This flag disables postulates, `primTrustMe`, and "unsafe" `OPTIONS`
+  pragmas, some of which are known to make Agda inconsistent.
+
+  Rejected pragmas:
+
+  ```
+  --allow-unsolved-metas
+  --experimental-irrelevance
+  --guardedness-preserving-type-construtors
+  --injective-type-constructors
+  --no-coverage-check
+  --no-positivity-check
+  --no-termination-check
+  --sized-types
+  --type-in-type
+  ```
+
+  Note that, at the moment, it is not possible to define the universe
+  level or coinduction primitives when `--safe` is used (because they
+  must be introduced as postulates). This can be worked around by
+  type-checking trusted files in a first pass, without using `--safe`,
+  and then using `--saf`e in a second pass. Modules which have already
+  been type-checked are not re-type-checked just because `--safe` is
+  used.
+
+* Dependency graphs.
+
+  The new flag `--dependency-graph=FILE` can be used to generate a DOT
+  file containing a module dependency graph. The generated file (FILE)
+  can be rendered using a tool like dot.
+
+* The `--no-unreachable-check` flag has been removed.
+
+* Projection functions are highlighted as functions instead of as
+  fields. Field names (in record definitions and record values) are
+  still highlighted as fields.
+
+* Support for jumping to positions mentioned in the information
+  buffer has been added.
+
+* The `make install` command no longer installs Agda globally (by
+  default).
diff --git a/doc/release-notes/2.3.2.1.md b/doc/release-notes/2.3.2.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.3.2.1.md
@@ -0,0 +1,16 @@
+Release notes for Agda 2 version 2.3.2.1
+========================================
+
+Installation
+------------
+
+* Made it possible to compile Agda with more recent versions of
+  hashable, QuickCheck and Win32.
+
+* Excluded mtl-2.1.
+
+Type checking
+-------------
+
+* Fixed bug in the termination checker
+  (Issue [#754](https://github.com/agda/agda/issues/754)).
diff --git a/doc/release-notes/2.3.2.2.md b/doc/release-notes/2.3.2.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.3.2.2.md
@@ -0,0 +1,10 @@
+Release notes for Agda 2 version 2.3.2.2
+========================================
+
+* Fixed a bug that sometimes made it tricky to use the Emacs mode on
+  Windows [Issue [#757](https://github.com/agda/agda/issues/757)].
+
+* Made Agda build with newer versions of some libraries.
+
+* Fixed a bug that caused ambiguous parse error messages
+  [Issue [#147](https://github.com/agda/agda/issues/147)].
diff --git a/doc/release-notes/2.3.2.md b/doc/release-notes/2.3.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.3.2.md
@@ -0,0 +1,806 @@
+Release notes for Agda 2 version 2.3.2
+======================================
+
+Installation
+------------
+
+* The Agda-executable package has been removed.
+
+  The executable is now provided as part of the Agda package.
+
+* The Emacs mode no longer depends on haskell-mode or GHCi.
+
+* Compilation of Emacs mode Lisp files.
+
+  You can now compile the Emacs mode Lisp files by running `agda-mode
+  compile`. This command is run by `make install`.
+
+  Compilation can, in some cases, give a noticeable speedup.
+
+  WARNING: If you reinstall the Agda mode without recompiling the
+  Emacs Lisp files, then Emacs may continue using the old, compiled
+  files.
+
+Pragmas and options
+-------------------
+
+* The `--without-K` check now reconstructs constructor parameters.
+
+  New specification of `--without-K`:
+
+  If the flag is activated, then Agda only accepts certain
+  case-splits. If the type of the variable to be split is
+  `D pars ixs`, where `D` is a data (or record) type, `pars` stands
+  for the parameters, and `ixs` the indices, then the following
+  requirements must be satisfied:
+
+  - The indices `ixs` must be applications of constructors (or
+    literals) to distinct variables. Constructors are usually not
+    applied to parameters, but for the purposes of this check
+    constructor parameters are treated as other arguments.
+
+  - These distinct variables must not be free in pars.
+
+* Irrelevant arguments are printed as `_` by default now.  To turn on
+  printing of irrelevant arguments, use option
+
+  ```
+  --show-irrelevant
+  ```
+
+* New: Pragma `NO_TERMINATION_CHECK` to switch off termination checker
+  for individual function definitions and mutual blocks.
+
+  The pragma must precede a function definition or a mutual block.
+  Examples (see `test/Succeed/NoTerminationCheck.agda`):
+
+  1. Skipping a single definition: before type signature.
+
+     ```agda
+     {-# NO_TERMINATION_CHECK #-}
+     a : A
+     a = a
+     ```
+
+  2. Skipping a single definition: before first clause.
+
+     ```agda
+     b : A
+     {-# NO_TERMINATION_CHECK #-}
+     b = b
+     ```
+
+  3. Skipping an old-style mutual block: Before `mutual` keyword.
+
+     ```agda
+     {-# NO_TERMINATION_CHECK #-}
+     mutual
+       c : A
+       c = d
+
+       d : A
+       d = c
+     ```
+
+  4. Skipping a new-style mutual block: Anywhere before a type
+     signature or first function clause in the block
+
+     ```agda
+     i : A
+     j : A
+
+     i = j
+     {-# NO_TERMINATION_CHECK #-}
+     j = i
+     ```
+
+  The pragma cannot be used in `--safe` mode.
+
+Language
+--------
+
+* Let binding record patterns
+
+  ```agda
+  record _×_ (A B : Set) : Set where
+    constructor _,_
+    field
+      fst : A
+      snd : B
+  open _×_
+
+  let (x , (y , z)) = t
+  in  u
+  ```
+
+  will now be interpreted as
+
+  ```agda
+  let x = fst t
+      y = fst (snd t)
+      z = snd (snd t)
+  in  u
+  ```
+
+  Note that the type of `t` needs to be inferable. If you need to
+  provide a type signature, you can write the following:
+
+  ```agda
+  let a : ...
+      a = t
+      (x , (y , z)) = a
+  in  u
+  ```
+
+* Pattern synonyms
+
+  A pattern synonym is a declaration that can be used on the left hand
+  side (when pattern matching) as well as the right hand side (in
+  expressions). For example:
+
+  ```agda
+  pattern z    = zero
+  pattern ss x = suc (suc x)
+
+  f : ℕ -> ℕ
+  f z       = z
+  f (suc z) = ss z
+  f (ss n)  = n
+  ```
+
+  Pattern synonyms are implemented by substitution on the abstract
+  syntax, so definitions are scope-checked but not type-checked. They
+  are particularly useful for universe constructions.
+
+* Qualified mixfix operators
+
+  It is now possible to use a qualified mixfix operator by qualifying
+  the first part of the name. For instance
+
+  ```agda
+  import Data.Nat as Nat
+  import Data.Bool as Bool
+
+  two = Bool.if true then 1 Nat.+ 1 else 0
+  ```
+
+* Sections [Issue [#735](https://github.com/agda/agda/issues/735)].
+  Agda now parses anonymous modules as sections:
+
+  ```agda
+  module _ {a} (A : Set a) where
+
+    data List : Set a where
+      []  : List
+      _∷_ : (x : A) (xs : List) → List
+
+  module _ {a} {A : Set a} where
+
+    _++_ : List A → List A → List A
+    []       ++ ys = ys
+    (x ∷ xs) ++ ys = x ∷ (xs ++ ys)
+
+  test : List Nat
+  test = (5 ∷ []) ++ (3 ∷ [])
+  ```
+
+  In general, now the syntax
+
+  ```agda
+  module _ parameters where
+    declarations
+  ```
+
+  is accepted and has the same effect as
+
+  ```agda
+  private
+    module M parameters where
+      declarations
+  open M public
+  ```
+
+  for a fresh name `M`.
+
+* Instantiating a module in an open import statement
+  [Issue [#481](https://github.com/agda/agda/issues/481)]. Now
+  accepted:
+
+  ```agda
+  open import Path.Module args [using/hiding/renaming (...)]
+  ```
+
+  This only brings the imported identifiers from `Path.Module` into scope,
+  not the module itself!  Consequently, the following is pointless, and raises
+  an error:
+
+  ```agda
+    import Path.Module args [using/hiding/renaming (...)]
+  ```
+
+  You can give a private name `M` to the instantiated module via
+
+  ```agda
+  import Path.Module args as M [using/hiding/renaming (...)]
+  open import Path.Module args as M [using/hiding/renaming (...)]
+  ```
+
+  Try to avoid `as` as part of the arguments.  `as` is not a keyword;
+  the following can be legal, although slightly obfuscated Agda code:
+
+  ```agda
+  open import as as as as as as
+  ```
+
+* Implicit module parameters can be given by name. E.g.
+
+  ```agda
+  open M {namedArg = bla}
+  ```
+
+  This feature has been introduced in Agda 2.3.0 already.
+
+* Multiple type signatures sharing a same type can now be written as a single
+  type signature.
+
+  ```agda
+  one two : ℕ
+  one = suc zero
+  two = suc one
+  ```
+
+Goal and error display
+----------------------
+
+* Meta-variables that were introduced by hidden argument `arg` are now
+  printed as `_arg_number` instead of just `_number`.
+  [Issue [#526](https://github.com/agda/agda/issues/526)]
+
+* Agda expands identifiers in anonymous modules when printing.  Should
+  make some goals nicer to read.
+  [Issue [#721](https://github.com/agda/agda/issues/721)]
+
+* When a module identifier is ambiguous, Agda tells you if one of them
+  is a data type module.
+  [Issues [#318](https://github.com/agda/agda/issues/318),
+  [#705](https://github.com/agda/agda/issues/705)]
+
+Type checking
+-------------
+
+* Improved coverage checker. The coverage checker splits on arguments
+  that have constructor or literal pattern, committing to the
+  left-most split that makes progress.  Consider the lookup function
+  for vectors:
+
+  ```agda
+  data Fin : Nat → Set where
+    zero : {n : Nat} → Fin (suc n)
+    suc  : {n : Nat} → Fin n → Fin (suc n)
+
+  data Vec (A : Set) : Nat → Set where
+    []  : Vec A zero
+    _∷_ : {n : Nat} → A → Vec A n → Vec A (suc n)
+
+  _!!_ : {A : Set}{n : Nat} → Vec A n → Fin n → A
+  (x ∷ xs) !! zero  = x
+  (x ∷ xs) !! suc i = xs !! i
+  ```
+
+  In Agda up to 2.3.0, this definition is rejected unless we add
+  an absurd clause
+
+  ```agda
+  [] !! ()
+  ```
+
+  This is because the coverage checker committed on splitting on the
+  vector argument, even though this inevitably lead to failed
+  coverage, because a case for the empty vector `[]` is missing.
+
+  The improvement to the coverage checker consists on committing only
+  on splits that have a chance of covering, since all possible
+  constructor patterns are present.  Thus, Agda will now split first
+  on the `Fin` argument, since cases for both `zero` and `suc` are
+  present.  Then, it can split on the `Vec` argument, since the empty
+  vector is already ruled out by instantiating `n` to a `suc _`.
+
+* Instance arguments resolution will now consider candidates which
+  still expect hidden arguments. For example:
+
+  ```agda
+  record Eq (A : Set) : Set where
+    field eq : A → A → Bool
+
+  open Eq {{...}}
+
+  eqFin : {n : ℕ} → Eq (Fin n)
+  eqFin = record { eq = primEqFin }
+
+  testFin : Bool
+  testFin = eq fin1 fin2
+  ```
+
+  The type-checker will now resolve the instance argument of the `eq`
+  function to `eqFin {_}`. This is only done for hidden arguments, not
+  instance arguments, so that the instance search stays non-recursive.
+
+* Constraint solving: Upgraded Miller patterns to record patterns.
+  [Issue [#456](https://github.com/agda/agda/issues/456)]
+
+  Agda now solves meta-variables that are applied to record patterns.
+  A typical (but here, artificial) case is:
+
+  ```agda
+  record Sigma (A : Set)(B : A -> Set) : Set where
+    constructor _,_
+    field
+      fst : A
+      snd : B fst
+
+  test : (A : Set)(B : A -> Set) ->
+    let X : Sigma A B -> Sigma A B
+        X = _
+    in  (x : A)(y : B x) -> X (x , y) ≡ (x , y)
+  test A B x y = refl
+  ```
+
+  This yields a constraint of the form
+
+  ```
+  _X A B (x , y) := t[x,y]
+  ```
+
+  (with `t[x,y] = (x, y)`) which is not a Miller pattern.
+  However, Agda now solves this as
+
+  ```
+  _X A B z := t[fst z,snd z].
+  ```
+
+* Changed: solving recursive constraints.
+  [Issue [#585](https://github.com/agda/agda/issues/585)]
+
+  Until 2.3.0, Agda sometimes inferred values that did not pass the
+  termination checker later, or would even make Agda loop. To prevent
+  this, the occurs check now also looks into the definitions of the
+  current mutual block, to avoid constructing recursive solutions. As
+  a consequence, also terminating recursive solutions are no longer
+  found automatically.
+
+  This effects a programming pattern where the recursively computed
+  type of a recursive function is left to Agda to solve.
+
+  ```agda
+  mutual
+
+    T : D -> Set
+    T pattern1 = _
+    T pattern2 = _
+
+    f : (d : D) -> T d
+    f pattern1 = rhs1
+    f pattern2 = rhs2
+  ```
+
+  This might no longer work from now on. See examples
+  `test/Fail/Issue585*.agda`.
+
+* Less eager introduction of implicit parameters.
+  [Issue [#679](https://github.com/agda/agda/issues/679)]
+
+  Until Agda 2.3.0, trailing hidden parameters were introduced eagerly
+  on the left hand side of a definition.  For instance, one could not
+  write
+
+  ```agda
+  test : {A : Set} -> Set
+  test = \ {A} -> A
+  ```
+
+  because internally, the hidden argument `{A : Set}` was added to the
+  left-hand side, yielding
+
+  ```agda
+  test {_} = \ {A} -> A
+  ```
+
+  which raised a type error.  Now, Agda only introduces the trailing
+  implicit parameters it has to, in order to maintain uniform function
+  arity.  For instance, in
+
+  ```agda
+  test : Bool -> {A B C : Set} -> Set
+  test true {A}      = A
+  test false {B = B} = B
+  ```
+
+  Agda will introduce parameters `A` and `B` in all clauses, but not
+  `C`, resulting in
+
+  ```agda
+  test : Bool -> {A B C : Set} -> Set
+  test true  {A} {_}     = A
+  test false {_} {B = B} = B
+  ```
+
+  Note that for checking `where`-clauses, still all hidden trailing
+  parameters are in scope.  For instance:
+
+  ```agda
+  id : {i : Level}{A : Set i} -> A -> A
+  id = myId
+    where myId : forall {A} -> A -> A
+          myId x = x
+  ```
+
+  To be able to fill in the meta variable `_1` in
+
+  ```agda
+  myId : {A : Set _1} -> A -> A
+  ```
+
+  the hidden parameter `{i : Level}` needs to be in scope.
+
+  As a result of this more lazy introduction of implicit parameters,
+  the following code now passes.
+
+  ```agda
+  data Unit : Set where
+    unit : Unit
+
+  T : Unit → Set
+  T unit = {u : Unit} → Unit
+
+  test : (u : Unit) → T u
+  test unit with unit
+  ... | _ = λ {v} → v
+  ```
+
+  Before, Agda would eagerly introduce the hidden parameter `{v}` as
+  unnamed left-hand side parameter, leaving no way to refer to it.
+
+  The related Issue [#655](https://github.com/agda/agda/issues/655)
+  has also been addressed.  It is now possible to make `synonym'
+  definitions
+
+  ```
+  name = expression
+  ```
+
+  even when the type of expression begins with a hidden quantifier.
+  Simple example:
+
+  ```
+  id2 = id
+  ```
+
+  That resulted in unsolved metas until 2.3.0.
+
+* Agda detects unused arguments and ignores them during equality
+  checking. [Issue [#691](https://github.com/agda/agda/issues/691),
+  solves also Issue [#44](https://github.com/agda/agda/issues/44)]
+
+  Agda's polarity checker now assigns 'Nonvariant' to arguments that
+  are not actually used (except for absurd matches).  If `f`'s first
+  argument is Nonvariant, then `f x` is definitionally equal to `f y`
+  regardless of `x` and `y`.  It is similar to irrelevance, but does
+  not require user annotation.
+
+  For instance, unused module parameters do no longer get in the way:
+
+  ```agda
+  module M (x : Bool) where
+
+    not : Bool → Bool
+    not true  = false
+    not false = true
+
+  open M true
+  open M false renaming (not to not′)
+
+  test : (y : Bool) → not y ≡ not′ y
+  test y = refl
+  ```
+
+  Matching against record or absurd patterns does not count as `use',
+  so we get some form of proof irrelevance:
+
+  ```agda
+  data ⊥ : Set where
+  record ⊤ : Set where
+    constructor trivial
+
+  data Bool : Set where
+    true false : Bool
+
+  True : Bool → Set
+  True true  = ⊤
+  True false = ⊥
+
+  fun : (b : Bool) → True b → Bool
+  fun true  trivial = true
+  fun false ()
+
+  test : (b : Bool) → (x y : True b) → fun b x ≡ fun b y
+  test b x y = refl
+  ```
+
+  More examples in `test/Succeed/NonvariantPolarity.agda`.
+
+  Phantom arguments:  Parameters of record and data types are considered
+  `used' even if they are not actually used.  Consider:
+
+  ```agda
+  False : Nat → Set
+  False zero    = ⊥
+  False (suc n) = False n
+
+  module Invariant where
+    record Bla (n : Nat)(p : False n) : Set where
+
+  module Nonvariant where
+    Bla : (n : Nat) → False n → Set
+    Bla n p = ⊤
+  ```
+
+  Even though record `Bla` does not use its parameters `n` and `p`,
+  they are considered as used, allowing "phantom type" techniques.
+
+  In contrast, the arguments of function `Bla` are recognized as
+  unused.  The following code type-checks if we open `Invariant` but
+  leaves unsolved metas if we open `Nonvariant`.
+
+  ```agda
+  drop-suc : {n : Nat}{p : False n} → Bla (suc n) p → Bla n p
+  drop-suc _ = _
+
+  bla : (n : Nat) → {p : False n} → Bla n p → ⊥
+  bla zero {()} b
+  bla (suc n) b = bla n (drop-suc b)
+  ```
+
+  If `Bla` is considered invariant, the hidden argument in the
+  recursive call can be inferred to be `p`.  If it is considered
+  non-variant, then `Bla n X = Bla n p` does not entail `X = p` and
+  the hidden argument remains unsolved.  Since `bla` does not actually
+  use its hidden argument, its value is not important and it could be
+  searched for.  Unfortunately, polarity analysis of `bla` happens
+  only after type checking, thus, the information that `bla` is
+  non-variant in `p` is not available yet when meta-variables are
+  solved.  (See
+  `test/Fail/BrokenInferenceDueToNonvariantPolarity.agda`)
+
+* Agda now expands simple definitions (one clause, terminating) to
+  check whether a function is constructor
+  headed. [Issue [#747](https://github.com/agda/agda/issues/747)] For
+  instance, the following now also works:
+
+  ```agda
+  MyPair : Set -> Set -> Set
+  MyPair A B = Pair A B
+
+  Vec : Set -> Nat -> Set
+  Vec A zero    = Unit
+  Vec A (suc n) = MyPair A (Vec A n)
+  ```
+
+  Here, `Unit` and `Pair` are data or record types.
+
+Compiler backends
+-----------------
+
+* `-Werror` is now overridable.
+
+  To enable compilation of Haskell modules containing warnings, the
+  `-Werror` flag for the MAlonzo backend has been made
+  overridable. If, for example, `--ghc-flag=-Wwarn` is passed when
+  compiling, one can get away with things like:
+
+  ```agda
+  data PartialBool : Set where
+    true : PartialBool
+
+  {-# COMPILED_DATA PartialBool Bool True #-}
+  ```
+
+  The default behavior remains as it used to be and rejects the above
+  program.
+
+Tools
+-----
+
+### Emacs mode
+
+* Asynchronous Emacs mode.
+
+  One can now use Emacs while a buffer is type-checked. If the buffer
+  is edited while the type-checker runs, then syntax highlighting will
+  not be updated when type-checking is complete.
+
+* Interactive syntax highlighting.
+
+  The syntax highlighting is updated while a buffer is type-checked:
+
+  - At first the buffer is highlighted in a somewhat crude way
+    (without go-to-definition information for overloaded
+    constructors).
+
+  - If the highlighting level is "interactive", then the piece of code
+    that is currently being type-checked is highlighted as such. (The
+    default is "non-interactive".)
+
+  - When a mutual block has been type-checked it is highlighted
+    properly (this highlighting includes warnings for potential
+    non-termination).
+
+  The highlighting level can be controlled via the new configuration
+  variable `agda2-highlight-level`.
+
+* Multiple case-splits can now be performed in one go.
+
+  Consider the following example:
+
+  ```agda
+  _==_ : Bool → Bool → Bool
+  b₁ == b₂ = {!!}
+  ```
+
+  If you split on `b₁ b₂`, then you get the following code:
+
+  ```agda
+  _==_ : Bool → Bool → Bool
+  true == true = {!!}
+  true == false = {!!}
+  false == true = {!!}
+  false == false = {!!}
+  ```
+
+  The order of the variables matters. Consider the following code:
+
+  ```agda
+  lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A
+  lookup xs i = {!!}
+  ```
+
+  If you split on `xs i`, then you get the following code:
+
+  ```agda
+  lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A
+  lookup [] ()
+  lookup (x ∷ xs) zero = {!!}
+  lookup (x ∷ xs) (suc i) = {!!}
+  ```
+
+  However, if you split on `i xs`, then you get the following code
+  instead:
+
+  ```agda
+  lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A
+  lookup (x ∷ xs) zero = ?
+  lookup (x ∷ xs) (suc i) = ?
+  ```
+
+  This code is rejected by Agda 2.3.0, but accepted by 2.3.2 thanks
+  to improved coverage checking (see above).
+
+* The Emacs mode now presents information about which module is
+  currently being type-checked.
+
+* New global menu entry: `Information about the character at point`.
+
+  If this entry is selected, then information about the character at
+  point is displayed, including (in many cases) information about how
+  to type the character.
+
+* Commenting/uncommenting the rest of the buffer.
+
+  One can now comment or uncomment the rest of the buffer by typing
+  `C-c C-x M-;` or by selecting the menu entry `Comment/uncomment` the
+  rest of the buffer".
+
+* The Emacs mode now uses the Agda executable instead of GHCi.
+
+  The `*ghci*` buffer has been renamed to `*agda2*`.
+
+  A new configuration variable has been introduced:
+  `agda2-program-name`, the name of the Agda executable (by default
+  `agda`).
+
+  The variable `agda2-ghci-options` has been replaced by
+  `agda2-program-args`: extra arguments given to the Agda executable
+  (by default `none`).
+
+  If you want to limit Agda's memory consumption you can add some
+  arguments to `agda2-program-args`, for instance `+RTS -M1.5G -RTS`.
+
+* The Emacs mode no longer depends on haskell-mode.
+
+  Users who have customised certain haskell-mode variables (such as
+  `haskell-ghci-program-args`) may want to update their configuration.
+
+### LaTeX-backend
+
+An experimental LaTeX-backend which does precise highlighting a la the
+HTML-backend and code alignment a la lhs2TeX has been added.
+
+Here is a sample input literate Agda file:
+
+  ```latex
+  \documentclass{article}
+
+  \usepackage{agda}
+
+  \begin{document}
+
+  The following module declaration will be hidden in the output.
+
+  \AgdaHide{
+  \begin{code}
+  module M where
+  \end{code}
+  }
+
+  Two or more spaces can be used to make the backend align stuff.
+
+  \begin{code}
+  data ℕ : Set where
+    zero  : ℕ
+    suc   : ℕ → ℕ
+
+  _+_ : ℕ → ℕ → ℕ
+  zero   + n = n
+  suc m  + n = suc (m + n)
+  \end{code}
+
+  \end{document}
+  ```
+
+To produce an output PDF issue the following commands:
+
+  ```
+  agda --latex -i . <file>.lagda
+  pdflatex latex/<file>.tex
+  ```
+
+Only the top-most module is processed, like with lhs2tex and unlike
+with the HTML-backend. If you want to process imported modules you
+have to call `agda --latex` manually on each of those modules.
+
+There are still issues related to formatting, see the bug tracker for
+more information:
+
+  https://code.google.com/p/agda/issues/detail?id=697
+
+The default `agda.sty` might therefore change in backwards-incompatible
+ways, as work proceeds in trying to resolve those problems.
+
+Implemented features:
+
+* Two or more spaces can be used to force alignment of things, like
+  with lhs2tex. See example above.
+
+* The highlighting information produced by the type checker is used to
+  generate the output. For example, the data declaration in the
+  example above, produces:
+
+  ```agda
+  \AgdaKeyword{data} \AgdaDatatype{ℕ} \AgdaSymbol{:}
+      \AgdaPrimitiveType{Set} \AgdaKeyword{where}
+  ```
+
+  These LaTeX commands are defined in `agda.sty` (which is imported by
+  `\usepackage{agda}`) and cause the highlighting.
+
+* The LaTeX-backend checks if `agda.sty` is found by the LaTeX
+  environment, if it isn't a default `agda.sty` is copied from Agda's
+  `data-dir` into the working directory (and thus made available to
+  the LaTeX environment).
+
+  If the default `agda.sty` isn't satisfactory (colors, fonts,
+  spacing, etc) then the user can modify it and make put it somewhere
+  where the LaTeX environment can find it. Hopefully most aspects
+  should be modifiable via `agda.sty` rather than having to tweak the
+  implementation.
+
+* `--latex-dir` can be used to change the default output directory.
diff --git a/doc/release-notes/2.4.0.1.md b/doc/release-notes/2.4.0.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.0.1.md
@@ -0,0 +1,8 @@
+Release notes for Agda 2 version 2.4.0.1
+========================================
+
+* The option `--compile-no-main` has been renamed to `--no-main`.
+
+* `COMPILED_DATA` pragmas can now be given for records.
+
+* Various bug fixes.
diff --git a/doc/release-notes/2.4.0.2.md b/doc/release-notes/2.4.0.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.0.2.md
@@ -0,0 +1,90 @@
+Release notes for Agda 2 version 2.4.0.2
+========================================
+
+* The Agda input mode now supports alphabetical super and subscripts,
+  in addition to the numerical ones that were already present.
+  [Issue [#1240](https://github.com/agda/agda/issues/1240)]
+
+* New feature: Interactively split result.
+
+  Make case (`C-c C-c`) with no variables given tries to split on the
+  result to introduce projection patterns.  The hole needs to be of
+  record type, of course.
+
+  ```agda
+  test : {A B : Set} (a : A) (b : B) → A × B
+  test a b = ?
+  ```
+
+  Result-splitting `?` will produce the new clauses:
+
+  ```agda
+  proj₁ (test a b) = ?
+  proj₂ (test a b) = ?
+  ```
+
+  If hole is of function type ending in a record type, the necessary
+  pattern variables will be introduced before the split.  Thus, the
+  same result can be obtained by starting from:
+
+  ```agda
+  test : {A B : Set} (a : A) (b : B) → A × B
+  test = ?
+  ```
+
+* The so far undocumented `ETA` pragma now throws an error if applied to
+  definitions that are not records.
+
+  `ETA` can be used to force eta-equality at recursive record types,
+  for which eta is not enabled automatically by Agda.  Here is such an
+  example:
+
+  ```agda
+  mutual
+    data Colist (A : Set) : Set where
+      [] : Colist A
+      _∷_ : A → ∞Colist A → Colist A
+
+    record ∞Colist (A : Set) : Set where
+      coinductive
+      constructor delay
+      field       force : Colist A
+
+  open ∞Colist
+
+  {-# ETA ∞Colist #-}
+
+  test : {A : Set} (x : ∞Colist A) → x ≡ delay (force x)
+  test x = refl
+  ```
+
+  Note: Unsafe use of `ETA` can make Agda loop, e.g. by triggering
+  infinite eta expansion!
+
+* Bugs fixed (see [bug tracker](https://github.com/agda/agda/issues)):
+
+  [#1203](https://github.com/agda/agda/issues/1203)
+
+  [#1205](https://github.com/agda/agda/issues/1205)
+
+  [#1209](https://github.com/agda/agda/issues/1209)
+
+  [#1213](https://github.com/agda/agda/issues/1213)
+
+  [#1214](https://github.com/agda/agda/issues/1214)
+
+  [#1216](https://github.com/agda/agda/issues/1216)
+
+  [#1225](https://github.com/agda/agda/issues/1225)
+
+  [#1226](https://github.com/agda/agda/issues/1226)
+
+  [#1231](https://github.com/agda/agda/issues/1231)
+
+  [#1233](https://github.com/agda/agda/issues/1233)
+
+  [#1239](https://github.com/agda/agda/issues/1239)
+
+  [#1241](https://github.com/agda/agda/issues/1241)
+
+  [#1243](https://github.com/agda/agda/issues/1243)
diff --git a/doc/release-notes/2.4.0.md b/doc/release-notes/2.4.0.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.0.md
@@ -0,0 +1,1211 @@
+Release notes for Agda 2 version 2.4.0
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* A new module called `Agda.Primitive` has been introduced. This
+  module is available to all users, even if the standard library is
+  not used.  Currently the module contains level primitives and their
+  representation in Haskell when compiling with MAlonzo:
+
+  ```agda
+  infixl 6 _⊔_
+
+  postulate
+    Level : Set
+    lzero : Level
+    lsuc  : (ℓ : Level) → Level
+    _⊔_   : (ℓ₁ ℓ₂ : Level) → Level
+
+  {-# COMPILED_TYPE Level ()      #-}
+  {-# COMPILED lzero ()           #-}
+  {-# COMPILED lsuc  (\_ -> ())   #-}
+  {-# COMPILED _⊔_   (\_ _ -> ()) #-}
+
+  {-# BUILTIN LEVEL     Level  #-}
+  {-# BUILTIN LEVELZERO lzero  #-}
+  {-# BUILTIN LEVELSUC  lsuc   #-}
+  {-# BUILTIN LEVELMAX  _⊔_    #-}
+  ```
+
+  To bring these declarations into scope you can use a declaration
+  like the following one:
+
+  ```agda
+  open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+  ```
+
+  The standard library reexports these primitives (using the names
+  `zero` and `suc` instead of `lzero` and `lsuc`) from the `Level`
+  module.
+
+  Existing developments using universe polymorphism might now trigger
+  the following error message:
+
+  ```
+  Duplicate binding for built-in thing LEVEL, previous binding to
+    .Agda.Primitive.Level
+  ```
+
+  To fix this problem, please remove the duplicate bindings.
+
+  Technical details (perhaps relevant to those who build Agda
+  packages):
+
+  The include path now always contains a directory
+  `<DATADIR>/lib/prim`, and this directory is supposed to contain a
+  subdirectory Agda containing a file `Primitive.agda`.
+
+  The standard location of `<DATADIR>` is system- and
+  installation-specific.  E.g., in a Cabal `--user` installation of
+  Agda-2.3.4 on a standard single-ghc Linux system it would be
+  `$HOME/.cabal/share/Agda-2.3.4` or something similar.
+
+  The location of the `<DATADIR>` directory can be configured at
+  compile-time using Cabal flags (`--datadir` and `--datasubdir`).
+  The location can also be set at run-time, using the `Agda_datadir`
+  environment variable.
+
+Pragmas and options
+-------------------
+
+* Pragma `NO_TERMINATION_CHECK` placed within a mutual block is now
+  applied to the whole mutual block (rather than being discarded
+  silently).  Adding to the uses 1.-4. outlined in the release notes
+  for 2.3.2 we allow:
+
+  3a. Skipping an old-style mutual block: Somewhere within `mutual`
+      block before a type signature or first function clause.
+
+   ```agda
+   mutual
+     {-# NO_TERMINATION_CHECK #-}
+     c : A
+     c = d
+
+     d : A
+     d = c
+   ```
+
+* New option `--no-pattern-matching`
+
+  Disables all forms of pattern matching (for the current file).
+  You can still import files that use pattern matching.
+
+* New option `-v profile:7`
+
+  Prints some stats on which phases Agda spends how much time.
+  (Number might not be very reliable, due to garbage collection
+  interruptions, and maybe due to laziness of Haskell.)
+
+* New option `--no-sized-types`
+
+  Option `--sized-types` is now default.  `--no-sized-types` will turn
+  off an extra (inexpensive) analysis on data types used for subtyping
+  of sized types.
+
+Language
+--------
+
+* Experimental feature: `quoteContext`
+
+  There is a new keyword `quoteContext` that gives users access to the
+  list of names in the current local context. For instance:
+
+  ```agda
+  open import Data.Nat
+  open import Data.List
+  open import Reflection
+
+  foo : ℕ → ℕ → ℕ
+  foo 0 m = 0
+  foo (suc n) m = quoteContext xs in ?
+  ```
+
+  In the remaining goal, the list `xs` will consist of two names, `n`
+  and `m`, corresponding to the two local variables. At the moment it
+  is not possible to access let bound variables (this feature may be
+  added in the future).
+
+* Experimental feature: Varying arity.
+  Function clauses may now have different arity, e.g.,
+
+  ```agda
+  Sum : ℕ → Set
+  Sum 0       = ℕ
+  Sum (suc n) = ℕ → Sum n
+
+  sum : (n : ℕ) → ℕ → Sum n
+  sum 0       acc   = acc
+  sum (suc n) acc m = sum n (m + acc)
+  ```
+
+  or,
+
+  ```agda
+  T : Bool → Set
+  T true  = Bool
+  T false = Bool → Bool
+
+  f : (b : Bool) → T b
+  f false true  = false
+  f false false = true
+  f true = true
+  ```
+
+  This feature is experimental.  Yet unsupported:
+  - Varying arity and `with`.
+
+  - Compilation of functions with varying arity to Haskell, JS, or Epic.
+
+* Experimental feature: copatterns.  (Activated with option `--copatterns`)
+
+  We can now define a record by explaining what happens if you project
+  the record.  For instance:
+
+  ```agda
+  {-# OPTIONS --copatterns #-}
+
+  record _×_ (A B : Set) : Set where
+    constructor _,_
+    field
+      fst : A
+      snd : B
+  open _×_
+
+  pair : {A B : Set} → A → B → A × B
+  fst (pair a b) = a
+  snd (pair a b) = b
+
+  swap : {A B : Set} → A × B → B × A
+  fst (swap p) = snd p
+  snd (swap p) = fst p
+
+  swap3 : {A B C : Set} → A × (B × C) → C × (B × A)
+  fst (swap3 t)       = snd (snd t)
+  fst (snd (swap3 t)) = fst (snd t)
+  snd (snd (swap3 t)) = fst t
+  ```
+
+  Taking a projection on the left hand side (lhs) is called a
+  projection pattern, applying to a pattern is called an application
+  pattern.  (Alternative terms: projection/application copattern.)
+
+  In the first example, the symbol `pair`, if applied to variable
+  patterns `a` and `b` and then projected via `fst`, reduces to
+  `a`. `pair` by itself does not reduce.
+
+  A typical application are coinductive records such as streams:
+
+  ```agda
+  record Stream (A : Set) : Set where
+    coinductive
+    field
+      head : A
+      tail : Stream A
+  open Stream
+
+  repeat : {A : Set} (a : A) -> Stream A
+  head (repeat a) = a
+  tail (repeat a) = repeat a
+  ```
+
+  Again, `repeat a` by itself will not reduce, but you can take a
+  projection (head or tail) and then it will reduce to the respective
+  rhs.  This way, we get the lazy reduction behavior necessary to
+  avoid looping corecursive programs.
+
+  Application patterns do not need to be trivial (i.e., variable
+  patterns), if we mix with projection patterns.  E.g., we can have
+
+  ```agda
+  nats : Nat -> Stream Nat
+  head (nats zero) = zero
+  tail (nats zero) = nats zero
+  head (nats (suc x)) = x
+  tail (nats (suc x)) = nats x
+  ```
+
+  Here is an example (not involving coinduction) which demostrates
+  records with fields of function type:
+
+  ```agda
+  -- The State monad
+
+  record State (S A : Set) : Set where
+    constructor state
+    field
+      runState : S → A × S
+  open State
+
+  -- The Monad type class
+
+  record Monad (M : Set → Set) : Set1 where
+    constructor monad
+    field
+      return : {A : Set}   → A → M A
+      _>>=_  : {A B : Set} → M A → (A → M B) → M B
+
+
+  -- State is an instance of Monad
+  -- Demonstrates the interleaving of projection and application patterns
+
+  stateMonad : {S : Set} → Monad (State S)
+  runState (Monad.return stateMonad a  ) s  = a , s
+  runState (Monad._>>=_  stateMonad m k) s₀ =
+    let a , s₁ = runState m s₀
+    in  runState (k a) s₁
+
+  module MonadLawsForState {S : Set} where
+
+    open Monad (stateMonad {S})
+
+    leftId : {A B : Set}(a : A)(k : A → State S B) →
+      (return a >>= k) ≡ k a
+    leftId a k = refl
+
+    rightId : {A B : Set}(m : State S A) →
+      (m >>= return) ≡ m
+    rightId m = refl
+
+    assoc : {A B C : Set}(m : State S A)(k : A → State S B)(l : B → State S C) →
+      ((m >>= k) >>= l) ≡ (m >>= λ a → (k a >>= l))
+    assoc m k l = refl
+  ```
+
+  Copatterns are yet experimental and the following does not work:
+
+  - Copatterns and `with` clauses.
+
+  - Compilation of copatterns to Haskell, JS, or Epic.
+
+  - Projections generated by
+
+    ```agda
+    open R {{...}}
+    ```
+
+    are not handled properly on lhss yet.
+
+  - Conversion checking is slower in the presence of copatterns, since
+    stuck definitions of record type do no longer count as neutral,
+    since they can become unstuck by applying a projection. Thus,
+    comparing two neutrals currently requires comparing all they
+    projections, which repeats a lot of work.
+
+* Top-level module no longer required.
+
+  The top-level module can be omitted from an Agda file. The module
+  name is then inferred from the file name by dropping the path and
+  the `.agda` extension. So, a module defined in `/A/B/C.agda` would get
+  the name `C`.
+
+  You can also suppress only the module name of the top-level module
+  by writing
+
+  ```agda
+  module _ where
+  ```
+
+  This works also for parameterised modules.
+
+* Module parameters are now always hidden arguments in projections.
+  For instance:
+
+  ```agda
+  module M (A : Set) where
+
+    record Prod (B : Set) : Set where
+      constructor _,_
+      field
+        fst : A
+        snd : B
+    open Prod public
+
+  open M
+  ```
+
+  Now, the types of `fst` and `snd` are
+
+  ```agda
+  fst : {A : Set}{B : Set} → Prod A B → A
+  snd : {A : Set}{B : Set} → Prod A B → B
+  ```
+
+  Until 2.3.2, they were
+
+  ```agda
+  fst : (A : Set){B : Set} → Prod A B → A
+  snd : (A : Set){B : Set} → Prod A B → B
+  ```
+
+  This change is a step towards symmetry of constructors and projections.
+  (Constructors always took the module parameters as hidden arguments).
+
+* Telescoping lets: Local bindings are now accepted in telescopes
+  of modules, function types, and lambda-abstractions.
+
+  The syntax of telescopes as been extended to support `let`:
+
+  ```agda
+  id : (let ★ = Set) (A : ★) → A → A
+  id A x = x
+  ```
+
+  In particular one can now `open` modules inside telescopes:
+
+  ```agda
+  module Star where
+    ★ : Set₁
+    ★ = Set
+
+
+  module MEndo (let open Star) (A : ★) where
+    Endo : ★
+    Endo = A → A
+  ```
+
+  Finally a shortcut is provided for opening modules:
+
+  ```agda
+  module N (open Star) (A : ★) (open MEndo A) (f : Endo) where
+    ...
+  ```
+
+  The semantics of the latter is
+
+  ```agda
+  module _ where
+    open Star
+    module _ (A : ★) where
+      open MEndo A
+      module N (f : Endo) where
+        ...
+  ```
+
+  The semantics of telescoping lets in function types and lambda
+  abstractions is just expanding them into ordinary lets.
+
+* More liberal left-hand sides in lets
+  [Issue [#1028](https://github.com/agda/agda/issues/1028)]:
+
+  You can now write left-hand sides with arguments also for let
+  bindings without a type signature. For instance,
+
+  ```agda
+  let f x = suc x in f zero
+  ```
+
+  Let bound functions still can't do pattern matching though.
+
+* Ambiguous names in patterns are now optimistically resolved in favor
+  of constructors. [Issue [#822](https://github.com/agda/agda/issues/822)]
+  In particular, the following succeeds now:
+
+  ```agda
+  module M where
+
+    data D : Set₁ where
+      [_] : Set → D
+
+  postulate [_] : Set → Set
+
+  open M
+
+  Foo : _ → Set
+  Foo [ A ] = A
+  ```
+
+* Anonymous `where`-modules are opened
+  public. [Issue [#848](https://github.com/agda/agda/issues/848)]
+
+  ```
+  <clauses>
+  f args = rhs
+    module _ telescope where
+      body
+  <more clauses>
+  ```
+
+  means the following (not proper Agda code, since you cannot put a
+  module in-between clauses)
+
+  ```
+  <clauses>
+  module _ {arg-telescope} telescope where
+    body
+
+  f args = rhs
+  <more clauses>
+  ```
+
+  Example:
+
+  ```agda
+  A : Set1
+  A = B module _ where
+    B : Set1
+    B = Set
+
+  C : Set1
+  C = B
+  ```
+
+* Builtin `ZERO` and `SUC` have been merged with `NATURAL`.
+
+  When binding the `NATURAL` builtin, `ZERO` and `SUC` are bound to
+  the appropriate constructors automatically. This means that instead
+  of writing
+
+  ```agda
+  {-# BUILTIN NATURAL Nat #-}
+  {-# BUILTIN ZERO zero #-}
+  {-# BUILTIN SUC suc #-}
+  ```
+
+  you just write
+
+  ```agda
+  {-# BUILTIN NATURAL Nat #-}
+  ```
+
+* Pattern synonym can now have implicit
+  arguments. [Issue [#860](https://github.com/agda/agda/issues/860)]
+
+  For example,
+
+  ```agda
+  pattern tail=_ {x} xs = x ∷ xs
+
+  len : ∀ {A} → List A → Nat
+  len []         = 0
+  len (tail= xs) = 1 + len xs
+  ```
+
+* Syntax declarations can now have implicit
+  arguments. [Issue [#400](https://github.com/agda/agda/issues/400)]
+
+  For example
+
+  ```agda
+  id : ∀ {a}{A : Set a} -> A -> A
+  id x = x
+
+  syntax id {A} x = x ∈ A
+  ```
+
+* Minor syntax changes
+
+  - `-}` is now parsed as end-comment even if no comment was begun. As
+    a consequence, the following definition gives a parse error
+
+    ```agda
+    f : {A- : Set} -> Set
+    f {A-} = A-
+    ```
+
+    because Agda now sees `ID(f) LBRACE ID(A) END-COMMENT`, and no
+    longer `ID(f) LBRACE ID(A-) RBRACE`.
+
+    The rational is that the previous lexing was to context-sensitive,
+    attempting to comment-out `f` using `{-` and `-}` lead to a parse
+    error.
+
+  - Fixities (binding strengths) can now be negative numbers as
+    well. [Issue [#1109](https://github.com/agda/agda/issues/1109)]
+
+    ```agda
+    infix -1 _myop_
+    ```
+
+  - Postulates are now allowed in mutual
+    blocks. [Issue [#977](https://github.com/agda/agda/issues/977)]
+
+  - Empty where blocks are now
+    allowed. [Issue [#947](https://github.com/agda/agda/issues/947)]
+
+  - Pattern synonyms are now allowed in parameterised
+    modules. [Issue [#941](https://github.com/agda/agda/issues/941)]
+
+  - Empty hiding and renaming lists in module directives are now allowed.
+
+  - Module directives `using`, `hiding`, `renaming` and `public` can
+    now appear in arbitrary order. Multiple
+    `using`/`hiding`/`renaming` directives are allowed, but you still
+    cannot have both using and `hiding` (because that doesn't make
+    sense). [Issue [#493](https://github.com/agda/agda/issues/493)]
+
+Goal and error display
+----------------------
+
+* The error message `Refuse to construct infinite term` has been
+  removed, instead one gets unsolved meta variables.  Reason: the
+  error was thrown over-eagerly.
+  [Issue [#795](https://github.com/agda/agda/issues/795)]
+
+* If an interactive case split fails with message
+
+  ```
+    Since goal is solved, further case distinction is not supported;
+    try `Solve constraints' instead
+  ```
+
+  then the associated interaction meta is assigned to a solution.
+  Press `C-c C-=` (Show constraints) to view the solution and `C-c
+  C-s` (Solve constraints) to apply it.
+  [Issue [#289](https://github.com/agda/agda/issues/289)]
+
+Type checking
+-------------
+
+* [ Issue [#376](https://github.com/agda/agda/issues/376) ]
+  Implemented expansion of bound record variables during meta
+  assignment.  Now Agda can solve for metas X that are applied to
+  projected variables, e.g.:
+
+  ```agda
+  X (fst z) (snd z) = z
+
+  X (fst z)         = fst z
+  ```
+
+  Technically, this is realized by substituting `(x , y)` for `z` with fresh
+  bound variables `x` and `y`.  Here the full code for the examples:
+
+  ```agda
+  record Sigma (A : Set)(B : A -> Set) : Set where
+    constructor _,_
+    field
+      fst : A
+      snd : B fst
+  open Sigma
+
+  test : (A : Set) (B : A -> Set) ->
+    let X : (x : A) (y : B x) -> Sigma A B
+        X = _
+    in  (z : Sigma A B) -> X (fst z) (snd z) ≡ z
+  test A B z = refl
+
+  test' : (A : Set) (B : A -> Set) ->
+    let X : A -> A
+        X = _
+    in  (z : Sigma A B) -> X (fst z) ≡ fst z
+  test' A B z = refl
+  ```
+
+  The fresh bound variables are named `fst(z)` and `snd(z)` and can appear
+  in error messages, e.g.:
+
+  ```agda
+  fail : (A : Set) (B : A -> Set) ->
+    let X : A -> Sigma A B
+        X = _
+    in  (z : Sigma A B) -> X (fst z) ≡ z
+  fail A B z = refl
+  ```
+
+  results in error:
+
+  ```
+  Cannot instantiate the metavariable _7 to solution fst(z) , snd(z)
+  since it contains the variable snd(z) which is not in scope of the
+  metavariable or irrelevant in the metavariable but relevant in the
+  solution
+  when checking that the expression refl has type _7 A B (fst z) ≡ z
+  ```
+
+* Dependent record types and definitions by copatterns require
+  reduction with previous function clauses while checking the current
+  clause. [Issue [#907](https://github.com/agda/agda/issues/907)]
+
+  For a simple example, consider
+
+  ```agda
+  test : ∀ {A} → Σ Nat λ n → Vec A n
+  proj₁ test = zero
+  proj₂ test = []
+  ```
+
+  For the second clause, the lhs and rhs are typed as
+
+  ```agda
+  proj₂ test : Vec A (proj₁ test)
+  []         : Vec A zero
+  ```
+
+  In order for these types to match, we have to reduce the lhs type
+  with the first function clause.
+
+  Note that termination checking comes after type checking, so be
+  careful to avoid non-termination!  Otherwise, the type checker
+  might get into an infinite loop.
+
+* The implementation of the primitive `primTrustMe` has changed.  It
+  now only reduces to `REFL` if the two arguments `x` and `y` have the
+  same computational normal form.  Before, it reduced when `x` and `y`
+  were definitionally equal, which included type-directed equality
+  laws such as eta-equality.  Yet because reduction is untyped,
+  calling conversion from reduction lead to Agda crashes
+  [Issue [#882](https://github.com/agda/agda/issues/882)].
+
+  The amended description of `primTrustMe` is (cf. release notes
+  for 2.2.6):
+
+  ```agda
+  primTrustMe : {A : Set} {x y : A} → x ≡ y
+  ```
+
+  Here `_≡_` is the builtin equality (see BUILTIN hooks for equality,
+  above).
+
+  If `x` and `y` have the same computational normal form, then
+  `primTrustMe {x = x} {y = y}` reduces to `refl`.
+
+  A note on `primTrustMe`'s runtime behavior: The MAlonzo compiler
+  replaces all uses of `primTrustMe` with the `REFL` builtin, without
+  any check for definitional equality. Incorrect uses of `primTrustMe`
+  can potentially lead to segfaults or similar problems of the
+  compiled code.
+
+* Implicit patterns of record type are now only eta-expanded if there
+  is a record constructor.
+  [Issues [#473](https://github.com/agda/agda/issues/473),
+  [#635](https://github.com/agda/agda/issues/635)]
+
+  ```agda
+  data D : Set where
+    d : D
+
+  data P : D → Set where
+    p : P d
+
+  record Rc : Set where
+    constructor c
+    field f : D
+
+  works : {r : Rc} → P (Rc.f r) → Set
+  works p = D
+  ```
+
+  This works since the implicit pattern `r` is eta-expanded to `c x`
+  which allows the type of `p` to reduce to `P x` and `x` to be
+  unified with `d`. The corresponding explicit version is:
+
+  ```agda
+  works' : (r : Rc) → P (Rc.f r) → Set
+  works' (c .d) p = D
+  ```
+
+  However, if the record constructor is removed, the same example will
+  fail:
+
+  ```agda
+  record R : Set where
+    field f : D
+
+  fails : {r : R} → P (R.f r) → Set
+  fails p = D
+
+  -- d != R.f r of type D
+  -- when checking that the pattern p has type P (R.f r)
+  ```
+
+  The error is justified since there is no pattern we could write down
+  for `r`.  It would have to look like
+
+  ```agda
+  record { f = .d }
+  ```
+
+  but anonymous record patterns are not part of the language.
+
+* Absurd lambdas at different source locations are no longer
+  different. [Issue [#857](https://github.com/agda/agda/issues/857)]
+  In particular, the following code type-checks now:
+
+  ```agda
+  absurd-equality : _≡_ {A = ⊥ → ⊥} (λ()) λ()
+  absurd-equality = refl
+  ```
+
+  Which is a good thing!
+
+* Printing of named implicit function types.
+
+  When printing terms in a context with bound variables Agda renames
+  new bindings to avoid clashes with the previously bound names. For
+  instance, if `A` is in scope, the type `(A : Set) → A` is printed as
+  `(A₁ : Set) → A₁`. However, for implicit function types the name of
+  the binding matters, since it can be used when giving implicit
+  arguments.
+
+  For this situation, the following new syntax has been introduced:
+  `{x = y : A} → B` is an implicit function type whose bound variable
+  (in scope in `B`) is `y`, but where the name of the argument is `x`
+  for the purposes of giving it explicitly. For instance, with `A` in
+  scope, the type `{A : Set} → A` is now printed as `{A = A₁ : Set} →
+  A₁`.
+
+  This syntax is only used when printing and is currently not being parsed.
+
+* Changed the semantics of `--without-K`.
+  [Issue [#712](https://github.com/agda/agda/issues/712),
+  Issue [#865](https://github.com/agda/agda/issues/865),
+  Issue [#1025](https://github.com/agda/agda/issues/1025)]
+
+  New specification of `--without-K`:
+
+  When `--without-K` is enabled, the unification of indices for
+  pattern matching is restricted in two ways:
+
+  1. Reflexive equations of the form `x == x` are no longer solved,
+     instead Agda gives an error when such an equation is encountered.
+
+  2. When unifying two same-headed constructor forms `c us` and `c vs`
+     of type `D pars ixs`, the datatype indices `ixs` (but not the
+     parameters) have to be *self-unifiable*, i.e. unification of
+     `ixs` with itself should succeed positively. This is a nontrivial
+     requirement because of point 1.
+
+  Examples:
+
+  - The J rule is accepted.
+
+    ```agda
+    J : {A : Set} (P : {x y : A} → x ≡ y → Set) →
+        (∀ x → P (refl x)) →
+        ∀ {x y} (x≡y : x ≡ y) → P x≡y
+    J P p (refl x) = p x
+    ```agda
+
+    This definition is accepted since unification of `x` with `y`
+    doesn't require deletion or injectivity.
+
+  - The K rule is rejected.
+
+    ```agda
+    K : {A : Set} (P : {x : A} → x ≡ x → Set) →
+        (∀ x → P (refl {x = x})) →
+       ∀ {x} (x≡x : x ≡ x) → P x≡x
+    K P p refl = p _
+    ```
+
+    Definition is rejected with the following error:
+
+    ```
+    Cannot eliminate reflexive equation x = x of type A because K has
+    been disabled.
+    when checking that the pattern refl has type x ≡ x
+    ```
+
+  - Symmetry of the new criterion.
+
+    ```agda
+    test₁ : {k l m : ℕ} → k + l ≡ m → ℕ
+    test₁ refl = zero
+
+    test₂ : {k l m : ℕ} → k ≡ l + m → ℕ
+    test₂ refl = zero
+    ```
+
+    Both versions are now accepted (previously only the first one was).
+
+  - Handling of parameters.
+
+    ```agda
+    cons-injective : {A : Set} (x y : A) → (x ∷ []) ≡ (y ∷ []) → x ≡ y
+    cons-injective x .x refl = refl
+    ```
+
+    Parameters are not unified, so they are ignored by the new criterion.
+
+  - A larger example: antisymmetry of ≤.
+
+    ```agda
+    data _≤_ : ℕ → ℕ → Set where
+      lz : (n : ℕ) → zero ≤ n
+      ls : (m n : ℕ) → m ≤ n → suc m ≤ suc n
+
+    ≤-antisym : (m n : ℕ) → m ≤ n → n ≤ m → m ≡ n
+    ≤-antisym .zero    .zero    (lz .zero) (lz .zero)   = refl
+    ≤-antisym .(suc m) .(suc n) (ls m n p) (ls .n .m q) =
+                 cong suc (≤-antisym m n p q)
+    ```
+
+  - [ Issue [#1025](https://github.com/agda/agda/issues/1025) ]
+
+    ```agda
+    postulate mySpace : Set
+    postulate myPoint : mySpace
+
+    data Foo : myPoint ≡ myPoint → Set where
+      foo : Foo refl
+
+    test : (i : foo ≡ foo) → i ≡ refl
+    test refl = {!!}
+    ```
+
+    When applying injectivity to the equation `foo ≡ foo` of type `Foo
+    refl`, it is checked that the index `refl` of type `myPoint ≡
+    myPoint` is self-unifiable. The equation `refl ≡ refl` again
+    requires injectivity, so now the index `myPoint` is checked for
+    self-unifiability, hence the error:
+
+    ```
+    Cannot eliminate reflexive equation myPoint = myPoint of type
+    mySpace because K has been disabled.
+    when checking that the pattern refl has type foo ≡ foo
+    ```
+
+Termination checking
+--------------------
+
+* A buggy facility coined "matrix-shaped orders" that supported
+  uncurried functions (which take tuples of arguments instead of one
+  argument after another) has been removed from the termination
+  checker. [Issue [#787](https://github.com/agda/agda/issues/787)]
+
+* Definitions which fail the termination checker are not unfolded any
+  longer to avoid loops or stack overflows in Agda.  However, the
+  termination checker for a mutual block is only invoked after
+  type-checking, so there can still be loops if you define a
+  non-terminating function.  But termination checking now happens
+  before the other supplementary checks: positivity, polarity,
+  injectivity and projection-likeness.  Note that with the pragma `{-#
+  NO_TERMINATION_CHECK #-}` you can make Agda treat any function as
+  terminating.
+
+* Termination checking of functions defined by `with` has been improved.
+
+  Cases which previously required `--termination-depth` to pass the
+  termination checker (due to use of `with`) no longer need the
+  flag. For example
+
+  ```agda
+  merge : List A → List A → List A
+  merge [] ys = ys
+  merge xs [] = xs
+  merge (x ∷ xs) (y ∷ ys) with x ≤ y
+  merge (x ∷ xs) (y ∷ ys)    | false = y ∷ merge (x ∷ xs) ys
+  merge (x ∷ xs) (y ∷ ys)    | true  = x ∷ merge xs (y ∷ ys)
+  ```
+
+  This failed to termination check previously, since the `with`
+  expands to an auxiliary function `merge-aux`:
+
+  ```agda
+  merge-aux x y xs ys false = y ∷ merge (x ∷ xs) ys
+  merge-aux x y xs ys true  = x ∷ merge xs (y ∷ ys)
+  ```
+
+  This function makes a call to `merge` in which the size of one of
+  the arguments is increasing. To make this pass the termination
+  checker now inlines the definition of `merge-aux` before checking,
+  thus effectively termination checking the original source program.
+
+  As a result of this transformation doing `with` on a variable no longer
+  preserves termination. For instance, this does not termination check:
+
+  ```agda
+  bad : Nat → Nat
+  bad n with n
+  ... | zero  = zero
+  ... | suc m = bad m
+  ```
+
+* The performance of the termination checker has been improved.  For
+  higher `--termination-depth` the improvement is significant.  While
+  the default `--termination-depth` is still 1, checking with higher
+  `--termination-depth` should now be feasible.
+
+Compiler backends
+-----------------
+
+* The MAlonzo compiler backend now has support for compiling modules
+  that are not full programs (i.e. don't have a main function). The
+  goal is that you can write part of a program in Agda and the rest in
+  Haskell, and invoke the Agda functions from the Haskell code. The
+  following features were added for this reason:
+
+  - A new command-line option `--compile-no-main`: the command
+
+    ```
+    agda --compile-no-main Test.agda
+    ```
+
+    will compile `Test.agda` and all its dependencies to Haskell and
+    compile the resulting Haskell files with `--make`, but (unlike
+    `--compile`) not tell GHC to treat `Test.hs` as the main
+    module. This type of compilation can be invoked from Emacs by
+    customizing the `agda2-backend` variable to value `MAlonzoNoMain` and
+    then calling `C-c C-x C-c` as before.
+
+  - A new pragma `COMPILED_EXPORT` was added as part of the MAlonzo
+    FFI. If we have an Agda file containing the following:
+
+    ```agda
+     module A.B where
+
+     test : SomeType
+     test = someImplementation
+
+     {-# COMPILED_EXPORT test someHaskellId #-}
+    ```
+
+    then test will be compiled to a Haskell function called
+    `someHaskellId` in module `MAlonzo.Code.A.B` that can be invoked
+    from other Haskell code. Its type will be translated according to
+    the normal MAlonzo rules.
+
+Tools
+-----
+
+### Emacs mode
+
+* A new goal command `Helper Function Type` (`C-c C-h`) has been added.
+
+  If you write an application of an undefined function in a goal, the
+  `Helper Function Type` command will print the type that the function
+  needs to have in order for it to fit the goal. The type is also
+  added to the Emacs kill-ring and can be pasted into the buffer using
+  `C-y`.
+
+  The application must be of the form `f args` where `f` is the name of the
+  helper function you want to create. The arguments can use all the normal
+  features like named implicits or instance arguments.
+
+  Example:
+
+  Here's a start on a naive reverse on vectors:
+
+  ```agda
+  reverse : ∀ {A n} → Vec A n → Vec A n
+  reverse [] = []
+  reverse (x ∷ xs) = {!snoc (reverse xs) x!}
+  ```
+
+  Calling `C-c C-h` in the goal prints
+
+  ```agda
+  snoc : ∀ {A} {n} → Vec A n → A → Vec A (suc n)
+  ```
+
+* A new command `Explain why a particular name is in scope` (`C-c
+  C-w`) has been added.
+  [Issue [#207](https://github.com/agda/agda/issues/207)]
+
+  This command can be called from a goal or from the top-level and will as the
+  name suggests explain why a particular name is in scope.
+
+  For each definition or module that the given name can refer to a trace is
+  printed of all open statements and module applications leading back to the
+  original definition of the name.
+
+  For example, given
+
+  ```agda
+  module A (X : Set₁) where
+    data Foo : Set where
+      mkFoo : Foo
+  module B (Y : Set₁) where
+    open A Y public
+  module C = B Set
+  open C
+  ```
+
+  Calling `C-c C-w` on `mkFoo` at the top-level prints
+
+  ```
+  mkFoo is in scope as
+  * a constructor Issue207.C._.Foo.mkFoo brought into scope by
+    - the opening of C at Issue207.agda:13,6-7
+    - the application of B at Issue207.agda:11,12-13
+    - the application of A at Issue207.agda:9,8-9
+    - its definition at Issue207.agda:6,5-10
+  ```
+
+  This command is useful if Agda complains about an ambiguous name and
+  you need to figure out how to hide the undesired interpretations.
+
+* Improvements to the `make case` command (`C-c C-c`)
+
+  - One can now also split on hidden variables, using the name
+    (starting with `.`) with which they are printed.  Use `C-c C-`, to
+    see all variables in context.
+
+  - Concerning the printing of generated clauses:
+
+    * Uses named implicit arguments to improve readability.
+
+    * Picks explicit occurrences over implicit ones when there is a
+      choice of binding site for a variable.
+
+    * Avoids binding variables in implicit positions by replacing dot
+      patterns that uses them by wildcards (`._`).
+
+* Key bindings for lots of "mathematical" characters (examples: 𝐴𝑨𝒜𝓐𝔄)
+  have been added to the Agda input method.  Example: type
+  `\MiA\MIA\McA\MCA\MfA` to get 𝐴𝑨𝒜𝓐𝔄.
+
+  Note: `\McB` does not exist in Unicode (as well as others in that style),
+  but the `\MC` (bold) alphabet is complete.
+
+* Key bindings for "blackboard bold" B (𝔹) and 0-9 (𝟘-𝟡) have been
+  added to the Agda input method (`\bb` and `\b[0-9]`).
+
+* Key bindings for controlling simplification/normalisation:
+
+  Commands like `Goal type and context` (`C-c C-,`) could previously
+  be invoked in two ways. By default the output was normalised, but if
+  a prefix argument was used (for instance via `C-u C-c C-,`), then no
+  explicit normalisation was performed. Now there are three options:
+
+  - By default (`C-c C-,`) the output is simplified.
+
+  - If `C-u` is used exactly once (`C-u C-c C-,`), then the result is
+    neither (explicitly) normalised nor simplified.
+
+  - If `C-u` is used twice (`C-u C-u C-c C-,`), then the result is
+    normalised.
+
+### LaTeX-backend
+
+* Two new color scheme options were added to `agda.sty`:
+
+  `\usepackage[bw]{agda}`, which highlights in black and white;
+  `\usepackage[conor]{agda}`, which highlights using Conor's colors.
+
+  The default (no options passed) is to use the standard colors.
+
+* If `agda.sty` cannot be found by the LateX environment, it is now
+  copied into the LateX output directory (`latex` by default) instead
+  of the working directory. This means that the commands needed to
+  produce a PDF now is
+
+  ```
+  agda --latex -i . <file>.lagda
+  cd latex
+  pdflatex <file>.tex
+  ```
+
+* The LaTeX-backend has been made more tool agnostic, in particular
+  XeLaTeX and LuaLaTeX should now work. Here is a small example
+  (`test/LaTeXAndHTML/succeed/UnicodeInput.lagda`):
+
+  ```latex
+  \documentclass{article}
+  \usepackage{agda}
+  \begin{document}
+
+  \begin{code}
+  data αβγδεζθικλμνξρστυφχψω : Set₁ where
+
+  postulate
+    →⇒⇛⇉⇄↦⇨↠⇀⇁ : Set
+  \end{code}
+
+  \[
+  ∀X [ ∅ ∉ X ⇒ ∃f:X ⟶  ⋃ X\ ∀A ∈ X (f(A) ∈ A) ]
+  \]
+  \end{document}
+  ```
+
+  Compiled as follows, it should produce a nice looking PDF (tested with
+  TeX Live 2012):
+
+  ```
+  agda --latex <file>.lagda
+  cd latex
+  xelatex <file>.tex (or lualatex <file>.tex)
+  ```
+
+  If symbols are missing or XeLaTeX/LuaLaTeX complains about the font
+  missing, try setting a different font using:
+
+  ```latex
+  \setmathfont{<math-font>}
+  ```
+
+  Use the `fc-list` tool to list available fonts.
+
+* Add experimental support for hyperlinks to identifiers
+
+  If the `hyperref` LateX package is loaded before the Agda package
+  and the links option is passed to the Agda package, then the Agda
+  package provides a function called `\AgdaTarget`. Identifiers which
+  have been declared targets, by the user, will become clickable
+  hyperlinks in the rest of the document. Here is a small example
+  (`test/LaTeXAndHTML/succeed/Links.lagda`):
+
+  ```latex
+  \documentclass{article}
+  \usepackage{hyperref}
+  \usepackage[links]{agda}
+  \begin{document}
+
+  \AgdaTarget{ℕ}
+  \AgdaTarget{zero}
+  \begin{code}
+  data ℕ : Set where
+    zero  : ℕ
+    suc   : ℕ → ℕ
+  \end{code}
+
+  See next page for how to define \AgdaFunction{two} (doesn't turn into a
+  link because the target hasn't been defined yet). We could do it
+  manually though; \hyperlink{two}{\AgdaDatatype{two}}.
+
+  \newpage
+
+  \AgdaTarget{two}
+  \hypertarget{two}{}
+  \begin{code}
+  two : ℕ
+  two = suc (suc zero)
+  \end{code}
+
+  \AgdaInductiveConstructor{zero} is of type
+  \AgdaDatatype{ℕ}. \AgdaInductiveConstructor{suc} has not been defined to
+  be a target so it doesn't turn into a link.
+
+  \newpage
+
+  Now that the target for \AgdaFunction{two} has been defined the link
+  works automatically.
+
+  \begin{code}
+  data Bool : Set where
+    true false : Bool
+  \end{code}
+
+  The AgdaTarget command takes a list as input, enabling several
+  targets to be specified as follows:
+
+  \AgdaTarget{if, then, else, if\_then\_else\_}
+  \begin{code}
+  if_then_else_ : {A : Set} → Bool → A → A → A
+  if true  then t else f = t
+  if false then t else f = f
+  \end{code}
+
+  \newpage
+
+  Mixfix identifier need their underscores escaped:
+  \AgdaFunction{if\_then\_else\_}.
+
+  \end{document}
+  ```
+
+  The boarders around the links can be suppressed using hyperref's
+  hidelinks option:
+
+  ```latex
+    \usepackage[hidelinks]{hyperref}
+  ```
+
+  Note that the current approach to links does not keep track of scoping
+  or types, and hence overloaded names might create links which point to
+  the wrong place. Therefore it is recommended to not overload names
+  when using the links option at the moment, this might get fixed in the
+  future.
diff --git a/doc/release-notes/2.4.2.1.md b/doc/release-notes/2.4.2.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.1.md
@@ -0,0 +1,214 @@
+Release notes for Agda version 2.4.2.1
+======================================
+
+Pragmas and options
+-------------------
+
+* New pragma `{-# TERMINATING #-}` replacing
+  `{-# NO_TERMINATION_CHECK #-}`
+
+  Complements the existing pragma `{-# NON_TERMINATING #-}`.  Skips
+  termination check for the associated definitions and marks them as
+  terminating.  Thus, it is a replacement for `{-#
+  NO_TERMINATION_CHECK #-}` with the same semantics.
+
+  You can no longer use pragma `{-# NO_TERMINATION_CHECK #-}` to skip
+  the termination check, but must label your definitions as either
+  `{-# TERMINATING #-}` or `{-# NON_TERMINATING #-}` instead.
+
+  Note: `{-# OPTION --no-termination-check #-}` labels all your
+  definitions as `{-# TERMINATING #-}`, putting you in the danger zone
+  of a loop in the type checker.
+
+Language
+--------
+
+* Referring to a local variable shadowed by module opening is now an
+  error.  Previous behavior was preferring the local over the imported
+  definitions. [Issue [#1266](https://github.com/agda/agda/issues/1266)]
+
+  Note that module parameters are locals as well as variables bound by
+  λ, dependent function type, patterns, and let.
+
+  Example:
+
+  ```agda
+  module M where
+    A = Set1
+
+  test : (A : Set) → let open M in A
+  ```
+
+  The last `A` produces an error, since it could refer to the local
+  variable `A` or to the definition imported from module `M`.
+
+* `with` on a variable bound by a module telescope or a pattern of a
+  parent function is now forbidden.
+  [Issue [#1342](https://github.com/agda/agda/issues/1342)]
+
+  ```agda
+  data Unit : Set where
+    unit : Unit
+
+  id : (A : Set) → A → A
+  id A a = a
+
+  module M (x : Unit) where
+
+    dx : Unit → Unit
+    dx unit = x
+
+    g : ∀ u → x ≡ dx u
+    g with x
+    g | unit  = id (∀ u → unit ≡ dx u) ?
+  ```
+
+  Even though this code looks right, Agda complains about the type
+  expression `∀ u → unit ≡ dx u`.  If you ask Agda what should go
+  there instead, it happily tells you that it wants `∀ u → unit ≡ dx
+  u`. In fact what you do not see and Agda will never show you is that
+  the two expressions actually differ in the invisible first argument
+  to `dx`, which is visible only outside module `M`.  What Agda wants
+  is an invisible `unit` after `dx`, but all you can write is an
+  invisible `x` (which is inserted behind the scenes).
+
+  To avoid those kinds of paradoxes, `with` is now outlawed on module
+  parameters.  This should ensure that the invisible arguments are
+  always exactly the module parameters.
+
+  Since a `where` block is desugared as module with pattern variables
+  of the parent clause as module parameters, the same strikes you for
+  uses of `with` on pattern variables of the parent function.
+
+  ```agda
+  f : Unit → Unit
+  f x = unit
+    where
+      dx : Unit → Unit
+      dx unit = x
+
+      g : ∀ u → x ≡ dx u
+      g with x
+      g | unit  = id ((u : Unit) → unit ≡ dx u) ?
+  ```
+
+  The `with` on pattern variable `x` of the parent clause `f x = unit`
+  is outlawed now.
+
+Type checking
+-------------
+
+* Termination check failure is now a proper error.
+
+  We no longer continue type checking after termination check
+  failures.  Use pragmas `{-# NON_TERMINATING #-}` and `{-#
+  NO_TERMINATION_CHECK #-}` near the offending definitions if you want
+  to do so.  Or switch off the termination checker altogether with
+  `{-# OPTIONS --no-termination-check #-}` (at your own risk!).
+
+* (Since Agda 2.4.2): Termination checking `--without-K` restricts
+  structural descent to arguments ending in data types or `Size`.
+  Likewise, guardedness is only tracked when result type is data or
+  record type.
+
+  ```agda
+  mutual
+    data WOne : Set where wrap : FOne → WOne
+    FOne = ⊥ → WOne
+
+  noo : (X : Set) → (WOne ≡ X) → X → ⊥
+  noo .WOne refl (wrap f) = noo FOne iso f
+  ```
+
+  `noo` is rejected since at type `X` the structural descent
+  `f < wrap f` is discounted `--without-K`.
+
+  ```agda
+  data Pandora : Set where
+    C : ∞ ⊥ → Pandora
+
+  loop : (A : Set) → A ≡ Pandora → A
+  loop .Pandora refl = C (♯ (loop ⊥ foo))
+  ```
+
+  `loop` is rejected since guardedness is not tracked at type `A`
+  `--without-K`.
+
+  See issues [#1023](https://github.com/agda/agda/issues/1023),
+  [#1264](https://github.com/agda/agda/issues/1264),
+  [#1292](https://github.com/agda/agda/issues/1292).
+
+Termination checking
+--------------------
+
+* The termination checker can now recognize simple subterms in dot
+  patterns.
+
+  ```agda
+  data Subst : (d : Nat) → Set where
+    c₁ : ∀ {d} → Subst d → Subst d
+    c₂ : ∀ {d₁ d₂} → Subst d₁ → Subst d₂ → Subst (suc d₁ + d₂)
+
+  postulate
+    comp : ∀ {d₁ d₂} → Subst d₁ → Subst d₂ → Subst (d₁ + d₂)
+
+  lookup : ∀ d → Nat → Subst d → Set₁
+  lookup d             zero    (c₁ ρ)             = Set
+  lookup d             (suc v) (c₁ ρ)             = lookup d v ρ
+  lookup .(suc d₁ + d₂) v      (c₂ {d₁} {d₂} ρ σ) = lookup (d₁ + d₂) v (comp ρ σ)
+  ```
+
+  The dot pattern here is actually normalized, so it is
+
+  ```agda
+  suc (d₁ + d₂)
+  ```
+
+  and the corresponding recursive call argument is `(d₁ + d₂)`.  In
+  such simple cases, Agda can now recognize that the pattern is
+  constructor applied to call argument, which is valid descent.
+
+  Note however, that Agda only looks for syntactic equality when
+  identifying subterms, since it is not allowed to normalize terms on
+  the rhs during termination checking.
+
+  Actually writing the dot pattern has no effect, this works as well,
+  and looks pretty magical... ;-)
+
+  ```agda
+  hidden : ∀{d} → Nat → Subst d → Set₁
+  hidden zero    (c₁ ρ)   = Set
+  hidden (suc v) (c₁ ρ)   = hidden v ρ
+  hidden v       (c₂ ρ σ) = hidden v (comp ρ σ)
+  ```
+
+Tools
+-----
+
+### LaTeX-backend
+
+* Fixed the issue of identifiers containing operators being typeset with
+  excessive math spacing.
+
+Bug fixes
+---------
+
+* Issue [#1194](https://github.com/agda/agda/issues/1194)
+
+* Issue [#836](https://github.com/agda/agda/issues/836): Fields and
+  constructors can be qualified by the record/data *type* as well as
+  by their record/data module.  This now works also for record/data
+  type imported from parametrized modules:
+
+  ```agda
+  module M (_ : Set₁) where
+
+    record R : Set₁ where
+      field
+        X : Set
+
+  open M Set using (R)  -- rather than using (module R)
+
+  X : R → Set
+  X = R.X
+  ```
diff --git a/doc/release-notes/2.4.2.2.md b/doc/release-notes/2.4.2.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.2.md
@@ -0,0 +1,20 @@
+Release notes for Agda version 2.4.2.2
+======================================
+
+Bug fixes
+---------
+
+* Compilation on Windows fixed.
+
+* Other issues fixed (see
+  [bug tracker](https://github.com/agda/agda/issues))
+
+  [#1332](https://github.com/agda/agda/issues/1322)
+
+  [#1353](https://github.com/agda/agda/issues/1353)
+
+  [#1360](https://github.com/agda/agda/issues/1360)
+
+  [#1366](https://github.com/agda/agda/issues/1366)
+
+  [#1369](https://github.com/agda/agda/issues/1369)
diff --git a/doc/release-notes/2.4.2.3.md b/doc/release-notes/2.4.2.3.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.3.md
@@ -0,0 +1,303 @@
+Release notes for Agda version 2.4.2.3
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 7.10.1.
+
+* Removed support for GHC 7.0.4.
+
+Language
+--------
+
+* `_ `is no longer a valid name for a definition.  The following fails
+  now: [Issue [#1465](https://github.com/agda/agda/issues/1465)]
+
+  ```agda
+  postulate _ : Set
+  ```
+
+* Typed bindings can now contain hiding information
+  [Issue [#1391](https://github.com/agda/agda/issues/1391)].  This
+  means you can now write
+
+  ```agda
+  assoc : (xs {ys zs} : List A) → ((xs ++ ys) ++ zs) ≡ (xs ++ (ys ++ zs))
+  ```
+
+  instead of the longer
+
+  ```agda
+  assoc : (xs : List A) {ys zs : List A} → ...
+  ```
+
+  It also works with irrelevance
+
+  ```agda
+  .(xs {ys zs} : List A) → ...
+  ```
+
+  but of course does not make sense if there is hiding information already.
+  Thus, this is (still) a parse error:
+
+  ```agda
+  {xs {ys zs} : List A} → ...
+  ```
+
+* The builtins for sized types no longer need accompanying postulates.
+  The BUILTIN pragmas for size stuff now also declare the identifiers
+  they bind to.
+
+  ```agda
+  {-# BUILTIN SIZEUNIV SizeUniv #-}  --  SizeUniv : SizeUniv
+  {-# BUILTIN SIZE     Size     #-}  --  Size     : SizeUniv
+  {-# BUILTIN SIZELT   Size<_   #-}  --  Size<_   : ..Size → SizeUniv
+  {-# BUILTIN SIZESUC  ↑_       #-}  --  ↑_       : Size → Size
+  {-# BUILTIN SIZEINF  ∞        #-}  --  ∞       : Size
+  ```
+
+  `Size` and `Size<` now live in the new universe `SizeUniv`.  It is
+  forbidden to build function spaces in this universe, in order to
+  prevent the malicious assumption of a size predecessor
+
+  ```agda
+  pred : (i : Size) → Size< i
+  ```
+
+  [Issue [#1428](https://github.com/agda/agda/issues/1428)].
+
+* Unambiguous notations (coming from syntax declarations) that resolve
+  to ambiguous names are now parsed unambiguously
+  [Issue [#1194](https://github.com/agda/agda/issues/1194)].
+
+* If only some instances of an overloaded name have a given associated
+  notation (coming from syntax declarations), then this name can only
+  be resolved to the given instances of the name, not to other
+  instances [Issue [#1194](https://github.com/agda/agda/issues/1194)].
+
+  Previously, if different instances of an overloaded name had
+  *different* associated notations, then none of the notations could
+  be used. Now all of them can be used.
+
+  Note that notation identity does not only involve the right-hand
+  side of the syntax declaration. For instance, the following
+  notations are not seen as identical, because the implicit argument
+  names are different:
+
+  ```agda
+  module A where
+
+    data D : Set where
+      c : {x y : D} → D
+
+    syntax c {x = a} {y = b} = a ∙ b
+
+  module B where
+
+    data D : Set where
+      c : {y x : D} → D
+
+    syntax c {y = a} {x = b} = a ∙ b
+  ```
+
+* If an overloaded operator is in scope with at least two distinct
+  fixities, then it gets the default fixity
+  [Issue [#1436](https://github.com/agda/agda/issues/1436)].
+
+  Similarly, if two or more identical notations for a given overloaded
+  name are in scope, and these notations do not all have the
+  same fixity, then they get the default fixity.
+
+Type checking
+-------------
+
+* Functions of varying arity can now have with-clauses and use rewrite.
+
+  Example:
+
+  ```agda
+  NPred : Nat → Set
+  NPred 0       = Bool
+  NPred (suc n) = Nat → NPred n
+
+  const : Bool → ∀{n} → NPred n
+  const b {0}       = b
+  const b {suc n} m = const b {n}
+
+  allOdd : ∀ n → NPred n
+  allOdd 0 = true
+  allOdd (suc n) m with even m
+  ... | true  = const false
+  ... | false = allOdd n
+  ```
+
+* Function defined by copattern matching can now have `with`-clauses
+  and use `rewrite`.
+
+  Example:
+
+  ```agda
+  {-# OPTIONS --copatterns #-}
+
+  record Stream (A : Set) : Set where
+    coinductive
+    constructor delay
+    field
+      force : A × Stream A
+  open Stream
+
+  map : ∀{A B} → (A → B) → Stream A → Stream B
+  force (map f s) with force s
+  ... | a , as = f a , map f as
+
+  record Bisim {A B} (R : A → B → Set) (s : Stream A) (t : Stream B) : Set where
+    coinductive
+    constructor ~delay
+    field
+      ~force : let a , as = force s
+                   b , bs = force t
+               in  R a b × Bisim R as bs
+  open Bisim
+
+  SEq : ∀{A} (s t : Stream A) → Set
+  SEq = Bisim (_≡_)
+
+  -- Slightly weird definition of symmetry to demonstrate rewrite.
+
+  ~sym' : ∀{A} {s t : Stream A} → SEq s t → SEq t s
+  ~force (~sym' {s = s} {t} p) with force s | force t | ~force p
+  ... | a , as | b , bs | r , q rewrite r = refl , ~sym' q
+  ```
+
+* Instances can now be defined by copattern
+  matching. [Issue [#1413](https://github.com/agda/agda/issues/1413)]
+  The following example extends the one in
+  [Abel, Pientka, Thibodeau, Setzer, POPL 2013, Section 2.2]:
+
+  ```agda
+  {-# OPTIONS --copatterns #-}
+
+  -- The Monad type class
+
+  record Monad (M : Set → Set) : Set1 where
+    field
+      return : {A : Set}   → A → M A
+      _>>=_  : {A B : Set} → M A → (A → M B) → M B
+  open Monad {{...}}
+
+  -- The State newtype
+
+  record State (S A : Set) : Set where
+    field
+      runState : S → A × S
+  open State
+
+  -- State is an instance of Monad
+
+  instance
+    stateMonad : {S : Set} → Monad (State S)
+    runState (return {{stateMonad}} a  ) s  = a , s    -- NEW
+    runState (_>>=_  {{stateMonad}} m k) s₀ =          -- NEW
+      let a , s₁ = runState m s₀
+      in  runState (k a) s₁
+
+  -- stateMonad fulfills the monad laws
+
+  leftId : {A B S : Set}(a : A)(k : A → State S B) →
+    (return a >>= k) ≡ k a
+  leftId a k = refl
+
+  rightId : {A B S : Set}(m : State S A) →
+    (m >>= return) ≡ m
+  rightId m = refl
+
+  assoc : {A B C S : Set}(m : State S A)(k : A → State S B)(l : B → State S C) →
+     ((m >>= k) >>= l) ≡ (m >>= λ a → k a >>= l)
+  assoc m k l = refl
+  ```
+
+Emacs mode
+----------
+
+* The new menu option `Switch to another version of Agda` tries to do
+  what it says.
+
+* Changed feature: Interactively split result.
+
+  [ This is as before: ]
+  Make-case (`C-c C-c`) with no variables given tries to split on the
+  result to introduce projection patterns.  The hole needs to be of
+  record type, of course.
+
+  ```agda
+  test : {A B : Set} (a : A) (b : B) → A × B
+  test a b = ?
+  ```
+
+  Result-splitting `?` will produce the new clauses:
+
+  ```agda
+  proj₁ (test a b) = ?
+  proj₂ (test a b) = ?
+  ```
+
+  [ This has changed: ]
+  If hole is of function type, `make-case` will introduce only pattern
+  variables (as much as it can).
+
+  ```agda
+  testFun : {A B : Set} (a : A) (b : B) → A × B
+  testFun = ?
+  ```
+
+  Result-splitting `?` will produce the new clause:
+
+  ```agda
+  testFun a b = ?
+  ```
+
+  A second invocation of `make-case` will then introduce projection
+  patterns.
+
+Error messages
+--------------
+
+* Agda now suggests corrections of misspelled options, e.g.
+
+  ```agda
+  {-# OPTIONS
+    --dont-termination-check
+    --without-k
+    --senf-gurke
+    #-}
+  ```
+
+  Unrecognized options:
+
+  ```
+  --dont-termination-check (did you mean --no-termination-check ?)
+  --without-k (did you mean --without-K ?)
+  --senf-gurke
+  ```
+
+  Nothing close to `--senf-gurke`, I am afraid.
+
+Compiler backends
+-----------------
+
+* The Epic backend has been removed
+  [Issue [#1481](https://github.com/agda/agda/issues/1481)].
+
+Bug fixes
+---------
+
+* Fixed bug with `unquoteDecl` not working in instance blocks
+  [Issue [#1491](https://github.com/agda/agda/issues/1491)].
+
+* Other issues fixed (see
+  [bug tracker](https://github.com/agda/agda/issues)
+
+  [#1497](https://github.com/agda/agda/issues/1497)
+
+  [#1500](https://github.com/agda/agda/issues/1500)
diff --git a/doc/release-notes/2.4.2.4.md b/doc/release-notes/2.4.2.4.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.4.md
@@ -0,0 +1,295 @@
+Release notes for Agda version 2.4.2.4
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Removed support for GHC 7.4.2.
+
+Pragmas and options
+-------------------
+
+* Option `--copatterns` is now on by default.  To switch off
+  parsing of copatterns, use:
+
+  ```agda
+  {-# OPTIONS --no-copatterns #-}
+  ```
+
+* Option `--rewriting` is now needed to use `REWRITE` pragmas and
+  rewriting during reduction.  Rewriting is not `--safe`.
+
+  To use rewriting, first specify a relation symbol `R` that will
+  later be used to add rewrite rules.  A canonical candidate would be
+  propositional equality
+
+  ```agda
+  {-# BUILTIN REWRITE _≡_ #-}
+  ```
+
+  but any symbol `R` of type `Δ → A → A → Set i` for some `A` and `i`
+  is accepted.  Then symbols `q` can be added to rewriting provided
+  their type is of the form `Γ → R ds l r`.  This will add a rewrite
+  rule
+
+  ```
+  Γ ⊢ l ↦ r : A[ds/Δ]
+  ```
+
+  to the signature, which fires whenever a term is an instance of `l`.
+  For example, if
+
+  ```agda
+  plus0 : ∀ x → x + 0 ≡ x
+  ```
+
+  (ideally, there is a proof for `plus0`, but it could be a
+  postulate), then
+
+  ```agda
+  {-# REWRITE plus0 #-}
+  ```
+
+  will prompt Agda to rewrite any well-typed term of the form `t + 0`
+  to `t`.
+
+  Some caveats: Agda accepts and applies rewrite rules naively, it is
+  very easy to break consistency and termination of type checking.
+  Some examples of rewrite rules that should *not* be added:
+
+  ```agda
+  refl     : ∀ x → x ≡ x             -- Agda loops
+  plus-sym : ∀ x y → x + y ≡ y + x   -- Agda loops
+  absurd   : true ≡ false            -- Breaks consistency
+  ```
+
+  Adding only proven equations should at least preserve consistency,
+  but this is only a conjecture, so know what you are doing!  Using
+  rewriting, you are entering into the wilderness, where you are on
+  your own!
+
+Language
+--------
+
+* `forall` / `∀` now parses like `λ`, i.e., the following parses now
+  [Issue [#1583](https://github.com/agda/agda/issues/1538)]:
+
+  ```agda
+  ⊤ × ∀ (B : Set) → B → B
+  ```
+
+* The underscore pattern `_` can now also stand for an inaccessible
+  pattern (dot pattern). This alleviates the need for writing `._`.
+  [Issue #[1605](https://github.com/agda/agda/issues/1605)] Instead of
+
+  ```agda
+  transVOld : ∀{A : Set} (a b c : A) → a ≡ b → b ≡ c → a ≡ c
+  transVOld _ ._ ._ refl refl = refl
+  ```
+
+  one can now write
+
+  ```agda
+    transVNew : ∀{A : Set} (a b c : A) → a ≡ b → b ≡ c → a ≡ c
+    transVNew _ _ _ refl refl = refl
+  ```
+
+  and let Agda decide where to put the dots.  This was always possible
+  by using hidden arguments
+
+  ```agda
+  transH : ∀{A : Set}{a b c : A} → a ≡ b → b ≡ c → a ≡ c
+  transH refl refl = refl
+  ```
+
+  which is now equivalent to
+
+  ```agda
+  transHNew : ∀{A : Set}{a b c : A} → a ≡ b → b ≡ c → a ≡ c
+  transHNew {a = _}{b = _}{c = _} refl refl = refl
+  ```
+
+  Before, underscore `_` stood for an unnamed variable that could not
+  be instantiated by an inaccessible pattern.  If one no wants to
+  prevent Agda from instantiating, one needs to use a variable name
+  other than underscore (however, in practice this situation seems
+  unlikely).
+
+Type checking
+-------------
+
+* Polarity of phantom arguments to data and record types has
+  changed. [Issue [#1596](https://github.com/agda/agda/issues/1596)]
+  Polarity of size arguments is Nonvariant (both monotone and
+  antitone).  Polarity of other arguments is Covariant (monotone).
+  Both were Invariant before (neither monotone nor antitone).
+
+  The following example type-checks now:
+
+  ```agda
+  open import Common.Size
+
+  -- List should be monotone in both arguments
+  -- (even when `cons' is missing).
+
+  data List (i : Size) (A : Set) : Set where
+    [] : List i A
+
+  castLL : ∀{i A} → List i (List i A) → List ∞ (List ∞ A)
+  castLL x = x
+
+  -- Stream should be antitone in the first and monotone in the second argument
+  -- (even with field `tail' missing).
+
+  record Stream (i : Size) (A : Set) : Set where
+    coinductive
+    field
+      head : A
+
+  castSS : ∀{i A} → Stream ∞ (Stream ∞ A) → Stream i (Stream i A)
+  castSS x = x
+  ```
+
+* `SIZELT` lambdas must be consistent
+  [Issue [#1523](https://github.com/agda/agda/issues/1523), see Abel
+  and Pientka, ICFP 2013].  When lambda-abstracting over type (`Size<
+  size`) then `size` must be non-zero, for any valid instantiation of
+  size variables.
+
+  - The good:
+
+    ```agda
+    data Nat (i : Size) : Set where
+      zero : ∀ (j : Size< i) → Nat i
+      suc  : ∀ (j : Size< i) → Nat j → Nat i
+
+    {-# TERMINATING #-}
+    -- This definition is fine, the termination checker is too strict at the moment.
+    fix : ∀ {C : Size → Set}
+       → (∀ i → (∀ (j : Size< i) → Nat j -> C j) → Nat i → C i)
+       → ∀ i → Nat i → C i
+    fix t i (zero j)  = t i (λ (k : Size< i) → fix t k) (zero j)
+    fix t i (suc j n) = t i (λ (k : Size< i) → fix t k) (suc j n)
+    ```
+
+    The `λ (k : Size< i)` is fine in both cases, as context
+
+    ```agda
+    i : Size, j : Size< i
+    ```
+
+    guarantees that `i` is non-zero.
+
+  - The bad:
+
+    ```agda
+    record Stream {i : Size} (A : Set) : Set where
+      coinductive
+      constructor _∷ˢ_
+      field
+        head  : A
+        tail  : ∀ {j : Size< i} → Stream {j} A
+    open Stream public
+
+    _++ˢ_ : ∀ {i A} → List A → Stream {i} A → Stream {i} A
+    []        ++ˢ s = s
+    (a ∷ as)  ++ˢ s = a ∷ˢ (as ++ˢ s)
+    ```
+
+    This fails, maybe unjustified, at
+
+    ```agda
+    i : Size, s : Stream {i} A
+      ⊢
+        a ∷ˢ (λ {j : Size< i} → as ++ˢ s)
+    ```
+
+    Fixed by defining the constructor by copattern matching:
+
+    ```agda
+    record Stream {i : Size} (A : Set) : Set where
+      coinductive
+      field
+        head  : A
+        tail  : ∀ {j : Size< i} → Stream {j} A
+    open Stream public
+
+    _∷ˢ_ : ∀ {i A} → A → Stream {i} A → Stream {↑ i} A
+    head  (a ∷ˢ as) = a
+    tail  (a ∷ˢ as) = as
+
+    _++ˢ_ : ∀ {i A} → List A → Stream {i} A → Stream {i} A
+    []        ++ˢ s = s
+    (a ∷ as)  ++ˢ s = a ∷ˢ (as ++ˢ s)
+    ```
+
+  - The ugly:
+
+    ```agda
+    fix : ∀ {C : Size → Set}
+       → (∀ i → (∀ (j : Size< i) → C j) → C i)
+       → ∀ i → C i
+    fix t i = t i λ (j : Size< i) → fix t j
+    ```
+
+    For `i=0`, there is no such `j` at runtime, leading to looping
+    behavior.
+
+Interaction
+-----------
+
+* Issue [#635](https://github.com/agda/agda/issues/635) has been
+  fixed.  Case splitting does not spit out implicit record patterns
+  any more.
+
+  ```agda
+  record Cont : Set₁ where
+    constructor _◃_
+    field
+      Sh  : Set
+      Pos : Sh → Set
+
+  open Cont
+
+  data W (C : Cont) : Set where
+    sup : (s : Sh C) (k : Pos C s → W C) → W C
+
+  bogus : {C : Cont} → W C → Set
+  bogus w = {!w!}
+  ```
+
+  Case splitting on `w` yielded, since the fix of
+  Issue [#473](https://github.com/agda/agda/issues/473),
+
+  ```agda
+  bogus {Sh ◃ Pos} (sup s k) = ?
+  ```
+
+  Now it gives, as expected,
+
+  ```agda
+  bogus (sup s k) = ?
+  ```
+
+Performance
+-----------
+
+* As one result of the 21st Agda Implementor's Meeting (AIM XXI),
+  serialization of the standard library is 50% faster (time reduced by
+  a third), without using additional disk space for the interface
+  files.
+
+
+Bug fixes
+---------
+
+Issues fixed (see [bug tracker](https://github.com/agda/agda/issues)):
+
+[#1546](https://github.com/agda/agda/issues/1546) (copattern matching
+and with-clauses)
+
+[#1560](https://github.com/agda/agda/issues/1560) (positivity checker
+inefficiency)
+
+[#1584](https://github.com/agda/agda/issues/1548) (let pattern with
+trailing implicit)
diff --git a/doc/release-notes/2.4.2.5.md b/doc/release-notes/2.4.2.5.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.5.md
@@ -0,0 +1,78 @@
+Release notes for Agda version 2.4.2.5
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 7.10.3.
+
+* Added `cpphs` Cabal flag
+
+  Turn on/off this flag to choose cpphs/cpp as the C preprocessor.
+
+  This flag is turn on by default.
+
+  (This flag was added in Agda 2.4.2.1 but it was not documented)
+
+Pragmas and options
+-------------------
+
+* Termination pragmas are no longer allowed inside `where` clauses
+  [Issue [#1137](https://github.com/agda/agda/issues/1137)].
+
+Type checking
+-------------
+
+* `with`-abstraction is more aggressive, abstracts also in types of
+  variables that are used in the `with`-expressions, unless they are
+  also used in the types of the
+  `with`-expressions. [Issue [#1692](https://github.com/agda/agda/issues/1692)]
+
+  Example:
+
+  ```agda
+  test : (f : (x : A) → a ≡ x) (b : A) → b ≡ a
+  test f b with a | f b
+  test f b | .b | refl = f b
+  ```
+
+  Previously, `with` would not abstract in types of variables that
+  appear in the `with`-expressions, in this case, both `f` and `b`,
+  leaving their types unchanged.  Now, it tries to abstract in `f`, as
+  only `b` appears in the types of the `with`-expressions which are
+  `A` (of `a`) and `a ≡ b` (of `f b`).  As a result, the type of `f`
+  changes to `(x : A) → b ≡ x` and the type of the goal to `b ≡ b` (as
+  previously).
+
+  This also affects `rewrite`, which is implemented in terms of
+  `with`.
+
+  ```agda
+  test : (f : (x : A) → a ≡ x) (b : A) → b ≡ a
+  test f b rewrite f b = f b
+  ```
+
+  As the new `with` is not fully backwards-compatible, some parts of
+  your Agda developments using `with` or `rewrite` might need
+  maintenance.
+
+Fixed issues
+------------
+
+See [bug tracker](https://github.com/agda/agda/issues)
+
+[#1407](https://github.com/agda/agda/issues/1497)
+
+[#1518](https://github.com/agda/agda/issues/1518)
+
+[#1670](https://github.com/agda/agda/issues/1670)
+
+[#1677](https://github.com/agda/agda/issues/1677)
+
+[#1698](https://github.com/agda/agda/issues/1698)
+
+[#1701](https://github.com/agda/agda/issues/1701)
+
+[#1710](https://github.com/agda/agda/issues/1710)
+
+[#1718](https://github.com/agda/agda/issues/1718)
diff --git a/doc/release-notes/2.4.2.md b/doc/release-notes/2.4.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.4.2.md
@@ -0,0 +1,391 @@
+Release notes for Agda version 2.4.2
+====================================
+
+Pragmas and options
+-------------------
+
+* New option: `--with-K`
+
+  This can be used to override a global `--without-K` in a file, by
+  adding a pragma `{-# OPTIONS --with-K #-}`.
+
+* New pragma `{-# NON_TERMINATING #-}`
+
+  This is a safer version of `NO_TERMINATION_CHECK` which doesn't
+  treat the affected functions as terminating. This means that
+  `NON_TERMINATING` functions do not reduce during type checking. They
+  do reduce at run-time and when invoking `C-c C-n` at top-level (but
+  not in a hole).
+
+Language
+--------
+
+* Instance search is now more efficient and recursive (see
+  Issue [#938](https://github.com/agda/agda/issues/938)) (but without
+  termination check yet).
+
+  A new keyword `instance` has been introduced (in the style of
+  `abstract` and `private`) which must now be used for every
+  definition/postulate that has to be taken into account during
+  instance resolution. For example:
+
+  ```agda
+  record RawMonoid (A : Set) : Set where
+    field
+      nil  : A
+      _++_ : A -> A -> A
+
+  open RawMonoid {{...}}
+
+  instance
+    rawMonoidList : {A : Set} -> RawMonoid (List A)
+    rawMonoidList = record { nil = []; _++_ = List._++_ }
+
+    rawMonoidMaybe : {A : Set} {{m : RawMonoid A}} -> RawMonoid (Maybe A)
+    rawMonoidMaybe {A} = record { nil = nothing ; _++_ = catMaybe }
+      where
+        catMaybe : Maybe A -> Maybe A -> Maybe A
+        catMaybe nothing mb = mb
+        catMaybe ma nothing = ma
+        catMaybe (just a) (just b) = just (a ++ b)
+  ```
+
+  Moreover, each type of an instance must end in (something that reduces
+  to) a named type (e.g. a record, a datatype or a postulate). This
+  allows us to build a simple index structure
+
+  ```
+  data/record name  -->  possible instances
+  ```
+
+  that speeds up instance search.
+
+  Instance search takes into account all local bindings and all global
+  `instance` bindings and the search is recursive. For instance,
+  searching for
+
+  ```agda
+  ? : RawMonoid (Maybe (List A))
+  ```
+
+  will consider the candidates {`rawMonoidList`, `rawMonoidMaybe`}, fail to
+  unify the first one, succeeding with the second one
+
+  ```agda
+  ? = rawMonoidMaybe {A = List A} {{m = ?m}} : RawMonoid (Maybe (List A))
+  ```
+
+  and continue with goal
+
+  ```agda
+  ?m : RawMonoid (List A)
+  ```
+
+  This will then find
+
+  ```agda
+  ?m = rawMonoidList {A = A}
+  ```
+
+  and putting together we have the solution.
+
+  Be careful that there is no termination check for now, you can
+  easily make Agda loop by declaring the identity function as an
+  instance. But it shouldn’t be possible to make Agda loop by only
+  declaring structurally recursive instances (whatever that means).
+
+  Additionally:
+
+  - Uniqueness of instances is up to definitional equality (see
+    Issue [#899](https://github.com/agda/agda/issues/899)).
+
+  - Instances of the following form are allowed:
+
+    ```agda
+    EqSigma : {A : Set} {B : A → Set} {{EqA : Eq A}}
+              {{EqB : {a : A} → Eq (B a)}}
+              → Eq (Σ A B)
+    ```
+
+    When searching recursively for an instance of type `{a : A} → Eq
+    (B a)`, a lambda will automatically be introduced and instance
+    search will search for something of type `Eq (B a)` in the context
+    extended by `a : A`. When searching for an instance, the `a`
+    argument does not have to be implicit, but in the definition of
+    `EqSigma`, instance search will only be able to use `EqB` if `a`
+    is implicit.
+
+  - There is no longer any attempt to solve irrelevant metas by instance
+    search.
+
+  - Constructors of records and datatypes are automatically added to the
+    instance table.
+
+* You can now use `quote` in patterns.
+
+  For instance, here is a function that unquotes a (closed) natural
+  number term.
+
+  ```agda
+  unquoteNat : Term → Maybe Nat
+  unquoteNat (con (quote Nat.zero) [])            = just zero
+  unquoteNat (con (quote Nat.suc) (arg _ n ∷ [])) = fmap suc (unquoteNat n)
+  unquoteNat _                                    = nothing
+  ```
+
+* The builtin constructors `AGDATERMUNSUPPORTED` and
+  `AGDASORTUNSUPPORTED` are now translated to meta variables when
+  unquoting.
+
+* New syntactic sugar `tactic e` and `tactic e | e1 | .. | en`.
+
+  It desugars as follows and makes it less unwieldy to call
+  reflection-based tactics.
+
+  ```agda
+  tactic e                --> quoteGoal g in unquote (e g)
+  tactic e | e1 | .. | en --> quoteGoal g in unquote (e g) e1 .. en
+  ```
+
+  Note that in the second form the tactic function should generate a
+  function from a number of new subgoals to the original goal. The
+  type of `e` should be `Term -> Term` in both cases.
+
+* New reflection builtins for literals.
+
+  The term data type `AGDATERM` now needs an additional constructor
+   `AGDATERMLIT` taking a reflected literal defined as follows (with
+   appropriate builtin bindings for the types `Nat`, `Float`, etc).
+
+  ```agda
+  data Literal : Set where
+    nat    : Nat    → Literal
+    float  : Float  → Literal
+    char   : Char   → Literal
+    string : String → Literal
+    qname  : QName  → Literal
+
+  {-# BUILTIN AGDALITERAL   Literal #-}
+  {-# BUILTIN AGDALITNAT    nat     #-}
+  {-# BUILTIN AGDALITFLOAT  float   #-}
+  {-# BUILTIN AGDALITCHAR   char    #-}
+  {-# BUILTIN AGDALITSTRING string  #-}
+  {-# BUILTIN AGDALITQNAME  qname   #-}
+  ```
+
+  When quoting (`quoteGoal` or `quoteTerm`) literals will be mapped to
+  the `AGDATERMLIT` constructor. Previously natural number literals
+  were quoted to `suc`/`zero` application and other literals were
+  quoted to `AGDATERMUNSUPPORTED`.
+
+* New reflection builtins for function definitions.
+
+  `AGDAFUNDEF` should now map to a data type defined as follows
+
+  (with
+  ```agda
+  {-# BUILTIN QNAME       QName   #-}
+  {-# BUILTIN ARG         Arg     #-}
+  {-# BUILTIN AGDATERM    Term    #-}
+  {-# BUILTIN AGDATYPE    Type    #-}
+  {-# BUILTIN AGDALITERAL Literal #-}
+  ```
+  ).
+
+  ```agda
+  data Pattern : Set where
+    con    : QName → List (Arg Pattern) → Pattern
+    dot    : Pattern
+    var    : Pattern
+    lit    : Literal → Pattern
+    proj   : QName → Pattern
+    absurd : Pattern
+
+  {-# BUILTIN AGDAPATTERN   Pattern #-}
+  {-# BUILTIN AGDAPATCON    con     #-}
+  {-# BUILTIN AGDAPATDOT    dot     #-}
+  {-# BUILTIN AGDAPATVAR    var     #-}
+  {-# BUILTIN AGDAPATLIT    lit     #-}
+  {-# BUILTIN AGDAPATPROJ   proj    #-}
+  {-# BUILTIN AGDAPATABSURD absurd  #-}
+
+  data Clause : Set where
+    clause        : List (Arg Pattern) → Term → Clause
+    absurd-clause : List (Arg Pattern) → Clause
+
+  {-# BUILTIN AGDACLAUSE       Clause        #-}
+  {-# BUILTIN AGDACLAUSECLAUSE clause        #-}
+  {-# BUILTIN AGDACLAUSEABSURD absurd-clause #-}
+
+  data FunDef : Set where
+    fun-def : Type → List Clause → FunDef
+
+  {-# BUILTIN AGDAFUNDEF    FunDef  #-}
+  {-# BUILTIN AGDAFUNDEFCON fun-def #-}
+  ```
+
+* New reflection builtins for extended (pattern-matching) lambda.
+
+  The `AGDATERM` data type has been augmented with a constructor
+
+  ```agda
+  AGDATERMEXTLAM : List AGDACLAUSE → List (ARG AGDATERM) → AGDATERM
+  ```
+
+  Absurd lambdas (`λ ()`) are quoted to extended lambdas with an
+  absurd clause.
+
+* Unquoting declarations.
+
+  You can now define (recursive) functions by reflection using the new
+  `unquoteDecl` declaration
+
+  ```agda
+  unquoteDecl x = e
+  ```
+
+  Here e should have type `AGDAFUNDEF` and evaluate to a closed
+  value. This value is then spliced in as the definition of `x`. In
+  the body `e`, `x` has type `QNAME` which lets you splice in
+  recursive definitions.
+
+  Standard modifiers, such as fixity declarations, can be applied to `x` as
+  expected.
+
+* Quoted levels
+
+  Universe levels are now quoted properly instead of being quoted to
+  `AGDASORTUNSUPPORTED`. `Setω` still gets an unsupported sort,
+  however.
+
+* Module applicants can now be operator applications.
+
+  Example:
+
+  ```agda
+  postulate
+    [_] : A -> B
+
+  module M (b : B) where
+
+  module N (a : A) = M [ a ]
+  ```
+
+  [See Issue [#1245](https://github.com/agda/agda/issues/1245)]
+
+* Minor change in module application
+  semantics. [Issue [#892](https://github.com/agda/agda/issues/892)]
+
+  Previously re-exported functions were not redefined when
+  instantiating a module. For instance
+
+  ```agda
+  module A where f = ...
+  module B (X : Set) where
+    open A public
+  module C = B Nat
+  ```
+
+  In this example `C.f` would be an alias for `A.f`, so if both `A`
+  and `C` were opened `f` would not be ambiguous. However, this
+  behaviour is not correct when `A` and `B` share some module
+  parameters
+  (Issue [#892](https://github.com/agda/agda/issues/892)). To fix this
+  `C` now defines its own copy of `f` (which evaluates to `A.f`),
+  which means that opening `A` and `C` results in an ambiguous `f`.
+
+Type checking
+-------------
+
+* Recursive records need to be declared as either `inductive` or
+  `coinductive`.  `inductive` is no longer default for recursive
+  records. Examples:
+
+  ```agda
+  record _×_ (A B : Set) : Set where
+    constructor _,_
+    field
+      fst : A
+      snd : B
+
+  record Tree (A : Set) : Set where
+    inductive
+    constructor tree
+    field
+      elem     : A
+      subtrees : List (Tree A)
+
+  record Stream (A : Set) : Set where
+    coinductive
+    constructor _::_
+    field
+      head : A
+      tail : Stream A
+  ```
+
+  If you are using old-style (musical) coinduction, a record may have
+  to be declared as inductive, paradoxically.
+
+  ```agda
+  record Stream (A : Set) : Set where
+    inductive -- YES, THIS IS INTENDED !
+    constructor _∷_
+    field
+      head : A
+      tail : ∞ (Stream A)
+  ```
+
+  This is because the "coinduction" happens in the use of `∞` and not
+  in the use of `record`.
+
+Tools
+-----
+
+### Emacs mode
+
+* A new menu option `Display` can be used to display the version of
+  the running Agda process.
+
+### LaTeX-backend
+
+* New experimental option `references` has been added. When specified,
+  i.e.:
+
+  ```latex
+  \usepackage[references]{agda}
+  ```
+
+  a new command called `\AgdaRef` is provided, which lets you
+  reference previously typeset commands, e.g.:
+
+  Let us postulate `\AgdaRef{apa}`.
+
+  ```agda
+  \begin{code}
+  postulate
+    apa : Set
+  \end{code}
+  ```
+
+  Above `apa` will be typeset (highlighted) the same in the text as in
+  the code, provided that the LaTeX output is post-processed using
+  `src/data/postprocess-latex.pl`, e.g.:
+
+  ```
+  cp $(dirname $(dirname $(agda-mode locate)))/postprocess-latex.pl .
+  agda -i. --latex Example.lagda
+  cd latex/
+  perl ../postprocess-latex.pl Example.tex > Example.processed
+  mv Example.processed Example.tex
+  xelatex Example.tex
+  ```
+
+  Mix-fix and Unicode should work as expected (Unicode requires
+  XeLaTeX/LuaLaTeX), but there are limitations:
+
+  - Overloading identifiers should be avoided, if multiples exist
+    `\AgdaRef` will typeset according to the first it finds.
+
+  - Only the current module is used, should you need to reference
+    identifiers in other modules then you need to specify which other
+    module manually, i.e. `\AgdaRef[module]{identifier}`.
diff --git a/doc/release-notes/2.5.1.1.md b/doc/release-notes/2.5.1.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.1.1.md
@@ -0,0 +1,79 @@
+Release notes for Agda version 2.5.1.1
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.0.1.
+
+* Documentation is now built with Python >=3.3, as done by
+  [readthedocs.org](https://readthedocs.org/).
+
+Bug fixes
+---------
+
+* Fixed a serious performance problem with instance search
+
+  Issues [#1952](https://github.com/agda/agda/issues/1952) and
+  [#1998](https://github.com/agda/agda/issues/1998). Also related:
+  [#1955](https://github.com/agda/agda/issues/1955) and
+  [#2025](https://github.com/agda/agda/issues/2025)
+
+* Interactively splitting variable with `C-c C-c` no longer introduces
+  new trailing patterns.  This fixes
+  Issue [#1950](https://github.com/agda/agda/issues/1950).
+
+  ```agda
+  data Ty : Set where
+    _⇒_ : Ty → Ty → Ty
+
+  ⟦_⟧ : Ty → Set
+  ⟦ A ⇒ B ⟧ = ⟦ A ⟧ → ⟦ B ⟧
+
+  data Term : Ty → Set where
+    K : (A B : Ty) → Term (A ⇒ (B ⇒ A))
+
+  test : (A : Ty) (a : Term A) → ⟦ A ⟧
+  test A a = {!a!}
+  ```
+
+  Before change, case splitting on `a` would give
+
+  ```agda
+  test .(A ⇒ (B ⇒ A)) (K A B) x x₁ = ?
+  ```
+
+  Now, it yields
+
+  ```agda
+  test .(A ⇒ (B ⇒ A)) (K A B) = ?
+  ```
+
+* In literate TeX files, `\begin{code}` and `\end{code}` can be
+  preceded (resp. followed) by TeX code on the same line. This fixes
+  Issue [#2077](https://github.com/agda/agda/issues/2077).
+
+* Other issues fixed (see
+  [bug tracker](https://github.com/agda/agda/issues)):
+
+  [#1951](https://github.com/agda/agda/issues/1951) (mixfix binders
+  not working in 'syntax')
+
+  [#1967](https://github.com/agda/agda/issues/1967) (too eager
+  insteance search error)
+
+  [#1974](https://github.com/agda/agda/issues/1974) (lost constraint
+  dependencies)
+
+  [#1982](https://github.com/agda/agda/issues/1982) (internal error in
+  unifier)
+
+  [#2034](https://github.com/agda/agda/issues/2034) (function type
+  instance goals)
+
+Compiler backends
+-----------------
+
+* UHC compiler backend
+
+  Added support for UHC 1.1.9.4.
diff --git a/doc/release-notes/2.5.1.2.md b/doc/release-notes/2.5.1.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.1.2.md
@@ -0,0 +1,5 @@
+Release notes for Agda version 2.5.1.2
+======================================
+
+* Fixed broken type signatures that were incorrectly accepted due to
+  [GHC #12784](https://ghc.haskell.org/trac/ghc/ticket/12784).
diff --git a/doc/release-notes/2.5.1.md b/doc/release-notes/2.5.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.1.md
@@ -0,0 +1,1600 @@
+Release notes for Agda version 2.5.1
+====================================
+
+Documentation
+-------------
+
+* There is now an official Agda User Manual:
+  https://agda.readthedocs.io/
+
+Installation and infrastructure
+-------------------------------
+
+* Builtins and primitives are now defined in a new set of modules available to
+  all users, independent of any particular library. The modules are
+
+  ```agda
+  Agda.Builtin.Bool
+  Agda.Builtin.Char
+  Agda.Builtin.Coinduction
+  Agda.Builtin.Equality
+  Agda.Builtin.Float
+  Agda.Builtin.FromNat
+  Agda.Builtin.FromNeg
+  Agda.Builtin.FromString
+  Agda.Builtin.IO
+  Agda.Builtin.Int
+  Agda.Builtin.List
+  Agda.Builtin.Nat
+  Agda.Builtin.Reflection
+  Agda.Builtin.Size
+  Agda.Builtin.Strict
+  Agda.Builtin.String
+  Agda.Builtin.TrustMe
+  Agda.Builtin.Unit
+  ```
+
+  The standard library reexports the primitives from the new modules.
+
+  The `Agda.Builtin` modules are installed in the same way as
+  `Agda.Primitive`, but unlike `Agda.Primitive` they are not loaded
+  automatically.
+
+Pragmas and options
+-------------------
+
+* Library management
+
+  There is a new 'library' concept for managing include paths. A library
+  consists of
+    - a name,
+    - a set of libraries it depends on, and
+    - a set of include paths.
+
+  A library is defined in a `.agda-lib` file using the following
+  format:
+
+  ```
+  name: LIBRARY-NAME  -- Comment
+  depend: LIB1 LIB2
+    LIB3
+    LIB4
+  include: PATH1
+    PATH2
+    PATH3
+  ```
+
+  Dependencies are library names, not paths to `.agda-lib` files, and
+  include paths are relative to the location of the library-file.
+
+  To be useable, a library file has to be listed (with its full path)
+  in `AGDA_DIR/libraries` (or `AGDA_DIR/libraries-VERSION`, for a
+  given Agda version). `AGDA_DIR` defaults to `~/.agda` on Unix-like
+  systems and `C:/Users/USERNAME/AppData/Roaming/agda` or similar on
+  Windows, and can be overridden by setting the `AGDA_DIR` environment
+  variable.
+
+  Environment variables in the paths (of the form `$VAR` or `${VAR}`)
+  are expanded. The location of the libraries file used can be
+  overridden using the `--library-file=FILE` flag, although this is
+  not expected to be very useful.
+
+  You can find out the precise location of the 'libraries' file by
+  calling `agda -l fjdsk Dummy.agda` and looking at the error message
+  (assuming you don't have a library called fjdsk installed).
+
+  There are three ways a library gets used:
+
+    - You supply the `--library=LIB` (or `-l LIB`) option to
+      Agda. This is equivalent to adding a `-iPATH` for each of the
+      include paths of `LIB` and its (transitive) dependencies.
+
+    - No explicit `--library` flag is given, and the current project
+      root (of the Agda file that is being loaded) or one of its
+      parent directories contains a `.agda-lib` file defining a
+      library `LIB`. This library is used as if a `--librarary=LIB`
+      option had been given, except that it is not necessary for the
+      library to be listed in the `AGDA_DIR/libraries` file.
+
+    - No explicit `--library` flag, and no `.agda-lib` file in the
+      project root. In this case the file `AGDA_DIR/defaults` is read
+      and all libraries listed are added to the path. The defaults
+      file should contain a list of library names, each on a separate
+      line. In this case the current directory is also added to the
+      path.
+
+      To disable default libraries, you can give the flag
+      `--no-default-libraries`.
+
+  Library names can end with a version number (for instance,
+  `mylib-1.2.3`). When resolving a library name (given in a `--library`
+  flag, or listed as a default library or library dependency) the
+  following rules are followed:
+
+    - If you don't give a version number, any version will do.
+
+    - If you give a version number an exact match is required.
+
+    - When there are multiple matches an exact match is preferred, and
+      otherwise the latest matching version is chosen.
+
+  For example, suppose you have the following libraries installed:
+  `mylib`, `mylib-1.0`, `otherlib-2.1`, and `otherlib-2.3`. In this
+  case, aside from the exact matches you can also say
+  `--library=otherlib` to get `otherlib-2.3`.
+
+* New Pragma `COMPILED_DECLARE_DATA` for binding recursively defined
+  Haskell data types to recursively defined Agda data types.
+
+  If you have a Haskell type like
+
+  ```haskell
+  {-# LANGUAGE GADTs #-}
+
+  module Issue223 where
+
+  data A where
+    BA :: B -> A
+
+  data B where
+    AB :: A -> B
+    BB :: B
+  ```
+
+  You can now bind it to corresponding mutual Agda inductive data
+  types as follows:
+
+  ```agda
+  {-# IMPORT Issue223 #-}
+
+  data A : Set
+  {-# COMPILED_DECLARE_DATA A Issue223.A #-}
+  data B : Set
+  {-# COMPILED_DECLARE_DATA B Issue223.B #-}
+
+  data A where
+    BA : B → A
+
+  {-# COMPILED_DATA A Issue223.A Issue223.BA #-}
+  data B where
+    AB : A → B
+    BB : B
+
+  {-# COMPILED_DATA B Issue223.B Issue223.AB Issue223.BB #-}
+  ```
+
+  This fixes Issue [#223](https://github.com/agda/agda/issues/223).
+
+* New pragma `HASKELL` for adding inline Haskell code (GHC backend only)
+
+  Arbitrary Haskell code can be added to a module using the `HASKELL`
+  pragma. For instance,
+
+  ```agda
+  {-# HASKELL
+    echo :: IO ()
+    echo = getLine >>= putStrLn
+  #-}
+
+  postulate echo : IO ⊤
+  {-# COMPILED echo echo #-}
+  ```
+
+* New option `--exact-split`.
+
+  The `--exact-split` flag causes Agda to raise an error whenever a
+  clause in a definition by pattern matching cannot be made to hold
+  definitionally (i.e. as a reduction rule). Specific clauses can be
+  excluded from this check by means of the `{-# CATCHALL #-}` pragma.
+
+  For instance, the following definition will be rejected as the second clause
+  cannot be made to hold definitionally:
+
+  ```agda
+  min : Nat → Nat → Nat
+  min zero    y       = zero
+  min x       zero    = zero
+  min (suc x) (suc y) = suc (min x y
+  ```
+
+  Catchall clauses have to be marked as such, for instance:
+
+  ```agda
+  eq : Nat → Nat → Bool
+  eq zero    zero    = true
+  eq (suc m) (suc n) = eq m n
+  {-# CATCHALL #-}
+  eq _       _       = false
+  ```
+
+* New option: `--no-exact-split`.
+
+  This option can be used to override a global `--exact-split` in a
+  file, by adding a pragma `{-# OPTIONS --no-exact-split #-}`.
+
+* New options: `--sharing` and `--no-sharing`.
+
+  These options are used to enable/disable sharing and call-by-need
+  evaluation.  The default is `--no-sharing`.
+
+  Note that they cannot appear in an `OPTIONS` pragma, but have to be
+  given as command line arguments or added to the Agda Program Args
+  from Emacs with `M-x customize-group agda2`.
+
+* New pragma `DISPLAY`.
+
+  ```agda
+  {-# DISPLAY f e1 .. en = e #-}
+  ```
+
+  This causes `f e1 .. en` to be printed in the same way as `e`, where
+  `ei` can bind variables used in `e`. The expressions `ei` and `e`
+  are scope checked, but not type checked.
+
+  For example this can be used to print overloaded (instance) functions with
+  the overloaded name:
+
+  ```agda
+  instance
+    NumNat : Num Nat
+    NumNat = record { ..; _+_ = natPlus }
+
+  {-# DISPLAY natPlus a b = a + b #-}
+  ```
+
+  Limitations
+
+  - Left-hand sides are restricted to variables, constructors, defined
+    functions or types, and literals. In particular, lambdas are not
+    allowed in left-hand sides.
+
+  - Since `DISPLAY` pragmas are not type checked implicit argument
+    insertion may not work properly if the type of `f` computes to an
+    implicit function space after pattern matching.
+
+* Removed pragma `{-# ETA R #-}`
+
+  The pragma `{-# ETA R #-}` is replaced by the `eta-equality` directive
+  inside record declarations.
+
+* New option `--no-eta-equality`.
+
+  The `--no-eta-equality` flag disables eta rules for declared record
+  types.  It has the same effect as `no-eta-equality` inside each
+  declaration of a record type `R`.
+
+  If used with the `OPTIONS` pragma it will not affect records defined
+  in other modules.
+
+* The semantics of `{-# REWRITE r #-}` pragmas in parametrized modules
+  has changed (see
+  Issue [#1652](https://github.com/agda/agda/issues/1652)).
+
+  Rewrite rules are no longer lifted to the top context. Instead, they
+  now only apply to terms in (extensions of) the module context. If
+  you want the old behaviour, you should put the `{-# REWRITE r #-}`
+  pragma outside of the module (i.e. unindent it).
+
+* New pragma `{-# INLINE f #-}` causes `f` to be inlined during
+  compilation.
+
+* The `STATIC` pragma is now taken into account during compilation.
+
+  Calls to a function marked `STATIC` are normalised before
+  compilation. The typical use case for this is to mark the
+  interpreter of an embedded language as `STATIC`.
+
+* Option `--type-in-type` no longer implies
+  `--no-universe-polymorphism`, thus, it can be used with explicit
+  universe
+  levels. [Issue [#1764](https://github.com/agda/agda/issues/1764)] It
+  simply turns off error reporting for any level mismatch now.
+  Examples:
+
+  ```agda
+  {-# OPTIONS --type-in-type #-}
+
+  Type : Set
+  Type = Set
+
+  data D {α} (A : Set α) : Set where
+    d : A → D A
+
+  data E α β : Set β where
+    e : Set α → E α β
+  ```
+
+* New `NO_POSITIVITY_CHECK` pragma to switch off the positivity checker
+  for data/record definitions and mutual blocks.
+
+  The pragma must precede a data/record definition or a mutual block.
+
+  The pragma cannot be used in `--safe` mode.
+
+  Examples (see `Issue1614*.agda` and `Issue1760*.agda` in
+  `test/Succeed/`):
+
+  1. Skipping a single data definition.
+
+     ```agda
+     {-# NO_POSITIVITY_CHECK #-}
+     data D : Set where
+       lam : (D → D) → D
+     ```
+
+  2. Skipping a single record definition.
+
+     ```agda
+     {-# NO_POSITIVITY_CHECK #-}
+     record U : Set where
+       field ap : U → U
+     ```
+
+  3. Skipping an old-style mutual block: Somewhere within a `mutual`
+     block before a data/record definition.
+
+     ```agda
+     mutual
+       data D : Set where
+         lam : (D → D) → D
+
+       {-# NO_POSITIVITY_CHECK #-}
+       record U : Set where
+         field ap : U → U
+     ```
+
+  4. Skipping an old-style mutual block: Before the `mutual` keyword.
+
+     ```agda
+     {-# NO_POSITIVITY_CHECK #-}
+     mutual
+       data D : Set where
+         lam : (D → D) → D
+
+       record U : Set where
+         field ap : U → U
+     ```
+
+  5. Skipping a new-style mutual block: Anywhere before the
+     declaration or the definition of data/record in the block.
+
+     ```agda
+     record U : Set
+     data D   : Set
+
+     record U where
+       field ap : U → U
+
+     {-# NO_POSITIVITY_CHECK #-}
+     data D where
+       lam : (D → D) → D
+     ```
+
+* Removed `--no-coverage-check`
+  option. [Issue [#1918](https://github.com/agda/agda/issues/1918)]
+
+Language
+--------
+
+### Operator syntax
+
+* The default fixity for syntax declarations has changed from -666 to 20.
+
+* Sections.
+
+  Operators can be sectioned by replacing arguments with underscores.
+  There must not be any whitespace between these underscores and the
+  adjacent nameparts. Examples:
+
+  ```agda
+  pred : ℕ → ℕ
+  pred = _∸ 1
+
+  T : Bool → Set
+  T = if_then ⊤ else ⊥
+
+  if : {A : Set} (b : Bool) → A → A → A
+  if b = if b then_else_
+  ```
+
+  Sections are translated into lambda expressions. Examples:
+
+  ```agda
+  _∸ 1              ↦  λ section → section ∸ 1
+
+  if_then ⊤ else ⊥  ↦  λ section → if section then ⊤ else ⊥
+
+  if b then_else_   ↦  λ section section₁ →
+                           if b then section else section₁
+  ```
+
+  Operator sections have the same fixity as the underlying operator
+  (except in cases like `if b then_else_`, in which the section is
+  "closed", but the operator is not).
+
+  Operator sections are not supported in patterns (with the exception
+  of dot patterns), and notations coming from syntax declarations
+  cannot be sectioned.
+
+* A long-standing operator fixity bug has been fixed. As a consequence
+  some programs that used to parse no longer do.
+
+  Previously each precedence level was (incorrectly) split up into
+  five separate ones, ordered as follows, with the earlier ones
+  binding less tightly than the later ones:
+
+    - Non-associative operators.
+
+    - Left associative operators.
+
+    - Right associative operators.
+
+    - Prefix operators.
+
+    - Postfix operators.
+
+  Now this problem has been addressed. It is no longer possible to mix
+  operators of a given precedence level but different associativity.
+  However, prefix and right associative operators are seen as having
+  the same associativity, and similarly for postfix and left
+  associative operators.
+
+  Examples
+  --------
+
+  The following code is no longer accepted:
+
+  ```agda
+  infixl 6 _+_
+  infix  6 _∸_
+
+  rejected : ℕ
+  rejected = 1 + 0 ∸ 1
+  ```
+
+  However, the following previously rejected code is accepted:
+
+  ```agda
+  infixr 4 _,_
+  infix  4 ,_
+
+  ,_ : {A : Set} {B : A → Set} {x : A} → B x → Σ A B
+  , y = _ , y
+
+  accepted : Σ ℕ λ i → Σ ℕ λ j → Σ (i ≡ j) λ _ → Σ ℕ λ k → j ≡ k
+  accepted = 5 , , refl , , refl
+  ```
+
+* The classification of notations with binders into the categories
+  infix, prefix, postfix or closed has
+  changed. [Issue [#1450](https://github.com/agda/agda/issues/1450)]
+
+  The difference is that, when classifying the notation, only
+  *regular* holes are taken into account, not *binding* ones.
+
+  Example: The notation
+
+  ```agda
+  syntax m >>= (λ x → f) = x <- m , f
+  ```
+
+  was previously treated as infix, but is now treated as prefix.
+
+* Notation can now include wildcard binders.
+
+  Example: `syntax Σ A (λ _ → B) = A × B`
+
+* If an overloaded operator is in scope with several distinct
+  precedence levels, then several instances of this operator will be
+  included in the operator grammar, possibly leading to ambiguity.
+  Previously the operator was given the default fixity
+  [Issue [#1436](https://github.com/agda/agda/issues/1436)].
+
+  There is an exception to this rule: If there are multiple precedences,
+  but at most one is explicitly declared, then only one instance will be
+  included in the grammar. If there are no explicitly declared
+  precedences, then this instance will get the default precedence, and
+  otherwise it will get the declared precedence.
+
+  If multiple occurrences of an operator are "merged" in the grammar,
+  and they have distinct associativities, then they are treated as
+  being non-associative.
+
+  The three paragraphs above also apply to identical notations (coming
+  from syntax declarations) for a given overloaded name.
+
+  Examples:
+
+  ```agda
+  module A where
+
+    infixr 5 _∷_
+    infixr 5 _∙_
+    infixl 3 _+_
+    infix  1 bind
+
+    syntax bind c (λ x → d) = x ← c , d
+
+  module B where
+
+    infix  5 _∷_
+    infixr 4 _∙_
+    -- No fixity declaration for _+_.
+    infixl 2 bind
+
+    syntax bind c d = c ∙ d
+
+  module C where
+
+    infixr 2 bind
+
+    syntax bind c d = c ∙ d
+
+  open A
+  open B
+  open C
+
+  -- _∷_ is infix 5.
+  -- _∙_ has two fixities: infixr 4 and infixr 5.
+  -- _+_ is infixl 3.
+  -- A.bind's notation is infix 1.
+  -- B.bind and C.bind's notations are infix 2.
+
+  -- There is one instance of "_ ∷ _" in the grammar, and one
+  -- instance of "_ + _".
+
+  -- There are three instances of "_ ∙ _" in the grammar, one
+  -- corresponding to A._∙_, one corresponding to B._∙_, and one
+  -- corresponding to both B.bind and C.bind.
+  ```
+
+### Reflection
+
+* The reflection framework has received a massive overhaul.
+
+  A new type of reflected type checking computations supplants most of
+  the old reflection primitives. The `quoteGoal`, `quoteContext` and
+  tactic primitives are deprecated and will be removed in the future,
+  and the `unquoteDecl` and `unquote` primitives have changed
+  behaviour. Furthermore the following primitive functions have been
+  replaced by builtin type checking computations:
+
+  ```agda
+  - primQNameType              --> AGDATCMGETTYPE
+  - primQNameDefinition        --> AGDATCMGETDEFINITION
+  - primDataConstructors       --> subsumed by AGDATCMGETDEFINITION
+  - primDataNumberOfParameters --> subsumed by AGDATCMGETDEFINITION
+  ```
+
+  See below for details.
+
+* Types are no longer packaged with a sort.
+
+  The `AGDATYPE` and `AGDATYPEEL` built-ins have been
+  removed. Reflected types are now simply terms.
+
+* Reflected definitions have more information.
+
+  The type for reflected definitions has changed to
+
+  ```agda
+  data Definition : Set where
+    fun-def     : List Clause  → Definition
+    data-type   : Nat → List Name → Definition -- parameters and constructors
+    record-type : Name → Definition            -- name of the data/record type
+    data-con    : Name → Definition            -- name of the constructor
+    axiom       : Definition
+    prim-fun    : Definition
+  ```
+
+  Correspondingly the built-ins for function, data and record
+  definitions (`AGDAFUNDEF`, `AGDAFUNDEFCON`, `AGDADATADEF`,
+  `AGDARECORDDEF`) have been removed.
+
+* Reflected type checking computations.
+
+  There is a primitive `TC` monad representing type checking
+  computations. The `unquote`, `unquoteDecl`, and the new `unquoteDef`
+  all expect computations in this monad (see below). The interface to
+  the monad is the following
+
+  ```agda
+  -- Error messages can contain embedded names and terms.
+  data ErrorPart : Set where
+    strErr  : String → ErrorPart
+    termErr : Term → ErrorPart
+    nameErr : Name → ErrorPart
+
+  {-# BUILTIN AGDAERRORPART       ErrorPart #-}
+  {-# BUILTIN AGDAERRORPARTSTRING strErr    #-}
+  {-# BUILTIN AGDAERRORPARTTERM   termErr   #-}
+  {-# BUILTIN AGDAERRORPARTNAME   nameErr   #-}
+
+  postulate
+    TC         : ∀ {a} → Set a → Set a
+    returnTC   : ∀ {a} {A : Set a} → A → TC A
+    bindTC     : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B
+
+    -- Unify two terms, potentially solving metavariables in the process.
+    unify      : Term → Term → TC ⊤
+
+    -- Throw a type error. Can be caught by catchTC.
+    typeError  : ∀ {a} {A : Set a} → List ErrorPart → TC A
+
+    -- Block a type checking computation on a metavariable. This will abort
+    -- the computation and restart it (from the beginning) when the
+    -- metavariable is solved.
+    blockOnMeta : ∀ {a} {A : Set a} → Meta → TC A
+
+    -- Backtrack and try the second argument if the first argument throws a
+    -- type error.
+    catchTC    : ∀ {a} {A : Set a} → TC A → TC A → TC A
+
+    -- Infer the type of a given term
+    inferType  : Term → TC Type
+
+    -- Check a term against a given type. This may resolve implicit arguments
+    -- in the term, so a new refined term is returned. Can be used to create
+    -- new metavariables: newMeta t = checkType unknown t
+    checkType  : Term → Type → TC Term
+
+    -- Compute the normal form of a term.
+    normalise  : Term → TC Term
+
+    -- Get the current context.
+    getContext : TC (List (Arg Type))
+
+    -- Extend the current context with a variable of the given type.
+    extendContext : ∀ {a} {A : Set a} → Arg Type → TC A → TC A
+
+    -- Set the current context.
+    inContext     : ∀ {a} {A : Set a} → List (Arg Type) → TC A → TC A
+
+    -- Quote a value, returning the corresponding Term.
+    quoteTC : ∀ {a} {A : Set a} → A → TC Term
+
+    -- Unquote a Term, returning the corresponding value.
+    unquoteTC : ∀ {a} {A : Set a} → Term → TC A
+
+    -- Create a fresh name.
+    freshName  : String → TC QName
+
+    -- Declare a new function of the given type. The function must be defined
+    -- later using 'defineFun'. Takes an Arg Name to allow declaring instances
+    -- and irrelevant functions. The Visibility of the Arg must not be hidden.
+    declareDef : Arg QName → Type → TC ⊤
+
+    -- Define a declared function. The function may have been declared using
+    -- 'declareDef' or with an explicit type signature in the program.
+    defineFun  : QName → List Clause → TC ⊤
+
+    -- Get the type of a defined name. Replaces 'primQNameType'.
+    getType    : QName → TC Type
+
+    -- Get the definition of a defined name. Replaces 'primQNameDefinition'.
+    getDefinition : QName → TC Definition
+
+  {-# BUILTIN AGDATCM                   TC                 #-}
+  {-# BUILTIN AGDATCMRETURN             returnTC           #-}
+  {-# BUILTIN AGDATCMBIND               bindTC             #-}
+  {-# BUILTIN AGDATCMUNIFY              unify              #-}
+  {-# BUILTIN AGDATCMNEWMETA            newMeta            #-}
+  {-# BUILTIN AGDATCMTYPEERROR          typeError          #-}
+  {-# BUILTIN AGDATCMBLOCKONMETA        blockOnMeta        #-}
+  {-# BUILTIN AGDATCMCATCHERROR         catchTC            #-}
+  {-# BUILTIN AGDATCMINFERTYPE          inferType          #-}
+  {-# BUILTIN AGDATCMCHECKTYPE          checkType          #-}
+  {-# BUILTIN AGDATCMNORMALISE          normalise          #-}
+  {-# BUILTIN AGDATCMGETCONTEXT         getContext         #-}
+  {-# BUILTIN AGDATCMEXTENDCONTEXT      extendContext      #-}
+  {-# BUILTIN AGDATCMINCONTEXT          inContext          #-}
+  {-# BUILTIN AGDATCMQUOTETERM          quoteTC            #-}
+  {-# BUILTIN AGDATCMUNQUOTETERM        unquoteTC          #-}
+  {-# BUILTIN AGDATCMFRESHNAME          freshName          #-}
+  {-# BUILTIN AGDATCMDECLAREDEF         declareDef         #-}
+  {-# BUILTIN AGDATCMDEFINEFUN          defineFun          #-}
+  {-# BUILTIN AGDATCMGETTYPE            getType            #-}
+  {-# BUILTIN AGDATCMGETDEFINITION      getDefinition      #-}
+  ```
+
+* Builtin type for metavariables
+
+  There is a new builtin type for metavariables used by the new reflection
+  framework. It is declared as follows and comes with primitive equality,
+  ordering and show.
+
+  ```agda
+  postulate Meta : Set
+  {-# BUILTIN AGDAMETA Meta #-}
+  primitive primMetaEquality : Meta → Meta → Bool
+  primitive primMetaLess : Meta → Meta → Bool
+  primitive primShowMeta : Meta → String
+  ```
+
+  There are corresponding new constructors in the `Term` and `Literal`
+  data types:
+
+  ```agda
+  data Term : Set where
+    ...
+    meta : Meta → List (Arg Term) → Term
+
+  {-# BUILTIN AGDATERMMETA meta #-}
+
+  data Literal : Set where
+    ...
+    meta : Meta → Literal
+
+  {-# BUILTIN AGDALITMETA meta #-}
+  ```
+
+* Builtin unit type
+
+  The type checker needs to know about the unit type, which you can
+  allow by
+
+  ```agda
+  record ⊤ : Set where
+  {-# BUILTIN UNIT ⊤ #-}
+  ```
+
+* Changed behaviour of `unquote`
+
+  The `unquote` primitive now expects a type checking computation
+  instead of a pure term. In particular `unquote e` requires
+
+  ```agda
+  e : Term → TC ⊤
+  ```
+
+  where the argument is the representation of the hole in which the
+  result should go. The old `unquote` behaviour (where `unquote`
+  expected a `Term` argument) can be recovered by
+
+  ```agda
+  OLD: unquote v
+  NEW: unquote λ hole → unify hole v
+  ```
+
+* Changed behaviour of `unquoteDecl`
+
+  The `unquoteDecl` primitive now expects a type checking computation
+  instead of a pure function definition. It is possible to define
+  multiple (mutually recursive) functions at the same time. More
+  specifically
+
+  ```agda
+  unquoteDecl x₁ .. xₙ = m
+  ```
+
+  requires `m : TC ⊤` and that `x₁ .. xₙ` are defined (using
+  `declareDef` and `defineFun`) after executing `m`. As before `x₁
+  .. xₙ : QName` in `m`, but have their declared types outside the
+  `unquoteDecl`.
+
+* New primitive `unquoteDef`
+
+  There is a new declaration
+
+  ```agda
+  unquoteDef x₁ .. xₙ = m
+  ```
+
+  This works exactly as `unquoteDecl` (see above) with the exception
+  that `x₁ ..  xₙ` are required to already be declared.
+
+  The main advantage of `unquoteDef` over `unquoteDecl` is that
+  `unquoteDef` is allowed in mutual blocks, allowing mutually
+  recursion between generated definitions and hand-written
+  definitions.
+
+* The reflection interface now exposes the name hint (as a string)
+  for variables. As before, the actual binding structure is with
+  de Bruijn indices. The String value is just a hint used as a prefix
+  to help display the variable. The type `Abs` is a new builtin type used
+  for the constructors `Term.lam`, `Term.pi`, `Pattern.var`
+  (bultins `AGDATERMLAM`, `AGDATERMPI` and `AGDAPATVAR`).
+
+  ```agda
+  data Abs (A : Set) : Set where
+    abs : (s : String) (x : A) → Abs A
+  {-# BUILTIN ABS    Abs #-}
+  {-# BUILTIN ABSABS abs #-}
+  ```
+
+  Updated constructor types:
+
+  ```agda
+  Term.lam    : Hiding   → Abs Term → Term
+  Term.pi     : Arg Type → Abs Type → Term
+  Pattern.var : String   → Pattern
+  ```
+
+* Reflection-based macros
+
+  Macros are functions of type `t1 → t2 → .. → Term → TC ⊤` that are
+  defined in a `macro` block. Macro application is guided by the type
+  of the macro, where `Term` arguments desugar into the `quoteTerm`
+  syntax and `Name` arguments into the `quote` syntax. Arguments of
+  any other type are preserved as-is. The last `Term` argument is the
+  hole term given to `unquote` computation (see above).
+
+  For example, the macro application `f u v w` where the macro `f` has
+  the type `Term → Name → Bool → Term → TC ⊤` desugars into `unquote
+  (f (quoteTerm u) (quote v) w)`
+
+  Limitations:
+
+    - Macros cannot be recursive. This can be worked around by defining the
+      recursive function outside the macro block and have the macro call the
+      recursive function.
+
+  Silly example:
+
+  ```agda
+  macro
+    plus-to-times : Term → Term → TC ⊤
+    plus-to-times (def (quote _+_) (a ∷ b ∷ [])) hole = unify hole (def (quote _*_) (a ∷ b ∷ []))
+    plus-to-times v hole = unify hole v
+
+  thm : (a b : Nat) → plus-to-times (a + b) ≡ a * b
+  thm a b = refl
+  ```
+
+  Macros are most useful when writing tactics, since they let you hide the
+  reflection machinery. For instance, suppose you have a solver
+
+  ```agda
+  magic : Type → Term
+  ```
+
+  that takes a reflected goal and outputs a proof (when successful). You can
+  then define the following macro
+
+  ```agda
+  macro
+    by-magic : Term → TC ⊤
+    by-magic hole =
+      bindTC (inferType hole) λ goal →
+      unify hole (magic goal)
+  ```
+
+  This lets you apply the magic tactic without any syntactic noise at all:
+
+  ```agda
+  thm : ¬ P ≡ NP
+  thm = by-magic
+  ```
+
+### Literals and built-ins
+
+* Overloaded number literals.
+
+  You can now overload natural number literals using the new builtin
+  `FROMNAT`:
+
+  ```agda
+  {-# BUILTIN FROMNAT fromNat #-}
+  ```
+
+  The target of the builtin should be a defined name. Typically you would do
+  something like
+
+  ```agda
+  record Number (A : Set) : Set where
+    field fromNat : Nat → A
+
+  open Number {{...}} public
+
+  {-# BUILTIN FROMNAT fromNat #-}
+  ```
+
+  This will cause number literals `n` to be desugared to `fromNat n`
+  before type checking.
+
+* Negative number literals.
+
+  Number literals can now be negative. For floating point literals it
+  works as expected. For integer literals there is a new builtin
+  `FROMNEG` that enables negative integer literals:
+
+  ```agda
+  {-# BUILTIN FROMNEG fromNeg #-}
+  ```
+
+  This causes negative literals `-n` to be desugared to `fromNeg n`.
+
+* Overloaded string literals.
+
+  String literals can be overladed using the `FROMSTRING` builtin:
+
+  ```agda
+  {-# BUILTIN FROMSTRING fromString #-}
+  ```
+
+  The will cause string literals `s` to be desugared to `fromString s`
+  before type checking.
+
+* Change to builtin integers.
+
+  The `INTEGER` builtin now needs to be bound to a datatype with two
+  constructors that should be bound to the new builtins `INTEGERPOS`
+  and `INTEGERNEGSUC` as follows:
+
+  ```agda
+  data Int : Set where
+    pos    : Nat -> Int
+    negsuc : Nat -> Int
+  {-# BUILTIN INTEGER       Int    #-}
+  {-# BUILTIN INTEGERPOS    pos    #-}
+  {-# BUILTIN INTEGERNEGSUC negsuc #-}
+  ```
+
+  where `negsuc n` represents the integer `-n - 1`. For instance, `-5`
+  is represented as `negsuc 4`. All primitive functions on integers
+  except `primShowInteger` have been removed, since these can be
+  defined without too much trouble on the above representation using
+  the corresponding functions on natural numbers.
+
+  The primitives that have been removed are
+
+  ```agda
+  primIntegerPlus
+  primIntegerMinus
+  primIntegerTimes
+  primIntegerDiv
+  primIntegerMod
+  primIntegerEquality
+  primIntegerLess
+  primIntegerAbs
+  primNatToInteger
+  ```
+
+* New primitives for strict evaluation
+
+  ```agda
+  primitive
+    primForce      : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) → (∀ x → B x) → B x
+    primForceLemma : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) (f : ∀ x → B x) → primForce x f ≡ f x
+  ```
+
+  `primForce x f` evaluates to `f x` if x is in weak head normal form,
+  and `primForceLemma x f` evaluates to `refl` in the same
+  situation. The following values are considered to be in weak head
+  normal form:
+
+    - constructor applications
+    - literals
+    - lambda abstractions
+    - type constructor (data/record types) applications
+    - function types
+    - Set a
+
+### Modules
+
+* Modules in import directives
+
+  When you use `using`/`hiding`/`renaming` on a name it now
+  automatically applies to any module of the same name, unless you
+  explicitly mention the module. For instance,
+
+  ```agda
+  open M using (D)
+  ```
+
+  is equivalent to
+
+  ```agda
+  open M using (D; module D)
+  ```
+
+  if `M` defines a module `D`. This is most useful for record and data
+  types where you always get a module of the same name as the type.
+
+  With this feature there is no longer useful to be able to qualify a
+  constructor (or field) by the name of the data type even when it
+  differs from the name of the corresponding module. The follow
+  (weird) code used to work, but doesn't work anymore:
+
+  ```agda
+  module M where
+    data D where
+      c : D
+  open M using (D) renaming (module D to MD)
+  foo : D
+  foo = D.c
+  ```
+
+  If you want to import only the type name and not the module you have to hide
+  it explicitly:
+
+  ```agda
+  open M using (D) hiding (module D)
+  ```
+
+  See discussion on
+  Issue [#836](https://github.com/agda/agda/issues/836).
+
+* Private definitions of a module are no longer in scope at the Emacs
+  mode top-level.
+
+  The reason for this change is that `.agdai-files` are stripped of
+  unused private definitions (which can yield significant performance
+  improvements for module-heavy code).
+
+  To test private definitions you can create a hole at the bottom of
+  the module, in which private definitions will be visible.
+
+### Records
+
+* New record directives `eta-equality`/`no-eta-equality`
+
+  The keywords `eta-equality`/`no-eta-equality` enable/disable eta
+  rules for the (inductive) record type being declared.
+
+  ```agda
+  record Σ (A : Set) (B : A -> Set) : Set where
+    no-eta-equality
+    constructor _,_
+    field
+      fst : A
+      snd : B fst
+  open Σ
+
+  -- fail : ∀ {A : Set}{B : A -> Set} → (x : Σ A B) → x ≡ (fst x , snd x)
+  -- fail x = refl
+  --
+  -- x != fst x , snd x of type Σ .A .B
+  -- when checking that the expression refl has type x ≡ (fst x , snd x)
+  ```
+
+* Building records from modules.
+
+  The `record { <fields> }` syntax is now extended to accept module
+  names as well. Fields are thus defined using the corresponding
+  definitions from the given module.
+
+  For instance assuming this record type `R` and module `M`:
+
+  ```agda
+  record R : Set where
+    field
+      x : X
+      y : Y
+      z : Z
+
+  module M where
+    x = {! ... !}
+    y = {! ... !}
+
+  r : R
+  r = record { M; z = {! ... !} }
+  ```
+
+  Previously one had to write `record { x = M.x; y = M.y; z = {! ... !} }`.
+
+  More precisely this construction now supports any combination of explicit
+  field definitions and applied modules.
+
+  If a field is both given explicitly and available in one of the modules,
+  then the explicit one takes precedence.
+
+  If a field is available in more than one module then this is ambiguous
+  and therefore rejected. As a consequence the order of assignments does
+  not matter.
+
+  The modules can be both applied to arguments and have import directives
+  such as `hiding`, `using`, and `renaming`. In particular this construct
+  subsumes the record update construction.
+
+  Here is an example of record update:
+
+  ```agda
+  -- Record update. Same as: record r { y = {! ... !} }
+  r2 : R
+  r2 = record { R r; y = {! ... !} }
+  ```
+
+  A contrived example showing the use of `hiding`/`renaming`:
+
+  ```agda
+  module M2 (a : A) where
+    w = {! ... !}
+    z = {! ... !}
+
+  r3 : A → R
+  r3 a = record { M hiding (y); M2 a renaming (w to y) }
+  ```
+
+* Record patterns are now accepted.
+
+  Examples:
+
+  ```agda
+  swap : {A B : Set} (p : A × B) → B × A
+  swap record{ proj₁ = a; proj₂ = b } = record{ proj₁ = b; proj₂ = a }
+
+  thd3 : ...
+  thd3 record{ proj₂ = record { proj₂ = c }} = c
+  ```
+
+* Record modules now properly hide all their parameters
+  [Issue [#1759](https://github.com/agda/agda/issues/1759)]
+
+  Previously parameters to parent modules were not hidden in the record
+  module, resulting in different behaviour between
+
+  ```agda
+  module M (A : Set) where
+    record R (B : Set) : Set where
+  ```
+
+  and
+
+  ```agda
+  module M where
+    record R (A B : Set) : Set where
+  ```
+
+  where in the former case, `A` would be an explicit argument to the module
+  `M.R`, but implicit in the latter case. Now `A` is implicit in both cases.
+
+### Instance search
+
+* Performance has been improved, recursive instance search which was
+  previously exponential in the depth is now only quadratic.
+
+* Constructors of records and datatypes are not anymore automatically
+  considered as instances, you have to do so explicitely, for
+  instance:
+
+  ```agda
+  -- only [b] is an instance of D
+  data D : Set where
+    a : D
+    instance
+      b : D
+    c : D
+
+  -- the constructor is now an instance
+  record tt : Set where
+    instance constructor tt
+  ```
+
+* Lambda-bound variables are no longer automatically considered
+  instances.
+
+  Lambda-bound variables need to be bound as instance arguments to be
+  considered for instance search. For example,
+
+  ```agda
+  _==_ : {A : Set} {{_ : Eq A}} → A → A → Bool
+
+  fails : {A : Set} → Eq A → A → Bool
+  fails eqA x = x == x
+
+  works : {A : Set} {{_ : Eq A}} → A → Bool
+  works x = x == x
+  ```
+
+* Let-bound variables are no longer automatically considered
+  instances.
+
+  To make a let-bound variable available as an instance it needs to be
+  declared with the `instance` keyword, just like top-level
+  instances. For example,
+
+  ```agda
+  mkEq : {A : Set} → (A → A → Bool) → Eq A
+
+  fails : {A : Set} → (A → A → Bool) → A → Bool
+  fails eq x = let eqA = mkEq eq in x == x
+
+  works : {A : Set} → (A → A → Bool) → A → Bool
+  works eq x = let instance eqA = mkEq eq in x == x
+  ```
+
+* Record fields can be declared instances.
+
+  For example,
+
+  ```agda
+  record EqSet : Set₁ where
+    field
+      set : Set
+      instance eq : Eq set
+  ```
+
+  This causes the projection function `eq : (E : EqSet) → Eq (set E)`
+  to be considered for instance search.
+
+* Instance search can now find arguments in variable types (but such
+  candidates can only be lambda-bound variables, they can’t be
+  declared as instances)
+
+  ```agda
+  module _ {A : Set} (P : A → Set) where
+
+    postulate
+      bla : {x : A} {{_ : P x}} → Set → Set
+
+    -- Works, the instance argument is found in the context
+    test :  {x : A} {{_ : P x}} → Set → Set
+    test B = bla B
+
+    -- Still forbidden, because [P] could be instantiated later to anything
+    instance
+     postulate
+      forbidden : {x : A} → P x
+  ```
+
+* Instance search now refuses to solve constraints with unconstrained
+  metavariables, since this can lead to non-termination.
+
+  See [Issue [#1532](https://github.com/agda/agda/issues/1523)] for an
+  example.
+
+* Top-level instances are now only considered if they are in
+  scope. [Issue [#1913](https://github.com/agda/agda/issues/1913)]
+
+  Note that lambda-bound instances need not be in scope.
+
+### Other changes
+
+* Unicode ellipsis character is allowed for the ellipsis token `...`
+  in `with` expressions.
+
+* `Prop` is no longer a reserved word.
+
+Type checking
+-------------
+
+* Large indices.
+
+  Force constructor arguments no longer count towards the size of a datatype.
+  For instance, the definition of equality below is accepted.
+
+  ```agda
+  data _≡_ {a} {A : Set a} : A → A → Set where
+    refl : ∀ x → x ≡ x
+  ```
+
+  This gets rid of the asymmetry that the version of equality which indexes
+  only on the second argument could be small, but not the version above which
+  indexes on both arguments.
+
+* Detection of datatypes that satisfy K (i.e. sets)
+
+  Agda will now try to detect datatypes that satisfy K when
+  `--without-K` is enabled. A datatype satisfies K when it follows
+  these three rules:
+
+  - The types of all non-recursive constructor arguments should satisfy K.
+
+  - All recursive constructor arguments should be first-order.
+
+  - The types of all indices should satisfy K.
+
+  For example, the types `Nat`, `List Nat`, and `x ≡ x` (where `x :
+  Nat`) are all recognized by Agda as satisfying K.
+
+* New unifier for case splitting
+
+  The unifier used by Agda for case splitting has been completely
+  rewritten. The new unifier takes a much more type-directed approach
+  in order to avoid the problems in issues
+  [#1406](https://github.com/agda/agda/issues/1406),
+  [#1408](https://github.com/agda/agda/issues/1408),
+  [#1427](https://github.com/agda/agda/issues/1427), and
+  [#1435](https://github.com/agda/agda/issues/1435).
+
+  The new unifier also has eta-equality for record types
+  built-in. This should avoid unnecessary case splitting on record
+  constructors and improve the performance of Agda on code that
+  contains deeply nested record patterns (see issues
+  [#473](https://github.com/agda/agda/issues/473),
+  [#635](https://github.com/agda/agda/issues/635),
+  [#1575](https://github.com/agda/agda/issues/1575),
+  [#1603](https://github.com/agda/agda/issues/1603),
+  [#1613](https://github.com/agda/agda/issues/1613), and
+  [#1645](https://github.com/agda/agda/issues/1645)).
+
+  In some cases, the locations of the dot patterns computed by the
+  unifier did not correspond to the locations given by the user (see
+  Issue [#1608](https://github.com/agda/agda/issues/1608)). This has
+  now been fixed by adding an extra step after case splitting that
+  checks whether the user-written patterns are compatible with the
+  computed ones.
+
+  In some rare cases, the new unifier is still too restrictive when
+  `--without-K` is enabled because it cannot generalize over the
+  datatype indices (yet). For example, the following code is rejected:
+
+  ```agda
+  data Bar : Set₁ where
+    bar : Bar
+    baz : (A : Set) → Bar
+
+  data Foo : Bar → Set where
+    foo : Foo bar
+
+  test : foo ≡ foo → Set₁
+  test refl = Set
+  ```
+
+* The aggressive behaviour of `with` introduced in 2.4.2.5 has been
+  rolled back
+  [Issue [#1692](https://github.com/agda/agda/issues/1692)]. With no
+  longer abstracts in the types of variables appearing in the
+  with-expressions. [Issue [#745](https://github.com/agda/agda/issues/745)]
+
+  This means that the following example no longer works:
+
+  ```agda
+  fails : (f : (x : A) → a ≡ x) (b : A) → b ≡ a
+  fails f b with a | f b
+  fails f b | .b | refl = f b
+  ```
+
+  The `with` no longer abstracts the type of `f` over `a`, since `f`
+  appears in the second with-expression `f b`. You can use a nested
+  `with` to make this example work.
+
+  This example does work again:
+
+  ```agda
+  test : ∀{A : Set}{a : A}{f : A → A} (p : f a ≡ a) → f (f a) ≡ a
+  test p rewrite p = p
+  ```
+
+  After `rewrite p` the goal has changed to `f a ≡ a`, but the type
+  of `p` has not been rewritten, thus, the final `p` solves the goal.
+
+  The following, which worked in 2.4.2.5, no longer works:
+
+  ```agda
+  fails : (f : (x : A) → a ≡ x) (b : A) → b ≡ a
+  fails f b rewrite f b = f b
+  ```
+
+  The rewrite with `f b : a ≡ b` is not applied to `f` as
+  the latter is part of the rewrite expression `f b`.  Thus,
+  the type of `f` remains untouched, and the changed goal
+  `b ≡ b` is not solved by `f b`.
+
+* When using `rewrite` on a term `eq` of type `lhs ≡ rhs`, the `lhs`
+  is no longer abstracted in `rhs`
+  [Issue [#520](https://github.com/agda/agda/issues/520)].  This means
+  that
+
+  ```agda
+  f pats rewrite eq = body
+  ```
+
+  is more than syntactic sugar for
+
+  ```agda
+  f pats with lhs | eq
+  f pats | _ | refl = body
+  ```
+
+  In particular, the following application of `rewrite` is now
+  possible
+
+  ```agda
+  id : Bool → Bool
+  id true  = true
+  id false = false
+
+  is-id : ∀ x → x ≡ id x
+  is-id true  = refl
+  is-id false = refl
+
+  postulate
+    P : Bool → Set
+    b : Bool
+    p : P (id b)
+
+  proof : P b
+  proof rewrite is-id b = p
+  ```
+
+  Previously, this was desugared to
+
+  ```agda
+  proof with b | is-id b
+  proof | _ | refl = p
+  ```
+
+  which did not type check as `refl` does not have type `b ≡ id b`.
+  Now, Agda gets the task of checking `refl : _ ≡ id b` leading to
+  instantiation of `_` to `id b`.
+
+Compiler backends
+-----------------
+
+* Major Bug Fixes:
+
+  - Function clauses with different arities are now always compiled
+    correctly by the GHC/UHC
+    backends. (Issue [#727](https://github.com/agda/agda/issues/727))
+
+* Co-patterns
+
+  - The GHC/UHC backends now support co-patterns. (Issues
+    [#1567](https://github.com/agda/agda/issues/1567),
+    [#1632](https://github.com/agda/agda/issues/1632))
+
+* Optimizations
+
+  - Builtin naturals are now represented as arbitrary-precision
+    Integers. See the user manual, section
+    "Agda Compilers -> Optimizations" for details.
+
+* GHC Haskell backend (MAlonzo)
+
+  - Pragmas
+
+    Since builtin naturals are compiled to `Integer` you can no longer
+    give a `{-# COMPILED_DATA #-}` pragma for `Nat`. The same goes for
+    builtin booleans, integers, floats, characters and strings which
+    are now hard-wired to appropriate Haskell types.
+
+* UHC compiler backend
+
+  A new backend targeting the Utrecht Haskell Compiler (UHC) is
+  available.  It targets the UHC Core language, and it's design is
+  inspired by the Epic backend. See the user manual, section "Agda
+  Compilers -> UHC Backend" for installation instructions.
+
+  - FFI
+
+    The UHC backend has a FFI to Haskell similar to MAlonzo's. The
+    target Haskell code also needs to be compilable using UHC, which
+    does not support the Haskell base library version 4.*.
+
+    FFI pragmas for the UHC backend are not checked in any way. If the
+    pragmas are wrong, bad things will happen.
+
+  - Imports
+
+    Additional Haskell modules can be brought into scope with the
+    `IMPORT_UHC` pragma:
+
+    ```agda
+    {-# IMPORT_UHC Data.Char #-}
+    ```
+
+    The Haskell modules `UHC.Base` and `UHC.Agda.Builtins` are always in
+    scope and don't need to be imported explicitly.
+
+  - Datatypes
+
+    Agda datatypes can be bound to Haskell datatypes as follows:
+
+    Haskell:
+    ```haskell
+    data HsData a = HsCon1 | HsCon2 (HsData a)
+    ```
+
+    Agda:
+    ```agda
+    data AgdaData (A : Set) : Set where
+      AgdaCon1 : AgdaData A
+      AgdaCon2 : AgdaData A -> AgdaData A
+    {-# COMPILED_DATA_UHC AgdaData HsData HsCon1 HsCon2 #-}
+    ```
+
+    The mapping has to cover all constructors of the used Haskell
+    datatype, else runtime behavior is undefined!
+
+    There are special reserved names to bind Agda datatypes to certain
+    Haskell datatypes. For example, this binds an Agda datatype to
+    Haskell's list datatype:
+
+    Agda:
+    ```agda
+    data AgdaList (A : Set) : Set where
+      Nil : AgdaList A
+      Cons : A -> AgdaList A -> AgdaList A
+    {-# COMPILED_DATA_UHC AgdaList __LIST__ __NIL__ __CONS__ #-}
+    ```
+
+    The following "magic" datatypes are available:
+
+    ```
+    HS Datatype | Datatype Pragma | HS Constructor | Constructor Pragma
+    ()            __UNIT__          ()               __UNIT__
+    List          __LIST__          (:)              __CONS__
+                                    []               __NIL__
+    Bool          __BOOL__          True             __TRUE__
+                                    False            __FALSE__
+    ```
+
+  - Functions
+
+    Agda postulates can be bound to Haskell functions. Similar as in
+    MAlonzo, all arguments of type `Set` need to be dropped before
+    calling Haskell functions. An example calling the return function:
+
+    Agda:
+    ```agda
+    postulate hs-return : {A : Set} -> A -> IO A
+    {-# COMPILED_UHC hs-return (\_ -> UHC.Agda.Builtins.primReturn) #-}
+    ```
+
+Emacs mode and interaction
+--------------------------
+
+* Module contents (`C-c C-o`) now also works for
+  records. [See Issue [#1926](https://github.com/agda/agda/issues/1926) ]
+  If you have an inferable expression of record type in an interaction
+  point, you can invoke `C-c C-o` to see its fields and types.
+  Example
+
+  ```agda
+  record R : Set where
+    field f : A
+
+  test : R → R
+  test r = {!r!}  -- C-c C-o here
+  ```
+
+* Less aggressive error notification.
+
+  Previously Emacs could jump to the position of an error even if the
+  type-checking process was not initiated in the current buffer. Now
+  this no longer happens: If the type-checking process was initiated
+  in another buffer, then the cursor is moved to the position of the
+  error in the buffer visiting the file (if any) and in every window
+  displaying the file, but focus should not change from one file to
+  another.
+
+  In the cases where focus does change from one file to another, one
+  can now use the go-back functionality to return to the previous
+  position.
+
+* Removed the `agda-include-dirs` customization parameter.
+
+  Use `agda-program-args` with `-iDIR` or `-lLIB` instead, or add
+  libraries to `~/.agda/defaults`
+  (`C:/Users/USERNAME/AppData/Roaming/agda/defaults` or similar on
+  Windows). See Library management, above, for more information.
+
+Tools
+-----
+
+### LaTeX-backend
+
+* The default font has been changed to XITS (which is part of TeX Live):
+
+    http://www.ctan.org/tex-archive/fonts/xits/
+
+  This font is more complete with respect to Unicode.
+
+### agda-ghc-names
+
+* New tool: The command
+
+  ```
+  agda-ghc-names fixprof <compile-dir> <ProgName>.prof
+  ```
+
+  converts `*.prof` files obtained from profiling runs of
+  MAlonzo-compiled code to `*.agdaIdents.prof`, with the original Agda
+  identifiers replacing the MAlonzo-generated Haskell identifiers.
+
+  For usage and more details, see `src/agda-ghc-names/README.txt`.
+
+Highlighting and textual backends
+---------------------------------
+
+* Names in import directives are now highlighted and are clickable.
+  [Issue [#1714](https://github.com/agda/agda/issues/1714)] This leads
+  also to nicer printing in the LaTeX and html backends.
+
+Fixed issues
+------------
+
+See
+[bug tracker (milestone 2.5.1)](https://github.com/agda/agda/issues?q=milestone%3A2.5.1+is%3Aclosed)
diff --git a/doc/release-notes/2.5.2.md b/doc/release-notes/2.5.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.2.md
@@ -0,0 +1,1184 @@
+Release notes for Agda version 2.5.2
+====================================
+
+Installation and infrastructure
+-------------------------------
+
+* Modular support for literate programming
+
+  Literate programming support has been moved out of the lexer and into the
+  `Agda.Syntax.Parser.Literate` module.
+
+  Files ending in `.lagda` are still interpreted as literate TeX.
+  The extension `.lagda.tex` may now also be used for literate TeX files.
+
+  Support for more literate code formats and extensions can be added
+  modularly.
+
+  By default, `.lagda.*` files are opened in the Emacs mode
+  corresponding to their last extension.  One may switch to and from
+  Agda mode manually.
+
+* reStructuredText
+
+  Literate Agda code can now be written in reStructuredText format, using
+  the `.lagda.rst` extension.
+
+  As a general rule, Agda will parse code following a line ending in `::`,
+  as long as that line does not start with `..`. The module name must
+  match the path of the file in the documentation, and must be given
+  explicitly.  Several files have been converted already, for instance:
+
+  - `language/mixfix-operators.lagda.rst`
+  - `tools/compilers.lagda.rst`
+
+  Note that:
+
+  - Code blocks inside an rST comment block will be type-checked by Agda,
+    but not rendered in the documentation.
+  - Code blocks delimited by `.. code-block:: agda` will be rendered in
+    the final documenation, but not type-checked by Agda.
+  - All lines inside a codeblock must be further indented than the first line
+    of the code block.
+  - Indentation must be consistent between code blocks. In other
+    words, the file as a whole must be a valid Agda file if all the
+    literate text is replaced by white space.
+
+* Documentation testing
+
+  All documentation files in the `doc/user-manual` directory that end
+  in `.lagda.rst` can be typechecked by running `make
+  user-manual-test`, and also as part of the general test suite.
+
+* Support installation through Stack
+
+  The Agda sources now also include a configuration for the stack install tool
+  (tested through continuous integration).
+
+  It should hence be possible to repeatably build any future Agda version
+  (including unreleased commits) from source by checking out that version and
+  running `stack install` from the checkout directory.
+  By using repeatable builds, this should keep selecting the same dependencies
+  in the face of new releases on Hackage.
+
+  For further motivation, see
+  Issue [#2005](https://github.com/agda/agda/issues/2005).
+
+* Removed the `--test` command-line option
+
+  This option ran the internal test-suite. This test-suite was
+  implemented using Cabal supports for
+  test-suites. [Issue [#2083](https://github.com/agda/agda/issues/2083)].
+
+* The `--no-default-libraries` flag has been split into two flags
+  [Issue [#1937](https://github.com/agda/agda/issues/1937)]
+
+  - `--no-default-libraries`: Ignore the defaults file but still look for local
+    `.agda-lib` files
+  - `--no-libraries`: Don't use any `.agda-lib` files (the previous behaviour
+    of `--no-default-libraries`).
+
+* If `agda` was built inside `git` repository, then the `--version` flag
+  will display the hash of the commit used, and whether the tree was
+  `-dirty` (i.e. there were uncommited changes in the working directory).
+  Otherwise, only the version number is shown.
+
+Language
+--------
+
+* Dot patterns are now optional
+
+  Consider the following program
+
+  ```agda
+  data Vec (A : Set) : Nat → Set where
+    []   : Vec A zero
+    cons : ∀ n → A → Vec A n → Vec A (suc n)
+
+  vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n
+  vmap .zero    f []            = []
+  vmap .(suc m) f (cons m x xs) = cons m (f x) (vmap m f xs)
+  ```
+
+  If we don't care about the dot patterns they can (and could previously) be
+  replaced by wildcards:
+
+  ```agda
+  vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n
+  vmap _ f []            = []
+  vmap _ f (cons m x xs) = cons m (f x) (vmap m f xs)
+  ```
+
+  Now it is also allowed to give a variable pattern in place of the dot
+  pattern. In this case the variable will be bound to the value of the dot
+  pattern. For our example:
+
+  ```agda
+  vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n
+  vmap n f []            = []
+  vmap n f (cons m x xs) = cons m (f x) (vmap m f xs)
+  ```
+
+  In the first clause `n` reduces to `zero` and in the second clause
+  `n` reduces to `suc m`.
+
+* Module parameters can now be refined by pattern matching
+
+  Previously, pattern matches that would refine a variable outside the
+  current left-hand side was disallowed. For instance, the following
+  would give an error, since matching on the vector would
+  instantiate `n`.
+
+  ```agda
+  module _ {A : Set} {n : Nat} where
+    f : Vec A n → Vec A n
+    f []       = []
+    f (x ∷ xs) = x ∷ xs
+  ```
+
+  Now this is no longer disallowed. Instead `n` is bound to the
+  appropriate value in each clause.
+
+* With-abstraction now abstracts also in module parameters
+
+  The change that allows pattern matching to refine module parameters also
+  allows with-abstraction to abstract in them. For instance,
+
+  ```agda
+  module _ (n : Nat) (xs : Vec Nat (n + n)) where
+    f : Nat
+    f with n + n
+    f    | nn = ? -- xs : Vec Nat nn
+  ```
+
+  Note: Any function argument or lambda-bound variable bound outside a given
+  function counts as a module parameter.
+
+  To prevent abstraction in a parameter you can hide it inside a definition. In
+  the above example,
+
+  ```agda
+  module _ (n : Nat) (xs : Vec Nat (n + n)) where
+
+    ys : Vec Nat (n + n)
+    ys = xs
+
+    f : Nat
+    f with n + n
+    f    | nn = ? -- xs : Vec Nat nn, ys : Vec Nat (n + n)
+  ```
+
+* As-patterns [Issue [#78](https://github.com/agda/agda/issues/78)].
+
+  As-patterns (`@`-patterns) are finally working and can be used to name a
+  pattern. The name has the same scope as normal pattern variables (i.e. the
+  right-hand side, where clause, and dot patterns). The name reduces to the
+  value of the named pattern. For example::
+
+  ```agda
+  module _ {A : Set} (_<_ : A → A → Bool) where
+    merge : List A → List A → List A
+    merge xs [] = xs
+    merge [] ys = ys
+    merge xs@(x ∷ xs₁) ys@(y ∷ ys₁) =
+      if x < y then x ∷ merge xs₁ ys
+               else y ∷ merge xs ys₁
+  ```
+
+* Idiom brackets.
+
+  There is new syntactic sugar for idiom brackets:
+
+    `(| e a1 .. an |)` expands to
+
+    `pure e <*> a1 <*> .. <*> an`
+
+  The desugaring takes place before scope checking and only requires names
+  `pure` and `_<*>_` in scope. Idiom brackets work well with operators, for
+  instance
+
+    `(| if a then b else c |)` desugars to
+
+    `pure if_then_else_ <*> a <*> b <*> c`
+
+  Limitations:
+
+    - The top-level application inside idiom brackets cannot include
+      implicit applications, so `(| foo {x = e} a b |)` is illegal. In
+      the case `e` is pure you can write `(| (foo {x = e}) a b |)`
+      which desugars to
+
+        `pure (foo {x = e}) <*> a <*> b`
+
+    - Binding syntax and operator sections cannot appear immediately inside
+      idiom brackets.
+
+* Layout for pattern matching lambdas.
+
+  You can now write pattern matching lambdas using the syntax
+
+  ```agda
+  λ where false → true
+          true  → false
+  ```
+
+  avoiding the need for explicit curly braces and semicolons.
+
+* Overloaded projections
+  [Issue [#1944](https://github.com/agda/agda/issues/1944)].
+
+  Ambiguous projections are no longer a scope error.  Instead they get
+  resolved based on the type of the record value they are
+  eliminating.  This corresponds to constructors, which can be
+  overloaded and get disambiguated based on the type they are
+  introducing.  Example:
+
+  ```agda
+  module _ (A : Set) (a : A) where
+
+  record R B : Set where
+    field f : B
+  open R public
+
+  record S B : Set where
+    field f : B
+  open S public
+  ```
+
+  Exporting `f` twice from both `R` and `S` is now allowed.  Then,
+
+  ```agda
+  r : R A
+  f r = a
+
+  s : S A
+  f s = f r
+  ```
+
+  disambiguates to:
+
+  ```agda
+  r : R A
+  R.f r = a
+
+  s : S A
+  S.f s = R.f r
+  ```
+
+  If the type of the projection is known, it can also be disambiguated
+  unapplied.
+
+  ```agda
+  unapplied : R A -> A
+  unapplied = f
+  ```
+
+* Postfix projections
+  [Issue [#1963](https://github.com/agda/agda/issues/1963)].
+
+  Agda now supports a postfix syntax for projection application.
+  This style is more in harmony with copatterns.  For example:
+
+  ```agda
+  record Stream (A : Set) : Set where
+    coinductive
+    field head : A
+          tail : Stream A
+
+  open Stream
+
+  repeat : ∀{A} (a : A) → Stream A
+  repeat a .head = a
+  repeat a .tail = repeat a
+
+  zipWith : ∀{A B C} (f : A → B → C) (s : Stream A) (t : Stream B) → Stream C
+  zipWith f s t .head = f (s .head) (t .head)
+  zipWith f s t .tail = zipWith f (s .tail) (t .tail)
+
+  module Fib (Nat : Set) (zero one : Nat) (plus : Nat → Nat → Nat) where
+
+    {-# TERMINATING #-}
+    fib : Stream Nat
+    fib .head = zero
+    fib .tail .head = one
+    fib .tail .tail = zipWith plus fib (fib .tail)
+  ```
+
+  The thing we eliminate with projection now is visibly the head,
+  i.e., the left-most expression of the sequence (e.g. `repeat` in
+  `repeat a .tail`).
+
+  The syntax overlaps with dot patterns, but for type correct left
+  hand sides there is no confusion: Dot patterns eliminate function
+  types, while (postfix) projection patterns eliminate record types.
+
+  By default, Agda prints system-generated projections (such as by
+  eta-expansion or case splitting) prefix.  This can be changed with
+  the new option:
+
+  ```agda
+  {-# OPTIONS --postfix-projections #-}
+  ```
+
+  Result splitting in extended lambdas (aka pattern lambdas) always
+  produces postfix projections, as prefix projection pattern do not
+  work here: a prefix projection needs to go left of the head, but the
+  head is omitted in extended lambdas.
+
+  ```agda
+  dup : ∀{A : Set}(a : A) → A × A
+  dup = λ{ a → ? }
+  ```
+
+  Result splitting (`C-c C-c RET`) here will yield:
+
+  ```agda
+  dup = λ{ a .proj₁ → ? ; a .proj₂ → ? }
+  ```
+
+* Projection parameters
+  [Issue [#1954](https://github.com/agda/agda/issues/1954)].
+
+  When copying a module, projection parameters will now stay hidden
+  arguments, even if the module parameters are visible.
+  This matches the situation we had for constructors since long.
+  Example:
+
+  ```agda
+  module P (A : Set) where
+    record R : Set where
+      field f : A
+
+  open module Q A = P A
+  ```
+
+  Parameter `A` is now hidden in `R.f`:
+
+  ```agda
+  test : ∀{A} → R A → A
+  test r = R.f r
+  ```
+
+  Note that a module parameter that corresponds to the record value
+  argument of a projection will not be hidden.
+
+  ```agda
+  module M (A : Set) (r : R A) where
+    open R A r public
+
+  test' : ∀{A} → R A → A
+  test' r = M.f r
+  ```
+
+* Eager insertion of implicit arguments
+  [Issue [#2001](https://github.com/agda/agda/issues/2001)]
+
+  Implicit arguments are now (again) eagerly inserted in left-hand sides. The
+  previous behaviour of inserting implicits for where blocks, but not
+  right-hand sides was not type safe.
+
+* Module applications can now be eta expanded/contracted without
+  changing their behaviour
+  [Issue #[1985](https://github.com/agda/agda/issues/1985)]
+
+  Previously definitions exported using `open public` got the
+  incorrect type for underapplied module applications.
+
+  Example:
+
+  ```agda
+  module A where
+    postulate A : Set
+
+  module B (X : Set) where
+    open A public
+
+  module C₁ = B
+  module C₂ (X : Set) = B X
+  ```
+
+  Here both `C₁.A` and `C₂.A` have type `(X : Set) → Set`.
+
+* Polarity pragmas.
+
+  Polarity pragmas can be attached to postulates. The polarities express
+  how the postulate's arguments are used. The following polarities
+  are available:
+
+  `_`:  Unused.
+
+  `++`: Strictly positive.
+
+  `+`:  Positive.
+
+  `-`:  Negative.
+
+  `*`:  Unknown/mixed.
+
+  Polarity pragmas have the form
+
+  ```
+  {-# POLARITY name <zero or more polarities> #-}
+  ```
+
+  and can be given wherever fixity declarations can be given. The
+  listed polarities apply to the given postulate's arguments
+  (explicit/implicit/instance), from left to right. Polarities
+  currently cannot be given for module parameters. If the postulate
+  takes n arguments (excluding module parameters), then the number of
+  polarities given must be between 0 and n (inclusive).
+
+  Polarity pragmas make it possible to use postulated type formers in
+  recursive types in the following way:
+
+  ```agda
+  postulate
+    ∥_∥ : Set → Set
+
+  {-# POLARITY ∥_∥ ++ #-}
+
+  data D : Set where
+    c : ∥ D ∥ → D
+  ```
+
+  Note that one can use postulates that may seem benign, together with
+  polarity pragmas, to prove that the empty type is inhabited:
+
+  ```agda
+  postulate
+    _⇒_    : Set → Set → Set
+    lambda : {A B : Set} → (A → B) → A ⇒ B
+    apply  : {A B : Set} → A ⇒ B → A → B
+
+  {-# POLARITY _⇒_ ++ #-}
+
+  data ⊥ : Set where
+
+  data D : Set where
+    c : D ⇒ ⊥ → D
+
+  not-inhabited : D → ⊥
+  not-inhabited (c f) = apply f (c f)
+
+  inhabited : D
+  inhabited = c (lambda not-inhabited)
+
+  bad : ⊥
+  bad = not-inhabited inhabited
+  ```
+
+  Polarity pragmas are not allowed in safe mode.
+
+* Declarations in a `where`-block are now
+  private. [Issue [#2101](https://github.com/agda/agda/issues/2101)]
+  This means that
+
+  ```agda
+  f ps = body where
+    decls
+  ```
+
+  is now equivalent to
+
+  ```agda
+  f ps = body where
+    private
+      decls
+  ```
+
+  This changes little, since the `decls` were anyway not in scope
+  outside `body`.  However, it makes a difference for abstract
+  definitions, because private type signatures can see through
+  abstract definitions.  Consider:
+
+  ```agda
+  record Wrap (A : Set) : Set where
+    field unwrap : A
+
+  postulate
+    P : ∀{A : Set} → A → Set
+
+  abstract
+
+    unnamedWhere : (A : Set) → Set
+    unnamedWhere A = A
+      where  -- the following definitions are private!
+      B : Set
+      B = Wrap A
+
+      postulate
+        b : B
+        test : P (Wrap.unwrap b)  -- succeeds
+  ```
+
+  The `abstract` is inherited in `where`-blocks from the parent (here:
+  function `unnamedWhere`).  Thus, the definition of `B` is opaque and
+  the type equation `B = Wrap A` cannot be used to check type
+  signatures, not even of abstract definitions.  Thus, checking the
+  type  `P (Wrap.unwrap b)` would fail.  However, if `test` is
+  private, abstract definitions are translucent in its type, and
+  checking succeeds.  With the implemented change, all
+  `where`-definitions are private, in this case `B`, `b`, and `test`,
+  and the example succeeds.
+
+  Nothing changes for the named forms of `where`,
+
+  ```agda
+  module M where
+  module _ where
+  ```
+
+  For instance, this still fails:
+
+  ```agda
+  abstract
+
+    unnamedWhere : (A : Set) → Set
+    unnamedWhere A = A
+      module M where
+      B : Set
+      B = Wrap A
+
+      postulate
+        b : B
+        test : P (Wrap.unwrap b)  -- fails
+  ```
+
+* Private anonymous modules now work as expected
+  [Issue [#2199](https://github.com/agda/agda/issues/2199)]
+
+  Previously the `private` was ignored for anonymous modules causing
+  its definitions to be visible outside the module containing the
+  anonymous module.  This is no longer the case. For instance,
+
+  ```agda
+  module M where
+    private
+      module _ (A : Set) where
+        Id : Set
+        Id = A
+
+    foo : Set → Set
+    foo = Id
+
+  open M
+
+  bar : Set → Set
+  bar = Id -- Id is no longer in scope here
+  ```
+
+* Pattern synonyms are now expanded on left hand sides of DISPLAY
+  pragmas [Issue [#2132](https://github.com/agda/agda/issues/2132)].
+  Example:
+
+  ```agda
+  data D : Set where
+    C c : D
+    g : D → D
+
+  pattern C′ = C
+
+  {-# DISPLAY C′ = C′ #-}
+  {-# DISPLAY g C′ = c #-}
+  ```
+
+  This now behaves as:
+
+  ```agda
+  {-# DISPLAY C = C′ #-}
+  {-# DISPLAY g C = c #-}
+  ```
+
+  Expected error for
+
+  ```agda
+  test : C ≡ g C
+  test = refl
+  ```
+
+  is thus:
+
+  ```
+  C′ != c of type D
+  ```
+
+* The built-in floats have new semantics to fix inconsistencies
+  and to improve cross-platform portability.
+
+  - Float equality has been split into two primitives.
+    ``primFloatEquality`` is designed to establish
+    decidable propositional equality while
+    ``primFloatNumericalEquality`` is intended for numerical
+    computations. They behave as follows:
+
+    ```
+    primFloatEquality NaN NaN = True
+    primFloatEquality 0.0 -0.0 = False
+
+    primFloatNumericalEquality NaN NaN = False
+    primFloatNumericalEquality 0.0 -0.0 = True
+    ```
+
+    This change fixes an inconsistency, see [Issue [#2169](https://github.com/agda/agda/issues/2169)].
+    For further detail see the [user manual](http://agda.readthedocs.io/en/v2.5.2/language/built-ins.html#floats).
+
+  - Floats now have only one `NaN` value. This is necessary
+    for proper Float support in the JavaScript backend,
+    as JavaScript (and some other platforms) only support
+    one `NaN` value.
+
+  - The primitive function `primFloatLess` was renamed
+    `primFloatNumericalLess`.
+
+* Added new primitives to built-in floats:
+
+  - `primFloatNegate : Float → Float`
+    [Issue [#2194](https://github.com/agda/agda/issues/2194)]
+
+  - Trigonometric primitives
+    [Issue [#2200](https://github.com/agda/agda/issues/2200)]:
+
+    ```agda
+    primCos   : Float → Float
+    primTan   : Float → Float
+    primASin  : Float → Float
+    primACos  : Float → Float
+    primATan  : Float → Float
+    primATan2 : Float → Float → Float
+    ```
+
+* Anonymous declarations
+  [Issue [#1465](https://github.com/agda/agda/issues/1465)].
+
+  A module can contain an arbitrary number of declarations
+  named `_` which will scoped-checked and type-checked but
+  won't be made available in the scope (nor exported). They
+  cannot introduce arguments on the LHS (but one can use
+  lambda-abstractions on the RHS) and they cannot be defined
+  by recursion.
+
+  ```agda
+  _ : Set → Set
+  _ = λ x → x
+  ```
+
+### Rewriting
+
+* The REWRITE pragma can now handle several names.  E.g.:
+  ```agda
+  {-# REWRITE eq1 eq2 #-}
+  ```
+
+### Reflection
+
+* You can now use macros in reflected terms
+  [Issue [#2130](https://github.com/agda/agda/issues/2130)].
+
+  For instance, given a macro
+
+  ```agda
+  macro
+    some-tactic : Term → TC ⊤
+    some-tactic = ...
+  ```
+
+  the term `def (quote some-tactic) []` represents a call to the
+  macro. This makes it a lot easier to compose tactics.
+
+* The reflection machinery now uses normalisation less often:
+
+  * Macros no longer normalise the (automatically quoted) term
+    arguments.
+
+  * The TC primitives `inferType`, `checkType` and `quoteTC` no longer
+    normalise their arguments.
+
+  * The following deprecated constructions may also have been changed:
+    `quoteGoal`, `quoteTerm`, `quoteContext` and `tactic`.
+
+* New TC primitive: `withNormalisation`.
+
+  To recover the old normalising behaviour of `inferType`, `checkType`,
+  `quoteTC` and `getContext`, you can wrap them inside a call to
+  `withNormalisation true`:
+
+  ```agda
+    withNormalisation : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  ```
+
+* New TC primitive: `reduce`.
+
+  ```agda
+  reduce : Term → TC Term
+  ```
+
+  Reduces its argument to weak head normal form.
+
+* Added new TC primitive: `isMacro`
+  [Issue [#2182](https://github.com/agda/agda/issues/2182)]
+
+  ```agda
+  isMacro : Name → TC Bool
+  ```
+
+  Returns `true` if the name refers to a macro, otherwise `false`.
+
+* The `record-type` constructor now has an extra argument containing
+  information about the record type's fields:
+  ```agda
+    data Definition : Set where
+      …
+      record-type : (c : Name) (fs : List (Arg Name)) → Definition
+      …
+  ```
+
+Type checking
+-------------
+
+* Files with open metas can be imported now
+  [Issue [#964](https://github.com/agda/agda/issues/964)].  This
+  should make simultaneous interactive development on several modules
+  more pleasant.
+
+  Requires option: `--allow-unsolved-metas`
+
+  Internally, before serialization, open metas are turned into postulates named
+
+  ```
+    unsolved#meta.<nnn>
+  ```
+
+  where `<nnn>` is the internal meta variable number.
+
+* The performance of the compile-time evaluator has been greatly improved.
+
+  - Fixed a memory leak in evaluator
+    (Issue [#2147](https://github.com/agda/agda/issues/2147)).
+
+  - Reduction speed improved by an order of magnitude and is now
+    comparable to the performance of GHCi. Still call-by-name though.
+
+* The detection of types that satisfy K added in Agda 2.5.1 has been
+  rolled back (see
+  Issue [#2003](https://github.com/agda/agda/issues/2003)).
+
+* Eta-equality for record types is now only on after the positivity
+  checker has confirmed it is safe to have it.  Eta-equality for
+  unguarded inductive records previously lead to looping of the type
+  checker.
+  [See Issue [#2197](https://github.com/agda/agda/issues/2197)]
+
+  ```agda
+  record R : Set where
+    inductive
+    field r : R
+
+    loops : R
+    loops = ?
+  ```
+
+  As a consequence of this change, the following example does not
+  type-check any more:
+
+  ```agda
+  mutual
+    record ⊤ : Set where
+
+    test : ∀ {x y : ⊤} → x ≡ y
+    test = refl
+  ```
+
+  It fails because the positivity checker is only run after the mutual
+  block, thus, eta-equality for `⊤` is not available when checking
+  test.
+
+  One can declare eta-equality explicitly, though, to make this
+  example work.
+
+  ```agda
+  mutual
+    record ⊤ : Set where
+      eta-equality
+
+    test : ∀ {x y : ⊤} → x ≡ y
+    test = refl
+  ```
+
+* Records with instance fields are now eta expanded before instance search.
+
+  For instance, assuming `Eq` and `Ord` with boolean functions `_==_` and `_<_`
+  respectively,
+
+  ```agda
+    record EqAndOrd (A : Set) : Set where
+      field {{eq}}  : Eq A
+            {{ord}} : Ord A
+
+
+    leq : {A : Set} {{_ : EqAndOrd A}} → A → A → Bool
+    leq x y = x == y || x < y
+  ```
+
+  Here the `EqAndOrd` record is automatically unpacked before instance search,
+  revealing the component `Eq` and `Ord` instances.
+
+  This can be used to simulate superclass dependencies.
+
+* Overlappable record instance fields.
+
+  Instance fields in records can be marked as overlappable using the new
+  `overlap` keyword:
+
+  ```agda
+    record Ord (A : Set) : Set where
+      field
+        _<_ : A → A → Bool
+        overlap {{eqA}} : Eq A
+  ```
+
+  When instance search finds multiple candidates for a given instance goal and
+  they are **all** overlappable it will pick the left-most candidate instead of
+  refusing to solve the instance goal.
+
+  This can be use to solve the problem arising from shared "superclass"
+  dependencies. For instance, if you have, in addition to `Ord` above, a `Num`
+  record that also has an `Eq` field and want to write a function requiring
+  both `Ord` and `Num`, any `Eq` constraint will be solved by the `Eq` instance
+  from whichever argument that comes first.
+
+  ```agda
+    record Num (A : Set) : Set where
+      field
+        fromNat : Nat → A
+        overlap {{eqA}} : Eq A
+
+    lessOrEqualFive : {A : Set} {{NumA : Num A}} {{OrdA : Ord A}} → A → Bool
+    lessOrEqualFive x = x == fromNat 5 || x < fromNat 5
+  ```
+
+  In this example the call to `_==_` will use the `eqA` field from `NumA`
+  rather than the one from `OrdA`. Note that these may well be different.
+
+* Instance fields can be left out of copattern matches
+  [Issue [#2288](https://github.com/agda/agda/issues/2288)]
+
+  Missing cases for instance fields (marked `{{` `}}`) in copattern matches
+  will be solved using instance search. This makes defining instances with
+  superclass fields much nicer. For instance, we can define `Nat` instances of
+  `Eq`, `Ord` and `Num` from above as follows:
+
+  ```agda
+    instance
+      EqNat : Eq Nat
+      _==_ {{EqNat}} n m = eqNat n m
+
+      OrdNat : Ord Nat
+      _<_ {{OrdNat}} n m = lessNat n m
+
+      NumNat : Num Nat
+      fromNat {{NumNat}} n = n
+  ```
+
+  The `eqA` fields of `Ord` and `Num` are filled in using instance search (with
+  `EqNat` in this case).
+
+* Limited instance search depth
+  [Issue [#2269](https://github.com/agda/agda/issues/2269)]
+
+  To prevent instance search from looping on bad instances
+  (see [Issue #1743](https://github.com/agda/agda/issues/1743)) the search
+  depth of instance search is now limited. The maximum depth can be set with
+  the `--instance-search-depth` flag and the default value is `500`.
+
+Emacs mode
+----------
+
+* New command `C-u C-u C-c C-n`: Use `show` to display the result of
+  normalisation.
+
+  Calling `C-u C-u C-c C-n` on an expression `e` (in a hole or at top level)
+  normalises `show e` and prints the resulting string, or an error message if
+  the expression does not normalise to a literal string.
+
+  This is useful when working with complex data structures for which you have
+  defined a nice `Show` instance.
+
+  Note that the name `show` is hardwired into the command.
+
+* Changed feature: Interactively split result.
+
+  Make-case (`C-c C-c`) with no variables will now *either* introduce
+  function arguments *or* do a copattern split (or fail).
+
+  This is as before:
+
+  ```agda
+  test : {A B : Set} (a : A) (b : B) → A × B
+  test a b = ?
+
+  -- expected:
+  -- proj₁ (test a b) = {!!}
+  -- proj₂ (test a b) = {!!}
+
+  testFun : {A B : Set} (a : A) (b : B) → A × B
+  testFun = ?
+
+  -- expected:
+  -- testFun a b = {!!}
+  ```
+
+  This is has changed:
+
+  ```agda
+  record FunRec A : Set where
+    field funField : A → A
+  open FunRec
+
+  testFunRec : ∀{A} → FunRec A
+  testFunRec = ?
+
+  -- expected (since 2016-05-03):
+  -- funField testFunRec = {!!}
+
+  -- used to be:
+  -- funField testFunRec x = {!!}
+  ```
+
+* Changed feature: Split on hidden variables.
+
+  Make-case (`C-c C-c`) will no longer split on the given hidden
+  variables, but only make them visible. (Splitting can then be
+  performed in a second go.)
+
+  ```agda
+  test : ∀{N M : Nat} → Nat → Nat → Nat
+  test N M = {!.N N .M!}
+  ```
+
+  Invoking splitting will result in:
+
+  ```agda
+  test {N} {M} zero M₁ = ?
+  test {N} {M} (suc N₁) M₁ = ?
+  ```
+
+  The hidden `.N` and `.M` have been brought into scope, the
+  visible `N` has been split upon.
+
+* Non-fatal errors/warnings.
+
+  Non-fatal errors and warnings are now displayed in the info buffer
+  and do not interrupt the typechecking of the file.
+
+  Currently termination errors, unsolved metavariables, unsolved
+  constraints, positivity errors, deprecated BUILTINs, and empty
+  REWRITING pragmas are non-fatal errors.
+
+* Highlighting for positivity check failures
+
+  Negative occurences of a datatype in its definition are now
+  highlighted in a way similar to termination errors.
+
+* The abbrev for codata was replaced by an abbrev for code
+  environments.
+
+  If you type `c C-x '` (on a suitably standard setup), then Emacs
+  will insert the following text:
+
+  ```agda
+  \begin{code}<newline>  <cursor><newline>\end{code}<newline>.
+  ```
+
+* The LaTeX backend can now be invoked from the Emacs mode.
+
+  Using the compilation command (`C-c C-x C-c`).
+
+  The flag `--latex-dir` can be used to set the output directory (by
+  default: `latex`). Note that if this directory is a relative path,
+  then it is interpreted relative to the "project root". (When the
+  LaTeX backend is invoked from the command line the path is
+  interpreted relative to the current working directory.) Example: If
+  the module `A.B.C` is located in the file `/foo/A/B/C.agda`, then
+  the project root is `/foo/`, and the default output directory is
+  `/foo/latex/`.
+
+* The compilation command (`C-c C-x C-c`) now by default asks for a
+  backend.
+
+  To avoid this question, set the customisation variable
+  `agda2-backend` to an appropriate value.
+
+* The command `agda2-measure-load-time` no longer "touches" the file,
+  and the optional argument `DONT-TOUCH` has been removed.
+
+* New command `C-u (C-u) C-c C-s`: Simplify or normalise the solution `C-c C-s` produces
+
+  When writing examples, it is nice to have the hole filled in with
+  a normalised version of the solution. Calling `C-c C-s` on
+
+  ```agda
+  _ : reverse (0 ∷ 1 ∷ []) ≡ ?
+  _ = refl
+  ```
+
+  used to yield the non informative `reverse (0 ∷ 1 ∷ [])` when we would
+  have hopped to get `1 ∷ 0 ∷ []` instead. We can now control finely the
+  degree to which the solution is simplified.
+
+* Changed feature: Solving the hole at point
+
+  Calling `C-c C-s` inside a specific goal does not solve *all* the goals
+  already instantiated internally anymore: it only solves the one at hand
+  (if possible).
+
+* New bindings: All the blackboard bold letters are now available
+  [Pull Request [#2305](https://github.com/agda/agda/pull/2305)]
+
+  The Agda input method only bound a handful of the blackboard bold letters
+  but programmers were actually using more than these. They are now all
+  available: lowercase and uppercase. Some previous bindings had to be
+  modified for consistency. The naming scheme is as follows:
+
+  * `\bx` for lowercase blackboard bold
+  * `\bX` for uppercase blackboard bold
+  * `\bGx` for lowercase greek blackboard bold (similar to `\Gx` for
+    greeks)
+  * `\bGX` for uppercase greek blackboard bold (similar to `\GX` for
+    uppercase greeks)
+
+* Replaced binding for go back
+
+  Use `M-,` (instead of `M-*`) for go back in Emacs ≥ 25.1 (and
+  continue using `M-*` with previous versions of Emacs).
+
+Compiler backends
+-----------------
+
+* JS compiler backend
+
+  The JavaScript backend has been (partially) rewritten. The
+  JavaScript backend now supports most Agda features, notably
+  copatterns can now be compiled to JavaScript. Furthermore, the
+  existing optimizations from the other backends now apply to the
+  JavaScript backend as well.
+
+* GHC, JS and UHC compiler backends
+
+  Added new primitives to built-in floats
+  [Issues [#2194](https://github.com/agda/agda/issues/2194) and
+  [#2200](https://github.com/agda/agda/issues/2200)]:
+
+  ```agda
+  primFloatNegate : Float → Float
+  primCos         : Float → Float
+  primTan         : Float → Float
+  primASin        : Float → Float
+  primACos        : Float → Float
+  primATan        : Float → Float
+  primATan2       : Float → Float → Float
+  ```
+
+LaTeX backend
+-------------
+
+* Code blocks are now (by default) surrounded by vertical space.
+  [Issue [#2198](https://github.com/agda/agda/issues/2198)]
+
+  Use `\AgdaNoSpaceAroundCode{}` to avoid this vertical space, and
+  `\AgdaSpaceAroundCode{}` to reenable it.
+
+  Note that, if `\AgdaNoSpaceAroundCode{}` is used, then empty lines
+  before or after a code block will not necessarily lead to empty
+  lines in the generated document. However, empty lines *inside* the
+  code block do (by default) lead to empty lines in the output.
+
+  If you prefer the previous behaviour, then you can use the `agda.sty`
+  file that came with the previous version of Agda.
+
+* `\AgdaHide{...}` now eats trailing spaces (using `\ignorespaces`).
+
+* New environments: `AgdaAlign`, `AgdaSuppressSpace` and
+  `AgdaMultiCode`.
+
+  Sometimes one might want to break up a code block into multiple
+  pieces, but keep code in different blocks aligned with respect to
+  each other. Then one can use the `AgdaAlign` environment. Example
+  usage:
+  ```latex
+    \begin{AgdaAlign}
+    \begin{code}
+      code
+        code  (more code)
+    \end{code}
+    Explanation...
+    \begin{code}
+      aligned with "code"
+        code  (aligned with (more code))
+    \end{code}
+    \end{AgdaAlign}
+  ```
+  Note that `AgdaAlign` environments should not be nested.
+
+  Sometimes one might also want to hide code in the middle of a code
+  block. This can be accomplished in the following way:
+  ```latex
+    \begin{AgdaAlign}
+    \begin{code}
+      visible
+    \end{code}
+    \AgdaHide{
+    \begin{code}
+      hidden
+    \end{code}}
+    \begin{code}
+      visible
+    \end{code}
+    \end{AgdaAlign}
+  ```
+  However, the result may be ugly: extra space is perhaps inserted
+  around the code blocks.
+
+  The `AgdaSuppressSpace` environment ensures that extra space is only
+  inserted before the first code block, and after the last one (but
+  not if `\AgdaNoSpaceAroundCode{}` is used).
+
+  The environment takes one argument, the number of wrapped code
+  blocks (excluding hidden ones). Example usage:
+  ```latex
+    \begin{AgdaAlign}
+    \begin{code}
+      code
+        more code
+    \end{code}
+    Explanation...
+    \begin{AgdaSuppressSpace}{2}
+    \begin{code}
+      aligned with "code"
+        aligned with "more code"
+    \end{code}
+    \AgdaHide{
+    \begin{code}
+      hidden code
+    \end{code}}
+    \begin{code}
+        also aligned with "more code"
+    \end{code}
+    \end{AgdaSuppressSpace}
+    \end{AgdaAlign}
+  ```
+
+  Note that `AgdaSuppressSpace` environments should not be nested.
+
+  There is also a combined environment, `AgdaMultiCode`, that combines
+  the effects of `AgdaAlign` and `AgdaSuppressSpace`.
+
+Tools
+-----
+
+### agda-ghc-names
+
+The `agda-ghc-names` now has its own repository at
+
+  https://github.com/agda/agda-ghc-names
+
+and is no longer distributed with Agda.
diff --git a/doc/release-notes/2.5.3.md b/doc/release-notes/2.5.3.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.3.md
@@ -0,0 +1,822 @@
+Release notes for Agda version 2.5.3
+====================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.0.2 and 8.2.1.
+
+* Removed support for GHC 7.6.3.
+
+* Markdown support for literate Agda
+  \[PR [#2357](https://github.com/agda/agda/pull/2357)].
+
+  Files ending in `.lagda.md` will be parsed as literate Markdown files.
+
+  + Code blocks start with  ```` ``` ```` or ```` ```agda ```` in its own line, and end with
+    ```` ``` ````, also in its own line.
+  + Code blocks which should be type-checked by Agda but should not be visible
+    when the Markdown is rendered may be enclosed in HTML comment delimiters
+    (`<!--`  and `-->`).
+  + Code blocks which should be ignored by Agda, but rendered in the final
+    document may be indented by four spaces.
+  + Note that inline code fragments are not supported due to the difficulty of
+    interpreting their indentation level with respect to the rest of the file.
+
+Language
+--------
+
+### Pattern matching
+
+* Dot patterns.
+
+  The dot in front of an inaccessible pattern can now be skipped if the
+  pattern consists entirely of constructors or literals. For example:
+  ```agda
+    open import Agda.Builtin.Bool
+
+    data D : Bool → Set where
+      c : D true
+
+    f : (x : Bool) → D x → Bool
+    f true c = true
+
+  ```
+  Before this change, you had to write `f .true c = true`.
+
+* With-clause patterns can be replaced by _
+  [Issue [#2363](https://github.com/agda/agda/issues/2363)].
+  Example:
+  ```agda
+    test : Nat → Set
+    test zero    with zero
+    test _       | _ = Nat
+    test (suc x) with zero
+    test _       | _ = Nat
+  ```
+  We do not have to spell out the pattern of the parent clause
+  (`zero` / `suc x`) in the with-clause if we do not need the
+  pattern variables.  Note that `x` is not in scope in the
+  with-clause!
+
+  A more elaborate example, which cannot be reduced to
+  an ellipsis `...`:
+  ```agda
+    record R : Set where
+      coinductive -- disallow matching
+      field f : Bool
+            n : Nat
+
+    data P (r : R) : Nat → Set where
+      fTrue  : R.f r ≡ true → P r zero
+      nSuc   : P r (suc (R.n r))
+
+    data Q : (b : Bool) (n : Nat) →  Set where
+      true! : Q true zero
+      suc!  : ∀{b n} → Q b (suc n)
+
+    test : (r : R) {n : Nat} (p : P r n) → Q (R.f r) n
+    test r nSuc       = suc!
+    test r (fTrue p)  with R.f r
+    test _ (fTrue ()) | false
+    test _ _          | true = true!  -- underscore instead of (isTrue _)
+  ```
+
+* Pattern matching lambdas (also known as extended lambdas) can now be
+  nullary, mirroring the behaviour for ordinary function definitions.
+  [Issue [#2671](https://github.com/agda/agda/issues/2671)]
+
+  This is useful for case splitting on the result inside an
+  expression: given
+  ```agda
+  record _×_ (A B : Set) : Set where
+    field
+      π₁ : A
+      π₂ : B
+  open _×_
+  ```
+  one may case split on the result (C-c C-c RET) in a hole
+  ```agda
+    λ { → {!!}}
+  ```
+  of type A × B to produce
+  ```agda
+    λ { .π₁ → {!!} ; .π₂ → {!!}}
+  ```
+
+* Records with a field of an empty type are now recognized as empty by Agda.
+  In particular, they can be matched against with an absurd pattern ().
+  For example:
+  ```agda
+    data ⊥ : Set where
+
+    record Empty : Set where
+      field absurdity : ⊥
+
+    magic : Empty → ⊥
+    magic ()
+  ```
+
+* Injective pragmas.
+
+  Injective pragmas can be used to mark a definition as injective for the
+  pattern matching unifier. This can be used as a version of
+  `--injective-type-constructors` that only applies to specific datatypes.
+  For example:
+  ```agda
+    open import Agda.Builtin.Equality
+    data Fin : Nat → Set where
+      zero : {n : Nat} → Fin (suc n)
+      suc  : {n : Nat} → Fin n → Fin (suc n)
+
+    {-# INJECTIVE Fin #-}
+
+    Fin-injective : {m n : Nat} → Fin m ≡ Fin n → m ≡ n
+    Fin-injective refl = refl
+  ```
+  Aside from datatypes, this pragma can also be used to mark other definitions
+  as being injective (for example postulates).
+
+* Metavariables can no longer be instantiated during case splitting. This means
+  Agda will refuse to split instead of taking the first constructor it finds.
+  For example:
+  ```agda
+    open import Agda.Builtin.Nat
+
+    data Vec (A : Set) : Nat → Set where
+      nil : Vec A 0
+      cons : {n : Nat} → A → Vec A n → Vec A (suc n)
+
+    foo : Vec Nat _ → Nat
+    foo x = {!x!}
+  ```
+  In Agda 2.5.2, case splitting on `x` produced the single clause
+  `foo nil = {!!}`, but now Agda refuses to split.
+
+### Reflection
+
+* New TC primitive: `debugPrint`.
+
+  ```agda
+    debugPrint : String → Nat → List ErrorPart → TC ⊤
+  ```
+
+  This maps to the internal function `reportSDoc`. Debug output is enabled with
+  the `-v` flag at the command line, or in an `OPTIONS` pragma. For instance,
+  giving `-v a.b.c:10` enables printing from `debugPrint "a.b.c.d" 10 msg`. In the
+  Emacs mode, debug output ends up in the `*Agda debug*` buffer.
+
+### Built-ins
+
+* BUILTIN REFL is now superfluous, subsumed by BUILTIN EQUALITY
+  [Issue [#2389](https://github.com/agda/agda/issues/2389)].
+
+* BUILTIN EQUALITY is now more liberal
+  [Issue [#2386](https://github.com/agda/agda/issues/2386)].
+  It accepts, among others, the following new definitions of equality:
+  ```agda
+    -- Non-universe polymorphic:
+    data _≡_ {A : Set} (x : A) : A → Set where
+      refl : x ≡ x
+
+    -- ... with explicit argument to refl;
+    data _≡_ {A : Set} : (x y : A) → Set where
+      refl : {x : A} → x ≡ x
+
+    -- ... even visible
+    data _≡_ {A : Set} : (x y : A) → Set where
+      refl : (x : A) → x ≡ x
+
+    -- Equality in a different universe than domain:
+    -- (also with explicit argument to refl)
+    data _≡_ {a} {A : Set a} (x : A) : A → Set where
+      refl : x ≡ x
+
+  ```
+  The standard definition is still:
+  ```agda
+    -- Equality in same universe as domain:
+    data _≡_ {a} {A : Set a} (x : A) : A → Set a where
+      refl : x ≡ x
+  ```
+
+### Miscellaneous
+
+* Rule change for omitted top-level module headers.
+  [Issue [#1077](https://github.com/agda/agda/issues/1077)]
+
+  If your file is named `Bla.agda`, then the following content
+  is rejected.
+  ```agda
+    foo = Set
+    module Bla where
+      bar = Set
+  ```
+  Before the fix of this issue, Agda would add the missing module
+  header `module Bla where` at the top of the file.
+  However, in this particular case it is more likely the user
+  put the declaration `foo = Set` before the module start in error.
+  Now you get the error
+  ```
+    Illegal declaration(s) before top-level module
+  ```
+  if the following conditions are met:
+
+    1. There is at least one non-import declaration or non-toplevel pragma
+       before the start of the first module.
+
+    2. The module has the same name as the file.
+
+    3. The module is the only module at this level
+       (may have submodules, of course).
+
+  If you should see this error, insert a top-level module
+  before the illegal declarations, or move them inside the
+  existing module.
+
+Emacs mode
+----------
+
+* New warnings:
+
+  - Unreachable clauses give rise to a simple warning. They are
+    highlighted in gray.
+
+  - Incomplete patterns are non-fatal warnings: it is possible
+    to keep interacting with the file (the reduction will simply
+    be stuck on arguments not matching any pattern).
+    The definition with incomplete patterns are highlighted in
+    wheat.
+
+* Clauses which do not hold definitionally are now highlighted in white smoke.
+
+* Fewer commands have the side effect that the buffer is saved.
+
+* Aborting commands.
+
+  Now one can (try to) abort an Agda command by using `C-c C-x C-a` or
+  a menu entry. The effect is similar to that of restarting Agda (`C-c
+  C-x C-r`), but some state is preserved, which could mean that it
+  takes less time to reload the module.
+
+  Warning: If a command is aborted while it is writing data to disk
+  (for instance `.agdai` files or Haskell files generated by the GHC
+  backend), then the resulting files may be corrupted. Note also that
+  external commands (like GHC) are not aborted, and their output may
+  continue to be sent to the Emacs mode.
+
+* New bindings for the Agda input method:
+
+  - All the bold digits are now available. The naming scheme is `\Bx` for digit `x`.
+
+  - Typing `\:` you can now get a whole slew of colons.
+
+    (The Agda input method originally only bound the standard unicode colon,
+    which looks deceptively like the normal colon.)
+
+* Case splitting now preserves underscores.
+  [Issue [#819](https://github.com/agda/agda/issues/819)]
+  ```agda
+    data ⊥ : Set where
+
+    test : {A B : Set} → A → ⊥ → B
+    test _ x = {! x !}
+  ```
+  Splitting on `x` yields
+  ```agda
+    test _ ()
+  ```
+
+* Interactively expanding ellipsis.
+  [Issue [#2589](https://github.com/agda/agda/issues/2589)]
+  An ellipsis in a with-clause can be expanded by splitting on "variable" "." (dot).
+  ```agda
+    test0 : Nat → Nat
+    test0 x with zero
+    ... | q = {! . !}  -- C-c C-c
+  ```
+  Splitting on dot here yields:
+  ```agda
+    test0 x | q = ?
+  ```
+
+* New command to check an expression against the type of the hole
+  it is in and see what it elaborates to.
+  [Issue [#2700](https://github.com/agda/agda/issues/2700)]
+  This is useful to determine e.g. what solution typeclass resolution yields.
+  The command is bound to `C-c C-;` and respects the `C-u` modifier.
+
+  ```agda
+    record Pointed (A : Set) : Set where
+      field point : A
+
+    it : ∀ {A : Set} {{x : A}} → A
+    it {{x}} = x
+
+    instance _ = record { point = 3 - 4 }
+
+    _ : Pointed Nat
+    _ = {! it !} -- C-u C-u C-c C-;
+  ```
+  yields
+  ```agda
+    Goal: Pointed Nat
+    Elaborates to: record { point = 0 }
+  ```
+
+* If `agda2-give` is called with a prefix, then giving is forced,
+  i.e., the safety checks are skipped,
+  including positivity, termination, and double type-checking.
+  [Issue [#2730](https://github.com/agda/agda/issues/2730)]
+
+  Invoke forced giving with key sequence `C-u C-c C-SPC`.
+
+
+Library management
+------------------
+
+* The `name` field in an `.agda-lib` file is now optional.
+  [Issue [#2708](https://github.com/agda/agda/issues/2708)]
+
+  This feature is convenient if you just want to specify the dependencies
+  and include pathes for your local project in an `.agda-lib` file.
+
+  Naturally, libraries without names cannot be depended on.
+
+
+Compiler backends
+-----------------
+
+* Unified compiler pragmas
+
+  The compiler pragmas (`COMPILED`, `COMPILED_DATA`, etc.) have been unified across
+  backends into two new pragmas:
+
+  ```
+    {-# COMPILE <Backend> <Name> <Text> #-}
+    {-# FOREIGN <Backend> <Text> #-}
+  ```
+
+  The old pragmas still work, but will emit a warning if used. They will be
+  removed completely in Agda 2.6.
+
+  The translation of old pragmas into new ones is as follows:
+
+  Old | New
+  --- | ---
+  `{-# COMPILED f e #-}` | `{-# COMPILE GHC f = e #-}`
+  `{-# COMPILED_TYPE A T #-}` | `{-# COMPILE GHC A = type T #-}`
+  `{-# COMPILED_DATA A D C1 .. CN #-}` | `{-# COMPILE GHC A = data D (C1 \| .. \| CN) #-}`
+  `{-# COMPILED_DECLARE_DATA #-}` | obsolete, removed
+  `{-# COMPILED_EXPORT f g #-}` | `{-# COMPILE GHC f as g #-}`
+  `{-# IMPORT M #-}` | `{-# FOREIGN GHC import qualified M #-}`
+  `{-# HASKELL code #-}` | `{-# FOREIGN GHC code #-}`
+  `{-# COMPILED_UHC f e #-}` | `{-# COMPILE UHC f = e #-}`
+  `{-# COMPILED_DATA_UHC A D C1 .. CN #-}` | `{-# COMPILE UHC A = data D (C1 \| .. \| CN) #-}`
+  `{-# IMPORT_UHC M #-}` | `{-# FOREIGN UHC __IMPORT__ M #-}`
+  `{-# COMPILED_JS f e #-}` | `{-# COMPILE JS f = e #-}`
+
+* GHC Haskell backend
+
+  The COMPILED pragma (and the corresponding COMPILE GHC pragma) is now also
+  allowed for functions. This makes it possible to have both an Agda
+  implementation and a native Haskell runtime implementation.
+
+  The GHC file header pragmas `LANGUAGE`, `OPTIONS_GHC`, and `INCLUDE`
+  inside a `FOREIGN GHC` pragma are recognized and printed correctly
+  at the top of the generated Haskell file.
+  [Issue [#2712](https://github.com/agda/agda/issues/2712)]
+
+
+* UHC compiler backend
+
+  The UHC backend has been moved to its own repository
+  [https://github.com/agda/agda-uhc] and is no longer part of the Agda
+  distribution.
+
+* Haskell imports are no longer transitively inherited from imported modules.
+
+  The (now deprecated) IMPORT and IMPORT_UHC pragmas no longer cause import
+  statements in modules importing the module containing the pragma.
+
+  The same is true for the corresponding FOREIGN pragmas.
+
+* Support for stand-alone backends.
+
+  There is a new API in `Agda.Compiler.Backend` for creating stand-alone
+  backends using Agda as a library. This allows prospective backend writers to
+  experiment with new backends without having to change the Agda code base.
+
+HTML backend
+------------
+
+* Anchors for identifiers (excluding bound variables) are now the
+  identifiers themselves rather than just the file position
+  [Issue [#2604](https://github.com/agda/agda/issues/2604)].
+
+  Symbolic anchors look like
+  ```html
+  <a id="test1">
+  <a id="M.bla">
+  ```
+  while other anchors just give the character position in the file:
+  ```html
+  <a id="42">
+  ```
+
+  Top-level module names do not get a symbolic anchor, since the position of
+  a top-level module is defined to be the beginning of the file.
+
+  Example:
+
+  ```agda
+  module Issue2604 where   -- Character position anchor
+
+  test1 : Set₁             -- Issue2604.html#test1
+  test1 = bla
+    where
+    bla = Set              -- Character position anchor
+
+  test2 : Set₁             -- Issue2604.html#test2
+  test2 = bla
+    where
+    bla = Set              -- Character position anchor
+
+  test3 : Set₁             -- Issue2604.html#test3
+  test3 = bla
+    module M where         -- Issue2604.html#M
+    bla = Set              -- Issue2604.html#M.bla
+
+  module NamedModule where -- Issue2604.html#NamedModule
+    test4 : Set₁           -- Issue2604.html#NamedModule.test4
+    test4 = M.bla
+
+  module _ where           -- Character position anchor
+    test5 : Set₁           -- Character position anchor
+    test5 = M.bla
+  ```
+
+* Some generated HTML files now have different file names [Issue
+  [#2725](https://github.com/agda/agda/issues/2725)].
+
+  Agda now uses an encoding that amounts to first converting the
+  module names to UTF-8, and then percent-encoding the resulting
+  bytes. For instance, HTML for the module `Σ` is placed in
+  `%CE%A3.html`.
+
+LaTeX backend
+-------------
+
+* The LaTeX backend now handles indentation in a different way [Issue
+  [#1832](https://github.com/agda/agda/issues/1832)].
+
+  A constraint on the indentation of the first token *t* on a line is
+  determined as follows:
+  * Let *T* be the set containing every previous token (in any code
+    block) that is either the initial token on its line or preceded by
+    at least one whitespace character.
+  * Let *S* be the set containing all tokens in *T* that are not
+    *shadowed* by other tokens in *T*. A token *t₁* is shadowed by
+    *t₂* if *t₂* is further down than *t₁* and does not start to the
+    right of *t₁*.
+  * Let *L* be the set containing all tokens in *S* that start to the
+    left of *t*, and *E* be the set containing all tokens in *S* that
+    start in the same column as *t*.
+  * The constraint is that *t* must be indented further than every
+    token in *L*, and aligned with every token in *E*.
+
+  Note that if any token in *L* or *E* belongs to a previous code
+  block, then the constraint may not be satisfied unless (say) the
+  `AgdaAlign` environment is used in an appropriate way.
+
+  If custom settings are used, for instance if `\AgdaIndent` is
+  redefined, then the constraint discussed above may not be satisfied.
+  (Note that the meaning of the `\AgdaIndent` command's argument has
+  changed, and that the command is now used in a different way in the
+  generated LaTeX files.)
+
+  Examples:
+  * Here `C` is indented further than `B`:
+
+    ```agda
+    postulate
+      A  B
+          C : Set
+    ```
+
+  * Here `C` is not (necessarily) indented further than `B`, because
+    `X` shadows `B`:
+
+    ```agda
+    postulate
+      A  B  : Set
+      X
+          C : Set
+    ```
+
+  The new rule is inspired by, but not identical to, the one used by
+  lhs2TeX's poly mode (see Section 8.4 of the [manual for lhs2TeX
+  version 1.17](https://www.andres-loeh.de/lhs2tex/Guide2-1.17.pdf)).
+
+* Some spacing issues
+  [[#2353](https://github.com/agda/agda/issues/2353),
+  [#2441](https://github.com/agda/agda/issues/2441),
+  [#2733](https://github.com/agda/agda/issues/2733),
+  [#2740](https://github.com/agda/agda/issues/2740)] have been fixed.
+
+* The user can now control the typesetting of (certain) individual tokens
+  by redefining the `\AgdaFormat` command. Example:
+  ```latex
+  \usepackage{ifthen}
+
+  % Insert extra space before some tokens.
+  \DeclareRobustCommand{\AgdaFormat}[2]{%
+    \ifthenelse{
+      \equal{#1}{≡⟨} \OR
+      \equal{#1}{≡⟨⟩} \OR
+      \equal{#1}{∎}
+    }{\ }{}#2}
+  ```
+  Note the use of `\DeclareRobustCommand`. The first argument to
+  `\AgdaFormat` is the token, and the second argument the thing to
+  be typeset.
+
+* One can now instruct the agda package not to select any fonts.
+
+  If the `nofontsetup` option is used, then some font packages are
+  loaded, but specific fonts are not selected:
+  ```latex
+  \usepackage[nofontsetup]{agda}
+  ```
+
+* The height of empty lines is now configurable
+  [[#2734](https://github.com/agda/agda/issues/2734)].
+
+  The height is controlled by the length `\AgdaEmptySkip`, which by
+  default is `\baselineskip`.
+
+* The alignment feature regards the string `+̲`, containing `+` and a
+  combining character, as having length two. However, it seems more
+  reasonable to treat it as having length one, as it occupies a single
+  column, if displayed "properly" using a monospace font. The new flag
+  `--count-clusters` is an attempt at fixing this. When this flag is
+  enabled the backend counts ["extended grapheme
+  clusters"](http://www.unicode.org/reports/tr29/#Grapheme_Cluster_Boundaries)
+  rather than code points.
+
+  Note that this fix is not perfect: a single extended grapheme
+  cluster might be displayed in different ways by different programs,
+  and might, in some cases, occupy more than one column. Here are some
+  examples of extended grapheme clusters, all of which are treated as
+  a single character by the alignment algorithm:
+  ```
+  │ │
+  │+̲│
+  │Ö̂│
+  │நி│
+  │ᄀힰᇹ│
+  │ᄀᄀᄀᄀᄀᄀힰᇹᇹᇹᇹᇹᇹ│
+  │ │
+  ```
+
+  Note also that the layout machinery does not count extended grapheme
+  clusters, but code points. The following code is syntactically
+  correct, but if `--count-clusters` is used, then the LaTeX backend
+  does not align the two `field` keywords:
+  ```agda
+    record +̲ : Set₁ where  field A : Set
+                            field B : Set
+  ```
+
+  The `--count-clusters` flag is not enabled in all builds of Agda,
+  because the implementation depends on the
+  [ICU](http://site.icu-project.org) library, the installation of
+  which could cause extra trouble for some users. The presence of this
+  flag is controlled by the Cabal flag `enable-cluster-counting`.
+
+* A faster variant of the LaTeX backend: QuickLaTeX.
+
+  When this variant of the backend is used the top-level module is not
+  type-checked, only scope-checked. This implies that some
+  highlighting information is not available. For instance, overloaded
+  constructors are not resolved.
+
+  QuickLaTeX can be invoked from the Emacs mode, or using `agda
+  --latex --only-scope-checking`. If the module has already been
+  type-checked successfully, then this information is reused; in this
+  case QuickLaTeX behaves like the regular LaTeX backend.
+
+  The `--only-scope-checking` flag can also be used independently, but
+  it is perhaps unclear what purpose that would serve. (The flag can
+  currently not be combined with `--html`, `--dependency-graph` or
+  `--vim`.) The flag is not allowed in safe mode.
+
+Pragmas and options
+-------------------
+
+* The `--safe` option is now a valid pragma.
+
+  This makes it possible to declare a module as being part of the safe
+  subset of the language by stating `{-# OPTIONS --safe #-}` at the top
+  of the corresponding file. Incompatibilities between the `--safe` option
+  and other options or language constructs are non-fatal errors.
+
+* The `--no-main` option is now a valid pragma.
+
+  One can now suppress the compiler warning about a missing main function by
+  putting
+  ```agda
+    {-# OPTIONS --no-main #-}
+  ```
+  on top of the file.
+
+* New command-line option and pragma `--warning=MODE` (or `-W MODE`) for
+  setting the warning mode. Current options are
+  - `warn` for displaying warnings (default)
+  - `error` for turning warnings into errors
+  - `ignore` for not displaying warnings
+
+List of fixed issues
+--------------------
+
+For 2.5.3, the following issues have been fixed
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  - [#142](https://github.com/agda/agda/issues/142): Inherited dot patterns in with functions are not checked
+  - [#623](https://github.com/agda/agda/issues/623): Error message points to importing module rather than imported module
+  - [#657](https://github.com/agda/agda/issues/657): Yet another display form problem
+  - [#668](https://github.com/agda/agda/issues/668): Ability to stop, or restart, typechecking somehow
+  - [#705](https://github.com/agda/agda/issues/705): confusing error message for ambiguous datatype module name
+  - [#719](https://github.com/agda/agda/issues/719): Error message for duplicate module definition points to external module instead of internal module
+  - [#776](https://github.com/agda/agda/issues/776): Unsolvable constraints should give error
+  - [#819](https://github.com/agda/agda/issues/819): Case-splitting doesn't preserve underscores
+  - [#883](https://github.com/agda/agda/issues/883): Rewrite loses type information
+  - [#899](https://github.com/agda/agda/issues/899): Instance search fails if there are several definitionally equal values in scope
+  - [#1077](https://github.com/agda/agda/issues/1077): problem with module syntax, with parametric module import
+  - [#1126](https://github.com/agda/agda/issues/1126): Port optimizations from the Epic backend
+  - [#1175](https://github.com/agda/agda/issues/1175): Internal Error in Auto
+  - [#1544](https://github.com/agda/agda/issues/1544): Positivity polymorphism needed for compositional positivity analysis
+  - [#1611](https://github.com/agda/agda/issues/1611): Interactive splitting instantiates meta
+  - [#1664](https://github.com/agda/agda/issues/1664): Add Reflection primitives to expose precedence and fixity
+  - [#1817](https://github.com/agda/agda/issues/1817): Solvable size constraints reported as unsolvable
+  - [#1832](https://github.com/agda/agda/issues/1832): Insufficient indentation in LaTeX-rendered Agda code
+  - [#1834](https://github.com/agda/agda/issues/1834): Copattern matching: order of clauses should not matter here
+  - [#1886](https://github.com/agda/agda/issues/1886): Second copies of telescopes not checked?
+  - [#1899](https://github.com/agda/agda/issues/1899): Positivity checker does not treat datatypes and record types in the same way
+  - [#1975](https://github.com/agda/agda/issues/1975): Type-incorrect instantiated overloaded constructor accepted in pattern
+  - [#1976](https://github.com/agda/agda/issues/1976): Type-incorrect instantiated projection accepted in pattern
+  - [#2035](https://github.com/agda/agda/issues/2035): Matching on string causes solver to fail with internal error
+  - [#2146](https://github.com/agda/agda/issues/2146): Unicode syntax for instance arguments
+  - [#2217](https://github.com/agda/agda/issues/2217): Abort Agda without losing state
+  - [#2229](https://github.com/agda/agda/issues/2229): Absence or presence of top-level module header affects scope
+  - [#2253](https://github.com/agda/agda/issues/2253): Wrong scope error for abstract constructors
+  - [#2261](https://github.com/agda/agda/issues/2261): Internal error in Auto/CaseSplit.hs:284
+  - [#2270](https://github.com/agda/agda/issues/2270): Printer does not use sections.
+  - [#2329](https://github.com/agda/agda/issues/2329): Size solver does not use type `Size< i` to gain the necessary information
+  - [#2354](https://github.com/agda/agda/issues/2354): Interaction between instance search, size solver, and ordinary constraint solver.
+  - [#2355](https://github.com/agda/agda/issues/2355): Literate Agda parser does not recognize TeX comments
+  - [#2360](https://github.com/agda/agda/issues/2360): With clause stripping chokes on ambiguous projection
+  - [#2362](https://github.com/agda/agda/issues/2362): Printing of parent patterns when with-clause does not match
+  - [#2363](https://github.com/agda/agda/issues/2363): Allow underscore in with-clause patterns
+  - [#2366](https://github.com/agda/agda/issues/2366): With-clause patterns renamed in error message
+  - [#2368](https://github.com/agda/agda/issues/2368): Internal error after refining a tactic @ MetaVars.hs:267
+  - [#2371](https://github.com/agda/agda/issues/2371): Shadowed module parameter crashes interaction
+  - [#2372](https://github.com/agda/agda/issues/2372): problems when instances are declared with inferred types
+  - [#2374](https://github.com/agda/agda/issues/2374): Ambiguous projection pattern could be disambiguated by visibility
+  - [#2376](https://github.com/agda/agda/issues/2376): Termination checking interacts badly with eta-contraction
+  - [#2377](https://github.com/agda/agda/issues/2377): open public is useless before module header
+  - [#2381](https://github.com/agda/agda/issues/2381): Search (`C-c C-z`) panics on pattern synonyms
+  - [#2386](https://github.com/agda/agda/issues/2386): Relax requirements of BUILTIN EQUALITY
+  - [#2389](https://github.com/agda/agda/issues/2389): BUILTIN REFL not needed
+  - [#2400](https://github.com/agda/agda/issues/2400): LaTeX backend error on LaTeX comments
+  - [#2402](https://github.com/agda/agda/issues/2402): Parameters not dropped when reporting incomplete patterns
+  - [#2403](https://github.com/agda/agda/issues/2403): Termination checker should reduce arguments in structural order check
+  - [#2405](https://github.com/agda/agda/issues/2405): instance search failing in parameterized module
+  - [#2408](https://github.com/agda/agda/issues/2408): DLub sorts are not serialized
+  - [#2412](https://github.com/agda/agda/issues/2412): Problem with checking  with sized types
+  - [#2413](https://github.com/agda/agda/issues/2413): Agda crashes on x@y pattern
+  - [#2415](https://github.com/agda/agda/issues/2415): Size solver reports "inconsistent upper bound" even though there is a solution
+  - [#2416](https://github.com/agda/agda/issues/2416): Cannot give size as computed by solver
+  - [#2422](https://github.com/agda/agda/issues/2422): Overloaded inherited projections don't resolve
+  - [#2423](https://github.com/agda/agda/issues/2423): Inherited projection on lhs
+  - [#2426](https://github.com/agda/agda/issues/2426): On just warning about missing cases
+  - [#2429](https://github.com/agda/agda/issues/2429): Irrelevant lambda should be accepted when relevant lambda is expected
+  - [#2430](https://github.com/agda/agda/issues/2430): Another regression related to parameter refinement?
+  - [#2433](https://github.com/agda/agda/issues/2433): rebindLocalRewriteRules re-adds global rewrite rules
+  - [#2434](https://github.com/agda/agda/issues/2434): Exact split analysis is too strict when matching on eta record constructor
+  - [#2441](https://github.com/agda/agda/issues/2441): Incorrect alignement in latex using the new ACM format
+  - [#2444](https://github.com/agda/agda/issues/2444): Generalising compiler pragmas
+  - [#2445](https://github.com/agda/agda/issues/2445): The LaTeX backend is slow
+  - [#2447](https://github.com/agda/agda/issues/2447): Cache loaded interfaces even if a type error is encountered
+  - [#2449](https://github.com/agda/agda/issues/2449): Agda depends on additional C library icu
+  - [#2451](https://github.com/agda/agda/issues/2451): Agda panics when attempting to rewrite a typeclass Eq
+  - [#2456](https://github.com/agda/agda/issues/2456): Internal error when postulating instance
+  - [#2458](https://github.com/agda/agda/issues/2458): Regression: Agda-2.5.3 loops where Agda-2.5.2 passes
+  - [#2462](https://github.com/agda/agda/issues/2462): Overloaded postfix projection does not resolve
+  - [#2464](https://github.com/agda/agda/issues/2464): Eta contraction for irrelevant functions breaks subject reduction
+  - [#2466](https://github.com/agda/agda/issues/2466): Case split to make hidden variable visible does not work
+  - [#2467](https://github.com/agda/agda/issues/2467): REWRITE without BUILTIN REWRITE crashes
+  - [#2469](https://github.com/agda/agda/issues/2469): "Partial" pattern match causes segfault at runtime
+  - [#2472](https://github.com/agda/agda/issues/2472): Regression related to the auto command
+  - [#2477](https://github.com/agda/agda/issues/2477): Sized data type analysis brittle, does not reduce size
+  - [#2478](https://github.com/agda/agda/issues/2478): Multiply defined labels on the user manual (pdf)
+  - [#2479](https://github.com/agda/agda/issues/2479): "Occurs check" error in generated Haskell code
+  - [#2480](https://github.com/agda/agda/issues/2480): Agda accepts incorrect (?) code, subject reduction broken
+  - [#2482](https://github.com/agda/agda/issues/2482): Wrong counting of data parameters with new-style mutual blocks
+  - [#2483](https://github.com/agda/agda/issues/2483): Files are sometimes truncated to a size of 201 bytes
+  - [#2486](https://github.com/agda/agda/issues/2486): Imports via FOREIGN are not transitively inherited anymore
+  - [#2488](https://github.com/agda/agda/issues/2488): Instance search inhibits holes for instance fields
+  - [#2493](https://github.com/agda/agda/issues/2493): Regression: Agda seems to loop when expression is given
+  - [#2494](https://github.com/agda/agda/issues/2494): Instance fields sometimes have incorrect goal types
+  - [#2495](https://github.com/agda/agda/issues/2495): Regression: termination checker of Agda-2.5.3 seemingly loops where Agda-2.5.2 passes
+  - [#2500](https://github.com/agda/agda/issues/2500): Adding fields to a record can cause Agda to reject previous definitions
+  - [#2510](https://github.com/agda/agda/issues/2510): Wrong error with --no-pattern-matching
+  - [#2517](https://github.com/agda/agda/issues/2517): "Not a variable error"
+  - [#2518](https://github.com/agda/agda/issues/2518): CopatternReductions in TreeLess
+  - [#2523](https://github.com/agda/agda/issues/2523): The documentation of `--without-K` is outdated
+  - [#2529](https://github.com/agda/agda/issues/2529): Unable to install Agda on Windows.
+  - [#2537](https://github.com/agda/agda/issues/2537): case splitting with 'with' creates {_} instead of replicating the arguments it found.
+  - [#2538](https://github.com/agda/agda/issues/2538): Internal error when parsing as-pattern
+  - [#2543](https://github.com/agda/agda/issues/2543): Case splitting with ellipsis produces spurious parentheses
+  - [#2545](https://github.com/agda/agda/issues/2545): Race condition in api tests
+  - [#2549](https://github.com/agda/agda/issues/2549): Rewrite rule for higher path constructor does not fire
+  - [#2550](https://github.com/agda/agda/issues/2550): Internal error in Agda.TypeChecking.Substitute
+  - [#2552](https://github.com/agda/agda/issues/2552): Let bindings in module telescopes crash Agda.Interaction.BasicOps
+  - [#2553](https://github.com/agda/agda/issues/2553): Internal error in Agda.TypeChecking.CheckInternal
+  - [#2554](https://github.com/agda/agda/issues/2554): More flexible size-assignment in successor style
+  - [#2555](https://github.com/agda/agda/issues/2555): Why does the positivity checker care about non-recursive occurrences?
+  - [#2558](https://github.com/agda/agda/issues/2558): Internal error in Warshall Solver
+  - [#2560](https://github.com/agda/agda/issues/2560): Internal Error in Reduce.Fast
+  - [#2564](https://github.com/agda/agda/issues/2564): Non-exact-split highlighting makes other highlighting disappear
+  - [#2568](https://github.com/agda/agda/issues/2568): agda2-infer-type-maybe-toplevel (in hole) does not respect "single-solution" requirement of instance resolution
+  - [#2571](https://github.com/agda/agda/issues/2571): Record pattern translation does not eta contract
+  - [#2573](https://github.com/agda/agda/issues/2573): Rewrite rules fail depending on unrelated changes
+  - [#2574](https://github.com/agda/agda/issues/2574): No link attached to module without toplevel name
+  - [#2575](https://github.com/agda/agda/issues/2575): Internal error, related to caching
+  - [#2577](https://github.com/agda/agda/issues/2577): deBruijn fail for higher order instance problem
+  - [#2578](https://github.com/agda/agda/issues/2578): Catch-all clause face used incorrectly for parent with pattern
+  - [#2579](https://github.com/agda/agda/issues/2579): Import statements with module instantiation should not trigger an error message
+  - [#2580](https://github.com/agda/agda/issues/2580): Implicit absurd match is NonVariant, explicit not
+  - [#2583](https://github.com/agda/agda/issues/2583): Wrong de Bruijn index introduced by absurd pattern
+  - [#2584](https://github.com/agda/agda/issues/2584): Duplicate warning printing
+  - [#2585](https://github.com/agda/agda/issues/2585): Definition by copatterns not modulo eta
+  - [#2586](https://github.com/agda/agda/issues/2586): "λ where" with single absurd clause not parsed
+  - [#2588](https://github.com/agda/agda/issues/2588): `agda --latex` produces invalid LaTeX when there are block comments
+  - [#2592](https://github.com/agda/agda/issues/2592): Internal Error in Agda/TypeChecking/Serialise/Instances/Common.hs
+  - [#2597](https://github.com/agda/agda/issues/2597): Inline record definitions confuse the reflection API
+  - [#2602](https://github.com/agda/agda/issues/2602): Debug output messes up AgdaInfo buffer
+  - [#2603](https://github.com/agda/agda/issues/2603): Internal error in MetaVars.hs
+  - [#2604](https://github.com/agda/agda/issues/2604): Use QNames as anchors in generated HTML
+  - [#2605](https://github.com/agda/agda/issues/2605): HTML backend generates anchors for whitespace
+  - [#2606](https://github.com/agda/agda/issues/2606): Check that LHS of a rewrite rule doesn't reduce is too strict
+  - [#2612](https://github.com/agda/agda/issues/2612): `exact-split` documentation is outdated and incomplete
+  - [#2613](https://github.com/agda/agda/issues/2613): Parametrised modules, with-abstraction and termination
+  - [#2620](https://github.com/agda/agda/issues/2620): Internal error in auto.
+  - [#2621](https://github.com/agda/agda/issues/2621): Case splitting instantiates meta
+  - [#2626](https://github.com/agda/agda/issues/2626): triggered internal error with sized types in MetaVars module
+  - [#2629](https://github.com/agda/agda/issues/2629): Exact splitting should not complain about absurd clauses
+  - [#2631](https://github.com/agda/agda/issues/2631): docs for auto aren't clear on how to use flags/options
+  - [#2632](https://github.com/agda/agda/issues/2632): some flags to auto dont seem to work in current agda 2.5.2
+  - [#2637](https://github.com/agda/agda/issues/2637): Internal error in Agda.TypeChecking.Pretty, possibly related to sized types
+  - [#2639](https://github.com/agda/agda/issues/2639): Performance regression, possibly related to the size solver
+  - [#2641](https://github.com/agda/agda/issues/2641): Required instance of FromNat when compiling imported files
+  - [#2642](https://github.com/agda/agda/issues/2642): Records with duplicate fields
+  - [#2644](https://github.com/agda/agda/issues/2644): Wrong substitution in expandRecordVar
+  - [#2645](https://github.com/agda/agda/issues/2645): Agda accepts postulated fields in a record
+  - [#2646](https://github.com/agda/agda/issues/2646): Only warn if fixities for undefined symbols are given
+  - [#2649](https://github.com/agda/agda/issues/2649): Empty list of "previous definition" in duplicate definition error
+  - [#2652](https://github.com/agda/agda/issues/2652): Added a new variant of the colon to the Agda input method
+  - [#2653](https://github.com/agda/agda/issues/2653): agda-mode: "cannot refine" inside instance argument even though term to be refined typechecks there
+  - [#2654](https://github.com/agda/agda/issues/2654): Internal error on result splitting without --postfix-projections
+  - [#2664](https://github.com/agda/agda/issues/2664): Segmentation fault with compiled programs using mutual record
+  - [#2665](https://github.com/agda/agda/issues/2665): Documentation: Record update syntax in wrong location
+  - [#2666](https://github.com/agda/agda/issues/2666): Internal error at Agda/Syntax/Abstract/Name.hs:113
+  - [#2667](https://github.com/agda/agda/issues/2667): Panic error on unbound variable.
+  - [#2669](https://github.com/agda/agda/issues/2669): Interaction: incorrect field variable name generation
+  - [#2671](https://github.com/agda/agda/issues/2671): Feature request: nullary pattern matching lambdas
+  - [#2679](https://github.com/agda/agda/issues/2679): Internal error at "Typechecking/Abstract.hs:133" and "TypeChecking/Telescope.hs:68"
+  - [#2682](https://github.com/agda/agda/issues/2682): What are the rules for projections of abstract records?
+  - [#2684](https://github.com/agda/agda/issues/2684): Bad error message for abstract constructor
+  - [#2686](https://github.com/agda/agda/issues/2686): Abstract constructors should be ignored when resolving overloading
+  - [#2690](https://github.com/agda/agda/issues/2690): [regression?] Agda engages in deep search instead of immediately failing
+  - [#2700](https://github.com/agda/agda/issues/2700): Add a command to check against goal type (and normalise)
+  - [#2703](https://github.com/agda/agda/issues/2703): Regression: Internal error for underapplied indexed constructor
+  - [#2705](https://github.com/agda/agda/issues/2705): The GHC backend might diverge in infinite file creation
+  - [#2708](https://github.com/agda/agda/issues/2708): Why is the `name` field in .agda-lib files mandatory?
+  - [#2710](https://github.com/agda/agda/issues/2710): Type checker hangs
+  - [#2712](https://github.com/agda/agda/issues/2712): Compiler Pragma for headers
+  - [#2714](https://github.com/agda/agda/issues/2714): Option --no-main should be allowed as file-local option
+  - [#2717](https://github.com/agda/agda/issues/2717): internal error at DisplayForm.hs:197
+  - [#2718](https://github.com/agda/agda/issues/2718): Interactive 'give' doesn't insert enough parenthesis
+  - [#2721](https://github.com/agda/agda/issues/2721): Without-K doesn't prevent heterogeneous conflict between literals
+  - [#2723](https://github.com/agda/agda/issues/2723): Unreachable clauses in definition by copattern matching trip clause compiler
+  - [#2725](https://github.com/agda/agda/issues/2725): File names for generated HTML files
+  - [#2726](https://github.com/agda/agda/issues/2726): Old regression related to with
+  - [#2727](https://github.com/agda/agda/issues/2727): Internal errors related to rewrite
+  - [#2729](https://github.com/agda/agda/issues/2729): Regression: case splitting uses variable name variants instead of the unused original names
+  - [#2730](https://github.com/agda/agda/issues/2730): Command to give in spite of termination errors
+  - [#2731](https://github.com/agda/agda/issues/2731): Agda fails to build with happy 1.19.6
+  - [#2733](https://github.com/agda/agda/issues/2733): Avoid some uses of \AgdaIndent?
+  - [#2734](https://github.com/agda/agda/issues/2734): Make height of empty lines configurable
+  - [#2736](https://github.com/agda/agda/issues/2736): Segfault using Alex 3.2.2 and cpphs
+  - [#2740](https://github.com/agda/agda/issues/2740): Indenting every line of code should be a no-op
diff --git a/doc/release-notes/2.5.4.1.md b/doc/release-notes/2.5.4.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.4.1.md
@@ -0,0 +1,16 @@
+Release notes for Agda version 2.5.4.1
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Generated the interface file for the `Sigma.agda` built-in when
+  installing Agda
+  [Issue [#3128](https://github.com/agda/agda/issues/3128)].
+
+Emacs mode
+----------
+
+* Light highlighting is no longer applied continuously, but only when
+  the file is saved [Issue
+  [#3119](https://github.com/agda/agda/issues/3119)].
diff --git a/doc/release-notes/2.5.4.2.md b/doc/release-notes/2.5.4.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.4.2.md
@@ -0,0 +1,23 @@
+Release notes for Agda version 2.5.4.2
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Fixed installation with some old versions of `cabal-install`
+  [Issue [#3225](https://github.com/agda/agda/issues/3225)].
+
+* Using `cpp` instead of `cpphs` as the default preprocessor
+  [Issue [#3223](https://github.com/agda/agda/issues/3223)].
+
+* Added support for GHC 8.4.4.
+
+Other closed issues
+--------------------
+
+For 2.5.4.2 the following issues have also been closed
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  - [#3177](https://github.com/agda/agda/issues/3177): Slow typechecking with unsolved instance constraint
+  - [#3199](https://github.com/agda/agda/issues/3199): Panics when serialising absolute paths
+  - [#3312](https://github.com/agda/agda/issues/3312): Crash in Substitute.hs
diff --git a/doc/release-notes/2.5.4.md b/doc/release-notes/2.5.4.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.5.4.md
@@ -0,0 +1,859 @@
+Release notes for Agda version 2.5.4
+====================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.2.2 and GHC 8.4.3.
+
+  Note that GHC 8.4.* requires `cabal-install` ≥ 2.2.0.0.
+
+* Removed support for GHC 7.8.4.
+
+* Included user manual in PDF format in `doc/user-manual.pdf`.
+
+Language
+--------
+
+* Call-by-need reduction.
+
+  Compile-time weak-head evaluation is now call-by-need, but each weak-head
+  reduction has a local heap, so sharing is not maintained between different
+  reductions.
+
+  The reduction machine has been rewritten from scratch and should be faster
+  than the old one in all cases, even those not exploiting laziness.
+
+* Compile-time inlining.
+
+  Simple definitions (that don't do any pattern matching) marked as INLINE are
+  now also inlined at compile time, whereas before they were only inlined by
+  the compiler backends. Inlining only triggers in function bodies and not in
+  type signatures, to preserve goal types as far as possible.
+
+* Automatic inlining.
+
+  Definitions satisfying the following criteria are now automatically inlined
+  (can be disabled using the new NOINLINE pragma):
+
+    - No pattern matching.
+    - Uses each argument at most once.
+    - Does not use all its arguments.
+
+  Automatic inlining can be turned off using the flag `--no-auto-inline`. This
+  can be useful when debugging tactics that may be affected by whether or not
+  a particular definition is being inlined.
+
+### Syntax
+
+* Do-notation.
+
+  There is now builtin do-notation syntax. This means that `do` is a reserved
+  keyword and cannot be used as an identifier.
+
+  Do-blocks support lets and pattern matching binds. If the pattern in a bind
+  is non-exhaustive the other patterns need to be handled in a `where`-clause
+  (see example below).
+
+  Example:
+
+  ```agda
+  filter : {A : Set} → (A → Bool) → List A → List A
+  filter p xs = do
+    x    ← xs
+    true ← return (p x)
+      where false → []
+    return x
+  ```
+
+  Do-blocks desugar to `_>>=_` and `_>>_` before scope checking, so whatever
+  definitions of these two functions are in scope of the do-block will be used.
+
+  More precisely:
+
+  - Simple bind
+
+    ```agda
+    do x ← m
+       m'
+    ```
+    desugars to `m >>= λ x → m'`.
+
+  - Pattern bind
+
+    ```agda
+    do p ← m where pᵢ → mᵢ
+       m'
+    ```
+    desugars to `m >>= λ { p → m'; pᵢ → mᵢ }`, where `pᵢ → mᵢ` is an arbitrary
+    sequence of clauses and follows the usual layout rules for `where`. If `p`
+    is exhaustive the `where` clause can be omitted.
+
+  - Non-binding operation
+
+    ```agda
+    do m
+       m'
+    ```
+    desugars to `m >> m'`.
+
+  - Let
+
+    ```agda
+    do let ds
+       m
+    ```
+    desugars to `let ds in m`, where `ds` is an arbitrary sequence of valid let-declarations.
+
+  - The last statement in the do block must be a plain expression (no let or bind).
+
+  Bind statements can use either `←` or `<-`. Neither of these are reserved, so
+  code outside do-blocks can use identifiers with these names, but inside a
+  do-block they would need to be used qualified or under different names.
+
+* Infix let declarations. [Issue [#917](https://github.com/agda/agda/issues/917)]
+
+  Let declarations can now be defined in infix (or mixfix) style. For instance:
+
+  ```agda
+    f : Nat → Nat
+    f n = let _!_ : Nat → Nat → Nat
+              x ! y = 2 * x + y
+          in n ! n
+  ```
+
+* Overloaded pattern synonyms. [Issue [#2787](https://github.com/agda/agda/issues/2787)]
+
+  Pattern synonyms can now be overloaded if all candidates have the same
+  *shape*. Two pattern synonym definitions have the same shape if they are
+  equal up to variable and constructor names. Shapes are checked at resolution
+  time.
+
+  For instance, the following is accepted:
+
+  ```agda
+    open import Agda.Builtin.Nat
+
+    data List (A : Set) : Set where
+      lnil  : List A
+      lcons : A → List A → List A
+
+    data Vec (A : Set) : Nat → Set where
+      vnil  : Vec A 0
+      vcons : ∀ {n} → A → Vec A n → Vec A (suc n)
+
+    pattern [] = lnil
+    pattern [] = vnil
+
+    pattern _∷_ x xs = lcons x xs
+    pattern _∷_ y ys = vcons y ys
+
+    lmap : ∀ {A B} → (A → B) → List A → List B
+    lmap f []       = []
+    lmap f (x ∷ xs) = f x ∷ lmap f xs
+
+    vmap : ∀ {A B n} → (A → B) → Vec A n → Vec B n
+    vmap f []       = []
+    vmap f (x ∷ xs) = f x ∷ vmap f xs
+  ```
+
+* If the file has no top-level module header, the first module
+  cannot have the same name as the file.
+  [Issues [#2808](https://github.com/agda/agda/issues/2808)
+   and [#1077](https://github.com/agda/agda/issues/1077)]
+
+  This means that the following file `File.agda` is rejected:
+  ```agda
+    -- no module header
+    postulate A : Set
+    module File where -- inner module with the same name as the file
+  ```
+  Agda reports `Illegal declarations(s) before top-level module`
+  at the `postulate`.
+  This is to avoid confusing scope errors in similar situations.
+
+  If a top-level module header is inserted manually, the file is accepted:
+
+  ```agda
+    module _ where    -- user written module header
+    postulate A : Set
+    module File where -- inner module with the same name as the file, ok
+  ```
+
+### Pattern matching
+
+* Forced constructor patterns.
+
+  Constructor patterns can now be dotted to indicate that Agda should not case
+  split on them but rather their value is forced by the type of the other
+  patterns. The difference between this and a regular dot pattern is that
+  forced constructor patterns can still bind variables in their arguments.
+  For example,
+
+  ```agda
+    open import Agda.Builtin.Nat
+
+    data Vec (A : Set) : Nat → Set where
+      nil  : Vec A zero
+      cons : (n : Nat) → A → Vec A n → Vec A (suc n)
+
+    append : {A : Set} (m n : Nat) → Vec A m → Vec A n → Vec A (m + n)
+    append .zero    n nil            ys = ys
+    append (.suc m) n (cons .m x xs) ys = cons (m + n) x (append m n xs ys)
+  ```
+
+* Inferring the type of a function based on its patterns
+
+  Agda no longer infers the type of a function based on the patterns used in
+  its definition. [Issue [#2834](https://github.com/agda/agda/issues/2834)]
+
+  This means that the following Agda program is no longer accepted:
+  ```agda
+    open import Agda.Builtin.Nat
+
+    f : _ → _
+    f zero    = zero
+    f (suc n) = n
+  ```
+  Agda now requires the type of the argument of `f` to be given explicitly.
+
+* Improved constraint solving for pattern matching functions
+
+  Constraint solving for functions where each right-hand side has a distinct
+  rigid head has been extended to also cover the case where some clauses return
+  an argument of the function. A typical example is append on lists:
+
+  ```agda
+    _++_ : {A : Set} → List A → List A → List A
+    []       ++ ys = ys
+    (x ∷ xs) ++ ys = x ∷ (xs ++ ys)
+  ```
+
+  Agda can now solve constraints like `?X ++ ys == 1 ∷ ys` when `ys` is a
+  neutral term.
+
+* Record expressions translated to copatterns
+
+  Definitions of the form
+
+  ```agda
+    f ps = record { f₁ = e₁; ..; fₙ = eₙ }
+  ```
+
+  are translated internally to use copatterns:
+
+  ```agda
+    f ps .f₁ = e₁
+    ...
+    f ps .fₙ = eₙ
+  ```
+
+  This means that `f ps` does not reduce, but thanks to η-equality the two
+  definitions are equivalent.
+
+  The change should lead to fewer big record expressions showing up in goal
+  types, and potentially significant performance improvement in some cases.
+
+  This may have a minor impact on with-abstraction and code using `--rewriting`
+  since η-equality is not used in these cases.
+
+* When using `with`, it is now allowed to replace any pattern from the parent
+  clause by a variable in the with clause. For example:
+
+  ```agda
+    f : List ℕ → List ℕ
+    f [] = []
+    f (x ∷ xs) with x ≤? 10
+    f xs | p = {!!}
+  ```
+
+  In the with clause, `xs` is treated as a let-bound variable with value
+  `.x ∷ .xs` (where `.x : ℕ` and `.xs : List ℕ` are out of scope) and
+  `p : Dec (.x ≤ 10)`.
+
+  Since with-abstraction may change the type of variables, instantiations
+  of variables in the with clause are type checked again after with-abstraction.
+
+### Builtins
+
+* Added support for built-in 64-bit machine words.
+
+  These are defined in `Agda.Builtin.Word` and come with two primitive
+  operations to convert to and from natural numbers.
+
+  ```agda
+    Word64 : Set
+    primWord64ToNat   : Word64 → Nat
+    primWord64FromNat : Nat → Word64
+  ```
+
+  Converting to a natural number is the trivial embedding, and converting from a natural number
+  gives you the remainder modulo 2^64. The proofs of these theorems are not
+  primitive, but can be defined in a library using `primTrustMe`.
+
+  Basic arithmetic operations can be defined on `Word64` by converting to
+  natural numbers, peforming the corresponding operation, and then converting
+  back. The compiler will optimise these to use 64-bit arithmetic. For
+  instance,
+
+  ```agda
+    addWord : Word64 → Word64 → Word64
+    addWord a b = primWord64FromNat (primWord64ToNat a + primWord64ToNat b)
+
+    subWord : Word64 → Word64 → Word64
+    subWord a b = primWord64FromNat (primWord64ToNat a + 18446744073709551616 - primWord64ToNat b)
+  ```
+
+  These compiles (in the GHC backend) to addition and subtraction on
+  `Data.Word.Word64`.
+
+* New primitive primFloatLess and changed semantics of primFloatNumericalLess.
+
+  `primFloatNumericalLess` now uses standard IEEE `<`, so for instance
+  `NaN < x = x < NaN = false`.
+
+  On the other hand `primFloatLess` provides a total order on `Float`, with
+  `-Inf < NaN < -1.0 < -0.0 < 0.0 < 1.0 < Inf`.
+
+* The `SIZEINF` builtin is now given the name `∞` in
+  `Agda.Builtin.Size` [Issue
+  [#2931](https://github.com/agda/agda/issues/2931)].
+
+  Previously it was given the name `ω`.
+
+### Reflection
+
+* New TC primitive: `declarePostulate`. [Issue
+  [#2782](https://github.com/agda/agda/issues/2782)]
+
+  ```agda
+    declarePostulate : Arg Name → Type → TC ⊤
+  ```
+
+  This can be used to declare new postulates. The Visibility of the
+  Arg must not be hidden. This feature fails when executed with
+  `--safe` flag from command-line.
+
+Pragmas and options
+-------------------
+
+* The `--caching` option is ON by default and is also a valid pragma.
+  Caching can (sometimes) speed up re-typechecking in `--interaction`
+  mode by reusing the result of the previous typechecking for the
+  prefix of the file that has not changed (with a granularity at the
+  level of declarations/mutual blocks).
+
+  It can be turned off by passing ```--no-caching``` to ```agda``` or
+  with the following at the top of your file.
+
+  ```agda
+    {-# OPTIONS --no-caching #-}
+  ```
+
+* The `--sharing` and `--no-sharing` options have been deprecated and do
+  nothing.
+
+  Compile-time evaluation is now always call-by-need.
+
+* BUILTIN pragmas can now appear before the top-level module header
+  and in parametrized modules.
+  [Issue [#2824](https://github.com/agda/agda/issues/2824)]
+  ```agda
+    {-# OPTIONS --rewriting #-}
+    open import Agda.Builtin.Equality
+    {-# BUILTIN REWRITE _≡_ #-}  -- here
+    module TopLevel (A : Set) where
+    {-# BUILTIN REWRITE _≡_ #-}  -- or here
+  ```
+  Note that it is still the case that built-ins cannot be bound if
+  they depend on module parameters from an enclosing module. For
+  instance, the following is illegal:
+  ```agda
+    module _ {a} {A : Set a} where
+      data _≡_ (x : A) : A → Set a where
+        refl : x ≡ x
+      {-# BUILTIN EQUALITY _≡_ #-}
+  ```
+
+* Builtin `NIL` and `CONS` have been merged with `LIST`.
+
+  When binding the `LIST` builtin, `NIL` and `CONS` are bound to
+  the appropriate constructors automatically. This means that instead
+  of writing
+
+  ```agda
+  {-# BUILTIN LIST List #-}
+  {-# BUILTIN NIL  []   #-}
+  {-# BUILTIN CONS _∷_  #-}
+  ```
+
+  you just write
+
+  ```agda
+  {-# BUILTIN LIST List #-}
+  ```
+
+  Attempting to bind `NIL` or `CONS` results in a warning and has otherwise no
+  effect.
+
+* The `--no-unicode` pragma prevents Agda from introducing unicode characters
+  when pretty printing a term. Lambda, Arrows and Forall quantifiers are all
+  replaced by their ascii only version. Instead of resorting to subscript
+  suffixes, Agda uses ascii digit characters.
+
+* New option `--inversion-max-depth=N`.
+
+  The depth is used to avoid looping due to inverting pattern matching for
+  unsatisfiable constraints [Issue [#431](https://github.com/agda/agda/issues/431)].
+  This option is only expected to be necessary in pathological cases.
+
+* New option `--no-print-pattern-synonyms`.
+
+  This disables the use of pattern synonyms in output from Agda.
+  See [Issue [#2902](https://github.com/agda/agda/issues/2902)] for situations
+  where this might be desirable.
+
+* New fine-grained control over the warning machinery: ability to (en/dis)able
+  warnings on a one-by-one basis.
+
+* The command line option `--help` now takes an optional argument which
+  allows the user to request more specific usage information about particular
+  topics. The only one added so far is `warning`.
+
+* New pragma NOINLINE.
+
+  ```agda
+  {-# NOINLINE f #-}
+  ```
+
+  Disables automatic inlining of `f`.
+
+* New pragma WARNING_ON_USAGE
+
+  ```
+  {-# WARNING_ON_USAGE QName Message #}
+  ```
+
+  Prints Message whenever QName is used.
+
+Emacs mode
+----------
+
+* Banana brackets have been added to the Agda input method.
+  ```
+    \((   #x2985  LEFT  WHITE PARENTHESIS
+    \))   #x2986  RIGHT WHITE PARENTHESIS
+  ```
+
+* Result splitting will introduce the trailing hidden arguments,
+  if there is nothing else todo
+  [Issue [#2871](https://github.com/agda/agda/issues/2871)].
+  Example:
+  ```agda
+    data Fun (A : Set) : Set where
+      mkFun : (A → A) → Fun A
+
+    test : {A : Set} → Fun A
+    test = ?
+
+  ```
+  Splitting on the result here (`C-c C-c RET`) will append
+  `{A}` to the left hand side.
+  ```agda
+    test {A} = ?
+  ```
+
+* Light highlighting is performed dynamically, even if the file is not
+  loaded [Issue [#2794](https://github.com/agda/agda/issues/2794)].
+
+  This light highlighting is based on the token stream generated by
+  Agda's lexer: the code is only highlighted if the file is lexically
+  correct. If the Agda backend is not busy with something else, then
+  the code is highlighted automatically in certain situations:
+
+  * When the file is saved.
+
+  * When Emacs has been idle, continuously, for a certain period of
+    time (by default 0.2 s) after the last modification of the file,
+    and the file has not been saved (or marked as being unmodified).
+    This functionality can be turned off, and the time period can be
+    customised.
+
+* Highlighting of comments is no longer handled by Font Lock mode
+  [Issue [#2794](https://github.com/agda/agda/issues/2794)].
+
+* The Emacs mode's syntax table has been changed.
+
+  Previously `_` was treated as punctuation. Now it is treated in the
+  same way as most other characters: if the standard syntax table
+  assigns it the syntax class "whitespace", "open parenthesis" or
+  "close parenthesis", then it gets that syntax class, and otherwise
+  it gets the syntax class "word constituent".
+
+Compiler backends
+-----------------
+
+* The GHC backend now automatically compiles BUILTIN LIST to Haskell lists.
+
+  This means that it's no longer necessary to give a COMPILE GHC pragma for the
+  builtin list type. Indeed, doing so has no effect on the compilation and
+  results in a warning.
+
+* The GHC backend performance improvements.
+
+  Generated Haskell code now contains approximate type signatures, which lets
+  GHC get rid of many of the `unsafeCoerce`s. This leads to performance
+  improvements of up to 50% of compiled code.
+
+* The GHC backend now compiles the `INFINITY`, `SHARP` and `FLAT`
+  builtins in a different way [Issue
+  [#2909](https://github.com/agda/agda/issues/2909)].
+
+  Previously these were compiled to (basically) nothing. Now the
+  `INFINITY` builtin is compiled to `Infinity`, available from
+  `MAlonzo.RTE`:
+
+  ```haskell
+  data Inf a            = Sharp { flat :: a }
+  type Infinity level a = Inf a
+  ```
+
+  The `SHARP` builtin is compiled to `Sharp`, and the `FLAT` builtin
+  is (by default) compiled to a corresponding destructor.
+
+  Note that code that interacts with Haskell libraries may have to be
+  updated. As an example, here is one way to print colists of
+  characters using the Haskell function `putStr`:
+
+  ```agda
+  open import Agda.Builtin.Char
+  open import Agda.Builtin.Coinduction
+  open import Agda.Builtin.IO
+  open import Agda.Builtin.Unit
+
+  data Colist {a} (A : Set a) : Set a where
+    []  : Colist A
+    _∷_ : A → ∞ (Colist A) → Colist A
+
+  {-# FOREIGN GHC
+    data Colist a    = Nil | Cons a (MAlonzo.RTE.Inf (Colist a))
+    type Colist' l a = Colist a
+
+    fromColist :: Colist a -> [a]
+    fromColist Nil         = []
+    fromColist (Cons x xs) = x : fromColist (MAlonzo.RTE.flat xs)
+    #-}
+
+  {-# COMPILE GHC Colist = data Colist' (Nil | Cons) #-}
+
+  postulate
+    putStr : Colist Char → IO ⊤
+
+  {-# COMPILE GHC putStr = putStr . fromColist #-}
+  ```
+
+* `COMPILE GHC` pragmas have been included for the size primitives
+  [Issue [#2879](https://github.com/agda/agda/issues/2879)].
+
+LaTeX backend
+-------------
+
+* The `code` environment can now take arguments [Issues
+  [#2744](https://github.com/agda/agda/issues/2744) and
+  [#2453](https://github.com/agda/agda/issues/2453)].
+
+  Everything from \begin{code} to the end of the line is preserved in
+  the generated LaTeX code, and not treated as Agda code.
+
+  The default implementation of the `code` environment recognises one
+  optional argument, `hide`, which can be used for code that should be
+  type-checked, but not typeset:
+  ```latex
+  \begin{code}[hide]
+    open import Module
+  \end{code}
+  ```
+
+  The `AgdaHide` macro has not been removed, but has been deprecated
+  in favour of `[hide]`.
+
+* The `AgdaSuppressSpace` and `AgdaMultiCode` environments no longer
+  take an argument.
+
+  Instead some documents need to be compiled multiple times.
+
+* The `--count-clusters` flag can now be given in `OPTIONS` pragmas.
+
+* The `nofontsetup` option to the LaTeX package `agda` was broken, and
+  has (hopefully) been fixed
+  [Issue [#2773](https://github.com/agda/agda/issues/2773)].
+
+  Fewer packages than before are loaded when `nofontsetup` is used,
+  see `agda.sty` for details. Furthermore, if LuaLaTeX or XeLaTeX are
+  not used, then the font encoding is no longer changed.
+
+* The new option `noinputencodingsetup` instructs the LaTeX package
+  `agda` to not change the input encoding, and to not load the `ucs`
+  package.
+
+* Underscores are now typeset using `\AgdaUnderscore{}`.
+
+  The default implementation is `\_` (the command that was previously
+  generated for underscores). Note that it is possible to override
+  this implementation.
+
+* OtherAspects (unsolved meta variables, catchall clauses, etc.) are
+  now correctly highlighted in the LaTeX backend (and the HTML one).
+  [Issue [#2474](https://github.com/agda/agda/issues/2474)]
+
+* `postprocess-latex.pl` does not add extra spaces around tagged `\Agda*{}`
+  commands anymore.
+
+HTML backend
+------------
+
+* An identifier (excluding bound variables),
+  gets the identifier itself as an anchor,
+  _in addition_ to the file position
+  [Issue [#2756](https://github.com/agda/agda/issues/2756)].
+  In Agda 2.5.3, the identifier anchor would _replace_ the file position anchor
+  [Issue [#2604](https://github.com/agda/agda/issues/2604)].
+
+  Symbolic anchors look like
+  ```html
+  <a id="test1">
+  <a id="M.bla">
+  ```
+  while file position anchors just give the character position in the file:
+  ```html
+  <a id="42">
+  ```
+
+  Top-level module names do not get a symbolic anchor, since the position of
+  a top-level module is defined to be the beginning of the file.
+
+  Example:
+
+  ```agda
+  module Issue2604 where   -- Character position anchor
+
+  test1 : Set₁             -- Issue2604.html#test1
+  test1 = bla
+    where
+    bla = Set              -- Only character position anchor
+
+  test2 : Set₁             -- Issue2604.html#test2
+  test2 = bla
+    where
+    bla = Set              -- Only character position anchor
+
+  test3 : Set₁             -- Issue2604.html#test3
+  test3 = bla
+    module M where         -- Issue2604.html#M
+    bla = Set              -- Issue2604.html#M.bla
+
+  module NamedModule where -- Issue2604.html#NamedModule
+    test4 : Set₁           -- Issue2604.html#NamedModule.test4
+    test4 = M.bla
+
+  module _ where           -- Only character position anchor
+    test5 : Set₁           -- Only character position anchor
+    test5 = M.bla
+  ```
+
+List of closed issues
+---------------------
+
+For 2.5.4, the following issues have been closed
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  - [#351](https://github.com/agda/agda/issues/351): Constraint solving for irrelevant metas
+  - [#421](https://github.com/agda/agda/issues/421): Higher order positivity
+  - [#431](https://github.com/agda/agda/issues/431): Constructor-headed function makes type-checker diverge
+  - [#437](https://github.com/agda/agda/issues/437): Detect when something cannot be a function type
+  - [#488](https://github.com/agda/agda/issues/488): Refining on user defined syntax mixes up the order of the subgoals
+  - [#681](https://github.com/agda/agda/issues/681): Lack of visual state indicators in new Emacs mode
+  - [#689](https://github.com/agda/agda/issues/689): Contradictory constraints should yield error
+  - [#708](https://github.com/agda/agda/issues/708): Coverage checker not taking literal patterns into account properly
+  - [#875](https://github.com/agda/agda/issues/875): Nonstrict irrelevance violated by implicit inference
+  - [#964](https://github.com/agda/agda/issues/964): Allow unsolved metas in imported files
+  - [#987](https://github.com/agda/agda/issues/987): --html anchors could be more informative
+  - [#1054](https://github.com/agda/agda/issues/1054): Inlined Agda code in LaTeX backend
+  - [#1131](https://github.com/agda/agda/issues/1131): Infix definitions not allowed in let definitions
+  - [#1169](https://github.com/agda/agda/issues/1169): Auto fails with non-terminating function
+  - [#1268](https://github.com/agda/agda/issues/1268): Hard to print type of variable if the type starts with an instance argument
+  - [#1384](https://github.com/agda/agda/issues/1384): Order of constructor arguments matters for coverage checker
+  - [#1425](https://github.com/agda/agda/issues/1425): Instances with relevant recursive instance arguments are not considered in irrelevant positions
+  - [#1548](https://github.com/agda/agda/issues/1548): Confusing error about ambiguous definition with parametrized modules
+  - [#1884](https://github.com/agda/agda/issues/1884): what is the format of the libraries and defaults files
+  - [#1906](https://github.com/agda/agda/issues/1906): Possible performance problem
+  - [#2056](https://github.com/agda/agda/issues/2056): Cannot instantiate meta to solution...: Pattern checking done too early in where block
+  - [#2067](https://github.com/agda/agda/issues/2067): Display forms in parameterised module too general
+  - [#2183](https://github.com/agda/agda/issues/2183): Allow splitting on dotted variables
+  - [#2226](https://github.com/agda/agda/issues/2226): open {{...}} gets hiding wrong
+  - [#2255](https://github.com/agda/agda/issues/2255): Performance issue with deeply-nested lambdas
+  - [#2306](https://github.com/agda/agda/issues/2306): Commands in the emacs-mode get confused if we add question marks to the file
+  - [#2384](https://github.com/agda/agda/issues/2384): More fine-grained blocking in constraint solver
+  - [#2401](https://github.com/agda/agda/issues/2401): LaTeX backend error
+  - [#2404](https://github.com/agda/agda/issues/2404): checkType doesn't accept a type-checking definition checked with the same type
+  - [#2420](https://github.com/agda/agda/issues/2420): Failed to solve level constraints in record type with hole
+  - [#2421](https://github.com/agda/agda/issues/2421): After emacs starts up, Agda does not process file without restart of Agda
+  - [#2436](https://github.com/agda/agda/issues/2436): Agda allows coinductive records with eta-equality
+  - [#2450](https://github.com/agda/agda/issues/2450): Irrelevant variables are pruned too eagerly
+  - [#2474](https://github.com/agda/agda/issues/2474): The LaTeX and HTML backends do not highlight (all) unsolved metas
+  - [#2484](https://github.com/agda/agda/issues/2484): Regression related to sized types
+  - [#2526](https://github.com/agda/agda/issues/2526): Better documentation of record modules
+  - [#2536](https://github.com/agda/agda/issues/2536): UTF8 parsed incorrectly for literate agda files
+  - [#2565](https://github.com/agda/agda/issues/2565): Options for the interaction action give to keep the overloaded literals and sections?
+  - [#2576](https://github.com/agda/agda/issues/2576): Shadowing data decl by data sig produces Missing type signature error
+  - [#2594](https://github.com/agda/agda/issues/2594): Valid partial cover rejected: "Cannot split on argument of non-datatype"
+  - [#2600](https://github.com/agda/agda/issues/2600): Stack complains about Agda.cabal
+  - [#2607](https://github.com/agda/agda/issues/2607): Instance search confused when an instance argument is sourced from a record
+  - [#2617](https://github.com/agda/agda/issues/2617): Installation instructions
+  - [#2623](https://github.com/agda/agda/issues/2623): Incorrect indentation when \AgdaHide is used
+  - [#2634](https://github.com/agda/agda/issues/2634): Fixity declaration ignored in definitions in record
+  - [#2636](https://github.com/agda/agda/issues/2636): The positivity checker complains when a new definition is added in the same where clause
+  - [#2640](https://github.com/agda/agda/issues/2640): Unifier dots the relevant pattern variables when it should dot the irrelevant ones
+  - [#2668](https://github.com/agda/agda/issues/2668): Changing the visibility of a module parameter breaks `with`
+  - [#2728](https://github.com/agda/agda/issues/2728): Bad interaction between caching and the warning machinery
+  - [#2738](https://github.com/agda/agda/issues/2738): Update Stackage LTS from 9.1 to version supporting Alex 3.2.3
+  - [#2744](https://github.com/agda/agda/issues/2744): It should be possible to give arguments to the code environment
+  - [#2745](https://github.com/agda/agda/issues/2745): Broken build with GHC 7.8.4 due to (new) version 1.2.2.0 of hashtables
+  - [#2749](https://github.com/agda/agda/issues/2749): Add --no-unicode cli option to Agda
+  - [#2751](https://github.com/agda/agda/issues/2751): Unsolved constraints, but no highlighting
+  - [#2752](https://github.com/agda/agda/issues/2752): Mutual blocks inside instance blocks
+  - [#2753](https://github.com/agda/agda/issues/2753): Unsolved constraint, related to instance arguments and sized types
+  - [#2756](https://github.com/agda/agda/issues/2756): HTML backend generates broken links
+  - [#2758](https://github.com/agda/agda/issues/2758): Relevant meta is instantiated with irrelevant solution
+  - [#2759](https://github.com/agda/agda/issues/2759): Empty mutual blocks should be warning rather than error
+  - [#2762](https://github.com/agda/agda/issues/2762): Automatically generate DISPLAY pragmas to fold pattern synonyms
+  - [#2763](https://github.com/agda/agda/issues/2763): Internal Error at "src/full/Agda/TypeChecking/Abstract.hs:138"
+  - [#2765](https://github.com/agda/agda/issues/2765): Inferred level expressions are often "reversed"
+  - [#2769](https://github.com/agda/agda/issues/2769): Agda prints ill-formed expression, record argument dropped
+  - [#2771](https://github.com/agda/agda/issues/2771): Erroneous 'with' error message
+  - [#2773](https://github.com/agda/agda/issues/2773): The nofontsetup option does not work as advertised
+  - [#2775](https://github.com/agda/agda/issues/2775): Irrelevance to be taken into account in 'with' abstraction.
+  - [#2776](https://github.com/agda/agda/issues/2776): Dotted variable in inferred type
+  - [#2780](https://github.com/agda/agda/issues/2780): Improve level constraint solving for groups of inequality constraints
+  - [#2782](https://github.com/agda/agda/issues/2782): Extending Agda reflection to introduce postulates
+  - [#2785](https://github.com/agda/agda/issues/2785): internal error @ ConcreteToAbstract.hs:721
+  - [#2787](https://github.com/agda/agda/issues/2787): Overloaded pattern synonyms
+  - [#2792](https://github.com/agda/agda/issues/2792): Safe modules can sometimes not be imported from unsafe modules
+  - [#2794](https://github.com/agda/agda/issues/2794): Using \texttt{-} destroys code coloring in literate file
+  - [#2796](https://github.com/agda/agda/issues/2796): Overloaded (inherited) projection resolution fails with parametrized record
+  - [#2798](https://github.com/agda/agda/issues/2798): The LaTeX backend ignores the "operator" aspect
+  - [#2802](https://github.com/agda/agda/issues/2802): Printing of overloaded functions broken due to eager normalization of projections
+  - [#2803](https://github.com/agda/agda/issues/2803): Case splitting loses names of hidden arguments
+  - [#2808](https://github.com/agda/agda/issues/2808): Confusing error when inserting declaration before top-level module
+  - [#2810](https://github.com/agda/agda/issues/2810): Make `--caching` a pragma option
+  - [#2811](https://github.com/agda/agda/issues/2811): OPTION --caching allowed in file (Issue #2810)
+  - [#2819](https://github.com/agda/agda/issues/2819): Forcing analysis doesn't consider relevance
+  - [#2821](https://github.com/agda/agda/issues/2821): BUILTIN BOOL gremlin
+  - [#2824](https://github.com/agda/agda/issues/2824): Allow {-# BUILTIN #-} in preamble and in parametrized modules
+  - [#2826](https://github.com/agda/agda/issues/2826): Case splitting on earlier variable uses duplicate variable name
+  - [#2827](https://github.com/agda/agda/issues/2827): Variables off in with-clauses.  Parameter refinement?
+  - [#2831](https://github.com/agda/agda/issues/2831): NO_POSITIVITY_CHECK pragma can be written before a mutual block without data or record types
+  - [#2832](https://github.com/agda/agda/issues/2832): BUILTIN NIL and CONS are not needed
+  - [#2834](https://github.com/agda/agda/issues/2834): Disambiguation of type based on pattern leads to non-unique meta solution
+  - [#2836](https://github.com/agda/agda/issues/2836): The Emacs mode does not handle .lagda.tex files
+  - [#2840](https://github.com/agda/agda/issues/2840): Internal error in positivity with modules/datatype definitions
+  - [#2841](https://github.com/agda/agda/issues/2841): Opting out of idiom brackets
+  - [#2844](https://github.com/agda/agda/issues/2844): Root documentation URL redirects to version 2.5.2
+  - [#2849](https://github.com/agda/agda/issues/2849): Internal error at absurd pattern followed by `rewrite`
+  - [#2854](https://github.com/agda/agda/issues/2854): Agda worries about possibly empty type of sizes even when no builtins for size are active
+  - [#2855](https://github.com/agda/agda/issues/2855): Single-clause definition is both unreachable and incomplete
+  - [#2856](https://github.com/agda/agda/issues/2856): Panic: unbound variable
+  - [#2859](https://github.com/agda/agda/issues/2859): Error "pattern variable shadows constructor" caused by parameter refinement
+  - [#2862](https://github.com/agda/agda/issues/2862): inconsistency from a mutual datatype declaration and module definition
+  - [#2867](https://github.com/agda/agda/issues/2867): Give does not insert parenthesis for module parameters
+  - [#2868](https://github.com/agda/agda/issues/2868): With --postfix-projections, record fields are printed preceded by a dot when working within the record
+  - [#2870](https://github.com/agda/agda/issues/2870): Lexical error for \- (hyphen)
+  - [#2871](https://github.com/agda/agda/issues/2871): Introduce just trailing hidden arguments by result splitting
+  - [#2873](https://github.com/agda/agda/issues/2873): Refinement problem in presence of overloaded constructors
+  - [#2874](https://github.com/agda/agda/issues/2874): Internal error in src/full/Agda/TypeChecking/Coverage/Match.hs:312
+  - [#2878](https://github.com/agda/agda/issues/2878): Support for GHC 8.4.1
+  - [#2879](https://github.com/agda/agda/issues/2879): Include COMPILE GHC pragmas for size primitives
+  - [#2881](https://github.com/agda/agda/issues/2881): Internal error in BasicOps
+  - [#2883](https://github.com/agda/agda/issues/2883): "internal error in TypeChecking/Substitute.hs:379"
+  - [#2884](https://github.com/agda/agda/issues/2884): Missing PDF user manual in the tarball
+  - [#2888](https://github.com/agda/agda/issues/2888): Internal error caused by new forcing translation
+  - [#2894](https://github.com/agda/agda/issues/2894): Unifier tries to eta expand non-eta record
+  - [#2896](https://github.com/agda/agda/issues/2896): Unifier throws away pattern
+  - [#2897](https://github.com/agda/agda/issues/2897): Internal error for local modules with refined parameters
+  - [#2904](https://github.com/agda/agda/issues/2904): No tab completion for GHCNoMain
+  - [#2906](https://github.com/agda/agda/issues/2906): Confusing "cannot be translated to a Haskell type" error message
+  - [#2908](https://github.com/agda/agda/issues/2908): primForce is compiled away
+  - [#2909](https://github.com/agda/agda/issues/2909): Agda uses newtypes incorrectly, causing wellformed programs to loop
+  - [#2911](https://github.com/agda/agda/issues/2911): Inferring missing instance clause panics in refined context
+  - [#2912](https://github.com/agda/agda/issues/2912): Add fine-grained control over the displayed warnings
+  - [#2914](https://github.com/agda/agda/issues/2914): Slicing ignores as pragma?
+  - [#2916](https://github.com/agda/agda/issues/2916): The GHC backend generates code with an incorrect number of constructor arguments
+  - [#2917](https://github.com/agda/agda/issues/2917): Very slow due to unsolved size?
+  - [#2919](https://github.com/agda/agda/issues/2919): Internal error in Agda.TypeChecking.Forcing
+  - [#2921](https://github.com/agda/agda/issues/2921): COMPILE data for data types with erased constructor arguments
+  - [#2923](https://github.com/agda/agda/issues/2923): Word.agda not included as builtin
+  - [#2925](https://github.com/agda/agda/issues/2925): Allow adding the same rewrite rules multiple times
+  - [#2927](https://github.com/agda/agda/issues/2927): Panic related to sized types
+  - [#2928](https://github.com/agda/agda/issues/2928): Internal error in Agda.TypeChecking.Rules.LHS
+  - [#2931](https://github.com/agda/agda/issues/2931): Rename Agda.Builtin.Size.ω to ∞?
+  - [#2941](https://github.com/agda/agda/issues/2941): "coinductive" record inconsistent
+  - [#2944](https://github.com/agda/agda/issues/2944): Regression, seemingly related to record expressions
+  - [#2945](https://github.com/agda/agda/issues/2945): Inversion warning in code that used to be accepted
+  - [#2947](https://github.com/agda/agda/issues/2947): Internal error in Agda.TypeChecking.Forcing
+  - [#2952](https://github.com/agda/agda/issues/2952): Wrong compilation of pattern matching to Haskell
+  - [#2953](https://github.com/agda/agda/issues/2953): Generated Haskell code does not typecheck
+  - [#2954](https://github.com/agda/agda/issues/2954): Pattern matching on string gives unexpected unreachable clause
+  - [#2957](https://github.com/agda/agda/issues/2957): Support for async 2.2.1
+  - [#2958](https://github.com/agda/agda/issues/2958): `as` names being duplicated in buffer after `with`
+  - [#2959](https://github.com/agda/agda/issues/2959): Repeating a successful command after revert + reload fails with caching enabled
+  - [#2960](https://github.com/agda/agda/issues/2960): Uncommenting indented lines doesn't work
+  - [#2963](https://github.com/agda/agda/issues/2963): Extended lambdas bypass positivity checking in records
+  - [#2966](https://github.com/agda/agda/issues/2966): Internal error in Auto
+  - [#2968](https://github.com/agda/agda/issues/2968): Bad Interaction with copatterns and eta?, leads to ill-typed terms in error messages.
+  - [#2971](https://github.com/agda/agda/issues/2971): Copattern split with `--no-irrelevant-projections` panics
+  - [#2974](https://github.com/agda/agda/issues/2974): Copatterns break canonicity
+  - [#2975](https://github.com/agda/agda/issues/2975): Termination checker runs too early for definitions inside record (or: positivity checker runs too late)
+  - [#2976](https://github.com/agda/agda/issues/2976): Emacs mode reports errors in connection with highlighting comments
+  - [#2978](https://github.com/agda/agda/issues/2978): Double solving of meta
+  - [#2985](https://github.com/agda/agda/issues/2985): The termination checker accepts non-terminating code
+  - [#2989](https://github.com/agda/agda/issues/2989): Internal error when checking record match in let expr
+  - [#2990](https://github.com/agda/agda/issues/2990): Performance regression related to the abstract machine
+  - [#2994](https://github.com/agda/agda/issues/2994): Solution accepted in hole is subsequently rejected on reload
+  - [#2996](https://github.com/agda/agda/issues/2996): Internal error with -v tc.cover:20
+  - [#2997](https://github.com/agda/agda/issues/2997): Internal error in Agda.TypeChecking.Rules.LHS
+  - [#2998](https://github.com/agda/agda/issues/2998): Regression: With clause pattern x is not an instance of its parent pattern "eta expansion of x"
+  - [#3002](https://github.com/agda/agda/issues/3002): Spurious 1 after simplification
+  - [#3004](https://github.com/agda/agda/issues/3004): Agda hangs on extended lambda
+  - [#3007](https://github.com/agda/agda/issues/3007): Internal error in Parser
+  - [#3012](https://github.com/agda/agda/issues/3012): Internal Error at : "src/full/Agda/TypeChecking/Reduce/Fast.hs:1030"
+  - [#3014](https://github.com/agda/agda/issues/3014): Internal error in Rules.LHS
+  - [#3020](https://github.com/agda/agda/issues/3020): Missing highlighting in record modules
+  - [#3023](https://github.com/agda/agda/issues/3023): Support for GHC 8.4.2
+  - [#3024](https://github.com/agda/agda/issues/3024): Postfix projection patterns not highlighted correctly with agda --latex
+  - [#3030](https://github.com/agda/agda/issues/3030): [ warning ] user defined warnings
+  - [#3031](https://github.com/agda/agda/issues/3031): Eta failure for record meta with irrelevant fields
+  - [#3033](https://github.com/agda/agda/issues/3033): Giving and solving don't insert parenthesis for applications in dot pattern
+  - [#3044](https://github.com/agda/agda/issues/3044): Internal error in src/full/Agda/TypeChecking/Substitute/Class.hs:209
+  - [#3045](https://github.com/agda/agda/issues/3045): GHC backend generates type without enough arguments
+  - [#3046](https://github.com/agda/agda/issues/3046): do-notation causes parse errors in subsequent where clauses
+  - [#3049](https://github.com/agda/agda/issues/3049): Positivity unsoundness
+  - [#3050](https://github.com/agda/agda/issues/3050): We revert back to call-by-name during positivity checking
+  - [#3051](https://github.com/agda/agda/issues/3051): Pattern synonyms should be allowed in mutual blocks
+  - [#3052](https://github.com/agda/agda/issues/3052): Another recent inference change
+  - [#3062](https://github.com/agda/agda/issues/3062): Literal match does not respect first-match semantics
+  - [#3063](https://github.com/agda/agda/issues/3063): Internal error in Agda.TypeChecking.Forcing
+  - [#3064](https://github.com/agda/agda/issues/3064): Coverage checker bogus on literals combined with copatterns
+  - [#3065](https://github.com/agda/agda/issues/3065): Internal error in coverage checker triggered by literal dot pattern
+  - [#3067](https://github.com/agda/agda/issues/3067): checking hangs on invalid program
+  - [#3072](https://github.com/agda/agda/issues/3072): invalid section printing
+  - [#3074](https://github.com/agda/agda/issues/3074): Wrong hiding causes internal error in LHS checker
+  - [#3075](https://github.com/agda/agda/issues/3075): Automatic inlining and tactics
+  - [#3078](https://github.com/agda/agda/issues/3078): Error building with GHC 7.10.2: Missing transformers library
+  - [#3079](https://github.com/agda/agda/issues/3079): Wrong parameter hiding for instance open
+  - [#3080](https://github.com/agda/agda/issues/3080): Case splitting prints out-of-scope pattern synonyms
+  - [#3082](https://github.com/agda/agda/issues/3082): Emacs mode regression: a ? inserted before existing hole hijacks its interaction point
+  - [#3083](https://github.com/agda/agda/issues/3083): Wrong hiding in module application
+  - [#3084](https://github.com/agda/agda/issues/3084): Changes to mode line do not take effect immediately
+  - [#3085](https://github.com/agda/agda/issues/3085): Postpone checking a pattern let binding when type is blocked
+  - [#3090](https://github.com/agda/agda/issues/3090): Internal error in parser when using parentheses in BUILTIN pragma
+  - [#3096](https://github.com/agda/agda/issues/3096): Support GHC 8.4.3
diff --git a/doc/release-notes/2.6.0.1.md b/doc/release-notes/2.6.0.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.0.1.md
@@ -0,0 +1,22 @@
+Release notes for Agda version 2.6.0.1
+======================================
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.6.5.
+
+List of all closed issues
+-------------------------
+
+For 2.6.0.1, the following issues have been closed
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  -  [#3685](https://github.com/agda/agda/issues/3685): Support GHC 8.6.5
+  -  [#3692](https://github.com/agda/agda/issues/3692): Omission of absurd patterns in automatically added absurd clauses causes too optimistic polarity.
+  -  [#3694](https://github.com/agda/agda/issues/3694): Importing Agda.Builtin.Size in one module affects another module
+  -  [#3696](https://github.com/agda/agda/issues/3696): Make `AgdaAny` polykinded?
+  -  [#3697](https://github.com/agda/agda/issues/3697): Panic when checking non-Setω data definitions with --type-in-type
+  -  [#3701](https://github.com/agda/agda/issues/3701): [ re agda/agda-stdlib#710 ] toNat for machine words is injective
+  -  [#3731](https://github.com/agda/agda/issues/3731): GHC backend thinks that a constructor called 'main' is the main program
+  -  [#3742](https://github.com/agda/agda/issues/3742): Strange error message for code that combines mutual and abstract
diff --git a/doc/release-notes/2.6.0.md b/doc/release-notes/2.6.0.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.0.md
@@ -0,0 +1,849 @@
+Release notes for Agda version 2.6.0
+====================================
+
+Highlights
+----------
+
+* Added support for [Cubical
+  Agda](https://agda.readthedocs.io/en/v2.6.0/language/cubical.html)
+  which adds new features such as univalence and higher inductive
+  types to Agda.
+
+* Added support for ML-style [automatic generalization of
+  variables](https://agda.readthedocs.io/en/v2.6.0/language/generalization-of-declared-variables.html).
+
+* Added a new sort ``Prop`` of [definitionally proof-irrelevant
+  propositions](https://agda.readthedocs.io/en/v2.6.0/language/prop.html).
+
+* The implementation of [instance
+  search](https://agda.readthedocs.io/en/v2.6.0/language/instance-arguments.html)
+  got a major overhaul and no longer supports overlapping instances
+  (unless enabled by a flag).
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.6.4.
+
+* Interface files for all builtin and primitive files are now
+  re-generated each time Agda is installed.
+
+Syntax
+------
+
+* Agda now supports implicit generalization of declared
+  variables. Variables to be generalized can declared with the new
+  keyword `variable`.  For example:
+
+  ```agda
+    postulate
+      Con : Set
+
+    variable
+      Γ Δ θ : Con
+  ```
+
+  Declared variables are automatically generalized in type signatures,
+  module telescopes and data type and record parameters and indices:
+
+  ```agda
+    postulate
+      Sub : Con → Con → Set
+
+      id  : Sub Γ Γ
+   -- -- equivalent to
+   -- id  : {Γ : Con} → Sub Γ Γ
+
+      _∘_ : Sub Θ Δ → Sub Γ Θ → Sub Γ Δ
+   -- -- equivalent to
+   -- _∘_ : {Γ Δ Θ : Con} → Sub Θ Δ → Sub Γ Θ → Sub Γ Δ
+  ```
+
+  See the [user manual](https://agda.readthedocs.io/en/v2.6.0/language/generalization-of-declared-variables.html)
+  for more details.
+
+* Data type and record definitions separated from their type signatures can no
+  longer repeat the types of the parameters, but can bind implicit parameters
+  by name [Issue [#1886](https://github.com/agda/agda/issues/1886)].
+
+  This is now allowed
+  ```agda
+    data D {a b} (A : Set a) (B : Set b) : Set (a ⊔ lsuc b)
+    data D {b = b} A B where
+      mkD : (A → Set b) → D A B
+  ```
+  but this is not
+  ```agda
+    data I (A : Set) : Set
+    data I (A : Set) where
+  ```
+
+* The label used for named implicit arguments can now be different from the
+  name of the bound variable [Issue [#952](https://github.com/agda/agda/issues/952)].
+
+  Example,
+  ```agda
+    id₁ : {A = X : Set} → X → X
+    id₁ x = x
+
+    id₂ : ∀ {B = X} → X → X
+    id₂ {B = X} x = id₁ {A = X} x
+
+    test : Nat
+    test = id₁ {A = Nat} 5 + id₂ {B = Nat} 6
+  ```
+  Only implicit and instance arguments can have a label and either or both of
+  the label and bound variable can be `_`. Labeled bindings with a type
+  signature can only bind a single variable. For instance, the type `Set` has
+  to be repeated here:
+  ```agda
+    const : {A = X : Set} {B = Y : Set} → X → Y → X
+    const x _ = x
+  ```
+
+* The rules for parsing of patterns have changed slightly [Issue
+  [#3400](https://github.com/agda/agda/issues/3400)].
+
+  Now projections are treated similarly to constructors: In a pattern
+  name parts coming from projections can only be used as part of
+  projections, constructors or pattern synonyms. They cannot be used
+  as variables, or as part of the name of the defined value.
+
+  Examples:
+
+  * The following code used to be syntactically ambiguous, but is now
+    parsed, because A can no longer be used as a variable:
+    ```agda
+    record R : Set₂ where
+      field
+        _A : Set₁
+
+    open R
+
+    r : R
+    r A = Set
+    ```
+
+  * On the other hand the following code is no longer parsed:
+    ```agda
+    record R : Set₁ where
+      field
+        ⟨_+_⟩ : Set
+
+    open R
+
+    + : Set → Set
+    + A = A
+    ```
+
+
+Type checking
+-------------
+
+* Agda now supports a cubical mode which adds new features from
+  [Cubical Type Theory](https://arxiv.org/abs/1611.02108), including
+  univalence and higher inductive types. Option `--cubical` enables
+  the cubical mode, and cubical primitives are defined in the module
+  `Agda.Primitive.Cubical`.  See the [user
+  manual](https://agda.readthedocs.io/en/v2.6.0/language/cubical.html)
+  for more info.
+
+* Agda now supports the new sort ``Prop`` of [definitionally
+  proof-irrelevant propositions](https://hal.inria.fr/hal-01859964).
+  Option `--prop` enables the `Prop` universe but is off by default.
+  Option `--no-prop` disables the `Prop` universe.  See the [user
+  manual](https://agda.readthedocs.io/en/v2.6.0/language/prop.html)
+  for more details.
+
+  In the absense of `Prop`, the sort `Set` is the lowest sort, thus,
+  the sort annotation `: Set` can be ommitted if the sort is
+  constrained to be weakly below `Set`.  For instance:
+
+  ```agda
+  {-# OPTIONS --no-prop #-}
+
+  data Wrap A : Set where
+    wrap : A → Wrap A
+  ```
+
+  In contrast, when `--prop` is enabled the sort of `A` could be
+  either `Set` or `Prop` so this code no longer typechecks.
+
+* Agda now allows omitting absurd clauses in case one of the pattern
+  variable inhabits an obviously empty type
+  [Issue [#1086](https://github.com/agda/agda/issues/1086)].
+  For example:
+  ```agda
+  f : Fin 1 → Nat
+  f zero = 0
+  -- f (suc ())   -- this clause is no longer required
+  ```
+  Absurd clauses are still required in case deep pattern matching is
+  needed to expose the absurd variable, or if there are no non-absurd
+  clauses.
+
+  Due to the changes to the coverage checker required for this new
+  feature, Agda will now sometimes construct a different case tree when
+  there are multiple valid splitting orders. In some cases this may
+  impact the constraints that Agda is able to solve (for example, see
+  [#673](https://github.com/agda/agda-stdlib/pull/673) on the
+  standard library).
+
+* Since Agda 2.5.3, the hiding is considered part of the name in the
+  insertion of implicit arguments.  Until Agda 2.5.2, the following
+  code was rejected:
+  ```agda
+    test : {{X : Set}} {X : Set} → Set
+    test {X = X} = X
+  ```
+  The rationale was that named argument `X` is given with the wrong hiding.
+  The new rationale is that the hiding is considered part of the name,
+  distinguishing `{{X}}` from `{X}`.
+  This language change was accidential and has not been documented in
+  the 2.5.3 release notes.
+
+* Agda no longer allows case splitting on irrelevant arguments of
+  record types (see Issue
+  [#3056](https://github.com/agda/agda/issues/3056)).
+
+* Metavariables in module telescopes are now sometimes frozen later
+  [Issue [#1063](https://github.com/agda/agda/issues/1063)].
+
+  Metavariables created in the types of module parameters used to be
+  frozen right after the module's first mutual block had been
+  type-checked (unless, perhaps, if the module itself was contained in
+  a mutual block). Now they are instead frozen at the end of the
+  module (with a similar caveat regarding an outer mutual block).
+
+* When `--without-K` is enabled, Agda no longer allows datatypes with
+  large indices. For example, the following definition of equality is
+  now forbidden when `--without-K` is enabled:
+  ```agda
+    data _≡₀_ {ℓ} {A : Set ℓ} (x : A) : A → Set where
+      refl : x ≡₀ x
+  ```
+
+* The termination checker now also looks for recursive calls in the type of definitions.
+  This fixes an issue where Agda allowed very dependent types
+  [Issue [#1556](https://github.com/agda/agda/issues/1556)].
+
+  This change affects induction-induction, e.g.
+  ```agda
+    mutual
+      data Cxt : Set where
+        ε    :  Cxt
+        _,_  :  (Γ : Cxt) (A : Ty Γ) → Cxt
+
+      data Ty : (Γ : Cxt) → Set where
+        u  :  ∀ Γ → Ty Γ
+        Π  :  ∀ Γ (A : Ty Γ) (B : Ty (Γ , A)) → Ty Γ
+
+    mutual
+      f : Cxt → Cxt
+      f ε        =  ε
+      f (Γ , T)  =  (f Γ , g Γ T)
+
+      g : ∀ Γ → Ty Γ → Ty (f Γ)
+      g Γ (u .Γ)      =  u (f Γ)
+      g Γ (Π .Γ A B)  =  Π (f Γ) (g Γ A) (g (Γ , A) B)
+
+  ```
+  The type of `g` contains a call `g Γ _ --> f Γ` which is now taken
+  into account during termination checking.
+
+Instance search
+---------------
+
+* Instance argument resolution now also applies when there are
+  unconstrained metavariables in the type of the argument. For
+  example, if there is a single instance `eqBool : Eq Bool` in scope,
+  then an instance argument `{{eq : Eq _}}` will be solved to
+  `eqBool`, setting the value of the metavariable `_` to `Bool` in the
+  process.
+
+* By default, Agda no longer allows overlapping instances. Two
+  instances are defined to overlap if they could both solve the
+  instance goal when given appropriate solutions for their recursive
+  (instance) arguments. Agda used to choose between undecidable
+  instances based on the result of recursive instance search, but this
+  lead to an exponential slowdown in instance resolution. Overlapping
+  instances can be enabled with the flag `--overlapping-instances`.
+
+* Explicit arguments are no longer automatically turned into instance
+  arguments for the purpose of recursive instance search. Instead,
+  explicit arguments are left unresolved and will thus never be used
+  for instance search.
+
+  If an instance is declared which has explicit arguments, Agda will
+  raise a warning that this instance will never be considered by
+  instance search.
+
+* Instance arguments that are already solved by conversion checking
+  are no longer ignored by instance search. Thus the constructor of
+  the unit type must now be explicitly be declared as an instance in
+  order to be considered by instance search:
+  ```agda
+    record ⊤ : Set where
+      instance constructor tt
+  ```
+
+* Instances are now (correctly) required to be in scope to be eligible
+  (see Issue [#1913](https://github.com/agda/agda/issues/1913)
+   and Issue [#2489](https://github.com/agda/agda/issues/2489)
+  ).
+  This means that you can no longer import instances from parameterised modules by
+  ```agda
+    import Some.Module Arg₁ Arg2
+  ```
+  without opening or naming the module.
+
+Reflection
+----------
+
+* New TC primitive `noConstraints` [Issue
+  [#2351](https://github.com/agda/agda/issues/2351)]:
+
+  ```agda
+    noConstraints : ∀ {a} {A : Set a} → TC A → TC A
+  ```
+
+  The computation `noConstraints m` fails if `m` gives rise to new,
+  unsolved
+  ["blocking"](https://github.com/agda/agda/blob/4900ef5fc61776381f3a5e9c94ef776375e9e1f1/src/full/Agda/TypeChecking/Monad/Constraints.hs#L160-L174)
+  constraints.
+
+* New TC primitive `runSpeculative` [Issue
+  [#3346](https://github.com/agda/agda/issues/3346)]:
+
+  ```
+    runSpeculative : ∀ {a} {A : Set a} → TC (Σ A λ _ → Bool) → TC A
+  ```
+
+  The computation `runSpeculative m` runs `m` and either keeps the new
+  TC state (if the second component is `true`) or resets to the old TC
+  state (if it is `false`).
+
+
+Interaction and error reporting
+-------------------------------
+
+* A new command `agda2-elaborate-give` (C-c C-m) normalizes a goal input
+  (it respects the C-u prefixes), type checks, and inserts the normalized
+  term into the goal.
+
+* 'Solve constraints' (C-c C-s) now turns unsolved metavariables into new
+  interaction holes (see Issue [#2273](https://github.com/agda/agda/issues/2273)).
+
+* Out-of-scope identifiers are no longer prefixed by a '.' dot [Issue
+  [#3127](https://github.com/agda/agda/issues/3127)].  This notation
+  could be confused with dot patterns, postfix projections, and
+  irrelevance. Now Agda will do its best to make up fresh names for
+  out-of-scope identifiers that do not conflict with any existing
+  names. In addition, these names are marked as "(out of scope)" when
+  printing the context.
+
+  The change affects the printing of terms, e.g. in error messages and
+  interaction, and the parsing of out-of-scope variables for
+  case splitting (`C-c C-c` in emacs).
+
+* Shadowed local variables are now assigned fresh names in error
+  messages and interactive goals [Issue
+  [#572](https://github.com/agda/agda/issues/572)]. For example,
+  consider the following piece of code:
+  ```agda
+    postulate P : Set -> Set
+
+    test : (B : Set) -> P B -> P B
+    test = λ p p -> {!!}
+  ```
+  When asking for the goal type, Agda will now print the following:
+  ```
+    Goal: P p₁
+    ————————————————————————————————————————————————————————————
+    p      : P p₁
+    p = p₁ : Set  (not in scope)
+  ```
+  Shadowed top-level identifiers are printed using the qualified name,
+  for example in
+  ```agda
+    module M where
+
+      postulate A : Set
+
+      test : Set → A
+      test A = {!!}
+  ```
+  Agda will now show the goal type as
+  ```
+    Goal: M.A
+    ————————————————————————————————————————————————————————————
+    A : Set
+  ```
+
+* When case splitting (`C-c C-c` in emacs), Agda will now filter out
+  impossible cases (i.e. ones where at least one of the variables
+  could be replaced by an absurd pattern `()`). If all the clauses
+  produced by a case split are impossible, Agda will not filter out
+  any of them.
+
+Pragmas and options
+-------------------
+
+* Consistency checking of options used.
+
+  Agda now checks that options used in imported modules are consistent
+  with each other, e.g. a module using `--safe`, `--without-K`,
+  `--no-universe-polymorphism` or `--no-sized-types` may only import
+  modules with the same option, and modules using `--cubical` or
+  `--prop` must in turn use the same option. If an interface file has
+  been generated using different options compared to the current ones,
+  Agda will now re-typecheck the file.
+  [Issue [#2487](https://github.com/agda/agda/issues/2487)].
+
+* New option `--cubical` to enable Cubical Agda.
+
+* New option `--prop` to enable the ``Prop`` sort, and `--no-prop` to
+  disable it (default).
+
+* New options `--guardedness` and `--no-guardedness` [Issue
+  [#1209](https://github.com/agda/agda/issues/1209)].
+
+  Constructor-based guarded corecursion is now only (meant to be)
+  allowed if the `--guardedness` option is active. This option is
+  active by default. The combination of constructor-based guarded
+  corecursion and sized types is not allowed if `--safe` is used,
+  and activating `--safe` turns off both `--guardedness` and
+  `--sized-types` (because this combination is known to be
+  inconsistent in the current implementation). If you want to use
+  either constructor-based guarded corecursion or sized types in
+  safe mode, then you can use `--safe --guardedness` or `--safe
+  --sized-types` respectively (in this order).
+
+  The option `--no-guardedness` turns off constructor-based guarded
+  corecursion.
+
+* Option `--irrelevant-projections` is now off by default and
+  not considered `--safe` any longer.
+  Reason: There are consistency issues that may be systemic
+  [Issue [#2170](https://github.com/agda/agda/issues/2170)].
+
+* New option `--no-syntactic-equality` disables the syntactic equality
+  shortcut used by the conversion checker. This will slow down
+  typechecking in most cases, but makes the performance more
+  predictable and stable under minor changes.
+
+* New option `--overlapping-instances` enables overlapping instances
+  by performing recursive instance search during pruning of instance
+  candidates (this used to be the default behaviour). Overlapping
+  instances can be disabled with `--no-overlapping-instances`
+  (default).
+
+* Option (and experimental feature)
+  `--guardedness-preserving-type-constructors`
+  has been removed.
+  [Issue [#3180](https://github.com/agda/agda/issues/3180)].
+
+* Deprecated options `--sharing` and `--no-sharing` now raise an error.
+
+* New primitive `primErase`. It takes a proof of equality and returns a proof of
+  the same equality. `primErase eq` reduces to `refl` on the diagonal. `trustMe`
+  is not a primitive anymore, it is implemented using `primErase`.
+
+  The primitive is declared in `Agda.Builtin.Equality.Erase`.
+
+* The `REWRITE` builtin is now bound to the builtin equality type from
+  `Agda.Builtin.Equality` in `Agda.Builtin.Equality.Rewrite` [Issue
+  [#3318](https://github.com/agda/agda/issues/3318)].
+
+* New primitives `primCharToNatInjective` and `primStringToListInjective`
+  internalising the fact that `primCharToNat` and `primStringtoList` are
+  injective functions. They are respectively bound in `Agda.Builtin.Char.Properties`
+  and `Agda.Builtin.String.Properties`.
+
+* The option `--only-scope-checking` is now allowed together with `--safe`.
+
+* The option `--ignore-interfaces` no longer ignores the interfaces of
+  builtin and primitive modules. For experts, there is the option
+  `--ignore-all-interfaces` which also rechecks builtin and primitive
+  files.
+
+* The following deprecated compiler pragmas have been removed:
+
+  ```
+    {-# COMPILED f e #-}
+    {-# COMPILED_TYPE A T #-}
+    {-# COMPILED_DATA A D C1 .. CN #-}
+    {-# COMPILED_DECLARE_DATA #-}
+    {-# COMPILED_EXPORT f g #-}
+    {-# IMPORT M #-}
+    {-# HASKELL code #-}
+    {-# COMPILED_UHC f e #-}
+    {-# COMPILED_DATA_UHC A D C1 .. CN #-}
+    {-# IMPORT_UHC M #-}
+    {-# COMPILED_JS f e #-}
+  ```
+
+  See the [user manual](https://agda.readthedocs.io/en/v2.6.0/language/foreign-function-interface.html)
+  for how to use the `COMPILE` and `FOREIGN` pragmas that replaced these in Agda 2.5.
+
+### New warnings
+
+* A declaration of the form `f : A` without an accompanying definition
+  is no longer an error, but instead raises a warning.
+
+* A clause that has both an absurd pattern and a right-hand side is no
+  longer an error, but instead raises a warning.
+
+* An import statement for `M` that mentions names not exported by `M`
+  (in either `using`, `hiding`, or `renaming`) is no longer an
+  error. Instead, Agda will raise a warning and ignore the names.
+
+* Pragma, primitive, module or import statements in a mutual block
+  are no longer errors. Instead, Agda will raise a warning and ignore
+  these statements.
+
+### Pragmas and options concerning universes
+
+* New pragma `{-# NO_UNIVERSE_CHECK #-}`.
+
+  The pragma `{-# NO_UNIVERSE_CHECK #-}` can be put in front of a data
+  or record type to disable universe consistency checking locally.
+  Example:
+  ```agda
+    {-# NO_UNIVERSE_CHECK #-}
+    data U : Set where
+      el : Set → U
+  ```
+  Like the similar pragmas for disabling termination and positivity
+  checking, `{-# NO_UNIVERSE_CHECK #-}` cannot be used with `--safe`.
+
+* New builtin `SETOMEGA`.
+
+  Agda's top sort `Setω` is now defined as a builtin in `Agda.Primitive`
+  and can be renamed when importing that module.
+
+* New option `--omega-in-omega`.
+
+  The option `--omega-in-omega` enables the typing rule `Setω : Setω`.
+  Example:
+  ```agda
+  {-# OPTIONS --omega-in-omega #-}
+  open import Agda.Primitive
+
+  data Type : Setω where
+    el : ∀ {ℓ} → Set ℓ → Type
+  ```
+  Like `--type-in-type`, this makes Agda inconsistent. However, code
+  written using `--omega-in-omega` is still compatible with normal
+  universe-polymorphic code and can be used in such files.
+
+Emacs mode
+----------
+
+* Jump-to-definition now works for record field names in record expressions
+  and patterns. [Issue [#3120](https://github.com/agda/agda/issues/3120)]
+  ```agda
+    record R : Set₂ where
+      field f : Set₁
+
+    exp : R
+    exp = record { f = Set }
+
+    pat : R → R
+    pat r@record { f = X } = record r { f = X }
+  ```
+  Jump-to-definition (`M-.` or middle-click) on any of these `f`s
+  now jumps to the field declaration.
+
+* Commas "ʻ،⸲⸴⹁⹉、︐︑﹐﹑，､" and semi-colons "؛⁏፤꛶；︔﹔⍮⸵;" added
+  to the input mode.
+
+* It is now possible to customise the highlighting of more text in
+  pragmas [Issue [#2452](https://github.com/agda/agda/issues/2452)].
+
+  Some text was already highlighted. Now there is a specific face for
+  the remaining text (`agda2-highlight-pragma-face`).
+
+LaTeX backend
+-------------
+
+* The code environment has two new options, `inline` and `inline*`.
+
+  These options are for typesetting inline code. The implementation of
+  these options is a bit of a hack. Only use these options for
+  typesetting a single line of code without multiple consecutive
+  whitespace characters (except at the beginning of the line).
+
+  When the option `inline*` is used space (`\AgdaSpace{}`) is added at
+  the end of the code, and when `inline` is used space is not added.
+
+* Now highlighting commands for things like "this is an unsolved
+  meta-variable" are applied on the outside of highlighting commands
+  for things like "this is a postulate" [Issue
+  [#2474](https://github.com/agda/agda/issues/2474)].
+
+  Example: Instead of generating
+  `\AgdaPostulate{\AgdaUnsolvedMeta{F}}` Agda now generates
+  `\AgdaUnsolvedMeta{\AgdaPostulate{F}}`.
+
+* The package `agda.sty` no longer selects any fonts, and no longer
+  changes the input or font encodings [Issue
+  [#3224](https://github.com/agda/agda/issues/3224)].
+
+  The new behaviour is the same as the old behaviour with the options
+  `nofontsetup` and `noinputencodingsetup`. These options have been
+  removed.
+
+  One reason for this change is that several persons have received
+  complaints from reviewers because they have unwittingly used
+  non-standard fonts in submitted papers. Another is that the `utf8x`
+  option to `inputenc` is now deprecated.
+
+  Note that Agda code is now less likely to typeset properly out of
+  the box. See the documentation for some hints about what to do if
+  this affects you.
+
+* Some text was by default typeset in math mode when LuaLaTeX or
+  XeLaTeX were used, and in text mode when pdfLaTeX was used. Now text
+  mode is the default for all of these engines.
+
+* Typesetting of pragmas should now work better [Issue
+  [#2452](https://github.com/agda/agda/issues/2452)].
+
+  The `\AgdaOption` command and `AgdaOption` colour have been replaced
+  by `\AgdaPragma` and `AgdaPragma`. The `\AgdaPragma` command is used
+  where `\AgdaOption` used to be used (for certain options), but also
+  in other cases (for other options and certain other text in
+  pragmas).
+
+* There is no longer any special treatment of the character `-` [Issue
+  [#2452](https://github.com/agda/agda/issues/2452)].
+
+  This might, depending on things like what font your are using, mean
+  that the token `--` is typeset like an en dash (–). However, this is
+  not the case for at least one common monospace font (in at least one
+  setting).
+
+* The default value of `\AgdaEmptySkip` has been changed from
+  `\baselineskip` to `\abovedisplayskip`. This could mean that less
+  vertical space is used to render empty lines in code blocks.
+
+HTML backend
+------------
+
+* New option `--html-highlight=[code,all,auto]`.
+
+  The option `--html-highlight=code` makes the HTML-backend generate
+  files with:
+
+  0. No HTML footer/header
+  1. Agda codes highlighted
+  2. Non-Agda code parts as-is
+  3. Output file extension as-is (i.e. `.lagda.md` becomes `.md`)
+  4. For ReStructuredText, a `.. raw:: html\n` will be inserted
+     before every code blocks
+
+  This makes it possible to use an ordinary Markdown/ReStructuredText
+  processor to render the generated HTML.
+
+  This will affect all the files involved in one compilation, making
+  pure Agda code files rendered without HTML footer/header as well.
+  To use `code` with literate Agda files and `all` with pure Agda
+  files, use `--html-highlight=auto`, which means auto-detection.
+
+  The old and default behaviour is still `--html-highlight=all`.
+
+List of all closed issues
+-------------------------
+
+For 2.6.0, the following issues have been closed
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  -  [#572](https://github.com/agda/agda/issues/572): Shadowed identifiers should be preceded by a dot when printed
+  -  [#723](https://github.com/agda/agda/issues/723): Instance search needs to know whether a meta must be a function type
+  -  [#758](https://github.com/agda/agda/issues/758): No highlighting for syntax declarations
+  -  [#887](https://github.com/agda/agda/issues/887): Case-split causes problems for coverage checker
+  -  [#952](https://github.com/agda/agda/issues/952): Parse named implicit pi {x = y : A} -> B
+  -  [#1003](https://github.com/agda/agda/issues/1003): No highlighting for ambiguous instance argument
+  -  [#1063](https://github.com/agda/agda/issues/1063): Freeze metas in module telescope after checking the module?
+  -  [#1086](https://github.com/agda/agda/issues/1086): Make absurd patterns not needed at toplevel
+  -  [#1209](https://github.com/agda/agda/issues/1209): Guardedness checker inconsistency with copatterns
+  -  [#1581](https://github.com/agda/agda/issues/1581): Fields of opened records sometimes highlighted, sometimes not
+  -  [#1602](https://github.com/agda/agda/issues/1602): NonStrict arguments should be allowed to occur relevantly in the type
+  -  [#1706](https://github.com/agda/agda/issues/1706): Feature request: ML-style forall-generalization
+  -  [#1764](https://github.com/agda/agda/issues/1764): Type in type and universe polymorphism
+  -  [#1886](https://github.com/agda/agda/issues/1886): Second copies of telescopes not checked?
+  -  [#1909](https://github.com/agda/agda/issues/1909): parameters are not dropped from reflected pattern lambda
+  -  [#1913](https://github.com/agda/agda/issues/1913): Names that are not in scope can sometimes be candidates for instance resolution
+  -  [#1995](https://github.com/agda/agda/issues/1995): Correct names in goal types after multiple renaming imports.
+  -  [#2044](https://github.com/agda/agda/issues/2044): Better diagnosis for failed instance search
+  -  [#2089](https://github.com/agda/agda/issues/2089): ''No such module'' is a rude error message for private modules
+  -  [#2153](https://github.com/agda/agda/issues/2153): PDF version of Language Documentation on readthedocs lacks most Unicode characters
+  -  [#2273](https://github.com/agda/agda/issues/2273): C-c C-s should put new goals instead of underscores for unknown subterms
+  -  [#2351](https://github.com/agda/agda/issues/2351): expose noConstraints to reflection framework
+  -  [#2452](https://github.com/agda/agda/issues/2452): The LaTeX backend does not handle options very well
+  -  [#2473](https://github.com/agda/agda/issues/2473): Don't reread the source code without checking that it is unchanged
+  -  [#2487](https://github.com/agda/agda/issues/2487): Options used for different modules must be consistent with each other, and options used when loading an interface must be consistent with those used when the interface was created
+  -  [#2489](https://github.com/agda/agda/issues/2489): Where clauses in functions leak instances to global instance search
+  -  [#2490](https://github.com/agda/agda/issues/2490): possible non-terminating inference of instance arguments?
+  -  [#2513](https://github.com/agda/agda/issues/2513): Extensible syntax for function space annotations
+  -  [#2548](https://github.com/agda/agda/issues/2548): Move the "Old Reference Manual" to the current documentation
+  -  [#2563](https://github.com/agda/agda/issues/2563): Improve documentation and error reporting related to instance resolution (especially unconstrained metavariables)
+  -  [#2579](https://github.com/agda/agda/issues/2579): Import statements with module instantiation should not trigger an error message
+  -  [#2618](https://github.com/agda/agda/issues/2618): Reflection and pattern-matching lambdas
+  -  [#2670](https://github.com/agda/agda/issues/2670): Instance arguments and multi-sorted algebras
+  -  [#2757](https://github.com/agda/agda/issues/2757): Proposal: split non-strict relevance into shape-irrelevance, parametricity, and runtime-irrelevance
+  -  [#2760](https://github.com/agda/agda/issues/2760): Relax instance search restriction on unconstrained metas
+  -  [#2774](https://github.com/agda/agda/issues/2774): Internal error with sized types
+  -  [#2783](https://github.com/agda/agda/issues/2783): Make more primitive/builtin modules safe?
+  -  [#2789](https://github.com/agda/agda/issues/2789): Narrow and broad options
+  -  [#2791](https://github.com/agda/agda/issues/2791): More illtyped meta solutions
+  -  [#2797](https://github.com/agda/agda/issues/2797): Relevance check missed for overloaded projection
+  -  [#2833](https://github.com/agda/agda/issues/2833): Coverage checker splits on result too eagerly
+  -  [#2837](https://github.com/agda/agda/issues/2837): The Emacs mode only handles LaTeX-based literate Agda
+  -  [#2872](https://github.com/agda/agda/issues/2872): Case splitting adds a dot in front of pattern matches on Chars
+  -  [#2880](https://github.com/agda/agda/issues/2880): Disallow FFI binding for defined functions when --safe is used
+  -  [#2892](https://github.com/agda/agda/issues/2892): 'With' should also abstract over the type of stripped dot patterns
+  -  [#2893](https://github.com/agda/agda/issues/2893): Display warnings also when an error is encountered
+  -  [#2899](https://github.com/agda/agda/issues/2899): Add a warning for infix notations without corresponding fixity declaration
+  -  [#2929](https://github.com/agda/agda/issues/2929): Turn "missing definition" into a warning
+  -  [#2936](https://github.com/agda/agda/issues/2936): Sort warning flags alphabetically in user manual
+  -  [#2939](https://github.com/agda/agda/issues/2939): make install-bin on a Mac can fail to install text-icu
+  -  [#2964](https://github.com/agda/agda/issues/2964): Mismatch between order of matching in clauses and case tree; subject reduction broken
+  -  [#2969](https://github.com/agda/agda/issues/2969): Module parameter is erased from dot pattern
+  -  [#2979](https://github.com/agda/agda/issues/2979): Rewriting matching does not respect eta rules
+  -  [#2993](https://github.com/agda/agda/issues/2993): Quadratic (failing) instance search
+  -  [#3010](https://github.com/agda/agda/issues/3010): Field of opened record does not get highlighted
+  -  [#3032](https://github.com/agda/agda/issues/3032): spurious meta in dot pattern
+  -  [#3056](https://github.com/agda/agda/issues/3056): Matching on irrelevant variable of dependent record type should not be allowed
+  -  [#3057](https://github.com/agda/agda/issues/3057): A module can export two definitions with the same name
+  -  [#3068](https://github.com/agda/agda/issues/3068): Add option to turn off syntactic equality check
+  -  [#3095](https://github.com/agda/agda/issues/3095): Would like to make hidden variable visible but it is created ambiguous
+  -  [#3102](https://github.com/agda/agda/issues/3102): Performance regression: very slow reduction in the presence of many module parameters
+  -  [#3114](https://github.com/agda/agda/issues/3114): Missing alpha-renaming when printing constraints
+  -  [#3120](https://github.com/agda/agda/issues/3120): No tooltips for record field names in record expressions
+  -  [#3122](https://github.com/agda/agda/issues/3122): Hidden record fields are not picked up from module in record expression
+  -  [#3124](https://github.com/agda/agda/issues/3124): De Bruijn index in lhs checking error message
+  -  [#3125](https://github.com/agda/agda/issues/3125): Internal error in InstanceArguments.hs:292
+  -  [#3127](https://github.com/agda/agda/issues/3127): Notation for out-of-scope variables conflicts with notation for irrelevance
+  -  [#3128](https://github.com/agda/agda/issues/3128): Sigma builtin not added to setup, agdai file missing.
+  -  [#3130](https://github.com/agda/agda/issues/3130): Conflict between dot pattern and postfix projection
+  -  [#3137](https://github.com/agda/agda/issues/3137): Preserve Markdown as-is when outputting HTML
+  -  [#3138](https://github.com/agda/agda/issues/3138): Result splitter introduces pattern variable that conflicts with constructor
+  -  [#3139](https://github.com/agda/agda/issues/3139): Internal error in parser
+  -  [#3147](https://github.com/agda/agda/issues/3147): Non-linear as-patterns
+  -  [#3152](https://github.com/agda/agda/issues/3152): `give` in a do-block inserts spurious parentheses
+  -  [#3153](https://github.com/agda/agda/issues/3153): Type checker fails to infer missing signature of module parameter.
+  -  [#3161](https://github.com/agda/agda/issues/3161): Case splitter produces end-of-comment
+  -  [#3169](https://github.com/agda/agda/issues/3169): Doc for rewriting
+  -  [#3170](https://github.com/agda/agda/issues/3170): UnicodeDeclare fails with pdflatex from TeX Live 2018
+  -  [#3175](https://github.com/agda/agda/issues/3175): Instance resolution fails with defined method
+  -  [#3176](https://github.com/agda/agda/issues/3176): Empty lambdas are sometimes considered definitionally equal, other times not
+  -  [#3180](https://github.com/agda/agda/issues/3180): Remove feature `--guardedness-preserving-type-constructors`
+  -  [#3188](https://github.com/agda/agda/issues/3188): Warnings disappear when fatal error is encountered
+  -  [#3195](https://github.com/agda/agda/issues/3195): Internal error at Auto/Typecheck.hs:373
+  -  [#3196](https://github.com/agda/agda/issues/3196): Turning MissingDefinition into a warning
+  -  [#3200](https://github.com/agda/agda/issues/3200): Function marked as irrelevant when it isn't
+  -  [#3201](https://github.com/agda/agda/issues/3201): [ warning ] AbsurdPatternRequiresNoRHS
+  -  [#3205](https://github.com/agda/agda/issues/3205): [ cleanup + warning ] ModuleDoesntExport can be recovered from
+  -  [#3224](https://github.com/agda/agda/issues/3224): Switch from utf8x to utf8? Make agda.sty easier to maintain?
+  -  [#3235](https://github.com/agda/agda/issues/3235): Cannot pass backend flags via emacs variable `agda2-program-args`
+  -  [#3247](https://github.com/agda/agda/issues/3247): Support cabal-install >= 2.4.1.0 in the Makefile
+  -  [#3248](https://github.com/agda/agda/issues/3248): Max of two sizes less than i
+  -  [#3253](https://github.com/agda/agda/issues/3253): [ fix ] ignore duplicate declarations of libraries
+  -  [#3254](https://github.com/agda/agda/issues/3254): `cpphs` doesn't build with GHC 8.6.*
+  -  [#3256](https://github.com/agda/agda/issues/3256): Internal error at src/full/Agda/TypeChecking/Reduce.hs:148
+  -  [#3257](https://github.com/agda/agda/issues/3257): Anonymous top-level modules can have names with multiple components
+  -  [#3258](https://github.com/agda/agda/issues/3258): Ordering the constructor names at Definition.
+  -  [#3262](https://github.com/agda/agda/issues/3262): Suboptimal placement of "missing with-clauses" error
+  -  [#3264](https://github.com/agda/agda/issues/3264): When refine leads to a termination error it should say so rather than "cannot refine"
+  -  [#3268](https://github.com/agda/agda/issues/3268): [ haddock ] Fix haddock formatting
+  -  [#3285](https://github.com/agda/agda/issues/3285): Internal error for syntax declaration
+  -  [#3302](https://github.com/agda/agda/issues/3302): Multiple definitions called _ are sometimes allowed, sometimes not
+  -  [#3307](https://github.com/agda/agda/issues/3307): `--no-unicode` bug: case splitting inside a pattern matching lambda still produces unicode arrows
+  -  [#3309](https://github.com/agda/agda/issues/3309): Use of irrelevant arguments with copatterns and irrelevant fields
+  -  [#3313](https://github.com/agda/agda/issues/3313): Add --html-highlight support for the HTML backend
+  -  [#3315](https://github.com/agda/agda/issues/3315): The primErase primitive is not safe
+  -  [#3318](https://github.com/agda/agda/issues/3318): Lots of primitives and builtins are not declared in the primitive/builtin modules
+  -  [#3320](https://github.com/agda/agda/issues/3320): Extra indentation when code is hidden
+  -  [#3323](https://github.com/agda/agda/issues/3323): Internal error with inconsistent irrelevance info between declaration and definition of data type
+  -  [#3338](https://github.com/agda/agda/issues/3338): Missing Definitions not recognised in instance search
+  -  [#3342](https://github.com/agda/agda/issues/3342): GHC panic on stack and GHC 7.10.3
+  -  [#3344](https://github.com/agda/agda/issues/3344): Disable compilation with GHC 8.6.1
+  -  [#3356](https://github.com/agda/agda/issues/3356): C-c C-s prints postfix projections by default
+  -  [#3363](https://github.com/agda/agda/issues/3363): The wiki should support HTTPS
+  -  [#3364](https://github.com/agda/agda/issues/3364): Funny scope error when trying to import as qualified
+  -  [#3366](https://github.com/agda/agda/issues/3366): Add a command line flag to change the extension of the files generated by the HTML backend
+  -  [#3368](https://github.com/agda/agda/issues/3368): Support GHC 8.6.2
+  -  [#3370](https://github.com/agda/agda/issues/3370): [ fix ] < and > need to be in math mode in latex
+  -  [#3371](https://github.com/agda/agda/issues/3371): Document common LaTeX backend pitfalls
+  -  [#3372](https://github.com/agda/agda/issues/3372): Provide some simple LaTeX backend templates
+  -  [#3373](https://github.com/agda/agda/issues/3373): Wrap HTML in `raw` directive when working with ReStructuredText
+  -  [#3379](https://github.com/agda/agda/issues/3379): Adding a tutorial set in the readthedocs frontpage
+  -  [#3380](https://github.com/agda/agda/issues/3380): Too much erasure in strict backends
+  -  [#3394](https://github.com/agda/agda/issues/3394): Internal error in mutual block with unsolved implicit argument in termination checker
+  -  [#3400](https://github.com/agda/agda/issues/3400): Obscure parse error with copattern and infix field
+  -  [#3403](https://github.com/agda/agda/issues/3403): Internal error in Agda.TypeChecking.Rules.Term
+  -  [#3404](https://github.com/agda/agda/issues/3404): Positivity checker marks postulates as constant in mutual block
+  -  [#3407](https://github.com/agda/agda/issues/3407): Internal error at "src/full/Agda/TypeChecking/Reduce/Fast.hs:1338"
+  -  [#3409](https://github.com/agda/agda/issues/3409): No error if mapping the empty type to non-empty Haskell type
+  -  [#3410](https://github.com/agda/agda/issues/3410): ghc backend generates program that segfaults
+  -  [#3419](https://github.com/agda/agda/issues/3419): Allow unconstrained instances & disallow overlapping instances
+  -  [#3420](https://github.com/agda/agda/issues/3420): Inductive definitions live in a larger set --without-K
+  -  [#3425](https://github.com/agda/agda/issues/3425): Internal error at src/full/Agda/Termination/Monad.hs:177
+  -  [#3426](https://github.com/agda/agda/issues/3426): Termination checking false positive when using "where"
+  -  [#3428](https://github.com/agda/agda/issues/3428): Another interal error in Substitute:72 when filling a hole
+  -  [#3431](https://github.com/agda/agda/issues/3431): Rewrite rule doesn't fire during conversion checking
+  -  [#3434](https://github.com/agda/agda/issues/3434): Regression related to instance resolution
+  -  [#3435](https://github.com/agda/agda/issues/3435): Performance regression
+  -  [#3439](https://github.com/agda/agda/issues/3439): Setω doesn’t respect --type-in-type
+  -  [#3441](https://github.com/agda/agda/issues/3441): Generate Level expressions with fewer parentheses
+  -  [#3442](https://github.com/agda/agda/issues/3442): Support GHC 8.6.3
+  -  [#3443](https://github.com/agda/agda/issues/3443): "internal error" in Agda of December 7, 2018
+  -  [#3444](https://github.com/agda/agda/issues/3444): `Setup.hs` is not generating the interface files
+  -  [#3445](https://github.com/agda/agda/issues/3445): case splitting attempts to shadow constructor
+  -  [#3451](https://github.com/agda/agda/issues/3451): The --no-sized-types option is broken
+  -  [#3452](https://github.com/agda/agda/issues/3452): Case split on irrelevant argument goes through but is later rejected
+  -  [#3454](https://github.com/agda/agda/issues/3454): Highlighting for incomplete pattern matching should be above highliting for non-exact split
+  -  [#3456](https://github.com/agda/agda/issues/3456): [ new ] Injectivity of prim(NatToChar/StringToList)
+  -  [#3461](https://github.com/agda/agda/issues/3461): Macro loop
+  -  [#3463](https://github.com/agda/agda/issues/3463): Impossible to give certain instance arguments by name?
+  -  [#3466](https://github.com/agda/agda/issues/3466): two definitionally equal terms are not equal
+  -  [#3471](https://github.com/agda/agda/issues/3471): Can't install via cabal-install on current Haskell Platform
+  -  [#3480](https://github.com/agda/agda/issues/3480): Parse error at EOF should be reported before EOF (especially if there is a long comment before EOF)
+  -  [#3483](https://github.com/agda/agda/issues/3483): Internal error at TypeChecking/Monad/Signature.hs:732
+  -  [#3485](https://github.com/agda/agda/issues/3485): [ warnings ] for empty primitive blocks
+  -  [#3491](https://github.com/agda/agda/issues/3491): Internal error src/full/Agda/TypeChecking/Rules/LHS.hs:294 after pattern matching
+  -  [#3498](https://github.com/agda/agda/issues/3498): Internal error in activateLoadedFileCache
+  -  [#3501](https://github.com/agda/agda/issues/3501): Case split in let clause causes internal error
+  -  [#3503](https://github.com/agda/agda/issues/3503): Internal error in BasicOps
+  -  [#3514](https://github.com/agda/agda/issues/3514): Accidential language change in 2.5.3: hiding is now part of name when resolving hidden argument insertion
+  -  [#3517](https://github.com/agda/agda/issues/3517): Option consistency checking bug
+  -  [#3518](https://github.com/agda/agda/issues/3518): Performance regression
+  -  [#3521](https://github.com/agda/agda/issues/3521): Documentation: fixes a plural issue in copatterns
+  -  [#3526](https://github.com/agda/agda/issues/3526): Do not generate trivially impossible clause when case-splitting
+  -  [#3533](https://github.com/agda/agda/issues/3533): [ fix #3526 ] Remove trivially impossible clauses from case-split
+  -  [#3534](https://github.com/agda/agda/issues/3534): Problem finding higher-order instances
+  -  [#3536](https://github.com/agda/agda/issues/3536): Patternmatching on coinductive record fields breaks
+  -  [#3544](https://github.com/agda/agda/issues/3544): internal error @ TypeChecking/Forcing.hs:227
+  -  [#3548](https://github.com/agda/agda/issues/3548): [ new ] Add support for compiling literate Org documents
+  -  [#3554](https://github.com/agda/agda/issues/3554): Type checker explosion
+  -  [#3561](https://github.com/agda/agda/issues/3561): fix typo: "FreBSD" => "FreeBSD"
+  -  [#3566](https://github.com/agda/agda/issues/3566): Missing name when printing type of definition of a record
+  -  [#3578](https://github.com/agda/agda/issues/3578): Pattern matching unifier normalizes too much
+  -  [#3586](https://github.com/agda/agda/issues/3586): Internal error in ConcreteToAbstract.hs:2217
+  -  [#3590](https://github.com/agda/agda/issues/3590): Superlinear time required for simple code
+  -  [#3597](https://github.com/agda/agda/issues/3597): Agda loops on simple code with a record and a hole
+  -  [#3600](https://github.com/agda/agda/issues/3600): Size solver complains, explicit sizes work
+  -  [#3610](https://github.com/agda/agda/issues/3610): Support GHC 8.6.4
+  -  [#3621](https://github.com/agda/agda/issues/3621): performance problem
+  -  [#3631](https://github.com/agda/agda/issues/3631): Performance with --no-universe-polymorphism
+  -  [#3638](https://github.com/agda/agda/issues/3638): Rewrite rules do not fire in goal normalization in parametrized module
+  -  [#3639](https://github.com/agda/agda/issues/3639): Argument to function created by tactic is lost
+  -  [#3640](https://github.com/agda/agda/issues/3640): Polarity: Size index check crashes due to wrong parameter number calculation
+  -  [#3641](https://github.com/agda/agda/issues/3641): Remove old compiler pragmas
+  -  [#3648](https://github.com/agda/agda/issues/3648): Agda could fail to build if a .agda-lib file exists in a parent directory
+  -  [#3651](https://github.com/agda/agda/issues/3651): internal error ghc backend
+  -  [#3657](https://github.com/agda/agda/issues/3657): Disable compilation with Windows and GHC 8.6.3
+  -  [#3678](https://github.com/agda/agda/issues/3678): Two out-of-scope variables are given the same name
+  -  [#3687](https://github.com/agda/agda/issues/3687): Show module contents (C-c C-o) prints garbled names in clause
diff --git a/doc/release-notes/2.6.1.1.md b/doc/release-notes/2.6.1.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.1.1.md
@@ -0,0 +1,4 @@
+Release notes for Agda version 2.6.1.1
+======================================
+
+* Added support for GHC 8.8.4 and GHC 8.10.2
diff --git a/doc/release-notes/2.6.1.2.md b/doc/release-notes/2.6.1.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.1.2.md
@@ -0,0 +1,8 @@
+Release notes for Agda version 2.6.1.2
+======================================
+
+* Build with latest versions of hackage packages:
+  - aeson (1.5.3), [issue #4838](https://github.com/agda/agda/issues/4838)
+  - strict (0.4), [commit 0497ec9](https://github.com/agda/agda/commit/0497ec9fdde159a56ee42821e500b52d66374201)
+
+* Build with dynamic linking, [issue #4569](https://github.com/agda/agda/issues/4569)
diff --git a/doc/release-notes/2.6.1.3.md b/doc/release-notes/2.6.1.3.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.1.3.md
@@ -0,0 +1,4 @@
+Release notes for Agda version 2.6.1.3
+======================================
+
+* Added support for GHC 8.10.3.
diff --git a/doc/release-notes/2.6.1.md b/doc/release-notes/2.6.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.1.md
@@ -0,0 +1,850 @@
+Release notes for Agda version 2.6.1
+====================================
+
+General
+-------
+
+* Agda now has an official logo: [![The official Agda
+  logo](../../doc/user-manual/agda.svg)](https://github.com/agda/agda/blob/master/doc/user-manual/agda.svg). The
+  logo was chosen by the Agda community from a list of candidates. The
+  winning design was submitted by Miëtek Bak. The list of candidates
+  and the outcome of the poll can be consulted
+  [here](https://civs.cs.cornell.edu/cgi-bin/results.pl?id=E_ce6fe5e2a518ac98).
+
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.8.2
+  [Issue [#4285](https://github.com/agda/agda/issues/4285)].
+
+* Removed support for GHC 7.10.3.
+
+* Interface files are now written in directory `_build/VERSION/agda/` at
+  the project root (the closest enclosing directory where an `.agda-lib`
+  file is present). If there is no project root then the interface file
+  is written alongside the module it corresponds to.
+  The flag `--local-interfaces` forces Agda to revert back to storing
+  interface files alongside module files no matter what.
+
+* Agda now uses the default RTS options `-M3.5G -I0`.  If
+  you run Agda on a 32-bit system or a system with less than 8GB of
+  RAM, it is recommended to set the RTS options explicitly to a lower
+  value by running `agda` with option `+RTS -M1.2G -RTS`
+  (for example) or by setting the GHCRTS enviroment variable. See the
+  [GHC User's Guide](https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/runtime_control.html#setting-rts-options)
+  for more information.
+
+* If Agda is compiled using GHC 8.4 or later, then one can expect to
+  see substantially lower memory consumption
+  [Issues [#4457](https://github.com/agda/agda/issues/4457)
+  and [#4316](https://github.com/agda/agda/issues/4316)].
+
+  This is due to the use of ["compact
+  regions"](https://hackage.haskell.org/package/ghc-compact-0.1.0.0/docs/GHC-Compact.html).
+
+* The `CHANGELOG.md` was split. Changes to previous versions of Agda
+  are in the directory `doc/release-notes`.
+
+Pragmas and options
+-------------------
+
+* New pragma `WARNING_ON_IMPORT` to let module authors raise a warning
+  when a module is imported. This can be use to tell users deprecations.
+
+* New option `--confluence-check` (off by default) enables confluence
+  checking of user-defined rewrite rules (this only has an effect when
+  `--rewriting` is also enabled).
+
+* New option `--no-projection-like` to turn off the analysis whether a
+  type signature likens that of a projection.
+  Projection-likeness is an optimization that reduces the size of
+  terms by dropping parameter-like reconstructible function arguments.
+  Thus, it is advisable to leave this optimization on, the flag is
+  meant for debugging Agda.
+
+* Option `--no-forcing` is now a pragma option, i.e., the forcing analysis
+  can be switched off on a per-file basis via
+
+  ```agda
+  {-# OPTIONS --no-forcing #-}
+  ```
+
+  at the beginning of the file
+  [Issue [#3872](https://github.com/agda/agda/issues/3872)].
+
+* New pragma option `--no-flat-split` disables pattern matching on `@♭` arguments.
+
+* New pragma option `--allow-incomplete-matches`. It is similar to
+  `--allow-unsolved-metas`: modules containing partial function definitions
+  can be imported. Its local equivalent is the `NON_COVERING` pragma to
+  be placed before the function (or the block of mutually defined functions)
+  which the user knows to be partial.
+
+* Option `--interaction-json` now brings more information about goals,
+  unsolved metas, warnings, errors.
+  It also displays pretty-printed terms.
+
+* New pragma option `--keep-pattern-variables` to prevent case
+  splitting from replacing variables with dot patterns.
+
+* Pragma `{-# ETA <record name> #-}` is no longer considered `--safe`.
+  See [Issue [#4450](https://github.com/agda/agda/issues/4450)].
+
+* New pragma options `--subtyping` and `--no-subtyping` (default) to
+  turn on/off subtyping rules globally [see
+  Issue_[#4474](https://github.com/agda/agda/issues/4474)]. Currently,
+  this includes subtyping for irrelevance, erasure, and flat
+  modalities. Additionally, `--subtyping` is implied by
+  `--cumulativity` (see below). `--subtyping` is currently NOT implied
+  by `--sized-types`, and subtyping for sized types is used even when
+  `--subtyping` is not enabled.
+
+* New profiling options to measure time spent per module or top-level
+  definition.
+
+  - `-v profile.modules:10` prints a breakdown per top-level module
+  - `-v profile.definitions:10` prints a breakdown per top-level
+    definition
+
+Language
+--------
+
+### Syntax
+
+* Fractional precedence levels are now supported, see
+  Issue [#3991](https://github.com/agda/agda/issues/3991). Example:
+
+  ```agda
+  infix 3.14 _<_
+  ```
+  Note that this includes a respective change in the reflected Agda syntax.
+
+* Fixities can now be changed during import in a `renaming` directive,
+  see
+  Issue [#1346](https://github.com/agda/agda/issues/1346). Example:
+
+  ```agda
+  open M using (_∙_)
+  open M renaming (_∙_ to infixl 10 _*_)
+  ```
+  After this, `_∙_` is in scope with its original fixity, and as `_*_` as left
+  associative operator of precedence 10.
+
+* Implicit non-dependent function spaces `{A} → B` and `{{A}} → B` are now supported.
+
+* Idiom brackets
+
+  Idiom brackets can accommodate none or multiple applications separated by a vertical bar `|`
+  if there are two additional operations
+  ```agda
+  empty : ∀ {A} → F A
+  _<|>_ : ∀ {A} → F A → F A → F A
+  ```
+  i.e. an Alternative type class in Haskell.
+  As usual, the new idiom brackets desugar before scope checking.
+
+  Idiom brackets with multiple applications
+  ```agda
+  (| e₁ a₁ .. aₙ | e₂ a₁ .. aₘ | .. | eₖ a₁ .. aₗ |)
+  ```
+  expand to (assuming right associative `_<|>_`)
+  ```agda
+  (pure e₁ <*> a₁ <*> .. <*> aₙ) <|> ((pure e₂ <*> a₁ <*> .. <*> aₘ) <|> (pure eₖ <*> a₁ <*> .. <*> aₗ))
+  ```
+  Idiom brackets with no application `(|)` or `⦇⦈` are equivalent to `empty`.
+
+
+* Irrefutable With
+
+  Users can now match on irrefutable patterns on the LHS using a
+  pattern-matching `with`. An expression of the form:
+
+  ```agda
+  f xs with p1 <- e1 | ... | pn <- en
+       with q1 <- f1 | ... | qm <- fm = rhs
+  ```
+
+  is translated to nested `with` clauses, essentially equivalent to:
+
+  ```agda
+  f xs with e1 | ... | en
+  ... | p1 | ... | pn
+       with f1 | ... | fm
+  ... | q1 | ... | qm = rhs
+  ```
+
+* Record patterns in telescopes
+
+  Users can now use record patterns in telescope and lambda abstractions.
+  The type of the second projection from a dependent pair is the prototypical
+  example It can be defined as follows:
+
+  ```agda
+  snd : ((a , _) : Σ A B) → B a
+  ```
+
+  And this second projection can be implemented with a lamba-abstraction using
+  one of these irrefutable patterns:
+
+  ```agda
+  snd = λ (a , b) → b
+  ```
+
+  Using an as-pattern, users can get a name for the value as well as for its
+  subparts. We can for instance prove that any pair is equal to the pairing
+  of its first and second projections:
+
+  ```agda
+  eta : (p@(a , b) : Σ A B) → p ≡ (a , b)
+  eta p = refl
+  ```
+
+* Absurd match in a do block
+  The last expression in a do block can now also be an absurd match `() <- f`.
+
+* Named `where` modules are now in scope in the rhs of the clause (see
+  Issue [#4050](https://github.com/agda/agda/issues/4050)).  Example:
+
+  ```agda
+  record Wrap : Set₂ where
+    field wrapped : Set₁
+
+  test : Wrap
+  test = record { M }
+    module M where
+      wrapped : Set₁
+      wrapped = Set
+  ```
+
+* `{{-` is now lexed as `{ {-` rather than `{{ -`,
+  see Issue [#3962](https://github.com/agda/agda/issues/3962).
+
+* Syntax for large numbers: you can now separate groups of 3 digits using `_`.
+  e.g. write `1_000_000` instead of `1000000`.
+
+* `quoteGoal` and `quoteContext` are no longer keywords.
+
+* Record constructors can no longer be qualified by the record module.
+  (See Issue [#4189](https://github.com/agda/agda/issues/4189).)
+
+  ```agda
+  record Foo : Set where
+    constructor foo
+
+  works = foo
+  fails = Foo.foo
+  ```
+
+* `codata` definitions have been removed from the concrete syntax
+  Previously they got accepted syntactically, but resulted in errors.
+
+* Imports can now be anonymous.
+  (See Issue_[#3727](https://github.com/agda/agda/issues/3727).)
+  For example, the following will **not** bring `Agda.Builtin.Unit` into scope:
+  ```agda
+  open import Agda.Builtin.Unit as _
+  blah :: ⊤
+  blah = tt
+  ```
+
+### Type checking
+
+* Type inference for record expressions no longer considers record types from
+  modules that have not been imported (Issue [#4267](https://github.com/agda/agda/issues/4267)).
+
+  For instance,
+  ```agda
+  -- A.agda
+  module A where
+    record R : Set₁ where
+      field f : Set
+  ```
+  ```agda
+  -- B.agda
+  module B where
+    import A
+  ```
+  ```agda
+  -- C.agda
+  module C where
+    import B
+    fails : Set → _
+    fails X = record {f = X}  -- import A required to infer record type R
+  ```
+
+* The fix of issue [#3903](https://github.com/agda/agda/issues/3903) changes
+  the algorithm computing the order of case splits, which in some cases may
+  lead to unsolved metavariables in previously working code. See issue
+  [#4353](https://github.com/agda/agda/issues/4353).
+
+### Modalities
+
+* New Flat Modality
+
+  New modality `@♭/@flat` (previously only available in the branch "flat").
+  An idempotent comonadic modality modeled after spatial/crisp type theory.
+  See [Flat Modality](https://agda.readthedocs.io/en/v2.6.1/language/flat.html)
+  in the documentation for more.
+
+* New run-time erasure modality (`@0` / `@erased`).
+  Terms marked as erased cannot influence computations and are erased
+  at run time
+  [Issue [#3855](https://github.com/agda/agda/issues/3855)]. See
+  [Run-time
+  Irrelevance](https://agda.readthedocs.io/en/v2.6.1/language/runtime-irrelevance.html)
+  in the documentation for more information.
+
+  Note that this feature can cause previously solved metavariables to become
+  unsolved even in code that doesn't use run-time erasure (see issue
+  [#4174](https://github.com/agda/agda/issues/4174)).
+
+* Subtyping rules for modalities are by default no longer used (see
+  Issue_[#4390](https://github.com/agda/agda/issues/4390)). For
+  example, if `f : .A → A`, Agda no longer accepts `f` at type `A →
+  A`. Instead, Agda accepts `λ x → f x : A → A`. The same holds for
+  erasure (`@0`) and flat (`@♭`) modalities. Consequently, it may be
+  required to eta-expand certain functions in order to make old code
+  work with Agda 2.6.1. Alternatively, enabling the new `--subtyping`
+  flag will restore the old behaviour but might negatively impact
+  typechecking performance.
+
+### Universe levels
+
+* New (experimental) option `--cumulativity`
+
+  When the ``--cumulativity`` flag is enabled, Agda uses the subtyping
+  rule ``Set i =< Set j`` whenever ``i =< j``. For example, in
+  addition to its usual type ``Set``, ``Nat`` also has the type
+  ``Set₁`` and even ``Set i`` for any ``i : Level``. More information
+  about this new option can be found in section
+  [Cumulativity](https://agda.readthedocs.io/en/v2.6.1/language/cumulativity.html)
+  of the user manual.
+
+### Termination checking
+
+* The "with inlining" feature of the termination checker has been
+  removed. As a consequence, some functions defined using `with` are
+  no longer accepted as terminating. See
+  Issue [#59](https://github.com/agda/agda/issues/59) for why this
+  feature was originally introduced and
+  [#3604](https://github.com/agda/agda/issues/3604) for why it had to
+  be removed.
+
+  The easiest way to fix termination problems caused by `with` is to abstract
+  over the offending recursive call before any other `with`s. For example
+
+  ```agda
+  data D : Set where
+    [_] : Nat → D
+
+  fails : D → Nat
+  fails [ zero  ] = zero
+  fails [ suc n ] with some-stuff
+  ... | _ = fails [ n ]
+  ```
+
+  This fails termination because the relation between `[ suc n ]` and `[ n ]`
+  is lost since the generated with-function only gets passed `n`. To fix it we
+  can abstract over the recursive call:
+
+  ```agda
+  fixed : D → Nat
+  fixed [ zero  ] = zero
+  fixed [ suc n ] with fixed [ n ] | some-stuff
+  ... | rec | _ = rec
+  ```
+
+  If the function takes more arguments you might need to abstract over a
+  partial application to just the structurally recursive argument. For instance,
+
+  ```agda
+  fails : Nat → D → Nat
+  fails _ [ zero  ] = zero
+  fails _ [ suc n ] with some-stuff
+  ... | m = fails m [ n ]
+
+  fixed : Nat → D → Nat
+  fixed _ [ zero  ] = zero
+  fixed _ [ suc n ] with (λ m → fixed m [ n ]) | some-stuff
+  ... | rec | m = rec m
+  ```
+
+  A possible complication is that later `with`-abstractions might change the
+  type of the abstracted recursive call:
+
+  ```agda
+  T      : D → Set
+  suc-T  : ∀ {n} → T [ n ] → T [ suc n ]
+  zero-T : T [ zero ]
+
+  fails : (d : D) → T d
+  fails [ zero  ] = zero-T
+  fails [ suc n ] with some-stuff
+  ... | _ with [ n ]
+  ...   | z = suc-T (fails [ n ])
+
+  still-fails : (d : D) → T d
+  still-fails [ zero ] = zero-T
+  still-fails [ suc n ] with still-fails [ n ] | some-stuff
+  ... | rec | _ with [ n ]
+  ...   | z = suc-T rec -- Type error because rec : T z
+  ```
+
+  To solve this problem you can add `rec` to the with-abstraction messing up
+  its type. This will prevent it from having its type changed:
+
+  ```agda
+  fixed : (d : D) → T d
+  fixed [ zero ] = zero-T
+  fixed [ suc n ] with fixed [ n ] | some-stuff
+  ... | rec | _ with rec | [ n ]
+  ...   | _ | z = suc-T rec
+  ```
+
+* The termination checker will now try to dispose of recursive calls
+  by reducing with the non-recursive function clauses.
+  This eliminates false positives common for definitions by copatterns
+  using dependent types,
+  see Issue [#906](https://github.com/agda/agda/issues/906).
+
+  For example, consider the following example using a dependent
+  coinductive record `Tree`:
+  ```agda
+  data Fin : Nat → Set where
+    fzero : ∀ n → Fin (suc n)
+    fsuc  : ∀ n (i : Fin n) → Fin (suc n)
+
+  toNat : ∀ n → Fin n → Nat
+  toNat .(suc n) (fzero n)  = zero
+  toNat .(suc n) (fsuc n i) = suc (toNat n i)
+
+  record Tree : Set where
+    coinductive
+    field label : Nat
+          child : Fin label → Tree
+  open Tree
+
+  tree : Nat → Tree
+  tree n .label   = n
+  tree n .child i = tree (n + toNat _ i)
+  ```
+  Agda solves the underscore by `tree n .label`, which is a corecursive
+  call in a non-guarded position, violating the guardedness criterion.
+  This lead to a complaint of the termination checker.
+  Now this call is reduced to `n` first using the non-recursive clause
+  `tree n .label = n`, which leaves us only with the guarded call
+  `tree (n + toNat n i)`, and the termination checker is happy.
+
+  Note: Similar false positives arose already for non-recursive dependent
+  records, e.g., when trying to define an inhabitant of the Σ-type by
+  copattern matching on the projects.
+  See Issue_[#2068](https://github.com/agda/agda/issues/2068) for a
+  non-recursive example.
+
+### Irrelevance and Prop
+
+* Agda will no longer reduce irrelevant definitions and definitions
+  with a type in `Prop`. This does not have an effect on the
+  semantics, but should lead to improved performance (see Issues
+  [#4115](https://github.com/agda/agda/issues/4115),
+  [#4118](https://github.com/agda/agda/issues/4118),
+  [#4120](https://github.com/agda/agda/issues/4120),
+  [#4122](https://github.com/agda/agda/issues/4122)).
+
+* Terms of a type in `Prop` are now printed as `_`. To show the actual
+  term, you can use the `--show-irrelevant` flag (see
+  Issue [#3337](https://github.com/agda/agda/issues/3337).
+
+### Rewrite rules
+
+* Rewrite rules (option `--rewriting`) with data or record types as
+  the head symbol are no longer allowed (see
+  Issue [#3846](https://github.com/agda/agda/issues/3846)).
+
+### Tactics & Reflection
+
+* Implicit arguments solved by user-defined tactics
+
+  You can declare tactics to be used to solve a particular implicit argument
+  using the following syntax:
+
+  ```agda
+  example : {@(tactic f) x : A} → B
+  ```
+
+  where `f : Term → TC ⊤`. At calls to `example`, `f` is called on the
+  metavariable inserted for `x`. `f` can be an arbitrary term and may depend on
+  previous arguments to the function. For instance,
+
+  ```agda
+  example₂ : (depth : Nat) {@(tactic search depth) x : A} → B
+  ```
+
+  Record fields can also be annotated with a tactic, allowing them to be
+  omitted in constructor applications, record constructions and co-pattern
+  matches:
+
+  ```agda
+  record Example : Set where
+    constructor mkExample
+    field x : A
+          @(tactic solveP x) {y} : P x
+  ```
+
+  where `solveP : (x : A) → Term → TC ⊤` is a tactic that tries to
+  prove `P x`
+  [Issue [#4124](https://github.com/agda/agda/issues/4124)].
+
+* The legacy reflection framework using `quoteGoal` and `quoteContext` has been
+  removed.
+
+### Builtins
+
+* New primitives
+
+  ```agda
+  primWord64ToNatInjective    : ∀ a b → primWord64ToNat a ≡ primWord64ToNat b → a ≡ b
+
+  primFloatToWord64           : Float → Word64
+  primFloatToWord64Injective  : ∀ a b → primFloatToWord64 a ≡ primFloatToWord64 b → a ≡ b
+
+  primMetaToNat               : Meta → Nat
+  primMetaToNatInjective      : ∀ a b → primMetaToNat a ≡ primMetaToNat b → a ≡ b
+
+  primQNameToWord64s          : Name → Word64 × Word64
+  primQNameToWord64sInjective : ∀ a b → primQNameToWord64s a ≡ primQNameToWord64s b → a ≡ b
+  ```
+
+  These can be used to define safe decidable propositional equality, see Issue [agda-stdlib#698](https://github.com/agda/agda-stdlib/issues/698).
+
+* New Primitive for showing Natural numbers:
+
+  ```agda
+  primShowNat : Nat → String
+  ```
+
+  placed in Agda.Builtin.String.
+
+* The builtin `IO` has been declared strictly positive in both its
+  level and type argument.
+
+### Warnings
+
+* New warning for a variable shadowing another in a telescope. If the two
+  variables are introduced in different telescopes then the warning is not
+  raised.
+
+  ```agda
+  f : {a : Level} {A : Set a} (a : A) → A   -- warning raised: repeated a
+  g : {a : Level} {A : Set a} → (a : A) → A -- warning not raised: two distinct telescopes
+  ```
+
+  Note that this warning is turned off by default (you can use
+  `-WShadowingInTelescope` or `--warning ShadowingInTelescope` to turn
+  it on, `-Wall` would also naturally work).
+
+
+Emacs mode
+----------
+
+* Agda input method: new key bindings `\ G h` and `\ G H` for `η` and
+  `H` (capital η)
+  [Issue [#3856](https://github.com/agda/agda/issues/3856)].
+
+* Syntax highlighting: in literate modes, the pure texts
+  (other than Agda code and the code-text separators) are no longer highlighted
+  (it was highlighted as comments before).
+  This somehow provides more information about how Agda lexes literate files.
+
+* Agda now also displays the values of let-bound variables in the
+  context instead of just their types
+  [Issue [#4199](https://github.com/agda/agda/issues/4199)].
+
+* Agda will now try to preserve the ellipsis (`...`) during case
+  splitting when possible. To manually expand the ellipsis, you may
+  ask Agda to case split on the special identifier `.`.
+  [Issue [#2589](https://github.com/agda/agda/issues/2589)]
+
+* Agda will now also show variables named `_` in the context if they
+  are instance arguments (see
+  [#4307](https://github.com/agda/agda/issues/4307)). Instance
+  arguments are now also marked as `(instance)` in the context. Example:
+
+  ```agda
+  f : {{_ : A}} → A
+  f = ?
+  ```
+
+  Agda will now display the goal as follows:
+
+  ```
+  Goal: A
+  ————————————————————————————————————————————————————————————
+  _ : A   (instance)
+  ```
+
+* It is now possible to ask Agda to terminate itself after any
+  previously invoked commands have completed, by giving a prefix
+  argument to `agda2-term`.
+
+* The command `agda2-measure-load-time` has been removed.
+
+GHC Backend
+-----------
+
+* Types which have a COMPILE GHC pragma are no longer erased
+  [Issue [#3732](https://github.com/agda/agda/issues/3732)].
+
+  ```agda
+  data I : Set where
+    bar : I
+
+  {-# FOREIGN GHC data I = Bar     #-}
+  {-# COMPILE GHC I = data I (Bar) #-}
+
+  data S : Set where
+    foo :  I → S
+
+  {-# FOREIGN GHC data S = Foo I #-}
+  {-# COMPILE GHC S = data S (Foo) #-}
+  ```
+  Previously [Issue [#2921](https://github.com/agda/agda/issues/2921)],
+  the last binding was incorrect, since the argument of
+  singleton type `I` was erased from the constructor `foo` during
+  compilation.  The required shape of `S` was previously
+  ```
+  {-# FOREIGN GHC data S = Foo #-}
+  ```
+  i.e., constructor `Foo` had to have no arguments.
+
+  For the sake of transparency, Haskell constructors bound to
+  Agda constructors now take the same arguments.
+  This is especially important if Haskell bindings are to be
+  produced automatically by third party tool.
+
+LaTeX backend
+-------------
+
+* Now the code environment complains if it is given unrecognised options.
+
+  It is also possible to write, say, `hide=true` instead of `hide`,
+  and `hide=false` means that the `hide` option should not be used.
+  Furthermore the same option can be given multiple times, in which
+  case later choices take precedence over earlier ones.
+
+* The code environment has a new option, `number`.
+
+  When the option `number` is used an equation number is generated for
+  the code listing. The number is set to the right, centered
+  vertically. By default the number is set in parentheses, but this
+  can be changed by redefining `\AgdaFormatCodeNumber`.
+
+  The option can optionally be given an argument: when `number=l` is
+  used a label `l`, referring to the code listing, is generated. It is
+  possible to use this option several times with different labels.
+
+  The option has no effect if used together with `hide`, `inline` or
+  `inline*`.
+
+API
+----
+* Removed module `Agda.Utils.HashMap`. It only re-exported `Data.HashMap.Strict`
+  from the package `unordered-containers`. Use `Data.HashMap.Strict` instead.
+
+* Removed module `Agda.Utils.Char`. It used to provide functions converting a
+  `Char` in base 8, 10, and 16 to the corresponding `Int`. Use `digitToInt` in
+  `Data.Char` instead. The rest of module was about Unicode test which was not
+  used.
+
+* `Agda.Utils.List` no longer provides `headMaybe`.
+  Use `listToMaybe` in `Data.Maybe` instead.
+
+* `Agda.Utils.Either` no longer provides `mapEither`. Use `bimap` in
+  `Data.Bifunctor` instead.
+
+* `Agda.Utils.Map` no longer provides `unionWithM`, `insertWithKeyM`,
+  `allWithKey`, `unzip`, and `unzip3`.
+
+Other issues
+------------
+
+For 2.6.1, the following issues were also closed (see [bug
+tracker](https://github.com/agda/agda/issues)):
+
+  -  [#470](https://github.com/agda/agda/issues/470): Constraint solving in heterogenous situations
+  -  [#471](https://github.com/agda/agda/issues/471): Emacs command to show goal with constraints on it
+  -  [#500](https://github.com/agda/agda/issues/500): Allow creation of implicit parameters in with blocks
+  -  [#543](https://github.com/agda/agda/issues/543): Irrelevant projections are inconsistent
+  -  [#760](https://github.com/agda/agda/issues/760): Warning for open public in an abstract block
+  -  [#1073](https://github.com/agda/agda/issues/1073): Solve C-c C-s inserts variables that are not in scope
+  -  [#1097](https://github.com/agda/agda/issues/1097): Allow record patterns in lambda-bound positions
+  -  [#1182](https://github.com/agda/agda/issues/1182): Request: allowing the use of patterns in syntax-bound variables
+  -  [#1381](https://github.com/agda/agda/issues/1381): Termination checker rejects function with with-clause
+  -  [#1445](https://github.com/agda/agda/issues/1445): Lack of subject reduction with REWRITE
+  -  [#1820](https://github.com/agda/agda/issues/1820): Case splitting should preserve existing names
+  -  [#2068](https://github.com/agda/agda/issues/2068): Copattern matching: Hyvernat termination would succeed
+  -  [#2148](https://github.com/agda/agda/issues/2148): Option to use use `stack exec` for GHC backend
+  -  [#2170](https://github.com/agda/agda/issues/2170): Two equal irrelevant definitions: one is type checked, the other is not
+  -  [#2284](https://github.com/agda/agda/issues/2284): Disallow duplicate bound variable in lambda and pi
+  -  [#2414](https://github.com/agda/agda/issues/2414): Case splitting loses as-patterns
+  -  [#2498](https://github.com/agda/agda/issues/2498): Resolution of unnamed instances
+  -  [#2512](https://github.com/agda/agda/issues/2512): Propose: Split the changelog
+  -  [#2530](https://github.com/agda/agda/issues/2530): --ignore-interfaces should not recompile Primitive.agda
+  -  [#2535](https://github.com/agda/agda/issues/2535): Expose name id in reflection API
+  -  [#2589](https://github.com/agda/agda/issues/2589): Preserve the ellipsis (dots) when case splitting "with" arguments
+  -  [#2610](https://github.com/agda/agda/issues/2610): Avoid rechecking by storing interfaces in separate directories?
+  -  [#2619](https://github.com/agda/agda/issues/2619): Feature request: link to `renaming` clause
+  -  [#2902](https://github.com/agda/agda/issues/2902): Case-splitting should not generate patterns containing pattern synonyms
+  -  [#3034](https://github.com/agda/agda/issues/3034): Pattern matching without K seemingly illogical for the inductive family of squares
+  -  [#3073](https://github.com/agda/agda/issues/3073): type-in-type and spurious levels
+  -  [#3081](https://github.com/agda/agda/issues/3081): Termination problem: copatterns and without-K
+  -  [#3089](https://github.com/agda/agda/issues/3089): Nicer syntax for implicit @-patterns
+  -  [#3095](https://github.com/agda/agda/issues/3095): Would like to make hidden variable visible but it is created ambiguous
+  -  [#3136](https://github.com/agda/agda/issues/3136): Spurious module parameters printed in extended lambda in termination error
+  -  [#3189](https://github.com/agda/agda/issues/3189): No information about which warnings are enabled by default
+  -  [#3233](https://github.com/agda/agda/issues/3233): Type declarations not accompanied by a definition should be highlighted in the emacs mode
+  -  [#3238](https://github.com/agda/agda/issues/3238): Printing of inserted hidden lambdas
+  -  [#3293](https://github.com/agda/agda/issues/3293): Absurd match in a do block
+  -  [#3295](https://github.com/agda/agda/issues/3295): Allow import of files with incomplete pattern matching
+  -  [#3353](https://github.com/agda/agda/issues/3353): Case splitting turns named arguments into positional arguments
+  -  [#3383](https://github.com/agda/agda/issues/3383): Document the DISPLAY pragma
+  -  [#3417](https://github.com/agda/agda/issues/3417): No highlighting for code that fails termination checking when an error is encountered
+  -  [#3423](https://github.com/agda/agda/issues/3423): Implicit arguments with custom macro for resolution
+  -  [#3432](https://github.com/agda/agda/issues/3432): Highlighting does not work for pattern synonyms in import lists
+  -  [#3493](https://github.com/agda/agda/issues/3493): Impossible to normalize elements in a proposition
+  -  [#3525](https://github.com/agda/agda/issues/3525): Rewrite rules with non-linear patterns do not work in presence of Prop
+  -  [#3545](https://github.com/agda/agda/issues/3545): JavaScript backend: mapping a function that returns Set fails
+  -  [#3574](https://github.com/agda/agda/issues/3574): Support precedent rebind / changing the precedents in builtin library
+  -  [#3582](https://github.com/agda/agda/issues/3582): Error message referring to Set instead of Prop
+  -  [#3594](https://github.com/agda/agda/issues/3594): Occurs check throws error when a solution is possible by eta expansion
+  -  [#3599](https://github.com/agda/agda/issues/3599): Bad performance on pathToEquiv
+  -  [#3606](https://github.com/agda/agda/issues/3606): Do not create/display superfluous metas and show constraints in a readable way
+  -  [#3654](https://github.com/agda/agda/issues/3654): Show non-blocked constraints first in list of unsolved constraints
+  -  [#3695](https://github.com/agda/agda/issues/3695): Generalisation introduces multiple explicit arguments for one generalisable variable
+  -  [#3698](https://github.com/agda/agda/issues/3698): Remove primComp?
+  -  [#3712](https://github.com/agda/agda/issues/3712): Sigma not listed in Built-ins documentation
+  -  [#3724](https://github.com/agda/agda/issues/3724): Internal error with Prop and inductive-inductive type
+  -  [#3725](https://github.com/agda/agda/issues/3725): Support GHC 8.8.1
+  -  [#3730](https://github.com/agda/agda/issues/3730): Internal error resulting from unused implicit argument
+  -  [#3735](https://github.com/agda/agda/issues/3735): Incorrect context when generalisable variable is used
+  -  [#3736](https://github.com/agda/agda/issues/3736): Safe decidability equality support for Name and Meta
+  -  [#3745](https://github.com/agda/agda/issues/3745): Update user manual on built-ins
+  -  [#3749](https://github.com/agda/agda/issues/3749): Inconsistency: Rounding op differentiates NaNs
+  -  [#3759](https://github.com/agda/agda/issues/3759): Change the default RTS options?
+  -  [#3774](https://github.com/agda/agda/issues/3774): de Bruijn index out of scope with rewrite rules
+  -  [#3776](https://github.com/agda/agda/issues/3776): Conversion check fails too quickly when type could be eta unit type
+  -  [#3779](https://github.com/agda/agda/issues/3779): Incorrectly ordered generalised variables
+  -  [#3785](https://github.com/agda/agda/issues/3785): Comparison of blocked terms doesn't respect eta
+  -  [#3791](https://github.com/agda/agda/issues/3791): Asking Agda to solve a constraint inside a macro
+  -  [#3803](https://github.com/agda/agda/issues/3803): Parse empty field lists
+  -  [#3805](https://github.com/agda/agda/issues/3805): Agda prelude: Internal error at src/full/Agda/TypeChecking/Reduce/Fast.hs:1347
+  -  [#3807](https://github.com/agda/agda/issues/3807): Internal error related to generalisable variables
+  -  [#3812](https://github.com/agda/agda/issues/3812): Rewriting projected symbols leads to loss of subject reduction
+  -  [#3813](https://github.com/agda/agda/issues/3813): Destructuring leads to invalid premises
+  -  [#3818](https://github.com/agda/agda/issues/3818): For open import M, Agda should remember that M is an external module
+  -  [#3824](https://github.com/agda/agda/issues/3824): rewrite drops named where module
+  -  [#3825](https://github.com/agda/agda/issues/3825): record{M} syntax reports unsolved metas in module M instead of in record expression
+  -  [#3828](https://github.com/agda/agda/issues/3828): Internal error in Agda/TypeChecking/Coverage.hs:467
+  -  [#3829](https://github.com/agda/agda/issues/3829): Case-split: don't generate pattern covered by unreachable clause
+  -  [#3830](https://github.com/agda/agda/issues/3830): primShow(Char/String) display spurious square brackets
+  -  [#3831](https://github.com/agda/agda/issues/3831): Wrong de Bruijn indices for reflected variables inside an extended context
+  -  [#3843](https://github.com/agda/agda/issues/3843): Internal error with-clause and unification
+  -  [#3851](https://github.com/agda/agda/issues/3851): C-c C-h should default to AsIs rather than Simplified
+  -  [#3866](https://github.com/agda/agda/issues/3866): `--no-unicode` option producing unicode variable names
+  -  [#3878](https://github.com/agda/agda/issues/3878): Case splitting should respect existing input
+  -  [#3879](https://github.com/agda/agda/issues/3879): Only unqualified pattern synonyms should be used for resugaring
+  -  [#3882](https://github.com/agda/agda/issues/3882): de Bruijn index out of scope
+  -  [#3892](https://github.com/agda/agda/issues/3892): Internal error with `data .. where` definitions
+  -  [#3898](https://github.com/agda/agda/issues/3898): Forcing analysis sensitive to normalization
+  -  [#3900](https://github.com/agda/agda/issues/3900): Abstract constructor not usable in function definition involving "with"
+  -  [#3901](https://github.com/agda/agda/issues/3901): Unnamed implicit non-dependent function space {A} -> B and {{A}} -> B
+  -  [#3912](https://github.com/agda/agda/issues/3912): Generalisable variables generate unknown and explicit parameters
+  -  [#3919](https://github.com/agda/agda/issues/3919): Case splitting fails in parameterized module
+  -  [#3927](https://github.com/agda/agda/issues/3927): `import … hiding …` should be documented
+  -  [#3928](https://github.com/agda/agda/issues/3928): The error message `Hiding … has no effect` should be improved
+  -  [#3930](https://github.com/agda/agda/issues/3930): BUILTIN NATURAL internal error at Forcing.hs:232
+  -  [#3932](https://github.com/agda/agda/issues/3932): Internal error when mixing implicit and explicit mutual blocks
+  -  [#3937](https://github.com/agda/agda/issues/3937): Internal error at "ConcreteToAbstract:1372"
+  -  [#3940](https://github.com/agda/agda/issues/3940): Weird error with piSort and generalization
+  -  [#3943](https://github.com/agda/agda/issues/3943): Print also hidden problematic unification terms
+  -  [#3955](https://github.com/agda/agda/issues/3955): Document module keyword in using/hiding/renaming
+  -  [#3956](https://github.com/agda/agda/issues/3956): Duplicate name in environment buffer with @-pattern
+  -  [#3964](https://github.com/agda/agda/issues/3964): Agda overwrites user-written dotted pattern
+  -  [#3965](https://github.com/agda/agda/issues/3965): Wrong indication of unreachable clauses
+  -  [#3966](https://github.com/agda/agda/issues/3966): All clauses marked when one clause has unification error
+  -  [#3972](https://github.com/agda/agda/issues/3972): Unreachable clause leads to internal error at Serialise/Instances/Internal.hs:94 (MetaV)
+  -  [#3974](https://github.com/agda/agda/issues/3974): Range for unexpected implicit argument on lhs too big
+  -  [#3983](https://github.com/agda/agda/issues/3983): TERMINATING accepted with --safe if hidden in a block
+  -  [#3989](https://github.com/agda/agda/issues/3989): Warn about duplicate bindings in a single telescope
+  -  [#4000](https://github.com/agda/agda/issues/4000): How to get Agda to ignore `~/.agda`?
+  -  [#4006](https://github.com/agda/agda/issues/4006): Internal error related to abstract and variable
+  -  [#4007](https://github.com/agda/agda/issues/4007): Cannot give pattern-matching lambda in abstract setting
+  -  [#4010](https://github.com/agda/agda/issues/4010): unquoteDef fails in abstract block
+  -  [#4012](https://github.com/agda/agda/issues/4012): Internal error when accessing abstract definitions created by unquoteDef/Decl
+  -  [#4020](https://github.com/agda/agda/issues/4020): Rewriting incorrectly considers level variables under lambdas as unbound in the LHS
+  -  [#4032](https://github.com/agda/agda/issues/4032): Loss of subject reduction involving --rewriting even when --confluence-check is on and everything passes the confluence checker
+  -  [#4038](https://github.com/agda/agda/issues/4038): Rewriting sometimes fails to rewrite in the presence of unsolved metas
+  -  [#4044](https://github.com/agda/agda/issues/4044): Equality checking uses too much memory in 2.6.0 (compared to 2.5.4)
+  -  [#4046](https://github.com/agda/agda/issues/4046): Remove (deprecated) codata keyword
+  -  [#4048](https://github.com/agda/agda/issues/4048): Rewriting rule fails to trigger
+  -  [#4049](https://github.com/agda/agda/issues/4049): Internal error with sized types if the target type of a constructor is an alias
+  -  [#4051](https://github.com/agda/agda/issues/4051): Internal error when importing a module with a hole in a type
+  -  [#4053](https://github.com/agda/agda/issues/4053): Emacs-mode: Case split leaves part of old line behind
+  -  [#4059](https://github.com/agda/agda/issues/4059): Two variants of irrefutable with?
+  -  [#4066](https://github.com/agda/agda/issues/4066): Regression related to instance resolution
+  -  [#4116](https://github.com/agda/agda/issues/4116): Internal error Forcing.hs:232
+  -  [#4121](https://github.com/agda/agda/issues/4121): Pattern synonyms cannot be made private
+  -  [#4125](https://github.com/agda/agda/issues/4125): Type checker normalizes too much
+  -  [#4134](https://github.com/agda/agda/issues/4134): Internal error triggered by missing check for irrelevant meta dependencies
+  -  [#4136](https://github.com/agda/agda/issues/4136): Overzealous pruning of metavariable with irrelevant argument
+  -  [#4141](https://github.com/agda/agda/issues/4141): Printing of DontCare should not use dot syntax
+  -  [#4142](https://github.com/agda/agda/issues/4142): defCopatternLHS needs to be set when record expression were translated to copatterns
+  -  [#4148](https://github.com/agda/agda/issues/4148): Internal error related to records and type-level indices
+  -  [#4152](https://github.com/agda/agda/issues/4152): Variables in Prop position should not raise hard error in occurs check
+  -  [#4154](https://github.com/agda/agda/issues/4154): Renaming declarations within a module may cause name clash
+  -  [#4158](https://github.com/agda/agda/issues/4158): Double check failure (unaware of rewrite rule)
+  -  [#4163](https://github.com/agda/agda/issues/4163): pattern matching in parametrized module leads to ill-typed definitions in where modules.
+  -  [#4170](https://github.com/agda/agda/issues/4170): Tactic causes Agda to enter into an infinite loop
+  -  [#4179](https://github.com/agda/agda/issues/4179): Coverage check false positive
+  -  [#4185](https://github.com/agda/agda/issues/4185): Agda uses η-equality for record types defined with no-eta-equality
+  -  [#4205](https://github.com/agda/agda/issues/4205): Internal error in connection with with, copatterns, and open record
+  -  [#4211](https://github.com/agda/agda/issues/4211): Cannot add as-pattern on literal pattern
+  -  [#4214](https://github.com/agda/agda/issues/4214): `with` abstraction fails with HIT constructors in the goal
+  -  [#4215](https://github.com/agda/agda/issues/4215): Case splitting should respect Nat literals
+  -  [#4255](https://github.com/agda/agda/issues/4255): Hole filler accepted, but type check error on reload
+  -  [#4261](https://github.com/agda/agda/issues/4261): Order of arguments affects lambda pattern matching
+  -  [#4268](https://github.com/agda/agda/issues/4268): Give failure with large quantification
+  -  [#4269](https://github.com/agda/agda/issues/4269): Universe levels are not solved
+  -  [#4283](https://github.com/agda/agda/issues/4283): DeBruijn issue(?) in standard library tests
+  -  [#4289](https://github.com/agda/agda/issues/4289): datatype scope and import guidelines
+  -  [#4297](https://github.com/agda/agda/issues/4297): Missing documentation: NO_UNIVERSE_CHECK pragma
+  -  [#4310](https://github.com/agda/agda/issues/4310): Anonymous .. binder should not lead to a parse error
+  -  [#4314](https://github.com/agda/agda/issues/4314): Internal error with generalize
+  -  [#4320](https://github.com/agda/agda/issues/4320): Path constructor overloading
+  -  [#4323](https://github.com/agda/agda/issues/4323): Internal error (Rewriting.hs:395) with generalize and rewrite rules
+  -  [#4330](https://github.com/agda/agda/issues/4330): Equations for cubical subtypes
+  -  [#4348](https://github.com/agda/agda/issues/4348): Seemingly needless repetition of highlighting of warnings
+  -  [#4360](https://github.com/agda/agda/issues/4360): Missing warning for declaring constructor instances for records with explicit fields
+  -  [#4361](https://github.com/agda/agda/issues/4361): Inconsistent highlighting of BUILTING EQUALITY/REWRITE
+  -  [#4371](https://github.com/agda/agda/issues/4371): Inconsistency with rewrite rules and assumptions in Prop
+  -  [#4373](https://github.com/agda/agda/issues/4373): Non-imported instances are used for instance resolution
+  -  [#4375](https://github.com/agda/agda/issues/4375): Internal error in Agda/TypeChecking/Monad/Context.hs:120
+  -  [#4380](https://github.com/agda/agda/issues/4380): Parse error with instance constructor and end of file
+  -  [#4382](https://github.com/agda/agda/issues/4382): Rewriting and records with eta
+  -  [#4387](https://github.com/agda/agda/issues/4387): Less responsive Emacs mode in v2.6.1 release candidate 1
+  -  [#4390](https://github.com/agda/agda/issues/4390): Unification finds solution with bound variable used at wrong modality
+  -  [#4391](https://github.com/agda/agda/issues/4391): Termination checking failed with guardedness
+  -  [#4399](https://github.com/agda/agda/issues/4399): Case split on unnamed argument produces non-sensical code
+  -  [#4401](https://github.com/agda/agda/issues/4401): Missing check on context variables leads to Set:Set with --cumulativity
+  -  [#4404](https://github.com/agda/agda/issues/4404): Disambiguation fails in Cubical Agda
+  -  [#4410](https://github.com/agda/agda/issues/4410): Rewrite rule matching does not respect Prop
+  -  [#4447](https://github.com/agda/agda/issues/4447): Positivity: internal error with projection in constructor type
+  -  [#4451](https://github.com/agda/agda/issues/4451): Highlighting: use several lookups rather than merging hash-maps?
+  -  [#4452](https://github.com/agda/agda/issues/4452): Compiler error when using REWRITE
+  -  [#4469](https://github.com/agda/agda/issues/4469): The warning machinery does not work correctly when interface files are involved
+
+
+The following previously closed issues were reopened:
+
+  -  [#1556](https://github.com/agda/agda/issues/1556): Agda allows "very dependent" types
diff --git a/doc/release-notes/2.6.2.1.md b/doc/release-notes/2.6.2.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.2.1.md
@@ -0,0 +1,149 @@
+Release notes for Agda version 2.6.2.1
+======================================
+
+Highlights
+----------
+
+* Agda 2.6.2.1 catches up to changes in the Haskell ecosystem
+  (GHC 9.2.1, `aeson-2.0`, `hashable-1.4.`).
+
+* Fixes some regressions introduced in 2.6.1:
+  [#5283](https://github.com/agda/agda/issues/5283)
+  [#5506](https://github.com/agda/agda/issues/5506)
+  [#5610](https://github.com/agda/agda/issues/5610)
+
+* Fixes some regressions introduced in 2.6.2:
+  [#5508](https://github.com/agda/agda/issues/5508)
+  [#5544](https://github.com/agda/agda/issues/5544)
+  [#5565](https://github.com/agda/agda/issues/5565)
+  [#5584](https://github.com/agda/agda/issues/5584)
+  [#5620](https://github.com/agda/agda/issues/5620)
+  [#5638](https://github.com/agda/agda/issues/5638)
+  [#5657](https://github.com/agda/agda/issues/5657)
+
+* Improvements to the compiler backends (see below).
+
+* Feature preview: `--ghc-strict`.
+
+Installation and infrastructure
+-------------------------------
+
+Agda 2.6.2.1 is expected to build with GHC versions 8.0 to 9.2.
+It has been tested with the latest minor version releases of GHC for
+each of these major versions:
+
+  - 8.0.2
+  - 8.2.2
+  - 8.4.4
+  - 8.6.5
+  - 8.8.4
+  - 8.10.7: Issue [#5539](https://github.com/agda/agda/issues/5539).
+  - 9.0.1
+  - 9.2.1:
+    Issue [#5442](https://github.com/agda/agda/issues/5442),
+    stackage issue [#6318](https://github.com/commercialhaskell/stackage/pull/6318).
+
+Agda 2.6.2.1 has been adapted to recent changes in the Haskell ecosystem, including:
+
+  - `Cabal-3.6.2`
+  - `aeson-2.0`:
+    Issue [#5593](https://github.com/agda/agda/issues/5593),
+    stackage issue [#6217](https://github.com/commercialhaskell/stackage/issues/6217).
+  - `hashable-1.4`:
+    Stackage issue [#6268](https://github.com/commercialhaskell/stackage/issues/6268).
+  - `transformers-0.6`
+
+Compiler backends
+-----------------
+
+* Both the GHC and JS backends now refuse to compile code that uses
+  `--cubical`.
+
+* The new option `--ghc-strict-data`, which is inspired by the GHC
+  language extension `StrictData`, makes the GHC backend compile
+  inductive data and record constructors to constructors with strict
+  arguments.
+
+  This does not apply to certain builtin types—lists, the maybe type,
+  and some types related to reflection—and might not apply to types
+  with `COMPILE GHC … = data …` pragmas.
+
+  This feature is experimental.
+
+* The new option `--ghc-strict`, which is inspired by the GHC language
+  extension `Strict`, makes the GHC backend generate mostly strict
+  code.
+
+  Functions might not be strict in unused arguments.
+
+  Function definitions coming from `COMPILE GHC` pragmas are not
+  affected.
+
+  This flag implies `--ghc-strict-data`, and the exceptions of that
+  flag applies to this flag as well.
+
+  Note that this option requires the use of GHC 9 or later.
+
+  This feature is experimental.
+
+* JS backend now uses the native `BigInt` instead of the
+  [biginteger.js](https://github.com/silentmatt/javascript-biginteger).
+  Fixes [#4878](https://github.com/agda/agda/issues/4878).
+
+LaTeX backend
+-------------
+
+* Files `agda.sty` and `postprocess-latex.pl` are now found in the `latex/`
+  subdirectory of the Agda data directory (`agda --print-agda-dir`).
+
+* `agda.sty` is now versioned (printed to the `.log` file by `latex`)
+  (see [#5473](https://github.com/agda/agda/issues/5473)).
+
+* Italics correction (inserted by `\textit` e.g. in `\AgdaBound`) now works,
+  thanks to moving the `\textcolor` wrapping to the outside in `agda.sty`
+  (see [#5471](https://github.com/agda/agda/issues/5471)).
+
+List of closed issues
+---------------------
+
+For 2.6.2.1, the following issues were
+[closed](https://github.com/agda/agda/issues?q=is%3Aissue+milestone%3A2.6.2.1+is%3Aclosed)
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+  - [#4878](https://github.com/agda/agda/issues/4878): Replace biginteger.js with native BigInt
+  - [#5283](https://github.com/agda/agda/issues/5283): Tactic command runs forever
+  - [#5291](https://github.com/agda/agda/issues/5291): `match` doesn't work for non-prefix-free cases
+  - [#5302](https://github.com/agda/agda/issues/5302): building tests with cabal
+  - [#5396](https://github.com/agda/agda/issues/5396): Internal error for rewriting without --confluence-check
+  - [#5398](https://github.com/agda/agda/issues/5398): Problem with LaTeX code for multi-line comments with blank lines
+  - [#5420](https://github.com/agda/agda/issues/5420): The JS backend generates incorrect code for Agda code that uses reflection
+  - [#5421](https://github.com/agda/agda/issues/5421): The GHC backend generates incorrect code for Agda code that uses reflection
+  - [#5431](https://github.com/agda/agda/issues/5431): --ghc-strict-data and --ghc-strict
+  - [#5433](https://github.com/agda/agda/issues/5433): The JS backend "installs" highlight-hover.js
+  - [#5440](https://github.com/agda/agda/issues/5440): (Re)Documenting `catchfilebetweentags` method of building latex files with Agda
+  - [#5442](https://github.com/agda/agda/issues/5442): Support GHC 9.2
+  - [#5463](https://github.com/agda/agda/issues/5463): Hole in the middle of a record is malformed
+  - [#5465](https://github.com/agda/agda/issues/5465): Compilation of Parser.y depends on the locale on Debian too
+  - [#5469](https://github.com/agda/agda/issues/5469): `onlyReduceDefs` should not prevent evaluation of macros
+  - [#5470](https://github.com/agda/agda/issues/5470): Internal error when using `REWRITE` in `private` block
+  - [#5471](https://github.com/agda/agda/issues/5471): LaTeX backend: italics correction
+  - [#5473](https://github.com/agda/agda/issues/5473): agda.sty has no version
+  - [#5478](https://github.com/agda/agda/issues/5478): Open goal inside record causes internal error (eta-contraction)
+  - [#5481](https://github.com/agda/agda/issues/5481): Pattern-matching on records in Prop allows eliminating into Set
+  - [#5489](https://github.com/agda/agda/issues/5489): C-c C-x C-a (abort) does not communicate well
+  - [#5490](https://github.com/agda/agda/issues/5490): Why does abort (C-c C-x C-a) remove highlighting from the buffer?
+  - [#5506](https://github.com/agda/agda/issues/5506): Agda panic: Pattern match failure
+  - [#5508](https://github.com/agda/agda/issues/5508): Internal error typechecking non-terminating function on case-insensitive filesystem
+  - [#5514](https://github.com/agda/agda/issues/5514): Support GHC 8.10.6
+  - [#5531](https://github.com/agda/agda/issues/5531): Internal bug: TypeChecking/Sort
+  - [#5532](https://github.com/agda/agda/issues/5532): "The module was successfully compiled" should mention with which backend
+  - [#5539](https://github.com/agda/agda/issues/5539): Support GHC 8.10.7
+  - [#5544](https://github.com/agda/agda/issues/5544): Internal error caused by addition of `Checkpoints` to `OpenThing`
+  - [#5557](https://github.com/agda/agda/issues/5557): Allow Agda to output data files
+  - [#5565](https://github.com/agda/agda/issues/5565): Internal error in Agda.TypeChecking.MetaVars
+  - [#5593](https://github.com/agda/agda/issues/5593): Compilation failure with `aeson-2`
+  - [#5602](https://github.com/agda/agda/issues/5602): The JS backend does not reduce constructor type signatures
+  - [#5610](https://github.com/agda/agda/issues/5610): Panic when checking pragma BUILTIN SHARP
+  - [#5620](https://github.com/agda/agda/issues/5620): Seemingly incorrect warning for abstract definition without type signature
+  - [#5633](https://github.com/agda/agda/issues/5633): Case splitting inserts one with pattern too much (regression in 2.6.2)
+  - [#5657](https://github.com/agda/agda/issues/5657): Internal error with postfix projection
diff --git a/doc/release-notes/2.6.2.2.md b/doc/release-notes/2.6.2.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.2.2.md
@@ -0,0 +1,109 @@
+Release notes for Agda version 2.6.2.2
+======================================
+
+Highlights
+----------
+
+* Agda 2.6.2.2 catches up to changes in the Haskell ecosystem
+  (`bytestring-0.11.2.0`, `mtl-2.3-rc3/4`, `text-icu-0.8.0.1`,
+  stackage `lts-19.0` and `nightly`).
+
+* Fixes inconsistency [#5838](https://github.com/agda/agda/issues/5838)
+  in `--cubical`.
+
+* Fixes some regressions introduced in 2.6.1:
+
+  - [#5809](https://github.com/agda/agda/issues/5809):
+    internal error with `--irrelevant-projections`.
+
+* Fixes some regressions introduced in 2.6.2:
+
+  - [#5705](https://github.com/agda/agda/issues/5705) and
+    [#5706](https://github.com/agda/agda/issues/5706):
+    inconsistency from universe level `Int` overflow.
+
+  - [#5784](https://github.com/agda/agda/issues/5784):
+    `primEraseEquality` does not compute.
+
+  - [#5805](https://github.com/agda/agda/issues/5805):
+    internal error involving holes and `with`.
+
+  - [#5819](https://github.com/agda/agda/issues/5819):
+    internal error when reducing in termination checker.
+
+* Other
+  [fixes](https://github.com/agda/agda/issues?q=is%3Aissue+milestone%3A2.6.2.2+is%3Aclosed)
+  and improvements (see below).
+
+Installation and infrastructure
+-------------------------------
+
+Agda supports GHC versions 8.0.2 to 9.2.2.
+
+* UTF-8 encoding is now used for the `libraries` and `executables`
+  configuration files (issue
+  [#5741](https://github.com/agda/agda/issues/5741)).
+
+Language
+--------
+
+* `macro` definitions can now be used even when they are declared as erased
+  (PR [#5744](https://github.com/agda/agda/pull/5744)).
+  For example, this is now accepted:
+  ```agda
+  macro
+    @0 trivial : Term → TC ⊤
+    trivial = unify (con (quote refl) [])
+
+  test : 42 ≡ 42
+  test = trivial
+  ```
+
+* Fixed inconsistent `--cubical` reductions for `transp`:
+  issue [#5838](https://github.com/agda/agda/issues/5838).
+
+* Fixed issues with reflection:
+
+  - [#5762](https://github.com/agda/agda/issues/5762):
+    do not eagerly check existence of commands in `executables` file.
+
+  - [#5695](https://github.com/agda/agda/issues/5695):
+    fix `elaborate-and-give` interaction command.
+
+  - [#5700](https://github.com/agda/agda/issues/5700):
+    scope of metas created during macro expansion.
+
+  - [#5712](https://github.com/agda/agda/issues/5712):
+    internal error with tactics on record fields of function type.
+
+* Fixed issues with instance search:
+
+  - [#5583](https://github.com/agda/agda/issues/5583):
+    constructor instances from parameterized modules.
+
+  - [#5787](https://github.com/agda/agda/issues/5787):
+    erased instance arguments.
+
+* Fixed issue [#5683](https://github.com/agda/agda/issues/5683) with
+  generalization in `let`.
+
+Compiler backends
+-----------------
+
+* `.hs` files generated by the GHC backend now switch off the
+  `warn-overlapping-patterns` warning (issue
+  [#5758](https://github.com/agda/agda/issues/5758)).
+
+* The GHC backend now calls `ghc` with environment setting
+  `GHC_CHARENC=UTF-8` (issue
+  [#5742](https://github.com/agda/agda/issues/5742)).
+
+Performance
+-----------
+
+* Better caching of interfaces
+  (issue [#2767](https://github.com/agda/agda/issues/2767)).
+
+* Various performance improvements concerning meta-variables:
+  issue [#5388](https://github.com/agda/agda/issues/5388)
+  and PR [#5733](https://github.com/agda/agda/pull/5733).
diff --git a/doc/release-notes/2.6.2.md b/doc/release-notes/2.6.2.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.2.md
@@ -0,0 +1,1250 @@
+Release notes for Agda version 2.6.2
+====================================
+
+Highlights
+----------
+
+* Several improvements and bug-fixes related to [Run-time
+  Irrelevance](https://agda.readthedocs.io/en/v2.6.2/language/runtime-irrelevance.html).
+
+* Several improvements and bug-fixes related to the [JavaScript
+  Backend](https://agda.readthedocs.io/en/v2.6.2/tools/compilers.html#javascript-backend).
+
+* Added experimental support for [Guarded Cubical
+  Agda](https://agda.readthedocs.io/en/v2.6.2/language/guarded-cubical.html).
+
+* The [Primitive
+  Sorts](https://agda.readthedocs.io/en/v2.6.2/language/built-ins.html#sorts)
+  of Agda (`Set` and `Prop`) are no longer keywords and can be renamed
+  when importing `Agda.Primitive`.
+
+* Added native support for the [Inspect
+  Idiom](https://agda.readthedocs.io/en/v2.6.2/language/with-abstraction.html#with-abstraction-equality).
+
+* Added support for making [System
+  Calls](https://agda.readthedocs.io/en/v2.6.2/language/reflection.html#system-calls)
+  from the reflection API.
+
+Installation and infrastructure
+-------------------------------
+
+* Added support for GHC 8.10.5 and 9.0.1.
+
+* Some expensive optimisations are now off by default
+  (see [#4521](https://github.com/agda/agda/issues/4521)).
+
+  These optimisations can in some cases make Agda substantially
+  faster, but they can also make the compilation of the Agda program
+  take more time and space.
+
+  The optimisations can be turned on manually (Cabal:
+  `-foptimise-heavily`, Stack: `--flag Agda:optimise-heavily`). They
+  are turned on (by default) when Agda is installed using `make
+  install`.
+
+  If the optimisations are turned on it might make sense to limit
+  GHC's memory usage (using something like `--ghc-options="+RTS -M6G
+  -RTS"`).
+
+Pragmas and options
+-------------------
+
+* New option `--auto-inline` turns on automatic compile-time inlining
+  of simple functions. This was previously enabled by default.
+
+  Note that the absence of automatic inlining can make typechecking
+  substantially slower.
+
+  The new default has repercussions on termination checking, for instance
+  (see [#4702](https://github.com/agda/agda/issues/4702)).
+  The following formulation of `plus` termination checks with `--auto-inline`
+  but not without:
+  ```agda
+  open import Agda.Builtin.Nat
+
+  case_of_ : {A B : Set} → A → (A → B) → B
+  case x of f = f x
+
+  plus : Nat → Nat → Nat
+  plus m n = case m of λ
+     { zero    → n
+     ; (suc m) → suc (plus m n)
+     }
+  ```
+  In this particular case, we can work around the limitation of the
+  termination checker with pragma `{-# INLINE case_of_ #-}`.
+
+* New options `--qualified-instances` (default) and
+  `--no-qualified-instances`. When `--no-qualified-instances` is
+  enabled, Agda will only consider candidates for instance search that
+  are in scope under an unqualified name (see
+  [#4522](https://github.com/agda/agda/pull/4522)).
+
+* New option `--call-by-name` turns off call-by-need evaluation at type
+  checking time.
+
+* New option `--highlight-occurrences` (off by default) enables the HTML
+  backend to include a JavaScript file that highlights all occurrences of
+  the mouse-hovered symbol (see
+  [#4535](https://github.com/agda/agda/pull/4535)).
+
+* New option `--no-import-sorts` disables the implicit `open
+  import Agda.Primitive using (Set; Prop)` at the top of each file
+  (see below).
+
+* New option `--local-confluence-check` to restore the old behaviour
+  of the `--confluence-check` flag (see below for the new behaviour).
+
+* New primitive `primStringFromListInjective` internalising the fact that
+  `primStringFromList` is an injective function. It is bound in
+  `Agda.Builtin.String.Properties`.
+
+* New option `--allow-exec` enables the use of system calls during
+  type checking using the `AGDATCMEXECTC` builtin.
+
+* New option `--show-identity-substitutions` shows all arguments of
+  metavariables when pretty-printing a term, even if they amount to
+  just applying all the variables in the context.
+
+* The option `--rewriting` is now considered infective: if a module has
+  `--rewriting` enabled, then all modules importing it must also have
+  `--rewriting` enabled.
+
+* New option `--no-double-check` (default), opposite of the existing
+  `--double-check`.
+
+* Due to several known soundness issues with sized types (see
+  [#1201](https://github.com/agda/agda/issues/1201),
+  [#1946](https://github.com/agda/agda/issues/1946),
+  [#2820](https://github.com/agda/agda/issues/2820),
+  [#3026](https://github.com/agda/agda/issues/3026)), the
+  `--sized-types` flag can no longer be used while `--safe` is active.
+
+* New option `--guarded` turns on the Guarded Cubical extension of Agda.
+
+  See [Guarded Cubical](https://agda.readthedocs.io/en/v2.6.2/language/guarded-cubical.html)
+  in the documentation for more.
+
+* The flags `--guardedness` and `--sized-types` are no longer enabled
+  by default.
+
+Command-line interaction
+------------------------
+
+* In the previous release, Agda exited with either status 0 when the
+  program type checks successfully, or status 1 when encountering any
+  kind of error.  Now Agda exits with status 42 for type errors, 71
+  for errors in the commandline arguments, and 154 for impossible
+  errors. Exit status 1 may be returned under other circumstances; for
+  instance, an incomplete pattern matching, or an error generated by
+  the Haskell runtime.  See PR
+  [#4540](https://github.com/agda/agda/pull/4540).
+
+Lexical syntax
+--------------
+
+* Layout handling has been improved so that block starters can be
+  stacked on the same line
+  [#1145](https://github.com/agda/agda/issues/1145).
+
+  If several layout blocks are started by layout keywords without line
+  break in between (where line breaks inside block comments do not
+  count), then those blocks indented *more* than the last block go
+  passive, meaning they cannot be further extended by new statements.
+  ```agda
+    private module M where postulate
+              A : Set                 -- module-block goes passive
+              B : Set                 -- postulate-block can still be extended
+            module N where            -- private-block can still be extended
+  ```
+  Previously, this was a parse error.
+
+Language
+--------
+
+* Inductive records without η-equality no longer support both matching
+  on the record constructor and construction of record elements by
+  copattern matching.  It has been discovered that the combination of
+  both leads to loss of subject reduction, i.e., reduction does not
+  preserve typing.  See issue
+  [#4560](https://github.com/agda/agda/issues/4560).
+
+  η-equality for a record can be turned off manually with directive
+  `no-eta-equality` or command-line option `--no-eta-equality`, but it
+  is also automatically turned off for some recursive records.  For
+  records without η, matching on the record constructor is now off by
+  default and construction by copattern matching is on.  If you want
+  the converse, you can add the new record directive `pattern`.
+
+  Example with record pattern:
+  ```agda
+  record N : Set where
+    inductive
+    no-eta-equality
+    pattern
+    field out : Maybe N
+
+  pred : N → Maybe N
+  pred record{ out = m } = m
+  ```
+  Example with record constructor and use of `;` instead of newline:
+  ```agda
+  record N : Set where
+    inductive; no-eta-equality
+    pattern; constructor inn
+    field out : Maybe N
+
+  pred : N → Maybe N
+  pred (inn m) = m
+  ```
+
+* `Set` and `Prop` are no longer keywords but are now primitives
+  defined in the module `Agda.Primitive`. They can be renamed when
+  importing this module, for example:
+
+  ```agda
+  open import Agda.Primitive renaming (Set to Type)
+
+  test : Type₁
+  test = Type
+  ```
+
+  To preserve backwards compatibility, each top-level Agda module now
+  starts with an implicit statement:
+
+  ```agda
+  open import Agda.Primitive using (Set; Prop)
+  ```
+
+  This implicit import can be disabled with the
+  `--no-import-sorts` flag.
+
+* Agda now has support for sorts `Setωᵢ` (alternative syntax: `Setωi`)
+  for natural numbers `i`, where `Setω₀ = Setω`. These sorts form a
+  second hierarchy `Setωᵢ : Setωᵢ₊₁` similar to the standard hierarchy
+  of `Setᵢ`, but do not support universe polymorphism. It should not
+  be necessary to refer to these sorts during normal usage of Agda,
+  but they might be useful for defining reflection-based macros (see
+  [#2119](https://github.com/agda/agda/issues/2119) and
+  [#4585](https://github.com/agda/agda/issues/4585)).
+
+* Changed the internal representation of literal strings: instead of using a
+  linked list of characters (`String`), we are now using `Data.Text`. This
+  should be a transparent change from the user's point of view: the backend
+  was already packing these strings as text.
+
+  Used this opportunity to introduce a `primStringUncons` primitive in
+  `Agda.Builtin.String` (and to correspondingly add the
+  `Agda.Builtin.Maybe` it needs).
+
+* The option `--confluence-check` for rewrite rules has been given a
+  new implementation that checks global confluence instead of local
+  confluence. Concretely, it does so by enforcing two properties:
+
+  1. For any two left-hand sides of the rewrite rules that overlap
+     (either at the root position or at a subterm), the most general
+     unifier of the two left-hand sides is again a left-hand side of a
+     rewrite rule. For example, if there are two rules `suc m + n =
+     suc (m + n)` and `m + suc n = suc (m + n)`, then there should
+     also be a rule `suc m + suc n = suc (suc (m + n))`.
+
+  2. Each rewrite rule should satisfy the *triangle property*: For any
+     rewrite rule `u = w` and any single-step parallel unfolding `u =>
+     v`, we should have another single-step parallel unfolding `v =>
+     w`.
+
+  The previous behaviour of the confluence checker that only ensures
+  local confluence can be restored by using the
+  `--local-confluence-check` flag.
+
+* Binary integer literals with prefix `0b` (for instance,
+  `0b11001001`) are now supported.
+
+* Overloaded literals now require the conversion function (`fromNat`,
+  `fromNeg`, or `fromString`) to be in scope *unqualified* to take
+  effect.
+
+  Previously, it was enough for the function to be in scope at all,
+  which meant you couldn't import the corresponding builtin module
+  without having overloaded literals turned on.
+
+* Added `interleaved mutual` blocks where users can forward-declare
+  function, record, and data types and interleave their
+  definitions. These blocks are elaborated to more traditional mutual
+  blocks by:
+
+    - leaving the signatures where they are
+    - grouping the clauses for a function together with the first of them
+    - grouping the constructors for a datatype together with the first of them
+
+  Example: two interleaved function definitions
+
+  ```agda
+
+  interleaved mutual
+
+    -- Declarations:
+    even : Nat → Bool
+    odd  : Nat → Bool
+
+    -- zero is even, not odd
+    even zero = true
+    odd  zero = false
+
+    -- suc case: switch evenness on the predecessor
+    even (suc n) = odd n
+    odd  (suc n) = even n
+  ```
+
+  Other example: the definition of universe of types closed under the
+  natural numbers and pairing:
+
+  ```agda
+
+  interleaved mutual
+
+    -- Declaration of a product record, a universe of codes, and a decoding function
+    record _×_ (A B : Set) : Set
+    data U : Set
+    El : U → Set
+
+    -- We have a code for the type of natural numbers in our universe
+    constructor `Nat : U
+    El `Nat = Nat
+
+    -- Btw we know how to pair values in a record
+    record _×_ A B where
+      constructor _,_
+      inductive
+      field fst : A; snd : B
+
+    -- And we have a code for pairs in our universe
+    constructor _`×_ : (A B : U) → U
+    El (A `× B) = El A × El B
+  ```
+
+* Erased constructors (see
+  [#4638](https://github.com/agda/agda/issues/4638)).
+
+  Constructors can be marked as erased. Example:
+  ```agda
+    {-# OPTIONS --cubical --safe #-}
+
+    open import Agda.Builtin.Cubical.Path
+    open import Agda.Primitive
+
+    private
+      variable
+        a   : Level
+        A B : Set a
+
+    Is-proposition : Set a → Set a
+    Is-proposition A = (x y : A) → x ≡ y
+
+    data ∥_∥ (A : Set a) : Set a where
+      ∣_∣        : A → ∥ A ∥
+      @0 trivial : Is-proposition ∥ A ∥
+
+    rec : @0 Is-proposition B → (A → B) → ∥ A ∥ → B
+    rec p f ∣ x ∣           = f x
+    rec p f (trivial x y i) = p (rec p f x) (rec p f y) i
+  ```
+  In the code above the constructor `trivial` is only available at
+  compile-time, whereas `∣_∣` is also available at run-time. Erased
+  names can be used in bodies of clauses that match on `trivial`, if
+  the match is done in a non-erased position, like in the final clause
+  of `rec`. (Note that Cubical Agda programs still cannot be
+  compiled.)
+
+* Erased pattern-matching lambdas (see
+  [#4525](https://github.com/agda/agda/issues/4525)).
+
+  Regular pattern-matching lambdas are treated as non-erased
+  function definitions. One can make a pattern-matching lambda erased
+  by writing `@0` or `@erased` after the lambda:
+  ```agda
+  @0 _ : @0 Set → Set
+  _ = λ @0 { A → A }
+
+  @0 _ : @0 Set → Set
+  _ = λ @erased where
+    A → A
+  ```
+
+  The reflection machinery currently does not support erased
+  pattern-matching lambdas (they are quoted as regular
+  pattern-matching lambdas).
+
+* New (?) rule for modalities of generalised variables
+  (see [#5058](https://github.com/agda/agda/issues/5058)).
+
+  The new rule is that generalisable variables get the modality that
+  they are declared with, whereas other variables always get the
+  default modality. (It is unclear what the old rule was, perhaps
+  nothing was changed.)
+
+* Private abstract type signatures can no longer see through abstract
+  (see [#418](https://github.com/agda/agda/issues/418)).
+
+  This means that abstract definitions no longer evaluate in *any*
+  type signatures in the same module. Previously they evaluated in
+  type signatures of definitions that were both private and abstract.
+
+  It also means that metavariables in type signatures have to be
+  solved locally, and cannot make use of information in the definition
+  body, and that constructors of abstract datatypes are not in scope
+  in type signatures.
+
+* Type inference is disabled for abstract definitions (see
+  [#418](https://github.com/agda/agda/issues/418)).
+
+  This means that abstract definitions (inluding functions defined in
+  `where` blocks of abstract definitions) need complete type
+  signatures.
+
+* One can now declare syntax with two name parts without any hole in
+  between, and syntax without any holes.
+
+  Examples:
+  ```agda
+  syntax Σ A (λ x → B) = [ x ∶ A ] × B
+  syntax []            = [ ]
+  ```
+
+* Internalised the *inspect idiom* that allows users to abstract over
+  an expression in a ``with`` clause while, at the same time,
+  remembering the origin of the abstracted pattern via an equation.
+
+  In the following example, abstracting over and then matching on the
+  result of ``p x`` allows the first call to ``filter p (x ∷ xs)`` to
+  reduce.
+
+  In case the element ``x`` is kept, the second call to ``filter`` on
+  the LHS then performs the same ``p x`` test. Because we have
+  retained the proof that ``p x ≡ true`` in ``eq``, we are able to
+  rewrite by this equality and get it to reduce too.
+
+  This leads to just enough computation that we can finish the proof
+  with an appeal to congruence and the induction hypothesis.
+
+  ```agda
+  filter-filter : ∀ p xs → filter p (filter p xs) ≡ filter p xs
+  filter-filter p []       = refl
+  filter-filter p (x ∷ xs) with p x in eq
+  ... | false = filter-filter p xs -- easy
+  ... | true -- second filter stuck on `p x`: rewrite by `eq`!
+    rewrite eq = cong (x ∷_) (filter-filter p xs)
+  ```
+
+* As a consequence of the above extensions to `with`, lambdas and lets
+  now need parentheses when appearing in a `with`. For instance,
+
+  ```agda
+  with-on-fun : Nat → Nat
+  with-on-fun n with (λ m → m + n)  -- parentheses required!
+  ... | f = f n
+  ```
+
+* It is now possible to add hiding and relevance annotations to `with`
+  expressions. For example:
+
+  ```agda
+  module _ (A B : Set) (recompute : .B → .{{A}} → B) where
+
+    _$_ : .(A → B) → .A → B
+    f $ x with .{f} | .(f x) | .{{x}}
+    ... | y = recompute y
+  ```
+
+Builtins
+--------
+
+- Primitive operations for floating-point numbers changed. The equalities now
+  follow IEEE 754 equality, after unifying all NaNs. Primitive inequality was
+  added:
+  ```agda
+  primFloatEquality   : Float -> Float -> Bool -- from primFloatNumericEquality
+  primFloatLess       : Float -> Float -> Bool -- from primFloatNumericLess
+  primFloatInequality : Float -> Float -> Bool -- new
+  ```
+  The “numeric” relations are now deprecated.
+
+  There are several new predicates on floating-point numbers:
+  ```agda
+  primFloatIsInfinite     : Float -> Bool -- new
+  primFloatIsNaN          : Float -> Bool -- new
+  primFloatIsSafeInteger  : Float -> Bool -- new
+  ```
+  The `primFloatIsSafeInteger` function determines whether the value is a number
+  that is a safe integer, i.e., is within the range where the arithmetic
+  operations do not lose precision.
+
+  The operations for conversion to integers (`primRound`, `primFloor`,
+  and `primCeiling`) were renamed for consistency, and return a value
+  of type `Maybe Int`, returning `nothing` for NaN and the infinities:
+  ```agda
+  primFloatRound   : Float → Maybe Int -- from primRound
+  primFloatFloor   : Float → Maybe Int -- from primFloor
+  primFloatCeiling : Float → Maybe Int -- from primCeiling
+  ```
+
+  There are several new conversions:
+  ```agda
+  primIntToFloat    : Int -> Float               -- new
+  primFloatToRatio  : Float -> (Int × Nat)       -- new
+  primRatioToFloat  : Int -> Nat -> Float        -- new
+  primFloatDecode   : Float -> Maybe (Int × Int) -- new
+  primFloatEncode   : Int -> Int -> Maybe Float  -- new
+  ```
+  The `primFloatDecode` function decodes a floating-point number f to a mantissa
+  and exponent, such that `f = mantissa * 2 ^ exponent`, normalised such that
+  the mantissa is the smallest possible number. The `primFloatEncode` function
+  encodes a pair of a mantissa and exponent to a floating-point number.
+
+  There are several new operations:
+  ```agda
+  primFloatPow        : Float -> Float -> Float -- new
+  primFloatATan2      : Float -> Float -> Float -- from primATan2
+  primFloatSinh       : Float -> Float          -- new
+  primFloatCosh       : Float -> Float          -- new
+  primFloatTanh       : Float -> Float          -- new
+  primFloatASinh      : Float -> Float          -- new
+  primFloatACosh      : Float -> Float          -- new
+  primFloatATanh      : Float -> Float          -- new
+  ```
+  Furthermore, the following operations were renamed for consistency:
+  ```agda
+  primFloatExp        : Float -> Float          -- from primExp
+  primFloatSin        : Float -> Float          -- from primSin
+  primFloatLog        : Float -> Float          -- from primLog
+  primFloatCos        : Float -> Float          -- from primCos
+  primFloatTan        : Float -> Float          -- from primTan
+  primFloatASin       : Float -> Float          -- from primASin
+  primFloatACos       : Float -> Float          -- from primACos
+  primFloatATan       : Float -> Float          -- from primATan
+  ```
+
+  All of these operations are implemented on the JavaScript backend.
+
+- `primNatToChar` maps surrogate code points to the replacement character
+  `'U+FFFD` and surrogate code points are disallowed in character literals
+
+  [Surrogate code points](https://www.unicode.org/glossary/#surrogate_code_point)
+  are characters in the range `U+D800` to `U+DFFF` and are reserved for use by
+  UTF-16.
+
+  The reason for this change is that strings are represented (at type-checking
+  time and in the GHC backend) by Data.Text byte strings, which cannot
+  represent surrogate code points and replaces them by `U+FFFD`. By doing the
+  same for characters we can have `primStringFromList` be injective (witnessed
+  by `Agda.Builtin.String.Properties.primStringFromListInjective`).
+
+
+Reflection
+----------
+
+- New operation in `TC` monad, similar to `quoteTC` but operating on
+  types in `Setω`
+  ```agda
+  quoteωTC : ∀ {A : Setω} → A → TC Term
+  ```
+- `typeError` and `debugPrint` no longer inserts spaces around `termErr` and
+  `nameErr` parts. They also do a better job of respecting line breaks in
+  `strErr` parts.
+
+- The reflection machinery now supports quantities in `Arg` (see
+  [#5317](https://github.com/agda/agda/issues/5317)). The `ArgInfo`
+  type has changed, and there are new types `Modality` and `Quantity`:
+  ```agda
+  data Quantity : Set where
+    quantity-0 quantity-ω : Quantity
+
+  {-# BUILTIN QUANTITY   Quantity   #-}
+  {-# BUILTIN QUANTITY-0 quantity-0 #-}
+  {-# BUILTIN QUANTITY-ω quantity-ω #-}
+
+  data Modality : Set where
+    modality : (r : Relevance) (q : Quantity) → Modality
+
+  {-# BUILTIN MODALITY             Modality #-}
+  {-# BUILTIN MODALITY-CONSTRUCTOR modality #-}
+
+  data ArgInfo : Set where
+    arg-info : (v : Visibility) (m : Modality) → ArgInfo
+  ```
+
+- The representation of reflected patterns and clauses has
+  changed. Each clause now includes a telescope with the names and
+  types of the pattern variables.
+
+  ```agda
+  data Clause where
+    clause        : (tel : List (Σ String λ _ → Arg Type)) (ps : List (Arg Pattern)) (t : Term) → Clause
+    absurd-clause : (tel : List (Σ String λ _ → Arg Type)) (ps : List (Arg Pattern)) → Clause
+  ```
+
+  These telescopes provide additional information on the types of
+  pattern variables that was previously hard to reconstruct (see
+  [#2151](https://github.com/agda/agda/issues/2151)). When unquoting a
+  clause, the types in the clause telescope are currently ignored (but
+  this is subject to change in the future).
+
+  Three constructors of the `Pattern` datatype were also changed:
+
+  * pattern variables now refer to a de Bruijn index (relative to the
+    clause telescope) rather than a string,
+  * absurd patterns take a de Bruijn index and are expected to be bound by the
+    clause telescope,
+  * dot patterns now include the actual dotted term.
+
+  ```agda
+  data Pattern where
+    con    : (c : Name) (ps : List (Arg Pattern)) → Pattern
+    dot    : (t : Term)    → Pattern   -- previously:   dot : Pattern
+    var    : (x : Nat)     → Pattern   -- previously:   var : (x : String) → Pattern
+    lit    : (l : Literal) → Pattern
+    proj   : (f : Name)    → Pattern
+    absurd : (x : Nat)     → Pattern
+  ```
+
+  It is likely that this change to the reflected syntax requires you
+  to update reflection code written for previous versions of
+  Agda. Here are some tips for updating your code:
+
+  * When quoting a clause, you can recover the name of a pattern
+    variable by looking up the given index in the clause
+    telescope. The contents of dot patterns can safely be ignored
+    (unless you have a use for them).
+
+  * When creating a new clause for unquoting, you need to create a
+    telescope for the types of the pattern variables. To get back the
+    old behaviour of Agda, it is sufficient to set all the types of
+    the pattern variables to `unknown`. So you can construct the
+    telescope by listing the names of all pattern variables and absurd
+    patterns together with their `ArgInfo`. Meanwhile, the pattern
+    variables should be numbered in order to update them to the new
+    representation. As for the telescope types, the contents of a
+    `dot` pattern can safely be set to `unknown`.
+
+- New operation in `TC` monad, `execTC`, which calls an external executable
+  ```agda
+  execTC : (exe : String) (args : List String) (stdIn : String)
+         → TC (Σ Nat (λ _ → Σ String (λ _ → String)))
+  ```
+  The `execTC` builtin takes three arguments: the basename of the
+  executable (e.g., `"echo"`), a list of arguments, and the contents
+  of the standard input. It returns a triple, consisting of the exit
+  code (as a natural number), the contents of the standard output, and
+  the contents of the standard error.
+
+  The builtin is only available when `--allow-exec` is passed. (Note
+  that `--allow-exec` is incompatible with ``--safe``.) To make an
+  executable available to Agda, add the absolute path on a new line in
+  `~/.agda/executables`.
+
+- Two new operations in the `TC` monad, `onlyReduceDefs` and
+  `dontReduceDefs`:
+  ```agda
+  onlyReduceDefs : ∀ {a} {A : Set a} → List Name → TC A → TC A
+  dontReduceDefs : ∀ {a} {A : Set a} → List Name → TC A → TC A
+  ```
+  These functions allow picking a specific set of functions that
+  should (resp. should not) be reduced while executing the given `TC`
+  computation.
+
+  For example, the following macro unifies the current hole with the
+  term `3 - 3`:
+  ```agda
+  macro₁ : Term -> TC ⊤
+  macro₁ goal = do
+    u   ← quoteTC ((1 + 2) - 3)
+    u'  ← onlyReduceDefs (quote _+_ ∷ []) (normalise u)
+    unify u' goal
+  ```
+- New operation in the `TC` monad, `withReconstructed`:
+  ```agda
+  withReconstructed : ∀ {a} {A : Set a} → TC A → TC A
+  ```
+
+  This function ensures reconstruction of hidden parameters
+  after performing the `TC` computation.  For example, consider the
+  following type and function:
+  ```agda
+  record RVec {a} (X : Set a) (n : Nat) : Set a where
+    constructor vec
+    field sel : Fin n → X
+
+  test-rvec : Nat → RVec Nat 5
+  test-rvec x = vec λ _ → x
+  ```
+
+  In the reflected syntax the body of the `test-rvec` would be represented
+  as `con vec (unknown ∷ unknown ∷ unknown ∷ (lam _ x)`.  The use of
+  `withReconstructed` replaces `unknown`s with the actual values:
+  ```agda
+  macro₂ : Name → Term → TC ⊤
+  macro₂ n hole = do
+    (function (clause tel ps t ∷ [])) ←
+      withReconstructed (getDefinition n)
+      where _ → quoteTC "ERROR" >>= unify hole
+    quoteTC t >>= unify hole
+  ```
+
+- Three new constructors in the `Sort` datatype, `prop : Level →
+  Sort`, `propLit : Nat → Sort`, and `inf : Nat → Sort`, representing
+  the sorts `Prop ℓ`, `Propᵢ`, and `Setωᵢ`.
+
+- Terms that belong to a type in `Prop` are no longer unquoted to
+  `unknown` but to a proper `Term`. (See
+  [#3553](https://github.com/agda/agda/issues/3553).)
+
+Library management
+------------------
+
+- `.agda-lib` files can now contain an extra field `flags:` with
+  default flags for the library. Flags can be any flags that are
+  accepted as part of an `{-# OPTIONS ... #-}` pragma. For example,
+  file `my-library.agda-lib` with
+
+  ```
+  flags: --without-K
+  ```
+
+  will apply the `--without-K` flag to all Agda files in the current
+  directory and (recursive) subdirectories that do not themselves
+  contain an `.agda-lib` file.
+
+
+Emacs mode
+----------
+
+* New command prefix `C-u C-u C-u` for weak-head normalization. For instance,
+  given
+
+  ```agda
+  downFrom : Nat → List Nat
+  downFrom 0 = []
+  downFrom (suc n) = n ∷ downFrom n
+  ```
+
+  `C-u C-u C-u C-c C-n downFrom 5` returns `4 ∷ downFrom 4`.
+
+* New keyboard shortcut `C-c C-x C-i` for toggling display of
+  irrelevant arguments.
+
+* One can no longer use commands like `M-;` (`comment-dwim`) to
+  uncomment block comments. In return one can use `M-;` to comment out
+  pragmas. (See [#3329](https://github.com/agda/agda/issues/3329).)
+
+JSON Interaction mode
+---------------------
+
+Changes have been made to the structure of error and warning
+messages. The changes are summarized below. See
+[#5052](https://github.com/agda/agda/issues/5052) for additional
+details.
+
+* The format of an error or warning was previously a bare string. Now, errors
+  and warnings are represented by an object with a `"message"` key.
+
+  This means that responses _previously_ structured like:
+
+  ```json
+  {"…": "…", "error": "Foo bar baz"}
+  ```
+
+  will now be structured:
+
+  ```json
+  {"…": "…", "error": {"message": "Foo bar baz"}}
+  ```
+
+  This applies directly to the `PostPonedCheckFunDef` response kind
+  and `Error` info kind of the `DisplayInfo` response kind.
+
+* The format of collections of errors or warnings, which previously were each
+  represented by a single newline-joined string, has been updated to represent
+  each warning or error individually in a list.
+
+  That means that responses _previously_ structured like:
+
+  ```json
+  { "…": "…"
+  , "errors": "Postulates overcooked\nAxioms too wiggly"
+  , "warnings": "Something wrong\nSomething else\nwrong"
+  }
+  ```
+
+  will now be structured:
+
+  ```json
+  { "…": "…"
+  , "errors":
+    [ { "message": "Postulates overcooked" }
+    , { "message": "Axioms too wiggly" }
+    ]
+  , "warnings":
+    [ { "message": "Something wrong" }
+    , { "message": "Something else\nwrong" }
+    ]
+  }
+  ```
+
+  This applies to `CompilationOk`, `AllGoalsWarning`, and `Error` info
+  kinds of the `DisplayInfo` response kind.
+
+* The `Error` info kind of the `DisplayInfo` response kind has
+  additionally been updated to distinguish warnings and errors.
+
+  An example of the _previous_ format of a `DisplayInfo` response with
+  an `Error` info kind was:
+  ```json
+  {
+    "kind": "DisplayInfo",
+    "info": {
+      "kind": "Error",
+      "message": "———— Error —————————————————————————————————————————————————\n/data/code/agda-test/Test.agda:2,1-9\nFailed to find source of module M in any of the following\nlocations:\n  /data/code/agda-test/M.agda\n  /data/code/agda-test/M.lagda\nwhen scope checking the declaration\n  import M\n\n———— Warning(s) ————————————————————————————————————————————\n/data/code/agda-test/Test.agda:3,1-10\nEmpty postulate block."
+    }
+  }
+  ```
+
+  The updated format is:
+  ```json
+  {
+    "kind": "DisplayInfo",
+    "info": {
+      "kind": "Error",
+      "error": {
+        "message": "/data/code/agda-test/Test.agda:2,1-9\nFailed to find source of module M in any of the following\nlocations:\n  /data/code/agda-test/M.agda\n  /data/code/agda-test/M.lagda\nwhen scope checking the declaration\n  import M"
+      },
+      "warnings": [
+        {
+          "message": "/data/code/agda-test/Test.agda:3,1-10\nEmpty postulate block."
+        }
+      ]
+    }
+  }
+  ```
+
+Compiler backends -----------------
+
+- With option `--allow-unsolved-metas`, code with holes can be compiled.
+  If a hole is reached at runtime, the compiled program crashes.
+  See issue [#5103](https://github.com/agda/agda/issues/5103)
+
+- Previously the GHC backend compiled at least one instance of Hinze's
+  memoisation technique from ["Memo functions,
+  polytypically!"](http://www.cs.ox.ac.uk/ralf.hinze/publications/index.html#P11)
+  to reasonably efficient code. That is no longer the case (at least
+  for that particular instance, see
+  [#5153](https://github.com/agda/agda/issues/5153)).
+
+LaTeX backend
+-------------
+
+- The spacing in comments is now preserved when generating LaTex files
+  from literate Agda.  See
+  [#5320](https://github.com/agda/agda/pull/5320) for more details.
+
+HTML backend
+------------
+
+- The named `id` attributes for local modules inside local modules are
+  now different (see [#5335](https://github.com/agda/agda/pull/5320)).
+
+  For instance, consider the following Agda file:
+  ```agda
+  module Top-level where
+
+    module Inner where
+
+      module Inside-inner where
+  ```
+  Previously one could link to the module `Inside-inner` using a URL
+  that ended with `#Inside-inner`. Now one can use
+  `#Inner.Inside-inner` instead.
+
+JS backend
+----------
+
+- Smaller local variable names in the generated JS code.
+
+  Previously: `x0`, `x1`, `x2`, ...
+
+  Now: `a`, `b`, `c`, ..., `z`, `a0`, `b0`, ..., `z0`, `a1`, `b1`, ...
+
+- Improved indentation of generated JS code.
+
+- More compact rendering of generated JS functions.
+
+  Previously:
+  ```js
+  exports["N"]["suc"] = function (x0) {
+      return function (x1) {
+        return x1["suc"](x0);
+      };
+    };
+  ```
+
+  Now:
+  ```js
+  exports["N"]["suc"] = a => b => b["suc"](a);
+  ```
+
+- Irrelevant arguments are now erased in the generated JS code.
+
+  Example Agda code:
+  ```agda
+  flip : {A B C : Set} -> (B -> A -> C) -> A -> B -> C
+  flip f a b = f b a
+  ```
+
+  Previously generated JS code:
+  ```js
+  exports["flip"] = function (x0) {
+      return function (x1) {
+        return function (x2) {
+          return function (x3) {
+            return function (x4) {
+              return function (x5) {
+                return x3(x5)(x4);
+              };
+            };
+          };
+        };
+      };
+    };
+  ```
+
+  JS code generated now:
+  ```js
+  exports["flip"] = a => b => c => a(c)(b);
+  ```
+
+- Record fields are not stored separately (the fields are stored only
+  in the constructor) in the generated JS code.
+
+  Example Agda code:
+  ```agda
+  record Sigma (A : Set) (B : A -> Set) : Set where
+    field
+      fst : A
+      snd : B fst
+  ```
+
+  Previously generated JS code (look at the `"fst"` and `"snd"` fields in the
+  return value of `exports["Sigma"]["record"]`:
+  ```js
+  exports["Sigma"] = {};
+  exports["Sigma"]["fst"] = function (x0) {
+      return x0["record"]({
+        "record": function (x1, x2) {
+          return x1;
+        }
+      });
+    };
+  exports["Sigma"]["snd"] = function (x0) {
+      return x0["record"]({
+        "record": function (x1, x2) {
+          return x2;
+        }
+      });
+    };
+  exports["Sigma"]["record"] = function (x0) {
+      return function (x1) {
+        return {
+          "fst": x0,
+          "record": function (x2) {
+            return x2["record"](x0, x1);
+          },
+          "snd": x1
+        };
+      };
+    };
+  ```
+
+  JS code generated now:
+  ```js
+  exports["Sigma"] = {};
+  exports["Sigma"]["fst"] = a => a["record"]({"record": (b,c) => b});
+  exports["Sigma"]["snd"] = a => a["record"]({"record": (b,c) => c});
+  exports["Sigma"]["record"] = a => b => ({"record": c => c["record"](a,b)});
+  ```
+
+- `--js-optimize` flag has been added to the `agda` compiler.
+
+  With `--js-optimize`, `agda` does not wrap records in JS objects.
+
+  Example Agda code:
+  ```agda
+  record Sigma (A : Set) (B : A -> Set) : Set where
+    field
+      fst : A
+      snd : B fst
+  ```
+
+  JS code generated without the `--js-optimize` flag:
+  ```js
+  exports["Sigma"] = {};
+  exports["Sigma"]["fst"] = a => a["record"]({"record": (b,c) => b});
+  exports["Sigma"]["snd"] = a => a["record"]({"record": (b,c) => c});
+  exports["Sigma"]["record"] = a => b => ({"record": c => c["record"](a,b)});
+  ```
+
+  JS code generated with the `--js-optimize` flag:
+  ```js
+  exports["Sigma"] = {};
+  exports["Sigma"]["fst"] = a => a((b,c) => b);
+  exports["Sigma"]["snd"] = a => a((b,c) => c);
+  exports["Sigma"]["record"] = a => b => c => c(a,b);
+  ```
+
+  With `--js-optimize`, `agda` uses JS arrays instead of JS objects.
+  This is possible because constructor names are not relevant during the evaluation.
+
+  Example Agda code:
+  ```agda
+  data Bool : Set where
+    false : Bool
+    true  : Bool
+
+  not : Bool -> Bool
+  not false = true
+  not true  = false
+  ```
+
+  JS code generated without the `--js-optimize` flag:
+  ```js
+  exports["Bool"] = {};
+  exports["Bool"]["false"] = a => a["false"]();
+  exports["Bool"]["true"] = a => a["true"]();
+  exports["not"] = a => a({
+      "false": () => exports["Bool"]["true"],
+      "true": () => exports["Bool"]["false"]
+    });
+  ```
+
+  JS code generated with the `--js-optimize` flag:
+  ```js
+  exports["Bool"] = {};
+  exports["Bool"]["false"] = a => a[0/* false */]();
+  exports["Bool"]["true"] = a => a[1/* true */]();
+  exports["not"] = a => a([
+      /* false */() => exports["Bool"]["true"],
+      /* true */() => exports["Bool"]["false"]
+    ]);
+  ```
+
+  Note that comments are added to generated JS code to help human readers.
+
+  Erased branches are replaced by `null` in the generated array.  If
+  more than the half of branches are erased, the array is compressed
+  to be a object like `{3: ..., 13: ...}`.
+
+- `--js-minify` flag has been added to the `agda` compiler.
+
+  With `--js-minify`, `agda` discards comments and whitespace in the
+  generated JS code.
+
+
+Agda as a library (API)
+-----------------------
+
+* The `SourceInfo` record has been renamed to `Source`, and the
+  `sourceInfo` function to `parseSource`.
+
+Other issues
+------------
+
+For 2.6.2, the following issues were also closed (see [bug
+tracker](https://github.com/agda/agda/issues)):
+
+  -  [#418](https://github.com/agda/agda/issues/418): Unifier ignores presence of abstract keyword
+  -  [#958](https://github.com/agda/agda/issues/958): Module application display forms in parameterised modules
+  -  [#1145](https://github.com/agda/agda/issues/1145): Allow multiple layout keywords on the same line
+  -  [#2151](https://github.com/agda/agda/issues/2151): Add TC primitive to check left-hand side
+  -  [#2461](https://github.com/agda/agda/issues/2461): Support with in the presence of IApply patterns
+  -  [#2858](https://github.com/agda/agda/issues/2858): Feature request: Interleaving mutually-defined functions & datatypes
+  -  [#3000](https://github.com/agda/agda/issues/3000): Interaction: iterated give encounters internal error
+  -  [#3118](https://github.com/agda/agda/issues/3118): Feature request: default flags in .agda-lib file
+  -  [#3289](https://github.com/agda/agda/issues/3289): Postfix projections should not have hiding information
+  -  [#3360](https://github.com/agda/agda/issues/3360): Make Emacs mode available as a normal package via MELPA
+  -  [#3365](https://github.com/agda/agda/issues/3365): Update GitHub linguist syntax highlight file
+  -  [#3398](https://github.com/agda/agda/issues/3398): With the option --allow-unsolved-metas, the unsolved metas are not shown, only yellow
+  -  [#3422](https://github.com/agda/agda/issues/3422): Show names of instance candidates in error message
+  -  [#3486](https://github.com/agda/agda/issues/3486): Elaborate-and-give shouldn't reduce solution
+  -  [#3532](https://github.com/agda/agda/issues/3532): Refine does not work for functions with 10 arguments or more
+  -  [#3538](https://github.com/agda/agda/issues/3538): Regression: Rewrite rule involving constructors rejected in parametrized module
+  -  [#3588](https://github.com/agda/agda/issues/3588): Refine suggests overloaded constructor which is not in scope
+  -  [#3627](https://github.com/agda/agda/issues/3627): Where-blocks of clauses with irrelevant projections can use irrelevant variables
+  -  [#3644](https://github.com/agda/agda/issues/3644): Error message without position
+  -  [#3672](https://github.com/agda/agda/issues/3672): Better error messages for generalize easter eggs
+  -  [#3684](https://github.com/agda/agda/issues/3684): Make error about non-existent record field a warning?
+  -  [#3734](https://github.com/agda/agda/issues/3734): WARNING_ON_USAGE is not raised for constructors
+  -  [#3744](https://github.com/agda/agda/issues/3744): Internal error related to abstract
+  -  [#3870](https://github.com/agda/agda/issues/3870): Internal error during instance search
+  -  [#3926](https://github.com/agda/agda/issues/3926): Document the effect of `mutual` to the order of type checking
+  -  [#3933](https://github.com/agda/agda/issues/3933): `import` can remove definitions from scope
+  -  [#3961](https://github.com/agda/agda/issues/3961): Missing documentation for coverage checking
+  -  [#4071](https://github.com/agda/agda/issues/4071): Ill-scoped code in error message
+  -  [#4088](https://github.com/agda/agda/issues/4088): Strange scoping rules for irrefutable with, part 2
+  -  [#4093](https://github.com/agda/agda/issues/4093): Make it possible to rename Set?
+  -  [#4109](https://github.com/agda/agda/issues/4109): cannot declare data types in Setω
+  -  [#4131](https://github.com/agda/agda/issues/4131): Record definition doesn't compile without a specific `let` binding
+  -  [#4132](https://github.com/agda/agda/issues/4132): The regular expression for floats in the lexer is too liberal
+  -  [#4135](https://github.com/agda/agda/issues/4135): Constructor disambiguation picks non-unique solution
+  -  [#4157](https://github.com/agda/agda/issues/4157): Agda gets confused by multiple anonymous definitions in a single mutual block
+  -  [#4160](https://github.com/agda/agda/issues/4160): Printing implicit lambdas with --show-implicit
+  -  [#4161](https://github.com/agda/agda/issues/4161): An alternative solution for hGetContent error on Windows when non-English
+  -  [#4166](https://github.com/agda/agda/issues/4166): Instances that are not in scope are candidates for instance resolution
+  -  [#4208](https://github.com/agda/agda/issues/4208): Field named `_` in `genTel` record
+  -  [#4252](https://github.com/agda/agda/issues/4252): Interaction ids get conflated after iterated give
+  -  [#4265](https://github.com/agda/agda/issues/4265): Unsolved constraints when --no-syntactic-equality is used
+  -  [#4280](https://github.com/agda/agda/issues/4280): Test case for #4169 fails in JS backend
+  -  [#4291](https://github.com/agda/agda/issues/4291): Incorrect names can be generated for generalised variables
+  -  [#4341](https://github.com/agda/agda/issues/4341): The documentation of inContext seems wrong.
+  -  [#4350](https://github.com/agda/agda/issues/4350): Scoping bug with let open in telescope
+  -  [#4365](https://github.com/agda/agda/issues/4365): Module fails to type check after parametrising it by postulates
+  -  [#4400](https://github.com/agda/agda/issues/4400): TERMINATING pragma in where clause
+  -  [#4425](https://github.com/agda/agda/issues/4425): [doc] What are .agdai files?
+  -  [#4456](https://github.com/agda/agda/issues/4456): No error highlighting for error warnings?
+  -  [#4458](https://github.com/agda/agda/issues/4458): The command agda2-measure-load-time is broken
+  -  [#4481](https://github.com/agda/agda/issues/4481): Named implicit arguments do not behave the same in anonymous lambdas & definitions
+  -  [#4482](https://github.com/agda/agda/issues/4482): "Unexpected implicit argument" should pinpoint exactly where the error starts
+  -  [#4486](https://github.com/agda/agda/issues/4486): "did you mean" hint also for failing imports
+  -  [#4491](https://github.com/agda/agda/issues/4491): Add a primitive for Data.Text's uncons
+  -  [#4516](https://github.com/agda/agda/issues/4516): Internal error if files cannot be written to the directory for temporary files
+  -  [#4518](https://github.com/agda/agda/issues/4518): Confusing error message if missing import
+  -  [#4520](https://github.com/agda/agda/issues/4520): Better error for ambiguous BUILTIN [FROMNAT no longer working]
+  -  [#4521](https://github.com/agda/agda/issues/4521): Massive increase in memory required to install Agda 2.6.1
+  -  [#4526](https://github.com/agda/agda/issues/4526): Agda 2.6.1 bad performance: findProjectConfig slow in big directories
+  -  [#4528](https://github.com/agda/agda/issues/4528): Internal error due to new forcing translation
+  -  [#4530](https://github.com/agda/agda/issues/4530): Less normalization of goal types for instance search
+  -  [#4534](https://github.com/agda/agda/issues/4534): [reflection] quote is not a defined name
+  -  [#4536](https://github.com/agda/agda/issues/4536): co-pattern matching on empty record type removes body
+  -  [#4538](https://github.com/agda/agda/issues/4538): changing the predefined precedence of an operator
+  -  [#4543](https://github.com/agda/agda/issues/4543): Access violation on Windows on GHC 8.8.3, 8.8.4, 8.10.1 and 8.10.2
+  -  [#4550](https://github.com/agda/agda/issues/4550): Documentation build: malformed code-block
+  -  [#4556](https://github.com/agda/agda/issues/4556): [documentation] update hello world
+  -  [#4557](https://github.com/agda/agda/issues/4557): activate github's discussions beta
+  -  [#4560](https://github.com/agda/agda/issues/4560): Loss of canonicity with no-eta record and copatterns.
+  -  [#4572](https://github.com/agda/agda/issues/4572): add PiSort and UnivSort to the documentation
+  -  [#4576](https://github.com/agda/agda/issues/4576): quoteTC for Setω
+  -  [#4580](https://github.com/agda/agda/issues/4580): No highlighting for pragmas FROMNAT, FROMNEG, FROMSTRING
+  -  [#4583](https://github.com/agda/agda/issues/4583): QuickLaTeX backend does not highlight coinductive constructors as such
+  -  [#4586](https://github.com/agda/agda/issues/4586): Better error message  for "Not a valid let declaration"
+  -  [#4593](https://github.com/agda/agda/issues/4593): The blocking machinery seems to be broken
+  -  [#4595](https://github.com/agda/agda/issues/4595): Should Setω be a type?
+  -  [#4596](https://github.com/agda/agda/issues/4596): Improve pattern matching on records in telescopes
+  -  [#4606](https://github.com/agda/agda/issues/4606): The combination of Cubical Agda with inductive families is logically inconsistent
+  -  [#4610](https://github.com/agda/agda/issues/4610): Support Emacs 27.1
+  -  [#4615](https://github.com/agda/agda/issues/4615): Enable --no-sort-comparison by default?
+  -  [#4621](https://github.com/agda/agda/issues/4621): Make --rewriting infective
+  -  [#4623](https://github.com/agda/agda/issues/4623): Empty where blocks should get dead code warnings
+  -  [#4631](https://github.com/agda/agda/issues/4631): Non-linear patterns handled in a buggy way
+  -  [#4637](https://github.com/agda/agda/issues/4637): recCon-NOT-PRINTED in termination error in connection to with
+  -  [#4638](https://github.com/agda/agda/issues/4638): Erased constructors
+  -  [#4649](https://github.com/agda/agda/issues/4649): Repair Agda's REPL (agda -I) to work with --safe flag
+  -  [#4656](https://github.com/agda/agda/issues/4656): Function name not wrapped in `\AgdaFunction` in generated LaTeX
+  -  [#4662](https://github.com/agda/agda/issues/4662): Current module contents
+  -  [#4665](https://github.com/agda/agda/issues/4665): Documentation: add install instructions for stack
+  -  [#4671](https://github.com/agda/agda/issues/4671): Weird error message on case-insensitive file systems
+  -  [#4679](https://github.com/agda/agda/issues/4679): Cubical: giving seems to skip the boundary condition check for extended lambdas
+  -  [#4681](https://github.com/agda/agda/issues/4681): Get rid of auto-inlining?
+  -  [#4684](https://github.com/agda/agda/issues/4684): Type error due to --no-syntactic-equality
+  -  [#4687](https://github.com/agda/agda/issues/4687): Instance search fails with two equal candidates
+  -  [#4704](https://github.com/agda/agda/issues/4704): Case-split generates invalid code
+  -  [#4707](https://github.com/agda/agda/issues/4707): Just warn when `using` directive has repetitions
+  -  [#4721](https://github.com/agda/agda/issues/4721): de Bruijn index out of scope when using rewriting
+  -  [#4727](https://github.com/agda/agda/issues/4727): Meta-variable solutions contain subterms with the wrong modality
+  -  [#4735](https://github.com/agda/agda/issues/4735): primShowQName creates not-in-scope names
+  -  [#4737](https://github.com/agda/agda/issues/4737): Turn error `Hiding ... has no effect` into a warning
+  -  [#4750](https://github.com/agda/agda/issues/4750): Unification failure in 2.6.1 and the master branch
+  -  [#4752](https://github.com/agda/agda/issues/4752): Panic on unbound variable with pattern synonym
+  -  [#4768](https://github.com/agda/agda/issues/4768): De Bruijn index @0 in error "Not a finite domain"
+  -  [#4769](https://github.com/agda/agda/issues/4769): mergeEqualPs ignores Name and ArgInfo of merged-in patterns
+  -  [#4772](https://github.com/agda/agda/issues/4772): C-u C-u C-c C-? should show all goals normalized (Cmd_metas)
+  -  [#4773](https://github.com/agda/agda/issues/4773): Missing does-not-export warning for `open` directive for parametrised module
+  -  [#4775](https://github.com/agda/agda/issues/4775): Internal error when trying to use incorrect lambda syntax to pattern match
+  -  [#4784](https://github.com/agda/agda/issues/4784): Make erasure compatible with univalence
+  -  [#4795](https://github.com/agda/agda/issues/4795): Build "agda-tests" fails using dynamic linking
+  -  [#4815](https://github.com/agda/agda/issues/4815): Current master fails compilation: binding for 'error' shadows the existing binding
+  -  [#4828](https://github.com/agda/agda/issues/4828): Symlinks are incorrectly followed during compilation
+  -  [#4833](https://github.com/agda/agda/issues/4833): Internal error: cannot type-check file
+  -  [#4851](https://github.com/agda/agda/issues/4851): BUILTIN SIGMA and --type-in-type
+  -  [#4852](https://github.com/agda/agda/issues/4852): First load the file
+  -  [#4857](https://github.com/agda/agda/issues/4857): Instance argument is printed as explicit argument
+  -  [#4869](https://github.com/agda/agda/issues/4869): Internal error at src/full/Agda/TypeChecking/Serialise/Instances/Internal.hs:147
+  -  [#4880](https://github.com/agda/agda/issues/4880): Non-dependent, irrelevant, nameless arguments aren't accepted in arrows
+  -  [#4882](https://github.com/agda/agda/issues/4882): Missing `reduce` in `literalStrategy`
+  -  [#4888](https://github.com/agda/agda/issues/4888): "Illegal declaration(s) before top-level module" in Agda 2.6.1
+  -  [#4909](https://github.com/agda/agda/issues/4909): Rewrite rule not accepted with --no-fast-reduce
+  -  [#4924](https://github.com/agda/agda/issues/4924): Instance resolution loops infinitely even when an instance is available
+  -  [#4925](https://github.com/agda/agda/issues/4925): Too aggressive literal overloading
+  -  [#4928](https://github.com/agda/agda/issues/4928): Internal error checking cubical library
+  -  [#4929](https://github.com/agda/agda/issues/4929): Regression in 2.6.1 connected to forcing translation (internal error)
+  -  [#4944](https://github.com/agda/agda/issues/4944): Generalize: stuck on constraint ↑ i =< ↑ (↑ i) : Size
+  -  [#4946](https://github.com/agda/agda/issues/4946): Size polarity brittle with generalization
+  -  [#4949](https://github.com/agda/agda/issues/4949): Cubical: internal error in eta-expansion under constraints
+  -  [#4950](https://github.com/agda/agda/issues/4950): Range too large in complaint about missing definitions
+  -  [#4951](https://github.com/agda/agda/issues/4951): Data types in Setω are treated as non-fibrant
+  -  [#4952](https://github.com/agda/agda/issues/4952): Incorrect HTML generated for renaming clause
+  -  [#4962](https://github.com/agda/agda/issues/4962): JS backend: bugs involving "null"
+  -  [#4967](https://github.com/agda/agda/issues/4967): Crazy bug when defining Ord instances for Int
+  -  [#4970](https://github.com/agda/agda/issues/4970): `variable` use adds explicit argument
+  -  [#4975](https://github.com/agda/agda/issues/4975): "no such meta variable" when calling `C-u C-c C-;`
+  -  [#4982](https://github.com/agda/agda/issues/4982): Internal error related to Cubical Agda
+  -  [#4986](https://github.com/agda/agda/issues/4986): Pattern matching allows you to turn `(x y : A) -> A` into `(@0 x y : A) -> A`
+  -  [#4995](https://github.com/agda/agda/issues/4995): No Cycle should not look under lambdas.
+  -  [#4998](https://github.com/agda/agda/issues/4998): Make case in clause with instance projection does not work
+  -  [#4999](https://github.com/agda/agda/issues/4999): `primStringFromList` is not injective because of surrogate code points
+  -  [#5002](https://github.com/agda/agda/issues/5002): Bad JavaScript generated
+  -  [#5005](https://github.com/agda/agda/issues/5005): Add flag to print AGDA_DIR and exit
+  -  [#5029](https://github.com/agda/agda/issues/5029): One can override --safe
+  -  [#5033](https://github.com/agda/agda/issues/5033): Internal error related to @tick
+  -  [#5048](https://github.com/agda/agda/issues/5048): Disturbing names in normalised reflected type
+  -  [#5064](https://github.com/agda/agda/issues/5064): Give more information in error "Pattern matching on no-eta record types is by default not allowed"
+  -  [#5065](https://github.com/agda/agda/issues/5065): The termination checker is too liberal
+  -  [#5079](https://github.com/agda/agda/issues/5079): Deep pattern-matching is sometimes allowed for erased arguments
+  -  [#5093](https://github.com/agda/agda/issues/5093): Weird instance propagation between parameterised modules
+  -  [#5112](https://github.com/agda/agda/issues/5112): `make install-fix-whitespace` shouldn't use the `stack-X.Y.Z.yaml` files used for Agda
+  -  [#5128](https://github.com/agda/agda/issues/5128): getDefinition sometimes loses patterns
+  -  [#5133](https://github.com/agda/agda/issues/5133): Current master fails LaTeX-related tests
+  -  [#5140](https://github.com/agda/agda/issues/5140): test/LaTeXAndHTML/succeed contains failing tests
+  -  [#5146](https://github.com/agda/agda/issues/5146): v2.6.1.2 does not contain MAlonzo/RTE/Float.hs
+  -  [#5161](https://github.com/agda/agda/issues/5161): No error location for error in imported module when .agdai file exists
+  -  [#5167](https://github.com/agda/agda/issues/5167): Fix broken compatibility with agda-bench
+  -  [#5168](https://github.com/agda/agda/issues/5168): User manual: Missing instructions for installing Agda from Hackage using stack
+  -  [#5176](https://github.com/agda/agda/issues/5176): `mutual` is deprecated in doc
+  -  [#5204](https://github.com/agda/agda/issues/5204): Investigate highlighting failures
+  -  [#5205](https://github.com/agda/agda/issues/5205): acmart examples in (user-manual) fail to build with latest TeXLive
+  -  [#5207](https://github.com/agda/agda/issues/5207): Agda generated code does not type-check with GHC 9.0
+  -  [#5210](https://github.com/agda/agda/issues/5210): Internal error
+  -  [#5230](https://github.com/agda/agda/issues/5230): When `stack.yaml` exists, `make` calls `stack`, even on `make debug`
+  -  [#5231](https://github.com/agda/agda/issues/5231): Problems compiling hello-world.agda
+  -  [#5237](https://github.com/agda/agda/issues/5237): `__IMPOSSIBLE__` from Agda.TypeChecking.Substitute
+  -  [#5238](https://github.com/agda/agda/issues/5238): Rewrites are conjuring elements out of thin air
+  -  [#5245](https://github.com/agda/agda/issues/5245): An infinite loop?
+  -  [#5250](https://github.com/agda/agda/issues/5250): Change of warning options ignored
+  -  [#5251](https://github.com/agda/agda/issues/5251): @0 annotation on lambda ignored
+  -  [#5252](https://github.com/agda/agda/issues/5252): Internal error when case splitting pattern-lambda with higher rank type
+  -  [#5286](https://github.com/agda/agda/issues/5286): Wrong error location with do notation and parse error in lhs
+  -  [#5288](https://github.com/agda/agda/issues/5288): Very weird behaviour with compiled Data.Nat.Show.readMaybe
+  -  [#5313](https://github.com/agda/agda/issues/5313): Documentation for internal level properties
+  -  [#5314](https://github.com/agda/agda/issues/5314): Warn about abstract definitions without type signatures
+  -  [#5317](https://github.com/agda/agda/issues/5317): The reflection machinery should support quantities
+  -  [#5326](https://github.com/agda/agda/issues/5326): The highlighting code should be optimised
+  -  [#5334](https://github.com/agda/agda/issues/5334): Meta-variable in constructor type busts interleaved mutual
+  -  [#5335](https://github.com/agda/agda/issues/5335): Incorrect id attributes for local modules inside local modules
+  -  [#5336](https://github.com/agda/agda/issues/5336): `data Foo constructor {cs : ts}` notation in `interleaved mutual`
+  -  [#5339](https://github.com/agda/agda/issues/5339): `constructor` blocks do not tolerate overloading in same block
+  -  [#5341](https://github.com/agda/agda/issues/5341): Do not make context variables non-erased
+  -  [#5356](https://github.com/agda/agda/issues/5356): `interleaved mutual`: `data _ where` instead of `constructor`
+  -  [#5358](https://github.com/agda/agda/issues/5358): tactic annotation on record field of function type drops domain in copattern definition
+  -  [#5367](https://github.com/agda/agda/issues/5367): Parser regression involving `with` and `let`
+  -  [#5370](https://github.com/agda/agda/issues/5370): Inconsistency in agda --help
+  -  [#5375](https://github.com/agda/agda/issues/5375): Efficient conversion between interaction points and meta-variables
+  -  [#5410](https://github.com/agda/agda/issues/5410): Module applications in where clauses of erased definitions yield non-erased code
+  -  [#5419](https://github.com/agda/agda/issues/5419): Missing licences?
+  -  [#5424](https://github.com/agda/agda/issues/5424): Internal error in v2.6.2 release candidate 1
+  -  [#5434](https://github.com/agda/agda/issues/5434): The user manual's explanation of how erasure is checked for constructors does not match the implementation
diff --git a/doc/release-notes/2.6.3.md b/doc/release-notes/2.6.3.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.3.md
@@ -0,0 +1,522 @@
+Release notes for Agda version 2.6.3
+====================================
+
+Highlights
+----------
+
+* Added support for [Erased Cubical
+  Agda](https://agda.readthedocs.io/en/v2.6.3/language/cubical.html#cubical-agda-with-erased-glue),
+  a variant of Cubical Agda that is supported by the GHC backend,
+  under the flag `--erased-cubical`.
+
+* Added a new flag `--cubical-compatible` to turn on generation of
+  Cubical Agda-specific support code (previously this behaviour was
+  part of `--without-K`).
+
+  Since `--cubical-compatible` mode implies that functions should work
+  with the preliminary support for [indexed inductive types in Cubical
+  Agda](https://agda.readthedocs.io/en/v2.6.3/language/cubical.html#indexed-inductive-types),
+  many pattern matching functions will now emit an
+  `UnsupportedIndexedMatch` warning, indicating that the function will
+  not compute when applied to transports (from `--cubical` code).
+
+  This warning can be disabled with `-WnoUnsupportedIndexedMatch`, which
+  can be used either in an `OPTIONS` pragma or in your `agda-lib` file.
+  The latter is recommended if your project is only
+  `--cubical-compatible`, or if it is already making extensive use of
+  indexed types.
+
+  Note that code that uses (only) `--without-K` can no longer be
+  imported from code that uses `--cubical`. Thus it may make sense to
+  replace `--without-K` with `--cubical-compatible` in library code,
+  if possible.
+
+  Note also that Agda tends to be quite a bit faster if `--without-K`
+  is used instead of `--cubical-compatible`.
+
+* Agda 2.6.3 seems to type-check one variant of the standard library
+  about [30%
+  faster](https://github.com/agda/agda/issues/6049#issuecomment-1329163727)
+  than Agda 2.6.2.2 (on one system; the library was changed in a small
+  way between the tests to accommodate changes to Agda). In that test
+  the standard library did not use the new flag
+  `--cubical-compatible`. With that flag enabled in all the files that
+  used to use `--without-K` (and the warning `UnsupportedIndexedMatch`
+  turned off) Agda 2.6.3 was still about 10% faster.
+
+* New primitives `declareData`, `defineData`, and `unquoteDecl data`
+  for generating new data types have been added to the [reflection
+  API](https://agda.readthedocs.io/en/v2.6.3/language/reflection.html#metaprogramming).
+
+Installation and infrastructure
+-------------------------------
+
+Agda supports GHC versions 8.0.2 to 9.4.4.
+
+Erasure
+-------
+
+* The new option `--erased-cubical` turns on a variant of Cubical Agda
+  (see [#4701](https://github.com/agda/agda/issues/4701)).
+
+  When this variant of Cubical Agda is used glue (and some related
+  builtins) may only be used in erased settings. One can import
+  regular Cubical Agda code from this variant of Cubical Agda, but
+  names defined using Cubical Agda are (mostly) treated as if they had
+  been marked as erased. See the [reference
+  manual](https://agda.readthedocs.io/en/v2.6.3/language/cubical.html#cubical-agda-with-erased-glue-and-erased-higher-constructors)
+  for more details.
+
+  The GHC backend can compile code that uses `--erased-cubical` if the
+  top-level module uses this flag.
+
+  This feature is experimental.
+
+* Added an option `--erase-record-parameters` that marks parameters to
+  record fields and definitions in a record module as erased (see
+  [#4786](https://github.com/agda/agda/issues/4786) and
+  [#5770](https://github.com/agda/agda/issues/5770)). For example:
+
+  ```agda
+  {-# OPTIONS --erase-record-parameters #-}
+
+  record R (A : Set) : Set where
+    field
+      f : A
+
+  test : {@0 A : Set} → R A → A
+  test = R.f
+  ```
+
+Cubical Agda
+------------
+
+* [**Breaking**] The generation of Cubical Agda-specific support code was removed
+  from `--without-K` and transferred to its own flag,
+  `--cubical-compatible` (see
+  [#5843](https://github.com/agda/agda/issues/5843) and
+  [#6049](https://github.com/agda/agda/issues/6049) for the
+  rationale).
+
+* Cubical Agda now has experimental support for indexed inductive types
+  ([#3733](https://github.com/agda/agda/issues/3733)).
+  See the [user guide](https://agda.readthedocs.io/en/v2.6.3/language/cubical.html#indexed-inductive-types)
+  for caveats.
+
+* The cubical interval `I` now belongs to its own sort, `IUniv`, rather
+  than `SSet`. For `J : IUniv` and `A : J → Set l`, we have
+  `(j : J) → A j : Set l`, that is, the type of functions from a type in `IUniv`
+  to a fibrant type is fibrant.
+
+* The option `--experimental-irrelevance` is now perhaps incompatible
+  with Cubical Agda and perhaps also postulated univalence (see
+  [#5611](https://github.com/agda/agda/issues/5611) and
+  [#5861](https://github.com/agda/agda/pull/5861)).
+
+  This is not meant to imply that the option was not already
+  incompatible with those things. Note that
+  `--experimental-irrelevance` cannot be used together with `--safe`.
+
+* A new built-in constructor `REFLID` was added to the cubical identity
+  types. This is definitionally equal to the reflexivity identification
+  built with `conid`, with the difference being that matching on
+  `REFLID` is allowed.
+
+  ```agda
+  symId : ∀ {a} {A : Set a} {x y : A} → Id x y → Id y x
+  symId reflId = reflId
+  ```
+
+* Definitions which pattern match on higher-inductive types are no
+  longer considered for injectivity analysis.
+  ([#6219](https://github.com/agda/agda/pull/6219))
+
+* [**Breaking**] Higher constructors are no longer considered as guarding in the productivity check.
+  ([#6108](https://github.com/agda/agda/issues/6108))
+
+* Rewrite rules with interval arguments are now supported.
+  ([#4384](https://github.com/agda/agda/issues/4384))
+
+The flat modality
+-----------------
+
+* [**Breaking**] The `@flat`/`@♭` modality is now by default disabled (see
+  [#4927](https://github.com/agda/agda/issues/4927)).
+
+  It can be enabled using the infective flag `--cohesion`.
+
+* [**Breaking**] Matching on `@flat` arguments is now disabled by default, the flag
+  `--no-flat-split` has been removed, and the flag `--flat-split` is
+  now infective (see [#6238](https://github.com/agda/agda/issues/6238)
+  and [#6263](https://github.com/agda/agda/issues/6263)).
+
+  Matching can be enabled using the `--flat-split` flag. Note that in
+  Cubical Agda functions that match on an argument marked with `@flat`
+  trigger the `UnsupportedIndexedMatch` warning, and the code might
+  not compute properly.
+
+Reflection
+----------
+
+* Two new reflection primitives
+
+  ```agda
+  declareData      : Name → Nat → Type → TC ⊤
+  defineData       : Name → List (Σ Name (λ _ → Type)) → TC ⊤
+  ```
+
+  are added for declaring and defining datatypes, similar to
+  `declareDef` and `defineDef`.
+
+* The construct `unquoteDecl` is extended with the ability of bringing
+  a datatype `d` and its constructors `c₁ ... cₙ` given by a `TC`
+  computation `m` into scope by the following syntax:
+
+  ```agda
+  unquoteDecl data x constructor c₁ .. cₙ = m
+  ```
+
+* A new reflection primitive `getInstances : Meta → TC (List Term)`
+  was added to `Agda.Builtin.Reflection`. This operation returns the
+  list of all possibly valid instance candidates for a given
+  metavariable. For example, the following macro instantiates the goal
+  with the first instance candidate, even if there are several:
+  ```agda
+  macro
+    pickWhatever : Term → TC ⊤
+    pickWhatever hole@(meta m _) = do
+      (cand ∷ _) ← getInstances m
+        where [] -> typeError (strErr "No candidates!" ∷ [])
+      unify hole cand
+    pickWhatever _ = typeError (strErr "Already solved!" ∷ [])
+  ```
+
+* [**Breaking**] The reflection primitives `getContext` and `inContext` use a nominal context
+  `List (Σ String λ _ → Arg Type)` instead of  `List (Arg Type)` for printing
+  type information better. Similarly, `extendContext` takes an extra argument
+  of type `String`.
+
+* `macro` definitions can now be used even when they are declared as erased.
+  For example, this is now accepted:
+  ```agda
+  macro
+    @0 trivial : Term → TC ⊤
+    trivial = unify (con (quote refl) [])
+
+  test : 42 ≡ 42
+  test = trivial
+  ```
+
+* A new reflection primitive `formatErrorParts : List ErrorPart → TC String`
+  is added. It takes a list of `ErrorPart` and return its formatted string.
+
+* [**Breaking**] A new constructor `pattErr : Pattern → ErrorPart` of `ErrorPart` for reflection
+  is added.
+
+* [**Breaking**] The reflection primitives `getType` and
+  `getDefinition` respect the module context they are invoked from
+  instead of returning information that would be expected in the top
+  context.
+
+* [**Breaking**] The reflection primitive `inContext` cannot step
+  outside of the context that the `TC` computation is invoked from
+  anymore. The telescope is now relative to that context instead.
+
+Syntax
+------
+
+* It is now OK to put lambda-bound variables anywhere in the
+  right-hand side of a syntax declaration. However, there must always
+  be at least one "identifier" between any two regular "holes". For
+  instance, the following syntax declaration is accepted because `-`
+  is between the holes `B` and `D`.
+
+  ```agda
+  postulate
+    F : (Set → Set) → (Set → Set) → Set
+
+  syntax F (λ A → B) (λ C → D) = B A C - D
+  ```
+
+* Syntax can now use lambdas with multiple arguments
+  ([#394](https://github.com/agda/agda/issues/394)).
+
+  Example:
+
+  ```agda
+  postulate
+    Σ₂ : (A : Set) → (A → A → Set) → Set
+
+  syntax Σ₂ A (λ x₁ x₂ → P) = [ x₁ x₂ ⦂ A ] × P
+  ```
+
+Builtins
+--------
+
+* [**Breaking**] Change `primFloatToWord64` to return `Maybe Word64`.
+  (See [#6093](https://github.com/agda/agda/issues/6093).)
+
+  The new type is
+  ```agda
+    primFloatToWord64 : Float → Maybe Word64
+  ```
+  and it returns `nothing` for `NaN`.
+
+* [**Breaking**] The type expected by the builtin `EQUIVPROOF` has been changed to
+  properly encode the condition that `EQUVIFUN` is an equivalence.
+  ([#5661](https://github.com/agda/agda/issues/5661),
+  [#6032](https://github.com/agda/agda/pull/6032))
+
+* [**Breaking**] The primitive `primIdJ` has been removed
+  ([#6032](https://github.com/agda/agda/pull/6032)) in favour of
+  matching on the cubical identity type.
+
+* [**Breaking**] The builtin `SUBIN` is now exported from `Agda.Builtin.Cubical.Sub` as
+  **`inS`** rather than `inc`. Similarly, the internal modules refer to
+  `primSubOut` as `outS`. ([#6032](https://github.com/agda/agda/pull/6032))
+
+Pragmas and options
+-------------------
+
+* It is now possible to declare several `BUILTIN REWRITE` relations.
+  Example:
+  ```agda
+  {-# OPTIONS --rewriting #-}
+
+  open import Agda.Builtin.Equality
+  open import Agda.Builtin.Equality.Rewrite  -- 1st rewrite relation
+
+  postulate
+    R : (A : Set) → A → A → Set
+    A : Set
+    a b c : A
+    foo : R A a b  -- using 2nd rewrite relation
+    bar : b ≡ c    -- using 1st rewrite relation
+
+  {-# BUILTIN REWRITE R #-}  -- 2nd rewrite relation
+  {-# REWRITE foo bar #-}
+
+  test : a ≡ c
+  test = refl
+  ```
+
+* [**Breaking**] The option `--experimental-lossy-unification` that
+  makes Agda sometimes use first-order unification has been renamed to
+  `--lossy-unification`
+  ([#1625](https://github.com/agda/agda/issues/1625)).
+
+  Note that use of this option is associated with some potential
+  [drawbacks](https://agda.readthedocs.io/en/v2.6.3/language/lossy-unification.html#drawbacks).
+
+* The new option `--no-load-primitives` complements `--no-import-sorts`
+  by foregoing loading of the primitive modules altogether. This option
+  leaves Agda in a very fragile state, as the built-in sorts are used
+  extensively throughout the implementation. It is intended to be used
+  by Literate Agda projects which want to bind `BUILTIN TYPE` (and
+  other primitives) in their own literate files.
+
+* If `--interaction-exit-on-error` is used, then Agda exits with a
+  non-zero exit code if `--interaction` or `--interaction-json` are
+  used and a type error is encountered. The option also makes Agda
+  exit with exit code 113 if Agda fails to parse a command.
+
+  This option might for instance be used if Agda is controlled from a
+  script.
+
+* Add a `NOT_PROJECTION_LIKE` pragma, which marks a function as not
+  suitable for projection-likeness. Projection-like functions have some of
+  their arguments erased, which can cause confusing behaviour when they
+  are printed instantiated (see [#6203](https://github.com/agda/agda/issues/6203)).
+
+* [**Breaking**] The options `--subtyping` and `--no-subtyping` have been removed
+  (see [#5427](https://github.com/agda/agda/issues/5427)).
+
+Profiling and performance
+-------------------------
+
+* New verbosity `-v debug.time:100` adds time stamps to debugging output.
+
+* [**Breaking**] Profiling options are now turned on with a new `--profile` flag
+  instead of abusing the debug verbosity option. (See
+  [#5781](https://github.com/agda/agda/issues/5781).)
+
+* The new profiling option `--profile=conversion` collects statistics
+  on how often various steps of the conversion algorithm are used
+  (reduction, eta-expansion, syntactic equality, etc).
+
+* Meta-variables can now be saved in `.agdai` files, instead
+  of being expanded. This can affect performance. (See
+  [#5731](https://github.com/agda/agda/issues/5731).)
+
+  Meta-variables are saved if the pragma option `--save-metas` is
+  used. This option can be overridden by `--no-save-metas`.
+
+* The new option `--syntactic-equality[=FUEL]` can be used to limit
+  how many times the syntactic equality shortcut is allowed to fail
+  (see [#5801](https://github.com/agda/agda/issues/5801)).
+
+  If `FUEL` is omitted, then the syntactic equality shortcut is
+  enabled without any restrictions.
+
+  If `FUEL` is given, then the syntactic equality shortcut is given
+  `FUEL` units of fuel. The exact meaning of this is
+  implementation-dependent, but successful uses of the shortcut do not
+  affect the amount of fuel. Currently the fuel is decreased in the
+  failure continuations of the implementation of the syntactic
+  equality shortcut. When a failure continuation completes the fuel is
+  restored to its previous amount.
+
+  The idea for this option comes from András Kovács'
+  [smalltt](https://github.com/AndrasKovacs/smalltt/blob/989b020309686e04374f1ab7844f468386d2eb2f/README.md#approximate-conversion-checking).
+
+  Note that this option is experimental and subject to change.
+
+Library management
+------------------
+
+* Library files below the "project root" are now ignored
+  (see [#5644](https://github.com/agda/agda/issues/5644)).
+
+  For instance, if you have a module called `A.B.C` in the directory
+  `Root/A/B`, then `.agda-lib` files in `Root/A` or `Root/A/B` do not
+  affect what options are used to type-check `A.B.C`: `.agda-lib`
+  files for `A.B.C` have to reside in `Root`, or further up the
+  directory hierarchy.
+
+Interaction
+-----------
+
+* Agsy ([automatic proof search](https://agda.readthedocs.io/en/v2.6.3/tools/auto.html)) can
+  now be invoked in the right-hand-sides of copattern matching clauses.
+  ([#5827](https://github.com/agda/agda/pull/5827))
+
+Compiler backends
+-----------------
+
+* [**Breaking**] Both the GHC and JS backends now refuse to compile code that uses
+  `--cubical`.
+
+  Note that support for compiling code that uses `--erased-cubical`
+  has been added to the GHC backend (see above).
+
+* If the GHC backend is invoked when `--interaction` or
+  `--interaction-json` is active (for instance when the Emacs mode is
+  used), then GHC is now invoked from the directory containing the
+  `MAlonzo` directory (see
+  [#6194](https://github.com/agda/agda/issues/6194)).
+
+  Before GHC was invoked from the Agda process's current working
+  directory, and that is still the case if `--interaction` and
+  `--interaction-json` are not used.
+
+DOT backend
+-----------
+
+* The new option `--dependency-graph-include=LIBRARY` can be used to
+  restrict the dependency graph to modules from one or more libraries
+  (see [#5634](https://github.com/agda/agda/issues/5634)).
+
+  Note that the module given on the command line might not be
+  included.
+
+* The generated graphs no longer contain "redundant" edges: if a
+  module is imported both directly and indirectly, then the edge
+  corresponding to the direct import is omitted.
+
+JSON API
+--------
+
+* [**Breaking**] The JSON API now represents meta-variables differently, using
+  objects containing two keys, `id` and `module`, both with values
+  that are (natural) numbers. See
+  [#5731](https://github.com/agda/agda/issues/5731).
+
+
+Other issues closed
+--------------------
+
+For 2.6.3, the following issues were also closed (see [bug
+tracker](https://github.com/agda/agda/issues)):
+
+  - [#3660](https://github.com/agda/agda/issues/3660): Wrong variable name in constraints for higher constructor
+  - [#3986](https://github.com/agda/agda/issues/3986): Subtyping `.A -> B <= A -> B` leads to wrong `ArgInfo`
+  - [#4103](https://github.com/agda/agda/issues/4103): Rewrite rule rejected because of projection likeness
+  - [#4506](https://github.com/agda/agda/issues/4506): Lack of unicode support in locale may result in uncaught `IOException`
+  - [#4725](https://github.com/agda/agda/issues/4725): Cubical Agda: Program rejected by termination checker due to moved dot pattern
+  - [#4755](https://github.com/agda/agda/issues/4755): Rewrite rule on constructor uses wrong type for matching
+  - [#4763](https://github.com/agda/agda/issues/4763): Cubical Agda: Unquote anonymous copattern involving path
+  - [#5191](https://github.com/agda/agda/issues/5191): Unifier can use erased variables in non-erased data parameters
+  - [#5257](https://github.com/agda/agda/issues/5257): Internal error when matching on user syntax with binding
+  - [#5378](https://github.com/agda/agda/issues/5378): Internal error with tactic on record field
+  - [#5448](https://github.com/agda/agda/issues/5448): Should the predicate be erasable in the subst rule (without-K)
+  - [#5462](https://github.com/agda/agda/issues/5462): Internal error caused by a REWRITE on a projection-like function
+  - [#5468](https://github.com/agda/agda/issues/5468): Disallow certain forms of pattern matching when an index is erased
+  - [#5525](https://github.com/agda/agda/issues/5525): Duplicate entries in `executables` file lead to undefined behavior
+  - [#5548](https://github.com/agda/agda/issues/5548): Agda infers an incorrect type with subtyping on
+  - [#5551](https://github.com/agda/agda/issues/5551): Panic when showing module contents with pattern synonym
+  - [#5563](https://github.com/agda/agda/issues/5563): Allow erased names in the type signatures of let-bound definitions
+  - [#5577](https://github.com/agda/agda/issues/5577): The "Could not generate equivalence" warning is not always emitted
+  - [#5581](https://github.com/agda/agda/issues/5581): Lexical error with tab character in literate Agda text
+  - [#5589](https://github.com/agda/agda/issues/5589): Internal error with REWRITE of function from path
+  - [#5681](https://github.com/agda/agda/issues/5681): Panic on record declaration with unknown sort
+  - [#5702](https://github.com/agda/agda/issues/5702): Can't case split an `HitInt` with some already existing cases
+  - [#5715](https://github.com/agda/agda/issues/5715): Reflection: Use `Telescope` for `getContext`, `inContext`, and `extendContext`
+  - [#5727](https://github.com/agda/agda/issues/5727): Reducing universe levels before checking is not sufficient
+  - [#5728](https://github.com/agda/agda/issues/5728): Internal error when pattern matching on `...` in with statement without providing a pattern match
+  - [#5734](https://github.com/agda/agda/issues/5734): Relevance check in reflection
+  - [#5751](https://github.com/agda/agda/issues/5751): json interaction produces Haskell output for `SolveAll`
+  - [#5754](https://github.com/agda/agda/issues/5754): Internal error when compiling program with quoted metavariable
+  - [#5760](https://github.com/agda/agda/issues/5760): Some code related to Cubical Agda runs also when the K rule is on
+  - [#5763](https://github.com/agda/agda/issues/5763): Internal parser error using syntax rules
+  - [#5765](https://github.com/agda/agda/issues/5765): Erasure check failure when pattern matching on refl in erased definition
+  - [#5775](https://github.com/agda/agda/issues/5775): JSON interaction produces fully qualified terms
+  - [#5794](https://github.com/agda/agda/issues/5794): Agsy/Auto crashes with `Prelude.!!: index too large`
+  - [#5823](https://github.com/agda/agda/issues/5823): Singleton check loops on recursive eta record
+  - [#5828](https://github.com/agda/agda/issues/5828): Agsy/Auto panics with `-r` in the presence of a pattern synonym
+  - [#5845](https://github.com/agda/agda/issues/5845): Internal error caused by abstracting `variables`
+  - [#5848](https://github.com/agda/agda/issues/5848): Internal error with `--confluence-check`
+  - [#5850](https://github.com/agda/agda/issues/5850): Warn about useless hiding in `variable` declaration
+  - [#5856](https://github.com/agda/agda/issues/5856): Lambda with irrefutable pattern is not rejected when used on Path
+  - [#5868](https://github.com/agda/agda/issues/5868): Document `--two-level`
+  - [#5875](https://github.com/agda/agda/issues/5875): Instance Search breaks Termination Highlighting
+  - [#5891](https://github.com/agda/agda/issues/5891): `SizeUniv : SizeUniv` is inconsistent
+  - [#5901](https://github.com/agda/agda/issues/5901): Use `emacs --batch` mode in `agda-mode` setup
+  - [#5920](https://github.com/agda/agda/issues/5920): Erased constructors skipped in modality check
+  - [#5922](https://github.com/agda/agda/issues/5922): Failure of termination checking for reflection-generated code due to data projections
+  - [#5923](https://github.com/agda/agda/issues/5923): Internal error in rewriting
+  - [#5944](https://github.com/agda/agda/issues/5944): Internal error in rewriting with `--two-level`
+  - [#5953](https://github.com/agda/agda/issues/5953): Recursor of inductive-inductive type does not pass termination check in Cubical Agda
+  - [#5955](https://github.com/agda/agda/issues/5955): Composition of Glue Type Causes Infinite Loop
+  - [#5956](https://github.com/agda/agda/issues/5956): Cubical Agda crashes when printing empty system
+  - [#5966](https://github.com/agda/agda/issues/5966): Improved performance by switching to `vector-hashtables`
+  - [#5989](https://github.com/agda/agda/issues/5989): Dead-code elimination crashes function with private tactic argument
+  - [#6003](https://github.com/agda/agda/issues/6003): de Bruijn index out of scope when rewriting
+  - [#6006](https://github.com/agda/agda/issues/6006): Internal error rewriting with holes
+  - [#6015](https://github.com/agda/agda/issues/6015): Pi types and Partial types should not be considered inter-convertible
+  - [#6022](https://github.com/agda/agda/issues/6022): Private bindings in imported modules defeat check for binding of primIdFace/primIdPath
+  - [#6042](https://github.com/agda/agda/issues/6042): De Bruijn index out of scope when rewriting without-K
+  - [#6043](https://github.com/agda/agda/issues/6043): de Bruijn error on unexpected implicit argument
+  - [#6059](https://github.com/agda/agda/issues/6059): Non-terminating function over tuples passed with `--termination-depth=2`
+  - [#6066](https://github.com/agda/agda/issues/6066): Document the meaning of `pattern` without `no-eta-equality`
+  - [#6067](https://github.com/agda/agda/issues/6067): Another de Bruijn error in rewriting
+  - [#6073](https://github.com/agda/agda/issues/6073): Constraint solving does not honour singleton types
+  - [#6074](https://github.com/agda/agda/issues/6074): `piSort`/`funSort` of `IUniv` should be blocked on the codomain
+  - [#6076](https://github.com/agda/agda/issues/6076): Agda input mode (emacs): Minibuffer display for `\;` is strange
+  - [#6080](https://github.com/agda/agda/issues/6080): A space leak due to `absName`
+  - [#6082](https://github.com/agda/agda/issues/6082): Elaborate-and-give does not respect `--postfix-projections`
+  - [#6095](https://github.com/agda/agda/issues/6095): Ambiguous pattern synonyms broken with anonymous module
+  - [#6112](https://github.com/agda/agda/issues/6112): Internal error: non-confluent rewriting to singletons
+  - [#6200](https://github.com/agda/agda/issues/6200): The reflection machinery does not treat the module telescope consistently
+  - [#6203](https://github.com/agda/agda/issues/6203): Projection-likeness and instance arguments
+  - [#6205](https://github.com/agda/agda/issues/6205): Internal error with `withReconstructed`
+  - [#6244](https://github.com/agda/agda/issues/6244): Make `--no-load-primitives` not `--safe`
+  - [#6250](https://github.com/agda/agda/issues/6250): Documentation says `--sized-types` is the default when it isn't
+  - [#6257](https://github.com/agda/agda/issues/6257): Document options `--prop`, `--guarded`, and `--two-level`.
+  - [#6265](https://github.com/agda/agda/issues/6265): Some options should be listed in `restartOptions`
+  - [#6273](https://github.com/agda/agda/issues/6273): Missing highlighting when interleaved mutual is used
+  - [#6276](https://github.com/agda/agda/issues/6276): LaTeX/HTML generation doesn't properly render parameters of pre-declared records
+  - [#6281](https://github.com/agda/agda/issues/6281): Special treatment of attribute followed by underscore in pretty-printer
+  - [#6337](https://github.com/agda/agda/issues/6337): `--lossy-unification` in Agda 2.6.3
+  - [#6338](https://github.com/agda/agda/issues/6338): internal error in Agda, perhaps related to `--rewriting`
+  - [#6377](https://github.com/agda/agda/issues/6377): Fix installation docs concerning icu libraries
+  - [#6379](https://github.com/agda/agda/issues/6379): Weird warning for instance declarations of bad type
diff --git a/doc/release-notes/2.6.4.1.md b/doc/release-notes/2.6.4.1.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.4.1.md
@@ -0,0 +1,75 @@
+Release notes for Agda version 2.6.4.1
+======================================
+
+This is a minor release of Agda 2.6.4 featuring a few changes:
+
+- Make recursion on proofs legal again.
+- Improve performance, e.g. by removing debug printing unless built with cabal flag `debug`.
+- Switch to XDG directory convention.
+- Reflection: change to order of results returned by `getInstances`.
+- Fix some internal errors.
+
+Installation
+------------
+
+* Agda supports GHC versions 8.6.5 to 9.8.1.
+
+* Verbose output printing via `-v` or `--verbose` is now only active if Agda is built with the `debug` cabal flag.
+  Without `debug`, no code is generated for verbose printing, which makes building Agda faster and Agda itself
+  faster as well. (PR [#6863](https://github.com/agda/agda/pull/6863))
+
+Language
+--------
+
+* A [change](https://github.com/agda/agda/pull/6639) in 2.6.4 that prevented all recursion on proofs,
+  i.e., members of a type `A : Prop ℓ`, has been [reverted](https://github.com/agda/agda/pull/6936).
+  It is possible again to use proofs as termination arguments.
+  (See [issue #6930](https://github.com/agda/agda/issues/6930).)
+
+Reflection
+----------
+
+Changes to the meta-programming facilities.
+
+* The reflection primitive `getInstances` will now return instance
+  candidates ordered by _specificity_, rather than in unspecified order:
+  If a candidate `c1 : T` has a type which is a substitution instance of
+  that of another candidate `c2 : S`, `c1` will appear earlier in the
+  list.
+
+  As a concrete example, if you have instances `F (Nat → Nat)`, `F (Nat
+  → a)`, and `F (a → b)`, they will be returned in this order. See
+  [issue #6944](https://github.com/agda/agda/issues/6944) for further
+  motivation.
+
+Library management
+------------------
+
+* Agda now follows the XDG base directory standard on Unix-like systems,
+  see [PR #6858](https://github.com/agda/agda/pull/6858).
+  This means, it will look for configuration files in `~/.config/agda` rather than `~/.agda`.
+
+  For backward compatibility, if you still have an `~/.agda` directory, it will look there first.
+
+  No change on Windows, it will continue to use `%APPDATA%` (e.g. `C:/Users/USERNAME/AppData/Roaming/agda`).
+
+
+Other issues closed
+-------------------
+
+For 2.6.4.1, the following issues were also
+[closed](https://github.com/agda/agda/issues?q=is%3Aissue+milestone%3A2.6.4.1+is%3Aclosed)
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+- [#6745](https://github.com/agda/agda/issues/6745): Strange interaction between `opaque` and `let open`
+- [#6746](https://github.com/agda/agda/issues/6746): Support GHC 9.8
+- [#6852](https://github.com/agda/agda/issues/6852): Follow XDG Base Directory Specification
+- [#6913](https://github.com/agda/agda/issues/6913): Internal error on `primLockUniv`-sorted functions
+- [#6930](https://github.com/agda/agda/issues/6930): Termination checking with --prop: change in 2.6.4 compared with 2.6.3
+- [#6931](https://github.com/agda/agda/issues/6931): Internal error with an empty parametrized module from a different file
+- [#6941](https://github.com/agda/agda/issues/6941): Interaction between opaque and instance arguments
+- [#6944](https://github.com/agda/agda/issues/6944): Order instances by specificity for reflection
+- [#6953](https://github.com/agda/agda/issues/6953): Emacs 30 breaks agda mode
+- [#6957](https://github.com/agda/agda/issues/6957): Agda stdlib installation instructions broken link
+- [#6959](https://github.com/agda/agda/issues/6959): Warn about opaque `unquoteDecl`/`unquoteDef`
+- [#6983](https://github.com/agda/agda/issues/6983): Refine command does not work on Emacs 30
diff --git a/doc/release-notes/2.6.4.md b/doc/release-notes/2.6.4.md
new file mode 100644
--- /dev/null
+++ b/doc/release-notes/2.6.4.md
@@ -0,0 +1,588 @@
+Release notes for Agda version 2.6.4
+====================================
+
+Highlights
+----------
+
+* Cubical Agda now displays boundary conditions in interactive mode
+  (PR [#6529](https://github.com/agda/agda/pull/6529)).
+
+* An inconsistency in the treatment of large indices has been fixed
+  (Issue [#6654](https://github.com/agda/agda/issues/6654)).
+
+* Unfolding of definitions can now be fine-controlled via `opaque` definitions.
+
+* Additions to the sort system: `LevelUniv` and `Propω`.
+
+* New flag `--erasure` with several improvements to erasure (declared run-time irrelevance).
+
+* New reflection primitives for meta-programming.
+
+Installation
+------------
+
+* Removed the cabal flag `cpphs` that enabled building Agda with `cpphs` instead of the default C preprocessor.
+
+* Agda supports GHC versions 8.6.5 to 9.6.3.
+
+Pragmas and options
+-------------------
+
+* New command-line option `--numeric-version` to just print the version number of Agda.
+
+* Option `--version` now also prints the cabal flags active in this build of Agda
+  (e.g. whether Agda was built with `-f enable-cluster-counting`).
+
+* New command-line option `--trace-imports` to switch on notification messages
+  on the end of compilation of an imported module
+  or on access to an interface file during the type-checking.
+
+  See [--trace-imports](https://agda.readthedocs.io/en/v2.6.4/tools/command-line-options.html#cmdoption-trace-imports)
+  in the documentation for more.
+
+* New option `--no-infer-absurd-clauses` to simplify coverage checking and case splitting:
+  Agda will then no longer attempt to automatically eliminate absurd clauses which can be a costly operation.
+  This means that these absurd clauses have to be written out in the Agda text.
+  Try this option if you experience type checking performance degradation with omitted absurd clauses.
+
+  Opposite: `--infer-absurd-clauses`.
+
+* Benign warnings are now printed together with their warning name, to give a hint how they can be disabled
+  (see [#6229](https://github.com/agda/agda/issues/6229)).
+
+* New option `--level-universe` to make `Level` inhabit its own universe `LevelUniv`:
+  When this option is turned on, `Level` can now only depend on terms of type `Level`.
+
+  Note: While compatible with the `--cubical` option, this option is currently not compatible with cubical builtin files, and an error will be raised when trying to import them in a file using `--level-universe`.
+
+  Opposite: `--no-level-universe`.
+
+* Most boolean options now have their opposite, e.g., `--allow-unsolved-metas` is complemented by `--no-allow-unsolved-metas`.
+  With the opposite one can override a previously given option.
+  Options given on the command line are overwritten by options given in the `.agda-lib` file,
+  which in turn get overwritten by options given in the individual `.agda` file.
+
+  New options (all on by default):
+  - `--no-allow-exec`
+  - `--no-allow-incomplete-matches`
+  - `--no-allow-unsolved-metas`
+  - `--no-call-by-name`
+  - `--no-cohesion`
+  - `--no-count-clusters`
+  - `--no-erased-matches`
+  - `--no-erasure`
+  - `--no-experimental-irrelevance`
+  - `--no-flat-split`
+  - `--no-guarded`
+  - `--no-injective-type-constructors`
+  - `--no-keep-covering-clauses`
+  - `--no-lossy-unification`
+  - `--no-keep-pattern-variables`
+  - `--no-omega-in-omega`
+  - `--no-postfix-projections`
+  - `--no-rewriting`
+  - `--no-show-identity-substitutions`
+  - `--no-show-implicit`
+  - `--no-show-irrelevant`
+  - `--no-two-level`
+  - `--no-type-in-type`
+  - `--eta-equality`
+  - `--fast-reduce`
+  - `--forcing`
+  - `--import-sorts`
+  - `--load-primitives`
+  - `--main`
+  - `--pattern-matching`
+  - `--positivity-check`
+  - `--print-pattern-synonyms`
+  - `--projection-like`
+  - `--termination-check`
+  - `--unicode`
+
+* Option `--flat-split` again implies `--cohesion`.
+  Reverts change introduced in Agda 2.6.3 where `--cohesion` was a prerequisite for `--flat-split`.
+
+* Pragma `INLINE` may now be applied to constructors of types supporting co-pattern matching.
+  It enables translation of right-hand-side constructor applications to left-hand-side co-pattern splits (see [PR #6682](https://github.com/agda/agda/pull/6682)).
+  For example, this translation allows the `nats` function to pass termination checking:
+  ```agda
+    record Stream (A : Set) : Set where
+      coinductive; constructor _∷_
+      field head : A
+            tail : Stream A
+    open Stream
+    {-# INLINE _∷_ #-}
+
+    nats : Nat → Stream Nat
+    nats n = n ∷ nats (1 + n)
+  ```
+  Inlining transforms the definition of `nats` to the following definition by copattern matching:
+  ```agda
+    nats n .head = n
+    nats n .tail = nats (1 + n)
+  ```
+  This form is accepted by the termination checker;
+  unlike the form before inlining, it does not admit any infinite reduction sequences.
+
+  If option `--exact-split` is on, the inlining will trigger a `InlineNoExactSplit` warning for `nats`.
+  This warning can be disabled as usual, with `-WnoInlineNoExactSplit`.
+
+* New option `--large-indices`, controlling whether constructors of
+  indexed data types are allowed to refer to data that would be "too
+  large" to fit in their declared sort. Large indices are disallowed by
+  default; see the [language changes](#language) for details.
+
+* New option `--forced-argument-recursion`, on by default, controlling
+  whether forced constructor arguments are usable for termination
+  checking. This flag may be necessary for Agda to accept nontrivial
+  uses of induction-induction.
+
+* The suffix `Warning` has been dropped from the warning names
+  `DuplicateFieldsWarning` and `TooManyFieldsWarning`.
+
+* The warning `GenericUseless` has been split into the three warnings
+  `UselessPragma`, `FaceConstraintCannotBeHidden` and `FaceConstraintCannotBeNamed`.
+
+* New warning `PatternShadowsConstructor` which used to be an error.
+
+Library management
+------------------
+
+* [**Breaking**] One can no longer have `.agda-lib` files that are
+  located below the "project root", on the path to the file that is
+  being type-checked (see
+  [#6465](https://github.com/agda/agda/issues/6465)).
+
+  For instance, if you have a module called `A.B.C` in the directory
+  `Root/A/B`, then an error is raised if there are `.agda-lib` files
+  in `Root/A` or `Root/A/B`.
+
+  Previously such `.agda-lib` files were ignored.
+
+Interaction and emacs mode
+--------------------------
+
+* Agda now supports reading files with extension `.lagda.typ`, and use the parser for
+  markdown files to parse them.
+  To edit such files in Emacs with Agda support, one needs to add the line
+  ```elisp
+  (add-to-list 'auto-mode-alist '("\\.lagda.typ\\'" . agda2-mode))
+  ```
+  to `.emacs`.
+
+  Generation for highlighted code like HTML is unsupported for Typst.
+  One may generate HTML with typst input, but that makes little sense,
+  and markdown is recommended instead when HTML export is desired.
+
+* Helper function (`C-c C-h`) does not abstract over module parameters anymore
+  (see [#2271](https://github.com/agda/agda/issues/2271))
+  and neither over generalized `variable`s
+  (see [#6689](https://github.com/agda/agda/pull/6689)).
+
+* New Agda input mode prefix `box` for APL boxed operators, e.g. `\box=` for ⌸;
+  see PR [#6510](https://github.com/agda/agda/pull/6510/files) for full list of bindings.
+
+* Cubical Agda will now report boundary information for interaction
+  points which are not at the top-level of their respective clauses.
+  This includes bodies of `Path`-typed values, the faces of a partial
+  element, arguments to functions returning paths, etc.
+
+  Since this information is available in a structured way _during
+  interaction_, the "goal type, context, and inferred type" command will
+  also display the value of the expression at each relevant face.
+
+  See also [PR #6529](https://github.com/agda/agda/pull/6529) for a
+  deeper explanation and a demo video.
+
+Syntax
+------
+
+* Agda now skips the UTF8 byte order mark (BOM) at beginning of files
+  (see [#6524](https://github.com/agda/agda/issues/6524)).
+  Previously, the BOM caused a parse error.
+
+* If the new option `--hidden-argument-puns` is used, then the pattern
+  `{x}` is interpreted as `{x = x}`, and the pattern `⦃ x ⦄` is
+  interpreted as `⦃ x = x ⦄` (see
+  [#6325](https://github.com/agda/agda/issues/6325)). Here `x` must be
+  an unqualified name that does not refer to a constructor that is in
+  scope: if `x` is qualified, then the pattern is not interpreted as a
+  pun, and if `x` is unqualified and refers to a constructor that is
+  in scope, then the code is rejected.
+
+  This feature can be turned off using `--no-hidden-argument-puns`.
+
+  Note that `{(x)}` and `⦃ (x) ⦄` are not interpreted as puns.
+
+  Note also that `{x}` is not interpreted as a pun in `λ {x} → …` or
+  `syntax f {x} = …`. However, `{x}` is interpreted as a pun in
+  `λ (c {x}) → …`.
+
+* `postulate` blocks may now contain `private` declarations
+  (see [#1702](https://github.com/agda/agda/issues/1702)).
+
+Language
+--------
+
+* [**Breaking**] Constructor arguments are no longer allowed to store
+  values of a type larger than their own sort, even when these values
+  are forced by the indices of a constructor.
+
+  This fixes a particular instance of the incompatibility between
+  structural recursion and impredicativity, which could previously be
+  exploited through the use of large data-type indices.
+  (see [#6654](https://github.com/agda/agda/issues/6654)).
+
+  This behaviour can be controlled with the flag `--large-indices`. Note
+  that, when `--large-indices` is enabled, forced constructor arguments
+  should not be used for termination checking. The flag
+  `--[no-]forced-argument-recursion` makes the termination checker skip
+  these arguments entirely. When `--safe` is given, `--large-indices` is
+  incompatible with `--without-K` _and_ incompatible with
+  `--forced-argument-recursion`.
+
+* Added [`opaque` definitions](https://agda.readthedocs.io/en/v2.6.4/language/opaque-definitions.html),
+  a mechanism for finer-grained control of unfolding. Unlike `abstract`
+  definitions, which can never be unfolded outside of (a child module
+  of) the defining module, opacity can be toggled at use-sites:
+
+  ```agda
+  opaque
+    foo : Set
+    foo = Nat
+
+  opaque
+    unfolding foo
+
+    _ : foo
+    _ = 123
+  ```
+
+* Unless `--no-import-sorts` is given, `Set` is in scope as before,
+  but `Prop` is only in scope when `--prop` is active.
+  Additionally `SSet` is now in scope when `--two-level` is active
+  (see [#6634](https://github.com/agda/agda/pull/6634)).
+
+* New sorts `Propω`, `Propω₁`, etc., in analogy to `Setω`, `Setω₁` etc.
+  Requires option `--prop`.
+
+  Example:
+  ```agda
+  {-# OPTIONS --prop --large-indices #-}
+
+  open Agda.Primitive
+
+  variable
+    ℓ : Level
+    A : Set ℓ
+
+  -- Lists of elements of types at any finite level.
+
+  data HList : Setω where
+    []  : HList
+    _∷_ : A → HList → HList
+
+  variable
+    x  : A
+    xs : HList
+
+  -- Predicate stating that all elements satisfy a given property.
+
+  data All (P : ∀{ℓ} {A : Set ℓ} → A → Prop ℓ) : HList → Propω where
+    []  : All P []
+    _∷_ : P x → All P xs → All P (x ∷ xs)
+  ```
+
+* [**Breaking**] The algorithm for resolution of instance arguments
+  has been simplified. It will now only rely on the type of instances
+  to determine which candidate it should use, and no longer on their
+  values.
+
+Erasure
+-------
+
+* [**Breaking**] The new flag `--erasure` turns on support for erasure
+  ([#6349](https://github.com/agda/agda/issues/6349)).
+
+  This flag is infective.
+  It is implied by `--erase-record-parameters` and `--erased-matches`.
+
+  Unless this flag is active the following things are prohibited:
+  * Use of the annotations `@0` and `@erased`.
+  * Use of names defined in Cubical Agda in Erased Cubical Agda.
+
+  When `--erasure` is used the parameter arguments of constructors and
+  projections are marked as erased
+  ([#4786](https://github.com/agda/agda/issues/4786)), with one
+  exception: for indexed data types this only happens if the
+  `--with-K` flag is active
+  ([#6297](https://github.com/agda/agda/issues/6297)).
+
+  For instance, the type of the constructor `c` below is `{@0 A :
+  Set} → D A`, and the type of the projection `R.f` is `{@0 A : Set}
+  → R A → A`:
+  ```agda
+  {-# OPTIONS --erasure #-}
+
+  data D (A : Set) : Set where
+    c : D A
+
+  record R (A : Set) : Set where
+    field
+      f : A
+  ```
+
+* [**Breaking**] Unless the new flag `--erased-matches` is used
+  matching is not allowed in erased positions for single-constructor
+  data types or record types without η-equality
+  ([#6349](https://github.com/agda/agda/issues/6349)).
+
+  This flag is infective and implied by `--with-K`.
+  If it is given explicitly, it implies `--erasure`.
+
+* [**Breaking**] Added a hard compile-time mode (see
+  [#4743](https://github.com/agda/agda/issues/4743)).
+
+  When the hard compile-time mode is used all definitions are treated
+  as erased. The hard compile-time mode is entered when an erased
+  definition is checked (including an erased data or record type or
+  module), but not when (for instance) a type-signature is checked.
+
+  Previously the following code was rejected:
+  ```agda
+  open import Agda.Builtin.Bool
+
+  @0 f : @0 Bool → Bool
+  f = λ where
+    true  → false
+    false → true
+  ```
+  Now this code is accepted (if `--erasure` is used). On the other
+  hand, the following code which used to be accepted is now rejected
+  (if `--erasure` is used), because the pattern-matching lambda is
+  treated as erased:
+  ```agda
+  open import Agda.Builtin.Equality
+
+  data Unit : Set where
+    unit : Unit
+
+  mutual
+
+    f : Unit → Unit
+    f = _
+
+    @0 f≡ : f ≡ λ { unit → unit }
+    f≡ = refl
+  ```
+
+* One can now mark data and record types and modules as erased (see
+  [#4743](https://github.com/agda/agda/issues/4743)).
+
+  If a data type is marked as erased, then it can only be used in
+  erased settings, and its constructors are erased. A data type is
+  marked as erased by writing `@0` or `@erased` right after the `data`
+  keyword of the data type's declaration:
+  ```agda
+  data @0 D₁ : Set where
+    c : D₁
+
+  data @0 D₂ : Set
+
+  data D₂ where
+    c : D₁ → D₂
+
+  interleaved mutual
+
+    data @0 D₃ : Set where
+
+    data D₃ where
+      c : D₃
+  ```
+
+  If a record type is marked as erased, then it can only be used in
+  erased settings, its constructors and fields are erased, and
+  definitions in the record module are erased. A record type is marked
+  as erased by writing `@0` or `@erased` right after the `record`
+  keyword of the record type's declaration:
+  ```agda
+  record @0 R₁ : Set where
+    field
+      x : D₁
+
+  record @0 R₂ : Set
+
+  record R₂ where
+    field
+      x : R₁
+  ```
+
+  If a module is marked as erased, then all definitions inside the
+  module (and in the module's telescope) are erased. A module is
+  marked as erased by writing `@0` or `@erased` right after the
+  `module` keyword:
+  ```agda
+  module @0 _ where
+
+    F : @0 Set → Set
+    F A = A
+
+  module M (A : Set) where
+
+    record R : Set where
+      field
+        @0 x : A
+
+  module @0 N (@0 A : Set) = M A
+
+  G : (@0 A : Set) → let module @0 M₂ = M A in Set
+  G A = M.R B
+    module @0 _ where
+      B : Set
+      B = A
+  ```
+  If an erased module is defined by a module application, then erased
+  names can be used in the application, as in the definition of `N`
+  above.
+
+* Equivalence primitives no longer require full `--cubical` mode,
+  `--erased-cubical` suffices. Equivalence definition is moved out of
+  `Agda.Builtin.Cubical.Glue` into its own module `Agda.Builtin.Cubical.Equiv`,
+  the former reexports the latter.
+
+Reflection
+----------
+
+* `FOREIGN` and `COMPILE` pragmas can now be generated using two new reflection primitives:
+
+  ```agda
+  pragmaForeign : String → String → TC ⊤
+  pragmaCompile : String → Name → String → TC ⊤
+  ```
+
+* Add 4 reflection primitives of the form `ask*` and `with*`:
+
+  ```agda
+  withNormalisation : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  askNormalisation  : TC Bool
+
+  withExpandLast : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  askExpandLast  : TC Bool
+
+  withReduceDefs : ∀ {a} {A : Set a} → (Σ Bool λ _ → List Name) → TC A → TC A
+  askReduceDefs  : TC (Σ Bool λ _ → List Name)
+
+  askReconstructed  : TC Bool
+  ```
+  to change the behaviour of `inferType`, `checkType`, `quoteTC`, `getContext`.
+
+* [**Breaking**] The type of `withReconstructed` has been changed from
+
+  ```agda
+  withReconstructed : ∀ {a} {A : Set a} →        TC A → TC A
+
+  ```
+  to
+  ```agda
+  withReconstructed : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  ```
+  to match the type of primitives of the form `with*`.
+
+* Two primitives `onlyReduceDefs` and `dontReduceDefs` are removed but re-implemented
+  using the new family of primitives `with*` and `ask*` for backward compatibility.
+
+* Blocking the type-checking monad can now be done with more precision
+  by using the `Blocker` type, and the `blockTC` primitive:
+
+  ```agda
+  data Blocker : Set where
+    blockerAny  : List Blocker → Blocker
+    blockerAll  : List Blocker → Blocker
+    blockerMeta : Meta → Blocker
+  ```
+
+  When blocking on a value of this type, the TCM computation will only
+  be retried when any (resp. all) of the mentioned metavariables have
+  been solved. This can avoid getting into loops where a macro blocks on
+  a meta, gets unblocked, traverses some term again, and then blocks on
+  a meta that was already present.
+
+  The `blockOnMeta` builtin has been deprecated, and an implementation
+  in terms of `blockTC` is given for backwards compatibility.
+
+
+Other issues closed
+-------------------
+
+For 2.6.4, the following issues were also
+[closed](https://github.com/agda/agda/issues?q=is%3Aissue+milestone%3A2.6.4+is%3Aclosed)
+(see [bug tracker](https://github.com/agda/agda/issues)):
+
+- [#1181](https://github.com/agda/agda/issues/1181): Display of let-bound variables in goals and error messages
+- [#2271](https://github.com/agda/agda/issues/2271): Helper function abstracts over module parameters, with sometimes disastrous consequences for printing
+- [#3437](https://github.com/agda/agda/issues/3437): Add Propω
+- [#3605](https://github.com/agda/agda/issues/3605): Improve constraint reporting for cubical
+- [#3690](https://github.com/agda/agda/issues/3690): Cubical interaction: Display inferred type with interval variables instantiated
+- [#5900](https://github.com/agda/agda/issues/5900): De Bruijn fail in Cubical (Was: Garbled boundary contexts & naming eta expansion.)
+- [#6124](https://github.com/agda/agda/issues/6124): Reflection: cannot reduce type because variable is erased
+- [#6140](https://github.com/agda/agda/issues/6140): Unapplied `List` and `Maybe` are sometimes translated to `[AgdaAny]` and `Maybe AgdaAny` by GHC backend
+- [#6229](https://github.com/agda/agda/issues/6229): Print warning name along with warning text
+- [#6269](https://github.com/agda/agda/issues/6269): Documentation is missing for `--keep-covering-clauses` and `--lossy-unification`
+- [#6271](https://github.com/agda/agda/issues/6271): Cubical: should generated code corresponding to erased constructors be erased?
+- [#6272](https://github.com/agda/agda/issues/6272): Put Level type in a different sort
+- [#6309](https://github.com/agda/agda/issues/6309): Drop support for GHC 8.0, 8.2, and 8.4
+- [#6325](https://github.com/agda/agda/issues/6325): Hidden argument puns
+- [#6333](https://github.com/agda/agda/issues/6333): Misleading file path in "Unrecognised option" error
+- [#6336](https://github.com/agda/agda/issues/6336): Paradoxical self-reference in endpoints for path constructors
+- [#6364](https://github.com/agda/agda/issues/6364): Instance candidates filtered out by type errors
+- [#6371](https://github.com/agda/agda/issues/6371): Preserve metavariable name suggestion when eta-expanding
+- [#6374](https://github.com/agda/agda/issues/6374): Refine does not work for overloaded record constructors
+- [#6380](https://github.com/agda/agda/issues/6380): Confusing warning about turning instances into instances
+- [#6395](https://github.com/agda/agda/issues/6395): `dataXXX` identifiers mis-parsed by {-# COMPILE GHC #-}
+- [#6407](https://github.com/agda/agda/issues/6407): Agsy produces clauses with out of scope variables
+- [#6413](https://github.com/agda/agda/issues/6413): Miscompilation of nested patterns in erased fields
+- [#6415](https://github.com/agda/agda/issues/6415): Apparent infinite loop in cubical with --lossy-unification
+- [#6418](https://github.com/agda/agda/issues/6418): Bug in rewriting with cubical primitives
+- [#6434](https://github.com/agda/agda/issues/6434): Option to increase performance: do not filter out absurd clauses automatically
+- [#6448](https://github.com/agda/agda/issues/6448): Don't define dependencies for elisp files included in the agda2-mode package
+- [#6506](https://github.com/agda/agda/issues/6506): Cubical: `with` abstraction failing to type check
+- [#6521](https://github.com/agda/agda/issues/6521): Support GHC 9.6 with cabal
+- [#6523](https://github.com/agda/agda/issues/6523): Soundness bug: Tick constraints not properly propogated in Guarded Cubical
+- [#6524](https://github.com/agda/agda/issues/6524): Ignore Unicode byte order mark
+- [#6525](https://github.com/agda/agda/issues/6525): Recent Emacs's escape character handling improvement leads to an error when loading agda-mode
+- [#6528](https://github.com/agda/agda/issues/6528): Guarded can block on solved metas
+- [#6530](https://github.com/agda/agda/issues/6530): Miscompilation of case split RHS lambdas
+- [#6541](https://github.com/agda/agda/issues/6541): Internal error in Agda.TypeChecking.Reduce.Fast
+- [#6551](https://github.com/agda/agda/issues/6551): Doc: the keywords `hiding`,`public`, `renaming`, and `using` are always reserved
+- [#6573](https://github.com/agda/agda/issues/6573): Check on presence of `--erasure` in `--erase-record-parameters` comes too early
+- [#6581](https://github.com/agda/agda/issues/6581): Cubical: no canonicity for record types without η-equality
+- [#6605](https://github.com/agda/agda/issues/6605): Doc: comments in "libraries" file
+- [#6621](https://github.com/agda/agda/issues/6621): Enable K also for SSetω (like for SSet)
+- [#6622](https://github.com/agda/agda/issues/6622): Bad error for `mutual` in implicit mutual block
+- [#6624](https://github.com/agda/agda/issues/6624): Suffix not working for SSet
+- [#6627](https://github.com/agda/agda/issues/6627): CheckArguments call exposes dummy checkArguments return type
+- [#6632](https://github.com/agda/agda/issues/6632): hcompU eta rule in conversion checker loses solution
+- [#6633](https://github.com/agda/agda/issues/6633): Bad interaction of Type:Type and SSet
+- [#6648](https://github.com/agda/agda/issues/6648): `--level-universe` not respected when solving funSort `_->_ : ? -> Set -> SetOmega`
+- [#6651](https://github.com/agda/agda/issues/6651): Agda fails on `univSort ? = SetOmega` even when `SizeUniv` is a solution
+- [#6654](https://github.com/agda/agda/issues/6654): Forcing analysis is inconsistent for large indices
+- [#6660](https://github.com/agda/agda/issues/6660): `{-# INLINE #-}` for copattern constructors
+- [#6662](https://github.com/agda/agda/issues/6662): Error message for unsafe option combinations has wrong pluralization
+- [#6677](https://github.com/agda/agda/issues/6677): Helper function type includes generalized parameters
+- [#6687](https://github.com/agda/agda/issues/6687): Termination checker bug with `CATCHALL`
+- [#6702](https://github.com/agda/agda/issues/6702): Inlining constructors to copattern should give warning with `--exact-split`
+- [#6706](https://github.com/agda/agda/issues/6706): Shape-irrelevant variables marked as irrelevant in human-readable context
+- [#6711](https://github.com/agda/agda/issues/6711): Internal error on `primStringUncons` when no builtin Sigma provided
+- [#6714](https://github.com/agda/agda/issues/6714): Docstring error with Emacs 29+ due to changed escape rules for single quote
+- [#6715](https://github.com/agda/agda/issues/6715): Type checking loops on certain pattern match in cubical (regression in 2.6.3)
+- [#6720](https://github.com/agda/agda/issues/6720): Cubical: internal error in `Sort.hs`
+- [#6725](https://github.com/agda/agda/issues/6725): Cubical: internal error in `Reduce.hs` (regression in 2.6.3)
+- [#6750](https://github.com/agda/agda/issues/6750): Order of deserialization depends on build of Agda (version of `hashable`)
+- [#6757](https://github.com/agda/agda/issues/6757): Incorrect `InteractionMetaBoundaries` warning
+- [#6767](https://github.com/agda/agda/issues/6767): Internal error related to forcing on literals
+- [#6786](https://github.com/agda/agda/issues/6786): Missing "when checking parameters of module M" in error message
+- [#6787](https://github.com/agda/agda/issues/6787): Refine doesn't find proof of refl=refl without K
+- [#6794](https://github.com/agda/agda/issues/6794): Safe Agda accepts `{-# TERMINATING #-}` pragma in `interleaved mutual` block
+- [#6795](https://github.com/agda/agda/issues/6795): Missing warning about discarded `{-# TERMINATING #-}` pragma in `where` block inside `interleaved mutual` block
+- [#6823](https://github.com/agda/agda/issues/6823): Suboptimal error location for missing definition before `mutual` block
+- [#6868](https://github.com/agda/agda/issues/6868): With-abstraction fails for trailing instance argument
diff --git a/doc/user-manual/agda.svg b/doc/user-manual/agda.svg
new file mode 100644
--- /dev/null
+++ b/doc/user-manual/agda.svg
@@ -0,0 +1,43 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<svg width="5217px" height="1707px" viewBox="0 0 5217 1707" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+    <!-- Generator: Sketch 52.6 (67491) - http://www.bohemiancoding.com/sketch -->
+    <title>logotype</title>
+    <desc>Created with Sketch.</desc>
+    <g id="Page-1" stroke="none" stroke-width="1" fill="none" fill-rule="evenodd">
+        <g id="Group" transform="translate(-4781.000000, -4784.000000)">
+            <rect id="white-background" fill="#FFFFFF" x="0" y="0" width="45624" height="78038"></rect>
+            <g id="black-logotypes" transform="translate(4781.000000, 4784.000000)">
+                <g id="logotype" transform="translate(219.000000, 219.000000)">
+                    <g id="logo">
+                        <circle id="left-eye" fill="#000000" cx="240" cy="270" r="27"></circle>
+                        <circle id="right-eye" fill="#000000" cx="340" cy="270" r="27"></circle>
+                        <path d="M1000,0 L600,400" id="wing" stroke="#000000" stroke-width="36" stroke-linecap="round" stroke-linejoin="round"></path>
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+                        <path d="M1200,0 L1000,200" id="tail-top" stroke="#000000" stroke-width="36" stroke-linecap="round" stroke-linejoin="round"></path>
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+                            <polyline id="A-body" stroke-linecap="round" stroke-linejoin="round" points="0 1000 1002 -2.27373675e-13 1002 1000"></polyline>
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+                        </g>
+                        <g id="g" transform="translate(1140.000000, 280.000000)">
+                            <circle id="g-body" cx="360" cy="360" r="360"></circle>
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+</svg>
diff --git a/src/agda-mode/Main.hs b/src/agda-mode/Main.hs
new file mode 100644
--- /dev/null
+++ b/src/agda-mode/Main.hs
@@ -0,0 +1,288 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+
+-- | A program which either tries to add setup code for Agda's Emacs
+-- mode to the users .emacs file, or provides information to Emacs
+-- about where the Emacs mode is installed.
+
+module Main (main) where
+
+import Control.Exception as E
+import Control.Monad
+import Data.Char
+import Data.List (intercalate, isInfixOf)
+import Data.Maybe
+import Data.Version
+import Numeric
+import System.Directory
+import System.Environment
+import System.Exit
+import System.FilePath
+import System.IO
+-- import System.IO.Error (isDoesNotExistError)
+import System.Process
+
+import Paths_Agda (getDataDir, version)
+
+-- | The program.
+
+main :: IO ()
+main = do
+  prog <- getProgName
+  args <- getArgs
+  case args of
+    [arg] | arg == locateFlag -> printEmacsModeFile
+          | arg == setupFlag  -> do
+             dotEmacs <- findDotEmacs
+             setupDotEmacs (Files { thisProgram = prog
+                                  , dotEmacs    = dotEmacs
+                                  })
+          | arg == compileFlag ->
+             compileElispFiles
+    _  -> do inform usage
+             exitFailure
+
+-- Command line options.
+
+setupFlag   = "setup"
+locateFlag  = "locate"
+compileFlag = "compile"
+
+-- | Usage information.
+
+usage :: String
+usage = unlines
+  [ "This program, which is part of Agda version " ++ ver ++ ", can be run"
+  , "in three modes, depending on which option it is invoked with:"
+  , ""
+  , setupFlag
+  , ""
+  , "  The program tries to add setup code for Agda's Emacs mode to the"
+  , "  current user's .emacs file. It is assumed that the .emacs file"
+  , "  uses the character encoding specified by the locale."
+  , ""
+  , locateFlag
+  , ""
+  , "  The path to the Emacs mode's main file is printed on standard"
+  , "  output (using the UTF-8 character encoding and no trailing"
+  , "  newline)."
+  , ""
+  , compileFlag
+  , ""
+  , "  The program tries to compile Agda's Emacs mode's source files."
+  , ""
+  , "  WARNING: If you reinstall the Agda mode without recompiling the Emacs"
+  , "  Lisp files, then Emacs may continue using the old, compiled files."
+  ]
+
+-- | The current version of Agda.
+
+ver :: String
+ver = intercalate "." $ map show $
+        versionBranch version
+
+------------------------------------------------------------------------
+-- Locating the Agda mode
+
+-- | Prints out the path to the Agda mode's main file (using UTF-8 and
+-- without any trailing newline).
+
+printEmacsModeFile :: IO ()
+printEmacsModeFile = do
+  dataDir <- getDataDir
+  let path = dataDir </> "emacs-mode" </> "agda2.el"
+  hSetEncoding stdout utf8
+  putStr path
+
+------------------------------------------------------------------------
+-- Setting up the .emacs file
+
+data Files = Files { dotEmacs :: FilePath
+                     -- ^ The .emacs file.
+                   , thisProgram :: FilePath
+                     -- ^ The name of the current program.
+                   }
+
+-- | Tries to set up the Agda mode in the given .emacs file.
+
+setupDotEmacs :: Files -> IO ()
+setupDotEmacs files = do
+  informLn $ "The .emacs file used: " ++ dotEmacs files
+
+  already <- alreadyInstalled files
+  if already then
+    informLn "It seems as if setup has already been performed."
+   else do
+
+    appendFile (dotEmacs files) (setupString files)
+    inform $ unlines $
+      [ "Setup done. Try to (re)start Emacs and open an Agda file."
+      , "The following text was appended to the .emacs file:"
+      ] ++ lines (setupString files)
+
+-- | Tries to find the user's .emacs file by querying Emacs.
+
+findDotEmacs :: IO FilePath
+findDotEmacs = askEmacs "(expand-file-name user-init-file)"
+
+-- | Has the Agda mode already been set up?
+
+alreadyInstalled :: Files -> IO Bool
+alreadyInstalled files = do
+  exists <- doesFileExist (dotEmacs files)
+  if not exists then return False else
+    withFile (dotEmacs files) ReadMode $ (evaluate . (identifier files `isInfixOf`)) <=< hGetContents
+      -- Uses evaluate to ensure that the file is not closed
+      -- prematurely.
+
+-- | If this string occurs in the .emacs file, then it is assumed that
+-- setup has already been performed.
+
+identifier :: Files -> String
+identifier files =
+  takeFileName (thisProgram files) ++ " " ++ locateFlag
+
+-- | The string appended to the end of the .emacs file.
+
+setupString :: Files -> String
+setupString files = unlines
+  [ ""
+  , "(load-file (let ((coding-system-for-read 'utf-8))"
+  , "                (shell-command-to-string \""
+                        ++ identifier files ++ "\")))"
+  ]
+
+------------------------------------------------------------------------
+-- Querying Emacs
+
+-- | Evaluates the given Elisp command using Emacs. The output of the
+-- command (whatever was written into the current buffer) is returned.
+--
+-- Note: The input is not checked. The input is assumed to come from a
+-- trusted source.
+
+askEmacs :: String -> IO String
+askEmacs query = do
+  tempDir <- getTemporaryDirectory
+  bracket (openTempFile tempDir "askEmacs")
+          (removeFile . fst) $ \(file, h) -> do
+    hClose h
+    exit <- rawSystemWithDiagnostics "emacs"
+      [ "--batch"
+          -- Andreas, 2022-10-15, issue #5901, suggested by Spencer Baugh (catern):
+          -- Use Emacs batch mode so that it can run without a terminal.
+      , "--user", ""
+          -- The flag --user is necessary with --batch so that user-init-file is defined.
+          -- The empty user is the default user.
+          -- (Option --batch includes --no-init-file, this is reverted by supplying --user.)
+      -- Andreas, 2022-05-25, issue #5901 reloaded:
+      -- Loading the init file without loading the site fails for some users:
+      -- , "--quick"
+      --     -- Option --quick includes --no-site-file.
+      , "--eval"
+      , apply [ "with-temp-file", escape file, apply [ "insert", query ] ]
+          -- Short cutting the temp file via just [ "princ", query ]
+          -- does not work if the loading of the user-init-file prints extra stuff.
+          -- Going via the temp file we can let this stuff go to stdout without
+          -- affecting the output we care about.
+      ]
+    unless (exit == ExitSuccess) $ do
+      informLn "Unable to query Emacs."
+      exitFailure
+    withFile file ReadMode $ \h -> do
+      result <- hGetContents h
+      evaluate (length result)
+      -- Uses evaluate to ensure that the file is not closed
+      -- prematurely.
+      return result
+
+-- | Like 'rawSystem' but handles 'IOException' by printing diagnostics
+-- (@PATH@) before 'exitFailure'.
+
+rawSystemWithDiagnostics
+  :: FilePath  -- ^ Command to run.
+  -> [String]  -- ^ Arguments to command.
+  -> IO ExitCode
+rawSystemWithDiagnostics cmd args =
+    rawSystem cmd args
+  `E.catch` \ (e :: IOException) -> do
+     informLn $ unwords [ "FAILED:", showCommandForUser cmd args ]
+     informLn $ unwords [ "Exception:", show e ]
+     -- The PATH might be useful in other exceptions, like "permission denied".
+     -- when (isDoesNotExistError e) $ do
+     path <- fromMaybe "(not found)" <$> findExecutable cmd
+     informLn $ unwords [ "Executable", cmd, "at:", path ]
+     informLn "PATH:"
+     mapM_ (informLn . ("  - " ++)) =<< getSearchPath
+     exitFailure
+
+-- | Escapes the string so that Emacs can parse it as an Elisp string.
+
+escape :: FilePath -> FilePath
+escape s = "\"" ++ concatMap esc s ++ "\""
+  where
+  esc c | c `elem` ['\\', '"']   = '\\' : [c]
+        | isAscii c && isPrint c = [c]
+        | otherwise              = "\\x" ++ showHex (fromEnum c) "\\ "
+
+------------------------------------------------------------------------
+-- Compiling Emacs Lisp files
+
+-- | The Agda mode's Emacs Lisp files, given in the order in which
+-- they should be compiled.
+
+emacsLispFiles :: [FilePath]
+emacsLispFiles =
+  [ "agda2-abbrevs.el"
+  , "annotation.el"
+  , "agda2-queue.el"
+  , "eri.el"
+  , "agda2.el"
+  , "agda-input.el"
+  , "agda2-highlight.el"
+  , "agda2-mode.el"
+  ]
+
+-- | Tries to compile the Agda mode's Emacs Lisp files.
+
+compileElispFiles :: IO ()
+compileElispFiles = do
+  dataDir <- (</> "emacs-mode") <$> getDataDir
+  let elFiles = map (dataDir </>) emacsLispFiles
+  elFiles <- filterM doesFileExist elFiles
+  results <- mapM (compile dataDir) elFiles
+  case catMaybes results of
+    [] -> return ()
+    fs -> do
+      informLn "Unable to compile the following Emacs Lisp files:"
+      mapM_ (informLn . ("  " ++)) fs
+      exitFailure
+  where
+  compile dataDir f = do
+    exit <- rawSystemWithDiagnostics "emacs" $
+      [ "--quick"                -- 'quick' implies 'no-site-file'
+      , "--directory", dataDir
+      , "--batch"                -- 'batch' implies 'no-init-file' but not 'no-site-file'.
+      , "--eval"
+      , "(progn \
+           \(setq byte-compile-error-on-warn t) \
+           \(byte-compile-disable-warning 'cl-functions) \
+           \(batch-byte-compile))"
+      , f
+      ]
+    return $ if exit == ExitSuccess then Nothing else Just f
+
+------------------------------------------------------------------------
+-- Helper functions
+
+-- These functions inform the user about something by printing on
+-- stderr.
+
+inform   = hPutStr   stderr
+informLn = hPutStrLn stderr
+
+parens :: String -> String
+parens s = concat [ "(", s, ")" ]
+
+-- LISP application
+apply :: [String] -> String
+apply = parens . unwords
diff --git a/src/data/JS/agda-rts.amd.js b/src/data/JS/agda-rts.amd.js
new file mode 100644
--- /dev/null
+++ b/src/data/JS/agda-rts.amd.js
@@ -0,0 +1,382 @@
+define([], function() {
+var exports = {};
+// Contains *most* of the primitives required by the JavaScript backend.
+// (Some, e.g., those using Agda types like Maybe, are defined in their
+// respective builtin modules.)
+//
+// Primitives prefixed by 'u' are uncurried variants, which are sometimes
+// emitted by the JavaScript backend. Whenever possible, the curried primitives
+// should be implemented in terms of the uncurried ones.
+//
+// Primitives prefixed by '_' are internal variants, usually for those primitives
+// which return Agda types like Maybe. These are never emitted by the compiler,
+// but can be used internally to define other prefixes.
+
+// Integers
+
+// primIntegerFromString : String -> Int
+exports.primIntegerFromString = BigInt;
+
+// primShowInteger : Int -> String
+exports.primShowInteger = x => x.toString();
+
+// uprimIntegerPlus : (Int, Int) -> Int
+exports.uprimIntegerPlus = (x, y) => x + y;
+
+// uprimIntegerMinus : (Int, Int) -> Int
+exports.uprimIntegerMinus = (x, y) => x - y;
+
+// uprimIntegerMultiply : (Int, Int) -> Int
+exports.uprimIntegerMultiply = (x, y) => x * y;
+
+// uprimIntegerRem : (Int, Int) -> Int
+exports.uprimIntegerRem = (x, y) => x % y;
+
+// uprimIntegerQuot : (Int, Int) -> Int
+exports.uprimIntegerQuot = (x, y) => x / y;
+
+// uprimIntegerEqual : (Int, Int) -> Bool
+exports.uprimIntegerEqual = (x, y) => x === y;
+
+// uprimIntegerGreaterOrEqualThan : (Int, Int) -> Bool
+exports.uprimIntegerGreaterOrEqualThan = (x, y) => x >= y;
+
+// uprimIntegerLessThan : (Int, Int) -> Bool
+exports.uprimIntegerLessThan = (x, y) => x < y;
+
+// Words
+const WORD64_MAX_VALUE = 18446744073709552000n;
+
+// primWord64ToNat : Word64 -> Nat
+exports.primWord64ToNat = x => x;
+
+// primWord64FromNat : Nat -> Word64
+exports.primWord64FromNat = x => x % WORD64_MAX_VALUE;
+
+// uprimWord64Plus : (Word64, Word64) -> Word64
+exports.uprimWord64Plus = (x, y) => (x + y) % WORD64_MAX_VALUE;
+
+// uprimWord64Minus : (Word64, Word64) -> Word64
+exports.uprimWord64Minus = (x, y) => (x + WORD64_MAX_VALUE - y) % WORD64_MAX_VALUE;
+
+// uprimWord64Multiply : (Word64, Word64) -> Word64
+exports.uprimWord64Multiply = (x, y) => (x * y) % WORD64_MAX_VALUE;
+
+// Natural numbers
+
+// primNatMinus : Nat -> Nat -> Nat
+exports.primNatMinus = x => y => {
+  const z = x - y;
+  return z < 0n ? 0n : z;
+};
+
+// Floating-point numbers
+var _primFloatGreatestCommonFactor = function(x, y) {
+    var z;
+    x = Math.abs(x);
+    y = Math.abs(y);
+    while (y) {
+        z = x % y;
+        x = y;
+        y = z;
+    }
+    return x;
+};
+exports._primFloatRound = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.round(x);
+    }
+};
+exports._primFloatFloor = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.floor(x);
+    }
+};
+exports._primFloatCeiling = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.ceil(x);
+    }
+};
+exports._primFloatToRatio = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return {numerator: 0.0, denominator: 0.0};
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return {numerator: -1.0, denominator: 0.0};
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return {numerator: 1.0, denominator: 0.0};
+    }
+    else if (exports.primFloatIsNegativeZero(x)) {
+        return {numerator: 0.0, denominator: 1.0};
+    }
+    else if (x == 0.0) {
+        return {numerator: 0.0, denominator: 1.0};
+    }
+    else {
+        var numerator = Math.round(x*1e9);
+        var denominator = 1e9;
+        var gcf = _primFloatGreatestCommonFactor(numerator, denominator);
+        numerator /= gcf;
+        denominator /= gcf;
+        return {numerator: numerator, denominator: denominator};
+    }
+};
+exports._primFloatDecode = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return null;
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        var mantissa = x, exponent = 0;
+        while (!Number.isInteger(mantissa)) {
+            mantissa *= 2.0;
+            exponent -= 1;
+        };
+        while (mantissa % 2.0 === 0) {
+            mantissa /= 2.0;
+            exponent += 1;
+        }
+        return {mantissa: mantissa, exponent: exponent};
+    }
+};
+exports.uprimFloatEquality = function(x, y) {
+    return x === y;
+};
+exports.primFloatEquality = function(x) {
+    return function(y) {
+        return exports.uprimFloatEquality(x, y);
+    };
+};
+exports.primFloatInequality = function(x) {
+    return function(y) {
+        return x <= y;
+    };
+};
+exports.primFloatLess = function(x) {
+    return function(y) {
+        return x < y;
+    };
+};
+exports.primFloatIsInfinite = function(x) {
+    return !Number.isNaN(x) && !Number.isFinite(x);
+};
+exports.primFloatIsNaN = function(x) {
+    return Number.isNaN(x);
+};
+exports.primFloatIsNegativeZero = function(x) {
+    return Object.is(x,-0.0);
+};
+exports.primFloatIsSafeInteger = function(x) {
+    return Number.isSafeInteger(x);
+};
+
+
+// These WORD64 values were obtained via `castDoubleToWord64` in Haskell:
+const WORD64_NAN      = 18444492273895866368n;
+const WORD64_POS_INF  = 9218868437227405312n;
+const WORD64_NEG_INF  = 18442240474082181120n;
+const WORD64_POS_ZERO = 0n;
+const WORD64_NEG_ZERO = 9223372036854775808n;
+
+exports.primFloatToWord64 = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return WORD64_NAN;
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return WORD64_NEG_INF;
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return WORD64_POS_INF;
+    }
+    else if (exports.primFloatIsNegativeZero(x)) {
+        return WORD64_NEG_ZERO;
+    }
+    else if (x == 0.0) {
+        return WORD64_POS_ZERO;
+    }
+    else {
+        var mantissa, exponent;
+        ({mantissa, exponent} = exports._primFloatDecode(x));
+        var sign = Math.sign(mantissa);
+        console.log(mantissa);
+        mantissa *= sign;
+        sign = (sign === -1 ? "1" : "0");
+        mantissa = (mantissa.toString(2)).padStart(11, "0");
+        exponent = (mantissa.toString(2)).padStart(52, "0");
+        return BigInt(parseInt(sign + mantissa + exponent, 2));
+    }
+};
+
+// primNatToFloat : Nat -> Float
+exports.primNatToFloat = Number;
+
+// primIntToFloat : Int -> Float
+exports.primIntToFloat = Number;
+
+// primRatioToFloat : Int -> Int -> Float
+exports.primRatioToFloat = x => y => Number(x) / Number(y);
+
+// uprimFloatEncode : (Int, Int) -> Maybe Float
+exports.uprimFloatEncode = (x, y) => {
+  const mantissa = Number(x);
+  const exponent = Number(y);
+
+  if (Number.isSafeInteger(mantissa) && -1024 <= exponent && exponent <= 1024) {
+    return mantissa * (2 ** exponent);
+  }
+
+  else {
+    return null;
+  }
+};
+
+exports.primShowFloat = function(x) {
+    // See Issue #2192.
+    if (Number.isInteger(x)) {
+        if (exports.primFloatIsNegativeZero(x)) {
+            return ("-0.0");
+        } else {
+            return (x.toString() + ".0");
+        }
+    } else {
+        return x.toString();
+    }
+};
+exports.primFloatPlus = function(x) {
+    return function(y) {
+        return x + y;
+    };
+};
+exports.primFloatMinus = function(x) {
+    return function(y) {
+        return x - y;
+    };
+};
+exports.primFloatTimes = function(x) {
+    return function(y) {
+        return x * y;
+    };
+};
+exports.primFloatNegate = function(x) {
+    return -x;
+};
+exports.primFloatDiv = function(x) {
+  return function(y) {
+    return x / y;
+  };
+};
+exports.primFloatPow = function(x) {
+    return function(y) {
+        return x ** y;
+    };
+};
+exports.primFloatSqrt = function(x) {
+    return Math.sqrt(x);
+};
+exports.primFloatExp = function(x) {
+    return Math.exp(x);
+};
+exports.primFloatLog = function(x) {
+    return Math.log(x);
+};
+exports.primFloatSin = function(x) {
+    return Math.sin(x);
+};
+exports.primFloatCos = function(x) {
+    return Math.cos(x);
+};
+exports.primFloatTan = function(x) {
+    return Math.tan(x);
+};
+exports.primFloatASin = function(x) {
+    return Math.asin(x);
+};
+exports.primFloatACos = function(x) {
+    return Math.acos(x);
+};
+exports.primFloatATan = function(x) {
+    return Math.atan(x);
+};
+exports.primFloatATan2 = function(x) {
+    return function(y){
+        return Math.atan2(x, y);
+    };
+};
+exports.primFloatSinh = function(x) {
+    return Math.sinh(x);
+};
+exports.primFloatCosh = function(x) {
+    return Math.cosh(x);
+};
+exports.primFloatTanh = function(x) {
+    return Math.tanh(x);
+};
+exports.primFloatASinh = function(x) {
+    return Math.asinh(x);
+};
+exports.primFloatACosh = function(x) {
+    return Math.acosh(x);
+};
+exports.primFloatATanh = function(x) {
+    return Math.atanh(x);
+};
+
+// Cubical primitives.
+exports.primIMin = x => y => x && y;
+exports.primIMax = x => y => x || y;
+exports.primINeg = x => !x;
+exports.primPartial = _ => _ => x => x;
+exports.primPartialP = _ => _ => x => x;
+exports.primPOr = _ => i => _ => _ => x => y => i ? x : y;
+exports.primComp = _ => _ => _ => _ => x => x;
+exports.primTransp = _ => _ => _ => x => x;
+exports.primHComp = _ => _ => _ => _ => x => x;
+exports.primSubOut = _ => _ => _ => _ => x => x;
+exports.prim_glueU = _ => _ => _ => _ => _ => x => x;
+exports.prim_unglueU = _ => _ => _ => _ => x => x;
+exports.primFaceForall = f => f(true) == true && f(false) == false;
+exports.primDepIMin =
+    i => f => i ? f({ "tt" : a => a["tt"]() }) : false;
+exports.primConId = _ => _ => _ => _ => i => p => { return { "i" : i, "p" : p } };
+exports.primIdFace = _ => _ => _ => _ => x => x["i"];
+exports.primIdPath = _ => _ => _ => _ => x => x["p"];
+exports.primIdJ = _ => _ => _ => _ => _ => x => _ => _ => x;
+exports.primIdElim =
+    _ => _ => _ => _ => _ => f => x => y => f(y["i"])(x)(y["p"]);
+
+// Other stuff
+
+// primSeq : (X, Y) -> Y
+exports.primSeq = (x, y) => y;
+
+// uprimQNameEquality : (Name, Name) -> Bool
+exports.uprimQNameEquality = (x, y) => x['id'] === y['id'] && x['moduleId'] === y['moduleId'];
+
+// primQNameEquality : Name -> Name -> Bool
+exports.primQNameEquality = x => y => exports.uprimQNameEquality(x, y);
+
+// primQNameLess : Name -> Name -> Bool
+exports.primQNameLess = x => y => x['id'] === y['id'] ? x['moduleId'] < y['moduleId'] : x['id'] < y['id'];
+
+// primShowQName : Name -> String
+exports.primShowQName = x => x['name'];
+
+// primQNameFixity : Name -> Fixity
+exports.primQNameFixity = x => x['fixity'];
+return exports;
+});
diff --git a/src/data/JS/agda-rts.js b/src/data/JS/agda-rts.js
new file mode 100644
--- /dev/null
+++ b/src/data/JS/agda-rts.js
@@ -0,0 +1,394 @@
+// Contains *most* of the primitives required by the JavaScript backend.
+// (Some, e.g., those using Agda types like Maybe, are defined in their
+// respective builtin modules.)
+//
+// Primitives prefixed by 'u' are uncurried variants, which are sometimes
+// emitted by the JavaScript backend. Whenever possible, the curried primitives
+// should be implemented in terms of the uncurried ones.
+//
+// Primitives prefixed by '_' are internal variants, usually for those primitives
+// which return Agda types like Maybe. These are never emitted by the compiler,
+// but can be used internally to define other prefixes.
+
+// Integers
+
+// primIntegerFromString : String -> Int
+exports.primIntegerFromString = BigInt;
+
+// primShowInteger : Int -> String
+exports.primShowInteger = x => x.toString();
+
+// uprimIntegerPlus : (Int, Int) -> Int
+exports.uprimIntegerPlus = (x, y) => x + y;
+
+// uprimIntegerMinus : (Int, Int) -> Int
+exports.uprimIntegerMinus = (x, y) => x - y;
+
+// uprimIntegerMultiply : (Int, Int) -> Int
+exports.uprimIntegerMultiply = (x, y) => x * y;
+
+// uprimIntegerRem : (Int, Int) -> Int
+exports.uprimIntegerRem = (x, y) => x % y;
+
+// uprimIntegerQuot : (Int, Int) -> Int
+exports.uprimIntegerQuot = (x, y) => x / y;
+
+// uprimIntegerEqual : (Int, Int) -> Bool
+exports.uprimIntegerEqual = (x, y) => x === y;
+
+// uprimIntegerGreaterOrEqualThan : (Int, Int) -> Bool
+exports.uprimIntegerGreaterOrEqualThan = (x, y) => x >= y;
+
+// uprimIntegerLessThan : (Int, Int) -> Bool
+exports.uprimIntegerLessThan = (x, y) => x < y;
+
+// Words
+const WORD64_MAX_VALUE = 18446744073709552000n;
+
+// primWord64ToNat : Word64 -> Nat
+exports.primWord64ToNat = x => x;
+
+// primWord64FromNat : Nat -> Word64
+exports.primWord64FromNat = x => x % WORD64_MAX_VALUE;
+
+// uprimWord64Plus : (Word64, Word64) -> Word64
+exports.uprimWord64Plus = (x, y) => (x + y) % WORD64_MAX_VALUE;
+
+// uprimWord64Minus : (Word64, Word64) -> Word64
+exports.uprimWord64Minus = (x, y) => (x + WORD64_MAX_VALUE - y) % WORD64_MAX_VALUE;
+
+// uprimWord64Multiply : (Word64, Word64) -> Word64
+exports.uprimWord64Multiply = (x, y) => (x * y) % WORD64_MAX_VALUE;
+
+// Natural numbers
+
+// primNatMinus : Nat -> Nat -> Nat
+exports.primNatMinus = x => y => {
+  const z = x - y;
+  return z < 0n ? 0n : z;
+};
+
+// Floating-point numbers
+var _primFloatGreatestCommonFactor = function(x, y) {
+    var z;
+    x = Math.abs(x);
+    y = Math.abs(y);
+    while (y) {
+        z = x % y;
+        x = y;
+        y = z;
+    }
+    return x;
+};
+exports._primFloatRound = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.round(x);
+    }
+};
+exports._primFloatFloor = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.floor(x);
+    }
+};
+exports._primFloatCeiling = function(x) {
+    if (exports.primFloatIsNaN(x) || exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        return Math.ceil(x);
+    }
+};
+exports._primFloatToRatio = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return {numerator: 0.0, denominator: 0.0};
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return {numerator: -1.0, denominator: 0.0};
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return {numerator: 1.0, denominator: 0.0};
+    }
+    else if (exports.primFloatIsNegativeZero(x)) {
+        return {numerator: 0.0, denominator: 1.0};
+    }
+    else if (x == 0.0) {
+        return {numerator: 0.0, denominator: 1.0};
+    }
+    else {
+        var numerator = Math.round(x*1e9);
+        var denominator = 1e9;
+        var gcf = _primFloatGreatestCommonFactor(numerator, denominator);
+        numerator /= gcf;
+        denominator /= gcf;
+        return {numerator: numerator, denominator: denominator};
+    }
+};
+exports._primFloatDecode = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return null;
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return null;
+    }
+    else {
+        var mantissa = x, exponent = 0;
+        while (!Number.isInteger(mantissa)) {
+            mantissa *= 2.0;
+            exponent -= 1;
+        };
+        while (mantissa % 2.0 === 0) {
+            mantissa /= 2.0;
+            exponent += 1;
+        }
+        return {mantissa: mantissa, exponent: exponent};
+    }
+};
+exports.uprimFloatEquality = function(x, y) {
+    return x === y;
+};
+exports.primFloatEquality = function(x) {
+    return function(y) {
+        return exports.uprimFloatEquality(x, y);
+    };
+};
+exports.primFloatInequality = function(x) {
+    return function(y) {
+        return x <= y;
+    };
+};
+exports.primFloatLess = function(x) {
+    return function(y) {
+        return x < y;
+    };
+};
+exports.primFloatIsInfinite = function(x) {
+    return !Number.isNaN(x) && !Number.isFinite(x);
+};
+exports.primFloatIsNaN = function(x) {
+    return Number.isNaN(x);
+};
+exports.primFloatIsNegativeZero = function(x) {
+    return Object.is(x,-0.0);
+};
+exports.primFloatIsSafeInteger = function(x) {
+    return Number.isSafeInteger(x);
+};
+
+
+// These WORD64 values were obtained via `castDoubleToWord64` in Haskell:
+const WORD64_POS_INF  = 9218868437227405312n;
+const WORD64_NEG_INF  = 18442240474082181120n;
+const WORD64_POS_ZERO = 0n;
+const WORD64_NEG_ZERO = 9223372036854775808n;
+
+exports.primFloatToWord64 = function(x) {
+    if (exports.primFloatIsNaN(x)) {
+        return null;
+    }
+    else if (x < 0.0 && exports.primFloatIsInfinite(x)) {
+        return WORD64_NEG_INF;
+    }
+    else if (x > 0.0 && exports.primFloatIsInfinite(x)) {
+        return WORD64_POS_INF;
+    }
+    else if (exports.primFloatIsNegativeZero(x)) {
+        return WORD64_NEG_ZERO;
+    }
+    else if (x == 0.0) {
+        return WORD64_POS_ZERO;
+    }
+    else {
+        var mantissa, exponent;
+        ({mantissa, exponent} = exports._primFloatDecode(x));
+        var sign = Math.sign(mantissa);
+        console.log(mantissa);
+        mantissa *= sign;
+        sign = (sign === -1 ? "1" : "0");
+        mantissa = (mantissa.toString(2)).padStart(11, "0");
+        exponent = (mantissa.toString(2)).padStart(52, "0");
+        return BigInt(parseInt(sign + mantissa + exponent, 2));
+    }
+};
+
+// primNatToFloat : Nat -> Float
+exports.primNatToFloat = Number;
+
+// primIntToFloat : Int -> Float
+exports.primIntToFloat = Number;
+
+// primRatioToFloat : Int -> Int -> Float
+exports.primRatioToFloat = x => y => Number(x) / Number(y);
+
+// uprimFloatEncode : (Int, Int) -> Maybe Float
+exports.uprimFloatEncode = (x, y) => {
+  const mantissa = Number(x);
+  const exponent = Number(y);
+
+  if (Number.isSafeInteger(mantissa) && -1024 <= exponent && exponent <= 1024) {
+    return mantissa * (2 ** exponent);
+  }
+
+  else {
+    return null;
+  }
+};
+
+exports.primShowFloat = function(x) {
+    // See Issue #2192.
+    if (Number.isInteger(x)) {
+        if (exports.primFloatIsNegativeZero(x)) {
+            return ("-0.0");
+        } else {
+            return (x.toString() + ".0");
+        }
+    } else {
+        return x.toString();
+    }
+};
+exports.primFloatPlus = function(x) {
+    return function(y) {
+        return x + y;
+    };
+};
+exports.primFloatMinus = function(x) {
+    return function(y) {
+        return x - y;
+    };
+};
+exports.primFloatTimes = function(x) {
+    return function(y) {
+        return x * y;
+    };
+};
+exports.primFloatNegate = function(x) {
+    return -x;
+};
+exports.primFloatDiv = function(x) {
+  return function(y) {
+    return x / y;
+  };
+};
+exports.primFloatPow = function(x) {
+    return function(y) {
+        return x ** y;
+    };
+};
+exports.primFloatSqrt = function(x) {
+    return Math.sqrt(x);
+};
+exports.primFloatExp = function(x) {
+    return Math.exp(x);
+};
+exports.primFloatLog = function(x) {
+    return Math.log(x);
+};
+exports.primFloatSin = function(x) {
+    return Math.sin(x);
+};
+exports.primFloatCos = function(x) {
+    return Math.cos(x);
+};
+exports.primFloatTan = function(x) {
+    return Math.tan(x);
+};
+exports.primFloatASin = function(x) {
+    return Math.asin(x);
+};
+exports.primFloatACos = function(x) {
+    return Math.acos(x);
+};
+exports.primFloatATan = function(x) {
+    return Math.atan(x);
+};
+exports.primFloatATan2 = function(x) {
+    return function(y){
+        return Math.atan2(x, y);
+    };
+};
+exports.primFloatSinh = function(x) {
+    return Math.sinh(x);
+};
+exports.primFloatCosh = function(x) {
+    return Math.cosh(x);
+};
+exports.primFloatTanh = function(x) {
+    return Math.tanh(x);
+};
+exports.primFloatASinh = function(x) {
+    return Math.asinh(x);
+};
+exports.primFloatACosh = function(x) {
+    return Math.acosh(x);
+};
+exports.primFloatATanh = function(x) {
+    return Math.atanh(x);
+};
+
+// Cubical primitives.
+exports.primIMin = x => y => x && y;
+exports.primIMax = x => y => x || y;
+exports.primINeg = x => !x;
+exports.primPartial = _ => _ => x => x;
+exports.primPartialP = _ => _ => x => x;
+exports.primPOr = _ => i => _ => _ => x => y => i ? x : y;
+exports.primComp = _ => _ => _ => _ => x => x;
+exports.primTransp = _ => _ => _ => x => x;
+exports.primHComp = _ => _ => _ => _ => x => x;
+exports.primSubOut = _ => _ => _ => _ => x => x;
+exports.prim_glueU = _ => _ => _ => _ => _ => x => x;
+exports.prim_unglueU = _ => _ => _ => _ => x => x;
+exports.primFaceForall = f => f(true) == true && f(false) == false;
+exports.primDepIMin =
+    i => f => i ? f({ "tt" : a => a["tt"]() }) : false;
+exports.primConId = _ => _ => _ => _ => i => p => { return { "i" : i, "p" : p } };
+exports.primIdFace = _ => _ => _ => _ => x => x["i"];
+exports.primIdPath = _ => _ => _ => _ => x => x["p"];
+exports.primIdElim =
+    _ => _ => _ => _ => _ => f => x => y => f(y["i"])(x)(y["p"]);
+
+// Other stuff
+
+// primSeq : (X, Y) -> Y
+exports.primSeq = (x, y) => y;
+
+// uprimQNameEquality : (Name, Name) -> Bool
+exports.uprimQNameEquality = (x, y) => x['id'] === y['id'] && x['moduleId'] === y['moduleId'];
+
+// primQNameEquality : Name -> Name -> Bool
+exports.primQNameEquality = x => y => exports.uprimQNameEquality(x, y);
+
+// primQNameLess : Name -> Name -> Bool
+exports.primQNameLess = x => y => x['id'] === y['id'] ? x['moduleId'] < y['moduleId'] : x['id'] < y['id'];
+
+// primShowQName : Name -> String
+exports.primShowQName = x => x['name'];
+
+// primQNameFixity : Name -> Fixity
+exports.primQNameFixity = x => x['fixity'];
+
+// Meta
+
+// primShowMeta : Meta -> String
+//   Should be kept in sync with version in `primitiveFunctions` in
+//   Agda.TypeChecking.Primitive
+exports.primShowMeta = x => "_" + x['id'] + "@" + x['module'];
+
+// primMetaToNat : Meta -> Nat
+//   Should be kept in sync with `metaToNat` in Agda.TypeChecking.Primitive
+exports.primMetaToNat = x => x['module'] * 2^64 + x['id'];
+
+// primMetaEquality : Meta -> Meta -> Bool
+exports.primMetaEquality = x => y => x['id'] === y['id'] && x['module'] === y['module'];
+
+// primMetaLess : Meta -> Meta -> Bool
+exports.primMetaLess = x => y => x['id'] === y['id'] ? x['module'] < y['module'] : x['id'] < y['id'];
+
diff --git a/src/data/MAlonzo/src/MAlonzo/RTE.hs b/src/data/MAlonzo/src/MAlonzo/RTE.hs
new file mode 100644
--- /dev/null
+++ b/src/data/MAlonzo/src/MAlonzo/RTE.hs
@@ -0,0 +1,121 @@
+{-# LANGUAGE PolyKinds #-}
+
+module MAlonzo.RTE where
+
+import Prelude
+  ( Bool, Char, Double, Integer, String
+  , Enum(..), Eq(..), Ord(..), Integral(..), Num(..)
+  , ($), error, otherwise
+  , (++), fromIntegral
+  )
+
+import Data.Char ( GeneralCategory(Surrogate), generalCategory )
+import Data.Kind ( Type)
+import qualified Data.Word
+import qualified GHC.Exts as GHC ( Any )
+import Unsafe.Coerce ( unsafeCoerce )
+
+type AgdaAny = GHC.Any
+
+-- Special version of coerce that plays well with rules.
+{-# INLINE [1] coe #-}
+coe :: a -> b
+coe = unsafeCoerce
+{-# RULES "coerce-id" forall (x :: a) . coe x = x #-}
+
+-- Builtin QNames.
+data QName = QName { nameId, moduleId :: Integer, qnameString :: String, qnameFixity :: Fixity }
+
+data Assoc      = NonAssoc | LeftAssoc | RightAssoc
+data Precedence = Unrelated | Related PrecedenceLevel
+data Fixity     = Fixity Assoc Precedence
+type PrecedenceLevel = Double
+
+instance Eq QName where
+  QName a b _ _ == QName c d _ _ = (a, b) == (c, d)
+
+instance Ord QName where
+  compare (QName a b _ _) (QName c d _ _) = compare (a, b) (c, d)
+
+erased :: a
+erased = coe (\ _ -> erased)
+
+mazUnreachableError :: a
+mazUnreachableError = error ("Agda: unreachable code reached.")
+
+mazHole :: String -> a
+mazHole s = error ("Agda: reached hole: " ++ s)
+
+addInt :: Integer -> Integer -> Integer
+addInt = (+)
+
+subInt :: Integer -> Integer -> Integer
+subInt = (-)
+
+mulInt :: Integer -> Integer -> Integer
+mulInt = (*)
+
+geqInt :: Integer -> Integer -> Bool
+geqInt = (>=)
+
+ltInt :: Integer -> Integer -> Bool
+ltInt = (<)
+
+eqInt :: Integer -> Integer -> Bool
+eqInt = (==)
+
+quotInt :: Integer -> Integer -> Integer
+quotInt = quot
+
+remInt :: Integer -> Integer -> Integer
+remInt = rem
+
+-- #4999: Data.Text maps surrogate code points (\xD800 - \xDFFF) to the replacement character
+-- \xFFFD, so to keep strings isomorphic to list of characters we do the same for characters.
+natToChar :: Integer -> Char
+natToChar n | generalCategory c == Surrogate = '\xFFFD'
+            | otherwise                      = c
+  where c = toEnum $ fromIntegral $ mod n 0x110000
+
+-- Words --
+
+type Word64 = Data.Word.Word64
+
+word64ToNat :: Word64 -> Integer
+word64ToNat = fromIntegral
+
+word64FromNat :: Integer -> Word64
+word64FromNat = fromIntegral
+
+{-# INLINE add64 #-}
+add64 :: Word64 -> Word64 -> Word64
+add64 = (+)
+
+{-# INLINE sub64 #-}
+sub64 :: Word64 -> Word64 -> Word64
+sub64 = (-)
+
+{-# INLINE mul64 #-}
+mul64 :: Word64 -> Word64 -> Word64
+mul64 = (*)
+
+{-# INLINE quot64 #-}
+quot64 :: Word64 -> Word64 -> Word64
+quot64 = quot
+
+{-# INLINE rem64 #-}
+rem64 :: Word64 -> Word64 -> Word64
+rem64 = rem
+
+{-# INLINE eq64 #-}
+eq64 :: Word64 -> Word64 -> Bool
+eq64 = (==)
+
+{-# INLINE lt64 #-}
+lt64 :: Word64 -> Word64 -> Bool
+lt64 = (<)
+
+-- Support for musical coinduction.
+
+data Inf                      a = Sharp { flat :: a }
+type Infinity (level :: Type) a = Inf a
diff --git a/src/data/MAlonzo/src/MAlonzo/RTE/Float.hs b/src/data/MAlonzo/src/MAlonzo/RTE/Float.hs
new file mode 100644
--- /dev/null
+++ b/src/data/MAlonzo/src/MAlonzo/RTE/Float.hs
@@ -0,0 +1,285 @@
+{-# LANGUAGE CPP #-}
+
+module MAlonzo.RTE.Float where
+
+import Prelude
+  ( Bool, Double, Int, Integer, Maybe(..), Ordering(..)
+  , Eq(..), Ord(..), Functor(..)
+  , Floating(..), Fractional(..), Integral(..), Num(..), Real(..), RealFloat(..), RealFrac(..)
+  , ($), (.), otherwise, uncurry, undefined
+  , (&&), fst, snd
+  , (^), even, fromIntegral
+  )
+
+import Data.Bifunctor   ( bimap, second )
+import Data.Function    ( on )
+import Data.Maybe       ( fromMaybe )
+import Data.Ratio       ( (%), numerator, denominator )
+import Data.Word        ( Word64 )
+
+#if __GLASGOW_HASKELL__ >= 804
+import GHC.Float (castDoubleToWord64, castWord64ToDouble)
+#else
+import System.IO.Unsafe (unsafePerformIO)
+import qualified Foreign          as F
+import qualified Foreign.Storable as F
+#endif
+
+#if __GLASGOW_HASKELL__ < 804
+castDoubleToWord64 :: Double -> Word64
+castDoubleToWord64 float = unsafePerformIO $ F.alloca $ \buf -> do
+  F.poke (F.castPtr buf) float
+  F.peek buf
+
+castWord64ToDouble :: Word64 -> Double
+castWord64ToDouble word = unsafePerformIO $ F.alloca $ \buf -> do
+  F.poke (F.castPtr buf) word
+  F.peek buf
+#endif
+
+{-# INLINE doubleEq #-}
+doubleEq :: Double -> Double -> Bool
+doubleEq = (==)
+
+{-# INLINE doubleLe #-}
+doubleLe :: Double -> Double -> Bool
+doubleLe = (<=)
+
+{-# INLINE doubleLt #-}
+doubleLt :: Double -> Double -> Bool
+doubleLt = (<)
+
+truncateDouble :: Double -> Double
+truncateDouble = castWord64ToDouble . castDoubleToWord64
+
+{-# INLINE intToDouble #-}
+intToDouble :: Integral a => a -> Double
+intToDouble = truncateDouble . fromIntegral
+
+{-# INLINE doublePlus #-}
+doublePlus :: Double -> Double -> Double
+doublePlus x y = truncateDouble (x + y)
+
+{-# INLINE doubleMinus #-}
+doubleMinus :: Double -> Double -> Double
+doubleMinus x y = truncateDouble (x - y)
+
+{-# INLINE doubleTimes #-}
+doubleTimes :: Double -> Double -> Double
+doubleTimes x y = truncateDouble (x * y)
+
+{-# INLINE doubleNegate #-}
+doubleNegate :: Double -> Double
+doubleNegate = negate -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleDiv #-}
+doubleDiv :: Double -> Double -> Double
+doubleDiv = (/) -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doublePow #-}
+doublePow :: Double -> Double -> Double
+doublePow x y = truncateDouble (x ** y)
+
+{-# INLINE doubleSqrt #-}
+doubleSqrt :: Double -> Double
+doubleSqrt = sqrt -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleExp #-}
+doubleExp :: Double -> Double
+doubleExp x = truncateDouble (exp x)
+
+{-# INLINE doubleLog #-}
+doubleLog :: Double -> Double
+doubleLog = log -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleSin #-}
+doubleSin :: Double -> Double
+doubleSin = sin -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleCos #-}
+doubleCos :: Double -> Double
+doubleCos = cos -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleTan #-}
+doubleTan :: Double -> Double
+doubleTan = tan -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleASin #-}
+doubleASin :: Double -> Double
+doubleASin = asin -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleACos #-}
+doubleACos :: Double -> Double
+doubleACos = acos -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATan #-}
+doubleATan :: Double -> Double
+doubleATan = atan -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATan2 #-}
+doubleATan2 :: Double -> Double -> Double
+doubleATan2 = atan2 -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleSinh #-}
+doubleSinh :: Double -> Double
+doubleSinh = sinh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleCosh #-}
+doubleCosh :: Double -> Double
+doubleCosh = cosh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleTanh #-}
+doubleTanh :: Double -> Double
+doubleTanh = tanh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleASinh #-}
+doubleASinh :: Double -> Double
+doubleASinh = asinh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleACosh #-}
+doubleACosh :: Double -> Double
+doubleACosh = acosh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATanh #-}
+doubleATanh :: Double -> Double
+doubleATanh = atanh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE negativeZero #-}
+negativeZero :: Double
+negativeZero = -0.0
+
+positiveInfinity :: Double
+positiveInfinity = 1.0 / 0.0
+
+negativeInfinity :: Double
+negativeInfinity = -positiveInfinity
+
+nan :: Double
+nan = 0.0 / 0.0
+
+isPosInf :: Double -> Bool
+isPosInf x = x > 0.0 && isInfinite x
+
+isNegInf :: Double -> Bool
+isNegInf x = x < 0.0 && isInfinite x
+
+isPosZero :: Double -> Bool
+isPosZero x = doubleDenotEq x 0.0
+
+isNegZero :: Double -> Bool
+isNegZero x = doubleDenotEq x (-0.0)
+
+doubleRound :: Double -> Maybe Integer
+doubleRound = fmap round . asFinite
+
+doubleFloor :: Double -> Maybe Integer
+doubleFloor = fmap floor . asFinite
+
+doubleCeiling :: Double -> Maybe Integer
+doubleCeiling = fmap ceiling . asFinite
+
+normaliseNaN :: Double -> Double
+normaliseNaN x
+  | isNaN x   = nan
+  | otherwise = x
+
+doubleToWord64 :: Double -> Maybe Word64
+doubleToWord64 x
+  | isNaN x   = Nothing
+  | otherwise = Just (castDoubleToWord64 x)
+
+-- |Denotational equality for floating point numbers, checks bitwise equality.
+--
+--  NOTE: Denotational equality distinguishes NaNs, so its results may vary
+--        depending on the architecture and compilation flags. Unfortunately,
+--        this is a problem with floating-point numbers in general.
+--
+doubleDenotEq :: Double -> Double -> Bool
+doubleDenotEq = (==) `on` doubleToWord64
+
+-- |I guess "denotational orderings" are now a thing? The point is that we need
+--  an Ord instance which provides a total ordering, and is consistent with the
+--  denotational equality.
+--
+--  NOTE: The ordering induced via `doubleToWord64` is total, and is consistent
+--        with `doubleDenotEq`. However, it is *deeply* unintuitive. For one, it
+--        considers all negative numbers to be larger than positive numbers.
+--
+doubleDenotOrd :: Double -> Double -> Ordering
+doubleDenotOrd = compare `on` doubleToWord64
+
+-- |Return Just x if it's a finite number, otherwise return Nothing.
+asFinite :: Double -> Maybe Double
+asFinite x
+  | isNaN      x = Nothing
+  | isInfinite x = Nothing
+  | otherwise    = Just x
+
+-- |Decode a Double to an integer ratio.
+doubleToRatio :: Double -> (Integer, Integer)
+doubleToRatio x
+  | isNaN      x = (0, 0)
+  | isInfinite x = (signum (floor x), 0)
+  | otherwise    = let r = toRational x in (numerator r, denominator r)
+
+-- |Encode an integer ratio as a double.
+ratioToDouble :: Integer -> Integer -> Double
+ratioToDouble n d
+  | d == 0 = case compare n 0 of
+      LT -> negativeInfinity
+      EQ -> nan
+      GT -> positiveInfinity
+  | otherwise = fromRational (n % d)
+
+-- |Decode a Double to its mantissa and its exponent, normalised such that the
+--  mantissa is the smallest possible number without loss of accuracy.
+doubleDecode :: Double -> Maybe (Integer, Integer)
+doubleDecode x
+  | isNaN      x = Nothing
+  | isInfinite x = Nothing
+  | otherwise    = Just (uncurry normalise (second toInteger (decodeFloat x)))
+  where
+    normalise :: Integer -> Integer -> (Integer, Integer)
+    normalise mantissa exponent
+      | even mantissa = normalise (mantissa `div` 2) (exponent + 1)
+      | otherwise = (mantissa, exponent)
+
+-- |Checks whether or not the Double is within a safe range of operation.
+isSafeInteger :: Double -> Bool
+isSafeInteger x = case properFraction x of
+  (n, f) -> f == 0.0 && minMantissa <= n && n <= maxMantissa
+
+doubleRadix :: Integer
+doubleRadix = floatRadix (undefined :: Double)
+
+doubleDigits :: Int
+doubleDigits = floatDigits (undefined :: Double)
+
+doubleRange :: (Int, Int)
+doubleRange = floatRange (undefined :: Double)
+
+-- |The smallest representable mantissa. Simultaneously, the smallest integer which can be
+--  represented as a Double without loss of precision.
+minMantissa :: Integer
+minMantissa = - maxMantissa
+
+-- |The largest representable mantissa. Simultaneously, the largest integer which can be
+--  represented as a Double without loss of precision.
+maxMantissa :: Integer
+maxMantissa = (doubleRadix ^ toInteger doubleDigits) - 1
+
+-- |The largest representable exponent.
+minExponent :: Integer
+minExponent = toInteger $ (fst doubleRange - doubleDigits) - 1
+
+-- |The smallest representable exponent.
+maxExponent :: Integer
+maxExponent = toInteger $ snd doubleRange - doubleDigits
+
+-- |Encode a mantissa and an exponent as a Double.
+doubleEncode :: Integer -> Integer -> Maybe Double
+doubleEncode mantissa exponent
+  = if minMantissa <= mantissa && mantissa <= maxMantissa &&
+       minExponent <= exponent && exponent <= maxExponent
+    then Just (encodeFloat mantissa (fromInteger exponent))
+    else Nothing
diff --git a/src/data/emacs-mode/agda-input.el b/src/data/emacs-mode/agda-input.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda-input.el
@@ -0,0 +1,1445 @@
+;;; -*- lexical-binding: t; -*-
+;;; agda-input.el --- The Agda input method
+
+;; SPDX-License-Identifier: MIT License
+;;; Commentary:
+
+;; A highly customisable input method which can inherit from other
+;; Quail input methods. By default the input method is geared towards
+;; the input of mathematical and other symbols in Agda programs.
+;;
+;; Use M-x customize-group agda-input to customise this input method.
+;; Note that the functions defined under "Functions used to tweak
+;; translation pairs" below can be used to tweak both the key
+;; translations inherited from other input methods as well as the
+;; ones added specifically for this one.
+;;
+;; Use agda-input-show-translations to see all the characters which
+;; can be typed using this input method (except for those
+;; corresponding to ASCII characters).
+
+;;; Code:
+
+(require 'quail)
+(require 'cl-lib)
+;; Quail is quite stateful, so be careful when editing this code.  Note
+;; that with-temp-buffer is used below whenever buffer-local state is
+;; modified.
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Utility functions
+
+(defun agda-input-concat-map (f xs)
+  "Concat (map F XS)."
+  (apply 'append (mapcar f xs)))
+
+(defun agda-input-to-string-list (s)
+  "Convert a string S to a list of one-character strings, after
+removing all space and newline characters."
+  (agda-input-concat-map
+   (lambda (c) (if (member c (string-to-list " \n"))
+              nil
+            (list (string c))))
+   (string-to-list s)))
+
+(defun agda-input-character-range (from to)
+  "A string consisting of the characters from FROM to TO."
+  (let (seq)
+    (dotimes (i (1+ (- to from)))
+      (setq seq (cons (+ from i) seq)))
+    (concat (nreverse seq))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Functions used to tweak translation pairs
+
+(defun agda-input-compose (f g)
+  "λ x -> concatMap F (G x)"
+    (lambda (x) (agda-input-concat-map f (funcall g x))))
+
+(defun agda-input-or (f g)
+  "λ x -> F x ++ G x"
+    (lambda (x) (append (funcall f x) (funcall g x))))
+
+(defun agda-input-nonempty ()
+  "Only keep pairs with a non-empty first component."
+  (lambda (x) (if (> (length (car x)) 0) (list x))))
+
+(defun agda-input-prepend (prefix)
+  "Prepend PREFIX to all key sequences."
+    (lambda (x) `((,(concat prefix (car x)) . ,(cdr x)))))
+
+(defun agda-input-prefix (prefix)
+  "Only keep pairs whose key sequence starts with PREFIX."
+    (lambda (x)
+      (if (equal (substring (car x) 0 (length prefix)) prefix)
+          (list x))))
+
+(defun agda-input-suffix (suffix)
+  "Only keep pairs whose key sequence ends with SUFFIX."
+    (lambda (x)
+      (if (equal (substring (car x)
+                            (- (length (car x)) (length suffix)))
+                 suffix)
+          (list x))))
+
+(defun agda-input-drop (ss)
+  "Drop pairs matching one of the given key sequences.
+SS should be a list of strings."
+    (lambda (x) (unless (member (car x) ss) (list x))))
+
+(defun agda-input-drop-beginning (n)
+  "Drop N characters from the beginning of each key sequence."
+    (lambda (x) `((,(substring (car x) n) . ,(cdr x)))))
+
+(defun agda-input-drop-end (n)
+  "Drop N characters from the end of each key sequence."
+    (lambda (x)
+      `((,(substring (car x) 0 (- (length (car x)) n)) .
+         ,(cdr x)))))
+
+(defun agda-input-drop-prefix (prefix)
+  "Only keep pairs whose key sequence starts with PREFIX.
+This prefix is dropped."
+  (agda-input-compose
+   (agda-input-drop-beginning (length prefix))
+   (agda-input-prefix prefix)))
+
+(defun agda-input-drop-suffix (suffix)
+  "Only keep pairs whose key sequence ends with SUFFIX.
+This suffix is dropped."
+    (agda-input-compose
+     (agda-input-drop-end (length suffix))
+     (agda-input-suffix suffix)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Customization
+
+;; The :set keyword is set to 'agda-input-incorporate-changed-setting
+;; so that the input method gets updated immediately when users
+;; customize it. However, the setup functions cannot be run before all
+;; variables have been defined. Hence the :initialize keyword is set to
+;; 'custom-initialize-default to ensure that the setup is not performed
+;; until agda-input-setup is called at the end of this file.
+
+(defgroup agda-input nil
+  "The Agda input method.
+After tweaking these settings you may want to inspect the resulting
+translations using `agda-input-show-translations'."
+  :group 'agda2
+  :group 'leim)
+
+(defcustom agda-input-tweak-all
+  '(agda-input-compose
+    (agda-input-prepend "\\")
+    (agda-input-nonempty))
+  "An expression yielding a function which can be used to tweak
+all translations before they are included in the input method.
+The resulting function (if non-nil) is applied to every
+\(KEY-SEQUENCE . TRANSLATION) pair and should return a list of such
+pairs. (Note that the translations can be anything accepted by
+`quail-defrule'.)
+
+If you change this setting manually (without using the
+customization buffer) you need to call `agda-input-setup' in
+order for the change to take effect."
+  :group 'agda-input
+  :set 'agda-input-incorporate-changed-setting
+  :initialize 'custom-initialize-default
+  :type 'sexp)
+
+(defcustom agda-input-inherit
+  `(("TeX" . (agda-input-compose
+              (agda-input-drop '("geq" "leq" "bullet" "qed" "par"))
+              (agda-input-or
+               (agda-input-drop-prefix "\\")
+               (agda-input-or
+                (agda-input-compose
+                 (agda-input-drop '("^l" "^o" "^r" "^v"))
+                 (agda-input-prefix "^"))
+                (agda-input-prefix "_")))))
+    )
+  "A list of Quail input methods whose translations should be
+inherited by the Agda input method (with the exception of
+translations corresponding to ASCII characters).
+
+The list consists of pairs (qp . tweak), where qp is the name of
+a Quail package, and tweak is an expression of the same kind as
+`agda-input-tweak-all' which is used to tweak the translation
+pairs of the input method.
+
+The inherited translation pairs are added last, after
+`agda-input-user-translations' and `agda-input-translations'.
+
+If you change this setting manually (without using the
+customization buffer) you need to call `agda-input-setup' in
+order for the change to take effect."
+  :group 'agda-input
+  :set 'agda-input-incorporate-changed-setting
+  :initialize 'custom-initialize-default
+  :type '(repeat (cons (string :tag "Quail package")
+                       (sexp :tag "Tweaking function"))))
+
+(defcustom agda-input-translations
+  (let ((max-lisp-eval-depth 2800)) `(
+
+  ;; Equality and similar symbols.
+
+  ("eq"  . ,(agda-input-to-string-list "=∼∽≈≋∻∾∿≀≃⋍≂≅ ≌≊≡≣≐≑≒≓≔≕≖≗≘≙≚≛≜≝≞≟≍≎≏≬⋕＝"))
+  ("eqn" . ,(agda-input-to-string-list "≠≁ ≉     ≄  ≇≆  ≢                 ≭    "))
+
+                    ("=n"  . ("≠"))
+  ("~"    . ,(agda-input-to-string-list "∼～"))
+                    ("~n"  . ("≁"))
+  ("~~"   . ("≈"))  ("~~n" . ("≉"))
+  ("~~~"  . ("≋"))
+  (":~"   . ("∻"))
+  ("~-"   . ("≃"))  ("~-n" . ("≄"))
+  ("-~"   . ("≂"))
+  ("~="   . ("≅"))  ("~=n" . ("≇"))
+  ("~~-"  . ("≊"))
+  ("=="   . ("≡"))  ("==n" . ("≢"))
+  ("==="  . ("≣"))
+  ("="    . ("＝"))
+  (".="   . ("≐"))  (".=." . ("≑"))
+  (":="   . ("≔"))  ("=:"  . ("≕"))
+  ("=o"   . ("≗"))
+  ("(="   . ("≘"))
+  ("and=" . ("≙"))  ("or=" . ("≚"))
+  ("*="   . ("≛"))
+  ("t="   . ("≜"))
+  ("def=" . ("≝"))
+  ("m="   . ("≞"))
+  ("?="   . ("≟"))
+
+  ;; Inequality and similar symbols.
+
+  ("leq"  . ,(agda-input-to-string-list "<≪⋘≤≦≲ ≶≺≼≾⊂⊆ ⋐⊏⊑ ⊰⊲⊴⋖⋚⋜⋞＜"))
+  ("leqn" . ,(agda-input-to-string-list "≮  ≰≨≴⋦≸⊀ ⋨⊄⊈⊊  ⋢⋤ ⋪⋬   ⋠"))
+  ("geq"  . ,(agda-input-to-string-list ">≫⋙≥≧≳ ≷≻≽≿⊃⊇ ⋑⊐⊒ ⊱⊳⊵⋗⋛⋝⋟＞"))
+  ("geqn" . ,(agda-input-to-string-list "≯  ≱≩≵⋧≹⊁ ⋩⊅⊉⊋  ⋣⋥ ⋫⋭   ⋡"))
+
+  ("<="   . ("≤"))  (">="   . ("≥"))
+  ("<=n"  . ("≰"))  (">=n"  . ("≱"))
+  ("len"  . ("≰"))  ("gen"  . ("≱"))
+  ("<n"   . ("≮"))  (">n"   . ("≯"))
+  ("<~"   . ("≲"))  (">~"   . ("≳"))
+  ("<~n"  . ("⋦"))  (">~n"  . ("⋧"))
+  ("<~nn" . ("≴"))  (">~nn" . ("≵"))
+
+  ("sub"   . ("⊂"))  ("sup"   . ("⊃"))
+  ("subn"  . ("⊄"))  ("supn"  . ("⊅"))
+  ("sub="  . ("⊆"))  ("sup="  . ("⊇"))
+  ("sub=n" . ("⊈"))  ("sup=n" . ("⊉"))
+
+  ("squb"   . ("⊏"))  ("squp"   . ("⊐"))
+  ("squb="  . ("⊑"))  ("squp="  . ("⊒"))
+  ("squb=n" . ("⋢"))  ("squp=n" . ("⋣"))
+
+  ;; Set membership etc.
+
+  ("member" . ,(agda-input-to-string-list "∈∉∊∋∌∍⋲⋳⋴⋵⋶⋷⋸⋹⋺⋻⋼⋽⋾⋿"))
+
+  ("inn" . ("∉"))
+  ("nin" . ("∌"))
+
+  ;; Intersections, unions etc.
+
+  ("intersection" . ,(agda-input-to-string-list "∩⋂∧⋀⋏⨇⊓⨅⋒∏ ⊼      ⨉"))
+  ("union"        . ,(agda-input-to-string-list "∪⋃∨⋁⋎⨈⊔⨆⋓∐⨿⊽⊻⊍⨃⊎⨄⊌∑⅀"))
+
+  ("and" . ("∧"))  ("or"  . ("∨"))
+  ("And" . ("⋀"))  ("Or"  . ("⋁"))
+  ("i"   . ("∩"))  ("un"  . ("∪"))  ("u+" . ("⊎"))  ("u." . ("⊍"))
+  ("I"   . ("⋂"))  ("Un"  . ("⋃"))  ("U+" . ("⨄"))  ("U." . ("⨃"))
+  ("glb" . ("⊓"))  ("lub" . ("⊔"))
+  ("Glb" . ("⨅"))  ("Lub" . ("⨆"))
+
+  ;; Entailment etc.
+
+  ("entails" . ,(agda-input-to-string-list "⊢⊣⊤⊥⊦⊧⊨⊩⊪⊫⊬⊭⊮⊯"))
+
+  ("|-"   . ("⊢"))  ("|-n"  . ("⊬"))
+  ("-|"   . ("⊣"))
+  ("|="   . ("⊨"))  ("|=n"  . ("⊭"))
+  ("||-"  . ("⊩"))  ("||-n" . ("⊮"))
+  ("||="  . ("⊫"))  ("||=n" . ("⊯"))
+  ("|||-" . ("⊪"))
+
+  ;; Divisibility, parallelity.
+
+  ("|"  . ("∣"))  ("|n"  . ("∤"))
+  ("||" . ("∥"))  ("||n" . ("∦"))
+
+  ;; Some symbols from logic and set theory.
+
+  ("all" . ("∀"))
+  ("ex"  . ("∃"))
+  ("exn" . ("∄"))
+  ("0"   . ("∅"))
+  ("C"   . ("∁"))
+
+  ;; Corners, ceilings and floors.
+
+  ("c"  . ,(agda-input-to-string-list "⌜⌝⌞⌟⌈⌉⌊⌋"))
+  ("cu" . ,(agda-input-to-string-list "⌜⌝  ⌈⌉  "))
+  ("cl" . ,(agda-input-to-string-list "  ⌞⌟  ⌊⌋"))
+
+  ("cul" . ("⌜"))  ("cuL" . ("⌈"))
+  ("cur" . ("⌝"))  ("cuR" . ("⌉"))
+  ("cll" . ("⌞"))  ("clL" . ("⌊"))
+  ("clr" . ("⌟"))  ("clR" . ("⌋"))
+
+  ;; Various operators/symbols.
+
+  ("qed"       . ("∎"))
+  ("x"         . ("×"))
+  ("o"         . ("∘"))
+  ("comp"      . ("∘"))
+  ("."         . ,(agda-input-to-string-list "∙．"))
+  ("*"         . ("⋆"))
+  (".+"        . ("∔"))
+  (".-"        . ("∸"))
+  (":"         . ,(agda-input-to-string-list "∶⦂ː꞉˸፥፦：﹕︓"))
+  (","         . ,(agda-input-to-string-list "ʻ،⸲⸴⹁⹉、︐︑﹐﹑，､"))
+  (";"         . ,(agda-input-to-string-list "⨾⨟⁏፤꛶；︔﹔⍮⸵;"))
+  ("::"        . ("∷"))
+  ("::-"       . ("∺"))
+  ("-:"        . ("∹"))
+  ("+ "        . ("⊹"))
+  ("+"         . ("＋"))
+  ("sqrt"      . ("√"))
+  ("surd3"     . ("∛"))
+  ("surd4"     . ("∜"))
+  ("increment" . ("∆"))
+  ("inf"       . ("∞"))
+  ("&"         . ("⅋"))
+  ("z;"        . ,(agda-input-to-string-list "⨟⨾"))
+  ("z:"        . ("⦂"))
+
+  ;; Circled operators.
+
+  ("o+"  . ("⊕"))
+  ("o--" . ("⊖"))
+  ("ox"  . ("⊗"))
+  ("o/"  . ("⊘"))
+  ("o."  . ("⊙"))
+  ("oo"  . ("⊚"))
+  ("o*"  . ("⊛"))
+  ("o="  . ("⊜"))
+  ("o-"  . ("⊝"))
+
+  ("O+"  . ("⨁"))
+  ("Ox"  . ("⨂"))
+  ("O."  . ("⨀"))
+  ("O*"  . ("⍟"))
+
+  ;; Boxed operators.
+
+  ("b+" . ("⊞"))
+  ("b-" . ("⊟"))
+  ("bx" . ("⊠"))
+  ("b." . ("⊡"))
+
+  ;; APL boxed operators
+
+  ("box="       . ("⌸"))
+  ("box?"       . ("⍰"))
+  ("box'"       . ("⍞"))
+  ("box:"       . ("⍠"))
+  ("box/"       . ("⍁"))
+  ("box\\"      . ("⍂"))
+  ("box<"       . ("⍃"))
+  ("box>"       . ("⍄"))
+  ("boxo"       . ("⌻"))
+  ("boxO"       . ("⌼"))
+
+  ("boxcomp"    . ("⌻"))
+  ("boxcircle"  . ("⌼"))
+  ("boxeq"      . ("⌸"))
+  ("boxneq"     . ("⍯"))
+  ("boxeqn"     . ("⍯"))
+
+  ("boxl"       . ("⍇"))
+  ("boxr"       . ("⍈"))
+  ("boxu"       . ("⍐"))
+  ("boxd"       . ("⍗"))
+
+  ("boxdi"      . ("⌺"))
+  ("boxdiv"     . ("⌹"))
+  ("boxwedge"   . ("⍓"))
+  ("boxvee"     . ("⍌"))
+  ("boxdelta"   . ("⍍"))
+  ("boxnabla"   . ("⍔"))
+
+  ;; Various symbols.
+
+  ("integral" . ,(agda-input-to-string-list "∫∬∭∮∯∰∱∲∳"))
+  ("angle"    . ,(agda-input-to-string-list "∟∡∢⊾⊿"))
+  ("join"     . ,(agda-input-to-string-list "⋈⋉⋊⋋⋌⨝⟕⟖⟗"))
+
+  ;; Arrows.
+
+  ("l"  . ,(agda-input-to-string-list "←⇐⇚⭅⇇⇆↤⇦↞↼↽⇠⇺↜⇽⟵⟸↚⇍⇷ ↹     ↢↩↫⇋⇜⇤⟻⟽⤆↶↺⟲                                     "))
+  ("r"  . ,(agda-input-to-string-list "→⇒⇛⭆⇉⇄↦⇨↠⇀⇁⇢⇻↝⇾⟶⟹↛⇏⇸⇶ ↴    ↣↪↬⇌⇝⇥⟼⟾⤇↷↻⟳⇰⇴⟴⟿ ➵➸➙➔➛➜➝➞➟➠➡➢➣➤➧➨➩➪➫➬➭➮➯➱➲➳➺➻➼➽➾⊸"))
+  ("u"  . ,(agda-input-to-string-list "↑⇑⤊⟰⇈⇅↥⇧↟↿↾⇡⇞          ↰↱➦ ⇪⇫⇬⇭⇮⇯                                           "))
+  ("d"  . ,(agda-input-to-string-list "↓⇓⤋⟱⇊⇵↧⇩↡⇃⇂⇣⇟         ↵↲↳➥ ↯                                                "))
+  ("ud" . ,(agda-input-to-string-list "↕⇕   ↨⇳                                                                    "))
+  ("lr" . ,(agda-input-to-string-list "↔⇔         ⇼↭⇿⟷⟺↮⇎⇹                                                        "))
+  ("ul" . ,(agda-input-to-string-list "↖⇖                        ⇱↸                                               "))
+  ("ur" . ,(agda-input-to-string-list "↗⇗                                         ➶➹➚                             "))
+  ("dr" . ,(agda-input-to-string-list "↘⇘                        ⇲                ➴➷➘                             "))
+  ("dl" . ,(agda-input-to-string-list "↙⇙                                                                         "))
+
+  ("l-"  . ("←"))  ("<-"  . ("←"))  ("l="  . ("⇐"))  ("<="  . ("⇐"))
+  ("r-"  . ("→"))  ("->"  . ("→"))  ("r="  . ("⇒"))  ("=>"  . ("⇒"))
+  ("u-"  . ("↑"))                   ("u="  . ("⇑"))
+  ("d-"  . ("↓"))                   ("d="  . ("⇓"))
+  ("ud-" . ("↕"))                   ("ud=" . ("⇕"))
+  ("lr-" . ("↔"))  ("<->" . ("↔"))  ("lr=" . ("⇔"))  ("<=>" . ("⇔"))
+  ("ul-" . ("↖"))                   ("ul=" . ("⇖"))
+  ("ur-" . ("↗"))                   ("ur=" . ("⇗"))
+  ("dr-" . ("↘"))                   ("dr=" . ("⇘"))
+  ("dl-" . ("↙"))                   ("dl=" . ("⇙"))
+
+  ("l==" . ("⇚"))  ("l-2" . ("⇇"))                   ("l-r-" . ("⇆"))
+  ("r==" . ("⇛"))  ("r-2" . ("⇉"))  ("r-3" . ("⇶"))  ("r-l-" . ("⇄"))
+  ("u==" . ("⟰"))  ("u-2" . ("⇈"))                   ("u-d-" . ("⇅"))
+  ("d==" . ("⟱"))  ("d-2" . ("⇊"))                   ("d-u-" . ("⇵"))
+
+  ("l--"  . ("⟵"))  ("<--"  . ("⟵"))  ("l~"  . ("↜" "⇜"))
+  ("r--"  . ("⟶"))  ("-->"  . ("⟶"))  ("r~"  . ("↝" "⇝" "⟿"))
+  ("lr--" . ("⟷"))  ("<-->" . ("⟷"))  ("lr~" . ("↭"))
+
+  ("l-n"  . ("↚"))  ("<-n"  . ("↚"))  ("l=n"  . ("⇍"))
+  ("r-n"  . ("↛"))  ("->n"  . ("↛"))  ("r=n"  . ("⇏"))  ("=>n"  . ("⇏"))
+  ("lr-n" . ("↮"))  ("<->n" . ("↮"))  ("lr=n" . ("⇎"))  ("<=>n" . ("⇎"))
+
+  ("l-|"  . ("↤"))  ("ll-" . ("↞"))
+  ("r-|"  . ("↦"))  ("rr-" . ("↠"))
+  ("u-|"  . ("↥"))  ("uu-" . ("↟"))
+  ("d-|"  . ("↧"))  ("dd-" . ("↡"))
+  ("ud-|" . ("↨"))
+
+  ("l->" . ("↢"))
+  ("r->" . ("↣"))
+
+  ("r-o" . ("⊸"))  ("-o"  . ("⊸"))
+
+  ("dz" . ("↯"))
+
+  ;; Ellipsis.
+
+  ("..." . ,(agda-input-to-string-list "⋯⋮⋰⋱"))
+
+  ;; Box-drawing characters.
+
+  ("---" . ,(agda-input-to-string-list "─│┌┐└┘├┤┬┼┴╴╵╶╷╭╮╯╰╱╲╳"))
+  ("--=" . ,(agda-input-to-string-list "═║╔╗╚╝╠╣╦╬╩     ╒╕╘╛╞╡╤╪╧ ╓╖╙╜╟╢╥╫╨"))
+  ("--_" . ,(agda-input-to-string-list "━┃┏┓┗┛┣┫┳╋┻╸╹╺╻
+                                        ┍┯┑┕┷┙┝┿┥┎┰┒┖┸┚┠╂┨┞╀┦┟╁┧┢╈┪┡╇┩
+                                        ┮┭┶┵┾┽┲┱┺┹╊╉╆╅╄╃ ╿╽╼╾"))
+  ("--." . ,(agda-input-to-string-list "╌╎┄┆┈┊
+                                        ╍╏┅┇┉┋"))
+
+  ;; Triangles.
+
+  ;; Big/small, black/white.
+
+  ("t" . ,(agda-input-to-string-list "◂◃◄◅▸▹►▻▴▵▾▿◢◿◣◺◤◸◥◹"))
+  ("T" . ,(agda-input-to-string-list "◀◁▶▷▲△▼▽◬◭◮"))
+
+  ("tb" . ,(agda-input-to-string-list "◂▸▴▾◄►◢◣◤◥"))
+  ("tw" . ,(agda-input-to-string-list "◃▹▵▿◅▻◿◺◸◹"))
+
+  ("Tb" . ,(agda-input-to-string-list "◀▶▲▼"))
+  ("Tw" . ,(agda-input-to-string-list "◁▷△▽"))
+
+  ;; Squares.
+
+  ("sq"  . ,(agda-input-to-string-list "■□◼◻◾◽▣▢▤▥▦▧▨▩◧◨◩◪◫◰◱◲◳"))
+  ("sqb" . ,(agda-input-to-string-list "■◼◾"))
+  ("sqw" . ,(agda-input-to-string-list "□◻◽"))
+  ("sq." . ("▣"))
+  ("sqo" . ("▢"))
+
+  ;; Rectangles.
+
+  ("re"  . ,(agda-input-to-string-list "▬▭▮▯"))
+  ("reb" . ,(agda-input-to-string-list "▬▮"))
+  ("rew" . ,(agda-input-to-string-list "▭▯"))
+
+  ;; Parallelograms.
+
+  ("pa"  . ,(agda-input-to-string-list "▰▱"))
+  ("pab" . ("▰"))
+  ("paw" . ("▱"))
+
+  ;; Diamonds.
+
+  ("di"  . ,(agda-input-to-string-list "◆◇◈"))
+  ("dib" . ("◆"))
+  ("diw" . ("◇"))
+  ("di." . ("◈"))
+
+  ;; Circles.
+
+  ("ci"   . ,(agda-input-to-string-list "●○◎◌◯◍◐◑◒◓◔◕◖◗◠◡◴◵◶◷⚆⚇⚈⚉"))
+  ("cib"  . ("●"))
+  ("ciw"  . ("○"))
+  ("ci."  . ("◎"))
+  ("ci.." . ("◌"))
+  ("ciO"  . ("◯"))
+
+  ;; Stars.
+
+  ("st"   . ,(agda-input-to-string-list "⋆✦✧✶✴✹ ★☆✪✫✯✰✵✷✸"))
+  ("st4"  . ,(agda-input-to-string-list "✦✧"))
+  ("st6"  . ("✶"))
+  ("st8"  . ("✴"))
+  ("st12" . ("✹"))
+
+  ;; Blackboard bold letters.
+
+  ("bA"   . ("𝔸"))
+  ("bB"   . ("𝔹"))
+  ("bC"   . ("ℂ"))
+  ("bD"   . ("𝔻"))
+  ("bE"   . ("𝔼"))
+  ("bF"   . ("𝔽"))
+  ("bG"   . ("𝔾"))
+  ("bH"   . ("ℍ"))
+  ("bI"   . ("𝕀"))
+  ("bJ"   . ("𝕁"))
+  ("bK"   . ("𝕂"))
+  ("bL"   . ("𝕃"))
+  ("bM"   . ("𝕄"))
+  ("bN"   . ("ℕ"))
+  ("bO"   . ("𝕆"))
+  ("bP"   . ("ℙ"))
+  ("bQ"   . ("ℚ"))
+  ("bR"   . ("ℝ"))
+  ("bS"   . ("𝕊"))
+  ("bT"   . ("𝕋"))
+  ("bU"   . ("𝕌"))
+  ("bV"   . ("𝕍"))
+  ("bW"   . ("𝕎"))
+  ("bX"   . ("𝕏"))
+  ("bY"   . ("𝕐"))
+  ("bZ"   . ("ℤ"))
+  ("bGG"  . ("ℾ"))
+  ("bGP"  . ("ℿ"))
+  ("bGS"  . ("⅀"))
+  ("ba"   . ("𝕒"))
+  ("bb"   . ("𝕓"))
+  ("bc"   . ("𝕔"))
+  ("bd"   . ("𝕕"))
+  ("be"   . ("𝕖"))
+  ("bf"   . ("𝕗"))
+  ("bg"   . ("𝕘"))
+  ("bh"   . ("𝕙"))
+  ("bi"   . ("𝕚"))
+  ("bj"   . ("𝕛"))
+  ("bk"   . ("𝕜"))
+  ("bl"   . ("𝕝"))
+  ("bm"   . ("𝕞"))
+  ("bn"   . ("𝕟"))
+  ("bo"   . ("𝕠"))
+  ("bp"   . ("𝕡"))
+  ("bq"   . ("𝕢"))
+  ("br"   . ("𝕣"))
+  ("bs"   . ("𝕤"))
+  ("bt"   . ("𝕥"))
+  ("bu"   . ("𝕦"))
+  ("bv"   . ("𝕧"))
+  ("bw"   . ("𝕨"))
+  ("bx"   . ("𝕩"))
+  ("by"   . ("𝕪"))
+  ("bz"   . ("𝕫"))
+  ("bGg"  . ("ℽ"))
+  ("bGp"  . ("ℼ"))
+
+  ;; Blackboard bold numbers.
+
+  ("b0"   . ("𝟘"))
+  ("b1"   . ("𝟙"))
+  ("b2"   . ("𝟚"))
+  ("b3"   . ("𝟛"))
+  ("b4"   . ("𝟜"))
+  ("b5"   . ("𝟝"))
+  ("b6"   . ("𝟞"))
+  ("b7"   . ("𝟟"))
+  ("b8"   . ("𝟠"))
+  ("b9"   . ("𝟡"))
+
+  ;; Mathematical bold letters.
+
+  ("BA"   . ("𝐀"))
+  ("BB"   . ("𝐁"))
+  ("BC"   . ("𝐂"))
+  ("BD"   . ("𝐃"))
+  ("BE"   . ("𝐄"))
+  ("BF"   . ("𝐅"))
+  ("BG"   . ("𝐆"))
+  ("BH"   . ("𝐇"))
+  ("BI"   . ("𝐈"))
+  ("BJ"   . ("𝐉"))
+  ("BK"   . ("𝐊"))
+  ("BL"   . ("𝐋"))
+  ("BM"   . ("𝐌"))
+  ("BN"   . ("𝐍"))
+  ("BO"   . ("𝐎"))
+  ("BP"   . ("𝐏"))
+  ("BQ"   . ("𝐐"))
+  ("BR"   . ("𝐑"))
+  ("BS"   . ("𝐒"))
+  ("BT"   . ("𝐓"))
+  ("BU"   . ("𝐔"))
+  ("BV"   . ("𝐕"))
+  ("BW"   . ("𝐖"))
+  ("BX"   . ("𝐗"))
+  ("BY"   . ("𝐘"))
+  ("BZ"   . ("𝐙"))
+  ("Ba"   . ("𝐚"))
+  ("Bb"   . ("𝐛"))
+  ("Bc"   . ("𝐜"))
+  ("Bd"   . ("𝐝"))
+  ("Be"   . ("𝐞"))
+  ("Bf"   . ("𝐟"))
+  ("Bg"   . ("𝐠"))
+  ("Bh"   . ("𝐡"))
+  ("Bi"   . ("𝐢"))
+  ("Bj"   . ("𝐣"))
+  ("Bk"   . ("𝐤"))
+  ("Bl"   . ("𝐥"))
+  ("Bm"   . ("𝐦"))
+  ("Bn"   . ("𝐧"))
+  ("Bo"   . ("𝐨"))
+  ("Bp"   . ("𝐩"))
+  ("Bq"   . ("𝐪"))
+  ("Br"   . ("𝐫"))
+  ("Bs"   . ("𝐬"))
+  ("Bt"   . ("𝐭"))
+  ("Bu"   . ("𝐮"))
+  ("Bv"   . ("𝐯"))
+  ("Bw"   . ("𝐰"))
+  ("Bx"   . ("𝐱"))
+  ("By"   . ("𝐲"))
+  ("Bz"   . ("𝐳"))
+
+  ;; Mathematical bold Greek letters.
+
+  ("BGA"  . ("𝚨"))
+  ("BGB"  . ("𝚩"))
+  ("BGC"  . ("𝚾"))
+  ("BGD"  . ("𝚫"))
+  ("BGE"  . ("𝚬"))
+  ("BGG"  . ("𝚪"))
+  ("BGH"  . ("𝚮"))
+  ("BGI"  . ("𝚰"))
+  ("BGK"  . ("𝚱"))
+  ("BGL"  . ("𝚲"))
+  ("BGM"  . ("𝚳"))
+  ("BGN"  . ("𝚴"))
+  ("BGO"  . ("𝛀"))
+  ("BOmicron" . ("𝚶"))
+  ("BGF"  . ("𝚽"))
+  ("BPi"  . ("𝚷"))
+  ("BGP"  . ("𝚿"))
+  ("BGR"  . ("𝚸"))
+  ("BGS"  . ("𝚺"))
+  ("BGT"  . ("𝚻"))
+  ("BGTH" . ("𝚯"))
+  ("BGU"  . ("𝚼"))
+  ("BGX"  . ("𝚵"))
+  ("BGZ"  . ("𝚭"))
+  ("BGa"  . ("𝛂"))
+  ("BGb"  . ("𝛃"))
+  ("BGc"  . ("𝛘"))
+  ("BGd"  . ("𝛅"))
+  ("BGe"  . ("𝛆"))
+  ("BGg"  . ("𝛄"))
+  ("BGh"  . ("𝛈"))
+  ("BGi"  . ("𝛊"))
+  ("BGk"  . ("𝛋"))
+  ("BGl"  . ("𝛌"))
+  ("BGm"  . ("𝛍"))
+  ("BGn"  . ("𝛎"))
+  ("BGo"  . ("𝛚"))
+  ("Bomicron" . ("𝛐"))
+  ("BGf"  . ("𝛗"))
+  ("Bpi"  . ("𝛑"))
+  ("BGp"  . ("𝛙"))
+  ("BGr"  . ("𝛒"))
+  ("BGs"  . ("𝛔"))
+  ("BGt"  . ("𝛕"))
+  ("BGth" . ("𝛉"))
+  ("BGu"  . ("𝛖"))
+  ("BGx"  . ("𝛏"))
+  ("BGz"  . ("𝛇"))
+
+  ;; Mathematical bold digits.
+
+  ("B0"   . ("𝟎"))
+  ("B1"   . ("𝟏"))
+  ("B2"   . ("𝟐"))
+  ("B3"   . ("𝟑"))
+  ("B4"   . ("𝟒"))
+  ("B5"   . ("𝟓"))
+  ("B6"   . ("𝟔"))
+  ("B7"   . ("𝟕"))
+  ("B8"   . ("𝟖"))
+  ("B9"   . ("𝟗"))
+
+  ;; Fullwidth letters
+
+  ("FA"   . ("Ａ"))
+  ("FB"   . ("Ｂ"))
+  ("FC"   . ("Ｃ"))
+  ("FD"   . ("Ｄ"))
+  ("FE"   . ("Ｅ"))
+  ("FF"   . ("Ｆ"))
+  ("FG"   . ("Ｇ"))
+  ("FH"   . ("Ｈ"))
+  ("FI"   . ("Ｉ"))
+  ("FJ"   . ("Ｊ"))
+  ("FK"   . ("Ｋ"))
+  ("FL"   . ("Ｌ"))
+  ("FM"   . ("Ｍ"))
+  ("FN"   . ("Ｎ"))
+  ("FO"   . ("Ｏ"))
+  ("FP"   . ("Ｐ"))
+  ("FQ"   . ("Ｑ"))
+  ("FR"   . ("Ｒ"))
+  ("FS"   . ("Ｓ"))
+  ("FT"   . ("Ｔ"))
+  ("FU"   . ("Ｕ"))
+  ("FV"   . ("Ｖ"))
+  ("FW"   . ("Ｗ"))
+  ("FX"   . ("Ｘ"))
+  ("FY"   . ("Ｙ"))
+  ("FZ"   . ("Ｚ"))
+  ("Fa"   . ("ａ"))
+  ("Fb"   . ("ｂ"))
+  ("Fc"   . ("ｃ"))
+  ("Fd"   . ("ｄ"))
+  ("Fe"   . ("ｅ"))
+  ("Ff"   . ("ｆ"))
+  ("Fg"   . ("ｇ"))
+  ("Fh"   . ("ｈ"))
+  ("Fi"   . ("ｉ"))
+  ("Fj"   . ("ｊ"))
+  ("Fk"   . ("ｋ"))
+  ("Fl"   . ("ｌ"))
+  ("Fm"   . ("ｍ"))
+  ("Fn"   . ("ｎ"))
+  ("Fo"   . ("ｏ"))
+  ("Fp"   . ("ｐ"))
+  ("Fq"   . ("ｑ"))
+  ("Fr"   . ("ｒ"))
+  ("Fs"   . ("ｓ"))
+  ("Ft"   . ("ｔ"))
+  ("Fu"   . ("ｕ"))
+  ("Fv"   . ("ｖ"))
+  ("Fw"   . ("ｗ"))
+  ("Fx"   . ("ｘ"))
+  ("Fy"   . ("ｙ"))
+  ("Fz"   . ("ｚ"))
+
+  ;; Fullwidth digits
+
+  ("F0"   . ("０"))
+  ("F1"   . ("１"))
+  ("F2"   . ("２"))
+  ("F3"   . ("３"))
+  ("F4"   . ("４"))
+  ("F5"   . ("５"))
+  ("F6"   . ("６"))
+  ("F7"   . ("７"))
+  ("F8"   . ("８"))
+  ("F9"   . ("９"))
+
+  ;; Parentheses.
+
+  ("(" . ,(agda-input-to-string-list "([{⁅⁽₍〈⎴⟅⟦⟨⟪⦃〈《「『【〔〖〚︵︷︹︻︽︿﹁﹃﹙﹛﹝（［｛｢❪❬❰❲❴⟮⦅⦗⧼⸨❮⦇⦉"))
+  (")" . ,(agda-input-to-string-list ")]}⁆⁾₎〉⎵⟆⟧⟩⟫⦄〉》」』】〕〗〛︶︸︺︼︾﹀﹂﹄﹚﹜﹞）］｝｣❫❭❱❳❵⟯⦆⦘⧽⸩❯⦈⦊"))
+
+  ("[[" . ("⟦"))
+  ("]]" . ("⟧"))
+  ("<"  . ,(agda-input-to-string-list "⟨<≪⋘≺⊂⋐⊏⊰⊲⋖＜"))
+  (">"  . ,(agda-input-to-string-list "⟩>≫⋙≻⊃⋑⊐⊱⊳⋗＞"))
+  ("<<" . ("⟪"))
+  (">>" . ("⟫"))
+  ("{{" . ("⦃"))
+  ("}}" . ("⦄"))
+
+  ("(b" . ("⟅"))
+  (")b" . ("⟆"))
+
+  ("lbag" . ("⟅"))
+  ("rbag" . ("⟆"))
+
+  ("<|" . ("⦉"))  ;; Angle bar brackets
+  ("|>" . ("⦊"))
+
+  ("(|" . ("⦇"))  ;; Idiom brackets
+  ("|)" . ("⦈"))
+
+  ("((" . ,(agda-input-to-string-list "⦅｟"))  ;; Banana brackets
+  ("))" . ,(agda-input-to-string-list "⦆｠"))
+
+  ;; Primes.
+
+  ("'" . ,(agda-input-to-string-list "′″‴⁗＇"))
+  ("`" . ,(agda-input-to-string-list "‵‶‷｀"))
+
+  ;; Fractions.
+
+  ("frac" . ,(agda-input-to-string-list "¼½¾⅓⅔⅕⅖⅗⅘⅙⅚⅛⅜⅝⅞⅟"))
+
+  ;; Bullets.
+
+  ("bu"  . ,(agda-input-to-string-list "•◦‣⁌⁍"))
+  ("bub" . ("•"))
+  ("buw" . ("◦"))
+  ("but" . ("‣"))
+
+  ;; Musical symbols.
+
+  ("note" . ,(agda-input-to-string-list "♩♪♫♬"))
+  ("b"    . ("♭"))
+  ("#"    . ("♯"))
+
+  ;; Other punctuation and symbols.
+
+  ("\\"         . ("\\"))
+  ("en"         . ("–"))
+  ("em"         . ("—"))
+  ("!"          . ("！"))
+  ("!!"         . ("‼"))
+  ("?"          . ("？"))
+  ("??"         . ("⁇"))
+  ("?!"         . ("‽" "⁈"))
+  ("!?"         . ("⁉"))
+  ("die"        . ,(agda-input-to-string-list "⚀⚁⚂⚃⚄⚅"))
+  ("asterisk"   . ,(agda-input-to-string-list "⁎⁑⁂✢✣✤✥✱✲✳✺✻✼✽❃❉❊❋＊"))
+  ("8<"         . ("✂" "✄"))
+  ("tie"        . ("⁀"))
+  ("undertie"   . ("‿"))
+  ("apl"        . ,(agda-input-to-string-list "⌶⌷⌸⌹⌺⌻⌼⌽⌾⌿⍀⍁⍂⍃⍄⍅⍆⍇⍈
+                                               ⍉⍊⍋⍌⍍⍎⍏⍐⍑⍒⍓⍔⍕⍖⍗⍘⍙⍚⍛
+                                               ⍜⍝⍞⍟⍠⍡⍢⍣⍤⍥⍦⍧⍨⍩⍪⍫⍬⍭⍮
+                                               ⍯⍰⍱⍲⍳⍴⍵⍶⍷⍸⍹⍺⎕"))
+  ("#"          . ("＃"))
+  ("%"          . ("％"))
+  ("&"          . ("＆"))
+  ("*"          . ("＊"))
+  ("/"          . ,(agda-input-to-string-list "／＼"))
+  ("@"          . ("＠"))
+  ("__"         . ("＿"))
+  ("\""         . ("＂"))
+
+  ;; Some combining characters.
+  ;;
+  ;; The following combining characters also have (other)
+  ;; translations:
+  ;; ̀ ́ ̂ ̃ ̄ ̆ ̇ ̈ ̋ ̌ ̣ ̧ ̱
+
+  ("^--" . ,(agda-input-to-string-list"̅̿"))
+  ("_--" . ,(agda-input-to-string-list"̲̳"))
+  ("^~"  . ,(agda-input-to-string-list"̃͌"))
+  ("_~"  .  (                         "̰"))
+  ("^."  . ,(agda-input-to-string-list"̇̈⃛⃜"))
+  ("_."  . ,(agda-input-to-string-list"̣̤"))
+  ("^l"  . ,(agda-input-to-string-list"⃖⃐⃔"))
+  ("^l-" .  (                         "⃖"))
+  ("^r"  . ,(agda-input-to-string-list"⃗⃑⃕"))
+  ("^r-" .  (                         "⃗"))
+  ("^lr" .  (                         "⃡"))
+  ("_lr" .  (                         "͍"))
+  ("^^"  . ,(agda-input-to-string-list"̂̑͆"))
+  ("_^"  . ,(agda-input-to-string-list"̭̯̪"))
+  ("^v"  . ,(agda-input-to-string-list"̌̆"))
+  ("_v"  . ,(agda-input-to-string-list"̬̮̺"))
+
+  ;; Shorter forms of many greek letters plus ƛ.
+
+  ("Ga"  . ("α"))  ("GA"  . ("Α"))
+  ("Gb"  . ("β"))  ("GB"  . ("Β"))
+  ("Gg"  . ("γ"))  ("GG"  . ("Γ"))
+  ("Gd"  . ("δ"))  ("GD"  . ("Δ"))
+  ("Ge"  . ("ε"))  ("GE"  . ("Ε"))
+  ("Gz"  . ("ζ"))  ("GZ"  . ("Ζ"))
+  ("Gh"  . ("η"))  ("GH"  . ("Η"))
+  ("Gth" . ("θ"))  ("GTH" . ("Θ"))
+  ("Gi"  . ("ι"))  ("GI"  . ("Ι"))
+  ("Gk"  . ("κ"))  ("GK"  . ("Κ"))
+  ("Gl"  . ("λ"))  ("GL"  . ("Λ"))  ("Gl-" . ("ƛ"))
+  ("Gm"  . ("μ"))  ("GM"  . ("Μ"))
+  ("Gn"  . ("ν"))  ("GN"  . ("Ν"))
+  ("Gx"  . ("ξ"))  ("GX"  . ("Ξ"))
+  ;; \omicron \Omicron
+  ;; \pi \Pi
+  ("Gr"  . ("ρ"))  ("GR"  . ("Ρ"))
+  ("Gs"  . ("σ"))  ("GS"  . ("Σ"))
+  ("Gt"  . ("τ"))  ("GT"  . ("Τ"))
+  ("Gu"  . ("υ"))  ("GU"  . ("Υ"))
+  ("Gf"  . ("φ"))  ("GF"  . ("Φ"))
+  ("Gc"  . ("χ"))  ("GC"  . ("Χ"))
+  ("Gp"  . ("ψ"))  ("GP"  . ("Ψ"))
+  ("Go"  . ("ω"))  ("GO"  . ("Ω"))
+
+  ;; Mathematical characters
+
+  ("MiA" . ("𝐴"))
+  ("MiB" . ("𝐵"))
+  ("MiC" . ("𝐶"))
+  ("MiD" . ("𝐷"))
+  ("MiE" . ("𝐸"))
+  ("MiF" . ("𝐹"))
+  ("MiG" . ("𝐺"))
+  ("MiH" . ("𝐻"))
+  ("MiI" . ("𝐼"))
+  ("MiJ" . ("𝐽"))
+  ("MiK" . ("𝐾"))
+  ("MiL" . ("𝐿"))
+  ("MiM" . ("𝑀"))
+  ("MiN" . ("𝑁"))
+  ("MiO" . ("𝑂"))
+  ("MiP" . ("𝑃"))
+  ("MiQ" . ("𝑄"))
+  ("MiR" . ("𝑅"))
+  ("MiS" . ("𝑆"))
+  ("MiT" . ("𝑇"))
+  ("MiU" . ("𝑈"))
+  ("MiV" . ("𝑉"))
+  ("MiW" . ("𝑊"))
+  ("MiX" . ("𝑋"))
+  ("MiY" . ("𝑌"))
+  ("MiZ" . ("𝑍"))
+  ("Mia" . ("𝑎"))
+  ("Mib" . ("𝑏"))
+  ("Mic" . ("𝑐"))
+  ("Mid" . ("𝑑"))
+  ("Mie" . ("𝑒"))
+  ("Mif" . ("𝑓"))
+  ("Mig" . ("𝑔"))
+  ("Mih" . ("ℎ"))
+  ("Mii" . ("𝑖"))
+  ("Mij" . ("𝑗"))
+  ("Mik" . ("𝑘"))
+  ("Mil" . ("𝑙"))
+  ("Mim" . ("𝑚"))
+  ("Min" . ("𝑛"))
+  ("Mio" . ("𝑜"))
+  ("Mip" . ("𝑝"))
+  ("Miq" . ("𝑞"))
+  ("Mir" . ("𝑟"))
+  ("Mis" . ("𝑠"))
+  ("Mit" . ("𝑡"))
+  ("Miu" . ("𝑢"))
+  ("Miv" . ("𝑣"))
+  ("Miw" . ("𝑤"))
+  ("Mix" . ("𝑥"))
+  ("Miy" . ("𝑦"))
+  ("Miz" . ("𝑧"))
+  ("MIA" . ("𝑨"))
+  ("MIB" . ("𝑩"))
+  ("MIC" . ("𝑪"))
+  ("MID" . ("𝑫"))
+  ("MIE" . ("𝑬"))
+  ("MIF" . ("𝑭"))
+  ("MIG" . ("𝑮"))
+  ("MIH" . ("𝑯"))
+  ("MII" . ("𝑰"))
+  ("MIJ" . ("𝑱"))
+  ("MIK" . ("𝑲"))
+  ("MIL" . ("𝑳"))
+  ("MIM" . ("𝑴"))
+  ("MIN" . ("𝑵"))
+  ("MIO" . ("𝑶"))
+  ("MIP" . ("𝑷"))
+  ("MIQ" . ("𝑸"))
+  ("MIR" . ("𝑹"))
+  ("MIS" . ("𝑺"))
+  ("MIT" . ("𝑻"))
+  ("MIU" . ("𝑼"))
+  ("MIV" . ("𝑽"))
+  ("MIW" . ("𝑾"))
+  ("MIX" . ("𝑿"))
+  ("MIY" . ("𝒀"))
+  ("MIZ" . ("𝒁"))
+  ("MIa" . ("𝒂"))
+  ("MIb" . ("𝒃"))
+  ("MIc" . ("𝒄"))
+  ("MId" . ("𝒅"))
+  ("MIe" . ("𝒆"))
+  ("MIf" . ("𝒇"))
+  ("MIg" . ("𝒈"))
+  ("MIh" . ("𝒉"))
+  ("MIi" . ("𝒊"))
+  ("MIj" . ("𝒋"))
+  ("MIk" . ("𝒌"))
+  ("MIl" . ("𝒍"))
+  ("MIm" . ("𝒎"))
+  ("MIn" . ("𝒏"))
+  ("MIo" . ("𝒐"))
+  ("MIp" . ("𝒑"))
+  ("MIq" . ("𝒒"))
+  ("MIr" . ("𝒓"))
+  ("MIs" . ("𝒔"))
+  ("MIt" . ("𝒕"))
+  ("MIu" . ("𝒖"))
+  ("MIv" . ("𝒗"))
+  ("MIw" . ("𝒘"))
+  ("MIx" . ("𝒙"))
+  ("MIy" . ("𝒚"))
+  ("MIz" . ("𝒛"))
+  ("McA" . ("𝒜"))
+  ("McB" . ("ℬ"))
+  ("McC" . ("𝒞"))
+  ("McD" . ("𝒟"))
+  ("McE" . ("ℰ"))
+  ("McF" . ("ℱ"))
+  ("McG" . ("𝒢"))
+  ("McH" . ("ℋ"))
+  ("McI" . ("ℐ"))
+  ("McJ" . ("𝒥"))
+  ("McK" . ("𝒦"))
+  ("McL" . ("ℒ"))
+  ("McM" . ("ℳ"))
+  ("McN" . ("𝒩"))
+  ("McO" . ("𝒪"))
+  ("McP" . ("𝒫"))
+  ("McQ" . ("𝒬"))
+  ("McR" . ("ℛ"))
+  ("McS" . ("𝒮"))
+  ("McT" . ("𝒯"))
+  ("McU" . ("𝒰"))
+  ("McV" . ("𝒱"))
+  ("McW" . ("𝒲"))
+  ("McX" . ("𝒳"))
+  ("McY" . ("𝒴"))
+  ("McZ" . ("𝒵"))
+  ("Mca" . ("𝒶"))
+  ("Mcb" . ("𝒷"))
+  ("Mcc" . ("𝒸"))
+  ("Mcd" . ("𝒹"))
+  ("Mce" . ("ℯ"))
+  ("Mcf" . ("𝒻"))
+  ("Mcg" . ("ℊ"))
+  ("Mch" . ("𝒽"))
+  ("Mci" . ("𝒾"))
+  ("Mcj" . ("𝒿"))
+  ("Mck" . ("𝓀"))
+  ("Mcl" . ("𝓁"))
+  ("Mcm" . ("𝓂"))
+  ("Mcn" . ("𝓃"))
+  ("Mco" . ("ℴ"))
+  ("Mcp" . ("𝓅"))
+  ("Mcq" . ("𝓆"))
+  ("Mcr" . ("𝓇"))
+  ("Mcs" . ("𝓈"))
+  ("Mct" . ("𝓉"))
+  ("Mcu" . ("𝓊"))
+  ("Mcv" . ("𝓋"))
+  ("Mcw" . ("𝓌"))
+  ("Mcx" . ("𝓍"))
+  ("Mcy" . ("𝓎"))
+  ("Mcz" . ("𝓏"))
+  ("MCA" . ("𝓐"))
+  ("MCB" . ("𝓑"))
+  ("MCC" . ("𝓒"))
+  ("MCD" . ("𝓓"))
+  ("MCE" . ("𝓔"))
+  ("MCF" . ("𝓕"))
+  ("MCG" . ("𝓖"))
+  ("MCH" . ("𝓗"))
+  ("MCI" . ("𝓘"))
+  ("MCJ" . ("𝓙"))
+  ("MCK" . ("𝓚"))
+  ("MCL" . ("𝓛"))
+  ("MCM" . ("𝓜"))
+  ("MCN" . ("𝓝"))
+  ("MCO" . ("𝓞"))
+  ("MCP" . ("𝓟"))
+  ("MCQ" . ("𝓠"))
+  ("MCR" . ("𝓡"))
+  ("MCS" . ("𝓢"))
+  ("MCT" . ("𝓣"))
+  ("MCU" . ("𝓤"))
+  ("MCV" . ("𝓥"))
+  ("MCW" . ("𝓦"))
+  ("MCX" . ("𝓧"))
+  ("MCY" . ("𝓨"))
+  ("MCZ" . ("𝓩"))
+  ("MCa" . ("𝓪"))
+  ("MCb" . ("𝓫"))
+  ("MCc" . ("𝓬"))
+  ("MCd" . ("𝓭"))
+  ("MCe" . ("𝓮"))
+  ("MCf" . ("𝓯"))
+  ("MCg" . ("𝓰"))
+  ("MCh" . ("𝓱"))
+  ("MCi" . ("𝓲"))
+  ("MCj" . ("𝓳"))
+  ("MCk" . ("𝓴"))
+  ("MCl" . ("𝓵"))
+  ("MCm" . ("𝓶"))
+  ("MCn" . ("𝓷"))
+  ("MCo" . ("𝓸"))
+  ("MCp" . ("𝓹"))
+  ("MCq" . ("𝓺"))
+  ("MCr" . ("𝓻"))
+  ("MCs" . ("𝓼"))
+  ("MCt" . ("𝓽"))
+  ("MCu" . ("𝓾"))
+  ("MCv" . ("𝓿"))
+  ("MCw" . ("𝔀"))
+  ("MCx" . ("𝔁"))
+  ("MCy" . ("𝔂"))
+  ("MCz" . ("𝔃"))
+  ("MfA" . ("𝔄"))
+  ("MfB" . ("𝔅"))
+  ("MfC" . ("ℭ"))
+  ("MfD" . ("𝔇"))
+  ("MfE" . ("𝔈"))
+  ("MfF" . ("𝔉"))
+  ("MfG" . ("𝔊"))
+  ("MfH" . ("ℌ"))
+  ("MfI" . ("ℑ"))
+  ("MfJ" . ("𝔍"))
+  ("MfK" . ("𝔎"))
+  ("MfL" . ("𝔏"))
+  ("MfM" . ("𝔐"))
+  ("MfN" . ("𝔑"))
+  ("MfO" . ("𝔒"))
+  ("MfP" . ("𝔓"))
+  ("MfQ" . ("𝔔"))
+  ("MfR" . ("ℜ"))
+  ("MfS" . ("𝔖"))
+  ("MfT" . ("𝔗"))
+  ("MfU" . ("𝔘"))
+  ("MfV" . ("𝔙"))
+  ("MfW" . ("𝔚"))
+  ("MfX" . ("𝔛"))
+  ("MfY" . ("𝔜"))
+  ("MfZ" . ("ℨ"))
+  ("Mfa" . ("𝔞"))
+  ("Mfb" . ("𝔟"))
+  ("Mfc" . ("𝔠"))
+  ("Mfd" . ("𝔡"))
+  ("Mfe" . ("𝔢"))
+  ("Mff" . ("𝔣"))
+  ("Mfg" . ("𝔤"))
+  ("Mfh" . ("𝔥"))
+  ("Mfi" . ("𝔦"))
+  ("Mfj" . ("𝔧"))
+  ("Mfk" . ("𝔨"))
+  ("Mfl" . ("𝔩"))
+  ("Mfm" . ("𝔪"))
+  ("Mfn" . ("𝔫"))
+  ("Mfo" . ("𝔬"))
+  ("Mfp" . ("𝔭"))
+  ("Mfq" . ("𝔮"))
+  ("Mfr" . ("𝔯"))
+  ("Mfs" . ("𝔰"))
+  ("Mft" . ("𝔱"))
+  ("Mfu" . ("𝔲"))
+  ("Mfv" . ("𝔳"))
+  ("Mfw" . ("𝔴"))
+  ("Mfx" . ("𝔵"))
+  ("Mfy" . ("𝔶"))
+  ("Mfz" . ("𝔷"))
+
+  ;; (Sub / Super) scripts
+  ;;
+  ;; Unicode 12.1 omits several latin characters from sub/superscript.
+  ;; https://www.quora.com/Why-is-there-no-character-for-superscript-q-in-Unicode
+  ;;
+  ;; Perhaps they will be added in future versions, however there are no
+  ;; proposals for it currently in the pipeline:
+  ;; https://www.unicode.org/alloc/Pipeline.html
+
+  ("_a" . ("ₐ"))
+  ;; ("_b" . ("b"))
+  ;; ("_c" . ("c"))
+  ;; ("_d" . ("d"))
+  ("_e" . ("ₑ"))
+  ;; ("_f" . ("f"))
+  ;; ("_g" . ("g"))
+  ("_h" . ("ₕ"))
+  ("_i" . ("ᵢ"))
+  ("_j" . ("ⱼ"))
+  ("_k" . ("ₖ"))
+  ("_l" . ("ₗ"))
+  ("_m" . ("ₘ"))
+  ("_n" . ("ₙ"))
+  ("_o" . ("ₒ"))
+  ("_p" . ("ₚ"))
+  ;; ("_q" . ("q"))
+  ("_r" . ("ᵣ"))
+  ("_s" . ("ₛ"))
+  ("_t" . ("ₜ"))
+  ("_u" . ("ᵤ"))
+  ("_v" . ("ᵥ"))
+  ;; ("_w" . ("w"))
+  ("_x" . ("ₓ"))
+  ;; ("_y" . ("y"))
+  ;; ("_z" . ("z"))
+
+  ("_Gb" . ("ᵦ"))
+  ("_Gg" . ("ᵧ"))
+  ("_Gr" . ("ᵨ"))
+  ("_Gf" . ("ᵩ"))
+  ("_Gc" . ("ᵪ"))
+
+  ("^a" . ("ᵃ"))
+  ("^b" . ("ᵇ"))
+  ("^c" . ("ᶜ"))
+  ("^d" . ("ᵈ"))
+  ("^e" . ("ᵉ"))
+  ("^f" . ("ᶠ"))
+  ("^g" . ("ᵍ"))
+  ("^h" . ("ʰ"))
+  ("^i" . ("ⁱ"))
+  ("^j" . ("ʲ"))
+  ("^k" . ("ᵏ"))
+  ("^l" . ("ˡ"))
+  ("^m" . ("ᵐ"))
+  ("^n" . ("ⁿ"))
+  ("^o" . ("ᵒ"))
+  ("^p" . ("ᵖ"))
+  ;; ("^q" . ("q"))
+  ("^r" . ("ʳ"))
+  ("^s" . ("ˢ"))
+  ("^t" . ("ᵗ"))
+  ("^u" . ("ᵘ"))
+  ("^v" . ("ᵛ"))
+  ("^w" . ("ʷ"))
+  ("^x" . ("ˣ"))
+  ("^y" . ("ʸ"))
+  ("^z" . ("ᶻ"))
+
+  ("^A" . ("ᴬ"))
+  ("^B" . ("ᴮ"))
+  ;; ("^C" . ("C"))
+  ("^D" . ("ᴰ"))
+  ("^E" . ("ᴱ"))
+  ;; ("^F" . ("F"))
+  ("^G" . ("ᴳ"))
+  ("^H" . ("ᴴ"))
+  ("^I" . ("ᴵ"))
+  ("^J" . ("ᴶ"))
+  ("^K" . ("ᴷ"))
+  ("^L" . ("ᴸ"))
+  ("^M" . ("ᴹ"))
+  ("^N" . ("ᴺ"))
+  ("^O" . ("ᴼ"))
+  ("^P" . ("ᴾ"))
+  ;; ("^Q" . ("Q"))
+  ("^R" . ("ᴿ"))
+  ;; ("^S" . ("S"))
+  ("^T" . ("ᵀ"))
+  ("^U" . ("ᵁ"))
+  ("^V" . ("ⱽ"))
+  ("^W" . ("ᵂ"))
+  ;; ("^X" . ("X"))
+  ;; ("^Y" . ("Y"))
+  ;; ("^Z" . ("Z"))
+
+  ("^Gb" . ("ᵝ"))
+  ("^Gg" . ("ᵞ"))
+  ("^Gd" . ("ᵟ"))
+  ("^Ge" . ("ᵋ"))
+  ("^Gth" . ("ᶿ"))
+  ("^Gf" . ("ᵠ"))
+  ("^Gc" . ("ᵡ"))
+
+  ;; Some ISO8859-1 characters.
+
+  (" "         . (" "))
+  ("!"         . ("¡"))
+  ("cent"      . ("¢"))
+  ("brokenbar" . ("¦"))
+  ("degree"    . ("°"))
+  ("?"         . ("¿"))
+  ("^a_"       . ("ª"))
+  ("^o_"       . ("º"))
+
+  ;; Circled, parenthesised etc. numbers and letters.
+
+  ( "(0)" . ,(agda-input-to-string-list " ⓪🄀⓿🄋🄌"))
+  ( "(1)" . ,(agda-input-to-string-list "⑴①⒈❶➀➊"))
+  ( "(2)" . ,(agda-input-to-string-list "⑵②⒉❷➁➋"))
+  ( "(3)" . ,(agda-input-to-string-list "⑶③⒊❸➂➌"))
+  ( "(4)" . ,(agda-input-to-string-list "⑷④⒋❹➃➍"))
+  ( "(5)" . ,(agda-input-to-string-list "⑸⑤⒌❺➄➎"))
+  ( "(6)" . ,(agda-input-to-string-list "⑹⑥⒍❻➅➏"))
+  ( "(7)" . ,(agda-input-to-string-list "⑺⑦⒎❼➆➐"))
+  ( "(8)" . ,(agda-input-to-string-list "⑻⑧⒏❽➇➑"))
+  ( "(9)" . ,(agda-input-to-string-list "⑼⑨⒐❾➈➒"))
+  ("(10)" . ,(agda-input-to-string-list "⑽⑩⒑❿➉➓"))
+  ("(11)" . ,(agda-input-to-string-list "⑾⑪⒒⓫"))
+  ("(12)" . ,(agda-input-to-string-list "⑿⑫⒓⓬"))
+  ("(13)" . ,(agda-input-to-string-list "⒀⑬⒔⓭"))
+  ("(14)" . ,(agda-input-to-string-list "⒁⑭⒕⓮"))
+  ("(15)" . ,(agda-input-to-string-list "⒂⑮⒖⓯"))
+  ("(16)" . ,(agda-input-to-string-list "⒃⑯⒗⓰"))
+  ("(17)" . ,(agda-input-to-string-list "⒄⑰⒘⓱"))
+  ("(18)" . ,(agda-input-to-string-list "⒅⑱⒙⓲"))
+  ("(19)" . ,(agda-input-to-string-list "⒆⑲⒚⓳"))
+  ("(20)" . ,(agda-input-to-string-list "⒇⑳⒛⓴"))
+
+  ("(a)"  . ,(agda-input-to-string-list "⒜Ⓐⓐ🅐🄰🅰"))
+  ("(b)"  . ,(agda-input-to-string-list "⒝Ⓑⓑ🅑🄱🅱"))
+  ("(c)"  . ,(agda-input-to-string-list "⒞Ⓒⓒ🅒🄲🅲"))
+  ("(d)"  . ,(agda-input-to-string-list "⒟Ⓓⓓ🅓🄳🅳"))
+  ("(e)"  . ,(agda-input-to-string-list "⒠Ⓔⓔ🅔🄴🅴"))
+  ("(f)"  . ,(agda-input-to-string-list "⒡Ⓕⓕ🅕🄵🅵"))
+  ("(g)"  . ,(agda-input-to-string-list "⒢Ⓖⓖ🅖🄶🅶"))
+  ("(h)"  . ,(agda-input-to-string-list "⒣Ⓗⓗ🅗🄷🅷"))
+  ("(i)"  . ,(agda-input-to-string-list "⒤Ⓘⓘ🅘🄸🅸"))
+  ("(j)"  . ,(agda-input-to-string-list "⒥Ⓙⓙ🅙🄹🅹"))
+  ("(k)"  . ,(agda-input-to-string-list "⒦Ⓚⓚ🅚🄺🅺"))
+  ("(l)"  . ,(agda-input-to-string-list "⒧Ⓛⓛ🅛🄻🅻"))
+  ("(m)"  . ,(agda-input-to-string-list "⒨Ⓜⓜ🅜🄼🅼"))
+  ("(n)"  . ,(agda-input-to-string-list "⒩Ⓝⓝ🅝🄽🅽"))
+  ("(o)"  . ,(agda-input-to-string-list "⒪Ⓞⓞ🅞🄾🅾"))
+  ("(p)"  . ,(agda-input-to-string-list "⒫Ⓟⓟ🅟🄿🅿"))
+  ("(q)"  . ,(agda-input-to-string-list "⒬Ⓠⓠ🅠🅀🆀"))
+  ("(r)"  . ,(agda-input-to-string-list "⒭Ⓡⓡ🅡🅁🆁"))
+  ("(s)"  . ,(agda-input-to-string-list "⒮Ⓢⓢ🅢🅂🆂"))
+  ("(t)"  . ,(agda-input-to-string-list "⒯Ⓣⓣ🅣🅃🆃"))
+  ("(u)"  . ,(agda-input-to-string-list "⒰Ⓤⓤ🅤🅄🆄"))
+  ("(v)"  . ,(agda-input-to-string-list "⒱Ⓥⓥ🅥🅅🆅"))
+  ("(w)"  . ,(agda-input-to-string-list "⒲Ⓦⓦ🅦🅆🆆"))
+  ("(x)"  . ,(agda-input-to-string-list "⒳Ⓧⓧ🅧🅇🆇"))
+  ("(y)"  . ,(agda-input-to-string-list "⒴Ⓨⓨ🅨🅈🆈"))
+  ("(z)"  . ,(agda-input-to-string-list "⒵Ⓩⓩ🅩🅉🆉"))
+
+  ))
+  "A list of translations specific to the Agda input method.
+Each element is a pair (KEY-SEQUENCE-STRING . LIST-OF-TRANSLATION-STRINGS).
+All the translation strings are possible translations
+of the given key sequence; if there is more than one you can choose
+between them using the arrow keys.
+
+Note that if you customize this setting you will not
+automatically benefit (or suffer) from modifications to its
+default value when the library is updated.  If you just want to
+add some bindings it is probably a better idea to customize
+`agda-input-user-translations'.
+
+These translation pairs are included after those in
+`agda-input-user-translations', but before the ones inherited
+from other input methods (see `agda-input-inherit').
+
+If you change this setting manually (without using the
+customization buffer) you need to call `agda-input-setup' in
+order for the change to take effect."
+  :group 'agda-input
+  :set 'agda-input-incorporate-changed-setting
+  :initialize 'custom-initialize-default
+  :type '(repeat (cons (string :tag "Key sequence")
+                       (repeat :tag "Translations" string))))
+
+(defcustom agda-input-user-translations nil
+  "Like `agda-input-translations', but more suitable for user
+customizations since by default it is empty.
+
+These translation pairs are included first, before those in
+`agda-input-translations' and the ones inherited from other input
+methods."
+  :group 'agda-input
+  :set 'agda-input-incorporate-changed-setting
+  :initialize 'custom-initialize-default
+  :type '(repeat (cons (string :tag "Key sequence")
+                       (repeat :tag "Translations" string))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Inspecting and modifying translation maps
+
+(defun agda-input-get-translations (qp)
+  "Return a list containing all translations from the Quail
+package QP (except for those corresponding to ASCII).
+Each pair in the list has the form (KEY-SEQUENCE . TRANSLATION)."
+  (with-temp-buffer
+    (activate-input-method qp) ; To make sure that the package is loaded.
+    (unless (quail-package qp)
+      (error "%s is not a Quail package." qp))
+    (let ((decode-map (list 'decode-map)))
+      (quail-build-decode-map (list (quail-map)) "" decode-map 0)
+      (cdr decode-map))))
+
+(defun agda-input-show-translations (qp)
+  "Display all translations used by the Quail package QP (a string).
+\(Except for those corresponding to ASCII)."
+  (interactive (list (read-input-method-name
+                      "Quail input method (default %s): " "Agda")))
+  (let ((buf (concat "*" qp " input method translations*")))
+    (with-output-to-temp-buffer buf
+      (with-current-buffer buf
+        (quail-insert-decode-map
+         (cons 'decode-map (agda-input-get-translations qp)))))))
+
+(defun agda-input-add-translations (trans)
+  "Add the given translations TRANS to the Agda input method.
+TRANS is a list of pairs (KEY-SEQUENCE . TRANSLATION). The
+translations are appended to the current translations."
+  (with-temp-buffer
+    (dolist (tr (agda-input-concat-map (eval agda-input-tweak-all) trans))
+      (quail-defrule (car tr) (cdr tr) "Agda" t))))
+
+(defun agda-input-inherit-package (qp &optional fun)
+  "Let the Agda input method inherit the translations from the
+Quail package QP (except for those corresponding to ASCII).
+
+The optional function FUN can be used to modify the translations.
+It is given a pair (KEY-SEQUENCE . TRANSLATION) and should return
+a list of such pairs."
+  (let ((trans (agda-input-get-translations qp)))
+    (agda-input-add-translations
+     (if fun (agda-input-concat-map fun trans)
+       trans))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Setting up the input method
+
+(defun agda-input-setup ()
+  "Set up the Agda input method based on the customisable
+variables and underlying input methods."
+
+  ;; Create (or reset) the input method.
+  (with-temp-buffer
+    (quail-define-package "Agda" "UTF-8" "∏" t ; guidance
+     "Agda input method.
+The purpose of this input method is to edit Agda programs, but
+since it is highly customisable it can be made useful for other
+tasks as well."
+     nil nil nil nil nil nil t ; maximum-shortest
+     ))
+
+  (agda-input-add-translations
+   (mapcar (lambda (tr) (cons (car tr) (vconcat (cdr tr))))
+           (append agda-input-user-translations
+                   agda-input-translations)))
+  (dolist (def agda-input-inherit)
+    (agda-input-inherit-package (car def)
+                                (eval (cdr def)))))
+
+(defun agda-input-incorporate-changed-setting (sym val)
+  "Update the Agda input method based on the customisable
+variables and underlying input methods.
+Suitable for use in the :set field of `defcustom'."
+  (set-default sym val)
+  (agda-input-setup))
+
+;; Set up the input method.
+
+(agda-input-setup)
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Administrative details
+
+(provide 'agda-input)
+;;; agda-input.el ends here
diff --git a/src/data/emacs-mode/agda2-abbrevs.el b/src/data/emacs-mode/agda2-abbrevs.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2-abbrevs.el
@@ -0,0 +1,106 @@
+;; agda2-abbrevs.el --- Default Agda abbrevs
+;; SPDX-License-Identifier: MIT License
+
+;;; Commentary:
+
+;;; Code:
+
+;; Skeletons
+
+(require 'skeleton)
+
+(define-skeleton agda2-abbrevs-module
+  "Inserts a module header template."
+  nil
+  "module " _ " where\n")
+
+(define-skeleton agda2-abbrevs-data
+  "Inserts a data template."
+  nil
+  "data " _ " : Set where\n")
+
+(define-skeleton agda2-abbrevs-record
+  "Inserts a record type template."
+  nil
+  "record " _ " : Set where\n"
+  "  field\n")
+
+(define-skeleton agda2-abbrevs-record-value
+  "Inserts a record value template."
+  nil
+  "record {" _ "}")
+
+(define-skeleton agda2-abbrevs-using
+  "Inserts a using template."
+  nil
+  "using (" _ ")")
+
+(define-skeleton agda2-abbrevs-hiding
+  "Inserts a hiding template."
+  nil
+  "hiding (" _ ")")
+
+(define-skeleton agda2-abbrevs-renaming
+  "Inserts a renaming template."
+  nil
+  "renaming (" _ " to " _ ")")
+
+(define-skeleton agda2-abbrevs-forall
+  "Inserts a forall template."
+  nil
+  "∀ {" _ "} ")
+
+(define-skeleton agda2-abbrevs-code-block
+  "Inserts a code block."
+  nil
+  "\\begin{code}\n  " _ "\n\\end{code}\n")
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Abbrevs
+
+(defvar agda2-abbrevs-defaults '(
+  ("m"   "" agda2-abbrevs-module)
+  ("d"   "" agda2-abbrevs-data)
+  ("c"   "" agda2-abbrevs-code-block)
+  ("re"  "" agda2-abbrevs-record)
+  ("rec" "" agda2-abbrevs-record-value)
+  ("u"   "" agda2-abbrevs-using)
+  ("h"   "" agda2-abbrevs-hiding)
+  ("r"   "" agda2-abbrevs-renaming)
+  ("w"   "where\n")
+  ("po"  "postulate")
+  ("a"   "abstract\n")
+  ("pr"  "private\n")
+  ("pu"  "public")
+  ("mu"  "mutual\n")
+  ("f"   "" agda2-abbrevs-forall)
+  ("oi"  "open import "))
+  "Abbreviations defined by default in the Agda mode.")
+
+(defcustom agda2-mode-abbrevs-use-defaults nil
+  "If non-nil include the default Agda mode abbrevs in `agda2-mode-abbrev-table'.
+The abbrevs are designed to be expanded explicitly, so users of `abbrev-mode'
+probably do not want to include them.
+
+Restart Emacs in order for this change to take effect."
+  :group 'agda2
+  :type '(choice (const :tag "Yes" t)
+                 (const :tag "No" nil)))
+
+(defvar agda2-mode-abbrev-table nil
+  "Agda mode abbrev table.")
+
+(define-abbrev-table
+  'agda2-mode-abbrev-table
+  (if agda2-mode-abbrevs-use-defaults
+      (mapcar (lambda (abbrev)
+                (append abbrev
+                        (make-list (- 4 (length abbrev)) nil)
+                        '((:system t))))
+              agda2-abbrevs-defaults)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Administrative details
+
+(provide 'agda2-abbrevs)
+;;; agda2-abbrevs.el ends here
diff --git a/src/data/emacs-mode/agda2-highlight.el b/src/data/emacs-mode/agda2-highlight.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2-highlight.el
@@ -0,0 +1,596 @@
+;;; agda2-highlight.el --- Syntax highlighting for Agda (version ≥ 2)
+;; SPDX-License-Identifier: MIT License
+
+;;; Commentary:
+
+;; Code to apply syntactic highlighting to Agda source code. This uses
+;; Agda's own annotations to figure out what is what, so the parsing
+;; is always done correctly, but highlighting is not done on the fly.
+
+;;; Code:
+
+(require 'annotation)
+(require 'font-lock)
+
+(defgroup agda2-highlight nil
+  "Syntax highlighting for Agda."
+  :group 'agda2)
+
+(defcustom agda2-highlight-level 'non-interactive
+  "How much syntax highlighting should be produced?
+Interactive highlighting includes highlighting of the expression
+that is currently being type-checked."
+  :type '(choice
+          (const :tag "None"            none)
+          (const :tag "Non-interactive" non-interactive)
+          (const :tag "Interactive"     interactive))
+  :group 'agda2-highlight)
+
+(defun agda2-highlight-level nil
+  "Formats the highlighting level in a Haskelly way."
+  (cond ((equal agda2-highlight-level 'none)            "None")
+        ((equal agda2-highlight-level 'non-interactive) "NonInteractive")
+        ((equal agda2-highlight-level 'interactive)     "Interactive")
+        (t                                              "None")))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Functions for setting faces
+
+(defun agda2-highlight-set-face-attribute (face attrs)
+  "Reset (globally) all attributes of the face FACE according to ATTRS.
+If the face does not exist, then it is created first."
+  (make-face face)
+  (set-face-attribute face nil
+                      :family         'unspecified
+                      :width          'unspecified
+                      :height         'unspecified
+                      :weight         'unspecified
+                      :slant          'unspecified
+                      :foreground     'unspecified
+                      :background     'unspecified
+                      :inverse-video  'unspecified
+                      :stipple        'unspecified
+                      :underline      'unspecified
+                      :overline       'unspecified
+                      :strike-through 'unspecified
+                      :inherit        'unspecified
+                      :box            'unspecified
+                      :font           'unspecified)
+  (eval `(set-face-attribute face nil ,@attrs)))
+
+(defun agda2-highlight-set-faces (variable group)
+  "Set all Agda faces according to the value of GROUP.
+Also sets the default value of VARIABLE to GROUP."
+  (set-default variable group)
+  (mapc (lambda (face-and-attrs)
+          (agda2-highlight-set-face-attribute
+           (car face-and-attrs) (cdr face-and-attrs)))
+        (cond
+         ((equal group 'conor)
+          '((agda2-highlight-keyword-face
+             :bold t)
+            (agda2-highlight-string-face
+             :foreground "firebrick3")
+            (agda2-highlight-number-face
+             :foreground "firebrick3")
+            (agda2-highlight-symbol-face
+             :foreground "grey25")
+            (agda2-highlight-primitive-type-face
+             :foreground "medium blue")
+            (agda2-highlight-bound-variable-face
+             :foreground "purple")
+            (agda2-highlight-generalizable-variable-face
+             :foreground "purple")
+            (agda2-highlight-inductive-constructor-face
+             :foreground "firebrick3")
+            (agda2-highlight-coinductive-constructor-face
+             :foreground "firebrick3")
+            (agda2-highlight-datatype-face
+             :foreground "medium blue")
+            (agda2-highlight-field-face
+             :foreground "deeppink")
+            (agda2-highlight-function-face
+             :foreground "darkgreen")
+            (agda2-highlight-module-face
+             :foreground "medium blue")
+            (agda2-highlight-postulate-face
+             :foreground "darkgreen")
+            (agda2-highlight-primitive-face
+             :foreground "darkgreen")
+            (agda2-highlight-macro-face
+             :foreground "aquamarine4")
+            (agda2-highlight-record-face
+             :foreground "medium blue")
+            (agda2-highlight-dotted-face)
+            (agda2-highlight-error-face
+             :foreground "red"
+             :underline t)
+            (agda2-highlight-error-warning-face
+             :background "light coral"
+             :underline t)
+            (agda2-highlight-unsolved-meta-face
+             :foreground "black"
+             :background "yellow")
+            (agda2-highlight-unsolved-constraint-face
+             :foreground "black"
+             :background "yellow")
+            (agda2-highlight-termination-problem-face
+             :foreground "black"
+             :background "light salmon")
+            (agda2-highlight-positivity-problem-face
+             :foreground "black"
+             :background "peru")
+            (agda2-highlight-incomplete-pattern-face
+             :foreground "black"
+             :background "purple")
+            (agda2-highlight-typechecks-face
+             :foreground "black"
+             :background "light blue")))
+         ((equal group 'default-faces)
+          (list (cons 'agda2-highlight-keyword-face
+                      (list :inherit font-lock-keyword-face))
+                (cons 'agda2-highlight-string-face
+                      (list :inherit font-lock-string-face))
+                (cons 'agda2-highlight-number-face
+                      (list :inherit font-lock-constant-face))
+                (cons 'agda2-highlight-symbol-face
+                      (list :inherit font-lock-keyword-face))
+                (cons 'agda2-highlight-primitive-type-face
+                      (list :inherit font-lock-keyword-face))
+                (cons 'agda2-highlight-bound-variable-face
+                      (list :inherit font-lock-variable-name-face))
+                (cons 'agda2-highlight-generalizable-variable-face
+                      (list :inherit font-lock-variable-name-face))
+                (cons 'agda2-highlight-inductive-constructor-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-coinductive-constructor-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-datatype-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-field-face
+                      (list :inherit font-lock-variable-name-face))
+                (cons 'agda2-highlight-function-face
+                      (list :inherit font-lock-function-name-face))
+                (cons 'agda2-highlight-module-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-postulate-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-primitive-face
+                      (list :inherit font-lock-constant-face))
+                (cons 'agda2-highlight-macro-face
+                      (list :inherit font-lock-function-name-face))
+                (cons 'agda2-highlight-record-face
+                      (list :inherit font-lock-variable-name-face))
+                (cons 'agda2-highlight-dotted-face
+                      (list :inherit font-lock-variable-name-face))
+                (cons 'agda2-highlight-operator-face
+                      (list :inherit font-lock-function-name-face))
+                (cons 'agda2-highlight-error-face
+                      (list :inherit font-lock-warning-face))
+                (cons 'agda2-highlight-typechecks-face
+                      (list :inherit font-lock-type-face))
+                (cons 'agda2-highlight-typechecking-face
+                      (list :inherit font-lock-preprocessor-face)))))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Faces
+
+(defcustom agda2-highlight-face-groups nil
+  "Colour scheme used in Agda buffers.
+Changes to this variable may not take full effect until you have
+restarted Emacs. Note also that if you are using the
+default-faces option and change your colour theme, then the
+changes may not take effect in Agda buffers until you have
+restarted Emacs."
+  :type '(choice
+          (const :tag "Use the settings in the \"Agda2 Highlight Faces\" subgroup." nil)
+          (const :tag "Use an approximation of Conor McBride's colour scheme."
+                 conor)
+          (const :tag "Use simplified highlighting and default font-lock faces."
+                 default-faces))
+  :group 'agda2-highlight
+  :set 'agda2-highlight-set-faces)
+
+(defgroup agda2-highlight-faces nil
+  "Faces used to highlight Agda code.
+If `agda2-highlight-face-groups' is nil."
+  :group 'agda2-highlight)
+
+(defface agda2-highlight-keyword-face
+  '((((background light))
+     (:foreground "DarkOrange3"))
+    (((background dark))
+     (:foreground "#FF9932")))
+  "The face used for keywords."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-string-face
+  '((((background light))
+     (:foreground "firebrick"))
+    (((background dark))
+     (:foreground "#DD4D4D")))
+  "The face used for strings."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-number-face
+  '((((background light))
+     (:foreground "purple"))
+    (((background dark))
+     (:foreground "#9010E0")))
+  "The face used for numbers."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-symbol-face
+  '((((background light))
+     (:foreground "gray25"))
+    (((background dark))
+     (:foreground "gray75")))
+  "The face used for symbols like forall, =, ->, etc."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-primitive-type-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for primitive types (like Set and Prop)."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-bound-variable-face
+  '((t nil))
+  "The face used for bound variables."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-generalizable-variable-face
+  '((t nil))
+  "The face used for generalizable variables."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-inductive-constructor-face
+  '((((background light))
+     :foreground "green4")
+    (((background dark))
+     :foreground "#29CC29"))
+  "The face used for inductive constructors."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-coinductive-constructor-face
+  '((((background light))
+     :foreground "gold4")
+    (((background dark))
+     :foreground "#FFEA75"))
+  "The face used for coinductive constructors."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-datatype-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for datatypes."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-field-face
+  '((((background light))
+     (:foreground "DeepPink2"))
+    (((background dark))
+     (:foreground "#F570B7")))
+  "The face used for record fields."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-function-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for functions."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-module-face
+  '((((background light))
+     (:foreground "purple"))
+    (((background dark))
+     (:foreground "#CD80FF")))
+  "The face used for module names."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-postulate-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for postulates."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-pragma-face
+  '((t nil))
+  "The face used for (some text in) pragmas."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-primitive-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for primitive functions."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-macro-face
+  '((((background light))
+     (:foreground "aquamarine4"))
+    (((background dark))
+     (:foreground "#73BAA2")))
+  "The face used for macros."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-record-face
+  '((((background light))
+     (:foreground "medium blue"))
+    (((background dark))
+     (:foreground "#8080FF")))
+  "The face used for record types."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-dotted-face
+  '((t nil))
+  "The face used for dotted patterns."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-operator-face
+  '((t nil))
+  "The face used for operators."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-error-face
+  '((((background light))
+     (:foreground "red" :underline t))
+    (((background dark))
+     (:foreground "#FF0000" :underline t)))
+  "The face used for errors."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-error-warning-face
+  '((((background light))
+     (:background "light coral" :underline t))
+    (((background dark))
+     (:background "#802400" :underline t)))
+  "The face used for fatal warnings."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-unsolved-meta-face
+  '((((background light))
+     (:background "yellow"))
+    (((background dark))
+     (:background "#806B00")))
+  "The face used for unsolved meta variables."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-unsolved-constraint-face
+  '((((background light))
+     (:background "yellow"))
+    (((background dark))
+     (:background "#806B00")))
+  "The face used for unsolved constraints which are not connected to metas."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-termination-problem-face
+  '((((background light))
+     (:background "light salmon"))
+    (((background dark))
+     (:background "#802400")))
+  "The face used for termination problems."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-positivity-problem-face
+  '((((background light))
+     (:background "peru"))
+    (((background dark))
+     (:background "#803F00")))
+  "The face used for positivity problems."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-deadcode-face
+  '((((background light))
+     (:background "dark gray"))
+    (((background dark))
+     (:background "#808080")))
+  "The face used for dead code (unreachable clauses, etc.)."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-shadowing-in-telescope-face
+  '((((background light))
+     (:background "dark gray"))
+    (((background dark))
+     (:background "#808080")))
+  "The face used for shadowed repeated variable names in telescopes."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-coverage-problem-face
+  '((((background light))
+     (:background "wheat"))
+    (((background dark))
+     (:background "#805300")))
+  "The face used for coverage problems."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-catchall-clause-face
+  '((((background light))
+     (:background "white smoke"))
+    (((background dark))
+     (:background "#404040")))
+  "The face used for catchall clauses."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-confluence-problem-face
+  '((((background light))
+     (:background "pink"))
+    (((background dark))
+     (:background "#800080")))
+  "The face used for confluence problems."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-missing-definition-face
+  '((((background light))
+     (:background "orange"))
+    (((background dark))
+     (:background "#804040")))
+  "The face used for type declarations with missing definitions."
+  :group 'agda2-highlight-faces)
+
+(defface agda2-highlight-typechecks-face
+  '((((background light))
+     (:background "light blue" :foreground "black"))
+    (((background dark))
+     (:background "#006080" :foreground "white")))
+  "The face used for code which is being type-checked."
+  :group 'agda2-highlight-faces)
+
+(defvar agda2-highlight-faces
+  '((keyword                . agda2-highlight-keyword-face)
+    (comment                . font-lock-comment-face)
+    (background             . default)
+    (markup                 . font-lock-comment-delimiter-face)
+    (string                 . agda2-highlight-string-face)
+    (number                 . agda2-highlight-number-face)
+    (symbol                 . agda2-highlight-symbol-face)
+    (primitivetype          . agda2-highlight-primitive-type-face)
+    (bound                  . agda2-highlight-bound-variable-face)
+    (generalizable          . agda2-highlight-generalizable-variable-face)
+    (inductiveconstructor   . agda2-highlight-inductive-constructor-face)
+    (coinductiveconstructor . agda2-highlight-coinductive-constructor-face)
+    (datatype               . agda2-highlight-datatype-face)
+    (field                  . agda2-highlight-field-face)
+    (function               . agda2-highlight-function-face)
+    (module                 . agda2-highlight-module-face)
+    (postulate              . agda2-highlight-postulate-face)
+    (pragma                 . agda2-highlight-pragma-face)
+    (primitive              . agda2-highlight-primitive-face)
+    (macro                  . agda2-highlight-macro-face)
+    (record                 . agda2-highlight-record-face)
+    (dotted                 . agda2-highlight-dotted-face)
+    (operator               . agda2-highlight-operator-face)
+    (error                  . agda2-highlight-error-face)
+    (errorwarning           . agda2-highlight-error-warning-face)
+    (unsolvedmeta           . agda2-highlight-unsolved-meta-face)
+    (unsolvedconstraint     . agda2-highlight-unsolved-constraint-face)
+    (terminationproblem     . agda2-highlight-termination-problem-face)
+    (deadcode               . agda2-highlight-deadcode-face)
+    (shadowingintelescope   . agda2-highlight-shadowing-in-telescope-face)
+    (coverageproblem        . agda2-highlight-coverage-problem-face)
+    (positivityproblem      . agda2-highlight-positivity-problem-face)
+    (incompletepattern      . agda2-highlight-incomplete-pattern-face)
+    (catchallclause         . agda2-highlight-catchall-clause-face)
+    (confluenceproblem      . agda2-highlight-confluence-problem-face)
+    (missingdefinition      . agda2-highlight-missing-definition-face)
+    (typechecks             . agda2-highlight-typechecks-face))
+  "Alist mapping code aspects to the face used when displaying them.
+
+The aspects currently recognised are the following:
+
+`background'             Non-Agda code contents in literate mode.
+`bound'                  Bound variables.
+`catchallclause'         Clause not holding definitionally.
+`coinductiveconstructor' Coinductive constructors.
+`comment'                Comments.
+`coverageproblem'        Coverage problems.
+`datatype'               Data types.
+`deadcode'               Deadcode (like unreachable clauses or RHS).
+`dotted'                 Dotted patterns.
+`error'                  Errors.
+`errorwarning'           Fatal warnings.
+`field'                  Record fields.
+`function'               Functions.
+`generalizable'          Generalizable variables.
+`incompletepattern'      Incomplete patterns.
+`inductiveconstructor'   Inductive constructors.
+`keyword'                Keywords.
+`macro'                  Macros.
+`markup'                 Delimiters to separate the Agda code blocks
+                           from other contents.
+`module'                 Module names.
+`number'                 Numbers.
+`operator'               Operators.
+`positivityproblem'      Positivity problems.
+`postulate'              Postulates.
+`pragma'                 Text occurring in pragmas that does not have
+                           a more specific (syntactic) aspect.
+`primitive'              Primitive functions.
+`primitivetype'          Primitive types (like Set and Prop).
+`record'                 Record types.
+`shadowingintelescope'   Shadowed repeated variable names in telescopes.
+`string'                 Strings.
+`symbol'                 Symbols like forall, =, ->, etc.
+`terminationproblem'     Termination problems.
+`typechecks'             Code which is being type-checked.
+`unsolvedconstraint'     Unsolved constraints, not connected to meta
+                           variables.
+`unsolvedmeta'           Unsolved meta variables.")
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Variables
+
+(defvar agda2-highlight-in-progress nil
+  "If nil, then highlighting annotations are not applied.")
+(make-variable-buffer-local 'agda2-highlight-in-progress)
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Functions
+
+(defun agda2-highlight-setup nil
+  "Set up the `annotation' library for use with `agda2-mode'."
+  (agda2-highlight-set-faces 'agda2-highlight-face-groups agda2-highlight-face-groups)
+  (setq annotation-bindings agda2-highlight-faces))
+
+(defun agda2-highlight-apply (remove &rest cmds)
+  "Adds the syntax highlighting information in the annotation list CMDS.
+
+If REMOVE is nil, then old syntax highlighting information is not
+removed. Otherwise all token-based syntax highlighting is removed."
+  (let (;; Ignore read-only status, otherwise this function may fail.
+        (inhibit-read-only t))
+    (apply 'annotation-load
+           "Click mouse-2 to jump to definition"
+           remove
+           cmds)))
+
+(defun agda2-highlight-add-annotations (remove &rest cmds)
+  "Like `agda2-highlight-apply'.
+But only if `agda2-highlight-in-progress' is non-nil."
+  (if agda2-highlight-in-progress
+      (apply 'agda2-highlight-apply remove cmds)))
+
+(defun agda2-highlight-load (file)
+  "Load syntax highlighting information from FILE.
+
+Old syntax highlighting information is not removed."
+  (let* ((coding-system-for-read 'utf-8)
+         (cmds (with-temp-buffer
+                 (insert-file-contents file)
+                 (goto-char (point-min))
+                 (read (current-buffer)))))
+      (apply 'agda2-highlight-apply cmds)))
+
+(defun agda2-highlight-load-and-delete-action (file)
+  "Like `agda2-highlight-load', but deletes FILE when done.
+And highlighting is only updated if `agda2-highlight-in-progress'
+is non-nil."
+  (unwind-protect
+      (if agda2-highlight-in-progress
+          (agda2-highlight-load file))
+    (delete-file file)))
+
+(defun agda2-highlight-clear (&optional token-based)
+  "Remove all syntax highlighting.
+
+If TOKEN-BASED is non-nil, then only token-based highlighting is
+removed."
+  (interactive)
+  (let ((inhibit-read-only t))
+       ; Ignore read-only status, otherwise this function may fail.
+    (annotation-remove-annotations token-based)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Administrative details
+
+(provide 'agda2-highlight)
+;;; agda2-highlight.el ends here
diff --git a/src/data/emacs-mode/agda2-mode-pkg.el b/src/data/emacs-mode/agda2-mode-pkg.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2-mode-pkg.el
@@ -0,0 +1,3 @@
+(define-package "agda2-mode" "2.6.4.2"
+  "interactive development for Agda, a dependently typed functional programming language"
+  '((emacs "24.3"))) ;; dep defs for `annotation.el` and `eri.el` are not required if they are packaged together
diff --git a/src/data/emacs-mode/agda2-mode.el b/src/data/emacs-mode/agda2-mode.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2-mode.el
@@ -0,0 +1,2063 @@
+;;; agda2-mode.el --- Major mode for Agda
+;; SPDX-License-Identifier: MIT License
+
+;;; Commentary:
+
+;; A major mode for editing Agda (the dependently typed programming
+;; language / interactive theorem prover).
+;;
+;; Major features include:
+;;
+;; - syntax highlighting.
+;;
+;; - on the fly Agda interpretation.
+;;
+;; - goal-driven development
+;;
+;; - interactive case-splitting
+;;
+;; - proof search
+;;
+;; - input support (for utf8 characters)
+;;
+;; see https://agda.readthedocs.io/ for more information
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; Dependency
+
+
+;;; Code:
+
+(defvar agda2-version "2.6.4.2"
+  "The version of the Agda mode.
+Note that the same version of the Agda executable must be used.")
+
+(require 'cl-lib)
+(require 'compile)
+(require 'time-date)
+(require 'eri)
+(require 'annotation)
+(require 'fontset)
+(require 'agda-input)
+(require 'agda2)
+(require 'agda2-highlight)
+(require 'agda2-abbrevs)
+(require 'agda2-queue)
+(eval-and-compile
+  ;; Load filladapt, if it is installed.
+  (condition-case nil
+      (require 'filladapt)
+    (error nil))
+  (unless (fboundp 'overlays-in) (load "overlay")) ; for Xemacs
+  (unless (fboundp 'propertize)                    ; for Xemacs 21.4
+    ;; FIXME: XEmacs-21.4 (patch 22) does have `propertize' and so does Emacs-22
+    ;; (and agda2-mode doesn't work in Emacs-21, AFAICT).
+    (defun propertize (string &rest properties)
+      "Return a copy of STRING with text properties added.
+First argument is the string to copy.
+Remaining arguments form a sequence of PROPERTY VALUE pairs for text
+properties to add to the result."
+      (let ((str (copy-sequence string)))
+        (add-text-properties 0 (length str) properties str)
+        str)))
+  (unless (fboundp 'prog-mode)          ;For Emacs<24.
+    (defalias 'prog-mode 'fundamental-mode)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; Utilities
+
+(defmacro agda2-let (varbind funcbind &rest body)
+  "Expands to (let* VARBIND (cl-labels FUNCBIND BODY...)).
+Or possibly (let* VARBIND (labels FUNCBIND BODY...))."
+  (declare (debug ((&rest [&or symbolp (symbolp form)])
+                   (&rest (cl-defun))
+                   body))
+           (indent 2))
+  ;; Use cl-labels if available to avoid obsolescence warnings.
+  `(let* ,varbind (,(if (fboundp 'cl-labels) 'cl-labels 'labels) ,funcbind ,@body)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; User options
+
+(defgroup agda2 nil
+  "Major mode for interactively developing Agda programs."
+  :group 'languages)
+
+(defcustom agda2-program-name "agda"
+  "The name of the Agda executable."
+  :type 'string
+  :group 'agda2)
+
+(defcustom agda2-program-args nil
+  "Command-line arguments given to the Agda executable (one per string).
+
+Note: Do not give several arguments in the same string.
+
+The flag \"--interaction\" is always included as the first
+argument, and does not need to be listed here."
+  :type '(repeat string)
+  :group 'agda2)
+
+(defvar agda2-backends '("GHC" "GHCNoMain" "JS" "LaTeX" "QuickLaTeX")
+  "Compilation backends.")
+
+(defcustom agda2-backend
+  ""
+  "The backend used to compile Agda programs (leave blank to ask every time)."
+  :type 'string
+  :group 'agda2)
+
+(defcustom agda2-information-window-max-height
+  0.35
+  "The maximum height of the information window.
+A multiple of the frame height."
+  :type 'number
+  :group 'agda2)
+
+(defcustom agda2-fontset-name
+  (unless (or (eq window-system 'mac)
+              ;; Emacs-23 uses a revamped font engine which should
+              ;; make agda2-fontset-name unnecessary in most cases.
+              ;; And if it turns out to be necessary, we should
+              ;; probably use face-remapping-alist rather than
+              ;; set-frame-font so the special font only applies to
+              ;; Agda buffers, and so it applies in all frames where
+              ;; Agda buffers are displayed.
+              (boundp 'face-remapping-alist))
+    "fontset-agda2")
+  "Default font to use in the selected frame when activating the Agda mode.
+This is only used if it's non-nil and Emacs is not running in a
+terminal.
+
+Note that this setting (if non-nil) affects non-Agda buffers as
+well, and that you have to restart Emacs if you want settings to
+this variable to take effect."
+  :type '(choice (string :tag "Fontset name")
+                 (const :tag "Do not change the font" nil))
+  :group 'agda2)
+
+(defcustom agda2-fontset-spec-of-fontset-agda2
+    "-*-fixed-Medium-r-Normal-*-18-*-*-*-c-*-fontset-agda2,
+    ascii:-Misc-Fixed-Medium-R-Normal--18-120-100-100-C-90-ISO8859-1,
+    latin-iso8859-2:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-2,
+    latin-iso8859-3:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-3,
+    latin-iso8859-4:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-4,
+    cyrillic-iso8859-5:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-5,
+    greek-iso8859-7:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-7,
+    latin-iso8859-9:-*-Fixed-*-r-*-*-18-*-*-*-c-*-iso8859-9,
+    mule-unicode-0100-24ff:-Misc-Fixed-Medium-R-Normal--18-120-100-100-C-90-ISO10646-1,
+    mule-unicode-2500-33ff:-Misc-Fixed-Medium-R-Normal--18-120-100-100-C-90-ISO10646-1,
+    mule-unicode-e000-ffff:-Misc-Fixed-Medium-R-Normal--18-120-100-100-C-90-ISO10646-1,
+    japanese-jisx0208:-Misc-Fixed-Medium-R-Normal-ja-18-*-*-*-C-*-JISX0208.1990-0,
+    japanese-jisx0212:-Misc-Fixed-Medium-R-Normal-ja-18-*-*-*-C-*-JISX0212.1990-0,
+    thai-tis620:-Misc-Fixed-Medium-R-Normal--24-240-72-72-C-120-TIS620.2529-1,
+    lao:-Misc-Fixed-Medium-R-Normal--24-240-72-72-C-120-MuleLao-1,
+    tibetan:-TibMdXA-fixed-medium-r-normal--16-160-72-72-m-160-MuleTibetan-0,
+    tibetan-1-column:-TibMdXA-fixed-medium-r-normal--16-160-72-72-m-80-MuleTibetan-1,
+    korean-ksc5601:-Daewoo-Mincho-Medium-R-Normal--16-120-100-100-C-160-KSC5601.1987-0,
+    chinese-gb2312:-ISAS-Fangsong ti-Medium-R-Normal--16-160-72-72-c-160-GB2312.1980-0,
+    chinese-cns11643-1:-HKU-Fixed-Medium-R-Normal--16-160-72-72-C-160-CNS11643.1992.1-0,
+    chinese-big5-1:-ETen-Fixed-Medium-R-Normal--16-150-75-75-C-160-Big5.ETen-0,
+    chinese-big5-2:-ETen-Fixed-Medium-R-Normal--16-150-75-75-C-160-Big5.ETen-0"
+  "Specification of the \"fontset-agda2\" fontset.
+This fontset is only created if `agda2-fontset-name' is
+\"fontset-agda2\" and Emacs is not run in a terminal.
+
+Note that the text \"fontset-agda2\" has to be part of the
+string (in a certain way; see the default setting) in order for the
+agda2 fontset to be created properly.
+
+Note also that the default setting may not work unless suitable
+fonts are installed on your system. Refer to the README file
+accompanying the Agda distribution for more details.
+
+Note finally that you have to restart Emacs if you want settings
+to this variable to take effect."
+  :group 'agda2
+  :type 'string)
+
+(if (and (equal agda2-fontset-name "fontset-agda2") window-system)
+    (create-fontset-from-fontset-spec agda2-fontset-spec-of-fontset-agda2 t t))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; Global and buffer-local vars, initialization
+
+(defvar agda2-mode-syntax-table
+  (let ((tbl (make-syntax-table)))
+    ;; Set the syntax of every char to "w" except for those whose default
+    ;; syntax in `standard-syntax-table' is `paren' or `whitespace'.
+    (map-char-table (lambda (keys val)
+                      ;; `keys' here can be a normal char, a generic char
+                      ;; (Emacs<23), or a char range (Emacs>=23).
+                      (unless (memq (car val)
+                                    (eval-when-compile
+                                      (mapcar 'car
+                                              (list (string-to-syntax "(")
+                                                    (string-to-syntax ")")
+                                                    (string-to-syntax " ")))))
+                        (modify-syntax-entry keys "w" tbl)))
+                    (standard-syntax-table))
+    ;; Then override the remaining special cases.
+    (dolist (cs '((?- . "w 12") (?\n . ">")
+                  (?. . ".") (?\; . ".") (?! . ".")))
+      (modify-syntax-entry (car cs) (cdr cs) tbl))
+    tbl)
+  "Syntax table used by the Agda mode:
+
+-   | Comment character, word constituent.
+\n  | Comment ender.
+.;! | Punctuation.
+
+Remaining characters inherit their syntax classes from the
+standard syntax table if that table treats them as matching
+parentheses or whitespace.  Otherwise they are treated as word
+constituents.")
+
+(defconst agda2-command-table
+  `(
+    (agda2-load                              "\C-c\C-l"           (global)       "Load")
+    (agda2-load                              "\C-c\C-x\C-l")
+    (agda2-compile                           "\C-c\C-x\C-c"       (global)       "Compile")
+    (agda2-quit                              "\C-c\C-x\C-q"       (global)       "Quit")
+    (agda2-restart                           "\C-c\C-x\C-r"       (global)       "Kill and restart Agda")
+    (agda2-abort                             "\C-c\C-x\C-a"       (global)       "Abort a command")
+    (agda2-remove-annotations                "\C-c\C-x\C-d"       (global)       "Remove goals and highlighting (\"deactivate\")")
+    (agda2-display-implicit-arguments        "\C-c\C-x\C-h"       (global)       "Toggle display of hidden arguments")
+    (agda2-display-irrelevant-arguments      "\C-c\C-x\C-i"       (global)       "Toggle display of irrelevant arguments")
+    (agda2-show-constraints                  ,(kbd "C-c C-=")     (global)       "Show constraints")
+    (agda2-solve-maybe-all                   ,(kbd "C-c C-s")     (local global) "Solve constraints")
+    (agda2-show-goals                        ,(kbd "C-c C-?")     (global)       "Show goals")
+    (agda2-next-goal                         "\C-c\C-f"           (global)       "Next goal") ; Forward.
+    (agda2-previous-goal                     "\C-c\C-b"           (global)       "Previous goal") ; Back.
+    (agda2-give                              ,(kbd "C-c C-SPC")   (local)        "Give")
+    (agda2-elaborate-give                    ,(kbd "C-c C-m")     (local)        "Elaborate and Give")
+    (agda2-refine                            "\C-c\C-r"           (local)        "Refine")
+    (agda2-auto-maybe-all                    "\C-c\C-a"           (local global) "Auto")
+    (agda2-make-case                         "\C-c\C-c"           (local)        "Case")
+    (agda2-goal-type                         "\C-c\C-t"           (local)        "Goal type")
+    (agda2-show-context                      "\C-c\C-e"           (local)        "Context (environment)")
+    (agda2-helper-function-type              "\C-c\C-h"           (local)        "Helper function type")
+    (agda2-infer-type-maybe-toplevel         "\C-c\C-d"           (local global) "Infer (deduce) type")
+    (agda2-why-in-scope-maybe-toplevel       "\C-c\C-w"           (local global) "Explain why a particular name is in scope")
+    (agda2-goal-and-context                  ,(kbd "C-c C-,")     (local)        "Goal type and context")
+    (agda2-goal-and-context-and-inferred     ,(kbd "C-c C-.")     (local)        "Goal type, context and inferred type")
+    (agda2-goal-and-context-and-checked      ,(kbd "C-c C-;")     (local)        "Goal type, context and checked type")
+    (agda2-search-about-toplevel             ,(kbd "C-c C-z")     (local global) "Search About")
+    (agda2-module-contents-maybe-toplevel    ,(kbd "C-c C-o")     (local global) "Module contents")
+    (agda2-compute-normalised-maybe-toplevel "\C-c\C-n"           (local global) "Evaluate term to normal form")
+    (describe-char                           nil                  (global)       "Information about the character at point")
+    (agda2-comment-dwim-rest-of-buffer       ,(kbd "C-c C-x M-;") (global)       "Comment/uncomment the rest of the buffer")
+    (agda2-display-program-version           nil                  (global)       "Version")
+    (agda2-set-program-version               "\C-c\C-x\C-s"       (global)       "Switch to another version of Agda")
+    (eri-indent                  ,(kbd "TAB"))
+    (eri-indent-reverse          [S-iso-lefttab])
+    (eri-indent-reverse          [S-lefttab])
+    (eri-indent-reverse          [S-tab])
+    (agda2-goto-definition-mouse [mouse-2])
+    (agda2-goto-definition-keyboard "\M-.")
+    (agda2-go-back                  ,(if (version< emacs-version "25.1") "\M-*" "\M-,"))
+    )
+  "Table of commands, used to build keymaps and menus.
+Each element has the form (CMD &optional KEYS WHERE DESC) where
+CMD is a command; KEYS is its key binding (if any); WHERE is a
+list which should contain \\='local if the command should exist in
+the goal menu and \\='global if the command should exist in the main
+menu; and DESC is the description of the command used in the
+menus.")
+
+(defvar agda2-mode-map
+  (let ((map (make-sparse-keymap "Agda mode")))
+    (define-key map [menu-bar Agda]
+      (cons "Agda" (make-sparse-keymap "Agda")))
+    (define-key map [down-mouse-3]  'agda2-popup-menu-3)
+    (dolist (d (reverse agda2-command-table))
+      (cl-destructuring-bind (f &optional keys kinds desc) d
+        (if keys (define-key map keys f))
+        (if (member 'global kinds)
+            (define-key map
+              (vector 'menu-bar 'Agda (intern desc)) (cons desc f)))))
+    map)
+  "Keymap for `agda2-mode'.")
+
+(defvar agda2-goal-map
+  (let ((map (make-sparse-keymap "Agda goal")))
+    (dolist (d (reverse agda2-command-table))
+      (cl-destructuring-bind (f &optional keys kinds desc) d
+        (if (member 'local kinds)
+            (define-key map
+              (vector (intern desc)) (cons desc f)))))
+    map)
+  "Keymap for agda2 goal menu.")
+
+(defvar agda2-info-buffer nil
+  "Agda information buffer.")
+
+(defvar agda2-process-buffer nil
+  "Agda subprocess buffer.
+Set in `agda2-restart'.")
+
+(defvar agda2-process nil
+  "Agda subprocess.
+Set in `agda2-restart'.")
+
+(defvar agda2-in-progress nil
+  "Is the Agda process currently busy?
+Valid values: `nil' (not busy), `busy' (busy),
+`not-so-busy' (busy with something that should typically
+terminate fairly quickly).")
+
+;; Some buffer locals
+(defvar agda2-buffer-external-status ""
+  "External status of an `agda2-mode' buffer (dictated by the Haskell side).")
+(make-variable-buffer-local 'agda2-buffer-external-status)
+
+(defvar agda2-output-prompt "Agda2> "
+  "The Agda2 buffer's prompt.")
+
+(defconst agda2-help-address
+  ""
+  "Address accepting submissions of bug reports and questions.")
+
+;; Annotation for a goal
+;; {! .... !}
+;; ----------  overlay:    agda2-gn num, face highlight, after-string num,
+;;                         modification-hooks (agda2-protect-goal-markers)
+;; -           text-props: category agda2-delim1
+;;  -          text-props: category agda2-delim2
+;;         -   text-props: category agda2-delim3
+;;          -  text-props: category agda2-delim4
+;;
+;; Char categories for {! ... !}
+(defvar agda2-open-brace  "{")
+(defvar agda2-close-brace " }")
+(setplist 'agda2-delim1 `(display ,agda2-open-brace))
+(setplist 'agda2-delim2 `(display ,agda2-open-brace rear-nonsticky t
+                                  agda2-delim2 t))
+(setplist 'agda2-delim3 `(display ,agda2-close-brace agda2-delim3 t))
+(setplist 'agda2-delim4 `(display ,agda2-close-brace rear-nonsticky t))
+
+;; Note that strings used with the display property are compared by
+;; reference. If the agda2-*-brace definitions were inlined, then
+;; goals would be displayed as "{{ }}n" instead of "{ }n".
+
+;; The following variables are used by the filter process,
+;; `agda2-output-filter'. Their values are only modified by the filter
+;; process, `agda2-go', `agda2-restart', `agda2-abort-highlighting',
+;; and `agda2-abort-done'.
+
+(defvar agda2-output-chunk-incomplete (agda2-queue-empty)
+  "Buffer for incomplete lines.
+\(See `agda2-output-filter'.)")
+(make-variable-buffer-local 'agda2-output-chunk-incomplete)
+
+(defvar agda2-last-responses nil
+  "Response commands which should be run after other commands.
+The command which arrived last is stored first in the list.")
+(make-variable-buffer-local 'agda2-last-responses)
+
+(defvar agda2-file-buffer nil
+  "The Agda buffer.
+Note that this variable is not buffer-local.")
+
+(defvar agda2-in-agda2-file-buffer nil
+  "Was `agda2-file-buffer' active when `agda2-output-filter' started?
+Note that this variable is not buffer-local.")
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; agda2-mode
+
+;;;###autoload
+(add-to-list 'auto-mode-alist '("\\.l?agda\\'" . agda2-mode))
+;;;###autoload
+(modify-coding-system-alist 'file "\\.l?agda\\'" 'utf-8)
+;;;###autoload
+(define-derived-mode agda2-mode prog-mode "Agda"
+  "Major mode for Agda files.
+
+The following paragraph does not apply to Emacs 23 or newer.
+
+  Note that when this mode is activated the default font of the
+  current frame is changed to the fontset `agda2-fontset-name'.
+  The reason is that Agda programs often use mathematical symbols
+  and other Unicode characters, so we try to provide a suitable
+  default font setting, which can display many of the characters
+  encountered. If you prefer to use your own settings, set
+  `agda2-fontset-name' to nil.
+
+Special commands:
+\\{agda2-mode-map}"
+
+ (if (boundp 'agda2-include-dirs)
+     (display-warning 'agda2 "Note that the variable agda2-include-dirs is
+no longer used. You may want to update your configuration. You
+have at least two choices:
+* Use the library management system.
+* Set the include path using agda2-program-args.
+
+One way to avoid seeing this warning is to make sure that
+agda2-include-dirs is not bound." :warning))
+
+ (setq local-abbrev-table agda2-mode-abbrev-table
+       indent-tabs-mode   nil
+       mode-line-process
+         '((:eval (unless (eq 0 (length agda2-buffer-external-status))
+                    (concat ":" agda2-buffer-external-status)))))
+ (let ((l '(max-specpdl-size    2600
+            max-lisp-eval-depth 2800)))
+   (while l (set (make-local-variable (pop l)) (pop l))))
+ (if (and window-system agda2-fontset-name)
+     (condition-case nil
+         (set-frame-font agda2-fontset-name)
+       (error (error "Unable to change the font; change agda2-fontset-name or tweak agda2-fontset-spec-of-fontset-agda2"))))
+ ;; Deactivate highlighting if the buffer is edited before
+ ;; typechecking is complete.
+ (add-hook 'first-change-hook 'agda2-abort-highlighting nil 'local)
+ ;; If Agda is not running syntax highlighting does not work properly.
+ (unless (eq 'run (agda2-process-status))
+   (agda2-restart))
+ ;; Make sure that Font Lock mode is not used.
+ (font-lock-mode 0)
+ (agda2-highlight-setup)
+ (condition-case err
+     (agda2-highlight-reload)
+   (error (message "Highlighting not loaded: %s"
+                   (error-message-string err))))
+ (agda2-comments-and-paragraphs-setup)
+ (force-mode-line-update)
+ ;; Protect global value of default-input-method from set-input-method.
+ (make-local-variable 'default-input-method)
+ ;; Don't take script into account when determining word boundaries
+ (set (make-local-variable 'word-combining-categories) (cons '(nil . nil) word-combining-categories))
+ (set-input-method "Agda")
+ ;; Highlighting etc. is removed when we switch from the Agda mode.
+ ;; Use case: When a file M.lagda with a local variables list
+ ;; including "mode: latex" is loaded chances are that the Agda mode
+ ;; is activated before the LaTeX mode, and the LaTeX mode does not
+ ;; seem to remove the text properties set by the Agda mode.
+ (add-hook 'change-major-mode-hook 'agda2-quit nil 'local))
+
+(defun agda2-restart ()
+  "Tries to start or restart the Agda process."
+  (interactive)
+
+  ;; Kill any running instance of the Agda process.
+  (condition-case nil
+      (agda2-term)
+    (error nil))
+
+  ;; Check that the right version of Agda is used.
+  (let* ((coding-system-for-read 'utf-8)
+         (output (with-output-to-string
+                   (call-process agda2-program-name
+                                 nil standard-output nil "--version")))
+         (version (and (string-match "^Agda version \\([0-9.]+\\)" output)
+                       (match-string 1 output))))
+    (unless (equal version agda2-version)
+      (error "The Agda mode's version (%s) does not match that of %s (%s)."
+             agda2-version
+             agda2-program-name (or version "unknown"))))
+
+  (let ((all-program-args (cons "--interaction" agda2-program-args)))
+
+    ;; Check that the arguments are not malformed.
+    (let* ((coding-system-for-read 'utf-8)
+           (status)
+           (output
+            (with-output-to-string
+              (setq status
+                    (apply 'call-process agda2-program-name
+                           nil standard-output nil all-program-args)))))
+      (unless (equal status 0)
+        (error "Failed to start the Agda process:\n%s" output)))
+
+    ;; Start the Agda process.
+    (let ((agda2-bufname "*agda2*"))
+
+      (let ((process-connection-type nil)) ; Pipes are faster than PTYs.
+        (setq agda2-process
+              (apply 'start-process "Agda2" agda2-bufname
+                     agda2-program-name all-program-args)))
+
+      (set-process-coding-system agda2-process 'utf-8 'utf-8)
+      (set-process-query-on-exit-flag agda2-process nil)
+      (set-process-filter agda2-process 'agda2-output-filter)
+      (setq agda2-in-progress nil
+            agda2-file-buffer (current-buffer))
+
+      (with-current-buffer agda2-bufname
+        (setq agda2-process-buffer (current-buffer)
+              mode-name            "Agda executable"
+              agda2-last-responses nil)
+        (set-buffer-file-coding-system 'utf-8))
+
+      (agda2-remove-annotations))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; Communicating with Agda
+
+(defun agda2-raise-error ()
+  "Raises an error.
+The error message directs the user to the *agda2* buffer."
+  (error "Problem encountered. The *agda2* buffer can perhaps explain why."))
+
+(defun agda2-running-p nil
+  "Does the *agda2* buffer exist, and is the Agda2 process running?"
+  (and (buffer-live-p agda2-process-buffer)
+       (eq (agda2-process-status) 'run)))
+
+(defun agda2-send-command (restart &rest args)
+  "Send a command to the Agda process.
+Sends the list of strings ARGS to the process. If RESTART is
+non-nil and the process is not running, or the *agda2*
+buffer does not exist, then an attempt is made to restart the
+process."
+  (when (and restart (not (agda2-running-p)))
+    ;; Try restarting automatically, but only once, in case there is
+    ;; some major problem.
+    (agda2-restart)
+    (unless (agda2-running-p)
+      (agda2-raise-error)))
+  (let ((command (apply 'concat (agda2-intersperse " " args))))
+    (with-current-buffer agda2-process-buffer
+      (goto-char (point-max))
+      (insert command)
+      (insert "\n")
+      (process-send-string agda2-process (concat command "\n")))))
+
+(defun agda2-go (save highlight how-busy do-abort &rest args)
+  "Executes commands in the Agda2 interpreter.
+Sends the list of strings ARGS to the Agda2 interpreter, waits
+for output and executes the responses, if any.
+
+If SAVE is \\='save, then the buffer is saved first.
+
+If HIGHLIGHT is non-nil, then the buffer's syntax highlighting
+may be updated. This is also the case if the Agda process is
+busy (or `not-so-busy') and `agda2-highlight-in-process' is
+non-nil.
+
+The value HOW-BUSY should be `busy' if it should not be possible
+to invoke other commands while this command is running (with the
+exception of commands for which DO-ABORT is nil). Otherwise it
+should be `not-so-busy' (which should only be used for commands
+that typically terminate fairly quickly).
+
+If the Agda process is busy (or `not-so-busy'), and the current
+buffer does not match `agda2-file-buffer', then the command is
+not executed and an error is raised. The same applies if DO-ABORT
+is non-nil and the Agda process is `busy'."
+
+  ; Check that how-busy is well-formed.
+  (cl-assert (or (equal how-busy 'busy)
+              (equal how-busy 'not-so-busy)))
+
+  (when (and agda2-in-progress
+             (not (equal agda2-file-buffer
+                         (current-buffer))))
+    (error "Agda is busy with something in the buffer %s"
+           agda2-file-buffer))
+
+  (when (and do-abort
+             (equal agda2-in-progress 'busy))
+    (error "Agda is busy with something
+\(you have the option to abort or restart Agda)"))
+
+  (setq agda2-file-buffer (current-buffer))
+
+  (setq agda2-highlight-in-progress
+        (or highlight
+            (and agda2-in-progress
+                 agda2-highlight-in-progress)))
+
+  (unless agda2-in-progress
+    (setq agda2-output-chunk-incomplete (agda2-queue-empty)))
+
+  (setq agda2-in-progress
+        (if (or (equal how-busy 'busy)
+                (equal agda2-in-progress 'busy))
+            'busy
+          'not-so-busy))
+
+  (when (equal save 'save) (save-buffer))
+
+  (apply 'agda2-send-command
+         'restart
+         "IOTCM"
+         (agda2-string-quote (buffer-file-name))
+         (if highlight (agda2-highlight-level) "None")
+         "Indirect"
+         "("
+         (append args '(")"))))
+
+(defun agda2-abort ()
+  "Tries to abort the current computation, if any.
+May be more efficient than restarting Agda."
+  (interactive)
+  (agda2-send-command nil
+                      "IOTCM"
+                      (agda2-string-quote (buffer-file-name))
+                      "None"
+                      "Indirect"
+                      "Cmd_abort"))
+
+(defun agda2-abort-done ()
+  "Resets certain variables.
+Intended to be used by the backend if an abort command was
+successful."
+  (agda2-info-action "*Aborted*" "Aborted." t)
+  (setq agda2-highlight-in-progress nil
+        agda2-last-responses        nil))
+
+(defun agda2-output-filter (proc chunk)
+  "Evaluate the Agda process's commands.
+This filter function assumes that every line contains either some
+kind of error message (which cannot be parsed as a list), or
+exactly one command. Incomplete lines are stored in a
+buffer (`agda2-output-chunk-incomplete').
+
+Every command is run by this function, unless it has the form
+\"(('last . priority) . cmd)\", in which case it is run by
+`agda2-run-last-commands' at the end, after the Agda2 prompt
+has reappeared, after all non-last commands, and after all
+interactive highlighting is complete. The last commands can have
+different integer priorities; those with the lowest priority are
+executed first.
+
+Non-last commands should not call the Agda process.
+
+All commands are echoed to the *agda2* buffer, with the exception
+of commands of the form \"(agda2-highlight-... ...)\".
+
+The non-last commands are run in the order in which they appear.
+
+When the prompt has been reached highlighting annotations are
+reloaded from `agda2-highlighting-file', unless
+`agda2-highlighting-in-progress' is nil."
+
+  ;; Beware: the buffer may have been killed in the mean time.  E.g. when
+  ;; viewing an attachment containing Agda code in Gnus, Gnus will
+  ;; create a temp buffer, set it in agda2-mode, call font-lock-ensure on it
+  ;; (which won't know that it needs to wait for some process to reply), then
+  ;; extract the fontified text and kill the temp buffer; so when Agda
+  ;; finally answers, the temp buffer is long gone.
+  (when (buffer-live-p agda2-file-buffer)
+  (setq agda2-in-agda2-file-buffer
+        (and agda2-file-buffer
+             (equal (current-buffer) agda2-file-buffer)))
+  (let (;; The input lines in the current chunk.
+        (lines (split-string chunk "\n"))
+
+        ;; Non-last commands found in the current chunk (reversed).
+        (non-last-commands ())
+
+        ;; Last incomplete line, if any.
+        (output-chunk-incomplete ""))
+    (with-current-buffer agda2-file-buffer
+      (when (consp lines)
+        (agda2-queue-enqueue agda2-output-chunk-incomplete (pop lines))
+        (when (consp lines)
+          ;; The previous uncomplete chunk is now complete.
+          (push (agda2-queue-to-string agda2-output-chunk-incomplete)
+                lines)
+
+          ;; Stash away the last incomplete line, if any. (Note that
+          ;; (split-string "...\n" "\n") evaluates to (... "").)
+          (setq output-chunk-incomplete (car (last lines))
+                agda2-output-chunk-incomplete
+                (agda2-queue-from-string output-chunk-incomplete))
+
+          ;; Handle every complete line.
+          (dolist (line (butlast lines))
+            (let* (;; The command. Lines which cannot be parsed as a single
+                   ;; list, without any junk, are ignored.
+                   (cmd (condition-case nil
+                            (let ((result (read-from-string line)))
+                              (if (and (listp (car result))
+                                       (= (cdr result) (length line)))
+                                  (car result)))
+                          (error nil)))
+                   (is-highlighting-command
+                    (and cmd
+                         (symbolp (car cmd))
+                         (let ((case-fold-search nil))
+                           (string-match "^agda2-highlight-"
+                                         (symbol-name (car cmd)))))))
+
+              ;; Do not echo highlighting commands.
+              (unless is-highlighting-command
+                (with-current-buffer agda2-process-buffer
+                  (save-excursion
+                    (goto-char (point-max))
+                    (insert line)
+                    (insert "\n"))))
+              (when cmd
+                (if (equal 'last (car-safe (car cmd)))
+                    (push (cons (cdr (car cmd)) (cdr cmd))
+                          agda2-last-responses)
+                  (push cmd non-last-commands)))))
+
+          ;; Run non-last commands.
+          (mapc 'agda2-exec-response (nreverse non-last-commands)))
+
+        ;; Check if the prompt has been reached. This function assumes
+        ;; that the prompt does not include any newline characters.
+        (when (agda2-queue-is-prefix-of agda2-output-prompt
+                                        agda2-output-chunk-incomplete)
+          (with-current-buffer agda2-process-buffer
+            (insert output-chunk-incomplete))
+          (setq agda2-output-chunk-incomplete (agda2-queue-empty)
+                agda2-in-progress nil
+                agda2-last-responses (nreverse agda2-last-responses))
+
+          (agda2-run-last-commands)))))))
+
+(defun agda2-run-last-commands nil
+  "Execute the last commands in the right order.
+\(After the prompt has reappeared.) See `agda2-output-filter'."
+
+  ;; with-current-buffer is used repeatedly below, because some last
+  ;; commands may switch the focus to another buffer.
+
+  (while (with-current-buffer agda2-file-buffer
+           (and (not agda2-in-progress) (consp agda2-last-responses)))
+    (with-current-buffer agda2-file-buffer
+      ;; The list is sorted repeatedly because this function may be
+      ;; called recursively (via `agda2-exec-response').
+      (setq agda2-last-responses (sort agda2-last-responses
+                                       (lambda (x y) (<= (car x) (car y)))))
+      (let ((r (pop agda2-last-responses)))
+        (agda2-exec-response (cdr r)))))
+
+  ;; Unset agda2-highlight-in-progress when all the asynchronous
+  ;; commands have terminated.
+  (unless agda2-in-progress
+      (setq agda2-highlight-in-progress nil)))
+
+(defun agda2-abort-highlighting nil
+  "Abort any interactive highlighting.
+This function should be used in `first-change-hook'."
+  (when agda2-highlight-in-progress
+    (setq agda2-highlight-in-progress nil)
+    (message "\"%s\" has been modified. Interrupting highlighting."
+             (buffer-name (current-buffer)))))
+
+(defun agda2-goal-cmd (cmd save &optional want ask &rest args)
+  "Reads input from goal or minibuffer and sends command to Agda.
+
+An error is raised if point is not in a goal.
+
+The command sent to Agda is
+
+  CMD <goal number> <goal range> <user input> ARGS.
+
+The user input is computed as follows:
+
+* If WANT is nil, then the user input is the empty string.
+
+* If WANT is a string, and either ASK is non-nil or the goal only
+  contains whitespace, then the input is taken from the
+  minibuffer. In this case WANT is used as the prompt string.
+
+* Otherwise (including if WANT is \\='goal) the goal contents are
+  used.
+
+If the user input is not taken from the goal, then an empty goal
+range is given.
+
+If SAVE is \\='save, then the buffer is saved just before the
+command is sent to Agda (if it is sent)."
+  (cl-multiple-value-bind (o g) (agda2-goal-at (point))
+    (unless g (error "For this command, please place the cursor in a goal"))
+    (let ((txt (buffer-substring-no-properties (+ (overlay-start o) 2)
+                                               (- (overlay-end   o) 2)))
+          (input-from-goal nil))
+      (cond ((null want) (setq txt ""))
+            ((and (stringp want)
+                  (or ask (string-match "\\`\\s *\\'" txt)))
+             (setq txt (read-string (concat want ": ") nil nil txt t)))
+            (t (setq input-from-goal t)))
+      (apply 'agda2-go save input-from-goal 'busy t cmd
+             (format "%d" g)
+             (if input-from-goal (agda2-goal-Range o) (agda2-mkRange nil))
+             (agda2-string-quote txt) args))))
+
+;; Note that the following function is a security risk, since it
+;; evaluates code without first inspecting it. The code (supposedly)
+;; comes from the Agda backend, but there could be bugs in the backend
+;; which can be exploited by an attacker which manages to trick
+;; someone into type-checking compromised Agda code.
+
+(defun agda2-exec-response (response)
+  "Interprets response."
+  (let ((inhibit-read-only t))
+    (eval response)))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; User commands and response processing
+
+(defun agda2-load ()
+  "Load current buffer."
+  (interactive)
+  (agda2-go 'save t 'busy t "Cmd_load"
+            (agda2-string-quote (buffer-file-name))
+            (agda2-list-quote agda2-program-args)
+            ))
+
+(defun agda2-compile ()
+  "Compile the current module.
+
+The variable `agda2-backend' determines which backend is used."
+  (interactive)
+  (let ((backend (cond ((equal agda2-backend "MAlonzo")       "GHC")
+                       ((equal agda2-backend "MAlonzoNoMain") "GHCNoMain")
+                       ((equal agda2-backend "")
+                        (completing-read "Backend: " agda2-backends
+                                         nil nil nil nil nil
+                                         'inherit-input-method))
+                       (t agda2-backend))))
+    (when (equal backend "") (error "No backend chosen"))
+    (agda2-go 'save t 'busy t "Cmd_compile"
+              backend
+              (agda2-string-quote (buffer-file-name))
+              (agda2-list-quote agda2-program-args)
+              )))
+
+(defmacro agda2-maybe-forced (name comment cmd save want)
+  "This macro constructs a function NAME which runs CMD.
+COMMENT is used to build the function's comment. The function
+NAME takes a prefix argument which tells whether it should
+apply force or not when running CMD (through
+`agda2-goal-cmd';
+SAVE is used as `agda2-goal-cmd's SAVE argument and
+WANT is used as `agda2-goal-cmd's WANT argument)."
+  (let ((eval (make-symbol "eval")))
+  `(defun ,name (&optional prefix)
+     ,(concat comment ".
+
+The action depends on the prefix argument:
+
+* If the prefix argument is `nil' (i.e., if no prefix argument is
+  given), then no force is applied.
+
+* If any other prefix argument is used (for instance, if C-u is
+  typed once or twice right before the command is invoked), then
+  force is applied.")
+     (interactive "P")
+     (let ((,eval (cond ((equal prefix nil) "WithoutForce")
+                        ("WithForce"))))
+       (agda2-goal-cmd (concat ,cmd " " ,eval)
+                       ,save ,want)))))
+
+(agda2-maybe-forced
+  agda2-give
+  "Give to the goal at point the expression in it"
+  "Cmd_give"
+  'save
+  "expression to give")
+
+;; (defun agda2-give()
+;;   "Give to the goal at point the expression in it" (interactive)
+;;   (agda2-goal-cmd "Cmd_give" 'save "expression to give"))
+
+(defun agda2-give-action (old-g paren)
+  "Update the goal OLD-G with the expression in it."
+  (let
+     ;; Don't run modification hooks: we don't want this to
+      ;; trigger agda2-abort-highlighting.
+      ((inhibit-modification-hooks t))
+  (agda2-update old-g paren)))
+
+(defun agda2-refine (pmlambda)
+  "Refine the goal at point.
+If the goal contains an expression e, and some \"suffix\" of the
+type of e unifies with the goal type, then the goal is replaced
+by e applied to a suitable number of new goals.
+
+PMLAMBDA is only used if the goal has a functional type.
+When the prefix argument is given a pattern maching lambda will
+be inserted, otherwise a standard lambda will be used.
+
+If the goal is empty, the goal type is a data type, and there is
+exactly one constructor which unifies with this type, then the
+goal is replaced by the constructor applied to a suitable number
+of new goals."
+  (interactive "P")
+  (if pmlambda
+      (agda2-goal-cmd "Cmd_refine_or_intro True" 'save 'goal)
+    (agda2-goal-cmd "Cmd_refine_or_intro False" 'save 'goal)))
+
+(defun agda2-autoOne ()
+ "Simple proof search" (interactive)
+ (agda2-goal-cmd "Cmd_autoOne" 'save 'goal))
+
+(defun agda2-autoAll ()
+  "Solves all goals by simple proof search."
+  (interactive)
+  (agda2-go nil nil 'busy t "Cmd_autoAll")
+)
+
+(defun agda2-make-case ()
+  "Refine the pattern variables given in the goal.
+Assumes that <clause> = {!<variables>!} is on one line."
+  (interactive)
+  (agda2-goal-cmd "Cmd_make_case" 'save "pattern variables to case (empty for split on result)"))
+
+(defun agda2-make-case-action (newcls)
+  "Replace the line at point with new clauses NEWCLS and reload."
+  (agda2-forget-all-goals);; we reload later anyway.
+  (let* ((p0 (point))
+         (p1 (goto-char (+ (current-indentation) (line-beginning-position))))
+         (indent (current-column))
+         cl)
+    (delete-region p1 (line-end-position))
+    (while (setq cl (pop newcls))
+      (insert cl)
+      (if newcls (insert "\n" (make-string indent ?  ))))
+    (goto-char p0))
+  (agda2-load))
+
+(defun agda2-make-case-action-extendlam (newcls)
+  "Replace definition of extended lambda with new clauses NEWCLS and reload."
+  (agda2-forget-all-goals);; we reload later anyway.
+  (let* ((p0 (point))
+         (pmax (re-search-forward "!}"))
+         (bracketCount 0)
+         (p1 (goto-char (+ (current-indentation) (line-beginning-position))))
+         (indent (current-column))
+         cl)
+    (goto-char p0)
+    (re-search-backward "{!")
+    (while (and (not (equal (preceding-char) ?\;)) (>= bracketCount 0) (> (point) p1))
+      (backward-char)
+      (if (equal (preceding-char) ?}) (cl-incf bracketCount))
+      (if (equal (preceding-char) ?{) (cl-decf bracketCount)))
+    (let* ((is-lambda-where (= (point) p1))
+           (p (point)))
+      (delete-region (point) pmax)
+      (if (not is-lambda-where) (insert " "))
+      (while (setq cl (pop newcls))
+        (insert cl)
+        (if newcls (if is-lambda-where (insert "\n" (make-string indent ? )) (insert " ; "))))
+      (goto-char p)))
+  (agda2-load))
+
+(defun agda2-status-action (status)
+  "Display the string STATUS in the current buffer's mode line.
+\(precondition: the current buffer has to use the Agda mode as the
+major mode)."
+  (setq agda2-buffer-external-status status)
+  (force-mode-line-update))
+
+(defmacro agda2-information-buffer (buffer kind title)
+  "Used to define functions like `agda2-info-buffer'."
+  `(defun ,buffer nil
+     ,(concat "Creates the Agda " kind
+              " buffer, if it does not already exist.
+The buffer is returned.")
+  (unless (buffer-live-p ,buffer)
+    (setq ,buffer
+          (generate-new-buffer ,title))
+
+    (with-current-buffer ,buffer
+      (compilation-mode "AgdaInfo")
+      ;; Support for jumping to positions mentioned in the text.
+      (set (make-local-variable 'compilation-error-regexp-alist)
+           '(("\\([\\\\/][^[:space:]]*\\):\\([0-9]+\\),\\([0-9]+\\)-\\(\\([0-9]+\\),\\)?\\([0-9]+\\)"
+              1 (2 . 5) (3 . 6))))
+      ;; Do not skip errors that start in the same position as the
+      ;; current one.
+      (set (make-local-variable 'compilation-skip-to-next-location) nil)
+      ;; No support for recompilation. The key binding is removed, and
+      ;; attempts to run `recompile' will (hopefully) result in an
+      ;; error.
+      (let ((map (copy-keymap (current-local-map))))
+        (define-key map (kbd "g") 'undefined)
+        (use-local-map map))
+      (set (make-local-variable 'compile-command)
+           'agda2-does-not-support-compilation-via-the-compilation-mode)
+
+      (set-syntax-table agda2-mode-syntax-table)
+      (set (make-local-variable 'word-combining-categories) (cons '(nil . nil) word-combining-categories))
+      (set-input-method "Agda")))
+
+  ,buffer))
+
+(agda2-information-buffer agda2-info-buffer "info" "*Agda information*")
+
+(defun agda2-info-action (name text &optional append)
+  "Insert TEXT into the Agda info buffer and display it.
+NAME is displayed in the buffer's mode line.
+
+If APPEND is non-nil, then TEXT is appended at the end of the
+buffer, and point placed after this text.
+
+If APPEND is nil, then any previous text is removed before TEXT
+is inserted, and point is placed before this text."
+  (interactive)
+  (let ((buf (agda2-info-buffer)))
+    (with-current-buffer buf
+      ;; In some cases the jump-to-position-mentioned-in-text
+      ;; functionality (see compilation-error-regexp-alist above)
+      ;; didn't work: Emacs jumped to the wrong position. However, it
+      ;; seems to work if compilation-forget-errors is used. This
+      ;; problem may be related to Emacs bug #9679
+      ;; (http://debbugs.gnu.org/cgi/bugreport.cgi?bug=9679). The idea
+      ;; to use compilation-forget-errors comes from a comment due to
+      ;; Oleksandr Manzyuk
+      ;; (https://github.com/haskell/haskell-mode/issues/67).
+      (compilation-forget-errors)
+      (unless append (erase-buffer))
+      (save-excursion
+        (goto-char (point-max))
+        (insert text))
+      (put-text-property 0 (length name) 'face '(:weight bold) name)
+      (setq mode-line-buffer-identification name)
+      (force-mode-line-update))
+    ;; If the current window displays the information buffer, then the
+    ;; window configuration is left untouched.
+    (unless (equal (window-buffer) buf)
+      (let ((agda-window
+              (and agda2-file-buffer
+                   (car-safe
+                     ;; All windows, including minibuffers, on any
+                     ;; frame on the current terminal, displaying the
+                     ;; present Agda file buffer.
+                     (get-buffer-window-list agda2-file-buffer t 0)))))
+        (save-selected-window
+          ;; Select a window displaying the Agda file buffer (if such
+          ;; a window exists). With certain configurations of
+          ;; display-buffer this should increase the likelihood that
+          ;; the info buffer will be displayed on the same frame.
+          (when agda-window
+            (select-window agda-window 'no-record))
+          (let* (;; If there is only one window, then the info window
+                 ;; should be created above or below the code window,
+                 ;; not to the left or right.
+                 (split-width-threshold nil)
+                 (window
+                   (display-buffer
+                     buf
+                     ;; Under Emacs 23 the effect of the following
+                     ;; argument is only that the current window
+                     ;; should not be used.
+                     '(nil
+                       .
+                       (;; Do not use the same window.
+                        (inhibit-same-window . t)
+                        ;; Do not raise or select another frame.
+                        (inhibit-switch-frame . t))))))
+            (if window
+                (fit-window-to-buffer window
+                  (truncate
+                    (* (frame-height)
+                       agda2-information-window-max-height))))))))
+    ;; Move point in every window displaying the information buffer.
+    ;; Exception: If we are appending, don't move point in selected
+    ;; windows.
+    (dolist (window (get-buffer-window-list buf 'no-minibuffer t))
+      (unless (and append
+                   (equal window (selected-window)))
+        (with-selected-window window
+          (if append
+              (goto-char (point-max))
+            (goto-char (point-min))))))))
+
+(defun agda2-info-action-and-copy (name text &optional append)
+  "Same as agda2-info-action but also puts TEXT in the kill ring."
+  (kill-new text)
+  (agda2-info-action name text append))
+
+(defun agda2-show-constraints()
+  "Show constraints." (interactive)
+  (agda2-go nil t 'busy t "Cmd_constraints"))
+
+(defun agda2-remove-annotations ()
+  "Removes buffer annotations (overlays and text properties)."
+  (interactive)
+  (dolist (o (overlays-in (point-min) (point-max)))
+    (delete-overlay o))
+  (let ((inhibit-read-only t))
+    (annotation-preserve-mod-p-and-undo
+     (set-text-properties (point-min) (point-max) '()))
+    (force-mode-line-update)))
+
+(defun agda2-next-goal ()     "Go to the next goal, if any."     (interactive)
+  (agda2-mv-goal 'next-single-property-change     'agda2-delim2 1 (point-min)))
+(defun agda2-previous-goal () "Go to the previous goal, if any." (interactive)
+  (agda2-mv-goal 'previous-single-property-change 'agda2-delim3 0 (point-max)))
+(defun agda2-mv-goal (change delim adjust wrapped)
+  (agda2-let ()
+      ((go (p) (while (and (setq p (funcall change p 'category))
+                           (not (eq (get-text-property p 'category) delim))))
+           (if p (goto-char (+ adjust p)))))
+    (or (go (point)) (go wrapped) (message "No goals in the buffer"))))
+
+(defun agda2-quit ()
+  "Quit and clean up after agda2."
+  (interactive)
+  (remove-hook 'first-change-hook 'agda2-abort-highlighting 'local)
+  (remove-hook 'after-save-hook 'agda2-highlight-tokens 'local)
+  (agda2-remove-annotations)
+  (agda2-term))
+
+(defun agda2-term (&optional nicely)
+  "Interrupt the Agda process and kill its buffer.
+If this function is invoked with a prefix argument, then Agda is
+asked nicely to terminate itself after any previously invoked
+commands have completed."
+  (interactive "P")
+  (if nicely
+      (progn
+        ;; Set up things so that if the Agda process terminates, then
+        ;; its buffer is killed.
+        (when (and agda2-process
+                   (process-status agda2-process))
+          (set-process-sentinel agda2-process 'agda2-kill-process-buffer))
+        ;; Kill the process buffer if the Agda process has already
+        ;; been killed.
+        (agda2-kill-process-buffer)
+        ;; Try to kill the Agda process.
+        (agda2-send-command nil
+                            "IOTCM"
+                            (agda2-string-quote (buffer-file-name))
+                            "None"
+                            "Indirect"
+                            "Cmd_exit"))
+    ;; Try to kill the Agda process and the process buffer.
+    (when (and agda2-process
+               (process-status agda2-process))
+      (interrupt-process agda2-process))
+    (when (buffer-live-p agda2-process-buffer)
+      (kill-buffer agda2-process-buffer))))
+
+(defun agda2-kill-process-buffer (&optional process event)
+  "Kills the Agda process buffer, if any.
+But only if the Agda process does not exist or has terminated.
+
+This function can be used as a process sentinel."
+  (when (and (or (null agda2-process)
+                 (member (process-status agda2-process)
+                         '(exit signal failed nil)))
+             (buffer-live-p agda2-process-buffer))
+    (kill-buffer agda2-process-buffer)))
+
+(cl-defmacro agda2--with-gensyms ((&rest names) &body body)
+  "Bind NAMES to fresh symbols in BODY"
+  (declare (indent 1))
+  `(let ,(cl-loop for x in names collecting `(,x (make-symbol (symbol-name',x))))
+     ,@body))
+
+;; This macro is meant to be used to generate other macros which define
+;; functions which can be used either directly from a goal or at a global
+;; level and are modifiable using one of three levels of normalisation.
+
+(defmacro agda2-proto-maybe-normalised (name comment cmd norm0 norm1 norm2 norm3 spec)
+  "This macro constructs a function NAME which runs CMD.
+COMMENT is used to build the function's comment.
+The function NAME takes a prefix argument which tells whether it
+should normalise types according to either NORM0, NORM1, NORM2, or NORM3
+when running CMD through `agda2-goal-cmd`.
+SPEC can be either (fromgoal want) or (global prompt).
+"
+
+  ;; Names bound in a macro should be ``uninterned'' to avoid name capture
+  ;; We use the macro `agda2--with-gensyms' to bind these.
+  (agda2--with-gensyms (eval prefix args)
+    `(defun ,name (,prefix &rest ,args)
+       ,(format "%s.
+
+The form of the result depends on the prefix argument:
+
+* If the prefix argument is `nil' (i.e., if no prefix argument is
+  given), then the result is %s.
+
+* If the prefix argument is `(4)' (for instance if C-u is typed
+  exactly once right before the command is invoked), then the
+  result is %s.
+
+* If the prefix argument is `(16)' (for instance if C-u is typed
+  exactly twice right before the command is invoked), then the
+  result is %s.
+
+* If any other prefix argument is used (for instance if C-u is
+  typed thrice right before the command is invoked), then the
+  result is %s." comment (nth 1 norm0) (nth 1 norm1) (nth 1 norm2) (nth 1 norm3))
+
+       ;; All the commands generated by the macro are interactive.
+       ;; Those called from a goal, grab the value present there (if any)
+       ;; Whereas those called globally always use a prompt
+       (interactive ,(pcase spec
+                       (`(fromgoal ,want)
+                        "P")
+                       (`(global ,prompt)
+                        (if prompt
+                            (concat "P\nM" prompt ": ")
+                          "P"))))
+       ;; Depending on the prefix's value we pick one of the three
+       ;; normalisation levels
+       (let ((,eval (cond ((null ,prefix)
+                           ,(car norm0))
+                          ((equal ,prefix '(4))
+                           ,(car norm1))
+                          ((equal ,prefix '(16))
+                           ,(car norm2))
+                          (t ,(car norm3)))))
+       ;; Finally, if the command is called from a goal, we use `agda2-goal-cmd'
+       ;; Otherwise we resort to `agda2-go'
+         ,(pcase spec
+            (`(fromgoal ,want)
+             `(agda2-goal-cmd (concat ,cmd " " ,eval) nil ,want))
+            (`(global ,prompt)
+             `(agda2-go nil t 'busy t
+                        (concat ,cmd " "
+                                ,eval " "
+                                (if ,prompt
+                                    (agda2-string-quote (car ,args))
+                                    "")))))))))
+
+(defmacro agda2-maybe-normalised (name comment cmd want)
+  `(agda2-proto-maybe-normalised
+    ,name ,comment ,cmd
+    ("Simplified"   "simplified")
+    ("Instantiated" "neither explicitly normalised nor simplified")
+    ("Normalised"   "normalised")
+    ("HeadNormal"   "head normalised")
+    (fromgoal ,want)))
+
+(defmacro agda2-maybe-normalised-asis (name comment cmd want)
+  `(agda2-proto-maybe-normalised
+    ,name ,comment ,cmd
+    ("AsIs"       "returned as is")
+    ("Simplified" "simplified")
+    ("Normalised" "normalised")
+    ("HeadNormal" "head normalised")
+    (fromgoal ,want)))
+
+(defmacro agda2-maybe-normalised-toplevel (name comment cmd prompt)
+  `(agda2-proto-maybe-normalised
+    ,name ,comment ,cmd
+    ("Simplified"   "simplified")
+    ("Instantiated" "neither explicitly normalised nor simplified")
+    ("Normalised"   "normalised")
+    ("HeadNormal"   "head normalised")
+    (global ,prompt)))
+
+(defmacro agda2-maybe-normalised-toplevel-asis-noprompt (name comment cmd)
+  `(agda2-proto-maybe-normalised
+    ,name ,comment ,cmd
+    ("AsIs"       "returned as is")
+    ("Simplified" "simplified")
+    ("Normalised" "normalised")
+    ("HeadNormal" "head normalised")
+    (global nil)))
+
+(agda2-maybe-normalised
+ agda2-goal-type
+ "Show the type of the goal at point"
+ "Cmd_goal_type"
+ nil)
+
+(agda2-maybe-normalised
+ agda2-infer-type
+ "Infer the type of the goal at point"
+ "Cmd_infer"
+ "expression to type")
+
+(agda2-maybe-normalised-toplevel
+   agda2-infer-type-toplevel
+   "Infers the type of the given expression. The scope used for
+the expression is that of the last point inside the current
+top-level module"
+   "Cmd_infer_toplevel"
+   "Expression")
+
+(defun agda2-infer-type-maybe-toplevel ()
+  "Infers the type of the given expression.
+Either uses the scope of the current goal or, if point is not in a goal, the
+top-level scope."
+  (interactive)
+  (call-interactively (if (agda2-goal-at (point))
+                          'agda2-infer-type
+                        'agda2-infer-type-toplevel)))
+
+(defun agda2-why-in-scope ()
+  "Explain why something is in scope in a goal."
+  (interactive)
+  (agda2-goal-cmd "Cmd_why_in_scope" nil "Name"))
+
+(defun agda2-why-in-scope-toplevel (name)
+  "Explain why something is in scope at the top level."
+  (interactive "MName: ")
+  (agda2-go nil t 'busy t
+            "Cmd_why_in_scope_toplevel"
+            (agda2-string-quote name)))
+
+(defun agda2-why-in-scope-maybe-toplevel ()
+  "Explains why a given name is in scope."
+  (interactive)
+  (call-interactively (if (agda2-goal-at (point))
+                          'agda2-why-in-scope
+                          'agda2-why-in-scope-toplevel)))
+
+(agda2-maybe-normalised
+ agda2-elaborate-give
+ "Elaborate check the given expression against the hole's type and fill in the
+ hole with the elaborated term"
+ "Cmd_elaborate_give"
+ "expression to elaborate and give")
+
+(agda2-maybe-normalised
+ agda2-goal-and-context
+ "Shows the type of the goal at point and the currect context"
+ "Cmd_goal_type_context"
+ nil)
+
+(agda2-maybe-normalised
+ agda2-goal-and-context-and-inferred
+ "Shows the context, the goal and the given expression's inferred type"
+ "Cmd_goal_type_context_infer"
+ "expression to type")
+
+(agda2-maybe-normalised
+ agda2-goal-and-context-and-checked
+ "Shows the context, the goal and check the given expression's against
+ the hole's type"
+ "Cmd_goal_type_context_check"
+ "expression to type")
+
+(agda2-maybe-normalised
+ agda2-show-context
+ "Show the context of the goal at point"
+ "Cmd_context"
+ nil)
+
+(agda2-maybe-normalised-asis
+ agda2-helper-function-type
+  "Compute the type of a hypothetical helper function."
+  "Cmd_helper_function"
+  "Expression")
+
+(agda2-maybe-normalised
+  agda2-module-contents
+  "Shows all the top-level names in the given module.
+Along with their types."
+  "Cmd_show_module_contents"
+  "Module name (empty for current module)")
+
+(agda2-maybe-normalised-toplevel
+  agda2-module-contents-toplevel
+  "Shows all the top-level names in the given module.
+Along with their types."
+  "Cmd_show_module_contents_toplevel"
+  "Module name (empty for top-level module)"
+)
+
+(agda2-maybe-normalised-toplevel
+  agda2-search-about-toplevel
+  "Search About an identifier"
+  "Cmd_search_about_toplevel"
+  "Name"
+)
+
+(defun agda2-module-contents-maybe-toplevel ()
+  "Shows all the top-level names in the given module.
+Along with their types.
+
+Uses either the scope of the current goal or, if point is not in
+a goal, the top-level scope."
+  (interactive)
+  (call-interactively (if (agda2-goal-at (point))
+                          'agda2-module-contents
+                        'agda2-module-contents-toplevel)))
+
+(defun agda2-solve-maybe-all ()
+  "Solves goals that are already instantiated internally.
+Either only one if point is a goal, or all of them."
+  (interactive)
+  (call-interactively (if (agda2-goal-at (point))
+                          'agda2-solveOne
+                          'agda2-solveAll))
+)
+
+(defun agda2-auto-maybe-all ()
+  "Run auto.
+Either only one if point is a goal, or all of them."
+  (interactive)
+  (call-interactively (if (agda2-goal-at (point))
+                          'agda2-autoOne
+                          'agda2-autoAll))
+)
+
+(agda2-maybe-normalised-toplevel-asis-noprompt
+ agda2-show-goals
+ "Show all goals."
+ "Cmd_metas"
+ )
+
+(agda2-maybe-normalised-toplevel-asis-noprompt
+ agda2-solveAll
+ "Solves all goals that are already instantiated internally."
+ "Cmd_solveAll"
+ )
+
+(agda2-maybe-normalised
+  agda2-solveOne
+  "Solves the goal at point if it is already instantiated internally"
+  "Cmd_solveOne"
+  nil
+)
+
+(defun agda2-solveAll-action (iss)
+  (while iss
+    (let* ((g (pop iss)) (txt (pop iss))
+           (cmd (cons 'agda2-solve-action (cons g (cons txt nil)))))
+      (if (null agda2-last-responses)
+          (push (cons 1 cmd) agda2-last-responses)
+        (nconc agda2-last-responses (cons (cons 3 cmd) nil))))))
+
+(defun agda2-solve-action (g txt)
+  (save-excursion
+    (agda2-replace-goal g txt)
+    (agda2-goto-goal g)
+    (agda2-give)))
+
+(defun agda2-compute-normalised (&optional arg)
+  "Compute the normal form of the expression in the goal at point.
+
+With the prefix argument `(4)' \"abstract\" is ignored during the
+computation.
+
+With a prefix argument `(16)' the normal form of
+\"show <expression>\" is computed, and then the resulting string
+is printed.
+
+With any other prefix the head normal form is computed."
+  (interactive "P")
+  (let ((cmd (concat "Cmd_compute"
+                      (cond ((equal arg nil) " DefaultCompute")
+                            ((equal arg '(4)) " IgnoreAbstract")
+                            ((equal arg '(16)) " UseShowInstance")
+                            (" HeadCompute")))))
+    (agda2-goal-cmd cmd nil "expression to normalise")))
+
+(defun agda2-compute-normalised-toplevel (expr &optional arg)
+  "Compute the normal form of the given expression.
+The scope used for the expression is that of the last point
+inside the current top-level module.
+
+With a prefix argument distinct from `(4)' the normal form of
+\"show <expression>\" is computed, and then the resulting string
+is printed.
+
+With the prefix argument `(4)' \"abstract\" is ignored during the
+computation."
+  (interactive "MExpression: \nP")
+  (let ((cmd (concat "Cmd_compute_toplevel"
+                     (cond ((equal arg nil) " DefaultCompute")
+                            ((equal arg '(4)) " IgnoreAbstract")
+                            ((equal arg '(16)) " UseShowInstance")
+                            (" HeadCompute")) " ")))
+    (agda2-go nil t 'busy t
+              (concat cmd (agda2-string-quote expr)))))
+
+(defun agda2-compute-normalised-maybe-toplevel ()
+  "Compute the normal form of the given expression.
+The scope used for the expression is that of the last point
+inside the current top-level module.
+
+With a prefix argument distinct from `(4)' the normal form of
+\"show <expression>\" is computed, and then the resulting string
+is printed.
+
+With the prefix argument `(4)' \"abstract\" is ignored during the
+computation."
+  (interactive)
+  (if (agda2-goal-at (point))
+      (call-interactively 'agda2-compute-normalised)
+    (call-interactively 'agda2-compute-normalised-toplevel)))
+
+(defun agda2-display-program-version ()
+  "Display version of Agda"
+  (interactive)
+  (agda2-go nil nil 'busy t "Cmd_show_version"))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;;
+
+(defun agda2-highlight-reload nil
+  "Loads precomputed syntax highlighting info for the current buffer.
+Only if the buffer is unmodified, and only if there is anything to load."
+ (unless (buffer-modified-p)
+   (agda2-go nil t 'not-so-busy t
+             "Cmd_load_highlighting_info"
+             (agda2-string-quote (buffer-file-name)))))
+
+(defun agda2-literate-p ()
+  "Is the current buffer a literate Agda buffer?"
+  (not (equal (file-name-extension (buffer-file-name)) "agda")))
+
+(defmacro agda2--case (exp &rest branches) ;FIXME: Use `pcase' instead!
+  (declare (debug t) (indent 1))
+  (let ((s (make-symbol "v")))
+    `(let ((,s ,exp))
+       (cond
+         ,@(mapcar (lambda (branch)
+                     `((equal ,s ,(car branch)) ,@(cdr branch)))
+                   branches)))))
+
+(defun agda2-goals-action (goals)
+  "Annotates the goals in the current buffer with text properties.
+GOALS is a list of the buffer's goal numbers, in the order in
+which they appear in the buffer. Note that this function should
+be run /after/ syntax highlighting information has been loaded,
+because the two highlighting mechanisms interact in unfortunate
+ways."
+  (agda2-forget-all-goals)
+  (agda2-let
+      ((literate (agda2-literate-p))
+       stk
+       top
+       ;; Don't run modification hooks: we don't want this function to
+       ;; trigger agda2-abort-highlighting.
+       (inhibit-modification-hooks t))
+      ((delims() (re-search-forward "[?]\\|[{][-!]\\|[-!][}]\\|--\\|^%.*\\\\begin{code}\\|\\\\begin{code}\\|\\\\end{code}\\|```\\|\\#\\+begin_src agda2\\|\\#\\+end_src agda2" nil t))
+       ;; is-proper checks whether string s (e.g. "?" or "--") is proper
+       ;; i.e., is not part of an identifier.
+       ;; comment-starter is true if s starts a comment (e.g. "--")
+       (is-proper (s comment-starter)
+          (save-excursion
+            (save-match-data
+              (backward-char (length s))
+              (unless (bolp) (backward-char 1))  ;; bolp = pointer at beginning of line
+              ;; Andreas, 2014-05-17 Issue 1132
+              ;; A questionmark can also follow immediately after a .
+              ;; for instance to be a place holder for a dot pattern.
+              (looking-at (concat "\\([.{}();]\\|^\\|\\s \\)"  ;; \\s = whitespace
+                                  (regexp-quote s)
+                                  (unless comment-starter
+                                    "\\([{}();]\\|$\\|\\s \\)"))))))
+       (make(p)  (agda2-make-goal p (point) (pop goals)))
+       (inside-comment() (and stk (null     (car stk))))
+       (inside-goal()    (and stk (integerp (car stk))))
+       (outside-code()   (and stk (eq (car stk) 'outside)))
+       (inside-code()    (not (outside-code)))
+       ;; inside a multi-line comment ignore everything but the multi-line comment markers
+       (safe-delims()
+          (if (inside-comment)
+               (re-search-forward "{-\\|-}" nil t)
+            (delims))))
+    (save-excursion
+      ;; In literate mode we should start out in the "outside of code"
+      ;; state.
+      (if literate (push 'outside stk))
+      (goto-char (point-min))
+      (while (and goals (safe-delims))
+        (agda2--case (match-string 0)
+          ("\\begin{code}"     (when (outside-code)               (pop stk)))
+          ("\\end{code}"       (when (not stk)                    (push 'outside stk)))
+          ("#+begin_src agda2" (when (outside-code)               (pop stk)))
+          ("#+end_src agda2"   (when (not stk)                    (push 'outside stk)))
+          ("```"               (if   (outside-code)               (pop stk)
+                               (when (not stk)                    (push 'outside stk))))
+          ("--"                (when (and (not stk)
+                                          (is-proper "--" t))     (end-of-line)))
+          ("{-"                (when (and (inside-code)
+                                          (not (inside-goal)))    (push nil           stk)))
+          ("-}"                (when (inside-comment)             (pop stk)))
+          ("{!"                (when (and (inside-code)
+                                          (not (inside-comment))) (push (- (point) 2) stk)))
+          ("!}"                (when (inside-goal)
+                                 (setq top (pop stk))
+                                 (unless stk (make top))))
+          ("?"                 (progn
+                                 (when (and (not stk) (is-proper "?" nil))
+                                   (delete-char -1)
+                                   (insert "{!!}")
+                                   (make (- (point) 4))))))))))
+
+(defun agda2-make-goal (p q n)
+  "Make a goal with number N at <P>{!...!}<Q>.  Assume the region is clean."
+  (annotation-preserve-mod-p-and-undo
+   (let ((atp (lambda (x ps) (add-text-properties x (1+ x) ps))))
+     (funcall atp p       '(category agda2-delim1))
+     (funcall atp (1+ p)  '(category agda2-delim2))
+     (funcall atp (- q 2) '(category agda2-delim3))
+     (funcall atp (1- q)  '(category agda2-delim4)))
+   (let ((o (make-overlay p q nil t nil)))
+     (overlay-put o 'modification-hooks '(agda2-protect-goal-markers))
+     (overlay-put o 'agda2-gn           n)
+     (overlay-put o 'face               'highlight)
+     (overlay-put o 'after-string       (propertize (format "%s" n) 'face 'highlight)))))
+
+(defun agda2-protect-goal-markers (ol action beg end &optional length)
+  "Ensures that the goal markers cannot be tampered with.
+Except if `inhibit-read-only' is non-nil or /all/ of the goal is
+modified."
+  (if action
+      ;; This is the after-change hook.
+      nil
+    ;; This is the before-change hook.
+    (cond
+     ((and (<= beg (overlay-start ol)) (>= end (overlay-end ol)))
+      ;; The user is trying to remove the whole goal:
+      ;; manually evaporate the overlay and add an undo-log entry so
+      ;; it gets re-added if needed.
+      (when (listp buffer-undo-list)
+        (push (list 'apply 0 (overlay-start ol) (overlay-end ol)
+                    'move-overlay ol (overlay-start ol) (overlay-end ol))
+              buffer-undo-list))
+      (delete-overlay ol))
+     ((or (< beg (+ (overlay-start ol) 2))
+          (> end (- (overlay-end ol) 2)))
+      (unless inhibit-read-only
+        (signal 'text-read-only nil))))))
+
+(defun agda2-update (old-g new-txt)
+  "Update the goal OLD-G.
+If NEW-TXT is a string, then the goal is replaced by the string,
+and otherwise the text inside the goal is retained (parenthesised
+if NEW-TXT is `'paren').
+
+Removes the goal braces, but does not remove the goal overlay or
+text properties."
+  (cl-multiple-value-bind (p q) (agda2-range-of-goal old-g)
+    (save-excursion
+      (cond ((stringp new-txt)
+             (agda2-replace-goal old-g new-txt))
+            ((equal new-txt 'paren)
+             (goto-char (- q 2)) (insert ")")
+             (goto-char (+ p 2)) (insert "(")))
+      (cl-multiple-value-bind (p q) (agda2-range-of-goal old-g)
+        (delete-region (- q 2) q)
+        (delete-region p (+ p 2)))
+        ;; Update highlighting
+        (if (and (not (equal new-txt 'paren)) (not (equal new-txt 'no-paren)))
+            (apply 'agda2-go 'save t 'busy nil "Cmd_highlight"
+              (format "%d" old-g)
+              (agda2-mkRange `(,p ,(- q 2)))
+              (agda2-string-quote new-txt) nil))
+    )))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;; Misc
+
+(defun agda2-process-status ()
+  "Status of `agda2-process-buffer', or \"no process\"."
+  (condition-case nil
+      (process-status agda2-process)
+    (error "no process")))
+
+(defun agda2-intersperse (sep xs)
+  (let (ys)
+    (while xs
+      (push (pop xs) ys)
+      (push sep ys))
+    (pop ys)
+    (nreverse ys)))
+
+(defun agda2-goal-Range (o)
+  "The Haskell Range of goal overlay O."
+  (agda2-mkRange `(,(+ (overlay-start o) 2)
+                   ,(- (overlay-end   o) 2))))
+
+(defun agda2-mkRange (points)
+  "A string representing a range corresponding to POINTS.
+POINTS must be a list of integers, and its length must be 0 or 2."
+  (if points
+      (format "(intervalsToRange (Just (mkAbsolute %s)) %s)"
+              (agda2-string-quote (file-truename (buffer-file-name)))
+              (format "[Interval %s %s]"
+                      (agda2-mkPos (car points))
+                      (agda2-mkPos (cadr points))))
+    "noRange"))
+
+(defun agda2-mkPos (&optional p)
+  "The Haskell PositionWithoutFile corresponding to P or `point'."
+  (save-excursion
+    (save-restriction
+      (widen)
+      (if p (goto-char p))
+      (format "(Pn () %d %d %d)"
+              (point)
+              (count-lines (point-min) (point))
+              (1+ (current-column))))))
+
+(defun agda2-char-quote (c)
+  "Convert character C to the notation used in Haskell strings.
+The non-ASCII characters are actually rendered as
+\"\\xNNNN\\&\", i.e. followed by a \"null character\", to avoid
+problems if they are followed by digits.  ASCII characters (code
+points < 128) are converted to singleton strings."
+  (if (< c 128)
+      (list c)
+    ;; FIXME: Why return a list rather than a string?  --Stef
+    (append (format "\\x%x\\&" (encode-char c 'ucs)) nil)))
+
+(defun agda2-string-quote (s)
+  "Format S as a Haskell string literal.
+Removes any text properties, escapes newlines, double quotes,
+etc., adds surrounding double quotes, and converts non-ASCII
+characters to the \\xNNNN notation used in Haskell strings."
+  (let ((print-escape-newlines t)
+        (s2 (copy-sequence s)))
+    (set-text-properties 0 (length s2) nil s2)
+    (mapconcat 'agda2-char-quote (prin1-to-string s2) "")))
+
+(defun agda2-list-quote (strings)
+  "Convert a list of STRINGS into a string representing it in Haskell syntax."
+  (concat "[" (mapconcat 'agda2-string-quote strings ", ") "]"))
+
+(defun agda2-goal-at(pos)
+  "Return (goal overlay, goal number) at POS, or nil."
+  (let ((os (and pos (overlays-at pos))) o g)
+    (while (and os (not(setq g (overlay-get (setq o (pop os)) 'agda2-gn)))))
+    (if g (list o g))))
+
+(defun agda2-goal-overlay (g)
+  "Returns the overlay of goal number G, if any."
+  (car
+   (remove nil
+           (mapcar (lambda (o) (if (equal (overlay-get o 'agda2-gn) g) o))
+                   (overlays-in (point-min) (point-max))))))
+
+(defun agda2-range-of-goal (g)
+  "The range of goal G."
+  (let ((o (agda2-goal-overlay g)))
+    (if o (list (overlay-start o) (overlay-end o)))))
+
+(defun agda2-goto-goal (g)
+  (let ((p (+ 2 (car (agda2-range-of-goal g)))))
+    (if p (goto-char p))))
+
+(defun agda2-replace-goal (g newtxt)
+  "Replace the content of goal G with NEWTXT." (interactive)
+  (save-excursion
+    (cl-multiple-value-bind (p q) (agda2-range-of-goal g)
+      (setq p (+ p 2) q (- q 2))
+      (let ((indent (and (goto-char p) (current-column))))
+        (delete-region p q) (insert newtxt)
+        (while (re-search-backward "^" p t)
+          (insert-char ?  indent) (backward-char (1+ indent)))))))
+
+(defun agda2-forget-all-goals ()
+  "Remove all goal annotations.
+\(Including some text properties which might be used by other
+\(minor) modes.)"
+  (annotation-preserve-mod-p-and-undo
+   (remove-text-properties (point-min) (point-max)
+                           '(category nil agda2-delim2 nil agda2-delim3 nil
+                             display nil rear-nonsticky nil)))
+  (let ((p (point-min)))
+    (while (< (setq p (next-single-char-property-change p 'agda2-gn))
+              (point-max))
+      (delete-overlay (car (agda2-goal-at p))))))
+
+(defun agda2-decl-beginning ()
+  "Find the beginning point of the declaration containing the point.
+To do: dealing with semicolon separated decls."
+  (interactive)
+  (save-excursion
+    (let* ((pEnd (point))
+           (pDef (progn (goto-char (point-min))
+                        (re-search-forward "\\s *" pEnd t)))
+           (cDef (current-column)))
+      (while (re-search-forward
+              "where\\(\\s +\\)\\S \\|^\\(\\s *\\)\\S " pEnd t)
+        (if (match-end 1)
+            (setq pDef (goto-char (match-end 1))
+                  cDef (current-column))
+          (goto-char (match-end 2))
+          (if (>= cDef (current-column))
+              (setq pDef (point)
+                    cDef (current-column))))
+        (forward-char))
+      (goto-char pDef)
+      (if (equal (current-word) "mutual")
+          (or (match-end 2) (match-end 1))
+        pDef))))
+
+(defun agda2-beginning-of-decl ()
+  (interactive)
+  (goto-char (agda2-decl-beginning)))
+
+(defvar agda2-debug-buffer-name "*Agda debug*"
+  "The name of the buffer used for Agda debug messages.")
+
+(defun agda2-verbose (msg)
+  "Appends the string MSG to the `agda2-debug-buffer-name' buffer.
+Note that this buffer's contents is not erased automatically when
+a file is loaded."
+  (with-current-buffer (get-buffer-create agda2-debug-buffer-name)
+    (save-excursion
+      (goto-char (point-max))
+      (insert msg))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Comments and paragraphs
+
+(defun agda2-comments-and-paragraphs-setup nil
+  "Set up comment and paragraph handling for the Agda mode."
+
+  ;; Empty lines (all white space according to Emacs) delimit
+  ;; paragraphs.
+  (set (make-local-variable 'paragraph-start) "\\s-*$")
+  (set (make-local-variable 'paragraph-separate) paragraph-start)
+
+  ;; Support for adding/removing comments.
+  (set (make-local-variable 'comment-start) "-- ")
+
+  ;; Use the syntax table to locate comments (and possibly other
+  ;; things). Syntax table setup for comments is done elsewhere.
+  (set (make-local-variable 'comment-use-syntax) t)
+
+  ;; Update token-based highlighting after the buffer has been saved.
+  (add-hook 'after-save-hook 'agda2-highlight-tokens nil 'local)
+
+  ;; Support for proper filling of text in comments (requires that
+  ;; Filladapt is activated).
+  (when (featurep 'filladapt)
+    (add-to-list (make-local-variable
+                  'filladapt-token-table)
+                 '("--" agda2-comment))
+    (add-to-list (make-local-variable 'filladapt-token-match-table)
+                 '(agda2-comment agda2-comment) t)
+    (add-to-list (make-local-variable 'filladapt-token-conversion-table)
+                 '(agda2-comment . exact))))
+
+(defun agda2-comment-dwim-rest-of-buffer ()
+  "Comment or uncomment the rest of the buffer.
+From the beginning of the current line to the end of the buffer."
+  (interactive)
+  (save-excursion
+    (forward-line 0)
+    (push-mark (point) 'no-message 'activate-mark)
+    (unwind-protect
+        (progn
+          (goto-char (point-max))
+          (comment-dwim nil))
+      (pop-mark))))
+
+(defun agda2-highlight-tokens nil
+  "Compute token-based highlighting information.
+
+Unless `agda2-highlight-level' is `none' or the Agda process is
+busy (or `not-so-busy') with something. This command might save
+the buffer."
+  (unless (or agda2-in-progress
+              (equal agda2-highlight-level 'none))
+    (agda2-go 'save t 'not-so-busy t
+              "Cmd_tokenHighlighting"
+              (agda2-string-quote (buffer-file-name))
+              "Keep")))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Go to definition site
+
+(defun agda2-goto-definition-keyboard (&optional other-window)
+  "Go to the definition site of the name under point (if any).
+If this function is invoked with a prefix argument then another window is used
+to display the given position."
+  (interactive "P")
+  (annotation-goto-indirect (point) other-window))
+
+(defun agda2-goto-definition-mouse (ev)
+  "Go to the definition site of the name clicked on, if any.
+Otherwise, yank (see `mouse-yank-primary')."
+  (interactive "e")
+  (unless (annotation-goto-indirect ev)
+    ;; FIXME: Shouldn't we use something like
+    ;; (call-interactively (key-binding ev))?  --Stef
+    (mouse-yank-primary ev)))
+
+(defun agda2-go-back nil
+  "Go back to the previous position in which
+`agda2-goto-definition-keyboard' or `agda2-goto-definition-mouse' was
+invoked."
+  (interactive)
+  (annotation-go-back))
+
+(defun agda2-maybe-goto (filepos)
+  "Might move point to the given error.
+FILEPOS should have the form (FILE . POSITION).
+
+If `agda2-highlight-in-progress' is nil, then nothing happens.
+Otherwise, if the current buffer is the one that is connected to
+the Agda process, then point is moved to POSITION in
+FILE (assuming that the FILE is readable). Otherwise point is
+moved to the given position in the buffer visiting the file, if
+any, and in every window displaying the buffer, but the window
+configuration and the selected window are not changed."
+  (when (and agda2-highlight-in-progress
+             (consp filepos)
+             (stringp (car filepos))
+             (integerp (cdr filepos)))
+    (if agda2-in-agda2-file-buffer
+        (annotation-goto-and-push (current-buffer) (point) filepos)
+      (save-excursion
+        (let ((buffer (find-buffer-visiting (car filepos))))
+          (when buffer
+            (let ((windows (get-buffer-window-list buffer
+                                                   'no-minibuffer t)))
+              (if windows
+                  (dolist (window windows)
+                    (with-selected-window window
+                      (goto-char (cdr filepos))))
+                (with-current-buffer buffer
+                  (goto-char (cdr filepos)))))))))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Implicit arguments
+
+(defun agda2-display-implicit-arguments (&optional arg)
+  "Toggle display of implicit arguments.
+With prefix argument, turn on display of implicit arguments if
+the argument is a positive number, otherwise turn it off."
+  (interactive "P")
+  (cond
+   ((eq arg nil)
+      (agda2-go nil t 'not-so-busy t "ToggleImplicitArgs"))
+   ((and (numberp arg) (> arg 0))
+      (agda2-go nil t 'not-so-busy t "ShowImplicitArgs" "True"))
+   (t (agda2-go nil t 'not-so-busy t "ShowImplicitArgs" "False"))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Irrelevant arguments
+
+(defun agda2-display-irrelevant-arguments (&optional arg)
+  "Toggle display of irrelevant arguments.
+With prefix argument, turn on display of irrelevant arguments if
+the argument is a positive number, otherwise turn it off."
+  (interactive "P")
+  (cond
+   ((eq arg nil)
+      (agda2-go nil t 'not-so-busy t "ToggleIrrelevantArgs"))
+   ((and (numberp arg) (> arg 0))
+      (agda2-go nil t 'not-so-busy t "ShowIrrelevantArgs" "True"))
+   (t (agda2-go nil t 'not-so-busy t "ShowIrrelevantArgs" "False"))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;;;;
+
+(defun agda2-popup-menu-3 (ev)
+  "If in a goal, popup the goal menu and call chosen command."
+  (interactive "e")
+  (let (choice)
+    (save-excursion
+      (and (agda2-goal-at (goto-char (posn-point (event-end ev))))
+           (setq choice (x-popup-menu ev agda2-goal-map))
+           (call-interactively
+            (lookup-key agda2-goal-map (apply 'vector choice)))))))
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Switching to a different version of Agda
+
+(defun agda2-get-agda-program-versions ()
+  "Get \"version strings\" of executables starting with
+\\='agda-mode\\=' in current path."
+  (delete-dups
+   (mapcar (lambda (path)
+             ;; strip 'agda-mode' prefix
+             (replace-regexp-in-string "^agda-mode-?" ""
+                                       (file-name-nondirectory path)))
+           (cl-remove-if-not 'file-executable-p
+             ;; concatenate result
+             (cl-reduce 'append
+                     ;; for each directory in exec-path, get list of
+                     ;; files whose name starts with 'agda-mode'
+                     (mapcar (lambda (path)
+                               (when (file-accessible-directory-p path)
+                                 (directory-files path 't "^agda-mode")))
+                             exec-path))))))
+
+;; Note that other versions of Agda may use different protocols, so
+;; this function unloads the Emacs mode.
+
+(defun agda2-set-program-version (version)
+  "Tries to switch to Agda version VERSION.
+
+This command assumes that the agda and agda-mode executables for
+Agda version VERSION are called agda-VERSION and
+agda-mode-VERSION, and that they are located on the PATH. (If
+VERSION is empty, then agda and agda-mode are used instead.)
+
+An attempt is made to preserve the default value of
+`agda2-mode-hook'."
+  (interactive
+   (list (completing-read "Version: " (agda2-get-agda-program-versions))))
+
+  (let*
+      ((agda-buffers
+        (cl-mapcan (lambda (buf)
+                  (with-current-buffer buf
+                    (when (equal major-mode 'agda2-mode)
+                      (list buf))))
+                (buffer-list)))
+
+       (default-hook (default-value 'agda2-mode-hook))
+
+       (version-suffix (if (or (equal version "")
+                               (equal version nil))
+                           ""
+                         (concat "-" version)))
+
+       ;; Run agda-mode<version-suffix> and make sure that it returns
+       ;; successfully.
+       (coding-system-for-read 'utf-8)
+       (agda-mode-prog (concat "agda-mode" version-suffix))
+       (agda-mode-path
+        (condition-case nil
+            (with-temp-buffer
+              (unless
+                  (equal 0 (call-process agda-mode-prog
+                                         nil (current-buffer) nil
+                                         "locate"))
+                (error "%s" (concat "Error when running "
+                                    agda-mode-prog)))
+              (buffer-string))
+          (file-error
+           (error "%s" (concat "Could not find " agda-mode-prog))))))
+
+    ;; Make sure that agda-mode<version-suffix> returns a valid file.
+    (unless (file-readable-p agda-mode-path)
+      (error "%s" (concat "Could not read " agda-mode-path)))
+
+    ;; Turn off the Agda mode.
+    (agda2-quit)
+
+    ;; Kill some buffers related to Agda.
+    (when (buffer-live-p agda2-info-buffer)
+      (kill-buffer agda2-info-buffer))
+    (when (and agda2-debug-buffer-name
+               (get-buffer agda2-debug-buffer-name))
+      (kill-buffer agda2-debug-buffer-name))
+
+    ;; Remove the Agda mode directory from the load path.
+    (setq load-path (delete agda2-directory load-path))
+
+    ;; Unload the Agda mode and its dependencies.
+    (unload-feature 'agda2-mode      'force)
+    (unload-feature 'agda2           'force)
+    (unload-feature 'eri             'force)
+    (unload-feature 'annotation      'force)
+    (unload-feature 'agda-input      'force)
+    (unload-feature 'agda2-highlight 'force)
+    (unload-feature 'agda2-abbrevs   'force)
+    (unload-feature 'agda2-queue     'force)
+
+    ;; Load the new version of Agda.
+    (load-file agda-mode-path)
+    (require 'agda2-mode)
+    (setq agda2-program-name (concat "agda" version-suffix))
+
+    ;; Restore the Agda mode's default hook (if any).
+    (when default-hook
+      (set-default 'agda2-mode-hook default-hook))
+
+    ;; Restart the Agda mode in all former Agda mode buffers.
+    (mapc (lambda (buf)
+            (with-current-buffer buf
+              (agda2-mode)))
+          agda-buffers)))
+
+(provide 'agda2-mode)
+;;; agda2-mode.el ends here
diff --git a/src/data/emacs-mode/agda2-queue.el b/src/data/emacs-mode/agda2-queue.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2-queue.el
@@ -0,0 +1,44 @@
+;;; agda2-queue.el --- Simple FIFO character queues.
+;; SPDX-License-Identifier: MIT License
+
+(defun agda2-queue-empty ()
+  "Creates a new empty FIFO character queue.
+Queues are represented as pairs. The car contains the queue. If
+the queue is empty, then the cdr contains the symbol nil, and
+otherwise it points to the queue's last cons-cell."
+  (cons nil nil))
+
+(defun agda2-queue-is-prefix-of (prefix queue)
+  "Returns a non-nil result iff the string PREFIX is a prefix of QUEUE.
+Linear in the length of PREFIX."
+  (let ((queue  (car queue))
+        (prefix (append prefix nil)))
+    (while (and (consp queue) (consp prefix)
+                (equal (car queue) (car prefix)))
+      (pop queue)
+      (pop prefix))
+    (null prefix)))
+
+(defun agda2-queue-enqueue (queue string)
+  "Adds the characters in STRING to the end of QUEUE.
+This function updates QUEUE destructively, and is linear in the
+length of STRING."
+  (let ((chars (append string nil)))
+    (when (consp chars)
+      (if (null (cdr queue))
+          (setcar queue chars)
+        (setcdr (cdr queue) chars))
+      (setcdr queue (last chars))))
+  queue)
+
+(defun agda2-queue-from-string (string)
+  "Creates a new FIFO containing the characters in STRING.
+Linear in the length of STRING."
+  (agda2-queue-enqueue (agda2-queue-empty) string))
+
+(defun agda2-queue-to-string (queue)
+  "Constructs a string containing all the characters in QUEUE.
+Linear in the length of QUEUE."
+  (concat "" (car queue)))
+
+(provide 'agda2-queue)
diff --git a/src/data/emacs-mode/agda2.el b/src/data/emacs-mode/agda2.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/agda2.el
@@ -0,0 +1,16 @@
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; Agda mode code which should run before the first Agda file is
+;; loaded
+;; SPDX-License-Identifier: MIT License
+
+(defvar agda2-directory (file-name-directory load-file-name)
+  "Path to the directory that contains agda2.el(c).")
+
+(add-to-list 'load-path (or agda2-directory (car load-path)))
+
+(autoload 'agda2-mode "agda2-mode"
+  "Major mode for editing Agda files (version ≥ 2)." t)
+(add-to-list 'auto-mode-alist '("\\.l?agda\\'" . agda2-mode))
+(modify-coding-system-alist 'file "\\.l?agda\\'" 'utf-8)
+
+(provide 'agda2)
diff --git a/src/data/emacs-mode/annotation.el b/src/data/emacs-mode/annotation.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/annotation.el
@@ -0,0 +1,301 @@
+;;; annotation.el --- Functions for annotating text with faces and help bubbles
+
+;; Version: 1.0
+
+;; SPDX-License-Identifier: MIT License
+;; URL: https://github.com/agda/agda
+;; Version: 1.0
+
+;;; Commentary:
+
+;; Note that this library enumerates buffer positions starting from 1,
+;; just like Emacs.
+
+(require 'cl-lib)
+
+(defvar annotation-bindings nil
+  "An association list mapping symbols to faces.")
+(make-variable-buffer-local 'annotation-bindings)
+
+(defvar annotation-goto-stack nil
+  "Positions from which `annotation-goto' was invoked.")
+
+(defun annotation-goto-indirect (link &optional other-window)
+  "Follow the `annotation-goto' hyperlink pointed to by LINK, if any.
+
+LINK should be a buffer position, or an event object (in which
+case the ending position is used).
+
+If the hyperlink exists and the jump is performed successfully,
+then `t' is returned, and otherwise `nil' (unless an error is
+raised).
+
+If OTHER-WINDOW is non-nil, then another window is used to
+display the target position."
+  (let (source-pos
+        source-window
+        source-buffer
+        source-file-name
+        target)
+    (cond ((eventp link)
+           (let ((pn (event-end link)))
+             (when (not (posn-area pn))
+               (setq source-pos (posn-point pn))
+               (setq source-window (posn-window pn))
+               (setq source-buffer (window-buffer source-window)))))
+          ((integerp link)
+           (setq source-pos link)
+           (setq source-window (selected-window))
+           (setq source-buffer (current-buffer)))
+          (t (error "Not an integer or event object: %S" link)))
+    (when (and source-pos source-buffer)
+      (with-current-buffer source-buffer
+        (setq target (get-text-property source-pos 'annotation-goto)))
+      (when target
+        (unless (equal source-window (selected-window))
+          (select-window source-window))
+        (annotation-goto-and-push source-buffer source-pos target
+                                  other-window)))))
+
+(defun annotation-go-back nil
+  "Go back to the previous position.
+The previous position in which `annotation-goto-and-push' was
+successfully invoked."
+  (when annotation-goto-stack
+    (let ((pos (pop annotation-goto-stack)))
+      (annotation-goto pos))))
+
+(defun annotation-goto-and-push (source-buffer source-pos filepos &optional other-window)
+  "Like `annotation-goto', but pushes a position when successful.
+The position consists of the file visited by SOURCE-BUFFER, and
+the position given by SOURCE-POS."
+  (let (source-file-name)
+    (with-current-buffer source-buffer
+      (setq source-file-name buffer-file-name))
+    (when (annotation-goto filepos other-window)
+      (unless (and (equal source-buffer (current-buffer))
+                   (eq source-pos (point)))
+        (push `(,source-file-name . ,source-pos)
+              annotation-goto-stack))
+      t)))
+
+(defun annotation-goto (filepos &optional other-window)
+  "Go to file position FILEPOS if the file is readable.
+FILEPOS should have the form (FILE . POS).  Return t if successful.
+
+If OTHER-WINDOW is non-nil, use another window to display the
+given position."
+  (when (consp filepos)
+    (let ((file (car filepos)))
+      (if (file-readable-p file)
+          (progn
+            (if other-window
+                (find-file-other-window file)
+              (find-file file))
+            (goto-char (cdr filepos))
+            t)
+        (error "File does not exist or is unreadable: %s." file)))))
+
+(defun annotation-merge-faces (start end faces)
+  "Helper procedure used by `annotation-annotate'.
+For each position in the range the FACES are merged
+with the current value of the annotation-faces text property, and
+both the face and the annotation-faces text properties are set to
+the resulting list of faces.
+
+Precondition: START and END must be numbers, and START must be
+less than END."
+  (cl-assert (condition-case nil (< start end) (error nil)))
+  (let ((pos start)
+        mid)
+    (while (< pos end)
+      (setq mid (next-single-property-change pos 'annotation-faces
+                                             nil end))
+      (let* ((old-faces (get-text-property pos 'annotation-faces))
+             (all-faces (cl-union old-faces faces)))
+        (mapc (lambda (prop) (put-text-property pos mid prop all-faces))
+              '(annotation-faces face))
+        (setq pos mid)))))
+
+(defun annotation-annotate
+    (start end anns &optional token-based info goto)
+  "Annotate text between START and END in the current buffer.
+
+Nothing happens if either START or END are out of bounds for the
+current (possibly narrowed) buffer, or END <= START.
+
+If ANNS is nil, then those text properties between START and END
+that have been set by this function are deleted. Otherwise the
+following happens.
+
+All the symbols in ANNS are looked up in `annotation-bindings',
+and the resulting list of faces is used to set the face text
+property. For each position in the range the faces are merged
+with the current value of the annotation-faces text property, and
+both the face and the annotation-faces text properties are set to
+the resulting list of faces.
+
+If TOKEN-BASED is non-nil, then the annotation-token-based
+property is set to t. This means that all text properties set by
+`annotation-annotate' in this range are interpreted as being
+token-based, including those set by previous calls to this
+procedure.
+
+If the string INFO is non-nil, the mouse-face
+property is set to highlight, and INFO is used as the help-echo
+string. If GOTO has the form (FILENAME . POSITION), then the
+mouse-face property is set to highlight, and the given
+filename/position will be used by `annotation-goto-indirect' when
+it is invoked with a position in the given range.
+
+Note that if a given attribute is defined by several faces, then
+the first face's setting takes precedence.
+
+All characters whose text properties get set also have the
+annotation-annotated property set to t, and
+annotation-annotations is set to a list with all the properties
+that have been set; this ensures that the text properties can
+later be removed (if the annotation-* properties are not tampered
+with)."
+  (when (and (<= (point-min) start)
+             (< start end)
+             (<= end (point-max)))
+    (if (null anns)
+        (annotation-remove-annotations nil start end)
+      (let ((faces (delq nil
+                         (mapcar (lambda (ann)
+                                   (cdr (assoc ann annotation-bindings)))
+                                 anns)))
+            (props nil))
+        (when faces
+          (annotation-merge-faces start end faces)
+          (add-to-list 'props 'face)
+          (add-to-list 'props 'annotation-faces))
+        (when token-based
+          (add-text-properties start end
+                               `(annotation-token-based t))
+          (add-to-list 'props 'annotation-token-based))
+        (when (consp goto)
+          (add-text-properties start end
+                               `(annotation-goto ,goto
+                                 mouse-face highlight))
+          (add-to-list 'props 'annotation-goto)
+          (add-to-list 'props 'mouse-face))
+        (when info
+          (add-text-properties start end
+                               `(mouse-face highlight help-echo ,info))
+          (add-to-list 'props 'mouse-face)
+          (add-to-list 'props 'help-echo))
+        (when props
+          (add-to-list 'props 'annotation-annotated)
+          (let ((pos start)
+                mid)
+            (while (< pos end)
+              (setq mid (next-single-property-change pos
+                           'annotation-annotations nil end))
+              (let* ((old-props (get-text-property pos 'annotation-annotations))
+                     (all-props (cl-union old-props props)))
+                (add-text-properties pos mid
+                   `(annotation-annotated t annotation-annotations ,all-props))
+                (setq pos mid)))))))))
+
+(defmacro annotation-preserve-mod-p-and-undo (&rest code)
+  "Run CODE preserving both the undo data and the modification bit.
+Modification hooks are also disabled."
+  (declare (debug (&rest form)))
+  (let ((modp (make-symbol "modp")))
+  `(let ((,modp (buffer-modified-p))
+         ;; Don't check if the file is being modified by some other process.
+         (buffer-file-name nil)
+         ;; Don't record those changes on the undo-log.
+         (buffer-undo-list t)
+         ;; Don't run modification hooks.
+         (inhibit-modification-hooks t))
+     (unwind-protect
+         (progn ,@code)
+       (restore-buffer-modified-p ,modp)))))
+
+(defun annotation-remove-annotations (&optional token-based start end)
+  "Remove text properties set by `annotation-annotate'.
+
+In the current buffer. If START and END are given, then
+properties are only removed between these positions. If
+TOKEN-BASED is non-nil, then only token-based properties are
+removed.
+
+This function preserves the file modification stamp of the
+current buffer, does not modify the undo list, and temporarily
+disables all modification hooks.
+
+Note: This function may fail if there is read-only text in the
+buffer."
+
+  ;; remove-text-properties fails for read-only text.
+
+  (annotation-preserve-mod-p-and-undo
+   (let ((tag (if token-based
+                  'annotation-token-based
+                'annotation-annotated))
+         (pos (or start (point-min)))
+         (end (or end (point-max)))
+         pos2)
+     (while pos
+       (let ((props (get-text-property pos 'annotation-annotations)))
+         (setq pos2 (next-single-property-change pos tag nil end))
+         (when (and props
+                    (or (not token-based)
+                        (member 'annotation-token-based props)))
+           (remove-text-properties pos (or pos2 (point-max))
+              (cl-mapcan (lambda (prop) (list prop nil))
+                      (cons 'annotation-annotations props)))))
+       (setq pos (unless (or (not pos2) (>= pos2 end)) pos2))))))
+
+(defun annotation-load (goto-help remove &rest cmds)
+  "Apply highlighting annotations in CMDS in the current buffer.
+
+The argument CMDS should be a list of lists (start end anns
+&optional info goto). Text between start and end will be
+annotated with the annotations in the list anns (using
+`annotation-annotate'). If info and/or goto are present they will
+be used as the corresponding arguments to `annotation-annotate'.
+
+If INFO is nil in a call to `annotation-annotate', and the GOTO
+argument is a cons-cell, then the INFO argument is set to
+GOTO-HELP. The intention is that the default help text should
+inform the user about the \"goto\" facility.
+
+If REMOVE is nil, then old syntax highlighting information is not
+removed. Otherwise all token-based syntax highlighting is
+removed. In order to reduce the risk of flicker this highlighting
+is removed step by step, in conjunction with the addition of new
+highlighting. (This process assumes that CMDS is ordered by the
+positions of the annotations. If it isn't, then the highlighting
+is still applied correctly, but perhaps with more flicker.)
+
+This function preserves the file modification stamp of the
+current buffer, does not modify the undo list, and temporarily
+disables all modification hooks.
+
+Note: This function may fail if there is read-only text in the
+buffer."
+  (annotation-preserve-mod-p-and-undo
+    (when (listp cmds)
+      (let ((pos (point-min)))
+        (dolist (cmd cmds)
+          (cl-destructuring-bind
+              (start end anns &optional token-based info goto) cmd
+            (let ((info (if (and (not info) (consp goto))
+                            goto-help
+                          info)))
+              (when remove
+                (annotation-remove-annotations
+                 'token-based pos end)
+                (setq pos end))
+              (annotation-annotate
+               start end anns token-based info goto))))
+        (when remove
+          (annotation-remove-annotations
+           'token-based pos (point-max)))))))
+
+(provide 'annotation)
+;;; annotation.el ends here
diff --git a/src/data/emacs-mode/eri.el b/src/data/emacs-mode/eri.el
new file mode 100644
--- /dev/null
+++ b/src/data/emacs-mode/eri.el
@@ -0,0 +1,212 @@
+;;; eri.el --- Enhanced relative indentation (eri)
+
+;; SPDX-License-Identifier: MIT License
+;; URL: https://github.com/agda/agda
+;; Version: 1.0
+
+;;; Commentary:
+
+;; Cycle between indentation points with enhanced relative indentation.
+
+;;; Code:
+
+(require 'cl-lib)
+
+(defun eri-current-line-length nil
+  "Calculate length of current line."
+  (- (line-end-position) (line-beginning-position)))
+
+(defun eri-current-line-empty nil
+  "Return non-nil if the current line is empty (not counting white space)."
+  (equal (current-indentation)
+         (eri-current-line-length)))
+
+(defun eri-maximum (xs)
+  "Calculate maximum element in XS.
+Returns nil if the list is empty."
+  (if xs (apply 'max xs)))
+
+(defun eri-take (n xs)
+  "Return the first N elements of XS."
+  (butlast xs (- (length xs) n)))
+
+(defun eri-split (x xs)
+  "Return a pair of lists (XS1 . XS2).
+If XS is sorted, then XS = (append XS1 XS2), and all elements in
+XS1 are <= X, whereas all elements in XS2 are > X."
+  (let* ((pos (or (cl-position-if (lambda (y) (> y x)) xs) (length xs)))
+         (xs1 (eri-take pos xs))
+         (xs2 (nthcdr pos xs)))
+    (cons xs1 xs2)))
+
+(defun eri-calculate-indentation-points-on-line (max)
+  "Calculate indentation points on current line.
+Only points left of column number MAX are included. If MAX is
+nil, then all points are included. Points are returned in
+ascending order.
+
+Example (positions marked with ^ are returned):
+
+  f x y = g 3 (Just y) 5 4
+  ^ ^ ^ ^ ^ ^ ^     ^  |
+                       |
+                       MAX"
+  (let ((result))
+    (save-excursion
+      (save-restriction
+        (beginning-of-line)
+        ; To make \\` work in the regexp below:
+        (narrow-to-region (line-beginning-position) (line-end-position))
+        (while
+            (progn
+              (let ((pos (and (search-forward-regexp
+                               "\\(?:\\s-\\|\\`\\)\\(\\S-\\)" nil t)
+                              (match-beginning 1))))
+                (when (not (null pos))
+                  (let ((pos1 (- pos (line-beginning-position))))
+                    (when (or (null max) (< pos1 max))
+                      (add-to-list 'result pos1))))
+                (and pos
+                     (< (point) (line-end-position))
+                     (or (null max) (< (current-column) max))))))
+        (nreverse result) ; Destructive operation.
+        ))))
+
+(defun eri-new-indentation-points ()
+  "Calculate new indentation points.
+Returns a singleton list containing the column number two steps
+in from the indentation of the first non-empty line (white space
+excluded) above the current line. If there is no such line,
+then the empty list is returned."
+  (let ((start (line-beginning-position)))
+    (save-excursion
+      ; Find a non-empty line above the current one, if any.
+      (while
+          (progn
+            (forward-line -1)
+            (not (or (bobp)
+                     (not (eri-current-line-empty))))))
+      (if (or (equal (point) start)
+              (eri-current-line-empty))
+          nil
+        (list (+ 2 (current-indentation)))))))
+
+(defun eri-calculate-indentation-points (reverse)
+  "Calculate points used to indent the current line.
+The points are given in reverse order if REVERSE is non-nil. See
+`eri-indent' for a description of how the indentation points are
+calculated; note that the current indentation is not included in
+the returned list."
+  ;; First find a bunch of indentations used above the current line.
+  (let ((points)
+        (max)
+        (start (line-beginning-position)))
+    (save-excursion
+      (while
+          (progn
+            (forward-line -1)
+            ; Skip the line we started from and lines with nothing but
+            ; white space.
+            (unless (or (equal (point) start)
+                        (eri-current-line-empty))
+              (setq points
+                    (append
+                     (eri-calculate-indentation-points-on-line max)
+                     points))
+              (setq max (car points)))
+            ;; Stop after hitting the beginning of the buffer or a
+            ;; non-empty, non-indented line.
+            (not (or (bobp)
+                     (and (equal (current-indentation) 0)
+                          (> (eri-current-line-length) 0)))))))
+    ;; Add new indentation points, but remove the current indentation.
+    ;; Sort the indentations. Rearrange the points so that the next
+    ;; point is the one after the current one. Reverse if necessary.
+    ;;
+    ;; Note: sort and nreverse are destructive.
+    (let* ((ps0 (remove (current-indentation)
+                        (append (eri-new-indentation-points) points)))
+           (ps1 (eri-split (current-indentation) (sort ps0 '<)))
+           (ps2 (append (cdr ps1) (car ps1))))
+      (if reverse
+          (nreverse ps2)
+        ps2))))
+
+(defun eri-indent (&optional reverse)
+  "Cycle between some possible indentation points.
+With prefix argument REVERSE, cycle in reverse order.
+
+Assume that a file contains the following lines of code, with
+point on the line with three dots:
+
+frob = loooooooooooooooooooooooooong identifier
+foo = f a b
+  where
+    f (Foo x) y = let bar = x
+                      baz = 3 + 5
+
+...
+
+^ ^ ^ ^    ^  ^ ^ ^   ^ * ^ ^ ^ ^
+
+Then the ^'s and the * mark the indentation points that this
+function cycles through. The indentation points are selected as
+follows:
+
+  * All lines before the current one, up to and including the
+    first non-indented line (or the beginning of the buffer) are
+    considered.
+
+      foo = f a b
+        where
+          f (Foo x) y = let bar = x
+                            baz = 3 + 5
+
+  * On these lines, erase all characters that stand to the right
+    of some non-white space character on a lower line.
+
+      foo
+        whe
+          f (Foo x) y = let b
+                            baz = 3 + 5
+
+  * Also erase all characters not immediately preceded by white
+    space.
+
+      f
+        w
+          f (    x  y = l   b
+                            b   = 3 + 5
+
+  * The columns of all remaining characters are indentation
+    points.
+
+      f w f (    x  y = l   b   = 3 + 5
+      ^ ^ ^ ^    ^  ^ ^ ^   ^   ^ ^ ^ ^
+
+  * A new indentation point is also added, two steps in from the
+    indentation of the first non-empty line (white space
+    excluded) above the current line (if there is such a line).
+
+      f w f (    x  y = l   b   = 3 + 5
+      ^ ^ ^ ^    ^  ^ ^ ^   ^ * ^ ^ ^ ^"
+  (interactive "P")
+  (let* ((points (eri-calculate-indentation-points reverse))
+         (remaining-points (cdr (member (current-indentation) points)))
+         (indentation (if remaining-points
+                          (car remaining-points)
+                        (car points))))
+    (when indentation
+      (save-excursion (indent-line-to indentation))
+      (if (< (current-column) indentation)
+          (indent-line-to indentation)))))
+
+(defun eri-indent-reverse nil
+  "Cycle between some possible indentation points (in reverse order).
+See `eri-indent' for a description of how the indentation points
+are calculated."
+  (interactive)
+  (eri-indent t))
+
+(provide 'eri)
+;;; eri.el ends here
diff --git a/src/data/html/Agda.css b/src/data/html/Agda.css
new file mode 100644
--- /dev/null
+++ b/src/data/html/Agda.css
@@ -0,0 +1,41 @@
+/* Aspects. */
+.Agda .Comment       { color: #B22222 }
+.Agda .Background    {}
+.Agda .Markup        { color: #000000 }
+.Agda .Keyword       { color: #CD6600 }
+.Agda .String        { color: #B22222 }
+.Agda .Number        { color: #A020F0 }
+.Agda .Symbol        { color: #404040 }
+.Agda .PrimitiveType { color: #0000CD }
+.Agda .Pragma        { color: black   }
+.Agda .Operator      {}
+.Agda .Hole          { background: #B4EEB4 }
+
+/* NameKinds. */
+.Agda .Bound                  { color: black   }
+.Agda .Generalizable          { color: black   }
+.Agda .InductiveConstructor   { color: #008B00 }
+.Agda .CoinductiveConstructor { color: #8B7500 }
+.Agda .Datatype               { color: #0000CD }
+.Agda .Field                  { color: #EE1289 }
+.Agda .Function               { color: #0000CD }
+.Agda .Module                 { color: #A020F0 }
+.Agda .Postulate              { color: #0000CD }
+.Agda .Primitive              { color: #0000CD }
+.Agda .Record                 { color: #0000CD }
+
+/* OtherAspects. */
+.Agda .DottedPattern        {}
+.Agda .UnsolvedMeta         { color: black; background: yellow         }
+.Agda .UnsolvedConstraint   { color: black; background: yellow         }
+.Agda .TerminationProblem   { color: black; background: #FFA07A        }
+.Agda .IncompletePattern    { color: black; background: #F5DEB3        }
+.Agda .Error                { color: red;   text-decoration: underline }
+.Agda .TypeChecks           { color: black; background: #ADD8E6        }
+.Agda .Deadcode             { color: black; background: #808080        }
+.Agda .ShadowingInTelescope { color: black; background: #808080        }
+
+/* Standard attributes. */
+.Agda a { text-decoration: none }
+.Agda a[href]:hover { background-color: #B4EEB4 }
+.Agda [href].hover-highlight { background-color: #B4EEB4; }
diff --git a/src/data/html/highlight-hover.js b/src/data/html/highlight-hover.js
new file mode 100644
--- /dev/null
+++ b/src/data/html/highlight-hover.js
@@ -0,0 +1,35 @@
+// Copyright 2023, Andreas Abel.
+// Falls under the Agda license at https://github.com/agda/agda/blob/master/LICENSE
+
+// When we hover over an Agda identifier, we highlight all occurrences of this identifier on the page.
+// To this end, we create a map from identifier to all of its occurrences in the beginning.
+
+// A dictionary from hrefs to 'a'-elements that have this href.
+const dict = new Map();
+
+window.onload = function () {
+
+  // Get all 'a' tags with an 'href' attribute.
+  // We call those "objects".
+  const objs  = document.querySelectorAll('a[href]');
+
+  // Build a dictionary mapping a href to a set of objects that have this href.
+  for (const obj of objs) {
+    const key = obj.href;
+    const set = dict.get(key) ?? new Set();
+    set.add(obj);
+    dict.set(key, set);
+  }
+
+  // Install 'onmouseover' and 'onmouseout' event handlers for all objects.
+  for (const obj of objs) {
+    // 'onmouseover' for an object adds attribute 'hover-highlight' to all objects with the same href.
+    obj.onmouseover = function () {
+      for (const o of dict.get(this.href)) { o.classList.add('hover-highlight'); }
+    }
+    // 'onmouseover' removes the added 'hover-highlight' attributes again.
+    obj.onmouseout = function () {
+      for (const o of dict.get(this.href)) { o.classList.remove('hover-highlight'); }
+    }
+  }
+};
diff --git a/src/data/latex/agda.sty b/src/data/latex/agda.sty
new file mode 100644
--- /dev/null
+++ b/src/data/latex/agda.sty
@@ -0,0 +1,722 @@
+% ----------------------------------------------------------------------
+% Some useful commands when doing highlighting of Agda code in LaTeX.
+% ----------------------------------------------------------------------
+
+% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+% !!! NOTE: when you make changes to this file, bump the date. !!!
+% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+\ProvidesPackage{agda}
+  [2021/07/14 version 2.6.4.2 Formatting LaTeX generated by Agda]
+
+\RequirePackage{ifxetex, ifluatex, xifthen, xcolor, polytable, etoolbox,
+                calc, environ, xparse, xkeyval}
+
+% https://tex.stackexchange.com/questions/47576/combining-ifxetex-and-ifluatex-with-the-logical-or-operation
+\newif\ifxetexorluatex
+\ifxetex
+  \xetexorluatextrue
+\else
+  \ifluatex
+    \xetexorluatextrue
+  \else
+    \xetexorluatexfalse
+  \fi
+\fi
+
+% ----------------------------------------------------------------------
+% Options
+
+\DeclareOption{bw}   {\newcommand{\AgdaColourScheme}{bw}}
+\DeclareOption{conor}{\newcommand{\AgdaColourScheme}{conor}}
+
+\newif\if@AgdaEnableReferences\@AgdaEnableReferencesfalse
+\DeclareOption{references}{
+  \@AgdaEnableReferencestrue
+}
+
+\newif\if@AgdaEnableLinks\@AgdaEnableLinksfalse
+\DeclareOption{links}{
+  \@AgdaEnableLinkstrue
+}
+
+\ProcessOptions\relax
+
+% ----------------------------------------------------------------------
+% Font setup
+
+\tracinglostchars=2 % If the font is missing some symbol, then say
+                    % so in the compilation output.
+
+% ----------------------------------------------------------------------
+% Colour schemes.
+
+\providecommand{\AgdaColourScheme}{standard}
+
+% ----------------------------------------------------------------------
+% References to code (needs additional post-processing of tex files to
+% work, see wiki for details).
+
+\if@AgdaEnableReferences
+  \RequirePackage{catchfilebetweentags, xstring}
+  \newcommand{\AgdaRef}[2][]{%
+    \StrSubstitute{#2}{\_}{AgdaUnderscore}[\tmp]%
+    \ifthenelse{\isempty{#1}}%
+               {\ExecuteMetaData{AgdaTag-\tmp}}%
+               {\ExecuteMetaData{#1}{AgdaTag-\tmp}}
+  }
+\fi
+
+\providecommand{\AgdaRef}[2][]{#2}
+
+% ----------------------------------------------------------------------
+% Links (only done if the option is passed and the user has loaded the
+% hyperref package).
+
+\if@AgdaEnableLinks
+  \@ifpackageloaded{hyperref}{
+
+    % List that holds added targets.
+    \newcommand{\AgdaList}[0]{}
+
+    \newtoggle{AgdaIsElem}
+    \newcounter{AgdaIndex}
+    \newcommand{\AgdaLookup}[3]{%
+      \togglefalse{AgdaIsElem}%
+      \setcounter{AgdaIndex}{0}%
+      \renewcommand*{\do}[1]{%
+      \ifstrequal{#1}{##1}%
+        {\toggletrue{AgdaIsElem}\listbreak}%
+        {\stepcounter{AgdaIndex}}}%
+      \dolistloop{\AgdaList}%
+      \iftoggle{AgdaIsElem}{#2}{#3}%
+    }
+
+    \newcommand*{\AgdaTargetHelper}[1]{%
+      \AgdaLookup{#1}%
+        {\PackageError{agda}{``#1'' used as target more than once}%
+                            {Overloaded identifiers and links do not%
+                             work well, consider using unique%
+                             \MessageBreak identifiers instead.}%
+        }%
+        {\listadd{\AgdaList}{#1}%
+         \hypertarget{Agda\theAgdaIndex}{}%
+        }%
+    }
+
+    \newcommand{\AgdaTarget}[1]{\forcsvlist{\AgdaTargetHelper}{#1}}
+
+    \newcommand{\AgdaLink}[1]{%
+      \AgdaLookup{#1}%
+        {\hyperlink{Agda\theAgdaIndex}{#1}}%
+        {#1}%
+    }
+  }{\PackageError{agda}{Load the hyperref package before the agda package}{}}
+\fi
+
+\providecommand{\AgdaTarget}[1]{}
+\providecommand{\AgdaLink}[1]{#1}
+
+% ----------------------------------------------------------------------
+% Font styles.
+
+\newcommand{\AgdaFontStyle}[1]{\textsf{#1}}
+\ifthenelse{\equal{\AgdaColourScheme}{bw}}{
+    \newcommand{\AgdaKeywordFontStyle}[1]{\underline{#1}}
+}{
+    \newcommand{\AgdaKeywordFontStyle}[1]{\textsf{#1}}
+}
+\newcommand{\AgdaStringFontStyle}[1]{\texttt{#1}}
+\newcommand{\AgdaCommentFontStyle}[1]{\texttt{#1}}
+\newcommand{\AgdaBoundFontStyle}[1]{\textit{#1}}
+
+% ----------------------------------------------------------------------
+% Colours.
+
+% ----------------------------------
+% The black and white colour scheme.
+\ifthenelse{\equal{\AgdaColourScheme}{bw}}{
+
+    % Aspect colours.
+    \definecolor{AgdaComment}      {HTML}{000000}
+    \definecolor{AgdaPragma}       {HTML}{000000}
+    \definecolor{AgdaKeyword}      {HTML}{000000}
+    \definecolor{AgdaString}       {HTML}{000000}
+    \definecolor{AgdaNumber}       {HTML}{000000}
+    \definecolor{AgdaSymbol}       {HTML}{000000}
+    \definecolor{AgdaPrimitiveType}{HTML}{000000}
+
+    % NameKind colours.
+    \definecolor{AgdaBound}                 {HTML}{000000}
+    \definecolor{AgdaGeneralizable}         {HTML}{000000}
+    \definecolor{AgdaInductiveConstructor}  {HTML}{000000}
+    \definecolor{AgdaCoinductiveConstructor}{HTML}{000000}
+    \definecolor{AgdaDatatype}              {HTML}{000000}
+    \definecolor{AgdaField}                 {HTML}{000000}
+    \definecolor{AgdaFunction}              {HTML}{000000}
+    \definecolor{AgdaMacro}                 {HTML}{000000}
+    \definecolor{AgdaModule}                {HTML}{000000}
+    \definecolor{AgdaPostulate}             {HTML}{000000}
+    \definecolor{AgdaPrimitive}             {HTML}{000000}
+    \definecolor{AgdaRecord}                {HTML}{000000}
+    \definecolor{AgdaArgument}              {HTML}{000000}
+
+    % Other aspect colours.
+    \definecolor{AgdaDottedPattern}     {HTML}{000000}
+    \definecolor{AgdaUnsolvedMeta}      {HTML}{D3D3D3}
+    \definecolor{AgdaUnsolvedConstraint}{HTML}{D3D3D3}
+    \definecolor{AgdaTerminationProblem}{HTML}{BEBEBE}
+    \definecolor{AgdaIncompletePattern} {HTML}{D3D3D3}
+    \definecolor{AgdaErrorWarning}      {HTML}{BEBEBE}
+    \definecolor{AgdaError}             {HTML}{696969}
+
+    % Misc.
+    \definecolor{AgdaHole}              {HTML}{BEBEBE}
+
+% ----------------------------------
+% Conor McBride's colour scheme.
+}{ \ifthenelse{\equal{\AgdaColourScheme}{conor}}{
+
+    % Aspect colours.
+    \definecolor{AgdaComment}      {HTML}{B22222}
+    \definecolor{AgdaPragma}       {HTML}{000000}
+    \definecolor{AgdaKeyword}      {HTML}{000000}
+    \definecolor{AgdaString}       {HTML}{000000}
+    \definecolor{AgdaNumber}       {HTML}{000000}
+    \definecolor{AgdaSymbol}       {HTML}{000000}
+    \definecolor{AgdaPrimitiveType}{HTML}{0000CD}
+
+    % NameKind colours.
+    \definecolor{AgdaBound}                 {HTML}{A020F0}
+    \definecolor{AgdaGeneralizable}         {HTML}{A020F0}
+    \definecolor{AgdaInductiveConstructor}  {HTML}{8B0000}
+    \definecolor{AgdaCoinductiveConstructor}{HTML}{8B0000}
+    \definecolor{AgdaDatatype}              {HTML}{0000CD}
+    \definecolor{AgdaField}                 {HTML}{8B0000}
+    \definecolor{AgdaFunction}              {HTML}{006400}
+    \definecolor{AgdaMacro}                 {HTML}{006400}
+    \definecolor{AgdaModule}                {HTML}{006400}
+    \definecolor{AgdaPostulate}             {HTML}{006400}
+    \definecolor{AgdaPrimitive}             {HTML}{006400}
+    \definecolor{AgdaRecord}                {HTML}{0000CD}
+    \definecolor{AgdaArgument}              {HTML}{404040}
+
+    % Other aspect colours.
+    \definecolor{AgdaDottedPattern}     {HTML}{000000}
+    \definecolor{AgdaUnsolvedMeta}      {HTML}{FFD700}
+    \definecolor{AgdaUnsolvedConstraint}{HTML}{FFD700}
+    \definecolor{AgdaTerminationProblem}{HTML}{FF0000}
+    \definecolor{AgdaIncompletePattern} {HTML}{A020F0}
+    \definecolor{AgdaErrorWarning}      {HTML}{FF0000}
+    \definecolor{AgdaError}             {HTML}{F4A460}
+
+    % Misc.
+    \definecolor{AgdaHole}              {HTML}{9DFF9D}
+
+% ----------------------------------
+% The standard colour scheme.
+}{
+    % Aspect colours.
+    \definecolor{AgdaComment}      {HTML}{B22222}
+    \definecolor{AgdaPragma}       {HTML}{000000}
+    \definecolor{AgdaKeyword}      {HTML}{CD6600}
+    \definecolor{AgdaString}       {HTML}{B22222}
+    \definecolor{AgdaNumber}       {HTML}{A020F0}
+    \definecolor{AgdaSymbol}       {HTML}{404040}
+    \definecolor{AgdaPrimitiveType}{HTML}{0000CD}
+
+    % NameKind colours.
+    \definecolor{AgdaBound}                 {HTML}{000000}
+    \definecolor{AgdaGeneralizable}         {HTML}{000000}
+    \definecolor{AgdaInductiveConstructor}  {HTML}{008B00}
+    \definecolor{AgdaCoinductiveConstructor}{HTML}{8B7500}
+    \definecolor{AgdaDatatype}              {HTML}{0000CD}
+    \definecolor{AgdaField}                 {HTML}{EE1289}
+    \definecolor{AgdaFunction}              {HTML}{0000CD}
+    \definecolor{AgdaMacro}                 {HTML}{458B74}
+    \definecolor{AgdaModule}                {HTML}{A020F0}
+    \definecolor{AgdaPostulate}             {HTML}{0000CD}
+    \definecolor{AgdaPrimitive}             {HTML}{0000CD}
+    \definecolor{AgdaRecord}                {HTML}{0000CD}
+    \definecolor{AgdaArgument}              {HTML}{404040}
+
+    % Other aspect colours.
+    \definecolor{AgdaDottedPattern}     {HTML}{000000}
+    \definecolor{AgdaUnsolvedMeta}      {HTML}{FFFF00}
+    \definecolor{AgdaUnsolvedConstraint}{HTML}{FFFF00}
+    \definecolor{AgdaTerminationProblem}{HTML}{FFA07A}
+    \definecolor{AgdaIncompletePattern} {HTML}{F5DEB3}
+    \definecolor{AgdaErrorWarning}      {HTML}{FFA07A}
+    \definecolor{AgdaError}             {HTML}{FF0000}
+
+    % Misc.
+    \definecolor{AgdaHole}              {HTML}{9DFF9D}
+}}
+
+% ----------------------------------------------------------------------
+% Commands.
+
+\newcommand{\AgdaNoSpaceMath}[1]
+    {\begingroup\thickmuskip=0mu\medmuskip=0mu#1\endgroup}
+
+% Aspect commands.
+\newcommand{\AgdaComment}     [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaComment}{\AgdaCommentFontStyle{#1}}}}
+\newcommand{\AgdaPragma}      [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaPragma}{\AgdaCommentFontStyle{#1}}}}
+\newcommand{\AgdaKeyword}     [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaKeyword}{\AgdaKeywordFontStyle{#1}}}}
+\newcommand{\AgdaString}      [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaString}{\AgdaStringFontStyle{#1}}}}
+\newcommand{\AgdaNumber}      [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaNumber}{\AgdaFontStyle{#1}}}}
+\newcommand{\AgdaSymbol}      [1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaSymbol}{\AgdaFontStyle{#1}}}}
+\newcommand{\AgdaPrimitiveType}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaPrimitiveType}{\AgdaFontStyle{#1}}}}
+%% Andreas, 2021-07-14, issue #5471
+%% To make italics correction \/ work, the font-style modifier
+%% needs to be inside, in particular inside the \textcolor modifier,
+%% as the \textcolor{} wrapping around something hides its content
+%% to the logic that resolves \/ into a space or not.
+
+% Note that, in code generated by the LaTeX backend, \AgdaOperator is
+% always applied to a NameKind command.
+\newcommand{\AgdaOperator}    [1]{#1}
+
+% NameKind commands.
+
+% The user can control the typesetting of (certain) individual tokens
+% by redefining the following command. The first argument is the token
+% and the second argument the thing to be typeset (sometimes just the
+% token, sometimes \AgdaLink{<the token>}). Example:
+%
+%   \usepackage{ifthen}
+%
+%   % Insert extra space before some tokens.
+%   \DeclareRobustCommand{\AgdaFormat}[2]{%
+%     \ifthenelse{
+%       \equal{#1}{≡⟨} \OR
+%       \equal{#1}{≡⟨⟩} \OR
+%       \equal{#1}{∎}
+%     }{\ }{}#2}
+%
+% Note the use of \DeclareRobustCommand.
+
+\newcommand{\AgdaFormat}[2]{#2}
+
+\newcommand{\AgdaBound}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaBound}{\AgdaBoundFontStyle{\AgdaFormat{#1}{#1}}}}}
+\newcommand{\AgdaGeneralizable}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaGeneralizable}{\AgdaBoundFontStyle{\AgdaFormat{#1}{#1}}}}}
+\newcommand{\AgdaInductiveConstructor}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaInductiveConstructor}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaCoinductiveConstructor}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaCoinductiveConstructor}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaDatatype}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaDatatype}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaField}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaField}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaFunction}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaFunction}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaMacro}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaMacro}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaModule}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaModule}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaPostulate}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaPostulate}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaPrimitive}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaPrimitive}{\AgdaFontStyle{\AgdaFormat{#1}{#1}}}}}
+\newcommand{\AgdaRecord}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaRecord}{\AgdaFontStyle{\AgdaFormat{#1}{\AgdaLink{#1}}}}}}
+\newcommand{\AgdaArgument}[1]
+    {\AgdaNoSpaceMath{\textcolor{AgdaArgument}{\AgdaBoundFontStyle{\AgdaFormat{#1}{#1}}}}}
+
+% Other aspect commands.
+\newcommand{\AgdaFixityOp}          [1]{\AgdaNoSpaceMath{$#1$}}
+\newcommand{\AgdaDottedPattern}     [1]{\textcolor{AgdaDottedPattern}{#1}}
+\newcommand{\AgdaUnsolvedMeta}      [1]
+    {\AgdaFontStyle{\colorbox{AgdaUnsolvedMeta}{#1}}}
+\newcommand{\AgdaUnsolvedConstraint}[1]
+    {\AgdaFontStyle{\colorbox{AgdaUnsolvedConstraint}{#1}}}
+\newcommand{\AgdaTerminationProblem}[1]
+    {\AgdaFontStyle{\colorbox{AgdaTerminationProblem}{#1}}}
+\newcommand{\AgdaIncompletePattern} [1]{\colorbox{AgdaIncompletePattern}{#1}}
+\newcommand{\AgdaErrorWarning}      [1]{\colorbox{AgdaErrorWarning}{#1}}
+\newcommand{\AgdaError}             [1]
+    {\textcolor{AgdaError}{\AgdaFontStyle{\underline{#1}}}}
+\newcommand{\AgdaCatchallClause}    [1]{#1} % feel free to change this
+
+% Used to hide code from LaTeX.
+%
+% Note that this macro has been deprecated in favour of giving the
+% hide argument to the code environment.
+\long\def\AgdaHide#1{\ignorespaces}
+
+% Misc.
+\newcommand{\AgdaHole}[1]{\colorbox{AgdaHole}{#1}}
+
+% ----------------------------------------------------------------------
+% The code environment.
+
+\newcommand{\AgdaCodeStyle}{}
+% \newcommand{\AgdaCodeStyle}{\tiny}
+
+\ifdefined\mathindent
+  {}
+\else
+  \newdimen\mathindent\mathindent\leftmargini
+\fi
+
+% Adds the given amount of vertical space and starts a new line.
+%
+% The implementation comes from lhs2TeX's polycode.fmt, written by
+% Andres Löh.
+\newcommand{\Agda@NewlineWithVerticalSpace}[1]{%
+  {\parskip=0pt\parindent=0pt\par\vskip #1\noindent}}
+
+% Should there be space around code?
+\newboolean{Agda@SpaceAroundCode}
+
+% Use this command to avoid extra space around code blocks.
+\newcommand{\AgdaNoSpaceAroundCode}{%
+  \setboolean{Agda@SpaceAroundCode}{false}}
+
+% Use this command to include extra space around code blocks.
+\newcommand{\AgdaSpaceAroundCode}{%
+  \setboolean{Agda@SpaceAroundCode}{true}}
+
+% By default space is inserted around code blocks.
+\AgdaSpaceAroundCode{}
+
+% Sometimes one might want to break up a code block into multiple
+% pieces, but keep code in different blocks aligned with respect to
+% each other. Then one can use the AgdaAlign environment. Example
+% usage:
+%
+%   \begin{AgdaAlign}
+%   \begin{code}
+%     code
+%       code  (more code)
+%   \end{code}
+%   Explanation...
+%   \begin{code}
+%     aligned with "code"
+%       code  (aligned with (more code))
+%   \end{code}
+%   \end{AgdaAlign}
+%
+% Note that AgdaAlign environments should not be nested.
+%
+% Sometimes one might also want to hide code in the middle of a code
+% block. This can be accomplished in the following way:
+%
+%   \begin{AgdaAlign}
+%   \begin{code}
+%     visible
+%   \end{code}
+%   \begin{code}[hide]
+%     hidden
+%   \end{code}
+%   \begin{code}
+%     visible
+%   \end{code}
+%   \end{AgdaAlign}
+%
+% However, the result may be ugly: extra space is perhaps inserted
+% around the code blocks.
+%
+% The AgdaSuppressSpace environment ensures that extra space is only
+% inserted before the first code block, and after the last one (but
+% not if \AgdaNoSpaceAroundCode{} is used). Example usage:
+%
+%   \begin{AgdaAlign}
+%   \begin{code}
+%     code
+%       more code
+%   \end{code}
+%   Explanation...
+%   \begin{AgdaSuppressSpace}
+%   \begin{code}
+%     aligned with "code"
+%       aligned with "more code"
+%   \end{code}
+%   \begin{code}[hide]
+%     hidden code
+%   \end{code}
+%   \begin{code}
+%       also aligned with "more code"
+%   \end{code}
+%   \end{AgdaSuppressSpace}
+%   \end{AgdaAlign}
+%
+% Note that AgdaSuppressSpace environments should not be nested.
+%
+% There is also a combined environment, AgdaMultiCode, that combines
+% the effects of AgdaAlign and AgdaSuppressSpace.
+
+% The number of the current/next code block (excluding hidden ones).
+\newcounter{Agda@Current}
+\setcounter{Agda@Current}{0}
+
+% The number of the previous code block (excluding hidden ones), used
+% locally in \Agda@SuppressEnd.
+\newcounter{Agda@Previous}
+
+% Is AgdaAlign active?
+\newboolean{Agda@Align}
+\setboolean{Agda@Align}{false}
+
+% The number of the first code block (if any) in a given AgdaAlign
+% environment.
+\newcounter{Agda@AlignStart}
+
+\newcommand{\Agda@AlignStart}{%
+  \ifthenelse{\boolean{Agda@Align}}{%
+    \PackageError{agda}{Nested AgdaAlign environments}{%
+      AgdaAlign and AgdaMultiCode environments must not be
+      nested.}}{%
+    \setboolean{Agda@Align}{true}%
+    \setcounter{Agda@AlignStart}{\value{Agda@Current}}}}
+
+\newcommand{\Agda@AlignEnd}{\setboolean{Agda@Align}{false}}
+
+\newenvironment{AgdaAlign}{%
+  \Agda@AlignStart{}}{%
+  \Agda@AlignEnd{}%
+  \ignorespacesafterend}
+
+% Is AgdaSuppressSpace active?
+\newboolean{Agda@Suppress}
+\setboolean{Agda@Suppress}{false}
+
+% The number of the first code block (if any) in a given
+% AgdaSuppressSpace environment.
+\newcounter{Agda@SuppressStart}
+
+% Does a "do not suppress space after" label exist for the current
+% code block? (This boolean is used locally in the code environment's
+% implementation.)
+\newboolean{Agda@DoNotSuppressSpaceAfter}
+
+\newcommand{\Agda@SuppressStart}{%
+  \ifthenelse{\boolean{Agda@Suppress}}{%
+    \PackageError{agda}{Nested AgdaSuppressSpace environments}{%
+      AgdaSuppressSpace and AgdaMultiCode environments must not be
+      nested.}}{%
+    \setboolean{Agda@Suppress}{true}%
+    \setcounter{Agda@SuppressStart}{\value{Agda@Current}}}}
+
+% Marks the given code block as one that space should not be
+% suppressed after (if AgdaSpaceAroundCode and AgdaSuppressSpace are
+% both active).
+\newcommand{\Agda@DoNotSuppressSpaceAfter}[1]{%
+  % The use of labels is intended to ensure that LaTeX will provide a
+  % warning if the document needs to be recompiled.
+  \label{Agda@DoNotSuppressSpaceAfter@#1}}
+
+\newcommand{\Agda@SuppressEnd}{%
+  \ifthenelse{\value{Agda@SuppressStart} = \value{Agda@Current}}{}{%
+    % Mark the previous code block in the .aux file.
+    \setcounter{Agda@Previous}{\theAgda@Current-1}%
+    \immediate\write\@auxout{%
+      \noexpand\Agda@DoNotSuppressSpaceAfter{\theAgda@Previous}}}%
+  \setboolean{Agda@Suppress}{false}}
+
+\newenvironment{AgdaSuppressSpace}{%
+  \Agda@SuppressStart{}}{%
+  \Agda@SuppressEnd{}%
+  \ignorespacesafterend}
+
+\newenvironment{AgdaMultiCode}{%
+  \Agda@AlignStart{}%
+  \Agda@SuppressStart{}}{%
+  \Agda@SuppressEnd{}%
+  \Agda@AlignEnd{}%
+  \ignorespacesafterend}
+
+% Vertical space used for empty lines. By default \abovedisplayskip.
+\newlength{\AgdaEmptySkip}
+\setlength{\AgdaEmptySkip}{\abovedisplayskip}
+
+% Extra space to be inserted for empty lines (the difference between
+% \AgdaEmptySkip and \baselineskip). Used internally.
+\newlength{\AgdaEmptyExtraSkip}
+
+% Counter used for code numbers.
+\newcounter{AgdaCodeNumber}
+% Formats a code number.
+\newcommand{\AgdaFormatCodeNumber}[1]{(#1)}
+
+% A boolean used to handle the option number.
+\newboolean{Agda@Number}
+\setboolean{Agda@Number}{false}
+
+% A boolean used to handle the option inline*. (For some reason the
+% approach used for hide and inline does not work for inline*.)
+\newboolean{Agda@InlineStar}
+\setboolean{Agda@InlineStar}{false}
+
+% Keys used by the code environment.
+\define@boolkey[Agda]{code}{hide}[true]{}
+\define@boolkey[Agda]{code}{inline}[true]{}
+\define@boolkey[Agda]{code}{inline*}[true]{%
+  \setboolean{Agda@InlineStar}{true}}
+\define@key[Agda]{code}{number}[]{%
+  \ifthenelse{\boolean{Agda@Number}}{}{%
+    \setboolean{Agda@Number}{true}%
+    % Increase the counter if this has not already been done.
+    \refstepcounter{AgdaCodeNumber}}%
+  % If the label is non-empty, set it. Note that it is possible to
+  % give several labels for a single code listing.
+  \ifthenelse{\equal{#1}{}}{}{\label{#1}}}
+
+% The code environment.
+%
+% Options:
+%
+% * hide: The code is hidden. Other options are ignored.
+%
+% * number: Give the code an equation number.
+%
+% * number=l: Give the code an equation number and the label l. It is
+%   possible to use this option several times with different labels.
+%
+% * inline/inline*: The code is inlined. In this case most of the
+%   discussion above does not apply, alignment is not respected, and so
+%   on. It is recommended to only use this option for a single line of
+%   code, and to not use two consecutive spaces in this piece of code.
+%
+%   Note that this environment ignores spaces after its end. If a space
+%   (\AgdaSpace{}) should be inserted after the inline code, use
+%   inline*, otherwise use inline.
+%
+%   When this option is used number is ignored.
+%
+% The implementation is based on plainhscode in lhs2TeX's
+% polycode.fmt, written by Andres Löh.
+\NewEnviron{code}[1][]{%
+  % Process the options. Complain about unknown options.
+  \setkeys[Agda]{code}[number]{#1}%
+  \ifAgda@code@hide%
+    % Hide the code.
+  \else%
+  \ifAgda@code@inline%
+    % Inline code.
+    %
+    % Make the polytable primitives emitted by the LaTeX backend
+    % do nothing.
+    \DeclareDocumentCommand{\>}{O{}O{}}{}%
+    \DeclareDocumentCommand{\<}{O{}}{}%
+    \AgdaCodeStyle\BODY%
+  \else%
+  \ifthenelse{\boolean{Agda@InlineStar}}{%
+    % Inline code with space at the end.
+    %
+    \DeclareDocumentCommand{\>}{O{}O{}}{}%
+    \DeclareDocumentCommand{\<}{O{}}{}%
+    \AgdaCodeStyle\BODY\AgdaSpace{}}{%
+    %
+    % Displayed code.
+    %
+    % Conditionally emit space before the code block. Unconditionally
+    % switch to a new line.
+    \ifthenelse{\boolean{Agda@SpaceAroundCode} \and%
+                \(\not \boolean{Agda@Suppress} \or%
+                  \value{Agda@SuppressStart} = \value{Agda@Current}\)}{%
+      \Agda@NewlineWithVerticalSpace{\abovedisplayskip}}{%
+      \Agda@NewlineWithVerticalSpace{0pt}}%
+    %
+    % Check if numbers have been requested. If they have, then a side
+    % effect of this call is that Agda@Number is set to true, the code
+    % number counter is increased, and the label (if any) is set.
+    \setkeys[Agda]{code}[hide,inline,inline*]{#1}%
+    \ifthenelse{\boolean{Agda@Number}}{%
+      % Equation numbers have been requested. Use a minipage, so that
+      % there is room for the code number to the right, and the code
+      % number becomes centered vertically.
+      \begin{minipage}{%
+          \linewidth-%
+          \widthof{%
+            \AgdaSpace{}%
+            \AgdaFormatCodeNumber{\theAgdaCodeNumber}}}}{}%
+    %
+    % Indent the entire code block.
+    \advance\leftskip\mathindent%
+    %
+    % The code's style can be customised.
+    \AgdaCodeStyle%
+    %
+    % Used to control the height of empty lines.
+    \setlength{\AgdaEmptyExtraSkip}{\AgdaEmptySkip - \baselineskip}%
+    %
+    % The environment used to handle indentation (of individual lines)
+    % and alignment.
+    \begin{pboxed}%
+      %
+      % Conditionally preserve alignment between code blocks.
+      \ifthenelse{\boolean{Agda@Align}}{%
+        \ifthenelse{\value{Agda@AlignStart} = \value{Agda@Current}}{%
+          \savecolumns}{%
+          \restorecolumns}}{}%
+      %
+      % The code.
+      \BODY%
+    \end{pboxed}%
+    %
+    \ifthenelse{\boolean{Agda@Number}}{%
+      % Equation numbers have been requested.
+      \end{minipage}%
+      % Insert the code number to the right.
+      \hfill \AgdaFormatCodeNumber{\theAgdaCodeNumber}}{}%
+    %
+    % Does the label Agda@DoNotSuppressAfter@<current code block
+    % number> exist?
+    \ifcsdef{r@Agda@DoNotSuppressSpaceAfter@\theAgda@Current}{%
+      \setboolean{Agda@DoNotSuppressSpaceAfter}{true}}{%
+      \setboolean{Agda@DoNotSuppressSpaceAfter}{false}}%
+    %
+    % Conditionally emit space after the code block. Unconditionally
+    % switch to a new line.
+    \ifthenelse{\boolean{Agda@SpaceAroundCode} \and%
+                \(\not \boolean{Agda@Suppress} \or%
+                  \boolean{Agda@DoNotSuppressSpaceAfter}\)}{%
+      \Agda@NewlineWithVerticalSpace{\belowdisplayskip}}{%
+      \Agda@NewlineWithVerticalSpace{0pt}}%
+    %
+    % Step the code block counter, but only for non-hidden code.
+    \stepcounter{Agda@Current}}%
+  \fi%
+  \fi%
+  % Reset Agda@Number and Agda@InlineStar.
+  \setboolean{Agda@Number}{false}%
+  \setboolean{Agda@InlineStar}{false}}
+
+% Space inserted after tokens.
+\newcommand{\AgdaSpace}{ }
+
+% Space inserted to indent something.
+\newcommand{\AgdaIndentSpace}{\AgdaSpace{}$\;\;$}
+
+% Default column for polytable.
+\defaultcolumn{@{}l@{\AgdaSpace{}}}
+
+% \AgdaIndent expects a non-negative integer as its only argument.
+% This integer should be the distance, in code blocks, to the thing
+% relative to which the text is indented.
+%
+% The default implementation only indents if the thing that the text
+% is indented relative to exists in the same code block or is wrapped
+% in the same AgdaAlign or AgdaMultiCode environment.
+\newcommand{\AgdaIndent}[1]{%
+  \ifthenelse{#1 = 0
+                \or
+              \( \boolean{Agda@Align}
+                   \and
+                 \cnttest{\value{Agda@Current} - #1}{>=}{
+                          \value{Agda@AlignStart}}
+              \)}{\AgdaIndentSpace{}}{}}
+
+% Underscores are typeset using \AgdaUnderscore{}.
+\newcommand{\AgdaUnderscore}{\_}
+
+\endinput
diff --git a/src/data/latex/postprocess-latex.pl b/src/data/latex/postprocess-latex.pl
new file mode 100644
--- /dev/null
+++ b/src/data/latex/postprocess-latex.pl
@@ -0,0 +1,24 @@
+#!/usr/bin/env perl
+
+use strict;
+use warnings;
+
+my $tag_prefix = "AgdaTag";
+my $underscore = "AgdaUnderscore";
+my $commands   = qr"(InductiveConstructor|CoinductiveConstructor\
+                    |Datatype|Field|Function|Module|Postulate|Record)";
+
+while (<>) {
+
+  s|(\\Agda$commands)\{(.*?)\}
+
+   | my $cmd = $1;
+     my $arg = $3;
+     my $tag = "$tag_prefix-$3" =~ s/\\_/$underscore/gr;
+
+     $_ = "%\n%<*$tag>\n$cmd\{$arg\}%\n%</$tag>\n";
+   |gxe;
+
+  print;
+
+}
diff --git a/src/data/lib/prim/Agda/Builtin/Bool.agda b/src/data/lib/prim/Agda/Builtin/Bool.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Bool.agda
@@ -0,0 +1,15 @@
+{-# OPTIONS --cubical-compatible --safe --no-universe-polymorphism
+            --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Bool where
+
+data Bool : Set where
+  false true : Bool
+
+{-# BUILTIN BOOL  Bool  #-}
+{-# BUILTIN FALSE false #-}
+{-# BUILTIN TRUE  true  #-}
+
+{-# COMPILE JS Bool  = function (x,v) { return ((x)? v["true"]() : v["false"]()); } #-}
+{-# COMPILE JS false = false #-}
+{-# COMPILE JS true  = true  #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Char.agda b/src/data/lib/prim/Agda/Builtin/Char.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Char.agda
@@ -0,0 +1,18 @@
+{-# OPTIONS --cubical-compatible --safe --no-universe-polymorphism
+            --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Char where
+
+open import Agda.Builtin.Nat
+open import Agda.Builtin.Bool
+
+postulate Char : Set
+{-# BUILTIN CHAR Char #-}
+
+primitive
+  primIsLower primIsDigit primIsAlpha primIsSpace primIsAscii
+    primIsLatin1 primIsPrint primIsHexDigit : Char → Bool
+  primToUpper primToLower : Char → Char
+  primCharToNat : Char → Nat
+  primNatToChar : Nat → Char
+  primCharEquality : Char → Char → Bool
diff --git a/src/data/lib/prim/Agda/Builtin/Char/Properties.agda b/src/data/lib/prim/Agda/Builtin/Char/Properties.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Char/Properties.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Char.Properties where
+
+open import Agda.Builtin.Char
+open import Agda.Builtin.Equality
+
+primitive
+
+  primCharToNatInjective : ∀ a b → primCharToNat a ≡ primCharToNat b → a ≡ b
diff --git a/src/data/lib/prim/Agda/Builtin/Coinduction.agda b/src/data/lib/prim/Agda/Builtin/Coinduction.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Coinduction.agda
@@ -0,0 +1,15 @@
+{-# OPTIONS --cubical-compatible --safe --universe-polymorphism --no-sized-types
+            --guardedness --level-universe #-}
+
+module Agda.Builtin.Coinduction where
+
+infix 1000 ♯_
+
+postulate
+  ∞  : ∀ {a} (A : Set a) → Set a
+  ♯_ : ∀ {a} {A : Set a} → A → ∞ A
+  ♭  : ∀ {a} {A : Set a} → ∞ A → A
+
+{-# BUILTIN INFINITY ∞  #-}
+{-# BUILTIN SHARP    ♯_ #-}
+{-# BUILTIN FLAT     ♭  #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/Equiv.agda b/src/data/lib/prim/Agda/Builtin/Cubical/Equiv.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/Equiv.agda
@@ -0,0 +1,107 @@
+{-# OPTIONS --erased-cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.Equiv where
+
+open import Agda.Primitive
+open import Agda.Builtin.Sigma
+open import Agda.Primitive.Cubical renaming (primINeg to ~_; primIMax to _∨_; primIMin to _∧_;
+                                             primHComp to hcomp; primTransp to transp; primComp to comp;
+                                             itIsOne to 1=1)
+open import Agda.Builtin.Cubical.Path
+open import Agda.Builtin.Cubical.Sub renaming (Sub to _[_↦_])
+import Agda.Builtin.Cubical.HCompU as HCompU
+
+module Helpers = HCompU.Helpers
+
+open Helpers
+
+
+-- We make this a record so that isEquiv can be proved using
+-- copatterns. This is good because copatterns don't get unfolded
+-- unless a projection is applied so it should be more efficient.
+record isEquiv {ℓ ℓ'} {A : Set ℓ} {B : Set ℓ'} (f : A → B) : Set (ℓ ⊔ ℓ') where
+  no-eta-equality
+  field
+    equiv-proof : (y : B) → isContr (fiber f y)
+
+open isEquiv public
+
+infix 4 _≃_
+
+_≃_ : ∀ {ℓ ℓ'} (A : Set ℓ) (B : Set ℓ') → Set (ℓ ⊔ ℓ')
+A ≃ B = Σ (A → B) \ f → (isEquiv f)
+
+equivFun : ∀ {ℓ ℓ'} {A : Set ℓ} {B : Set ℓ'} → A ≃ B → A → B
+equivFun e = fst e
+
+-- Improved version of equivProof compared to Lemma 5 in CCHM. We put
+-- the (φ = i0) face in contr' making it be definitionally c in this
+-- case. This makes the computational behavior better, in particular
+-- for transp in Glue.
+equivProof : ∀ {la lt} (T : Set la) (A : Set lt) → (w : T ≃ A) → (a : A)
+           → ∀ ψ (f : Partial ψ (fiber (w .fst) a)) → fiber (w .fst) a [ ψ ↦ f ]
+equivProof A B w a ψ fb =
+  inS (contr' {A = fiber (w .fst) a} (w .snd .equiv-proof a) ψ fb)
+  where
+    contr' : ∀ {ℓ} {A : Set ℓ} → isContr A → (φ : I) → (u : Partial φ A) → A
+    contr' {A = A} (c , p) φ u = hcomp (λ i → λ { (φ = i1) → p (u 1=1) i
+                                                ; (φ = i0) → c }) c
+
+
+{-# BUILTIN EQUIV      _≃_        #-}
+{-# BUILTIN EQUIVFUN   equivFun   #-}
+{-# BUILTIN EQUIVPROOF equivProof #-}
+
+module _ {ℓ : I → Level} (P : (i : I) → Set (ℓ i)) where
+  private
+    E : (i : I) → Set (ℓ i)
+    E  = λ i → P i
+    ~E : (i : I) → Set (ℓ (~ i))
+    ~E = λ i → P (~ i)
+
+    A = P i0
+    B = P i1
+
+    f : A → B
+    f x = transp E i0 x
+
+    g : B → A
+    g y = transp ~E i0 y
+
+    u : ∀ i → A → E i
+    u i x = transp (λ j → E (i ∧ j)) (~ i) x
+
+    v : ∀ i → B → E i
+    v i y = transp (λ j → ~E ( ~ i ∧ j)) i y
+
+    fiberPath : (y : B) → (xβ0 xβ1 : fiber f y) → xβ0 ≡ xβ1
+    fiberPath y (x0 , β0) (x1 , β1) k = ω , λ j → δ (~ j) where
+      module _ (j : I) where
+        private
+          sys : A → ∀ i → PartialP (~ j ∨ j) (λ _ → E (~ i))
+          sys x i (j = i0) = v (~ i) y
+          sys x i (j = i1) = u (~ i) x
+        ω0 = comp ~E (sys x0) ((β0 (~ j)))
+        ω1 = comp ~E (sys x1) ((β1 (~ j)))
+        θ0 = fill ~E (sys x0) (inS (β0 (~ j)))
+        θ1 = fill ~E (sys x1) (inS (β1 (~ j)))
+      sys = λ {j (k = i0) → ω0 j ; j (k = i1) → ω1 j}
+      ω = hcomp sys (g y)
+      θ = hfill sys (inS (g y))
+      δ = λ (j : I) → comp E
+            (λ i → λ { (j = i0) → v i y ; (k = i0) → θ0 j (~ i)
+                     ; (j = i1) → u i ω ; (k = i1) → θ1 j (~ i) })
+             (θ j)
+
+    γ : (y : B) → y ≡ f (g y)
+    γ y j = comp E (λ i → λ { (j = i0) → v i y
+                            ; (j = i1) → u i (g y) }) (g y)
+
+  pathToisEquiv : isEquiv f
+  pathToisEquiv .equiv-proof y .fst .fst = g y
+  pathToisEquiv .equiv-proof y .fst .snd = sym (γ y)
+  pathToisEquiv .equiv-proof y .snd = fiberPath y _
+
+  pathToEquiv : A ≃ B
+  pathToEquiv .fst = f
+  pathToEquiv .snd = pathToisEquiv
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/Glue.agda b/src/data/lib/prim/Agda/Builtin/Cubical/Glue.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/Glue.agda
@@ -0,0 +1,18 @@
+{-# OPTIONS --cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.Glue where
+
+open import Agda.Primitive
+open import Agda.Primitive.Cubical
+open import Agda.Builtin.Cubical.Equiv public
+
+primitive
+    primGlue    : ∀ {ℓ ℓ'} (A : Set ℓ) {φ : I}
+      → (T : Partial φ (Set ℓ')) → (e : PartialP φ (λ o → T o ≃ A))
+      → Set ℓ'
+    prim^glue   : ∀ {ℓ ℓ'} {A : Set ℓ} {φ : I}
+      → {T : Partial φ (Set ℓ')} → {e : PartialP φ (λ o → T o ≃ A)}
+      → (t : PartialP φ T) → (a : A) → primGlue A T e
+    prim^unglue : ∀ {ℓ ℓ'} {A : Set ℓ} {φ : I}
+      → {T : Partial φ (Set ℓ')} → {e : PartialP φ (λ o → T o ≃ A)}
+      → primGlue A T e → A
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/HCompU.agda b/src/data/lib/prim/Agda/Builtin/Cubical/HCompU.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/HCompU.agda
@@ -0,0 +1,78 @@
+{-# OPTIONS --erased-cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.HCompU where
+
+open import Agda.Primitive
+open import Agda.Builtin.Sigma
+open import Agda.Primitive.Cubical renaming (primINeg to ~_; primIMax to _∨_; primIMin to _∧_;
+                                             primHComp to hcomp; primTransp to transp; primComp to comp;
+                                             itIsOne to 1=1)
+open import Agda.Builtin.Cubical.Path
+open import Agda.Builtin.Cubical.Sub renaming (Sub to _[_↦_]; primSubOut to outS)
+
+module Helpers where
+    -- Homogeneous filling
+    hfill : ∀ {ℓ} {A : Set ℓ} {φ : I}
+              (u : ∀ i → Partial φ A)
+              (u0 : A [ φ ↦ u i0 ]) (i : I) → A
+    hfill {φ = φ} u u0 i =
+      hcomp (λ j → \ { (φ = i1) → u (i ∧ j) 1=1
+                     ; (i = i0) → outS u0 })
+            (outS u0)
+
+    -- Heterogeneous filling defined using comp
+    fill : ∀ {ℓ : I → Level} (A : ∀ i → Set (ℓ i)) {φ : I}
+             (u : ∀ i → Partial φ (A i))
+             (u0 : A i0 [ φ ↦ u i0 ]) →
+             ∀ i →  A i
+    fill A {φ = φ} u u0 i =
+      comp (λ j → A (i ∧ j))
+           (λ j → \ { (φ = i1) → u (i ∧ j) 1=1
+                    ; (i = i0) → outS u0 })
+           (outS {φ = φ} u0)
+
+    module _ {ℓ} {A : Set ℓ} where
+      refl : {x : A} → x ≡ x
+      refl {x = x} = λ _ → x
+
+      sym : {x y : A} → x ≡ y → y ≡ x
+      sym p = λ i → p (~ i)
+
+      cong : ∀ {ℓ'} {B : A → Set ℓ'} {x y : A}
+             (f : (a : A) → B a) (p : x ≡ y)
+           → PathP (λ i → B (p i)) (f x) (f y)
+      cong f p = λ i → f (p i)
+
+    isContr : ∀ {ℓ} → Set ℓ → Set ℓ
+    isContr A = Σ A \ x → (∀ y → x ≡ y)
+
+    fiber : ∀ {ℓ ℓ'} {A : Set ℓ} {B : Set ℓ'} (f : A → B) (y : B) → Set (ℓ ⊔ ℓ')
+    fiber {A = A} f y = Σ A \ x → f x ≡ y
+
+open Helpers
+
+
+primitive
+  prim^glueU : {la : Level} {φ : I} {T : I → Partial φ (Set la)}
+                 {A : Set la [ φ ↦ T i0 ]} →
+                 PartialP φ (T i1) → outS A → hcomp T (outS A)
+  prim^unglueU : {la : Level} {φ : I} {T : I → Partial φ (Set la)}
+                   {A : Set la [ φ ↦ T i0 ]} →
+                   hcomp T (outS A) → outS A
+  -- Needed for transp.
+  primFaceForall : (I → I) → I
+
+transpProof : ∀ {l} → (e : I → Set l) → (φ : I) → (a : Partial φ (e i0)) → (b : e i1 [ φ ↦ (\ o → transp (\ i → e i) i0 (a o)) ] ) → fiber (transp (\ i → e i) i0) (outS b)
+transpProof e φ a b = f , \ j → comp (\ i → e i) (\ i →
+                                               \ { (φ = i1) → transp (\ j → e (j ∧ i)) (~ i) (a 1=1)
+                                                 ; (j = i0) → transp (\ j → e (j ∧ i)) (~ i) f
+                                                 ; (j = i1) → g (~ i) })
+                                        f
+    where
+      b' = outS {u = (\ o → transp (\ i → e i) i0 (a o))} b
+      g : (k : I) → e (~ k)
+      g k = fill (\ i → e (~ i)) (\ i → \ { (φ = i1) → transp (\ j → e (j ∧ ~ i)) i (a 1=1)
+                                          ; (φ = i0) → transp (\ j → e (~ j ∨ ~ i)) (~ i) b' }) (inS b') k
+      f = comp (\ i → e (~ i)) (\ i → \ { (φ = i1) → transp (\ j → e (j ∧ ~ i)) i (a 1=1); (φ = i0) → transp (\ j → e (~ j ∨ ~ i)) (~ i) b' }) b'
+
+{-# BUILTIN TRANSPPROOF transpProof #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/Id.agda b/src/data/lib/prim/Agda/Builtin/Cubical/Id.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/Id.agda
@@ -0,0 +1,49 @@
+{-# OPTIONS --erased-cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.Id where
+
+  open import Agda.Primitive.Cubical
+  open import Agda.Builtin.Cubical.Path
+  open import Agda.Builtin.Cubical.Sub renaming (primSubOut to outS; Sub to _[_↦_])
+
+  {-# BUILTIN ID           Id       #-}
+  {-# BUILTIN REFLID       reflId   #-}
+
+  private
+    module ConId where
+      primitive
+        primConId : ∀ {ℓ} {A : Set ℓ} {x y : A} → I → x ≡ y → Id x y
+
+  open ConId public renaming (primConId to conid)
+
+  -- Id x y is treated as a pair of I and x ≡ y, using "i" for the
+  -- first component and "p" for the second.
+  {-# COMPILE JS conid =
+      _ => _ => _ => _ => i => p => { return { "i" : i, "p" : p } }
+    #-}
+
+  primitive
+    primDepIMin : _
+    primIdFace : ∀ {ℓ} {A : Set ℓ} {x y : A} → Id x y → I
+    primIdPath : ∀ {ℓ} {A : Set ℓ} {x y : A} → Id x y → x ≡ y
+
+  primitive
+    primIdElim : ∀ {a c} {A : Set a} {x : A}
+                   (C : (y : A) → Id x y → Set c) →
+                   ((φ : I) (y : A [ φ ↦ (λ _ → x) ])
+                    (w : (x ≡ outS y) [ φ ↦ (λ { (φ = i1) → \ _ → x}) ]) →
+                    C (outS y) (conid φ (outS w))) →
+                   {y : A} (p : Id x y) → C y p
+
+  -- IdJ can be defined in terms of pattern matching on the reflId
+  -- constructor. This equality is definitional; For non-reflId
+  -- identifications, it computes in terms of primIdElim and primComp.
+  IdJ : ∀ {ℓ ℓ'} {A : Set ℓ} {x : A} (P : ∀ y → Id x y → Set ℓ') →
+      P x (conid i1 (λ i → x)) → ∀ {y} (p : Id x y) → P y p
+  IdJ {x = x} P prefl reflId = prefl
+
+  -- Test computational behaviour of IdJ:
+  _ : ∀ {ℓ ℓ'} {A : Set ℓ} {x : A} (P : ∀ y → Id x y → Set ℓ')
+    → (a : P x (conid i1 (λ i → x)))
+    → IdJ P a (conid i1 (λ i → x)) ≡ a
+  _ = λ P a i → a
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/Path.agda b/src/data/lib/prim/Agda/Builtin/Cubical/Path.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/Path.agda
@@ -0,0 +1,15 @@
+{-# OPTIONS --erased-cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.Path where
+
+  open import Agda.Primitive.Cubical using (PathP) public
+
+
+  infix 4 _≡_
+
+  -- We have a variable name in `(λ i → A)` as a hint for case
+  -- splitting.
+  _≡_ : ∀ {ℓ} {A : Set ℓ} → A → A → Set ℓ
+  _≡_ {A = A} = PathP (λ i → A)
+
+  {-# BUILTIN PATH         _≡_     #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Cubical/Sub.agda b/src/data/lib/prim/Agda/Builtin/Cubical/Sub.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Cubical/Sub.agda
@@ -0,0 +1,18 @@
+{-# OPTIONS --erased-cubical --safe --no-sized-types --no-guardedness #-}
+
+module Agda.Builtin.Cubical.Sub where
+
+  open import Agda.Primitive.Cubical
+
+  {-# BUILTIN SUB Sub #-}
+
+  postulate
+    inS : ∀ {ℓ} {A : Set ℓ} {φ} (x : A) → Sub A φ (λ _ → x)
+
+  {-# BUILTIN SUBIN inS #-}
+
+  -- Sub A φ u is treated as A.
+  {-# COMPILE JS inS = _ => _ => _ => x => x #-}
+
+  primitive
+    primSubOut : ∀ {ℓ} {A : Set ℓ} {φ : I} {u : Partial φ A} → Sub _ φ u → A
diff --git a/src/data/lib/prim/Agda/Builtin/Equality.agda b/src/data/lib/prim/Agda/Builtin/Equality.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Equality.agda
@@ -0,0 +1,9 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Equality where
+
+infix 4 _≡_
+data _≡_ {a} {A : Set a} (x : A) : A → Set a where
+  instance refl : x ≡ x
+
+{-# BUILTIN EQUALITY _≡_ #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Equality/Erase.agda b/src/data/lib/prim/Agda/Builtin/Equality/Erase.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Equality/Erase.agda
@@ -0,0 +1,7 @@
+{-# OPTIONS --with-K --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Equality.Erase where
+
+open import Agda.Builtin.Equality
+
+primitive primEraseEquality : ∀ {a} {A : Set a} {x y : A} → x ≡ y → x ≡ y
diff --git a/src/data/lib/prim/Agda/Builtin/Equality/Rewrite.agda b/src/data/lib/prim/Agda/Builtin/Equality/Rewrite.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Equality/Rewrite.agda
@@ -0,0 +1,7 @@
+{-# OPTIONS --cubical-compatible --rewriting --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Equality.Rewrite where
+
+open import Agda.Builtin.Equality
+
+{-# BUILTIN REWRITE _≡_ #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Float.agda b/src/data/lib/prim/Agda/Builtin/Float.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Float.agda
@@ -0,0 +1,209 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Float where
+
+open import Agda.Builtin.Bool
+open import Agda.Builtin.Int
+open import Agda.Builtin.Maybe
+open import Agda.Builtin.Nat
+open import Agda.Builtin.Sigma
+open import Agda.Builtin.String
+open import Agda.Builtin.Word
+
+postulate Float : Set
+{-# BUILTIN FLOAT Float #-}
+
+primitive
+  -- Relations
+  primFloatInequality        : Float → Float → Bool
+  primFloatEquality          : Float → Float → Bool
+  primFloatLess              : Float → Float → Bool
+  primFloatIsInfinite        : Float → Bool
+  primFloatIsNaN             : Float → Bool
+  primFloatIsNegativeZero    : Float → Bool
+  primFloatIsSafeInteger     : Float → Bool
+  -- Conversions
+  primFloatToWord64          : Float → Maybe Word64
+  primNatToFloat             : Nat → Float
+  primIntToFloat             : Int → Float
+  primFloatRound             : Float → Maybe Int
+  primFloatFloor             : Float → Maybe Int
+  primFloatCeiling           : Float → Maybe Int
+  primFloatToRatio           : Float → (Σ Int λ _ → Int)
+  primRatioToFloat           : Int → Int → Float
+  primFloatDecode            : Float → Maybe (Σ Int λ _ → Int)
+  primFloatEncode            : Int → Int → Maybe Float
+  primShowFloat              : Float → String
+  -- Operations
+  primFloatPlus              : Float → Float → Float
+  primFloatMinus             : Float → Float → Float
+  primFloatTimes             : Float → Float → Float
+  primFloatDiv               : Float → Float → Float
+  primFloatPow               : Float → Float → Float
+  primFloatNegate            : Float → Float
+  primFloatSqrt              : Float → Float
+  primFloatExp               : Float → Float
+  primFloatLog               : Float → Float
+  primFloatSin               : Float → Float
+  primFloatCos               : Float → Float
+  primFloatTan               : Float → Float
+  primFloatASin              : Float → Float
+  primFloatACos              : Float → Float
+  primFloatATan              : Float → Float
+  primFloatATan2             : Float → Float → Float
+  primFloatSinh              : Float → Float
+  primFloatCosh              : Float → Float
+  primFloatTanh              : Float → Float
+  primFloatASinh             : Float → Float
+  primFloatACosh             : Float → Float
+  primFloatATanh             : Float → Float
+
+{-# COMPILE JS
+    primFloatRound = function(x) {
+        x = agdaRTS._primFloatRound(x);
+        if (x === null) {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"];
+        }
+        else {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](x);
+        }
+    };
+#-}
+{-# COMPILE JS
+    primFloatFloor = function(x) {
+        x = agdaRTS._primFloatFloor(x);
+        if (x === null) {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"];
+        }
+        else {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](x);
+        }
+    };
+#-}
+{-# COMPILE JS
+    primFloatCeiling = function(x) {
+        x = agdaRTS._primFloatCeiling(x);
+        if (x === null) {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"];
+        }
+        else {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](x);
+        }
+    };
+#-}
+{-# COMPILE JS
+    primFloatToRatio = function(x) {
+        x = agdaRTS._primFloatToRatio(x);
+        return z_jAgda_Agda_Builtin_Sigma["_,_"](x.numerator)(x.denominator);
+    };
+#-}
+{-# COMPILE JS
+    primFloatDecode = function(x) {
+        x = agdaRTS._primFloatDecode(x);
+        if (x === null) {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"];
+        }
+        else {
+            return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](
+                z_jAgda_Agda_Builtin_Sigma["_,_"](x.mantissa)(x.exponent));
+        }
+    };
+#-}
+{-# COMPILE JS
+    primFloatEncode = function(x) {
+        return function (y) {
+            x = agdaRTS.uprimFloatEncode(x, y);
+            if (x === null) {
+                return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"];
+            }
+            else {
+                return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](x);
+            }
+        }
+    };
+#-}
+
+primFloatNumericalEquality = primFloatEquality
+{-# WARNING_ON_USAGE primFloatNumericalEquality
+"Warning: primFloatNumericalEquality was deprecated in Agda v2.6.2.
+Please use primFloatEquality instead."
+#-}
+
+primFloatNumericalLess = primFloatLess
+{-# WARNING_ON_USAGE primFloatNumericalLess
+"Warning: primFloatNumericalLess was deprecated in Agda v2.6.2.
+Please use primFloatLess instead."
+#-}
+
+primRound = primFloatRound
+{-# WARNING_ON_USAGE primRound
+"Warning: primRound was deprecated in Agda v2.6.2.
+Please use primFloatRound instead."
+#-}
+
+primFloor = primFloatFloor
+{-# WARNING_ON_USAGE primFloor
+"Warning: primFloor was deprecated in Agda v2.6.2.
+Please use primFloatFloor instead."
+#-}
+
+primCeiling = primFloatCeiling
+{-# WARNING_ON_USAGE primCeiling
+"Warning: primCeiling was deprecated in Agda v2.6.2.
+Please use primFloatCeiling instead."
+#-}
+
+primExp = primFloatExp
+{-# WARNING_ON_USAGE primExp
+"Warning: primExp was deprecated in Agda v2.6.2.
+Please use primFloatExp instead."
+#-}
+
+primLog = primFloatLog
+{-# WARNING_ON_USAGE primLog
+"Warning: primLog was deprecated in Agda v2.6.2.
+Please use primFloatLog instead."
+#-}
+
+primSin = primFloatSin
+{-# WARNING_ON_USAGE primSin
+"Warning: primSin was deprecated in Agda v2.6.2.
+Please use primFloatSin instead."
+#-}
+
+primCos = primFloatCos
+{-# WARNING_ON_USAGE primCos
+"Warning: primCos was deprecated in Agda v2.6.2.
+Please use primFloatCos instead."
+#-}
+
+primTan = primFloatTan
+{-# WARNING_ON_USAGE primTan
+"Warning: primTan was deprecated in Agda v2.6.2.
+Please use primFloatTan instead."
+#-}
+
+primASin = primFloatASin
+{-# WARNING_ON_USAGE primASin
+"Warning: primASin was deprecated in Agda v2.6.2.
+Please use primFloatASin instead."
+#-}
+
+
+primACos = primFloatACos
+{-# WARNING_ON_USAGE primACos
+"Warning: primACos was deprecated in Agda v2.6.2.
+Please use primFloatACos instead."
+#-}
+
+primATan = primFloatATan
+{-# WARNING_ON_USAGE primATan
+"Warning: primATan was deprecated in Agda v2.6.2.
+Please use primFloatATan instead."
+#-}
+
+primATan2 = primFloatATan2
+{-# WARNING_ON_USAGE primATan2
+"Warning: primATan2 was deprecated in Agda v2.6.2.
+Please use primFloatATan2 instead."
+#-}
diff --git a/src/data/lib/prim/Agda/Builtin/Float/Properties.agda b/src/data/lib/prim/Agda/Builtin/Float/Properties.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Float/Properties.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Float.Properties where
+
+open import Agda.Builtin.Float
+open import Agda.Builtin.Equality
+
+primitive
+
+  primFloatToWord64Injective : ∀ a b → primFloatToWord64 a ≡ primFloatToWord64 b → a ≡ b
diff --git a/src/data/lib/prim/Agda/Builtin/FromNat.agda b/src/data/lib/prim/Agda/Builtin/FromNat.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/FromNat.agda
@@ -0,0 +1,16 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.FromNat where
+
+open import Agda.Primitive
+open import Agda.Builtin.Nat
+
+record Number {a} (A : Set a) : Set (lsuc a) where
+  field
+    Constraint : Nat → Set a
+    fromNat : ∀ n → {{_ : Constraint n}} → A
+
+open Number {{...}} public using (fromNat)
+
+{-# BUILTIN FROMNAT fromNat #-}
+{-# DISPLAY Number.fromNat _ n = fromNat n #-}
diff --git a/src/data/lib/prim/Agda/Builtin/FromNeg.agda b/src/data/lib/prim/Agda/Builtin/FromNeg.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/FromNeg.agda
@@ -0,0 +1,16 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.FromNeg where
+
+open import Agda.Primitive
+open import Agda.Builtin.Nat
+
+record Negative {a} (A : Set a) : Set (lsuc a) where
+  field
+    Constraint : Nat → Set a
+    fromNeg : ∀ n → {{_ : Constraint n}} → A
+
+open Negative {{...}} public using (fromNeg)
+
+{-# BUILTIN FROMNEG fromNeg #-}
+{-# DISPLAY Negative.fromNeg _ n = fromNeg n #-}
diff --git a/src/data/lib/prim/Agda/Builtin/FromString.agda b/src/data/lib/prim/Agda/Builtin/FromString.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/FromString.agda
@@ -0,0 +1,16 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.FromString where
+
+open import Agda.Primitive
+open import Agda.Builtin.String
+
+record IsString {a} (A : Set a) : Set (lsuc a) where
+  field
+    Constraint : String → Set a
+    fromString : (s : String) {{_ : Constraint s}} → A
+
+open IsString {{...}} public using (fromString)
+
+{-# BUILTIN FROMSTRING fromString #-}
+{-# DISPLAY IsString.fromString _ s = fromString s #-}
diff --git a/src/data/lib/prim/Agda/Builtin/IO.agda b/src/data/lib/prim/Agda/Builtin/IO.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/IO.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.IO where
+
+postulate IO : ∀ {a} → Set a → Set a
+{-# POLARITY IO ++ ++ #-}
+{-# BUILTIN IO IO #-}
+
+{-# FOREIGN GHC type AgdaIO a b = IO b #-}
+{-# COMPILE GHC IO = type AgdaIO #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Int.agda b/src/data/lib/prim/Agda/Builtin/Int.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Int.agda
@@ -0,0 +1,18 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Int where
+
+open import Agda.Builtin.Nat
+open import Agda.Builtin.String
+
+infix 8 pos  -- Standard library uses this as +_
+
+data Int : Set where
+  pos    : (n : Nat) → Int
+  negsuc : (n : Nat) → Int
+
+{-# BUILTIN INTEGER       Int    #-}
+{-# BUILTIN INTEGERPOS    pos    #-}
+{-# BUILTIN INTEGERNEGSUC negsuc #-}
+
+primitive primShowInteger : Int → String
diff --git a/src/data/lib/prim/Agda/Builtin/List.agda b/src/data/lib/prim/Agda/Builtin/List.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/List.agda
@@ -0,0 +1,16 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.List where
+
+infixr 5 _∷_
+data List {a} (A : Set a) : Set a where
+  []  : List A
+  _∷_ : (x : A) (xs : List A) → List A
+
+{-# BUILTIN LIST List #-}
+
+{-# COMPILE JS  List = function(x,v) {
+  if (x.length < 1) { return v["[]"](); } else { return v["_∷_"](x[0], x.slice(1)); }
+} #-}
+{-# COMPILE JS [] = Array() #-}
+{-# COMPILE JS _∷_ = function (x) { return function(y) { return Array(x).concat(y); }; } #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Maybe.agda b/src/data/lib/prim/Agda/Builtin/Maybe.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Maybe.agda
@@ -0,0 +1,9 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Maybe where
+
+data Maybe {a} (A : Set a) : Set a where
+  just : A → Maybe A
+  nothing : Maybe A
+
+{-# BUILTIN MAYBE Maybe #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Nat.agda b/src/data/lib/prim/Agda/Builtin/Nat.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Nat.agda
@@ -0,0 +1,134 @@
+{-# OPTIONS --cubical-compatible --safe --no-universe-polymorphism
+            --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Nat where
+
+open import Agda.Builtin.Bool
+
+data Nat : Set where
+  zero : Nat
+  suc  : (n : Nat) → Nat
+
+{-# BUILTIN NATURAL Nat #-}
+
+infix  4 _==_ _<_
+infixl 6 _+_ _-_
+infixl 7 _*_
+
+_+_ : Nat → Nat → Nat
+zero  + m = m
+suc n + m = suc (n + m)
+
+{-# BUILTIN NATPLUS _+_ #-}
+
+_-_ : Nat → Nat → Nat
+n     - zero = n
+zero  - suc m = zero
+suc n - suc m = n - m
+
+{-# BUILTIN NATMINUS _-_ #-}
+
+_*_ : Nat → Nat → Nat
+zero  * m = zero
+suc n * m = m + n * m
+
+{-# BUILTIN NATTIMES _*_ #-}
+
+_==_ : Nat → Nat → Bool
+zero  == zero  = true
+suc n == suc m = n == m
+_     == _     = false
+
+{-# BUILTIN NATEQUALS _==_ #-}
+
+_<_ : Nat → Nat → Bool
+_     < zero  = false
+zero  < suc _ = true
+suc n < suc m = n < m
+
+{-# BUILTIN NATLESS _<_ #-}
+
+-- Helper function  div-helper  for Euclidean division.
+---------------------------------------------------------------------------
+--
+-- div-helper computes n / 1+m via iteration on n.
+--
+--   n div (suc m) = div-helper 0 m n m
+--
+-- The state of the iterator has two accumulator variables:
+--
+--   k: The quotient, returned once n=0.  Initialized to 0.
+--
+--   j: A counter, initialized to the divisor m, decreased on each iteration step.
+--      Once it reaches 0, the quotient k is increased and j reset to m,
+--      starting the next countdown.
+--
+-- Under the precondition j ≤ m, the invariant is
+--
+--   div-helper k m n j = k + (n + m - j) div (1 + m)
+
+div-helper : (k m n j : Nat) → Nat
+div-helper k m  zero    j      = k
+div-helper k m (suc n)  zero   = div-helper (suc k) m n m
+div-helper k m (suc n) (suc j) = div-helper k       m n j
+
+{-# BUILTIN NATDIVSUCAUX div-helper #-}
+
+-- Proof of the invariant by induction on n.
+--
+--   clause 1: div-helper k m 0 j
+--           = k                                        by definition
+--           = k + (0 + m - j) div (1 + m)              since m - j < 1 + m
+--
+--   clause 2: div-helper k m (1 + n) 0
+--           = div-helper (1 + k) m n m                 by definition
+--           = 1 + k + (n + m - m) div (1 + m)          by induction hypothesis
+--           = 1 + k +          n  div (1 + m)          by simplification
+--           = k +   (n + (1 + m)) div (1 + m)          by expansion
+--           = k + (1 + n + m - 0) div (1 + m)          by expansion
+--
+--   clause 3: div-helper k m (1 + n) (1 + j)
+--           = div-helper k m n j                       by definition
+--           = k + (n + m - j) div (1 + m)              by induction hypothesis
+--           = k + ((1 + n) + m - (1 + j)) div (1 + m)  by expansion
+--
+-- Q.e.d.
+
+-- Helper function  mod-helper  for the remainder computation.
+---------------------------------------------------------------------------
+--
+-- (Analogous to div-helper.)
+--
+-- mod-helper computes n % 1+m via iteration on n.
+--
+--   n mod (suc m) = mod-helper 0 m n m
+--
+-- The invariant is:
+--
+--   m = k + j  ==>  mod-helper k m n j = (n + k) mod (1 + m).
+
+mod-helper : (k m n j : Nat) → Nat
+mod-helper k m  zero    j      = k
+mod-helper k m (suc n)  zero   = mod-helper 0       m n m
+mod-helper k m (suc n) (suc j) = mod-helper (suc k) m n j
+
+{-# BUILTIN NATMODSUCAUX mod-helper #-}
+
+-- Proof of the invariant by induction on n.
+--
+--   clause 1: mod-helper k m 0 j
+--           = k                               by definition
+--           = (0 + k) mod (1 + m)             since m = k + j, thus k < m
+--
+--   clause 2: mod-helper k m (1 + n) 0
+--           = mod-helper 0 m n m              by definition
+--           = (n + 0)       mod (1 + m)       by induction hypothesis
+--           = (n + (1 + m)) mod (1 + m)       by expansion
+--           = (1 + n) + k)  mod (1 + m)       since k = m (as l = 0)
+--
+--   clause 3: mod-helper k m (1 + n) (1 + j)
+--           = mod-helper (1 + k) m n j        by definition
+--           = (n + (1 + k)) mod (1 + m)       by induction hypothesis
+--           = ((1 + n) + k) mod (1 + m)       by commutativity
+--
+-- Q.e.d.
diff --git a/src/data/lib/prim/Agda/Builtin/Reflection.agda b/src/data/lib/prim/Agda/Builtin/Reflection.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Reflection.agda
@@ -0,0 +1,470 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Reflection where
+
+open import Agda.Builtin.Unit
+open import Agda.Builtin.Bool
+open import Agda.Builtin.Nat
+open import Agda.Builtin.Word
+open import Agda.Builtin.List
+open import Agda.Builtin.String
+open import Agda.Builtin.Char
+open import Agda.Builtin.Float
+open import Agda.Builtin.Int
+open import Agda.Builtin.Sigma
+open import Agda.Primitive
+
+-- Names --
+
+postulate Name : Set
+{-# BUILTIN QNAME Name #-}
+
+primitive
+  primQNameEquality : Name → Name → Bool
+  primQNameLess     : Name → Name → Bool
+  primShowQName     : Name → String
+
+-- Fixity --
+
+data Associativity : Set where
+  left-assoc  : Associativity
+  right-assoc : Associativity
+  non-assoc   : Associativity
+
+data Precedence : Set where
+  related   : Float → Precedence
+  unrelated : Precedence
+
+data Fixity : Set where
+  fixity : Associativity → Precedence → Fixity
+
+{-# BUILTIN ASSOC      Associativity #-}
+{-# BUILTIN ASSOCLEFT  left-assoc    #-}
+{-# BUILTIN ASSOCRIGHT right-assoc   #-}
+{-# BUILTIN ASSOCNON   non-assoc     #-}
+
+{-# BUILTIN PRECEDENCE    Precedence #-}
+{-# BUILTIN PRECRELATED   related    #-}
+{-# BUILTIN PRECUNRELATED unrelated  #-}
+
+{-# BUILTIN FIXITY       Fixity #-}
+{-# BUILTIN FIXITYFIXITY fixity #-}
+
+{-# COMPILE GHC Associativity = data MAlonzo.RTE.Assoc (MAlonzo.RTE.LeftAssoc | MAlonzo.RTE.RightAssoc | MAlonzo.RTE.NonAssoc) #-}
+{-# COMPILE GHC Precedence    = data MAlonzo.RTE.Precedence (MAlonzo.RTE.Related | MAlonzo.RTE.Unrelated) #-}
+{-# COMPILE GHC Fixity        = data MAlonzo.RTE.Fixity (MAlonzo.RTE.Fixity) #-}
+
+{-# COMPILE JS Associativity  = function (x,v) { return v[x](); } #-}
+{-# COMPILE JS left-assoc     = "left-assoc"  #-}
+{-# COMPILE JS right-assoc    = "right-assoc" #-}
+{-# COMPILE JS non-assoc      = "non-assoc"   #-}
+
+{-# COMPILE JS Precedence     =
+  function (x,v) {
+    if (x === "unrelated") { return v[x](); } else { return v["related"](x); }} #-}
+{-# COMPILE JS related        = function(x) { return x; } #-}
+{-# COMPILE JS unrelated      = "unrelated"               #-}
+
+{-# COMPILE JS Fixity         = function (x,v) { return v["fixity"](x["assoc"], x["prec"]); } #-}
+{-# COMPILE JS fixity         = function (x) { return function (y) { return { "assoc": x, "prec": y}; }; } #-}
+
+primitive
+  primQNameFixity : Name → Fixity
+  primQNameToWord64s : Name → Σ Word64 (λ _ → Word64)
+
+-- Metavariables --
+
+postulate Meta : Set
+{-# BUILTIN AGDAMETA Meta #-}
+
+primitive
+  primMetaEquality : Meta → Meta → Bool
+  primMetaLess     : Meta → Meta → Bool
+  primShowMeta     : Meta → String
+  primMetaToNat    : Meta → Nat
+
+-- Arguments --
+
+-- Arguments can be (visible), {hidden}, or {{instance}}.
+data Visibility : Set where
+  visible hidden instance′ : Visibility
+
+{-# BUILTIN HIDING   Visibility #-}
+{-# BUILTIN VISIBLE  visible    #-}
+{-# BUILTIN HIDDEN   hidden     #-}
+{-# BUILTIN INSTANCE instance′  #-}
+
+-- Arguments can be relevant or irrelevant.
+data Relevance : Set where
+  relevant irrelevant : Relevance
+
+{-# BUILTIN RELEVANCE  Relevance  #-}
+{-# BUILTIN RELEVANT   relevant   #-}
+{-# BUILTIN IRRELEVANT irrelevant #-}
+
+-- Arguments also have a quantity.
+data Quantity : Set where
+  quantity-0 quantity-ω : Quantity
+
+{-# BUILTIN QUANTITY   Quantity   #-}
+{-# BUILTIN QUANTITY-0 quantity-0 #-}
+{-# BUILTIN QUANTITY-ω quantity-ω #-}
+
+-- Relevance and quantity are combined into a modality.
+data Modality : Set where
+  modality : (r : Relevance) (q : Quantity) → Modality
+
+{-# BUILTIN MODALITY             Modality #-}
+{-# BUILTIN MODALITY-CONSTRUCTOR modality #-}
+
+data ArgInfo : Set where
+  arg-info : (v : Visibility) (m : Modality) → ArgInfo
+
+data Arg {a} (A : Set a) : Set a where
+  arg : (i : ArgInfo) (x : A) → Arg A
+
+{-# BUILTIN ARGINFO    ArgInfo  #-}
+{-# BUILTIN ARGARGINFO arg-info #-}
+{-# BUILTIN ARG        Arg      #-}
+{-# BUILTIN ARGARG     arg      #-}
+
+data Blocker : Set where
+  blockerAny  : List Blocker → Blocker
+  blockerAll  : List Blocker → Blocker
+  blockerMeta : Meta → Blocker
+
+{-# BUILTIN AGDABLOCKER     Blocker #-}
+{-# BUILTIN AGDABLOCKERANY  blockerAny #-}
+{-# BUILTIN AGDABLOCKERALL  blockerAll #-}
+{-# BUILTIN AGDABLOCKERMETA blockerMeta #-}
+
+-- Name abstraction --
+
+data Abs {a} (A : Set a) : Set a where
+  abs : (s : String) (x : A) → Abs A
+
+{-# BUILTIN ABS    Abs #-}
+{-# BUILTIN ABSABS abs #-}
+
+-- Literals --
+
+data Literal : Set where
+  nat    : (n : Nat)    → Literal
+  word64 : (n : Word64) → Literal
+  float  : (x : Float)  → Literal
+  char   : (c : Char)   → Literal
+  string : (s : String) → Literal
+  name   : (x : Name)   → Literal
+  meta   : (x : Meta)   → Literal
+
+{-# BUILTIN AGDALITERAL   Literal #-}
+{-# BUILTIN AGDALITNAT    nat     #-}
+{-# BUILTIN AGDALITWORD64 word64  #-}
+{-# BUILTIN AGDALITFLOAT  float   #-}
+{-# BUILTIN AGDALITCHAR   char    #-}
+{-# BUILTIN AGDALITSTRING string  #-}
+{-# BUILTIN AGDALITQNAME  name    #-}
+{-# BUILTIN AGDALITMETA   meta    #-}
+
+
+-- Terms and patterns --
+
+data Term    : Set
+data Sort    : Set
+data Pattern : Set
+data Clause  : Set
+Type = Term
+Telescope = List (Σ String λ _ → Arg Type)
+
+data Term where
+  var       : (x : Nat) (args : List (Arg Term)) → Term
+  con       : (c : Name) (args : List (Arg Term)) → Term
+  def       : (f : Name) (args : List (Arg Term)) → Term
+  lam       : (v : Visibility) (t : Abs Term) → Term
+  pat-lam   : (cs : List Clause) (args : List (Arg Term)) → Term
+  pi        : (a : Arg Type) (b : Abs Type) → Term
+  agda-sort : (s : Sort) → Term
+  lit       : (l : Literal) → Term
+  meta      : (x : Meta) → List (Arg Term) → Term
+  unknown   : Term
+
+data Sort where
+  set     : (t : Term) → Sort
+  lit     : (n : Nat) → Sort
+  prop    : (t : Term) → Sort
+  propLit : (n : Nat) → Sort
+  inf     : (n : Nat) → Sort
+  unknown : Sort
+
+data Pattern where
+  con    : (c : Name) (ps : List (Arg Pattern)) → Pattern
+  dot    : (t : Term)    → Pattern
+  var    : (x : Nat)     → Pattern
+  lit    : (l : Literal) → Pattern
+  proj   : (f : Name)    → Pattern
+  absurd : (x : Nat)     → Pattern  -- absurd patterns counts as variables
+
+data Clause where
+  clause        : (tel : Telescope) (ps : List (Arg Pattern)) (t : Term) → Clause
+  absurd-clause : (tel : Telescope) (ps : List (Arg Pattern)) → Clause
+
+{-# BUILTIN AGDATERM      Term    #-}
+{-# BUILTIN AGDASORT      Sort    #-}
+{-# BUILTIN AGDAPATTERN   Pattern #-}
+{-# BUILTIN AGDACLAUSE    Clause  #-}
+
+{-# BUILTIN AGDATERMVAR         var       #-}
+{-# BUILTIN AGDATERMCON         con       #-}
+{-# BUILTIN AGDATERMDEF         def       #-}
+{-# BUILTIN AGDATERMMETA        meta      #-}
+{-# BUILTIN AGDATERMLAM         lam       #-}
+{-# BUILTIN AGDATERMEXTLAM      pat-lam   #-}
+{-# BUILTIN AGDATERMPI          pi        #-}
+{-# BUILTIN AGDATERMSORT        agda-sort #-}
+{-# BUILTIN AGDATERMLIT         lit       #-}
+{-# BUILTIN AGDATERMUNSUPPORTED unknown   #-}
+
+{-# BUILTIN AGDASORTSET         set     #-}
+{-# BUILTIN AGDASORTLIT         lit     #-}
+{-# BUILTIN AGDASORTPROP        prop    #-}
+{-# BUILTIN AGDASORTPROPLIT     propLit #-}
+{-# BUILTIN AGDASORTINF         inf     #-}
+{-# BUILTIN AGDASORTUNSUPPORTED unknown #-}
+
+{-# BUILTIN AGDAPATCON    con     #-}
+{-# BUILTIN AGDAPATDOT    dot     #-}
+{-# BUILTIN AGDAPATVAR    var     #-}
+{-# BUILTIN AGDAPATLIT    lit     #-}
+{-# BUILTIN AGDAPATPROJ   proj    #-}
+{-# BUILTIN AGDAPATABSURD absurd  #-}
+
+{-# BUILTIN AGDACLAUSECLAUSE clause        #-}
+{-# BUILTIN AGDACLAUSEABSURD absurd-clause #-}
+
+-- Definitions --
+
+data Definition : Set where
+  function    : (cs : List Clause) → Definition
+  data-type   : (pars : Nat) (cs : List Name) → Definition
+  record-type : (c : Name) (fs : List (Arg Name)) → Definition
+  data-cons   : (d : Name) → Definition
+  axiom       : Definition
+  prim-fun    : Definition
+
+{-# BUILTIN AGDADEFINITION                Definition  #-}
+{-# BUILTIN AGDADEFINITIONFUNDEF          function    #-}
+{-# BUILTIN AGDADEFINITIONDATADEF         data-type   #-}
+{-# BUILTIN AGDADEFINITIONRECORDDEF       record-type #-}
+{-# BUILTIN AGDADEFINITIONDATACONSTRUCTOR data-cons   #-}
+{-# BUILTIN AGDADEFINITIONPOSTULATE       axiom       #-}
+{-# BUILTIN AGDADEFINITIONPRIMITIVE       prim-fun    #-}
+
+-- Errors --
+
+data ErrorPart : Set where
+  strErr  : String → ErrorPart
+  termErr : Term → ErrorPart
+  pattErr : Pattern → ErrorPart
+  nameErr : Name → ErrorPart
+
+{-# BUILTIN AGDAERRORPART       ErrorPart #-}
+{-# BUILTIN AGDAERRORPARTSTRING strErr    #-}
+{-# BUILTIN AGDAERRORPARTTERM   termErr   #-}
+{-# BUILTIN AGDAERRORPARTPATT   pattErr   #-}
+{-# BUILTIN AGDAERRORPARTNAME   nameErr   #-}
+
+-- TC monad --
+
+postulate
+  TC               : ∀ {a} → Set a → Set a
+  returnTC         : ∀ {a} {A : Set a} → A → TC A
+  bindTC           : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B
+  unify            : Term → Term → TC ⊤
+  typeError        : ∀ {a} {A : Set a} → List ErrorPart → TC A
+  inferType        : Term → TC Type
+  checkType        : Term → Type → TC Term
+  normalise        : Term → TC Term
+  reduce           : Term → TC Term
+  catchTC          : ∀ {a} {A : Set a} → TC A → TC A → TC A
+  quoteTC          : ∀ {a} {A : Set a} → A → TC Term
+  unquoteTC        : ∀ {a} {A : Set a} → Term → TC A
+  quoteωTC         : ∀ {A : Setω} → A → TC Term
+  getContext       : TC Telescope
+  extendContext    : ∀ {a} {A : Set a} → String → Arg Type → TC A → TC A
+  inContext        : ∀ {a} {A : Set a} → Telescope → TC A → TC A
+  freshName        : String → TC Name
+  declareDef       : Arg Name → Type → TC ⊤
+  declarePostulate : Arg Name → Type → TC ⊤
+  declareData      : Name → Nat → Type → TC ⊤
+  defineData       : Name → List (Σ Name (λ _ → Type)) → TC ⊤
+  defineFun        : Name → List Clause → TC ⊤
+  getType          : Name → TC Type
+  getDefinition    : Name → TC Definition
+  blockTC          : ∀ {a} {A : Set a} → Blocker → TC A
+  commitTC         : TC ⊤
+  isMacro          : Name → TC Bool
+  pragmaForeign    : String → String → TC ⊤
+  pragmaCompile    : String → Name → String → TC ⊤
+
+  -- If 'true', makes the following primitives also normalise
+  -- their results: inferType, checkType, quoteTC, getType, and getContext
+  withNormalisation : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  askNormalisation  : TC Bool
+
+  -- If 'true', makes the following primitives to reconstruct hidden arguments:
+  -- getDefinition, normalise, reduce, inferType, checkType and getContext
+  withReconstructed : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  askReconstructed  : TC Bool
+
+  -- Whether implicit arguments at the end should be turned into metavariables
+  withExpandLast : ∀ {a} {A : Set a} → Bool → TC A → TC A
+  askExpandLast  : TC Bool
+
+  -- White/blacklist specific definitions for reduction while executing the TC computation
+  -- 'true' for whitelist, 'false' for blacklist
+  withReduceDefs : ∀ {a} {A : Set a} → (Σ Bool λ _ → List Name) → TC A → TC A
+  askReduceDefs  : TC (Σ Bool λ _ → List Name)
+
+  formatErrorParts : List ErrorPart → TC String
+  -- Prints the third argument if the corresponding verbosity level is turned
+  -- on (with the -v flag to Agda).
+  debugPrint : String → Nat → List ErrorPart → TC ⊤
+
+  -- Fail if the given computation gives rise to new, unsolved
+  -- "blocking" constraints.
+  noConstraints : ∀ {a} {A : Set a} → TC A → TC A
+
+  -- Run the given TC action and return the first component. Resets to
+  -- the old TC state if the second component is 'false', or keep the
+  -- new TC state if it is 'true'.
+  runSpeculative : ∀ {a} {A : Set a} → TC (Σ A λ _ → Bool) → TC A
+
+  -- Get a list of all possible instance candidates for the given meta
+  -- variable (it does not have to be an instance meta).
+  getInstances : Meta → TC (List Term)
+
+{-# BUILTIN AGDATCM                           TC                         #-}
+{-# BUILTIN AGDATCMRETURN                     returnTC                   #-}
+{-# BUILTIN AGDATCMBIND                       bindTC                     #-}
+{-# BUILTIN AGDATCMUNIFY                      unify                      #-}
+{-# BUILTIN AGDATCMTYPEERROR                  typeError                  #-}
+{-# BUILTIN AGDATCMINFERTYPE                  inferType                  #-}
+{-# BUILTIN AGDATCMCHECKTYPE                  checkType                  #-}
+{-# BUILTIN AGDATCMNORMALISE                  normalise                  #-}
+{-# BUILTIN AGDATCMREDUCE                     reduce                     #-}
+{-# BUILTIN AGDATCMCATCHERROR                 catchTC                    #-}
+{-# BUILTIN AGDATCMQUOTETERM                  quoteTC                    #-}
+{-# BUILTIN AGDATCMUNQUOTETERM                unquoteTC                  #-}
+{-# BUILTIN AGDATCMQUOTEOMEGATERM             quoteωTC                   #-}
+{-# BUILTIN AGDATCMGETCONTEXT                 getContext                 #-}
+{-# BUILTIN AGDATCMEXTENDCONTEXT              extendContext              #-}
+{-# BUILTIN AGDATCMINCONTEXT                  inContext                  #-}
+{-# BUILTIN AGDATCMFRESHNAME                  freshName                  #-}
+{-# BUILTIN AGDATCMDECLAREDEF                 declareDef                 #-}
+{-# BUILTIN AGDATCMDECLAREPOSTULATE           declarePostulate           #-}
+{-# BUILTIN AGDATCMDECLAREDATA                declareData                #-}
+{-# BUILTIN AGDATCMDEFINEDATA                 defineData                 #-}
+{-# BUILTIN AGDATCMDEFINEFUN                  defineFun                  #-}
+{-# BUILTIN AGDATCMGETTYPE                    getType                    #-}
+{-# BUILTIN AGDATCMGETDEFINITION              getDefinition              #-}
+{-# BUILTIN AGDATCMBLOCK                      blockTC                    #-}
+{-# BUILTIN AGDATCMCOMMIT                     commitTC                   #-}
+{-# BUILTIN AGDATCMISMACRO                    isMacro                    #-}
+{-# BUILTIN AGDATCMPRAGMAFOREIGN              pragmaForeign              #-}
+{-# BUILTIN AGDATCMPRAGMACOMPILE              pragmaCompile              #-}
+{-# BUILTIN AGDATCMWITHNORMALISATION          withNormalisation          #-}
+{-# BUILTIN AGDATCMWITHRECONSTRUCTED          withReconstructed          #-}
+{-# BUILTIN AGDATCMWITHEXPANDLAST             withExpandLast             #-}
+{-# BUILTIN AGDATCMWITHREDUCEDEFS             withReduceDefs             #-}
+{-# BUILTIN AGDATCMASKNORMALISATION           askNormalisation           #-}
+{-# BUILTIN AGDATCMASKRECONSTRUCTED           askReconstructed           #-}
+{-# BUILTIN AGDATCMASKEXPANDLAST              askExpandLast              #-}
+{-# BUILTIN AGDATCMASKREDUCEDEFS              askReduceDefs              #-}
+{-# BUILTIN AGDATCMFORMATERRORPARTS           formatErrorParts           #-}
+{-# BUILTIN AGDATCMDEBUGPRINT                 debugPrint                 #-}
+{-# BUILTIN AGDATCMNOCONSTRAINTS              noConstraints              #-}
+{-# BUILTIN AGDATCMRUNSPECULATIVE             runSpeculative             #-}
+{-# BUILTIN AGDATCMGETINSTANCES               getInstances               #-}
+
+-- All the TC primitives are compiled to functions that return
+-- undefined, rather than just undefined, in an attempt to make sure
+-- that code will run properly.
+{-# COMPILE JS returnTC          = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS bindTC            = _ => _ => _ => _ =>
+                                   _ => _ =>           undefined #-}
+{-# COMPILE JS unify             = _ => _ =>           undefined #-}
+{-# COMPILE JS typeError         = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS inferType         = _ =>                undefined #-}
+{-# COMPILE JS checkType         = _ => _ =>           undefined #-}
+{-# COMPILE JS normalise         = _ =>                undefined #-}
+{-# COMPILE JS reduce            = _ =>                undefined #-}
+{-# COMPILE JS catchTC           = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS quoteTC           = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS unquoteTC         = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS quoteωTC          = _ => _ =>           undefined #-}
+{-# COMPILE JS getContext        =                     undefined #-}
+{-# COMPILE JS extendContext     = _ => _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS inContext         = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS freshName         = _ =>                undefined #-}
+{-# COMPILE JS declareDef        = _ => _ =>           undefined #-}
+{-# COMPILE JS declarePostulate  = _ => _ =>           undefined #-}
+{-# COMPILE JS declareData       = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS defineData        = _ => _ =>           undefined #-}
+{-# COMPILE JS defineFun         = _ => _ =>           undefined #-}
+{-# COMPILE JS getType           = _ =>                undefined #-}
+{-# COMPILE JS getDefinition     = _ =>                undefined #-}
+{-# COMPILE JS blockTC           = _ => _ =>           undefined #-}
+{-# COMPILE JS commitTC          =                     undefined #-}
+{-# COMPILE JS isMacro           = _ =>                undefined #-}
+{-# COMPILE JS pragmaForeign     = _ => _ =>           undefined #-}
+{-# COMPILE JS pragmaCompile     = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS withNormalisation = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS withReconstructed = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS withExpandLast    = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS withReduceDefs    = _ => _ => _ => _ => undefined #-}
+{-# COMPILE JS askNormalisation  =                     undefined #-}
+{-# COMPILE JS askReconstructed  =                     undefined #-}
+{-# COMPILE JS askExpandLast     =                     undefined #-}
+{-# COMPILE JS askReduceDefs     =                     undefined #-}
+{-# COMPILE JS debugPrint        = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS noConstraints     = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS runSpeculative    = _ => _ => _ =>      undefined #-}
+{-# COMPILE JS getInstances      = _ =>                undefined #-}
+
+private
+  filter : (Name → Bool) → List Name → List Name
+  filter p [] = []
+  filter p (x ∷ xs) with p x
+  ... | true  = x ∷ filter p xs
+  ... | false = filter p xs
+
+  _∈_ : Name → List Name → Bool
+  n ∈ []      = false
+  n ∈ (n' ∷ l) with primQNameEquality n n'
+  ... | true  = true
+  ... | false = n ∈ l
+
+  _∉_ : Name → List Name → Bool
+  n ∉ l with n ∈ l
+  ... | true  = false
+  ... | false = true
+
+  _++_ : List Name → List Name → List Name
+  [] ++ l       = l
+  (x ∷ xs) ++ l = x ∷ (xs ++ l)
+
+  combineReduceDefs : (Σ Bool λ _ → List Name) → (Σ Bool λ _ → List Name) → (Σ Bool λ _ → List Name)
+  combineReduceDefs (true  , defs₁) (true  , defs₂) = (true  , filter (_∈ defs₁) defs₂)
+  combineReduceDefs (false , defs₁) (true  , defs₂) = (true  , filter (_∉ defs₁) defs₂)
+  combineReduceDefs (true  , defs₁) (false , defs₂) = (true  , filter (_∉ defs₂) defs₁)
+  combineReduceDefs (false , defs₁) (false , defs₂) = (false , defs₁ ++ defs₂)
+
+onlyReduceDefs dontReduceDefs : ∀ {a} {A : Set a} → List Name → TC A → TC A
+onlyReduceDefs defs x = bindTC askReduceDefs (λ exDefs → withReduceDefs (combineReduceDefs (true  , defs) exDefs) x)
+dontReduceDefs defs x = bindTC askReduceDefs (λ exDefs → withReduceDefs (combineReduceDefs (false , defs) exDefs) x)
+
+blockOnMeta   : ∀ {a} {A : Set a} → Meta → TC A
+blockOnMeta m = blockTC (blockerMeta m)
+
+{-# WARNING_ON_USAGE onlyReduceDefs "DEPRECATED: Use `withReduceDefs` instead of `onlyReduceDefs`" #-}
+{-# WARNING_ON_USAGE dontReduceDefs "DEPRECATED: Use `withReduceDefs` instead of `dontReduceDefs`" #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Reflection/External.agda b/src/data/lib/prim/Agda/Builtin/Reflection/External.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Reflection/External.agda
@@ -0,0 +1,17 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Reflection.External where
+
+open import Agda.Builtin.List
+open import Agda.Builtin.Nat
+open import Agda.Builtin.Sigma
+open import Agda.Builtin.String
+open import Agda.Builtin.Reflection
+
+postulate
+  execTC : String → List String → String
+         → TC (Σ Nat (λ _ → Σ String (λ _ → String)))
+
+{-# BUILTIN AGDATCMEXEC execTC #-}
+
+{-# COMPILE JS execTC = _ => _ => _ => undefined #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Reflection/Properties.agda b/src/data/lib/prim/Agda/Builtin/Reflection/Properties.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Reflection/Properties.agda
@@ -0,0 +1,11 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Reflection.Properties where
+
+open import Agda.Builtin.Reflection
+open import Agda.Builtin.Equality
+
+primitive
+
+  primMetaToNatInjective : ∀ a b → primMetaToNat a ≡ primMetaToNat b → a ≡ b
+  primQNameToWord64sInjective : ∀ a b → primQNameToWord64s a ≡ primQNameToWord64s b → a ≡ b
diff --git a/src/data/lib/prim/Agda/Builtin/Sigma.agda b/src/data/lib/prim/Agda/Builtin/Sigma.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Sigma.agda
@@ -0,0 +1,17 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Sigma where
+
+open import Agda.Primitive
+
+record Σ {a b} (A : Set a) (B : A → Set b) : Set (a ⊔ b) where
+  constructor _,_
+  field
+    fst : A
+    snd : B fst
+
+open Σ public
+
+infixr 4 _,_
+
+{-# BUILTIN SIGMA Σ #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Size.agda b/src/data/lib/prim/Agda/Builtin/Size.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Size.agda
@@ -0,0 +1,21 @@
+{-# OPTIONS --cubical-compatible --no-universe-polymorphism --sized-types
+            --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Size where
+
+{-# BUILTIN SIZEUNIV SizeUniv #-}
+{-# BUILTIN SIZE     Size     #-}
+{-# BUILTIN SIZELT   Size<_   #-}
+{-# BUILTIN SIZESUC  ↑_       #-}
+{-# BUILTIN SIZEINF  ∞        #-}
+{-# BUILTIN SIZEMAX  _⊔ˢ_     #-}
+
+{-# FOREIGN GHC
+  type SizeLT i = ()
+  #-}
+
+{-# COMPILE GHC Size   = type ()     #-}
+{-# COMPILE GHC Size<_ = type SizeLT #-}
+{-# COMPILE GHC ↑_     = \_ -> ()    #-}
+{-# COMPILE GHC ∞      = ()          #-}
+{-# COMPILE GHC _⊔ˢ_   = \_ _ -> ()  #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Strict.agda b/src/data/lib/prim/Agda/Builtin/Strict.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Strict.agda
@@ -0,0 +1,9 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Strict where
+
+open import Agda.Builtin.Equality
+
+primitive
+  primForce      : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) → (∀ x → B x) → B x
+  primForceLemma : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) (f : ∀ x → B x) → primForce x f ≡ f x
diff --git a/src/data/lib/prim/Agda/Builtin/String.agda b/src/data/lib/prim/Agda/Builtin/String.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/String.agda
@@ -0,0 +1,36 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.String where
+
+open import Agda.Builtin.Bool
+open import Agda.Builtin.Char
+open import Agda.Builtin.List
+open import Agda.Builtin.Maybe
+open import Agda.Builtin.Nat using (Nat)
+open import Agda.Builtin.Sigma
+
+postulate String : Set
+{-# BUILTIN STRING String #-}
+
+primitive
+  primStringUncons   : String → Maybe (Σ Char (λ _ → String))
+  primStringToList   : String → List Char
+  primStringFromList : List Char → String
+  primStringAppend   : String → String → String
+  primStringEquality : String → String → Bool
+  primShowChar       : Char → String
+  primShowString     : String → String
+  primShowNat        : Nat → String
+
+{-# COMPILE JS primStringUncons = function(x) {
+   if (x === "") { return z_jAgda_Agda_Builtin_Maybe["Maybe"]["nothing"]; };
+   return z_jAgda_Agda_Builtin_Maybe["Maybe"]["just"](z_jAgda_Agda_Builtin_Sigma["_,_"](x.charAt(0))(x.slice(1)));
+   }
+ #-}
+{-# COMPILE JS primStringToList = function(x) { return x.split(""); } #-}
+{-# COMPILE JS primStringFromList = function(x) { return x.join(""); } #-}
+{-# COMPILE JS primStringAppend = function(x) { return function(y) { return x+y; }; } #-}
+{-# COMPILE JS primStringEquality = function(x) { return function(y) { return x===y; }; } #-}
+{-# COMPILE JS primShowChar = function(x) { return JSON.stringify(x); } #-}
+{-# COMPILE JS primShowString = function(x) { return JSON.stringify(x); } #-}
+{-# COMPILE JS primShowNat = function(x) { return JSON.stringify(x); } #-}
diff --git a/src/data/lib/prim/Agda/Builtin/String/Properties.agda b/src/data/lib/prim/Agda/Builtin/String/Properties.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/String/Properties.agda
@@ -0,0 +1,11 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.String.Properties where
+
+open import Agda.Builtin.String
+open import Agda.Builtin.Equality
+
+primitive
+
+  primStringToListInjective : ∀ a b → primStringToList a ≡ primStringToList b → a ≡ b
+  primStringFromListInjective : ∀ a b → primStringFromList a ≡ primStringFromList b → a ≡ b
diff --git a/src/data/lib/prim/Agda/Builtin/TrustMe.agda b/src/data/lib/prim/Agda/Builtin/TrustMe.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/TrustMe.agda
@@ -0,0 +1,15 @@
+{-# OPTIONS --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.TrustMe where
+
+open import Agda.Builtin.Equality
+open import Agda.Builtin.Equality.Erase
+
+private
+  postulate
+    unsafePrimTrustMe : ∀ {a} {A : Set a} {x y : A} → x ≡ y
+
+primTrustMe : ∀ {a} {A : Set a} {x y : A} → x ≡ y
+primTrustMe = primEraseEquality unsafePrimTrustMe
+
+{-# DISPLAY primEraseEquality unsafePrimTrustMe = primTrustMe #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Unit.agda b/src/data/lib/prim/Agda/Builtin/Unit.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Unit.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --cubical-compatible --safe --no-universe-polymorphism
+            --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Unit where
+
+record ⊤ : Set where
+  instance constructor tt
+
+{-# BUILTIN UNIT ⊤ #-}
+{-# COMPILE GHC ⊤ = data () (()) #-}
diff --git a/src/data/lib/prim/Agda/Builtin/Word.agda b/src/data/lib/prim/Agda/Builtin/Word.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Word.agda
@@ -0,0 +1,13 @@
+{-# OPTIONS --cubical-compatible --safe --no-universe-polymorphism
+            --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Word where
+
+open import Agda.Builtin.Nat
+
+postulate Word64 : Set
+{-# BUILTIN WORD64 Word64 #-}
+
+primitive
+  primWord64ToNat   : Word64 → Nat
+  primWord64FromNat : Nat → Word64
diff --git a/src/data/lib/prim/Agda/Builtin/Word/Properties.agda b/src/data/lib/prim/Agda/Builtin/Word/Properties.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Builtin/Word/Properties.agda
@@ -0,0 +1,10 @@
+{-# OPTIONS --cubical-compatible --safe --no-sized-types --no-guardedness --level-universe #-}
+
+module Agda.Builtin.Word.Properties where
+
+open import Agda.Builtin.Word
+open import Agda.Builtin.Equality
+
+primitive
+
+  primWord64ToNatInjective : ∀ a b → primWord64ToNat a ≡ primWord64ToNat b → a ≡ b
diff --git a/src/data/lib/prim/Agda/Primitive.agda b/src/data/lib/prim/Agda/Primitive.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Primitive.agda
@@ -0,0 +1,41 @@
+-- The Agda primitives (preloaded).
+
+{-# OPTIONS --cubical-compatible --no-import-sorts --level-universe #-}
+
+module Agda.Primitive where
+
+------------------------------------------------------------------------
+-- Universe levels
+------------------------------------------------------------------------
+
+infixl 6 _⊔_
+
+{-# BUILTIN PROP           Prop      #-}
+{-# BUILTIN TYPE           Set       #-}
+{-# BUILTIN STRICTSET      SSet      #-}
+
+{-# BUILTIN PROPOMEGA      Propω     #-}
+{-# BUILTIN SETOMEGA       Setω      #-}
+{-# BUILTIN STRICTSETOMEGA SSetω     #-}
+
+{-# BUILTIN LEVELUNIV      LevelUniv #-}
+
+-- Level is the first thing we need to define.
+-- The other postulates can only be checked if built-in Level is known.
+
+postulate
+  Level : LevelUniv
+
+-- MAlonzo compiles Level to (). This should be safe, because it is
+-- not possible to pattern match on levels.
+
+{-# BUILTIN LEVEL Level #-}
+
+postulate
+  lzero : Level
+  lsuc  : (ℓ : Level) → Level
+  _⊔_   : (ℓ₁ ℓ₂ : Level) → Level
+
+{-# BUILTIN LEVELZERO lzero #-}
+{-# BUILTIN LEVELSUC  lsuc  #-}
+{-# BUILTIN LEVELMAX  _⊔_   #-}
diff --git a/src/data/lib/prim/Agda/Primitive/Cubical.agda b/src/data/lib/prim/Agda/Primitive/Cubical.agda
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/Agda/Primitive/Cubical.agda
@@ -0,0 +1,78 @@
+{-# OPTIONS --erased-cubical #-}
+
+module Agda.Primitive.Cubical where
+
+{-# BUILTIN CUBEINTERVALUNIV IUniv #-}  -- IUniv : SSet₁
+{-# BUILTIN INTERVAL I  #-}  -- I : IUniv
+
+{-# BUILTIN IZERO    i0 #-}
+{-# BUILTIN IONE     i1 #-}
+
+-- I is treated as the type of booleans.
+{-# COMPILE JS i0 = false #-}
+{-# COMPILE JS i1 = true  #-}
+
+infix  30 primINeg
+infixr 20 primIMin primIMax
+
+primitive
+    primIMin : I → I → I
+    primIMax : I → I → I
+    primINeg : I → I
+
+{-# BUILTIN ISONE    IsOne    #-}  -- IsOne : I → Setω
+
+postulate
+  itIsOne : IsOne i1
+  IsOne1  : ∀ i j → IsOne i → IsOne (primIMax i j)
+  IsOne2  : ∀ i j → IsOne j → IsOne (primIMax i j)
+
+{-# BUILTIN ITISONE  itIsOne  #-}
+{-# BUILTIN ISONE1   IsOne1   #-}
+{-# BUILTIN ISONE2   IsOne2   #-}
+
+-- IsOne i is treated as the unit type.
+{-# COMPILE JS itIsOne = { "tt" : a => a["tt"]() } #-}
+{-# COMPILE JS IsOne1 =
+  _ => _ => _ => { return { "tt" : a => a["tt"]() } }
+  #-}
+{-# COMPILE JS IsOne2 =
+  _ => _ => _ => { return { "tt" : a => a["tt"]() } }
+  #-}
+
+-- Partial : ∀{ℓ} (i : I) (A : Set ℓ) → Set ℓ
+-- Partial i A = IsOne i → A
+
+{-# BUILTIN PARTIAL  Partial  #-}
+{-# BUILTIN PARTIALP PartialP #-}
+
+postulate
+  isOneEmpty : ∀ {ℓ} {A : Partial i0 (Set ℓ)} → PartialP i0 A
+
+{-# BUILTIN ISONEEMPTY isOneEmpty #-}
+
+-- Partial i A and PartialP i A are treated as IsOne i → A.
+{-# COMPILE JS isOneEmpty =
+  _ => x => _ => x({ "tt" : a => a["tt"]() })
+  #-}
+
+primitive
+  primPOr : ∀ {ℓ} (i j : I) {A : Partial (primIMax i j) (Set ℓ)}
+            → (u : PartialP i (λ z → A (IsOne1 i j z)))
+            → (v : PartialP j (λ z → A (IsOne2 i j z)))
+            → PartialP (primIMax i j) A
+
+  -- Computes in terms of primHComp and primTransp
+  primComp : ∀ {ℓ} (A : (i : I) → Set (ℓ i)) {φ : I} (u : ∀ i → Partial φ (A i)) (a : A i0) → A i1
+
+syntax primPOr p q u t = [ p ↦ u , q ↦ t ]
+
+primitive
+  primTransp : ∀ {ℓ} (A : (i : I) → Set (ℓ i)) (φ : I) (a : A i0) → A i1
+  primHComp  : ∀ {ℓ} {A : Set ℓ} {φ : I} (u : ∀ i → Partial φ A) (a : A) → A
+
+
+postulate
+  PathP : ∀ {ℓ} (A : I → Set ℓ) → A i0 → A i1 → Set ℓ
+
+{-# BUILTIN PATHP        PathP     #-}
diff --git a/src/data/lib/prim/agda-builtins.agda-lib b/src/data/lib/prim/agda-builtins.agda-lib
new file mode 100644
--- /dev/null
+++ b/src/data/lib/prim/agda-builtins.agda-lib
@@ -0,0 +1,2 @@
+name: agda-builtins
+include: .
diff --git a/src/full/Agda/Auto/Auto.hs b/src/full/Agda/Auto/Auto.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/Auto.hs
@@ -0,0 +1,512 @@
+
+module Agda.Auto.Auto
+      (auto
+      , AutoResult(..)
+      , AutoProgress(..)
+      ) where
+
+import Prelude hiding ((!!), null)
+
+import Control.Monad          ( filterM, forM, guard, join, when )
+import Control.Monad.Except
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.State
+
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Data.IORef
+import qualified System.Timeout
+import Data.Maybe
+import qualified Data.Traversable as Trav
+import qualified Data.HashMap.Strict as HMap
+
+import Agda.Utils.Permutation (permute, takeP)
+import Agda.TypeChecking.Monad hiding (withCurrentModule)
+import Agda.TypeChecking.Telescope
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pretty (prettyA)
+import qualified Agda.Syntax.Concrete.Name as C
+import qualified Text.PrettyPrint.Annotated as PP
+import qualified Agda.TypeChecking.Pretty as TCM
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Translation.AbstractToConcrete (abstractToConcreteScope, abstractToConcrete_, runAbsToCon, toConcrete)
+import Agda.Interaction.Base
+import Agda.Interaction.BasicOps hiding (refine)
+import Agda.TypeChecking.Reduce (normalise)
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Scope.Base as Scope
+import Agda.Syntax.Scope.Monad (withCurrentModule)
+import qualified Agda.Syntax.Abstract.Name as AN
+import qualified Agda.TypeChecking.Monad.Base as TCM
+import Agda.TypeChecking.EtaContract (etaContract)
+
+import Agda.Auto.Options
+import Agda.Auto.Convert
+import Agda.Auto.NarrowingSearch
+import Agda.Auto.Syntax
+import Agda.Auto.SearchControl
+import Agda.Auto.Typecheck
+
+import Agda.Auto.CaseSplit
+
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+import Agda.Utils.List
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+
+insertAbsurdPattern :: String -> String
+insertAbsurdPattern [] = []
+insertAbsurdPattern s@(_:_) | take (length abspatvarname) s == abspatvarname = "()" ++ drop (length abspatvarname) s
+insertAbsurdPattern (c:s) = c : insertAbsurdPattern s
+
+getHeadAsHint :: A.Expr -> Maybe Hint
+getHeadAsHint (A.ScopedExpr _ e) = getHeadAsHint e
+getHeadAsHint (A.Def qname)      = Just $ Hint False qname
+getHeadAsHint (A.Proj _ qname)   = Just $ Hint False $ AN.headAmbQ qname
+getHeadAsHint (A.Con qname)      = Just $ Hint True  $ AN.headAmbQ qname
+getHeadAsHint _ = Nothing
+
+-- | Result type: Progress & potential Message for the user
+--
+--   The  of the Auto tactic can be one of the following three:
+--
+--   1. @Solutions [(ii,s)]@
+--      A list of solutions @s@ for interaction ids @ii@.
+--      In particular, @Solutions []@ means Agsy found no solution.
+--
+--   2. @FunClauses cs@
+--      A list of clauses for the interaction id @ii@ in which Auto
+--      was invoked with case-splitting turned on.
+--
+--   3. @Refinement s@
+--      A refinement for the interaction id @ii@ in which Auto was invoked.
+
+data AutoProgress =
+    Solutions  [(InteractionId, String)]
+  | FunClauses [String]
+  | Refinement String
+
+data AutoResult = AutoResult
+  { autoProgress :: AutoProgress
+  , autoMessage  :: Maybe String
+  }
+
+stopWithMsg :: String -> TCM AutoResult
+stopWithMsg msg = return $ AutoResult (Solutions []) (Just msg)
+
+-- | Entry point for Auto tactic (Agsy).
+--
+--   If the @autoMessage@ part of the result is set to @Just msg@, the
+--   message @msg@ produced by Agsy should be displayed to the user.
+
+{-# SPECIALIZE auto :: InteractionId -> Range -> String -> TCM AutoResult #-}
+auto
+  :: MonadTCM tcm
+  => InteractionId
+  -> Range
+  -> String
+  -> tcm AutoResult
+auto ii rng argstr = liftTCM $ locallyTC eMakeCase (const True) $ do
+
+  -- Parse hints and other configuration.
+  let autoOptions = parseArgs argstr
+  let hints    = autoOptions ^. aoHints
+  let timeout  = autoOptions ^. aoTimeOut
+  let pick     = autoOptions ^. aoPick
+  let mode     = autoOptions ^. aoMode
+  let hintmode = autoOptions ^. aoHintMode
+  ahints <- case mode of
+    MRefine{} -> return []
+    _         -> mapM (parseExprIn ii rng) hints
+  let failHints = stopWithMsg "Hints must be a list of constant names"
+
+  eqstuff <- getEqCombinators ii rng
+
+  caseMaybe (mapM getHeadAsHint ahints) failHints $ \ ehints -> do
+
+    -- Get the meta variable for the interaction point we are trying to fill.
+    -- Add the @autohints@ for that meta to the hints collection.
+    mi <- lookupInteractionId ii
+    thisdefinfo <- findClauseDeep ii
+    ehints <- (ehints ++) <$> do autohints hintmode mi $ fmap fst3 thisdefinfo
+
+    -- If @thisdefinfo /= Nothing@ get the its type (normalized).
+    mrectyp <- maybeToList <$> do
+      Trav.forM thisdefinfo $ \ (def, _, _) -> do
+        normalise =<< do TCM.defType <$> getConstInfo def
+
+    (myhints', mymrectyp, tccons, eqcons, cmap) <- tomy mi (ehints ++ eqstuff) mrectyp
+
+    let (myhints, c1to6) = splitAt (length myhints' - length eqstuff) myhints'
+        meqr = ifNull eqstuff Nothing $ \ _ -> {- else -}
+                 let [c1, c2, c3, c4, c5, c6] = c1to6
+                 in  Just $ EqReasoningConsts c1 c2 c3 c4 c5 c6
+
+
+    let tcSearchSC isdep ctx typ trm = caseMaybe meqr a $ \ eqr ->
+          mpret $ Sidecondition (calcEqRState eqr trm) a
+          where a = tcSearch isdep ctx typ trm
+
+    let (mainm, _, _, _) = tccons Map.! mi
+    case mode of
+     MNormal listmode disprove -> do
+        let numsols = if listmode then 10 else 1
+          -- Andreas, 2015-05-17 Issue 1504:
+          -- wish to produce several solutions, as
+          -- the first one might be ill-typed.
+          -- However, currently changing the 1 to something higher makes Agsy loop.
+        sols <- liftIO $ newIORef ([] :: [[I.Term]])
+        nsol <- liftIO $ newIORef $ pick + numsols
+        let hsol = do
+             nsol' <- readIORef nsol
+             let cond = nsol' <= numsols
+             when cond $ do
+               trms <- runExceptT
+                       $ mapM (\ (m , _, _, _) -> convert (Meta m) :: MOT I.Term)
+                       $ Map.elems tccons
+               case trms of
+                 Left{}     -> writeIORef nsol $! nsol' + 1
+                 Right trms -> modifyIORef sols (trms :)
+                 -- Right trms -> if listmode then modifyIORef sols (trms :)
+                 --                           else writeIORef sols [trms]
+        ticks <- liftIO $ newIORef 0
+
+        let exsearch initprop recinfo defdfv =
+             liftIO $ System.Timeout.timeout (getTimeOut timeout * 1000)
+                    $ loop 0
+             where
+               loop d = do
+                 let rechint x = case recinfo of
+                                  Nothing -> x
+                                  Just (_, recdef) -> (recdef, HMRecCall) : x
+                     env = RIEnv { rieHints             = rechint $ map (,HMNormal) myhints
+                                 , rieDefFreeVars       = defdfv
+                                 , rieEqReasoningConsts = meqr
+                                 }
+                 depreached <- topSearch ticks nsol hsol env (initprop) d costIncrease
+                 nsol' <- readIORef nsol
+                 if nsol' /= 0 && depreached then loop (d + costIncrease) else return depreached
+
+        let getsols :: [I.Term] -> TCM [(MetaId, A.Expr)]
+            getsols sol = do
+             exprs <- forM (zip (Map.keys tccons) sol) $ \ (mi, e) -> do
+               mv   <- lookupLocalMetaAuto mi
+               e    <- etaContract e
+               expr <- modifyAbstractExpr <$> do withMetaInfo (getMetaInfo mv) $ reify e
+               return (mi, expr)
+
+             let loop :: I.MetaId -> StateT [I.MetaId] TCM [(I.MetaId, A.Expr)]
+                 loop midx = do
+                   let (m, _, _, deps) = tccons Map.! midx
+                   asolss <- mapM loop deps
+                   dones  <- get
+                   asols  <- if midx `elem` dones then return [] else do
+                     put (midx : dones)
+                     return [(midx, fromMaybe __IMPOSSIBLE__ $ lookup midx exprs)]
+                   return $ concat asolss ++ asols
+             (asols, _) <- runStateT (loop mi) []
+             return asols
+
+        if disprove then
+          case eqcons of
+           [] -> case Map.elems tccons of
+            (m, mytype, mylocalVars, _) : [] -> do
+                defdfv <- case thisdefinfo of
+                           Just (def, _, _) -> getdfv mi def
+                           Nothing -> return 0
+                ee <- liftIO $ newIORef $ ConstDef {cdname = "T", cdorigin = __IMPOSSIBLE__, cdtype = NotM $ Sort (Set 0), cdcont = Postulate, cddeffreevars = 0}
+                let (restargs, modargs) = splitAt (length mylocalVars - defdfv) mylocalVars
+                    mytype' = foldl (\x y -> NotM $ Pi Nothing NotHidden (freeIn 0 y) y (Abs NoId x)) mytype restargs
+                    htyp = negtype ee mytype'
+                    sctx = (Id "h", closify htyp) : map (\x -> (NoId, closify x)) modargs
+                    ntt = closify (NotM $ App Nothing (NotM OKVal) (Const ee) (NotM ALNil))
+                res <- exsearch (tcSearchSC False sctx ntt (Meta m)) Nothing defdfv
+                rsols <- fmap reverse $ liftIO $ readIORef sols
+                if null rsols then do
+                  nsol' <- liftIO $ readIORef nsol
+                  stopWithMsg $ insuffsols (pick + numsols - nsol')
+                 else do
+                  aexprss <- mapM getsols rsols
+                  cexprss <- forM aexprss $ mapM $ \(mi, e) -> do
+                    mv <- lookupLocalMetaAuto mi
+                    withMetaInfo (getMetaInfo mv) $ do
+                      (mi,) <$> abstractToConcrete_ e
+                  let ss = dropWhile (== ' ') . dropWhile (/= ' ') . prettyShow
+                      disp [(_, cexpr)] = ss cexpr
+                      disp cexprs = concatMap (\ (mi, cexpr) -> ss cexpr ++ " ") cexprs
+                  ticks <- liftIO $ readIORef ticks
+                  stopWithMsg $ unlines $
+                    ("Listing disproof(s) " ++ show pick ++ "-" ++ show (pick + length rsols - 1)) :
+                    for (zip cexprss [pick..]) (\ (x, y) -> show y ++ "  " ++ disp x)
+            _ -> stopWithMsg "Metavariable dependencies not allowed in disprove mode"
+           _ -> stopWithMsg "Metavariable dependencies not allowed in disprove mode"
+         else do
+          (recinfo, defdfv) <-
+           case thisdefinfo of
+            Just (def, clause, _) -> do
+             let [rectyp'] = mymrectyp
+             defdfv <- getdfv mi def
+             myrecdef <- liftIO $ newIORef $ ConstDef {cdname = "", cdorigin = (Nothing, def), cdtype = rectyp', cdcont = Postulate, cddeffreevars = defdfv}
+             (_, pats) <- constructPats cmap mi clause
+             defdfv <- getdfv mi def
+             return $ if contains_constructor pats then
+               (Just (pats, myrecdef), defdfv)
+              else
+               (Nothing, defdfv)
+            Nothing -> return (Nothing, 0)
+          let tc (m, mytype, mylocalVars) isdep = tcSearchSC isdep (map (\x -> (NoId, closify x)) mylocalVars) (closify mytype) (Meta m)
+              initprop =
+                foldl (\x (ineq, e, i) -> mpret $ And Nothing x (comp' ineq (closify e) (closify i)))
+                 (foldl (\x (m, mt, mlv, _) ->
+                   if hequalMetavar m mainm then
+                    case recinfo of
+                     Just (recpats, recdef) ->
+                      mpret $ Sidecondition (localTerminationSidecond (localTerminationEnv recpats) recdef (Meta m))
+                                            (tc (m, mt, mlv) False)
+                     Nothing -> mpret $ And Nothing x (tc (m, mt, mlv) False)
+                   else
+                    mpret $ And Nothing x (tc (m, mt, mlv) True)
+                  )
+                  (mpret OK)
+                  (Map.elems tccons)
+                 ) eqcons
+          res <- exsearch initprop recinfo defdfv
+          riis <- map swap <$> getInteractionIdsAndMetas
+          let timeoutString | isNothing res = " after timeout (" ++ show timeout ++ "ms)"
+                            | otherwise     = ""
+          if listmode then do
+            rsols <- fmap reverse $ liftIO $ readIORef sols
+            if null rsols then do
+              nsol' <- liftIO $ readIORef nsol
+              stopWithMsg $ insuffsols (pick + numsols - nsol') ++ timeoutString
+             else do
+              aexprss <- mapM getsols rsols
+              -- cexprss <- mapM (mapM (\(mi, e) -> lookupMeta mi >>= \mv -> withMetaInfo (getMetaInfo mv) $ abstractToConcrete_ e >>= \e' -> return (mi, e'))) aexprss
+              cexprss <- forM aexprss $ do
+                mapM $ \ (mi, e) -> do
+                  mv <- lookupLocalMetaAuto mi
+                  withMetaInfo (getMetaInfo mv) $ do
+                    e' <- abstractToConcrete_ e
+                    return (mi, e')
+              let disp [(_, cexpr)] = prettyShow cexpr
+                  disp cexprs = concat $ for cexprs $ \ (mi, cexpr) ->
+                    maybe (show mi) show (lookup mi riis)
+                      ++ " := " ++ prettyShow cexpr ++ " "
+              ticks <- liftIO $ readIORef ticks
+              stopWithMsg $ "Listing solution(s) " ++ show pick ++ "-" ++ show (pick + length rsols - 1) ++ timeoutString ++
+                        "\n" ++ unlines (zipWith (\x y -> show y ++ "  " ++ disp x) cexprss [pick..])
+           else {- not listmode -}
+            case res of
+             Nothing -> do
+              nsol' <- liftIO $ readIORef nsol
+              stopWithMsg $ insuffsols (pick + numsols - nsol') ++ timeoutString
+             Just depthreached -> do
+              ticks <- liftIO $ readIORef ticks
+              rsols <- liftIO $ readIORef sols
+              case rsols of
+                [] -> do
+                  nsol' <- liftIO $ readIORef nsol
+                  stopWithMsg $ insuffsols (pick + numsols - nsol')
+                terms -> loop terms where
+                  -- Andreas, 2015-05-17  Issue 1504
+                  -- If giving a solution failed (e.g. ill-typed)
+                  -- we could try the next one.
+                  -- However, currently @terms@ is always a singleton list.
+                  -- Thus, the following @loop@ is not doing something very
+                  -- meaningful.
+                  loop :: [[I.Term]] -> TCM AutoResult
+                  loop [] = return $ AutoResult (Solutions []) (Just "")
+                  loop (term : terms') = do
+                    -- On exception, try next solution
+                    flip catchError (\ e -> do reportSDoc "auto" 40 $ "Solution failed:" TCM.<?> TCM.prettyTCM e
+                                               loop terms') $ do
+                      exprs <- getsols term
+                      reportSDoc "auto" 20 $ "Trying solution " TCM.<+> TCM.prettyTCM exprs
+                      giveress <- forM exprs $ \ (mi, expr0) -> do
+                        let expr = killRange expr0
+                        case lookup mi riis of
+                         Nothing ->
+                          -- catchError
+                           (giveExpr WithoutForce Nothing mi expr >> return (Nothing, Nothing))
+                           -- (const retry)
+                           -- (\_ -> return (Nothing, Just ("Failed to give expr for side solution of " ++ show mi)))
+                         Just ii' -> do ae <- give WithoutForce ii' Nothing expr
+                                        mv <- lookupLocalMetaAuto mi
+                                        let scope = getMetaScope mv
+                                        ce <- abstractToConcreteScope scope ae
+                                        let cmnt = if ii' == ii then agsyinfo ticks else ""
+                                        return (Just (ii', prettyShow ce ++ cmnt), Nothing)
+                           -- Andreas, 2015-05-17, Issue 1504
+                           -- When Agsy produces an ill-typed solution, return nothing.
+                           -- TODO: try other solution.
+                           -- `catchError` const retry -- (return (Nothing, Nothing))
+                      let msg = if natSize exprs == 1 then
+                                 Nothing
+                                else
+                                 Just $ "Also gave solution(s) for hole(s)" ++
+                                         concatMap (\(mi', _) ->
+                                          if mi' == mi then "" else (" " ++ case lookup mi' riis of {Nothing -> show mi'; Just ii -> show ii})
+                                         ) exprs
+                      let msgs = catMaybes $ msg : map snd giveress
+                          msg' = unlines msgs <$ guard (not $ null msgs)
+                      return $ AutoResult (Solutions $ mapMaybe fst giveress) msg'
+
+     MCaseSplit -> do
+      case thisdefinfo of
+       Just (def, clause, True) ->
+        case Map.elems tccons of
+         [(m, mytype, mylocalVars, _)] | null eqcons -> do
+          (ids, pats) <- constructPats cmap mi clause
+          let ctx = zipWith (\(hid, id) t -> HI hid (id, t)) ids mylocalVars
+          ticks <- liftIO $ newIORef 0
+          let [rectyp'] = mymrectyp
+          defdfv <- getdfv mi def
+          myrecdef <- liftIO $ newIORef $ ConstDef {cdname = "", cdorigin = (Nothing, def), cdtype = rectyp', cdcont = Postulate, cddeffreevars = defdfv}
+          sols <- liftIO $ System.Timeout.timeout (getTimeOut timeout * 1000) (
+             let r d = do
+                  sols <- liftIO $ caseSplitSearch ticks __IMPOSSIBLE__ myhints meqr __IMPOSSIBLE__ d myrecdef ctx mytype pats
+                  case sols of
+                   [] -> r (d + costIncrease)
+                   (_:_) -> return sols
+             in r 0)
+          case sols of
+           Just (cls : _) -> withInteractionId ii $ do
+            cls' <- liftIO $ runExceptT (mapM frommyClause cls)
+            case cls' of
+             Left{} -> stopWithMsg "No solution found"
+             Right cls' -> do
+              cls'' <- forM cls' $ \ (I.Clause _ _ tel ps body t catchall exact recursive reachable ell wm) -> do
+                withCurrentModule (AN.qnameModule def) $ do
+                 -- Normalise the dot patterns
+                 ps <- addContext tel $ normalise ps
+                 body <- etaContract body
+                 fmap modifyAbstractClause $ inTopContext $ reify $ AN.QNamed def $ I.Clause noRange noRange tel ps body t catchall exact recursive reachable ell wm
+              moduleTel <- lookupSection (AN.qnameModule def)
+              pcs <- withInteractionId ii $ inTopContext $ addContext moduleTel $ mapM prettyA cls''
+              ticks <- liftIO $ readIORef ticks
+
+
+              return $ AutoResult (FunClauses $ map (insertAbsurdPattern . PP.renderStyle (PP.style { PP.mode = PP.OneLineMode })) pcs) Nothing
+
+           Just [] -> stopWithMsg "No solution found" -- case not possible at the moment because case split doesnt care about search exhaustiveness
+           Nothing -> stopWithMsg $ "No solution found at time out (" ++ show timeout ++ "s)"
+         _ -> stopWithMsg "Metavariable dependencies not allowed in case split mode"
+       _ -> stopWithMsg "Metavariable is not at top level of clause RHS"
+
+     MRefine listmode -> do
+      mv <- lookupLocalMetaAuto mi
+      let tt = jMetaType $ mvJudgement mv
+          minfo = getMetaInfo mv
+      targettyp <- withMetaInfo minfo $ do
+       vs <- getContextArgs
+       targettype <- tt `piApplyM` permute (takeP (length vs) $ mvPermutation mv) vs
+       normalise targettype
+      let tctx = length $ envContext $ clEnv minfo
+
+      hits <- if "-a" `elem` hints then do
+        st <- liftTCM $ join $ pureTCM $ \st _ -> return st
+        let defs    = st ^. stSignature . sigDefinitions
+            idefs   = st ^. stImports   . sigDefinitions
+            alldefs = HMap.keys defs ++ HMap.keys idefs
+        catMaybes <$> mapM (\n ->
+          case thisdefinfo of
+           Just (def, _, _) | def == n -> return Nothing
+           _ -> do
+            cn <- withMetaInfo minfo $ runAbsToCon $ toConcrete n
+            if C.isInScope cn == C.NotInScope then
+              return Nothing
+            else getConstInfo' n >>= \case
+              Left{} -> return Nothing
+              Right c -> do
+                ctyp <- normalise $ defType c
+                cdfv <- withMetaInfo minfo $ getDefFreeVars n
+                return $ case matchType cdfv tctx ctyp targettyp of
+                  Nothing -> Nothing
+                  Just score -> Just (prettyShow cn, score)
+         ) alldefs
+       else do
+        let scopeinfo = clScope (getMetaInfo mv)
+            namespace = Scope.everythingInScope scopeinfo
+            names = Scope.nsNames namespace
+            qnames = map (\(x, y) -> (x, Scope.anameName $ List1.head y)) $ Map.toList names
+            modnames = case thisdefinfo of
+                        Just (def, _, _) -> filter (\(_, n) -> n /= def) qnames
+                        Nothing -> qnames
+        catMaybes <$> mapM (\(cn, n) -> getConstInfo' n >>= \case
+          Left{} -> return Nothing
+          Right c -> do
+            ctyp <- normalise $ defType c
+            cdfv <- withMetaInfo minfo $ getDefFreeVars n
+            return $ case matchType cdfv tctx ctyp targettyp of
+              Nothing -> Nothing
+              Just score -> Just (prettyShow cn, score)
+         ) modnames
+
+      let sorthits = List.sortBy (\(_, (pa1, pb1)) (_, (pa2, pb2)) -> case compare pa2 pa1 of {EQ -> compare pb1 pb2; o -> o}) hits
+      if listmode || pick == (-1) then
+        let pick' = max 0 pick
+        in if pick' >= length sorthits then
+             stopWithMsg $ insuffcands $ length sorthits
+            else
+             let showhits = take 10 $ drop pick' sorthits
+             in stopWithMsg $ "Listing candidate(s) " ++ show pick' ++ "-" ++ show (pick' + length showhits - 1) ++ " (found " ++ show (length sorthits) ++ " in total)\n" ++
+                           unlines (zipWith (\i (cn, _) -> show i ++ "  " ++ cn) [pick'..pick' + length showhits - 1] showhits)
+       else
+        if pick >= length sorthits then
+         stopWithMsg $ insuffcands $ length sorthits
+        else
+         return $ AutoResult (Refinement $ fst $ sorthits !! pick) Nothing
+  where
+    agsyinfo ticks = ""
+
+-- Get the functions and axioms defined in the same module as @def@.
+autohints :: AutoHintMode -> I.MetaId -> Maybe AN.QName -> TCM [Hint]
+autohints AHMModule mi (Just def) = do
+  scope <- clScope . getMetaInfo <$> lookupLocalMetaAuto mi
+  let names     = Scope.nsNames $ Scope.everythingInScope scope
+      qnames    = map (Scope.anameName . List1.head) $ Map.elems names
+      modnames  = filter (\n -> AN.qnameModule n == AN.qnameModule def && n /= def) qnames
+  map (Hint False) <$> do
+    (`filterM` modnames) $ \ n -> getConstInfo' n >>= \case
+      Left{} -> return False
+      Right c -> case theDef c of
+        Axiom{}    -> return True
+        AbstractDefn{} -> return True
+        Function{} -> return True
+        _          -> return False
+
+autohints _ _ _ = return []
+
+
+
+-- | Names for the equality reasoning combinators
+--   Empty if any of these names is not defined.
+
+getEqCombinators :: InteractionId -> Range -> TCM [Hint]
+getEqCombinators ii rng = do
+  let eqCombinators = ["_≡_", "begin_", "_≡⟨_⟩_", "_∎", "sym", "cong"]
+  raw <- mapM (parseExprIn ii rng) eqCombinators `catchError` const (pure [])
+  return $ fromMaybe [] $ mapM getHeadAsHint raw
+
+-- | Templates for error messages
+
+genericNotEnough :: String -> Int -> String
+genericNotEnough str n = unwords $ case n of
+  0 -> ["No", str, "found"]
+  1 -> ["Only 1", str, "found"]
+  _ -> ["Only", show n, str ++ "s", "found"]
+
+insuffsols :: Int -> String
+insuffsols  = genericNotEnough "solution"
+
+insuffcands :: Int -> String
+insuffcands = genericNotEnough "candidate"
diff --git a/src/full/Agda/Auto/CaseSplit.hs b/src/full/Agda/Auto/CaseSplit.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/CaseSplit.hs
@@ -0,0 +1,668 @@
+
+module Agda.Auto.CaseSplit where
+
+import Prelude hiding ((!!))
+
+import Control.Monad.State as St hiding (lift)
+import Control.Monad.Reader as Rd hiding (lift)
+import qualified Control.Monad.State as St
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+import Data.Function (on)
+import Data.IORef
+import Data.Tuple (swap)
+import Data.List (elemIndex)
+-- Import of <> needed for 8.2.2, but redundant in 8.8.3
+import Data.Monoid ((<>), Sum(..))
+import qualified Data.Set    as Set
+import qualified Data.IntMap as IntMap
+
+import Agda.Syntax.Common (Hiding(..))
+import Agda.Auto.NarrowingSearch
+import Agda.Auto.Syntax
+
+import Agda.Auto.SearchControl
+import Agda.Auto.Typecheck
+
+import Agda.Utils.Impossible
+import Agda.Utils.Monad (or2M)
+import Agda.Utils.List ((!!), last1)
+
+abspatvarname :: String
+abspatvarname = "\0absurdPattern"
+
+costCaseSplitVeryHigh, costCaseSplitHigh, costCaseSplitLow, costAddVarDepth
+  :: Cost
+costCaseSplitVeryHigh = 10000
+costCaseSplitHigh     = 5000
+costCaseSplitLow      = 2000
+costAddVarDepth       = 1000
+
+data HI a = HI Hiding a
+
+drophid :: [HI a] -> [a]
+drophid = map (\(HI _ x) -> x)
+
+type CSPat o = HI (CSPatI o)
+type CSCtx o = [HI (MId, MExp o)]
+
+data CSPatI o = CSPatConApp (ConstRef o) [CSPat o]
+              | CSPatProj (ConstRef o)
+              | CSPatVar Nat
+              | CSPatExp (MExp o)
+              | CSWith (MExp o) -- always an App
+              | CSAbsurd
+
+              | CSOmittedArg
+type Sol o = [(CSCtx o, [CSPat o], Maybe (MExp o))]
+
+caseSplitSearch ::
+  forall o . IORef Int -> Int -> [ConstRef o] ->
+  Maybe (EqReasoningConsts o) -> Int -> Cost -> ConstRef o ->
+  CSCtx o -> MExp o -> [CSPat o] -> IO [Sol o]
+caseSplitSearch ticks nsolwanted chints meqr depthinterval depth recdef ctx tt pats = do
+ let branchsearch :: Cost -> CSCtx o -> MExp o ->
+                     ([Nat], Nat, [Nat]) -> IO (Maybe (MExp o))
+     branchsearch depth ctx tt termcheckenv = do
+
+      nsol <- newIORef 1
+      m <- initMeta
+      sol <- newIORef Nothing
+      let trm = Meta m
+          hsol = do trm' <- expandMetas trm
+                    writeIORef sol (Just trm')
+          initcon = mpret
+                  $ Sidecondition
+                    (localTerminationSidecond termcheckenv recdef trm)
+                  $ (case meqr of
+                        Nothing  -> id
+                        Just eqr -> mpret . Sidecondition (calcEqRState eqr trm)
+                     ) $ tcSearch False (map (fmap closify) (drophid ctx))
+                         (closify tt) trm
+      recdefd <- readIORef recdef
+      let env = RIEnv { rieHints = (recdef, HMRecCall) : map (, HMNormal) chints
+                      , rieDefFreeVars = cddeffreevars recdefd
+                      , rieEqReasoningConsts = meqr
+                      }
+      depreached <- topSearch ticks nsol hsol env initcon depth (depth + 1)
+      readIORef sol
+     ctx' = ff 1 ctx
+     ff _ [] = []
+     ff n (HI hid (id, t) : ctx) = HI hid (id, lift n t) : ff (n + 1) ctx
+ caseSplitSearch' branchsearch depthinterval depth recdef ctx' tt pats
+
+caseSplitSearch' :: forall o .
+  (Cost -> CSCtx o -> MExp o -> ([Nat], Nat, [Nat]) -> IO (Maybe (MExp o))) ->
+  Int -> Cost -> ConstRef o -> CSCtx o -> MExp o -> [CSPat o] -> IO [Sol o]
+caseSplitSearch' branchsearch depthinterval depth recdef ctx tt pats = do
+  recdefd <- readIORef recdef
+  rc depth (cddeffreevars recdefd) ctx tt pats
+ where
+  rc :: Cost -> Int -> CSCtx o -> MExp o -> [CSPat o] -> IO [Sol o]
+  rc depth _ _ _ _ | depth < 0 = return []
+  rc depth nscrutavoid ctx tt pats = do
+
+    mblkvar <- getblks tt
+    fork
+     mblkvar
+   where
+   fork :: [Nat] -> IO [Sol o]
+   fork mblkvar = do
+    sols1 <- dobody
+    case sols1 of
+     (_:_) -> return sols1
+     [] -> do
+      let r :: [Nat] -> IO [Sol o]
+          r [] = return []
+          r (v:vs) = do
+           sols2 <- splitvar mblkvar v
+           case sols2 of
+            (_:_) -> return sols2
+            [] -> r vs
+      r [nv - x | x <- [0..nv]] -- [0..length ctx - 1 - nscrutavoid]
+    where nv = length ctx - 1
+   dobody :: IO [Sol o]
+   dobody = do
+    case findperm (map snd (drophid ctx)) of
+     Just perm -> do
+      let (ctx', tt', pats') = applyperm perm ctx tt pats
+      res <- branchsearch depth ctx' tt' (localTerminationEnv pats')
+      return $ case res of
+       Just trm -> [[(ctx', pats', Just trm)]]
+       Nothing -> []
+     Nothing -> __IMPOSSIBLE__ -- no permutation found
+   splitvar :: [Nat] -> Nat -> IO [Sol o]
+   splitvar mblkvar scrut = do
+    let scruttype = infertypevar ctx scrut
+    case rm __IMPOSSIBLE__ scruttype of
+     App _ _ (Const c) _ -> do
+      cd <- readIORef c
+      case cdcont cd of
+       Datatype cons _ -> do
+         sols <- dobranches cons
+         return $ map (\sol -> case sol of
+          [] ->
+           case findperm (map snd (drophid ctx)) of
+            Just perm ->
+             let HI scrhid(_, scrt) = ctx !! scrut
+                 ctx1 = take scrut ctx ++ (HI scrhid (Id abspatvarname, scrt)) : drop (scrut + 1) ctx
+                 (ctx', _, pats') = applyperm perm ctx1 tt ({-map (replacep scrut 1 CSAbsurd __IMPOSSIBLE__) -}pats)
+             in [(ctx', pats', Nothing)]
+            Nothing -> __IMPOSSIBLE__ -- no permutation found
+          _ -> sol
+          ) sols
+        where
+         dobranches :: [ConstRef o] -> IO [Sol o]
+         dobranches [] = return [[]]
+         dobranches (con : cons) = do
+          cond <- readIORef con
+          let ff t = case rm __IMPOSSIBLE__ t of
+                        Pi _ h _ it (Abs id ot) ->
+                         let (xs, inft) = ff ot
+                         in (((h, scrut + length xs), id, lift (scrut + length xs + 1) it) : xs, inft)
+                        _ -> ([], lift scrut t)
+              (newvars, inftype) = ff (cdtype cond)
+              constrapp = NotM $ App Nothing (NotM OKVal) (Const con) (foldl (\xs ((h, v), _, _) -> NotM $ ALCons h (NotM $ App Nothing (NotM OKVal) (Var v) (NotM ALNil)) xs) (NotM ALNil) (reverse newvars))
+              pconstrapp = CSPatConApp con (map (\((hid, v), _, _) -> HI hid (CSPatVar v)) newvars)
+              thesub = replace scrut (length newvars) constrapp
+              Id newvarprefix = fst $ (drophid ctx) !! scrut
+              ctx1 = map (\(HI hid (id, t)) -> HI hid (id, thesub t)) (take scrut ctx) ++
+                     reverse (zipWith (\((hid, _), id, t) i ->
+                       HI hid (Id (case id of {NoId -> newvarprefix{- ++ show i-}; Id id -> id}), t)
+                      ) newvars [0..]) ++
+                     map (\(HI hid (id, t)) -> HI hid (id, thesub t)) (drop (scrut + 1) ctx)
+              tt' = thesub tt
+              pats' = map (replacep scrut (length newvars) pconstrapp constrapp) pats
+              scruttype' = thesub scruttype  -- scruttype shouldn't really refer to scrutvar so lift is enough, but what if circular ref has been created and this is not detected until case split is done
+          case unifyexp inftype scruttype' of
+           Nothing -> do
+            res <- notequal scrut (length newvars) scruttype' inftype
+            if res then -- branch absurd
+              dobranches cons
+             else -- branch dont know
+              return []
+           Just unif ->
+            do
+             let (ctx2, tt2, pats2) = removevar ctx1 tt' pats' unif
+                 --cost = if elem scrut mblkvar then costCaseSplit - (costCaseSplit - costCaseSplitFollow) `div` (length mblkvar) else costCaseSplit
+                 cost
+                   | null mblkvar && scrut < length ctx - nscrutavoid && nothid
+                                                                = costCaseSplitLow +
+                                                                  costAddVarDepth *
+                                                                  Cost (depthofvar scrut pats)
+                   | null mblkvar                               = costCaseSplitVeryHigh
+                   | scrut `elem` mblkvar                       = costCaseSplitLow
+                   | scrut < length ctx - nscrutavoid && nothid = costCaseSplitHigh
+                   | otherwise                                  = costCaseSplitVeryHigh
+
+                 nothid = let HI hid _ = ctx !! scrut
+                          in hid == NotHidden
+
+
+             sols <- rc (depth - cost) (length ctx - 1 - scrut) ctx2 tt2 pats2
+             case sols of
+              [] -> return []
+              _ -> do
+               sols2 <- dobranches cons
+               return $ concatMap (\sol -> map (\sol2 -> sol ++ sol2) sols2) sols
+       _ -> return [] -- split failed "scrut type is not datatype"
+     _ -> return [] -- split failed "scrut type is not datatype"
+
+infertypevar :: CSCtx o -> Nat -> MExp o
+infertypevar ctx v = snd $ (drophid ctx) !! v
+
+class Replace t u where
+  type ReplaceWith t u
+  replace' :: Nat -> MExp (ReplaceWith t u) -> t -> Reader (Nat, Nat) u
+
+replace :: Replace t u => Nat -> Nat -> MExp (ReplaceWith t u) -> t -> u
+replace sv nnew e t = replace' 0 e t `runReader` (sv, nnew)
+
+instance Replace t u => Replace (Abs t) (Abs u) where
+  type ReplaceWith (Abs t) (Abs u) = ReplaceWith t u
+  replace' n re (Abs mid b) = Abs mid <$> replace' (n + 1) re b
+
+instance Replace (Exp o) (MExp o) where
+  type ReplaceWith (Exp o) (MExp o) = o
+  replace' n re = \case
+    App uid ok elr@(Var v) args -> do
+      ih         <- NotM <$> replace' n re args
+      (sv, nnew) <- ask
+      return $
+        if v >= n
+        then if v - n == sv
+             then betareduce (lift n re) ih
+             else if v - n > sv
+                  then NotM $ App uid ok (Var (v + nnew - 1)) ih
+                  else NotM $ App uid ok elr ih
+        else NotM $ App uid ok elr ih
+    App uid ok elr@Const{} args ->
+      NotM . App uid ok elr . NotM <$> replace' n re args
+    Lam hid b -> NotM . Lam hid <$> replace' (n + 1) re b
+    Pi uid hid possdep it b ->
+      fmap NotM $ Pi uid hid possdep <$> replace' n re it <*> replace' n re b
+    e@Sort{} -> return $ NotM e
+    e@AbsurdLambda{} -> return $ NotM e
+
+instance Replace t u => Replace (MM t (RefInfo o)) u where
+  type ReplaceWith (MM t (RefInfo o)) u = ReplaceWith t u
+  replace' n re = replace' n re . rm __IMPOSSIBLE__
+
+instance Replace (ArgList o) (ArgList o) where
+  type ReplaceWith (ArgList o) (ArgList o) = o
+  replace' n re args = case args of
+    ALNil           -> return ALNil
+    ALCons hid a as ->
+      ALCons hid <$> replace' n re a <*> (NotM <$> replace' n re as)
+    ALProj{}        -> __IMPOSSIBLE__
+    ALConPar as     -> ALConPar . NotM <$> replace' n re as
+
+
+betareduce :: MExp o -> MArgList o -> MExp o
+betareduce e args = case rm __IMPOSSIBLE__ args of
+ ALNil -> e
+ ALCons _ a rargs -> case rm __IMPOSSIBLE__ e of
+  App uid ok elr eargs -> NotM $ App uid ok elr (concatargs eargs args)
+  Lam _ (Abs _ b) -> betareduce (replace 0 0 a b) rargs
+  _ -> __IMPOSSIBLE__ -- not type correct if this happens
+ ALProj{} -> __IMPOSSIBLE__
+ ALConPar as -> __IMPOSSIBLE__
+
+concatargs :: MArgList o -> MArgList o -> MArgList o
+concatargs xs ys = case rm __IMPOSSIBLE__ xs of
+  ALNil -> ys
+
+  ALCons hid x xs -> NotM $ ALCons hid x (concatargs xs ys)
+
+  ALProj{} -> __IMPOSSIBLE__
+
+  ALConPar as -> NotM $ ALConPar (concatargs xs ys)
+
+replacep :: forall o. Nat -> Nat -> CSPatI o -> MExp o -> CSPat o -> CSPat o
+replacep sv nnew rp re = r
+ where
+  r :: CSPat o -> CSPat o
+  r (HI hid (CSPatConApp c ps)) = HI hid (CSPatConApp c (map r ps))
+  r (HI hid (CSPatVar v)) | v == sv   = HI hid rp
+                          | v > sv    = HI hid (CSPatVar (v + nnew - 1))
+                          | otherwise = HI hid (CSPatVar v)
+  r (HI hid (CSPatExp e)) = HI hid (CSPatExp $ replace sv nnew re e)
+
+  r p@(HI _ CSOmittedArg) = p
+
+  r _ = __IMPOSSIBLE__ -- other constructors dont appear in indata Pats
+
+
+
+-- Unification takes two values of the same type and generates a list
+-- of assignments making the two terms equal.
+
+type Assignments o = [(Nat, Exp o)]
+
+class Unify t where
+  type UnifiesTo t
+  unify'    :: t -> t -> StateT (Assignments (UnifiesTo t)) Maybe ()
+  notequal' :: t -> t -> ReaderT (Nat, Nat) (StateT (Assignments (UnifiesTo t)) IO) Bool
+
+unify :: Unify t => t -> t -> Maybe (Assignments (UnifiesTo t))
+unify t u = unify' t u `execStateT` []
+
+notequal :: Unify t => Nat -> Nat -> t -> t -> IO Bool
+notequal fstnew nbnew t1 t2 = notequal' t1 t2 `runReaderT` (fstnew, nbnew)
+                                              `evalStateT` []
+
+instance (Unify t, o ~ UnifiesTo t) => Unify (MM t (RefInfo o)) where
+  type UnifiesTo (MM t (RefInfo o)) = o
+
+  unify' = unify' `on` rm __IMPOSSIBLE__
+
+  notequal' = notequal' `on` rm __IMPOSSIBLE__
+
+unifyVar :: Nat -> Exp o -> StateT (Assignments o) Maybe ()
+unifyVar v e = do
+  unif <- get
+  case lookup v unif of
+    Nothing -> modify ((v, e) :)
+    Just e' -> unify' e e'
+
+instance Unify t => Unify (Abs t) where
+  type UnifiesTo (Abs t) = UnifiesTo t
+  unify' (Abs _ b1) (Abs _ b2) = unify' b1 b2
+
+  notequal' (Abs _ b1) (Abs _ b2) = notequal' b1 b2
+
+instance Unify (Exp o) where
+  type UnifiesTo (Exp o) = o
+
+  unify' e1 e2 = case (e1, e2) of
+   (App _ _ elr1 args1, App _ _ elr2 args2) | elr1 == elr2 -> unify' args1 args2
+   (Lam hid1 b1, Lam hid2 b2)               | hid1 == hid2 -> unify' b1 b2
+   (Pi _ hid1 _ a1 b1, Pi _ hid2 _ a2 b2)   | hid1 == hid2 -> unify' a1 a2
+                                                           >> unify' b1 b2
+   (Sort _, Sort _) -> return () -- a bit sloppy
+   (App _ _ (Var v) (NotM ALNil), _)
+     | v `Set.member` (freeVars e2) -> St.lift Nothing -- Occurs check
+   (_, App _ _ (Var v) (NotM ALNil))
+     | v `Set.member` (freeVars e1) -> St.lift Nothing -- Occurs check
+   (App _ _ (Var v) (NotM ALNil), _) -> unifyVar v e2
+   (_, App _ _ (Var v) (NotM ALNil)) -> unifyVar v e1
+   _ -> St.lift Nothing
+
+  notequal' e1 e2 = do
+    (fstnew, nbnew) <- ask
+    unifier         <- get
+    case (e1, e2) of
+      (App _ _ elr1 es1, App _ _ elr2 es2) | elr1 == elr2 -> notequal' es1 es2
+      (_, App _ _ (Var v2) (NotM ALNil)) -- why is this not symmetric?!
+        | fstnew <= v2 && v2 < fstnew + nbnew ->
+        case lookup v2 unifier of
+          Nothing  -> modify ((v2, e1):) >> return False
+          Just e2' -> notequal' e1 e2'
+{-
+  GA: Skipped these: Not sure why we'd claim they're impossible
+      (_, App _ _ (Var v2) (NotM ALProj{})) -> __IMPOSSIBLE__
+      (_, App _ _ (Var v2) (NotM ALConPar{})) -> __IMPOSSIBLE__
+-}
+      (App _ _ (Const c1) es1, App _ _ (Const c2) es2) -> do
+        cd1 <- liftIO $ readIORef c1
+        cd2 <- liftIO $ readIORef c2
+        case (cdcont cd1, cdcont cd2) of
+          (Constructor{}, Constructor{}) -> if c1 == c2 then notequal' es1 es2
+                                            else return True
+          _ -> return False
+{- GA: Why don't we have a case for distinct heads after all these
+       unification cases for vars with no spines & metas that can
+       be looked up?
+      (App _ _ elr1 _, App _ _ elr2 _) | elr1 <> elr2 -> return True
+-}
+      _ -> return False
+
+instance Unify (ArgList o) where
+  type UnifiesTo (ArgList o) = o
+
+  unify' args1 args2 = case (args1, args2) of
+   (ALNil, ALNil) -> pure ()
+   (ALCons hid1 a1 as1, ALCons hid2 a2 as2) | hid1 == hid2 -> unify' a1 a2
+                                                           >> unify' as1 as2
+   (ALConPar as1, ALCons _ _ as2) -> unify' as1 as2
+   (ALCons _ _ as1, ALConPar as2) -> unify' as1 as2
+   (ALConPar as1, ALConPar as2)   -> unify' as1 as2
+   _ -> St.lift Nothing
+
+  notequal' args1 args2 = case (args1, args2) of
+    (ALCons _ e es, ALCons _ f fs) -> notequal' e f `or2M` notequal' es fs
+    (ALConPar es1, ALConPar es2)   -> notequal' es1 es2
+    _                              -> return False
+
+-- This definition is only here to respect the previous interface.
+unifyexp :: MExp o -> MExp o -> Maybe ([(Nat, MExp o)])
+unifyexp e1 e2 = fmap (NotM <$>) <$> unify e1 e2
+
+class Lift t where
+  lift' :: Nat -> Nat -> t -> t
+
+lift :: Lift t => Nat -> t -> t
+lift 0 = id
+lift n = lift' n 0
+
+instance Lift t => Lift (Abs t) where
+  lift' n j (Abs mid b) = Abs mid (lift' n (j + 1) b)
+
+instance Lift t => Lift (MM t r) where
+  lift' n j = NotM . lift' n j . rm __IMPOSSIBLE__
+
+instance Lift (Exp o) where
+  lift' n j = \case
+    App uid ok elr args -> case elr of
+      Var v | v >= j -> App uid ok (Var (v + n)) (lift' n j args)
+      _ -> App uid ok elr (lift' n j args)
+    Lam hid b -> Lam hid (lift' n j b)
+    Pi uid hid possdep it b -> Pi uid hid possdep (lift' n j it) (lift' n j b)
+    e@Sort{} -> e
+    e@AbsurdLambda{} -> e
+
+instance Lift (ArgList o) where
+  lift' n j args = case args of
+    ALNil           -> ALNil
+    ALCons hid a as -> ALCons hid (lift' n j a) (lift' n j as)
+    ALProj{}        -> __IMPOSSIBLE__
+    ALConPar as     -> ALConPar (lift' n j as)
+
+
+removevar :: CSCtx o -> MExp o -> [CSPat o] -> [(Nat, MExp o)] -> (CSCtx o, MExp o, [CSPat o])
+removevar ctx tt pats [] = (ctx, tt, pats)
+removevar ctx tt pats ((v, e) : unif) =
+ let
+  e2 = replace v 0 __IMPOSSIBLE__ {- occurs check failed -} e
+  thesub = replace v 0 e2
+  ctx1 = map (\(HI hid (id, t)) -> HI hid (id, thesub t)) (take v ctx) ++
+         map (\(HI hid (id, t)) -> HI hid (id, thesub t)) (drop (v + 1) ctx)
+  tt' = thesub tt
+  pats' = map (replacep v 0 (CSPatExp e2) e2) pats
+  unif' = map (\(uv, ue) -> (if uv > v then uv - 1 else uv, thesub ue)) unif
+ in
+  removevar ctx1 tt' pats' unif'
+
+findperm :: [MExp o] -> Maybe [Nat]
+findperm ts =
+ let
+  frees = map freevars ts
+  m = IntMap.fromList $
+      map (\i -> (i, length (filter (elem i) frees)))
+          [0..length ts - 1]
+  r _ perm 0 = Just $ reverse perm
+  r m perm n =
+   case lookup 0 (map swap (IntMap.toList m)) of
+    Nothing -> Nothing
+    Just i -> r (foldl (flip $ IntMap.adjust (subtract 1))
+                       (IntMap.insert i (-1) m)
+                       (frees !! i))
+                 (i : perm) (n - 1)
+ in r m [] (length ts)
+
+
+freevars :: FreeVars t => t -> [Nat]
+freevars = Set.toList . freeVars
+
+applyperm :: [Nat] -> CSCtx o -> MExp o -> [CSPat o] ->
+             (CSCtx o, MExp o, [CSPat o])
+applyperm perm ctx tt pats =
+ let ctx1 = map (\(HI hid (id, t)) -> HI hid (id, rename (ren perm) t)) ctx
+     ctx2 = map (\i -> ctx1 !! i) perm
+     ctx3 = seqctx ctx2
+     tt' = rename (ren perm) tt
+     pats' = map (rename (ren perm)) pats
+ in (ctx3, tt', pats')
+
+ren :: [Nat] -> Nat -> Int
+ren n i = let Just j = elemIndex i n in j
+
+instance Renaming t => Renaming (HI t) where
+  renameOffset j ren (HI hid t) = HI hid $ renameOffset j ren t
+
+instance Renaming (CSPatI o) where
+  renameOffset j ren = \case
+    CSPatConApp c pats -> CSPatConApp c $ map (renameOffset j ren) pats
+    CSPatVar i         -> CSPatVar $ j + ren i
+    CSPatExp e         -> CSPatExp $ renameOffset j ren e
+    e@CSOmittedArg     -> e
+    _                  -> __IMPOSSIBLE__
+
+seqctx :: CSCtx o -> CSCtx o
+seqctx = r (-1)
+ where
+  r _ [] = []
+  r n (HI hid (id, t) : ctx) = HI hid (id, lift n t) : r (n - 1) ctx
+-- --------------------
+
+depthofvar :: Nat -> [CSPat o] -> Nat
+depthofvar v pats =
+ let [depth] = concatMap (f 0) (drophid pats)
+     f d (CSPatConApp _ pats) = concatMap (f (d + 1)) (drophid pats)
+     f d (CSPatVar v') = [d | v == v']
+     f _ _ = []
+ in depth
+
+-- --------------------
+-- | Speculation: Type class computing the size (?) of a pattern
+--   and collecting the vars it introduces
+class LocalTerminationEnv a where
+  sizeAndBoundVars :: a -> (Sum Nat, [Nat])
+
+instance LocalTerminationEnv a => LocalTerminationEnv (HI a) where
+  sizeAndBoundVars (HI _ p) = sizeAndBoundVars p
+
+instance LocalTerminationEnv (CSPatI o) where
+  sizeAndBoundVars = \case
+    CSPatConApp _ ps -> (1, []) <> sizeAndBoundVars ps
+    CSPatVar n       -> (0, [n])
+    CSPatExp e       -> sizeAndBoundVars e
+    _                -> (0, [])
+
+instance LocalTerminationEnv a => LocalTerminationEnv [a] where
+  sizeAndBoundVars = foldMap sizeAndBoundVars
+
+instance LocalTerminationEnv (MExp o) where
+--  sizeAndBoundVars e = case rm __IMPOSSIBLE__ e of
+-- GA: 2017 06 27: Not actually impossible! (cf. #2620)
+  sizeAndBoundVars Meta{} = (0, [])
+-- Does this default behaviour even make sense? The catchall in the
+-- following match seems to suggest it does
+  sizeAndBoundVars (NotM e) = case e of
+    App _ _ (Var v) _      -> (0, [v])
+    App _ _ (Const _) args -> (1, []) <> sizeAndBoundVars args
+    _                      -> (0, [])
+
+instance (LocalTerminationEnv a, LocalTerminationEnv b) => LocalTerminationEnv (a, b) where
+  sizeAndBoundVars (a, b) = sizeAndBoundVars a <> sizeAndBoundVars b
+
+instance LocalTerminationEnv (MArgList o) where
+  sizeAndBoundVars as = case rm __IMPOSSIBLE__ as of
+    ALNil         -> (0, [])
+    ALCons _ a as -> sizeAndBoundVars (a, as)
+    ALProj{}      -> __IMPOSSIBLE__
+    ALConPar as   -> sizeAndBoundVars as
+
+
+-- | Take a list of patterns and returns (is, size, vars) where (speculation):
+---  * the is are the pattern indices the vars are contained in
+--   * size is total number of constructors removed (?) to access vars
+localTerminationEnv :: [CSPat o] -> ([Nat], Nat, [Nat])
+localTerminationEnv pats = (is, getSum s, vs) where
+
+  (is , s , vs) = g 0 pats
+
+  g :: Nat -> [CSPat o] -> ([Nat], Sum Nat, [Nat])
+  g _ [] = ([], 0, [])
+  g i (hp@(HI _ p) : ps) = case p of
+    CSPatConApp{} -> let (size, vars) = sizeAndBoundVars hp
+                     in ([i], size, vars) <> g (i + 1) ps
+    _ -> g (i + 1) ps
+
+localTerminationSidecond :: ([Nat], Nat, [Nat]) -> ConstRef o -> MExp o -> EE (MyPB o)
+localTerminationSidecond (is, size, vars) reccallc b =
+  ok b
+ where
+     ok e = mmpcase (False, prioNo, Nothing) e $ \e -> case e of
+      App _ _ elr args -> mpret $ Sidecondition
+       (oks args)
+       (case elr of
+          Const c | c == reccallc -> if size == 0 then mpret (Error "localTerminationSidecond: no size to decrement") else okcall 0 size vars args
+          _ -> mpret OK
+       )
+      Lam _ (Abs _ e) -> ok e
+      Pi _ _ _ it (Abs _ ot) -> mpret $ Sidecondition
+       (ok it)
+       (ok ot)
+      Sort{} -> mpret OK
+
+      AbsurdLambda{} -> mpret OK
+
+
+     oks as = mmpcase (False, prioNo, Nothing) as $ \as -> case as of
+      ALNil -> mpret OK
+      ALCons _ a as -> mpret $ Sidecondition
+       (ok a)
+       (oks as)
+
+      ALProj eas _ _ as -> mpret $ Sidecondition (oks eas) (oks as)
+
+
+      ALConPar as -> oks as
+
+     okcall i size vars as = mmpcase (False, prioNo, Nothing) as $ \as -> case as of
+      ALNil -> mpret OK
+      ALCons _ a as | i `elem` is ->
+       mbpcase prioNo Nothing (he size vars a) $ \x -> case x of
+        Nothing -> mpret $ Error "localTerminationSidecond: reccall not ok"
+        Just (size', vars') -> okcall (i + 1) size' vars' as
+      ALCons _ a as -> okcall (i + 1) size vars as
+
+      ALProj{} -> mpret OK
+
+
+      ALConPar as -> __IMPOSSIBLE__
+
+     he size vars e = mmcase e $ \e -> case e of
+      App _ _ (Var v) _ ->
+       case remove v vars of
+        Nothing -> mbret Nothing
+        Just vars' -> mbret $ Just (size, vars')
+      App _ _ (Const c) args -> do
+       cd <- readIORef c
+       case cdcont cd of
+        Constructor{} ->
+         if size == 1 then
+          mbret Nothing
+         else
+          hes (size - 1) vars args
+        _ -> mbret Nothing
+      _ -> mbret Nothing
+     hes size vars as = mmcase as $ \as -> case as of
+      ALNil -> mbret $ Just (size, vars)
+      ALCons _ a as ->
+       mbcase (he size vars a) $ \x -> case x of
+        Nothing -> mbret Nothing
+        Just (size', vars') -> hes size' vars' as
+
+      ALProj{} -> __IMPOSSIBLE__
+
+
+      ALConPar as -> __IMPOSSIBLE__
+
+     remove _ [] = Nothing
+     remove x (y : ys) | x == y = Just ys
+     remove x (y : ys) = case remove x ys of {Nothing -> Nothing; Just ys' -> Just (y : ys')}
+
+-- ---------------------------
+
+
+getblks :: MExp o -> IO [Nat]
+getblks tt = do
+ NotB (hntt, blks) <- hnn_blks (Clos [] tt)
+ case f blks of
+  Just v -> return [v]
+  Nothing -> case rawValue hntt of
+   HNApp (Const c) args -> do
+    cd <- readIORef c
+    case cdcont cd of
+     Datatype{} -> g [] args
+     _ -> return []
+   _ -> return []
+ where
+  f blks = case blks of
+             (b : bs) -> case rawValue (last1 b bs) of
+              HNApp (Var v) _ -> Just v
+              _ -> Nothing
+             _ -> Nothing
+  g vs args = do
+   NotB hnargs <- hnarglist args
+   case hnargs of
+    HNALCons _ a as -> do
+     NotB (_, blks) <- hnn_blks a
+     let vs' = case f blks of
+                Just v | v `notElem` vs -> v : vs
+                _ -> vs
+     g vs' as
+    _ -> return vs
+-- ---------------------------
diff --git a/src/full/Agda/Auto/Convert.hs b/src/full/Agda/Auto/Convert.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/Convert.hs
@@ -0,0 +1,788 @@
+
+module Agda.Auto.Convert where
+
+import Prelude hiding ((!!))
+
+import Control.Monad          ( when )
+import Control.Monad.Except
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.State
+
+import Data.Bifunctor (first)
+import Data.IORef
+import Data.Maybe (catMaybes)
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.Syntax.Common (Hiding(..), getHiding, Arg)
+import Agda.Syntax.Concrete (exprFieldA)
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Internal (Dom'(..),domInfo,unDom)
+import qualified Agda.Syntax.Internal.Pattern as IP
+import qualified Agda.Syntax.Common as Cm
+import qualified Agda.Syntax.Abstract.Name as AN
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Position as SP
+
+import qualified Agda.TypeChecking.Monad.Base as MB
+
+import Agda.TypeChecking.Monad.Signature (getConstInfo, getDefFreeVars, ignoreAbstractMode)
+import Agda.TypeChecking.Level (reallyUnLevelView)
+import Agda.TypeChecking.Monad.Base (mvJudgement, mvPermutation, getMetaInfo, envContext, clEnv)
+import Agda.TypeChecking.Monad.MetaVars
+  (lookupMeta, withMetaInfo, lookupInteractionPoint)
+import Agda.TypeChecking.Monad.Context (getContextArgs)
+import Agda.TypeChecking.Monad.Constraints (getAllConstraints)
+import Agda.TypeChecking.Substitute (applySubst, renamingR)
+import Agda.TypeChecking.Telescope (piApplyM)
+import qualified Agda.TypeChecking.Substitute as I (absBody)
+import Agda.TypeChecking.Reduce (normalise, instantiate)
+import Agda.TypeChecking.EtaContract (etaContract)
+import Agda.TypeChecking.Monad.Builtin (constructorForm)
+import Agda.TypeChecking.Free as Free (freeIn)
+
+import Agda.Interaction.MakeCase (getClauseZipperForIP)
+
+import Agda.Auto.NarrowingSearch
+import Agda.Auto.Syntax hiding (getConst)
+
+import Agda.Auto.CaseSplit hiding (lift)
+
+import Agda.Utils.Either
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Monad       ( forMaybeMM )
+import Agda.Utils.Permutation ( Permutation(Perm), permute, takeP, compactP )
+import Agda.Syntax.Common.Pretty      ( prettyShow )
+
+import Agda.Utils.Impossible
+
+
+data Hint = Hint
+  { hintIsConstructor :: Bool
+  , hintQName         :: I.QName
+  }
+
+type O = (Maybe (Int, [Arg AN.QName]),AN.QName)
+  -- Nothing - Def
+  -- Just npar - Con with npar parameters which don't appear in Agda
+
+data TMode = TMAll -- can be extended to distinguish between different modes (all, only def)
+ deriving Eq
+
+type MapS a b = (Map a b, [a])
+
+initMapS :: MapS a b
+initMapS = (Map.empty, [])
+
+popMapS :: (S -> (a, [b])) -> ((a, [b]) -> S -> S) -> TOM (Maybe b)
+popMapS r w = do (m, xs) <- gets r
+                 case xs of
+                  [] -> return Nothing
+                  (x:xs) -> do
+                   modify (w (m, xs))
+                   return $ Just x
+
+data S = S {sConsts :: MapS AN.QName (TMode, ConstRef O),
+            sMetas :: MapS I.MetaId (Metavar (Exp O) (RefInfo O), Maybe (MExp O, [MExp O]), [I.MetaId]),
+            sEqs :: MapS Int (Maybe (Bool, MExp O, MExp O)),
+            sCurMeta :: Maybe I.MetaId,
+            sMainMeta :: I.MetaId
+           }
+
+type TOM = StateT S MB.TCM
+type MOT = ExceptT String IO
+
+tomy :: I.MetaId -> [Hint] -> [I.Type] ->
+        MB.TCM ([ConstRef O]
+               , [MExp O]
+               , Map I.MetaId (Metavar (Exp O) (RefInfo O), MExp O, [MExp O], [I.MetaId])
+               , [(Bool, MExp O, MExp O)]
+               , Map AN.QName (TMode, ConstRef O))
+tomy imi icns typs = do
+ eqs <- getEqs
+ let
+  r :: [AN.QName] -> TOM [AN.QName]
+  r projfcns = do
+   nxt <- popMapS sConsts (\x y -> y {sConsts = x})
+   case nxt of
+    Just cn -> do
+     cmap <- gets (fst . sConsts)
+     let (mode, c) = cmap Map.! cn
+     def <- lift $ getConstInfo cn
+     let typ = MB.defType def
+         defn = MB.theDef def
+     typ <- lift $ normalise typ
+     typ' <- convert typ
+     let clausesToDef clauses = do
+           clauses' <- convert clauses
+           let narg = case clauses of
+                        [] -> 0
+                        I.Clause {I.namedClausePats = xs} : _ -> length xs
+           return (Def narg clauses' Nothing Nothing, [])
+     (cont, projfcns2) <- case defn of
+      MB.Axiom {} -> return (Postulate, [])
+      MB.DataOrRecSig{} -> return (Postulate, [])
+      MB.GeneralizableVar{} -> __IMPOSSIBLE__
+      MB.AbstractDefn{} -> return (Postulate, [])
+      MB.Function {MB.funClauses = clauses} -> clausesToDef clauses
+      -- MB.Primitive {MB.primClauses = []} -> throwError $ strMsg "Auto: Primitive functions are not supported" -- Andreas, 2013-06-17 breaks interaction/AutoMisc
+      MB.Primitive {MB.primClauses = clauses} -> clausesToDef clauses
+      MB.PrimitiveSort{} -> __IMPOSSIBLE__
+      MB.Datatype {MB.dataCons = cons} -> do
+       cons2 <- mapM (\con -> getConst True con TMAll) cons
+       return (Datatype cons2 [], [])
+      MB.Record {MB.recFields = fields, MB.recTel = tel} -> do -- the value of recPars seems unreliable or don't know what it signifies
+       let pars n (I.El _ (I.Pi it typ)) = Cm.Arg (I.domInfo it) (I.var n) :
+                                           pars (n - 1) (I.unAbs typ)
+           pars _ (I.El _ _) = []
+           contyp npar I.EmptyTel = I.El (I.mkType 0 {- arbitrary -}) $
+                                      I.Def cn $ map I.Apply $ pars (npar - 1) typ
+           contyp npar (I.ExtendTel it (I.Abs v tel)) = I.El (I.mkType 0 {- arbitrary -}) (I.Pi it (I.Abs v (contyp (npar + 1) tel)))
+           contyp npar (I.ExtendTel it I.NoAbs{})     = __IMPOSSIBLE__
+       contyp' <- convert $ contyp 0 tel
+       cc <- lift $ liftIO $ readIORef c
+       let Datatype [con] [] = cdcont cc
+       lift $ liftIO $ modifyIORef con (\cdef -> cdef {cdtype = contyp'})
+
+       projfcns <- mapM (\ dom -> getConst False (I.unDom dom) TMAll) fields
+       -- Equivalently projfcns <- mapM (($ TMAll) . getConst False . I.unDom) fields
+
+       return (Datatype [con] projfcns, []{-map snd fields-})
+      MB.Constructor {MB.conData = dt} -> do
+       _ <- getConst False dt TMAll -- make sure that datatype is included
+       cc <- lift $ liftIO $ readIORef c
+       let (Just (nomi,_), _) = cdorigin cc
+       return (Constructor (nomi - cddeffreevars cc), [])
+     lift $ liftIO $ modifyIORef c (\cdef -> cdef {cdtype = typ', cdcont = cont})
+     r $ projfcns2 ++ projfcns
+    Nothing -> do
+     nxt <- popMapS sMetas (\x y -> y {sMetas = x})
+     case nxt of
+      Just mi -> do
+       mapM_ (\((_, e, i), eqi) -> do
+         when (fmExp mi e || fmExp mi i) $ do
+          (eqsm, eqsl) <- gets sEqs
+          when (Map.notMember eqi eqsm) $ do
+           modify $ \s -> s {sEqs = (Map.insert eqi Nothing eqsm, eqi : eqsl)}
+        ) (zip eqs [0..])
+       mv <- lift $ lookupLocalMetaAuto mi
+       msol <- case MB.mvInstantiation mv of
+                     MB.InstV{} ->
+                      lift $ withMetaInfo (getMetaInfo mv) $ do
+                       args <- getContextArgs
+                       --sol <- norm (I.MetaV mi args)
+                       sol <- instantiate $ I.MetaV mi $ map I.Apply $ permute (takeP (length args) $ mvPermutation mv) args
+                       return $ Just sol
+                     _ -> return Nothing
+       case msol of
+        Nothing -> return ()
+        Just sol -> do
+         m <- getMeta mi
+         sol' <- convert sol
+         modify $ \s -> s {sEqs = first (Map.insert (Map.size (fst $ sEqs s)) (Just (False, Meta m, sol'))) (sEqs s)}
+       let tt = MB.jMetaType $ mvJudgement mv
+           minfo = getMetaInfo mv
+           localVars = map (snd . I.unDom) . envContext . clEnv $ minfo
+       (targettype, localVars) <- lift $ withMetaInfo minfo $ do
+        vs <- getContextArgs
+        targettype <- tt `piApplyM` permute (takeP (length vs) $ mvPermutation mv) vs
+        targettype <- normalise targettype
+        localVars <- mapM normalise localVars
+        return (targettype, localVars)
+       modify (\s -> s {sCurMeta = Just mi})
+       typ' <- convert targettype
+       ctx' <- mapM convert localVars
+       modify (\s -> s {sCurMeta = Nothing})
+       modify (\s -> s {sMetas = first (Map.adjust (\(m, _, deps) -> (m, Just (typ', ctx'), deps)) mi) (sMetas s)})
+       r projfcns
+      Nothing -> do
+       nxt <- popMapS sEqs (\x y -> y {sEqs = x})
+       case nxt of
+        Just eqi -> do
+         let (ineq, e, i) = eqs !! eqi
+         e' <- convert e
+         i' <- convert i
+         modify (\s -> s {sEqs = first (Map.adjust (\_ -> Just (ineq, e', i')) eqi) (sEqs s)})
+         r projfcns
+        Nothing ->
+         return projfcns
+ ((icns', typs'), s) <- runStateT
+  (do _ <- getMeta imi
+      icns' <- mapM (\ (Hint iscon name) -> getConst iscon name TMAll) icns
+      typs' <- mapM convert typs
+      projfcns <- r []
+      projfcns' <- mapM (\name -> getConst False name TMAll) projfcns
+      [] <- r []
+      return (projfcns' ++ icns', typs')
+  ) (S {sConsts = initMapS, sMetas = initMapS, sEqs = initMapS, sCurMeta = Nothing, sMainMeta = imi})
+ lift $ liftIO $ mapM_ categorizedecl icns'
+ return (icns', typs', Map.map flatten (fst (sMetas s)), map fromJust $ Map.elems (fst (sEqs s)), fst (sConsts s))
+ where
+ flatten (x, Just (y, z), w) = (x, y, z, w)
+ flatten (x, Nothing, w) = __IMPOSSIBLE__
+
+ fromJust (Just x) = x
+ fromJust Nothing = __IMPOSSIBLE__
+
+getConst :: Bool -> AN.QName -> TMode -> TOM (ConstRef O)
+getConst iscon name mode = do
+ def <- lift $ getConstInfo name
+ case MB.theDef def of
+  MB.Record {MB.recConHead = con} -> do
+   let conname = I.conName con
+       conflds = I.conFields con
+   cmap <- gets (fst . sConsts)
+   case Map.lookup name cmap of
+    Just (mode', c) ->
+     if iscon then do
+      cd <- lift $ liftIO $ readIORef c
+      let Datatype [con] _ = cdcont cd
+      return con
+     else
+      return c
+    Nothing -> do
+     mainm <- gets sMainMeta
+     dfv <- lift $ getdfv mainm name
+     let nomi = I.arity (MB.defType def)
+     ccon <- lift $ liftIO $ newIORef (ConstDef {cdname = prettyShow name ++ ".CONS", cdorigin = (Just (nomi,conflds), conname), cdtype = __IMPOSSIBLE__, cdcont = Constructor (nomi - dfv), cddeffreevars = dfv}) -- ?? correct value of deffreevars for records?
+     c <- lift $ liftIO $ newIORef (ConstDef {cdname = prettyShow name, cdorigin = (Nothing, name), cdtype = __IMPOSSIBLE__, cdcont = Datatype [ccon] [], cddeffreevars = dfv}) -- ?? correct value of deffreevars for records?
+     modify (\s -> s {sConsts = (Map.insert name (mode, c) cmap, name : snd (sConsts s))})
+     return $ if iscon then ccon else c
+  _ -> do
+   cmap <- gets (fst . sConsts)
+   case Map.lookup name cmap of
+    Just (mode', c) ->
+     return c
+    Nothing -> do
+     (miscon, sname) <- if iscon then do
+       let MB.Constructor {MB.conPars = npar, MB.conData = dname, MB.conSrcCon = ch} = MB.theDef def
+       return (Just (npar,I.conFields ch), prettyShow dname ++ "." ++ prettyShow (I.qnameName name))
+      else
+       return (Nothing, prettyShow name)
+     mainm <- gets sMainMeta
+     dfv <- lift $ getdfv mainm name
+     c <- lift $ liftIO $ newIORef (ConstDef {cdname = sname, cdorigin = (miscon, name), cdtype = __IMPOSSIBLE__, cdcont = __IMPOSSIBLE__, cddeffreevars = dfv})
+     modify (\s -> s {sConsts = (Map.insert name (mode, c) cmap, name : snd (sConsts s))})
+     return c
+
+getdfv :: I.MetaId -> A.QName -> MB.TCM Cm.Nat
+getdfv mainm name = do
+ mv <- lookupLocalMetaAuto mainm
+ withMetaInfo (getMetaInfo mv) $ getDefFreeVars name
+
+-- | A variant of 'lookupLocalMeta' that, if applied to a remote
+-- meta-variable, raises a special error message noting that remote
+-- meta-variables are not handled by the auto command.
+
+lookupLocalMetaAuto :: I.MetaId -> MB.TCM MB.MetaVariable
+lookupLocalMetaAuto m = do
+  mv <- lookupMeta m
+  case mv of
+    Just (Right mv) -> return mv
+    Nothing         -> __IMPOSSIBLE__
+    Just Left{}     -> MB.typeError $ MB.GenericError $
+      "The auto command does not support remote meta-variables," ++
+      "consider using --no-save-metas"
+
+getMeta :: I.MetaId -> TOM (Metavar (Exp O) (RefInfo O))
+getMeta name = do
+ mmap <- gets (fst . sMetas)
+ case Map.lookup name mmap of
+  Just (m, _, _) ->
+   return m
+  Nothing -> do
+   m <- lift $ liftIO initMeta
+   modify $ \ s -> s { sMetas = (Map.insert name (m, Nothing, []) mmap, name : snd (sMetas s)) }
+   return m
+
+getEqs :: MB.TCM [(Bool, I.Term, I.Term)]
+getEqs = forMaybeMM getAllConstraints $ \ eqc -> do
+  neqc <- normalise eqc
+  case MB.clValue $ MB.theConstraint neqc of
+    MB.ValueCmp ineq _ i e -> do
+      ei <- etaContract i
+      ee <- etaContract e
+      return $ Just (tomyIneq ineq, ee, ei)
+    _ -> return Nothing
+
+literalsNotImplemented :: MB.TCM a
+literalsNotImplemented = MB.typeError $ MB.NotImplemented $
+  "The Agda synthesizer (Agsy) does not support literals yet"
+
+hitsNotImplemented :: MB.TCM a
+hitsNotImplemented = MB.typeError $ MB.NotImplemented $
+  "The Agda synthesizer (Agsy) does not support HITs yet"
+
+class Conversion m a b where
+  convert :: a -> m b
+
+instance Conversion TOM [I.Clause] [([Pat O], MExp O)] where
+  convert = fmap catMaybes . mapM convert
+
+instance Conversion TOM I.Clause (Maybe ([Pat O], MExp O)) where
+  convert cl = do
+    let -- Jesper, 2016-07-28:
+     -- I can't figure out if this should be the old or new
+     -- clause body (i.e. relative to the positions of pattern variables or
+     -- relative to the clauseTel). Both options pass the test suite, so I
+     -- have the impression it doesn't actually matter.
+     -- ALTERNATIVE CODE:
+     -- perm = fromMaybe __IMPOSSIBLE__ $ IP.clausePerm cl
+     -- body = applySubst (renamingR perm) $ I.clauseBody cl
+        body = I.clauseBody cl
+        pats = I.clausePats cl
+    pats' <- mapM convert (IP.unnumberPatVars pats :: [Cm.Arg I.Pattern])
+    body' <- traverse convert =<< lift (normalise body)
+    return $ (pats',) <$> body'
+
+instance Conversion TOM (Cm.Arg I.Pattern) (Pat O) where
+  convert p = case Cm.unArg p of
+    I.IApplyP _ _ _ n  -> return $ PatVar (prettyShow n)
+    I.VarP _ n  -> return $ PatVar (prettyShow n)
+    I.DotP _ _  -> return $ PatVar "_"
+      -- because Agda includes these when referring to variables in the body
+    I.ConP con _ pats -> do
+      let n = I.conName con
+      c     <- getConst True n TMAll
+      pats' <- mapM (convert . fmap Cm.namedThing) pats
+      def   <- lift $ getConstInfo n
+      cc    <- lift $ liftIO $ readIORef c
+      let Just (npar,_) = fst $ cdorigin cc
+      return $ PatConApp c (replicate npar PatExp ++ pats')
+    I.ProjP _ q -> PatProj <$> getConst True q TMAll
+
+    -- UNSUPPORTED CASES
+    I.LitP{}    -> lift literalsNotImplemented
+    I.DefP{}    -> lift hitsNotImplemented
+
+instance Conversion TOM I.Type (MExp O) where
+  convert (I.El _ t) = convert t -- sort info is thrown away
+
+instance Conversion TOM I.Term (MExp O) where
+  convert v0 =
+    case I.unSpine v0 of
+      I.Var v es -> do
+        let Just as = I.allApplyElims es
+        as' <- convert as
+        return $ NotM $ App Nothing (NotM OKVal) (Var v) as'
+      I.Lam info b -> do
+        b' <- convert (I.absBody b)
+        return $ NotM $ Lam (getHiding info) (Abs (Id $ I.absName b) b')
+      t@I.Lit{} -> do
+        t <- lift $ constructorForm t
+        case t of
+          I.Lit{} -> lift literalsNotImplemented
+          _       -> convert t
+      I.Level l -> convert =<< lift (reallyUnLevelView l)
+      I.Def name es -> do
+        let Just as = I.allApplyElims es
+        c   <- getConst False name TMAll
+        as' <- convert as
+        return $ NotM $ App Nothing (NotM OKVal) (Const c) as'
+      I.Con con ci es -> do
+        let Just as = I.allApplyElims es
+        let name = I.conName con
+        c   <- getConst True name TMAll
+        as' <- convert as
+        def <- lift $ getConstInfo name
+        cc  <- lift $ liftIO $ readIORef c
+        let Just (npar,_) = fst $ cdorigin cc
+        return $ NotM $ App Nothing (NotM OKVal) (Const c) (foldl (\x _ -> NotM $ ALConPar x) as' [1..npar])
+      I.Pi (I.Dom{domInfo = info, unDom = x}) b -> do
+        let y    = I.absBody b
+            name = I.absName b
+        x' <- convert x
+        y' <- convert y
+        return $ NotM $ Pi Nothing (getHiding info) (Free.freeIn 0 y) x' (Abs (Id name) y')
+      I.Sort (I.Type (I.ClosedLevel l)) -> return $ NotM $ Sort $ Set $ fromIntegral l
+      I.Sort _ -> return $ NotM $ Sort UnknownSort
+      I.Dummy{}-> return $ NotM $ Sort UnknownSort
+      t@I.MetaV{} -> do
+        t <- lift $ instantiate t
+        case t of
+          I.MetaV mid _ -> do
+            mcurmeta <- gets sCurMeta
+            case mcurmeta of
+              Nothing -> return ()
+              Just curmeta ->
+                modify $ \ s -> s { sMetas = first (Map.adjust (\(m, x, deps) -> (m, x, mid : deps)) curmeta) (sMetas s) }
+            m <- getMeta mid
+            return $ Meta m
+          _ -> convert t
+      I.DontCare _ -> return $ NotM dontCare
+
+instance Conversion TOM a b => Conversion TOM (Cm.Arg a) (Hiding, b) where
+  convert (Cm.Arg info a) = (getHiding info,) <$> convert a
+
+instance Conversion TOM I.Args (MM (ArgList O) (RefInfo O)) where
+  convert as = NotM . foldr (\ (hid,t) -> ALCons hid t . NotM) ALNil
+               <$> mapM convert as
+
+tomyIneq :: MB.Comparison -> Bool
+tomyIneq MB.CmpEq = False
+tomyIneq MB.CmpLeq = True
+
+-- ---------------------------------------------
+
+fmType :: I.MetaId -> I.Type -> Bool
+fmType m (I.El _ t) = fmExp m t
+
+fmExp :: I.MetaId -> I.Term -> Bool
+fmExp m (I.Var _ as) = fmExps m $ I.argsFromElims as
+fmExp m (I.Lam _ b) = fmExp m (I.unAbs b)
+fmExp m (I.Lit _) = False
+fmExp m (I.Level (I.Max _ as)) = any (fmLevel m) as
+fmExp m (I.Def _ as) = fmExps m $ I.argsFromElims as
+fmExp m (I.Con _ ci as) = fmExps m $ I.argsFromElims as
+fmExp m (I.Pi x y)  = fmType m (I.unDom x) || fmType m (I.unAbs y)
+fmExp m (I.Sort _) = False
+fmExp m (I.MetaV mid _) = mid == m
+fmExp m (I.DontCare _) = False
+fmExp _ I.Dummy{} = False
+
+fmExps :: I.MetaId -> I.Args -> Bool
+fmExps m as = any (fmExp m . Cm.unArg) as
+
+fmLevel :: I.MetaId -> I.PlusLevel -> Bool
+fmLevel m (I.Plus _ l) = fmExp m l
+
+-- ---------------------------------------------
+
+icnvh :: Hiding -> Cm.ArgInfo
+icnvh h = Cm.setHiding h $
+          Cm.setOrigin o $
+          Cm.defaultArgInfo
+    where
+    -- Andreas, 2017-01-18, issue #819.
+    -- Visible arguments are made UserWritten,
+    -- otherwise they might not be printed in patterns.
+    o = case h of
+          NotHidden  -> Cm.UserWritten
+          Instance{} -> Cm.Inserted
+          Hidden     -> Cm.Inserted
+
+-- ---------------------------------------------
+
+instance Conversion MOT a b => Conversion MOT (MM a (RefInfo O)) b where
+  convert meta = case meta of
+    NotM a -> convert a
+    Meta m -> do
+      ma <- lift $ readIORef $ mbind m
+      case ma of
+        Nothing -> throwError "meta not bound"
+        Just a  -> convert a
+
+instance Conversion MOT a b => Conversion MOT (Abs a) (I.Abs b) where
+  convert (Abs mid t) = I.Abs id <$> convert t where
+    id = case mid of
+           NoId  -> "x"
+           Id id -> id
+
+instance Conversion MOT (Exp O) I.Type where
+  convert e = I.El (I.mkType 0) <$> convert e
+              -- 0 is arbitrary, sort not read by Agda when reifying
+
+instance Conversion MOT (Exp O) I.Term where
+  convert = \case
+    App _ _ (Var v) as -> frommyExps 0 as (I.Var v [])
+    App _ _ (Const c) as -> do
+      cdef <- lift $ readIORef c
+      let (iscon, name) = cdorigin cdef
+{-
+   case iscon of
+      Just n -> do
+        v <- getConTerm name -- We are not in TCM
+        frommyExps n as v
+-}
+          (ndrop, h) = case iscon of
+                         Just (n,fs) -> (n, \ q -> I.Con (I.ConHead q I.IsData Cm.Inductive fs) Cm.ConOSystem)
+                         Nothing -> (0, \ f vs -> I.Def f vs)
+      frommyExps ndrop as (h name [])
+    Lam hid t -> I.Lam (icnvh hid) <$> convert t
+    Pi _ hid _ x y -> do
+      x' <- convert x
+      let dom = (I.defaultDom x') {domInfo = icnvh hid}
+      I.Pi dom <$> convert y
+   -- maybe have case for Pi where possdep is False which produces Fun (and has to unweaken y), return $ I.Fun (Cm.Arg (icnvh hid) x') y'
+    Sort (Set l) -> return $ I.Sort (I.mkType (fromIntegral l))
+    Sort Type -> __IMPOSSIBLE__
+    Sort UnknownSort -> return $ I.Sort (I.mkType 0) -- hoping it's thrown away
+
+    AbsurdLambda hid -> return $ I.Lam (icnvh hid)
+                               $ I.Abs abslamvarname (I.Var 0 [])
+
+frommyExps :: Nat -> MArgList O -> I.Term -> ExceptT String IO I.Term
+frommyExps ndrop (Meta m) trm = do
+ bind <- lift $ readIORef $ mbind m
+ case bind of
+  Nothing -> throwError "meta not bound"
+  Just e -> frommyExps ndrop (NotM e) trm
+frommyExps ndrop (NotM as) trm =
+ case as of
+  ALNil -> return trm
+  ALCons _ _ xs | ndrop > 0 -> frommyExps (ndrop - 1) xs trm
+  ALCons hid x xs -> do
+   x' <- convert x
+   frommyExps ndrop xs (addend (Cm.Arg (icnvh hid) x') trm)
+
+  -- Andreas, 2013-10-19 TODO: restore postfix projections
+  ALProj eas idx hid xs -> do
+   idx <- lift $ expandbind idx
+   c <- case idx of
+            NotM c -> return c
+            Meta{} -> throwError "meta not bound"
+   cdef <- lift $ readIORef c
+   let name = snd $ cdorigin cdef
+   trm2 <- frommyExps 0 eas (I.Def name [])
+   frommyExps 0 xs (addend (Cm.Arg (icnvh hid) trm) trm2)
+
+  ALConPar xs | ndrop > 0 -> frommyExps (ndrop - 1) xs trm
+  ALConPar _ -> __IMPOSSIBLE__
+ where
+  addend x (I.Var h xs) = I.Var h (xs ++ [I.Apply x])
+  addend x (I.Con h ci xs) = I.Con h ci (xs ++ [I.Apply x])
+  addend x (I.Def h xs) = I.Def h (xs ++ [I.Apply x])
+  addend _ _ = __IMPOSSIBLE__
+
+-- --------------------------------
+
+abslamvarname :: String
+abslamvarname = "\0absurdlambda"
+
+modifyAbstractExpr :: A.Expr -> A.Expr
+modifyAbstractExpr = f
+ where
+  f (A.App i e1 (Cm.Arg info (Cm.Named n e2))) =
+        A.App i (f e1) (Cm.Arg info (Cm.Named n (f e2)))
+  f (A.Lam i (A.DomainFree _ x) _)
+     | A.Binder _ (A.BindName{unBind = n}) <- Cm.namedArg x
+     , prettyShow (A.nameConcrete n) == abslamvarname =
+        A.AbsurdLam i $ Cm.getHiding x
+  f (A.Lam i b e) = A.Lam i b (f e)
+  f (A.Rec i xs) = A.Rec i (map (mapLeft (over exprFieldA f)) xs)
+  f (A.RecUpdate i e xs) = A.RecUpdate i (f e) (map (over exprFieldA f) xs)
+  f (A.ScopedExpr i e) = A.ScopedExpr i (f e)
+  f e = e
+
+modifyAbstractClause :: A.Clause -> A.Clause
+modifyAbstractClause (A.Clause lhs spats (A.RHS e mc) decls catchall) =
+  A.Clause lhs spats (A.RHS (modifyAbstractExpr e) mc) decls catchall
+modifyAbstractClause cl = cl
+
+-- ---------------------------------
+
+
+constructPats :: Map AN.QName (TMode, ConstRef O) -> I.MetaId -> I.Clause -> MB.TCM ([(Hiding, MId)], [CSPat O])
+constructPats cmap mainm clause = do
+ let cnvps ns [] = return (ns, [])
+     cnvps ns (p : ps) = do
+      (ns', ps') <- cnvps ns ps
+      (ns'', p') <- cnvp ns' p
+      return (ns'', p' : ps')
+     cnvp ns p =
+      let hid = getHiding $ Cm.argInfo p
+      in case Cm.namedArg p of
+       I.VarP _ n -> return ((hid, Id n) : ns, HI hid (CSPatVar $ length ns))
+       I.IApplyP _ _ _ n -> return ((hid, Id n) : ns, HI hid (CSPatVar $ length ns))
+       I.ConP con _ ps -> do
+        let c = I.conName con
+        (c2, _) <- runStateT (getConst True c TMAll) (S {sConsts = (cmap, []), sMetas = initMapS, sEqs = initMapS, sCurMeta = Nothing, sMainMeta = mainm})
+        (ns', ps') <- cnvps ns ps
+        cc <- liftIO $ readIORef c2
+        let Just (npar,_) = fst $ cdorigin cc
+        return (ns', HI hid (CSPatConApp c2 (replicate npar (HI Hidden CSOmittedArg) ++ ps')))
+       I.DotP _ t -> do
+        (t2, _) <- runStateT (convert t) (S {sConsts = (cmap, []), sMetas = initMapS, sEqs = initMapS, sCurMeta = Nothing, sMainMeta = mainm})
+        return (ns, HI hid (CSPatExp t2))
+       I.ProjP po c -> do
+        (c2, _) <- runStateT (getConst True c TMAll) (S {sConsts = (cmap, []), sMetas = initMapS, sEqs = initMapS, sCurMeta = Nothing, sMainMeta = mainm})
+        cc <- liftIO $ readIORef c2
+        return (ns, HI hid (CSPatProj c2))
+       I.LitP{} -> literalsNotImplemented
+       I.DefP{} -> hitsNotImplemented
+
+ (names, pats) <- cnvps [] (IP.unnumberPatVars $ I.namedClausePats clause)
+ return (reverse names, pats)
+
+
+frommyClause :: (CSCtx O, [CSPat O], Maybe (MExp O)) -> ExceptT String IO I.Clause
+frommyClause (ids, pats, mrhs) = do
+ let ctel [] = return I.EmptyTel
+     ctel (HI hid (mid, t) : ctx) = do
+      let Id id = mid
+      tel <- ctel ctx
+      t' <- convert t
+      let dom = (I.defaultDom t') {domInfo = icnvh hid}
+      return $ I.ExtendTel dom (I.Abs id tel)
+ tel <- ctel $ reverse ids
+ let getperms 0 [] perm nv = return (perm, nv)
+     getperms n [] _ _ = __IMPOSSIBLE__
+     getperms 0 (p : ps) perm nv = do
+      (perm, nv) <- getperm p perm nv
+      getperms 0 ps perm nv
+     getperms n (HI _ CSPatExp{} : ps) perm nv = getperms (n - 1) ps perm nv
+     getperms n (HI _ CSOmittedArg{} : ps) perm nv = getperms (n - 1) ps perm nv
+     getperms n (_ : _) _ _ = __IMPOSSIBLE__
+     getperm (HI _ p) perm nv =
+      case p of
+       --CSPatVar v -> return (length ids + nv - 1 - v : perm, nv)
+       CSPatVar v -> return ((length ids - 1 - v, nv) : perm, nv + 1)
+       CSPatConApp c ps -> do
+        cdef <- lift $ readIORef c
+        let (Just (ndrop,_), _) = cdorigin cdef
+        getperms ndrop ps perm nv
+       CSPatExp e -> return (perm, nv + 1)
+       _ -> __IMPOSSIBLE__
+ (rperm, nv) <- getperms 0 pats [] 0
+ let --perm = reverse rperm
+     perm = map (\i -> let Just x = lookup i rperm in x) [0..length ids - 1]
+     --renperm = map (\i -> length ids + nv - 1 - i) rperm
+     --renm = rename (\i -> renperm !! i)
+     cnvps 0 [] = return []
+     cnvps n [] = __IMPOSSIBLE__
+     cnvps 0 (p : ps) = do
+      p' <- cnvp p
+      ps' <- cnvps 0 ps
+      return (p' : ps')
+     cnvps n (HI _ CSPatExp{} : ps) = cnvps (n - 1) ps
+     cnvps n (HI _ CSOmittedArg{} : ps) = cnvps (n - 1) ps
+     cnvps n (_ : _) = __IMPOSSIBLE__
+     cnvp (HI hid p) = do
+      p' <- case p of
+       CSPatVar v -> return (I.varP $ let HI _ (Id n, _) = ids !! v in n)
+       CSPatConApp c ps -> do
+        cdef <- lift $ readIORef c
+        let (Just (ndrop,_), name) = cdorigin cdef
+        ps' <- cnvps ndrop ps
+        let con = I.ConHead name I.IsData Cm.Inductive [] -- TODO: restore DataOrRecord and record fields!
+        return (I.ConP con I.noConPatternInfo ps')
+       CSPatExp e -> do
+        e' <- convert e {- renm e -} -- renaming before adding to clause below
+        return (I.dotP e')
+       CSAbsurd -> __IMPOSSIBLE__ -- CSAbsurd not used
+       _ -> __IMPOSSIBLE__
+      return $ Cm.Arg (icnvh hid) $ Cm.unnamed p'   -- TODO: recover names
+ ps <- cnvps 0 pats
+ body <- case mrhs of
+          Nothing -> return $ Nothing
+          Just e -> Just <$> convert e
+ let cperm =  Perm nv perm
+ return I.Clause
+   { I.clauseLHSRange  = SP.noRange
+   , I.clauseFullRange = SP.noRange
+   , I.clauseTel       = tel
+   , I.namedClausePats = IP.numberPatVars __IMPOSSIBLE__ cperm $ applySubst (renamingR $ compactP cperm) ps
+   , I.clauseBody      = body
+   , I.clauseType      = Nothing -- TODO: compute clause type
+   , I.clauseCatchall    = False
+   , I.clauseExact       = Nothing -- TODO
+   , I.clauseRecursive   = Nothing -- TODO: Don't know here whether recursive or not !?
+   , I.clauseUnreachable = Nothing -- TODO: Don't know here whether reachable or not !?
+   , I.clauseEllipsis    = Cm.NoEllipsis
+   , I.clauseWhereModule = Nothing
+   }
+
+contains_constructor :: [CSPat O] -> Bool
+contains_constructor = any f
+ where
+  f (HI _ p) = case p of
+         CSPatConApp{} -> True
+         _ -> False
+
+-- ---------------------------------
+
+freeIn :: Nat -> MExp o -> Bool
+freeIn = f
+ where
+  mr x = let NotM x' = x in x'
+  f v e = case mr e of
+   App _ _ elr args -> case elr of
+    Var v' | v' == v -> False
+    _ -> fs v args
+   Lam _ (Abs _ b) -> f (v + 1) b
+   Pi _ _ _ it (Abs _ ot) -> f v it && f (v + 1) ot
+   Sort{} -> True
+
+   AbsurdLambda{} -> True
+
+
+  fs v es = case mr es of
+   ALNil -> True
+   ALCons _ a as -> f v a && fs v as
+
+   ALProj{} -> __IMPOSSIBLE__
+
+
+   ALConPar as -> fs v as
+
+
+negtype :: ConstRef o -> MExp o -> MExp o
+negtype ee = f (0 :: Int)
+ where
+  mr x = let NotM x' = x in x'
+  f n e = case mr e of
+   Pi uid hid possdep it (Abs id ot) -> NotM $ Pi uid hid possdep it (Abs id (f (n + 1) ot))
+   _ -> NotM $ Pi Nothing NotHidden False (NotM $ Pi Nothing NotHidden False e (Abs NoId (NotM $ Pi Nothing NotHidden True (NotM $ Sort (Set 0)) (Abs NoId (NotM $ App Nothing (NotM OKVal) (Var 0) (NotM ALNil)))))) (Abs NoId (NotM $ App Nothing (NotM OKVal) (Const ee) (NotM ALNil)))
+
+-- ---------------------------------------
+
+findClauseDeep :: Cm.InteractionId -> MB.TCM (Maybe (AN.QName, I.Clause, Bool))
+findClauseDeep ii = ignoreAbstractMode $ do  -- Andreas, 2016-09-04, issue #2162
+  MB.InteractionPoint { MB.ipClause = ipCl} <- lookupInteractionPoint ii
+  case ipCl of
+    MB.IPNoClause -> return Nothing
+    MB.IPClause f clauseNo _ _ _ _ -> do
+      (_, (_, c, _)) <- getClauseZipperForIP f clauseNo
+      return $ Just (f, c, maybe __IMPOSSIBLE__ toplevel $ I.clauseBody c)
+  where
+    toplevel e =
+     case e of
+      I.MetaV{} -> True
+      _ -> False
+
+-- ---------------------------------------
+
+matchType :: Int -> Int -> I.Type -> I.Type -> Maybe (Nat, Nat) -- Nat is deffreevars of const, Nat is ctx length of target type, left arg is const type, right is target type
+matchType cdfv tctx ctyp ttyp = trmodps cdfv ctyp
+ where
+  trmodps 0 ctyp = tr 0 0 ctyp
+  trmodps n ctyp = case I.unEl ctyp of
+   I.Pi _ ot -> trmodps (n - 1) (I.absBody ot)
+   _ -> __IMPOSSIBLE__
+  tr narg na ctyp =
+   case ft 0 0 Just ctyp ttyp of
+    Just n -> Just (n, narg)
+    Nothing -> case I.unEl ctyp of
+     I.Pi _ (I.Abs _ ot) -> tr (narg + 1) (na + 1) ot
+     I.Pi _ (I.NoAbs _ ot) -> tr (narg + 1) na ot
+     _ -> Nothing
+   where
+    ft nl n c (I.El _ e1) (I.El _ e2) = f nl n c e1 e2
+    f nl n c e1 e2 = case e1 of
+     I.Var v1 as1 | v1 < nl -> case e2 of
+      I.Var v2 as2 | v1 == v2 -> fes nl (n + 1) c as1 as2
+      _ -> Nothing
+     I.Var v1 _ | v1 < nl + na -> c n -- unify vars with no args?
+     I.Var v1 as1 -> case e2 of
+      I.Var v2 as2 | cdfv + na + nl - v1 == tctx + nl - v2 -> fes nl (n + 1) c as1 as2
+      _ -> Nothing
+     _ -> case (e1, e2) of
+      (I.MetaV{}, _) -> c n
+      (_, I.MetaV{}) -> c n
+      (I.Lam hid1 b1, I.Lam hid2 b2) | hid1 == hid2 -> f (nl + 1) n c (I.absBody b1) (I.absBody b2)
+      (I.Lit lit1, I.Lit lit2) | lit1 == lit2 -> c (n + 1)
+      (I.Def n1 as1, I.Def n2 as2) | n1 == n2 -> fes nl (n + 1) c as1 as2
+      (I.Con n1 _ as1, I.Con n2 _ as2) | n1 == n2 -> fs nl (n + 1) c as1 as2
+      (I.Pi (I.Dom{domInfo = info1, unDom = it1})  ot1, I.Pi (I.Dom{domInfo = info2, unDom = it2})  ot2) | Cm.argInfoHiding info1 == Cm.argInfoHiding info2 -> ft nl n (\n -> ft (nl + 1) n c (I.absBody ot1) (I.absBody ot2)) it1 it2
+      (I.Sort{}, I.Sort{}) -> c n -- sloppy
+      _ -> Nothing
+    fs nl n c es1 es2 = case (es1, es2) of
+     ([], []) -> c n
+     (I.Apply (Cm.Arg info1 e1) : es1, I.Apply (Cm.Arg info2 e2) : es2) | Cm.argInfoHiding info1 == Cm.argInfoHiding info2 -> f nl n (\n -> fs nl n c es1 es2) e1 e2
+     _ -> Nothing
+    fes nl n c es1 es2 = case (es1, es2) of
+     ([], []) -> c n
+     (I.Proj _ f : es1, I.Proj _ f' : es2) | f == f' -> fes nl n c es1 es2
+     (I.Apply (Cm.Arg info1 e1) : es1, I.Apply (Cm.Arg info2 e2) : es2) | Cm.argInfoHiding info1 == Cm.argInfoHiding info2 -> f nl n (\n -> fes nl n c es1 es2) e1 e2
+     _ -> Nothing
diff --git a/src/full/Agda/Auto/NarrowingSearch.hs b/src/full/Agda/Auto/NarrowingSearch.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/NarrowingSearch.hs
@@ -0,0 +1,670 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Auto.NarrowingSearch where
+
+import Control.Monad       ( foldM, when )
+import Control.Monad.State ( MonadState(..), modify, StateT, evalStateT, runStateT )
+import Control.Monad.Trans ( lift )
+
+import Data.IORef hiding (writeIORef, modifyIORef)
+import qualified Data.IORef as NoUndo (writeIORef, modifyIORef)
+
+import Agda.Utils.Impossible
+import Agda.Utils.Empty
+
+newtype Prio = Prio { getPrio :: Int }
+ deriving (Eq, Ord, Num)
+
+class Trav a where
+  type Block a
+  trav :: Monad m => (forall b. TravWith b (Block a) => MM b (Block b) -> m ()) -> a -> m ()
+
+-- | Trav instance 'a' with block type 'blk'
+type TravWith a blk = (Trav a, Block a ~ blk)
+
+instance TravWith a blk => Trav (MM a blk) where
+  type Block (MM a blk) = blk
+  trav f me = f me
+
+data Term blk = forall a. TravWith a blk => Term a
+
+-- | Result of type-checking.
+data Prop blk
+  = OK
+    -- ^ Success.
+  | Error String
+    -- ^ Definite failure.
+  | forall a . AddExtraRef String (Metavar a blk) (Move' blk a)
+    -- ^ Experimental.
+  | And (Maybe [Term blk]) (MetaEnv (PB blk)) (MetaEnv (PB blk))
+    -- ^ Parallel conjunction of constraints.
+  | Sidecondition (MetaEnv (PB blk)) (MetaEnv (PB blk))
+    -- ^ Experimental, related to 'mcompoint'.
+    -- First arg is sidecondition.
+  | Or Prio (MetaEnv (PB blk)) (MetaEnv (PB blk))
+    -- ^ Forking proof on something that is not part of the term language.
+    --   E.g. whether a term will reduce or not.
+  | ConnectHandle (OKHandle blk) (MetaEnv (PB blk))
+    -- ^ Obsolete.
+
+data OKVal = OKVal
+type OKHandle blk = MM OKVal blk
+type OKMeta blk = Metavar OKVal blk
+
+-- | Agsy's meta variables.
+--
+--   @a@ the type of the metavariable (what it can be instantiated with).
+--   @blk@ the search control information (e.g. the scope of the meta).
+
+data Metavar a blk = Metavar
+  { mbind :: IORef (Maybe a)
+    -- ^ Maybe an instantiation (refinement).  It is usually shallow,
+    --   i.e., just one construct(or) with arguments again being metas.
+  , mprincipalpresent :: IORef Bool
+    -- ^ Does this meta block a principal constraint
+    --   (i.e., a type-checking constraint).
+  , mobs :: IORef [(QPB a blk, Maybe (CTree blk))]
+    -- ^ List of observers, i.e., constraints blocked by this meta.
+  , mcompoint :: IORef [SubConstraints blk]
+    -- ^ Used for experiments with independence of subproofs.
+  , mextrarefs :: IORef [Move' blk a]
+    -- ^ Experimental.
+  }
+
+hequalMetavar :: Metavar a1 blk1 -> Metavar a2 bkl2 -> Bool
+hequalMetavar m1 m2 = mprincipalpresent m1 == mprincipalpresent m2
+
+instance Eq (Metavar a blk) where
+ x == y = hequalMetavar x y
+
+newMeta :: IORef [SubConstraints blk] -> IO (Metavar a blk)
+newMeta mcompoint = do
+ bind <- newIORef Nothing
+ pp <- newIORef False
+ obs <- newIORef []
+ erefs <- newIORef []
+ return $ Metavar bind pp obs mcompoint erefs
+
+initMeta :: IO (Metavar a blk)
+initMeta = do
+ cp <- newIORef []
+ newMeta cp
+
+data CTree blk = CTree
+ {ctpriometa :: IORef (PrioMeta blk),
+  ctsub :: IORef (Maybe (SubConstraints blk)),
+  ctparent :: IORef (Maybe (CTree blk)), -- Nothing - root
+  cthandles :: IORef [OKMeta blk]
+ }
+
+data SubConstraints blk = SubConstraints
+ {scflip :: IORef Bool,
+  sccomcount :: IORef Int,
+  scsub1 :: CTree blk,
+  scsub2 :: CTree blk
+ }
+
+
+newCTree :: Maybe (CTree blk) -> IO (CTree blk)
+newCTree parent = do
+ priometa <- newIORef (NoPrio False)
+ sub <- newIORef Nothing
+ rparent <- newIORef parent
+ handles <- newIORef []
+ return $ CTree priometa sub rparent handles
+
+newSubConstraints :: CTree blk -> IO (SubConstraints blk)
+newSubConstraints node = do
+ flip <- newIORef True -- False -- initially (and always) True, trying out prefer rightmost subterm when none have priority
+ comcount <- newIORef 0
+ sub1 <- newCTree $ Just node
+ sub2 <- newCTree $ Just node
+ return $ SubConstraints flip comcount sub1 sub2
+
+
+data PrioMeta blk = forall a . Refinable a blk => PrioMeta Prio (Metavar a blk)
+                  | NoPrio Bool -- True if subconstraint is done (all OK)
+
+instance Eq (PrioMeta blk) where
+ NoPrio d1 == NoPrio d2 = d1 == d2
+ PrioMeta p1 m1 == PrioMeta p2 m2 = p1 == p2 && hequalMetavar m1 m2
+ _ == _ = False
+
+-- -----------------------
+
+data Restore = forall a . Restore (IORef a) a
+
+type Undo = StateT [Restore] IO
+
+ureadIORef :: IORef a -> Undo a
+ureadIORef ptr = lift $ readIORef ptr
+
+uwriteIORef :: IORef a -> a -> Undo ()
+uwriteIORef ptr newval = do
+ oldval <- ureadIORef ptr
+ modify (Restore ptr oldval :)
+ lift $ NoUndo.writeIORef ptr newval
+
+umodifyIORef :: IORef a -> (a -> a) -> Undo ()
+umodifyIORef ptr f = do
+ oldval <- ureadIORef ptr
+ modify (Restore ptr oldval :)
+ lift $ NoUndo.writeIORef ptr (f oldval)
+
+ureadmodifyIORef :: IORef a -> (a -> a) -> Undo a
+ureadmodifyIORef ptr f = do
+ oldval <- ureadIORef ptr
+ modify (Restore ptr oldval :)
+ lift $ NoUndo.writeIORef ptr (f oldval)
+ return oldval
+
+runUndo :: Undo a -> IO a
+runUndo x = do
+ (res, restores) <- runStateT x []
+ mapM_ (\(Restore ptr oldval) -> NoUndo.writeIORef ptr oldval) restores
+ return res
+
+-- -----------------------
+
+newtype RefCreateEnv blk a = RefCreateEnv
+  { runRefCreateEnv :: StateT ((IORef [SubConstraints blk]), Int) IO a }
+
+instance Functor (RefCreateEnv blk) where
+  fmap f = RefCreateEnv . fmap f . runRefCreateEnv
+
+instance Applicative (RefCreateEnv blk) where
+  pure    = RefCreateEnv . pure
+  f <*> t = RefCreateEnv $ runRefCreateEnv f <*> runRefCreateEnv t
+
+instance Monad (RefCreateEnv blk) where
+  return = pure
+  t >>= f = RefCreateEnv $ runRefCreateEnv t >>= runRefCreateEnv . f
+
+
+newtype Cost = Cost { getCost :: Int }
+  deriving (Num, Eq, Ord)
+
+data Move' blk a = Move
+  { moveCost :: Cost
+  , moveNext :: RefCreateEnv blk a
+  }
+
+class Refinable a blk where
+ refinements :: blk -> [blk] -> Metavar a blk -> IO [Move' blk a]
+
+
+newPlaceholder :: RefCreateEnv blk (MM a blk)
+newPlaceholder = RefCreateEnv $ do
+ (mcompoint, c) <- get
+ m <- lift $ newMeta mcompoint
+ put (mcompoint, (c + 1))
+ return $ Meta m
+
+newOKHandle :: RefCreateEnv blk (OKHandle blk)
+newOKHandle = RefCreateEnv $ do
+ (e, c) <- get
+ cp <- lift $ newIORef []
+ m  <- lift $ newMeta cp
+ put (e, (c + 1))
+ return $ Meta m
+
+dryInstantiate :: RefCreateEnv blk a -> IO a
+dryInstantiate bind = evalStateT (runRefCreateEnv bind) (__IMPOSSIBLE__, 0)
+
+type BlkInfo blk = (Bool, Prio, Maybe blk) -- Bool - is principal
+
+data MM a blk = NotM a
+              | Meta (Metavar a blk)
+
+rm :: Empty -> MM a b -> a
+rm _ (NotM x) = x
+rm e Meta{}   = absurd e
+
+type MetaEnv = IO
+
+
+data MB a blk = NotB a
+              | forall b . Refinable b blk => Blocked (Metavar b blk) (MetaEnv (MB a blk))
+              | Failed String
+
+data PB blk = NotPB (Prop blk)
+            | forall b . Refinable b blk => PBlocked (Metavar b blk) (BlkInfo blk) (MetaEnv (PB blk))
+            | forall b1 b2 . (Refinable b1 blk, Refinable b2 blk) => PDoubleBlocked (Metavar b1 blk) (Metavar b2 blk) (MetaEnv (PB blk))
+
+data QPB b blk = QPBlocked (BlkInfo blk) (MetaEnv (PB blk))
+               | QPDoubleBlocked (IORef Bool) (MetaEnv (PB blk)) -- flag set True by first observer that continues
+
+mmcase :: Refinable a blk => MM a blk -> (a -> MetaEnv (MB b blk)) -> MetaEnv (MB b blk)
+mmcase x f = case x of
+ NotM x -> f x
+ x@(Meta m) -> do
+  bind <- readIORef $ mbind m
+  case bind of
+   Just x -> f x
+   Nothing -> return $ Blocked m (mmcase x f)
+
+mmmcase :: MM a blk -> MetaEnv (MB b blk) -> (a -> MetaEnv (MB b blk)) -> MetaEnv (MB b blk)
+mmmcase x fm f = case x of
+ NotM x -> f x
+ Meta m -> do
+  bind <- readIORef $ mbind m
+  maybe fm f bind
+
+mmpcase :: Refinable a blk => BlkInfo blk -> MM a blk -> (a -> MetaEnv (PB blk)) -> MetaEnv (PB blk)
+mmpcase blkinfo x f = case x of
+ NotM x -> f x
+ x@(Meta m) -> do
+  bind <- readIORef $ mbind m
+  case bind of
+   Just x -> f x
+   Nothing -> return $ PBlocked m blkinfo (mmpcase __IMPOSSIBLE__ x f) -- blkinfo not needed because will be notb next time
+
+doubleblock :: (Refinable a blk, Refinable b blk) => MM a blk -> MM b blk -> MetaEnv (PB blk) -> MetaEnv (PB blk)
+doubleblock (Meta m1) (Meta m2) cont = return $ PDoubleBlocked m1 m2 cont
+doubleblock _ _ _ = __IMPOSSIBLE__
+
+mbcase :: MetaEnv (MB a blk) -> (a -> MetaEnv (MB b blk)) -> MetaEnv (MB b blk)
+mbcase x f = do
+ x' <- x
+ case x' of
+  NotB x -> f x
+  Blocked m x -> return $ Blocked m (mbcase x f)
+  Failed msg -> return $ Failed msg
+
+mbpcase :: Prio -> Maybe blk -> MetaEnv (MB a blk) -> (a -> MetaEnv (PB blk)) -> MetaEnv (PB blk)
+mbpcase prio bi x f = do
+ x' <- x
+ case x' of
+  NotB x -> f x
+  Blocked m x -> return $ PBlocked m (False, prio, bi) (mbpcase prio bi x f)
+  Failed msg -> return $ NotPB $ Error msg
+
+mmbpcase :: MetaEnv (MB a blk) -> (forall b . Refinable b blk => MM b blk -> MetaEnv (PB blk)) -> (a -> MetaEnv (PB blk)) -> MetaEnv (PB blk)
+mmbpcase x fm f = do
+ x' <- x
+ case x' of
+  NotB x -> f x
+  Blocked m _ -> fm (Meta m)
+  Failed msg -> return $ NotPB $ Error msg
+
+waitok :: OKHandle blk -> MetaEnv (MB b blk) -> MetaEnv (MB b blk)
+waitok okh f =
+ mmcase okh $ \ OKVal -> f -- principle constraint is never present for okhandle so it will not be refined
+
+mbret :: a -> MetaEnv (MB a blk)
+mbret x = return $ NotB x
+
+mbfailed :: String -> MetaEnv (MB a blk)
+mbfailed msg = return $ Failed msg
+
+mpret :: Prop blk -> MetaEnv (PB blk)
+mpret p = return $ NotPB p
+
+expandbind :: MM a blk -> MetaEnv (MM a blk)
+expandbind x = case x of
+ NotM{} -> return x
+ Meta m -> do
+  bind <- readIORef $ mbind m
+  case bind of
+   Just x -> return $ NotM x
+   Nothing -> return x
+
+
+-- -----------------------
+
+type HandleSol = IO ()
+
+
+type SRes = Either Bool Int
+
+topSearch :: forall blk . IORef Int -> IORef Int -> HandleSol -> blk -> MetaEnv (PB blk) -> Cost -> Cost -> IO Bool
+topSearch ticks nsol hsol envinfo p searchdepth depthinterval = do
+ depthreached <- newIORef False
+
+
+ mainroot <- newCTree Nothing
+
+ let
+  searchSubProb :: [(CTree blk, Maybe (IORef Bool))] -> Cost -> IO SRes
+  searchSubProb [] depth = do
+   when (depth < depthinterval) $ do
+
+
+    hsol
+    n <- readIORef nsol
+    NoUndo.writeIORef nsol $! n - 1
+
+
+   return $ Left True
+  searchSubProb ((root, firstdone) : restprobs) depth =
+   let
+    search :: Cost -> IO SRes
+    search depth = do
+     pm <- readIORef $ ctpriometa root
+     case pm of
+      NoPrio False -> return $ Left False -- nothing to refine but not done, this can happen when eq constraints are passed along with main constraint in agdaplugin
+      NoPrio True ->
+       searchSubProb restprobs depth -- ?? what should depth be
+      PrioMeta _ m -> do
+       let carryon = fork m depth
+       sub <- readIORef $ ctsub root
+       case sub of
+        Nothing -> carryon
+        Just sc -> do
+         let sub1 = scsub1 sc
+             sub2 = scsub2 sc
+         pm1 <- readIORef $ ctpriometa sub1
+         pm2 <- readIORef $ ctpriometa sub2
+         let split = carryon -- split disabled
+         case pm1 of
+          NoPrio True -> split
+          _ ->
+           case pm2 of
+            NoPrio True -> split
+            _ -> do
+             comc <- readIORef $ sccomcount sc
+             case comc of
+              0 -> split
+              _ -> carryon
+
+    fork :: forall a. Refinable a blk => Metavar a blk -> Cost -> IO SRes
+    fork m depth = do
+      blkinfos <- extractblkinfos m
+      refs <- refinements envinfo blkinfos m
+      f refs
+     where
+      f :: [Move' blk a] -> IO SRes
+      f [] = do
+       erefs <- readIORef $ mextrarefs m
+       case erefs of
+        [] -> return (Left False)
+        _ -> do
+         NoUndo.writeIORef (mextrarefs m) []
+         f erefs
+      f (Move cost bind : binds) = hsres (refine m bind (depth - cost)) (f binds)
+    hsres :: IO SRes -> IO SRes -> IO SRes
+    hsres x1 x2 = do
+     res <- x1
+     case res of
+      Right _ -> return res
+      Left found -> do
+       n <- readIORef nsol
+       if n == 0 then
+         return res
+        else do
+         res2 <- x2
+         case res2 of
+          Right _ -> if found then __IMPOSSIBLE__ else return res2
+          Left found2 -> return $ Left (found || found2)
+
+    refine :: Metavar a blk -> RefCreateEnv blk a -> Cost -> IO SRes
+
+    refine _ _ depthleft | depthleft < 0 = do
+     NoUndo.writeIORef depthreached True
+     return $ Left False
+
+
+    refine m bind depthleft = runUndo $
+     do t <- ureadIORef ticks
+        lift $ NoUndo.writeIORef ticks $! t + 1
+
+
+        (bind, (_, nnewmeta)) <- lift $ runStateT (runRefCreateEnv bind) (mcompoint m, 0)
+        uwriteIORef (mbind m) (Just bind)
+        mcomptr <- ureadIORef $ mcompoint m
+        mapM_ (\comptr ->
+          umodifyIORef (sccomcount comptr) (+ (nnewmeta - 1))
+          -- umodifyIORef (scflip comptr) not -- don't flip now since trying prefer rightmost subterm if non have prio
+         ) mcomptr
+        obs <- ureadIORef (mobs m)
+        res <- recalcs obs
+        if res
+          then
+            return $ Left False     -- failed
+          else
+            lift $ search depthleft -- succeeded
+
+    doit = do
+     res <- search depth
+     return $ case res of
+      Right n ->
+       case firstdone of
+        Nothing ->
+         if n == 0 then
+          Left False
+         else
+          Right (n - 1)
+        Just _ ->
+         Right (n + 1)
+      res@(Left True) -> res
+      res@(Left False) ->
+       case firstdone of
+        Nothing -> res
+        Just _ -> Right 0
+   in
+    case firstdone of
+     Nothing -> doit
+     Just rdone -> do
+      done <- readIORef rdone
+      if done then
+        searchSubProb restprobs depth
+       else do
+        NoUndo.writeIORef rdone True
+        doit
+
+ runUndo $ do
+  res <- reccalc p (Just mainroot)
+  if res -- failed immediately
+    then
+        return False
+    else
+      do
+        Left _solFound <- lift $ searchSubProb [(mainroot, Nothing)] searchdepth
+        lift $ readIORef depthreached
+
+
+extractblkinfos :: Metavar a blk -> IO [blk]
+extractblkinfos m = do
+ obs <- readIORef $ mobs m
+ return $ f obs
+ where
+  f [] = []
+  f ((QPBlocked (_,_,mblkinfo) _, _) : cs) =
+   case mblkinfo of
+    Nothing -> f cs
+    Just blkinfo -> blkinfo : f cs
+  f ((QPDoubleBlocked{}, _) : cs) = f cs
+
+recalcs :: [(QPB a blk, Maybe (CTree blk))] -> Undo Bool
+recalcs cs = foldr (seqc . recalc) (return False) cs
+
+seqc :: Undo Bool -> Undo Bool -> Undo Bool
+seqc x y = do
+ res1 <- x
+ case res1 of
+  res1@True -> return res1
+  False -> y
+
+recalc :: (QPB a blk, Maybe (CTree blk)) -> Undo Bool
+recalc (con, node) = case con of
+  QPBlocked       _    cont -> reccalc cont node
+  QPDoubleBlocked flag cont -> do
+    fl <- ureadIORef flag
+    if fl
+      then return False
+      else do
+        uwriteIORef flag True
+        reccalc cont node
+
+reccalc :: MetaEnv (PB blk) -> Maybe (CTree blk) -> Undo Bool
+reccalc cont node = do
+  res <- calc cont node
+  case res of
+    Nothing -> return True
+    Just pendhandles ->
+      foldM
+        ( \res1 h ->
+            if res1
+              then return res1
+              else do
+                uwriteIORef (mbind h) $ Just OKVal
+                obs <- ureadIORef (mobs h)
+                recalcs obs
+        )
+        False
+        pendhandles
+
+calc :: forall blk . MetaEnv (PB blk) -> Maybe (CTree blk) -> Undo (Maybe [OKMeta blk])
+calc cont node = do
+  res <- donewp node cont
+  case res of
+   Just (_, pendhandles) -> do
+    pendhandles2 <- case node of
+     Just node -> propagatePrio node
+     Nothing -> return []
+    return $ Just (pendhandles ++ pendhandles2)
+   Nothing -> return Nothing
+ where
+  storeprio (Just node) pm pendhandles = do
+   pendhandles' <- case pm of
+    NoPrio True -> do
+     handles <- ureadIORef (cthandles node)
+     return $ handles ++ pendhandles
+    _ -> return pendhandles
+   uwriteIORef (ctpriometa node) pm
+   return $ Just (pm, pendhandles')
+  storeprio Nothing _ _ =
+   return $ Just (NoPrio False, [])
+  donewp node p = do
+   bp <- lift p
+   case bp of
+    NotPB p ->
+     doprop node p
+    PBlocked m blkinfo cont -> do
+     oldobs <- ureadmodifyIORef (mobs m) ((QPBlocked blkinfo cont, node) :)
+     let (princ, prio, _) = blkinfo
+     pp <- ureadIORef (mprincipalpresent m)
+     when (princ && not pp) $ do
+      uwriteIORef (mprincipalpresent m) True
+      mapM_ (\(qpb, node) -> case node of
+         Just node ->
+          case qpb of
+           QPBlocked (_, prio, _) _ -> do
+
+
+            uwriteIORef (ctpriometa node) (PrioMeta prio m)
+            propagatePrio node
+           QPDoubleBlocked _flag _ ->
+            return []
+         Nothing -> return []
+       ) oldobs
+     if pp || princ then
+       storeprio node (PrioMeta prio m) []
+      else
+       storeprio node (NoPrio False) []
+    PDoubleBlocked m1 m2 cont -> do
+     flag <- lift $ newIORef False
+
+     let newobs :: forall b. [(QPB b blk, Maybe (CTree blk))]
+                          -> [(QPB b blk, Maybe (CTree blk))]
+         newobs = ((QPDoubleBlocked flag cont, node) :)
+     umodifyIORef (mobs m1) newobs
+     umodifyIORef (mobs m2) newobs
+     storeprio node (NoPrio False) []
+  doprop node p =
+   case p of
+    OK -> storeprio node (NoPrio True) []
+    Error _ -> return Nothing
+
+
+    AddExtraRef _ m eref -> do
+     lift $ NoUndo.modifyIORef (mextrarefs m) (eref :)
+     return Nothing
+    And coms p1 p2 -> do
+     let Just jnode = node
+     sc <- lift $ newSubConstraints jnode
+
+
+     uwriteIORef (ctsub jnode) $ Just sc
+     ndep <- case coms of
+      Nothing -> return 1 -- no metas pointing to it so will never decrement to 0
+      Just _coms  -> return 1 -- dito
+     lift $ NoUndo.writeIORef (sccomcount sc) ndep -- OK since sc was just created
+     resp1 <- donewp (Just $ scsub1 sc) p1
+     case resp1 of
+      Just (pm1, phs1) -> do
+       resp2 <- donewp (Just $ scsub2 sc) p2
+       case resp2 of
+        Just (pm2, phs2) ->
+         storeprio node (choosePrioMeta False pm1 pm2) (phs1 ++ phs2)
+        resp2@Nothing -> return resp2
+      resp1@Nothing -> return resp1
+    Sidecondition sidep mainp -> do
+     resp1 <- donewp Nothing sidep
+     case resp1 of
+      Just{} -> do
+       resp2 <- donewp node mainp
+       case resp2 of
+        Just (pm2, phs2) ->
+         storeprio node pm2 phs2
+        resp2@Nothing -> return resp2
+      resp1@Nothing -> return resp1
+    Or prio p1 p2 -> do
+     cm <- lift $ initMeta
+     donewp node (choose (Meta cm) prio p1 p2)
+    ConnectHandle (Meta handle) p' -> do
+     let Just jnode = node
+     umodifyIORef (cthandles jnode) (handle :)
+     donewp node p'
+    ConnectHandle (NotM _) _ -> __IMPOSSIBLE__
+
+choosePrioMeta :: Bool -> PrioMeta blk -> PrioMeta blk -> PrioMeta blk
+choosePrioMeta flip pm1@(PrioMeta p1 _) pm2@(PrioMeta p2 _)
+  | p1 > p2 = pm1
+  | p2 > p1 = pm2
+  | flip = pm2
+  | otherwise = pm1
+choosePrioMeta _ pm@(PrioMeta _ _) (NoPrio _) = pm
+choosePrioMeta _ (NoPrio _) pm@(PrioMeta _ _) = pm
+choosePrioMeta _ (NoPrio d1) (NoPrio d2) = NoPrio (d1 && d2)
+
+propagatePrio :: CTree blk -> Undo [OKMeta blk]
+propagatePrio node = do
+  parent <- lift $ readIORef $ ctparent node
+  case parent of
+    Nothing     -> return []
+    Just parent -> do
+      Just sc <- ureadIORef (ctsub parent)
+      pm1     <- ureadIORef $ ctpriometa $ scsub1 sc
+      pm2     <- ureadIORef $ ctpriometa $ scsub2 sc
+      flip    <- ureadIORef $ scflip sc
+      let pm = choosePrioMeta flip pm1 pm2
+      opm <- ureadIORef (ctpriometa parent)
+      if (pm /= opm)
+        then do
+          uwriteIORef (ctpriometa parent) pm
+          phs <- case pm of
+            NoPrio True -> ureadIORef (cthandles parent)
+            _           -> return []
+          phs2 <- propagatePrio parent
+          return $ phs ++ phs2
+        else
+          return []
+
+data Choice = LeftDisjunct | RightDisjunct
+
+choose :: MM Choice blk -> Prio -> MetaEnv (PB blk) -> MetaEnv (PB blk) -> MetaEnv (PB blk)
+choose c prio p1 p2 =
+ mmpcase (True, prio, Nothing) c $ \c -> case c of
+  LeftDisjunct -> p1
+  RightDisjunct -> p2
+
+instance Refinable Choice blk where
+ refinements _ _ _ = return $ Move 0 . return <$> [LeftDisjunct, RightDisjunct]
+
+
+instance Refinable OKVal blk where
+ refinements _ _ _ = __IMPOSSIBLE__ -- OKVal should never be refined
+
+
+-- ------------------------------------
diff --git a/src/full/Agda/Auto/Options.hs b/src/full/Agda/Auto/Options.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/Options.hs
@@ -0,0 +1,122 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Auto.Options where
+
+import Data.Char
+import Control.Monad.State
+import Agda.Utils.Lens
+
+data Mode = MNormal Bool Bool -- true if list mode, true if disprove
+
+          | MCaseSplit
+
+          | MRefine Bool -- true if list mode
+
+
+data AutoHintMode = AHMNone
+                  | AHMModule
+
+type Hints = [String]
+
+newtype TimeOut = TimeOut { getTimeOut :: Int } -- in ms
+
+instance Show TimeOut where
+  show = show . getTimeOut
+
+-- | Options for Auto, default value and lenses
+
+data AutoOptions = AutoOptions
+  { autoHints    :: Hints
+  , autoTimeOut  :: TimeOut
+  , autoPick     :: Int
+  , autoMode     :: Mode
+  , autoHintMode :: AutoHintMode
+  }
+
+initAutoOptions :: AutoOptions
+initAutoOptions = AutoOptions
+  { autoHints    = []
+  , autoTimeOut  = TimeOut 1000
+  , autoPick     = 0
+  , autoMode     = MNormal False False
+  , autoHintMode = AHMNone
+  }
+
+aoHints :: Lens' AutoOptions Hints
+aoHints f s =
+  f (autoHints s) <&>
+  \x -> s {autoHints = x}
+
+aoTimeOut :: Lens' AutoOptions TimeOut
+aoTimeOut f s =
+  f (autoTimeOut s) <&>
+  \x -> s {autoTimeOut = x}
+
+aoPick :: Lens' AutoOptions Int
+aoPick f s =
+  f (autoPick s) <&>
+  \x -> s {autoPick = x}
+
+aoMode :: Lens' AutoOptions Mode
+aoMode f s =
+  f (autoMode s) <&>
+  \x -> s {autoMode = x}
+
+aoHintMode :: Lens' AutoOptions AutoHintMode
+aoHintMode f s =
+  f (autoHintMode s) <&>
+  \x -> s {autoHintMode = x}
+
+-- | Tokenising the input (makes `parseArgs` cleaner)
+
+data AutoToken =
+    M | C | R | D | L
+  | T String | S Int | H String
+
+autoTokens :: [String] -> [AutoToken]
+autoTokens []              = []
+autoTokens ("-t" : t : ws) = T t        : autoTokens ws
+autoTokens ("-s" : s : ws) = S (read s) : autoTokens ws
+autoTokens ("-l"     : ws) = L          : autoTokens ws
+autoTokens ("-d"     : ws) = D          : autoTokens ws
+autoTokens ("-m"     : ws) = M          : autoTokens ws
+autoTokens ("-c"     : ws) = C          : autoTokens ws
+autoTokens ("-r"     : ws) = R          : autoTokens ws
+autoTokens (h        : ws) = H h        : autoTokens ws
+
+parseTime :: String -> Int
+parseTime [] = 0
+parseTime xs = read ds * modifier + parseTime r where
+  (ds , modr) = span isDigit xs
+  (mod , r)   = break isDigit modr
+
+  modifier = case mod of
+    "ms" -> 1
+    "cs" -> 10
+    "ds" -> 100
+    "s"  -> 1000
+    _    -> 1000
+
+parseArgs :: String -> AutoOptions
+parseArgs s = mapM_ step (autoTokens $ words s)
+              `execState` initAutoOptions where
+
+  step :: AutoToken -> State AutoOptions ()
+  step M     = aoHintMode .= AHMModule
+  step C     = aoMode     .= MCaseSplit
+  step R     = aoPick     .= (-1)
+            >> aoMode     .= MRefine False
+  step (T t) = aoTimeOut  .= TimeOut (parseTime t)
+  step (S p) = aoPick     .= p
+  step (H h) = aoHints    %= (h :)
+  step D     = do
+    mode <- use aoMode
+    case mode of
+      MNormal lm _ -> aoMode .= MNormal lm True
+      _            -> return ()
+  step L     = do
+    mode <- use aoMode
+    case mode of
+      MNormal _ dp -> aoMode .= MNormal True dp
+      MRefine _    -> aoMode .= MRefine True
+      _            -> return ()
diff --git a/src/full/Agda/Auto/SearchControl.hs b/src/full/Agda/Auto/SearchControl.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/SearchControl.hs
@@ -0,0 +1,451 @@
+{-# LANGUAGE CPP #-}
+
+{-# OPTIONS_GHC -Wunused-imports #-}
+{-# OPTIONS_GHC -Wno-orphans #-}
+#if __GLASGOW_HASKELL__ > 907
+{-# OPTIONS_GHC -Wno-x-partial #-}
+#endif
+
+
+
+module Agda.Auto.SearchControl where
+
+import Control.Monad
+import Data.IORef
+import Control.Monad.State
+import Data.Maybe (mapMaybe, fromMaybe)
+
+import Agda.Syntax.Common (Hiding(..))
+import Agda.Auto.NarrowingSearch
+import Agda.Auto.Syntax
+
+import Agda.Utils.Impossible
+
+instance Refinable (ArgList o) (RefInfo o) where
+ refinements _ infos _ = return $ fmap (Move 0) $
+   [ return ALNil, cons NotHidden, cons Hidden ]
+   ++ if getIsDep infos then []
+      else [ proj NotHidden, proj Hidden ]
+
+   where
+
+    getIsDep :: [RefInfo o] -> Bool
+    getIsDep (x : xs) = case x of
+      RICheckElim isDep -> isDep
+      _                 -> getIsDep xs
+    getIsDep _ = __IMPOSSIBLE__
+
+    proj :: Hiding -> RefCreateEnv (RefInfo o) (ArgList o)
+    proj hid = ALProj <$> newPlaceholder <*> newPlaceholder
+                      <*> return hid     <*> newPlaceholder
+
+    cons :: Hiding -> RefCreateEnv (RefInfo o) (ArgList o)
+    cons hid = ALCons hid <$> newPlaceholder <*> newPlaceholder
+
+
+data ExpRefInfo o = ExpRefInfo
+  { eriMain           :: Maybe (RefInfo o)
+  , eriUnifs          :: [RefInfo o]
+  , eriInfTypeUnknown :: Bool
+  , eriIsEliminand    :: Bool
+  , eriUsedVars       :: Maybe ([UId o], [Elr o])
+  , eriIotaStep       :: Maybe Bool
+  , eriPickSubsVar    :: Bool
+  , eriEqRState       :: Maybe EqReasoningState
+  }
+
+initExpRefInfo :: ExpRefInfo o
+initExpRefInfo = ExpRefInfo
+  { eriMain           = Nothing
+  , eriUnifs          = []
+  , eriInfTypeUnknown = False
+  , eriIsEliminand    = False
+  , eriUsedVars       = Nothing
+  , eriIotaStep       = Nothing
+  , eriPickSubsVar    = False
+  , eriEqRState       = Nothing
+  }
+
+getinfo :: [RefInfo o] -> ExpRefInfo o
+getinfo = foldl step initExpRefInfo where
+
+  step :: ExpRefInfo o -> RefInfo o -> ExpRefInfo o
+  step eri x@RIMainInfo{}           = eri { eriMain  = Just x }
+  step eri x@RIUnifInfo{}           = eri { eriUnifs = x : eriUnifs eri }
+  step eri RIInferredTypeUnknown    = eri { eriInfTypeUnknown = True }
+  step eri RINotConstructor         = eri { eriIsEliminand = True }
+  step eri (RIUsedVars nuids nused) = eri { eriUsedVars = Just (nuids, nused) }
+  step eri (RIIotaStep semif)       = eri { eriIotaStep = Just iota' } where
+    iota' = semif || (Just True ==) (eriIotaStep eri)
+  step eri RIPickSubsvar            = eri { eriPickSubsVar = True }
+  step eri (RIEqRState s)           = eri { eriEqRState = Just s }
+  step eri _ = __IMPOSSIBLE__
+
+
+-- | @univar sub v@ figures out what the name of @v@ "outside" of
+--   the substitution @sub@ ought to be, if anything.
+
+univar :: [CAction o] -> Nat -> Maybe Nat
+univar cl v = getOutsideName cl v 0 where
+
+  getOutsideName :: [CAction o] -> Nat -> Nat -> Maybe Nat
+  -- @v@ is offset by @v'@ binders
+  getOutsideName []            v v' = Just (v' + v)
+  -- @v@ was introduced by the weakening: disappears
+  getOutsideName (Weak n : _)  v v' | v < n = Nothing
+  -- @v@ was introduced before the weakening: strengthened
+  getOutsideName (Weak n : xs) v v' = getOutsideName xs (v - n) v'
+  -- Name of @v@ before the substitution was pushed in
+  -- had to be offset by 1
+  getOutsideName (Sub _  : xs) v v' = getOutsideName xs v (v' + 1)
+  -- If this is the place where @v@ was bound, it used to
+  -- be called 0 + offset of all the vars substituted for
+  getOutsideName (Skip   : _)  0 v' = Just v'
+  -- Going over a binder: de Bruijn name of @v@ decreased
+  -- but offset increased
+  getOutsideName (Skip   : xs) v v' = getOutsideName xs (v - 1) (v' + 1)
+
+-- | List of the variables instantiated by the substitution
+subsvars :: [CAction o] -> [Nat]
+subsvars = f 0 where
+
+  f :: Nat -> [CAction o] -> [Nat]
+  f n []            = []
+  f n (Weak _ : xs) = f n xs -- why?
+  f n (Sub _  : xs) = n : f (n + 1) xs
+  f n (Skip   : xs) = f (n + 1) xs
+
+-- | Moves
+--   A move is composed of a @Cost@ together with an action
+--   computing the refined problem.
+
+type Move o = Move' (RefInfo o) (Exp o)
+
+-- | New constructors
+--   Taking a step towards a solution consists in picking a
+--   constructor and filling in the missing parts with
+--   placeholders to be discharged later on.
+
+newAbs :: MId -> RefCreateEnv blk (Abs (MM a blk))
+newAbs mid = Abs mid <$> newPlaceholder
+
+newLam :: Hiding -> MId -> RefCreateEnv (RefInfo o) (Exp o)
+newLam hid mid = Lam hid <$> newAbs mid
+
+newPi :: UId o -> Bool -> Hiding -> RefCreateEnv (RefInfo o) (Exp o)
+newPi uid dep hid = Pi (Just uid) hid dep <$> newPlaceholder <*> newAbs NoId
+
+foldArgs :: [(Hiding, MExp o)] -> MArgList o
+foldArgs = foldr (\ (h, a) sp -> NotM $ ALCons h a sp) (NotM ALNil)
+
+-- | New spine of arguments potentially using placeholders
+
+newArgs' :: [Hiding] -> [MExp o] -> RefCreateEnv (RefInfo o) (MArgList o)
+newArgs' h tms = foldArgs . zip h . (++ tms) <$> replicateM size newPlaceholder
+  where size = length h - length tms
+
+newArgs :: [Hiding] -> RefCreateEnv (RefInfo o) (MArgList o)
+newArgs h = newArgs' h []
+
+-- | New @App@lication node using a new spine of arguments
+--   respecting the @Hiding@ annotation
+
+newApp' :: UId o -> ConstRef o -> [Hiding] -> [MExp o] ->
+           RefCreateEnv (RefInfo o) (Exp o)
+newApp' meta cst hds tms =
+  App (Just meta) <$> newOKHandle <*> return (Const cst) <*> newArgs' hds tms
+
+newApp :: UId o -> ConstRef o -> [Hiding] -> RefCreateEnv (RefInfo o) (Exp o)
+newApp meta cst hds = newApp' meta cst hds []
+
+-- | Equality reasoning steps
+--   The begin token is accompanied by two steps because
+--   it does not make sense to have a derivation any shorter
+--   than that.
+
+eqStep :: UId o -> EqReasoningConsts o -> Move o
+eqStep meta eqrc = Move costEqStep $ newApp meta (eqrcStep eqrc)
+  [Hidden, Hidden, NotHidden, Hidden, Hidden, NotHidden, NotHidden]
+
+eqEnd :: UId o -> EqReasoningConsts o -> Move o
+eqEnd meta eqrc = Move costEqEnd $ newApp meta (eqrcEnd eqrc)
+  [Hidden, Hidden, NotHidden]
+
+eqCong :: UId o -> EqReasoningConsts o -> Move o
+eqCong meta eqrc = Move costEqCong $ newApp meta (eqrcCong eqrc)
+  [Hidden, Hidden, Hidden, Hidden, NotHidden, Hidden, Hidden, NotHidden]
+
+eqSym :: UId o -> EqReasoningConsts o -> Move o
+eqSym meta eqrc = Move costEqSym $ newApp meta (eqrcSym eqrc)
+  [Hidden, Hidden, Hidden, Hidden, NotHidden]
+
+eqBeginStep2 :: UId o -> EqReasoningConsts o -> Move o
+eqBeginStep2 meta eqrc = Move costEqStep $ do
+  e1 <- newApp meta (eqrcStep eqrc)
+          [Hidden, Hidden, NotHidden, Hidden, Hidden, NotHidden, NotHidden]
+  e2 <- newApp' meta (eqrcStep eqrc)
+          [Hidden, Hidden, NotHidden, Hidden, Hidden, NotHidden, NotHidden]
+          [NotM e1]
+  newApp' meta (eqrcBegin eqrc) [Hidden, Hidden, Hidden, Hidden, NotHidden]
+    [NotM e2]
+
+
+-- | Pick the first unused UId amongst the ones you have seen (GA: ??)
+--   Defaults to the head of the seen ones.
+
+pickUid :: forall o. [UId o] -> [Maybe (UId o)] -> (Maybe (UId o), Bool)
+pickUid used seen = maybe (head seen, False) (, True) $ firstUnused seen where
+  {- ?? which uid to pick -}
+
+  firstUnused :: [Maybe (UId o)] -> Maybe (Maybe (UId o))
+  firstUnused []                 = Nothing
+  firstUnused (Nothing     : _)  = Just Nothing
+  firstUnused (mu@(Just u) : us) =
+    if u `elem` used then firstUnused us else Just mu
+
+instance Refinable (Exp o) (RefInfo o) where
+ refinements envinfo infos meta =
+  let
+   hints = rieHints envinfo
+   deffreevars = rieDefFreeVars envinfo
+
+   meqr = rieEqReasoningConsts envinfo
+
+   ExpRefInfo { eriMain  = Just (RIMainInfo n tt iotastepdone)
+              , eriUnifs = unis
+              , eriInfTypeUnknown = inftypeunknown
+              , eriIsEliminand = iseliminand -- TODO:: Defined but not used
+              , eriUsedVars = Just (uids, usedvars)
+              , eriIotaStep = iotastep
+              , eriPickSubsVar = picksubsvar -- TODO:: Defined but not used
+              , eriEqRState = meqrstate
+              } = getinfo infos
+
+   eqrstate = fromMaybe EqRSNone meqrstate
+
+   set l = return $ Sort (Set l)
+  in case unis of
+   [] ->
+    let
+
+     eqr = fromMaybe __IMPOSSIBLE__ meqr
+     eq_end         = eqEnd  meta eqr
+     eq_step        = eqStep meta eqr
+     eq_cong        = eqCong meta eqr
+     eq_sym         = eqSym  meta eqr
+     eq_begin_step2 = eqBeginStep2 meta eqr
+
+     adjustCost i = if inftypeunknown then costInferredTypeUnkown else i
+     varcost v | v < n - deffreevars = adjustCost $
+       if v `elem` (mapMaybe getVar usedvars)
+       then costAppVarUsed else costAppVar
+     varcost v | otherwise           = adjustCost costAppHint
+     varapps  = map (\ v -> Move (varcost v) $ app n meta Nothing (Var v)) [0..n - 1]
+     hintapps = map (\(c, hm) -> Move (cost c hm) (app n meta Nothing (Const c))) hints
+       where
+         cost :: ConstRef o -> HintMode -> Cost
+         cost c hm = adjustCost $ case (iotastep , hm) of
+           (Just _  , _       ) -> costIotaStep
+           (Nothing , HMNormal) ->
+             if c `elem` (mapMaybe getConst usedvars)
+             then costAppHintUsed else costAppHint
+           (Nothing , HMRecCall) ->
+             if c `elem` (mapMaybe getConst usedvars)
+             then costAppRecCallUsed else costAppRecCall
+     generics = varapps ++ hintapps
+    in case rawValue tt of
+
+     _ | eqrstate == EqRSChain ->
+      return [eq_end, eq_step]
+
+     HNPi hid _ _ (Abs id _) -> return $
+         Move (adjustCost (if iotastepdone then costLamUnfold else costLam)) (newLam hid id)
+       : Move costAbsurdLam (return $ AbsurdLambda hid)
+       : generics
+
+     HNSort (Set l) -> return $
+          map (Move (adjustCost costSort) . set) [0..l - 1]
+       ++ map (Move (adjustCost costPi) . newPi meta True) [NotHidden, Hidden]
+       ++ generics
+
+
+     HNApp (Const c) _ -> do
+      cd <- readIORef c
+      return $ case cdcont cd of
+
+       Datatype cons _ | eqrstate == EqRSNone ->
+         map (\c -> Move (adjustCost $ case iotastep of
+                                         Just True -> costUnification
+                                         _ -> if length cons <= 1
+                                              then costAppConstructorSingle
+                                              else costAppConstructor)
+                         $ app n meta Nothing (Const c)) cons
+         ++ generics
+         ++ (guard (maybe False ((c ==) . eqrcId) meqr)
+            *> [eq_sym, eq_cong, eq_begin_step2])
+
+       _ | eqrstate == EqRSPrf1 -> generics ++ [eq_sym, eq_cong]
+       _ | eqrstate == EqRSPrf2 -> generics ++ [eq_cong]
+
+       _ -> generics
+     _ -> return generics
+   (RIUnifInfo cl hne : _) ->
+    let
+     subsvarapps = map (Move costUnification . app n meta Nothing . Var) (subsvars cl)
+     mlam = case rawValue tt of
+      HNPi hid _ _ (Abs id _) -> [Move costUnification (newLam hid id)]
+      _ -> []
+     generics = mlam ++ subsvarapps
+
+    in
+     return $ case rawValue hne of
+      HNApp (Var v) _ ->
+       let (uid, isunique) = pickUid uids $ seenUIds hne
+           uni = case univar cl v of
+                  Just v | v < n -> [Move (costUnificationIf isunique) $ app n meta uid (Var v)]
+                  _ -> []
+       in uni ++ generics
+      HNApp (Const c) _ ->
+       let (uid, isunique) = pickUid uids $ seenUIds hne
+       in Move (costUnificationIf isunique) (app n meta uid (Const c)) : generics
+      HNLam{} -> generics
+      HNPi hid possdep _ _ ->
+       let (uid, isunique) = pickUid uids $ seenUIds hne
+       in Move (costUnificationIf isunique) (newPi (fromMaybe meta uid) possdep hid) : generics
+      HNSort (Set l) -> map (Move costUnification . set) [0..l] ++ generics
+      HNSort _ -> generics
+   _ -> __IMPOSSIBLE__
+
+  where
+
+    app :: Nat -> UId o -> Maybe (UId o) -> Elr o ->
+           RefCreateEnv (RefInfo o) (Exp o)
+    app n meta muid elr = do
+      p <- newPlaceholder
+      p <- case elr of
+        Var{}   -> return p
+        Const c -> do
+          cd <- RefCreateEnv $ lift $ readIORef c
+          let dfvapp 0 _ = p
+              dfvapp i n = NotM $ ALCons NotHidden
+                          (NotM $ App Nothing (NotM $ OKVal) (Var n) (NotM ALNil))
+                          (dfvapp (i - 1) (n - 1))
+         -- NotHidden is ok because agda reification throws these arguments
+         -- away and agsy skips typechecking them
+          return $ dfvapp (cddeffreevars cd) (n - 1)
+      okh <- newOKHandle
+      return $ App (Just $ fromMaybe meta muid) okh elr p
+
+
+extraref :: UId o -> [Maybe (UId o)] -> ConstRef o -> Move o
+extraref meta seenuids c = Move costAppExtraRef $ app (head seenuids) (Const c)
+ where
+   app muid elr = App (Just $ fromMaybe meta muid)
+              <$> newOKHandle <*> return elr <*> newPlaceholder
+
+instance Refinable (ICExp o) (RefInfo o) where
+ refinements _ infos _ =
+  let (RICopyInfo e : _) = infos
+  in return [Move 0 (return e)]
+
+
+instance Refinable (ConstRef o) (RefInfo o) where
+ refinements _ [RICheckProjIndex projs] _ = return $ map (Move 0 . return) projs
+ refinements _ _ _ = __IMPOSSIBLE__
+
+
+-- ---------------------------------
+
+costIncrease, costUnificationOccurs, costUnification, costAppVar,
+  costAppVarUsed, costAppHint, costAppHintUsed, costAppRecCall,
+  costAppRecCallUsed, costAppConstructor, costAppConstructorSingle,
+  costAppExtraRef, costLam, costLamUnfold, costPi, costSort, costIotaStep,
+  costInferredTypeUnkown, costAbsurdLam
+  :: Cost
+
+costUnificationIf :: Bool -> Cost
+costUnificationIf b = if b then costUnification else costUnificationOccurs
+
+costIncrease = 1000
+costUnificationOccurs = 100 -- 1000001 -- 1 -- 100
+costUnification = 0000
+costAppVar = 0000 -- 0, 1
+costAppVarUsed = 1000 -- 5
+costAppHint = 3000 -- 2, 5
+costAppHintUsed = 5000
+costAppRecCall = 0 -- 1000?
+costAppRecCallUsed = 10000 -- 1000?
+costAppConstructor = 1000
+costAppConstructorSingle = 0000
+costAppExtraRef = 1000
+costLam = 0000 -- 1, 0
+costLamUnfold = 1000 -- 1, 0
+costPi = 1000003 -- 100 -- 5
+costSort = 1000004 -- 0
+costIotaStep = 3000 -- 1000005 -- 2 -- 100
+costInferredTypeUnkown = 1000006 -- 100
+costAbsurdLam = 0
+
+costEqStep, costEqEnd, costEqSym, costEqCong :: Cost
+costEqStep = 2000
+costEqEnd = 0
+costEqSym = 0
+costEqCong = 500
+
+prioNo, prioTypeUnknown, prioTypecheckArgList, prioInferredTypeUnknown,
+  prioCompBeta, prioCompBetaStructured, prioCompareArgList, prioCompIota,
+  prioCompChoice, prioCompUnif, prioCompCopy, prioNoIota, prioAbsurdLambda,
+  prioProjIndex
+  :: Prio
+prioNo = (-1)
+prioTypeUnknown = 0
+prioTypecheckArgList = 3000
+prioInferredTypeUnknown = 4000
+prioCompBeta = 4000
+prioCompBetaStructured = 4000
+prioCompIota = 4000
+prioCompChoice = 5000 -- 700 -- 5000
+prioCompUnif = 6000 -- 2
+prioCompCopy = 8000
+prioCompareArgList = 7000 -- 5 -- 2
+prioNoIota = 500 -- 500
+prioAbsurdLambda = 1000
+
+prioProjIndex = 3000
+
+prioTypecheck :: Bool -> Prio
+prioTypecheck False = 1000
+prioTypecheck True = 0
+
+-- ---------------------------------
+
+instance Trav a => Trav [a] where
+  type Block [a] = Block a
+  trav _ []     = return ()
+  trav f (x:xs) = trav f x >> trav f xs
+
+instance Trav (MId, CExp o) where
+  type Block (MId, CExp o) = RefInfo o
+  trav f (_, ce) = trav f ce
+
+instance Trav (TrBr a o) where
+  type Block (TrBr a o) = RefInfo o
+  trav f (TrBr es _) = trav f es
+
+instance Trav (Exp o) where
+  type Block (Exp o) = RefInfo o
+  trav f = \case
+    App _ _ _ args         -> trav f args
+    Lam _ (Abs _ b)        -> trav f b
+    Pi _ _ _ it (Abs _ ot) -> trav f it >> trav f ot
+    Sort _                 -> return ()
+    AbsurdLambda{}         -> return ()
+
+instance Trav (ArgList o) where
+  type Block (ArgList o) = RefInfo o
+  trav _ ALNil               = return ()
+  trav f (ALCons _ arg args) = trav f arg >> trav f args
+  trav f (ALProj eas _ _ as) = trav f eas >> trav f as
+  trav f (ALConPar args)     = trav f args
+
+-- ---------------------------------
diff --git a/src/full/Agda/Auto/Syntax.hs b/src/full/Agda/Auto/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/Syntax.hs
@@ -0,0 +1,463 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Auto.Syntax where
+
+import Data.IORef
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common (Hiding)
+import Agda.Auto.NarrowingSearch
+
+import Agda.Utils.Impossible
+
+-- | Unique identifiers for variable occurrences in unification.
+type UId o = Metavar (Exp o) (RefInfo o)
+
+data HintMode = HMNormal
+              | HMRecCall
+
+data EqReasoningConsts o = EqReasoningConsts
+  { eqrcId    -- "_≡_"
+  , eqrcBegin -- "begin_"
+  , eqrcStep  -- "_≡⟨_⟩_"
+  , eqrcEnd   -- "_∎"
+  , eqrcSym   -- "sym"
+  , eqrcCong  -- "cong"
+  :: ConstRef o
+  }
+
+data EqReasoningState = EqRSNone | EqRSChain | EqRSPrf1 | EqRSPrf2 | EqRSPrf3
+ deriving (Eq, Show)
+
+-- | The concrete instance of the 'blk' parameter in 'Metavar'.
+--   I.e., the information passed to the search control.
+
+data RefInfo o
+  = RIEnv
+    { rieHints :: [(ConstRef o, HintMode)]
+    , rieDefFreeVars :: Nat
+      -- ^ Nat - deffreevars
+      --   (to make cost of using module parameters correspond to that of hints).
+    , rieEqReasoningConsts :: Maybe (EqReasoningConsts o)
+    }
+  | RIMainInfo
+    { riMainCxtLength :: Nat
+      -- ^ Size of typing context in which meta was created.
+    , riMainType      :: HNExp o
+      -- ^ Head normal form of type of meta.
+    , riMainIota      :: Bool
+       -- ^ True if iota steps performed when normalising target type
+       --   (used to put cost when traversing a definition
+       --    by construction instantiation).
+    }
+  | RIUnifInfo [CAction o] (HNExp o)
+    -- meta environment, opp hne
+  | RICopyInfo (ICExp o)
+  | RIIotaStep Bool -- True - semiflex
+  | RIInferredTypeUnknown
+  | RINotConstructor
+  | RIUsedVars [UId o] [Elr o]
+  | RIPickSubsvar
+
+  | RIEqRState EqReasoningState
+
+
+  | RICheckElim Bool -- isdep
+  | RICheckProjIndex [ConstRef o] -- noof proj functions
+
+
+type MyPB o = PB (RefInfo o)
+type MyMB a o = MB a (RefInfo o)
+
+type Nat = Int
+
+data MId = Id String
+         | NoId
+
+-- | Abstraction with maybe a name.
+--
+--   Different from Agda, where there is also info
+--   whether function is constant.
+data Abs a = Abs MId a
+
+-- | Constant signatures.
+
+data ConstDef o = ConstDef
+  { cdname        :: String
+    -- ^ For debug printing.
+  , cdorigin      :: o
+    -- ^ Reference to the Agda constant.
+  , cdtype        :: MExp o
+    -- ^ Type of constant.
+  , cdcont        :: DeclCont o
+    -- ^ Constant definition.
+  , cddeffreevars :: Nat
+    -- ^ Free vars of the module where the constant is defined..
+  } -- contains no metas
+
+-- | Constant definitions.
+
+data DeclCont o
+  = Def Nat [Clause o] (Maybe Nat) -- maybe an index to elimand argument
+                       (Maybe Nat) -- maybe index to elim arg if semiflex
+  | Datatype [ConstRef o] -- constructors
+             [ConstRef o] -- projection functions (in case it is a record)
+
+  | Constructor Nat -- number of omitted args
+  | Postulate
+
+type Clause o = ([Pat o], MExp o)
+
+data Pat o
+  = PatConApp (ConstRef o) [Pat o]
+  | PatVar String
+  | PatExp
+    -- ^ Dot pattern.
+  | PatProj (ConstRef o)
+    -- ^ Projection pattern.
+
+type ConstRef o = IORef (ConstDef o)
+
+-- | Head of application (elimination).
+data Elr o
+  = Var Nat
+  | Const (ConstRef o)
+  deriving (Eq)
+
+getVar :: Elr o -> Maybe Nat
+getVar (Var n) = Just n
+getVar Const{} = Nothing
+
+getConst :: Elr o -> Maybe (ConstRef o)
+getConst (Const c) = Just c
+getConst Var{}     = Nothing
+
+data Sort
+  = Set Nat
+  | UnknownSort
+  | Type
+
+-- | Agsy's internal syntax.
+data Exp o
+  = App
+    { appUId   :: Maybe (UId o)
+      -- ^ Unique identifier of the head.
+    , appOK    :: OKHandle (RefInfo o)
+      -- ^ This application has been type-checked.
+    , appHead  :: Elr o
+      -- ^ Head.
+    , appElims :: MArgList o
+      -- ^ Arguments.
+    }
+  | Lam Hiding (Abs (MExp o))
+    -- ^ Lambda with hiding information.
+  | Pi (Maybe (UId o)) Hiding Bool (MExp o) (Abs (MExp o))
+    -- ^ @True@ if possibly dependent (var not known to not occur).
+    --   @False@ if non-dependent.
+  | Sort Sort
+  | AbsurdLambda Hiding
+    -- ^ Absurd lambda with hiding information.
+
+dontCare :: Exp o
+dontCare = Sort UnknownSort
+
+-- | "Maybe expression":  Expression or reference to meta variable.
+type MExp o = MM (Exp o) (RefInfo o)
+
+data ArgList o
+  = ALNil
+    -- ^ No more eliminations.
+  | ALCons Hiding (MExp o) (MArgList o)
+    -- ^ Application and tail.
+
+  | ALProj (MArgList o) (MM (ConstRef o) (RefInfo o)) Hiding (MArgList o)
+    -- ^ proj pre args, projfcn idx, tail
+
+  | ALConPar (MArgList o)
+    -- ^ Constructor parameter (missing in Agda).
+    --   Agsy has monomorphic constructors.
+    --   Inserted to cover glitch of polymorphic constructor
+    --   applications coming from Agda
+
+type MArgList o = MM (ArgList o) (RefInfo o)
+
+data WithSeenUIds a o = WithSeenUIds
+  { seenUIds :: [Maybe (UId o)]
+  , rawValue :: a
+  }
+
+type HNExp o = WithSeenUIds (HNExp' o) o
+
+data HNExp' o =
+    HNApp  (Elr o) (ICArgList o)
+  | HNLam  Hiding (Abs (ICExp o))
+  | HNPi   Hiding Bool (ICExp o) (Abs (ICExp o))
+  | HNSort Sort
+
+-- | Head-normal form of 'ICArgList'.  First entry is exposed.
+--
+--   Q: Why are there no projection eliminations?
+data HNArgList o = HNALNil
+                 | HNALCons Hiding (ICExp o) (ICArgList o)
+                 | HNALConPar (ICArgList o)
+
+-- | Lazy concatenation of argument lists under explicit substitutions.
+data ICArgList o = CALNil
+                 | CALConcat (Clos (MArgList o) o) (ICArgList o)
+
+-- | An expression @a@ in an explicit substitution @[CAction a]@.
+type ICExp o  = Clos (MExp o) o
+data Clos a o = Clos [CAction o] a
+
+type CExp o   = TrBr (ICExp o) o
+data TrBr a o = TrBr [MExp o] a
+
+-- | Entry of an explicit substitution.
+--
+--   An explicit substitution is a list of @CAction@s.
+--   This is isomorphic to the usual presentation where
+--   @Skip@ and @Weak@ would be constructors of exp. substs.
+
+data CAction o
+  = Sub (ICExp o)
+    -- ^ Instantation of variable.
+  | Skip
+    -- ^ For going under a binder, often called "Lift".
+  | Weak Nat
+    -- ^ Shifting substitution (going to a larger context).
+
+type Ctx o = [(MId, CExp o)]
+
+type EE = IO
+
+-- -------------------------------------------
+
+detecteliminand :: [Clause o] -> Maybe Nat
+detecteliminand cls =
+ case map cleli cls of
+  [] -> Nothing
+  (i:is) -> if all (i ==) is then i else Nothing
+ where
+  cleli (pats, _) = pateli 0 pats
+  pateli i (PatConApp _ args : pats) = if all notcon (args ++ pats) then Just i else Nothing
+  pateli i (_ : pats) = pateli (i + 1) pats
+  pateli i [] = Nothing
+  notcon PatConApp{} = False
+  notcon _ = True
+
+detectsemiflex :: ConstRef o -> [Clause o] -> IO Bool
+detectsemiflex _ _ = return False -- disabled
+
+categorizedecl :: ConstRef o -> IO ()
+categorizedecl c = do
+ cd <- readIORef c
+ case cdcont cd of
+  Def narg cls _ _ -> do
+   semif <- detectsemiflex c cls
+   let elim = detecteliminand cls
+       semifb = case (semif, elim) of
+                 (True, Just i) -> Just i -- just copying val of elim arg. this should be changed
+                 (_, _) -> Nothing
+   writeIORef c (cd {cdcont = Def narg cls elim semifb})
+  _ -> return ()
+
+-- -------------------------------------------
+
+class MetaliseOKH t where
+  metaliseOKH :: t -> IO t
+
+instance MetaliseOKH t => MetaliseOKH (MM t a) where
+  metaliseOKH = \case
+    Meta m -> return $ Meta m
+    NotM e -> NotM <$> metaliseOKH e
+
+instance MetaliseOKH t => MetaliseOKH (Abs t) where
+  metaliseOKH (Abs id b) = Abs id <$> metaliseOKH b
+
+instance MetaliseOKH (Exp o) where
+  metaliseOKH = \case
+    App uid okh elr args ->
+      (\ m -> App uid m elr) <$> (Meta <$> initMeta) <*> metaliseOKH args
+    Lam hid b -> Lam hid <$> metaliseOKH b
+    Pi uid hid dep it ot ->
+      Pi uid hid dep <$> metaliseOKH it <*> metaliseOKH ot
+    e@Sort{} -> return e
+    e@AbsurdLambda{} -> return e
+
+instance MetaliseOKH (ArgList o) where
+  metaliseOKH = \case
+    ALNil -> return ALNil
+    ALCons hid a as -> ALCons hid <$> metaliseOKH a <*> metaliseOKH as
+    ALProj eas idx hid as ->
+      (\ eas -> ALProj eas idx hid) <$> metaliseOKH eas <*> metaliseOKH as
+    ALConPar as -> ALConPar <$> metaliseOKH as
+
+metaliseokh :: MExp o -> IO (MExp o)
+metaliseokh = metaliseOKH
+
+-- -------------------------------------------
+
+class ExpandMetas t where
+  expandMetas :: t -> IO t
+
+instance ExpandMetas t => ExpandMetas (MM t a) where
+  expandMetas = \case
+    NotM e -> NotM <$> expandMetas e
+    Meta m -> do
+      mb <- readIORef (mbind m)
+      case mb of
+        Nothing -> return $ Meta m
+        Just e  -> NotM <$> expandMetas e
+
+instance ExpandMetas t => ExpandMetas (Abs t) where
+  expandMetas (Abs id b) = Abs id <$> expandMetas b
+
+instance ExpandMetas (Exp o) where
+  expandMetas = \case
+    App uid okh elr args -> App uid okh elr <$> expandMetas args
+    Lam hid b -> Lam hid <$> expandMetas b
+    Pi uid hid dep it ot ->
+      Pi uid hid dep <$> expandMetas it <*> expandMetas ot
+    t@Sort{} -> return t
+    t@AbsurdLambda{} -> return t
+
+instance ExpandMetas (ArgList o) where
+  expandMetas = \case
+    ALNil -> return ALNil
+    ALCons hid a as -> ALCons hid <$> expandMetas a <*> expandMetas as
+    ALProj eas idx hid as ->
+      (\ a b -> ALProj a b hid) <$> expandMetas eas
+      <*> expandbind idx <*> expandMetas as
+    ALConPar as -> ALConPar <$> expandMetas as
+
+-- ---------------------------------
+
+addtrailingargs :: Clos (MArgList o) o -> ICArgList o -> ICArgList o
+addtrailingargs newargs CALNil = CALConcat newargs CALNil
+addtrailingargs newargs (CALConcat x xs) = CALConcat x (addtrailingargs newargs xs)
+
+-- ---------------------------------
+
+closify :: MExp o -> CExp o
+closify e = TrBr [e] (Clos [] e)
+
+sub :: MExp o -> CExp o -> CExp o
+-- sub e (Clos [] x) = Clos [Sub e] x
+sub e (TrBr trs (Clos (Skip : as) x)) = TrBr (e : trs) (Clos (Sub (Clos [] e) : as) x)
+{-sub e (Clos (Weak n : as) x) = if n == 1 then
+                                Clos as x
+                               else
+                                Clos (Weak (n - 1) : as) x-}
+sub _ _ = __IMPOSSIBLE__
+
+subi :: MExp o -> ICExp o -> ICExp o
+subi e (Clos (Skip : as) x) = Clos (Sub (Clos [] e) : as) x
+subi _ _ = __IMPOSSIBLE__
+
+weak :: Weakening t => Nat -> t -> t
+weak 0 = id
+weak n = weak' n
+
+class Weakening t where
+  weak' :: Nat -> t -> t
+
+instance Weakening a => Weakening (TrBr a o) where
+  weak' n (TrBr trs e) = TrBr trs (weak' n e)
+
+instance Weakening (Clos a o) where
+  weak' n (Clos as x) = Clos (Weak n : as) x
+
+instance Weakening (ICArgList o) where
+  weak' n = \case
+    CALNil         -> CALNil
+    CALConcat a as -> CALConcat (weak' n a) (weak' n as)
+
+instance Weakening (Elr o) where
+  weak' n = rename (n +)
+
+-- | Substituting for a variable.
+doclos :: [CAction o] -> Nat -> Either Nat (ICExp o)
+doclos = f 0
+ where
+  -- ns is the number of weakenings
+  f ns []            i = Left (ns + i)
+  f ns (Weak n : xs) i = f (ns + n) xs i
+  f ns (Sub s  : _ ) 0 = Right (weak ns s)
+  f ns (Skip   : _ ) 0 = Left ns
+  f ns (Skip   : xs) i = f (ns + 1) xs (i - 1)
+  f ns (Sub _  : xs) i = f ns xs (i - 1)
+
+
+-- | FreeVars class and instances
+
+freeVars :: FreeVars t => t -> Set.Set Nat
+freeVars = freeVarsOffset 0
+
+class FreeVars t where
+  freeVarsOffset :: Nat -> t -> Set.Set Nat
+
+instance (FreeVars a, FreeVars b) => FreeVars (a, b) where
+  freeVarsOffset n (a, b) = Set.union (freeVarsOffset n a) (freeVarsOffset n b)
+
+instance FreeVars t => FreeVars (MM t a) where
+  freeVarsOffset n e = freeVarsOffset n (rm __IMPOSSIBLE__ e)
+
+instance FreeVars t => FreeVars (Abs t) where
+  freeVarsOffset n (Abs id e) = freeVarsOffset (n + 1) e
+
+instance FreeVars (Elr o) where
+  freeVarsOffset n = \case
+    Var v   -> Set.singleton (v - n)
+    Const{} -> Set.empty
+
+instance FreeVars (Exp o) where
+  freeVarsOffset n = \case
+   App _ _ elr args -> freeVarsOffset n (elr, args)
+   Lam _ b          -> freeVarsOffset n b
+   Pi _ _ _ it ot   -> freeVarsOffset n (it, ot)
+   Sort{}           -> Set.empty
+   AbsurdLambda{}   -> Set.empty
+
+instance FreeVars (ArgList o) where
+  freeVarsOffset n es = case es of
+    ALNil         -> Set.empty
+    ALCons _ e es -> freeVarsOffset n (e, es)
+    ALConPar es   -> freeVarsOffset n es
+    ALProj{}      -> __IMPOSSIBLE__
+
+
+-- | Renaming Typeclass and instances
+rename :: Renaming t => (Nat -> Nat) -> t -> t
+rename = renameOffset 0
+
+class Renaming t where
+  renameOffset :: Nat -> (Nat -> Nat) -> t -> t
+
+instance (Renaming a, Renaming b) => Renaming (a, b) where
+  renameOffset j ren (a, b) = (renameOffset j ren a, renameOffset j ren b)
+
+instance Renaming t => Renaming (MM t a) where
+  renameOffset j ren e = NotM $ renameOffset j ren (rm __IMPOSSIBLE__ e)
+
+instance Renaming t => Renaming (Abs t) where
+  renameOffset j ren (Abs id e) = Abs id $ renameOffset (j + 1) ren e
+
+instance Renaming (Elr o) where
+  renameOffset j ren = \case
+    Var v | v >= j -> Var (ren (v - j) + j)
+    e              -> e
+
+instance Renaming (Exp o) where
+  renameOffset j ren = \case
+    App uid ok elr args -> uncurry (App uid ok) $ renameOffset j ren (elr, args)
+    Lam hid e -> Lam hid (renameOffset j ren e)
+    Pi a b c it ot -> uncurry (Pi a b c) $ renameOffset j ren (it, ot)
+    e@Sort{}         -> e
+    e@AbsurdLambda{} -> e
+
+instance Renaming (ArgList o) where
+  renameOffset j ren = \case
+    ALNil           -> ALNil
+    ALCons hid a as -> uncurry (ALCons hid) $ renameOffset j ren (a, as)
+    ALConPar as     -> ALConPar (renameOffset j ren as)
+    ALProj{}        -> __IMPOSSIBLE__
diff --git a/src/full/Agda/Auto/Typecheck.hs b/src/full/Agda/Auto/Typecheck.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Auto/Typecheck.hs
@@ -0,0 +1,846 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.Auto.Typecheck where
+
+import Prelude hiding ((!!))
+
+import Data.IORef
+
+import Agda.Syntax.Common (Hiding (..))
+import Agda.Auto.NarrowingSearch
+import Agda.Auto.Syntax
+import Agda.Auto.SearchControl
+
+import Agda.Utils.Impossible
+import Agda.Utils.List
+import Agda.Utils.Maybe
+
+-- ---------------------------------
+
+-- | Typechecker drives the solution of metas.
+tcExp :: Bool -> Ctx o -> CExp o -> MExp o -> EE (MyPB o)
+tcExp isdep ctx typ@(TrBr typtrs ityp@(Clos _ itypexp)) trm =
+  mbpcase prioTypeUnknown Nothing (hnn_checkstep ityp) $ \(hntyp, iotastepdone) ->
+  mmpcase (True, prioTypecheck isdep, Just (RIMainInfo (length ctx) hntyp iotastepdone)) trm $ \case
+   App _ okh elr args -> case rawValue hntyp of
+    HNPi{} | isdep -> mpret $ Error "tcExp, dep terms should be eta-long"
+    _ -> do
+     res <- case elr of
+              Var v ->
+                case ctx !!! v of
+                  Nothing     -> return Nothing
+                  Just (_, a) -> return $ Just (weak (v + 1) a, id)
+              Const c -> do
+               cdef <- readIORef c
+               return $ Just (closify (cdtype cdef), mpret . And (Just [Term args]) (noiotastep_term c args))
+     caseMaybe res (mpret $ Error "tcExp, variable not in scope") $ \ (ityp, sc) -> do
+
+     ndfv <- case elr of
+              Var{} -> return 0
+              Const c -> cddeffreevars <$> readIORef c
+
+
+     isconstructor <- case elr of
+      Var{} -> return False
+      Const c -> do
+       cdef <- readIORef c
+       return $ case cdcont cdef of {Constructor{} -> True; _ -> False}
+
+     sc $ tcargs ndfv isdep ctx ityp args (NotM $ App Nothing (NotM OKVal) elr (NotM ALNil)) isconstructor $ \ityp _ -> mpret $ ConnectHandle okh (comp' True typ ityp)
+   Lam hid (Abs id1 b) -> case rawValue hntyp of
+    HNPi hid2 _ it (Abs id2 ot) | hid == hid2 ->
+     tcExp isdep ((pickid id1 id2, t it) : ctx) (t ot) b
+    _ -> mpret $ Error "tcExp, type of lam should be fun or pi (and same hid)"
+   Pi _ _ _ it (Abs id ot) -> case rawValue hntyp of
+    HNSort s ->
+     mpret $ And (Just [Term ctx, Term it])
+      (tcExp True ctx (closify (NotM $ Sort s)) it)
+      (tcExp isdep ((id, closify it) : ctx) (closify (NotM $ Sort s)) ot)
+    _ -> mpret $ Error "tcExp, type of pi should be set"
+   Sort (Set i) -> case rawValue hntyp of
+    HNSort s2 -> case s2 of
+     Set j -> mpret $ if i < j then OK else Error "tcExp, type of set should be larger set"
+
+     UnknownSort -> mpret OK -- mpret $ Error "tcExp, type of set i unknown sort" -- OK instead? (prev __IMPOSSIBLE__)
+
+     Type -> mpret OK
+    _ -> mpret $ Error "tcExp, type of set should be set"
+
+   Sort UnknownSort -> __IMPOSSIBLE__
+
+   Sort Type -> __IMPOSSIBLE__
+
+   AbsurdLambda hid -> case rawValue hntyp of
+    HNPi hid2 _ it _ | hid == hid2 ->
+     mbpcase prioAbsurdLambda Nothing (getDatatype it) $ \res -> case res of
+      Just (indeces, cons) ->
+       foldl (\p con -> mpret $ And Nothing p (
+        constructorImpossible indeces con
+       )) (mpret OK) cons
+      Nothing -> mpret $ Error "tcExp, absurd lambda, datatype needed"
+    _ -> mpret $ Error "tcExp, type of absurd lam should be fun or pi (and same hid)"
+
+
+  where
+   t = TrBr typtrs
+
+
+getDatatype :: ICExp o -> EE (MyMB (Maybe (ICArgList o, [ConstRef o])) o)
+getDatatype t =
+ mbcase (hnn t) $ \hnt -> case rawValue hnt of
+  HNApp (Const c) args -> do
+   cd <- readIORef c
+   case cdcont cd of
+    Datatype cons _ -> mbret $ Just (args, cons) -- ?? check that lenth args corresponds to type of datatype
+    _ -> mbret Nothing
+  _ -> mbret Nothing
+
+constructorImpossible :: ICArgList o -> ConstRef o -> EE (MyPB o)
+constructorImpossible args c = do
+ cd <- readIORef c
+ mbpcase prioAbsurdLambda Nothing (traversePi (-1) (Clos [] $ cdtype cd)) $ \hnot ->
+  case rawValue hnot of
+   HNApp _ args2 -> unequals args args2 (\_ -> mpret $ Error "not unequal") []
+   _ -> mpret $ Error "constructorImpossible 1"
+
+unequals :: ICArgList o -> ICArgList o -> ([(Nat, HNExp o)] -> EE (MyPB o)) -> [(Nat, HNExp o)] -> EE (MyPB o)
+unequals es1 es2 cont unifier2 =
+ mbpcase prioAbsurdLambda Nothing (hnarglist es1) $ \hnes1 ->
+ mbpcase prioAbsurdLambda Nothing (hnarglist es2) $ \hnes2 ->
+ case (hnes1, hnes2) of
+  (HNALCons _ e1 es1, HNALCons _ e2 es2) -> unequal e1 e2 (unequals es1 es2 cont) unifier2
+
+  (HNALConPar es1, HNALConPar es2) -> unequals es1 es2 cont unifier2
+
+  _ -> cont unifier2
+
+unequal :: ICExp o -> ICExp o -> ([(Nat, HNExp o)] -> EE (MyPB o)) -> [(Nat, HNExp o)] -> EE (MyPB o)
+unequal e1 e2 cont unifier2 =
+ mbpcase prioAbsurdLambda Nothing (hnn e1) $ \hne1 ->
+ mbpcase prioAbsurdLambda Nothing (hnn e2) $ \hne2 ->
+  case rawValue hne2 of
+   HNApp (Var v2) es2 | v2 < 0 ->
+    mbpcase prioAbsurdLambda Nothing (hnarglist es2) $ \hnes2 -> case hnes2 of
+     HNALNil ->
+      case lookup v2 unifier2 of
+       Nothing -> cont ((v2, hne1) : unifier2)
+       Just hne2' -> cc hne1 hne2'
+     HNALCons{} -> cont unifier2
+
+     HNALConPar{} -> __IMPOSSIBLE__
+
+   _ -> cc hne1 hne2
+ where
+  cc hne1 hne2 = case (rawValue hne1, rawValue hne2) of
+   (HNApp (Const c1) es1, HNApp (Const c2) es2) -> do
+    cd1 <- readIORef c1
+    cd2 <- readIORef c2
+    case (cdcont cd1, cdcont cd2) of
+     (Constructor{}, Constructor{}) ->
+      if c1 == c2 then
+       unequals es1 es2 cont unifier2
+      else
+       mpret OK
+     _ -> cont unifier2
+   _ -> cont unifier2
+
+traversePi :: Int -> ICExp o -> EE (MyMB (HNExp o) o)
+traversePi v t =
+ mbcase (hnn t) $ \hnt ->
+ case rawValue hnt of
+  HNPi _ _ _ (Abs _ ot) -> traversePi (v - 1) $ subi (NotM $ App Nothing (NotM OKVal) (Var v) (NotM ALNil)) ot
+  _ -> mbret hnt
+
+tcargs :: Nat -> Bool -> Ctx o -> CExp o -> MArgList o -> MExp o -> Bool ->
+          (CExp o -> MExp o -> EE (MyPB o)) -> EE (MyPB o)
+tcargs ndfv isdep ctx ityp@(TrBr ityptrs iityp) args elimtrm isconstructor cont = mmpcase (True, prioTypecheckArgList, (Just $ RICheckElim $ isdep || isconstructor)) args $ \args' -> case args' of
+ ALNil -> cont ityp elimtrm
+ ALCons hid a as ->
+  mbpcase prioInferredTypeUnknown (Just RIInferredTypeUnknown) (hnn iityp) $ \hnityp -> case rawValue hnityp of
+   HNPi hid2 possdep it (Abs _ ot)
+     | ndfv > 0 || copyarg a || hid == hid2 -> mpret $
+    And (Just ([Term a | possdep] ++ [Term ctx, Term ityptrs]))
+        (if ndfv > 0 then mpret OK else tcExp (isdep || possdep) ctx (t it) a)
+        (tcargs (ndfv - 1) isdep ctx (sub a (t ot)) as (addend hid a elimtrm) isconstructor cont)
+   _ -> mpret $ Error "tcargs, inf type should be fun or pi (and same hid)"
+
+
+ ALProj{} | ndfv > 0 -> __IMPOSSIBLE__
+
+ ALProj preas projidx hid as ->
+  mbpcase prioInferredTypeUnknown (Just RIInferredTypeUnknown) (hnn iityp) $ \hnityp -> case rawValue hnityp of
+   HNApp (Const dd) _ -> do
+    dddef <- readIORef dd
+    case cdcont dddef of
+     Datatype _ projs ->
+      mmpcase (True, prioProjIndex, Just (RICheckProjIndex projs)) projidx $
+      \projidx -> do
+       projd <- readIORef projidx
+       tcargs (cddeffreevars projd) isdep ctx (closify $ cdtype projd) preas (NotM $ App Nothing (NotM OKVal) (Const projidx) (NotM ALNil)) True $
+        \ityp2@(TrBr ityp2trs iityp2) elimtrm2 ->
+         case iityp2 of
+          Clos _ (NotM (Pi _ _ _ (NotM (App _ _ (Const dd2) _)) _)) | dd2 == dd ->
+           mbpcase prioInferredTypeUnknown (Just RIInferredTypeUnknown) (hnn iityp2) $ \hnityp2 -> case rawValue hnityp2 of
+            HNPi hid2 possdep it (Abs _ ot) | hid == hid2 -> mpret $
+             And Nothing
+                 (comp' True (TrBr ityp2trs it) ityp)
+                 (tcargs 0 isdep ctx (sub elimtrm (t ot)) as (addend hid elimtrm elimtrm2) isconstructor cont)
+            _ -> mpret $ Error "proj function type is not a Pi"
+          _ -> mpret $ Error "proj function type is not correct"
+     _ -> mpret $ Error "proj, not a datatype"
+   _ -> mpret $ Error "proj, not a const app"
+
+
+ ALConPar _ -> __IMPOSSIBLE__
+
+ where
+  t = TrBr ityptrs
+
+addend :: Hiding -> MExp o -> MM (Exp o) blk -> MM (Exp o) blk
+addend hid a (NotM (App uid okh elr as)) = NotM $ App uid okh elr (f as)
+ where
+   f (NotM ALNil)             = NotM $ ALCons hid a (NotM $ ALNil)
+   f (NotM (ALCons hid a as)) = NotM $ ALCons hid a (f as)
+   f _                        = __IMPOSSIBLE__
+addend _ _ _ = __IMPOSSIBLE__
+
+copyarg :: MExp o -> Bool
+copyarg _ = False
+
+-- ---------------------------------
+
+type HNNBlks o = [HNExp o]
+
+noblks :: HNNBlks o
+noblks = []
+
+addblk :: HNExp o -> HNNBlks o -> HNNBlks o
+addblk = (:)
+
+hnn :: ICExp o -> EE (MyMB (HNExp o) o)
+hnn e = mbcase (hnn_blks e) $ \(hne, _) -> mbret hne
+
+hnn_blks :: ICExp o -> EE (MyMB (HNExp o, HNNBlks o) o)
+hnn_blks e = hnn' e CALNil
+
+hnn_checkstep :: ICExp o -> EE (MyMB (HNExp o, Bool) o)
+hnn_checkstep e =
+ mbcase (hnb e CALNil) $ \hne ->
+  mbcase (iotastep True hne) $ \res -> case res of
+   Right _ -> mbret (hne, False)
+   Left (e, as) ->
+    mbcase (hnn' e as) $ \(hne, _) -> mbret (hne, True)
+
+
+hnn' :: ICExp o -> ICArgList o -> EE (MyMB (HNExp o, HNNBlks o) o)
+hnn' e as =
+ mbcase (hnb e as) $ \hne ->
+  mbcase (iotastep True hne) $ \res -> case res of
+   Right blks -> mbret (hne, blks)
+   Left (e, as) -> hnn' e as
+
+hnb :: ICExp o -> ICArgList o -> EE (MyMB (HNExp o) o)
+hnb e as = mbcase (hnc False e as []) $ \res -> case res of
+            HNDone _ hne -> mbret hne
+            HNMeta{} -> __IMPOSSIBLE__
+
+data HNRes o = HNDone (Maybe (Metavar (Exp o) (RefInfo o))) (HNExp o)
+             | HNMeta (ICExp o) (ICArgList o) [Maybe (UId o)]
+
+hnc :: Bool -> ICExp o -> ICArgList o -> [Maybe (UId o)] -> EE (MyMB (HNRes o) o)
+hnc haltmeta = loop
+ where
+  loop ce@(Clos cl e) cargs seenuids =
+   (if haltmeta then mmmcase e (mbret $ HNMeta ce cargs seenuids) else mmcase e) $
+   \ee -> case ee of
+    App uid okh elr args ->
+     let ncargs = CALConcat (Clos cl args) cargs
+     in case elr of
+      Var v -> case doclos cl v of
+       Left v' -> mbret $ HNDone expmeta
+                        $ WithSeenUIds (uid : seenuids)
+                        $ HNApp (Var v') ncargs
+       Right f -> loop f ncargs (uid : seenuids)
+      Const _ -> mbret $ HNDone expmeta
+                       $ WithSeenUIds (uid : seenuids)
+                       $ HNApp elr ncargs
+    Lam hid (Abs id b) ->
+     mbcase (hnarglist cargs) $ \hncargs -> case hncargs of
+      HNALNil -> mbret $ HNDone expmeta
+                       $ WithSeenUIds seenuids
+                       $ HNLam hid (Abs id (Clos (Skip : cl) b))
+      HNALCons _ arg cargs' -> loop (Clos (Sub arg : cl) b) cargs' seenuids
+
+      HNALConPar{} -> __IMPOSSIBLE__
+
+    Pi uid hid possdep it (Abs id ot) ->
+       checkNoArgs cargs $ mbret $ HNDone expmeta
+         $ WithSeenUIds (uid : seenuids)
+         $ HNPi hid possdep (Clos cl it) (Abs id (Clos (Skip : cl) ot))
+    Sort s -> checkNoArgs cargs $ mbret
+            $ HNDone expmeta $ WithSeenUIds [] $ HNSort s
+
+    AbsurdLambda{} -> mbfailed "hnc: encountered absurdlambda"
+
+
+   where expmeta = case e of {Meta m -> Just m; NotM _ -> Nothing}
+  checkNoArgs cargs c =
+   mbcase (hnarglist cargs) $ \hncargs -> case hncargs of
+    HNALNil -> c
+    HNALCons{} -> mbfailed "hnc: there should be no args"
+
+    HNALConPar{} -> __IMPOSSIBLE__
+
+
+hnarglist :: ICArgList o -> EE (MyMB (HNArgList o) o)
+hnarglist args =
+ case args of
+  CALNil -> mbret HNALNil
+  CALConcat (Clos cl args) args2 ->
+   mmcase args $ \args -> case args of
+    ALNil -> hnarglist args2
+    ALCons hid arg argsb -> mbret $ HNALCons hid (Clos cl arg) (CALConcat (Clos cl argsb) args2)
+
+    ALProj{} -> mbret HNALNil -- dirty hack to make check of no-iota in term work
+
+
+    ALConPar args -> mbret $ HNALConPar (CALConcat (Clos cl args) args2)
+-- -----------------------------
+
+getNArgs :: Nat -> ICArgList o -> EE (MyMB (Maybe ([ICExp o], ICArgList o)) o)
+getNArgs 0 args = mbret $ Just ([], args)
+getNArgs narg args =
+ mbcase (hnarglist args) $ \hnargs -> case hnargs of
+  HNALNil -> mbret Nothing
+  HNALCons _ arg args' ->
+   mbcase (getNArgs (narg - 1) args') $ \res -> case res of
+    Nothing -> mbret Nothing
+    Just (pargs, rargs) -> mbret $ Just (arg : pargs, rargs)
+
+  HNALConPar{} -> __IMPOSSIBLE__
+
+
+getAllArgs :: ICArgList o -> EE (MyMB [ICExp o] o)
+getAllArgs args =
+ mbcase (hnarglist args) $ \hnargs -> case hnargs of
+  HNALNil -> mbret []
+  HNALCons _ arg args' ->
+   mbcase (getAllArgs args') $ \args'' ->
+    mbret (arg : args'')
+
+  HNALConPar args2 ->
+   mbcase (getAllArgs args2) $ \args3 -> mbret (__IMPOSSIBLE__ : args3)
+
+
+data PEval o = PENo (ICExp o)
+             | PEConApp (ICExp o) (ConstRef o) [PEval o]
+
+iotastep :: Bool -> HNExp o -> EE (MyMB (Either (ICExp o, ICArgList o) (HNNBlks o)) o)
+iotastep smartcheck e = case rawValue e of
+ HNApp (Const c) args -> do
+  cd <- readIORef c
+  case cdcont cd of
+   Def narg cls _ _ ->
+    mbcase (getNArgs narg args) $ \res -> case res of
+     Nothing -> mbret (Right noblks)
+     Just (pargs, rargs) ->
+      mbcase (dorules cls (map PENo pargs)) $ \res -> case res of
+       Right blks -> mbret (Right blks)
+       Left rhs -> mbret $ Left (rhs, rargs)
+   _ -> mbret $ Right noblks
+ _ -> mbret $ Right noblks
+ where
+ dorules :: [Clause o] -> [PEval o] -> EE (MyMB (Either (ICExp o) (HNNBlks o)) o)
+ dorules [] _ = mbret $ Right noblks
+ dorules (rule:rules') as =
+  mbcase (dorule rule as) $ \x -> case x of
+   Left (Left as') -> dorules rules' as'
+   Left (Right blks) -> mbret (Right blks)
+   Right rhs -> mbret $ Left rhs
+
+ dorule :: Clause o -> [PEval o] -> EE (MyMB (Either (Either [PEval o] (HNNBlks o)) (ICExp o)) o)
+ dorule (pats, rhs) as =
+  mbcase (dopats pats as) $ \x -> case x of
+   Right (_, ss) -> mbret $ Right (Clos (map Sub ss) rhs)
+   Left hnas -> mbret $ Left hnas
+
+ dopats :: [Pat o] -> [PEval o] -> EE (MyMB (Either (Either [PEval o] (HNNBlks o)) ([PEval o], [ICExp o])) o)
+ dopats [] [] = mbret $ Right ([], [])
+ dopats (p:ps') (a:as') =
+  mbcase (dopat p a) $ \x -> case x of
+   Right (hna, ss) ->
+    mbcase (dopats ps' as') $ \x -> case x of
+     Right (hnas, ss2) -> mbret $ Right (hna : hnas, ss2 ++ ss)
+     Left (Right blks) -> mbret $ Left (Right blks)
+     Left (Left hnas) -> mbret $ Left $ Left (hna : hnas)
+   Left (Right blks) -> mbret $ Left (Right blks)
+   Left (Left hna) -> mbret $ Left $ Left (hna : as')
+ dopats _ _ = mbfailed "bad patterns"
+
+ dopat :: Pat o -> PEval o -> EE (MyMB (Either (Either (PEval o) (HNNBlks o)) (PEval o, [ICExp o])) o)
+ dopat (PatConApp c pas) a =
+  case a of
+   PENo a ->
+    if smartcheck then
+     mbcase (meta_not_constructor a) $ \notcon -> if notcon then mbret $ Left $ Right noblks else qq -- to know more often if iota step is possible
+    else
+     qq
+    where
+     qq =
+      mbcase (hnn_blks a) $ \(hna, blks) -> case rawValue hna of
+       HNApp (Const c') as ->
+        if c == c' then
+         mbcase (getAllArgs as) $ \as' ->
+          if length as' == length pas then
+           mbcase (dopats pas (map PENo as')) $ \x -> case x of
+            Right (hnas, ss) -> mbret $ Right (PEConApp a c' hnas, ss)
+            Left (Right blks) -> mbret $ Left (Right blks)
+            Left (Left hnas) -> mbret $ Left $ Left (PEConApp a c' hnas)
+          else
+           mbfailed "dopat: wrong amount of args"
+        else do
+         cd <- readIORef c'
+         case cdcont cd of
+          Constructor{} -> mbcase (getAllArgs as) $ \as' ->
+           mbret $ Left (Left (PEConApp a c' (map PENo as')))
+          _ -> mbret $ Left (Right (addblk hna blks))
+       _ -> mbret $ Left (Right (addblk hna blks))
+   aa@(PEConApp a c' as) ->
+    if c == c' then
+     if length as == length pas then
+      mbcase (dopats pas as) $ \x -> case x of
+       Right (hnas, ss) -> mbret $ Right (PEConApp a c' hnas, ss)
+       Left (Right blks) -> mbret $ Left (Right blks)
+       Left (Left hnas) -> mbret $ Left $ Left (PEConApp a c' hnas)
+     else
+      mbfailed "dopat: wrong amount of args"
+    else
+     mbret $ Left (Left aa)
+ dopat (PatProj cs) a =
+  case a of
+   PENo a ->
+    if smartcheck then
+     mbcase (meta_not_constructor a) $ \notcon -> if notcon then mbret $ Left $ Right noblks else qq -- to know more often if iota step is possible
+    else
+     qq
+    where
+     qq =
+      mbcase (hnn_blks a) $ \(hna, blks) -> case rawValue hna of
+       HNApp (Const c') as ->
+        do
+         cd <- readIORef c'
+         case cdcont cd of
+          Constructor{} -> mbcase (getAllArgs as) $ \as' ->
+           mbret $ Left (Left (PEConApp a c' (map PENo as')))
+          _ -> mbret $ Left (Right (addblk hna blks))
+       _ -> mbret $ Left (Right (addblk hna blks))
+   aa@(PEConApp a c' as) -> mbret $ Left (Left aa)
+ dopat PatVar{} a@(PENo a') = mbret $ Right (a, [a'])
+ dopat PatVar{} a@(PEConApp a' _ _) = mbret $ Right (a, [a'])
+ dopat PatExp a = mbret $ Right (a, [])
+
+-- -----------------------------
+
+noiotastep :: HNExp o -> EE (MyPB o)
+noiotastep hne =
+ mbpcase prioNoIota Nothing (iotastep False hne) $ \res -> case res of
+  Left _ -> mpret $ Error "iota step possible contrary to assumed"
+  Right _ -> mpret OK
+
+noiotastep_term :: ConstRef o -> MArgList o -> EE (MyPB o)
+noiotastep_term c args = do
+  cd <- readIORef c
+  case cdcont cd of
+    Def _ [(pats, _)] _ _ -> mpret OK
+      -- all (\pat -> case pat of {PatConApp{} -> False; _ -> True}) pats
+    _ -> noiotastep $ WithSeenUIds []
+                    $ HNApp (Const c) $ CALConcat (Clos [] args) CALNil
+
+data CMode o = CMRigid (Maybe (Metavar (Exp o) (RefInfo o))) (HNExp o)
+             | forall b . Refinable b (RefInfo o) => CMFlex (MM b (RefInfo o)) (CMFlex o)
+data CMFlex o = CMFFlex (ICExp o) (ICArgList o) [Maybe (UId o)]
+              | CMFSemi (Maybe (Metavar (Exp o) (RefInfo o))) (HNExp o)
+              | CMFBlocked (Maybe (Metavar (Exp o) (RefInfo o))) (HNExp o)
+
+comp' :: forall o . Bool -> CExp o -> CExp o -> EE (MyPB o)
+comp' ineq lhs@(TrBr trs1 e1) rhs@(TrBr trs2 e2) = comp ineq e1 e2
+ where
+  comp :: Bool -> ICExp o -> ICExp o -> EE (MyPB o)
+  comp ineq e1 e2 =
+   proc e1 e2
+
+   where
+    proc e1 e2 = f True e1 CALNil [] $ \res1 -> f True e2 CALNil [] $ \res2 -> g res1 res2
+    f semifok e as seenuids cont =
+     mbpcase prioCompBeta Nothing (hnc True e as seenuids) $ \res ->
+      case res of
+       HNDone mexpmeta hne -> fhn semifok mexpmeta hne cont
+
+       HNMeta ce@(Clos cl m) cargs seenuids -> do
+        b1 <- boringClos cl
+        b2 <- boringArgs cargs
+        if b1 && b2 then
+          cont $ CMFlex m (CMFFlex ce cargs seenuids)
+         else
+          mbpcase prioCompBetaStructured Nothing (hnc False ce cargs seenuids) $ \res ->
+           case res of
+            HNDone mexpmeta hne -> cont $ CMFlex m (CMFBlocked mexpmeta hne)
+            HNMeta{} -> __IMPOSSIBLE__
+
+
+    fhn semifok mexpmeta hne cont =
+     mmbpcase (iotastep True hne)
+      (\m -> do
+        let sf = False {- semiflex hne -}
+        if semifok && sf then
+          cont (CMFlex m (CMFSemi mexpmeta hne))
+         else
+          cont (CMFlex m (CMFBlocked mexpmeta hne))
+      )
+      (\res -> case res of
+        Right _ -> cont (CMRigid mexpmeta hne)
+        Left (e, as) -> f semifok e as [] cont
+      )
+    g res1 res2 =
+     case (res1, res2) of
+      (CMRigid mexpmeta1 hne1, CMRigid mexpmeta2 hne2) -> comphn ineq mexpmeta1 hne1 mexpmeta2 hne2
+      (CMFlex m1 (CMFBlocked mexpmeta1 hne1), _) -> mstp False mexpmeta1 hne1 $ \res1 -> g res1 res2
+      (_, CMFlex m2 (CMFBlocked mexpmeta2 hne2)) -> mstp False mexpmeta2 hne2 $ \res2 -> g res1 res2
+      (CMRigid mexpmeta1 hne1, CMFlex _ fl2) -> unif True mexpmeta1 hne1 fl2
+      (CMFlex _ fl1, CMRigid mexpmeta2 hne2) -> unif False mexpmeta2 hne2 fl1
+
+
+      (CMFlex m1 fl1, CMFlex m2 fl2) -> doubleblock m1 m2 $ fcm fl1 $ \res1 -> fcm fl2 $ \res2 -> g res1 res2
+    fcm (CMFFlex ce cargs seenuids) = f True ce cargs seenuids
+    fcm (CMFSemi mexpmeta hne) = fhn True mexpmeta hne
+    fcm (CMFBlocked _ hne) = __IMPOSSIBLE__ -- not used. if so should be: fhn False hne
+    mstp semif mexpmeta hne cont =
+     mpret $ Or prioCompChoice
+      (mpret $ And (Just [Term lhs, Term rhs])
+       (noiotastep hne)
+       (cont (CMRigid mexpmeta hne))
+      )
+      (stp semif hne cont)
+    stp semif hne cont =
+     mbpcase prioCompIota (Just $ RIIotaStep semif) (iotastep True hne) $ \res -> case res of
+      Right _ -> mpret $ Error "no iota step possible, contrary to assumed"
+      Left (e, as) -> f semif e as [] cont
+    unif oppis1 oppmexpmeta opphne res =
+     let iter res = if oppis1 then
+                     g (CMRigid oppmexpmeta opphne) res
+                    else
+                     g res (CMRigid oppmexpmeta opphne)
+     in case res of
+      CMFFlex ce cargs seenuids -> do
+       poss <- iotapossmeta ce cargs
+       maybeor poss prioCompChoice
+        (loop ce cargs seenuids)
+-- (mbpcase prioCompBeta (Just $ RIIotaStep False) (hnb ce cargs) $ \hne ->
+        (mbpcase prioCompBeta (Just $ RIIotaStep False) (hnc False ce cargs seenuids) $ \res ->
+          -- RIIotaStep here on beta-norm to make cost high when guessing elim const in type par
+          case res of
+           HNDone mexpmeta hne -> stp False hne iter
+           HNMeta{} -> __IMPOSSIBLE__
+        )
+       where
+        loop ce@(Clos cl m) cargs seenuids =
+         mmpcase (False, prioCompUnif, Just (RIUnifInfo cl opphne)) m $ \_ ->
+         mbpcase prioCompBeta Nothing (hnc True ce cargs seenuids) $ \res -> case res of
+          HNDone mexpmeta hne ->
+           mpret $ And (Just [Term lhs, Term rhs])
+            (noiotastep hne)
+            (iter (CMRigid mexpmeta hne))
+          HNMeta ce cargs seenuids -> loop ce cargs seenuids
+      CMFSemi _ hne ->
+       __IMPOSSIBLE__ -- CMFSemi disabled, if used should be: stp True hne iter
+      CMFBlocked{} -> __IMPOSSIBLE__
+    comphn :: Bool -> Maybe (Metavar (Exp o) (RefInfo o)) -> HNExp o -> Maybe (Metavar (Exp o) (RefInfo o)) -> HNExp o -> EE (MyPB o)
+    comphn ineq mexpmeta1 hne1 mexpmeta2 hne2 =
+     case (rawValue hne1, rawValue hne2) of
+      (HNApp elr1 args1, HNApp elr2 args2) ->
+       let ce = case (elr1, elr2) of
+                 (Var v1, Var v2) ->
+                     if v1 == v2 then Nothing
+                     else Just "comphn, elr, vars not equal"
+                 (Const c1, Const c2) ->
+                    if c1 == c2 then Nothing
+                    else Just "comphn, elr, consts not equal"
+                 (_, _) -> Just "comphn, elrs not equal"
+       in case ce of
+            Nothing -> compargs args1 args2
+            Just msg -> mpret $ Error msg
+      (HNLam hid1 (Abs id1 b1), HNLam hid2 (Abs id2 b2)) -> comp False b1 b2
+      (HNLam _ (Abs _ b1), HNApp elr2 args2) ->
+       f True b1 CALNil (seenUIds hne1) $ \res1 ->
+       fhn True mexpmeta2 (WithSeenUIds (seenUIds hne2) $ HNApp (weak 1 elr2) (addtrailingargs (Clos [] $ NotM $ ALCons NotHidden{- arbitrary -} (NotM $ App Nothing (NotM OKVal) (Var 0) (NotM ALNil)) (NotM ALNil)) (weak 1 args2))) $ \res2 -> g res1 res2
+      (HNApp elr1 args1, HNLam _ (Abs _ b2)) ->
+       fhn True mexpmeta1 (WithSeenUIds (seenUIds hne1) $ HNApp (weak 1 elr1) (addtrailingargs (Clos [] $ NotM $ ALCons NotHidden{- arbitrary -} (NotM $ App Nothing (NotM OKVal) (Var 0) (NotM ALNil)) (NotM ALNil)) (weak 1 args1))) $ \res1 -> f True b2 CALNil (seenUIds hne2) $ \res2 -> g res1 res2
+{-
+      (HNLam _ (Abs _ b1), HNApp uid2 elr2 args2) ->
+       f True b1 CALNil $ \res1 -> g res1
+        (CMRigid mexpmeta2 (HNApp uid2 (weak 1 elr2) (addtrailingargs (Clos [] $ NotM $ ALCons NotHidden{- arbitrary -} (NotM $ App Nothing (NotM OKVal) (Var 0) (NotM ALNil)) (NotM ALNil)) (weak 1 args2))))
+      (HNApp uid1 elr1 args1, HNLam _ (Abs _ b2)) ->
+       f True b2 CALNil $ \res2 -> g
+        (CMRigid mexpmeta1 (HNApp uid1 (weak 1 elr1) (addtrailingargs (Clos [] $ NotM $ ALCons NotHidden{- arbitrary -} (NotM $ App Nothing (NotM OKVal) (Var 0) (NotM ALNil)) (NotM ALNil)) (weak 1 args1))))
+        res2
+-}
+      (HNPi hid1 _ it1 (Abs id1 ot1), HNPi hid2 _ it2 (Abs id2 ot2)) -> mpret $
+       And (Just [Term trs1, Term trs2]) (comp False it1 it2) (comp ineq ot1 ot2)
+      (HNSort s1, HNSort s2) -> mpret $
+       case (s1, s2) of
+        (Set i1, Set i2) -> if i1 == i2 || ineq && i1 > i2 then OK else Error "comphn, set levels not matching"
+        (Set _, UnknownSort) -> OK
+        (UnknownSort, Set _) -> OK
+        (UnknownSort, UnknownSort) -> OK
+        (Type, Set _) | ineq -> OK
+        (Type, UnknownSort) | ineq -> OK
+        _ -> __IMPOSSIBLE__
+      (HNApp (Const c1) _, _) -> case mexpmeta2 of
+       Nothing -> mpret $ Error "comphn, not equal (2)"
+       Just m2 -> mpret $ AddExtraRef "comphn: not equal, adding extra ref"
+                          m2 (extraref m2 (seenUIds hne1) c1)
+      (_, HNApp (Const c2) _) -> case mexpmeta1 of
+       Nothing -> mpret $ Error "comphn, not equal (3)"
+       Just m1 -> mpret $ AddExtraRef "comphn: not equal, adding extra ref"
+                          m1 (extraref m1 (seenUIds hne2) c2)
+      (_, _) -> mpret $ Error "comphn, not equal"
+
+    compargs :: ICArgList o -> ICArgList o -> EE (MyPB o)
+    compargs args1 args2 =
+     mbpcase prioCompareArgList Nothing (hnarglist args1) $ \hnargs1 ->
+     mbpcase prioCompareArgList Nothing (hnarglist args2) $ \hnargs2 ->
+     case (hnargs1, hnargs2) of
+      (HNALNil, HNALNil) -> mpret OK
+      (HNALCons hid1 arg1 args1b, HNALCons hid2 arg2 args2b) -> mpret $
+       And (Just [Term trs1, Term trs2]) (comp False arg1 arg2) (compargs args1b args2b)
+
+      (HNALConPar args1b, HNALCons _ _ args2b) -> compargs args1b args2b
+      (HNALCons _ _ args1b, HNALConPar args2b) -> compargs args1b args2b
+      (HNALConPar args1', HNALConPar args2') -> compargs args1' args2'
+
+      (_, _) -> mpret $ Error $ "comphnargs, not equal"
+
+
+    boringExp :: ICExp o -> EE Bool
+    boringExp (Clos cl e) = do
+     e <- expandbind e
+     case e of
+      Meta{} -> boringClos cl
+      NotM e -> case e of
+       App _ _ (Var v) as -> do
+        as <- expandbind as
+        case as of
+         Meta{} -> return False
+         NotM as -> case as of
+          ALNil -> case doclos cl v of
+           Left _ -> return True
+           Right e -> boringExp e
+          ALCons{} -> return False
+          ALProj{} -> return False
+          ALConPar{} -> return False
+
+       _ -> return False
+
+    boringClos :: [CAction o] -> EE Bool
+    boringClos cl = and <$> mapM f cl
+     where f (Sub e) = boringExp e
+           f Skip = return True
+           f (Weak _) = return True
+
+    boringArgs :: ICArgList o -> EE Bool
+    boringArgs CALNil = return True
+    boringArgs (CALConcat (Clos cl as) as2) = do
+     b1 <- f cl as
+     b2 <- boringArgs as2
+     return $ b1 && b2
+     where
+      f cl as = do
+       as <- expandbind as
+       case as of
+        Meta{} -> return False
+        NotM as -> case as of
+         ALNil -> return True
+         ALCons _ a as -> do
+          b1 <- boringExp (Clos cl a)
+          b2 <- f cl as
+          return $ b1 && b2
+
+         ALProj{} -> return False  -- Not impossible: #2966
+
+
+         ALConPar as -> f cl as
+-- ---------------------------------
+
+checkeliminand :: MExp o -> EE (MyPB o)
+checkeliminand = f [] []
+ where
+  f uids used e =
+   mmpcase (False, prioNo, Just (RIUsedVars uids used)) e $ \e -> case e of
+    App uid _ elr@(Var{}) args -> fs (adduid uid uids) (elr : used) args
+    App uid _ elr@(Const c) args -> do
+     cd <- readIORef c
+     case cdcont cd of
+      Def _ _ (Just i) _ -> mpret $ Sidecondition (fs (adduid uid uids) (elr : used) args) (g i args)
+       where
+        g i as = mmpcase (False, prioNo, Nothing) as $ \as -> case as of
+                  ALNil -> mpret OK
+                  ALCons _ a as -> case i of
+                   0 -> mmpcase (False, prioNo, Just RINotConstructor) a $ \_ ->
+                         mpret OK
+                   _ -> g (i - 1) as
+
+                  ALProj eas _ _ as -> mpret OK
+
+
+                  ALConPar as -> case i of
+                   0 -> __IMPOSSIBLE__
+                   _ -> g (i - 1) as
+
+      _ -> fs (adduid uid uids) (elr : used) args
+    Lam _ (Abs _ e) -> f uids (w used) e
+    Pi uid _ _ e1 (Abs _ e2) -> mpret $ Sidecondition (f (adduid uid uids) used e1) (f (adduid uid uids) (w used) e2)
+    Sort _ -> mpret OK
+
+    AbsurdLambda{} -> mpret OK
+
+
+  fs uids used as =
+   mmpcase (False, prioNo, Nothing) as $ \as -> case as of
+    ALNil -> mpret OK
+    ALCons _ a as -> mpret $ Sidecondition (f uids used a) (fs uids used as)
+
+    ALProj eas _ _ as -> mpret $ Sidecondition (fs uids used eas) (fs uids used as)
+
+
+    ALConPar as -> fs uids used as
+
+  w = map (\x -> case x of {Var v -> Var (v + 1); Const{} -> x})
+  adduid (Just uid) uids = uid : uids
+  adduid Nothing uids = uids
+
+-- ---------------------------------
+
+maybeor :: Bool -> Prio -> IO (PB (RefInfo o)) -> IO (PB (RefInfo o)) ->
+           IO (PB (RefInfo o))
+maybeor _ _ mainalt _ = mainalt
+
+iotapossmeta :: ICExp o -> ICArgList o -> EE Bool
+iotapossmeta ce@(Clos cl _) cargs = do
+ xs <- mapM ncaction cl
+ y <- nccargs cargs
+ return $ not (and xs && y)
+ where
+  ncaction (Sub ce) = nonconstructor ce
+  ncaction Skip = return True
+  ncaction (Weak{}) = return True
+  nccargs CALNil = return True
+  nccargs (CALConcat (Clos cl margs) cargs) = do
+   x <- ncmargs cl margs
+   y <- nccargs cargs
+   return $ x && y
+  ncmargs cl (Meta m) = do
+   mb <- readIORef (mbind m)
+   case mb of
+    Nothing -> return False
+    Just x -> ncargs cl x
+  ncmargs cl (NotM args) = ncargs cl args
+  ncargs cl ALNil = return True
+  ncargs cl (ALCons _ a args) = do
+   x <- nonconstructor (Clos cl a)
+   y <- ncmargs cl args
+   return $ x && y
+
+  ncargs _ (ALProj{}) = __IMPOSSIBLE__
+
+
+  ncargs cl (ALConPar args) = ncmargs cl args
+
+  nonconstructor :: ICExp o -> EE Bool
+  nonconstructor ce = do
+   res <- hnc True ce CALNil []
+   case res of
+    Blocked{} -> return False
+    Failed{} -> return False
+    NotB res -> case res of
+     HNMeta ce _ _ -> do
+      let (Clos _ (Meta m)) = ce
+      infos <- extractblkinfos m
+      if any (\info -> case info of {RINotConstructor -> True; _ -> False}) infos then do
+        return True
+       else
+        return False
+      -- return False -- return True -- ?? removes completeness - Yes, in DavidW1.additionRight
+     HNDone{} -> do
+      res <- hnn ce
+      case res of
+       NotB hne -> case rawValue hne of
+        HNApp (Const c) _ -> do
+         cd <- readIORef c
+         case cdcont cd of
+          Constructor{} -> return False
+          _ -> return True
+        _ -> return True
+       Blocked m _ -> return False -- not necessary to do check here because already done by hnn (!! if it's known that m stands for an eliminator then it cannot be constructor so True instead)
+       Failed _ -> return False
+
+meta_not_constructor :: ICExp o -> EE (MB Bool (RefInfo o))
+meta_not_constructor a =
+ mbcase (hnc True a CALNil []) $ \res -> case res of
+  HNMeta ce _ _ -> do
+    let (Clos _ (Meta m)) = ce
+    infos <- extractblkinfos m
+    if any (\info -> case info of {RINotConstructor -> True; _ -> False}) infos then do
+      b <- iotapossmeta ce CALNil
+      mbret $ not b
+     else
+      mbret False
+  HNDone{} -> mbret False
+
+-- ---------------------------------
+
+calcEqRState :: EqReasoningConsts o -> MExp o -> EE (MyPB o)
+calcEqRState cs = f EqRSNone
+ where
+  f s e =
+   mmpcase (False, prioNo, Just (RIEqRState s)) e $ \e -> case e of
+    App _ _ (Const c) args -> case () of
+     _ | c == eqrcBegin cs -> fs [EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSChain] args
+     _ | c == eqrcStep cs -> fs [EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSPrf1, EqRSChain] args
+     _ | c == eqrcSym cs -> fs [EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSPrf2] args
+     _ | c == eqrcCong cs -> fs [EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSNone, EqRSPrf3] args
+     _ -> fs [] args
+    App _ _ (Var{}) args -> fs [] args
+    Lam _ (Abs _ b) -> f EqRSNone b
+    Pi _ _ _ it (Abs _ ot) -> mpret $ Sidecondition (f EqRSNone it) (f EqRSNone ot)
+    Sort{} -> mpret OK
+
+    AbsurdLambda{} -> mpret OK
+
+
+  fs ss args =
+   mmpcase (False, prioNo, Nothing) args $ \args -> case (ss, args) of
+    (_, ALNil) -> mpret OK
+    (s : ss, ALCons _ a args) -> mpret $ Sidecondition (f s a) (fs ss args)
+    ([], ALCons _ a args) -> mpret $ Sidecondition (f EqRSNone a) (fs [] args)
+
+    (_, ALProj eas _ _ as) -> mpret $ Sidecondition (fs [] eas) (fs [] as) -- when eqr-hint is given manually, ss can be non-empty here
+
+
+    (_ : ss, ALConPar args) -> fs ss args
+    ([], ALConPar args) -> fs [] args
+
+-- ---------------------------------
+
+pickid :: MId -> MId -> MId
+pickid mid1@(Id _) _ = mid1
+pickid _ mid2 = mid2
+
+-- ---------------------------------
+
+tcSearch :: Bool -> Ctx o -> CExp o -> MExp o -> EE (MyPB o)
+tcSearch isdep ctx typ trm = mpret $ Sidecondition (checkeliminand trm)
+                              (tcExp isdep ctx typ trm)
+
+-- ----------------------------
diff --git a/src/full/Agda/Benchmarking.hs b/src/full/Agda/Benchmarking.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Benchmarking.hs
@@ -0,0 +1,153 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-- | Agda-specific benchmarking structure.
+
+module Agda.Benchmarking where
+
+import Control.DeepSeq
+import qualified Control.Exception as E
+
+import Data.IORef
+
+import GHC.Generics (Generic)
+
+import System.IO.Unsafe
+
+import Agda.Syntax.Concrete.Pretty () --instance only
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+import Agda.Utils.Benchmark (MonadBench(..))
+import qualified Agda.Utils.Benchmark as B
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+-- | Phases to allocate CPU time to.
+data Phase
+  = Parsing
+    -- ^ Happy parsing and operator parsing.
+  | Import
+    -- ^ Import chasing.
+  | Deserialization
+    -- ^ Reading interface files.
+  | Scoping
+    -- ^ Scope checking and translation to abstract syntax.
+  | Typing
+    -- ^ Type checking and translation to internal syntax.
+  | Termination
+    -- ^ Termination checking.
+  | Positivity
+    -- ^ Positivity checking and polarity computation.
+  | Injectivity
+    -- ^ Injectivity checking.
+  | ProjectionLikeness
+    -- ^ Checking for projection likeness.
+  | Coverage
+    -- ^ Coverage checking and compilation to case trees.
+  | Highlighting
+    -- ^ Generating highlighting info.
+  | Serialization
+    -- ^ Writing interface files.
+  | DeadCode
+    -- ^ Dead code elimination.
+  | DeadCodeInstantiateFull
+    -- ^ Unfolding all metas before serialization.
+  | DeadCodeReachable
+    -- ^ Dead code reachable definitions subphase.
+  | Graph
+    -- ^ Subphase for 'Termination'.
+  | RecCheck
+    -- ^ Subphase for 'Termination'.
+  | Reduce
+    -- ^ Subphase for 'Termination'.
+  | Level
+    -- ^ Subphase for 'Termination'.
+  | Compare
+    -- ^ Subphase for 'Termination'.
+  | With
+    -- ^ Subphase for 'Termination'.
+  | ModuleName
+    -- ^ Subphase for 'Import'.
+  | Compaction
+    -- ^ Subphase for 'Deserialization': compacting interfaces.
+  | BuildInterface
+    -- ^ Subphase for 'Serialization'.
+  | Sort
+    -- ^ Subphase for 'Serialization'.
+  | BinaryEncode
+    -- ^ Subphase for 'Serialization'.
+  | Compress
+    -- ^ Subphase for 'Serialization'.
+  | OperatorsExpr
+    -- ^ Subphase for 'Parsing'.
+  | OperatorsPattern
+    -- ^ Subphase for 'Parsing'.
+  | Free
+    -- ^ Subphase for 'Typing': free variable computation.
+  | OccursCheck
+    -- ^ Subphase for 'Typing': occurs check for solving metas.
+  | CheckLHS
+    -- ^ Subphase for 'Typing': checking the LHS
+  | CheckRHS
+    -- ^ Subphase for 'Typing': checking the RHS
+  | TypeSig
+    -- ^ Subphase for 'Typing': checking a type signature
+  | Generalize
+    -- ^ Subphase for 'Typing': generalizing over `variable`s
+  | InstanceSearch
+    -- ^ Subphase for 'Typing': solving instance goals
+  | UnifyIndices
+    -- ^ Subphase for 'CheckLHS': unification of the indices
+  | InverseScopeLookup
+    -- ^ Pretty printing names.
+  | TopModule TopLevelModuleName
+  | Definition QName
+  deriving (Eq, Ord, Show, Generic)
+
+instance Pretty Phase where
+  pretty (TopModule m)  = pretty m
+  pretty (Definition q) = pretty q
+  pretty a = text (show a)
+
+instance NFData Phase
+
+type Benchmark = B.Benchmark Phase
+type Account   = B.Account Phase
+
+isModuleAccount :: Account -> Bool
+isModuleAccount []                = True
+isModuleAccount (TopModule{} : _) = True
+isModuleAccount _                 = False
+
+isDefAccount :: Account -> Bool
+isDefAccount []                 = True
+isDefAccount (Definition{} : _) = True
+isDefAccount _                  = False
+
+isInternalAccount :: Account -> Bool
+isInternalAccount (TopModule{}  : _) = False
+isInternalAccount (Definition{} : _) = False
+isInternalAccount _                  = True
+
+-- * Benchmarking in the IO monad.
+
+-- | Global variable to store benchmark statistics.
+{-# NOINLINE benchmarks #-}
+benchmarks :: IORef Benchmark
+benchmarks = unsafePerformIO $ newIORef empty
+
+instance MonadBench IO where
+  type BenchPhase IO = Phase
+  getBenchmark = readIORef benchmarks
+  putBenchmark = writeIORef benchmarks
+  finally = E.finally
+
+-- | Benchmark an IO computation and bill it to the given account.
+billToIO :: Account -> IO a -> IO a
+billToIO = B.billTo
+
+-- | Benchmark a pure computation and bill it to the given account.
+billToPure :: Account -> a -> a
+billToPure acc a = unsafePerformIO $ billToIO acc $ return a
+{-# NOINLINE billToPure #-}
diff --git a/src/full/Agda/Compiler/Backend.hs b/src/full/Agda/Compiler/Backend.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Backend.hs
@@ -0,0 +1,290 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PolyKinds #-}
+
+-- | Interface for compiler backend writers.
+module Agda.Compiler.Backend
+  ( Backend(..), Backend'(..), Recompile(..), IsMain(..)
+  , Flag
+  , toTreeless
+  , module Agda.Syntax.Treeless
+  , module Agda.TypeChecking.Monad
+  , module CheckResult
+  , activeBackendMayEraseType
+    -- For Agda.Main
+  , backendInteraction
+  , parseBackendOptions
+    -- For InteractionTop
+  , callBackend
+    -- Tools
+  , lookupBackend
+  , activeBackend
+  ) where
+
+import Control.DeepSeq
+import Control.Monad              ( (<=<) )
+import Control.Monad.Trans        ( lift )
+import Control.Monad.Trans.Maybe
+
+import qualified Data.List as List
+import Data.Maybe
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import GHC.Generics (Generic)
+
+import System.Console.GetOpt
+
+import Agda.Syntax.TopLevelModuleName
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Errors (getAllWarnings)
+-- Agda.TypeChecking.Monad.Base imports us, relying on the .hs-boot file to
+-- resolve the circular dependency. Fine. However, ghci loads the module after
+-- compilation, so it brings in all of the symbols. That causes .Base to see
+-- getBenchmark (defined in Agda.TypeChecking.Monad.State) *and* the one
+-- defined in Agda.Utils.Benchmark, which causes an error. So we explicitly
+-- hide it here to prevent it from being seen there and causing an error.
+import Agda.TypeChecking.Monad hiding (getBenchmark)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty as P
+
+import Agda.Interaction.Options
+import Agda.Interaction.FindFile
+import Agda.Interaction.Imports as CheckResult (CheckResult(CheckResult), crInterface, crWarnings, crMode)
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.FileName
+import Agda.Utils.Functor
+import Agda.Utils.IndexedList
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+
+import Agda.Compiler.ToTreeless
+import Agda.Compiler.Common
+
+import Agda.Utils.Impossible
+
+-- Public interface -------------------------------------------------------
+
+data Backend where
+  Backend :: NFData opts => Backend' opts env menv mod def -> Backend
+
+data Backend' opts env menv mod def = Backend'
+  { backendName      :: String
+  , backendVersion   :: Maybe String
+      -- ^ Optional version information to be printed with @--version@.
+  , options          :: opts
+      -- ^ Default options
+  , commandLineFlags :: [OptDescr (Flag opts)]
+      -- ^ Backend-specific command-line flags. Should at minimum contain a
+      --   flag to enable the backend.
+  , isEnabled        :: opts -> Bool
+      -- ^ Unless the backend has been enabled, @runAgda@ will fall back to
+      --   vanilla Agda behaviour.
+  , preCompile       :: opts -> TCM env
+      -- ^ Called after type checking completes, but before compilation starts.
+  , postCompile      :: env -> IsMain -> Map TopLevelModuleName mod ->
+                        TCM ()
+      -- ^ Called after module compilation has completed. The @IsMain@ argument
+      --   is @NotMain@ if the @--no-main@ flag is present.
+  , preModule        :: env -> IsMain -> TopLevelModuleName ->
+                        Maybe FilePath -> TCM (Recompile menv mod)
+      -- ^ Called before compilation of each module. Gets the path to the
+      --   @.agdai@ file to allow up-to-date checking of previously written
+      --   compilation results. Should return @Skip m@ if compilation is not
+      --   required. Will be @Nothing@ if only scope checking.
+  , postModule       :: env -> menv -> IsMain -> TopLevelModuleName ->
+                        [def] -> TCM mod
+      -- ^ Called after all definitions of a module have been compiled.
+  , compileDef       :: env -> menv -> IsMain -> Definition -> TCM def
+      -- ^ Compile a single definition.
+  , scopeCheckingSuffices :: Bool
+      -- ^ True if the backend works if @--only-scope-checking@ is used.
+  , mayEraseType     :: QName -> TCM Bool
+      -- ^ The treeless compiler may ask the Backend if elements
+      --   of the given type maybe possibly erased.
+      --   The answer should be 'False' if the compilation of the type
+      --   is used by a third party, e.g. in a FFI binding.
+  }
+  deriving Generic
+
+data Recompile menv mod = Recompile menv | Skip mod
+
+-- | Call the 'compilerMain' function of the given backend.
+
+callBackend :: String -> IsMain -> CheckResult -> TCM ()
+callBackend name iMain checkResult = lookupBackend name >>= \case
+  Just (Backend b) -> compilerMain b iMain checkResult
+  Nothing -> do
+    backends <- useTC stBackends
+    genericError $
+      "No backend called '" ++ name ++ "' " ++
+      "(installed backends: " ++
+      List.intercalate ", "
+        (List.sort $ otherBackends ++
+                     [ backendName b | Backend b <- backends ]) ++
+      ")"
+
+-- | Backends that are not included in the state, but still available
+--   to the user.
+
+otherBackends :: [String]
+otherBackends = ["GHCNoMain", "QuickLaTeX"]
+
+-- | Look for a backend of the given name.
+
+lookupBackend :: BackendName -> TCM (Maybe Backend)
+lookupBackend name = useTC stBackends <&> \ backends ->
+  listToMaybe [ b | b@(Backend b') <- backends, backendName b' == name ]
+
+-- | Get the currently active backend (if any).
+
+activeBackend :: TCM (Maybe Backend)
+activeBackend = runMaybeT $ do
+  bname <- MaybeT $ asksTC envActiveBackendName
+  lift $ fromMaybe __IMPOSSIBLE__ <$> lookupBackend bname
+
+-- | Ask the active backend whether a type may be erased.
+--   See issue #3732.
+
+activeBackendMayEraseType :: QName -> TCM Bool
+activeBackendMayEraseType q = do
+  Backend b <- fromMaybe __IMPOSSIBLE__ <$> activeBackend
+  mayEraseType b q
+
+instance NFData Backend where
+  rnf (Backend b) = rnf b
+
+instance NFData opts => NFData (Backend' opts env menv mod def) where
+  rnf (Backend' a b c d e f g h i j k l) =
+    rnf a `seq` rnf b `seq` rnf c `seq` rnf' d `seq` rnf e `seq`
+    rnf f `seq` rnf g `seq` rnf h `seq` rnf i `seq` rnf j `seq`
+    rnf k `seq` rnf l
+    where
+    rnf' []                   = ()
+    rnf' (Option a b c d : e) =
+      rnf a `seq` rnf b `seq` rnf'' c `seq` rnf d `seq` rnf' e
+
+    rnf'' (NoArg a)    = rnf a
+    rnf'' (ReqArg a b) = rnf a `seq` rnf b
+    rnf'' (OptArg a b) = rnf a `seq` rnf b
+
+-- Internals --------------------------------------------------------------
+
+data BackendWithOpts opts where
+  BackendWithOpts ::
+    NFData opts =>
+    Backend' opts env menv mod def ->
+    BackendWithOpts opts
+
+backendWithOpts :: Backend -> Some BackendWithOpts
+backendWithOpts (Backend backend) = Some (BackendWithOpts backend)
+
+forgetOpts :: BackendWithOpts opts -> Backend
+forgetOpts (BackendWithOpts backend) = Backend backend
+
+bOptions :: Lens' (BackendWithOpts opts) opts
+bOptions f (BackendWithOpts b) = f (options b) <&> \ opts -> BackendWithOpts b{ options = opts }
+
+embedFlag :: Lens' b a -> Flag a -> Flag b
+embedFlag l flag = l flag
+
+embedOpt :: Lens' b a -> OptDescr (Flag a) -> OptDescr (Flag b)
+embedOpt l = fmap (embedFlag l)
+
+parseBackendOptions :: [Backend] -> [String] -> CommandLineOptions -> OptM ([Backend], CommandLineOptions)
+parseBackendOptions backends argv opts0 =
+  case makeAll backendWithOpts backends of
+    Some bs -> do
+      let agdaFlags    = map (embedOpt lSnd) (deadStandardOptions ++ standardOptions)
+          backendFlags = do
+            Some i            <- forgetAll Some $ allIndices bs
+            BackendWithOpts b <- [lookupIndex bs i]
+            opt               <- commandLineFlags b
+            return $ embedOpt (lFst . lIndex i . bOptions) opt
+      (backends, opts) <- getOptSimple (stripRTS argv)
+                                       (agdaFlags ++ backendFlags) (embedFlag lSnd . inputFlag)
+                                       (bs, opts0)
+      opts <- checkOpts opts
+      return (forgetAll forgetOpts backends, opts)
+
+backendInteraction :: AbsolutePath -> [Backend] -> TCM () -> (AbsolutePath -> TCM CheckResult) -> TCM ()
+backendInteraction mainFile backends setup check = do
+  setup
+  checkResult <- check mainFile
+
+  -- reset warnings
+  stTCWarnings `setTCLens` []
+
+  noMain <- optCompileNoMain <$> pragmaOptions
+  let isMain | noMain    = NotMain
+             | otherwise = IsMain
+
+  unlessM (optAllowUnsolved <$> pragmaOptions) $ do
+    let ws = crWarnings checkResult
+        mode = crMode checkResult
+    -- Possible warnings, but only scope checking: ok.
+    -- (Compatibility with scope checking done during options validation).
+    unless (mode == ModuleScopeChecked || null ws) $
+      genericError $ "You can only compile modules without unsolved metavariables."
+
+  sequence_ [ compilerMain backend isMain checkResult | Backend backend <- backends ]
+
+  -- print warnings that might have accumulated during compilation
+  ws <- filter (not . isUnsolvedWarning . tcWarning) <$> getAllWarnings AllWarnings
+  unless (null ws) $ alwaysReportSDoc "warning" 1 $ P.vcat $ P.prettyTCM <$> ws
+
+
+compilerMain :: Backend' opts env menv mod def -> IsMain -> CheckResult -> TCM ()
+compilerMain backend isMain0 checkResult = inCompilerEnv checkResult $ do
+  locallyTC eActiveBackendName (const $ Just $ backendName backend) $ do
+    -- BEWARE: Do not use @optOnlyScopeChecking@ here; it does not authoritatively describe the type-checking mode!
+    -- InteractionTop currently may invoke type-checking with scope checking regardless of that flag.
+    when (not (scopeCheckingSuffices backend) && crMode checkResult == ModuleScopeChecked) $
+      genericError $
+        "The --only-scope-checking flag cannot be combined with " ++
+        backendName backend ++ "."
+
+    let i = crInterface checkResult
+    -- Andreas, 2017-08-23, issue #2714
+    -- If the backend is invoked from Emacs, we can only get the --no-main
+    -- pragma option now, coming from the interface file.
+    isMain <- ifM (optCompileNoMain <$> pragmaOptions)
+      {-then-} (return NotMain)
+      {-else-} (return isMain0)
+
+    env  <- preCompile backend (options backend)
+    mods <- doCompile
+        -- This inner function is called for both `Agda.Primitive` and the module in question,
+        -- and all (distinct) imported modules. So avoid shadowing "isMain" or "i".
+        (\ifaceIsMain iface ->
+          Map.singleton (iTopLevelModuleName iface) <$>
+          compileModule backend env ifaceIsMain iface)
+        isMain i
+    -- Note that `doCompile` calls `setInterface` for each distinct module in the graph prior to calling into
+    -- `compileModule`. This last one is just to ensure it's reset to _this_ module.
+    setInterface i
+    postCompile backend env isMain mods
+
+compileModule :: Backend' opts env menv mod def -> env -> IsMain -> Interface -> TCM mod
+compileModule backend env isMain i = do
+  mName <- curMName
+  -- The interface file will only exist if performing af full type-check, vs scoping.
+  -- FIXME: Expecting backends to read the timestamp of the output path of the interface
+  --        file for dirtiness checking is very roundabout and heavily couples backend
+  --        implementations to the filesystem as the source of cache state.
+  mifile <- (Just . filePath . intFilePath =<<) <$> findInterfaceFile mName
+  r      <- preModule backend env isMain (iTopLevelModuleName i) mifile
+  case r of
+    Skip m         -> return m
+    Recompile menv -> do
+      defs <- map snd . sortDefs <$> curDefs
+      res  <- mapM (compileDef' backend env menv isMain <=< instantiateFull) defs
+      postModule backend env menv isMain (iTopLevelModuleName i) res
+
+compileDef' :: Backend' opts env menv mod def -> env -> menv -> IsMain -> Definition -> TCM def
+compileDef' backend env menv isMain def =
+  setCurrentRange (defName def) $
+    compileDef backend env menv isMain def
diff --git a/src/full/Agda/Compiler/Backend.hs-boot b/src/full/Agda/Compiler/Backend.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Backend.hs-boot
@@ -0,0 +1,34 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Backend
+  ( module Agda.Syntax.Treeless
+  , Backend
+  , activeBackendMayEraseType
+  , lookupBackend
+  )
+  where
+
+import Control.DeepSeq
+
+-- Explicitly adding the Agda.Syntax.Treeless import to the .hs-boot file
+-- so that the `Args` symbol can be hidden by the `SOURCE` import in
+-- TypeChecking.Monad.Base.
+--
+-- Without exporting it here, a `hiding` clause there causes a compilation
+-- error. But without hiding it there, the name conflicts with the one
+-- imported from Agda.Syntax.Internal.
+--
+-- This is only a problem with ghci, which will load a fully-compiled module if
+-- available; but that module will contain more symbols than just the few in
+-- the .hs-boot
+import Agda.Syntax.Treeless (TTerm, Args)
+
+import Agda.Syntax.Abstract.Name (QName)
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Base (TCM, BackendName)
+
+data Backend
+
+instance NFData Backend
+
+activeBackendMayEraseType :: QName -> TCM Bool
+lookupBackend :: BackendName -> TCM (Maybe Backend)
diff --git a/src/full/Agda/Compiler/Builtin.hs b/src/full/Agda/Compiler/Builtin.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Builtin.hs
@@ -0,0 +1,24 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-|
+  Built-in backends.
+-}
+
+module Agda.Compiler.Builtin where
+
+import Agda.Compiler.Backend (Backend)
+
+import Agda.Compiler.MAlonzo.Compiler (ghcBackend)
+import Agda.Compiler.JS.Compiler (jsBackend)
+import Agda.Interaction.Highlighting.Dot (dotBackend)
+import Agda.Interaction.Highlighting.HTML (htmlBackend)
+import Agda.Interaction.Highlighting.LaTeX (latexBackend)
+
+builtinBackends :: [Backend]
+builtinBackends =
+  [ ghcBackend
+  , jsBackend
+  , dotBackend
+  , htmlBackend
+  , latexBackend
+  ]
diff --git a/src/full/Agda/Compiler/Builtin.hs-boot b/src/full/Agda/Compiler/Builtin.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Builtin.hs-boot
@@ -0,0 +1,7 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Builtin where
+
+import {-# SOURCE #-} Agda.Compiler.Backend
+
+builtinBackends :: [Backend]
diff --git a/src/full/Agda/Compiler/CallCompiler.hs b/src/full/Agda/Compiler/CallCompiler.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/CallCompiler.hs
@@ -0,0 +1,106 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | A command which calls a compiler
+------------------------------------------------------------------------
+
+module Agda.Compiler.CallCompiler where
+
+import qualified Control.Exception as E
+import Control.Monad.Trans
+
+import System.Exit
+import System.IO
+import System.Process
+
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.Impossible
+
+-- | Calls a compiler:
+--
+-- * Checks the exit code to see if the compiler exits successfully.
+--   If not, then an exception is raised, containing the text the
+--   compiler printed to stderr (if any).
+--
+-- * Uses the debug printout machinery to relay any progress
+--   information the compiler prints to stdout.
+
+callCompiler
+  :: Bool
+     -- ^ Should we actually call the compiler
+  -> FilePath
+     -- ^ The path to the compiler
+  -> [String]
+     -- ^ Command-line arguments.
+  -> Maybe FilePath
+     -- ^ The working directory that should be used when the compiler
+     -- is invoked. The default is the current working directory.
+  -> Maybe TextEncoding
+     -- ^ Use the given text encoding, if any, when reading the output
+     -- from the process (stdout and stderr).
+  -> TCM ()
+callCompiler doCall cmd args cwd enc =
+  if doCall then do
+    merrors <- callCompiler' cmd args cwd enc
+    case merrors of
+      Nothing     -> return ()
+      Just errors -> typeError (CompilationError errors)
+  else
+    alwaysReportSLn "compile.cmd" 1 $ "NOT calling: " ++ unwords (cmd : args)
+
+-- | Generalisation of @callCompiler@ where the raised exception is
+-- returned.
+callCompiler'
+  :: FilePath
+     -- ^ The path to the compiler
+  -> [String]
+     -- ^ Command-line arguments.
+  -> Maybe FilePath
+     -- ^ The working directory that should be used when the compiler
+     -- is invoked. The default is the current working directory.
+  -> Maybe TextEncoding
+     -- ^ Use the given text encoding, if any, when reading the output
+     -- from the process (stdout and stderr).
+  -> TCM (Maybe String)
+callCompiler' cmd args cwd enc = do
+  alwaysReportSLn "compile.cmd" 1 $ "Calling: " ++ unwords (cmd : args)
+  (_, out, err, p) <-
+    liftIO $ createProcess
+               (proc cmd args) { std_err = CreatePipe
+                               , std_out = CreatePipe
+                               , cwd     = cwd
+                               }
+
+  -- In -v0 mode we throw away any progress information printed to
+  -- stdout.
+  case out of
+    Nothing  -> __IMPOSSIBLE__
+    Just out -> forkTCM $ do
+      -- The handle should be in text mode.
+      liftIO $ hSetBinaryMode out False
+      case enc of
+        Nothing  -> return ()
+        Just enc -> liftIO $ hSetEncoding out enc
+      progressInfo <- liftIO $ hGetContents out
+      mapM_ (alwaysReportSLn "compile.output" 1) $ lines progressInfo
+
+  errors <- liftIO $ case err of
+    Nothing  -> __IMPOSSIBLE__
+    Just err -> do
+      -- The handle should be in text mode.
+      hSetBinaryMode err False
+      case enc of
+        Nothing  -> return ()
+        Just enc -> liftIO $ hSetEncoding err enc
+      hGetContents err
+
+  exitcode <- liftIO $ do
+    -- Ensure that the output has been read before waiting for the
+    -- process.
+    _ <- E.evaluate (length errors)
+    waitForProcess p
+
+  case exitcode of
+    ExitFailure _ -> return $ Just errors
+    _             -> return Nothing
diff --git a/src/full/Agda/Compiler/Common.hs b/src/full/Agda/Compiler/Common.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Common.hs
@@ -0,0 +1,199 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Common where
+
+import Prelude hiding ((!!))
+
+import Data.List (sortBy, isPrefixOf)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.HashMap.Strict as HMap
+import Data.Char
+import Data.Function (on)
+
+import Control.Monad
+import Control.Monad.State
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.Interaction.FindFile ( srcFilePath )
+import Agda.Interaction.Options
+import Agda.Interaction.Imports  ( CheckResult, crInterface, crSource, Source(..) )
+import Agda.Interaction.Library
+
+import Agda.TypeChecking.Monad as TCM
+
+import Agda.Utils.FileName
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1          ( pattern (:|) )
+import Agda.Utils.Maybe
+import Agda.Utils.WithDefault    ( lensCollapseDefault )
+
+import Agda.Utils.Impossible
+
+data IsMain = IsMain | NotMain
+  deriving (Eq, Show)
+
+-- | Conjunctive semigroup ('NotMain' is absorbing).
+instance Semigroup IsMain where
+  NotMain <> _ = NotMain
+  _       <> NotMain = NotMain
+  IsMain  <> IsMain = IsMain
+
+instance Monoid IsMain where
+  mempty = IsMain
+  mappend = (<>)
+
+doCompile :: Monoid r => (IsMain -> Interface -> TCM r) -> IsMain -> Interface -> TCM r
+doCompile f isMain i = do
+  flip evalStateT Set.empty $ compilePrim $ doCompile' f isMain i
+  where
+  -- The Agda.Primitive module is only loaded if the --no-load-primitives flag was not given,
+  -- thus, only try to compile it if we have visited it.
+  compilePrim cont = do
+    agdaPrim <- lift $ do
+      agdaPrim <- TCM.topLevelModuleName agdaPrim
+      Map.lookup agdaPrim <$> getVisitedModules
+    case agdaPrim of
+      Nothing   -> cont
+      Just prim ->
+        mappend <$> doCompile' f NotMain (miInterface prim) <*> cont
+    where
+    agdaPrim = RawTopLevelModuleName
+      { rawModuleNameRange = mempty
+      , rawModuleNameParts = "Agda" :| "Primitive" : []
+      }
+      -- N.B. The Range in TopLevelModuleName is ignored for Ord, so we can set it to mempty.
+
+-- This helper function is called for both `Agda.Primitive` and the module in question.
+-- It's also called for each imported module, recursively. (Avoiding duplicates).
+doCompile'
+  :: Monoid r
+  => (IsMain -> Interface -> TCM r) -> (IsMain -> Interface -> StateT (Set ModuleName) TCM r)
+doCompile' f isMain i = do
+  alreadyDone <- gets (Set.member (iModuleName i))
+  if alreadyDone then return mempty else do
+    imps <- lift $
+      map miInterface . catMaybes <$>
+        mapM (getVisitedModule . fst) (iImportedModules i)
+    ri <- mconcat <$> mapM (doCompile' f NotMain) imps
+    lift $ setInterface i
+    r <- lift $ f isMain i
+    modify (Set.insert $ iModuleName i)
+    return $ mappend ri r
+
+setInterface :: Interface -> TCM ()
+setInterface i = do
+  opts <- getsTC (stPersistentOptions . stPersistentState)
+  setCommandLineOptions opts
+  mapM_ setOptionsFromPragma (iDefaultPragmaOptions i ++ iFilePragmaOptions i)
+  -- One could perhaps make the following command lazy. Note, however,
+  -- that it doesn't suffice to replace setTCLens' with setTCLens,
+  -- because the stPreImportedModules field is strict.
+  stImportedModules `setTCLens'`
+    Set.fromList (map fst (iImportedModules i))
+  stCurrentModule `setTCLens'`
+    Just (iModuleName i, iTopLevelModuleName i)
+
+curIF :: ReadTCState m => m Interface
+curIF = do
+  name <- curMName
+  maybe __IMPOSSIBLE__ miInterface <$> getVisitedModule name
+
+curMName :: ReadTCState m => m TopLevelModuleName
+curMName = maybe __IMPOSSIBLE__ snd <$> useTC stCurrentModule
+
+curDefs :: ReadTCState m => m Definitions
+curDefs = HMap.filter (not . defNoCompilation) . (^. sigDefinitions) . iSignature <$> curIF
+
+sortDefs :: Definitions -> [(QName, Definition)]
+sortDefs defs =
+  -- The list is sorted to ensure that the order of the generated
+  -- definitions does not depend on things like the number of bits
+  -- in an Int (see Issue 1900).
+  sortBy (compare `on` fst) $
+  HMap.toList defs
+
+compileDir :: HasOptions m => m FilePath
+compileDir = do
+  mdir <- optCompileDir <$> commandLineOptions
+  maybe __IMPOSSIBLE__ return mdir
+
+
+repl :: [String] -> String -> String
+repl subs = go where
+  go ('<':'<':c:'>':'>':s) | 0 <= i && i < length subs = subs !! i ++ go s
+     where i = ord c - ord '0'
+  go (c:s) = c : go s
+  go []    = []
+
+
+-- | Sets up the compilation environment.
+inCompilerEnv :: CheckResult -> TCM a -> TCM a
+inCompilerEnv checkResult cont = do
+  let mainI = crInterface checkResult
+      checkedSource = crSource checkResult
+
+  -- Preserve the state (the compiler modifies the state).
+  -- Andreas, 2014-03-23 But we might want to collect Benchmark info,
+  -- so use localTCState.
+  -- FNF, 2017-02-22 we also want to keep the warnings we have encountered,
+  -- so use localTCStateSaving and pick them out.
+  (a , s) <- localTCStateSaving $ do
+
+    -- Compute the output directory. Note: using commandLineOptions would make
+    -- the current pragma options persistent when we setCommandLineOptions
+    -- below.
+    opts <- getsTC $ stPersistentOptions . stPersistentState
+    let compileDir = case optCompileDir opts of
+          Just dir -> dir
+          Nothing  ->
+            -- The default output directory is the project root.
+            let tm = iTopLevelModuleName mainI
+                f  = srcFilePath $ srcOrigin checkedSource
+            in filePath $ projectRoot f tm
+    setCommandLineOptions $
+      opts { optCompileDir = Just compileDir }
+
+    -- Andreas, 2017-08-23, issue #2714 recover pragma option --no-main
+    -- Unfortunately, a pragma option is stored in the interface file as
+    -- just a list of strings, thus, the solution is a bit of hack:
+    -- We match on whether @["--no-main"]@ is one of the stored options.
+    let iFilePragmaStrings = map pragmaStrings . iFilePragmaOptions
+    when (["--no-main"] `elem` iFilePragmaStrings mainI) $
+      setTCLens (stPragmaOptions . lensOptCompileMain . lensCollapseDefault) False
+
+    -- Perhaps all pragma options from the top-level module should be
+    -- made available to the compiler in a suitable way. Here are more
+    -- hacks:
+    when (any ("--cubical" `elem`) $ iFilePragmaStrings mainI) $
+      setTCLens (stPragmaOptions . lensOptCubical) $ Just CFull
+    when (any ("--erased-cubical" `elem`) $ iFilePragmaStrings mainI) $
+      setTCLens (stPragmaOptions . lensOptCubical) $ Just CErased
+
+    setScope (iInsideScope mainI) -- so that compiler errors don't use overly qualified names
+    ignoreAbstractMode cont
+  -- keep generated warnings
+  let newWarnings = stPostTCWarnings $  stPostScopeState $ s
+  stTCWarnings `setTCLens` newWarnings
+  return a
+
+topLevelModuleName ::
+  ReadTCState m => ModuleName -> m TopLevelModuleName
+topLevelModuleName m = do
+  -- Interfaces of visited modules.
+  visited <- map miInterface . Map.elems <$> getVisitedModules
+  -- find the module with the longest matching prefix to m
+  let is = sortBy (compare `on` (length . mnameToList . iModuleName)) $
+           filter (\i -> mnameToList (iModuleName i) `isPrefixOf`
+                         mnameToList m)
+             visited
+  case is of
+    (i : _) -> return (iTopLevelModuleName i)
+    -- if we did not get anything, it may be because m is a section
+    -- (a module _ ), see e.g. #1866
+    []       -> curMName
diff --git a/src/full/Agda/Compiler/JS/Compiler.hs b/src/full/Agda/Compiler/JS/Compiler.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/JS/Compiler.hs
@@ -0,0 +1,877 @@
+-- | Main module for JS backend.
+
+module Agda.Compiler.JS.Compiler where
+
+import Prelude hiding ( null, writeFile )
+
+import Control.DeepSeq
+import Control.Monad.Trans
+
+import Data.Char     ( isSpace )
+import Data.Foldable ( forM_ )
+import Data.List     ( dropWhileEnd, elemIndex, intercalate, partition )
+import Data.Set      ( Set )
+
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+import qualified Data.Text as T
+
+import GHC.Generics (Generic)
+
+import System.Directory   ( createDirectoryIfMissing )
+import System.Environment ( setEnv )
+import System.FilePath    ( splitFileName, (</>) )
+import System.Process     ( callCommand )
+
+import Paths_Agda
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Name ( isNoName )
+import Agda.Syntax.Abstract.Name
+  ( QName,
+    mnameToList, qnameName, qnameModule, nameId )
+import Agda.Syntax.Internal
+  ( Name, Type
+  , nameFixity, unDom, telToList )
+import Agda.Syntax.Literal       ( Literal(..) )
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName, TopLevelModuleName'(..))
+import Agda.Syntax.Treeless      ( ArgUsage(..), filterUsed )
+import qualified Agda.Syntax.Treeless as T
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce ( instantiateFull )
+import Agda.TypeChecking.Substitute as TC ( TelV(..), raise, subst )
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Telescope ( telViewPath )
+
+import Agda.Utils.FileName ( isNewerThan )
+import Agda.Utils.Function ( iterate' )
+import Agda.Utils.List ( downFrom, headWithDefault )
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe ( boolToMaybe, catMaybes, caseMaybeM, fromMaybe, whenNothing )
+import Agda.Utils.Monad ( ifM, when )
+import Agda.Utils.Null  ( null )
+import Agda.Syntax.Common.Pretty (prettyShow, render)
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.IO.Directory
+import Agda.Utils.IO.UTF8 ( writeFile )
+import Agda.Utils.Singleton ( singleton )
+import Agda.Utils.Size (size)
+
+import Agda.Compiler.Common as CC
+import Agda.Compiler.ToTreeless
+import Agda.Compiler.Treeless.EliminateDefaults
+import Agda.Compiler.Treeless.EliminateLiteralPatterns
+import Agda.Compiler.Treeless.GuardsToPrims
+import Agda.Compiler.Treeless.Erase ( computeErasedConstructorArgs )
+import Agda.Compiler.Treeless.Subst ()
+import Agda.Compiler.Backend (Backend(..), Backend'(..), Recompile(..))
+
+import Agda.Compiler.JS.Syntax
+  ( Exp(Self,Local,Global,Undefined,Null,String,Char,Integer,Double,Lambda,Object,Array,Apply,Lookup,If,BinOp,PlainJS),
+    LocalId(LocalId), GlobalId(GlobalId), MemberId(MemberId,MemberIndex), Export(Export), Module(Module, modName, callMain), Comment(Comment),
+    modName, expName, uses
+  , JSQName
+  )
+import Agda.Compiler.JS.Substitution
+  ( curriedLambda, curriedApply, emp, apply )
+import qualified Agda.Compiler.JS.Pretty as JSPretty
+import Agda.Compiler.JS.Pretty (JSModuleStyle(..))
+
+import Agda.Utils.Impossible (__IMPOSSIBLE__)
+
+--------------------------------------------------
+-- Entry point into the compiler
+--------------------------------------------------
+
+jsBackend :: Backend
+jsBackend = Backend jsBackend'
+
+jsBackend' :: Backend' JSOptions JSOptions JSModuleEnv Module (Maybe Export)
+jsBackend' = Backend'
+  { backendName           = jsBackendName
+  , backendVersion        = Nothing
+  , options               = defaultJSOptions
+  , commandLineFlags      = jsCommandLineFlags
+  , isEnabled             = optJSCompile
+  , preCompile            = jsPreCompile
+  , postCompile           = jsPostCompile
+  , preModule             = jsPreModule
+  , postModule            = jsPostModule
+  , compileDef            = jsCompileDef
+  , scopeCheckingSuffices = False
+  , mayEraseType          = const $ return True
+      -- Andreas, 2019-05-09, see issue #3732.
+      -- If you want to use JS data structures generated from Agda
+      -- @data@/@record@, you might want to tell the treeless compiler
+      -- not to erase these types even if they have no content,
+      -- to get a stable interface.
+  }
+
+--- Options ---
+
+data JSOptions = JSOptions
+  { optJSCompile  :: Bool
+  , optJSOptimize :: Bool
+  , optJSMinify   :: Bool
+      -- ^ Remove spaces etc. See https://en.wikipedia.org/wiki/Minification_(programming).
+  , optJSVerify   :: Bool
+      -- ^ Run generated code through interpreter.
+  , optJSModuleStyle :: JSModuleStyle
+  }
+  deriving Generic
+
+instance NFData JSModuleStyle
+
+instance NFData JSOptions
+
+defaultJSOptions :: JSOptions
+defaultJSOptions = JSOptions
+  { optJSCompile  = False
+  , optJSOptimize = False
+  , optJSMinify   = False
+  , optJSVerify   = False
+  , optJSModuleStyle = JSCJS
+  }
+
+jsCommandLineFlags :: [OptDescr (Flag JSOptions)]
+jsCommandLineFlags =
+    [ Option [] ["js"] (NoArg enable) "compile program using the JS backend"
+    , Option [] ["js-optimize"] (NoArg enableOpt) "turn on optimizations during JS code generation"
+    -- Minification is described at https://en.wikipedia.org/wiki/Minification_(programming)
+    , Option [] ["js-minify"] (NoArg enableMin) "minify generated JS code"
+    , Option [] ["js-verify"] (NoArg enableVerify) "except for main module, run generated JS modules through `node` (needs to be in PATH)"
+    , Option [] ["js-cjs"] (NoArg setCJS) "use CommonJS module style (default)"
+    , Option [] ["js-amd"] (NoArg setAMD) "use AMD module style for JS"
+    ]
+  where
+    enable       o = pure o{ optJSCompile  = True }
+    enableOpt    o = pure o{ optJSOptimize = True }
+    enableMin    o = pure o{ optJSMinify   = True }
+    enableVerify o = pure o{ optJSVerify   = True }
+    setCJS       o = pure o{ optJSModuleStyle = JSCJS }
+    setAMD       o = pure o{ optJSModuleStyle = JSAMD }
+
+--- Top-level compilation ---
+
+jsPreCompile :: JSOptions -> TCM JSOptions
+jsPreCompile opts = do
+  cubical <- optCubical <$> pragmaOptions
+  let notSupported s =
+        typeError $ GenericError $
+          "Compilation of code that uses " ++ s ++ " is not supported."
+  case cubical of
+    Nothing      -> return ()
+    Just CErased -> notSupported "--erased-cubical"
+    Just CFull   -> notSupported "--cubical"
+
+  return opts
+
+-- | After all modules have been compiled, copy RTE modules and verify compiled modules.
+
+jsPostCompile ::
+  JSOptions -> IsMain -> Map.Map TopLevelModuleName Module -> TCM ()
+jsPostCompile opts _ ms = do
+
+  -- Copy RTE modules.
+
+  compDir  <- compileDir
+  liftIO $ do
+    dataDir <- getDataDir
+    let fname = case optJSModuleStyle opts of
+          JSCJS -> "agda-rts.js"
+          JSAMD -> "agda-rts.amd.js"
+        srcPath = dataDir </> "JS" </> fname
+        compPath = compDir </> fname
+    copyIfChanged srcPath compPath
+
+  -- Verify generated JS modules (except for main).
+
+  reportSLn "compile.js.verify" 10 $ "Considering to verify generated JS modules"
+  when (optJSVerify opts) $ do
+
+    reportSLn "compile.js.verify" 10 $ "Verifying generated JS modules"
+    liftIO $ setEnv "NODE_PATH" compDir
+
+    forM_ ms $ \ Module{ modName, callMain } -> do
+      jsFile <- outFile modName
+      reportSLn "compile.js.verify" 30 $ unwords [ "Considering JS module:" , jsFile ]
+
+      -- Since we do not run a JS program for real, we skip all modules that could
+      -- have a call to main.
+      -- Atm, modules whose compilation was skipped are also skipped during verification
+      -- (they appear here as main modules).
+      whenNothing callMain $ do
+        let cmd = unwords [ "node", "-", "<", jsFile ]
+        reportSLn "compile.js.verify" 20 $ unwords [ "calling:", cmd ]
+        liftIO $ callCommand cmd
+
+--- Module compilation ---
+
+data JSModuleEnv = JSModuleEnv
+  { jsCoinductionKit :: Maybe CoinductionKit
+  , jsCompile        :: Bool
+    -- ^ Should this module be compiled?
+  }
+
+jsPreModule ::
+  JSOptions -> IsMain -> TopLevelModuleName -> Maybe FilePath ->
+  TCM (Recompile JSModuleEnv Module)
+jsPreModule _opts _ m mifile = do
+  cubical <- optCubical <$> pragmaOptions
+  let compile = case cubical of
+        -- Code that uses --cubical is not compiled.
+        Just CFull   -> False
+        Just CErased -> True
+        Nothing      -> True
+  ifM uptodate noComp (yesComp compile)
+  where
+    uptodate = case mifile of
+      Nothing -> pure False
+      Just ifile -> liftIO =<< isNewerThan <$> outFile_ <*> pure ifile
+    ifileDesc = fromMaybe "(memory)" mifile
+
+    noComp = do
+      reportSLn "compile.js" 2 . (++ " : no compilation is needed.") . prettyShow =<< curMName
+      return $ Skip skippedModule
+
+    -- A skipped module acts as a fake main module, to be skipped by --js-verify as well.
+    skippedModule = Module (jsMod m) mempty mempty (Just __IMPOSSIBLE__)
+
+    yesComp compile = do
+      m   <- prettyShow <$> curMName
+      out <- outFile_
+      alwaysReportSLn "compile.js" 1 $ repl [m, ifileDesc, out] "Compiling <<0>> in <<1>> to <<2>>"
+      kit <- coinductionKit
+      return $ Recompile $ JSModuleEnv
+        { jsCoinductionKit = kit
+        , jsCompile        = compile
+        }
+
+jsPostModule ::
+  JSOptions -> JSModuleEnv -> IsMain -> TopLevelModuleName ->
+  [Maybe Export] -> TCM Module
+jsPostModule opts _ isMain _ defs = do
+  m  <- jsMod <$> curMName
+  is <- map (jsMod . fst) . iImportedModules <$> curIF
+  let mod = Module m is (reorder es) callMain
+  writeModule (optJSMinify opts) (optJSModuleStyle opts) mod
+  return mod
+  where
+  es       = catMaybes defs
+  main     = MemberId "main"
+  -- Andreas, 2020-10-27, only add invocation of "main" if such function is defined.
+  -- This allows loading of generated .js files into an interpreter
+  -- even if they do not define "main".
+  hasMain  = isMain == IsMain && any ((singleton main ==) . expName) es
+  callMain :: Maybe Exp
+  callMain = boolToMaybe hasMain $ Apply (Lookup Self main) [Lambda 1 emp]
+
+
+jsCompileDef :: JSOptions -> JSModuleEnv -> IsMain -> Definition -> TCM (Maybe Export)
+jsCompileDef opts kit _isMain def = definition (opts, kit) (defName def, def)
+
+--------------------------------------------------
+-- Naming
+--------------------------------------------------
+
+prefix :: [Char]
+prefix = "jAgda"
+
+jsMod :: TopLevelModuleName -> GlobalId
+jsMod m =
+  GlobalId (prefix : map T.unpack (List1.toList (moduleNameParts m)))
+
+jsFileName :: GlobalId -> String
+jsFileName (GlobalId ms) = intercalate "." ms ++ ".js"
+
+jsMember :: Name -> MemberId
+jsMember n
+  -- Anonymous fields are used for where clauses,
+  -- and they're all given the concrete name "_",
+  -- so we disambiguate them using their name id.
+  | isNoName n = MemberId ("_" ++ show (nameId n))
+  | otherwise  = MemberId $ prettyShow n
+
+global' :: QName -> TCM (Exp, JSQName)
+global' q = do
+  i   <- iTopLevelModuleName <$> curIF
+  top <- CC.topLevelModuleName (qnameModule q)
+  let
+    -- Global module prefix
+    qms = mnameToList $ qnameModule q
+    -- File-local module prefix
+    localms = drop (size top) qms
+    nm = fmap jsMember $ List1.snoc localms $ qnameName q
+  if top == i
+    then return (Self, nm)
+    else return (Global (jsMod top), nm)
+
+global :: QName -> TCM (Exp, JSQName)
+global q = do
+  d <- getConstInfo q
+  case d of
+    Defn { theDef = Constructor { conData = p } } -> do
+      getConstInfo p >>= \case
+        -- Andreas, 2020-10-27, comment quotes outdated fact.
+        -- anon. constructors are now M.R.constructor.
+        -- We could simplify/remove the workaround by switching "record"
+        -- to "constructor", but this changes the output of the JS compiler
+        -- maybe in ways that break user's developments
+        -- (if they link to Agda-generated JS).
+        -- -- Rather annoyingly, the anonymous constructor of a record R in module M
+        -- -- is given the name M.recCon, but a named constructor C
+        -- -- is given the name M.R.C, sigh. This causes a lot of hoop-jumping
+        -- -- in the map from Agda names to JS names, which we patch by renaming
+        -- -- anonymous constructors to M.R.record.
+        Defn { theDef = Record { recNamedCon = False } } -> do
+          (m,ls) <- global' p
+          return (m, ls <> singleton (MemberId "record"))
+        _ -> global' (defName d)
+    _ -> global' (defName d)
+
+-- Reorder a list of exports to ensure def-before-use.
+-- Note that this can diverge in the case when there is no such reordering.
+
+-- Only top-level values are evaluated before definitions are added to the
+-- module, so we put those last, ordered in dependency order. There can't be
+-- any recursion between top-level values (unless termination checking has been
+-- disabled and someone's written a non-sensical program), so reordering will
+-- terminate.
+
+reorder :: [Export] -> [Export]
+reorder es = datas ++ funs ++ reorder' (Set.fromList $ map expName $ datas ++ funs) vals
+  where
+    (vs, funs)    = partition isTopLevelValue es
+    (datas, vals) = partition isEmptyObject vs
+
+reorder' :: Set JSQName -> [Export] -> [Export]
+reorder' defs [] = []
+reorder' defs (e : es) =
+  let us = uses e `Set.difference` defs
+  in  if null us
+        then e : (reorder' (Set.insert (expName e) defs) es)
+        else reorder' defs (insertAfter us e es)
+
+isTopLevelValue :: Export -> Bool
+isTopLevelValue (Export _ e) = case e of
+  Object m | flatName `Map.member` m -> False
+  Lambda{} -> False
+  _        -> True
+
+isEmptyObject :: Export -> Bool
+isEmptyObject (Export _ e) = case e of
+  Object m -> null m
+  Lambda{} -> True
+  _        -> False
+
+insertAfter :: Set JSQName -> Export -> [Export] -> [Export]
+insertAfter us e []                   = [e]
+insertAfter us e (f : fs) | null us   = e : f : fs
+insertAfter us e (f : fs) | otherwise =
+  f : insertAfter (Set.delete (expName f) us) e fs
+
+--------------------------------------------------
+-- Main compiling clauses
+--------------------------------------------------
+
+type EnvWithOpts = (JSOptions, JSModuleEnv)
+
+definition :: EnvWithOpts -> (QName,Definition) -> TCM (Maybe Export)
+definition kit (q,d) = do
+  reportSDoc "compile.js" 10 $ "compiling def:" <+> prettyTCM q
+  (_,ls) <- global q
+  d <- instantiateFull d
+
+  definition' kit q d (defType d) ls
+
+-- | Ensure that there is at most one pragma for a name.
+checkCompilerPragmas :: QName -> TCM ()
+checkCompilerPragmas q =
+  caseMaybeM (getUniqueCompilerPragma jsBackendName q) (return ()) $ \ (CompilerPragma r s) ->
+  setCurrentRange r $ case words s of
+    "=" : _ -> return ()
+    _       -> genericDocError $ P.sep [ "Badly formed COMPILE JS pragma. Expected",
+                                         "{-# COMPILE JS <name> = <js> #-}" ]
+
+defJSDef :: Definition -> Maybe String
+defJSDef def =
+  case defCompilerPragmas jsBackendName def of
+    [CompilerPragma _ s] -> Just (dropEquals s)
+    []                   -> Nothing
+    _:_:_                -> __IMPOSSIBLE__
+  where
+    dropEquals = dropWhile $ \ c -> isSpace c || c == '='
+
+definition' :: EnvWithOpts -> QName -> Definition -> Type -> JSQName -> TCM (Maybe Export)
+definition' kit q d t ls =
+  if not (jsCompile (snd kit)) || not (usableModality d)
+  then return Nothing
+  else do
+  checkCompilerPragmas q
+  case theDef d of
+    -- coinduction
+    Constructor{}
+      | Just q == (nameOfSharp <$> jsCoinductionKit (snd kit)) -> do
+      return Nothing
+    Function{}
+      | Just q == (nameOfFlat <$> jsCoinductionKit (snd kit)) -> do
+      ret $ Lambda 1 $ Apply (Lookup (local 0) flatName) []
+
+    DataOrRecSig{} -> __IMPOSSIBLE__
+
+    Axiom{} | Just e <- defJSDef d -> plainJS e
+    Axiom{} | otherwise -> ret Undefined
+
+    GeneralizableVar{} -> return Nothing
+
+    Function{} | Just e <- defJSDef d -> plainJS e
+    Function{} | otherwise -> do
+
+      reportSDoc "compile.js" 5 $ "compiling fun:" <+> prettyTCM q
+      caseMaybeM (toTreeless T.EagerEvaluation q) (pure Nothing) $ \ treeless -> do
+        used <- fromMaybe [] <$> getCompiledArgUse q
+        funBody <- eliminateCaseDefaults =<<
+          eliminateLiteralPatterns
+          (convertGuards treeless)
+        reportSDoc "compile.js" 30 $ " compiled treeless fun:" <+> pretty funBody
+        reportSDoc "compile.js" 40 $ " argument usage:" <+> (text . show) used
+
+        let (body, given) = lamView funBody
+              where
+                lamView :: T.TTerm -> (T.TTerm, Int)
+                lamView (T.TLam t) = (+ 1) <$> lamView t
+                lamView t = (t, 0)
+
+            -- number of eta expanded args
+            etaN = length $ dropWhileEnd (== ArgUsed) $ drop given used
+
+            unusedN = length $ filter (== ArgUnused) used
+
+        funBody' <- compileTerm kit
+                  $ iterate' (given + etaN - unusedN) T.TLam
+                  $ eraseLocalVars (map (== ArgUnused) used)
+                  $ T.mkTApp (raise etaN body) (T.TVar <$> downFrom etaN)
+
+        reportSDoc "compile.js" 30 $ " compiled JS fun:" <+> (text . show) funBody'
+        return $
+          if funBody' == Null then Nothing
+          else Just $ Export ls funBody'
+
+    Primitive{primName = p}
+      | p == builtin_glueU ->
+        -- The string prim^glueU is not a valid JS name.
+        plainJS "agdaRTS.prim_glueU"
+      | p == builtin_unglueU ->
+        -- The string prim^unglueU is not a valid JS name.
+        plainJS "agdaRTS.prim_unglueU"
+      | p `Set.member` primitives ->
+        plainJS $ "agdaRTS." ++ getBuiltinId p
+      | Just e <- defJSDef d ->
+        plainJS e
+      | otherwise ->
+        ret Undefined
+    PrimitiveSort{} -> return Nothing
+
+    Datatype{} -> do
+        computeErasedConstructorArgs q
+        ret emp
+    Record{} -> do
+        computeErasedConstructorArgs q
+        return Nothing
+
+    Constructor{} | Just e <- defJSDef d -> plainJS e
+    Constructor{conData = p, conPars = nc} -> do
+      TelV tel _ <- telViewPath t
+      let np = length (telToList tel) - nc
+      erased <- getErasedConArgs q
+      let nargs = np - length (filter id erased)
+          args = [ Local $ LocalId $ nargs - i | i <- [0 .. nargs-1] ]
+      d <- getConstInfo p
+      let l = List1.last ls
+      case theDef d of
+        Record { recFields = flds } -> ret $ curriedLambda nargs $
+          if optJSOptimize (fst kit)
+            then Lambda 1 $ Apply (Local (LocalId 0)) args
+            else Object $ Map.singleton l $ Lambda 1 $ Apply (Lookup (Local (LocalId 0)) l) args
+        dt -> do
+          i <- index
+          ret $ curriedLambda (nargs + 1) $ Apply (Lookup (Local (LocalId 0)) i) args
+          where
+            index :: TCM MemberId
+            index
+              | Datatype{} <- dt
+              , optJSOptimize (fst kit) = do
+                  q  <- canonicalName q
+                  cs <- mapM canonicalName $ defConstructors dt
+                  case q `elemIndex` cs of
+                    Just i  -> return $ MemberIndex i (mkComment l)
+                    Nothing -> __IMPOSSIBLE_VERBOSE__ $ unwords [ "Constructor", prettyShow q, "not found in", prettyShow cs ]
+              | otherwise = return l
+            mkComment (MemberId s) = Comment s
+            mkComment _ = mempty
+
+    AbstractDefn{} -> __IMPOSSIBLE__
+  where
+    ret = return . Just . Export ls
+    plainJS = return . Just . Export ls . PlainJS
+
+compileTerm :: EnvWithOpts -> T.TTerm -> TCM Exp
+compileTerm kit t = go t
+  where
+    go :: T.TTerm -> TCM Exp
+    go = \case
+      T.TVar x -> return $ Local $ LocalId x
+      T.TDef q -> do
+        d <- getConstInfo q
+        case theDef d of
+          -- Datatypes and records are erased
+          Datatype {} -> return (String "*")
+          Record {} -> return (String "*")
+          _ -> qname q
+      T.TApp (T.TCon q) [x]
+        | Just q == (nameOfSharp <$> jsCoinductionKit (snd kit)) -> do
+        x <- go x
+        let evalThunk = unlines
+              [ "function() {"
+              , "  delete this.flat;"
+              , "  var result = this.__flat_helper();"
+              , "  delete this.__flat_helper;"
+              , "  this.flat = function() { return result; };"
+              , "  return result;"
+              , "}"
+              ]
+        return $ Object $ Map.fromListWith __IMPOSSIBLE__
+          [(flatName, PlainJS evalThunk)
+          ,(MemberId "__flat_helper", Lambda 0 x)]
+      T.TApp t' xs | Just f <- getDef t' -> do
+        used <- case f of
+          Left  q -> fromMaybe [] <$> getCompiledArgUse q
+          Right c -> map (\ b -> if b then ArgUnused else ArgUsed) <$> getErasedConArgs c
+            -- Andreas, 2021-02-10 NB: could be @map (bool ArgUsed ArgUnused)@
+            -- but I find it unintuitive that 'bool' takes the 'False'-branch first.
+        let given = length xs
+
+            -- number of eta expanded args
+            etaN = length $ dropWhile (== ArgUsed) $ reverse $ drop given used
+
+            args = filterUsed used $
+                     raise etaN xs ++ (T.TVar <$> downFrom etaN)
+
+        curriedLambda etaN <$> (curriedApply <$> go (raise etaN t') <*> mapM go args)
+
+      T.TApp t xs -> do
+            curriedApply <$> go t <*> mapM go xs
+      T.TLam t -> Lambda 1 <$> go t
+      -- TODO This is not a lazy let, but it should be...
+      T.TLet t e -> apply <$> (Lambda 1 <$> go e) <*> traverse go [t]
+      T.TLit l -> return $ literal l
+      T.TCon q -> do
+        d <- getConstInfo q
+        qname q
+      T.TCase sc ct def alts | T.CTData dt <- T.caseType ct -> do
+        dt <- getConstInfo dt
+        alts' <- traverse (compileAlt kit) alts
+        let cs  = defConstructors $ theDef dt
+            obj = Object $ Map.fromListWith __IMPOSSIBLE__ [(snd x, y) | (x, y) <- alts']
+            arr = mkArray [headWithDefault (mempty, Null) [(Comment s, y) | ((c', MemberId s), y) <- alts', c' == c] | c <- cs]
+        case (theDef dt, defJSDef dt) of
+          (_, Just e) -> do
+            return $ apply (PlainJS e) [Local (LocalId sc), obj]
+          (Record{}, _) | optJSOptimize (fst kit) -> do
+            return $ apply (Local $ LocalId sc) [snd $ headWithDefault __IMPOSSIBLE__ alts']
+          (Record{}, _) -> do
+            memId <- visitorName $ recCon $ theDef dt
+            return $ apply (Lookup (Local $ LocalId sc) memId) [obj]
+          (Datatype{}, _) | optJSOptimize (fst kit) -> do
+            return $ curriedApply (Local (LocalId sc)) [arr]
+          (Datatype{}, _) -> do
+            return $ curriedApply (Local (LocalId sc)) [obj]
+          _ -> __IMPOSSIBLE__
+      T.TCase _ _ _ _ -> __IMPOSSIBLE__
+
+      T.TPrim p -> return $ compilePrim p
+      T.TUnit -> unit
+      T.TSort -> unit
+      T.TErased -> unit
+      T.TError T.TUnreachable -> return Undefined
+      T.TError T.TMeta{}      -> return Undefined
+      T.TCoerce t -> go t
+
+    getDef (T.TDef f) = Just (Left f)
+    getDef (T.TCon c) = Just (Right c)
+    getDef (T.TCoerce x) = getDef x
+    getDef _ = Nothing
+
+    unit = return Null
+
+    mkArray xs
+        | 2 * length (filter ((== Null) . snd) xs) <= length xs = Array xs
+        | otherwise = Object $ Map.fromListWith __IMPOSSIBLE__
+            [ (MemberIndex i c, x) | (i, (c, x)) <- zip [0..] xs, x /= Null ]
+
+compilePrim :: T.TPrim -> Exp
+compilePrim p =
+  case p of
+    T.PIf -> curriedLambda 3 $ If (local 2) (local 1) (local 0)
+    T.PEqI -> binOp "agdaRTS.uprimIntegerEqual"
+    T.PEqF -> binOp "agdaRTS.uprimFloatEquality"
+    T.PEqQ -> binOp "agdaRTS.uprimQNameEquality"
+    T.PEqS -> primEq
+    T.PEqC -> primEq
+    T.PGeq -> binOp "agdaRTS.uprimIntegerGreaterOrEqualThan"
+    T.PLt -> binOp "agdaRTS.uprimIntegerLessThan"
+    T.PAdd -> binOp "agdaRTS.uprimIntegerPlus"
+    T.PSub -> binOp "agdaRTS.uprimIntegerMinus"
+    T.PMul -> binOp "agdaRTS.uprimIntegerMultiply"
+    T.PRem -> binOp "agdaRTS.uprimIntegerRem"
+    T.PQuot -> binOp "agdaRTS.uprimIntegerQuot"
+    T.PAdd64 -> binOp "agdaRTS.uprimWord64Plus"
+    T.PSub64 -> binOp "agdaRTS.uprimWord64Minus"
+    T.PMul64 -> binOp "agdaRTS.uprimWord64Multiply"
+    T.PRem64 -> binOp "agdaRTS.uprimIntegerRem"     -- -|
+    T.PQuot64 -> binOp "agdaRTS.uprimIntegerQuot"   --  > These can use the integer functions
+    T.PEq64 -> binOp "agdaRTS.uprimIntegerEqual"    --  |
+    T.PLt64 -> binOp "agdaRTS.uprimIntegerLessThan" -- -|
+    T.PITo64 -> unOp "agdaRTS.primWord64FromNat"
+    T.P64ToI -> unOp "agdaRTS.primWord64ToNat"
+    T.PSeq -> binOp "agdaRTS.primSeq"
+  where binOp js = curriedLambda 2 $ apply (PlainJS js) [local 1, local 0]
+        unOp js  = curriedLambda 1 $ apply (PlainJS js) [local 0]
+        primEq   = curriedLambda 2 $ BinOp (local 1) "===" (local 0)
+
+
+compileAlt :: EnvWithOpts -> T.TAlt -> TCM ((QName, MemberId), Exp)
+compileAlt kit = \case
+  T.TACon con ar body -> do
+    erased <- getErasedConArgs con
+    let nargs = ar - length (filter id erased)
+    memId <- visitorName con
+    body <- Lambda nargs <$> compileTerm kit (eraseLocalVars erased body)
+    return ((con, memId), body)
+  _ -> __IMPOSSIBLE__
+
+eraseLocalVars :: [Bool] -> T.TTerm -> T.TTerm
+eraseLocalVars [] x = x
+eraseLocalVars (False: es) x = eraseLocalVars es x
+eraseLocalVars (True: es) x = eraseLocalVars es (TC.subst (length es) T.TErased x)
+
+visitorName :: QName -> TCM MemberId
+visitorName q = do (m,ls) <- global q; return (List1.last ls)
+
+flatName :: MemberId
+flatName = MemberId "flat"
+
+local :: Nat -> Exp
+local = Local . LocalId
+
+qname :: QName -> TCM Exp
+qname q = do
+  (e,ls) <- global q
+  return (foldl Lookup e ls)
+
+literal :: Literal -> Exp
+literal = \case
+  (LitNat    x) -> Integer x
+  (LitWord64 x) -> Integer (fromIntegral x)
+  (LitFloat  x) -> Double  x
+  (LitString x) -> String  x
+  (LitChar   x) -> Char    x
+  (LitQName  x) -> litqname x
+  (LitMeta _ m) -> litmeta m
+
+litqname :: QName -> Exp
+litqname q =
+  Object $ Map.fromListWith __IMPOSSIBLE__
+    [ (mem "id", Integer $ fromIntegral n)
+    , (mem "moduleId", Integer $ fromIntegral m)
+    , (mem "name", String $ T.pack $ prettyShow q)
+    , (mem "fixity", litfixity fx)]
+  where
+    mem = MemberId
+    NameId n (ModuleNameHash m) = nameId $ qnameName q
+    fx = theFixity $ nameFixity $ qnameName q
+
+    litfixity :: Fixity -> Exp
+    litfixity fx = Object $ Map.fromListWith __IMPOSSIBLE__
+      [ (mem "assoc", litAssoc $ fixityAssoc fx)
+      , (mem "prec", litPrec $ fixityLevel fx)]
+
+    -- TODO this will probably not work well together with the necessary FFI bindings
+    litAssoc NonAssoc   = String "non-assoc"
+    litAssoc LeftAssoc  = String "left-assoc"
+    litAssoc RightAssoc = String "right-assoc"
+
+    litPrec Unrelated   = String "unrelated"
+    litPrec (Related l) = Double l
+
+litmeta :: MetaId -> Exp
+litmeta (MetaId m h) =
+  Object $ Map.fromListWith __IMPOSSIBLE__
+    [ (MemberId "id", Integer $ fromIntegral m)
+    , (MemberId "module", Integer $ fromIntegral $ moduleNameHash h) ]
+
+
+--------------------------------------------------
+-- Writing out an ECMAScript module
+--------------------------------------------------
+
+writeModule :: Bool -> JSModuleStyle -> Module -> TCM ()
+writeModule minify ms m = do
+  out <- outFile (modName m)
+  liftIO (writeFile out (JSPretty.prettyShow minify ms m))
+
+outFile :: GlobalId -> TCM FilePath
+outFile m = do
+  mdir <- compileDir
+  let (fdir, fn) = splitFileName (jsFileName m)
+  let dir = mdir </> fdir
+      fp  = dir </> fn
+  liftIO $ createDirectoryIfMissing True dir
+  return fp
+
+outFile_ :: TCM FilePath
+outFile_ = do
+  m <- curMName
+  outFile (jsMod m)
+
+-- | Primitives implemented in the JS Agda RTS.
+--
+-- TODO: Primitives that are not part of this set, and for which
+-- 'defJSDef' does not return anything, are silently compiled to
+-- 'Undefined'. A better approach might be to list exactly those
+-- primitives which should be compiled to 'Undefined'.
+primitives :: Set PrimitiveId
+primitives = Set.fromList
+  [ PrimShowInteger
+
+  -- Natural number functions
+  -- , PrimNatPlus                 -- missing
+  , PrimNatMinus
+  -- , PrimNatTimes                -- missing
+  -- , PrimNatDivSucAux            -- missing
+  -- , PrimNatModSucAux            -- missing
+  -- , PrimNatEquality             -- missing
+  -- , PrimNatLess                 -- missing
+  -- , PrimShowNat                 -- missing
+
+  -- Machine words
+  , PrimWord64ToNat
+  , PrimWord64FromNat
+  -- , PrimWord64ToNatInjective    -- missing
+
+  -- Level functions
+  -- , PrimLevelZero               -- missing
+  -- , PrimLevelSuc                -- missing
+  -- , PrimLevelMax                -- missing
+
+  -- Floating point functions
+  , PrimFloatEquality
+  , PrimFloatInequality
+  , PrimFloatLess
+  , PrimFloatIsInfinite
+  , PrimFloatIsNaN
+  , PrimFloatIsNegativeZero
+  , PrimFloatIsSafeInteger
+  , PrimFloatToWord64
+  -- , PrimFloatToWord64Injective  -- missing
+  , PrimNatToFloat
+  , PrimIntToFloat
+  -- , PrimFloatRound              -- in Agda.Builtin.Float
+  -- , PrimFloatFloor              -- in Agda.Builtin.Float
+  -- , PrimFloatCeiling            -- in Agda.Builtin.Float
+  -- , PrimFloatToRatio            -- in Agda.Builtin.Float
+  , PrimRatioToFloat
+  -- , PrimFloatDecode             -- in Agda.Builtin.Float
+  -- , PrimFloatEncode             -- in Agda.Builtin.Float
+  , PrimShowFloat
+  , PrimFloatPlus
+  , PrimFloatMinus
+  , PrimFloatTimes
+  , PrimFloatNegate
+  , PrimFloatDiv
+  , PrimFloatSqrt
+  , PrimFloatExp
+  , PrimFloatLog
+  , PrimFloatSin
+  , PrimFloatCos
+  , PrimFloatTan
+  , PrimFloatASin
+  , PrimFloatACos
+  , PrimFloatATan
+  , PrimFloatATan2
+  , PrimFloatSinh
+  , PrimFloatCosh
+  , PrimFloatTanh
+  , PrimFloatASinh
+  , PrimFloatACosh
+  , PrimFloatATanh
+  , PrimFloatPow
+
+  -- Character functions
+  -- , PrimCharEquality            -- missing
+  -- , PrimIsLower                 -- missing
+  -- , PrimIsDigit                 -- missing
+  -- , PrimIsAlpha                 -- missing
+  -- , PrimIsSpace                 -- missing
+  -- , PrimIsAscii                 -- missing
+  -- , PrimIsLatin1                -- missing
+  -- , PrimIsPrint                 -- missing
+  -- , PrimIsHexDigit              -- missing
+  -- , PrimToUpper                 -- missing
+  -- , PrimToLower                 -- missing
+  -- , PrimCharToNat               -- missing
+  -- , PrimCharToNatInjective      -- missing
+  -- , PrimNatToChar               -- missing
+  -- , PrimShowChar                -- in Agda.Builtin.String
+
+  -- String functions
+  -- , PrimStringToList            -- in Agda.Builtin.String
+  -- , PrimStringToListInjective   -- missing
+  -- , PrimStringFromList          -- in Agda.Builtin.String
+  -- , PrimStringFromListInjective -- missing
+  -- , PrimStringAppend            -- in Agda.Builtin.String
+  -- , PrimStringEquality          -- in Agda.Builtin.String
+  -- , PrimShowString              -- in Agda.Builtin.String
+  -- , PrimStringUncons            -- in Agda.Builtin.String
+
+  -- Other stuff
+  -- , PrimEraseEquality           -- missing
+  -- , PrimForce                   -- missing
+  -- , PrimForceLemma              -- missing
+  , PrimQNameEquality
+  , PrimQNameLess
+  , PrimShowQName
+  , PrimQNameFixity
+  -- , PrimQNameToWord64s          -- missing
+  -- , PrimQNameToWord64sInjective -- missing
+  , PrimMetaEquality
+  , PrimMetaLess
+  , PrimShowMeta
+  , PrimMetaToNat
+  -- , PrimMetaToNatInjective      -- missing
+  , builtinIMin
+  , builtinIMax
+  , builtinINeg
+  , PrimPartial
+  , PrimPartialP
+  , builtinPOr
+  , builtinComp
+  , builtinTrans
+  , builtinHComp
+  , builtinSubOut
+  , builtin_glueU
+  , builtin_unglueU
+  , builtinFaceForall
+  , PrimDepIMin
+  , PrimIdFace
+  , PrimIdPath
+  , builtinIdElim
+  , builtinConId
+  -- , builtinGlue                   -- missing
+  -- , builtin_glue                  -- missing
+  -- , builtin_unglue                -- missing
+  ]
diff --git a/src/full/Agda/Compiler/JS/Pretty.hs b/src/full/Agda/Compiler/JS/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/JS/Pretty.hs
@@ -0,0 +1,349 @@
+module Agda.Compiler.JS.Pretty where
+
+import GHC.Generics (Generic)
+
+import Data.Char ( isAsciiLower, isAsciiUpper, isDigit )
+import Data.List ( intercalate )
+import Data.String ( IsString (fromString) )
+import Data.Semigroup ( Semigroup, (<>) )
+import Data.Set ( Set, toList, insert, member )
+import qualified Data.Set as Set
+import Data.Map ( Map, toAscList )
+import qualified Data.Text as T
+
+import Agda.Syntax.Common ( Nat )
+
+import Agda.Utils.Function ( applyWhen )
+import Agda.Utils.Hash
+import Agda.Utils.List ( indexWithDefault )
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+
+import Agda.Utils.Impossible
+
+import Agda.Compiler.JS.Syntax hiding (exports)
+
+-- Pretty-print a lambda-calculus expression as ECMAScript.
+
+--- The indentation combinators of the pretty library does not fit C-like languages
+--- like ECMAScript.
+--- A simple pretty printer is implemented with a better `indent` and punctuation compaction.
+---
+--- More explanation:
+---
+--- I have struggled with different pretty printers, and at the end it was much easier
+--- to implement and use this ~100 SLOC code pretty printer library.
+--- It produces really better quality indentation than I could achieve with the
+--  standard pretty printers.
+--- This library code is only used in this module, and it is specialized to pretty
+--- print JavaScript code for the Agda backend, so I think its best place is in this module.
+data JSModuleStyle = JSCJS | JSAMD
+  deriving Generic
+
+data Doc
+    = Doc String
+    | Indent Int Doc
+    | Group Doc
+    | Beside Doc Doc
+    | Above Doc Doc
+    | Enclose Doc Doc Doc
+    | Space
+    | Empty
+
+minifiedCodeLinesLength :: Int
+minifiedCodeLinesLength = 500
+
+render :: Bool -> Doc -> String
+render minify = intercalate "\n" . joinLines . map (uncurry mkIndent) . go 0
+  where
+    joinLines :: [String] -> [String]
+    joinLines = applyWhen minify $ chunks 0 []
+      where
+        chunks len acc [] = [concat (reverse acc)]
+        chunks len acc (s: ss)
+            | len + n <= minifiedCodeLinesLength = chunks (len + n) (s: acc) ss
+            | otherwise = concat (reverse acc): chunks n [s] ss
+          where
+            n = length s
+
+    joinBy f [x] (y: ys) = f x y ++ ys
+    joinBy f (x:xs) ys = x: joinBy f xs ys
+    joinBy f xs ys = xs ++ ys
+
+    mkIndent n s | minify = s
+    mkIndent n "" = ""
+    mkIndent n s = replicate n ' ' ++ s
+
+    overlay (i, s) (j, s') | all punctuation (s ++ s') && n > 0 = [(i, s ++ mkIndent n s')]
+      where n = j - (i + length s)
+    overlay (j, s') (i, s) | all punctuation (s ++ s') && n > 0 = [(i, s' ++ mkIndent n s)]
+      where n = j - (i + length s)
+    overlay a b = [a, b]
+
+    punctuation = (`elem` ("(){}[];:, " :: String))
+
+    go i Space = if minify then [] else [(i, " ")]
+    go i Empty = []
+    go i (Doc s) = [(i, s)]
+    go i (Beside d d') = joinBy (\(i, s) (_, s') -> [(i, s ++ s')]) (go i d) (go i d')
+    go i (Above d d') = joinBy overlay (go i d) (go i d')
+    go i (Indent j d) = go (i + j) d
+    go i (Enclose open close d) = go i $ Group $ Above open $ Above d close
+    go i (Group d)
+        | size ss < 40 = compact ss
+        | otherwise    = ss
+      where
+        ss = go i d
+        size = sum . map (length . snd)
+        compact [] = []
+        compact ((i, x): xs) = [(i, x ++ concatMap snd xs)]
+
+instance IsString Doc where
+    fromString = Doc
+
+instance Semigroup Doc where
+    Empty <> d = d
+    d <> Empty = d
+    d <> d' = Beside d d'
+
+instance Monoid Doc where
+    mempty = Empty
+    mappend = (<>)
+
+infixr 5 $+$
+infixr 5 $++$
+infixr 6 <+>  -- fixity has to match the one of Semigroup.(<>)
+
+($+$) :: Doc -> Doc -> Doc
+Empty $+$ d = d
+d $+$ Empty = d
+d $+$ d' = Above d d'
+
+-- | Separate by blank line.
+
+($++$) :: Doc -> Doc -> Doc
+Empty $++$ d = d
+d $++$ Empty = d
+d $++$ d' = d `Above` "" `Above` d'
+
+-- | Separate by space that will be removed by minify.
+--
+-- For non-removable space, use @d <> " " <> d'@.
+
+(<+>) :: Doc -> Doc -> Doc
+Empty <+> d = d
+d <+> Empty = d
+d <+> d' = d `Beside` Space `Beside` d'
+
+text :: String -> Doc
+text = Doc
+
+group :: Doc -> Doc
+group = Group
+
+indentBy :: Int -> Doc -> Doc
+indentBy i Empty = Empty
+indentBy i (Indent j d) = Indent (i + j) d
+indentBy i d = Indent i d
+
+enclose :: Doc -> Doc -> Doc -> Doc
+enclose open close (Enclose o c d) = Enclose (open <> o) (c <> close) d
+enclose open close (Indent _ (Enclose o c d)) = Enclose (open <> o) (c <> close) d
+enclose open close d = Enclose open close d
+
+----------------------------------------------------------------------------------------------
+
+space :: Doc
+space = Space
+
+indent :: Doc -> Doc
+indent = indentBy 2
+
+hcat :: [Doc] -> Doc
+hcat = foldr (<>) mempty
+
+vcat :: [Doc] -> Doc
+vcat = foldr ($+$) mempty
+
+-- | Concatenate vertically, separated by blank lines.
+
+vsep :: [Doc] -> Doc
+vsep = foldr ($++$) mempty
+
+punctuate :: Doc -> [Doc] -> Doc
+punctuate _ []     = mempty
+punctuate p (x:xs) = indent $ vcat $ go x xs
+                   where go y []     = [y]
+                         go y (z:zs) = (y <> p) : go z zs
+
+parens, brackets, braces :: Doc -> Doc
+parens   = enclose "(" ")"
+brackets = enclose "[" "]"
+braces   = enclose "{" "}"
+
+-- | Apply 'parens' to 'Doc' if boolean is true.
+mparens :: Bool -> Doc -> Doc
+mparens True  d = parens d
+mparens False d = d
+
+----------------------------------------------------------------------------------------------
+
+unescape :: Char -> String
+unescape '"'      = "\\\""
+unescape '\\'     = "\\\\"
+unescape '\n'     = "\\n"
+unescape '\r'     = "\\r"
+unescape '\x2028' = "\\u2028"
+unescape '\x2029' = "\\u2029"
+unescape c        = [c]
+
+unescapes :: String -> Doc
+unescapes s = text $ concatMap unescape s
+
+-- pretty (n,b) i e pretty-prints e, under n levels of de Bruijn binding
+--   if b is true then the output is minified
+
+class Pretty a where
+    pretty :: (Nat, Bool, JSModuleStyle) -> a -> Doc
+
+prettyShow :: Pretty a => Bool -> JSModuleStyle -> a -> String
+prettyShow minify ms = render minify . pretty (0, minify, ms)
+
+instance Pretty a => Pretty (Maybe a) where
+  pretty n = maybe mempty (pretty n)
+
+instance (Pretty a, Pretty b) => Pretty (a,b) where
+  pretty n (x,y) = pretty n x <> ":" <+> pretty n y
+
+-- Pretty-print collections
+
+class Pretties a where
+    pretties :: (Nat, Bool, JSModuleStyle) -> a -> [Doc]
+
+instance Pretty a => Pretties [a] where
+  pretties n = map (pretty n)
+
+instance Pretty a => Pretties (List1 a) where
+  pretties n = pretties n . List1.toList
+
+instance (Pretty a, Pretty b) => Pretties (Map a b) where
+  pretties n = pretties n . toAscList
+
+-- Pretty print identifiers
+
+instance Pretty LocalId where
+  pretty (n, _, _) (LocalId x) = text $ indexWithDefault __IMPOSSIBLE__ vars (n - x - 1)
+    where
+      vars = ("": map show [0..]) >>= \s -> map (:s) ['a'..'z']
+
+instance Pretty GlobalId where
+  pretty n (GlobalId m) = text $ variableName $ intercalate "_" m
+
+instance Pretty MemberId where
+  pretty _ (MemberId s) = "\"" <> unescapes s <> "\""
+  pretty n (MemberIndex i comment) = text (show i) <> pretty n comment
+
+instance Pretty Comment where
+  pretty _ (Comment "") = mempty
+  pretty (_, True, _) _ = mempty
+  pretty _ (Comment s) = text $ "/* " ++ s ++ " */"
+
+-- Pretty print expressions
+
+instance Pretty Exp where
+  pretty n (Self)            = "exports"
+  pretty n (Local x)         = pretty n x
+  pretty n (Global m)        = pretty n m
+  pretty n (Undefined)       = "undefined"
+  pretty n (Null)            = "null"
+  pretty n (String s)        = "\"" <> unescapes (T.unpack s) <> "\""
+  pretty n (Char c)          = "\"" <> unescapes [c] <> "\""
+  pretty n (Integer x)       = "agdaRTS.primIntegerFromString(\"" <> text (show x) <> "\")"
+  pretty n (Double x)        = text $ show x
+  pretty (n, min, ms) (Lambda x e) =
+    mparens (x /= 1) (punctuate "," (pretties (n + x, min, ms) (map LocalId [x-1, x-2 .. 0])))
+    <+> "=>" <+> block (n + x, min, ms) e
+  pretty n (Object o)        = braces $ punctuate "," $ pretties n o
+  pretty n (Array es)        = brackets $ punctuate "," [pretty n c <> pretty n e | (c, e) <- es]
+  pretty n (Apply f es)      = pretty n f <> parens (punctuate "," $ pretties n es)
+  pretty n (Lookup e l)      = pretty n e <> brackets (pretty n l)
+  pretty n (If e f g)        = parens $ pretty n e <> "?" <+> pretty n f <> ":" <+> pretty n g
+  pretty n (PreOp op e)      = parens $ text op <> " " <> pretty n e
+  pretty n (BinOp e op f)    = parens $ pretty n e <> " " <> text op <> " " <> pretty n f
+  pretty n (Const c)         = text c
+  pretty n (PlainJS js)      = text js
+
+block :: (Nat, Bool, JSModuleStyle) -> Exp -> Doc
+block n e = mparens (doNest e) $ pretty n e
+  where
+    doNest Object{} = True
+    doNest _ = False
+
+modname :: GlobalId -> Doc
+modname (GlobalId ms) = text $ "\"" ++ intercalate "." ms ++ "\""
+
+exports :: (Nat, Bool, JSModuleStyle) -> Set JSQName -> [Export] -> Doc
+exports n lss [] = Empty
+exports n lss es0@(Export ls e : es)
+  -- If the parent of @ls@ is already defined (or no parent exists), @ls@ can be defined
+  | maybe True (`member` lss) parent =
+      "exports" <> hcat (map brackets (pretties n ls)) <+> "=" <+> indent (pretty n e) <> ";" $+$
+      exports n (insert ls lss) es
+  -- If the parent is not yet defined, first define it as empty object, and then continue with @ls@.
+  | otherwise =
+      exports n lss $ maybe es0 (\ ls' -> Export ls' (Object mempty) : es0) parent
+  where
+  parent = List1.nonEmpty $ List1.init ls
+
+instance Pretty [(GlobalId, Export)] where
+  pretty n es
+    = vcat [ pretty n g <> hcat (map brackets (pretties n ls)) <+> "=" <+> indent (pretty n e) <> ";"
+           | (g, Export ls e) <- es ]
+
+instance Pretty Module where
+  pretty opt@(n, min, JSCJS) (Module m is es callMain) = vsep
+    [ "var agdaRTS" <+> "=" <+> "require(\"agda-rts\");"
+    , imports
+    , exports opt Set.empty es
+    , pretty opt callMain
+    ]
+    $+$ ""
+    where
+      imports = vcat [
+        "var " <> indent (pretty opt e) <+> "=" <+> "require(" <> modname e <> ");"
+        | e <- toList (globals es <> Set.fromList is)
+        ]
+      les = toList (globals es <> Set.fromList is)
+  pretty opt@(n, min, JSAMD) (Module m is es callMain) = vsep
+    [ "define(['agda-rts'"
+      <+> hcat [ ", " <+> modname e | e <- les ]
+      <+> "],"
+    , "function(agdaRTS"
+      <+> hcat [ ", " <+> pretty opt e | e <- les ]
+      <+> ") {"
+    , "var exports = {};"
+    , exports opt Set.empty es
+    , pretty opt callMain
+    , "; return exports; });"
+    ]
+    $+$ "" -- Final newline
+    where
+      les = toList (globals es <> Set.fromList is)
+
+
+variableName :: String -> String
+variableName s = if isValidJSIdent s then "z_" ++ s else "h_" ++ show (hashString s)
+
+-- | Check if a string is a valid JS identifier. The check ignores keywords
+-- as we prepend z_ to our identifiers. The check
+-- is conservative and may not admit all valid JS identifiers.
+
+isValidJSIdent :: String -> Bool
+isValidJSIdent []     = False
+isValidJSIdent (c:cs) = validFirst c && all validOther cs
+  where
+  validFirst :: Char -> Bool
+  validFirst c = isAsciiUpper c || isAsciiLower c || c == '_' || c == '$'
+
+  validOther :: Char -> Bool
+  validOther c = validFirst c || isDigit c
diff --git a/src/full/Agda/Compiler/JS/Substitution.hs b/src/full/Agda/Compiler/JS/Substitution.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/JS/Substitution.hs
@@ -0,0 +1,125 @@
+module Agda.Compiler.JS.Substitution where
+
+import Prelude hiding ( map, lookup )
+import Data.Map ( empty, unionWith, singleton, findWithDefault )
+import qualified Data.Map as Map
+import Data.List ( genericIndex )
+import qualified Data.List as List
+
+import Agda.Syntax.Common ( Nat )
+import Agda.Compiler.JS.Syntax
+  ( Exp(Self,Undefined,Local,Lambda,Object,Array,Apply,Lookup,If,BinOp,PreOp),
+    MemberId, LocalId(LocalId) )
+import Agda.Utils.Function ( iterate' )
+
+-- Map for expressions
+
+map :: Nat -> (Nat -> LocalId -> Exp) -> Exp -> Exp
+map m f (Local i)       = f m i
+map m f (Lambda i e)    = Lambda i (map (m + i) f e)
+map m f (Object o)      = Object (Map.map (map m f) o)
+map m f (Array es)      = Array (List.map (\(c, e) -> (c, map m f e)) es)
+map m f (Apply e es)    = Apply (map m f e) (List.map (map m f) es)
+map m f (Lookup e l)    = Lookup (map m f e) l
+map m f (If e e' e'')   = If (map m f e) (map m f e') (map m f e'')
+map m f (PreOp op e)    = PreOp op (map m f e)
+map m f (BinOp e op e') = BinOp (map m f e) op (map m f e')
+map m f e               = e
+
+-- Shifting
+
+shift :: Nat -> Exp -> Exp
+shift = shiftFrom 0
+
+shiftFrom :: Nat -> Nat -> Exp -> Exp
+shiftFrom m 0 e = e
+shiftFrom m n e = map m (shifter n) e
+
+shifter :: Nat -> Nat -> LocalId -> Exp
+shifter n m (LocalId i) | i < m     = Local (LocalId i)
+shifter n m (LocalId i) | otherwise = Local (LocalId (i + n))
+
+-- Substitution
+
+subst :: Nat -> [Exp] -> Exp -> Exp
+subst 0 es e = e
+subst n es e = map 0 (substituter n es) e
+
+substituter :: Nat -> [Exp] -> Nat -> LocalId -> Exp
+substituter n es m (LocalId i) | i < m       = Local (LocalId i)
+substituter n es m (LocalId i) | (i - m) < n = shift m (genericIndex (es ++ repeat Undefined) (n - (i + 1 - m)))
+substituter n es m (LocalId i) | otherwise   = Local (LocalId (i - n))
+
+-- A variant on substitution which performs beta-reduction
+
+map' :: Nat -> (Nat -> LocalId -> Exp) -> Exp -> Exp
+map' m f (Local i)       = f m i
+map' m f (Lambda i e)    = Lambda i (map' (m + i) f e)
+map' m f (Object o)      = Object (Map.map (map' m f) o)
+map' m f (Array es)      = Array (List.map (\(c, e) -> (c, map' m f e)) es)
+map' m f (Apply e es)    = apply (map' m f e) (List.map (map' m f) es)
+map' m f (Lookup e l)    = lookup (map' m f e) l
+map' m f (If e e' e'')   = If (map' m f e) (map' m f e') (map' m f e'')
+map' m f (PreOp op e)    = PreOp op (map' m f e)
+map' m f (BinOp e op e') = BinOp (map' m f e) op (map' m f e')
+map' m f e               = e
+
+subst' :: Nat -> [Exp] -> Exp -> Exp
+subst' 0 es e = e
+subst' n es e = map' 0 (substituter n es) e
+
+-- Beta-reducing application and field access
+
+apply :: Exp -> [Exp] -> Exp
+apply (Lambda i e) es = subst' i es e
+apply e            es = Apply e es
+
+lookup :: Exp -> MemberId -> Exp
+lookup (Object o) l = findWithDefault Undefined l o
+lookup e          l = Lookup e l
+
+-- Replace any top-level occurrences of self
+-- (needed because JS is a cbv language, so any top-level
+-- recursions would evaluate before the module has been defined,
+-- e.g. exports = { x: 1, y: exports.x } results in an exception,
+-- as exports is undefined at the point that exports.x is evaluated),
+
+self :: Exp -> Exp -> Exp
+self e (Self)         = e
+self e (Object o)     = Object (Map.map (self e) o)
+self e (Array es)     = Array (List.map (\(c, x) -> (c, self e x)) es)
+self e (Apply f es)   = case (self e f) of
+  (Lambda n g) -> self e (subst' n es g)
+  g            -> Apply g (List.map (self e) es)
+self e (Lookup f l)   = lookup (self e f) l
+self e (If f g h)     = If (self e f) (self e g) (self e h)
+self e (BinOp f op g) = BinOp (self e f) op (self e g)
+self e (PreOp op f)   = PreOp op (self e f)
+self e f              = f
+
+-- Find the fixed point of an expression, with no top-level occurrences
+-- of self.
+
+fix :: Exp -> Exp
+fix f = e where e = self e f
+
+-- Some helper functions
+
+curriedApply :: Exp -> [Exp] -> Exp
+curriedApply = foldl (\ f e -> apply f [e])
+
+curriedLambda :: Nat -> Exp -> Exp
+curriedLambda n = iterate' n (Lambda 1)
+
+emp :: Exp
+emp = Object (empty)
+
+union :: Exp -> Exp -> Exp
+union (Object o) (Object p) = Object (unionWith union o p)
+union e          f          = e
+
+vine :: [MemberId] -> Exp -> Exp
+vine ls e = foldr (\ l e -> Object (singleton l e)) e ls
+
+object :: [([MemberId],Exp)] -> Exp
+object = foldr (\ (ls,e) -> (union (vine ls e))) emp
diff --git a/src/full/Agda/Compiler/JS/Syntax.hs b/src/full/Agda/Compiler/JS/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/JS/Syntax.hs
@@ -0,0 +1,156 @@
+
+module Agda.Compiler.JS.Syntax where
+
+import Data.Map (Map)
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Semigroup ( Semigroup )
+
+import Data.Text (Text)
+
+import Agda.Syntax.Common ( Nat )
+
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+
+-- An untyped lambda calculus with records,
+-- and a special self-binder for recursive declarations
+
+data Exp =
+  Self |
+  Local LocalId |
+  Global GlobalId |
+  Undefined |
+  Null |
+  String Text |
+  Char Char |
+  Integer Integer |
+  Double Double |
+  Lambda Nat Exp |
+  Object (Map MemberId Exp) |
+  Array [(Comment, Exp)] |
+  Apply Exp [Exp] |
+  Lookup Exp MemberId |
+  If Exp Exp Exp |
+  BinOp Exp String Exp |
+  PreOp String Exp |
+  Const String |
+  PlainJS String -- ^ Arbitrary JS code.
+  deriving (Show, Eq)
+
+-- Local identifiers are named by De Bruijn indices.
+-- Global identifiers are named by string lists.
+-- Object members are named by strings.
+
+newtype LocalId = LocalId Nat
+  deriving (Eq, Ord, Show)
+
+newtype GlobalId = GlobalId [String]
+  deriving (Eq, Ord, Show)
+
+data MemberId
+    = MemberId String
+    | MemberIndex Int Comment
+  deriving (Eq, Ord, Show)
+
+newtype Comment = Comment String
+  deriving (Show, Semigroup, Monoid)
+
+instance Eq Comment where _ == _ = True
+instance Ord Comment where compare _ _ = EQ
+
+-- The top-level compilation unit is a module, which names
+-- the GId of its exports, and a list of definitions
+
+data Export = Export { expName :: JSQName, defn :: Exp }
+  deriving Show
+
+type JSQName = List1 MemberId
+
+data Module = Module
+  { modName  :: GlobalId
+  , imports  :: [GlobalId]
+  , exports  :: [Export]
+  , callMain :: Maybe Exp
+  }
+  deriving Show
+
+-- Note that modules are allowed to be recursive, via the Self expression,
+-- which is bound to the exported module.
+
+-- Top-level uses of the form exports.l1....lN.
+
+class Uses a where
+  uses :: a -> Set JSQName
+
+  default uses :: (a ~ t b, Foldable t, Uses b) => a -> Set JSQName
+  uses = foldMap uses
+
+instance Uses a => Uses [a]
+instance Uses a => Uses (Map k a)
+
+instance (Uses a, Uses b) => Uses (a, b) where
+  uses (a, b) = uses a `Set.union` uses b
+
+instance (Uses a, Uses b, Uses c) => Uses (a, b, c) where
+  uses (a, b, c) = uses a `Set.union` uses b `Set.union` uses c
+
+instance Uses Comment where
+  uses _ = Set.empty
+
+instance Uses Exp where
+  uses (Object o)     = uses o
+  uses (Array es)     = uses es
+  uses (Apply e es)   = uses (e, es)
+  uses (Lookup e l)   = uses' e (List1.singleton l)
+    where
+      uses' :: Exp -> JSQName -> Set JSQName
+      uses' Self         ls = Set.singleton ls
+      uses' (Lookup e l) ls = uses' e (l <| ls)
+      uses' e            ls = uses e
+  uses (If e f g)     = uses (e, f, g)
+  uses (BinOp e op f) = uses (e, f)
+  uses (PreOp op e)   = uses e
+  uses e              = Set.empty
+
+instance Uses Export where
+  uses (Export _ e) = uses e
+
+-- All global ids
+
+class Globals a where
+  globals :: a -> Set GlobalId
+
+  default globals :: (a ~ t b, Foldable t, Globals b) => a -> Set GlobalId
+  globals = foldMap globals
+
+instance Globals a => Globals [a]
+instance Globals a => Globals (Maybe a)
+instance Globals a => Globals (Map k a)
+
+instance (Globals a, Globals b) => Globals (a, b) where
+  globals (a, b) = globals a `Set.union` globals b
+
+instance (Globals a, Globals b, Globals c) => Globals (a, b, c) where
+  globals (a, b, c) = globals a `Set.union` globals b `Set.union` globals c
+
+instance Globals Comment where
+  globals _ = Set.empty
+
+instance Globals Exp where
+  globals (Global i) = Set.singleton i
+  globals (Lambda n e) = globals e
+  globals (Object o) = globals o
+  globals (Array es) = globals es
+  globals (Apply e es) = globals (e, es)
+  globals (Lookup e l) = globals e
+  globals (If e f g) = globals (e, f, g)
+  globals (BinOp e op f) = globals (e, f)
+  globals (PreOp op e) = globals e
+  globals _ = Set.empty
+
+instance Globals Export where
+  globals (Export _ e) = globals e
+
+instance Globals Module where
+  globals (Module _ _ es me) = globals (es, me)
diff --git a/src/full/Agda/Compiler/MAlonzo/Coerce.hs b/src/full/Agda/Compiler/MAlonzo/Coerce.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Coerce.hs
@@ -0,0 +1,81 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.MAlonzo.Coerce (addCoercions, erasedArity) where
+
+import Agda.Syntax.Common (Nat)
+import Agda.Syntax.Treeless
+
+import Agda.TypeChecking.Monad
+  ( HasConstInfo
+  , getErasedConArgs
+  , getTreeless
+  )
+
+-- | Insert unsafeCoerce (in the form of 'TCoerce') everywhere it's needed in
+--   the right-hand side of a definition.
+addCoercions :: HasConstInfo m => TTerm -> m TTerm
+addCoercions = coerceTop
+  where
+    -- Don't coerce top-level lambdas.
+    coerceTop (TLam b) = TLam <$> coerceTop b
+    coerceTop t        = coerce t
+
+    -- Coerce a term `t`. The result (when translated to Haskell) has type
+    -- `forall a. a`.
+    coerce t =
+      case t of
+        TVar{}    -> return $ TCoerce t
+        TPrim{}   -> return $ TCoerce t
+        TDef{}    -> return $ TCoerce t
+        TCon{}    -> return $ TCoerce t
+        TLit{}    -> return $ TCoerce t
+        TUnit{}   -> return $ TCoerce t
+        TSort{}   -> return $ TCoerce t
+        TErased{} -> return t
+        TCoerce{} -> return t
+        TError{}  -> return t
+        TApp f vs -> do
+          ar <- funArity f
+          if length vs > ar
+            then TApp (TCoerce f) <$> mapM softCoerce vs
+            else TCoerce . TApp f <$> mapM coerce vs
+        TLam b         -> TCoerce . TLam <$> softCoerce b
+        TLet e b       -> TLet <$> softCoerce e <*> coerce b
+        TCase x t d bs -> TCase x t <$> coerce d <*> mapM coerceAlt bs
+
+    coerceAlt (TACon c a b) = TACon c a <$> coerce b
+    coerceAlt (TAGuard g b) = TAGuard   <$> coerce g <*> coerce b
+    coerceAlt (TALit l b)   = TALit l   <$> coerce b
+
+    -- Insert TCoerce in subterms. When translated to Haskell, the resulting
+    -- term is well-typed with some type arbitrary type.
+    softCoerce t =
+      case t of
+        TVar{}    -> return t
+        TPrim{}   -> return t
+        TDef{}    -> return t
+        TCon{}    -> return t
+        TLit{}    -> return t
+        TUnit{}   -> return t
+        TSort{}   -> return t
+        TErased{} -> return t
+        TCoerce{} -> return t
+        TError{}  -> return t
+        TApp f vs -> do
+          ar <- funArity f
+          if length vs > ar
+            then TApp (TCoerce f) <$> mapM softCoerce vs
+            else TApp f <$> mapM coerce vs
+        TLam b         -> TLam <$> softCoerce b
+        TLet e b       -> TLet <$> softCoerce e <*> softCoerce b
+        TCase x t d bs -> TCase x t <$> coerce d <*> mapM coerceAlt bs
+
+funArity :: HasConstInfo m => TTerm -> m Nat
+funArity (TDef q)  = maybe 0 (fst . tLamView) <$> getTreeless q
+funArity (TCon q)  = erasedArity q
+funArity (TPrim _) = return 3 -- max arity of any primitive
+funArity _         = return 0
+
+-- | The number of retained arguments after erasure.
+erasedArity :: HasConstInfo m => QName -> m Nat
+erasedArity q = length . filter not <$> getErasedConArgs q
diff --git a/src/full/Agda/Compiler/MAlonzo/Compiler.hs b/src/full/Agda/Compiler/MAlonzo/Compiler.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Compiler.hs
@@ -0,0 +1,1373 @@
+
+module Agda.Compiler.MAlonzo.Compiler
+  ( ghcBackend
+  , ghcInvocationStrings
+  )
+  where
+
+import Control.Arrow (second)
+import Control.DeepSeq
+import Control.Monad
+import Control.Monad.Except   ( throwError )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Reader   ( MonadReader(..), asks, ReaderT, runReaderT, withReaderT)
+import Control.Monad.Trans    ( lift )
+import Control.Monad.Writer   ( MonadWriter(..), WriterT, runWriterT )
+
+import qualified Data.HashSet as HashSet
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Text (Text)
+import qualified Data.Text as Text
+import Data.Monoid (Monoid, mempty, mappend)
+import Data.Semigroup ((<>))
+
+import GHC.Generics (Generic)
+
+import qualified Agda.Utils.Haskell.Syntax as HS
+
+import System.Directory (createDirectoryIfMissing)
+import System.Environment (setEnv)
+import System.FilePath hiding (normalise)
+import System.IO (utf8)
+
+import Agda.Compiler.CallCompiler
+import Agda.Compiler.Common
+import Agda.Compiler.MAlonzo.Coerce
+import Agda.Compiler.MAlonzo.Misc
+import Agda.Compiler.MAlonzo.Pretty
+import Agda.Compiler.MAlonzo.Primitives
+import Agda.Compiler.MAlonzo.HaskellTypes
+import Agda.Compiler.MAlonzo.Pragmas
+import Agda.Compiler.MAlonzo.Strict
+import Agda.Compiler.ToTreeless
+import Agda.Compiler.Treeless.Unused
+import Agda.Compiler.Treeless.Erase
+import Agda.Compiler.Backend
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty (prettyShow, render)
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Names (namesIn)
+import qualified Agda.Syntax.Treeless as T
+import Agda.Syntax.Literal
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Primitive (getBuiltinName)
+import Agda.TypeChecking.Pretty hiding ((<>))
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.FileName (isNewerThan)
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Float
+import Agda.Utils.IO.Directory
+import Agda.Utils.Lens
+import Agda.Utils.List
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Singleton
+import qualified Agda.Utils.IO.UTF8 as UTF8
+
+import Paths_Agda
+
+import Agda.Utils.Impossible
+
+-- The backend callbacks --------------------------------------------------
+
+ghcBackend :: Backend
+ghcBackend = Backend ghcBackend'
+
+ghcBackend' :: Backend' GHCFlags GHCEnv GHCModuleEnv GHCModule GHCDefinition
+ghcBackend' = Backend'
+  { backendName           = "GHC"
+  , backendVersion        = Nothing
+  , options               = defaultGHCFlags
+  , commandLineFlags      = ghcCommandLineFlags
+  , isEnabled             = flagGhcCompile
+  , preCompile            = ghcPreCompile
+  , postCompile           = ghcPostCompile
+  , preModule             = ghcPreModule
+  , postModule            = ghcPostModule
+  , compileDef            = ghcCompileDef
+  , scopeCheckingSuffices = False
+  , mayEraseType          = ghcMayEraseType
+  }
+
+--- Command-line flags ---
+
+data GHCFlags = GHCFlags
+  { flagGhcCompile :: Bool
+  , flagGhcCallGhc :: Bool
+  , flagGhcBin     :: Maybe FilePath
+    -- ^ Use the compiler at PATH instead of "ghc"
+  , flagGhcFlags      :: [String]
+  , flagGhcStrictData :: Bool
+    -- ^ Make inductive constructors strict?
+  , flagGhcStrict :: Bool
+    -- ^ Make functions strict?
+  }
+  deriving Generic
+
+instance NFData GHCFlags
+
+defaultGHCFlags :: GHCFlags
+defaultGHCFlags = GHCFlags
+  { flagGhcCompile    = False
+  , flagGhcCallGhc    = True
+  , flagGhcBin        = Nothing
+  , flagGhcFlags      = []
+  , flagGhcStrictData = False
+  , flagGhcStrict     = False
+  }
+
+-- | The option to activate the GHC backend.
+--
+ghcInvocationFlag :: OptDescr (Flag GHCFlags)
+ghcInvocationFlag =
+      Option ['c']  ["compile", "ghc"] (NoArg enable)
+                    "compile program using the GHC backend"
+  where
+    enable      o = pure o{ flagGhcCompile    = True }
+
+ghcCommandLineFlags :: [OptDescr (Flag GHCFlags)]
+ghcCommandLineFlags =
+    [ ghcInvocationFlag
+    , Option []     ["ghc-dont-call-ghc"] (NoArg dontCallGHC)
+                    "don't call GHC, just write the GHC Haskell files."
+    , Option []     ["ghc-flag"] (ReqArg ghcFlag "GHC-FLAG")
+                    "give the flag GHC-FLAG to GHC"
+    , Option []     ["with-compiler"] (ReqArg withCompilerFlag "PATH")
+                    "use the compiler available at PATH"
+    , Option []     ["ghc-strict-data"] (NoArg strictData)
+                    "make inductive constructors strict"
+    , Option []     ["ghc-strict"] (NoArg strict)
+                    "make functions strict"
+    ]
+  where
+    dontCallGHC o = pure o{ flagGhcCallGhc    = False }
+    ghcFlag f   o = pure o{ flagGhcFlags      = flagGhcFlags o ++ [f] }
+    strictData  o = pure o{ flagGhcStrictData = True }
+    strict      o = pure o{ flagGhcStrictData = True
+                          , flagGhcStrict     = True
+                          }
+
+withCompilerFlag :: FilePath -> Flag GHCFlags
+withCompilerFlag fp o = case flagGhcBin o of
+ Nothing -> pure o { flagGhcBin = Just fp }
+ Just{}  -> throwError "only one compiler path allowed"
+
+-- | Option strings to activate the GHC backend.
+--
+ghcInvocationStrings :: [String]
+ghcInvocationStrings = optionStrings ghcInvocationFlag
+
+-- | Get all flags that activate the given option.
+--
+optionStrings :: OptDescr a -> [String]
+optionStrings (Option short long _ _) = map (\ c -> '-' : c : []) short ++ long
+
+--- Context types ---
+
+-- | Monads that can read @GHCOptions@
+class Monad m => ReadGHCOpts m where
+  askGhcOpts :: m GHCOptions
+
+instance Monad m => ReadGHCOpts (ReaderT GHCOptions m) where
+  askGhcOpts = ask
+
+instance Monad m => ReadGHCOpts (ReaderT GHCEnv m) where
+  askGhcOpts = withReaderT ghcEnvOpts askGhcOpts
+
+instance Monad m => ReadGHCOpts (ReaderT GHCModuleEnv m) where
+  askGhcOpts = withReaderT ghcModEnv askGhcOpts
+
+data GHCModule = GHCModule
+  { ghcModModuleEnv :: GHCModuleEnv
+  , ghcModMainFuncs :: [MainFunctionDef]
+  -- ^ The `main` function definition(s), if both the module is
+  --   the @IsMain@ module (root/focused) and a suitable `main`
+  --   function was defined.
+  }
+
+instance Monad m => ReadGHCOpts (ReaderT GHCModule m) where
+  askGhcOpts = withReaderT ghcModModuleEnv askGhcOpts
+
+instance Monad m => ReadGHCModuleEnv (ReaderT GHCModule m) where
+  askGHCModuleEnv = withReaderT ghcModModuleEnv askGHCModuleEnv
+
+data GHCDefinition = GHCDefinition
+  { ghcDefUsesFloat  :: UsesFloat
+  , ghcDefDecls      :: [HS.Decl]
+  , ghcDefDefinition :: Definition
+  , ghcDefMainDef    :: Maybe MainFunctionDef
+  , ghcDefImports    :: Set TopLevelModuleName
+  }
+
+--- Top-level compilation ---
+
+ghcPreCompile :: GHCFlags -> TCM GHCEnv
+ghcPreCompile flags = do
+  cubical <- optCubical <$> pragmaOptions
+  let notSupported s =
+        typeError $ GenericError $
+          "Compilation of code that uses " ++ s ++ " is not supported."
+  case cubical of
+    Nothing      -> return ()
+    Just CErased -> return ()
+    Just CFull   -> notSupported "--cubical"
+
+  outDir <- compileDir
+  let ghcOpts = GHCOptions
+                { optGhcCallGhc    = flagGhcCallGhc flags
+                , optGhcBin        = fromMaybe "ghc" (flagGhcBin flags)
+                , optGhcFlags      = flagGhcFlags flags
+                , optGhcCompileDir = outDir
+                , optGhcStrictData = flagGhcStrictData flags
+                , optGhcStrict     = flagGhcStrict flags
+                }
+
+  mbool       <- getBuiltinName builtinBool
+  mtrue       <- getBuiltinName builtinTrue
+  mfalse      <- getBuiltinName builtinFalse
+  mlist       <- getBuiltinName builtinList
+  mnil        <- getBuiltinName builtinNil
+  mcons       <- getBuiltinName builtinCons
+  mmaybe      <- getBuiltinName builtinMaybe
+  mnothing    <- getBuiltinName builtinNothing
+  mjust       <- getBuiltinName builtinJust
+  mnat        <- getBuiltinName builtinNat
+  minteger    <- getBuiltinName builtinInteger
+  mword64     <- getBuiltinName builtinWord64
+  minf        <- getBuiltinName builtinInf
+  msharp      <- getBuiltinName builtinSharp
+  mflat       <- getBuiltinName builtinFlat
+  minterval   <- getBuiltinName builtinInterval
+  mizero      <- getBuiltinName builtinIZero
+  mione       <- getBuiltinName builtinIOne
+  misone      <- getBuiltinName builtinIsOne
+  mitisone    <- getBuiltinName builtinItIsOne
+  misone1     <- getBuiltinName builtinIsOne1
+  misone2     <- getBuiltinName builtinIsOne2
+  misoneempty <- getBuiltinName builtinIsOneEmpty
+  mpathp      <- getBuiltinName builtinPathP
+  msub        <- getBuiltinName builtinSub
+  msubin      <- getBuiltinName builtinSubIn
+  mid         <- getBuiltinName builtinId
+  mconid      <- getPrimitiveName' builtinConId
+
+  istcbuiltin <- do
+    builtins <- mapM getBuiltinName
+      [ builtinAgdaTCMReturn
+      , builtinAgdaTCMBind
+      , builtinAgdaTCMUnify
+      , builtinAgdaTCMTypeError
+      , builtinAgdaTCMInferType
+      , builtinAgdaTCMCheckType
+      , builtinAgdaTCMNormalise
+      , builtinAgdaTCMReduce
+      , builtinAgdaTCMCatchError
+      , builtinAgdaTCMQuoteTerm
+      , builtinAgdaTCMUnquoteTerm
+      , builtinAgdaTCMQuoteOmegaTerm
+      , builtinAgdaTCMGetContext
+      , builtinAgdaTCMExtendContext
+      , builtinAgdaTCMInContext
+      , builtinAgdaTCMFreshName
+      , builtinAgdaTCMDeclareDef
+      , builtinAgdaTCMDeclarePostulate
+      , builtinAgdaTCMDeclareData
+      , builtinAgdaTCMDefineData
+      , builtinAgdaTCMDefineFun
+      , builtinAgdaTCMGetType
+      , builtinAgdaTCMGetDefinition
+      , builtinAgdaTCMBlock
+      , builtinAgdaTCMCommit
+      , builtinAgdaTCMIsMacro
+      , builtinAgdaTCMWithNormalisation
+      , builtinAgdaTCMWithReconstructed
+      , builtinAgdaTCMWithExpandLast
+      , builtinAgdaTCMWithReduceDefs
+      , builtinAgdaTCMAskNormalisation
+      , builtinAgdaTCMAskReconstructed
+      , builtinAgdaTCMAskExpandLast
+      , builtinAgdaTCMAskReduceDefs
+      , builtinAgdaTCMFormatErrorParts
+      , builtinAgdaTCMDebugPrint
+      , builtinAgdaTCMNoConstraints
+      , builtinAgdaTCMRunSpeculative
+      , builtinAgdaTCMExec
+      , builtinAgdaTCMGetInstances
+      , builtinAgdaTCMPragmaForeign
+      , builtinAgdaTCMPragmaCompile
+      , builtinAgdaBlocker
+      , builtinAgdaBlockerAll
+      , builtinAgdaBlockerAny
+      , builtinAgdaBlockerMeta
+      ]
+    return $
+      flip HashSet.member $
+      HashSet.fromList $
+      catMaybes builtins
+
+  let defArity q = arity . defType <$> getConstInfo q
+  listArity <- traverse defArity mlist
+  maybeArity <- traverse defArity mmaybe
+
+  return $ GHCEnv
+    { ghcEnvOpts        = ghcOpts
+    , ghcEnvBool        = mbool
+    , ghcEnvTrue        = mtrue
+    , ghcEnvFalse       = mfalse
+    , ghcEnvMaybe       = mmaybe
+    , ghcEnvNothing     = mnothing
+    , ghcEnvJust        = mjust
+    , ghcEnvList        = mlist
+    , ghcEnvNil         = mnil
+    , ghcEnvCons        = mcons
+    , ghcEnvNat         = mnat
+    , ghcEnvInteger     = minteger
+    , ghcEnvWord64      = mword64
+    , ghcEnvInf         = minf
+    , ghcEnvSharp       = msharp
+    , ghcEnvFlat        = mflat
+    , ghcEnvInterval    = minterval
+    , ghcEnvIZero       = mizero
+    , ghcEnvIOne        = mione
+    , ghcEnvIsOne       = misone
+    , ghcEnvItIsOne     = mitisone
+    , ghcEnvIsOne1      = misone1
+    , ghcEnvIsOne2      = misone2
+    , ghcEnvIsOneEmpty  = misoneempty
+    , ghcEnvPathP       = mpathp
+    , ghcEnvSub         = msub
+    , ghcEnvSubIn       = msubin
+    , ghcEnvId          = mid
+    , ghcEnvConId       = mconid
+    , ghcEnvIsTCBuiltin = istcbuiltin
+    , ghcEnvListArity   = listArity
+    , ghcEnvMaybeArity  = maybeArity
+    }
+
+ghcPostCompile ::
+  GHCEnv -> IsMain -> Map TopLevelModuleName GHCModule -> TCM ()
+ghcPostCompile _cenv _isMain mods = do
+  -- FIXME: @curMName@ and @curIF@ are evil TCM state, but there does not appear to be
+  --------- another way to retrieve the compilation root ("main" module or interaction focused).
+  rootModuleName <- curMName
+  rootModule <- ifJust (Map.lookup rootModuleName mods) pure
+                $ genericError $ "Module " <> prettyShow rootModuleName <> " was not compiled!"
+  flip runReaderT rootModule $ do
+    copyRTEModules
+    callGHC
+
+--- Module compilation ---
+
+ghcPreModule
+  :: GHCEnv
+  -> IsMain      -- ^ Are we looking at the main module?
+  -> TopLevelModuleName
+  -> Maybe FilePath    -- ^ Path to the @.agdai@ file.
+  -> TCM (Recompile GHCModuleEnv GHCModule)
+                 -- ^ Could we confirm the existence of a main function?
+ghcPreModule cenv isMain m mifile =
+  (do let check = ifM uptodate noComp yesComp
+      cubical <- optCubical <$> pragmaOptions
+      case cubical of
+        -- Code that uses --cubical is not compiled.
+        Just CFull   -> noComp
+        Just CErased -> check
+        Nothing      -> check)
+    `runReaderT` GHCModuleEnv cenv (HsModuleEnv m (isMain == IsMain))
+  where
+    uptodate = case mifile of
+      Nothing -> pure False
+      Just ifile -> liftIO =<< isNewerThan <$> curOutFile <*> pure ifile
+    ifileDesc = fromMaybe "(memory)" mifile
+
+    noComp = do
+      reportSLn "compile.ghc" 2 .
+        (++ " : no compilation is needed.") . prettyShow =<< curMName
+      menv <- ask
+      mainDefs <- ifM curIsMainModule
+                         (mainFunctionDefs <$> curIF)
+                         (pure [])
+      return . Skip $ GHCModule menv mainDefs
+
+    yesComp = do
+      m   <- prettyShow <$> curMName
+      out <- curOutFile
+      alwaysReportSLn "compile.ghc" 1 $ repl [m, ifileDesc, out] "Compiling <<0>> in <<1>> to <<2>>"
+      asks Recompile
+
+ghcPostModule
+  :: GHCEnv
+  -> GHCModuleEnv
+  -> IsMain        -- ^ Are we looking at the main module?
+  -> TopLevelModuleName
+  -> [GHCDefinition]   -- ^ Compiled module content.
+  -> TCM GHCModule
+ghcPostModule _cenv menv _isMain _moduleName ghcDefs = do
+  builtinThings <- getsTC stBuiltinThings
+
+  -- Accumulate all of the modules, definitions, declarations, etc.
+  let (usedFloat, decls, defs, mainDefs, usedModules) = mconcat $
+        (\(GHCDefinition useFloat' decls' def' md' imps')
+         -> (useFloat', decls', [def'], maybeToList md', imps'))
+        <$> ghcDefs
+
+  let imps = mazRTEFloatImport usedFloat ++ imports builtinThings usedModules defs
+
+  i <- curIF
+
+  -- Get content of FOREIGN pragmas.
+  let (headerPragmas, hsImps, code) = foreignHaskell i
+
+  flip runReaderT menv $ do
+    hsModuleName <- curHsMod
+    writeModule $ HS.Module
+      hsModuleName
+      (map HS.OtherPragma headerPragmas)
+      imps
+      (map fakeDecl (hsImps ++ code) ++ decls)
+
+  return $ GHCModule menv mainDefs
+
+ghcCompileDef :: GHCEnv -> GHCModuleEnv -> IsMain -> Definition -> TCM GHCDefinition
+ghcCompileDef _cenv menv _isMain def = do
+  ((usesFloat, decls, mainFuncDef), (HsCompileState imps)) <-
+    definition def `runHsCompileT` menv
+  return $ GHCDefinition usesFloat decls def (checkedMainDef <$> mainFuncDef) imps
+
+-- | We do not erase types that have a 'HsData' pragma.
+--   This is to ensure a stable interface to third-party code.
+ghcMayEraseType :: QName -> TCM Bool
+ghcMayEraseType q = getHaskellPragma q <&> \case
+  -- Andreas, 2019-05-09, issue #3732.
+  -- We restrict this to 'HsData' since types like @Size@, @Level@
+  -- should be erased although they have a 'HsType' binding to the
+  -- Haskell unit type.
+  Just HsData{} -> False
+  _ -> True
+
+-- Compilation ------------------------------------------------------------
+
+imports ::
+  BuiltinThings PrimFun -> Set TopLevelModuleName -> [Definition] ->
+  [HS.ImportDecl]
+imports builtinThings usedModules defs = hsImps ++ imps where
+  hsImps :: [HS.ImportDecl]
+  hsImps = [unqualRTE, decl mazRTE]
+
+  unqualRTE :: HS.ImportDecl
+  unqualRTE = HS.ImportDecl mazRTE False $ Just $
+              (False, [ HS.IVar $ HS.Ident x
+                      | x <- [mazCoerceName, mazErasedName, mazAnyTypeName] ++
+                             map treelessPrimName rtePrims ])
+
+  rtePrims = [T.PAdd, T.PSub, T.PMul, T.PQuot, T.PRem, T.PGeq, T.PLt, T.PEqI,
+              T.PAdd64, T.PSub64, T.PMul64, T.PQuot64, T.PRem64, T.PLt64, T.PEq64,
+              T.PITo64, T.P64ToI] -- Excludes T.PEqF, which is defined in MAlonzo.RTE.Float
+
+  imps :: [HS.ImportDecl]
+  imps = map decl $ uniq $ importsForPrim builtinThings defs ++ map mazMod mnames
+
+  decl :: HS.ModuleName -> HS.ImportDecl
+  decl m = HS.ImportDecl m True Nothing
+
+  mnames :: [TopLevelModuleName]
+  mnames = Set.elems usedModules
+
+  uniq :: [HS.ModuleName] -> [HS.ModuleName]
+  uniq = List.map List1.head . List1.group . List.sort
+
+-- Should we import MAlonzo.RTE.Float
+newtype UsesFloat = UsesFloat Bool deriving (Eq, Show)
+
+pattern YesFloat :: UsesFloat
+pattern YesFloat = UsesFloat True
+
+pattern NoFloat :: UsesFloat
+pattern NoFloat = UsesFloat False
+
+instance Semigroup UsesFloat where
+  UsesFloat a <> UsesFloat b = UsesFloat (a || b)
+
+instance Monoid UsesFloat where
+  mempty  = NoFloat
+  mappend = (<>)
+
+mazRTEFloatImport :: UsesFloat -> [HS.ImportDecl]
+mazRTEFloatImport (UsesFloat b) = [ HS.ImportDecl mazRTEFloat True Nothing | b ]
+
+--------------------------------------------------
+-- Main compiling clauses
+--------------------------------------------------
+
+definition :: Definition -> HsCompileM (UsesFloat, [HS.Decl], Maybe CheckedMainFunctionDef)
+-- ignore irrelevant definitions
+{- Andreas, 2012-10-02: Invariant no longer holds
+definition kit (Defn NonStrict _ _  _ _ _ _ _ _) = __IMPOSSIBLE__
+-}
+definition Defn{defArgInfo = info, defName = q} | not $ usableModality info = do
+  reportSDoc "compile.ghc.definition" 10 $
+    ("Not compiling" <+> prettyTCM q) <> "."
+  return (mempty, mempty, Nothing)
+definition def@Defn{defName = q, defType = ty, theDef = d} = do
+  reportSDoc "compile.ghc.definition" 10 $ vcat
+    [ ("Compiling" <+> prettyTCM q) <> ":"
+    , nest 2 $ pretty d
+    ]
+  pragma <- liftTCM $ getHaskellPragma q
+  env <- askGHCEnv
+  let is p = Just q == p env
+  typeCheckedMainDef <- checkTypeOfMain def
+  let mainDecl = maybeToList $ checkedMainDecl <$> typeCheckedMainDef
+  let retDecls ds = return (mempty, ds)
+  (uncurry (,,typeCheckedMainDef)) . second ((mainDecl ++) . infodecl q) <$>
+    case d of
+
+      _ | Just (HsDefn r hs) <- pragma -> setCurrentRange r $
+          if is ghcEnvFlat
+          then genericError
+                "\"COMPILE GHC\" pragmas are not allowed for the FLAT builtin."
+          else do
+            -- Make sure we have imports for all names mentioned in the type.
+            hsty <- haskellType q
+            mapM_ (`xqual` HS.Ident "_") (namesIn ty :: Set QName)
+
+          -- Check that the function isn't INLINE (since that will make this
+          -- definition pointless).
+            inline <- (^. funInline) . theDef <$> getConstInfo q
+            when inline $ warning $ UselessInline q
+
+            retDecls $ fbWithType hsty (fakeExp hs)
+
+      -- Compiling Bool
+      Datatype{} | is ghcEnvBool -> do
+        sequence_ [primTrue, primFalse] -- Just to get the proper error for missing TRUE/FALSE
+        let d = dname q
+        Just true  <- getBuiltinName builtinTrue
+        Just false <- getBuiltinName builtinFalse
+        cs <- mapM (compiledcondecl Nothing) [false, true]
+        retDecls $ [ compiledTypeSynonym q "Bool" 0
+                   , HS.FunBind [HS.Match d [] (HS.UnGuardedRhs HS.unit_con) emptyBinds] ] ++
+                   cs
+
+      -- Compiling List
+      Datatype{ dataPars = np } | is ghcEnvList -> do
+        sequence_ [primNil, primCons] -- Just to get the proper error for missing NIL/CONS
+        caseMaybe pragma (return ()) $ \ p -> setCurrentRange p $ warning . GenericWarning =<< do
+          fsep $ pwords "Ignoring GHC pragma for builtin lists; they always compile to Haskell lists."
+        let d = dname q
+            t = unqhname TypeK q
+        Just nil  <- getBuiltinName builtinNil
+        Just cons <- getBuiltinName builtinCons
+        let vars f n = map (f . ihname A) [0 .. n - 1]
+        cs <- mapM (compiledcondecl Nothing) [nil, cons]
+        retDecls $ [ HS.TypeDecl t (vars HS.UnkindedVar (np - 1)) (HS.FakeType "[]")
+                   , HS.FunBind [HS.Match d (vars HS.PVar np) (HS.UnGuardedRhs HS.unit_con) emptyBinds] ] ++
+                   cs
+
+      -- Compiling Maybe
+      Datatype{ dataPars = np } | is ghcEnvMaybe -> do
+        sequence_ [primNothing, primJust] -- Just to get the proper error for missing NOTHING/JUST
+        caseMaybe pragma (return ()) $ \ p -> setCurrentRange p $ warning . GenericWarning =<< do
+          fsep $ pwords "Ignoring GHC pragma for builtin maybe; they always compile to Haskell lists."
+        let d = dname q
+            t = unqhname TypeK q
+        Just nothing <- getBuiltinName builtinNothing
+        Just just    <- getBuiltinName builtinJust
+        let vars f n = map (f . ihname A) [0 .. n - 1]
+        cs <- mapM (compiledcondecl Nothing) [nothing, just]
+        retDecls $ [ HS.TypeDecl t (vars HS.UnkindedVar (np - 1)) (HS.FakeType "Maybe")
+                   , HS.FunBind [HS.Match d (vars HS.PVar np) (HS.UnGuardedRhs HS.unit_con) emptyBinds] ] ++
+                   cs
+
+      -- Compiling Inf
+      _ | is ghcEnvInf -> do
+        _ <- primSharp -- To get a proper error for missing SHARP.
+        Just sharp <- getBuiltinName builtinSharp
+        sharpC     <- (compiledcondecl Nothing) sharp
+        let d   = dname q
+            err = "No term-level implementation of the INFINITY builtin."
+        retDecls $ [ compiledTypeSynonym q "MAlonzo.RTE.Infinity" 2
+                   , HS.FunBind [HS.Match d [HS.PVar (ihname A 0)]
+                       (HS.UnGuardedRhs (HS.FakeExp ("error " ++ show err)))
+                       emptyBinds]
+                   , sharpC
+                   ]
+
+      -- The interval is compiled as the type of booleans: 0 is
+      -- compiled as False and 1 as True.
+      Axiom{} | is ghcEnvInterval -> do
+        sequence_ [primIZero, primIOne]
+        Just i0 <- getBuiltinName builtinIZero
+        Just i1 <- getBuiltinName builtinIOne
+        cs      <- mapM (compiledcondecl (Just 0)) [i0, i1]
+        retDecls $
+          [ compiledTypeSynonym q "Bool" 0
+          , HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs HS.unit_con) emptyBinds]
+          ] ++
+          cs
+
+      -- IsOne is compiled as the constant function to the unit type.
+      -- Partial/PartialP are compiled as functions from the unit type
+      -- to the underlying type.
+      Axiom{} | is ghcEnvIsOne -> do
+        retDecls $
+          [ HS.TypeDecl (unqhname TypeK q) [HS.UnkindedVar (ihname A 0)]
+              (HS.FakeType "()")
+          , HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs HS.unit_con) emptyBinds]
+          ]
+
+      -- itIsOne.
+      Axiom{} | is ghcEnvItIsOne -> do
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs HS.unit_con) emptyBinds]
+          ]
+
+      -- IsOne1/IsOne2.
+      Axiom{} | is ghcEnvIsOne1 || is ghcEnvIsOne2 -> do
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ _ _ -> ()"))
+                 emptyBinds]
+          ]
+
+      -- isOneEmpty.
+      Axiom{} | is ghcEnvIsOneEmpty -> do
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ x _ -> x ()"))
+                 emptyBinds]
+          ]
+
+      -- PathP is compiled as a function from the interval (booleans)
+      -- to the underlying type.
+      Axiom{} | is ghcEnvPathP -> do
+        sequence_ [primInterval]
+        Just int <- getBuiltinName builtinInterval
+        int      <- xhqn TypeK int
+        retDecls $
+          [ HS.TypeDecl (unqhname TypeK q)
+              [HS.UnkindedVar (ihname A i) | i <- [0..3]]
+              (HS.TyFun (HS.TyCon int) mazAnyType)
+          , HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ _ _ _ -> ()"))
+                 emptyBinds]
+          ]
+
+      -- Sub is compiled as the underlying type.
+      Axiom{} | is ghcEnvSub -> do
+        retDecls $
+          [ HS.TypeDecl (unqhname TypeK q)
+              [HS.UnkindedVar (ihname A i) | i <- [0..3]]
+              (HS.TyVar (ihname A 1))
+          , HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ _ _ _ -> ()"))
+                 emptyBinds]
+          ]
+
+      -- subIn.
+      Axiom{} | is ghcEnvSubIn -> do
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ _ _ x -> x"))
+                 emptyBinds]
+          ]
+
+      -- Id x y is compiled as a pair of a boolean and whatever
+      -- Path x y is compiled to.
+      Datatype{} | is ghcEnvId -> do
+        sequence_ [primInterval]
+        Just int <- getBuiltinName builtinInterval
+        int      <- xhqn TypeK int
+        -- re  #3733: implement reflId
+        retDecls $
+          [ HS.TypeDecl (unqhname TypeK q)
+              [] -- [HS.UnkindedVar (ihname A i) | i <- [0..3]]
+              (HS.TyApp (HS.FakeType "(,) Bool")
+                 (HS.TyFun (HS.TyCon int) mazAnyType))
+          , HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp "\\_ _ _ _ -> ()"))
+                 emptyBinds]
+          ]
+
+      -- conid.
+      Primitive{} | is ghcEnvConId -> do
+        strict <- optGhcStrictData <$> askGhcOpts
+        let var = applyWhen strict HS.PBangPat . HS.PVar
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q)
+                 [ var (ihname A i) | i <- [0..1] ]
+                 (HS.UnGuardedRhs $
+                  HS.App (HS.App (HS.FakeExp "(,)")
+                            (HS.Var (HS.UnQual (ihname A 0))))
+                    (HS.Var (HS.UnQual (ihname A 1))))
+                 emptyBinds]
+          ]
+
+      -- TC builtins are compiled to erased, which is an ∞-ary
+      -- function.
+      Axiom{} | ghcEnvIsTCBuiltin env q -> do
+        retDecls $
+          [ HS.FunBind
+              [HS.Match (dname q) []
+                 (HS.UnGuardedRhs (HS.FakeExp mazErasedName))
+                 emptyBinds]
+          ]
+
+      DataOrRecSig{} -> __IMPOSSIBLE__
+
+      Axiom{} -> do
+        ar <- liftTCM $ typeArity ty
+        retDecls $ [ compiledTypeSynonym q ty ar | Just (HsType r ty) <- [pragma] ] ++
+                   fb axiomErr
+      Primitive{ primName = s } -> (mempty,) . fb <$> (liftTCM . primBody) s
+
+      PrimitiveSort{} -> retDecls []
+
+      Function{} -> function pragma $ functionViaTreeless q
+
+      Datatype{ dataPars = np, dataIxs = ni, dataClause = cl
+              , dataPathCons = pcs
+              } | Just hsdata@(HsData r ty hsCons) <- pragma ->
+        setCurrentRange r $ do
+        reportSDoc "compile.ghc.definition" 40 $ hsep $
+          [ "Compiling data type with COMPILE pragma ...", pretty hsdata ]
+        liftTCM $ computeErasedConstructorArgs q
+        cs <- liftTCM $ getNotErasedConstructors q
+        ccscov <- constructorCoverageCode q (np + ni) cs ty hsCons
+        cds <- mapM (compiledcondecl Nothing) cs
+        let result = concat $
+              [ tvaldecl q Inductive (np + ni) [] (Just __IMPOSSIBLE__)
+              , [ compiledTypeSynonym q ty np ]
+              , cds
+              , ccscov
+              ]
+        retDecls result
+      Datatype{ dataPars = np, dataIxs = ni, dataClause = cl
+              , dataPathCons = pcs
+              } -> do
+        liftTCM $ computeErasedConstructorArgs q
+        cs <- liftTCM $ getNotErasedConstructors q
+        cds <- mapM (flip condecl Inductive) cs
+        retDecls $ tvaldecl q Inductive (np + ni) cds cl
+      Constructor{} -> retDecls []
+      GeneralizableVar{} -> retDecls []
+      Record{ recPars = np, recClause = cl, recConHead = con,
+              recInduction = ind } ->
+        let -- Non-recursive record types are treated as being
+            -- inductive.
+            inductionKind = fromMaybe Inductive ind
+        in case pragma of
+          Just (HsData r ty hsCons) -> setCurrentRange r $ do
+            let cs = [conName con]
+            liftTCM $ computeErasedConstructorArgs q
+            ccscov <- constructorCoverageCode q np cs ty hsCons
+            cds <- mapM (compiledcondecl Nothing) cs
+            retDecls $
+              tvaldecl q inductionKind np [] (Just __IMPOSSIBLE__) ++
+              [compiledTypeSynonym q ty np] ++ cds ++ ccscov
+          _ -> do
+            liftTCM $ computeErasedConstructorArgs q
+            cd <- condecl (conName con) inductionKind
+            retDecls $ tvaldecl q inductionKind (I.arity ty) [cd] cl
+      AbstractDefn{} -> __IMPOSSIBLE__
+  where
+  function :: Maybe HaskellPragma -> HsCompileM (UsesFloat, [HS.Decl]) -> HsCompileM (UsesFloat, [HS.Decl])
+  function mhe fun = do
+    (imp, ccls) <- fun
+    case mhe of
+      Just (HsExport r name) -> setCurrentRange r $ do
+        env <- askGHCEnv
+        if Just q == ghcEnvFlat env
+        then genericError
+              "\"COMPILE GHC as\" pragmas are not allowed for the FLAT builtin."
+        else do
+          t <- setCurrentRange r $ haskellType q
+          let tsig :: HS.Decl
+              tsig = HS.TypeSig [HS.Ident name] t
+
+              def :: HS.Decl
+              def = HS.FunBind [HS.Match (HS.Ident name) [] (HS.UnGuardedRhs (hsCoerce $ hsVarUQ $ dname q)) emptyBinds]
+          return (imp, [tsig,def] ++ ccls)
+      _ -> return (imp, ccls)
+
+  functionViaTreeless :: QName -> HsCompileM (UsesFloat, [HS.Decl])
+  functionViaTreeless q = do
+    strict <- optGhcStrict <$> askGhcOpts
+    let eval = if strict then EagerEvaluation else LazyEvaluation
+    caseMaybeM (liftTCM $ toTreeless eval q) (pure mempty) $ \ treeless -> do
+
+      used <- fromMaybe [] <$> getCompiledArgUse q
+      let dostrip = ArgUnused `elem` used
+
+      -- Compute the type approximation
+      def <- getConstInfo q
+      (argTypes0, resType) <- hsTelApproximation $ defType def
+      let pars = case theDef def of
+                   Function{ funProjection = Right Projection{ projIndex = i } } | i > 0 -> i - 1
+                   _ -> 0
+          argTypes  = drop pars argTypes0
+          argTypesS = filterUsed used argTypes
+
+      (e, useFloat) <- if dostrip then closedTerm (stripUnusedArguments used treeless)
+                                  else closedTerm treeless
+      let (ps, b) = lamView e
+          lamView e =
+            case e of
+              HS.Lambda ps b -> (ps, b)
+              b              -> ([], b)
+
+          tydecl  f ts t = HS.TypeSig [f] (foldr HS.TyFun t ts)
+          funbind f ps b = HS.FunBind [HS.Match f ps (HS.UnGuardedRhs b) emptyBinds]
+          tyfunbind f ts t ps b =
+            let ts' = ts ++ (replicate (length ps - length ts) mazAnyType)
+            in [tydecl f ts' t, funbind f ps b]
+
+      -- The definition of the non-stripped function
+      (ps0, _) <- lamView <$> closedTerm_ (foldr ($) T.TErased $ replicate (length used) T.TLam)
+      let b0 = foldl HS.App (hsVarUQ $ duname q) [ hsVarUQ x | (~(HS.PVar x), ArgUsed) <- zip ps0 used ]
+          ps0' = zipWith (\p u -> case u of
+                                    ArgUsed   -> p
+                                    ArgUnused -> HS.PIrrPat p)
+                   ps0 used
+
+      return (useFloat,
+              if dostrip
+                then tyfunbind (dname q) argTypes resType ps0' b0 ++
+                     tyfunbind (duname q) argTypesS resType ps b
+                else tyfunbind (dname q) argTypes resType ps b)
+
+  fbWithType :: HS.Type -> HS.Exp -> [HS.Decl]
+  fbWithType ty e =
+    HS.TypeSig [dname q] ty : fb e
+
+  fb :: HS.Exp -> [HS.Decl]
+  fb e  = [HS.FunBind [HS.Match (dname q) []
+                                (HS.UnGuardedRhs e) emptyBinds]]
+
+  axiomErr :: HS.Exp
+  axiomErr = rtmError $ Text.pack $ "postulate evaluated: " ++ prettyShow q
+
+constructorCoverageCode :: QName -> Int -> [QName] -> HaskellType -> [HaskellCode] -> HsCompileM [HS.Decl]
+constructorCoverageCode q np cs hsTy hsCons = do
+  liftTCM $ checkConstructorCount q cs hsCons
+  ifM (liftTCM $ noCheckCover q) (return []) $ do
+    ccs <- List.concat <$> zipWithM checkConstructorType cs hsCons
+    cov <- liftTCM $ checkCover q hsTy np cs hsCons
+    return $ ccs ++ cov
+
+-- | Environment for naming of local variables.
+--   Invariant: @reverse ccCxt ++ ccNameSupply@
+data CCEnv = CCEnv
+  { _ccNameSupply :: NameSupply  -- ^ Supply of fresh names
+  , _ccContext    :: CCContext   -- ^ Names currently in scope
+  }
+
+type NameSupply = [HS.Name]
+type CCContext  = [HS.Name]
+
+ccNameSupply :: Lens' CCEnv NameSupply
+ccNameSupply f e =  (\ ns' -> e { _ccNameSupply = ns' }) <$> f (_ccNameSupply e)
+
+ccContext :: Lens' CCEnv CCContext
+ccContext f e = (\ cxt -> e { _ccContext = cxt }) <$> f (_ccContext e)
+
+-- | Initial environment for expression generation.
+initCCEnv :: CCEnv
+initCCEnv = CCEnv
+  { _ccNameSupply = map (ihname V) [0..]  -- DON'T CHANGE THESE NAMES!
+  , _ccContext    = []
+  }
+
+-- | Term variables are de Bruijn indices.
+lookupIndex :: Int -> CCContext -> HS.Name
+lookupIndex i xs = fromMaybe __IMPOSSIBLE__ $ xs !!! i
+
+-- | Constructor coverage monad transformer
+type CCT m = ReaderT CCEnv (WriterT UsesFloat (HsCompileT m))
+
+-- | Constructor coverage monad
+type CC = CCT TCM
+
+liftCC :: Monad m => HsCompileT m a -> CCT m a
+liftCC = lift . lift
+
+freshNames :: Monad m => Int -> ([HS.Name] -> CCT m a) -> CCT m a
+freshNames n _ | n < 0 = __IMPOSSIBLE__
+freshNames n cont = do
+  (xs, rest) <- splitAt n <$> view ccNameSupply
+  local (over ccNameSupply (const rest)) $ cont xs
+
+-- | Introduce n variables into the context.
+intros :: Monad m => Int -> ([HS.Name] -> CCT m a) -> CCT m a
+intros n cont = freshNames n $ \xs ->
+  local (over ccContext (reverse xs ++)) $ cont xs
+
+checkConstructorType :: QName -> HaskellCode -> HsCompileM [HS.Decl]
+checkConstructorType q hs = do
+  ty <- haskellType q
+  return [ HS.TypeSig [unqhname CheckK q] ty
+         , HS.FunBind [HS.Match (unqhname CheckK q) []
+                                (HS.UnGuardedRhs $ fakeExp hs) emptyBinds]
+         ]
+
+checkCover :: HasConstInfo m => QName -> HaskellType -> Nat -> [QName] -> [HaskellCode] -> m [HS.Decl]
+checkCover q ty n cs hsCons = do
+  let tvs = [ "a" ++ show i | i <- [1..n] ]
+      makeClause c hsc = do
+        a <- erasedArity c
+        let pat = HS.PApp (HS.UnQual $ HS.Ident hsc) $ replicate a HS.PWildCard
+        return $ HS.Alt pat (HS.UnGuardedRhs $ HS.unit_con) emptyBinds
+
+  cs <- zipWithM makeClause cs hsCons
+  let rhs = HS.Case (HS.Var $ HS.UnQual $ HS.Ident "x") cs
+
+  return [ HS.TypeSig [unqhname CoverK q] $ fakeType $ unwords (ty : tvs) ++ " -> ()"
+         , HS.FunBind [HS.Match (unqhname CoverK q) [HS.PVar $ HS.Ident "x"]
+                                (HS.UnGuardedRhs rhs) emptyBinds]
+         ]
+
+closedTerm_ :: T.TTerm -> HsCompileM HS.Exp
+closedTerm_ t = fst <$> closedTerm t
+
+closedTerm :: T.TTerm -> HsCompileM (HS.Exp, UsesFloat)
+closedTerm v = do
+  v <- liftTCM $ addCoercions v
+  runWriterT (term v `runReaderT` initCCEnv)
+
+-- Translate case on bool to if
+mkIf :: T.TTerm -> CC T.TTerm
+mkIf t@(TCase e _ d [TACon c1 0 b1, TACon c2 0 b2]) | T.isUnreachable d = do
+  env <- liftCC askGHCEnv
+  let isTrue  c = Just c == ghcEnvTrue  env
+      isFalse c = Just c == ghcEnvFalse env
+  if | isTrue c1, isFalse c2 -> return $ T.tIfThenElse (TCoerce $ TVar e) b1 b2
+     | isTrue c2, isFalse c1 -> return $ T.tIfThenElse (TCoerce $ TVar e) b2 b1
+     | otherwise             -> return t
+mkIf t = return t
+
+-- | Extract Agda term to Haskell expression.
+--   Erased arguments are extracted as @()@.
+--   Types are extracted as @()@.
+term :: T.TTerm -> CC HS.Exp
+term tm0 = mkIf tm0 >>= \ tm0 -> do
+  let ((hasCoerce, t), ts) = coerceAppView tm0
+  -- let (t0, ts)       = tAppView tm0
+  -- let (hasCoerce, t) = coerceView t0
+  let coe            = applyWhen hasCoerce hsCoerce
+  case (t, ts) of
+    (T.TPrim T.PIf, [c, x, y]) -> coe <$> do HS.If <$> term c <*> term x <*> term y
+
+    (T.TDef f, ts) -> do
+      used <- liftCC $ fromMaybe [] <$> getCompiledArgUse f
+      -- #2248: no unused argument pruning for COMPILE'd functions
+      isCompiled <- liftTCM $ isJust <$> getHaskellPragma f
+      let given   = length ts
+          needed  = length used
+          missing = drop given used
+      if not isCompiled && ArgUnused `elem` used
+        then if ArgUnused `elem` missing then term (etaExpand (needed - given) tm0) else do
+          f <- liftCC $ HS.Var <$> xhqn (FunK NoUnused) f
+                                   -- use stripped function
+          -- Andreas, 2019-11-07, issue #4169.
+          -- Insert coercion unconditionally as erasure of arguments
+          -- that are matched upon might remove the unfolding of codomain types.
+          -- (Hard to explain, see test/Compiler/simple/Issue4169.)
+          hsCoerce f `apps` filterUsed used ts
+        else do
+          f <- liftCC $ HS.Var <$> xhqn (FunK PossiblyUnused) f
+                                   -- use original (non-stripped) function
+          coe f `apps` ts
+
+    (T.TCon c, ts) -> do
+      erased  <- liftCC $ getErasedConArgs c
+      let missing = drop (length ts) erased
+          notErased = not
+      if all notErased missing
+        then do
+                f <- liftCC $ HS.Con <$> conhqn c
+                hsCoerce f `apps` [ t | (t, False) <- zip ts erased ]
+        else do
+                let n = length missing
+                unless (n >= 1) __IMPOSSIBLE__  -- We will add at least on TLam, not getting a busy loop here.
+                term $ etaExpand (length missing) tm0
+
+    -- Other kind of application: fall back to apps.
+    (t, ts) -> noApplication t >>= \ t' -> coe t' `apps` ts
+  where
+  apps = foldM (\ h a -> HS.App h <$> term a)
+  etaExpand n t = mkTLam n $ raise n t `T.mkTApp` map T.TVar (downFrom n)
+
+-- | Translate a non-application, non-coercion, non-constructor, non-definition term.
+noApplication :: T.TTerm -> CC HS.Exp
+noApplication = \case
+  T.TApp{}    -> __IMPOSSIBLE__
+  T.TCoerce{} -> __IMPOSSIBLE__
+  T.TCon{}    -> __IMPOSSIBLE__
+  T.TDef{}    -> __IMPOSSIBLE__
+
+  T.TVar i    -> hsVarUQ . lookupIndex i <$> view ccContext
+  T.TLam t    -> intros 1 $ \ [x] -> hsLambda [HS.PVar x] <$> term t
+
+  T.TLet t1 t2 -> do
+    t1' <- term t1
+    intros 1 $ \[x] -> do
+      hsLet x t1' . hsCoerce <$> term t2
+
+  T.TCase sc ct def alts -> do
+    sc'   <- term $ T.TVar sc
+    alts' <- traverse (alt sc) alts
+    def'  <- term def
+    let defAlt = HS.Alt HS.PWildCard (HS.UnGuardedRhs def') emptyBinds
+    return $ HS.Case (hsCoerce sc') (alts' ++ [defAlt])
+
+  T.TLit l    -> literal l
+  T.TPrim p   -> return $ compilePrim p
+  T.TUnit     -> return $ HS.unit_con
+  T.TSort     -> return $ HS.unit_con
+  T.TErased   -> return $ hsVarUQ $ HS.Ident mazErasedName
+  T.TError e  -> return $ case e of
+    T.TUnreachable -> rtmUnreachableError
+    T.TMeta s      -> rtmHole s
+
+hsCoerce :: HS.Exp -> HS.Exp
+hsCoerce t = HS.App mazCoerce t
+
+compilePrim :: T.TPrim -> HS.Exp
+compilePrim s = HS.Var $ hsName $ treelessPrimName s
+
+alt :: Int -> T.TAlt -> CC HS.Alt
+alt sc a = do
+  case a of
+    T.TACon {T.aCon = c} -> do
+      intros (T.aArity a) $ \ xs -> do
+        erased <- liftCC $ getErasedConArgs c
+        env    <- liftCC askGHCEnv
+        hConNm <-
+          if | Just c == ghcEnvNil env ->
+               return $ HS.UnQual $ HS.Ident "[]"
+             | Just c == ghcEnvCons env ->
+               return $ HS.UnQual $ HS.Symbol ":"
+             | otherwise -> liftCC $ conhqn c
+        mkAlt (HS.PApp hConNm $ [HS.PVar x | (x, False) <- zip xs erased])
+    T.TAGuard g b -> do
+      g <- term g
+      b <- term b
+      return $ HS.Alt HS.PWildCard
+                      (HS.GuardedRhss [HS.GuardedRhs [HS.Qualifier g] b])
+                      emptyBinds
+    T.TALit { T.aLit = LitQName q } -> mkAlt (litqnamepat q)
+    T.TALit { T.aLit = LitMeta _ m } -> mkAlt (litmetapat m)
+    T.TALit { T.aLit = l@LitFloat{}, T.aBody = b } -> do
+      tell YesFloat
+      l <- literal l
+      mkGuarded (treelessPrimName T.PEqF) l b
+    T.TALit { T.aLit = LitString s , T.aBody = b } -> mkGuarded "(==)" (litString s) b
+    T.TALit {} -> mkAlt (HS.PLit $ hslit $ T.aLit a)
+  where
+    mkGuarded eq lit b = do
+      b  <- term b
+      let varName = HS.Ident "l" -- only used locally in the guard
+          pv = HS.PVar varName
+          v  = hsVarUQ varName
+          guard =
+            HS.Var (HS.UnQual (HS.Ident eq)) `HS.App`
+              v `HS.App` lit
+      return $ HS.Alt pv
+                      (HS.GuardedRhss [HS.GuardedRhs [HS.Qualifier guard] b])
+                      emptyBinds
+
+    mkAlt :: HS.Pat -> CC HS.Alt
+    mkAlt pat = do
+        body' <- term $ T.aBody a
+        let body'' = case body' of
+                       HS.Lambda{} -> hsCoerce body'
+                       _           -> body'
+        return $ HS.Alt pat (HS.UnGuardedRhs body'') emptyBinds
+
+literal :: forall m. Monad m => Literal -> CCT m HS.Exp
+literal l = case l of
+  LitNat    _   -> return $ typed "Integer"
+  LitWord64 _   -> return $ typed "MAlonzo.RTE.Word64"
+  LitFloat  x   -> floatExp x "Double"
+  LitQName  x   -> return $ litqname x
+  LitString s   -> return $ litString s
+  LitMeta _ m   ->
+    return $ HS.FakeExp "(,)" `HS.App`
+             hsTypedInt (metaId m) `HS.App`
+             (hsTypedInt (moduleNameHash $ metaModule m))
+  _             -> return $ l'
+  where
+    l'    = HS.Lit $ hslit l
+    typed = HS.ExpTypeSig l' . HS.TyCon . rtmQual
+
+    -- ASR (2016-09-14): See Issue #2169.
+    -- Ulf, 2016-09-28: and #2218.
+    floatExp :: Double -> String -> CCT m HS.Exp
+    floatExp x s
+      | isPosInf  x = rte "positiveInfinity"
+      | isNegInf  x = rte "negativeInfinity"
+      | isNegZero x = rte "negativeZero"
+      | isNaN     x = rte "nan"
+      | otherwise   = return $ typed s
+      where
+        rte s = do tell YesFloat; return $ HS.Var $ HS.Qual mazRTEFloat $ HS.Ident s
+
+hslit :: Literal -> HS.Literal
+hslit = \case
+  LitNat    x -> HS.Int    x
+  LitWord64 x -> HS.Int    (fromIntegral x)
+  LitFloat  x -> HS.Frac   (toRational x)
+  LitChar   x -> HS.Char   x
+  LitQName  x -> __IMPOSSIBLE__
+  LitString _ -> __IMPOSSIBLE__
+  LitMeta{}   -> __IMPOSSIBLE__
+
+litString :: Text -> HS.Exp
+litString s = HS.Ann (HS.Lit (HS.String s))
+                     (HS.TyCon (HS.Qual (HS.ModuleName "Data.Text") (HS.Ident "Text")))
+
+litqname :: QName -> HS.Exp
+litqname x =
+  rteCon "QName" `apps`
+  [ hsTypedInt n
+  , hsTypedInt m
+  , HS.Lit $ HS.String $ Text.pack $ prettyShow x
+  , rteCon "Fixity" `apps`
+    [ litAssoc (fixityAssoc fx)
+    , litPrec  (fixityLevel fx)
+    ]
+  ]
+  where
+    apps = foldl HS.App
+    rteCon name = HS.Con $ HS.Qual mazRTE $ HS.Ident name
+    NameId n (ModuleNameHash m) = nameId $ qnameName x
+    fx = theFixity $ nameFixity $ qnameName x
+
+    litAssoc NonAssoc   = rteCon "NonAssoc"
+    litAssoc LeftAssoc  = rteCon "LeftAssoc"
+    litAssoc RightAssoc = rteCon "RightAssoc"
+
+    litPrec Unrelated   = rteCon "Unrelated"
+    litPrec (Related l) = rteCon "Related" `HS.App` hsTypedDouble l
+
+litqnamepat :: QName -> HS.Pat
+litqnamepat x =
+  HS.PApp (HS.Qual mazRTE $ HS.Ident "QName")
+          [ HS.PLit (HS.Int $ fromIntegral n)
+          , HS.PLit (HS.Int $ fromIntegral m)
+          , HS.PWildCard, HS.PWildCard ]
+  where
+    NameId n (ModuleNameHash m) = nameId $ qnameName x
+
+litmetapat :: MetaId -> HS.Pat
+litmetapat (MetaId m h) =
+  HS.PApp (hsName "(,)")
+          [ HS.PLit (HS.Int $ fromIntegral m)
+          , HS.PLit (HS.Int $ fromIntegral $ moduleNameHash h) ]
+
+condecl :: QName -> Induction -> HsCompileM HS.ConDecl
+condecl q _ind = do
+  opts <- askGhcOpts
+  def <- getConstInfo q
+  let Constructor{ conPars = np, conSrcCon, conErased = erased } = theDef def
+  (argTypes0, _) <- hsTelApproximation (defType def)
+  let strict     = if conInductive conSrcCon == Inductive &&
+                      optGhcStrictData opts
+                   then HS.Strict
+                   else HS.Lazy
+      argTypes   = [ (Just strict, t)
+                   | (t, False) <- zip (drop np argTypes0)
+                                       (fromMaybe [] erased ++ repeat False)
+                   ]
+  return $ HS.ConDecl (unqhname ConK q) argTypes
+
+compiledcondecl
+  :: Maybe Nat  -- ^ The constructor's arity (after erasure).
+  -> QName -> HsCompileM HS.Decl
+compiledcondecl mar q = do
+  ar <- case mar of
+    Nothing -> liftTCM $ erasedArity q
+    Just ar -> return ar
+  hsCon <- fromMaybe __IMPOSSIBLE__ <$> getHaskellConstructor q
+  let patVars = map (HS.PVar . ihname A) [0 .. ar - 1]
+  return $ HS.PatSyn (HS.PApp (HS.UnQual $ unqhname ConK q) patVars)
+             (HS.PApp (hsName hsCon) patVars)
+
+compiledTypeSynonym :: QName -> String -> Nat -> HS.Decl
+compiledTypeSynonym q hsT arity =
+  HS.TypeDecl (unqhname TypeK q) (map HS.UnkindedVar vs)
+              (foldl HS.TyApp (HS.FakeType hsT) $ map HS.TyVar vs)
+  where
+    vs = [ ihname A i | i <- [0 .. arity - 1]]
+
+tvaldecl :: QName
+         -> Induction
+            -- ^ Is the type inductive or coinductive?
+         -> Nat -> [HS.ConDecl] -> Maybe Clause -> [HS.Decl]
+tvaldecl q ind npar cds cl =
+  HS.FunBind [HS.Match vn pvs (HS.UnGuardedRhs HS.unit_con) emptyBinds] :
+  maybe [HS.DataDecl kind tn [] cds' []]
+        (const []) cl
+  where
+  (tn, vn) = (unqhname TypeK q, dname q)
+  pvs = [ HS.PVar $ ihname A i | i <- [0 .. npar - 1]]
+
+  -- Inductive data types consisting of a single constructor with a
+  -- single argument are translated into newtypes.
+  (kind, cds') = case (ind, cds) of
+    (Inductive, [HS.ConDecl c [(_, t)]]) ->
+      (HS.NewType, [HS.ConDecl c [(Nothing, t)]])
+      -- The strictness annotations are removed for newtype
+      -- constructors.
+    _ -> (HS.DataType, cds)
+
+infodecl :: QName -> [HS.Decl] -> [HS.Decl]
+infodecl _ [] = []
+infodecl q ds = HS.Comment (prettyShow q) : ds
+
+--------------------------------------------------
+-- Writing out a haskell module
+--------------------------------------------------
+
+type MonadGHCIO m = (MonadIO m, ReadGHCOpts m)
+
+copyRTEModules :: MonadGHCIO m => m ()
+copyRTEModules = do
+  dataDir <- liftIO getDataDir
+  let srcDir = dataDir </> "MAlonzo" </> "src"
+  dstDir <- optGhcCompileDir <$> askGhcOpts
+  liftIO $ copyDirContent srcDir dstDir
+
+writeModule :: MonadGHCIO m => HS.Module -> m ()
+writeModule (HS.Module m ps imp ds) = do
+  -- Note that GHC assumes that sources use ASCII or UTF-8.
+  out <- snd <$> outFileAndDir m
+  strict <- optGhcStrict <$> askGhcOpts
+  let languagePragmas =
+        List.map (HS.LanguagePragma . singleton . HS.Ident) $
+          List.sort $
+            [ "QualifiedDo" | strict ] ++
+                -- If --ghc-strict is used, then the language extension
+                -- QualifiedDo is activated. At the time of writing no
+                -- code is generated that depends on this extension
+                -- (except for the pragmas), but --ghc-strict is broken
+                -- with at least some versions of GHC prior to version 9,
+                -- and QualifiedDo was introduced with GHC 9.
+            [ "BangPatterns"
+            , "EmptyDataDecls"
+            , "EmptyCase"
+            , "ExistentialQuantification"
+            , "ScopedTypeVariables"
+            , "NoMonomorphismRestriction"
+            , "RankNTypes"
+            , "PatternSynonyms"
+            , "OverloadedStrings"
+            ]
+  let ghcOptions =
+        List.map HS.OtherPragma
+          [ ""  -- to separate from LANGUAGE pragmas
+          , "{-# OPTIONS_GHC -Wno-overlapping-patterns #-}"
+              -- Andreas, 2022-01-26, issue #5758:
+              -- Place this in generated file rather than
+              -- passing it only when calling GHC from within Agda.
+              -- This will silence the warning for the Agda-generated .hs
+              -- files while it can be on for other .hs files in the same
+              -- project.  (E.g., when using cabal/stack to compile.)
+          ]
+  liftIO $ UTF8.writeFile out $ (++ "\n") $ prettyPrint $
+    -- TODO: It might make sense to skip bang patterns for the unused
+    -- arguments of the "non-stripped" functions.
+    applyWhen strict makeStrict $
+    HS.Module m (concat [languagePragmas, ghcOptions, ps]) imp ds
+
+outFileAndDir :: MonadGHCIO m => HS.ModuleName -> m (FilePath, FilePath)
+outFileAndDir m = do
+  mdir <- optGhcCompileDir <$> askGhcOpts
+  let (fdir, fn) = splitFileName $ repldot pathSeparator $
+                   prettyPrint m
+  let dir = mdir </> fdir
+      fp  = dir </> replaceExtension fn "hs"
+  liftIO $ createDirectoryIfMissing True dir
+  return (mdir, fp)
+  where
+  repldot c = List.map $ \ c' -> if c' == '.' then c else c'
+
+curOutFileAndDir :: (MonadGHCIO m, ReadGHCModuleEnv m) => m (FilePath, FilePath)
+curOutFileAndDir = outFileAndDir =<< curHsMod
+
+curOutFile :: (MonadGHCIO m, ReadGHCModuleEnv m) => m FilePath
+curOutFile = snd <$> curOutFileAndDir
+
+callGHC :: ReaderT GHCModule TCM ()
+callGHC = do
+  opts     <- askGhcOpts
+  agdaOpts <- lift commandLineOptions
+  hsmod    <- prettyPrint <$> curHsMod
+  agdaMod  <- curAgdaMod
+  let outputName = Text.unpack $ List1.last $ moduleNameParts agdaMod
+  (mdir, fp) <- curOutFileAndDir
+  let ghcopts = optGhcFlags opts
+
+  modIsMain <- curIsMainModule
+  modHasMainFunc <- asks (not . null . ghcModMainFuncs)
+  let isMain = modIsMain && modHasMainFunc  -- both need to be IsMain
+
+  -- Warn if no main function and not --no-main
+  when (modIsMain /= isMain) $
+    genericWarning =<< fsep (pwords "No main function defined in" ++ [prettyTCM agdaMod <> "."] ++
+                             pwords "Use --no-main to suppress this warning.")
+
+  let overridableArgs =
+        [ "-O"] ++
+        (if isMain then ["-o", mdir </> outputName] else []) ++
+        [ "-Werror"]
+      otherArgs       =
+        [ "-i" ++ mdir] ++
+        (if isMain then ["-main-is", hsmod] else []) ++
+        [ fp
+        , "--make"
+        , "-fwarn-incomplete-patterns"
+        ]
+      args     = overridableArgs ++ ghcopts ++ otherArgs
+
+  let ghcBin = optGhcBin opts
+
+  -- Make GHC use UTF-8 when writing to stdout and stderr.
+  liftIO $ setEnv "GHC_CHARENC" "UTF-8"
+  -- Note: Some versions of GHC use stderr for progress reports. For
+  -- those versions of GHC we don't print any progress information
+  -- unless an error is encountered.
+  let doCall = optGhcCallGhc opts
+      cwd    = if optGHCiInteraction agdaOpts ||
+                  optJSONInteraction agdaOpts
+               then Just mdir
+               else Nothing
+  liftTCM $ callCompiler doCall ghcBin args cwd (Just utf8)
diff --git a/src/full/Agda/Compiler/MAlonzo/Encode.hs b/src/full/Agda/Compiler/MAlonzo/Encode.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Encode.hs
@@ -0,0 +1,69 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- Module name encoding
+------------------------------------------------------------------------
+
+module Agda.Compiler.MAlonzo.Encode
+  ( encodeModuleName
+  ) where
+
+import Data.Char
+import qualified Data.List as List
+import qualified Agda.Utils.Haskell.Syntax as HS
+
+import Agda.Compiler.MAlonzo.Misc
+
+-- | Haskell module names have to satisfy the Haskell (including the
+-- hierarchical module namespace extension) lexical syntax:
+--
+--   @modid -> [modid.] large {small | large | digit | ' }@
+--
+-- 'encodeModuleName' is an injective function into the set of module
+-- names defined by @modid@. The function preserves @.@s, and it also
+-- preserves module names whose first name part is not 'mazstr'.
+--
+-- Precondition: The input must not start or end with @.@, and no two
+-- @.@s may be adjacent.
+
+encodeModuleName :: HS.ModuleName -> HS.ModuleName
+encodeModuleName (HS.ModuleName s) = HS.ModuleName $ case List.stripPrefix mazstr s of
+  Just s' -> mazstr ++ foldr encNamePart "" (splitUp' s')
+  Nothing -> s
+  where
+  -- splitUp ".apa.bepa." == [".","apa",".","bepa","."]
+  -- splitUp = groupBy ((&&) `on` (/= '.'))
+
+  -- Since comparison against "." is wasteful, and modules name components are nonempty,
+  -- we can use "" as the separator.
+  -- Since modules name components are nonempty,
+  -- this is more efficient than adding a Maybe wrapper:
+  -- We are effectively using ``String = Maybe NEString''.
+  --
+  -- splitUp' ".apa.bepa." == ["","apa","","bepa",""]
+  splitUp' :: String -> [String]
+  splitUp' = h
+    where
+      h [] = []
+      h (c : cs) = case c of
+        '.' -> "" : h cs
+        _ -> g (c :) cs
+      g acc [] = [acc []]
+      g acc (c : cs) = case c of
+        '.' -> acc [] : "" : h cs
+        _ -> g (acc . (c :)) cs
+
+  encNamePart "" r = '.' : r
+  encNamePart s  r = ensureFirstCharLarge s $ foldr enc r s
+
+  ensureFirstCharLarge s r = case s of
+    c : cs | isUpper c && c /= largeChar -> r
+    _                                    -> largeChar : r
+
+  largeChar  = 'Q'
+  escapeChar = 'Z'
+
+  isOK c = c /= escapeChar && isModChar c
+
+  enc c r | isOK c    = c : r
+          | otherwise = escapeChar : shows (fromEnum c) (escapeChar : r)
diff --git a/src/full/Agda/Compiler/MAlonzo/HaskellTypes.hs b/src/full/Agda/Compiler/MAlonzo/HaskellTypes.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/HaskellTypes.hs
@@ -0,0 +1,299 @@
+
+-- | Translating Agda types to Haskell types. Used to ensure that imported
+--   Haskell functions have the right type.
+
+module Agda.Compiler.MAlonzo.HaskellTypes
+  ( haskellType
+  , checkConstructorCount
+  , hsTelApproximation, hsTelApproximation'
+  ) where
+
+import Control.Monad         ( zipWithM )
+import Control.Monad.Except  ( ExceptT(ExceptT), runExceptT, mapExceptT, catchError, throwError )
+import Control.Monad.Trans   ( lift )
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+import Data.Maybe (fromMaybe)
+import Data.List (intercalate)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Telescope
+
+import Agda.Compiler.MAlonzo.Pragmas
+import Agda.Compiler.MAlonzo.Misc
+import Agda.Compiler.MAlonzo.Pretty () --instance only
+
+import qualified Agda.Utils.Haskell.Syntax as HS
+import Agda.Utils.List
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.Utils.Impossible
+
+hsQCon :: String -> String -> HS.Type
+hsQCon m f = HS.TyCon $ HS.Qual (HS.ModuleName m) (HS.Ident f)
+
+hsCon :: String -> HS.Type
+hsCon = HS.TyCon . HS.UnQual . HS.Ident
+
+hsUnit :: HS.Type
+hsUnit = hsCon "()"
+
+hsVar :: HS.Name -> HS.Type
+hsVar = HS.TyVar
+
+hsApp :: HS.Type -> [HS.Type] -> HS.Type
+hsApp d ds = foldl HS.TyApp d ds
+
+hsForall :: HS.Name -> HS.Type -> HS.Type
+hsForall x = HS.TyForall [HS.UnkindedVar x]
+
+-- Issue #5207: From ghc-9.0 we have to be careful with nested foralls.
+hsFun :: HS.Type -> HS.Type -> HS.Type
+hsFun a (HS.TyForall vs b) = HS.TyForall vs $ hsFun a b
+hsFun a b = HS.TyFun a b
+
+data WhyNot = NoPragmaFor QName
+            | WrongPragmaFor Range QName
+            | BadLambda Term
+            | BadMeta Term
+            | BadDontCare Term
+            | NotCompiled QName
+
+type ToHs = ExceptT WhyNot HsCompileM
+
+notAHaskellType :: Term -> WhyNot -> TCM a
+notAHaskellType top offender = typeError . GenericDocError =<< do
+  fsep (pwords "The type" ++ [prettyTCM top] ++
+        pwords "cannot be translated to a corresponding Haskell type, because it contains" ++
+        reason offender) $$ possibleFix offender
+  where
+    reason (BadLambda        v) = pwords "the lambda term" ++ [prettyTCM v <> "."]
+    reason (BadMeta          v) = pwords "a meta variable" ++ [prettyTCM v <> "."]
+    reason (BadDontCare      v) = pwords "an erased term" ++ [prettyTCM v <> "."]
+    reason (NotCompiled      x) = pwords "a name that is not compiled"
+                                  ++ [parens (prettyTCM x) <> "."]
+    reason (NoPragmaFor      x) = prettyTCM x : pwords "which does not have a COMPILE pragma."
+    reason (WrongPragmaFor _ x) = prettyTCM x : pwords "which has the wrong kind of COMPILE pragma."
+
+    possibleFix BadLambda{}     = empty
+    possibleFix BadMeta{}       = empty
+    possibleFix BadDontCare{}   = empty
+    possibleFix NotCompiled{}   = empty
+    possibleFix (NoPragmaFor d) = suggestPragma d $ "add a pragma"
+    possibleFix (WrongPragmaFor r d) = suggestPragma d $
+      sep [ "replace the value-level pragma at", nest 2 $ pretty r, "by" ]
+
+    suggestPragma d action = do
+      def    <- theDef <$> getConstInfo d
+      let dataPragma n = ("data type HsD", "data HsD (" ++ intercalate " | " [ "C" ++ show i | i <- [1..n] ] ++ ")")
+          typePragma   = ("type HsT", "type HsT")
+          (hsThing, pragma) =
+            case def of
+              Datatype{ dataCons = cs } -> dataPragma (length cs)
+              Record{}                  -> dataPragma 1
+              _                         -> typePragma
+      vcat [ sep ["Possible fix:", action]
+           , nest 2 $ hsep [ "{-# COMPILE GHC", prettyTCM d, "=", text pragma, "#-}" ]
+           , text ("for a suitable Haskell " ++ hsThing ++ ".")
+           ]
+
+runToHs :: Term -> ToHs a -> HsCompileM a
+runToHs top m = either (liftTCM . notAHaskellType top) return =<< runExceptT m
+
+liftE1' :: (forall b. (a -> m b) -> m b) -> (a -> ExceptT e m b) -> ExceptT e m b
+liftE1' f k = ExceptT (f (runExceptT . k))
+
+-- Only used in hsTypeApproximation below, and in that case we catch the error.
+getHsType' :: QName -> HsCompileM HS.Type
+getHsType' q = runToHs (Def q []) (getHsType q)
+
+getHsType :: QName -> ToHs HS.Type
+getHsType x = do
+  unlessM (isCompiled x) $ throwError $ NotCompiled x
+
+  d   <- liftTCM $ getHaskellPragma x
+  env <- askGHCEnv
+  let is t p = Just t == p env
+
+      namedType = do
+        -- For these builtin types, the type name (xhqn ...) refers to the
+        -- generated, but unused, datatype and not the primitive type.
+        if  | x `is` ghcEnvNat ||
+              x `is` ghcEnvInteger -> return $ hsCon "Integer"
+            | x `is` ghcEnvBool    -> return $ hsCon "Bool"
+            | otherwise            ->
+              lift $ hsCon . prettyShow <$> xhqn TypeK x
+  mapExceptT (setCurrentRange d) $ case d of
+    _ | x `is` ghcEnvList ->
+        lift $ hsCon . prettyShow <$> xhqn TypeK x
+        -- we ignore Haskell pragmas for List
+    _ | x `is` ghcEnvMaybe ->
+        lift $ hsCon . prettyShow <$> xhqn TypeK x
+        -- we ignore Haskell pragmas for Maybe
+    _ | x `is` ghcEnvInf ->
+        return $ hsQCon "MAlonzo.RTE" "Infinity"
+    Just HsDefn{}      -> throwError $ WrongPragmaFor (getRange d) x
+    Just HsType{}      -> namedType
+    Just HsData{}      -> namedType
+    _                  -> throwError $ NoPragmaFor x
+
+-- | Is the given thing compiled?
+
+isCompiled :: HasConstInfo m => QName -> m Bool
+isCompiled q = usableModality <$> getConstInfo q
+
+-- | Does the name stand for a data or record type?
+
+isData :: HasConstInfo m => QName -> m Bool
+isData q = do
+  def <- theDef <$> getConstInfo q
+  return $ case def of
+    Datatype{} -> True
+    Record{}   -> True
+    _          -> False
+
+getHsVar :: (MonadFail tcm, MonadTCM tcm) => Nat -> tcm HS.Name
+getHsVar i =
+  HS.Ident . encodeString (VarK X) . prettyShow <$> nameOfBV i
+
+haskellType' :: Type -> HsCompileM HS.Type
+haskellType' t = runToHs (unEl t) (fromType t)
+  where
+    fromArgs = mapM (fromTerm . unArg)
+    fromType = fromTerm . unEl
+    fromTerm v = do
+      v   <- liftTCM $ unSpine <$> reduce v
+      reportSDoc "compile.haskell.type" 25 $ "toHaskellType " <+> prettyTCM v
+      reportSDoc "compile.haskell.type" 50 $ "toHaskellType " <+> pretty v
+      kit <- liftTCM coinductionKit
+      case v of
+        Var x es -> do
+          let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          hsApp . hsVar <$> getHsVar x <*> fromArgs args
+        Def d es -> do
+          let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          hsApp <$> getHsType d <*> fromArgs args
+        Pi a b ->
+          if isBinderUsed b  -- Andreas, 2012-04-03.  Q: could we rely on Abs/NoAbs instead of again checking freeness of variable?
+          then do
+            hsA <- fromType (unDom a)
+            liftE1' (underAbstraction a b) $ \ b ->
+              hsForall <$> getHsVar 0 <*> (hsFun hsA <$> fromType b)
+          else hsFun <$> fromType (unDom a) <*> fromType (noabsApp __IMPOSSIBLE__ b)
+        Con c ci es -> do
+          let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          hsApp <$> getHsType (conName c) <*> fromArgs args
+        Lam{}      -> throwError (BadLambda v)
+        Level{}    -> return hsUnit
+        Lit{}      -> return hsUnit
+        Sort{}     -> return hsUnit
+        MetaV{}    -> throwError (BadMeta v)
+        DontCare{} -> throwError (BadDontCare v)
+        Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+haskellType :: QName -> HsCompileM HS.Type
+haskellType q = do
+  def <- getConstInfo q
+  let (np, erased) =
+        case theDef def of
+          Constructor{ conPars, conErased }
+            -> (conPars, fromMaybe [] conErased ++ repeat False)
+          _ -> (0, repeat False)
+      stripErased (True  : es) (HS.TyFun _ t)     = stripErased es t
+      stripErased (False : es) (HS.TyFun s t)     = HS.TyFun s $ stripErased es t
+      stripErased es           (HS.TyForall xs t) = HS.TyForall xs $ stripErased es t
+      stripErased _            t                  = t
+      underPars 0 a = stripErased erased <$> haskellType' a
+      underPars n a = do
+        a <- reduce a
+        case unEl a of
+          Pi a (NoAbs _ b) -> underPars (n - 1) b
+          Pi a b  -> underAbstraction a b $ \b -> hsForall <$> getHsVar 0 <*> underPars (n - 1) b
+          _       -> __IMPOSSIBLE__
+  ty <- underPars np $ defType def
+  reportSDoc "tc.pragma.compile" 10 $ (("Haskell type for" <+> prettyTCM q) <> ":") <?> pretty ty
+  return ty
+
+checkConstructorCount :: QName -> [QName] -> [HaskellCode] -> TCM ()
+checkConstructorCount d cs hsCons
+  | n == hn   = return ()
+  | otherwise = do
+    let n_forms_are = case hn of
+          1 -> "1 Haskell constructor is"
+          n -> show n ++ " Haskell constructors are"
+        only | hn == 0   = ""
+             | hn < n    = "only "
+             | otherwise = ""
+
+    genericDocError =<<
+      fsep (prettyTCM d : pwords ("has " ++ show n ++
+            " constructors, but " ++ only ++ n_forms_are ++ " given [" ++ unwords hsCons ++ "]"))
+  where
+    n  = length cs
+    hn = length hsCons
+
+-- Type approximations ----------------------------------------------------
+
+data PolyApprox = PolyApprox | NoPolyApprox
+  deriving (Eq)
+
+hsTypeApproximation :: PolyApprox -> Int -> Type -> HsCompileM HS.Type
+hsTypeApproximation poly fv t = do
+  env <- askGHCEnv
+  let is q b = Just q == b env
+      tyCon  = HS.TyCon . HS.UnQual . HS.Ident
+      rteCon = HS.TyCon . HS.Qual mazRTE . HS.Ident
+      tyVar n i = HS.TyVar $ HS.Ident $ "a" ++ show (n - i)
+  let go n t = do
+        reportSDoc "compile.haskell.type" 25 $ "hsTypeApproximation " <+> prettyTCM t
+        reportSDoc "compile.haskell.type" 50 $ "hsTypeApproximation " <+> pretty t
+        t <- unSpine <$> reduce t
+        case t of
+          Var i _ | poly == PolyApprox -> return $ tyVar n i
+          Pi a b -> hsFun <$> go n (unEl $ unDom a) <*> go (n + k) (unEl $ unAbs b)
+            where k = case b of Abs{} -> 1; NoAbs{} -> 0
+          Def q els
+            | q `is` ghcEnvList
+            , Just k <- ghcEnvListArity env
+            , [Apply t] <- drop (k-1) els ->
+              HS.TyApp (tyCon "[]") <$> go n (unArg t)
+            | q `is` ghcEnvMaybe
+            , Just k <- ghcEnvMaybeArity env
+            , [Apply t] <- drop (k-1) els ->
+              HS.TyApp (tyCon "Maybe") <$> go n (unArg t)
+            | q `is` ghcEnvBool    -> return $ tyCon "Bool"
+            | q `is` ghcEnvInteger -> return $ tyCon "Integer"
+            | q `is` ghcEnvNat     -> return $ tyCon "Integer"
+            | q `is` ghcEnvWord64  -> return $ rteCon "Word64"
+            | otherwise -> do
+                let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims els
+                foldl HS.TyApp <$> getHsType' q <*> mapM (go n . unArg) args
+              `catchError` \ _ -> -- Not a Haskell type
+                ifM (and2M (isCompiled q) (isData q))
+                  (HS.TyCon <$> xhqn TypeK q)
+                  (return mazAnyType)
+          Sort{} -> return $ HS.FakeType "()"
+          _ -> return mazAnyType
+  go fv (unEl t)
+
+-- Approximating polymorphic types is not actually a good idea unless we
+-- actually keep track of type applications in recursive functions, and
+-- generate parameterised datatypes. Otherwise we'll just coerce all type
+-- variables to `Any` at the first `unsafeCoerce`.
+hsTelApproximation :: Type -> HsCompileM ([HS.Type], HS.Type)
+hsTelApproximation = hsTelApproximation' NoPolyApprox
+
+hsTelApproximation' :: PolyApprox -> Type -> HsCompileM ([HS.Type], HS.Type)
+hsTelApproximation' poly t = do
+  TelV tel res <- telViewPath t
+  let args = map (snd . unDom) (telToList tel)
+  (,) <$> zipWithM (hsTypeApproximation poly) [0..] args <*> hsTypeApproximation poly (length args) res
diff --git a/src/full/Agda/Compiler/MAlonzo/Misc.hs b/src/full/Agda/Compiler/MAlonzo/Misc.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Misc.hs
@@ -0,0 +1,422 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.MAlonzo.Misc where
+
+import Control.Monad.Reader ( ask )
+import Control.Monad.State ( modify )
+import Control.Monad.Trans ( MonadTrans(lift) )
+import Control.Monad.Trans.Except ( ExceptT )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Trans.Maybe ( MaybeT )
+import Control.Monad.Trans.Reader ( ReaderT(runReaderT) )
+import Control.Monad.Trans.State ( StateT(runStateT) )
+
+import Data.Char
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Text (Text)
+import qualified Data.Text as T
+
+import qualified Agda.Utils.Haskell.Syntax as HS
+
+import Agda.Compiler.Common as CC
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Monad
+
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+--------------------------------------------------
+-- Setting up Interface before compile
+--------------------------------------------------
+
+data HsModuleEnv = HsModuleEnv
+  { mazModuleName :: TopLevelModuleName
+    -- ^ The name of the Agda module
+  , mazIsMainModule :: Bool
+  -- ^ Whether this is the compilation root and therefore should have the `main` function.
+  --   This corresponds to the @IsMain@ flag provided to the backend,
+  --   not necessarily whether the GHC module has a `main` function defined.
+  }
+
+-- | The options derived from
+-- 'Agda.Compiler.MAlonzo.Compiler.GHCFlags' and other shared options.
+
+data GHCOptions = GHCOptions
+  { optGhcCallGhc    :: Bool
+  , optGhcBin        :: FilePath
+    -- ^ Use the compiler at PATH instead of "ghc"
+  , optGhcFlags      :: [String]
+  , optGhcCompileDir :: FilePath
+  , optGhcStrictData :: Bool
+    -- ^ Make inductive constructors strict?
+  , optGhcStrict :: Bool
+    -- ^ Make functions strict?
+  }
+
+-- | A static part of the GHC backend's environment that does not
+-- change from module to module.
+
+data GHCEnv = GHCEnv
+  { ghcEnvOpts :: GHCOptions
+  , ghcEnvBool
+  , ghcEnvTrue
+  , ghcEnvFalse
+  , ghcEnvMaybe
+  , ghcEnvNothing
+  , ghcEnvJust
+  , ghcEnvList
+  , ghcEnvNil
+  , ghcEnvCons
+  , ghcEnvNat
+  , ghcEnvInteger
+  , ghcEnvWord64
+  , ghcEnvInf
+  , ghcEnvSharp
+  , ghcEnvFlat
+  , ghcEnvInterval
+  , ghcEnvIZero
+  , ghcEnvIOne
+  , ghcEnvIsOne
+  , ghcEnvItIsOne
+  , ghcEnvIsOne1
+  , ghcEnvIsOne2
+  , ghcEnvIsOneEmpty
+  , ghcEnvPathP
+  , ghcEnvSub
+  , ghcEnvSubIn
+  , ghcEnvId
+  , ghcEnvConId
+    :: Maybe QName
+    -- Various (possibly) builtin names.
+  , ghcEnvIsTCBuiltin :: QName -> Bool
+  , ghcEnvListArity   :: Maybe Int
+  , ghcEnvMaybeArity  :: Maybe Int
+  }
+
+-- | Module compilation environment, bundling the overall
+--   backend session options along with the module's basic
+--   readable properties.
+data GHCModuleEnv = GHCModuleEnv
+  { ghcModEnv         :: GHCEnv
+  , ghcModHsModuleEnv :: HsModuleEnv
+  }
+
+-- | Monads that can produce a 'GHCModuleEnv'.
+class Monad m => ReadGHCModuleEnv m where
+  askGHCModuleEnv :: m GHCModuleEnv
+
+  default askGHCModuleEnv
+    :: (MonadTrans t, Monad n, m ~ (t n), ReadGHCModuleEnv n)
+    => m GHCModuleEnv
+  askGHCModuleEnv = lift askGHCModuleEnv
+
+  askHsModuleEnv :: m HsModuleEnv
+  askHsModuleEnv = ghcModHsModuleEnv <$> askGHCModuleEnv
+
+  askGHCEnv :: m GHCEnv
+  askGHCEnv = ghcModEnv <$> askGHCModuleEnv
+
+instance Monad m => ReadGHCModuleEnv (ReaderT GHCModuleEnv m) where
+  askGHCModuleEnv = ask
+
+instance ReadGHCModuleEnv m => ReadGHCModuleEnv (ExceptT e m)
+instance ReadGHCModuleEnv m => ReadGHCModuleEnv (IdentityT m)
+instance ReadGHCModuleEnv m => ReadGHCModuleEnv (MaybeT m)
+instance ReadGHCModuleEnv m => ReadGHCModuleEnv (StateT s m)
+
+newtype HsCompileState = HsCompileState
+  { mazAccumlatedImports :: Set TopLevelModuleName
+  } deriving (Eq, Semigroup, Monoid)
+
+-- | Transformer adding read-only module info and a writable set of imported modules
+type HsCompileT m = ReaderT GHCModuleEnv (StateT HsCompileState m)
+
+-- | The default compilation monad is the entire TCM (☹️) enriched with our state and module info
+type HsCompileM = HsCompileT TCM
+
+runHsCompileT' :: HsCompileT m a -> GHCModuleEnv -> HsCompileState -> m (a, HsCompileState)
+runHsCompileT' t e s = (flip runStateT s) . (flip runReaderT e) $ t
+
+runHsCompileT :: HsCompileT m a -> GHCModuleEnv -> m (a, HsCompileState)
+runHsCompileT t e = runHsCompileT' t e mempty
+
+--------------------------------------------------
+-- utilities for haskell names
+--------------------------------------------------
+
+-- | Whether the current module is expected to have the `main` function.
+--   This corresponds to the @IsMain@ flag provided to the backend,
+--   not necessarily whether the GHC module actually has a `main` function defined.
+curIsMainModule :: ReadGHCModuleEnv m => m Bool
+curIsMainModule = mazIsMainModule <$> askHsModuleEnv
+
+-- | This is the same value as @curMName@, but does not rely on the TCM's state.
+--   (@curMName@ and co. should be removed, but the current @Backend@ interface
+--   is not sufficient yet to allow that)
+curAgdaMod :: ReadGHCModuleEnv m => m TopLevelModuleName
+curAgdaMod = mazModuleName <$> askHsModuleEnv
+
+-- | Get the Haskell module name of the currently-focused Agda module
+curHsMod :: ReadGHCModuleEnv m => m HS.ModuleName
+curHsMod = mazMod <$> curAgdaMod
+
+-- | There are two kinds of functions: those definitely without unused
+-- arguments, and those that might have unused arguments.
+
+data FunctionKind = NoUnused | PossiblyUnused
+
+-- | Different kinds of variables: those starting with @a@, those
+-- starting with @v@, and those starting with @x@.
+
+data VariableKind = A | V | X
+
+-- | Different kinds of names.
+
+data NameKind
+  = TypeK
+    -- ^ Types.
+  | ConK
+    -- ^ Constructors.
+  | VarK VariableKind
+    -- ^ Variables.
+  | CoverK
+    -- ^ Used for coverage checking.
+  | CheckK
+    -- ^ Used for constructor type checking.
+  | FunK FunctionKind
+    -- ^ Other functions.
+
+-- | Turns strings into valid Haskell identifiers.
+--
+-- In order to avoid clashes with names of regular Haskell definitions
+-- (those not generated from Agda definitions), make sure that the
+-- Haskell names are always used qualified, with the exception of
+-- names from the prelude.
+
+encodeString :: NameKind -> String -> String
+encodeString k s = prefix ++ concatMap encode s
+  where
+  encode '\'' = "''"
+  encode c
+    | isLower c || isUpper c || c == '_' ||
+      generalCategory c == DecimalNumber =
+      [c]
+    | otherwise =
+      "'" ++ show (fromEnum c) ++ "'"
+
+  prefix = case k of
+    TypeK               -> "T"
+    ConK                -> "C"
+    VarK A              -> "a"
+    VarK V              -> "v"
+    VarK X              -> "x"
+    CoverK              -> "cover"
+    CheckK              -> "check"
+    FunK NoUnused       -> "du"
+    FunK PossiblyUnused -> "d"
+
+ihname :: VariableKind -> Nat -> HS.Name
+ihname k i = HS.Ident $ encodeString (VarK k) (show i)
+
+unqhname :: NameKind -> QName -> HS.Name
+unqhname k q =
+  HS.Ident $ encodeString k $
+    "_" ++ prettyShow (nameCanonical n) ++ "_" ++ idnum (nameId n)
+  where
+  n = qnameName q
+
+  idnum (NameId x _) = show (fromIntegral x)
+
+-- the toplevel module containing the given one
+tlmodOf :: ReadTCState m => ModuleName -> m HS.ModuleName
+tlmodOf = fmap mazMod . CC.topLevelModuleName
+
+
+-- qualify HS.Name n by the module of QName q, if necessary;
+-- accumulates the used module in stImportedModules at the same time.
+xqual :: QName -> HS.Name -> HsCompileM HS.QName
+xqual q n = do
+  m1 <- CC.topLevelModuleName (qnameModule q)
+  m2 <- curAgdaMod
+  if m1 == m2
+    then return (HS.UnQual n)
+    else do
+      modify (HsCompileState . Set.insert m1 . mazAccumlatedImports)
+      return (HS.Qual (mazMod m1) n)
+
+xhqn :: NameKind -> QName -> HsCompileM HS.QName
+xhqn k q = xqual q (unqhname k q)
+
+hsName :: String -> HS.QName
+hsName s = HS.UnQual (HS.Ident s)
+
+-- always use the original name for a constructor even when it's redefined.
+conhqn :: QName -> HsCompileM HS.QName
+conhqn q = xhqn ConK =<< canonicalName q
+
+-- qualify name s by the module of builtin b
+bltQual :: BuiltinId -> String -> HsCompileM HS.QName
+bltQual b s = do
+  Def q _ <- getBuiltin b
+  xqual q (HS.Ident s)
+
+dname :: QName -> HS.Name
+dname q = unqhname (FunK PossiblyUnused) q
+
+-- | Name for definition stripped of unused arguments
+duname :: QName -> HS.Name
+duname q = unqhname (FunK NoUnused) q
+
+hsPrimOp :: String -> HS.QOp
+hsPrimOp s = HS.QVarOp $ HS.UnQual $ HS.Symbol s
+
+hsPrimOpApp :: String -> HS.Exp -> HS.Exp -> HS.Exp
+hsPrimOpApp op e e1 = HS.InfixApp e (hsPrimOp op) e1
+
+hsInt :: Integer -> HS.Exp
+hsInt n = HS.Lit (HS.Int n)
+
+hsTypedInt :: Integral a => a -> HS.Exp
+hsTypedInt n = HS.ExpTypeSig (HS.Lit (HS.Int $ fromIntegral n)) (HS.TyCon (hsName "Integer"))
+
+hsTypedDouble :: Real a => a -> HS.Exp
+hsTypedDouble n = HS.ExpTypeSig (HS.Lit (HS.Frac $ toRational n)) (HS.TyCon (hsName "Double"))
+
+hsLet :: HS.Name -> HS.Exp -> HS.Exp -> HS.Exp
+hsLet x e b =
+  HS.Let (HS.BDecls [HS.LocalBind HS.Lazy x (HS.UnGuardedRhs e)]) b
+
+hsVarUQ :: HS.Name -> HS.Exp
+hsVarUQ = HS.Var . HS.UnQual
+
+hsAppView :: HS.Exp -> [HS.Exp]
+hsAppView = reverse . view
+  where
+    view (HS.App e e1) = e1 : view e
+    view (HS.InfixApp e1 op e2) = [e2, e1, hsOpToExp op]
+    view e = [e]
+
+hsOpToExp :: HS.QOp -> HS.Exp
+hsOpToExp (HS.QVarOp x) = HS.Var x
+
+hsLambda :: [HS.Pat] -> HS.Exp -> HS.Exp
+hsLambda ps (HS.Lambda ps1 e) = HS.Lambda (ps ++ ps1) e
+hsLambda ps e = HS.Lambda ps e
+
+hsMapAlt :: (HS.Exp -> HS.Exp) -> HS.Alt -> HS.Alt
+hsMapAlt f (HS.Alt p rhs wh) = HS.Alt p (hsMapRHS f rhs) wh
+
+hsMapRHS :: (HS.Exp -> HS.Exp) -> HS.Rhs -> HS.Rhs
+hsMapRHS f (HS.UnGuardedRhs def) = HS.UnGuardedRhs (f def)
+hsMapRHS f (HS.GuardedRhss es)   = HS.GuardedRhss [ HS.GuardedRhs g (f e) | HS.GuardedRhs g e <- es ]
+
+--------------------------------------------------
+-- Hard coded module names
+--------------------------------------------------
+
+mazstr :: String
+mazstr = "MAlonzo.Code"
+
+mazName :: Name
+mazName = mkName_ __IMPOSSIBLE__ mazstr
+
+mazMod' :: String -> HS.ModuleName
+mazMod' s = HS.ModuleName $ mazstr ++ "." ++ s
+
+mazMod :: TopLevelModuleName -> HS.ModuleName
+mazMod = mazMod' . prettyShow
+
+mazCoerceName :: String
+mazCoerceName = "coe"
+
+mazErasedName :: String
+mazErasedName = "erased"
+
+mazAnyTypeName :: String
+mazAnyTypeName = "AgdaAny"
+
+mazCoerce :: HS.Exp
+-- mazCoerce = HS.Var $ HS.Qual unsafeCoerceMod (HS.Ident "unsafeCoerce")
+-- mazCoerce = HS.Var $ HS.Qual mazRTE $ HS.Ident mazCoerceName
+mazCoerce = HS.Var $ HS.UnQual $ HS.Ident mazCoerceName
+
+mazUnreachableError :: HS.Exp
+mazUnreachableError = HS.Var $ HS.Qual mazRTE $ HS.Ident "mazUnreachableError"
+
+rtmUnreachableError :: HS.Exp
+rtmUnreachableError = mazUnreachableError
+
+mazHole :: HS.Exp
+mazHole = HS.Var $ HS.Qual mazRTE $ HS.Ident "mazHole"
+
+rtmHole :: String -> HS.Exp
+rtmHole s = mazHole `HS.App` HS.Lit (HS.String $ T.pack s)
+
+mazAnyType :: HS.Type
+mazAnyType = HS.TyCon (hsName mazAnyTypeName)
+
+mazRTE :: HS.ModuleName
+mazRTE = HS.ModuleName "MAlonzo.RTE"
+
+mazRTEFloat :: HS.ModuleName
+mazRTEFloat = HS.ModuleName "MAlonzo.RTE.Float"
+
+rtmQual :: String -> HS.QName
+rtmQual = HS.UnQual . HS.Ident
+
+rtmVar :: String -> HS.Exp
+rtmVar  = HS.Var . rtmQual
+
+rtmError :: Text -> HS.Exp
+rtmError s = rtmVar "error" `HS.App`
+             HS.Lit (HS.String $ T.append "MAlonzo Runtime Error: " s)
+
+unsafeCoerceMod :: HS.ModuleName
+unsafeCoerceMod = HS.ModuleName "Unsafe.Coerce"
+
+--------------------------------------------------
+-- Sloppy ways to declare <name> = <string>
+--------------------------------------------------
+
+fakeD :: HS.Name -> String -> HS.Decl
+fakeD v s = HS.FunBind [HS.Match v [] (HS.UnGuardedRhs $ fakeExp s) emptyBinds]
+
+fakeDS :: String -> String -> HS.Decl
+fakeDS = fakeD . HS.Ident
+
+fakeDQ :: QName -> String -> HS.Decl
+fakeDQ = fakeD . dname
+
+fakeType :: String -> HS.Type
+fakeType = HS.FakeType
+
+fakeExp :: String -> HS.Exp
+fakeExp = HS.FakeExp
+
+fakeDecl :: String -> HS.Decl
+fakeDecl = HS.FakeDecl
+
+--------------------------------------------------
+-- Auxiliary definitions
+--------------------------------------------------
+
+emptyBinds :: Maybe HS.Binds
+emptyBinds = Nothing
+
+--------------------------------------------------
+-- Utilities for Haskell modules names
+--------------------------------------------------
+
+-- | Can the character be used in a Haskell module name part
+-- (@conid@)? This function is more restrictive than what the Haskell
+-- report allows.
+
+isModChar :: Char -> Bool
+isModChar c =
+  isLower c || isUpper c || isDigit c || c == '_' || c == '\''
diff --git a/src/full/Agda/Compiler/MAlonzo/Pragmas.hs b/src/full/Agda/Compiler/MAlonzo/Pragmas.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Pragmas.hs
@@ -0,0 +1,224 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.MAlonzo.Pragmas where
+
+import Control.Monad
+import Data.Maybe
+import Data.Char
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Text.ParserCombinators.ReadP
+
+import Agda.Syntax.Position
+import Agda.Syntax.Abstract.Name
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive
+
+import Agda.Syntax.Common.Pretty hiding (char)
+import Agda.Utils.String ( ltrim )
+import Agda.Utils.Three
+
+import Agda.Compiler.MAlonzo.Misc
+
+import Agda.Utils.Impossible
+
+type HaskellCode = String
+type HaskellType = String
+
+-- | GHC backend translation pragmas.
+data HaskellPragma
+  = HsDefn Range HaskellCode
+      --  ^ @COMPILE GHC x = <code>@
+  | HsType Range HaskellType
+      --  ^ @COMPILE GHC X = type <type>@
+  | HsData Range HaskellType [HaskellCode]
+      -- ^ @COMPILE GHC X = data D (c₁ | ... | cₙ)
+  | HsExport Range HaskellCode
+      -- ^ @COMPILE GHC x as f@
+  deriving (Show, Eq)
+
+instance HasRange HaskellPragma where
+  getRange (HsDefn   r _)   = r
+  getRange (HsType   r _)   = r
+  getRange (HsData   r _ _) = r
+  getRange (HsExport r _)   = r
+
+instance Pretty HaskellPragma where
+  pretty = \case
+    HsDefn   _r hsCode        -> equals <+> text hsCode
+    HsType   _r hsType        -> equals <+> text hsType
+    HsData   _r hsType hsCons -> hsep $
+      [ equals, "data", text hsType
+      , parens $ hsep $ map text $ List.intersperse "|" hsCons
+      ]
+    HsExport _r hsCode        -> "as" <+> text hsCode
+
+-- Syntax for Haskell pragmas:
+--  HsDefn CODE       "= CODE"
+--  HsType TYPE       "= type TYPE"
+--  HsData NAME CONS  "= data NAME (CON₁ | .. | CONₙ)"
+--  HsExport NAME     "as NAME"
+parsePragma :: CompilerPragma -> Either String HaskellPragma
+parsePragma (CompilerPragma r s) =
+  case [ p | (p, "") <- readP_to_S pragmaP s ] of
+    []  -> Left $ "Failed to parse GHC pragma '" ++ s ++ "'"
+    [p] -> Right p
+    ps  -> Left $ "Ambiguous parse of pragma '" ++ s ++ "':\n" ++ unlines (map show ps)  -- shouldn't happen
+  where
+    pragmaP :: ReadP HaskellPragma
+    pragmaP = choice [ exportP, typeP, dataP, defnP ]
+
+    whitespace = many1 (satisfy isSpace)
+
+    wordsP []     = return ()
+    wordsP (w:ws) = skipSpaces *> string w *> wordsP ws
+
+    barP = skipSpaces *> char '|'
+
+    -- quite liberal
+    isIdent c = isAlphaNum c || elem c ("_.':[]" :: String)
+    isOp c    = not $ isSpace c || elem c ("()" :: String)
+    hsIdent = fst <$> gather (choice
+                [ string "()"
+                , many1 (satisfy isIdent)
+                , between (char '(') (char ')') (many1 (satisfy isOp))
+                ])
+    hsCode  = many1 get -- very liberal
+
+    paren = between (skipSpaces *> char '(') (skipSpaces *> char ')')
+
+    isPrefixSpaceOf pre s = case List.stripPrefix pre s of
+      Just (x:_) -> isSpace x
+      _ -> False
+
+    notTypeOrData = do
+      s <- look
+      guard $ not $ any (`isPrefixSpaceOf` s) ["type", "data"]
+
+    exportP = HsExport r <$ wordsP ["as"]        <* whitespace <*> hsIdent <* skipSpaces
+    typeP   = HsType   r <$ wordsP ["=", "type"] <* whitespace <*> hsCode
+    dataP   = HsData   r <$ wordsP ["=", "data"] <* whitespace <*> hsIdent <*>
+                                                    paren (sepBy (skipSpaces *> hsIdent) barP) <* skipSpaces
+    defnP   = HsDefn   r <$ wordsP ["="]         <* whitespace <*  notTypeOrData <*> hsCode
+
+parseHaskellPragma :: (MonadTCError m, MonadTrace m) => CompilerPragma -> m HaskellPragma
+parseHaskellPragma p = setCurrentRange p $
+  case parsePragma p of
+    Left err -> genericError err
+    Right p  -> return p
+
+getHaskellPragma :: QName -> TCM (Maybe HaskellPragma)
+getHaskellPragma q = do
+  pragma <- traverse parseHaskellPragma =<< getUniqueCompilerPragma ghcBackendName q
+  def <- getConstInfo q
+  setCurrentRange pragma $ pragma <$ sanityCheckPragma def pragma
+
+sanityCheckPragma :: (HasBuiltins m, MonadTCError m, MonadReduce m) => Definition -> Maybe HaskellPragma -> m ()
+sanityCheckPragma _ Nothing = return ()
+sanityCheckPragma def (Just HsDefn{}) =
+  case theDef def of
+    Axiom{}        -> return ()
+    Function{}     -> return ()
+    AbstractDefn{} -> __IMPOSSIBLE__
+    Datatype{}     -> recOrDataErr "data"
+    Record{}       -> recOrDataErr "record"
+    _              -> typeError $ GenericError "Haskell definitions can only be given for postulates and functions."
+    where
+      recOrDataErr which =
+        typeError $ GenericDocError $
+          sep [ text $ "Bad COMPILE GHC pragma for " ++ which ++ " type. Use"
+              , "{-# COMPILE GHC <Name> = data <HsData> (<HsCon1> | .. | <HsConN>) #-}" ]
+sanityCheckPragma def (Just HsData{}) =
+  case theDef def of
+    Datatype{} -> return ()
+    Record{}   -> return ()
+    _          -> typeError $ GenericError "Haskell data types can only be given for data or record types."
+sanityCheckPragma def (Just HsType{}) =
+  case theDef def of
+    Axiom{} -> return ()
+    Datatype{} -> do
+      -- We use HsType pragmas for Nat, Int and Bool
+      nat  <- getBuiltinName builtinNat
+      int  <- getBuiltinName builtinInteger
+      bool <- getBuiltinName builtinBool
+      unless (Just (defName def) `elem` [nat, int, bool]) err
+    _ -> err
+  where
+    err = typeError $ GenericError "Haskell types can only be given for postulates."
+sanityCheckPragma def (Just HsExport{}) =
+  case theDef def of
+    Function{} -> return ()
+    _ -> typeError $ GenericError "Only functions can be exported to Haskell using {-# COMPILE GHC <Name> as <HsName> #-}"
+
+
+
+-- TODO: cache this to avoid parsing the pragma for every constructor
+--       occurrence!
+getHaskellConstructor :: QName -> HsCompileM (Maybe HaskellCode)
+getHaskellConstructor c = do
+  c    <- canonicalName c
+  cDef <- theDef <$> getConstInfo c
+  env  <- askGHCEnv
+  let is c p = Just c == p env
+  case cDef of
+    _ | c `is` ghcEnvTrue    -> return $ Just "True"
+      | c `is` ghcEnvFalse   -> return $ Just "False"
+      | c `is` ghcEnvNil     -> return $ Just "[]"
+      | c `is` ghcEnvCons    -> return $ Just "(:)"
+      | c `is` ghcEnvNothing -> return $ Just "Nothing"
+      | c `is` ghcEnvJust    -> return $ Just "Just"
+      | c `is` ghcEnvSharp   -> return $ Just "MAlonzo.RTE.Sharp"
+      | c `is` ghcEnvIZero   -> return $ Just "False"
+      | c `is` ghcEnvIOne    -> return $ Just "True"
+    Constructor{conData = d} -> do
+      mp <- liftTCM $ getHaskellPragma d
+      case mp of
+        Just (HsData _ _ hsCons) -> do
+          cons <- defConstructors . theDef <$> getConstInfo d
+          return $ Just $ fromMaybe __IMPOSSIBLE__ $ lookup c $ zip cons hsCons
+        _ -> return Nothing
+    _ -> return Nothing
+
+-- | Get content of @FOREIGN GHC@ pragmas, sorted by 'KindOfForeignCode':
+--   file header pragmas, import statements, rest.
+foreignHaskell :: Interface -> ([String], [String], [String])
+foreignHaskell = partitionByKindOfForeignCode classifyForeign
+    . map getCode . maybe [] (reverse . getForeignCodeStack) . Map.lookup ghcBackendName . iForeignCode
+  where getCode (ForeignCode _ code) = code
+
+-- | Classify @FOREIGN@ Haskell code.
+data KindOfForeignCode
+  = ForeignFileHeaderPragma
+      -- ^ A pragma that must appear before the module header.
+  | ForeignImport
+      -- ^ An import statement.  Must appear right after the module header.
+  | ForeignOther
+      -- ^ The rest.  To appear after the import statements.
+
+-- | Classify a @FOREIGN GHC@ declaration.
+classifyForeign :: String -> KindOfForeignCode
+classifyForeign s0 = case ltrim s0 of
+  s | "import " `List.isPrefixOf` s -> ForeignImport
+  s | "{-#" `List.isPrefixOf` s -> classifyPragma $ drop 3 s
+  _ -> ForeignOther
+
+-- | Classify a Haskell pragma into whether it is a file header pragma or not.
+classifyPragma :: String -> KindOfForeignCode
+classifyPragma s0 = case ltrim s0 of
+  s | any (`List.isPrefixOf` s) fileHeaderPragmas -> ForeignFileHeaderPragma
+  _ -> ForeignOther
+  where
+  fileHeaderPragmas =
+    [ "LANGUAGE"
+    , "OPTIONS_GHC"
+    , "INCLUDE"
+    ]
+
+-- | Partition a list by 'KindOfForeignCode' attribute.
+partitionByKindOfForeignCode :: (a -> KindOfForeignCode) -> [a] -> ([a], [a], [a])
+partitionByKindOfForeignCode f = partition3 $ toThree . f
+  where
+  toThree = \case
+    ForeignFileHeaderPragma -> One
+    ForeignImport           -> Two
+    ForeignOther            -> Three
diff --git a/src/full/Agda/Compiler/MAlonzo/Pretty.hs b/src/full/Agda/Compiler/MAlonzo/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Pretty.hs
@@ -0,0 +1,243 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- Pretty-printing of Haskell modules
+------------------------------------------------------------------------
+
+module Agda.Compiler.MAlonzo.Pretty where
+
+import qualified Agda.Utils.Haskell.Syntax as HS
+
+import Agda.Compiler.MAlonzo.Encode
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Null (empty)
+import Agda.Utils.Function (applyWhen)
+
+
+prettyPrint :: Pretty a => a -> String
+prettyPrint = show . pretty
+
+instance Pretty HS.Module where
+  pretty (HS.Module m pragmas imps decls) =
+    vcat $ concat
+      [ map pretty pragmas
+      , [ "" | not $ null pragmas ]
+      , [ "module" <+> pretty m <+> "where" ]
+      , [ "" ]
+      , map pretty imps
+      , [ "" ]
+      , map pretty decls
+      ]
+
+instance Pretty HS.ModulePragma where
+  pretty (HS.LanguagePragma ps) =
+    "{-#" <+> "LANGUAGE" <+> fsep (punctuate comma $ map pretty ps) <+> "#-}"
+  pretty (HS.OtherPragma p) =
+    text p
+
+instance Pretty HS.ImportDecl where
+  pretty HS.ImportDecl{ HS.importModule    = m
+                      , HS.importQualified = q
+                      , HS.importSpecs     = specs } =
+      hsep [ "import"
+           , if q then "qualified" else empty
+           , pretty m
+           , maybe empty prSpecs specs ]
+    where prSpecs (hide, specs) =
+            hsep [ if hide then "hiding" else empty
+                 , parens $ fsep $ punctuate comma $ map pretty specs ]
+
+instance Pretty HS.ImportSpec where
+  pretty (HS.IVar x) = pretty x
+
+instance Pretty HS.Decl where
+  pretty = \case
+    HS.TypeDecl f xs t ->
+      sep [ "type" <+> pretty f <+> fsep (map pretty xs) <+> "="
+          , nest 2 $ pretty t ]
+    HS.DataDecl newt d xs cons derv ->
+      sep [ pretty newt <+> pretty d <+> fsep (map pretty xs)
+          , nest 2 $ if null cons then empty
+                     else "=" <+> fsep (punctuate " |" $ map pretty cons)
+          , nest 2 $ prDeriving derv ]
+      where
+        prDeriving [] = empty
+        prDeriving ds = "deriving" <+> parens (fsep $ punctuate comma $ map prDer ds)
+        prDer (d, ts) = pretty (foldl HS.TyApp (HS.TyCon d) ts)
+    HS.TypeSig fs t ->
+      sep [ hsep (punctuate comma (map pretty fs)) <+> "::"
+          , nest 2 $ pretty t ]
+    HS.FunBind ms -> vcat $ map pretty ms
+    HS.LocalBind s f rhs ->
+      sep [ pretty s <> pretty f
+          , nest 2 $ prettyRhs "=" rhs
+          ]
+    HS.PatSyn p1 p2 -> sep [ "pattern" <+> pretty p1 <+> "=" <+> pretty p2 ]
+    HS.FakeDecl s -> text s
+    HS.Comment s -> vcat $ map (("--" <+>) . text) (lines s)
+
+instance Pretty HS.ConDecl where
+  pretty (HS.ConDecl c sts) =
+    pretty c <+>
+    fsep (map (\(s, t) -> maybe empty pretty s <> prettyPrec 10 t) sts)
+
+instance Pretty HS.Strictness where
+  pretty HS.Strict = "!"
+  pretty HS.Lazy   = empty
+
+instance Pretty HS.Match where
+  pretty (HS.Match f ps rhs wh) =
+    prettyWhere wh $
+      sep [ pretty f <+> fsep (map (prettyPrec 10) ps)
+          , nest 2 $ prettyRhs "=" rhs ]
+
+prettyWhere :: Maybe HS.Binds -> Doc -> Doc
+prettyWhere Nothing  doc = doc
+prettyWhere (Just b) doc =
+  vcat [ doc, nest 2 $ sep [ "where", nest 2 $ pretty b ] ]
+
+instance Pretty HS.Pat where
+  prettyPrec pr pat =
+    case pat of
+      HS.PVar x         -> pretty x
+      HS.PLit l         -> prettyPrec pr l
+      HS.PAsPat x p     -> mparens (pr > 10) $ pretty x <> "@" <> prettyPrec 11 p
+      HS.PWildCard      -> "_"
+      HS.PBangPat p     -> "!" <> prettyPrec 11 p
+      HS.PApp c ps      -> mparens (pr > 9) $ pretty c <+> hsep (map (prettyPrec 10) ps)
+      HS.PatTypeSig p t -> mparens (pr > 0) $ sep [ pretty p <+> "::", nest 2 $ pretty t ]
+      HS.PIrrPat p      -> mparens (pr > 10) $ "~" <> prettyPrec 11 p
+
+prettyRhs :: String -> HS.Rhs -> Doc
+prettyRhs eq (HS.UnGuardedRhs e)   = text eq <+> pretty e
+prettyRhs eq (HS.GuardedRhss rhss) = vcat $ map (prettyGuardedRhs eq) rhss
+
+prettyGuardedRhs :: String -> HS.GuardedRhs -> Doc
+prettyGuardedRhs eq (HS.GuardedRhs ss e) =
+    sep [ "|" <+> sep (punctuate comma $ map pretty ss) <+> text eq
+        , nest 2 $ pretty e ]
+
+instance Pretty HS.Binds where
+  pretty (HS.BDecls ds) = vcat $ map pretty ds
+
+instance Pretty HS.DataOrNew where
+  pretty HS.DataType = "data"
+  pretty HS.NewType  = "newtype"
+
+instance Pretty HS.TyVarBind where
+  pretty (HS.UnkindedVar x) = pretty x
+
+instance Pretty HS.Type where
+  prettyPrec pr t =
+    case t of
+      HS.TyForall xs t ->
+        mparens (pr > 0) $
+          sep [ ("forall" <+> fsep (map pretty xs)) <> "."
+              , nest 2 $ pretty t ]
+      HS.TyFun a b ->
+        mparens (pr > 4) $
+          sep [ prettyPrec 5 a <+> "->", prettyPrec 4 b ]
+      HS.TyCon c -> pretty c
+      HS.TyVar x -> pretty x
+      HS.TyApp (HS.TyCon (HS.UnQual (HS.Ident "[]"))) t ->
+        brackets $ pretty t
+      t@HS.TyApp{} ->
+        mparens (pr > 9) $
+          sep [ prettyPrec 9 f
+              , nest 2 $ fsep $ map (prettyPrec 10) ts ]
+        where
+          f : ts = appView t []
+          appView (HS.TyApp a b) as = appView a (b : as)
+          appView t as = t : as
+      HS.FakeType s -> text s
+
+instance Pretty HS.Stmt where
+  pretty (HS.Qualifier e) = pretty e
+  pretty (HS.Generator p e) = sep [ pretty p <+> "<-", nest 2 $ pretty e ]
+
+instance Pretty HS.Literal where
+  prettyPrec pr = \case
+    HS.Int n    -> parensIfNeg n $ integer n
+    HS.Frac x   -> parensIfNeg d $ double d
+                   where
+                   d = fromRational x
+    HS.Char c   -> text (show c)
+    HS.String s -> text (show s)
+    where
+    parensIfNeg :: (Ord n, Num n) => n -> Doc -> Doc
+    parensIfNeg x = applyWhen (x < 0) $ mparens (pr > 10)
+
+instance Pretty HS.Exp where
+  prettyPrec pr e =
+    case e of
+      HS.Var x -> pretty x
+      HS.Con c -> pretty c
+      HS.Lit l -> pretty l
+      HS.InfixApp a qop b -> mparens (pr > 0) $
+        sep [ prettyPrec 1 a
+            , pretty qop <+> prettyPrec 1 b ]
+      HS.Ann e ty -> mparens (pr > 0) $
+        sep [ prettyPrec 1 e
+            , "::"
+            , prettyPrec 1 ty
+            ]
+      HS.App{} -> mparens (pr > 9) $
+        sep [ prettyPrec 9 f
+            , nest 2 $ fsep $ map (prettyPrec 10) es ]
+        where
+          f : es = appView e []
+          appView (HS.App f e) es = appView f (e : es)
+          appView f es = f : es
+      HS.Lambda ps e -> mparens (pr > 0) $
+        sep [ "\\" <+> fsep (map (prettyPrec 10) ps) <+> "->"
+            , nest 2 $ pretty e ]
+      HS.Let bs e -> mparens (pr > 0) $
+        sep [ "let" <+> pretty bs <+> "in"
+            , pretty e ]
+      HS.If a b c -> mparens (pr > 0) $
+        sep [ "if" <+> pretty a
+            , nest 2 $ "then" <+> pretty b
+            , nest 2 $ "else" <+> prettyPrec 1 c ]
+      HS.Case e bs -> mparens (pr > 0) $
+        vcat [ "case" <+> pretty e <+> "of"
+             , nest 2 $ vcat $ map pretty bs ]
+      HS.ExpTypeSig e t -> mparens (pr > 0) $
+        sep [ pretty e <+> "::"
+            , nest 2 $ pretty t ]
+      HS.NegApp exp -> parens $ "-" <> pretty exp
+      HS.FakeExp s -> text s
+
+instance Pretty HS.Alt where
+  pretty (HS.Alt pat rhs wh) =
+    prettyWhere wh $
+      sep [ pretty pat, nest 2 $ prettyRhs "->" rhs ]
+
+instance Pretty HS.ModuleName where
+  pretty m = text s
+    where HS.ModuleName s = encodeModuleName m
+
+instance Pretty HS.QName where
+  pretty q = mparens (isOperator q) (prettyQName q)
+
+instance Pretty HS.Name where
+  pretty (HS.Ident  s) = text s
+  pretty (HS.Symbol s) = text s
+
+instance Pretty HS.QOp where
+  pretty (HS.QVarOp x)
+    | isOperator x = prettyQName x
+    | otherwise    = "`" <> prettyQName x <> "`"
+
+isOperator :: HS.QName -> Bool
+isOperator q =
+  case q of
+    HS.Qual _ x           -> isOp x
+    HS.UnQual x           -> isOp x
+  where
+    isOp HS.Symbol{} = True
+    isOp HS.Ident{}  = False
+
+prettyQName :: HS.QName -> Doc
+prettyQName (HS.Qual m x)           = pretty m <> "." <> pretty x
+prettyQName (HS.UnQual x)           = pretty x
diff --git a/src/full/Agda/Compiler/MAlonzo/Primitives.hs b/src/full/Agda/Compiler/MAlonzo/Primitives.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Primitives.hs
@@ -0,0 +1,328 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.MAlonzo.Primitives where
+
+import Control.Arrow ( second )
+import Control.Monad.Trans.Maybe ( MaybeT(MaybeT, runMaybeT) )
+
+import qualified Data.List as List
+import           Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.HashMap.Strict as HMap
+import Data.Maybe
+
+import Agda.Compiler.Common
+import Agda.Compiler.MAlonzo.Misc
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Syntax.Internal
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty
+
+import Agda.Utils.Either
+import Agda.Utils.Lens
+import Agda.Utils.List   (hasElem)
+import qualified Agda.Utils.Haskell.Syntax as HS
+
+import Agda.Utils.Impossible
+
+newtype MainFunctionDef = MainFunctionDef Definition
+
+data CheckedMainFunctionDef = CheckedMainFunctionDef
+  { checkedMainDef :: MainFunctionDef
+  , checkedMainDecl :: HS.Decl
+  }
+
+-- Andreas, 2019-04-29, issue #3731: exclude certain kinds of names, like constructors.
+-- TODO: Also only consider top-level definition (not buried inside a module).
+asMainFunctionDef :: Definition -> Maybe MainFunctionDef
+asMainFunctionDef d = case (theDef d) of
+    Axiom{}                              -> perhaps
+    Function{ funProjection = Left _ }   -> perhaps
+    Function{ funProjection = Right{}  } -> no
+    AbstractDefn{}                       -> no
+    GeneralizableVar{}                   -> no
+    DataOrRecSig{}                       -> no
+    Datatype{}                           -> no
+    Record{}                             -> no
+    Constructor{}                        -> no
+    Primitive{}                          -> no
+    PrimitiveSort{}                      -> no
+  where
+  isNamedMain = "main" == prettyShow (nameConcrete . qnameName . defName $ d)  -- ignores the qualification!?
+  perhaps | isNamedMain = Just $ MainFunctionDef d
+          | otherwise   = no
+  no                    = Nothing
+
+mainFunctionDefs :: Interface -> [MainFunctionDef]
+mainFunctionDefs i = catMaybes $ asMainFunctionDef <$> defs
+  where
+    defs = HMap.elems $ iSignature i ^. sigDefinitions
+
+-- | Check that the main function has type IO a, for some a.
+checkTypeOfMain :: Definition -> HsCompileM (Maybe CheckedMainFunctionDef)
+checkTypeOfMain def = runMaybeT $ do
+  -- Only indicate main functions in the main module.
+  isMainModule <- curIsMainModule
+  mainDef <- MaybeT $ pure $ if isMainModule then asMainFunctionDef def else Nothing
+  liftTCM $ checkTypeOfMain' mainDef
+
+checkTypeOfMain' :: MainFunctionDef -> TCM CheckedMainFunctionDef
+checkTypeOfMain' m@(MainFunctionDef def) = CheckedMainFunctionDef m <$> do
+    Def io _ <- primIO
+    ty <- reduce $ defType def
+    case unEl ty of
+      Def d _ | d == io -> return mainAlias
+      _                 -> do
+        err <- fsep $
+          pwords "The type of main should be" ++
+          [prettyTCM io] ++ pwords " A, for some A. The given type is" ++ [prettyTCM ty]
+        typeError $ GenericError $ show err
+  where
+    mainAlias = HS.FunBind [HS.Match mainLHS [] mainRHS emptyBinds ]
+    mainLHS   = HS.Ident "main"
+    mainRHS   = HS.UnGuardedRhs $ HS.App mazCoerce (HS.Var $ HS.UnQual $ dname $ defName def)
+
+treelessPrimName :: TPrim -> String
+treelessPrimName p =
+  case p of
+    PQuot   -> "quotInt"
+    PRem    -> "remInt"
+    PSub    -> "subInt"
+    PAdd    -> "addInt"
+    PMul    -> "mulInt"
+    PGeq    -> "geqInt"
+    PLt     -> "ltInt"
+    PEqI    -> "eqInt"
+    PQuot64 -> "quot64"
+    PRem64  -> "rem64"
+    PSub64  -> "sub64"
+    PAdd64  -> "add64"
+    PMul64  -> "mul64"
+    PLt64   -> "lt64"
+    PEq64   -> "eq64"
+    PITo64  -> "word64FromNat"
+    P64ToI  -> "word64ToNat"
+    PEqF    -> "MAlonzo.RTE.Float.doubleDenotEq"
+    -- MAlonzo uses literal patterns, so we don't need equality for the other primitive types
+    PEqC    -> __IMPOSSIBLE__
+    PEqS    -> __IMPOSSIBLE__
+    PEqQ    -> __IMPOSSIBLE__
+    PSeq    -> "seq"
+    -- primitives only used by GuardsToPrims transformation, which MAlonzo doesn't use
+    PIf     -> __IMPOSSIBLE__
+
+-- | Haskell modules to be imported for BUILT-INs
+importsForPrim :: BuiltinThings PrimFun -> [Definition] -> [HS.ModuleName]
+importsForPrim builtinThings defs = xForPrim table builtinThings defs ++ [HS.ModuleName "Data.Text"]
+  where
+  table = Map.fromList $ map (second HS.ModuleName)
+    [ someBuiltin BuiltinChar                |-> "Data.Char"
+    , someBuiltin PrimFloatCeiling           |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatDecode            |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatEncode            |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatEquality          |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatFloor             |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatInequality        |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatIsSafeInteger     |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatLess              |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatRound             |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatToRatio           |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimFloatToWord64          |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimIsAlpha                |-> "Data.Char"
+    , someBuiltin PrimIsAscii                |-> "Data.Char"
+    , someBuiltin PrimIsDigit                |-> "Data.Char"
+    , someBuiltin PrimIsHexDigit             |-> "Data.Char"
+    , someBuiltin PrimIsLatin1               |-> "Data.Char"
+    , someBuiltin PrimIsLower                |-> "Data.Char"
+    , someBuiltin PrimIsPrint                |-> "Data.Char"
+    , someBuiltin PrimIsSpace                |-> "Data.Char"
+    , someBuiltin PrimRatioToFloat           |-> "MAlonzo.RTE.Float"
+    , someBuiltin PrimToLower                |-> "Data.Char"
+    , someBuiltin PrimToUpper                |-> "Data.Char"
+    ]
+  (|->) = (,)
+
+--------------
+
+xForPrim :: Map SomeBuiltin a -> BuiltinThings PrimFun -> [Definition] -> [a]
+xForPrim table builtinThings defs = catMaybes
+    [ Map.lookup s table
+    | (s, def) <- Map.toList builtinThings
+    , maybe False elemDefs $ getName def
+    ]
+  where
+  elemDefs = hasElem $ map defName defs
+  getName = \case
+    Builtin t                 -> Just $ getPrimName t
+    Prim (PrimFun q _ _ _)    -> Just q
+    BuiltinRewriteRelations _ -> Nothing
+
+
+-- | Definition bodies for primitive functions
+primBody :: MonadTCError m => PrimitiveId -> m HS.Exp
+primBody s = maybe unimplemented (fromRight (hsVarUQ . HS.Ident) <$>) $ List.lookup s $
+  [
+  -- Integer functions
+    PrimShowInteger      |-> return "(Data.Text.pack . show :: Integer -> Data.Text.Text)"
+
+  -- Levels
+  , PrimLevelZero        |-> return "()"
+  , PrimLevelSuc         |-> return "(\\ _ -> ())"
+  , PrimLevelMax         |-> return "(\\ _ _ -> ())"
+
+  -- Natural number functions
+  , PrimNatPlus         |-> binNat "(+)"
+  , PrimNatMinus        |-> binNat "(\\ x y -> max 0 (x - y))"
+  , PrimNatTimes        |-> binNat "(*)"
+  , PrimNatDivSucAux    |-> binNat4 "(\\ k m n j -> k + div (max 0 $ n + m - j) (m + 1))"
+  , PrimNatModSucAux    |-> binNat4 "(\\ k m n j -> if n > j then mod (n - j - 1) (m + 1) else (k + n))"
+  , PrimNatEquality     |-> relNat "(==)"
+  , PrimNatLess         |-> relNat "(<)"
+  , PrimShowNat         |-> return "(Data.Text.pack . show :: Integer -> Data.Text.Text)"
+
+  -- Machine word functions
+  , PrimWord64ToNat     |-> return "MAlonzo.RTE.word64ToNat"
+  , PrimWord64FromNat   |-> return "MAlonzo.RTE.word64FromNat"
+  , PrimWord64ToNatInjective   |-> return mazErasedName
+
+  -- Floating point functions
+  , PrimFloatEquality            |-> return "MAlonzo.RTE.Float.doubleEq"
+  , PrimFloatInequality          |-> return "MAlonzo.RTE.Float.doubleLe"
+  , PrimFloatLess                |-> return "MAlonzo.RTE.Float.doubleLt"
+  , PrimFloatIsInfinite          |-> return "(isInfinite :: Double -> Bool)"
+  , PrimFloatIsNaN               |-> return "(isNaN :: Double -> Bool)"
+  , PrimFloatIsNegativeZero      |-> return "(isNegativeZero :: Double -> Bool)"
+  , PrimFloatIsSafeInteger       |-> return "MAlonzo.RTE.Float.isSafeInteger"
+  , PrimFloatToWord64            |-> return "MAlonzo.RTE.Float.doubleToWord64"
+  , PrimFloatToWord64Injective   |-> return mazErasedName
+  , PrimNatToFloat               |-> return "(MAlonzo.RTE.Float.intToDouble :: Integer -> Double)"
+  , PrimIntToFloat               |-> return "(MAlonzo.RTE.Float.intToDouble :: Integer -> Double)"
+  , PrimFloatRound               |-> return "MAlonzo.RTE.Float.doubleRound"
+  , PrimFloatFloor               |-> return "MAlonzo.RTE.Float.doubleFloor"
+  , PrimFloatCeiling             |-> return "MAlonzo.RTE.Float.doubleCeiling"
+  , PrimFloatToRatio             |-> return "MAlonzo.RTE.Float.doubleToRatio"
+  , PrimRatioToFloat             |-> return "MAlonzo.RTE.Float.ratioToDouble"
+  , PrimFloatDecode              |-> return "MAlonzo.RTE.Float.doubleDecode"
+  , PrimFloatEncode              |-> return "MAlonzo.RTE.Float.doubleEncode"
+  , PrimShowFloat                |-> return "(Data.Text.pack . show :: Double -> Data.Text.Text)"
+  , PrimFloatPlus                |-> return "MAlonzo.RTE.Float.doublePlus"
+  , PrimFloatMinus               |-> return "MAlonzo.RTE.Float.doubleMinus"
+  , PrimFloatTimes               |-> return "MAlonzo.RTE.Float.doubleTimes"
+  , PrimFloatNegate              |-> return "MAlonzo.RTE.Float.doubleNegate"
+  , PrimFloatDiv                 |-> return "MAlonzo.RTE.Float.doubleDiv"
+  , PrimFloatPow                 |-> return "MAlonzo.RTE.Float.doublePow"
+  , PrimFloatSqrt                |-> return "MAlonzo.RTE.Float.doubleSqrt"
+  , PrimFloatExp                 |-> return "MAlonzo.RTE.Float.doubleExp"
+  , PrimFloatLog                 |-> return "MAlonzo.RTE.Float.doubleLog"
+  , PrimFloatSin                 |-> return "MAlonzo.RTE.Float.doubleSin"
+  , PrimFloatCos                 |-> return "MAlonzo.RTE.Float.doubleCos"
+  , PrimFloatTan                 |-> return "MAlonzo.RTE.Float.doubleTan"
+  , PrimFloatASin                |-> return "MAlonzo.RTE.Float.doubleASin"
+  , PrimFloatACos                |-> return "MAlonzo.RTE.Float.doubleACos"
+  , PrimFloatATan                |-> return "MAlonzo.RTE.Float.doubleATan"
+  , PrimFloatATan2               |-> return "MAlonzo.RTE.Float.doubleATan2"
+  , PrimFloatSinh                |-> return "MAlonzo.RTE.Float.doubleSinh"
+  , PrimFloatCosh                |-> return "MAlonzo.RTE.Float.doubleCosh"
+  , PrimFloatTanh                |-> return "MAlonzo.RTE.Float.doubleTanh"
+  , PrimFloatASinh               |-> return "MAlonzo.RTE.Float.doubleASinh"
+  , PrimFloatACosh               |-> return "MAlonzo.RTE.Float.doubleACosh"
+  , PrimFloatATanh               |-> return "MAlonzo.RTE.Float.doubleATanh"
+
+  -- Character functions
+  , PrimCharEquality     |-> rel "(==)" "Char"
+  , PrimIsLower          |-> return "Data.Char.isLower"
+  , PrimIsDigit          |-> return "Data.Char.isDigit"
+  , PrimIsAlpha          |-> return "Data.Char.isAlpha"
+  , PrimIsSpace          |-> return "Data.Char.isSpace"
+  , PrimIsAscii          |-> return "Data.Char.isAscii"
+  , PrimIsLatin1         |-> return "Data.Char.isLatin1"
+  , PrimIsPrint          |-> return "Data.Char.isPrint"
+  , PrimIsHexDigit       |-> return "Data.Char.isHexDigit"
+  , PrimToUpper          |-> return "Data.Char.toUpper"
+  , PrimToLower          |-> return "Data.Char.toLower"
+  , PrimCharToNat   |-> return "(fromIntegral . fromEnum :: Char -> Integer)"
+  , PrimNatToChar   |-> return "MAlonzo.RTE.natToChar"
+  , PrimShowChar    |-> return "(Data.Text.pack . show :: Char -> Data.Text.Text)"
+  , PrimCharToNatInjective   |-> return mazErasedName
+
+  -- String functions
+  , PrimStringUncons     |-> return "Data.Text.uncons"
+  , PrimStringToList     |-> return "Data.Text.unpack"
+  , PrimStringFromList   |-> return "Data.Text.pack"
+  , PrimStringAppend     |-> binAsis "Data.Text.append" "Data.Text.Text"
+  , PrimStringEquality   |-> rel "(==)" "Data.Text.Text"
+  , PrimShowString       |-> return "(Data.Text.pack . show :: Data.Text.Text -> Data.Text.Text)"
+  , PrimStringToListInjective   |-> return mazErasedName
+  , PrimStringFromListInjective   |-> return mazErasedName
+
+  -- Reflection
+  , PrimQNameEquality     |-> rel "(==)" "MAlonzo.RTE.QName"
+  , PrimQNameLess         |-> rel "(<)" "MAlonzo.RTE.QName"
+  , PrimShowQName         |-> return "Data.Text.pack . MAlonzo.RTE.qnameString"
+  , PrimQNameFixity       |-> return "MAlonzo.RTE.qnameFixity"
+  , PrimQNameToWord64s    |-> return "\\ qn -> (MAlonzo.RTE.nameId qn, MAlonzo.RTE.moduleId qn)"
+  , PrimQNameToWord64sInjective   |-> return mazErasedName
+  , PrimMetaEquality      |-> rel "(==)" "(Integer, Integer)"
+  , PrimMetaLess          |-> rel "(<)" "(Integer, Integer)"
+  -- Should be kept in sync with version in `primitiveFunctions` in
+  -- Agda.TypeChecking.Primitive
+  , PrimShowMeta          |-> return "\\ (m, h) -> Data.Text.pack (\"_\" ++ show (m :: Integer) ++ \"@\" ++ show (h :: Integer))"
+  -- Should be kept in sync with `metaToNat` in Agda.TypeChecking.Primitive
+  , PrimMetaToNat         |-> return "\\ (m, h) -> (h :: Integer) * 2^64 + (m :: Integer)"
+  , PrimMetaToNatInjective   |-> return mazErasedName
+
+  -- Seq
+  , PrimForce        |-> return "\\ _ _ _ _ x f -> f $! x"
+  , PrimForceLemma   |-> return mazErasedName
+
+  -- Lock universe
+  , PrimLockUniv |-> return "()"
+
+  -- Erase
+  , PrimEraseEquality |-> return mazErasedName
+
+  -- Cubical
+  , PrimIMin          |-> return "(&&)"
+  , PrimIMax          |-> return "(||)"
+  , PrimINeg          |-> return "not"
+  , PrimPartial       |-> return "\\_ _ x -> x"
+  , PrimPartialP      |-> return "\\_ _ x -> x"
+  , PrimPOr           |-> return "\\_ i _ _ x y -> if i then x else y"
+  , PrimComp          |-> return "\\_ _ _ _ x -> x"
+  , PrimTrans         |-> return "\\_ _ _ x -> x"
+  , PrimHComp         |-> return "\\_ _ _ _ x -> x"
+  , PrimSubOut        |-> return "\\_ _ _ _ x -> x"
+  , Prim_glueU        |-> return "\\_ _ _ _ _ x -> x"
+  , Prim_unglueU      |-> return "\\_ _ _ _ x -> x"
+  , PrimFaceForall    |-> return
+                            "\\f -> f True == True && f False == True"
+  , PrimDepIMin       |-> return "\\i f -> if i then f () else False"
+  , PrimIdFace        |-> return "\\_ _ _ _ -> fst"
+  , PrimIdPath        |-> return "\\_ _ _ _ -> snd"
+  , PrimIdElim        |-> return
+                            "\\_ _ _ _ _ f x y -> f (fst y) x (snd y)"
+  ]
+  where
+  x |-> s = (x, Left <$> s)
+  binNat  op = return $ repl [op] "(<<0>> :: Integer -> Integer -> Integer)"
+  binNat4 op = return $ repl [op] "(<<0>> :: Integer -> Integer -> Integer -> Integer -> Integer)"
+  binAsis op ty = return $ repl [op, opty ty] $ "((<<0>>) :: <<1>>)"
+  rel' toTy op ty = do
+    return $ repl [op, ty, toTy] $
+      "(\\ x y -> (<<0>> :: <<1>> -> <<1>> -> Bool) (<<2>> x) (<<2>> y))"
+  relNat op = do
+    return $ repl [op] $
+      "(<<0>> :: Integer -> Integer -> Bool)"
+  rel op ty  = rel' "" op ty
+  opty t = t ++ "->" ++ t ++ "->" ++ t
+  unimplemented = typeError $ NotImplemented (getBuiltinId s)
+
+  hLam x t = Lam (setHiding Hidden defaultArgInfo) (Abs x t)
+  nLam x t = Lam (setHiding NotHidden defaultArgInfo) (Abs x t)
+
+noCheckCover :: (HasBuiltins m, MonadReduce m) => QName -> m Bool
+noCheckCover q = (||) <$> isBuiltin q builtinNat <*> isBuiltin q builtinInteger
diff --git a/src/full/Agda/Compiler/MAlonzo/Strict.hs b/src/full/Agda/Compiler/MAlonzo/Strict.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/MAlonzo/Strict.hs
@@ -0,0 +1,91 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | Strictification of Haskell code
+------------------------------------------------------------------------
+
+module Agda.Compiler.MAlonzo.Strict where
+
+import Agda.Utils.Haskell.Syntax
+
+-- | The function 'makeStrict' makes every function argument, case and
+-- generator pattern, and 'LocalBind' binding strict (except for those
+-- patterns that are marked as irrefutable, and anything in a
+-- 'FakeDecl' or 'FakeExp'). Note that only the outermost patterns are
+-- made strict.
+
+class MakeStrict a where
+  makeStrict :: a -> a
+
+instance MakeStrict a => MakeStrict [a] where
+  makeStrict = map makeStrict
+
+instance MakeStrict a => MakeStrict (Maybe a) where
+  makeStrict = fmap makeStrict
+
+instance MakeStrict Module where
+  makeStrict (Module m pragmas imps decls) =
+    Module m pragmas imps (makeStrict decls)
+
+instance MakeStrict Decl where
+  makeStrict = \case
+    d@TypeDecl{}      -> d
+    d@DataDecl{}      -> d
+    d@TypeSig{}       -> d
+    FunBind ms        -> FunBind (makeStrict ms)
+    LocalBind s f rhs -> LocalBind Strict f (makeStrict rhs)
+    d@PatSyn{}        -> d
+    d@FakeDecl{}      -> d
+    d@Comment{}       -> d
+
+instance MakeStrict Match where
+  makeStrict (Match f ps rhs wh) =
+    Match f (makeStrict ps) (makeStrict rhs) (makeStrict wh)
+
+instance MakeStrict Pat where
+  makeStrict = \case
+    p@PVar{}       -> PBangPat p
+    p@PLit{}       -> PBangPat p
+    PAsPat x p     -> PAsPat x (makeStrict p)
+    p@PWildCard{}  -> PBangPat p
+    p@PBangPat{}   -> p
+    p@PApp{}       -> PBangPat p
+    PatTypeSig p t -> PatTypeSig (makeStrict p) t
+    p@PIrrPat{}    -> p
+
+instance MakeStrict Binds where
+  makeStrict (BDecls ds) = BDecls (makeStrict ds)
+
+instance MakeStrict Rhs where
+  makeStrict (UnGuardedRhs e) = UnGuardedRhs (makeStrict e)
+  makeStrict (GuardedRhss rs) = GuardedRhss (makeStrict rs)
+
+instance MakeStrict GuardedRhs where
+  makeStrict (GuardedRhs ss e) =
+    GuardedRhs (makeStrict ss) (makeStrict e)
+
+instance MakeStrict Stmt where
+  makeStrict = \case
+    Qualifier e   -> Qualifier (makeStrict e)
+    Generator p e -> Generator (makeStrict p) (makeStrict e)
+
+instance MakeStrict Exp where
+  makeStrict e =
+    case e of
+      Var{}           -> e
+      Con{}           -> e
+      Lit{}           -> e
+      InfixApp a op b -> InfixApp (makeStrict a) op (makeStrict b)
+      Ann e ty        -> Ann (makeStrict e) ty
+      App a b         -> App (makeStrict a) (makeStrict b)
+      Lambda ps e     -> Lambda (makeStrict ps) (makeStrict e)
+      Let bs e        -> Let (makeStrict bs) (makeStrict e)
+      If a b c        -> If (makeStrict a) (makeStrict b) (makeStrict c)
+      Case e bs       -> Case (makeStrict e) (makeStrict bs)
+      ExpTypeSig e t  -> ExpTypeSig (makeStrict e) t
+      NegApp e        -> NegApp (makeStrict e)
+      FakeExp s       -> FakeExp s
+
+instance MakeStrict Alt where
+  makeStrict (Alt pat rhs wh) =
+    Alt (makeStrict pat) (makeStrict rhs) (makeStrict wh)
diff --git a/src/full/Agda/Compiler/ToTreeless.hs b/src/full/Agda/Compiler/ToTreeless.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/ToTreeless.hs
@@ -0,0 +1,610 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.ToTreeless
+  ( toTreeless
+  , closedTermToTreeless
+  ) where
+
+import Prelude hiding ((!!))
+
+import Control.Monad        ( filterM, foldM, forM, zipWithM )
+import Control.Monad.Reader ( MonadReader(..), asks, ReaderT, runReaderT )
+import Control.Monad.Trans  ( lift )
+
+import Data.Maybe
+import Data.Map (Map)
+import qualified Data.Map  as Map
+import qualified Data.List as List
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Literal
+import qualified Agda.Syntax.Treeless as C
+import Agda.Syntax.Treeless (TTerm, EvaluationStrategy, ArgUsage(..))
+
+import Agda.TypeChecking.CompiledClause as CC
+import qualified Agda.TypeChecking.CompiledClause.Compile as CC
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.EtaContract (binAppView, BinAppView(..))
+import Agda.TypeChecking.Monad as TCM
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records (getRecordConstructor)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+
+import Agda.Compiler.Treeless.AsPatterns
+import Agda.Compiler.Treeless.Builtin
+import Agda.Compiler.Treeless.Erase
+import Agda.Compiler.Treeless.Identity
+import Agda.Compiler.Treeless.Simplify
+import Agda.Compiler.Treeless.Uncase
+import Agda.Compiler.Treeless.Unused
+
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Syntax.Common.Pretty as P
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+
+prettyPure :: P.Pretty a => a -> TCM Doc
+prettyPure = return . P.pretty
+
+-- | Recompile clauses with forcing translation turned on.
+getCompiledClauses :: QName -> TCM CC.CompiledClauses
+getCompiledClauses q = do
+  def <- getConstInfo q
+  let cs = defClauses def
+      isProj | Function{ funProjection = Right x } <- theDef def = isJust (projProper x)
+             | otherwise = False
+      translate | isProj    = CC.DontRunRecordPatternTranslation
+                | otherwise = CC.RunRecordPatternTranslation
+  reportSDoc "treeless.convert" 40 $ "-- before clause compiler" $$ (pretty q <+> "=") <?> vcat (map pretty cs)
+  let mst = funSplitTree $ theDef def
+  reportSDoc "treeless.convert" 70 $
+    caseMaybe mst "-- not using split tree" $ \st ->
+      "-- using split tree" $$ pretty st
+  CC.compileClauses' translate cs mst
+
+-- | Converts compiled clauses to treeless syntax.
+--
+-- Note: Do not use any of the concrete names in the returned
+-- term for identification purposes! If you wish to do so,
+-- first apply the Agda.Compiler.Treeless.NormalizeNames
+-- transformation.
+toTreeless :: EvaluationStrategy -> QName -> TCM (Maybe C.TTerm)
+toTreeless eval q = ifM (alwaysInline q) (pure Nothing) $ Just <$> toTreeless' eval q
+
+toTreeless' :: EvaluationStrategy -> QName -> TCM C.TTerm
+toTreeless' eval q =
+  flip fromMaybeM (getTreeless q) $ verboseBracket "treeless.convert" 20 ("compiling " ++ prettyShow q) $ do
+    cc <- getCompiledClauses q
+    unlessM (alwaysInline q) $ setTreeless q (C.TDef q)
+      -- so recursive inlining doesn't loop, but not for always inlined
+      -- functions, since that would risk inlining to fail.
+    ccToTreeless eval q cc
+
+-- | Does not require the name to refer to a function.
+cacheTreeless :: EvaluationStrategy -> QName -> TCM ()
+cacheTreeless eval q = do
+  def <- theDef <$> getConstInfo q
+  case def of
+    Function{} -> () <$ toTreeless' eval q
+    _          -> return ()
+
+ccToTreeless :: EvaluationStrategy -> QName -> CC.CompiledClauses -> TCM C.TTerm
+ccToTreeless eval q cc = do
+  let pbody b = pbody' "" b
+      pbody' suf b = sep [ text (prettyShow q ++ suf) <+> "=", nest 2 $ prettyPure b ]
+  v <- ifM (alwaysInline q) (return 20) (return 0)
+  reportSDoc "treeless.convert" (30 + v) $ "-- compiled clauses of" <+> prettyTCM q $$ nest 2 (prettyPure cc)
+  body <- casetreeTop eval cc
+  reportSDoc "treeless.opt.converted" (30 + v) $ "-- converted" $$ pbody body
+  body <- runPipeline eval q (compilerPipeline v q) body
+  used <- usedArguments q body
+  when (ArgUnused `elem` used) $
+    reportSDoc "treeless.opt.unused" (30 + v) $
+      "-- used args:" <+> hsep [ if u == ArgUsed then text [x] else "_" | (x, u) <- zip ['a'..] used ] $$
+      pbody' "[stripped]" (stripUnusedArguments used body)
+  reportSDoc "treeless.opt.final" (20 + v) $ pbody body
+  setTreeless q body
+  setCompiledArgUse q used
+  return body
+
+data Pipeline = FixedPoint Int Pipeline
+              | Sequential [Pipeline]
+              | SinglePass CompilerPass
+
+data CompilerPass = CompilerPass
+  { passTag       :: String
+  , passVerbosity :: Int
+  , passName      :: String
+  , passCode      :: EvaluationStrategy -> TTerm -> TCM TTerm
+  }
+
+compilerPass :: String -> Int -> String -> (EvaluationStrategy -> TTerm -> TCM TTerm) -> Pipeline
+compilerPass tag v name code = SinglePass (CompilerPass tag v name code)
+
+compilerPipeline :: Int -> QName -> Pipeline
+compilerPipeline v q =
+  Sequential
+    -- Issue #4967: No simplification step before builtin translation! Simplification relies
+    --              on either all or no builtins being translated. Since we might have inlined
+    --              functions that have had the builtin translation applied, we need to apply it
+    --              first.
+    -- [ compilerPass "simpl"   (35 + v) "simplification"      $ const simplifyTTerm
+    [ compilerPass "builtin" (30 + v) "builtin translation" $ const translateBuiltins
+    , FixedPoint 5 $ Sequential
+      [ compilerPass "simpl"  (30 + v) "simplification"     $ const simplifyTTerm
+      , compilerPass "erase"  (30 + v) "erasure"            $ eraseTerms q
+      , compilerPass "uncase" (30 + v) "uncase"             $ const caseToSeq
+      , compilerPass "aspat"  (30 + v) "@-pattern recovery" $ const recoverAsPatterns
+      ]
+    , compilerPass "id" (30 + v) "identity function detection" $ const (detectIdentityFunctions q)
+    ]
+
+runPipeline :: EvaluationStrategy -> QName -> Pipeline -> TTerm -> TCM TTerm
+runPipeline eval q pipeline t = case pipeline of
+  SinglePass p   -> runCompilerPass eval q p t
+  Sequential ps  -> foldM (flip $ runPipeline eval q) t ps
+  FixedPoint n p -> runFixedPoint n eval q p t
+
+runCompilerPass :: EvaluationStrategy -> QName -> CompilerPass -> TTerm -> TCM TTerm
+runCompilerPass eval q p t = do
+  t' <- passCode p eval t
+  let dbg f   = reportSDoc ("treeless.opt." ++ passTag p) (passVerbosity p) $ f $ text ("-- " ++ passName p)
+      pbody b = sep [ text (prettyShow q) <+> "=", nest 2 $ prettyPure b ]
+  dbg $ if | t == t'   -> (<+> "(No effect)")
+           | otherwise -> ($$ pbody t')
+  return t'
+
+runFixedPoint :: Int -> EvaluationStrategy -> QName -> Pipeline -> TTerm -> TCM TTerm
+runFixedPoint n eval q pipeline = go 1
+  where
+    go i t | i > n = do
+      reportSLn "treeless.opt.loop" 20 $ "++ Optimisation loop reached maximum iterations (" ++ show n ++ ")"
+      return t
+    go i t = do
+      reportSLn "treeless.opt.loop" 30 $ "++ Optimisation loop iteration " ++ show i
+      t' <- runPipeline eval q pipeline t
+      if | t == t'   -> do
+            reportSLn "treeless.opt.loop" 30 $ "++ Optimisation loop terminating after " ++ show i ++ " iterations"
+            return t'
+         | otherwise -> go (i + 1) t'
+
+closedTermToTreeless :: EvaluationStrategy -> I.Term -> TCM C.TTerm
+closedTermToTreeless eval t = do
+  substTerm t `runReaderT` initCCEnv eval
+
+alwaysInline :: QName -> TCM Bool
+alwaysInline q = do
+  def <- theDef <$> getConstInfo q
+  pure $ case def of  -- always inline with functions and pattern lambdas
+    Function{funClauses = cs} -> (isJust (funExtLam def) && not recursive) || isJust (funWith def)
+            where
+              recursive = any (fromMaybe True . clauseRecursive) cs
+    _ -> False
+
+-- | Initial environment for expression generation.
+initCCEnv :: EvaluationStrategy -> CCEnv
+initCCEnv eval = CCEnv
+  { ccCxt        = []
+  , ccCatchAll   = Nothing
+  , ccEvaluation = eval
+  }
+
+-- | Environment for naming of local variables.
+data CCEnv = CCEnv
+  { ccCxt        :: CCContext  -- ^ Maps case tree de-bruijn indices to TTerm de-bruijn indices
+  , ccCatchAll   :: Maybe Int  -- ^ TTerm de-bruijn index of the current catch all
+  -- If an inner case has no catch-all clause, we use the one from its parent.
+  , ccEvaluation :: EvaluationStrategy
+  }
+
+type CCContext = [Int]
+type CC = ReaderT CCEnv TCM
+
+shift :: Int -> CCContext -> CCContext
+shift n = map (+ n)
+
+-- | Term variables are de Bruijn indices.
+lookupIndex :: Int -- ^ Case tree de bruijn index.
+    -> CCContext
+    -> Int -- ^ TTerm de bruijn index.
+lookupIndex i xs = fromMaybe __IMPOSSIBLE__ $ xs !!! i
+
+-- | Case variables are de Bruijn levels.
+lookupLevel :: Int -- ^ case tree de bruijn level
+    -> CCContext
+    -> Int -- ^ TTerm de bruijn index
+lookupLevel l xs = fromMaybe __IMPOSSIBLE__ $ xs !!! (length xs - 1 - l)
+
+-- | Compile a case tree into nested case and record expressions.
+casetreeTop :: EvaluationStrategy -> CC.CompiledClauses -> TCM C.TTerm
+casetreeTop eval cc = flip runReaderT (initCCEnv eval) $ do
+  let a = commonArity cc
+  lift $ reportSLn "treeless.convert.arity" 40 $ "-- common arity: " ++ show a
+  lambdasUpTo a $ casetree cc
+
+casetree :: CC.CompiledClauses -> CC C.TTerm
+casetree cc = do
+  case cc of
+    CC.Fail xs -> withContextSize (length xs) $ return C.tUnreachable
+    CC.Done xs v -> withContextSize (length xs) $ do
+      -- Issue 2469: Body context size (`length xs`) may be smaller than current context size
+      -- if some arguments are not used in the body.
+      v <- lift (putAllowedReductions (SmallSet.fromList [ProjectionReductions, CopatternReductions]) $ normalise v)
+      cxt <- asks ccCxt
+      v' <- substTerm v
+      reportS "treeless.convert.casetree" 40 $
+        [ "-- casetree, calling substTerm:"
+        , "--   cxt =" <+> prettyPure cxt
+        , "--   v   =" <+> prettyPure v
+        , "--   v'  =" <+> prettyPure v'
+        ]
+      return v'
+    CC.Case _ (CC.Branches True _ _ _ Just{} _ _) -> __IMPOSSIBLE__
+      -- Andreas, 2016-06-03, issue #1986: Ulf: "no catch-all for copatterns!"
+      -- lift $ do
+      --   typeError . GenericDocError =<< do
+      --     "Not yet implemented: compilation of copattern matching with catch-all clause"
+    CC.Case (Arg _ n) (CC.Branches True conBrs _ _ Nothing _ _) -> lambdasUpTo n $ do
+      mkRecord =<< traverse casetree (CC.content <$> conBrs)
+    CC.Case (Arg i n) (CC.Branches False conBrs etaBr litBrs catchAll _ lazy) -> lambdasUpTo (n + 1) $ do
+      -- re #3733 TODO: revise when compiling --cubical
+      conBrs <- fmap Map.fromList $ filterM (isConstructor . fst) (Map.toList conBrs)
+                    -- We can treat eta-matches as regular matches here.
+      let conBrs' = caseMaybe etaBr conBrs $ \ (c, br) -> Map.insertWith (\ new old -> old) (conName c) br conBrs
+      if Map.null conBrs' && Map.null litBrs then do
+        -- there are no branches, just return default
+        updateCatchAll catchAll fromCatchAll
+      else do
+        -- Get the type of the scrutinee.
+        caseTy <-
+          case (Map.keys conBrs', Map.keys litBrs) of
+            (cs, []) -> lift $ go cs
+              where
+              go (c:cs) = canonicalName c >>= getConstInfo <&> theDef >>= \case
+                Constructor{conData} ->
+                  return $ C.CTData conData
+                _ -> go cs
+              go [] = __IMPOSSIBLE__
+            ([], LitChar   _ : _) -> return C.CTChar
+            ([], LitString _ : _) -> return C.CTString
+            ([], LitFloat  _ : _) -> return C.CTFloat
+            ([], LitQName  _ : _) -> return C.CTQName
+            _ -> __IMPOSSIBLE__
+
+        updateCatchAll catchAll $ do
+          x <- asks (lookupLevel n . ccCxt)
+          def <- fromCatchAll
+          let caseInfo = C.CaseInfo
+                { caseType   = caseTy
+                , caseLazy   = lazy
+                , caseErased = fromMaybe __IMPOSSIBLE__ $
+                               erasedFromQuantity (getQuantity i)
+                }
+          C.TCase x caseInfo def <$> do
+            br1 <- conAlts n conBrs'
+            br2 <- litAlts n litBrs
+            return (br1 ++ br2)
+  where
+    -- normally, Agda should make sure that a pattern match is total,
+    -- so we set the default to unreachable if no default has been provided.
+    fromCatchAll :: CC C.TTerm
+    fromCatchAll = asks (maybe C.tUnreachable C.TVar . ccCatchAll)
+
+commonArity :: CC.CompiledClauses -> Int
+commonArity cc =
+  case arities 0 cc of
+    [] -> 0
+    as -> minimum as
+  where
+    arities cxt (Case (Arg _ x) (Branches False cons eta lits def _ _)) =
+      concatMap (wArities cxt') (Map.elems cons) ++
+      concatMap ((wArities cxt') . snd) (maybeToList eta) ++
+      concatMap (wArities cxt' . WithArity 0) (Map.elems lits) ++
+      concat [ arities cxt' c | Just c <- [def] ] -- ??
+      where cxt' = max (x + 1) cxt
+    arities cxt (Case _ Branches{projPatterns = True}) = [cxt]
+    arities cxt (Done xs _) = [max cxt (length xs)]
+    arities cxt (Fail xs)   = [max cxt (length xs)]
+
+
+    wArities cxt (WithArity k c) = map (\ x -> x - k + 1) $ arities (cxt - 1 + k) c
+
+updateCatchAll :: Maybe CC.CompiledClauses -> (CC C.TTerm -> CC C.TTerm)
+updateCatchAll Nothing cont = cont
+updateCatchAll (Just cc) cont = do
+  def <- casetree cc
+  cxt <- asks ccCxt
+  reportS "treeless.convert.lambdas" 40 $
+    [ "-- updateCatchAll:"
+    , "--   cxt =" <+> prettyPure cxt
+    , "--   def =" <+> prettyPure def
+    ]
+  local (\ e -> e { ccCatchAll = Just 0, ccCxt = shift 1 cxt }) $ do
+    C.mkLet def <$> cont
+
+-- | Shrinks or grows the context to the given size.
+-- Does not update the catchAll expression, the catchAll expression
+-- MUST NOT be used inside `cont`.
+withContextSize :: Int -> CC C.TTerm -> CC C.TTerm
+withContextSize n cont = do
+  diff <- asks (((n -) . length) . ccCxt)
+  if diff >= 1 then createLambdas diff cont else do
+    let diff' = -diff
+    cxt <- -- shift diff .
+       -- Andreas, 2021-04-10, issue #5288
+       -- The @shift diff@ is wrong, since we are returning to the original
+       -- context from @cont@, and then we would have to reverse
+       -- the effect of @shift diff@.
+       -- We need to make sure that the result of @cont@ make sense
+       -- in the **present** context, not the changed context
+       -- where it is constructed.
+       --
+       -- Ulf, 2021-04-12, https://github.com/agda/agda/pull/5311/files#r611452551
+       --
+       -- This looks correct, but I can't quite follow the explanation. Here's my understanding:
+       --
+       -- We are building a `TTerm` case tree from `CompiledClauses`. In order
+       -- to be able to match we bind all variables we'll need in a top-level
+       -- lambda `λ a b c d → ..` (say). As we compute the `TTerm` we keep a
+       -- context (list) of `TTerm` deBruijn indices for each `CompiledClause`
+       -- variable. This is a renaming from the *source* context of the
+       -- `CompiledClause` to the *target* context of the `TTerm`.
+       --
+       -- After some pattern matching we might have
+       -- ```
+       -- λ a b c d →
+       --   case c of
+       --     e :: f → {cxt = [d, f, e, b, a]}
+       -- ```
+       -- Now, what's causing the problems here is that `CompiledClauses` can be
+       -- underapplied, so you might have matched on a variable only to find
+       -- that in the catch-all the variable you matched on is bound in a lambda
+       -- in the right-hand side! Extending the example, we might have
+       -- `CompiledClauses` looking like this:
+       -- ```
+       -- case 2 of
+       --   _::_ → done[d, f, e, b, a] ...
+       --   _    → done[b, a] (λ c d → ...)
+       -- ```
+       -- When we get to the catch-all, the context will be `[d, c, b, a]` but
+       -- the right-hand side is only expecting `a` and `b` to be bound. What we
+       -- need to do is compile the right-hand side and then apply it to the
+       -- variables `c` and `d` that we already bound. This is what
+       -- `withContextSize` does.
+       --
+       -- Crucially (and this is where the bug was), we are not changing the
+       -- target context, only the source context (we want a `TTerm` that makes
+       -- sense at this point). This means that the correct move is to drop the
+       -- entries for the additional source variables, but not change what
+       -- target variables the remaining source variables map to. Hence, `drop`
+       -- but no `shift`.
+       --
+       drop diff' <$> asks ccCxt
+    local (\ e -> e { ccCxt = cxt }) $ do
+      reportS "treeless.convert.lambdas" 40 $
+        [ "-- withContextSize:"
+        , "--   n   =" <+> prettyPure n
+        , "--   diff=" <+> prettyPure diff
+        , "--   cxt =" <+> prettyPure cxt
+        ]
+      cont <&> (`C.mkTApp` map C.TVar (downFrom diff'))
+
+-- | Prepend the given positive number of lambdas.
+-- Does not update the catchAll expression,
+-- the catchAll expression must be updated separately (or not be used).
+createLambdas :: Int -> CC C.TTerm -> CC C.TTerm
+createLambdas diff cont = do
+  unless (diff >= 1) __IMPOSSIBLE__
+  cxt <- ([0 .. diff-1] ++) . shift diff <$> asks ccCxt
+  local (\ e -> e { ccCxt = cxt }) $ do
+    reportS "treeless.convert.lambdas" 40 $
+      [ "-- createLambdas:"
+      , "--   diff =" <+> prettyPure diff
+      , "--   cxt  =" <+> prettyPure cxt
+      ]
+    -- Prepend diff lambdas
+    cont <&> \ t -> List.iterate C.TLam t !! diff
+
+-- | Adds lambdas until the context has at least the given size.
+-- Updates the catchAll expression to take the additional lambdas into account.
+lambdasUpTo :: Int -> CC C.TTerm -> CC C.TTerm
+lambdasUpTo n cont = do
+  diff <- asks (((n -) . length) . ccCxt)
+
+  if diff <= 0 then cont -- no new lambdas needed
+  else do
+    createLambdas diff $ do
+      asks ccCatchAll >>= \case
+        Just catchAll -> do
+          cxt <- asks ccCxt
+          reportS "treeless.convert.lambdas" 40 $
+            [ "lambdasUpTo: n =" <+> (text . show) n
+            , "  diff         =" <+> (text . show) n
+            , "  catchAll     =" <+> prettyPure catchAll
+            , "  ccCxt        =" <+> prettyPure cxt
+            ]
+          -- the catch all doesn't know about the additional lambdas, so just directly
+          -- apply it again to the newly introduced lambda arguments.
+          -- we also bind the catch all to a let, to avoid code duplication
+          local (\e -> e { ccCatchAll = Just 0
+                         , ccCxt = shift 1 cxt }) $ do
+            let catchAllArgs = map C.TVar $ downFrom diff
+            C.mkLet (C.mkTApp (C.TVar $ catchAll + diff) catchAllArgs)
+              <$> cont
+        Nothing -> cont
+
+conAlts :: Int -> Map QName (CC.WithArity CC.CompiledClauses) -> CC [C.TAlt]
+conAlts x br = forM (Map.toList br) $ \ (c, CC.WithArity n cc) -> do
+  c' <- lift $ canonicalName c
+  replaceVar x n $ do
+    branch (C.TACon c' n) cc
+
+litAlts :: Int -> Map Literal CC.CompiledClauses -> CC [C.TAlt]
+litAlts x br = forM (Map.toList br) $ \ (l, cc) ->
+  -- Issue1624: we need to drop the case scrutinee from the environment here!
+  replaceVar x 0 $ do
+    branch (C.TALit l ) cc
+
+branch :: (C.TTerm -> C.TAlt) -> CC.CompiledClauses -> CC C.TAlt
+branch alt cc = alt <$> casetree cc
+
+-- | Replace de Bruijn Level @x@ by @n@ new variables.
+replaceVar :: Int -> Int -> CC a -> CC a
+replaceVar x n cont = do
+  let upd cxt = shift n ys ++ ixs ++ shift n zs
+       where
+         -- compute the de Bruijn index
+         i = length cxt - 1 - x
+         -- discard index i
+         (ys, _:zs) = splitAt i cxt
+         -- compute the de-bruijn indexes of the newly inserted variables
+         ixs = [0..(n - 1)]
+  local (\e -> e { ccCxt = upd (ccCxt e) , ccCatchAll = (+ n) <$> ccCatchAll e }) $
+    cont
+
+
+-- | Precondition: Map not empty.
+mkRecord :: Map QName C.TTerm -> CC C.TTerm
+mkRecord fs = lift $ do
+  -- Get the name of the first field
+  let p1 = fst $ headWithDefault __IMPOSSIBLE__ $ Map.toList fs
+  -- Use the field name to get the record constructor and the field names.
+  I.ConHead c IsRecord{} _ind xs <- conSrcCon . theDef <$> (getConstInfo =<< canonicalName . I.conName =<< recConFromProj p1)
+  reportSDoc "treeless.convert.mkRecord" 60 $ vcat
+    [ text "record constructor fields: xs      = " <+> (text . show) xs
+    , text "to be filled with content: keys fs = " <+> (text . show) (Map.keys fs)
+    ]
+  -- Convert the constructor
+  let (args :: [C.TTerm]) = for xs $ \ x -> Map.findWithDefault __IMPOSSIBLE__ (unArg x) fs
+  return $ C.mkTApp (C.TCon c) args
+
+
+recConFromProj :: QName -> TCM I.ConHead
+recConFromProj q = do
+  caseMaybeM (isProjection q) __IMPOSSIBLE__ $ \ proj -> do
+    -- Get the record type name @d@ from the projection.
+    let d = unArg $ projFromType proj
+    getRecordConstructor d
+
+
+-- | Translate the actual Agda terms, with an environment of all the bound variables
+--   from patternmatching. Agda terms are in de Bruijn indices, but the expected
+--   TTerm de bruijn indexes may differ. This is due to additional let-bindings
+--   introduced by the catch-all machinery, so we need to lookup casetree de bruijn
+--   indices in the environment as well.
+substTerm :: I.Term -> CC C.TTerm
+substTerm term = normaliseStatic term >>= \ term ->
+  case I.unSpine $ etaContractErased term of
+    I.Var ind es -> do
+      ind' <- asks (lookupIndex ind . ccCxt)
+      let args = fromMaybe __IMPOSSIBLE__ $ I.allApplyElims es
+      C.mkTApp (C.TVar ind') <$> substArgs args
+    I.Lam _ ab ->
+      C.TLam <$>
+        local (\e -> e { ccCxt = 0 : shift 1 (ccCxt e) })
+          (substTerm $ I.unAbs ab)
+    I.Lit l -> return $ C.TLit l
+    I.Level _ -> return C.TUnit
+    I.Def q es -> do
+      let args = fromMaybe __IMPOSSIBLE__ $ I.allApplyElims es
+      maybeInlineDef q args
+    I.Con c ci es -> do
+        let args = fromMaybe __IMPOSSIBLE__ $ I.allApplyElims es
+        c' <- lift $ canonicalName $ I.conName c
+        C.mkTApp (C.TCon c') <$> substArgs args
+    I.Pi _ _ -> return C.TUnit
+    I.Sort _  -> return C.TSort
+    I.MetaV x _ -> return $ C.TError $ C.TMeta $ prettyShow x
+    I.DontCare _ -> return C.TErased
+    I.Dummy{} -> __IMPOSSIBLE__
+
+-- Andreas, 2019-07-10, issue #3792
+-- | Eta-contract erased lambdas.
+--
+-- Should also be fine for strict backends:
+--
+--   * eta-contraction is semantics-preserving for total, effect-free languages.
+--   * should a user rely on thunking, better not used an erased abstraction!
+--
+-- A live-or-death issue for the GHC 8.0 backend.  Consider:
+-- @
+--   foldl : ∀ {A} (B : Nat → Set)
+--         → (f : ∀ {@0 n} → B n → A → B (suc n))
+--         → (z : B 0)
+--         → ∀ {@0 n} → Vec A n → B n
+--   foldl B f z (x ∷ xs) = foldl (λ n → B (suc n)) (λ{@0 x} → f {suc x}) (f z x) xs
+--   foldl B f z [] = z
+-- @
+-- The hidden composition of @f@ with @suc@, term @(λ{@0 x} → f {suc x})@,
+-- can be eta-contracted to just @f@ by the compiler, since the first argument
+-- of @f@ is erased.
+--
+-- GHC >= 8.2 seems to be able to do the optimization himself, but not 8.0.
+--
+etaContractErased :: I.Term -> I.Term
+etaContractErased = trampoline etaErasedOnce
+  where
+  etaErasedOnce :: I.Term -> Either I.Term I.Term  -- Left = done, Right = jump again
+  etaErasedOnce t =
+    case t of
+
+      -- If the abstraction is void, we don't have to strengthen.
+      I.Lam _ (NoAbs _ v) ->
+        case binAppView v of
+          -- If the body is an application ending with an erased argument, eta-reduce!
+          App u arg | not (usableModality arg) -> Right u
+          _ -> done
+
+      -- If the abstraction is non-void, only eta-contract if erased.
+      I.Lam ai (Abs _ v) | not (usableModality ai) ->
+        case binAppView v of
+          -- If the body is an application ending with an erased argument, eta-reduce!
+          -- We need to strengthen the function part then.
+          App u arg | not (usableModality arg) -> Right $ subst 0 (DontCare __DUMMY_TERM__) u
+          _ -> done
+
+      _ -> done
+    where
+    done = Left t
+
+normaliseStatic :: I.Term -> CC I.Term
+normaliseStatic v@(I.Def f es) = lift $ do
+  static <- isStaticFun . theDef <$> getConstInfo f
+  if static then normalise v else pure v
+normaliseStatic v = pure v
+
+maybeInlineDef :: I.QName -> I.Args -> CC C.TTerm
+maybeInlineDef q vs = do
+  eval <- asks ccEvaluation
+  ifM (lift $ alwaysInline q) (doinline eval) $ do
+    lift $ cacheTreeless eval q
+    def <- lift $ getConstInfo q
+    case theDef def of
+      fun@Function{}
+        | fun ^. funInline -> doinline eval
+        | otherwise -> do
+        -- If ArgUsage hasn't been computed yet, we assume all arguments are used.
+        used <- lift $ fromMaybe [] <$> getCompiledArgUse q
+        let substUsed _   ArgUnused = pure C.TErased
+            substUsed arg ArgUsed   = substArg arg
+        C.mkTApp (C.TDef q) <$> zipWithM substUsed vs (used ++ repeat ArgUsed)
+      _ -> C.mkTApp (C.TDef q) <$> substArgs vs
+  where
+    doinline eval = C.mkTApp <$> inline eval q <*> substArgs vs
+    inline eval q = lift $ toTreeless' eval q
+
+substArgs :: [Arg I.Term] -> CC [C.TTerm]
+substArgs = traverse substArg
+
+substArg :: Arg I.Term -> CC C.TTerm
+substArg x | usableModality x = substTerm (unArg x)
+           | otherwise = return C.TErased
diff --git a/src/full/Agda/Compiler/Treeless/AsPatterns.hs b/src/full/Agda/Compiler/Treeless/AsPatterns.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/AsPatterns.hs
@@ -0,0 +1,76 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.AsPatterns (recoverAsPatterns) where
+
+import Control.Monad.Reader
+
+import Agda.Syntax.Treeless
+
+data AsPat = AsPat Int QName [Int]  -- x@(c ys)
+  deriving (Show)
+
+wk :: Int -> AsPat -> AsPat
+wk n (AsPat x c ys) = AsPat (n + x) c (map (n +) ys)
+
+type S = Reader [AsPat]
+
+runS :: S a -> a
+runS m = runReader m []
+
+underBinds :: Int -> S a -> S a
+underBinds 0 = id
+underBinds n = local (map $ wk n)
+
+bindAsPattern :: AsPat -> S a -> S a
+bindAsPattern p = local (p :)
+
+lookupAsPattern :: QName -> [TTerm] -> S TTerm
+lookupAsPattern c vs
+  | Just xs <- allVars vs = do
+    ps <- ask
+    case [ x | AsPat x c' ys <- ps, c == c', xs == ys ] of
+      x : _ -> pure $ TVar x
+      _     -> pure $ mkTApp (TCon c) vs
+  | otherwise = pure $ mkTApp (TCon c) vs
+  where
+    allVars = mapM getVar
+    getVar (TVar x) = Just x
+    getVar _        = Nothing   -- what about erased?
+
+-- | We lose track of @-patterns in the internal syntax. This pass puts them
+--   back.
+recoverAsPatterns :: Monad m => TTerm -> m TTerm
+recoverAsPatterns t = return $ runS (recover t)
+
+recover :: TTerm -> S TTerm
+recover t =
+  case t of
+    TApp f vs -> do
+      f  <- recover f
+      vs <- mapM recover vs
+      tApp f vs
+    TLam b -> TLam <$> underBinds 1 (recover b)
+    TCon{} -> tApp t []   -- need to recover nullary constructors as well (to make deep @-patterns work)
+    TLet v b -> TLet <$> recover v <*> underBinds 1 (recover b)
+    TCase x ct d bs -> TCase x ct <$> recover d <*> mapM (recoverAlt x) bs
+    TCoerce t -> TCoerce <$> recover t
+    TLit{}    -> pure t
+    TVar{}    -> pure t
+    TPrim{}   -> pure t
+    TDef{}    -> pure t
+    TUnit{}   -> pure t
+    TSort{}   -> pure t
+    TErased{} -> pure t
+    TError{}  -> pure t
+
+recoverAlt :: Int -> TAlt -> S TAlt
+recoverAlt x b =
+  case b of
+    TACon c n b -> TACon c n <$> underBinds n (bindAsPattern (AsPat (x + n) c [n - 1, n - 2..0]) $ recover b)
+    TAGuard g b -> TAGuard <$> recover g <*> recover b
+    TALit l b   -> TALit l <$> recover b
+
+tApp :: TTerm -> [TTerm] -> S TTerm
+tApp (TCon c) vs = lookupAsPattern c vs
+tApp f vs        = pure $ mkTApp f vs
+
diff --git a/src/full/Agda/Compiler/Treeless/Builtin.hs b/src/full/Agda/Compiler/Treeless/Builtin.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Builtin.hs
@@ -0,0 +1,188 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Translates the Agda builtin nat datatype to arbitrary-precision integers.
+--
+-- Philipp, 20150921:
+-- At the moment, this optimization is the reason that there is a
+-- TAPlus alternative. For Haskell, this can easily be translated to guards. However, in
+-- the long term it would be easier for the backends if these things were translated
+-- directly to a less-than primitive and if-then-else expressions or similar. This would
+-- require us to add some internal Bool-datatype as compiler-internal type and
+-- a primitive less-than function, which will be much easier once Treeless
+-- is used for whole modules.
+--
+-- Ulf, 2015-09-21: No, actually we need the n+k patterns, or at least guards.
+-- Representing them with if-then-else would make it a lot harder to do
+-- optimisations that analyse case tree, like impossible case elimination.
+--
+-- Ulf, 2015-10-30: Guards are actually a better primitive. Fixed that.
+module Agda.Compiler.Treeless.Builtin (translateBuiltins) where
+
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Treeless
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Monad
+
+import Agda.Compiler.Treeless.Subst () --instance only
+import Agda.Utils.Impossible
+
+
+data BuiltinKit = BuiltinKit
+  { isZero   :: QName -> Bool
+  , isSuc    :: QName -> Bool
+  , isPos    :: QName -> Bool
+  , isNegSuc :: QName -> Bool
+  , isPlus   :: QName -> Bool
+  , isTimes  :: QName -> Bool
+  , isLess   :: QName -> Bool
+  , isEqual  :: QName -> Bool
+  , isForce  :: QName -> Bool
+  , isWord64FromNat :: QName -> Bool
+  , isWord64ToNat   :: QName -> Bool
+  }
+
+builtinKit :: TCM BuiltinKit
+builtinKit =
+  BuiltinKit <$> isB con builtinZero
+             <*> isB con builtinSuc
+             <*> isB con builtinIntegerPos
+             <*> isB con builtinIntegerNegSuc
+             <*> isB def builtinNatPlus
+             <*> isB def builtinNatTimes
+             <*> isB def builtinNatLess
+             <*> isB def builtinNatEquals
+             <*> isP pf  PrimForce
+             <*> isP pf  PrimWord64FromNat
+             <*> isP pf  PrimWord64ToNat
+  where
+    con (I.Con c _ _) = pure $ I.conName c
+    con _           = Nothing
+    def (I.Def d _) = pure d
+    def _           = Nothing
+
+    pf = Just . primFunName
+
+    is  a b = maybe (const False) (==) . (a =<<) <$> b
+    isB a b = is a (getBuiltin' b)
+    isP a p = is a (getPrimitive' p)
+
+translateBuiltins :: TTerm -> TCM TTerm
+translateBuiltins t = do
+  kit <- builtinKit
+  return $ transform kit t
+
+transform :: BuiltinKit -> TTerm -> TTerm
+transform BuiltinKit{..} = tr
+  where
+    tr = \case
+
+      TCon c | isZero c   -> tInt 0
+             | isSuc c    -> TLam (tPlusK 1 (TVar 0))
+             | isPos c    -> TLam (TVar 0)
+             | isNegSuc c -> TLam $ tNegPlusK 1 (TVar 0)
+
+      TDef f | isPlus f   -> TPrim PAdd
+             | isTimes f  -> TPrim PMul
+             | isLess f   -> TPrim PLt
+             | isEqual f  -> TPrim PEqI
+             | isWord64ToNat f   -> TPrim P64ToI
+             | isWord64FromNat f -> TPrim PITo64
+        -- Note: Don't do this for builtinNatMinus! PSub is integer minus and
+        --       builtin minus is monus. The simplifier will do it if it can see
+        --       that it won't underflow.
+
+      TApp (TDef q) (_ : _ : _ : _ : e : f : es)
+        | isForce q -> tr $ TLet e $ mkTApp (tOp PSeq (TVar 0) $ mkTApp (raise 1 f) [TVar 0]) es
+
+      TApp (TCon s) [e] | isSuc s ->
+        case tr e of
+          TLit (LitNat n) -> tInt (n + 1)
+          e | Just (i, e) <- plusKView e -> tPlusK (i + 1) e
+          e                 -> tPlusK 1 e
+
+      TApp (TCon c) [e]
+        | isPos c    -> tr e
+        | isNegSuc c ->
+        case tr e of
+          TLit (LitNat n) -> tInt (-n - 1)
+          e | Just (i, e) <- plusKView e -> tNegPlusK (i + 1) e
+          e -> tNegPlusK 1 e
+
+      TCase e t d bs -> TCase e (inferCaseType t bs) (tr d) $ concatMap trAlt bs
+        where
+          trAlt = \case
+            TACon c 0 b | isZero c -> [TALit (LitNat 0) (tr b)]
+            TACon c 1 b | isSuc c  ->
+              case tr b of
+                -- Collapse nested n+k patterns
+                TCase 0 _ d bs' -> map sucBranch bs' ++ [nPlusKAlt 1 d]
+                b -> [nPlusKAlt 1 b]
+              where
+                sucBranch (TALit (LitNat i) b) = TALit (LitNat (i + 1)) $ TLet (tInt i) b
+                sucBranch alt | Just (k, b) <- nPlusKView alt =
+                  nPlusKAlt (k + 1) $ TLet (tOp PAdd (TVar 0) (tInt 1)) $
+                    applySubst ([TVar 1, TVar 0] ++# wkS 2 idS) b
+                sucBranch _ = __IMPOSSIBLE__
+
+                nPlusKAlt k b = TAGuard (tOp PGeq (TVar e) (tInt k)) $
+                                TLet (tOp PSub (TVar e) (tInt k)) b
+            TACon c 1 b | isPos c ->
+              case tr b of
+                -- collapse nested nat patterns
+                TCase 0 _ d bs -> map sub bs ++ [posAlt d]
+                b -> [posAlt  b]
+              where
+                -- subst scrutinee for the pos argument
+                sub :: SubstWith TTerm a => a -> a
+                sub = applySubst (TVar e :# IdS)
+
+                posAlt b = TAGuard (tOp PGeq (TVar e) (tInt 0)) $ sub b
+
+            TACon c 1 b | isNegSuc c ->
+              case tr b of
+                -- collapse nested nat patterns
+                TCase 0 _ d bs -> map negsucBranch bs ++ [negAlt d]
+                b -> [negAlt b]
+              where
+                body b   = TLet (tNegPlusK 1 (TVar e)) b
+                negAlt b = TAGuard (tOp PLt (TVar e) (tInt 0)) $ body b
+
+                negsucBranch (TALit (LitNat i) b) = TALit (LitNat (-i - 1)) $ body b
+                negsucBranch alt | Just (k, b) <- nPlusKView alt =
+                  TAGuard (tOp PLt (TVar e) (tInt (-k))) $
+                  body $ TLet (tNegPlusK (k + 1) (TVar $ e + 1)) b
+                negsucBranch _ = __IMPOSSIBLE__
+
+            TACon c a b -> [TACon c a (tr b)]
+            TALit l b   -> [TALit l (tr b)]
+            TAGuard g b -> [TAGuard (tr g) (tr b)]
+
+      t@TVar{}    -> t
+      t@TDef{}    -> t
+      t@TCon{}    -> t
+      t@TPrim{}   -> t
+      t@TLit{}    -> t
+      t@TUnit{}   -> t
+      t@TSort{}   -> t
+      t@TErased{} -> t
+      t@TError{}  -> t
+
+      TCoerce a -> TCoerce (tr a)
+
+      TLam b                  -> TLam (tr b)
+      TApp a bs               -> TApp (tr a) (map tr bs)
+      TLet e b                -> TLet (tr e) (tr b)
+
+    inferCaseType t (TACon c _ _ : _)
+      | isZero c   = t { caseType = CTNat }
+      | isSuc c    = t { caseType = CTNat }
+      | isPos c    = t { caseType = CTInt }
+      | isNegSuc c = t { caseType = CTInt }
+    inferCaseType t _ = t
+
+    nPlusKView (TAGuard (TApp (TPrim PGeq) [TVar 0, (TLit (LitNat k))])
+                        (TLet (TApp (TPrim PSub) [TVar 0, (TLit (LitNat j))]) b))
+      | k == j = Just (k, b)
+    nPlusKView _ = Nothing
diff --git a/src/full/Agda/Compiler/Treeless/Compare.hs b/src/full/Agda/Compiler/Treeless/Compare.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Compare.hs
@@ -0,0 +1,66 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Compare (equalTerms) where
+
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Substitute
+import Agda.Compiler.Treeless.Subst () --instance only
+
+equalTerms :: TTerm -> TTerm -> Bool
+equalTerms u v =
+  case (evalPrims u, evalPrims v) of
+    (TLet s u@(TCase 0 _ _ _), TLet t v@(TCase 0 _ _ _)) ->
+      equalTerms s t && equalTerms u v
+    (TLet _ (TCase 0 _ _ _), _)      -> False
+    (_, TLet _ (TCase 0 _ _ _))      -> False
+    (TLet t u, v)                    -> equalTerms (subst 0 t u) v
+    (u, TLet t v)                    -> equalTerms u (subst 0 t v)
+    (u, v) | u == v                  -> True
+    (TApp f us, TApp g vs)           -> eqList equalTerms (f : us) (g : vs)
+    (TCase x _ d as, TCase y _ e bs) -> x == y && equalTerms d e && eqList equalAlts as bs
+    (TLam u, TLam v)                 -> equalTerms u v
+    _                                -> False
+
+equalAlts :: TAlt -> TAlt -> Bool
+equalAlts (TACon c a b) (TACon c1 a1 b1) = (c, a) == (c1, a1) && equalTerms b b1
+equalAlts (TALit l b)   (TALit l1 b1)    = l == l1 && equalTerms b b1
+equalAlts (TAGuard g b) (TAGuard g1 b1)  = equalTerms g g1 && equalTerms b b1
+equalAlts _ _ = False
+
+eqList :: (a -> a -> Bool) -> [a] -> [a] -> Bool
+eqList eq xs ys = length xs == length ys && and (zipWith eq xs ys)
+
+evalPrims :: TTerm -> TTerm
+evalPrims (TApp (TPrim op) [a, b])
+  | Just n <- intView (evalPrims a),
+    Just m <- intView (evalPrims b),
+    Just r <- applyPrim op n m = tInt r
+evalPrims t = t
+
+applyPrim :: TPrim -> Integer -> Integer -> Maybe Integer
+applyPrim PAdd a b = Just (a + b)
+applyPrim PSub a b = Just (a - b)
+applyPrim PMul a b = Just (a * b)
+applyPrim PQuot a b | b /= 0    = Just (quot a b)
+                   | otherwise = Nothing
+applyPrim PRem a b | b /= 0    = Just (rem a b)
+                   | otherwise = Nothing
+applyPrim PGeq _ _ = Nothing
+applyPrim PLt  _ _ = Nothing
+applyPrim PEqI _ _ = Nothing
+applyPrim PEqF _ _ = Nothing
+applyPrim PEqC _ _ = Nothing
+applyPrim PEqS _ _ = Nothing
+applyPrim PEqQ _ _ = Nothing
+applyPrim PIf  _ _ = Nothing
+applyPrim PSeq _ _ = Nothing
+applyPrim PAdd64 _ _ = Nothing
+applyPrim PSub64 _ _ = Nothing
+applyPrim PMul64 _ _ = Nothing
+applyPrim PQuot64 _ _ = Nothing
+applyPrim PRem64 _ _ = Nothing
+applyPrim PLt64  _ _ = Nothing
+applyPrim PEq64 _ _ = Nothing
+applyPrim PITo64 _ _ = Nothing
+applyPrim P64ToI _ _ = Nothing
+
diff --git a/src/full/Agda/Compiler/Treeless/EliminateDefaults.hs b/src/full/Agda/Compiler/Treeless/EliminateDefaults.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/EliminateDefaults.hs
@@ -0,0 +1,55 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Eliminates case defaults by adding an alternative for all possible
+-- constructors. Literal cases are preserved as-is.
+module Agda.Compiler.Treeless.EliminateDefaults where
+
+import Control.Monad
+import qualified Data.List as List
+
+import Agda.Syntax.Treeless
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+
+import Agda.Compiler.Treeless.Subst () --instance only
+
+eliminateCaseDefaults :: TTerm -> TCM TTerm
+eliminateCaseDefaults = tr
+  where
+    tr :: TTerm -> TCM TTerm
+    tr = \case
+      TCase sc ct@CaseInfo{caseType = CTData qn} def alts
+        | not (isUnreachable def) -> do
+        dtCons <- defConstructors . theDef <$> getConstInfo qn
+        let missingCons = dtCons List.\\ map aCon alts
+        def <- tr def
+        newAlts <- forM missingCons $ \con -> do
+          Constructor {conArity = ar} <- theDef <$> getConstInfo con
+          return $ TACon con ar (TVar ar)
+
+        alts' <- (++ newAlts) <$> mapM (trAlt . raise 1) alts
+
+        return $ TLet def $ TCase (sc + 1) ct tUnreachable alts'
+      TCase sc ct def alts -> TCase sc ct <$> tr def <*> mapM trAlt alts
+
+      t@TVar{}    -> return t
+      t@TDef{}    -> return t
+      t@TCon{}    -> return t
+      t@TPrim{}   -> return t
+      t@TLit{}    -> return t
+      t@TUnit{}   -> return t
+      t@TSort{}   -> return t
+      t@TErased{} -> return t
+      t@TError{}  -> return t
+
+      TCoerce a               -> TCoerce <$> tr a
+      TLam b                  -> TLam <$> tr b
+      TApp a bs               -> TApp <$> tr a <*> mapM tr bs
+      TLet e b                -> TLet <$> tr e <*> tr b
+
+    trAlt :: TAlt -> TCM TAlt
+    trAlt = \case
+      TAGuard g b -> TAGuard <$> tr g <*> tr b
+      TACon q a b -> TACon q a <$> tr b
+      TALit l b   -> TALit l <$> tr b
diff --git a/src/full/Agda/Compiler/Treeless/EliminateLiteralPatterns.hs b/src/full/Agda/Compiler/Treeless/EliminateLiteralPatterns.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/EliminateLiteralPatterns.hs
@@ -0,0 +1,77 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Converts case matches on literals to if cascades with equality comparisons.
+module Agda.Compiler.Treeless.EliminateLiteralPatterns where
+
+import Data.Maybe
+
+import Agda.Syntax.Treeless
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive
+
+import Agda.Utils.Impossible
+
+
+eliminateLiteralPatterns :: TTerm -> TCM TTerm
+eliminateLiteralPatterns t = do
+  kit <- BuiltinKit <$> getBuiltinName builtinNat <*> getBuiltinName builtinInteger
+  return $ transform kit t
+
+data BuiltinKit = BuiltinKit
+  { nat :: Maybe QName
+  , int :: Maybe QName
+  }
+
+transform :: BuiltinKit -> TTerm -> TTerm
+transform kit = tr
+  where
+    tr :: TTerm -> TTerm
+    tr = \case
+      TCase sc t def alts | caseType t `elem` [CTChar, CTString, CTQName, CTNat, CTInt, CTFloat] ->
+        foldr litAlt (tr def) alts
+        where
+          litAlt :: TAlt -> TTerm -> TTerm
+          litAlt (TALit l body) cont =
+            tIfThenElse
+              (tOp (eqFromLit l) (TLit l) (TVar sc))
+              (tr body)
+              cont
+          litAlt _ _ = __IMPOSSIBLE__
+      TCase sc t@CaseInfo{caseType = CTData dt} def alts ->
+        TCase sc t (tr def) (map trAlt alts)
+        where
+          trAlt = \case
+            TAGuard g b -> TAGuard (tr g) (tr b)
+            TACon q a b -> TACon q a (tr b)
+            TALit l b   -> TALit l (tr b)
+      TCase _ _ _ _ -> __IMPOSSIBLE__
+
+      t@TVar{}    -> t
+      t@TDef{}    -> t
+      t@TCon{}    -> t
+      t@TPrim{}   -> t
+      t@TLit{}    -> t
+      t@TUnit{}   -> t
+      t@TSort{}   -> t
+      t@TErased{} -> t
+      t@TError{}  -> t
+
+      TCoerce a               -> TCoerce (tr a)
+      TLam b                  -> TLam (tr b)
+      TApp a bs               -> TApp (tr a) (map tr bs)
+      TLet e b                -> TLet (tr e) (tr b)
+
+    -- TODO:: Defined but not used
+    isCaseOn (CTData dt) xs = dt `elem` mapMaybe ($ kit) xs
+    isCaseOn _ _ = False
+
+    eqFromLit :: Literal -> TPrim
+    eqFromLit = \case
+      LitNat _     -> PEqI
+      LitFloat _   -> PEqF
+      LitString _  -> PEqS
+      LitChar _    -> PEqC
+      LitQName _   -> PEqQ
+      _ -> __IMPOSSIBLE__
diff --git a/src/full/Agda/Compiler/Treeless/Erase.hs b/src/full/Agda/Compiler/Treeless/Erase.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Erase.hs
@@ -0,0 +1,379 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE PatternSynonyms #-}
+
+module Agda.Compiler.Treeless.Erase
+       ( eraseTerms
+       , computeErasedConstructorArgs
+       , isErasable
+       ) where
+
+import Control.Arrow (first, second)
+import Control.Monad
+import Control.Monad.State
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Treeless
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Monad as I
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive
+
+import {-# SOURCE #-} Agda.Compiler.Backend
+import Agda.Compiler.Treeless.Subst
+import Agda.Compiler.Treeless.Unused
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+import Agda.Utils.Memo
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.IntSet.Infinite (IntSet)
+import qualified Agda.Utils.IntSet.Infinite as IntSet
+
+import Agda.Utils.Impossible
+
+-- | State of the eraser.
+data ESt = ESt
+  { _funMap  :: Map QName FunInfo
+      -- ^ Memoize computed `FunInfo` for functions/constructors/... `QName`.
+  , _typeMap :: Map QName TypeInfo
+      -- ^ Memoize computed `TypeInfo` for data/record types `QName`.
+  }
+
+funMap :: Lens' ESt (Map QName FunInfo)
+funMap f r = f (_funMap r) <&> \ a -> r { _funMap = a }
+
+typeMap :: Lens' ESt (Map QName TypeInfo)
+typeMap f r = f (_typeMap r) <&> \ a -> r { _typeMap = a }
+
+-- | Eraser monad.
+type E = StateT ESt TCM
+
+runE :: E a -> TCM a
+runE m = evalStateT m (ESt Map.empty Map.empty)
+
+-- | Takes the name of the data/record type.
+computeErasedConstructorArgs :: QName -> TCM ()
+computeErasedConstructorArgs d = do
+  cs <- getNotErasedConstructors d
+  runE $ mapM_ getFunInfo cs
+
+eraseTerms :: QName -> EvaluationStrategy -> TTerm -> TCM TTerm
+eraseTerms q eval t = usedArguments q t *> runE (eraseTop q t)
+  where
+    eraseTop q t = do
+      (_, h) <- getFunInfo q
+      case h of
+        Erasable -> pure TErased
+        Empty    -> pure TErased
+        _        -> erase t
+
+    erase t = case tAppView t of
+
+      (TCon c, vs) -> do
+        (rs, h) <- getFunInfo c
+        when (length rs < length vs) __IMPOSSIBLE__
+        case h of
+          Erasable -> pure TErased
+          Empty    -> pure TErased
+          _        -> tApp (TCon c) <$> zipWithM eraseRel rs vs
+
+      (TDef f, vs) -> do
+        (rs, h) <- getFunInfo f
+        case h of
+          Erasable -> pure TErased
+          Empty    -> pure TErased
+          _        -> tApp (TDef f) <$> zipWithM eraseRel (rs ++ repeat NotErasable) vs
+
+      _ -> case t of
+        TVar{}         -> pure t
+        TDef{}         -> pure t
+        TPrim{}        -> pure t
+        TLit{}         -> pure t
+        TCon{}         -> pure t
+        TApp f es      -> tApp <$> erase f <*> mapM erase es
+        TLam b         -> tLam <$> erase b
+        TLet e b       -> do
+          e <- erase e
+          if isErased e
+            then case b of
+                   TCase 0 _ _ _ -> tLet TErased <$> erase b
+                   _             -> erase $ subst 0 TErased b
+            else tLet e <$> erase b
+        TCase x t d bs -> do
+          (d, bs) <- pruneUnreachable x (caseErased t) (caseType t) d bs
+          d       <- erase d
+          bs      <- mapM eraseAlt bs
+          tCase x t d bs
+
+        TUnit          -> pure t
+        TSort          -> pure t
+        TErased        -> pure t
+        TError{}       -> pure t
+        TCoerce e      -> TCoerce <$> erase e
+
+    -- #3380: this is not safe for strict backends
+    tLam TErased | eval == LazyEvaluation = TErased
+    tLam t                                = TLam t
+
+    tLet e b
+      | freeIn 0 b = TLet e b
+      | otherwise  = strengthen impossible b
+
+    tApp f []                  = f
+    tApp TErased _             = TErased
+    tApp f _ | isUnreachable f = tUnreachable
+    tApp f es                  = mkTApp f es
+
+    tCase x t d bs
+      | isErased d && all (isErased . aBody) bs = pure TErased
+      | otherwise = case bs of
+        [b@(TACon c _ _)] -> do
+          h <- snd <$> getFunInfo c
+          case h of
+            NotErasable -> fallback
+            Empty       -> pure TErased
+            Erasable    -> erasedBody b
+        _ -> fallback
+      where
+        noerase = pure $ TCase x t d bs
+
+        erasedBody = \case
+          TACon _ arity body ->
+            (if arity == 0 then pure else erase) $
+               -- might enable more erasure
+            applySubst (replicate arity TErased ++# idS) body
+          TALit _ body   -> pure body
+          TAGuard _ body -> pure body
+
+        fallback = case (caseErased t, bs) of
+          (Erased{}, [b]) ->
+            -- The case variable is erased, and there is exactly one
+            -- case: use the case's body.
+            erasedBody b
+          (Erased{}, [])  ->
+            -- The case variable is erased, and there is no case: use
+            -- the default.
+            pure $ if isErased d then TErased else d
+          (Erased{}, _ : _ : _) ->
+            -- The case variable is erased, and there are at least two
+            -- cases: crash.
+            __IMPOSSIBLE__
+          _ ->
+            -- The case variable is not erased: do not erase anything.
+            noerase
+
+    isErased t = t == TErased || isUnreachable t
+
+    eraseRel r t | erasable r = pure TErased
+                 | otherwise  = erase t
+
+    eraseAlt = \case
+      TALit l b   -> TALit l   <$> erase b
+      TACon c a b -> do
+        rs <- map erasable . fst <$> getFunInfo c
+        let sub = foldr (\ e -> if e then (TErased :#) . wkS 1 else liftS 1) idS $ reverse rs
+        TACon c a <$> erase (applySubst sub b)
+      TAGuard g b -> TAGuard   <$> erase g <*> erase b
+
+pruneUnreachable ::
+  Int -> Erased -> CaseType -> TTerm -> [TAlt] -> E (TTerm, [TAlt])
+pruneUnreachable x erased t d bs = case erased of
+  NotErased{} -> pruneUnreachable' x erased t d bs
+  Erased{}    ->
+    -- If the match is on an erased argument, then the first branch
+    -- should match.
+    case bs of
+      []    -> pruneUnreachable' x erased t d            []
+      b : _ -> pruneUnreachable' x erased t tUnreachable [b]
+
+-- | Doesn't have any type information (other than the name of the data type),
+--   so we can't do better than checking if all constructors are present.
+pruneUnreachable' ::
+  Int -> Erased -> CaseType -> TTerm -> [TAlt] -> E (TTerm, [TAlt])
+pruneUnreachable' _ erased (CTData q) d bs' = do
+  -- Erased constructors are pruned iff the match is made on a
+  -- non-erased argument.
+  cs <- lift $
+        if isErased erased
+        then getConstructors q
+        else getNotErasedConstructors q
+  let bs | isErased erased = bs'
+         | otherwise       =
+           flip filter bs' $ \case
+             a@TACon{} -> (aCon a) `elem` cs
+             TAGuard{} -> True
+             TALit{}   -> True
+  let -- In the case of a match on an erased argument the value d is
+      -- equal to tUnreachable, except perhaps if bs is empty. In the
+      -- latter case complete is True exactly when the type has zero
+      -- constructors (erased or not), in which case it makes sense to
+      -- replace d with tUnreachable.
+      complete = length cs == length [ b | b@TACon{} <- bs ]
+      d' | complete  = tUnreachable
+         | otherwise = d
+  return (d', bs)
+pruneUnreachable' x _ CTNat d bs =
+  return $ pruneIntCase x d bs (IntSet.below 0)
+pruneUnreachable' x _ CTInt d bs =
+  return $ pruneIntCase x d bs IntSet.empty
+pruneUnreachable' _ _ _ d bs =
+  pure (d, bs)
+
+-- These are the guards we generate for Int/Nat pattern matching
+pattern Below :: Int -> Integer -> TTerm
+pattern Below x n = TApp (TPrim PLt)  [TVar x, TLit (LitNat n)]
+
+pattern Above :: Int -> Integer -> TTerm
+pattern Above x n = TApp (TPrim PGeq) [TVar x, TLit (LitNat n)]
+
+-- | Strip unreachable clauses (replace by tUnreachable for the default).
+--   Fourth argument is the set of ints covered so far.
+pruneIntCase :: Int -> TTerm -> [TAlt] -> IntSet -> (TTerm, [TAlt])
+pruneIntCase x d bs cover = go bs cover
+  where
+    go [] cover
+      | cover == IntSet.full = (tUnreachable, [])
+      | otherwise            = (d, [])
+    go (b : bs) cover =
+      case b of
+        TAGuard (Below y n) _ | x == y -> rec (IntSet.below n)
+        TAGuard (Above y n) _ | x == y -> rec (IntSet.above n)
+        TALit (LitNat n) _             -> rec (IntSet.singleton n)
+        _                                -> second (b :) $ go bs cover
+      where
+        rec this = second addAlt $ go bs cover'
+          where
+            this'  = IntSet.difference this cover
+            cover' = this' <> cover
+            addAlt = case IntSet.toFiniteList this' of
+                       Just []  -> id                                     -- unreachable case
+                       Just [n] -> (TALit (LitNat n) (aBody b) :) -- possibly refined case
+                       _        -> (b :)                                  -- unchanged case
+
+data TypeInfo = Empty | Erasable | NotErasable
+  deriving (Eq, Show)
+
+sumTypeInfo :: [TypeInfo] -> TypeInfo
+sumTypeInfo is = foldr plus Empty is
+  where
+    plus Empty       r           = r
+    plus r           Empty       = r
+    plus Erasable    r           = r
+    plus r           Erasable    = r
+    plus NotErasable NotErasable = NotErasable
+
+erasable :: TypeInfo -> Bool
+erasable Erasable    = True
+erasable Empty       = True
+erasable NotErasable = False
+
+type FunInfo = ([TypeInfo], TypeInfo)
+
+getFunInfo :: QName -> E FunInfo
+getFunInfo q = memo (funMap . key q) $ getInfo q
+  where
+    getInfo :: QName -> E FunInfo
+    getInfo q = do
+      (rs, t) <- do
+        (tel, t) <- lift $ typeWithoutParams q
+        is     <- mapM (getTypeInfo . snd . dget) tel
+        used   <- lift $ (++ repeat ArgUsed) . fromMaybe [] <$> getCompiledArgUse q
+        forced <- lift $ (++ repeat NotForced) <$> getForcedArgs q
+        return (zipWith3 (uncurry . mkR . getModality) tel (zip forced used) is, t)
+      h <- if isAbsurdLambdaName q then pure Erasable else getTypeInfo t
+      lift $ reportSLn "treeless.opt.erase.info" 50 $ "type info for " ++ prettyShow q ++ ": " ++ show rs ++ " -> " ++ show h
+      lift $ setErasedConArgs q $ map erasable rs
+      return (rs, h)
+
+    -- Treat empty, erasable, or unused arguments as Erasable
+    mkR :: Modality -> IsForced -> ArgUsage -> TypeInfo -> TypeInfo
+    mkR m f u i
+      | not (usableModality m) = Erasable
+      | ArgUnused <- u         = Erasable
+      | Forced <- f            = Erasable
+      | otherwise              = i
+
+isErasable :: QName -> TCM Bool
+isErasable qn =
+  -- The active backend should be set
+  caseMaybeM (viewTC eActiveBackendName) __IMPOSSIBLE__ $ \ bname ->
+  -- However it may not be part of the set of available backends
+  -- in which case we default to not erasable to avoid false negatives.
+  caseMaybeM (lookupBackend bname)       (pure False)   $ \ _ ->
+  erasable . snd <$> runE (getFunInfo qn)
+
+telListView :: Type -> TCM (ListTel, Type)
+telListView t = do
+  TelV tel t <- telViewPath t
+  return (telToList tel, t)
+
+typeWithoutParams :: QName -> TCM (ListTel, Type)
+typeWithoutParams q = do
+  def <- getConstInfo q
+  let d = case I.theDef def of
+        Function{ funProjection = Right Projection{ projIndex = i } } -> i - 1
+        Constructor{ conPars = n } -> n
+        _                          -> 0
+  first (drop d) <$> telListView (defType def)
+
+getTypeInfo :: Type -> E TypeInfo
+getTypeInfo t0 = do
+  (tel, t) <- lift $ telListView t0
+  et <- case I.unEl t of
+    I.Def d _ -> do
+      -- #2916: Only update the memo table for d. Results for other types are
+      -- under the assumption that d is erasable!
+      oldMap <- use typeMap
+      dInfo <- typeInfo d
+      typeMap .= Map.insert d dInfo oldMap
+      return dInfo
+    Sort{}    -> return Erasable
+    _         -> return NotErasable
+  is <- mapM (getTypeInfo . snd . dget) tel
+  let e | Empty `elem` is = Erasable
+        | null is         = et        -- TODO: guard should really be "all inhabited is"
+        | et == Empty     = Erasable
+        | otherwise       = et
+  lift $ reportSDoc "treeless.opt.erase.type" 50 $ prettyTCM t0 <+> text ("is " ++ show e)
+  return e
+  where
+  typeInfo :: QName -> E TypeInfo
+  typeInfo q = ifM (erasureForbidden q) (return NotErasable) $ {-else-} do
+    memoRec (typeMap . key q) Erasable $ do  -- assume recursive occurrences are erasable
+      mId    <- lift $ getName' builtinId
+      msizes <- lift $ mapM getBuiltinName
+                         [builtinSize, builtinSizeLt]
+      def    <- lift $ getConstInfo q
+      let mcs = case I.theDef def of
+                  I.Datatype{ dataCons = cs } -> Just cs
+                  I.Record{ recConHead = c }  -> Just [conName c]
+                  _                           -> Nothing
+      case mcs of
+        _ | Just q == mId        -> return NotErasable
+        _ | Just q `elem` msizes -> return Erasable
+        Just [c] -> do
+          (ts, _) <- lift $ typeWithoutParams c
+          let rs = map getModality ts
+          is <- mapM (getTypeInfo . snd . dget) ts
+          let er = and [ erasable i || not (usableModality r) | (i, r) <- zip is rs ]
+          return $ if er then Erasable else NotErasable
+        Just []      -> return Empty
+        Just (_:_:_) -> return NotErasable
+        Nothing ->
+          case I.theDef def of
+            I.Function{ funClauses = cs } ->
+              sumTypeInfo <$> mapM (maybe (return Empty) (getTypeInfo . El __DUMMY_SORT__) . clauseBody) cs
+            _ -> return NotErasable
+  -- The backend also has a say whether a type is eraseable or not.
+  erasureForbidden :: QName -> E Bool
+  erasureForbidden q = lift $ not <$> activeBackendMayEraseType q
diff --git a/src/full/Agda/Compiler/Treeless/Erase.hs-boot b/src/full/Agda/Compiler/Treeless/Erase.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Erase.hs-boot
@@ -0,0 +1,8 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Erase where
+
+import Agda.TypeChecking.Monad.Base (TCM)
+import Agda.Syntax.Abstract.Name (QName)
+
+isErasable :: QName -> TCM Bool
diff --git a/src/full/Agda/Compiler/Treeless/GuardsToPrims.hs b/src/full/Agda/Compiler/Treeless/GuardsToPrims.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/GuardsToPrims.hs
@@ -0,0 +1,56 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Translates guard alternatives to if-then-else cascades.
+--
+-- The builtin translation must be run before this transformation.
+module Agda.Compiler.Treeless.GuardsToPrims ( convertGuards ) where
+
+import qualified Data.List as List
+
+import Agda.Syntax.Treeless
+
+import Agda.Utils.Impossible
+
+
+convertGuards :: TTerm -> TTerm
+convertGuards = tr
+  where
+    tr = \case
+      TCase sc t def alts ->
+        if null otherAlts
+          then
+            def'
+          else
+            TCase sc t def' (fmap trAlt otherAlts)
+        where
+          (plusAlts, otherAlts) = splitAlts alts
+
+          guardedAlt :: TAlt -> TTerm -> TTerm
+          guardedAlt (TAGuard g body) cont = tIfThenElse (tr g) (tr body) (tr cont)
+          guardedAlt _ _ = __IMPOSSIBLE__
+
+          def' = foldr guardedAlt (tr def) plusAlts
+
+          trAlt (TAGuard{}) = __IMPOSSIBLE__
+          trAlt a = a { aBody = tr (aBody a) }
+
+      t@TVar{}    -> t
+      t@TDef{}    -> t
+      t@TCon{}    -> t
+      t@TPrim{}   -> t
+      t@TLit{}    -> t
+      t@TUnit{}   -> t
+      t@TSort{}   -> t
+      t@TErased{} -> t
+      t@TError{}  -> t
+
+      TCoerce a               -> TCoerce (tr a)
+      TLam b                  -> TLam (tr b)
+      TApp a bs               -> TApp (tr a) (map tr bs)
+      TLet e b                -> TLet (tr e) (tr b)
+
+-- | Split alts into TAGuard alts and other alts.
+splitAlts :: [TAlt] -> ([TAlt], [TAlt])
+splitAlts = List.partition isGuardAlt
+  where isGuardAlt (TAGuard _ _) = True
+        isGuardAlt _ = False
diff --git a/src/full/Agda/Compiler/Treeless/Identity.hs b/src/full/Agda/Compiler/Treeless/Identity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Identity.hs
@@ -0,0 +1,106 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Identity
+  ( detectIdentityFunctions ) where
+
+import Prelude hiding ((!!))  -- don't use partial functions
+
+import Control.Applicative ( Alternative((<|>), empty) )
+import Data.Semigroup
+import qualified Data.List as List
+
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.List
+import Agda.Utils.List1 (pattern (:|))
+
+import Agda.Utils.Impossible
+
+detectIdentityFunctions :: QName -> TTerm -> TCM TTerm
+detectIdentityFunctions q t =
+  case isIdentity q t of
+    Nothing     -> return t
+    Just (n, k) -> do
+      markInline True q
+      def <- theDef <$> getConstInfo q
+      return $ mkTLam n $ TVar k
+
+-- If isIdentity f t = Just (n, k) then
+-- f = t is equivalent to f = λ xn₋₁ .. x₀ → xk
+isIdentity :: QName -> TTerm -> Maybe (Int, Int)
+isIdentity q t =
+  trivialIdentity q t <|> recursiveIdentity q t
+
+-- Does the function recurse on an argument, rebuilding the same value again.
+recursiveIdentity :: QName -> TTerm -> Maybe (Int, Int)
+recursiveIdentity q t =
+  case b of
+    TCase x _ (TError TUnreachable) bs
+      | all (identityBranch x) bs -> pure (n, x)
+    _ -> empty -- TODO: lets?
+  where
+    (n, b) = tLamView t
+
+    identityBranch _ TALit{}   = False
+    identityBranch _ TAGuard{} = False
+    identityBranch x (TACon c a b) =
+      case b of
+        TApp (TCon c') args -> c == c' && identityArgs a args
+        TVar y              -> y == x + a  -- from @-pattern recovery
+        _                   -> False -- TODO: nested cases
+      where
+        identityArgs a args =
+          length args == a && and (zipWith match (reverse args) [0..])
+
+        proj x args = indexWithDefault __IMPOSSIBLE__ (reverse args) x
+
+        match TErased              _  = True
+        match (TVar z)             y = z == y
+        match (TApp (TDef f) args) y = f == q && length args == n && match (proj x args) y
+        match _                    _ = False
+
+data IdentityIn = IdIn [Int]
+
+notId :: IdentityIn
+notId = IdIn []
+
+instance Semigroup IdentityIn where
+  IdIn xs <> IdIn ys = IdIn $ List.intersect xs ys
+
+-- Does the function always return one of its arguments unchanged (possibly
+-- through recursive calls).
+trivialIdentity :: QName -> TTerm -> Maybe (Int, Int)
+trivialIdentity q t =
+  case go 0 b of
+    IdIn [x]     -> pure (n, x)
+    IdIn []      -> Nothing
+    IdIn (_:_:_) -> Nothing  -- only happens for empty functions (which will never be called)
+  where
+    (n, b) = tLamView t
+
+    go :: Int -> TTerm -> IdentityIn
+    go k t =
+      case t of
+        TVar x | x >= k    -> IdIn [x - k]
+               | otherwise -> notId
+        TLet _ b           -> go (k + 1) b
+        TCase _ _ d bs     -> sconcat (go k d :| map (goAlt k) bs)
+        TApp (TDef f) args
+          | f == q         -> IdIn [ y | (TVar x, y) <- zip (reverse args) [0..], y + k == x ]
+        TCoerce v          -> go k v
+        TApp{}             -> notId
+        TLam{}             -> notId
+        TLit{}             -> notId
+        TDef{}             -> notId
+        TCon{}             -> notId
+        TPrim{}            -> notId
+        TUnit{}            -> notId
+        TSort{}            -> notId
+        TErased{}          -> notId
+        TError{}           -> notId
+
+    goAlt :: Int -> TAlt -> IdentityIn
+    goAlt k (TALit _ b)   = go k b
+    goAlt k (TAGuard _ b) = go k b
+    goAlt k (TACon _ n b) = go (k + n) b
diff --git a/src/full/Agda/Compiler/Treeless/NormalizeNames.hs b/src/full/Agda/Compiler/Treeless/NormalizeNames.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/NormalizeNames.hs
@@ -0,0 +1,43 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Ensures that all occurences of an abstract name share
+-- the same concrete name.
+--
+-- Apply this transformation if your backend uses concrete names
+-- for identification purposes!
+--
+-- The identity of an abstract name is only the nameId, the concrete
+-- name is only a naming suggestion. If renaming imports are used,
+-- the concrete name may change. This transformation makes sure
+-- that all occurences of an abstract name share the same
+-- concrete name.
+--
+-- This transfomation should be run as the last transformation.
+module Agda.Compiler.Treeless.NormalizeNames ( normalizeNames ) where
+
+import Agda.TypeChecking.Monad
+import Agda.Syntax.Treeless
+
+normalizeNames :: TTerm -> TCM TTerm
+normalizeNames = tr
+  where
+    tr = \case
+      TDef q              -> TDef . defName <$> getConstInfo q
+      t@TVar{}            -> return t
+      t@TCon{}            -> return t
+      t@TPrim{}           -> return t
+      t@TLit{}            -> return t
+      t@TUnit{}           -> return t
+      t@TSort{}           -> return t
+      t@TErased{}         -> return t
+      t@TError{}          -> return t
+      TLam b              -> TLam <$> tr b
+      TApp a bs           -> TApp <$> tr a <*> mapM tr bs
+      TLet e b            -> TLet <$> tr e <*> tr b
+      TCase sc t def alts -> TCase sc t <$> tr def <*> mapM trAlt alts
+      TCoerce a           -> TCoerce <$> tr a
+
+    trAlt = \case
+      TAGuard g b -> TAGuard <$> tr g <*> tr b
+      TACon q a b -> TACon q a <$> tr b
+      TALit l b   -> TALit l <$> tr b
diff --git a/src/full/Agda/Compiler/Treeless/Pretty.hs b/src/full/Agda/Compiler/Treeless/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Pretty.hs
@@ -0,0 +1,197 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.Compiler.Treeless.Pretty () where
+
+import Prelude hiding ((!!)) -- don't use partial functions!
+
+import Control.Arrow (first)
+import Control.Monad.Reader
+import Data.Maybe
+import qualified Data.Map as Map
+
+import Agda.Syntax.Treeless
+import Agda.Syntax.Common.Pretty
+
+import Agda.Compiler.Treeless.Subst
+
+import Agda.Utils.Impossible
+import Agda.Utils.Function
+import Agda.Utils.List
+
+instance Pretty Compiled where
+  pretty Compiled {cTreeless, cArgUsage} =
+    "Compiled {" <?> vcat
+      [ "cTreeless   =" <?> pretty cTreeless
+      , "funCompiled =" <?> pshow cArgUsage
+      ] <?> "}"
+
+data PEnv = PEnv { pPrec :: Int
+                 , pFresh :: [String]
+                 , pBound :: [String] }
+
+type P = Reader PEnv
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--withName :: (String -> P a) -> P a
+--withName k = withNames 1 $ \[x] -> k x
+
+withNames :: Int -> ([String] -> P a) -> P a
+withNames n k = do
+  (xs, ys) <- asks $ splitAt n . pFresh
+  local (\ e -> e { pFresh = ys }) (k xs)
+
+-- | Don't generate fresh names for unused variables.
+withNames' :: HasFree a => Int -> a -> ([String] -> P b) -> P b
+withNames' n tm k = withNames n' $ k . insBlanks
+  where
+    fv = freeVars tm
+    n'  = length $ filter (< n) $ Map.keys fv
+    insBlanks = go n
+      where
+        go 0 _ = []
+        go i xs0@(~(x : xs))
+          | Map.member (i - 1) fv = x   : go (i - 1) xs
+          | otherwise             = "_" : go (i - 1) xs0
+
+bindName :: String -> P a -> P a
+bindName x = local $ \ e -> e { pBound = x : pBound e }
+
+bindNames :: [String] -> P a -> P a
+bindNames xs p = foldr bindName p xs
+
+paren :: Int -> P Doc -> P Doc
+paren p doc = do
+  n <- asks pPrec
+  applyWhen (p < n) parens <$> doc
+
+prec :: Int -> P a -> P a
+prec p = local $ \ e -> e { pPrec = p }
+
+name :: Int -> P String
+name x = asks
+  $ (\ xs -> indexWithDefault __IMPOSSIBLE__ xs x)
+  . (++ map (("^" ++) . show) [1..])
+  . pBound
+
+runP :: P a -> a
+runP p = runReader p PEnv{ pPrec = 0, pFresh = names, pBound = [] }
+  where
+    names = [ x ++ i | i <- "" : map show [1..], x <- map (:[]) ['a'..'z'] ]
+
+instance Pretty TTerm where
+  prettyPrec p t = runP $ prec p (pTerm t)
+
+opName :: TPrim -> String
+opName PAdd = "+"
+opName PSub = "-"
+opName PMul = "*"
+opName PQuot = "quot"
+opName PRem = "rem"
+opName PGeq = ">="
+opName PLt  = "<"
+opName PEqI = "==I"
+opName PAdd64 = "+64"
+opName PSub64 = "-64"
+opName PMul64 = "*64"
+opName PQuot64 = "quot64"
+opName PRem64 = "rem64"
+opName PLt64  = "<64"
+opName PEq64 = "==64"
+opName PEqF = "==F"
+opName PEqS = "==S"
+opName PEqC = "==C"
+opName PEqQ = "==Q"
+opName PIf  = "if_then_else_"
+opName PSeq = "seq"
+opName PITo64 = "toWord64"
+opName P64ToI = "fromWord64"
+
+
+isInfix :: TPrim -> Maybe (Int, Int, Int)
+isInfix op =
+  case op of
+    PMul -> l 7
+    PAdd -> l 6
+    PSub -> l 6
+    PGeq -> non 4
+    PLt  -> non 4
+    PMul64 -> l 7
+    PAdd64 -> l 6
+    PSub64 -> l 6
+    PLt64  -> non 4
+    p | isPrimEq p -> non 4
+    _    -> Nothing
+  where
+    l n   = Just (n, n, n + 1)
+    r n   = Just (n, n + 1, n) -- NB:: Defined but not used
+    non n = Just (n, n + 1, n + 1)
+
+pTerm' :: Int -> TTerm -> P Doc
+pTerm' p = prec p . pTerm
+
+pTerm :: TTerm -> P Doc
+pTerm = \case
+  TVar x -> text <$> name x
+  TApp (TPrim op) [a, b] | Just (c, l, r) <- isInfix op ->
+    paren c $ sep <$> sequence [ pTerm' l a
+                               , pure $ text $ opName op
+                               , pTerm' r b ]
+  TApp (TPrim PIf) [a, b, c] ->
+    paren 0 $ (\ a b c -> sep [ "if" <+> a
+                              , nest 2 $ "then" <+> b
+                              , nest 2 $ "else" <+> c ])
+              <$> pTerm' 0 a
+              <*> pTerm' 0 b
+              <*> pTerm c
+  TDef f -> pure $ pretty f
+  TCon c -> pure $ pretty c
+  TLit l -> pure $ pretty l
+  TPrim op | isJust (isInfix op) -> pure $ text ("_" ++ opName op ++ "_")
+           | otherwise -> pure $ text (opName op)
+  TApp f es ->
+    paren 9 $ (\a bs -> sep [a, nest 2 $ fsep bs])
+              <$> pTerm' 9 f
+              <*> mapM (pTerm' 10) es
+  t@TLam{} -> paren 0 $ withNames' n b $ \ xs -> bindNames xs $
+    (\b -> sep [ text ("λ " ++ unwords xs ++ " →")
+               , nest 2 b ]) <$> pTerm' 0 b
+    where
+      (n, b) = tLamView t
+  t@TLet{} -> paren 0 $ withNames (length es) $ \ xs ->
+    (\ (binds, b) -> sep [ "let" <+> vcat [ sep [ text x <+> "="
+                                                , nest 2 e ] | (x, e) <- binds ]
+                              <+> "in", b ])
+      <$> pLets (zip xs es) b
+    where
+      (es, b) = tLetView t
+
+      pLets [] b = ([],) <$> pTerm' 0 b
+      pLets ((x, e) : bs) b = do
+        e <- pTerm' 0 e
+        first ((x, e) :) <$> bindName x (pLets bs b)
+
+  TCase x _ def alts -> paren 0 $
+    (\ sc alts defd ->
+      sep [ "case" <+> sc <+> "of"
+          , nest 2 $ vcat (alts ++ [ "_ →" <+> defd | null alts || def /= TError TUnreachable ]) ]
+    ) <$> pTerm' 0 (TVar x)
+      <*> mapM pAlt alts
+      <*> pTerm' 0 def
+    where
+      pAlt (TALit l b) = pAlt' <$> pTerm' 0 (TLit l) <*> pTerm' 0 b
+      pAlt (TAGuard g b) =
+        pAlt' <$> (("_" <+> "|" <+>) <$> pTerm' 0 g)
+              <*> (pTerm' 0 b)
+      pAlt (TACon c a b) =
+        withNames' a b $ \ xs -> bindNames xs $
+        pAlt' <$> pTerm' 0 (TApp (TCon c) [TVar i | i <- reverse [0..a - 1]])
+              <*> pTerm' 0 b
+      pAlt' p b = sep [p <+> "→", nest 2 b]
+
+  TUnit -> pure "()"
+  TSort -> pure "Set"
+  TErased -> pure "_"
+  TError err -> paren 9 $ pure $ "error" <+> text (show (show err))
+  TCoerce t -> paren 9 $ ("coe" <+>) <$> pTerm' 10 t
diff --git a/src/full/Agda/Compiler/Treeless/Pretty.hs-boot b/src/full/Agda/Compiler/Treeless/Pretty.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Pretty.hs-boot
@@ -0,0 +1,7 @@
+
+module Agda.Compiler.Treeless.Pretty () where
+
+import Agda.Syntax.Treeless
+import Agda.Syntax.Common.Pretty
+
+instance Pretty Compiled
diff --git a/src/full/Agda/Compiler/Treeless/Simplify.hs b/src/full/Agda/Compiler/Treeless/Simplify.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Simplify.hs
@@ -0,0 +1,525 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Simplify (simplifyTTerm) where
+
+import Control.Arrow        ( (***), second )
+import Control.Monad        ( (>=>), guard )
+import Control.Monad.Reader ( MonadReader(..), asks, Reader, runReader )
+import qualified Data.List as List
+
+import Agda.Syntax.Treeless
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Substitute
+
+import Agda.Compiler.Treeless.Compare
+
+import Agda.Utils.List
+import Agda.Utils.Maybe
+
+import Agda.Utils.Impossible
+
+data SEnv = SEnv
+  { envSubst   :: Substitution' TTerm
+  , envRewrite :: [(TTerm, TTerm)] }
+
+type S = Reader SEnv
+
+runS :: S a -> a
+runS m = runReader m $ SEnv IdS []
+
+lookupVar :: Int -> S TTerm
+lookupVar i = asks $ (`lookupS` i) . envSubst
+
+onSubst :: (Substitution' TTerm -> Substitution' TTerm) -> S a -> S a
+onSubst f = local $ \ env -> env { envSubst = f (envSubst env) }
+
+onRewrite :: Substitution' TTerm -> S a -> S a
+onRewrite rho = local $ \ env -> env { envRewrite = map (applySubst rho *** applySubst rho) (envRewrite env) }
+
+addRewrite :: TTerm -> TTerm -> S a -> S a
+addRewrite lhs rhs = local $ \ env -> env { envRewrite = (lhs, rhs) : envRewrite env }
+
+underLams :: Int -> S a -> S a
+underLams i = onRewrite (raiseS i) . onSubst (liftS i)
+
+underLam :: S a -> S a
+underLam = underLams 1
+
+underLet :: TTerm -> S a -> S a
+underLet u = onRewrite (raiseS 1) . onSubst (\rho -> wkS 1 $ u :# rho)
+
+bindVar :: Int -> TTerm -> S a -> S a
+bindVar x u = onSubst (inplaceS x u `composeS`)
+
+rewrite :: TTerm -> S TTerm
+rewrite t = do
+  rules <- asks envRewrite
+  case [ rhs | (lhs, rhs) <- rules, equalTerms t lhs ] of
+    rhs : _ -> pure rhs
+    []      -> pure t
+
+data FunctionKit = FunctionKit
+  { modAux, divAux, natMinus, true, false :: Maybe QName }
+
+simplifyTTerm :: TTerm -> TCM TTerm
+simplifyTTerm t = do
+  kit <- FunctionKit <$> getBuiltinName builtinNatModSucAux
+                     <*> getBuiltinName builtinNatDivSucAux
+                     <*> getBuiltinName builtinNatMinus
+                     <*> getBuiltinName builtinTrue
+                     <*> getBuiltinName builtinFalse
+  return $ runS $ simplify kit t
+
+simplify :: FunctionKit -> TTerm -> S TTerm
+simplify FunctionKit{..} = simpl
+  where
+    simpl = rewrite' >=> unchainCase >=> \case
+
+      t@TDef{}  -> pure t
+      t@TPrim{} -> pure t
+      t@TVar{}  -> pure t
+
+      TApp (TDef f) [TLit (LitNat 0), m, n, m']
+        -- div/mod are equivalent to quot/rem on natural numbers.
+        | m == m', Just f == divAux -> simpl $ tOp PQuot n (tPlusK 1 m)
+        | m == m', Just f == modAux -> simpl $ tOp PRem n (tPlusK 1 m)
+
+      -- Word64 primitives --
+
+      --  toWord (a ∙ b) == toWord a ∙64 toWord b
+      TPFn PITo64 (TPOp op a b)
+        | Just op64 <- opTo64 op -> simpl $ tOp op64 (TPFn PITo64 a) (TPFn PITo64 b)
+        where
+          opTo64 op = lookup op [(PAdd, PAdd64), (PSub, PSub64), (PMul, PMul64),
+                                 (PQuot, PQuot64), (PRem, PRem64)]
+
+      t@(TApp (TPrim _) _) -> pure t  -- taken care of by rewrite'
+
+      TCoerce t -> TCoerce <$> simpl t
+
+      TApp f es -> do
+        f  <- simpl f
+        es <- traverse simpl es
+        maybeMinusToPrim f es
+      TLam b    -> TLam <$> underLam (simpl b)
+      t@TLit{}  -> pure t
+      t@TCon{}  -> pure t
+      TLet e b  -> do
+        simpl e >>= \case
+          TPFn P64ToI a -> do
+            -- Inline calls to P64ToI since these trigger optimisations.
+            -- Ideally, the optimisations would trigger anyway, but at the
+            -- moment they only do if inlining the entire let looks like a
+            -- good idea.
+            let rho = inplaceS 0 (TPFn P64ToI (TVar 0))
+            tLet a <$> underLet a (simpl (applySubst rho b))
+          e -> tLet e <$> underLet e (simpl b)
+
+      TCase x t d bs -> do
+        v <- lookupVar x
+        let (lets, u) = tLetView v
+        (d, bs) <- pruneBoolGuards d <$> traverse (simplAlt x) bs
+        case u of                          -- TODO: also for literals
+          _ | Just (c, as)     <- conView u   -> simpl $ matchCon lets c as d bs
+            | Just (k, TVar y) <- plusKView u -> simpl . mkLets lets . TCase y t d =<< mapM (matchPlusK y x k) bs
+          TCase y t1 d1 bs1 -> simpl $ mkLets lets $ TCase y t1 (distrDef case1 d1) $
+                                       map (distrCase case1) bs1
+            where
+              -- Γ x Δ -> Γ _ Δ Θ y, where x maps to y and Θ are the lets
+              n     = length lets
+              rho   = liftS (x + n + 1) (raiseS 1)    `composeS`
+                      singletonS (x + n + 1) (TVar 0) `composeS`
+                      raiseS (n + 1)
+              case1 = applySubst rho (TCase x t d bs)
+
+              distrDef v d | isUnreachable d = tUnreachable
+                           | otherwise       = tLet d v
+
+              distrCase v (TACon c a b) = TACon c a $ TLet b $ raiseFrom 1 a v
+              distrCase v (TALit l b)   = TALit l   $ TLet b v
+              distrCase v (TAGuard g b) = TAGuard g $ TLet b v
+
+          _ -> do
+            d <- simpl d
+            tCase x t d bs
+
+      t@TUnit    -> pure t
+      t@TSort    -> pure t
+      t@TErased  -> pure t
+      t@TError{} -> pure t
+
+    conView (TCon c)    = Just (c, [])
+    conView (TApp f as) = second (++ as) <$> conView f
+    conView e           = Nothing
+
+    -- Collapse chained cases (case x of bs -> vs; _ -> case x of bs' -> vs'  ==>
+    --                         case x of bs -> vs; bs' -> vs')
+    unchainCase :: TTerm -> S TTerm
+    unchainCase e@(TCase x t d bs) = do
+      let (lets, u) = tLetView d
+          k = length lets
+      return $ case u of
+        TCase y _ d' bs' | x + k == y ->
+          mkLets lets $ TCase y t d' $ raise k bs ++ bs'
+        _ -> e
+    unchainCase e = return e
+
+
+    mkLets es b = foldr TLet b es
+
+    matchCon _ _ _ d [] = d
+    matchCon lets c as d (TALit{}   : bs) = matchCon lets c as d bs
+    matchCon lets c as d (TAGuard{} : bs) = matchCon lets c as d bs
+    matchCon lets c as d (TACon c' a b : bs)
+      | c == c'        = flip (foldr TLet) lets $ mkLet 0 as (raiseFrom a (length lets) b)
+      | otherwise      = matchCon lets c as d bs
+      where
+        mkLet _ []       b = b
+        mkLet i (a : as) b = TLet (raise i a) $ mkLet (i + 1) as b
+
+    -- Simplify let y = x + k in case y of j     -> u; _ | g[y]     -> v
+    -- to       let y = x + k in case x of j - k -> u; _ | g[x + k] -> v
+    matchPlusK :: Int -> Int -> Integer -> TAlt -> S TAlt
+    matchPlusK x y k (TALit (LitNat j) b) = return $ TALit (LitNat (j - k)) b
+    matchPlusK x y k (TAGuard g b) = flip TAGuard b <$> simpl (applySubst (inplaceS y (tPlusK k (TVar x))) g)
+    matchPlusK x y k TACon{} = __IMPOSSIBLE__
+    matchPlusK x y k TALit{} = __IMPOSSIBLE__
+
+    simplPrim (TApp f@TPrim{} args) = do
+        args    <- mapM simpl args
+        inlined <- mapM inline args
+        let u = TApp f args
+            v = simplPrim' (TApp f inlined)
+        pure $ if v `betterThan` u then v else u
+      where
+        inline (TVar x)                   = do
+          v <- lookupVar x
+          if v == TVar x then pure v else inline v
+        inline (TApp f@TPrim{} args)      = TApp f <$> mapM inline args
+        inline u@(TLet _ (TCase 0 _ _ _)) = pure u
+        inline (TLet e b)                 = inline (subst 0 e b)
+        inline u                          = pure u
+    simplPrim t = pure t
+
+    simplPrim' :: TTerm -> TTerm
+    simplPrim' (TApp (TPrim PSeq) (u : v : vs))
+      | u == v             = mkTApp v vs
+      | TApp TCon{} _ <- u = mkTApp v vs
+      | TApp TLit{} _ <- u = mkTApp v vs
+    simplPrim' (TApp (TPrim PLt) [u, v])
+      | Just (PAdd, k, u) <- constArithView u,
+        Just (PAdd, j, v) <- constArithView v,
+        k == j = tOp PLt u v
+      | Just (PSub, k, u) <- constArithView u,
+        Just (PSub, j, v) <- constArithView v,
+        k == j = tOp PLt v u
+      | Just (PAdd, k, v) <- constArithView v,
+        TApp (TPrim P64ToI) [u] <- u,
+        k >= 2 ^ 64, Just trueCon <- true = TCon trueCon
+      | Just k <- intView u
+      , Just j <- intView v
+      , Just trueCon <- true
+      , Just falseCon <- false = if k < j then TCon trueCon else TCon falseCon
+    simplPrim' (TApp (TPrim PGeq) [u, v])
+      | Just (PAdd, k, u) <- constArithView u,
+        Just (PAdd, j, v) <- constArithView v,
+        k == j = tOp PGeq u v
+      | Just (PSub, k, u) <- constArithView u,
+        Just (PSub, j, v) <- constArithView v,
+        k == j = tOp PGeq v u
+      | Just k <- intView u
+      , Just j <- intView v
+      , Just trueCon <- true
+      , Just falseCon <- false = if k >= j then TCon trueCon else TCon falseCon
+    simplPrim' (TApp (TPrim op) [u, v])
+      | op `elem` [PGeq, PLt, PEqI]
+      , Just (PAdd, k, u) <- constArithView u
+      , Just j <- intView v = TApp (TPrim op) [u, tInt (j - k)]
+    simplPrim' (TApp (TPrim PEqI) [u, v])
+      | Just (op1, k, u) <- constArithView u,
+        Just (op2, j, v) <- constArithView v,
+        op1 == op2, k == j,
+        op1 `elem` [PAdd, PSub] = tOp PEqI u v
+    simplPrim' (TPOp op u v)
+      | zeroL, isMul || isDiv = tInt 0
+      | zeroL, isAdd          = v
+      | zeroR, isMul          = tInt 0
+      | zeroR, isAdd || isSub = u
+      where zeroL = Just 0 == intView u || Just 0 == word64View u
+            zeroR = Just 0 == intView v || Just 0 == word64View v
+            isAdd = op `elem` [PAdd, PAdd64]
+            isSub = op `elem` [PSub, PSub64]
+            isMul = op `elem` [PMul, PMul64]
+            isDiv = op `elem` [PQuot, PQuot64, PRem, PRem64]
+    simplPrim' (TApp (TPrim op) [u, v])
+      | Just u <- negView u,
+        Just v <- negView v,
+        op `elem` [PMul, PQuot] = tOp op u v
+      | Just u <- negView u,
+        op `elem` [PMul, PQuot] = simplArith $ tOp PSub (tInt 0) (tOp op u v)
+      | Just v <- negView v,
+        op `elem` [PMul, PQuot] = simplArith $ tOp PSub (tInt 0) (tOp op u v)
+    simplPrim' (TApp (TPrim PRem) [u, v])
+      | Just u <- negView u  = simplArith $ tOp PSub (tInt 0) (tOp PRem u (unNeg v))
+      | Just v <- negView v  = tOp PRem u v
+
+      -- (fromWord a == fromWord b) = (a ==64 b)
+    simplPrim' (TPOp op (TPFn P64ToI a) (TPFn P64ToI b))
+        | Just op64 <- opTo64 op = tOp op64 a b
+        where
+          opTo64 op = lookup op [(PEqI, PEq64), (PLt, PLt64)]
+
+      -- toWord/fromWord k == fromIntegral k
+    simplPrim' (TPFn PITo64 (TLit (LitNat n)))    = TLit (LitWord64 (fromIntegral n))
+    simplPrim' (TPFn P64ToI (TLit (LitWord64 n))) = TLit (LitNat    (fromIntegral n))
+
+      -- toWord (fromWord a) == a
+    simplPrim' (TPFn PITo64 (TPFn P64ToI a)) = a
+
+    simplPrim' (TApp f@(TPrim op) [u, v]) = simplArith $ TApp f [simplPrim' u, simplPrim' v]
+    simplPrim' u = u
+
+    unNeg u | Just v <- negView u = v
+            | otherwise           = u
+
+    negView (TApp (TPrim PSub) [a, b])
+      | Just 0 <- intView a = Just b
+    negView _ = Nothing
+
+    -- Count arithmetic operations
+    betterThan u v = operations u <= operations v
+      where
+        operations (TApp (TPrim _) [a, b]) = 1 + operations a + operations b
+        operations (TApp (TPrim PSeq) (a : _))
+          | notVar a                       = 1000000  -- only seq on variables!
+        operations (TApp (TPrim _) [a])    = 1 + operations a
+        operations TVar{}                  = 0
+        operations TLit{}                  = 0
+        operations TCon{}                  = 0
+        operations TDef{}                  = 0
+        operations _                       = 1000
+
+        notVar TVar{} = False
+        notVar _      = True
+
+    rewrite' t = rewrite =<< simplPrim t
+
+    constArithView :: TTerm -> Maybe (TPrim, Integer, TTerm)
+    constArithView (TApp (TPrim op) [TLit (LitNat k), u])
+      | op `elem` [PAdd, PSub] = Just (op, k, u)
+    constArithView (TApp (TPrim op) [u, TLit (LitNat k)])
+      | op == PAdd = Just (op, k, u)
+      | op == PSub = Just (PAdd, -k, u)
+    constArithView _ = Nothing
+
+    simplAlt x (TACon c a b) = TACon c a <$> underLams a (maybeAddRewrite (x + a) conTerm $ simpl b)
+      where conTerm = mkTApp (TCon c) $ map TVar $ downFrom a
+    simplAlt x (TALit l b)   = TALit l   <$> maybeAddRewrite x (TLit l) (simpl b)
+    simplAlt x (TAGuard g b) = TAGuard   <$> simpl g <*> simpl b
+
+    -- If x is already bound we add a rewrite, otherwise we bind x to rhs.
+    maybeAddRewrite x rhs cont = do
+      v <- lookupVar x
+      case v of
+        TVar y | x == y -> bindVar x rhs $ cont
+        _ -> addRewrite v rhs cont
+
+    isTrue (TCon c) = Just c == true
+    isTrue _        = False
+
+    isFalse (TCon c) = Just c == false
+    isFalse _        = False
+
+    maybeMinusToPrim f@(TDef minus) es@[a, b]
+      | Just minus == natMinus = do
+      leq  <- checkLeq b a
+      if leq then pure $ tOp PSub a b
+             else tApp f es
+
+    maybeMinusToPrim f es = tApp f es
+
+    tLet (TVar x) b = subst 0 (TVar x) b
+    tLet e (TVar 0) = e
+    tLet e b        = TLet e b
+
+    tCase :: Int -> CaseInfo -> TTerm -> [TAlt] -> S TTerm
+    tCase x t d [] = pure d
+    tCase x t d bs
+      | isUnreachable d =
+        case reverse bs' of
+          [] -> pure d
+          TALit _ b   : as  -> tCase x t b (reverse as)
+          TAGuard _ b : as  -> tCase x t b (reverse as)
+          TACon c a b : _   -> tCase' x t d bs'
+      | otherwise = do
+        d' <- lookupIfVar d
+        case d' of
+          TCase y _ d bs'' | x == y ->
+            tCase x t d (bs' ++ filter noOverlap bs'')
+          _ -> tCase' x t d bs'
+      where
+        bs' = filter (not . isUnreachable) bs
+
+        lookupIfVar (TVar i) = lookupVar i
+        lookupIfVar t = pure t
+
+        noOverlap b = not $ any (overlapped b) bs'
+        overlapped (TACon c _ _)  (TACon c' _ _) = c == c'
+        overlapped (TALit l _)    (TALit l' _)   = l == l'
+        overlapped _              _              = False
+
+    -- Drop unreachable cases for Nat and Int cases.
+    pruneLitCases :: Int -> CaseInfo -> TTerm -> [TAlt] -> S TTerm
+    pruneLitCases x t d bs | CTNat == caseType t =
+      case complete bs [] Nothing of
+        Just bs' -> tCase x t tUnreachable bs'
+        Nothing  -> return $ TCase x t d bs
+      where
+        complete bs small (Just upper)
+          | null $ [0..upper - 1] List.\\ small = Just []
+        complete (b@(TALit (LitNat n) _) : bs) small upper =
+          (b :) <$> complete bs (n : small) upper
+        complete (b@(TAGuard (TApp (TPrim PGeq) [TVar y, TLit (LitNat j)]) _) : bs) small upper | x == y =
+          (b :) <$> complete bs small (Just $ maybe j (min j) upper)
+        complete _ _ _ = Nothing
+
+    pruneLitCases x t d bs
+      | CTInt == caseType t = return $ TCase x t d bs -- TODO
+      | otherwise           = return $ TCase x t d bs
+
+    -- Drop 'false' branches and drop everything after 'true' branches (including the default
+    -- branch)
+    pruneBoolGuards d [] = (d, [])
+    pruneBoolGuards d (b@(TAGuard (TCon c) _) : bs)
+      | Just c == true  = (tUnreachable, [b])
+      | Just c == false = pruneBoolGuards d bs
+    pruneBoolGuards d (b : bs) =
+      second (b :) $ pruneBoolGuards d bs
+
+    tCase' x t d [] = return d
+    tCase' x t d bs = pruneLitCases x t d bs
+
+    tApp :: TTerm -> [TTerm] -> S TTerm
+    tApp (TLet e b) es = TLet e <$> underLet e (tApp b (raise 1 es))
+    tApp (TCase x t d bs) es = do
+      d  <- tApp d es
+      bs <- mapM (`tAppAlt` es) bs
+      simpl $ TCase x t d bs    -- will resimplify branches
+    tApp (TVar x) es = do
+      v <- lookupVar x
+      case v of
+        _ | v /= TVar x && isAtomic v -> tApp v es
+        TLam{} -> tApp v es   -- could blow up the code
+        _      -> pure $ mkTApp (TVar x) es
+    tApp f [] = pure f
+    tApp (TLam b) (TVar i : es) = tApp (subst 0 (TVar i) b) es
+    tApp (TLam b) (e : es) = tApp (TLet e b) es
+    tApp f es = pure $ TApp f es
+
+    tAppAlt (TACon c a b) es = TACon c a <$> underLams a (tApp b (raise a es))
+    tAppAlt (TALit l b) es   = TALit l   <$> tApp b es
+    tAppAlt (TAGuard g b) es = TAGuard g <$> tApp b es
+
+    isAtomic = \case
+      TVar{}    -> True
+      TCon{}    -> True
+      TPrim{}   -> True
+      TDef{}    -> True
+      TLit{}    -> True
+      TSort{}   -> True
+      TErased{} -> True
+      TError{}  -> True
+      _         -> False
+
+    checkLeq a b = do
+      rho  <- asks envSubst
+      rwr  <- asks envRewrite
+      let nf = toArith . applySubst rho
+          less = [ (nf a, nf b) | (TPOp PLt a b, rhs) <- rwr, isTrue  rhs ]
+          leq  = [ (nf b, nf a) | (TPOp PLt a b, rhs) <- rwr, isFalse rhs ]
+
+          match (j, as) (k, bs)
+            | as == bs  = Just (j - k)
+            | otherwise = Nothing
+
+          -- Do we have x ≤ y given x' < y' + d ?
+          matchEqn d x y (x', y') = isJust $ do
+            k <- match x x'     -- x = x' + k
+            j <- match y y'     -- y = y' + j
+            guard (k <= j + d)  -- x ≤ y if k ≤ j + d
+
+          matchLess = matchEqn 1
+          matchLeq  = matchEqn 0
+
+          literal (j, []) (k, []) = j <= k
+          literal _ _ = False
+
+          -- k + fromWord x ≤ y  if  k + 2^64 - 1 ≤ y
+          wordUpperBound (k, [Pos (TApp (TPrim P64ToI) _)]) y = go (k + 2 ^ 64 - 1, []) y
+          wordUpperBound _ _ = False
+
+          -- x ≤ k + fromWord y  if  x ≤ k
+          wordLowerBound a (k, [Pos (TApp (TPrim P64ToI) _)]) = go a (k, [])
+          wordLowerBound _ _ = False
+
+          go x y = or
+            [ literal x y
+            , wordUpperBound x y
+            , wordLowerBound x y
+            , any (matchLess x y) less
+            , any (matchLeq x y) leq ]
+
+      return $ go (nf a) (nf b)
+
+type Arith = (Integer, [Atom])
+
+data Atom = Pos TTerm | Neg TTerm
+  deriving (Show, Eq, Ord)
+
+aNeg :: Atom -> Atom
+aNeg (Pos a) = Neg a
+aNeg (Neg a) = Pos a
+
+aCancel :: [Atom] -> [Atom]
+aCancel (a : as)
+  | (aNeg a) `elem` as = aCancel (List.delete (aNeg a) as)
+  | otherwise          = a : aCancel as
+aCancel [] = []
+
+sortR :: Ord a => [a] -> [a]
+sortR = List.sortBy (flip compare)
+
+aAdd :: Arith -> Arith -> Arith
+aAdd (a, xs) (b, ys) = (a + b, aCancel $ sortR $ xs ++ ys)
+
+aSub :: Arith -> Arith -> Arith
+aSub (a, xs) (b, ys) = (a - b, aCancel $ sortR $ xs ++ map aNeg ys)
+
+fromArith :: Arith -> TTerm
+fromArith (n, []) = tInt n
+fromArith (0, xs)
+  | (ys, Pos a : zs) <- break isPos xs = foldl addAtom a (ys ++ zs)
+fromArith (n, xs)
+  | n < 0, (ys, Pos a : zs) <- break isPos xs =
+    tOp PSub (foldl addAtom a (ys ++ zs)) (tInt (-n))
+fromArith (n, xs) = foldl addAtom (tInt n) xs
+
+isPos :: Atom -> Bool
+isPos Pos{} = True
+isPos Neg{} = False
+
+addAtom :: TTerm -> Atom -> TTerm
+addAtom t (Pos a) = tOp PAdd t a
+addAtom t (Neg a) = tOp PSub t a
+
+toArith :: TTerm -> Arith
+toArith t | Just n <- intView t = (n, [])
+toArith (TApp (TPrim PAdd) [a, b]) = aAdd (toArith a) (toArith b)
+toArith (TApp (TPrim PSub) [a, b]) = aSub (toArith a) (toArith b)
+toArith t = (0, [Pos t])
+
+simplArith :: TTerm -> TTerm
+simplArith = fromArith . toArith
diff --git a/src/full/Agda/Compiler/Treeless/Subst.hs b/src/full/Agda/Compiler/Treeless/Subst.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Subst.hs
@@ -0,0 +1,141 @@
+{-# OPTIONS_GHC -fno-warn-orphans       #-}
+
+module Agda.Compiler.Treeless.Subst where
+
+import qualified Data.Map as Map
+import Data.Map (Map)
+import Data.Maybe
+import Data.Semigroup ( Semigroup, (<>), All(..), Any(..) )
+
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Impossible
+
+instance DeBruijn TTerm where
+  deBruijnVar = TVar
+  deBruijnView (TVar i) = Just i
+  deBruijnView _ = Nothing
+
+instance Subst TTerm where
+  type SubstArg TTerm = TTerm
+
+  applySubst IdS = id
+  applySubst rho = \case
+      t@TDef{}    -> t
+      t@TLit{}    -> t
+      t@TCon{}    -> t
+      t@TPrim{}   -> t
+      t@TUnit{}   -> t
+      t@TSort{}   -> t
+      t@TErased{} -> t
+      t@TError{}  -> t
+      TVar i         -> lookupS rho i
+      TApp f ts      -> tApp (applySubst rho f) (applySubst rho ts)
+      TLam b         -> TLam (applySubst (liftS 1 rho) b)
+      TLet e b       -> TLet (applySubst rho e) (applySubst (liftS 1 rho) b)
+      TCase i t d bs ->
+        case applySubst rho (TVar i) of
+          TVar j  -> TCase j t (applySubst rho d) (applySubst rho bs)
+          e       -> TLet e $ TCase 0 t (applySubst rho' d) (applySubst rho' bs)
+            where rho' = wkS 1 rho
+      TCoerce e -> TCoerce (applySubst rho e)
+    where
+      tApp (TPrim PSeq) [TErased, b] = b
+      tApp f ts = TApp f ts
+
+instance Subst TAlt where
+  type SubstArg TAlt = TTerm
+  applySubst rho (TACon c i b) = TACon c i (applySubst (liftS i rho) b)
+  applySubst rho (TALit l b)   = TALit l (applySubst rho b)
+  applySubst rho (TAGuard g b) = TAGuard (applySubst rho g) (applySubst rho b)
+
+newtype UnderLambda = UnderLambda Any
+  deriving (Eq, Ord, Show, Semigroup, Monoid)
+
+newtype SeqArg = SeqArg All
+  deriving (Eq, Ord, Show, Semigroup, Monoid)
+
+data Occurs = Occurs Int UnderLambda SeqArg
+  deriving (Eq, Ord, Show)
+
+once :: Occurs
+once = Occurs 1 mempty (SeqArg $ All False)
+
+inSeq :: Occurs -> Occurs
+inSeq (Occurs n l _) = Occurs n l mempty
+
+underLambda :: Occurs -> Occurs
+underLambda o = o <> Occurs 0 (UnderLambda $ Any True) mempty
+
+instance Semigroup Occurs where
+  Occurs a k s <> Occurs b l t = Occurs (a + b) (k <> l) (s <> t)
+
+instance Monoid Occurs where
+  mempty  = Occurs 0 mempty mempty
+  mappend = (<>)
+
+
+-- Andreas, 2019-07-10: this free variable computation should be rewritten
+-- in the style of TypeChecking.Free.Lazy.
+-- https://github.com/agda/agda/commit/03eb3945114a4ccdb449f22d69db8d6eaa4699b8#commitcomment-34249120
+
+class HasFree a where
+  freeVars :: a -> Map Int Occurs
+
+freeIn :: HasFree a => Int -> a -> Bool
+freeIn i x = Map.member i (freeVars x)
+
+occursIn :: HasFree a => Int -> a -> Occurs
+occursIn i x = fromMaybe mempty $ Map.lookup i (freeVars x)
+
+instance HasFree Int where
+  freeVars x = Map.singleton x once
+
+instance HasFree a => HasFree [a] where
+  freeVars xs = Map.unionsWith mappend $ map freeVars xs
+
+instance (HasFree a, HasFree b) => HasFree (a, b) where
+  freeVars (x, y) = Map.unionWith mappend (freeVars x) (freeVars y)
+
+data Binder a = Binder Int a
+
+instance HasFree a => HasFree (Binder a) where
+  freeVars (Binder 0 x) = freeVars x
+  freeVars (Binder k x) = Map.filterWithKey (\ k _ -> k >= 0) $ Map.mapKeysMonotonic (subtract k) $ freeVars x
+
+newtype InSeq a = InSeq a
+
+instance HasFree a => HasFree (InSeq a) where
+  freeVars (InSeq x) = inSeq <$> freeVars x
+
+instance HasFree TTerm where
+  freeVars = \case
+    TDef{}    -> Map.empty
+    TLit{}    -> Map.empty
+    TCon{}    -> Map.empty
+    TPrim{}   -> Map.empty
+    TUnit{}   -> Map.empty
+    TSort{}   -> Map.empty
+    TErased{} -> Map.empty
+    TError{}  -> Map.empty
+    TVar i         -> freeVars i
+    TApp (TPrim PSeq) [TVar x, b] -> freeVars (InSeq x, b)
+    TApp f ts      -> freeVars (f, ts)
+    TLam b         -> underLambda <$> freeVars (Binder 1 b)
+    TLet e b       -> freeVars (e, Binder 1 b)
+    TCase i _ d bs -> freeVars (i, (d, bs))
+    TCoerce t      -> freeVars t
+
+instance HasFree TAlt where
+  freeVars = \case
+    TACon _ i b -> freeVars (Binder i b)
+    TALit _ b   -> freeVars b
+    TAGuard g b -> freeVars (g, b)
+
+-- | Strenghtening.
+tryStrengthen :: (HasFree a, Subst a) => Int -> a -> Maybe a
+tryStrengthen n t =
+  case Map.minViewWithKey (freeVars t) of
+    Just ((i, _), _) | i < n -> Nothing
+    _ -> Just $ applySubst (strengthenS impossible n) t
diff --git a/src/full/Agda/Compiler/Treeless/Uncase.hs b/src/full/Agda/Compiler/Treeless/Uncase.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Uncase.hs
@@ -0,0 +1,70 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Uncase (caseToSeq) where
+
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Substitute
+import Agda.Compiler.Treeless.Subst
+import Agda.Compiler.Treeless.Compare
+
+import Agda.Utils.List
+
+import Agda.Utils.Impossible
+
+caseToSeq :: Monad m => TTerm -> m TTerm
+caseToSeq t = return $ uncase t
+
+uncase :: TTerm -> TTerm
+uncase t = case t of
+  TVar{}    -> t
+  TPrim{}   -> t
+  TDef{}    -> t
+  TApp f es -> tApp (uncase f) (map uncase es)
+  TLam b    -> TLam $ uncase b
+  TLit{}    -> t
+  TCon{}    -> t
+  TLet e b  -> tLet (uncase e) (uncase b)
+  TCase x t d bs -> doCase x t (uncase d) (map uncaseAlt bs)
+  TUnit{}   -> t
+  TSort{}   -> t
+  TErased{} -> t
+  TError{}  -> t
+  TCoerce t -> TCoerce (uncase t)
+  where
+    uncaseAlt (TACon c a b) = TACon c a $ uncase b
+    uncaseAlt (TALit l b)   = TALit l $ uncase b
+    uncaseAlt (TAGuard g b) = TAGuard (uncase g) (uncase b)
+
+    doCase x t d bs
+      | Just u <- mu,
+        all (equalTo x u) bs = maybeSeq u
+      | otherwise            = fallback
+      where
+        maybeSeq u | caseLazy t = u
+                   | otherwise  = tApp (TPrim PSeq) [TVar x, u]
+        fallback = TCase x t d bs
+        (fv, mu)
+          | isUnreachable d =
+            case lastWithDefault __IMPOSSIBLE__ bs of
+              TACon _ a b -> (a, tryStrengthen a b)
+              TALit l b   -> (0, Just b)
+              TAGuard _ b -> (0, Just b)
+          | otherwise = (0, Just d)
+
+    equalTo :: Int -> TTerm -> TAlt -> Bool
+    equalTo x t (TACon c a b)
+      | Just b' <- tryStrengthen a b = equalTerms (subst x v t) (subst x v b')
+      | otherwise                    = False
+      where v = mkTApp (TCon c) (replicate a TErased)
+    equalTo x t (TALit l b)   = equalTerms (subst x (TLit l) t) (subst x (TLit l) b)
+    equalTo x t (TAGuard _ b) = equalTerms t b
+
+    tLet e b =
+      case occursIn 0 b of
+        Occurs 0 _ _ -> strengthen impossible b
+        _            -> TLet e b
+
+    -- Primitive operations are already strict
+    tApp (TPrim PSeq) [_, b@(TApp (TPrim op) _)]
+      | op `elem` [PAdd, PSub, PMul, PLt, PGeq, PRem, PQuot] || isPrimEq op = b
+    tApp f es = TApp f es
diff --git a/src/full/Agda/Compiler/Treeless/Unused.hs b/src/full/Agda/Compiler/Treeless/Unused.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Compiler/Treeless/Unused.hs
@@ -0,0 +1,104 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Compiler.Treeless.Unused
+  ( usedArguments
+  , stripUnusedArguments
+  ) where
+
+import Data.Maybe
+
+import qualified Data.Set as Set
+  -- Andreas, 2021-02-10
+  -- TODO: Replace Set by IntSet.
+  -- However, this has to wait until we can comfortably bump to
+  -- containers-0.6.3.1, which is the first to contain IntSet.mapMonotonic.
+  -- Currently, such a constraints gets us into cabal hell.
+  -- GHC 8.10 is still shipped with 0.6.2.1, so we either have to wait
+  -- until we drop GHC 8 or until we adopt v2-cabal.
+
+import Agda.Syntax.Common
+import Agda.Syntax.Treeless
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+
+import Agda.Compiler.Treeless.Pretty () -- instance only
+
+import Agda.Utils.Function ( iterateUntilM )
+import Agda.Utils.List     ( downFrom )
+import Agda.Syntax.Common.Pretty   ( prettyShow )
+
+usedArguments :: QName -> TTerm -> TCM [ArgUsage]
+usedArguments q t = computeUnused q b (replicate n ArgUnused)
+  where (n, b) = tLamView t
+
+-- | Saturation algorithm, starting with all unused arguments
+--   and adding usages until fixed-point has been reached.
+
+computeUnused :: QName -> TTerm -> [ArgUsage] -> TCM [ArgUsage]
+computeUnused q t = iterateUntilM (==) $ \ used -> do
+
+  reportSLn "treeless.opt.unused" 50 $ concat
+    [ "Unused approximation for ", prettyShow q, ": "
+    , unwords [ if u == ArgUsed then [x] else "_" | (x, u) <- zip ['a'..] used ]
+    ]
+  -- Update usage information q to so far "best" value.
+  setCompiledArgUse q used
+
+  -- The new usage information is the free variables of @t@,
+  -- computed under the current usage assumptions of the functions it calls.
+  fv <- go t
+  return $ [ if Set.member i fv then ArgUsed else ArgUnused
+           | i <- downFrom (length used)
+           ]
+  where
+    go = \case
+      TVar x    -> pure $ Set.singleton x
+      TPrim{}   -> pure Set.empty
+      TDef{}    -> pure Set.empty
+      TLit{}    -> pure Set.empty
+      TCon{}    -> pure Set.empty
+
+      TApp (TDef f) ts -> do
+        used <- fromMaybe [] <$> getCompiledArgUse f
+        Set.unions <$> sequence [ go t | (t, ArgUsed) <- zip ts $ used ++ repeat ArgUsed ]
+
+      TApp f ts -> Set.unions <$> mapM go (f : ts)
+      TLam b    -> underBinder <$> go b
+      TLet e b  -> do
+        uses <- go b
+        if | Set.member 0 uses -> Set.union (underBinder uses) <$> go e
+           | otherwise         -> pure (underBinder uses)
+      TCase x i d bs ->
+        let e    = caseErased i
+            cont = Set.unions <$> ((:) <$> go d <*> mapM (goAlt e) bs) in
+        case e of
+          Erased{}    -> cont
+          NotErased{} -> Set.insert x <$> cont
+      TUnit{}   -> pure Set.empty
+      TSort{}   -> pure Set.empty
+      TErased{} -> pure Set.empty
+      TError{}  -> pure Set.empty
+      TCoerce t -> go t
+
+    goAlt _ (TALit _   b) = go b
+    goAlt e (TAGuard g b) = case e of
+      NotErased{} -> Set.union <$> go g <*> go b
+      Erased{}    -> -- The guard will not be executed if the match
+                     -- is on an erased argument.
+                     go b
+    goAlt _ (TACon _ a b) = underBinders a <$> go b
+
+    underBinder = underBinders 1
+    underBinders 0 = id
+    underBinders n = Set.filter (>= 0) . Set.mapMonotonic (subtract n)
+
+stripUnusedArguments :: [ArgUsage] -> TTerm -> TTerm
+stripUnusedArguments used t = mkTLam m $ applySubst rho b
+  where
+    (n, b) = tLamView t
+    m      = length $ filter (== ArgUsed) used'
+    used'  = reverse $ take n $ used ++ repeat ArgUsed
+    rho = computeSubst used'
+    computeSubst (ArgUnused : bs) = TErased :# computeSubst bs
+    computeSubst (ArgUsed   : bs) = liftS 1 $ computeSubst bs
+    computeSubst []               = idS
diff --git a/src/full/Agda/ImpossibleTest.hs b/src/full/Agda/ImpossibleTest.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/ImpossibleTest.hs
@@ -0,0 +1,22 @@
+-- | Facility to test throwing internal errors.
+
+module Agda.ImpossibleTest where
+
+import Agda.TypeChecking.Monad.Base   ( TCM, ReduceM, runReduceM )
+import Agda.TypeChecking.Monad.Debug  ( MonadDebug, __IMPOSSIBLE_VERBOSE__ )
+import Agda.TypeChecking.Reduce.Monad ()
+
+import Agda.Utils.CallStack           ( HasCallStack )
+import Agda.Utils.Impossible          ( __IMPOSSIBLE__ )
+
+-- | If the given list of words is non-empty, print them as debug message
+--   (using '__IMPOSSIBLE_VERBOSE__') before raising the internal error.
+impossibleTest :: (MonadDebug m, HasCallStack) => [String] -> m a
+impossibleTest = \case
+  []   -> __IMPOSSIBLE__
+  strs -> __IMPOSSIBLE_VERBOSE__ $ unwords strs
+
+impossibleTestReduceM :: (HasCallStack) => [String] -> TCM a
+impossibleTestReduceM = runReduceM . \case
+  []   -> __IMPOSSIBLE__
+  strs -> __IMPOSSIBLE_VERBOSE__ $ unwords strs
diff --git a/src/full/Agda/Interaction/AgdaTop.hs b/src/full/Agda/Interaction/AgdaTop.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/AgdaTop.hs
@@ -0,0 +1,86 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.AgdaTop
+    ( repl
+    ) where
+
+import Control.Monad                ( unless )
+import Control.Monad.IO.Class       ( MonadIO(..) )
+import Control.Monad.State          ( evalStateT, runStateT )
+import Control.Monad.Trans          ( lift )
+
+import Data.Char
+
+import System.IO
+
+import Agda.Interaction.Base
+import Agda.Interaction.ExitCode
+import Agda.Interaction.Response as R
+import Agda.Interaction.InteractionTop
+import Agda.Interaction.Options
+
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+----------------------------------
+
+-- | 'repl' is a fake ghci interpreter for both the Emacs the JSON frontend
+repl :: InteractionOutputCallback -> String -> TCM () -> TCM ()
+repl callback prompt setup = do
+    liftIO $ do
+      hSetBuffering stdout LineBuffering
+      hSetBuffering stdin  LineBuffering
+      hSetEncoding  stdout utf8
+      hSetEncoding  stdin  utf8
+
+    setInteractionOutputCallback callback
+
+    commands <- liftIO $ initialiseCommandQueue readCommand
+
+    handleCommand_ (lift setup) `evalStateT` initCommandState commands
+
+    opts <- commandLineOptions
+    _ <- interact' `runStateT`
+           (initCommandState commands)
+             { optionsOnReload = opts{ optAbsoluteIncludePaths = [] } }
+    return ()
+  where
+  interact' :: CommandM ()
+  interact' = do
+    Bench.reset
+    done <- Bench.billTo [] $ do
+
+      liftIO $ do
+        putStr prompt
+        hFlush stdout
+      r <- maybeAbort runInteraction
+      case r of
+        Done      -> return True -- Done.
+        Command _ -> return False
+        Error s   -> do
+          exit <- optExitOnError <$> commandLineOptions
+          if exit
+            then liftIO (exitAgdaWith CommandError)
+            else do
+              liftIO (putStrLn s)
+              return False
+
+    lift Bench.print
+    unless done interact'
+
+  -- Reads the next command from stdin.
+
+  readCommand :: IO Command
+  readCommand = do
+    done <- isEOF
+    if done then
+      return Done
+    else do
+      r <- getLine
+      _ <- return $! length r     -- force to read the full input line
+      case dropWhile isSpace r of
+        ""          -> readCommand
+        ('-':'-':_) -> readCommand
+        _           -> case parseIOTCM r of
+          Right cmd -> return $ Command cmd
+          Left err  -> return $ Error err
diff --git a/src/full/Agda/Interaction/Base.hs b/src/full/Agda/Interaction/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Base.hs
@@ -0,0 +1,495 @@
+{-# OPTIONS_GHC -fno-cse #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.Interaction.Base where
+
+import           Control.Concurrent.STM.TChan
+import           Control.Concurrent.STM.TVar
+
+import           Control.Monad                ( mplus, liftM2, liftM4 )
+import           Control.Monad.Except
+import           Control.Monad.Identity
+import           Control.Monad.State
+
+import qualified Data.List                    as List
+import           Data.Map                     (Map)
+import qualified Data.Map                     as Map
+import           Data.Maybe                   (listToMaybe)
+
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Base
+  (HighlightingLevel, HighlightingMethod, TCM, Comparison, Polarity, TCErr)
+
+import           Agda.Syntax.Abstract         (QName)
+import           Agda.Syntax.Common           (InteractionId (..), Modality)
+import           Agda.Syntax.Internal         (ProblemId, Blocker)
+import           Agda.Syntax.Position
+import           Agda.Syntax.Scope.Base       (ScopeInfo)
+import           Agda.Syntax.TopLevelModuleName
+
+import           Agda.Interaction.Options     (CommandLineOptions,
+                                               defaultOptions)
+
+import           Agda.Utils.FileName          (AbsolutePath, mkAbsolute)
+import           Agda.Syntax.Common.Pretty            (Pretty(..), prettyShow, text)
+import           Agda.Utils.Time              (ClockTime)
+
+------------------------------------------------------------------------
+-- The CommandM monad
+
+-- | Auxiliary state of an interactive computation.
+
+data CommandState = CommandState
+  { theInteractionPoints :: [InteractionId]
+    -- ^ The interaction points of the buffer, in the order in which
+    --   they appear in the buffer. The interaction points are
+    --   recorded in 'theTCState', but when new interaction points are
+    --   added by give or refine Agda does not ensure that the ranges
+    --   of later interaction points are updated.
+  , theCurrentFile       :: Maybe CurrentFile
+    -- ^ The file which the state applies to. Only stored if the
+    -- module was successfully type checked (potentially with
+    -- warnings).
+  , optionsOnReload      :: CommandLineOptions
+    -- ^ Reset the options on each reload to these.
+  , oldInteractionScopes :: !OldInteractionScopes
+    -- ^ We remember (the scope of) old interaction points to make it
+    --   possible to parse and compute highlighting information for the
+    --   expression that it got replaced by.
+  , commandQueue         :: !CommandQueue
+    -- ^ The command queue.
+    --
+    -- This queue should only be manipulated by
+    -- 'initialiseCommandQueue' and 'maybeAbort'.
+  }
+
+type OldInteractionScopes = Map InteractionId ScopeInfo
+
+-- | Initial auxiliary interaction state
+
+initCommandState :: CommandQueue -> CommandState
+initCommandState commandQueue =
+  CommandState
+    { theInteractionPoints = []
+    , theCurrentFile       = Nothing
+    , optionsOnReload      = defaultOptions
+    , oldInteractionScopes = Map.empty
+    , commandQueue         = commandQueue
+    }
+
+-- | Monad for computing answers to interactive commands.
+--
+--   'CommandM' is 'TCM' extended with state 'CommandState'.
+
+type CommandM = StateT CommandState TCM
+
+-- | Information about the current main module.
+data CurrentFile = CurrentFile
+  { currentFilePath  :: AbsolutePath
+      -- ^ The file currently loaded into interaction.
+  , currentFileModule :: TopLevelModuleName
+      -- ^ The top-level module name of the currently loaded file.
+  , currentFileArgs  :: [String]
+      -- ^ The arguments to Agda used for loading the file.
+  , currentFileStamp :: ClockTime
+      -- ^ The modification time stamp of the file when it was loaded.
+  } deriving (Show)
+
+------------------------------------------------------------------------
+-- Command queues
+
+-- | A generalised command type.
+
+data Command' a
+  = Command !a
+    -- ^ A command.
+  | Done
+    -- ^ Stop processing commands.
+  | Error String
+    -- ^ An error message for a command that could not be parsed.
+  deriving Show
+
+-- | IOTCM commands.
+
+type Command = Command' IOTCM
+
+-- | IOTCM commands.
+--
+-- The commands are obtained by applying the functions to the current
+-- top-level module name, if any. Note that the top-level module name
+-- is not used by independent commands. For other commands the
+-- top-level module name should be known.
+
+type IOTCM = Maybe TopLevelModuleName -> IOTCM' Range
+
+-- | Command queues.
+
+data CommandQueue = CommandQueue
+  { commands :: !(TChan (Integer, Command))
+    -- ^ Commands that should be processed, in the order in which they
+    -- should be processed. Each command is associated with a number,
+    -- and the numbers are strictly increasing. Abort commands are not
+    -- put on this queue.
+  , abort    :: !(TVar (Maybe Integer))
+    -- ^ When this variable is set to @Just n@ an attempt is made to
+    -- abort all commands with a command number that is at most @n@.
+  }
+
+
+----------------------------------------------------------------------------
+-- | An interactive computation.
+
+type Interaction = Interaction' Range
+
+data Interaction' range
+    -- | @cmd_load m argv@ loads the module in file @m@, using
+    -- @argv@ as the command-line options.
+  = Cmd_load            FilePath [String]
+
+    -- | @cmd_compile b m argv@ compiles the module in file @m@ using
+    -- the backend @b@, using @argv@ as the command-line options.
+  | Cmd_compile         CompilerBackend FilePath [String]
+
+  | Cmd_constraints
+
+    -- | Show unsolved metas. If there are no unsolved metas but unsolved constraints
+    -- show those instead.
+  | Cmd_metas Rewrite
+
+    -- | A command that fails if there are any unsolved
+    -- meta-variables. By default no output is generated if the
+    -- command is successful.
+  | Cmd_no_metas
+
+    -- | Shows all the top-level names in the given module, along with
+    -- their types. Uses the top-level scope.
+  | Cmd_show_module_contents_toplevel
+                        Rewrite
+                        String
+
+    -- | Shows all the top-level names in scope which mention all the given
+    -- identifiers in their type.
+  | Cmd_search_about_toplevel Rewrite String
+
+    -- | Solve (all goals / the goal at point) whose values are determined by
+    -- the constraints.
+  | Cmd_solveAll Rewrite
+  | Cmd_solveOne Rewrite InteractionId range String
+
+    -- | Solve (all goals / the goal at point) by using Auto.
+  | Cmd_autoOne            InteractionId range String
+  | Cmd_autoAll
+
+    -- | Parse the given expression (as if it were defined at the
+    -- top-level of the current module) and infer its type.
+  | Cmd_infer_toplevel  Rewrite  -- Normalise the type?
+                        String
+
+
+    -- | Parse and type check the given expression (as if it were defined
+    -- at the top-level of the current module) and normalise it.
+  | Cmd_compute_toplevel ComputeMode
+                         String
+
+    ------------------------------------------------------------------------
+    -- Syntax highlighting
+
+    -- | @cmd_load_highlighting_info source@ loads syntax highlighting
+    -- information for the module in @source@, and asks Emacs to apply
+    -- highlighting info from this file.
+    --
+    -- If the module does not exist, or its module name is malformed or
+    -- cannot be determined, or the module has not already been visited,
+    -- or the cached info is out of date, then no highlighting information
+    -- is printed.
+    --
+    -- This command is used to load syntax highlighting information when a
+    -- new file is opened, and it would probably be annoying if jumping to
+    -- the definition of an identifier reset the proof state, so this
+    -- command tries not to do that. One result of this is that the
+    -- command uses the current include directories, whatever they happen
+    -- to be.
+  | Cmd_load_highlighting_info FilePath
+
+    -- | Tells Agda to compute token-based highlighting information
+    -- for the file.
+    --
+    -- This command works even if the file's module name does not
+    -- match its location in the file system, or if the file is not
+    -- scope-correct. Furthermore no file names are put in the
+    -- generated output. Thus it is fine to put source code into a
+    -- temporary file before calling this command. However, the file
+    -- extension should be correct.
+    --
+    -- If the second argument is 'Remove', then the (presumably
+    -- temporary) file is removed after it has been read.
+  | Cmd_tokenHighlighting FilePath Remove
+
+    -- | Tells Agda to compute highlighting information for the expression just
+    --   spliced into an interaction point.
+  | Cmd_highlight InteractionId range String
+
+    ------------------------------------------------------------------------
+    -- Implicit arguments
+
+    -- | Tells Agda whether or not to show implicit arguments.
+  | ShowImplicitArgs    Bool -- Show them?
+
+
+    -- | Toggle display of implicit arguments.
+  | ToggleImplicitArgs
+
+    ------------------------------------------------------------------------
+    -- Irrelevant arguments
+
+    -- | Tells Agda whether or not to show irrelevant arguments.
+  | ShowIrrelevantArgs    Bool -- Show them?
+
+
+    -- | Toggle display of irrelevant arguments.
+  | ToggleIrrelevantArgs
+
+    ------------------------------------------------------------------------
+    -- | Goal commands
+    --
+    -- If the range is 'noRange', then the string comes from the
+    -- minibuffer rather than the goal.
+
+  | Cmd_give            UseForce InteractionId range String
+
+  | Cmd_refine          InteractionId range String
+
+  | Cmd_intro           Bool InteractionId range String
+
+  | Cmd_refine_or_intro Bool InteractionId range String
+
+  | Cmd_context         Rewrite InteractionId range String
+
+  | Cmd_helper_function Rewrite InteractionId range String
+
+  | Cmd_infer           Rewrite InteractionId range String
+
+  | Cmd_goal_type       Rewrite InteractionId range String
+
+  -- | Grabs the current goal's type and checks the expression in the hole
+  -- against it. Returns the elaborated term.
+  | Cmd_elaborate_give
+                        Rewrite InteractionId range String
+
+    -- | Displays the current goal and context.
+  | Cmd_goal_type_context Rewrite InteractionId range String
+
+    -- | Displays the current goal and context /and/ infers the type of an
+    -- expression.
+  | Cmd_goal_type_context_infer
+                        Rewrite InteractionId range String
+
+  -- | Grabs the current goal's type and checks the expression in the hole
+  -- against it.
+  | Cmd_goal_type_context_check
+                        Rewrite InteractionId range String
+
+    -- | Shows all the top-level names in the given module, along with
+    -- their types. Uses the scope of the given goal.
+  | Cmd_show_module_contents
+                        Rewrite InteractionId range String
+
+  | Cmd_make_case       InteractionId range String
+
+  | Cmd_compute         ComputeMode
+                        InteractionId range String
+
+  | Cmd_why_in_scope    InteractionId range String
+  | Cmd_why_in_scope_toplevel String
+    -- | Displays version of the running Agda
+  | Cmd_show_version
+  | Cmd_abort
+    -- ^ Abort the current computation.
+    --
+    -- Does nothing if no computation is in progress.
+  | Cmd_exit
+    -- ^ Exit the program.
+        deriving (Show, Read, Functor, Foldable, Traversable)
+
+data IOTCM' range
+    = IOTCM
+        FilePath
+         -- -^ The current file. If this file does not match
+         -- 'theCurrentFile, and the 'Interaction' is not
+         -- \"independent\", then an error is raised.
+        HighlightingLevel
+        HighlightingMethod
+        (Interaction' range)
+         -- -^ What to do
+            deriving (Show, Read, Functor, Foldable, Traversable)
+
+-- | Used to indicate whether something should be removed or not.
+
+data Remove
+  = Remove
+  | Keep
+  deriving (Show, Read)
+
+
+
+
+---------------------------------------------------------
+-- Read instances
+
+-- | An 'IOTCM' parser.
+--
+-- If the parse fails, then an error message is returned.
+
+parseIOTCM ::
+  String -> Either String IOTCM
+parseIOTCM s = case listToMaybe $ reads s of
+  Just (x, "")  -> Right $ \top -> case x of
+    IOTCM f l m i -> IOTCM f l m $
+      (fmap . fmap . fmap) (\rf -> mkRangeFile (rangeFilePath rf) top) i
+  Just (_, rem) -> Left $ "not consumed: " ++ rem
+  _             -> Left $ "cannot read: " ++ s
+
+-- | The 'Parse' monad.
+--   'StateT' state holds the remaining input.
+
+type Parse a = ExceptT String (StateT String Identity) a
+
+-- | Converter from the type of 'reads' to 'Parse'
+--   The first paramter is part of the error message
+--   in case the parse fails.
+
+readsToParse :: String -> (String -> Maybe (a, String)) -> Parse a
+readsToParse s f = do
+  st <- lift get
+  case f st of
+    Nothing -> throwError s
+    Just (a, st) -> do
+        lift $ put st
+        return a
+
+parseToReadsPrec :: Parse a -> Int -> String -> [(a, String)]
+parseToReadsPrec p i s = case runIdentity . flip runStateT s . runExceptT $ parens' p of
+  (Right a, s) -> [(a,s)]
+  _            -> []
+
+-- | Demand an exact string.
+
+exact :: String -> Parse ()
+exact s = readsToParse (show s) $ fmap ((),) . List.stripPrefix s . dropWhile (== ' ')
+
+readParse :: Read a => Parse a
+readParse = readsToParse "read failed" $ listToMaybe . reads
+
+parens' :: Parse a -> Parse a
+parens' p = do
+    exact "("
+    x <- p
+    exact ")"
+    return x
+  `mplus`
+    p
+
+instance Read InteractionId where
+    readsPrec = parseToReadsPrec $
+        fmap InteractionId readParse
+
+-- | Note that the grammar implemented by this instance does not
+-- necessarily match the current representation of ranges.
+
+instance Read a => Read (Range' a) where
+    readsPrec = parseToReadsPrec $
+      (exact "intervalsToRange" >>
+       liftM2 intervalsToRange readParse readParse)
+        `mplus`
+      (exact "noRange" >> return noRange)
+
+instance Read a => Read (Interval' a) where
+    readsPrec = parseToReadsPrec $ do
+        exact "Interval"
+        liftM2 Interval readParse readParse
+
+instance Read AbsolutePath where
+    readsPrec = parseToReadsPrec $ do
+        exact "mkAbsolute"
+        fmap mkAbsolute readParse
+
+-- | This instance fills in the 'TopLevelModuleName's using 'Nothing'.
+-- Note that these occurrences of 'Nothing' are \"overwritten\" by
+-- 'parseIOTCM'.
+
+instance Read RangeFile where
+    readsPrec = parseToReadsPrec $
+      fmap (flip mkRangeFile Nothing) readParse
+
+instance Read a => Read (Position' a) where
+    readsPrec = parseToReadsPrec $ do
+        exact "Pn"
+        liftM4 Pn readParse readParse readParse readParse
+
+---------------------------------------------------------
+-- | Available backends.
+
+data CompilerBackend = LaTeX | QuickLaTeX | OtherBackend String
+    deriving (Eq)
+
+-- TODO 2021-08-25 get rid of custom Show instance
+instance Show CompilerBackend where
+  show = prettyShow
+
+instance Pretty CompilerBackend where
+  pretty = \case
+    LaTeX          -> "LaTeX"
+    QuickLaTeX     -> "QuickLaTeX"
+    OtherBackend s -> text s
+
+instance Read CompilerBackend where
+  readsPrec _ s = do
+    (t, s) <- lex s
+    let b = case t of
+              "LaTeX"      -> LaTeX
+              "QuickLaTeX" -> QuickLaTeX
+              _            -> OtherBackend t
+    return (b, s)
+
+-- | Ordered ascendingly by degree of normalization.
+data Rewrite =  AsIs | Instantiated | HeadNormal | Simplified | Normalised
+    deriving (Show, Read, Eq, Ord)
+
+data ComputeMode = DefaultCompute | HeadCompute | IgnoreAbstract | UseShowInstance
+  deriving (Show, Read, Eq)
+
+data UseForce
+  = WithForce     -- ^ Ignore additional checks, like termination/positivity...
+  | WithoutForce  -- ^ Don't ignore any checks.
+  deriving (Eq, Read, Show)
+
+data OutputForm a b = OutputForm Range [ProblemId] Blocker (OutputConstraint a b)
+  deriving (Functor)
+
+data OutputConstraint a b
+      = OfType b a | CmpInType Comparison a b b
+                   | CmpElim [Polarity] a [b] [b]
+      | JustType b | CmpTypes Comparison b b
+                   | CmpLevels Comparison b b
+                   | CmpTeles Comparison b b
+      | JustSort b | CmpSorts Comparison b b
+      | Assign b a | TypedAssign b a a | PostponedCheckArgs b [a] a a
+      | IsEmptyType a
+      | SizeLtSat a
+      | FindInstanceOF b a [(a,a,a)]
+      | PTSInstance b b
+      | PostponedCheckFunDef QName a TCErr
+      | CheckLock b b
+      | DataSort QName b
+      | UsableAtMod Modality b
+  deriving (Functor)
+
+-- | A subset of 'OutputConstraint'.
+
+data OutputConstraint' a b = OfType'
+  { ofName :: b
+  , ofExpr :: a
+  }
+
+data OutputContextEntry name ty val
+  = ContextVar name ty
+  | ContextLet name ty val
diff --git a/src/full/Agda/Interaction/BasicOps.hs b/src/full/Agda/Interaction/BasicOps.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/BasicOps.hs
@@ -0,0 +1,1438 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.Interaction.BasicOps where
+
+import Prelude hiding (null)
+
+import Control.Arrow          ( first )
+import Control.Monad          ( (<=<), (>=>), forM, filterM, guard )
+import Control.Monad.Except
+import Control.Monad.State
+import Control.Monad.Identity
+import Control.Monad.Trans.Maybe
+
+import qualified Data.Map as Map
+import qualified Data.IntMap as IntMap
+import qualified Data.Map.Strict as MapS
+import qualified Data.Set as Set
+import qualified Data.List as List
+import Data.Maybe
+import Data.Monoid
+import Data.Function (on)
+import Data.Text (Text)
+import qualified Data.Text as T
+
+import Agda.Interaction.Base
+import Agda.Interaction.Options
+import Agda.Interaction.Response (Goals, ResponseContextEntry(..))
+
+import qualified Agda.Syntax.Concrete as C -- ToDo: Remove with instance of ToConcrete
+import Agda.Syntax.Position
+import Agda.Syntax.Abstract as A hiding (Open, Apply, Assign)
+import Agda.Syntax.Abstract.Views as A
+import Agda.Syntax.Abstract.Pretty
+import Agda.Syntax.Common
+import Agda.Syntax.Info (MetaInfo(..),emptyMetaInfo,exprNoRange,defaultAppInfo_,defaultAppInfo)
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Literal
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Translation.AbstractToConcrete
+import Agda.Syntax.Translation.ConcreteToAbstract
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad
+import Agda.Syntax.Fixity(Precedence(..), argumentCtx_)
+import Agda.Syntax.Parser
+
+import Agda.TheTypeChecker
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Errors ( getAllWarnings, stringTCErr, Verbalize(..) )
+import Agda.TypeChecking.Monad as M hiding (MetaInfo)
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.MetaVars.Mention
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.With
+import Agda.TypeChecking.Coverage
+import Agda.TypeChecking.Coverage.Match ( SplitPattern )
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Pretty ( PrettyTCM, prettyTCM )
+import Agda.TypeChecking.Pretty.Constraint (prettyRangeConstraint)
+import Agda.TypeChecking.IApplyConfluence
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.ProjectionLike (reduceProjectionLike)
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.CheckInternal
+import Agda.TypeChecking.SizedTypes.Solve
+import qualified Agda.TypeChecking.Pretty as TP
+import Agda.TypeChecking.Warnings
+  ( runPM, warning, WhichWarnings(..), classifyWarnings, isMetaTCWarning
+  , WarningsAndNonFatalErrors, emptyWarningsAndNonFatalErrors )
+
+import Agda.Termination.TermCheck (termMutual)
+
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Permutation
+import Agda.Utils.Size
+import Agda.Utils.String
+import Agda.Utils.WithDefault ( WithDefault'(Value) )
+
+import Agda.Utils.Impossible
+
+-- | Parses an expression.
+
+parseExpr :: Range -> String -> TCM C.Expr
+parseExpr rng s = do
+  (C.ExprWhere e wh, attrs) <-
+    runPM $ parsePosString exprWhereParser pos s
+  checkAttributes attrs
+  unless (null wh) $ typeError $ GenericError $
+    "where clauses are not supported in holes"
+  return e
+  where pos = fromMaybe (startPos Nothing) $ rStart rng
+
+parseExprIn :: InteractionId -> Range -> String -> TCM Expr
+parseExprIn ii rng s = do
+    mId <- lookupInteractionId ii
+    updateMetaVarRange mId rng
+    mi  <- getMetaInfo <$> lookupLocalMeta mId
+    e   <- parseExpr rng s
+    -- Andreas, 2019-08-19, issue #4007
+    -- We need to be in the TCEnv of the meta variable
+    -- such that the scope checker can label the clause
+    -- of a parsed extended lambda as IsAbstract if the
+    -- interaction point was created in AbstractMode.
+    withMetaInfo mi $
+      concreteToAbstract (clScope mi) e
+
+-- Type check the given expression and assign its value to the meta
+-- Precondition: we are in the context where the given meta was created.
+giveExpr :: UseForce -> Maybe InteractionId -> MetaId -> Expr -> TCM Term
+giveExpr force mii mi e = do
+    mv <- lookupLocalMeta mi
+    let t = case mvJudgement mv of
+              IsSort{}    -> __IMPOSSIBLE__
+              HasType _ _ t -> t
+    reportSDoc "interaction.give" 20 $
+      "give: meta type =" TP.<+> prettyTCM t
+    -- Here, we must be in the same context where the meta was created.
+    -- Thus, we can safely apply its type to the context variables.
+    ctx <- getContextArgs
+    t' <- t `piApplyM` permute (takeP (length ctx) $ mvPermutation mv) ctx
+    traceCall (CheckExprCall CmpLeq e t') $ do
+      reportSDoc "interaction.give" 20 $ do
+        a <- asksTC envAbstractMode
+        TP.hsep
+          [ TP.text ("give(" ++ show a ++ "): instantiated meta type =")
+          , prettyTCM t'
+          ]
+      -- Andreas, 2020-05-27 AIM XXXII, issue #4679
+      -- Clear envMutualBlock since cubical only executes
+      -- certain checks (checkIApplyConfluence) for an extended lambda
+      -- when not in a mutual block.
+      v <- locallyTC eMutualBlock (const Nothing) $
+        checkExpr e t'
+      reportSDoc "interaction.give" 40 $ "give: checked expression:" TP.<+> pure (pretty v)
+      case mvInstantiation mv of
+
+        InstV{} -> unlessM ((Irrelevant ==) <$> viewTC eRelevance) $ do
+          v' <- instantiate $ MetaV mi $ map Apply ctx
+          reportSDoc "interaction.give" 20 $ TP.sep
+            [ "meta was already set to value v' = " TP.<+> prettyTCM v'
+            , "now comparing it to given value v = " TP.<+> prettyTCM v
+            , "in context " TP.<+> inTopContext (prettyTCM ctx)
+            ]
+          equalTerm t' v v'
+
+        _ -> do -- updateMeta mi v
+          reportSLn "interaction.give" 20 "give: meta unassigned, assigning..."
+          args <- getContextArgs
+          nowSolvingConstraints $ assign DirEq mi args v (AsTermsOf t')
+
+      reportSDoc "interaction.give" 20 $ "give: meta variable updated!"
+      unless (force == WithForce) $ redoChecks mii
+      wakeupConstraints mi
+      solveSizeConstraints DontDefaultToInfty
+      cubical <- isJust . optCubical <$> pragmaOptions
+      -- don't double check with cubical, because it gets in the way too often.
+      unless (cubical || force == WithForce) $ do
+        -- Double check.
+        reportSDoc "interaction.give" 20 $ "give: double checking"
+        vfull <- instantiateFull v
+        checkInternal vfull CmpLeq t'
+      return v
+
+-- | After a give, redo termination etc. checks for function which was complemented.
+redoChecks :: Maybe InteractionId -> TCM ()
+redoChecks Nothing = return ()
+redoChecks (Just ii) = do
+  reportSLn "interaction.give" 20 $
+    "give: redoing termination check for function surrounding " ++ show ii
+  ip <- lookupInteractionPoint ii
+  case ipClause ip of
+    IPNoClause -> return ()
+    IPClause{ipcQName = f} -> do
+      mb <- mutualBlockOf f
+      terErrs <- localTC (\ e -> e { envMutualBlock = Just mb }) $ termMutual []
+      unless (null terErrs) $ warning $ TerminationIssue terErrs
+  -- TODO redo positivity check!
+
+-- | Try to fill hole by expression.
+--
+--   Returns the given expression unchanged
+--   (for convenient generalization to @'refine'@).
+give
+  :: UseForce       -- ^ Skip safety checks?
+  -> InteractionId  -- ^ Hole.
+  -> Maybe Range
+  -> Expr           -- ^ The expression to give.
+  -> TCM Expr       -- ^ If successful, the very expression is returned unchanged.
+give force ii mr e = liftTCM $ do
+  -- if Range is given, update the range of the interaction meta
+  mi  <- lookupInteractionId ii
+  whenJust mr $ updateMetaVarRange mi
+  reportSDoc "interaction.give" 10 $ "giving expression" TP.<+> prettyTCM e
+  reportSDoc "interaction.give" 50 $ TP.text $ show $ deepUnscope e
+  -- Try to give mi := e
+  _ <- withInteractionId ii $ do
+     setMetaOccursCheck mi DontRunMetaOccursCheck -- #589, #2710: Allow giving recursive solutions.
+     giveExpr force (Just ii) mi e
+    `catchError` \ case
+      -- Turn PatternErr into proper error:
+      PatternErr{} -> typeError . GenericDocError =<< do
+        withInteractionId ii $ "Failed to give" TP.<+> prettyTCM e
+      err -> throwError err
+  removeInteractionPoint ii
+  return e
+
+-- | Try to fill hole by elaborated expression.
+elaborate_give
+  :: Rewrite        -- ^ Normalise result?
+  -> UseForce       -- ^ Skip safety checks?
+  -> InteractionId  -- ^ Hole.
+  -> Maybe Range
+  -> Expr           -- ^ The expression to give.
+  -> TCM Expr       -- ^ If successful, return the elaborated expression.
+elaborate_give norm force ii mr e = withInteractionId ii $ do
+  -- if Range is given, update the range of the interaction meta
+  mi  <- lookupInteractionId ii
+  whenJust mr $ updateMetaVarRange mi
+  reportSDoc "interaction.give" 10 $ "giving expression" TP.<+> prettyTCM e
+  reportSDoc "interaction.give" 50 $ TP.text $ show $ deepUnscope e
+  -- Try to give mi := e
+  v <- withInteractionId ii $ do
+     setMetaOccursCheck mi DontRunMetaOccursCheck -- #589, #2710: Allow giving recursive solutions.
+     locallyTC eCurrentlyElaborating (const True) $
+       giveExpr force (Just ii) mi e
+    `catchError` \ case
+      -- Turn PatternErr into proper error:
+      PatternErr{} -> typeError . GenericDocError =<< do
+        withInteractionId ii $ "Failed to give" TP.<+> prettyTCM e
+      err -> throwError err
+  mv <- lookupLocalMeta mi
+  -- Reduce projection-likes before quoting, otherwise instance
+  -- selection may fail on reload (see #6203).
+  nv <- reduceProjectionLike =<< normalForm norm v
+  reportSDoc "interaction.give" 40 $ "nv = " TP.<+> pure (pretty v)
+  locallyTC ePrintMetasBare (const True) $ reify nv
+
+-- | Try to refine hole by expression @e@.
+--
+--   This amounts to successively try to give @e@, @e ?@, @e ? ?@, ...
+--   Returns the successfully given expression.
+refine
+  :: UseForce       -- ^ Skip safety checks when giving?
+  -> InteractionId  -- ^ Hole.
+  -> Maybe Range
+  -> Expr           -- ^ The expression to refine the hole with.
+  -> TCM Expr       -- ^ The successfully given expression.
+refine force ii mr e = do
+  mi <- lookupInteractionId ii
+  mv <- lookupLocalMeta mi
+  let range = fromMaybe (getRange mv) mr
+      scope = M.getMetaScope mv
+  reportSDoc "interaction.refine" 10 $
+    "refining with expression" TP.<+> prettyTCM e
+  reportSDoc "interaction.refine" 50 $
+    TP.text $ show $ deepUnscope e
+  -- We try to append up to 10 meta variables
+  tryRefine 10 range scope e
+  where
+    tryRefine :: Int -> Range -> ScopeInfo -> Expr -> TCM Expr
+    tryRefine nrOfMetas r scope = try nrOfMetas Nothing
+      where
+        try :: Int -> Maybe TCErr -> Expr -> TCM Expr
+        try 0 err e = throwError . stringTCErr $ case err of
+           Just (TypeError _ _ cl) | UnequalTerms _ I.Pi{} _ _ <- clValue cl ->
+             "Cannot refine functions with 10 or more arguments"
+           _ ->
+             "Cannot refine"
+        try n _ e = give force ii (Just r) e `catchError` \err -> try (n - 1) (Just err) =<< appMeta e
+
+        -- Apply A.Expr to a new meta
+        appMeta :: Expr -> TCM Expr
+        appMeta e = do
+          let rng = rightMargin r -- Andreas, 2013-05-01 conflate range to its right margin to ensure that appended metas are last in numbering.  This fixes issue 841.
+          -- Make new interaction point
+          ii <- registerInteractionPoint False rng Nothing
+          let info = Info.MetaInfo
+                { Info.metaRange = rng
+                , Info.metaScope = set scopePrecedence [argumentCtx_] scope
+                    -- Ulf, 2017-09-07: The `argumentCtx_` above is causing #737.
+                    -- If we're building an operator application the precedence
+                    -- should be something else.
+                , metaNumber = Nothing -- in order to print just as ?, not ?n
+                , metaNameSuggestion = ""
+                }
+              metaVar = QuestionMark info ii
+
+              count x e = getSum $ foldExpr isX e
+                where isX (A.Var y) | x == y = Sum 1
+                      isX _                  = mempty
+
+              lamView (A.Lam _ (DomainFree _ x) e) = Just (namedArg x, e)
+              lamView (A.Lam i (DomainFull (TBind r t (x :| xs) a)) e) =
+                List1.ifNull xs {-then-} (Just (namedArg x, e)) {-else-} $ \ xs ->
+                  Just (namedArg x, A.Lam i (DomainFull $ TBind r t xs a) e)
+              lamView _ = Nothing
+
+              -- reduce beta-redexes where the argument is used at most once
+              smartApp i e arg =
+                case fmap (first A.binderName) (lamView $ unScope e) of
+                  Just (A.BindName{unBind = x}, e) | count x e < 2 -> mapExpr subX e
+                    where subX (A.Var y) | x == y = namedArg arg
+                          subX e = e
+                  _ -> App i e arg
+          return $ smartApp (defaultAppInfo r) e $ defaultNamedArg metaVar
+
+-- Andreas, 2017-12-16:
+-- Ulf, your attempt to fix #737 introduced regression #2873.
+-- Going through concrete syntax does some arbitrary disambiguation
+-- of constructors, which subsequently makes refine fail.
+-- I am not convinced of the printing-parsing shortcut to address problems.
+-- (Unless you prove the roundtrip property.)
+--
+--           rescopeExpr scope $ smartApp (defaultAppInfo r) e $ defaultNamedArg metaVar
+-- -- | Turn an abstract expression into concrete syntax and then back into
+-- --   abstract. This ensures that context precedences are set correctly for
+-- --   abstract expressions built by hand. Used by refine above.
+-- rescopeExpr :: ScopeInfo -> Expr -> TCM Expr
+-- rescopeExpr scope = withScope_ scope . (concreteToAbstract_ <=< runAbsToCon . preserveInteractionIds . toConcrete)
+
+{-| Evaluate the given expression in the current environment -}
+evalInCurrent :: ComputeMode -> Expr -> TCM Expr
+evalInCurrent cmode e = do
+  (v, _t) <- inferExpr e
+  vb <- reduceB v
+  reportSDoc "interaction.eval" 30 $ "evaluated to" TP.<+> TP.pretty vb
+  v  <- pure $ ignoreBlocking vb
+  reify =<< if cmode == HeadCompute then pure v else normalise v
+
+
+evalInMeta :: InteractionId -> ComputeMode -> Expr -> TCM Expr
+evalInMeta ii cmode e =
+   do   m <- lookupInteractionId ii
+        mi <- getMetaInfo <$> lookupLocalMeta m
+        withMetaInfo mi $
+            evalInCurrent cmode e
+
+-- | Modifier for interactive commands,
+--   specifying the amount of normalization in the output.
+--
+normalForm :: (Reduce t, Simplify t, Instantiate t, Normalise t) => Rewrite -> t -> TCM t
+normalForm = \case
+  AsIs         -> instantiate   -- #4975: reify will also instantiate by for goal-type-and-context-and-check
+  Instantiated -> instantiate   --        we get a top-level fresh meta which has disappeared from state by the
+  HeadNormal   -> reduce        --        time we get to reification. Hence instantiate here.
+  Simplified   -> simplify
+  Normalised   -> normalise
+
+-- | Modifier for the interactive computation command,
+--   specifying the mode of computation and result display.
+--
+computeIgnoreAbstract :: ComputeMode -> Bool
+computeIgnoreAbstract DefaultCompute  = False
+computeIgnoreAbstract HeadCompute     = False
+computeIgnoreAbstract IgnoreAbstract  = True
+computeIgnoreAbstract UseShowInstance = True
+  -- UseShowInstance requires the result to be a string literal so respecting
+  -- abstract can only ever break things.
+
+computeWrapInput :: ComputeMode -> String -> String
+computeWrapInput UseShowInstance s = "show (" ++ s ++ ")"
+computeWrapInput _               s = s
+
+showComputed :: ComputeMode -> Expr -> TCM Doc
+showComputed UseShowInstance e =
+  case e of
+    A.Lit _ (LitString s) -> pure (text $ T.unpack s)
+    _                     -> ("Not a string:" $$) <$> prettyATop e
+showComputed _ e = prettyATop e
+
+-- | Modifier for interactive commands,
+--   specifying whether safety checks should be ignored.
+outputFormId :: OutputForm a b -> b
+outputFormId (OutputForm _ _ _ o) = out o
+  where
+    out = \case
+      OfType i _                 -> i
+      CmpInType _ _ i _          -> i
+      CmpElim _ _ (i:_) _        -> i
+      CmpElim _ _ [] _           -> __IMPOSSIBLE__
+      JustType i                 -> i
+      CmpLevels _ i _            -> i
+      CmpTypes _ i _             -> i
+      CmpTeles _ i _             -> i
+      JustSort i                 -> i
+      CmpSorts _ i _             -> i
+      Assign i _                 -> i
+      TypedAssign i _ _          -> i
+      PostponedCheckArgs i _ _ _ -> i
+      IsEmptyType _              -> __IMPOSSIBLE__   -- Should never be used on IsEmpty constraints
+      SizeLtSat{}                -> __IMPOSSIBLE__
+      FindInstanceOF _ _ _        -> __IMPOSSIBLE__
+      PTSInstance i _            -> i
+      PostponedCheckFunDef{}     -> __IMPOSSIBLE__
+      DataSort _ i               -> i
+      CheckLock i _              -> i
+      UsableAtMod _ i            -> i
+
+instance Reify ProblemConstraint where
+  type ReifiesTo ProblemConstraint = Closure (OutputForm Expr Expr)
+  reify (PConstr pids unblock cl) = withClosure cl $ \ c ->
+    OutputForm (getRange c) (Set.toList pids) unblock <$> reify c
+
+reifyElimToExpr :: MonadReify m => I.Elim -> m Expr
+reifyElimToExpr = \case
+    I.IApply _ _ v -> appl "iapply" <$> reify (defaultArg $ v) -- TODO Andrea: endpoints?
+    I.Apply v -> appl "apply" <$> reify v
+    I.Proj _o f -> appl "proj" <$> reify ((defaultArg $ I.Def f []) :: Arg Term)
+  where
+    appl :: Text -> Arg Expr -> Expr
+    appl s v = A.App defaultAppInfo_ (A.Lit empty (LitString s)) $ fmap unnamed v
+
+instance Reify Constraint where
+  type ReifiesTo Constraint = OutputConstraint Expr Expr
+
+  reify (ValueCmp cmp (AsTermsOf t) u v) = CmpInType cmp <$> reify t <*> reify u <*> reify v
+  reify (ValueCmp cmp AsSizes u v) = CmpInType cmp <$> (reify =<< sizeType) <*> reify u <*> reify v
+  reify (ValueCmp cmp AsTypes u v) = CmpTypes cmp <$> reify u <*> reify v
+  reify (ValueCmpOnFace cmp p t u v) = CmpInType cmp <$> (reify =<< ty) <*> reify (lam_o u) <*> reify (lam_o v)
+    where
+      lam_o = I.Lam (setRelevance Irrelevant defaultArgInfo) . NoAbs "_"
+      ty = runNamesT [] $ do
+        p <- open p
+        t <- open t
+        pPi' "o" p (\ o -> t)
+  reify (ElimCmp cmp _ t v es1 es2) =
+    CmpElim cmp <$> reify t <*> mapM reifyElimToExpr es1
+                            <*> mapM reifyElimToExpr es2
+  reify (LevelCmp cmp t t')    = CmpLevels cmp <$> reify t <*> reify t'
+  reify (SortCmp cmp s s')     = CmpSorts cmp <$> reify s <*> reify s'
+  reify (UnquoteTactic tac _ goal) = do
+      tac <- A.App defaultAppInfo_ (A.Unquote exprNoRange) . defaultNamedArg <$> reify tac
+      OfType tac <$> reify goal
+  reify (UnBlock m) = do
+      mi <- lookupMetaInstantiation m
+      m' <- reify (MetaV m [])
+      case mi of
+        BlockedConst t -> do
+          e  <- reify t
+          return $ Assign m' e
+        PostponedTypeCheckingProblem cl -> enterClosure cl $ \case
+          CheckExpr cmp e a -> do
+              a  <- reify a
+              return $ TypedAssign m' e a
+          CheckLambda cmp (Arg ai (xs, mt)) body target -> do
+            domType <- maybe (return underscore) reify mt
+            target  <- reify target
+            let mkN (WithHiding h x) = setHiding h $ defaultNamedArg $ A.mkBinder_ x
+                bs = mkTBind noRange (fmap mkN xs) domType
+                e  = A.Lam Info.exprNoRange (DomainFull bs) body
+            return $ TypedAssign m' e target
+          CheckArgs _ _ _ args t0 t1 _ -> do
+            t0 <- reify t0
+            t1 <- reify t1
+            return $ PostponedCheckArgs m' (map (namedThing . unArg) args) t0 t1
+          CheckProjAppToKnownPrincipalArg cmp e _ _ _ t _ _ _ _ -> TypedAssign m' e <$> reify t
+          DoQuoteTerm cmp v t -> do
+            tm <- A.App defaultAppInfo_ (A.QuoteTerm exprNoRange) . defaultNamedArg <$> reify v
+            OfType tm <$> reify t
+        Open{}  -> __IMPOSSIBLE__
+        OpenInstance{}  -> __IMPOSSIBLE__
+        InstV{} -> __IMPOSSIBLE__
+  reify (FindInstance m mcands) = FindInstanceOF
+    <$> reify (MetaV m [])
+    <*> (reify =<< getMetaType m)
+    <*> forM (fromMaybe [] mcands) (\ (Candidate q tm ty _) -> do
+          (,,) <$> reify tm <*> reify tm <*> reify ty)
+  reify (IsEmpty r a) = IsEmptyType <$> reify a
+  reify (CheckSizeLtSat a) = SizeLtSat  <$> reify a
+  reify (CheckFunDef i q cs err) = do
+    a <- reify =<< defType <$> getConstInfo q
+    return $ PostponedCheckFunDef q a err
+  reify (HasBiggerSort a) = OfType <$> reify a <*> reify (UnivSort a)
+  reify (HasPTSRule a b) = do
+    (a,(x,b)) <- reify (unDom a,b)
+    return $ PTSInstance a b
+  reify (CheckDataSort q s) = DataSort q <$> reify s
+  reify (CheckLockedVars t _ lk _) = CheckLock <$> reify t <*> reify (unArg lk)
+  reify (CheckMetaInst m) = do
+    t <- jMetaType . mvJudgement <$> lookupLocalMeta m
+    OfType <$> reify (MetaV m []) <*> reify t
+  reify (CheckType t) = JustType <$> reify t
+  reify (UsableAtModality _ _ mod t) = UsableAtMod mod <$> reify t
+  {-# SPECIALIZE reify :: Constraint -> TCM (ReifiesTo Constraint) #-}
+
+instance (Pretty a, Pretty b) => PrettyTCM (OutputForm a b) where
+  prettyTCM (OutputForm r pids unblock c) =
+    prettyRangeConstraint r pids unblock (pretty c)
+  {-# SPECIALIZE prettyTCM :: (Pretty a, Pretty b) => (OutputForm a b) -> TCM Doc #-}
+
+instance (Pretty a, Pretty b) => Pretty (OutputForm a b) where
+  pretty (OutputForm r pids unblock c) =
+    pretty c <?>
+      sep [ prange r, parensNonEmpty (sep [blockedOn unblock, prPids pids]) ]
+    where
+      prPids []    = empty
+      prPids [pid] = "belongs to problem" <+> pretty pid
+      prPids pids  = "belongs to problems" <+> fsep (punctuate "," $ map pretty pids)
+
+      comma | null pids = empty
+            | otherwise = ","
+
+      blockedOn (UnblockOnAll bs) | Set.null bs = empty
+      blockedOn (UnblockOnAny bs) | Set.null bs = "stuck" P.<> comma
+      blockedOn u = "blocked on" <+> (pretty u P.<> comma)
+
+      prange r | null s = empty
+               | otherwise = text $ " [ at " ++ s ++ " ]"
+        where s = prettyShow r
+
+instance (Pretty a, Pretty b) => Pretty (OutputConstraint a b) where
+  pretty oc =
+    case oc of
+      OfType e t           -> pretty e .: t
+      JustType e           -> "Type" <+> pretty e
+      JustSort e           -> "Sort" <+> pretty e
+      CmpInType cmp t e e' -> pcmp cmp e e' .: t
+      CmpElim cmp t e e'   -> pcmp cmp e e' .: t
+      CmpTypes  cmp t t'   -> pcmp cmp t t'
+      CmpLevels cmp t t'   -> pcmp cmp t t'
+      CmpTeles  cmp t t'   -> pcmp cmp t t'
+      CmpSorts cmp s s'    -> pcmp cmp s s'
+      Assign m e           -> bin (pretty m) ":=" (pretty e)
+      TypedAssign m e a    -> bin (pretty m) ":=" $ bin (pretty e) ":?" (pretty a)
+      PostponedCheckArgs m es t0 t1 ->
+        bin (pretty m) ":=" $ (parens ("_" .: t0) <+> fsep (map (paren . pretty) es)) .: t1
+        where paren d = mparens (any (`elem` [' ', '\n']) $ show d) d
+      IsEmptyType a        -> "Is empty:" <+> pretty a
+      SizeLtSat a          -> "Not empty type of sizes:" <+> pretty a
+      FindInstanceOF s t cs -> vcat
+        [ "Resolve instance argument" <?> (pretty s .: t)
+        , nest 2 $ "Candidate:"
+        , nest 4 $ vcat [ bin (pretty q) "=" (pretty v) .: t | (q, v, t) <- cs ] ]
+      PTSInstance a b      -> "PTS instance for" <+> pretty (a, b)
+      PostponedCheckFunDef q a _err ->
+        vcat [ "Check definition of" <+> pretty q <+> ":" <+> pretty a ]
+             -- , nest 2 "stuck because" <?> pretty err ] -- We don't have Pretty for TCErr
+      DataSort q s         -> "Sort" <+> pretty s <+> "allows data/record definitions"
+      CheckLock t lk       -> "Check lock" <+> pretty lk <+> "allows" <+> pretty t
+      UsableAtMod mod t    -> "Is usable at" <+> text (verbalize mod) <+> "modality:" <+> pretty t
+    where
+      bin a op b = sep [a, nest 2 $ op <+> b]
+      pcmp cmp a b = bin (pretty a) (pretty cmp) (pretty b)
+      val .: ty = bin val ":" (pretty ty)
+
+
+instance (ToConcrete a, ToConcrete b) => ToConcrete (OutputForm a b) where
+    type ConOfAbs (OutputForm a b) = OutputForm (ConOfAbs a) (ConOfAbs b)
+    toConcrete (OutputForm r pid u c) = OutputForm r pid u <$> toConcrete c
+
+instance (ToConcrete a, ToConcrete b) => ToConcrete (OutputConstraint a b) where
+    type ConOfAbs (OutputConstraint a b) = OutputConstraint (ConOfAbs a) (ConOfAbs b)
+
+    toConcrete (OfType e t) = OfType <$> toConcrete e <*> toConcreteCtx TopCtx t
+    toConcrete (JustType e) = JustType <$> toConcrete e
+    toConcrete (JustSort e) = JustSort <$> toConcrete e
+    toConcrete (CmpInType cmp t e e') =
+      CmpInType cmp <$> toConcreteCtx TopCtx t <*> toConcreteCtx TopCtx e
+                                               <*> toConcreteCtx TopCtx e'
+    toConcrete (CmpElim cmp t e e') =
+      CmpElim cmp <$> toConcreteCtx TopCtx t <*> toConcreteCtx TopCtx e <*> toConcreteCtx TopCtx e'
+    toConcrete (CmpTypes cmp e e') = CmpTypes cmp <$> toConcreteCtx TopCtx e
+                                                  <*> toConcreteCtx TopCtx e'
+    toConcrete (CmpLevels cmp e e') = CmpLevels cmp <$> toConcreteCtx TopCtx e
+                                                    <*> toConcreteCtx TopCtx e'
+    toConcrete (CmpTeles cmp e e') = CmpTeles cmp <$> toConcrete e <*> toConcrete e'
+    toConcrete (CmpSorts cmp e e') = CmpSorts cmp <$> toConcreteCtx TopCtx e
+                                                  <*> toConcreteCtx TopCtx e'
+    toConcrete (Assign m e) = noTakenNames $ Assign <$> toConcrete m <*> toConcreteCtx TopCtx e
+    toConcrete (TypedAssign m e a) = TypedAssign <$> toConcrete m <*> toConcreteCtx TopCtx e
+                                                                  <*> toConcreteCtx TopCtx a
+    toConcrete (PostponedCheckArgs m args t0 t1) =
+      PostponedCheckArgs <$> toConcrete m <*> toConcrete args <*> toConcrete t0 <*> toConcrete t1
+    toConcrete (IsEmptyType a) = IsEmptyType <$> toConcreteCtx TopCtx a
+    toConcrete (SizeLtSat a) = SizeLtSat <$> toConcreteCtx TopCtx a
+    toConcrete (FindInstanceOF s t cs) =
+      FindInstanceOF <$> toConcrete s <*> toConcrete t
+                     <*> mapM (\(q,tm,ty) -> (,,) <$> toConcrete q <*> toConcrete tm <*> toConcrete ty) cs
+    toConcrete (PTSInstance a b) = PTSInstance <$> toConcrete a <*> toConcrete b
+    toConcrete (DataSort a b)  = DataSort a <$> toConcrete b
+    toConcrete (CheckLock a b) = CheckLock <$> toConcrete a <*> toConcrete b
+    toConcrete (PostponedCheckFunDef q a err) = PostponedCheckFunDef q <$> toConcrete a <*> pure err
+    toConcrete (UsableAtMod a b) = UsableAtMod a <$> toConcrete b
+
+instance (Pretty a, Pretty b) => Pretty (OutputConstraint' a b) where
+  pretty (OfType' e t) = pretty e <+> ":" <+> pretty t
+
+instance (ToConcrete a, ToConcrete b) => ToConcrete (OutputConstraint' a b) where
+  type ConOfAbs (OutputConstraint' a b) = OutputConstraint' (ConOfAbs a) (ConOfAbs b)
+  toConcrete (OfType' e t) = OfType' <$> toConcrete e <*> toConcreteCtx TopCtx t
+
+instance Reify a => Reify (IPBoundary' a) where
+  type ReifiesTo (IPBoundary' a) = IPBoundary' (ReifiesTo a)
+  reify = traverse reify
+
+instance ToConcrete a => ToConcrete (IPBoundary' a) where
+  type ConOfAbs (IPBoundary' a) = IPBoundary' (ConOfAbs a)
+
+  toConcrete = traverse (toConcreteCtx TopCtx)
+
+instance Pretty c => Pretty (IPFace' c) where
+  pretty (IPFace' eqs val) = do
+    let
+      xs = map (\ (l,r) -> pretty l <+> "=" <+> pretty r) eqs
+      -- rhs = case over of
+      --         Overapplied    -> "=" <+> pretty meta
+      --         NotOverapplied -> mempty
+    prettyList_ xs <+> "⊢" <+> pretty val -- <+> rhs
+
+prettyConstraints :: [Closure Constraint] -> TCM [OutputForm C.Expr C.Expr]
+prettyConstraints cs = do
+  forM cs $ \ c -> do
+            cl <- reify (PConstr Set.empty alwaysUnblock c)
+            enterClosure cl abstractToConcrete_
+
+getConstraints :: TCM [OutputForm C.Expr C.Expr]
+getConstraints = getConstraints' return $ const True
+
+namedMetaOf :: OutputConstraint A.Expr a -> a
+namedMetaOf (OfType i _) = i
+namedMetaOf (JustType i) = i
+namedMetaOf (JustSort i) = i
+namedMetaOf (Assign i _) = i
+namedMetaOf _ = __IMPOSSIBLE__
+
+getConstraintsMentioning :: Rewrite -> MetaId -> TCM [OutputForm C.Expr C.Expr]
+getConstraintsMentioning norm m = getConstrs instantiateBlockingFull (mentionsMeta m)
+  -- could be optimized by not doing a full instantiation up front, with a more clever mentionsMeta.
+  where
+    instantiateBlockingFull p
+      = locallyTCState stInstantiateBlocking (const True) $
+          instantiateFull p
+
+    nay :: MaybeT TCM Elims
+    nay = MaybeT $ pure Nothing
+
+    -- Trying to find the actual meta application, as long as it's not
+    -- buried too deep.
+    -- We could look further but probably not under binders as that would mess with
+    -- the call to @unifyElimsMeta@ below.
+    hasHeadMeta c =
+      case c of
+        ValueCmp _ _ u v           -> isMeta u `mplus` isMeta v
+        ValueCmpOnFace cmp p t u v -> isMeta u `mplus` isMeta v
+        -- TODO: extend to other comparisons?
+        ElimCmp cmp fs t v as bs   -> Nothing
+        LevelCmp cmp u v           -> Nothing
+        SortCmp cmp a b            -> Nothing
+        UnBlock{}                  -> Nothing
+        FindInstance{}             -> Nothing
+        IsEmpty r t                -> isMeta (unEl t)
+        CheckSizeLtSat t           -> isMeta t
+        CheckFunDef{}              -> Nothing
+        HasBiggerSort a            -> Nothing
+        HasPTSRule a b             -> Nothing
+        UnquoteTactic{}            -> Nothing
+        CheckDataSort _ s          -> isMetaS s
+        CheckMetaInst{}            -> Nothing
+        CheckType t                -> isMeta (unEl t)
+        CheckLockedVars t _ _ _    -> isMeta t
+        UsableAtModality _ ms _ t  -> caseMaybe ms (isMeta t) $ \ s -> isMetaS s `mplus` isMeta t
+
+    isMeta :: Term -> Maybe Elims
+    isMeta (MetaV m' es_m) | m == m' = pure es_m
+    isMeta _  = Nothing
+
+    isMetaS :: I.Sort -> Maybe Elims
+    isMetaS (MetaS m' es_m)
+      | m == m' = pure es_m
+    isMetaS _  = Nothing
+
+    getConstrs g f = liftTCM $ do
+      cs <- stripConstraintPids . filter f <$> (mapM g =<< M.getAllConstraints)
+      cs <- caseMaybeM (traverse lookupInteractionPoint =<< isInteractionMeta m) (pure cs) $ \ip -> do
+        let
+          boundary = MapS.keysSet (getBoundary (ipBoundary ip))
+          isRedundant c = case allApplyElims =<< hasHeadMeta c of
+            Just apps -> caseMaybeM (isFaceConstraint m apps) (pure False) $ \(_, endps, _, _) ->
+              pure $ Set.member endps boundary
+            Nothing -> pure False
+        filterM (flip enterClosure (fmap not . isRedundant) . theConstraint) cs
+
+      reportSDoc "tc.constr.mentioning" 20 $ "getConstraintsMentioning"
+      forM cs $ \(PConstr s ub c) -> do
+        reportSDoc "tc.constr.mentioning" 20 $ "constraint:  " TP.<+> prettyTCM c
+        c <- normalForm norm c
+        let hm = hasHeadMeta (clValue c)
+        reportSDoc "tc.constr.mentioning" 20 $ "constraint:  " TP.<+> prettyTCM c
+        reportSDoc "tc.constr.mentioning" 20 $ "hasHeadMeta: " TP.<+> prettyTCM hm
+        case allApplyElims =<< hm of
+          Just as_m -> do
+            -- unifyElimsMeta tries to move the constraint into
+            -- (an extension of) the context where @m@ comes from.
+            unifyElimsMeta m as_m c $ \ eqs c -> do
+              flip enterClosure abstractToConcrete_ =<< reify . PConstr s ub =<< buildClosure c
+          _ -> do
+            cl <- reify $ PConstr s ub c
+            enterClosure cl abstractToConcrete_
+
+-- Copied from Agda.TypeChecking.Pretty.Warning.prettyConstraints
+stripConstraintPids :: Constraints -> Constraints
+stripConstraintPids cs = List.sortBy (compare `on` isBlocked) $ map stripPids cs
+  where
+    isBlocked = not . null . allBlockingProblems . constraintUnblocker
+    interestingPids = Set.unions $ map (allBlockingProblems . constraintUnblocker) cs
+    stripPids (PConstr pids unblock c) = PConstr (Set.intersection pids interestingPids) unblock c
+
+{-# SPECIALIZE interactionIdToMetaId :: InteractionId -> TCM MetaId #-}
+-- | Converts an 'InteractionId' to a 'MetaId'.
+interactionIdToMetaId :: ReadTCState m => InteractionId -> m MetaId
+interactionIdToMetaId i = do
+  h <- currentModuleNameHash
+  return MetaId
+    { metaId     = fromIntegral i
+    , metaModule = h
+    }
+
+getConstraints' :: (ProblemConstraint -> TCM ProblemConstraint) -> (ProblemConstraint -> Bool) -> TCM [OutputForm C.Expr C.Expr]
+getConstraints' g f = liftTCM $ do
+    cs <- stripConstraintPids . filter f <$> (mapM g =<< M.getAllConstraints)
+    cs <- forM cs $ \c -> do
+            cl <- reify c
+            enterClosure cl abstractToConcrete_
+    ss <- mapM toOutputForm =<< getSolvedInteractionPoints True AsIs -- get all
+    return $ ss ++ cs
+  where
+    toOutputForm (ii, mi, e) = do
+      mv <- getMetaInfo <$> lookupLocalMeta mi
+      withMetaInfo mv $ do
+        mi <- interactionIdToMetaId ii
+        let m = QuestionMark emptyMetaInfo{ metaNumber = Just mi } ii
+        abstractToConcrete_ $ OutputForm noRange [] alwaysUnblock $ Assign m e
+
+-- | Reify the boundary of an interaction point as something that can be
+-- shown to the user.
+getIPBoundary :: Rewrite -> InteractionId -> TCM [IPFace' C.Expr]
+getIPBoundary norm ii = withInteractionId ii $ do
+  ip <- lookupInteractionPoint ii
+
+  io <- primIOne
+  iz <- primIZero
+
+  lookupInteractionMeta ii >>= \case
+    Just mi -> do
+      mv <- lookupLocalMeta mi
+
+      let t = jMetaType $ mvJudgement mv
+      telv@(TelV tel a) <- telView t
+
+      reportSDoc "tc.ip.boundary" 30 $ TP.vcat
+        [ "reifying interaction point boundary"
+        , "tel:       " TP.<+> prettyTCM tel
+        , "meta:      " TP.<+> prettyTCM mi
+        ]
+      reportSDoc "tc.ip.boundary" 30 $ "boundary:  " TP.<+> pure (pretty (getBoundary (ipBoundary ip)))
+
+      withInteractionId ii $ do
+      -- The boundary is a map associating terms (lambda abstractions)
+      -- to IntMap Bools. The meta solver will wrap each LHS in lambdas
+      -- corresponding to the interaction point's context. Each key of
+      -- the boundary has a subset of (the interval variables in) the
+      -- interaction point's context as a keysSet.
+      as <- getContextArgs
+      let
+        c = abstractToConcrete_ <=< reifyUnblocked <=< normalForm norm
+        go (im, rhs) = do
+          reportSDoc "tc.ip.boundary" 30 $ TP.vcat
+            [ "reifying constraint for face" TP.<+> TP.pretty im
+            ]
+          reportSDoc "tc.ip.boundary" 30 $ "term " TP.<+> TP.prettyTCM rhs
+          -- Since the RHS is a lambda we have to apply it to the
+          -- context:
+          rhs <- c (rhs `apply` as)
+
+          -- Reify the IntMap Bool as a list of (i = i0) (j = i1) terms:
+          eqns <- forM (IntMap.toList im) $ \(a, b) -> do
+            a <- c (I.Var a [])
+            (,) a <$> c (if b then io else iz)
+          pure $ IPFace' eqns rhs
+      traverse go $ MapS.toList (getBoundary (ipBoundary ip))
+    Nothing -> pure []
+
+typeAndFacesInMeta :: InteractionId -> Rewrite -> Expr -> TCM (Expr, [IPFace' C.Expr])
+typeAndFacesInMeta ii norm expr = withInteractionId ii $ do
+  (ex, ty) <- inferExpr expr
+  ty <- normalForm norm ty
+  ip <- lookupInteractionPoint ii
+
+  io <- primIOne
+  iz <- primIZero
+  let
+    go im = do
+      let
+        c = abstractToConcrete_ <=< reifyUnblocked <=< normalForm norm
+        fa = IntMap.toList im
+        face (i, m) = inplaceS i $ if m then io else iz
+        sub = foldr (\f s -> composeS (face f) s) idS fa
+      eqns <- forM fa $ \(a, b) -> do
+        a <- c (I.Var a [])
+        (,) a <$> c (if b then io else iz)
+      fmap (IPFace' eqns) . c =<< simplify (applySubst sub ex)
+
+  faces <- traverse go $ MapS.keys (getBoundary (ipBoundary ip))
+  ty <- reifyUnblocked ty
+  pure (ty, faces)
+
+-- | Goals and Warnings
+
+getGoals :: TCM Goals
+getGoals = getGoals' AsIs Simplified
+  -- visible metas (as-is)
+  -- hidden metas (unsolved implicit arguments simplified)
+
+getGoals'
+  :: Rewrite    -- ^ Degree of normalization of goals.
+  -> Rewrite    -- ^ Degree of normalization of hidden goals.
+  -> TCM Goals
+getGoals' normVisible normHidden = do
+  visibleMetas <- typesOfVisibleMetas normVisible
+  hiddenMetas <- typesOfHiddenMetas normHidden
+  return (visibleMetas, hiddenMetas)
+
+-- | Print open metas nicely.
+showGoals :: Goals -> TCM String
+showGoals (ims, hms) = do
+  di <- forM ims $ \ i ->
+    withInteractionId (outputFormId $ OutputForm noRange [] alwaysUnblock i) $
+      prettyATop i
+  dh <- mapM showA' hms
+  return $ unlines $ map show di ++ dh
+  where
+    showA' :: OutputConstraint A.Expr NamedMeta -> TCM String
+    showA' m = do
+      let i = nmid $ namedMetaOf m
+      r <- getMetaRange i
+      d <- withMetaId i (prettyATop m)
+      return $ show d ++ "  [ at " ++ prettyShow r ++ " ]"
+
+getWarningsAndNonFatalErrors :: TCM WarningsAndNonFatalErrors
+getWarningsAndNonFatalErrors = do
+  mws <- getAllWarnings AllWarnings
+  let notMetaWarnings = filter (not . isMetaTCWarning) mws
+  return $ case notMetaWarnings of
+    ws@(_:_) -> classifyWarnings ws
+    _ -> emptyWarningsAndNonFatalErrors
+
+-- | Collecting the context of the given meta-variable.
+getResponseContext
+  :: Rewrite      -- ^ Normalise?
+  -> InteractionId
+  -> TCM [ResponseContextEntry]
+getResponseContext norm ii = contextOfMeta ii norm
+
+-- | @getSolvedInteractionPoints True@ returns all solutions,
+--   even if just solved by another, non-interaction meta.
+--
+--   @getSolvedInteractionPoints False@ only returns metas that
+--   are solved by a non-meta.
+
+getSolvedInteractionPoints :: Bool -> Rewrite -> TCM [(InteractionId, MetaId, Expr)]
+getSolvedInteractionPoints all norm = concat <$> do
+  mapM solution =<< getInteractionIdsAndMetas
+  where
+    solution (i, m) = do
+      mv <- lookupLocalMeta m
+      withMetaInfo (getMetaInfo mv) $ do
+        args  <- getContextArgs
+        scope <- getScope
+        let sol v = do
+              -- Andreas, 2014-02-17 exclude metas solved by metas
+              v <- instantiate v
+              let isMeta = case v of MetaV{} -> True; _ -> False
+              if isMeta && not all then return [] else do
+                e <- blankNotInScope =<< reify =<< normalForm norm v
+                return [(i, m, ScopedExpr scope e)]
+            unsol = return []
+        case mvInstantiation mv of
+          InstV{}                        -> sol (MetaV m $ map Apply args)
+          Open{}                         -> unsol
+          OpenInstance{}                 -> unsol
+          BlockedConst{}                 -> unsol
+          PostponedTypeCheckingProblem{} -> unsol
+
+typeOfMetaMI :: Rewrite -> MetaId -> TCM (OutputConstraint Expr NamedMeta)
+typeOfMetaMI norm mi =
+     do mv <- lookupLocalMeta mi
+        withMetaInfo (getMetaInfo mv) $
+          rewriteJudg mv (mvJudgement mv)
+   where
+    rewriteJudg :: MetaVariable -> Judgement MetaId ->
+                   TCM (OutputConstraint Expr NamedMeta)
+    rewriteJudg mv (HasType i cmp t) = do
+      ms <- getMetaNameSuggestion i
+      -- Andreas, 2019-03-17, issue #3638:
+      -- Need to put meta type into correct context _before_ normalizing,
+      -- otherwise rewrite rules in parametrized modules will not fire.
+      vs <- getContextArgs
+      t <- t `piApplyM` permute (takeP (size vs) $ mvPermutation mv) vs
+      t <- normalForm norm t
+      let x = NamedMeta ms i
+      reportSDoc "interactive.meta" 10 $ TP.vcat
+        [ TP.text $ unwords ["permuting", show i, "with", show $ mvPermutation mv]
+        , TP.nest 2 $ TP.vcat
+          [ "len  =" TP.<+> TP.text (show $ length vs)
+          , "args =" TP.<+> prettyTCM vs
+          , "t    =" TP.<+> prettyTCM t
+          , "x    =" TP.<+> TP.pretty x
+          ]
+        ]
+      reportSDoc "interactive.meta.scope" 20 $ TP.text $ show $ getMetaScope mv
+      -- Andreas, 2016-01-19, issue #1783: need piApplyM instead of just piApply
+      OfType x <$> reifyUnblocked t
+    rewriteJudg mv (IsSort i t) = do
+      ms <- getMetaNameSuggestion i
+      return $ JustSort $ NamedMeta ms i
+
+
+typeOfMeta :: Rewrite -> InteractionId -> TCM (OutputConstraint Expr InteractionId)
+typeOfMeta norm ii = typeOfMeta' norm . (ii,) =<< lookupInteractionId ii
+
+typeOfMeta' :: Rewrite -> (InteractionId, MetaId) -> TCM (OutputConstraint Expr InteractionId)
+typeOfMeta' norm (ii, mi) = fmap (\_ -> ii) <$> typeOfMetaMI norm mi
+
+typesOfVisibleMetas :: Rewrite -> TCM [OutputConstraint Expr InteractionId]
+typesOfVisibleMetas norm =
+  liftTCM $ mapM (typeOfMeta' norm) =<< getInteractionIdsAndMetas
+
+typesOfHiddenMetas :: Rewrite -> TCM [OutputConstraint Expr NamedMeta]
+typesOfHiddenMetas norm = liftTCM $ do
+  is    <- getInteractionMetas
+  store <- MapS.filterWithKey (implicit is) <$> useR stOpenMetaStore
+  mapM (typeOfMetaMI norm) $ MapS.keys store
+  where
+  implicit is x m | isJust (mvTwin m) = False
+  implicit is x m =
+    case mvInstantiation m of
+      M.InstV{} -> __IMPOSSIBLE__
+      M.Open    -> x `notElem` is
+      M.OpenInstance -> x `notElem` is  -- OR: True !?
+      M.BlockedConst{} -> False
+      M.PostponedTypeCheckingProblem{} -> False
+
+-- | Create type of application of new helper function that would solve the goal.
+metaHelperType :: Rewrite -> InteractionId -> Range -> String -> TCM (OutputConstraint' Expr Expr)
+metaHelperType norm ii rng s = case words s of
+  []    -> failure
+  f : _ -> withInteractionId ii $ do
+    ensureName f
+    A.Application h args <- A.appView . getBody . deepUnscope <$> parseExprIn ii rng ("let " ++ f ++ " = _ in " ++ s)
+    inCxt   <- hasElem <$> getContextNames
+    cxtArgs <- getContextArgs
+    enclosingFunctionName <- ipcQName . envClause <$> getEnv
+    a0      <- (`piApply` cxtArgs) <$> (getMetaType =<< lookupInteractionId ii)
+
+    -- Konstantin, 2022-10-23: We don't want to print section parameters in helper type.
+    freeVars <- getCurrentModuleFreeVars
+    contextForAbstracting <- drop freeVars . reverse <$> getContext
+
+    -- Andreas, 2019-10-11: I actually prefer pi-types over ->.
+    let runInPrintingEnvironment = localTC (\e -> e { envPrintDomainFreePi = True, envPrintMetasBare = True })
+                                 . escapeContext impossible (length contextForAbstracting)
+                                 . withoutPrintingGeneralization
+                                 . dontFoldLetBindings
+
+    case mapM (isVar . namedArg) args >>= \ xs -> xs <$ guard (all inCxt xs) of
+
+     -- Andreas, 2019-10-11
+     -- If all arguments are variables, there is no need to abstract.
+     -- We simply make exactly the given arguments visible and all other hidden.
+     Just xs -> do
+      let inXs = hasElem xs
+      let hideButXs dom = setHiding (if inXs $ fst $ unDom dom then NotHidden else Hidden) dom
+      let tel = telFromList . map (fmap (first nameToArgName) . hideButXs) $ contextForAbstracting
+      OfType' h <$> do
+        runInPrintingEnvironment $ reify $ telePiVisible tel a0
+
+     -- If some arguments are not variables.
+     Nothing -> do
+      -- cleanupType relies on with arguments being named 'w',
+      -- so we'd better rename any actual 'w's to avoid confusion.
+      let tel = runIdentity . onNamesTel unW . telFromList' nameToArgName $ contextForAbstracting
+      let a = runIdentity . onNames unW $ a0
+      vtys <- mapM (\ a -> fmap (Arg (getArgInfo a) . fmap OtherType) $ inferExpr $ namedArg a) args
+      -- Remember the arity of a
+      TelV atel _ <- telView a
+      let arity = size atel
+          (delta1, delta2, _, a', vtys') = splitTelForWith tel a vtys
+      a <- runInPrintingEnvironment $ do
+        reify =<< cleanupType arity args =<< normalForm norm =<< fst <$> withFunctionType delta1 vtys' delta2 a' []
+      reportSDoc "interaction.helper" 10 $ TP.vcat $
+        let extractOtherType = \case { OtherType a -> a; _ -> __IMPOSSIBLE__ } in
+        let (vs, as)   = unzipWith (fmap extractOtherType . unArg) vtys in
+        let (vs', as') = unzipWith (fmap extractOtherType . unArg) vtys' in
+        [ "generating helper function"
+        , TP.nest 2 $ "tel    = " TP.<+> inTopContext (prettyTCM tel)
+        , TP.nest 2 $ "a      = " TP.<+> prettyTCM a
+        , TP.nest 2 $ "vs     = " TP.<+> prettyTCM vs
+        , TP.nest 2 $ "as     = " TP.<+> prettyTCM as
+        , TP.nest 2 $ "delta1 = " TP.<+> inTopContext (prettyTCM delta1)
+        , TP.nest 2 $ "delta2 = " TP.<+> inTopContext (addContext delta1 $ prettyTCM delta2)
+        , TP.nest 2 $ "a'     = " TP.<+> inTopContext (addContext delta1 $ addContext delta2 $ prettyTCM a')
+        , TP.nest 2 $ "as'    = " TP.<+> inTopContext (addContext delta1 $ prettyTCM as')
+        , TP.nest 2 $ "vs'    = " TP.<+> inTopContext (addContext delta1 $ prettyTCM vs')
+        ]
+      return $ OfType' h a
+  where
+    failure = typeError $ GenericError $ "Expected an argument of the form f e1 e2 .. en"
+    ensureName f = do
+      ce <- parseExpr rng f
+      flip (caseMaybe $ isName ce) (\ _ -> return ()) $ do
+         reportSLn "interaction.helper" 10 $ "ce = " ++ show ce
+         failure
+    isVar :: A.Expr -> Maybe A.Name
+    isVar = \case
+      A.Var x -> Just x
+      _ -> Nothing
+    cleanupType arity args t = do
+      -- Get the arity of t
+      TelV ttel _ <- telView t
+      -- Compute the number of pi-types subject to stripping.
+      let n = size ttel - arity
+      -- It cannot be negative, otherwise we would have performed a
+      -- negative number of with-abstractions.
+      unless (n >= 0) __IMPOSSIBLE__
+      return $ evalState (renameVars $ stripUnused n t) args
+
+    getBody (A.Let _ _ e)      = e
+    getBody _                  = __IMPOSSIBLE__
+
+    -- Strip the non-dependent abstractions from the first n abstractions.
+    stripUnused n (El s v) = El s $ strip n v
+    strip 0 = id
+    strip n = \case
+      I.Pi a b -> case stripUnused (n-1) <$> b of
+        b | absName b == "w"   -> I.Pi a b
+        NoAbs _ b              -> unEl b
+        Abs s b | 0 `freeIn` b -> I.Pi (hide a) (Abs s b)
+                | otherwise    -> strengthen impossible (unEl b)
+      v -> v  -- todo: handle if goal type is a Pi
+
+    -- renameVars = onNames (stringToArgName <.> renameVar . argNameToString)
+    renameVars = onNames renameVar
+
+    -- onNames :: Applicative m => (ArgName -> m ArgName) -> I.Type -> m I.Type
+    onNames :: Applicative m => (String -> m String) -> I.Type -> m I.Type
+    onNames f (El s v) = El s <$> onNamesTm f v
+
+    -- onNamesTel :: Applicative f => (ArgName -> f ArgName) -> I.Telescope -> f I.Telescope
+    onNamesTel :: Applicative f => (String -> f String) -> I.Telescope -> f I.Telescope
+    onNamesTel f I.EmptyTel = pure I.EmptyTel
+    onNamesTel f (I.ExtendTel a b) = I.ExtendTel <$> traverse (onNames f) a <*> onNamesAbs f onNamesTel b
+
+    onNamesTm f = \case
+      I.Var x es   -> I.Var x <$> onNamesElims f es
+      I.Def q es   -> I.Def q <$> onNamesElims f es
+      I.Con c ci args -> I.Con c ci <$> onNamesArgs f args
+      I.Lam i b    -> I.Lam i <$> onNamesAbs f onNamesTm b
+      I.Pi a b     -> I.Pi <$> traverse (onNames f) a <*> onNamesAbs f onNames b
+      I.DontCare v -> I.DontCare <$> onNamesTm f v
+      v@I.Lit{}    -> pure v
+      v@I.Sort{}   -> pure v
+      v@I.Level{}  -> pure v
+      v@I.MetaV{}  -> pure v
+      v@I.Dummy{}  -> pure v
+    onNamesElims f = traverse $ traverse $ onNamesTm f
+    onNamesArgs f  = traverse $ traverse $ onNamesTm f
+    onNamesAbs f   = onNamesAbs' f (stringToArgName <.> f . argNameToString)
+    onNamesAbs' f f' nd (Abs   s x) = Abs   <$> f' s <*> nd f x
+    onNamesAbs' f f' nd (NoAbs s x) = NoAbs <$> f' s <*> nd f x
+
+    unW "w" = return ".w"
+    unW s   = return s
+
+    renameVar "w" = betterName
+    renameVar s   = pure s
+
+    betterName = do
+      xs <- get
+      case xs of
+        []         -> __IMPOSSIBLE__
+        arg : args -> do
+          put args
+          return $ if
+            | Arg _ (Named _ (A.Var x)) <- arg -> prettyShow $ A.nameConcrete x
+            | Just x <- bareNameOf arg         -> argNameToString x
+            | otherwise                        -> "w"
+
+
+-- | Gives a list of names and corresponding types.
+--   This list includes not only the local variables in scope, but also the let-bindings.
+
+contextOfMeta :: InteractionId -> Rewrite -> TCM [ResponseContextEntry]
+contextOfMeta ii norm = withInteractionId ii $ do
+  info <- getMetaInfo <$> (lookupLocalMeta =<< lookupInteractionId ii)
+  withMetaInfo info $ do
+    -- List of local variables.
+    cxt <- getContext
+    let localVars = zipWith raise [1..] cxt
+    -- List of let-bindings.
+    letVars <- Map.toAscList <$> asksTC envLetBindings
+    -- Reify the types and filter out bindings without a name.
+    (++) <$> forMaybeM (reverse localVars) mkVar
+         <*> forMaybeM letVars mkLet
+
+  where
+    mkVar :: ContextEntry -> TCM (Maybe ResponseContextEntry)
+    mkVar Dom{ domInfo = ai, unDom = (name, t) } = do
+      if shouldHide ai name then return Nothing else Just <$> do
+        let n = nameConcrete name
+        x  <- abstractToConcrete_ name
+        let s = C.isInScope x
+        ty <- reifyUnblocked =<< normalForm norm t
+        return $ ResponseContextEntry n x (Arg ai ty) Nothing s
+
+    mkLet :: (Name, Open M.LetBinding) -> TCM (Maybe ResponseContextEntry)
+    mkLet (name, lb) = do
+      LetBinding _ tm !dom <- getOpen lb
+      if shouldHide (domInfo dom) name then return Nothing else Just <$> do
+        let n = nameConcrete name
+        x  <- abstractToConcrete_ name
+        let s = C.isInScope x
+        ty <- reifyUnblocked =<< normalForm norm dom
+              -- Remove let bindings from x and later, to avoid folding to x = x, or using bindings
+              -- not introduced when x was defined.
+        v  <- removeLetBindingsFrom name $ reifyUnblocked =<< normalForm norm tm
+        return $ ResponseContextEntry n x ty (Just v) s
+
+    shouldHide :: ArgInfo -> A.Name -> Bool
+    shouldHide ai n = not (isInstance ai) && (isNoName n || nameIsRecordName n)
+
+-- | Returns the type of the expression in the current environment
+--   We wake up irrelevant variables just in case the user want to
+--   invoke that command in an irrelevant context.
+typeInCurrent :: Rewrite -> Expr -> TCM Expr
+typeInCurrent norm e =
+    do  (_,t) <- wakeIrrelevantVars $ inferExpr e
+        v <- normalForm norm t
+        reifyUnblocked v
+
+
+
+typeInMeta :: InteractionId -> Rewrite -> Expr -> TCM Expr
+typeInMeta ii norm e =
+   do   m <- lookupInteractionId ii
+        mi <- getMetaInfo <$> lookupLocalMeta m
+        withMetaInfo mi $
+            typeInCurrent norm e
+
+-- | The intro tactic.
+--
+-- Returns the terms (as strings) that can be
+-- used to refine the goal. Uses the coverage checker
+-- to find out which constructors are possible.
+--
+introTactic :: Bool -> InteractionId -> TCM [String]
+introTactic pmLambda ii = do
+  mi <- lookupInteractionId ii
+  mv <- lookupLocalMeta mi
+  withMetaInfo (getMetaInfo mv) $ case mvJudgement mv of
+    HasType _ _ t -> do
+        t <- reduce =<< piApplyM t =<< getContextArgs
+        -- Andreas, 2013-03-05 Issue 810: skip hidden domains in introduction
+        -- of constructor.
+        TelV tel' t <- telViewUpTo' (-1) notVisible t
+        -- if we cannot introduce a constructor, we try a lambda
+        let fallback = do
+              cubical <- isJust . optCubical <$> pragmaOptions
+              TelV tel _ <- (if cubical then telViewPath else telView) t
+              reportSDoc "interaction.intro" 20 $ TP.sep
+                [ "introTactic/fallback"
+                , "tel' = " TP.<+> prettyTCM tel'
+                , "tel  = " TP.<+> prettyTCM tel
+                ]
+              case (tel', tel) of
+                (EmptyTel, EmptyTel) -> return []
+                _ -> introFun (telToList tel' ++ telToList tel)
+
+        case unEl t of
+          I.Def d _ -> do
+            def <- getConstInfo d
+            case theDef def of
+              Datatype{}    -> addContext tel' $ introData AmbiguousNothing t
+              Record{ recNamedCon = name }
+                | name      -> addContext tel' $ introData AmbiguousConProjs t
+                | otherwise -> addContext tel' $ introRec d
+              _ -> fallback
+          _ -> fallback
+     `catchError` \_ -> return []
+    _ -> __IMPOSSIBLE__
+  where
+    conName :: [NamedArg SplitPattern] -> [I.ConHead]
+    conName [p] = [ c | I.ConP c _ _ <- [namedArg p] ]
+    conName _   = __IMPOSSIBLE__
+
+    showUnambiguousConName amb v =
+       render . pretty <$> runAbsToCon (lookupQName amb $ I.conName v)
+
+    showTCM :: PrettyTCM a => a -> TCM String
+    showTCM v = render <$> prettyTCM v
+
+    introFun :: ListTel -> TCM [String]
+    introFun tel = addContext tel' $ do
+        reportSDoc "interaction.intro" 10 $ do "introFun" TP.<+> prettyTCM (telFromList tel)
+        imp <- showImplicitArguments
+        let okHiding0 h = imp || h == NotHidden
+            -- if none of the vars were displayed, we would get a parse error
+            -- thus, we switch to displaying all
+            allHidden   = not (any okHiding0 hs)
+            okHiding    = if allHidden then const True else okHiding0
+        vars <- -- setShowImplicitArguments (imp || allHidden) $
+                applyWhen allHidden withShowAllArguments $
+                  mapM showTCM [ setHiding h $ defaultArg $ var i :: Arg Term
+                               | (h, i) <- zip hs $ downFrom n
+                               , okHiding h
+                               ]
+        if pmLambda
+           then return [ unwords $ ["λ", "{"] ++ vars ++ ["→", "?", "}"] ]
+           else return [ unwords $ ["λ"]      ++ vars ++ ["→", "?"] ]
+      where
+        n = size tel
+        hs   = map getHiding tel
+        tel' = telFromList [ fmap makeName b | b <- tel ]
+        makeName ("_", t) = ("x", t)
+        makeName (x, t)   = (x, t)
+
+    introData :: AllowAmbiguousNames -> I.Type -> TCM [String]
+    introData amb t = do
+      let tel  = telFromList [defaultDom ("_", t)]
+          pat  = [defaultArg $ unnamed $ debruijnNamedVar "c" 0]
+      -- Gallais, 2023-08-24: #6787 we need to locally ignore the
+      -- --without-K or --cubical-compatible options to figure out
+      -- that refl is a valid constructor for refl ≡ refl.
+      cubical <- isJust . optCubical <$> pragmaOptions
+      r <- (if cubical then id else
+            locallyTCState (stPragmaOptions . lensOptWithoutK) (const (Value False)))
+           $ splitLast CoInductive tel pat
+      case r of
+        Left err -> return []
+        Right cov ->
+           mapM (showUnambiguousConName amb) $ concatMap (conName . scPats) $ splitClauses cov
+
+    introRec :: QName -> TCM [String]
+    introRec d = do
+      hfs <- getRecordFieldNames d
+      fs <- ifM showImplicitArguments
+            (return $ map unDom hfs)
+            (return [ unDom a | a <- hfs, visible a ])
+      let e = C.Rec noRange $ for fs $ \ f ->
+            Left $ C.FieldAssignment f $ C.QuestionMark noRange Nothing
+      return [ prettyShow e ]
+      -- Andreas, 2019-02-25, remark:
+      -- prettyShow is ok here since we are just printing something like
+      -- record { f1 = ? ; ... ; fn = ?}
+      -- which does not involve any qualified names, and the fi are C.Name.
+
+-- | Runs the given computation as if in an anonymous goal at the end
+--   of the top-level module.
+--
+--   Sets up current module, scope, and context.
+atTopLevel :: TCM a -> TCM a
+atTopLevel m = inConcreteMode $ do
+  let err = typeError $ GenericError "The file has not been loaded yet."
+  caseMaybeM (useTC stCurrentModule) err $ \(current, topCurrent) -> do
+    caseMaybeM (getVisitedModule topCurrent) __IMPOSSIBLE__ $ \ mi -> do
+      let scope = iInsideScope $ miInterface mi
+      tel <- lookupSection current
+      -- Get the names of the local variables from @scope@
+      -- and put them into the context.
+      --
+      -- Andreas, 2017-04-24, issue #2552:
+      --
+      -- Delete the let-bound ones, since they are not represented
+      -- in the module telescope.
+      --
+      -- This is a temporary fix until a better solution is available,
+      -- e.g., when the module telescope represents let-bound variables.
+      --
+      -- Unfortunately, referring to let-bound variables
+      -- from the top level module telescope will for now result in a not-in-scope error.
+      let names :: [A.Name]
+          names = map localVar $ filter ((LetBound /=) . localBindingSource)
+                               $ map snd $ reverse $ scope ^. scopeLocals
+      -- Andreas, 2016-12-31, issue #2371
+      -- The following is an unnecessary complication, as shadowed locals
+      -- are not in scope anyway (they are ambiguous).
+      -- -- Replace the shadowed names by fresh names (such that they do not shadow imports)
+      -- let mnames :: [Maybe A.Name]
+      --     mnames = map (notShadowedLocal . snd) $ reverse $ scopeLocals scope
+      -- names <- mapM (maybe freshNoName_ return) mnames
+      let types :: [Dom I.Type]
+          types = map (snd <$>) $ telToList tel
+          gamma :: ListTel' A.Name
+          gamma = fromMaybe __IMPOSSIBLE__ $
+                    zipWith' (\ x dom -> (x,) <$> dom) names types
+      reportSDoc "interaction.top" 20 $ TP.vcat
+        [ "BasicOps.atTopLevel"
+        , "  names = " TP.<+> TP.sep (map prettyA   names)
+        , "  types = " TP.<+> TP.sep (map prettyTCM types)
+        ]
+      M.withCurrentModule current $
+        withScope_ scope $
+          addContext gamma $ do
+            -- We're going inside the top-level module, so we have to set the
+            -- checkpoint for it and all its submodules to the new checkpoint.
+            cp <- viewTC eCurrentCheckpoint
+            stModuleCheckpoints `modifyTCLens` fmap (const cp)
+            m
+
+-- | Parse a name.
+parseName :: Range -> String -> TCM C.QName
+parseName r s = do
+  e <- parseExpr r s
+  let failure = typeError $ GenericError $ "Not an identifier: " ++ show e ++ "."
+  maybe failure return $ isQName e
+
+-- | Check whether an expression is a (qualified) identifier.
+isQName :: C.Expr -> Maybe C.QName
+isQName = \case
+  C.Ident x                    -> return x
+  _ -> Nothing
+
+isName :: C.Expr -> Maybe C.Name
+isName = isQName >=> \case
+  C.QName x -> return x
+  _ -> Nothing
+
+-- | Returns the contents of the given module or record.
+
+moduleContents
+  :: Rewrite
+     -- ^ How should the types be presented?
+  -> Range
+     -- ^ The range of the next argument.
+  -> String
+     -- ^ The module name.
+  -> TCM ([C.Name], I.Telescope, [(C.Name, I.Type)])
+     -- ^ Module names,
+     --   context extension needed to print types,
+     --   names paired up with corresponding types.
+
+moduleContents norm rng s = traceCall ModuleContents $ do
+  if null (trim s) then getModuleContents norm Nothing else do
+  e <- parseExpr rng s
+  case isQName e of
+    -- If the expression is not a single identifier, it is not a module name
+    -- and treated as a record expression.
+    Nothing -> getRecordContents norm e
+    -- Otherwise, if it is not in scope as a module name, it is treated
+    -- as a record name.
+    Just x  -> do
+      ms :: [AbstractModule] <- scopeLookup x <$> getScope
+      if null ms then getRecordContents norm e else getModuleContents norm $ Just x
+
+-- | Returns the contents of the given record identifier.
+
+getRecordContents
+  :: Rewrite  -- ^ Amount of normalization in types.
+  -> C.Expr   -- ^ Expression presumably of record type.
+  -> TCM ([C.Name], I.Telescope, [(C.Name, I.Type)])
+              -- ^ Module names,
+              --   context extension,
+              --   names paired up with corresponding types.
+getRecordContents norm ce = do
+  e <- toAbstract ce
+  (_, t) <- inferExpr e
+  let notRecordType = typeError $ ShouldBeRecordType t
+  (q, vs, defn) <- fromMaybeM notRecordType $ isRecordType t
+  case defn of
+    Record{ recFields = fs, recTel = rtel } -> do
+      let xs   = map (nameConcrete . qnameName . unDom) fs
+          tel  = apply rtel vs
+          doms = flattenTel tel
+      -- Andreas, 2019-04-10, issue #3687: use flattenTel
+      -- to bring types into correct scope.
+      reportSDoc "interaction.contents.record" 20 $ TP.vcat
+        [ "getRecordContents"
+        , "  cxt  = " TP.<+> (prettyTCM =<< getContextTelescope)
+        , "  tel  = " TP.<+> prettyTCM tel
+        , "  doms = " TP.<+> prettyTCM doms
+        , "  doms'= " TP.<+> addContext tel (prettyTCM doms)
+        ]
+      ts <- mapM (normalForm norm . unDom) doms
+      return ([], tel, zip xs ts)
+    _ -> __IMPOSSIBLE__
+
+-- | Returns the contents of the given module.
+
+getModuleContents
+  :: Rewrite
+       -- ^ Amount of normalization in types.
+  -> Maybe C.QName
+       -- ^ Module name, @Nothing@ if top-level module.
+  -> TCM ([C.Name], I.Telescope, [(C.Name, I.Type)])
+       -- ^ Module names,
+       --   context extension,
+       --   names paired up with corresponding types.
+getModuleContents norm mm = do
+  modScope <- case mm of
+    Nothing -> getCurrentScope
+    Just m  -> getNamedScope . amodName =<< resolveModule m
+  let modules :: ThingsInScope AbstractModule
+      modules = exportedNamesInScope modScope
+      names :: ThingsInScope AbstractName
+      names = exportedNamesInScope modScope
+      xns = [ (x,n) | (x, ns) <- Map.toList names, n <- List1.toList ns ]
+  types <- forMaybeM xns $ \(x, n) -> do
+    getConstInfo' (anameName n) >>= \case
+      Right d -> do
+        t <- normalForm norm =<< (defType <$> instantiateDef d)
+        return $ Just (x, t)
+      Left{} -> return Nothing
+  return (Map.keys modules, EmptyTel, types)
+
+
+whyInScope :: FilePath -> String -> TCM WhyInScopeData
+whyInScope cwd s = do
+  x     <- parseName noRange s
+  scope <- getScope
+  return $ WhyInScopeData
+    x
+    cwd
+    (lookup x $ map (first C.QName) $ scope ^. scopeLocals)
+    (scopeLookup x scope)
+    (scopeLookup x scope)
diff --git a/src/full/Agda/Interaction/CommandLine.hs b/src/full/Agda/Interaction/CommandLine.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/CommandLine.hs
@@ -0,0 +1,355 @@
+
+module Agda.Interaction.CommandLine
+  ( runInteractionLoop
+  ) where
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.State
+import Control.Monad.Reader
+
+import qualified Data.List as List
+import Data.Maybe
+
+import Text.Read (readMaybe)
+
+import Agda.Interaction.Base hiding (Command)
+import Agda.Interaction.BasicOps as BasicOps hiding (parseExpr)
+import Agda.Interaction.Imports ( CheckResult, crInterface )
+import Agda.Interaction.Monad
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.Internal (telToList, alwaysUnblock)
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Parser
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Translation.ConcreteToAbstract
+import Agda.Syntax.Abstract.Pretty
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Pretty ( PrettyTCM(prettyTCM) )
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Warnings (runPM)
+
+import Agda.Utils.FileName (absolute, AbsolutePath)
+import Agda.Utils.Maybe (caseMaybeM)
+
+import Agda.Utils.Impossible
+
+data ReplEnv = ReplEnv
+    { replSetupAction     :: TCM ()
+    , replTypeCheckAction :: AbsolutePath -> TCM CheckResult
+    }
+
+data ReplState = ReplState
+    { currentFile :: Maybe AbsolutePath
+    }
+
+newtype ReplM a = ReplM { unReplM :: ReaderT ReplEnv (StateT ReplState IM) a }
+    deriving
+    ( Functor, Applicative, Monad, MonadIO
+    , HasOptions, MonadTCEnv, ReadTCState, MonadTCState, MonadTCM
+    , MonadError TCErr
+    , MonadReader ReplEnv, MonadState ReplState
+    )
+
+runReplM :: Maybe AbsolutePath -> TCM () -> (AbsolutePath -> TCM CheckResult) -> ReplM () -> TCM ()
+runReplM initialFile setup checkInterface
+    = runIM
+    . flip evalStateT (ReplState initialFile)
+    . flip runReaderT replEnv
+    . unReplM
+  where
+  replEnv = ReplEnv
+    { replSetupAction     = setup
+    , replTypeCheckAction = checkInterface
+    }
+
+data ExitCode a = Continue | ContinueIn TCEnv | Return a
+
+type Command a = (String, [String] -> ReplM (ExitCode a))
+
+matchCommand :: String -> [Command a] -> Either [String] ([String] -> ReplM (ExitCode a))
+matchCommand x cmds =
+    case List.filter (List.isPrefixOf x . fst) cmds of
+        [(_,m)] -> Right m
+        xs      -> Left $ List.map fst xs
+
+interaction :: String -> [Command a] -> (String -> TCM (ExitCode a)) -> ReplM a
+interaction prompt cmds eval = loop
+    where
+        go (Return x)       = return x
+        go Continue         = loop
+        go (ContinueIn env) = localTC (const env) loop
+
+        loop =
+            do  ms <- ReplM $ lift $ lift $ readline prompt
+                case fmap words ms of
+                    Nothing               -> return $ error "** EOF **"
+                    Just []               -> loop
+                    Just ((':':cmd):args) ->
+                        do  case matchCommand cmd cmds of
+                                Right c -> go =<< (c args)
+                                Left [] ->
+                                    do  liftIO $ putStrLn $ "Unknown command '" ++ cmd ++ "'"
+                                        loop
+                                Left xs ->
+                                    do  liftIO $ putStrLn $ "More than one command match: " ++
+                                                            List.intercalate ", " xs
+                                        loop
+                    Just _ ->
+                        do  go =<< liftTCM (eval $ fromJust ms)
+            `catchError` \e ->
+                do  s <- renderError e
+                    liftIO $ putStrLn s
+                    loop
+
+runInteractionLoop :: Maybe AbsolutePath -> TCM () -> (AbsolutePath -> TCM CheckResult) -> TCM ()
+runInteractionLoop initialFile setup check = runReplM initialFile setup check interactionLoop
+
+replSetup :: ReplM ()
+replSetup = do
+    liftTCM =<< asks replSetupAction
+    liftIO $ putStr splashScreen
+
+checkCurrentFile :: ReplM (Maybe CheckResult)
+checkCurrentFile = traverse checkFile =<< gets currentFile
+
+checkFile :: AbsolutePath -> ReplM CheckResult
+checkFile file = liftTCM . ($ file) =<< asks replTypeCheckAction
+
+-- | The interaction loop.
+interactionLoop :: ReplM ()
+interactionLoop = do
+    -- Run the setup action
+    replSetup
+    reload
+    interaction "Main> " commands evalTerm
+    where
+        reload :: ReplM () = do
+            checked <- checkCurrentFile
+            liftTCM $ setScope $ maybe emptyScopeInfo (iInsideScope . crInterface) checked
+            -- Andreas, 2021-01-27, issue #5132, make Set and Prop available from Agda.Primitive
+            -- if no module is loaded.
+            when (isNothing checked) $ do
+              -- @open import Agda.Primitive using (Set; Prop)@
+              void $ liftTCM importPrimitives
+          `catchError` \e -> do
+            s <- renderError e
+            liftIO $ putStrLn s
+            liftIO $ putStrLn "Failed."
+
+        commands =
+            [ "quit"        |>  \_ -> return $ Return ()
+            , "?"           |>  \_ -> continueAfter $ liftIO $ help commands
+            , "reload"      |>  \_ -> do reload
+                                         ContinueIn <$> askTC
+            , "constraints" |> \args -> continueAfter $ liftTCM $ showConstraints args
+            , "Context"     |> \args -> continueAfter $ liftTCM $ showContext args
+            , "give"        |> \args -> continueAfter $ liftTCM $ giveMeta args
+            , "Refine"      |> \args -> continueAfter $ liftTCM $ refineMeta args
+            , "metas"       |> \args -> continueAfter $ liftTCM $ showMetas args
+            , "load"        |> \args -> continueAfter $ loadFile reload args
+            , "eval"        |> \args -> continueAfter $ liftTCM $ evalIn args
+            , "typeOf"      |> \args -> continueAfter $ liftTCM $ typeOf args
+            , "typeIn"      |> \args -> continueAfter $ liftTCM $ typeIn args
+            , "wakeup"      |> \_ -> continueAfter $ liftTCM $ retryConstraints
+            , "scope"       |> \_ -> continueAfter $ liftTCM $ showScope
+            ]
+            where
+                (|>) = (,)
+
+continueAfter :: ReplM a -> ReplM (ExitCode b)
+continueAfter m = withCurrentFile $ do
+  m >> return Continue
+
+-- | Set 'envCurrentPath' to the repl's current file
+withCurrentFile :: ReplM a -> ReplM a
+withCurrentFile cont = do
+  mpath <- gets currentFile
+  localTC (\ e -> e { envCurrentPath = mpath }) cont
+
+loadFile :: ReplM () -> [String] -> ReplM ()
+loadFile reload [file] = do
+  absPath <- liftIO $ absolute file
+  modify (\(ReplState _prevFile) -> ReplState (Just absPath))
+  withCurrentFile reload
+loadFile _ _ = liftIO $ putStrLn ":load file"
+
+showConstraints :: [String] -> TCM ()
+showConstraints [] =
+    do  cs <- BasicOps.getConstraints
+        liftIO $ putStrLn $ unlines (List.map prettyShow cs)
+showConstraints _ = liftIO $ putStrLn ":constraints [cid]"
+
+
+showMetas :: [String] -> TCM ()
+showMetas [m] =
+    do  i <- InteractionId <$> readM m
+        withInteractionId i $ do
+          s <- typeOfMeta AsIs i
+          r <- getInteractionRange i
+          d <- prettyA s
+          liftIO $ putStrLn $ render d ++ " " ++ prettyShow r
+showMetas [m,"normal"] =
+    do  i <- InteractionId <$> readM m
+        withInteractionId i $ do
+          s <- prettyA =<< typeOfMeta Normalised i
+          r <- getInteractionRange i
+          liftIO $ putStrLn $ render s ++ " " ++ prettyShow r
+showMetas [] =
+    do  interactionMetas <- typesOfVisibleMetas AsIs
+        hiddenMetas      <- typesOfHiddenMetas  AsIs
+        mapM_ (liftIO . print) =<< mapM showII interactionMetas
+        mapM_ print' hiddenMetas
+    where
+        showII o = withInteractionId (outputFormId $ OutputForm noRange [] alwaysUnblock o) $ prettyA o
+        showM  o = withMetaId (nmid $ outputFormId $ OutputForm noRange [] alwaysUnblock o) $ prettyA o
+
+        metaId (OfType i _) = i
+        metaId (JustType i) = i
+        metaId (JustSort i) = i
+        metaId (Assign i e) = i
+        metaId _ = __IMPOSSIBLE__
+        print' x = do
+            r <- getMetaRange $ nmid $ metaId x
+            d <- showM x
+            liftIO $ putStrLn $ render d ++ "  [ at " ++ prettyShow r ++ " ]"
+showMetas _ = liftIO $ putStrLn $ ":meta [metaid]"
+
+
+showScope :: TCM ()
+showScope = do
+  scope <- getScope
+  liftIO $ putStrLn $ prettyShow scope
+
+metaParseExpr ::  InteractionId -> String -> TCM A.Expr
+metaParseExpr ii s =
+    do  m <- lookupInteractionId ii
+        scope <- getMetaScope <$> lookupLocalMeta m
+        r <- getRange <$> lookupLocalMeta m
+        -- liftIO $ putStrLn $ prettyShow scope
+        let pos = fromMaybe __IMPOSSIBLE__ (rStart r)
+        (e, attrs) <- runPM $ parsePosString exprParser pos s
+        checkAttributes attrs
+        concreteToAbstract scope e
+
+actOnMeta :: [String] -> (InteractionId -> A.Expr -> TCM a) -> TCM a
+actOnMeta (is:es) f =
+     do  i <- readM is
+         let ii = InteractionId i
+         e <- metaParseExpr ii (unwords es)
+         withInteractionId ii $ f ii e
+actOnMeta _ _ = __IMPOSSIBLE__
+
+
+giveMeta :: [String] -> TCM ()
+giveMeta s | length s >= 2 = do
+  _ <- actOnMeta s $ \ ii e -> give WithoutForce ii Nothing e
+  return ()
+giveMeta _ = liftIO $ putStrLn $ ": give" ++ " metaid expr"
+
+
+
+refineMeta :: [String] -> TCM ()
+refineMeta s | length s >= 2 = do
+  _ <- actOnMeta s $ \ ii e -> refine WithoutForce ii Nothing e
+  return ()
+refineMeta _ = liftIO $ putStrLn $ ": refine" ++ " metaid expr"
+
+
+
+retryConstraints :: TCM ()
+retryConstraints = wakeupConstraints_
+
+
+evalIn :: [String] -> TCM ()
+evalIn s | length s >= 2 =
+    do  d <- actOnMeta s $ \_ e -> prettyA =<< evalInCurrent DefaultCompute e
+        liftIO $ print d
+evalIn _ = liftIO $ putStrLn ":eval metaid expr"
+
+parseExpr :: String -> TCM A.Expr
+parseExpr s = do
+    (e, attrs) <- runPM $ parse exprParser s
+    checkAttributes attrs
+    localToAbstract e return
+
+evalTerm :: String -> TCM (ExitCode a)
+evalTerm s =
+    do  e <- parseExpr s
+        v <- evalInCurrent DefaultCompute e
+        e <- prettyTCM v
+        liftIO $ print e
+        return Continue
+
+typeOf :: [String] -> TCM ()
+typeOf s =
+    do  e  <- parseExpr (unwords s)
+        e0 <- typeInCurrent Normalised e
+        e1 <- typeInCurrent AsIs e
+        liftIO . putStrLn =<< showA e1
+
+typeIn :: [String] -> TCM ()
+typeIn s@(_:_:_) =
+    actOnMeta s $ \i e ->
+    do  e1 <- typeInMeta i Normalised e
+        e2 <- typeInMeta i AsIs e
+        liftIO . putStrLn =<< showA e1
+typeIn _ = liftIO $ putStrLn ":typeIn meta expr"
+
+showContext :: [String] -> TCM ()
+showContext (meta:args) = do
+    i <- InteractionId <$> readM meta
+    mi <- lookupLocalMeta =<< lookupInteractionId i
+    withMetaInfo (getMetaInfo mi) $ do
+      ctx <- List.map I.unDom . telToList <$> getContextTelescope
+      zipWithM_ display ctx $ reverse $ zipWith const [1..] ctx
+    where
+        display (x, t) n = do
+            t <- case args of
+                    ["normal"] -> normalise $ raise n t
+                    _          -> return $ raise n t
+            d <- prettyTCM t
+            liftIO $ print $ text (argNameToString x) <+> ":" <+> d
+showContext _ = liftIO $ putStrLn ":Context meta"
+
+-- | The logo that prints when Agda is started in interactive mode.
+splashScreen :: String
+splashScreen = unlines
+    [ "                 _ "
+    , "   ____         | |"
+    , "  / __ \\        | |"
+    , " | |__| |___  __| | ___"
+    , " |  __  / _ \\/ _  |/ __\\     Agda Interactive"
+    , " | |  |/ /_\\ \\/_| / /_| \\"
+    , " |_|  |\\___  /____\\_____/    Type :? for help."
+    , "        __/ /"
+    , "        \\__/"
+    , ""
+    -- , "The interactive mode is no longer supported. Don't complain if it doesn't work."
+    , "The interactive mode is no longer under active development. Use at your own risk."
+    ]
+
+-- | The help message
+help :: [Command a] -> IO ()
+help cs = putStr $ unlines $
+    [ "Command overview" ] ++ List.map explain cs ++
+    [ "<exp> Infer type of expression <exp> and evaluate it." ]
+    where
+        explain (x,_) = ":" ++ x
+
+-- Read -------------------------------------------------------------------
+
+readM :: Read a => String -> TCM a
+readM s = maybe err return $ readMaybe s
+  where
+  err    = throwError $ strMsg $ "Cannot parse: " ++ s
+  strMsg = Exception noRange . text
diff --git a/src/full/Agda/Interaction/EmacsCommand.hs b/src/full/Agda/Interaction/EmacsCommand.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/EmacsCommand.hs
@@ -0,0 +1,102 @@
+
+------------------------------------------------------------------------
+-- | Code for instructing Emacs to do things
+------------------------------------------------------------------------
+
+module Agda.Interaction.EmacsCommand
+  ( Lisp(..)
+  , response
+  , putResponse
+  , display_info'
+  , clearRunningInfo
+  , clearWarning
+  , displayRunningInfo
+  ) where
+
+-- import qualified Data.List as List
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.String
+
+-- | Simple Emacs Lisp expressions.
+
+data Lisp a
+  = A a
+    -- ^ Atom.
+  | Cons (Lisp a) (Lisp a)
+    -- Cons cell.
+  | L [Lisp a]
+    -- ^ List.
+  | Q (Lisp a)
+    -- Quoted expression.
+  deriving Eq
+
+instance Pretty a => Pretty (Lisp a) where
+  pretty (A a )     = pretty a
+  pretty (Cons a b) = parens (pretty a <+> "." <+> pretty b)
+  pretty (L xs)     = parens (hsep (map pretty xs))
+  pretty (Q x)      = "'" <> pretty x
+
+-- instance Show (Lisp String) where
+--   showsPrec _ (A a)      = showString a
+--   showsPrec p (Cons a b) = showString "(" . showsPrec p a . showString " . " .
+--                                             showsPrec p b . showString ")"
+--   showsPrec p (L xs)     = showString "(" . foldr (.) (showString ")")
+--                                               (List.intersperse (showString " ")
+--                                                  (map (showsPrec p) xs))
+--   showsPrec p (Q x)      = showString "'" . showsPrec p x
+
+-- | Formats a response command.
+--
+--   Replaces @'\n'@ with spaces to ensure that each command is a
+--   single line.
+response :: Lisp String -> String
+response = (++ "\n") . map replaceNewLines . show . pretty
+  where
+  replaceNewLines '\n' = ' '
+  replaceNewLines c    = c
+
+-- | Writes a response command to standard output.
+
+putResponse :: Lisp String -> IO ()
+putResponse = putStr . response
+
+-- | @displayInBuffer buffername append header content@ displays @content@
+-- (with header @header@) in some suitable way in the buffer @buffername@.
+-- If @append@ is @True@, then the content is appended to previous content
+-- (if any), otherwise any previous content is deleted.
+
+displayInBuffer :: String -> Bool -> String -> String -> Lisp String
+displayInBuffer buffername append header content =
+    L [ A buffername
+      , A (quote header)
+      , A (quote content)
+      , A (if append then "t" else "nil")
+      ]
+
+display_info' :: Bool -> String -> String -> Lisp String
+display_info' = displayInBuffer "agda2-info-action"
+
+------------------------------------------------------------------------
+-- Running info
+
+-- | The name of the running info buffer.
+
+runningInfoBufferName :: String
+runningInfoBufferName = "*Type-checking*"
+
+-- | Clear the running info buffer.
+
+clearRunningInfo :: Lisp String
+clearRunningInfo =
+    display_info' False runningInfoBufferName ""
+
+-- | Clear the warning buffer
+clearWarning :: Lisp String
+clearWarning = L [ A "agda2-close-warning" ]
+
+-- | Display running information about what the type-checker is up to.
+
+displayRunningInfo :: String -> Lisp String
+displayRunningInfo s =
+    display_info' True runningInfoBufferName s
diff --git a/src/full/Agda/Interaction/EmacsTop.hs b/src/full/Agda/Interaction/EmacsTop.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/EmacsTop.hs
@@ -0,0 +1,382 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.EmacsTop
+    ( mimicGHCi
+    , namedMetaOf
+    , showGoals
+    , showInfoError
+    , explainWhyInScope
+    , prettyResponseContext
+    , prettyTypeOfMeta
+    ) where
+
+import Control.Monad
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.State    ( evalStateT )
+import Control.Monad.Trans    ( lift )
+
+import qualified Data.List as List
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.Abstract.Pretty (prettyATop)
+import Agda.Syntax.Concrete as C
+
+import Agda.TypeChecking.Errors ( explainWhyInScope, getAllWarningsOfTCErr, renderError, verbalize )
+import qualified Agda.TypeChecking.Pretty as TCP
+import Agda.TypeChecking.Pretty (prettyTCM)
+import Agda.TypeChecking.Pretty.Warning (prettyTCWarnings, renderTCWarnings')
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Warnings (WarningsAndNonFatalErrors(..))
+import Agda.Interaction.AgdaTop
+import Agda.Interaction.Base
+import Agda.Interaction.BasicOps as B
+import Agda.Interaction.Response as R
+import Agda.Interaction.EmacsCommand hiding (putResponse)
+import Agda.Interaction.Highlighting.Emacs
+import Agda.Interaction.Highlighting.Precise (TokenBased(..))
+import Agda.Interaction.InteractionTop (localStateCommandM)
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Null (empty)
+import Agda.Utils.Maybe
+import Agda.Utils.String
+import Agda.Utils.Time (CPUTime)
+import Agda.VersionCommit
+
+----------------------------------
+
+-- | 'mimicGHCi' is a fake ghci interpreter for the Emacs frontend
+--   and for interaction tests.
+--
+--   'mimicGHCi' reads the Emacs frontend commands from stdin,
+--   interprets them and print the result into stdout.
+mimicGHCi :: TCM () -> TCM ()
+mimicGHCi = repl (liftIO . mapM_ (putStrLn . prettyShow) <=< lispifyResponse) "Agda2> "
+
+-- | Convert Response to an elisp value for the interactive emacs frontend.
+
+lispifyResponse :: Response -> TCM [Lisp String]
+lispifyResponse (Resp_HighlightingInfo info remove method modFile) =
+  (:[]) <$> liftIO (lispifyHighlightingInfo info remove method modFile)
+lispifyResponse (Resp_DisplayInfo info) = lispifyDisplayInfo info
+lispifyResponse (Resp_ClearHighlighting tokenBased) =
+  return [ L $ A "agda2-highlight-clear" :
+               case tokenBased of
+                 NotOnlyTokenBased -> []
+                 TokenBased        ->
+                   [ Q (lispifyTokenBased tokenBased) ]
+         ]
+lispifyResponse Resp_DoneAborting = return [ L [ A "agda2-abort-done" ] ]
+lispifyResponse Resp_DoneExiting  = return [ L [ A "agda2-exit-done"  ] ]
+lispifyResponse Resp_ClearRunningInfo = return [ clearRunningInfo ]
+lispifyResponse (Resp_RunningInfo n s)
+  | n <= 1    = return [ displayRunningInfo s ]
+  | otherwise = return [ L [A "agda2-verbose", A (quote s)] ]
+lispifyResponse (Resp_Status s)
+    = return [ L [ A "agda2-status-action"
+                 , A (quote $ List.intercalate "," $ catMaybes [checked, showImpl, showIrr])
+                 ]
+             ]
+  where
+    checked  = boolToMaybe (sChecked                 s) "Checked"
+    showImpl = boolToMaybe (sShowImplicitArguments   s) "ShowImplicit"
+    showIrr  = boolToMaybe (sShowIrrelevantArguments s) "ShowIrrelevant"
+
+lispifyResponse (Resp_JumpToError f p) = return
+  [ lastTag 3 $
+      L [ A "agda2-maybe-goto", Q $ L [A (quote f), A ".", A (show p)] ]
+  ]
+lispifyResponse (Resp_InteractionPoints is) = return
+  [ lastTag 1 $
+      L [A "agda2-goals-action", Q $ L $ map showNumIId is]
+  ]
+lispifyResponse (Resp_GiveAction ii s)
+    = return [ L [ A "agda2-give-action", showNumIId ii, A s' ] ]
+  where
+    s' = case s of
+        Give_String str -> quote str
+        Give_Paren      -> "'paren"
+        Give_NoParen    -> "'no-paren"
+lispifyResponse (Resp_MakeCase ii variant pcs) = return
+  [ lastTag 2 $ L [ A cmd, Q $ L $ map (A . quote) pcs ] ]
+  where
+  cmd = case variant of
+    R.Function       -> "agda2-make-case-action"
+    R.ExtendedLambda -> "agda2-make-case-action-extendlam"
+lispifyResponse (Resp_SolveAll ps) = return
+  [ lastTag 2 $
+      L [ A "agda2-solveAll-action", Q . L $ concatMap prn ps ]
+  ]
+  where
+    prn (ii,e)= [showNumIId ii, A $ quote $ prettyShow e]
+
+lispifyDisplayInfo :: DisplayInfo -> TCM [Lisp String]
+lispifyDisplayInfo info = case info of
+    Info_CompilationOk backend ws -> do
+      warnings <- prettyTCWarnings (tcWarnings ws)
+      errors <- prettyTCWarnings (nonFatalErrors ws)
+      let
+        msg = concat
+          [ "The module was successfully compiled with backend "
+          , prettyShow backend
+          , ".\n"
+          ]
+      -- abusing the goals field since we ignore the title
+        (body, _) = formatWarningsAndErrors msg warnings errors
+      format body "*Compilation result*"
+    Info_Constraints s -> do
+      doc <- TCP.vcat $ map prettyTCM s
+      format (render doc) "*Constraints*"
+    Info_AllGoalsWarnings ms ws -> do
+      goals <- showGoals ms
+      warnings <- prettyTCWarnings (tcWarnings ws)
+      errors <- prettyTCWarnings (nonFatalErrors ws)
+      let (body, title) = formatWarningsAndErrors goals warnings errors
+      format body ("*All" ++ title ++ "*")
+    Info_Auto s -> format s "*Auto*"
+    Info_Error err -> do
+      s <- showInfoError err
+      format s "*Error*"
+    Info_Time s -> format (render $ prettyTimed s) "*Time*"
+    Info_NormalForm state cmode time expr -> do
+      exprDoc <- evalStateT prettyExpr state
+      let doc = maybe empty prettyTimed time $$ exprDoc
+          lbl | cmode == HeadCompute = "*Head Normal Form*"
+              | otherwise            = "*Normal Form*"
+      format (render doc) lbl
+      where
+        prettyExpr = localStateCommandM
+            $ lift
+            $ B.atTopLevel
+            $ allowNonTerminatingReductions
+            $ (if computeIgnoreAbstract cmode then ignoreAbstractMode else inConcreteMode)
+            $ (B.showComputed cmode)
+            $ expr
+    Info_InferredType state time expr -> do
+      exprDoc <- evalStateT prettyExpr state
+      let doc = maybe empty prettyTimed time $$ exprDoc
+      format (render doc) "*Inferred Type*"
+      where
+        prettyExpr = localStateCommandM
+            $ lift
+            $ B.atTopLevel
+            $ TCP.prettyA
+            $ expr
+    Info_ModuleContents modules tel types -> do
+      doc <- localTCState $ do
+        typeDocs <- addContext tel $ forM types $ \ (x, t) -> do
+          doc <- prettyTCM t
+          return (prettyShow x, ":" <+> doc)
+        return $ vcat
+          [ "Modules"
+          , nest 2 $ vcat $ map pretty modules
+          , "Names"
+          , nest 2 $ align 10 typeDocs
+          ]
+      format (render doc) "*Module contents*"
+    Info_SearchAbout hits names -> do
+      hitDocs <- forM hits $ \ (x, t) -> do
+        doc <- prettyTCM t
+        return (prettyShow x, ":" <+> doc)
+      let doc = "Definitions about" <+>
+                text (List.intercalate ", " $ words names) $$ nest 2 (align 10 hitDocs)
+      format (render doc) "*Search About*"
+    Info_WhyInScope why -> do
+      doc <- explainWhyInScope why
+      format (render doc) "*Scope Info*"
+    Info_Context ii ctx -> do
+      doc <- localTCState (prettyResponseContext ii False ctx)
+      format (render doc) "*Context*"
+    Info_Intro_NotFound -> format "No introduction forms found." "*Intro*"
+    Info_Intro_ConstructorUnknown ss -> do
+      let doc = sep [ "Don't know which constructor to introduce of"
+                    , let mkOr []     = []
+                          mkOr [x, y] = [text x <+> "or" <+> text y]
+                          mkOr (x:xs) = text x : mkOr xs
+                      in nest 2 $ fsep $ punctuate comma (mkOr ss)
+                    ]
+      format (render doc) "*Intro*"
+    Info_Version -> format ("Agda version " ++ versionWithCommitInfo) "*Agda Version*"
+    Info_GoalSpecific ii kind -> lispifyGoalSpecificDisplayInfo ii kind
+
+lispifyGoalSpecificDisplayInfo :: InteractionId -> GoalDisplayInfo -> TCM [Lisp String]
+lispifyGoalSpecificDisplayInfo ii kind = localTCState $ withInteractionId ii $
+  case kind of
+    Goal_HelperFunction helperType -> do
+      doc <- inTopContext $ prettyATop helperType
+      return [ L [ A "agda2-info-action-and-copy"
+                 , A $ quote "*Helper function*"
+                 , A $ quote (render doc ++ "\n")
+                 , A "nil"
+                 ]
+             ]
+    Goal_NormalForm cmode expr -> do
+      doc <- showComputed cmode expr
+      format (render doc) "*Normal Form*"   -- show?
+    Goal_GoalType norm aux ctx bndry constraints -> do
+      ctxDoc <- prettyResponseContext ii True ctx
+      goalDoc <- prettyTypeOfMeta norm ii
+      let boundaryDoc hd bndry
+            | null bndry = []
+            | otherwise  = [ text $ delimiter hd
+                           , vcat $ map pretty bndry
+                           ]
+      auxDoc <- case aux of
+            GoalOnly -> return empty
+            GoalAndHave expr bndry -> do
+              doc <- prettyATop expr
+              return $ ("Have:" <+> doc) $$ vcat (boundaryDoc ("Boundary (actual)") bndry)
+            GoalAndElaboration term -> do
+              doc <- TCP.prettyTCM term
+              return $ "Elaborates to:" <+> doc
+      let constraintsDoc
+            | null constraints = []
+            | otherwise        =
+              [ TCP.text $ delimiter "Constraints"
+              , TCP.vcat $ map prettyTCM constraints
+              ]
+      doc <- TCP.vcat $
+        [ "Goal:" TCP.<+> return goalDoc
+        , return (vcat (boundaryDoc "Boundary (wanted)" bndry))
+        , return auxDoc
+        , TCP.text (replicate 60 '\x2014')
+        , return ctxDoc
+        ] ++ constraintsDoc
+      format (render doc) "*Goal type etc.*"
+    Goal_CurrentGoal norm -> do
+      doc <- prettyTypeOfMeta norm ii
+      format (render doc) "*Current Goal*"
+    Goal_InferredType expr -> do
+      doc <- prettyATop expr
+      format (render doc) "*Inferred Type*"
+
+-- | Format responses of DisplayInfo
+
+format :: String -> String -> TCM [Lisp String]
+format content bufname = return [ display_info' False bufname content ]
+
+-- | Adds a \"last\" tag to a response.
+
+lastTag :: Integer -> Lisp String -> Lisp String
+lastTag n r = Cons (Cons (A "last") (A $ show n)) r
+
+-- | Show an iteraction point identifier as an elisp expression.
+
+showNumIId :: InteractionId -> Lisp String
+showNumIId = A . show . interactionId
+
+--------------------------------------------------------------------------------
+
+-- | Given strings of goals, warnings and errors, return a pair of the
+--   body and the title for the info buffer
+formatWarningsAndErrors :: String -> String -> String -> (String, String)
+formatWarningsAndErrors g w e = (body, title)
+  where
+    isG = not $ null g
+    isW = not $ null w
+    isE = not $ null e
+    title = List.intercalate "," $ catMaybes
+              [ " Goals"    <$ guard isG
+              , " Errors"   <$ guard isE
+              , " Warnings" <$ guard isW
+              , " Done"     <$ guard (not (isG || isW || isE))
+              ]
+
+    body = List.intercalate "\n" $ catMaybes
+             [ g                    <$ guard isG
+             , delimiter "Errors"   <$ guard (isE && (isG || isW))
+             , e                    <$ guard isE
+             , delimiter "Warnings" <$ guard (isW && (isG || isE))
+             , w                    <$ guard isW
+             ]
+
+
+-- | Serializing Info_Error
+showInfoError :: Info_Error -> TCM String
+showInfoError (Info_GenericError err) = do
+  e <- renderError err
+  w <- renderTCWarnings' =<< getAllWarningsOfTCErr err
+
+  let errorMsg  = if null w
+                      then e
+                      else delimiter "Error" ++ "\n" ++ e
+  let warningMsg = List.intercalate "\n" $ delimiter "Warning(s)"
+                                      : filter (not . null) w
+  return $ if null w
+            then errorMsg
+            else errorMsg ++ "\n\n" ++ warningMsg
+showInfoError (Info_CompilationError warnings) = do
+  s <- prettyTCWarnings warnings
+  return $ unlines
+            [ "You need to fix the following errors before you can compile"
+            , "the module:"
+            , ""
+            , s
+            ]
+showInfoError (Info_HighlightingParseError ii) =
+  return $ "Highlighting failed to parse expression in " ++ show ii
+showInfoError (Info_HighlightingScopeCheckError ii) =
+  return $ "Highlighting failed to scope check expression in " ++ show ii
+
+-- | Pretty-prints the context of the given meta-variable.
+
+prettyResponseContext
+  :: InteractionId  -- ^ Context of this meta-variable.
+  -> Bool           -- ^ Print the elements in reverse order?
+  -> [ResponseContextEntry]
+  -> TCM Doc
+prettyResponseContext ii rev ctx = withInteractionId ii $ do
+  mod <- currentModality
+  align 10 . concat . applyWhen rev reverse <$> do
+    forM ctx $ \ (ResponseContextEntry n x (Arg ai expr) letv nis) -> do
+      let
+        prettyCtxName :: String
+        prettyCtxName
+          | n == x                 = prettyShow x
+          | isInScope n == InScope = prettyShow n ++ " = " ++ prettyShow x
+          | otherwise              = prettyShow x
+
+        -- Some attributes are useful to report whenever they are not
+        -- in the default state.
+        attribute :: String
+        attribute = c ++ if null c then "" else " "
+          where c = prettyShow (getCohesion ai)
+
+        extras :: [Doc]
+        extras = concat $
+          [ [ "not in scope" | isInScope nis == C.NotInScope ]
+            -- Print "erased" if hypothesis is erased but goal is non-erased.
+          , [ "erased"       | not $ getQuantity  ai `moreQuantity` getQuantity  mod ]
+            -- Print relevance of hypothesis relative to relevance of the goal. (Issue #6706.)
+          , [ text $ verbalize r
+                             | let r = getRelevance mod `inverseComposeRelevance` getRelevance ai
+                             , r /= Relevant ]
+            -- Print "instance" if variable is considered by instance search.
+          , [ "instance"     | isInstance ai ]
+          ]
+      ty <- prettyATop expr
+      maybeVal <- traverse prettyATop letv
+
+      return $
+        (attribute ++ prettyCtxName, ":" <+> ty <+> (parenSep extras)) :
+        [ (prettyShow x, "=" <+> val) | val <- maybeToList maybeVal ]
+
+  where
+    parenSep :: [Doc] -> Doc
+    parenSep docs
+      | null docs = empty
+      | otherwise = (" " <+>) $ parens $ fsep $ punctuate comma docs
+
+
+-- | Pretty-prints the type of the meta-variable.
+
+prettyTypeOfMeta :: Rewrite -> InteractionId -> TCM Doc
+prettyTypeOfMeta norm ii = do
+  form <- B.typeOfMeta norm ii
+  case form of
+    OfType _ e -> prettyATop e
+    _            -> prettyATop form
+
+-- | Prefix prettified CPUTime with "Time:"
+prettyTimed :: CPUTime -> Doc
+prettyTimed time = "Time:" <+> pretty time
diff --git a/src/full/Agda/Interaction/ExitCode.hs b/src/full/Agda/Interaction/ExitCode.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/ExitCode.hs
@@ -0,0 +1,37 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.ExitCode (
+  AgdaError(..),
+  agdaErrorToInt,
+  agdaErrorFromInt,
+  exitSuccess,
+  exitAgdaWith)
+  where
+
+import System.Exit (exitSuccess, exitWith, ExitCode(ExitFailure))
+
+data AgdaError = UnknownError      -- ^ 1
+               | TCMError          -- ^ 42
+               | OptionError       -- ^ 71
+               | CommandError      -- ^ 113
+               | ImpossibleError   -- ^ 154
+               deriving (Show, Eq, Enum, Bounded)
+
+agdaErrorToInt :: AgdaError -> Int
+agdaErrorToInt UnknownError    = 1
+agdaErrorToInt TCMError        = 42
+agdaErrorToInt OptionError     = 71
+agdaErrorToInt CommandError    = 113
+agdaErrorToInt ImpossibleError = 154
+
+-- ^ Return the error corresponding to an exit code from the
+--   Agda process
+agdaErrorFromInt :: Int -> Maybe AgdaError
+agdaErrorFromInt = -- We implement this in a somewhat more inefficient
+                   -- way for the sake of consistency
+                   flip lookup [(agdaErrorToInt error, error)
+                               | error  <- [minBound..maxBound]
+                               ]
+
+exitAgdaWith :: AgdaError -> IO a
+exitAgdaWith = exitWith . ExitFailure . agdaErrorToInt
diff --git a/src/full/Agda/Interaction/FindFile.hs b/src/full/Agda/Interaction/FindFile.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/FindFile.hs
@@ -0,0 +1,301 @@
+------------------------------------------------------------------------
+-- | Functions which map between module names and file names.
+--
+-- Note that file name lookups are cached in the 'TCState'. The code
+-- assumes that no Agda source files are added or removed from the
+-- include directories while the code is being type checked.
+------------------------------------------------------------------------
+
+module Agda.Interaction.FindFile
+  ( SourceFile(..), InterfaceFile(intFilePath)
+  , toIFile, mkInterfaceFile
+  , FindError(..), findErrorToTypeError
+  , findFile, findFile', findFile''
+  , findInterfaceFile', findInterfaceFile
+  , checkModuleName
+  , moduleName
+  , rootNameModule
+  , replaceModuleExtension
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans
+import Data.Maybe (catMaybes)
+import qualified Data.Map as Map
+import qualified Data.Text as T
+import System.FilePath
+
+import Agda.Interaction.Library ( findProjectRoot )
+
+import Agda.Syntax.Concrete
+import Agda.Syntax.Parser
+import Agda.Syntax.Parser.Literate (literateExtsShortList)
+import Agda.Syntax.Position
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.Interaction.Options ( optLocalInterfaces )
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Benchmark (billTo)
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Options
+  (getIncludeDirs, libToTCM)
+import Agda.TypeChecking.Monad.State (topLevelModuleName)
+import Agda.TypeChecking.Warnings (runPM, warning)
+
+import Agda.Version ( version )
+
+import Agda.Utils.Applicative ( (?$>) )
+import Agda.Utils.FileName
+import Agda.Utils.List  ( stripSuffix, nubOn )
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Monad ( ifM, unlessM )
+import Agda.Syntax.Common.Pretty ( Pretty(..), prettyShow )
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+-- | Type aliases for source files and interface files.
+--   We may only produce one of these if we know for sure that the file
+--   does exist. We can always output an @AbsolutePath@ if we are not sure.
+
+-- TODO: do not export @SourceFile@ and force users to check the
+-- @AbsolutePath@ does exist.
+newtype SourceFile    = SourceFile    { srcFilePath :: AbsolutePath } deriving (Eq, Ord, Show)
+newtype InterfaceFile = InterfaceFile { intFilePath :: AbsolutePath }
+
+instance Pretty SourceFile    where pretty = pretty . srcFilePath
+instance Pretty InterfaceFile where pretty = pretty . intFilePath
+
+-- | Makes an interface file from an AbsolutePath candidate.
+--   If the file does not exist, then fail by returning @Nothing@.
+
+mkInterfaceFile
+  :: AbsolutePath             -- ^ Path to the candidate interface file
+  -> IO (Maybe InterfaceFile) -- ^ Interface file iff it exists
+mkInterfaceFile fp = do
+  ex <- doesFileExistCaseSensitive $ filePath fp
+  pure (ex ?$> InterfaceFile fp)
+
+-- | Converts an Agda file name to the corresponding interface file
+--   name. Note that we do not guarantee that the file exists.
+
+toIFile :: SourceFile -> TCM AbsolutePath
+toIFile (SourceFile src) = do
+  let fp = filePath src
+  let localIFile = replaceModuleExtension ".agdai" src
+  mroot <- libToTCM $ findProjectRoot (takeDirectory fp)
+  case mroot of
+    Nothing   -> pure localIFile
+    Just root ->
+      let buildDir = root </> "_build" </> version </> "agda"
+          fileName = makeRelative root (filePath localIFile)
+          separatedIFile = mkAbsolute $ buildDir </> fileName
+          ifilePreference = ifM (optLocalInterfaces <$> commandLineOptions)
+            (pure (localIFile, separatedIFile))
+            (pure (separatedIFile, localIFile))
+      in do
+        separatedIFileExists <- liftIO $ doesFileExistCaseSensitive $ filePath separatedIFile
+        localIFileExists <- liftIO $ doesFileExistCaseSensitive $ filePath localIFile
+        case (separatedIFileExists, localIFileExists) of
+          (False, False) -> fst <$> ifilePreference
+          (False, True) -> pure localIFile
+          (True, False) -> pure separatedIFile
+          (True, True) -> do
+            ifiles <- ifilePreference
+            warning $ uncurry DuplicateInterfaceFiles ifiles
+            pure $ fst ifiles
+
+replaceModuleExtension :: String -> AbsolutePath -> AbsolutePath
+replaceModuleExtension ext@('.':_) = mkAbsolute . (++ ext) .  dropAgdaExtension . filePath
+replaceModuleExtension ext = replaceModuleExtension ('.':ext)
+
+-- | Errors which can arise when trying to find a source file.
+--
+-- Invariant: All paths are absolute.
+
+data FindError
+  = NotFound [SourceFile]
+    -- ^ The file was not found. It should have had one of the given
+    -- file names.
+  | Ambiguous [SourceFile]
+    -- ^ Several matching files were found.
+    --
+    -- Invariant: The list of matching files has at least two
+    -- elements.
+  deriving Show
+
+-- | Given the module name which the error applies to this function
+-- converts a 'FindError' to a 'TypeError'.
+
+findErrorToTypeError :: TopLevelModuleName -> FindError -> TypeError
+findErrorToTypeError m (NotFound  files) = FileNotFound m (map srcFilePath files)
+findErrorToTypeError m (Ambiguous files) =
+  AmbiguousTopLevelModuleName m (map srcFilePath files)
+
+-- | Finds the source file corresponding to a given top-level module
+-- name. The returned paths are absolute.
+--
+-- Raises an error if the file cannot be found.
+
+findFile :: TopLevelModuleName -> TCM SourceFile
+findFile m = do
+  mf <- findFile' m
+  case mf of
+    Left err -> typeError $ findErrorToTypeError m err
+    Right f  -> return f
+
+-- | Tries to find the source file corresponding to a given top-level
+--   module name. The returned paths are absolute.
+--
+--   SIDE EFFECT:  Updates 'stModuleToSource'.
+findFile' :: TopLevelModuleName -> TCM (Either FindError SourceFile)
+findFile' m = do
+    dirs         <- getIncludeDirs
+    modFile      <- useTC stModuleToSource
+    (r, modFile) <- liftIO $ findFile'' dirs m modFile
+    stModuleToSource `setTCLens` modFile
+    return r
+
+-- | A variant of 'findFile'' which does not require 'TCM'.
+
+findFile''
+  :: [AbsolutePath]
+  -- ^ Include paths.
+  -> TopLevelModuleName
+  -> ModuleToSource
+  -- ^ Cached invocations of 'findFile'''. An updated copy is returned.
+  -> IO (Either FindError SourceFile, ModuleToSource)
+findFile'' dirs m modFile =
+  case Map.lookup m modFile of
+    Just f  -> return (Right (SourceFile f), modFile)
+    Nothing -> do
+      files          <- fileList acceptableFileExts
+      filesShortList <- fileList parseFileExtsShortList
+      existingFiles  <-
+        liftIO $ filterM (doesFileExistCaseSensitive . filePath . srcFilePath) files
+      return $ case nubOn id existingFiles of
+        []     -> (Left (NotFound filesShortList), modFile)
+        [file] -> (Right file, Map.insert m (srcFilePath file) modFile)
+        files  -> (Left (Ambiguous existingFiles), modFile)
+  where
+    fileList exts = mapM (fmap SourceFile . absolute)
+                    [ filePath dir </> file
+                    | dir  <- dirs
+                    , file <- map (moduleNameToFileName m) exts
+                    ]
+
+-- | Finds the interface file corresponding to a given top-level
+-- module file. The returned paths are absolute.
+--
+-- Raises 'Nothing' if the interface file cannot be found.
+
+findInterfaceFile'
+  :: SourceFile                 -- ^ Path to the source file
+  -> TCM (Maybe InterfaceFile)  -- ^ Maybe path to the interface file
+findInterfaceFile' fp = liftIO . mkInterfaceFile =<< toIFile fp
+
+-- | Finds the interface file corresponding to a given top-level
+-- module file. The returned paths are absolute.
+--
+-- Raises an error if the source file cannot be found, and returns
+-- 'Nothing' if the source file can be found but not the interface
+-- file.
+
+findInterfaceFile :: TopLevelModuleName -> TCM (Maybe InterfaceFile)
+findInterfaceFile m = findInterfaceFile' =<< findFile m
+
+-- | Ensures that the module name matches the file name. The file
+-- corresponding to the module name (according to the include path)
+-- has to be the same as the given file name.
+
+checkModuleName
+  :: TopLevelModuleName
+     -- ^ The name of the module.
+  -> SourceFile
+     -- ^ The file from which it was loaded.
+  -> Maybe TopLevelModuleName
+     -- ^ The expected name, coming from an import statement.
+  -> TCM ()
+checkModuleName name (SourceFile file) mexpected = do
+  findFile' name >>= \case
+
+    Left (NotFound files)  -> typeError $
+      case mexpected of
+        Nothing -> ModuleNameDoesntMatchFileName name (map srcFilePath files)
+        Just expected -> ModuleNameUnexpected name expected
+
+    Left (Ambiguous files) -> typeError $
+      AmbiguousTopLevelModuleName name (map srcFilePath files)
+
+    Right src -> do
+      let file' = srcFilePath src
+      file <- liftIO $ absolute (filePath file)
+      unlessM (liftIO $ sameFile file file') $
+        typeError $ ModuleDefinedInOtherFile name file file'
+
+  -- Andreas, 2020-09-28, issue #4671:  In any case, make sure
+  -- that we do not end up with a mismatch between expected
+  -- and actual module name.
+
+  forM_ mexpected $ \ expected ->
+    unless (name == expected) $
+      typeError $ OverlappingProjects file name expected
+      -- OverlappingProjects is the correct error for
+      -- test/Fail/customized/NestedProjectRoots
+      -- -- typeError $ ModuleNameUnexpected name expected
+
+
+-- | Computes the module name of the top-level module in the given
+-- file.
+--
+-- If no top-level module name is given, then an attempt is made to
+-- use the file name as a module name.
+
+-- TODO: Perhaps it makes sense to move this procedure to some other
+-- module.
+
+moduleName
+  :: AbsolutePath
+     -- ^ The path to the file.
+  -> Module
+     -- ^ The parsed module.
+  -> TCM TopLevelModuleName
+moduleName file parsedModule = billTo [Bench.ModuleName] $ do
+  let defaultName = rootNameModule file
+      raw         = rawTopLevelModuleNameForModule parsedModule
+  topLevelModuleName =<< if isNoName raw
+    then do
+      m <- runPM (fst <$> parse moduleNameParser defaultName)
+             `catchError` \_ ->
+           typeError $ GenericError $
+             "The file name " ++ prettyShow file ++
+             " is invalid because it does not correspond to a valid module name."
+      case m of
+        Qual {} ->
+          typeError $ GenericError $
+            "The file name " ++ prettyShow file ++ " is invalid because " ++
+            defaultName ++ " is not an unqualified module name."
+        QName {} ->
+          return $ RawTopLevelModuleName
+            { rawModuleNameRange = getRange m
+            , rawModuleNameParts = singleton (T.pack defaultName)
+            }
+    else return raw
+
+parseFileExtsShortList :: [String]
+parseFileExtsShortList = ".agda" : literateExtsShortList
+
+dropAgdaExtension :: String -> String
+dropAgdaExtension s = case catMaybes [ stripSuffix ext s
+                                     | ext <- acceptableFileExts ] of
+    [name] -> name
+    _      -> __IMPOSSIBLE__
+
+rootNameModule :: AbsolutePath -> String
+rootNameModule = dropAgdaExtension . snd . splitFileName . filePath
diff --git a/src/full/Agda/Interaction/Highlighting/Common.hs b/src/full/Agda/Interaction/Highlighting/Common.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Common.hs
@@ -0,0 +1,49 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Common syntax highlighting functions for Emacs and JSON
+
+module Agda.Interaction.Highlighting.Common
+  ( toAtoms
+  , chooseHighlightingMethod
+  ) where
+
+import Agda.Interaction.Highlighting.Precise
+import Agda.Syntax.Common
+import Agda.TypeChecking.Monad (HighlightingMethod(..))
+import Data.Maybe (maybeToList)
+import Data.Char (toLower)
+import qualified Data.Set as Set
+
+-- | Converts the 'aspect' and 'otherAspects' fields to strings that are
+-- friendly to editors.
+toAtoms :: Aspects -> [String]
+toAtoms m = map toAtom (Set.toList $ otherAspects m)
+         ++ toAtoms' (aspect m)
+  where
+
+  toAtom :: Show a => a -> String
+  toAtom = map toLower . show
+
+  kindToAtom (Constructor Inductive)   = "inductiveconstructor"
+  kindToAtom (Constructor CoInductive) = "coinductiveconstructor"
+  kindToAtom k                         = toAtom k
+
+  toAtoms' Nothing               = []
+  toAtoms' (Just (Name mKind op)) =
+    map kindToAtom (maybeToList mKind) ++ opAtom
+    where opAtom | op        = ["operator"]
+                 | otherwise = []
+  toAtoms' (Just a) = [toAtom a]
+
+-- | Choose which method to use based on HighlightingInfo and HighlightingMethod
+chooseHighlightingMethod
+  :: HighlightingInfo
+  -> HighlightingMethod
+  -> HighlightingMethod
+chooseHighlightingMethod info method = case toList info of
+  _             | method == Direct -> Direct
+  ((_, mi) : _) | check mi         -> Direct
+  _                                -> Indirect
+
+  where check mi = otherAspects mi == Set.singleton TypeChecks
+                || mi == mempty
diff --git a/src/full/Agda/Interaction/Highlighting/Dot.hs b/src/full/Agda/Interaction/Highlighting/Dot.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Dot.hs
@@ -0,0 +1,7 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Highlighting.Dot
+  ( dotBackend
+  ) where
+
+import Agda.Interaction.Highlighting.Dot.Backend ( dotBackend )
diff --git a/src/full/Agda/Interaction/Highlighting/Dot/Backend.hs b/src/full/Agda/Interaction/Highlighting/Dot/Backend.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Dot/Backend.hs
@@ -0,0 +1,247 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Highlighting.Dot.Backend
+  ( dotBackend
+  ) where
+
+import Agda.Interaction.Highlighting.Dot.Base (renderDotToFile)
+
+import Control.Monad.Except
+  ( ExceptT
+  , runExceptT
+  , MonadError(throwError)
+  )
+import Control.Monad.IO.Class
+  ( MonadIO(..)
+  )
+import Control.DeepSeq
+
+import Data.HashSet (HashSet)
+import Data.Map (Map)
+import Data.Set (Set)
+import qualified Data.HashSet as HashSet
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.Maybe
+import qualified Data.Text.Lazy as L
+
+import GHC.Generics (Generic)
+
+import Agda.Compiler.Backend (Backend(..), Backend'(..), Definition, Recompile(..))
+import Agda.Compiler.Common (curIF, IsMain)
+
+import Agda.Interaction.FindFile (findFile, srcFilePath)
+import Agda.Interaction.Library
+import Agda.Interaction.Options
+  ( ArgDescr(ReqArg)
+  , Flag
+  , OptDescr(..)
+  )
+
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+
+import Agda.TypeChecking.Monad
+  ( Interface(iImportedModules)
+  , MonadTCError
+  , ReadTCState
+  , MonadTCM(..)
+  , genericError
+  , reportSDoc
+  , getAgdaLibFiles
+  )
+import Agda.TypeChecking.Pretty
+
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional
+  (Graph, WithUniqueInt)
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+import Agda.Syntax.Common.Pretty ( prettyShow )
+
+-- ------------------------------------------------------------------------
+
+data DotFlags = DotFlags
+  { dotFlagDestination :: Maybe FilePath
+  , dotFlagLibraries   :: Maybe (HashSet String)
+    -- ^ Only include modules from the given libraries.
+  } deriving (Eq, Generic)
+
+instance NFData DotFlags
+
+defaultDotFlags :: DotFlags
+defaultDotFlags = DotFlags
+  { dotFlagDestination = Nothing
+  , dotFlagLibraries   = Nothing
+  }
+
+dotFlagsDescriptions :: [OptDescr (Flag DotFlags)]
+dotFlagsDescriptions =
+  [ Option [] ["dependency-graph"] (ReqArg dependencyGraphFlag "FILE")
+              "generate a Dot file with a module dependency graph"
+  , Option [] ["dependency-graph-include"]
+      (ReqArg includeFlag "LIBRARY")
+      "include modules from the given library (default: all modules)"
+  ]
+
+dependencyGraphFlag :: FilePath -> Flag DotFlags
+dependencyGraphFlag f o = return $ o { dotFlagDestination = Just f }
+
+includeFlag :: String -> Flag DotFlags
+includeFlag l o = return $
+  o { dotFlagLibraries =
+        case dotFlagLibraries o of
+          Nothing -> Just (HashSet.singleton l)
+          Just s  -> Just (HashSet.insert l s)
+    }
+
+data DotCompileEnv = DotCompileEnv
+  { dotCompileEnvDestination :: FilePath
+  , dotCompileEnvLibraries   :: Maybe (HashSet String)
+    -- ^ Only include modules from the given libraries.
+  }
+
+-- Currently unused
+data DotModuleEnv = DotModuleEnv
+
+data DotModule = DotModule
+  { dotModuleName          :: TopLevelModuleName
+  , dotModuleImportedNames :: Set TopLevelModuleName
+  , dotModuleInclude       :: Bool
+    -- ^ Include the module in the graph?
+  }
+
+-- | Currently unused
+data DotDef = DotDef
+
+dotBackend :: Backend
+dotBackend = Backend dotBackend'
+
+dotBackend' :: Backend' DotFlags DotCompileEnv DotModuleEnv DotModule DotDef
+dotBackend' = Backend'
+  { backendName           = "Dot"
+  , backendVersion        = Nothing
+  , options               = defaultDotFlags
+  , commandLineFlags      = dotFlagsDescriptions
+  , isEnabled             = isJust . dotFlagDestination
+  , preCompile            = asTCErrors . preCompileDot
+  , preModule             = preModuleDot
+  , compileDef            = compileDefDot
+  , postModule            = postModuleDot
+  , postCompile           = postCompileDot
+  , scopeCheckingSuffices = True
+  , mayEraseType          = const $ return True
+  }
+
+-- | Convert a general "MonadError String m" into "MonadTCError m".
+asTCErrors :: MonadTCError m => ExceptT String m b -> m b
+asTCErrors t = either genericError return =<< runExceptT t
+
+preCompileDot
+  :: MonadError String m
+  => DotFlags
+  -> m DotCompileEnv
+preCompileDot d = case dotFlagDestination d of
+  Just dest -> return $ DotCompileEnv
+    { dotCompileEnvDestination = dest
+    , dotCompileEnvLibraries   = dotFlagLibraries d
+    }
+  Nothing ->
+    throwError "The Dot backend was invoked without being enabled!"
+
+preModuleDot
+  :: Applicative m
+  => DotCompileEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> Maybe FilePath
+  -> m (Recompile DotModuleEnv DotModule)
+preModuleDot _cenv _main _moduleName _ifacePath = pure $ Recompile DotModuleEnv
+
+compileDefDot
+  :: Applicative m
+  => DotCompileEnv
+  -> DotModuleEnv
+  -> IsMain
+  -> Definition
+  -> m DotDef
+compileDefDot _cenv _menv _main _def = pure DotDef
+
+postModuleDot
+  :: (MonadTCM m, ReadTCState m)
+  => DotCompileEnv
+  -> DotModuleEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> [DotDef]
+  -> m DotModule
+postModuleDot cenv DotModuleEnv _main m _defs = do
+  i <- curIF
+  let importedModuleNames = Set.fromList $ fst <$> (iImportedModules i)
+  include <- case dotCompileEnvLibraries cenv of
+    Nothing -> return True
+    Just ls -> liftTCM $ do
+      f    <- findFile m
+      libs <- getAgdaLibFiles (srcFilePath f) m
+
+      let incLibs = filter (\l -> _libName l `HashSet.member` ls) libs
+          inLib   = not (null incLibs)
+
+      reportSDoc "dot.include" 10 $ do
+        let name = pretty m
+            list = nest 2 . vcat . map (text . _libName)
+        if inLib then
+          fsep
+            ([ "Including"
+             , name
+             ] ++
+             pwords "because it is in the following libraries:") $$
+          list incLibs
+        else
+          fsep
+            (pwords "Not including" ++
+             [name <> ","] ++
+             pwords "which is in the following libraries:") $$
+          list libs
+
+      return inLib
+
+  return $ DotModule
+    { dotModuleName          = m
+    , dotModuleImportedNames = importedModuleNames
+    , dotModuleInclude       = include
+    }
+
+postCompileDot
+  :: (MonadIO m, ReadTCState m)
+  => DotCompileEnv
+  -> IsMain
+  -> Map TopLevelModuleName DotModule
+  -> m ()
+postCompileDot cenv _main modulesByName =
+  renderDotToFile moduleGraph (dotCompileEnvDestination cenv)
+  where
+  -- Only the keys of this map are used.
+  modulesToInclude =
+    Map.filter dotModuleInclude modulesByName
+
+  moduleGraph :: Graph (WithUniqueInt L.Text) ()
+  moduleGraph =
+    Graph.renameNodesMonotonic (fmap (L.pack . prettyShow)) $
+    Graph.transitiveReduction $
+    Graph.filterNodesKeepingEdges
+      (\n -> Graph.otherValue n `Map.member` modulesToInclude) $
+    -- The following use of transitive reduction should not affect the
+    -- semantics. It tends to make the graph smaller, so it might
+    -- improve the overall performance of the code, but I did not
+    -- verify this.
+    Graph.transitiveReduction $
+    Graph.addUniqueInts $
+    Graph.fromEdges $
+    concatMap
+       (\ (name, m) ->
+          [ Graph.Edge
+              { source = name
+              , target = target
+              , label  = ()
+              }
+          | target <- Set.toList $ dotModuleImportedNames m
+          ]) $
+    Map.toList modulesByName
diff --git a/src/full/Agda/Interaction/Highlighting/Dot/Base.hs b/src/full/Agda/Interaction/Highlighting/Dot/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Dot/Base.hs
@@ -0,0 +1,45 @@
+{-# LANGUAGE GADTs #-}
+-- | Generate an import dependency graph for a given module.
+
+module Agda.Interaction.Highlighting.Dot.Base
+  ( renderDotToFile
+  , renderDot
+  , DotGraph
+  ) where
+
+import Control.Monad.IO.Class
+
+import qualified Data.Set as S
+
+import qualified Data.Text.Lazy as L
+import qualified Data.Text.Lazy.Encoding as E
+import qualified Data.ByteString.Lazy as BS
+
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional
+  (Graph, WithUniqueInt)
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+
+-- | Graph structure
+type DotGraph = Graph (WithUniqueInt L.Text) ()
+
+-- * Graph rendering
+
+renderDot :: DotGraph -> L.Text
+renderDot g = L.unlines $ concat
+  [ [ "digraph dependencies {" ]
+  , [ L.concat ["   ", show' nodeId, "[label=\"", label, "\"];"]
+    | Graph.WithUniqueInt nodeId label <- S.toList $ Graph.nodes g
+    ]
+  , [ L.concat ["   ", show' r1, " -> ", show' r2, ";"]
+    | Graph.Edge
+        { source = Graph.WithUniqueInt r1 _
+        , target = Graph.WithUniqueInt r2 _
+        } <- Graph.edges g
+    ]
+  , ["}"]
+  ]
+  where
+  show' = L.pack . ("m" ++) . show
+
+renderDotToFile :: MonadIO m => DotGraph -> FilePath -> m ()
+renderDotToFile dot fp = liftIO $ BS.writeFile fp $ E.encodeUtf8 $ renderDot dot
diff --git a/src/full/Agda/Interaction/Highlighting/Emacs.hs b/src/full/Agda/Interaction/Highlighting/Emacs.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Emacs.hs
@@ -0,0 +1,100 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Functions which give precise syntax highlighting info to Emacs.
+
+module Agda.Interaction.Highlighting.Emacs
+  ( lispifyHighlightingInfo
+  , lispifyTokenBased
+  ) where
+
+import Prelude hiding (null)
+
+import Agda.Interaction.Highlighting.Common
+import Agda.Interaction.Highlighting.Precise
+import Agda.Interaction.Highlighting.Range (Range(..))
+import Agda.Interaction.EmacsCommand
+import Agda.Interaction.Response
+import Agda.TypeChecking.Monad (HighlightingMethod(..), ModuleToSource)
+import Agda.Utils.FileName (filePath)
+import Agda.Utils.IO.TempFile (writeToTempFile)
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.String (quote)
+
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Data.Maybe
+
+import Agda.Utils.Null
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- Read/show functions
+
+-- | Shows meta information in such a way that it can easily be read
+-- by Emacs.
+
+showAspects
+  :: ModuleToSource
+     -- ^ Must contain a mapping for the definition site's module, if any.
+  -> (Range, Aspects) -> Lisp String
+showAspects modFile (r, m) = L $
+    (map (A . show) [from r, to r])
+      ++
+    [L $ map A $ toAtoms m]
+      ++
+    dropNils (
+      [lispifyTokenBased (tokenBased m)]
+        ++
+      [A $ ifNull (note m) "nil" quote]
+        ++
+      maybeToList (defSite <$> definitionSite m))
+  where
+  defSite (DefinitionSite m p _ _) =
+    Cons (A $ quote $ filePath f) (A $ show p)
+    where f = Map.findWithDefault __IMPOSSIBLE__ m modFile
+
+  dropNils = List.dropWhileEnd (== A "nil")
+
+-- | Formats the 'TokenBased' tag for the Emacs backend. No quotes are
+-- added.
+
+lispifyTokenBased :: TokenBased -> Lisp String
+lispifyTokenBased TokenBased        = A "t"
+lispifyTokenBased NotOnlyTokenBased = A "nil"
+
+-- | Turns syntax highlighting information into a list of
+-- S-expressions.
+
+-- TODO: The "go-to-definition" targets can contain long strings
+-- (absolute paths to files). At least one of these strings (the path
+-- to the current module) can occur many times. Perhaps it would be a
+-- good idea to use a more compact format.
+
+lispifyHighlightingInfo
+  :: HighlightingInfo
+  -> RemoveTokenBasedHighlighting
+  -> HighlightingMethod
+  -> ModuleToSource
+     -- ^ Must contain a mapping for every definition site's module.
+  -> IO (Lisp String)
+lispifyHighlightingInfo h remove method modFile =
+  case chooseHighlightingMethod h method of
+    Direct   -> direct
+    Indirect -> indirect
+  where
+  info :: [Lisp String]
+  info = (case remove of
+                RemoveHighlighting -> A "remove"
+                KeepHighlighting   -> A "nil") :
+             map (showAspects modFile) (toList h)
+
+  direct :: IO (Lisp String)
+  direct = return $ L (A "agda2-highlight-add-annotations" :
+                         map Q info)
+
+  indirect :: IO (Lisp String)
+  indirect = do
+    filepath <- writeToTempFile (prettyShow $ L info)
+    return $ L [ A "agda2-highlight-load-and-delete-action"
+               , A (quote filepath)
+               ]
diff --git a/src/full/Agda/Interaction/Highlighting/FromAbstract.hs b/src/full/Agda/Interaction/Highlighting/FromAbstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/FromAbstract.hs
@@ -0,0 +1,705 @@
+-- | Extract highlighting syntax from abstract syntax.
+--
+-- Implements one big fold over abstract syntax.
+
+-- {-# OPTIONS_GHC -fwarn-unused-imports #-}  -- Data.Semigroup is redundant in later GHC versions
+{-# OPTIONS_GHC -fwarn-unused-binds   #-}
+
+module Agda.Interaction.Highlighting.FromAbstract
+  ( runHighlighter
+  , NameKinds
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Applicative
+import Control.Monad.Reader  ( MonadReader(..), asks, Reader, runReader )
+
+import qualified Data.Map      as Map
+import           Data.Maybe
+import           Data.Semigroup       ( Semigroup(..) )          -- for ghc 8.0
+import           Data.Void            ( Void )
+
+import           Agda.Interaction.Highlighting.Precise hiding ( singleton )
+import qualified Agda.Interaction.Highlighting.Precise as H
+import           Agda.Interaction.Highlighting.Range   ( rToR )  -- Range is ambiguous
+
+import           Agda.Syntax.Abstract                ( IsProjP(..) )
+import qualified Agda.Syntax.Abstract      as A
+import           Agda.Syntax.Common        as Common
+import           Agda.Syntax.Concrete                ( FieldAssignment'(..) )
+import qualified Agda.Syntax.Concrete.Name as C
+import           Agda.Syntax.Info                    ( ModuleInfo(..) )
+import           Agda.Syntax.Literal
+import qualified Agda.Syntax.Position      as P
+import           Agda.Syntax.Position                ( Range, HasRange, getRange, noRange )
+import           Agda.Syntax.Scope.Base              ( AbstractName(..), ResolvedName(..), exactConName )
+import           Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Monad
+  hiding (ModuleInfo, MetaInfo, Primitive, Constructor, Record, Function, Datatype)
+
+import           Agda.Utils.Function
+import           Agda.Utils.Functor
+import           Agda.Utils.List                     ( initLast1 )
+import           Agda.Utils.List1                    ( List1 )
+import qualified Agda.Utils.List1          as List1
+import           Agda.Utils.Maybe
+import qualified Agda.Utils.Maybe.Strict   as Strict
+import           Agda.Syntax.Common.Pretty
+import           Agda.Utils.Singleton
+import           Agda.Utils.Size
+
+-- Entry point:
+-- | Create highlighting info for some piece of syntax.
+runHighlighter
+  :: Hilite a
+  => TopLevelModuleName
+     -- ^ The current top-level module's name.
+  -> NameKinds -> a -> HighlightingInfoBuilder
+runHighlighter top kinds x =
+  runReader (hilite x) $
+  HiliteEnv
+    { hleNameKinds         = kinds
+    , hleCurrentModuleName = top
+    }
+
+-- | Environment of the highlighter.
+data HiliteEnv = HiliteEnv
+  { hleNameKinds :: NameKinds
+      -- ^ Function mapping qualified names to their kind.
+  , hleCurrentModuleName :: TopLevelModuleName
+      -- ^ The current top-level module's name. Used for consistency
+      -- checking.
+  }
+
+-- | A function mapping names to the kind of name they stand for.
+type NameKinds = A.QName -> Maybe NameKind
+
+-- | Highlighting monad.
+type HiliteM = Reader HiliteEnv
+
+-- | Highlighter.
+
+type Hiliter = HiliteM HighlightingInfoBuilder
+
+instance Monoid Hiliter where
+  mempty  = pure mempty
+  mappend = (<>)
+
+-- | Traversal to extract highlighting information.
+
+class Hilite a where
+  hilite :: a -> Hiliter
+
+  default hilite :: (Foldable t, Hilite b, t b ~ a) => a -> Hiliter
+  hilite = foldMap hilite
+
+-- * Generic instances
+---------------------------------------------------------------------------
+
+instance Hilite a => Hilite [a]
+instance Hilite a => Hilite (List1 a)
+instance Hilite a => Hilite (Maybe a)
+instance Hilite a => Hilite (Ranged a)
+instance Hilite a => Hilite (WithHiding a)
+
+instance Hilite Void where
+  hilite _ = mempty
+
+instance (Hilite a, Hilite b) => Hilite (Either a b) where
+  hilite = either hilite hilite
+
+instance (Hilite a, Hilite b) => Hilite (a, b) where
+  hilite (a, b) = hilite a <> hilite b
+
+-- * Major syntactic categories
+---------------------------------------------------------------------------
+
+-- | Reengineered from the old Geniplate-implemented highlighting extraction.
+-- This was the old procedure:
+--
+-- Traversal over declaration in abstract syntax that collects the
+-- following hiliting information:
+--
+-- [1. @constructorInfo@ (highest prio)]
+-- 2. @theRest@ (medium prio)
+-- 3. @nameInfo@ (lowest prio)
+--
+-- @nameInfo@:
+--   "All names mentioned in the syntax tree (not bound variables)."
+-- For each possibly ambiguous name (QName and AmbiguousQName)
+-- that not isExtendedLambdaName,
+-- do @hiliteAmbiguous@ (used to be called@generate@).
+--
+-- @constructorInfo@ (only when highlighting level == Full):
+--   "After the code has been type checked more information may be
+--   available for overloaded constructors, and
+--   generateConstructorInfo takes advantage of this information.
+--   Note, however, that highlighting for overloaded constructors is
+--   included also in nameInfo."
+-- This is not computed by recursion over the abstract syntax,
+-- but gets the constructor names stDisambiguatedNames
+-- that fall within the bounds of the current declaration.
+--
+-- @theRest@:
+--   Bound variables, dotted patterns, record fields, module names,
+--   the "as" and "to" symbols and some other things.
+--
+-- Here is a table what @theRest@ used to collect:
+--
+-- ---------------------------------------------------------------------
+-- | A.Expr
+-- ---------------------------------------------------------------------
+-- | getVarAndField (Expr) | A.Var                       | bound
+-- | getVarAndField        | A.Rec(Update)               | field
+-- | getExpr        (Expr) | A.PatternSyn                | patsyn
+-- | getExpr               | A.Macro                     | macro
+-- ---------------------------------------------------------------------
+-- | A.LetBinding
+-- ---------------------------------------------------------------------
+-- | getLet                | A.LetBind                   | bound
+-- | getLet                | A.LetDeclaredVariable       | bound
+-- ---------------------------------------------------------------------
+-- | A.LamBinding
+-- ---------------------------------------------------------------------
+-- | getLam                | A.Binder under A.DomainFree | bound
+-- | getTyped              | A.Binder under A.TBind      | bound
+-- ---------------------------------------------------------------------
+-- | A.Pattern'
+-- ---------------------------------------------------------------------
+-- | getPattern(Syn)       | A.VarP                      | bound
+-- | getPattern(Syn)       | A.AsP                       | bound
+-- | getPattern(Syn)       | A.DotP (not isProjP)        | DottedPattern
+-- | getPattern(Syn)       | A.RecP                      | field
+-- | getPattern(Syn)       | A.PatternSynP               | patsyn
+-- ---------------------------------------------------------------------
+-- | A.Declaration
+-- ---------------------------------------------------------------------
+-- | getFieldDecl          | A.Field under A.RecDef      | field
+-- | getPatSynArgs         | A.PatternSynDef             | bound
+-- | getPragma             | A.BuiltinPragma...          | keyword
+-- ---------------------------------------------------------------------
+-- | A.NamedArg (polymorphism not supported in geniplate)
+-- ---------------------------------------------------------------------
+-- | getNamedArg           | NamedArg a                  | nameOf
+-- | getNamedArgE          | NamedArg Exp                | nameOf
+-- | getNamedArgP          | NamedArg Pattern            | nameOf
+-- | getNamedArgB          | NamedArg BindName           | nameOf
+-- | getNamedArgL          | NamedArg LHSCore            | nameOf
+--
+-- | getModuleName         | A.MName                     | mod
+-- | getModuleInfo         | ModuleInfo                  | asName, (range of as,to)
+-- | getQuantityAttr       | Common.Quantity             | Symbol (if range)
+
+instance Hilite A.RecordDirectives where
+  hilite (RecordDirectives _ _ _ c) = hilite c
+
+instance Hilite A.Declaration where
+  hilite = \case
+      A.Axiom _ax _di ai _occ x e            -> hl ai <> hl x <> hl e
+      A.Generalize _names _di ai x e         -> hl ai <> hl x <> hl e
+      A.Field _di x e                        -> hlField x <> hl e
+      A.Primitive _di x e                    -> hl x <> hl e
+      A.Mutual _mi ds                        -> hl ds
+      A.Section _r er x tel ds               -> hl er <> hl x <> hl tel <> hl ds
+      A.Apply mi er x a _ci dir              -> hl mi <> hl er <> hl x <>
+                                                hl a <> hl dir
+      A.Import mi x dir                      -> hl mi <> hl x <> hl dir
+      A.Open mi x dir                        -> hl mi <> hl x <> hl dir
+      A.FunDef _di x cs                      -> hl x <> hl cs
+      A.DataSig _di er x tel e               -> hl er <> hl x <> hl tel <> hl e
+      A.DataDef _di x _uc pars cs            -> hl x <> hl pars <> hl cs
+      A.RecSig _di er x tel e                -> hl er <> hl x <> hl tel <> hl e
+      A.RecDef _di x _uc dir bs e ds         -> hl x <> hl dir <> hl bs <> hl e <> hl ds
+      A.PatternSynDef x xs p                 -> hl x <> hl xs <> hl p
+      A.UnquoteDecl _mi _di xs e             -> hl xs <> hl e
+      A.UnquoteDef _di xs e                  -> hl xs <> hl e
+      A.UnquoteData _i xs _uc _j cs e        -> hl xs <> hl cs <> hl e
+      A.ScopedDecl s ds                      -> hl ds
+      A.Pragma _r pragma                     -> hl pragma
+      A.UnfoldingDecl _r names               -> hl names
+    where
+    hl      a = hilite a
+    hlField x = hiliteField (concreteQualifier x) (concreteBase x) (Just $ bindingSite x)
+
+instance Hilite A.Pragma where
+  hilite = \case
+    A.OptionsPragma _strings     -> mempty
+    A.BuiltinPragma b x          -> singleAspect Keyword b <> hilite x
+    A.BuiltinNoDefPragma b k x   -> singleAspect Keyword b <> hiliteQName (Just $ kindOfNameToNameKind k) x
+    A.CompilePragma b x _foreign -> singleAspect Keyword b <> hilite x
+    A.RewritePragma r xs         -> singleAspect Keyword r <> hilite xs
+    A.StaticPragma x             -> hilite x
+    A.EtaPragma x                -> hilite x
+    A.InjectivePragma x          -> hilite x
+    A.NotProjectionLikePragma x  -> hilite x
+    A.InlinePragma _inline x     -> hilite x
+    A.DisplayPragma x ps e       -> hilite x <> hilite ps <> hilite e
+
+instance Hilite A.Expr where
+  hilite = \case
+      A.Var x                       -> hl $ A.BindName x        -- bound variable like binder
+      A.Def' q _                    -> hiliteQName Nothing q
+      A.Proj _o qs                  -> hiliteAmbiguousQName Nothing qs  -- Issue #4604: not: hiliteProjection qs
+                                         -- Names from @open R r@ should not be highlighted as projections
+      A.Con qs                      -> hiliteAmbiguousQName Nothing qs  -- TODO? Con aspect
+      A.PatternSyn qs               -> hilitePatternSynonym qs
+      A.Macro q                     -> hiliteQName (Just Macro) q
+      A.Lit _r l                    -> hl l
+      A.QuestionMark _mi _ii        -> mempty
+      A.Underscore _mi              -> mempty
+      A.Dot _r e                    -> hl e                   -- TODO? Projection?
+      A.App _r e es                 -> hl e <> hl es
+      A.WithApp _r e es             -> hl e <> hl es
+      A.Lam _r bs e                 -> hl bs <> hl e
+      A.AbsurdLam _r _h             -> mempty
+      A.ExtendedLam _r _di er _q cs -> hl er <> hl cs -- No hilighting of generated extended lambda name!
+      A.Pi _r tel b                 -> hl tel <> hl b
+      A.Generalized _qs e           -> hl e
+      A.Fun _r a b                  -> hl a <> hl b
+      A.Let _r bs e                 -> hl bs <> hl e
+      A.Rec _r ass                  -> hl ass
+      A.RecUpdate _r e ass          -> hl e <> hl ass
+      A.ScopedExpr _ e              -> hl e
+      A.Quote _r                    -> mempty
+      A.QuoteTerm _r                -> mempty
+      A.Unquote _r                  -> mempty
+      A.DontCare e                  -> hl e
+    where
+    hl a = hilite a
+
+instance (Hilite a, IsProjP a) => Hilite (A.Pattern' a) where
+  hilite = \case
+      A.VarP x               -> hl x
+      A.ConP _i qs es        -> hiliteInductiveConstructor qs <> hl es
+        -- No matching on coinductive constructors, thus, can determine NameKind here.
+      A.ProjP _r _o qs       -> hiliteProjection qs
+      A.DefP _r qs es        -> hl qs <> hl es
+      A.WildP _r             -> mempty
+      A.AsP _r x p           -> hl x <> hl p
+      A.DotP r e             -> case isProjP e of
+                                  Nothing       -> singleOtherAspect DottedPattern r <> hl e
+                                  Just (_o, qs) -> hiliteProjection qs
+      A.AbsurdP _r           -> mempty
+      A.LitP _r l            -> hl l
+      A.PatternSynP _r qs es -> hilitePatternSynonym qs <> hl es
+      A.RecP _r ps           -> hl ps
+      A.EqualP _r ps         -> hl ps
+      A.WithP _ p            -> hl p
+      A.AnnP _r a p          -> hl p
+
+    where
+    hl a = hilite a
+
+instance Hilite Literal where
+  hilite = \case
+    LitNat{}                 -> mempty
+    LitWord64{}              -> mempty
+    LitFloat{}               -> mempty
+    LitString{}              -> mempty
+    LitChar{}                -> mempty
+    LitQName x               -> hilite x
+    LitMeta _fileName _id    -> mempty
+
+-- * Minor syntactic categories
+---------------------------------------------------------------------------
+
+instance Hilite A.LHS where
+  hilite (A.LHS _r lhs) = hilite lhs
+
+instance (Hilite a, IsProjP a) => Hilite (A.LHSCore' a) where
+  hilite = \case
+    A.LHSHead q ps       -> hilite q   <> hilite ps
+    A.LHSProj q lhs ps   -> hilite lhs <> hilite q   <> hilite ps -- TODO? Projection?
+    A.LHSWith lhs wps ps -> hilite lhs <> hilite wps <> hilite ps
+
+instance Hilite A.RHS where
+  hilite = \case
+      A.RHS e _ce                          -> hl e
+      A.AbsurdRHS                          -> mempty
+      A.WithRHS _q es cs                   -> hl es  <> hl cs  -- No highlighting for with-function-name!
+      A.RewriteRHS eqs strippedPats rhs wh -> hl eqs <> hl strippedPats <> hl rhs <> hl wh
+    where
+    hl a = hilite a
+
+instance (HasRange n, Hilite p, Hilite e) => Hilite (RewriteEqn' x n p e) where
+  hilite = \case
+    Rewrite es    -> hilite $ fmap snd es
+    Invert _x pes -> hilite pes
+
+instance Hilite a => Hilite (A.Clause' a) where
+  hilite (A.Clause lhs strippedPats rhs wh _catchall) =
+    hilite lhs <> hilite strippedPats <> hilite rhs <> hilite wh
+
+instance Hilite A.ProblemEq where
+  hilite (A.ProblemEq p _t _dom) = hilite p
+
+instance Hilite A.WhereDeclarations where
+  hilite (A.WhereDecls m _ ds) = hilite m <> hilite ds
+
+instance Hilite A.GeneralizeTelescope where
+  hilite (A.GeneralizeTel _gen tel) = hilite tel
+
+instance Hilite A.DataDefParams where
+  hilite (A.DataDefParams _gen pars) = hilite pars
+
+instance Hilite A.ModuleApplication where
+  hilite = \case
+    A.SectionApp tel x es    -> hilite tel <> hilite x <> hilite es
+    A.RecordModuleInstance x -> hilite x
+
+instance Hilite A.LetBinding where
+  hilite = \case
+      A.LetBind    _r ai x t e     -> hl ai <> hl x <> hl t <> hl e
+      A.LetPatBind _r p e          -> hl p  <> hl e
+      A.LetApply mi er x es _c dir -> hl mi <> hl er <> hl x <>
+                                      hl es <> hl dir
+      A.LetOpen mi x dir           -> hl mi <> hl x <> hl dir
+      A.LetDeclaredVariable x      -> hl x
+    where
+    hl x = hilite x
+
+instance Hilite A.TypedBindingInfo where
+  hilite (A.TypedBindingInfo x _) = hilite x
+
+instance Hilite A.TypedBinding where
+  hilite = \case
+    A.TBind _r tac binds e -> hilite tac <> hilite binds <> hilite e
+    A.TLet _r binds        -> hilite binds
+
+instance Hilite A.LamBinding where
+  hilite = \case
+    A.DomainFree tac binds -> hilite tac <> hilite binds
+    A.DomainFull bind      -> hilite bind
+
+instance Hilite a => Hilite (A.Binder' a) where
+  hilite (A.Binder p x) = hilite p <> hilite x
+
+instance Hilite A.BindName where
+  hilite (A.BindName x) = hiliteBound x
+
+instance Hilite a => Hilite (FieldAssignment' a) where
+  hilite (FieldAssignment x e) = hiliteField [] x Nothing <> hilite e
+
+instance (Hilite a, HasRange n) => Hilite (Named n a) where
+  hilite (Named mn e)
+    =  maybe mempty (singleAspect $ Name (Just Argument) False) mn
+    <> hilite e
+
+instance Hilite a => Hilite (Arg a) where
+  hilite (Arg ai e) = hilite ai <> hilite e
+
+instance Hilite ArgInfo where
+  hilite (ArgInfo _hiding modality _origin _fv _a) = hilite modality
+
+instance Hilite Modality where
+  hilite (Modality _relevance quantity _cohesion) = hilite quantity
+
+-- | If the 'Quantity' attribute comes with a 'Range', highlight the
+-- corresponding attribute as 'Symbol'.
+instance Hilite Quantity where
+  hilite = singleAspect Symbol
+
+-- | Erasure attributes are highlighted as symbols.
+instance Hilite Erased where
+  hilite = singleAspect Symbol
+
+instance Hilite ModuleInfo where
+  hilite (ModuleInfo _r rAsTo asName _open _impDir)
+    =  singleAspect Symbol rAsTo            -- TODO: 'to' already covered by A.ImportDirective
+    <> maybe mempty hiliteAsName asName
+    -- <> hilite impDir                     -- Should be covered by A.ImportDirective
+    where
+    hiliteAsName :: C.Name -> Hiliter
+    hiliteAsName n = hiliteCName [] n noRange Nothing $ nameAsp Module
+
+instance (Hilite m, Hilite n, Hilite (RenamingTo m), Hilite (RenamingTo n))
+       => Hilite (ImportDirective' m n) where
+  hilite (ImportDirective _r using hiding renaming _ropen) =
+    hilite using <> hilite hiding <> hilite renaming
+
+instance (Hilite m, Hilite n) => Hilite (Using' m n) where
+  hilite = \case
+    UseEverything -> mempty
+    Using using   -> hilite using
+
+instance (Hilite m, Hilite n, Hilite (RenamingTo m), Hilite (RenamingTo n))
+       => Hilite (Renaming' m n) where
+  hilite (Renaming from to _fixity rangeKwTo)
+    =  hilite from
+    <> singleAspect Symbol rangeKwTo
+         -- Currently, the "to" is already highlited by rAsTo above.
+         -- TODO: remove the "to" ranges from rAsTo.
+    <> hilite (RenamingTo to)
+
+instance (Hilite m, Hilite n) => Hilite (ImportedName' m n) where
+  hilite = \case
+    ImportedModule m -> hilite m
+    ImportedName   n -> hilite n
+
+-- * Highlighting of names
+---------------------------------------------------------------------------
+
+instance Hilite DisambiguatedName where
+  hilite (DisambiguatedName k x) = hiliteQName (Just k) x
+
+instance Hilite ResolvedName where
+  hilite = \case
+    VarName           x _bindSrc -> hiliteBound x
+    DefinedName  _acc x _suffix  -> hilite $ anameName x
+    FieldName         xs         -> hiliteProjection $ A.AmbQ $ fmap anameName xs
+    ConstructorName i xs         -> hiliteAmbiguousQName k $ A.AmbQ $ fmap anameName xs
+      where k = kindOfNameToNameKind <$> exactConName i
+    PatternSynResName xs         -> hilitePatternSynonym $ A.AmbQ $ fmap anameName xs
+    UnknownName                  -> mempty
+
+instance Hilite A.QName where
+  hilite = hiliteQName Nothing
+
+instance Hilite A.AmbiguousQName where
+  hilite = hiliteAmbiguousQName Nothing
+
+instance Hilite A.ModuleName where
+  hilite m@(A.MName xs) = hiliteModule (isTopLevelModule, m)
+    where
+    isTopLevelModule =
+      case mapMaybe (P.rangeModule . A.nameBindingSite) xs of
+        []      -> False
+        top : _ ->
+          rawTopLevelModuleName top ==
+          rawTopLevelModuleNameForModuleName m
+
+  -- Andreas, 2020-09-29, issue #4952.
+-- The target of a @renaming@ clause needs to be highlighted in a special way.
+newtype RenamingTo a = RenamingTo a
+
+instance Hilite (RenamingTo A.QName) where
+  -- Andreas, 2020-09-29, issue #4952.
+  -- Do not include the bindingSite, because the HTML backed turns it into garbage.
+  hilite (RenamingTo q) = do
+    kind <- asks hleNameKinds <&> ($ q)
+    hiliteAName q False $ nameAsp' kind
+
+instance Hilite (RenamingTo A.ModuleName) where
+  -- Andreas, 2020-09-29, issue #4952.
+  -- Do not include the bindingSite, because the HTML backed turns it into garbage.
+  hilite (RenamingTo (A.MName ns)) = flip foldMap ns $ \ n ->
+    hiliteCName [] (A.nameConcrete n) noRange Nothing $ nameAsp Module
+
+instance (Hilite (RenamingTo m), Hilite (RenamingTo n))
+       => Hilite (RenamingTo (ImportedName' m n)) where
+  hilite (RenamingTo x) = case x of
+    ImportedModule m -> hilite (RenamingTo m)
+    ImportedName   n -> hilite (RenamingTo n)
+
+hiliteQName
+  :: Maybe NameKind   -- ^ Is 'NameKind' already known from the context?
+  -> A.QName
+  -> Hiliter
+hiliteQName mkind q
+  | isExtendedLambdaName q = mempty
+  | isAbsurdLambdaName   q = mempty
+  | otherwise = do
+      kind <- ifJust mkind (pure . Just) {-else-} $ asks hleNameKinds <&> ($ q)
+      hiliteAName q True $ nameAsp' kind
+
+-- | Takes the first 'NameKind'.  Binding site only included if unique.
+hiliteAmbiguousQName
+  :: Maybe NameKind   -- ^ Is 'NameKind' already known from the context?
+  -> A.AmbiguousQName
+  -> Hiliter
+hiliteAmbiguousQName mkind (A.AmbQ qs) = do
+  kind <- ifJust mkind (pure . Just) {-else-} $ do
+    kinds <- asks hleNameKinds
+    pure $ listToMaybe $ List1.catMaybes $ fmap kinds qs
+      -- Ulf, 2014-06-03: [issue1064] It's better to pick the first rather
+      -- than doing no highlighting if there's an ambiguity between an
+      -- inductive and coinductive constructor.
+  flip foldMap qs $ \ q ->
+    hiliteAName q include $ nameAsp' kind
+  where
+  include = List1.allEqual $ fmap bindingSite qs
+
+hiliteBound :: A.Name -> Hiliter
+hiliteBound x =
+  hiliteCName [] (A.nameConcrete x) noRange (Just $ A.nameBindingSite x) $ nameAsp Bound
+
+hiliteInductiveConstructor :: A.AmbiguousQName -> Hiliter
+hiliteInductiveConstructor = hiliteAmbiguousQName $ Just $ Constructor Inductive
+
+hilitePatternSynonym :: A.AmbiguousQName -> Hiliter
+hilitePatternSynonym = hiliteInductiveConstructor  -- There are no coinductive pattern synonyms!?
+
+hiliteProjection :: A.AmbiguousQName -> Hiliter
+hiliteProjection = hiliteAmbiguousQName (Just Field)
+
+hiliteField :: [C.Name] -> C.Name -> Maybe Range -> Hiliter
+hiliteField xs x bindingR = hiliteCName xs x noRange bindingR $ nameAsp Field
+
+-- For top level modules, we set the binding site to the beginning of the file
+-- so that clicking on an imported module will jump to the beginning of the file
+-- which defines this module.
+hiliteModule :: (Bool, A.ModuleName) -> Hiliter
+hiliteModule (isTopLevelModule, A.MName []) = mempty
+hiliteModule (isTopLevelModule, A.MName (n:ns)) =
+  hiliteCName
+    (map A.nameConcrete ms)
+    (A.nameConcrete m)
+    noRange
+    mR
+    (nameAsp Module)
+  where
+  (ms, m) = initLast1 n ns
+  mR = Just $
+       applyWhen isTopLevelModule P.beginningOfFile $
+       A.nameBindingSite m
+
+-- This was Highlighting.Generate.nameToFile:
+-- | Converts names to suitable 'File's.
+hiliteCName
+  :: [C.Name]
+     -- ^ The name qualifier (may be empty).
+  -> C.Name     -- ^ The base name.
+  -> Range
+     -- ^ The 'Range' of the name in its fixity declaration (if any).
+  -> Maybe Range
+     -- ^ The definition site of the name. The calculated
+     --   meta information is extended with this information, if possible.
+  -> (Bool -> Aspects)
+     -- ^ Meta information to be associated with the name.
+     --   The argument is 'True' iff the name is an operator.
+  -> Hiliter
+hiliteCName xs x fr mR asp = do
+  env <- ask
+  -- We don't care if we get any funny ranges.
+  if all (== Just (hleCurrentModuleName env)) moduleNames
+  then pure $
+    frFile <>
+    H.singleton (rToR rs) (aspects { definitionSite = mFilePos })
+  else mempty
+  where
+  aspects     = asp $ C.isOperator x
+  moduleNames = mapMaybe (P.rangeModule' . getRange) (x : xs)
+  frFile      = H.singleton (rToR fr) $
+                aspects { definitionSite = notHere <$> mFilePos }
+  rs          = getRange (x : xs)
+
+  -- The fixity declaration should not get a symbolic anchor.
+  notHere d = d { defSiteHere = False }
+
+  mFilePos :: Maybe DefinitionSite
+  mFilePos = do
+    r <- mR
+    P.Pn { P.srcFile = Strict.Just f, P.posPos = p } <- P.rStart r
+    mod <- P.rangeFileName f
+    -- Andreas, 2017-06-16, Issue #2604: Symbolic anchors.
+    -- We drop the file name part from the qualifiers, since
+    -- this is contained in the html file name already.
+    -- We want to get anchors of the form:
+    -- @<a name="TopLevelModule.html#LocalModule.NestedModule.identifier">@
+    let qualifiers = drop (size mod) xs
+    -- For bound variables, we do not create symbolic anchors.
+        local = maybe True isLocalAspect $ aspect aspects
+    return $ DefinitionSite
+      { defSiteModule = mod
+      , defSitePos    = fromIntegral p
+        -- Is our current position the definition site?
+      , defSiteHere   = r == getRange x
+        -- For bound variables etc. we do not create a symbolic anchor name.
+        -- Also not for names that include anonymous modules,
+        -- otherwise, we do not get unique anchors.
+      , defSiteAnchor = if local || C.isNoName x || any Common.isUnderscore qualifiers
+          then Nothing
+          else Just $ prettyShow $ foldr C.Qual (C.QName x) qualifiers
+      }
+
+  -- Is the name a bound variable or similar? If in doubt, yes.
+  isLocalAspect :: Aspect -> Bool
+  isLocalAspect = \case
+    Name (Just kind) _ -> isLocal kind
+    _ -> True
+  isLocal :: NameKind -> Bool
+  isLocal = \case
+    Bound         -> True
+    Generalizable -> True
+    Argument      -> True
+    Constructor{} -> False
+    Datatype      -> False
+    Field         -> False
+    Function      -> False
+    Module        -> False
+    Postulate     -> False
+    Primitive     -> False
+    Record        -> False
+    Macro         -> False
+
+-- This was Highlighting.Generate.nameToFileA:
+-- | A variant of 'hiliteCName' for qualified abstract names.
+hiliteAName
+  :: A.QName
+     -- ^ The name.
+  -> Bool
+     -- ^ Should the binding site be included in the file?
+  -> (Bool -> Aspects)
+     -- ^ Meta information to be associated with the name.
+     -- ^ The argument is 'True' iff the name is an operator.
+  -> Hiliter
+hiliteAName x include asp = do
+  currentModule <- asks hleCurrentModuleName
+  hiliteCName (concreteQualifier x)
+              (concreteBase x)
+              (rangeOfFixityDeclaration currentModule)
+              (if include then Just $ bindingSite x else Nothing)
+              asp
+    <> notationFile currentModule
+  where
+  -- TODO: Currently we highlight fixity and syntax declarations by
+  -- producing highlighting something like once per occurrence of the
+  -- related name(s) in the file of the declaration (and we explicitly
+  -- avoid doing this for other files). Perhaps it would be better to
+  -- only produce this highlighting once.
+
+  rangeOfFixityDeclaration currentModule =
+    if P.rangeModule r == Just currentModule
+    then r else noRange
+    where
+    r = theNameRange $ A.nameFixity $ A.qnameName x
+
+  notationFile currentModule = pure $
+    if P.rangeModule (getRange notation) == Just currentModule
+    then mconcat $ map genPartFile notation
+    else mempty
+    where
+    notation = theNotation $ A.nameFixity $ A.qnameName x
+
+    boundAspect = nameAsp Bound False
+
+    genPartFile (VarPart r i)  = several [rToR r, rToR $ getRange i] boundAspect
+    genPartFile (HolePart r i) = several [rToR r, rToR $ getRange i] boundAspect
+    genPartFile WildPart{}     = mempty
+    genPartFile (IdPart x)     = H.singleton (rToR $ getRange x) (asp False)
+
+-- * Short auxiliary functions.
+---------------------------------------------------------------------------
+
+singleAspect :: HasRange a => Aspect -> a -> Hiliter
+singleAspect a x = pure $ H.singleton (rToR $ getRange x) $ parserBased { aspect = Just a }
+
+singleOtherAspect :: HasRange a => OtherAspect -> a -> Hiliter
+singleOtherAspect a x = pure $ H.singleton (rToR $ getRange x) $ parserBased { otherAspects = singleton a }
+
+nameAsp' :: Maybe NameKind -> Bool -> Aspects
+nameAsp' k isOp = parserBased { aspect = Just $ Name k isOp }
+
+nameAsp :: NameKind -> Bool -> Aspects
+nameAsp = nameAsp' . Just
+
+concreteBase :: A.QName -> C.Name
+concreteBase = A.nameConcrete . A.qnameName
+
+concreteQualifier :: A.QName -> [C.Name]
+concreteQualifier = map A.nameConcrete . A.mnameToList . A.qnameModule
+
+bindingSite :: A.QName -> Range
+bindingSite = A.nameBindingSite . A.qnameName
diff --git a/src/full/Agda/Interaction/Highlighting/Generate.hs b/src/full/Agda/Interaction/Highlighting/Generate.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Generate.hs
@@ -0,0 +1,714 @@
+
+-- | Generates data used for precise syntax highlighting.
+
+-- {-# OPTIONS_GHC -fwarn-unused-imports #-}  -- Semigroup import obsolete in later ghcs
+-- {-# OPTIONS_GHC -fwarn-unused-binds   #-}
+
+module Agda.Interaction.Highlighting.Generate
+  ( Level(..)
+  , generateAndPrintSyntaxInfo
+  , generateTokenInfo, generateTokenInfoFromSource
+  , generateTokenInfoFromString
+  , printSyntaxInfo
+  , printErrorInfo, errorHighlighting
+  , printUnsolvedInfo
+  , printHighlightingInfo
+  , highlightAsTypeChecked
+  , highlightWarning, warningHighlighting
+  , computeUnsolvedInfo
+  , storeDisambiguatedConstructor, storeDisambiguatedProjection
+  , disambiguateRecordFields
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad
+
+import qualified Data.Foldable as Fold
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.List ((\\))
+import qualified Data.List as List
+import qualified Data.IntMap as IntMap
+import Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as HMap
+import Data.Semigroup (Semigroup(..))
+import Data.Sequence (Seq)
+import qualified Data.Set as Set
+import qualified Data.Text.Lazy as Text
+
+import Agda.Interaction.Response
+  ( RemoveTokenBasedHighlighting( KeepHighlighting ) )
+import Agda.Interaction.Highlighting.Precise as H
+import Agda.Interaction.Highlighting.Range
+  (rToR, rangeToRange, overlappings, Ranges)
+import Agda.Interaction.Highlighting.FromAbstract
+
+import qualified Agda.TypeChecking.Errors as TCM
+import Agda.TypeChecking.MetaVars (isBlockedTerm, hasTwinMeta)
+import Agda.TypeChecking.Monad
+  hiding (ModuleInfo, MetaInfo, Primitive, Constructor, Record, Function, Datatype)
+import qualified Agda.TypeChecking.Monad  as TCM
+import qualified Agda.TypeChecking.Monad.Base.Warning as W
+import qualified Agda.TypeChecking.Pretty as TCM
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Warnings ( raiseWarningsOnUsage, runPM )
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Concrete.Definitions as W ( DeclarationWarning(..), DeclarationWarning'(..) )
+import Agda.Syntax.Common (Induction(..), pattern Ranged)
+import qualified Agda.Syntax.Concrete.Name as C
+import qualified Agda.Syntax.Internal as I
+import qualified Agda.Syntax.Literal as L
+import qualified Agda.Syntax.Parser as Pa
+import qualified Agda.Syntax.Parser.Tokens as T
+import qualified Agda.Syntax.Position as P
+import Agda.Syntax.Position
+  (RangeFile, Range, HasRange, getRange, noRange)
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.Syntax.Scope.Base     ( WithKind(..) )
+import Agda.Syntax.Abstract.Views ( KName, declaredNames )
+
+import Agda.Utils.FileName
+import Agda.Utils.List            ( caseList, last1 )
+import Agda.Utils.List2           ( List2 )
+import qualified Agda.Utils.List2 as List2
+import Agda.Utils.Maybe
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+-- | Highlighting levels.
+
+data Level
+  = Full
+    -- ^ Full highlighting. Should only be used after typechecking has
+    --   completed successfully.
+  | Partial
+    -- ^ Highlighting without disambiguation of overloaded
+    --   constructors.
+
+-- | Highlight a warning.
+--   We do not generate highlighting for unsolved metas and
+--   constraints, as that gets handled in bulk after typechecking.
+highlightWarning :: TCWarning -> TCM ()
+highlightWarning tcwarn = do
+  let h = convert $ warningHighlighting' False tcwarn
+  -- Highlighting for warnings coming from the Happy parser is placed
+  -- together with token highlighting.
+  case tcWarning tcwarn of
+    ParseWarning{} -> modifyTCLens stTokens     (h <>)
+    _              -> modifyTCLens stSyntaxInfo (h <>)
+  ifTopLevelAndHighlightingLevelIs NonInteractive $
+    printHighlightingInfo KeepHighlighting h
+
+-- | Generate syntax highlighting information for the given
+-- declaration, and (if appropriate) print it. If the boolean is
+-- 'True', then the state is additionally updated with the new
+-- highlighting info (in case of a conflict new info takes precedence
+-- over old info).
+--
+-- The procedure makes use of some of the highlighting info
+-- corresponding to 'stTokens' (that corresponding to the interval
+-- covered by the declaration). If the boolean is 'True', then this
+-- highlighting info is additionally removed from the data structure
+-- that 'stTokens' refers to.
+
+generateAndPrintSyntaxInfo
+  :: A.Declaration
+       -- ^ Declaration to highlight.
+  -> Level
+       -- ^ Amount of highlighting.
+  -> Bool
+       -- ^ Update the state?
+  -> TCM ()
+generateAndPrintSyntaxInfo decl _ _ | null $ getRange decl = return ()
+generateAndPrintSyntaxInfo decl hlLevel updateState = do
+  top <- fromMaybe __IMPOSSIBLE__ <$> currentTopLevelModule
+
+  reportSDoc "import.iface.create" 15 $
+    TCM.fwords
+      ("Generating syntax info for the following declaration " ++
+       case hlLevel of
+         Full   {} -> "(final):"
+         Partial{} -> "(first approximation):")
+      TCM.$$
+    TCM.prettyA decl
+
+  ignoreAbstractMode $ do
+    kinds <- nameKinds hlLevel decl
+
+    -- After the code has been type checked more information may be
+    -- available for overloaded constructors, and
+    -- @generateConstructorInfo@ takes advantage of this information.
+    -- Note, however, that highlighting for overloaded constructors is
+    -- included also in @nameInfo@.
+    constructorInfo <- case hlLevel of
+      Full{} -> generateConstructorInfo top kinds decl
+      _      -> return mempty
+
+    -- Main source of scope-checker generated highlighting:
+    let nameInfo = runHighlighter top kinds decl
+
+    reportSDoc "highlighting.warning" 60 $ TCM.hcat
+      [ "current path = "
+      , Strict.maybe "(nothing)" (return . pretty) =<< do
+          P.rangeFile <$> viewTC eRange
+      ]
+
+    -- Highlighting from the lexer and Happy parser:
+    (curTokens, otherTokens) <-
+      insideAndOutside (rangeToRange (getRange decl)) <$> useTC stTokens
+
+    -- @constructorInfo@ needs
+    -- to be placed before @nameInfo@ since, when typechecking is done,
+    -- constructors are included in both lists. Finally the token
+    -- information is placed last since token highlighting is more
+    -- crude than the others.
+    let syntaxInfo = convert (constructorInfo <> nameInfo)
+                       <>
+                     curTokens
+
+    when updateState $ do
+      stSyntaxInfo `modifyTCLens` mappend syntaxInfo
+      stTokens     `setTCLens`    otherTokens
+
+    ifTopLevelAndHighlightingLevelIs NonInteractive $
+      printHighlightingInfo KeepHighlighting syntaxInfo
+
+-- | Generate and return the syntax highlighting information for the
+-- tokens in the given file.
+
+generateTokenInfo :: AbsolutePath -> TCM HighlightingInfo
+generateTokenInfo file =
+  generateTokenInfoFromSource rf . Text.unpack =<<
+    runPM (Pa.readFilePM rf)
+  where
+  -- Note the use of Nothing here. The file might not even parse, but
+  -- it should still be possible to obtain token-based highlighting
+  -- information. The top-level module names seem to be *mostly*
+  -- unused, but one cannot use __IMPOSSIBLE__ instead of Nothing,
+  -- because the top-level module names are used by interleaveRanges,
+  -- which is used by parseLiterateWithComments, which is used by
+  -- generateTokenInfoFromSource.
+  rf = P.mkRangeFile file Nothing
+
+-- | Generate and return the syntax highlighting information for the
+-- tokens in the given file.
+
+generateTokenInfoFromSource
+  :: RangeFile
+     -- ^ The module to highlight.
+  -> String
+     -- ^ The file contents. Note that the file is /not/ read from
+     -- disk.
+  -> TCM HighlightingInfo
+generateTokenInfoFromSource file input =
+  runPM $ tokenHighlighting . fst . fst <$>
+          Pa.parseFile Pa.tokensParser file input
+
+-- | Generate and return the syntax highlighting information for the
+-- tokens in the given string, which is assumed to correspond to the
+-- given range.
+
+generateTokenInfoFromString :: Range -> String -> TCM HighlightingInfo
+generateTokenInfoFromString r _ | r == noRange = return mempty
+generateTokenInfoFromString r s = do
+  runPM $ tokenHighlighting . fst <$>
+          Pa.parsePosString Pa.tokensParser p s
+  where
+    Just p = P.rStart r
+
+-- | Compute syntax highlighting for the given tokens.
+tokenHighlighting :: [T.Token] -> HighlightingInfo
+tokenHighlighting = convert . mconcat . map tokenToHI
+  where
+  -- Converts an aspect and a range to a file.
+  aToF a r = H.singleton (rToR r) (mempty { aspect = Just a })
+
+  tokenToHI :: T.Token -> HighlightingInfoBuilder
+  tokenToHI (T.TokKeyword T.KwForall i)  = aToF Symbol (getRange i)
+  tokenToHI (T.TokKeyword T.KwREWRITE _) = mempty  -- #4361, REWRITE is not always a Keyword
+  tokenToHI (T.TokKeyword _ i)           = aToF Keyword (getRange i)
+  tokenToHI (T.TokSymbol T.SymQuestionMark i) = aToF Hole (getRange i)
+  tokenToHI (T.TokSymbol  _ i)                = aToF Symbol (getRange i)
+  tokenToHI (T.TokLiteral (Ranged r (L.LitNat    _))) = aToF Number r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitWord64 _))) = aToF Number r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitFloat  _))) = aToF Number r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitString _))) = aToF String r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitChar   _))) = aToF String r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitQName  _))) = aToF String r
+  tokenToHI (T.TokLiteral (Ranged r (L.LitMeta _ _))) = aToF String r
+  tokenToHI (T.TokComment (i, _))            = aToF Comment (getRange i)
+  tokenToHI (T.TokTeX (i, _))                = aToF Background (getRange i)
+  tokenToHI (T.TokMarkup (i, _))             = aToF Markup (getRange i)
+  tokenToHI (T.TokId {})                     = mempty
+  tokenToHI (T.TokQId {})                    = mempty
+  tokenToHI (T.TokString (i,s))              = aToF Pragma (getRange i)
+  tokenToHI (T.TokDummy {})                  = mempty
+  tokenToHI (T.TokEOF {})                    = mempty
+
+-- | Builds a 'NameKinds' function.
+
+nameKinds :: Level
+             -- ^ This should only be @'Full'@ if
+             -- type-checking completed successfully (without any
+             -- errors).
+          -> A.Declaration
+          -> TCM NameKinds
+nameKinds hlLevel decl = do
+  imported <- useTC $ stImports . sigDefinitions
+  local    <- case hlLevel of
+    Full{} -> useTC $ stSignature . sigDefinitions
+    _      -> return HMap.empty
+  impPatSyns <- useTC stPatternSynImports
+  locPatSyns <- case hlLevel of
+    Full{} -> useTC stPatternSyns
+    _      -> return empty
+      -- Traverses the syntax tree and constructs a map from qualified
+      -- names to name kinds. TODO: Handle open public.
+  let syntax :: NameKindMap
+      syntax = runBuilder (declaredNames decl :: NameKindBuilder) HMap.empty
+  return $ \ n -> unionsMaybeWith mergeNameKind
+    [ defnToKind . theDef <$> HMap.lookup n local
+    , con <$ Map.lookup n locPatSyns
+    , defnToKind . theDef <$> HMap.lookup n imported
+    , con <$ Map.lookup n impPatSyns
+    , HMap.lookup n syntax
+    ]
+  where
+  defnToKind :: TCM.Defn -> NameKind
+  defnToKind   TCM.Axiom{}                           = Postulate
+  defnToKind   TCM.DataOrRecSig{}                    = Postulate
+  defnToKind   TCM.GeneralizableVar{}                = Generalizable
+  defnToKind d@TCM.Function{} | isProperProjection d = Field
+                            | otherwise            = Function
+  defnToKind   TCM.Datatype{}                        = Datatype
+  defnToKind   TCM.Record{}                          = Record
+  defnToKind   TCM.Constructor{ TCM.conSrcCon = c }  = Constructor $ I.conInductive c
+  defnToKind   TCM.Primitive{}                       = Primitive
+  defnToKind   TCM.PrimitiveSort{}                   = Primitive
+  defnToKind   TCM.AbstractDefn{}                    = __IMPOSSIBLE__
+
+  con :: NameKind
+  con = Constructor Inductive
+
+-- | The 'TCM.Axiom' constructor is used to represent various things
+-- which are not really axioms, so when maps are merged 'Postulate's
+-- are thrown away whenever possible. The 'declaredNames' function
+-- below can return several explanations for one qualified name; the
+-- 'Postulate's are bogus.
+mergeNameKind :: NameKind -> NameKind -> NameKind
+mergeNameKind Postulate k = k
+mergeNameKind _     Macro = Macro  -- If the abstract syntax says macro, it's a macro.
+mergeNameKind k         _ = k
+
+-- Auxiliary types for @nameKinds@ generation
+
+type NameKindMap     = HashMap A.QName NameKind
+data NameKindBuilder = NameKindBuilder
+  { runBuilder :: NameKindMap -> NameKindMap
+  }
+
+instance Semigroup (NameKindBuilder) where
+  NameKindBuilder f <> NameKindBuilder g = NameKindBuilder $ f . g
+
+instance Monoid (NameKindBuilder) where
+  mempty = NameKindBuilder id
+  mappend = (<>)
+
+instance Singleton KName NameKindBuilder where
+  singleton (WithKind k q) = NameKindBuilder $
+    HMap.insertWith mergeNameKind q $ kindOfNameToNameKind k
+
+instance Collection KName NameKindBuilder
+
+-- | Generates syntax highlighting information for all constructors
+-- occurring in patterns and expressions in the given declaration.
+--
+-- This function should only be called after type checking.
+-- Constructors can be overloaded, and the overloading is resolved by
+-- the type checker.
+
+generateConstructorInfo
+  :: TopLevelModuleName
+     -- ^ The module to highlight.
+  -> NameKinds
+  -> A.Declaration
+  -> TCM HighlightingInfoBuilder
+generateConstructorInfo top kinds decl = do
+
+  -- Get boundaries of current declaration.
+  -- @noRange@ should be impossible, but in case of @noRange@
+  -- it makes sense to return mempty.
+  caseList (P.rangeIntervals $ getRange decl)
+           (return mempty) $ \ i is -> do
+    let start = fromIntegral $ P.posPos $ P.iStart i
+        end   = fromIntegral $ P.posPos $ P.iEnd $ last1 i is
+
+    -- Get all disambiguated names that fall within the range of decl.
+    m0 <- useTC stDisambiguatedNames
+    let (_, m1) = IntMap.split (pred start) m0
+        (m2, _) = IntMap.split end m1
+        constrs = IntMap.elems m2
+
+    -- Return suitable syntax highlighting information.
+    return $ foldMap (runHighlighter top kinds) constrs
+
+printSyntaxInfo :: Range -> TCM ()
+printSyntaxInfo r = do
+  syntaxInfo <- useTC stSyntaxInfo
+  ifTopLevelAndHighlightingLevelIs NonInteractive $
+    printHighlightingInfo KeepHighlighting
+      (restrictTo (rangeToRange r) syntaxInfo)
+
+-- | Prints syntax highlighting info for an error.
+
+printErrorInfo :: TCErr -> TCM ()
+printErrorInfo e =
+  printHighlightingInfo KeepHighlighting . convert =<<
+    errorHighlighting e
+
+-- | Generate highlighting for error.
+
+errorHighlighting :: TCErr -> TCM HighlightingInfoBuilder
+errorHighlighting e = errorHighlighting' (getRange e) <$> TCM.renderError e
+
+errorHighlighting'
+  :: Range     -- ^ Error range.
+  -> String    -- ^ Error message for tooltip.
+  -> HighlightingInfoBuilder
+errorHighlighting' r s = mconcat
+  [ -- Erase previous highlighting.
+    H.singleton (rToR $ P.continuousPerLine r) mempty
+  , -- Print new highlighting.
+    H.singleton (rToR r)
+         $ parserBased { otherAspects = Set.singleton Error
+                       , note         = s
+                       }
+  ]
+
+-- | Highlighting for warnings that are considered fatal.
+
+errorWarningHighlighting :: HasRange a => a -> HighlightingInfoBuilder
+errorWarningHighlighting w =
+  H.singleton (rToR $ P.continuousPerLine $ getRange w) $
+    parserBased { otherAspects = Set.singleton ErrorWarning }
+-- errorWarningHighlighting w = errorHighlighting' (getRange w) ""
+  -- MonadPretty not available here, so, no tooltip.
+  -- errorHighlighting' (getRange w) . render <$> TCM.prettyWarning (tcWarning w)
+
+-- | Generate syntax highlighting for warnings.
+
+warningHighlighting :: TCWarning -> HighlightingInfoBuilder
+warningHighlighting = warningHighlighting' True
+
+warningHighlighting' :: Bool -- ^ should we generate highlighting for unsolved metas and constrains?
+                     -> TCWarning -> HighlightingInfoBuilder
+warningHighlighting' b w = case tcWarning w of
+  TerminationIssue terrs     -> terminationErrorHighlighting terrs
+  NotStrictlyPositive d ocs  -> positivityErrorHighlighting d ocs
+  -- #3965 highlight each unreachable clause independently: they
+  -- may be interleaved with actually reachable clauses!
+  UnreachableClauses _ rs    -> foldMap deadcodeHighlighting rs
+  CoverageIssue{}            -> coverageErrorHighlighting $ getRange w
+  CoverageNoExactSplit{}     -> catchallHighlighting $ getRange w
+  InlineNoExactSplit{}       -> catchallHighlighting $ getRange w
+  UnsolvedConstraints cs     -> if b then constraintsHighlighting [] cs else mempty
+  UnsolvedMetaVariables rs   -> if b then metasHighlighting rs          else mempty
+  AbsurdPatternRequiresNoRHS{} -> deadcodeHighlighting w
+  ModuleDoesntExport{}         -> deadcodeHighlighting w
+  DuplicateUsing xs            -> foldMap deadcodeHighlighting xs
+  FixityInRenamingModule rs    -> foldMap deadcodeHighlighting rs
+  -- expanded catch-all case to get a warning for new constructors
+  CantGeneralizeOverSorts{}  -> mempty
+  UnsolvedInteractionMetas{} -> mempty
+  InteractionMetaBoundaries{} -> mempty
+  OldBuiltin{}               -> mempty
+  EmptyRewritePragma{}       -> deadcodeHighlighting w
+  EmptyWhere{}               -> deadcodeHighlighting w
+  IllformedAsClause{}        -> deadcodeHighlighting w
+  UselessPragma r _          -> deadcodeHighlighting r
+  UselessPublic{}            -> deadcodeHighlighting w
+  UselessHiding xs           -> foldMap deadcodeHighlighting xs
+  UselessInline{}            -> mempty
+  UselessPatternDeclarationForRecord{} -> deadcodeHighlighting w
+  ClashesViaRenaming _ xs    -> foldMap deadcodeHighlighting xs
+    -- #4154, TODO: clashing renamings are not dead code, but introduce problems.
+    -- Should we have a different color?
+  WrongInstanceDeclaration{} -> mempty
+  InstanceWithExplicitArg{}  -> deadcodeHighlighting w
+  InstanceNoOutputTypeName{} -> mempty
+  InstanceArgWithExplicitArg{} -> mempty
+  InversionDepthReached{}    -> mempty
+  NoGuardednessFlag{}        -> mempty
+  GenericWarning{}           -> mempty
+  -- Andreas, 2020-03-21, issue #4456:
+  -- Error warnings that do not have dedicated highlighting
+  -- are highlighted as errors.
+  InvalidCharacterLiteral{}             -> errorWarningHighlighting w
+  SafeFlagPostulate{}                   -> errorWarningHighlighting w
+  SafeFlagPragma{}                      -> errorWarningHighlighting w
+  SafeFlagWithoutKFlagPrimEraseEquality -> errorWarningHighlighting w
+  InfectiveImport{}                     -> errorWarningHighlighting w
+  CoInfectiveImport{}                   -> errorWarningHighlighting w
+  WithoutKFlagPrimEraseEquality -> mempty
+  DeprecationWarning{}       -> mempty
+  UserWarning{}              -> mempty
+  LibraryWarning{}           -> mempty
+  RewriteNonConfluent{}      -> confluenceErrorHighlighting w
+  RewriteMaybeNonConfluent{} -> confluenceErrorHighlighting w
+  RewriteAmbiguousRules{}    -> confluenceErrorHighlighting w
+  RewriteMissingRule{}       -> confluenceErrorHighlighting w
+  PragmaCompileErased{}      -> deadcodeHighlighting w
+  NotInScopeW{}              -> deadcodeHighlighting w
+  UnsupportedIndexedMatch{}  -> mempty
+  AsPatternShadowsConstructorOrPatternSynonym{}
+                             -> deadcodeHighlighting w
+  PatternShadowsConstructor{}-> errorWarningHighlighting w  -- or mempty ?
+  PlentyInHardCompileTimeMode o
+                             -> deadcodeHighlighting o
+  RecordFieldWarning w       -> recordFieldWarningHighlighting w
+  OptionWarning w            -> mempty
+  ParseWarning w             -> case w of
+    Pa.UnsupportedAttribute{}     -> deadcodeHighlighting w
+    Pa.MultipleAttributes{}       -> deadcodeHighlighting w
+    Pa.OverlappingTokensWarning{} -> mempty
+  NotAffectedByOpaque{}           -> deadcodeHighlighting w
+  UselessOpaque{}                 -> deadcodeHighlighting w
+  UnfoldTransparentName r         -> deadcodeHighlighting r
+  FaceConstraintCannotBeHidden{}  -> deadcodeHighlighting w
+  FaceConstraintCannotBeNamed{}   -> deadcodeHighlighting w
+
+  NicifierIssue (DeclarationWarning _ w) -> case w of
+    -- we intentionally override the binding of `w` here so that our pattern of
+    -- using `getRange w` still yields the most precise range information we
+    -- can get.
+    NotAllowedInMutual{}             -> deadcodeHighlighting w
+    EmptyAbstract{}                  -> deadcodeHighlighting w
+    EmptyConstructor{}               -> deadcodeHighlighting w
+    EmptyInstance{}                  -> deadcodeHighlighting w
+    EmptyMacro{}                     -> deadcodeHighlighting w
+    EmptyMutual{}                    -> deadcodeHighlighting w
+    EmptyPostulate{}                 -> deadcodeHighlighting w
+    EmptyPrimitive{}                 -> deadcodeHighlighting w
+    EmptyPrivate{}                   -> deadcodeHighlighting w
+    EmptyGeneralize{}                -> deadcodeHighlighting w
+    EmptyField{}                     -> deadcodeHighlighting w
+    HiddenGeneralize{}               -> mempty
+      -- Andreas, 2022-03-25, issue #5850
+      -- We would like @deadcodeHighlighting w@ for the braces in
+      -- @variable {x} : A@, but these have no range, so we cannot highlight them.
+      -- Highlighting the variable instead might be misleading,
+      -- suggesting that it is not generalized over.
+    UselessAbstract{}                -> deadcodeHighlighting w
+    UselessInstance{}                -> deadcodeHighlighting w
+    UselessPrivate{}                 -> deadcodeHighlighting w
+    InvalidNoPositivityCheckPragma{} -> deadcodeHighlighting w
+    InvalidNoUniverseCheckPragma{}   -> deadcodeHighlighting w
+    InvalidTerminationCheckPragma{}  -> deadcodeHighlighting w
+    InvalidCoverageCheckPragma{}     -> deadcodeHighlighting w
+    InvalidConstructor{}             -> deadcodeHighlighting w
+    InvalidConstructorBlock{}        -> deadcodeHighlighting w
+    InvalidRecordDirective{}         -> deadcodeHighlighting w
+    OpenPublicAbstract{}             -> deadcodeHighlighting w
+    OpenPublicPrivate{}              -> deadcodeHighlighting w
+    SafeFlagEta                   {} -> errorWarningHighlighting w
+    SafeFlagInjective             {} -> errorWarningHighlighting w
+    SafeFlagNoCoverageCheck       {} -> errorWarningHighlighting w
+    SafeFlagNoPositivityCheck     {} -> errorWarningHighlighting w
+    SafeFlagNoUniverseCheck       {} -> errorWarningHighlighting w
+    SafeFlagNonTerminating        {} -> errorWarningHighlighting w
+    SafeFlagPolarity              {} -> errorWarningHighlighting w
+    SafeFlagTerminating           {} -> errorWarningHighlighting w
+    W.ShadowingInTelescope nrs       -> foldMap
+                                          (shadowingTelHighlighting . snd)
+                                          nrs
+    MissingDeclarations{}            -> missingDefinitionHighlighting w
+    MissingDefinitions{}             -> missingDefinitionHighlighting w
+    -- TODO: explore highlighting opportunities here!
+    InvalidCatchallPragma{}           -> mempty
+    PolarityPragmasButNotPostulates{} -> mempty
+    PragmaNoTerminationCheck{}        -> mempty
+    PragmaCompiled{}                  -> errorWarningHighlighting w
+    UnknownFixityInMixfixDecl{}       -> mempty
+    UnknownNamesInFixityDecl{}        -> mempty
+    UnknownNamesInPolarityPragmas{}   -> mempty
+
+  -- Not source code related
+  DuplicateInterfaceFiles{} -> mempty
+
+recordFieldWarningHighlighting ::
+  RecordFieldWarning -> HighlightingInfoBuilder
+recordFieldWarningHighlighting = \case
+  W.DuplicateFields xrs      -> dead xrs
+  W.TooManyFields _q _ys xrs -> dead xrs
+  where
+  dead :: [(C.Name, Range)] -> HighlightingInfoBuilder
+  dead = mconcat . map deadcodeHighlighting
+  -- Andreas, 2020-03-27 #3684: This variant seems to only highlight @x@:
+  -- dead = mconcat . map f
+  -- f (x, r) = deadcodeHighlighting (getRange x) `mappend` deadcodeHighlighting r
+
+-- | Generate syntax highlighting for termination errors.
+
+terminationErrorHighlighting ::
+  [TerminationError] -> HighlightingInfoBuilder
+terminationErrorHighlighting termErrs = functionDefs `mappend` callSites
+  where
+    m            = parserBased { otherAspects = Set.singleton TerminationProblem }
+    functionDefs = foldMap (\x -> H.singleton (rToR $ bindingSite x) m) $
+                   concatMap termErrFunctions termErrs
+    callSites    = foldMap (\r -> H.singleton (rToR r) m) $
+                   concatMap (map getRange . termErrCalls) termErrs
+    bindingSite  = A.nameBindingSite . A.qnameName
+
+-- | Generate syntax highlighting for not-strictly-positive inductive
+-- definitions.
+
+positivityErrorHighlighting ::
+  I.QName -> Seq OccursWhere -> HighlightingInfoBuilder
+positivityErrorHighlighting q os =
+  several (rToR <$> getRange q : rs) m
+  where
+    rs = map (\(OccursWhere r _ _) -> r) (Fold.toList os)
+    m  = parserBased { otherAspects = Set.singleton PositivityProblem }
+
+deadcodeHighlighting :: HasRange a => a -> HighlightingInfoBuilder
+deadcodeHighlighting a = H.singleton (rToR $ P.continuous $ getRange a) m
+  where m = parserBased { otherAspects = Set.singleton Deadcode }
+
+coverageErrorHighlighting :: Range -> HighlightingInfoBuilder
+coverageErrorHighlighting r = H.singleton (rToR $ P.continuousPerLine r) m
+  where m = parserBased { otherAspects = Set.singleton CoverageProblem }
+
+shadowingTelHighlighting :: List2 Range -> HighlightingInfoBuilder
+shadowingTelHighlighting =
+  -- we do not want to highlight the one variable in scope so we take
+  -- the @init@ segment of the ranges in question
+  foldMap (\r -> H.singleton (rToR $ P.continuous r) m) . List2.init
+  where
+  m = parserBased { otherAspects =
+                      Set.singleton H.ShadowingInTelescope }
+
+catchallHighlighting :: Range -> HighlightingInfoBuilder
+catchallHighlighting r = H.singleton (rToR $ P.continuousPerLine r) m
+  where m = parserBased { otherAspects = Set.singleton CatchallClause }
+
+confluenceErrorHighlighting ::
+  HasRange a => a -> HighlightingInfoBuilder
+confluenceErrorHighlighting a = H.singleton (rToR $ P.continuousPerLine $ getRange a) m
+  where m = parserBased { otherAspects = Set.singleton ConfluenceProblem }
+
+missingDefinitionHighlighting ::
+  HasRange a => a -> HighlightingInfoBuilder
+missingDefinitionHighlighting a = H.singleton (rToR $ P.continuousPerLine $ getRange a) m
+  where m = parserBased { otherAspects = Set.singleton MissingDefinition }
+
+-- | Generates and prints syntax highlighting information for unsolved
+-- meta-variables and certain unsolved constraints.
+
+printUnsolvedInfo :: TCM ()
+printUnsolvedInfo = do
+  info <- computeUnsolvedInfo
+
+  printHighlightingInfo KeepHighlighting (convert info)
+
+computeUnsolvedInfo :: TCM HighlightingInfoBuilder
+computeUnsolvedInfo = do
+  (rs, metaInfo) <- computeUnsolvedMetaWarnings
+  constraintInfo <- computeUnsolvedConstraints rs
+
+  return $ metaInfo `mappend` constraintInfo
+
+-- | Generates syntax highlighting information for unsolved meta
+-- variables.
+--   Also returns ranges of unsolved or interaction metas.
+computeUnsolvedMetaWarnings :: TCM ([Ranges], HighlightingInfoBuilder)
+computeUnsolvedMetaWarnings = do
+  is <- getInteractionMetas
+
+  -- We don't want to highlight blocked terms, since
+  --   * there is always at least one proper meta responsible for the blocking
+  --   * in many cases the blocked term covers the highlighting for this meta
+  --   * for the same reason we skip metas with a twin, since the twin will be blocked.
+  let notBlocked m = not <$> isBlockedTerm m
+  let notHasTwin m = not <$> hasTwinMeta m
+  ms <- filterM notHasTwin =<< filterM notBlocked =<< getOpenMetas
+
+  let extend = map (rToR . P.continuousPerLine)
+
+  rs <- extend <$> mapM getMetaRange (ms \\ is)
+
+  rs' <- extend <$> mapM getMetaRange is
+  return $ (rs ++ rs', metasHighlighting' rs)
+
+metasHighlighting :: [Range] -> HighlightingInfoBuilder
+metasHighlighting rs = metasHighlighting' (map (rToR . P.continuousPerLine) rs)
+
+metasHighlighting' :: [Ranges] -> HighlightingInfoBuilder
+metasHighlighting' rs = several rs
+                     $ parserBased { otherAspects = Set.singleton UnsolvedMeta }
+
+-- | Generates syntax highlighting information for unsolved constraints
+--   (ideally: that are not connected to a meta variable).
+
+computeUnsolvedConstraints :: [Ranges] -- ^ does not add ranges that would overlap with these.
+                           -> TCM HighlightingInfoBuilder
+computeUnsolvedConstraints ms = constraintsHighlighting ms <$> getAllConstraints
+
+constraintsHighlighting ::
+  [Ranges] -> Constraints -> HighlightingInfoBuilder
+constraintsHighlighting ms cs =
+  several (filter noOverlap $ map (rToR . P.continuousPerLine) rs)
+          (parserBased { otherAspects = Set.singleton UnsolvedConstraint })
+  where
+  noOverlap r = not $ any (overlappings $ r) $ ms
+  -- get ranges of interesting unsolved constraints
+  rs = (`mapMaybe` (map theConstraint cs)) $ \case
+    Closure{ clValue = IsEmpty r t           } -> Just r
+    Closure{ clEnv = e, clValue = ValueCmp{} } -> Just $ getRange (envRange e)
+    Closure{ clEnv = e, clValue = ElimCmp{}  } -> Just $ getRange (envRange e)
+    Closure{ clEnv = e, clValue = SortCmp{}  } -> Just $ getRange (envRange e)
+    Closure{ clEnv = e, clValue = LevelCmp{} } -> Just $ getRange (envRange e)
+    Closure{ clEnv = e, clValue = CheckSizeLtSat{} } -> Just $ getRange (envRange e)
+    _ -> Nothing
+
+
+-- * Disambiguation of constructors and projections.
+
+storeDisambiguatedField :: A.QName -> TCM ()
+storeDisambiguatedField = storeDisambiguatedName Field
+
+storeDisambiguatedProjection :: A.QName -> TCM ()
+storeDisambiguatedProjection = storeDisambiguatedField
+
+storeDisambiguatedConstructor :: Induction -> A.QName -> TCM ()
+storeDisambiguatedConstructor i = storeDisambiguatedName $ Constructor i
+
+-- TODO: move the following function to a new module TypeChecking.Overloading
+-- that gathers functions concerning disambiguation of overloading.
+
+-- | Remember a name disambiguation (during type checking).
+--   To be used later during syntax highlighting.
+--   Also: raise user warnings associated with the name.
+storeDisambiguatedName :: NameKind -> A.QName -> TCM ()
+storeDisambiguatedName k q = do
+  raiseWarningsOnUsage q
+  whenJust (start $ getRange q) $ \ i ->
+    modifyTCLens stDisambiguatedNames $ IntMap.insert i $ DisambiguatedName k q
+  where
+  start r = fromIntegral . P.posPos <$> P.rStart' r
+
+-- | Store a disambiguation of record field tags for the purpose of highlighting.
+disambiguateRecordFields
+  :: [C.Name]   -- ^ Record field names in a record expression.
+  -> [A.QName]  -- ^ Record field names in the corresponding record type definition
+  -> TCM ()
+disambiguateRecordFields cxs axs = forM_ cxs $ \ cx -> do
+  caseMaybe (List.find ((cx ==) . A.nameConcrete . A.qnameName) axs) (return ()) $ \ ax -> do
+    storeDisambiguatedField ax{ A.qnameName = (A.qnameName ax) { A.nameConcrete = cx } }
diff --git a/src/full/Agda/Interaction/Highlighting/Generate.hs-boot b/src/full/Agda/Interaction/Highlighting/Generate.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Generate.hs-boot
@@ -0,0 +1,7 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Highlighting.Generate where
+
+import Agda.TypeChecking.Monad.Base (TCM, TCWarning)
+
+highlightWarning :: TCWarning -> TCM ()
diff --git a/src/full/Agda/Interaction/Highlighting/HTML.hs b/src/full/Agda/Interaction/Highlighting/HTML.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/HTML.hs
@@ -0,0 +1,11 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Backend for generating highlighted, hyperlinked HTML from Agda sources.
+
+module Agda.Interaction.Highlighting.HTML
+  ( htmlBackend
+  ) where
+
+import Agda.Interaction.Highlighting.HTML.Backend as Exports
+  ( htmlBackend
+  )
diff --git a/src/full/Agda/Interaction/Highlighting/HTML/Backend.hs b/src/full/Agda/Interaction/Highlighting/HTML/Backend.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/HTML/Backend.hs
@@ -0,0 +1,202 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Backend for generating highlighted, hyperlinked HTML from Agda sources.
+
+module Agda.Interaction.Highlighting.HTML.Backend
+  ( htmlBackend
+  ) where
+
+import Agda.Interaction.Highlighting.HTML.Base
+
+import Prelude hiding ((!!), concatMap)
+
+import Control.DeepSeq
+import Control.Monad.Trans ( MonadIO )
+import Control.Monad.Except ( MonadError(throwError) )
+
+import Data.Map (Map)
+
+import GHC.Generics (Generic)
+
+import Agda.Interaction.Options
+    ( ArgDescr(ReqArg, NoArg)
+    , OptDescr(..)
+    , Flag
+    )
+import Agda.Compiler.Backend (Backend(..), Backend'(..), Recompile(..))
+import Agda.Compiler.Common (IsMain(..), curIF)
+
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+
+import Agda.TypeChecking.Monad
+  ( MonadDebug
+  , ReadTCState
+  , Definition
+  , reportS
+  )
+
+-- | Options for HTML generation
+
+data HtmlFlags = HtmlFlags
+  { htmlFlagEnabled              :: Bool
+  , htmlFlagDir                  :: FilePath
+  , htmlFlagHighlight            :: HtmlHighlight
+  , htmlFlagHighlightOccurrences :: Bool
+  , htmlFlagCssFile              :: Maybe FilePath
+  } deriving (Eq, Generic)
+
+instance NFData HtmlFlags
+
+data HtmlCompileEnv = HtmlCompileEnv
+  { htmlCompileEnvOpts :: HtmlOptions
+  }
+
+data HtmlModuleEnv = HtmlModuleEnv
+  { htmlModEnvCompileEnv :: HtmlCompileEnv
+  , htmlModEnvName       :: TopLevelModuleName
+  }
+
+data HtmlModule = HtmlModule
+data HtmlDef = HtmlDef
+
+htmlBackend :: Backend
+htmlBackend = Backend htmlBackend'
+
+htmlBackend' :: Backend' HtmlFlags HtmlCompileEnv HtmlModuleEnv HtmlModule HtmlDef
+htmlBackend' = Backend'
+  { backendName           = "HTML"
+  , backendVersion        = Nothing
+  , options               = initialHtmlFlags
+  , commandLineFlags      = htmlFlags
+  , isEnabled             = htmlFlagEnabled
+  , preCompile            = preCompileHtml
+  , preModule             = preModuleHtml
+  , compileDef            = compileDefHtml
+  , postModule            = postModuleHtml
+  , postCompile           = postCompileHtml
+  -- --only-scope-checking works, but with the caveat that cross-module links
+  -- will not have their definition site populated.
+  , scopeCheckingSuffices = True
+  , mayEraseType          = const $ return False
+  }
+
+initialHtmlFlags :: HtmlFlags
+initialHtmlFlags = HtmlFlags
+  { htmlFlagEnabled   = False
+  , htmlFlagDir       = defaultHTMLDir
+  , htmlFlagHighlight = HighlightAll
+  -- Don't enable by default because it causes potential
+  -- performance problems
+  , htmlFlagHighlightOccurrences = False
+  , htmlFlagCssFile              = Nothing
+  }
+
+htmlOptsOfFlags :: HtmlFlags -> HtmlOptions
+htmlOptsOfFlags flags = HtmlOptions
+  { htmlOptDir = htmlFlagDir flags
+  , htmlOptHighlight = htmlFlagHighlight flags
+  , htmlOptHighlightOccurrences = htmlFlagHighlightOccurrences flags
+  , htmlOptCssFile = htmlFlagCssFile flags
+  }
+
+-- | The default output directory for HTML.
+
+defaultHTMLDir :: FilePath
+defaultHTMLDir = "html"
+
+htmlFlags :: [OptDescr (Flag HtmlFlags)]
+htmlFlags =
+    [ Option []     ["html"] (NoArg htmlFlag)
+                    "generate HTML files with highlighted source code"
+    , Option []     ["html-dir"] (ReqArg htmlDirFlag "DIR")
+                    ("directory in which HTML files are placed (default: " ++
+                     defaultHTMLDir ++ ")")
+    , Option []     ["highlight-occurrences"] (NoArg highlightOccurrencesFlag)
+                    ("highlight all occurrences of hovered symbol in generated " ++
+                     "HTML files")
+    , Option []     ["css"] (ReqArg cssFlag "URL")
+                    "the CSS file used by the HTML files (can be relative)"
+    , Option []     ["html-highlight"] (ReqArg htmlHighlightFlag "[code,all,auto]")
+                    ("whether to highlight only the code parts (code) or " ++
+                     "the file as a whole (all) or " ++
+                     "decide by source file type (auto)")
+    ]
+
+htmlFlag :: Flag HtmlFlags
+htmlFlag o = return $ o { htmlFlagEnabled = True }
+
+htmlDirFlag :: FilePath -> Flag HtmlFlags
+htmlDirFlag d o = return $ o { htmlFlagDir = d }
+
+cssFlag :: FilePath -> Flag HtmlFlags
+cssFlag f o = return $ o { htmlFlagCssFile = Just f }
+
+highlightOccurrencesFlag :: Flag HtmlFlags
+highlightOccurrencesFlag o = return $ o { htmlFlagHighlightOccurrences = True }
+
+parseHtmlHighlightFlag :: MonadError String m => String -> m HtmlHighlight
+parseHtmlHighlightFlag "code" = return HighlightCode
+parseHtmlHighlightFlag "all"  = return HighlightAll
+parseHtmlHighlightFlag "auto" = return HighlightAuto
+parseHtmlHighlightFlag opt    = throwError $ concat ["Invalid option <", opt, ">, expected <all>, <auto> or <code>"]
+
+htmlHighlightFlag :: String -> Flag HtmlFlags
+htmlHighlightFlag opt    o = do
+  flag <- parseHtmlHighlightFlag opt
+  return $ o { htmlFlagHighlight = flag }
+
+runLogHtmlWithMonadDebug :: MonadDebug m => LogHtmlT m a -> m a
+runLogHtmlWithMonadDebug = runLogHtmlWith $ reportS "html" 1
+
+preCompileHtml
+  :: (MonadIO m, MonadDebug m)
+  => HtmlFlags
+  -> m HtmlCompileEnv
+preCompileHtml flags = runLogHtmlWithMonadDebug $ do
+  logHtml $ unlines
+    [ "Warning: HTML is currently generated for ALL files which can be"
+    , "reached from the given module, including library files."
+    ]
+  let opts = htmlOptsOfFlags flags
+  prepareCommonDestinationAssets opts
+  return $ HtmlCompileEnv opts
+
+preModuleHtml
+  :: Applicative m
+  => HtmlCompileEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> Maybe FilePath
+  -> m (Recompile HtmlModuleEnv HtmlModule)
+preModuleHtml cenv _isMain modName _ifacePath = pure $ Recompile (HtmlModuleEnv cenv modName)
+
+compileDefHtml
+  :: Applicative m
+  => HtmlCompileEnv
+  -> HtmlModuleEnv
+  -> IsMain
+  -> Definition
+  -> m HtmlDef
+compileDefHtml _env _menv _isMain _def = pure HtmlDef
+
+postModuleHtml
+  :: (MonadIO m, MonadDebug m, ReadTCState m)
+  => HtmlCompileEnv
+  -> HtmlModuleEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> [HtmlDef]
+  -> m HtmlModule
+postModuleHtml _env menv _isMain _modName _defs = do
+  let generatePage = defaultPageGen . htmlCompileEnvOpts . htmlModEnvCompileEnv $ menv
+  htmlSrc <- srcFileOfInterface (htmlModEnvName menv) <$> curIF
+  runLogHtmlWithMonadDebug $ generatePage htmlSrc
+  return HtmlModule
+
+postCompileHtml
+  :: Applicative m
+  => HtmlCompileEnv
+  -> IsMain
+  -> Map TopLevelModuleName HtmlModule
+  -> m ()
+postCompileHtml _cenv _isMain _modulesByName = pure ()
diff --git a/src/full/Agda/Interaction/Highlighting/HTML/Base.hs b/src/full/Agda/Interaction/Highlighting/HTML/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/HTML/Base.hs
@@ -0,0 +1,427 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Function for generating highlighted, hyperlinked HTML from Agda
+-- sources.
+
+module Agda.Interaction.Highlighting.HTML.Base
+  ( HtmlOptions(..)
+  , HtmlHighlight(..)
+  , prepareCommonDestinationAssets
+  , srcFileOfInterface
+  , defaultPageGen
+  , MonadLogHtml(logHtml)
+  , LogHtmlT
+  , runLogHtmlWith
+  ) where
+
+import Prelude hiding ((!!), concatMap)
+
+import Control.DeepSeq
+import Control.Monad
+import Control.Monad.Trans ( MonadIO(..), lift )
+import Control.Monad.Trans.Reader ( ReaderT(runReaderT), ask )
+
+import Data.Function ( on )
+import Data.Foldable (toList, concatMap)
+import Data.Maybe
+import qualified Data.IntMap as IntMap
+import Data.List.Split (splitWhen)
+import Data.Text.Lazy (Text)
+import qualified Data.Text.Lazy as T
+
+import GHC.Generics (Generic)
+
+import qualified Network.URI.Encode
+
+import System.FilePath
+import System.Directory
+
+import Text.Blaze.Html5
+    ( preEscapedToHtml
+    , toHtml
+    , stringValue
+    , Html
+    , (!)
+    , Attribute
+    )
+import qualified Text.Blaze.Html5 as Html5
+import qualified Text.Blaze.Html5.Attributes as Attr
+import Text.Blaze.Html.Renderer.Text ( renderHtml )
+  -- The imported operator (!) attaches an Attribute to an Html value
+  -- The defined operator (!!) attaches a list of such Attributes
+
+import Paths_Agda
+
+import Agda.Interaction.Highlighting.Precise hiding (toList)
+
+import Agda.Syntax.Common
+import Agda.Syntax.TopLevelModuleName
+
+import qualified Agda.TypeChecking.Monad as TCM
+  ( Interface(..)
+  )
+
+import Agda.Utils.Function
+import Agda.Utils.List1 (String1, pattern (:|))
+import qualified Agda.Utils.List1   as List1
+import qualified Agda.Utils.IO.UTF8 as UTF8
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+-- | The Agda data directory containing the files for the HTML backend.
+
+htmlDataDir :: FilePath
+htmlDataDir = "html"
+
+-- | The name of the default CSS file.
+
+defaultCSSFile :: FilePath
+defaultCSSFile = "Agda.css"
+
+-- | The name of the occurrence-highlighting JS file.
+
+occurrenceHighlightJsFile :: FilePath
+occurrenceHighlightJsFile = "highlight-hover.js"
+
+-- | The directive inserted before the rendered code blocks
+
+rstDelimiter :: String
+rstDelimiter = ".. raw:: html\n"
+
+-- | The directive inserted before rendered code blocks in org
+
+orgDelimiterStart :: String
+orgDelimiterStart = "#+BEGIN_EXPORT html\n<pre class=\"Agda\">\n"
+
+-- | The directive inserted after rendered code blocks in org
+
+orgDelimiterEnd :: String
+orgDelimiterEnd = "</pre>\n#+END_EXPORT\n"
+
+-- | Determine how to highlight the file
+
+data HtmlHighlight = HighlightAll | HighlightCode | HighlightAuto
+  deriving (Show, Eq, Generic)
+
+instance NFData HtmlHighlight
+
+highlightOnlyCode :: HtmlHighlight -> FileType -> Bool
+highlightOnlyCode HighlightAll  _ = False
+highlightOnlyCode HighlightCode _ = True
+highlightOnlyCode HighlightAuto AgdaFileType  = False
+highlightOnlyCode HighlightAuto MdFileType    = True
+highlightOnlyCode HighlightAuto RstFileType   = True
+highlightOnlyCode HighlightAuto OrgFileType   = True
+highlightOnlyCode HighlightAuto TypstFileType = True
+highlightOnlyCode HighlightAuto TexFileType   = False
+
+-- | Determine the generated file extension
+
+highlightedFileExt :: HtmlHighlight -> FileType -> String
+highlightedFileExt hh ft
+  | not $ highlightOnlyCode hh ft = "html"
+  | otherwise = case ft of
+      AgdaFileType  -> "html"
+      MdFileType    -> "md"
+      RstFileType   -> "rst"
+      TexFileType   -> "tex"
+      OrgFileType   -> "org"
+      TypstFileType -> "typ"
+
+-- | Options for HTML generation
+
+data HtmlOptions = HtmlOptions
+  { htmlOptDir                  :: FilePath
+  , htmlOptHighlight            :: HtmlHighlight
+  , htmlOptHighlightOccurrences :: Bool
+  , htmlOptCssFile              :: Maybe FilePath
+  } deriving Eq
+
+-- | Internal type bundling the information related to a module source file
+
+data HtmlInputSourceFile = HtmlInputSourceFile
+  { _srcFileModuleName :: TopLevelModuleName
+  , _srcFileType :: FileType
+  -- ^ Source file type
+  , _srcFileText :: Text
+  -- ^ Source text
+  , _srcFileHighlightInfo :: HighlightingInfo
+  -- ^ Highlighting info
+  }
+
+-- | Bundle up the highlighting info for a source file
+
+srcFileOfInterface ::
+  TopLevelModuleName -> TCM.Interface -> HtmlInputSourceFile
+srcFileOfInterface m i = HtmlInputSourceFile m (TCM.iFileType i) (TCM.iSource i) (TCM.iHighlighting i)
+
+-- | Logging during HTML generation
+
+type HtmlLogMessage = String
+type HtmlLogAction m = HtmlLogMessage -> m ()
+
+class MonadLogHtml m where
+  logHtml :: HtmlLogAction m
+
+type LogHtmlT m = ReaderT (HtmlLogAction m) m
+
+instance Monad m => MonadLogHtml (LogHtmlT m) where
+  logHtml message = do
+    doLog <- ask
+    lift $ doLog message
+
+runLogHtmlWith :: Monad m => HtmlLogAction m -> LogHtmlT m a -> m a
+runLogHtmlWith = flip runReaderT
+
+renderSourceFile :: HtmlOptions -> HtmlInputSourceFile -> Text
+renderSourceFile opts = renderSourcePage
+  where
+  cssFile = fromMaybe defaultCSSFile (htmlOptCssFile opts)
+  highlightOccur = htmlOptHighlightOccurrences opts
+  htmlHighlight = htmlOptHighlight opts
+  renderSourcePage (HtmlInputSourceFile moduleName fileType sourceCode hinfo) =
+    page cssFile highlightOccur onlyCode moduleName pageContents
+    where
+      tokens = tokenStream sourceCode hinfo
+      onlyCode = highlightOnlyCode htmlHighlight fileType
+      pageContents = code onlyCode fileType tokens
+
+defaultPageGen :: (MonadIO m, MonadLogHtml m) => HtmlOptions -> HtmlInputSourceFile -> m ()
+defaultPageGen opts srcFile@(HtmlInputSourceFile moduleName ft _ _) = do
+  logHtml $ render $ "Generating HTML for"  <+> pretty moduleName <+> ((parens (pretty target)) <> ".")
+  writeRenderedHtml html target
+  where
+    ext = highlightedFileExt (htmlOptHighlight opts) ft
+    target = (htmlOptDir opts) </> modToFile moduleName ext
+    html = renderSourceFile opts srcFile
+
+prepareCommonDestinationAssets :: MonadIO m => HtmlOptions -> m ()
+prepareCommonDestinationAssets options = liftIO $ do
+  -- There is a default directory given by 'defaultHTMLDir'
+  let htmlDir = htmlOptDir options
+  createDirectoryIfMissing True htmlDir
+
+  -- If the default CSS file should be used, then it is copied to
+  -- the output directory.
+  let cssFile = htmlOptCssFile options
+  when (isNothing $ cssFile) $ do
+    defCssFile <- getDataFileName $
+      htmlDataDir </> defaultCSSFile
+    copyFile defCssFile (htmlDir </> defaultCSSFile)
+
+  let highlightOccurrences = htmlOptHighlightOccurrences options
+  when highlightOccurrences $ do
+    highlightJsFile <- getDataFileName $
+      htmlDataDir </> occurrenceHighlightJsFile
+    copyFile highlightJsFile (htmlDir </> occurrenceHighlightJsFile)
+
+-- | Converts module names to the corresponding HTML file names.
+
+modToFile :: TopLevelModuleName -> String -> FilePath
+modToFile m ext = Network.URI.Encode.encode $ render (pretty m) <.> ext
+
+-- | Generates a highlighted, hyperlinked version of the given module.
+
+writeRenderedHtml
+  :: MonadIO m
+  => Text       -- ^ Rendered page
+  -> FilePath   -- ^ Output path.
+  -> m ()
+writeRenderedHtml html target = liftIO $ UTF8.writeTextToFile target html
+
+
+-- | Attach multiple Attributes
+
+(!!) :: Html -> [Attribute] -> Html
+h !! as = h ! mconcat as
+
+-- | Constructs the web page, including headers.
+
+page :: FilePath              -- ^ URL to the CSS file.
+     -> Bool                  -- ^ Highlight occurrences
+     -> Bool                  -- ^ Whether to reserve literate
+     -> TopLevelModuleName    -- ^ Module to be highlighted.
+     -> Html
+     -> Text
+page css
+     highlightOccurrences
+     htmlHighlight
+     modName
+     pageContent =
+  renderHtml $ if htmlHighlight
+               then pageContent
+               else Html5.docTypeHtml $ hdr <> rest
+  where
+
+    hdr = Html5.head $ mconcat
+      [ Html5.meta !! [ Attr.charset "utf-8" ]
+      , Html5.title (toHtml . render $ pretty modName)
+      , Html5.link !! [ Attr.rel "stylesheet"
+                      , Attr.href $ stringValue css
+                      ]
+      , if highlightOccurrences
+        then Html5.script mempty !!
+          [ Attr.type_ "text/javascript"
+          , Attr.src $ stringValue occurrenceHighlightJsFile
+          ]
+        else mempty
+      ]
+
+    rest = Html5.body $ (Html5.pre ! Attr.class_ "Agda") pageContent
+
+-- | Position, Contents, Infomation
+
+type TokenInfo =
+  ( Int
+  , String1
+  , Aspects
+  )
+
+-- | Constructs token stream ready to print.
+
+tokenStream
+     :: Text             -- ^ The contents of the module.
+     -> HighlightingInfo -- ^ Highlighting information.
+     -> [TokenInfo]
+tokenStream contents info =
+  map (\ ((mi, (pos, c)) :| xs) ->
+            (pos, c :| map (snd . snd) xs, fromMaybe mempty mi)) $
+  List1.groupBy ((==) `on` fst) $
+  zipWith (\pos c -> (IntMap.lookup pos infoMap, (pos, c))) [1..] (T.unpack contents)
+  where
+  infoMap = toMap info
+
+-- | Constructs the HTML displaying the code.
+
+code :: Bool     -- ^ Whether to generate non-code contents as-is
+     -> FileType -- ^ Source file type
+     -> [TokenInfo]
+     -> Html
+code onlyCode fileType = mconcat . if onlyCode
+  then case fileType of
+         -- Explicitly written all cases, so people
+         -- get compile error when adding new file types
+         -- when they forget to modify the code here
+         RstFileType   -> map mkRst . splitByMarkup
+         MdFileType    -> map mkMd . splitByMarkup
+         AgdaFileType  -> map mkHtml
+         OrgFileType   -> map mkOrg . splitByMarkup
+         -- Two useless cases, probably will never used by anyone
+         TexFileType   -> map mkMd . splitByMarkup
+         TypstFileType -> map mkMd . splitByMarkup
+  else map mkHtml
+  where
+  trd (_, _, a) = a
+
+  splitByMarkup :: [TokenInfo] -> [[TokenInfo]]
+  splitByMarkup = splitWhen $ (== Just Markup) . aspect . trd
+
+  mkHtml :: TokenInfo -> Html
+  mkHtml (pos, s, mi) =
+    -- Andreas, 2017-06-16, issue #2605:
+    -- Do not create anchors for whitespace.
+    applyUnless (mi == mempty) (annotate pos mi) $ toHtml $ List1.toList s
+
+  backgroundOrAgdaToHtml :: TokenInfo -> Html
+  backgroundOrAgdaToHtml token@(_, s, mi) = case aspect mi of
+    Just Background -> preEscapedToHtml $ List1.toList s
+    Just Markup     -> __IMPOSSIBLE__
+    _               -> mkHtml token
+
+  -- Proposed in #3373, implemented in #3384
+  mkRst :: [TokenInfo] -> Html
+  mkRst = mconcat . (toHtml rstDelimiter :) . map backgroundOrAgdaToHtml
+
+  -- The assumption here and in mkOrg is that Background tokens and Agda tokens are always
+  -- separated by Markup tokens, so these runs only contain one kind.
+  mkMd :: [TokenInfo] -> Html
+  mkMd tokens = if containsCode then formatCode else formatNonCode
+    where
+      containsCode = any ((/= Just Background) . aspect . trd) tokens
+
+      formatCode = Html5.pre ! Attr.class_ "Agda" $ mconcat $ backgroundOrAgdaToHtml <$> tokens
+      formatNonCode = mconcat $ backgroundOrAgdaToHtml <$> tokens
+
+  mkOrg :: [TokenInfo] -> Html
+  mkOrg tokens = mconcat $ if containsCode then formatCode else formatNonCode
+    where
+      containsCode = any ((/= Just Background) . aspect . trd) tokens
+
+      startDelimiter = preEscapedToHtml orgDelimiterStart
+      endDelimiter = preEscapedToHtml orgDelimiterEnd
+
+      formatCode = startDelimiter : foldr (\x -> (backgroundOrAgdaToHtml x :)) [endDelimiter] tokens
+      formatNonCode = map backgroundOrAgdaToHtml tokens
+
+  -- Put anchors that enable referencing that token.
+  -- We put a fail safe numeric anchor (file position) for internal references
+  -- (issue #2756), as well as a heuristic name anchor for external references
+  -- (issue #2604).
+  annotate :: Int -> Aspects -> Html -> Html
+  annotate pos mi =
+    applyWhen hereAnchor (anchorage nameAttributes mempty <>) . anchorage posAttributes
+    where
+    -- Warp an anchor (<A> tag) with the given attributes around some HTML.
+    anchorage :: [Attribute] -> Html -> Html
+    anchorage attrs html = Html5.a html !! attrs
+
+    -- File position anchor (unique, reliable).
+    posAttributes :: [Attribute]
+    posAttributes = concat
+      [ [Attr.id $ stringValue $ show pos ]
+      , toList $ link <$> definitionSite mi
+      , Attr.class_ (stringValue $ unwords classes) <$ guard (not $ null classes)
+      ]
+
+    -- Named anchor (not reliable, but useful in the general case for outside refs).
+    nameAttributes :: [Attribute]
+    nameAttributes = [ Attr.id $ stringValue $ fromMaybe __IMPOSSIBLE__ $ mDefSiteAnchor ]
+
+    classes = concat
+      [ concatMap noteClasses (note mi)
+      , otherAspectClasses (toList $ otherAspects mi)
+      , concatMap aspectClasses (aspect mi)
+      ]
+
+    aspectClasses (Name mKind op) = kindClass ++ opClass
+      where
+      kindClass = toList $ fmap showKind mKind
+
+      showKind (Constructor Inductive)   = "InductiveConstructor"
+      showKind (Constructor CoInductive) = "CoinductiveConstructor"
+      showKind k                         = show k
+
+      opClass = ["Operator" | op]
+    aspectClasses a = [show a]
+
+
+    otherAspectClasses = map show
+
+    -- Notes are not included.
+    noteClasses _s = []
+
+    -- Should we output a named anchor?
+    -- Only if we are at the definition site now (@here@)
+    -- and such a pretty named anchor exists (see 'defSiteAnchor').
+    hereAnchor      :: Bool
+    hereAnchor      = here && isJust mDefSiteAnchor
+
+    mDefinitionSite :: Maybe DefinitionSite
+    mDefinitionSite = definitionSite mi
+
+    -- Are we at the definition site now?
+    here            :: Bool
+    here            = maybe False defSiteHere mDefinitionSite
+
+    mDefSiteAnchor  :: Maybe String
+    mDefSiteAnchor  = maybe __IMPOSSIBLE__ defSiteAnchor mDefinitionSite
+
+    link (DefinitionSite m defPos _here _aName) = Attr.href $ stringValue $
+      -- If the definition site points to the top of a file,
+      -- we drop the anchor part and just link to the file.
+      applyUnless (defPos <= 1)
+        (++ "#" ++
+         Network.URI.Encode.encode (show defPos))
+         -- Network.URI.Encode.encode (fromMaybe (show defPos) aName)) -- Named links disabled
+        (Network.URI.Encode.encode $ modToFile m "html")
diff --git a/src/full/Agda/Interaction/Highlighting/JSON.hs b/src/full/Agda/Interaction/Highlighting/JSON.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/JSON.hs
@@ -0,0 +1,79 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Functions which give precise syntax highlighting info in JSON format.
+
+module Agda.Interaction.Highlighting.JSON (jsonifyHighlightingInfo) where
+
+import Agda.Interaction.Highlighting.Common
+import Agda.Interaction.Highlighting.Precise hiding (String)
+import Agda.Interaction.Highlighting.Range (Range(..))
+import Agda.Interaction.JSON
+import Agda.Interaction.Response
+import Agda.TypeChecking.Monad (HighlightingMethod(..), ModuleToSource)
+import Agda.Utils.FileName (filePath)
+import Agda.Utils.IO.TempFile (writeToTempFile)
+
+import qualified Data.ByteString.Lazy.Char8 as BS
+import qualified Data.Map as Map
+
+import Agda.Utils.Impossible
+
+-- | Encode meta information into a JSON Value
+showAspects
+  :: ModuleToSource
+     -- ^ Must contain a mapping for the definition site's module, if any.
+  -> (Range, Aspects) -> Value
+showAspects modFile (range, aspect) = object
+  [ "range" .= [from range, to range]
+  , "atoms" .= toAtoms aspect
+  , "tokenBased" .= tokenBased aspect
+  , "note" .= note aspect
+  , "definitionSite" .= fmap defSite (definitionSite aspect)
+  ]
+  where
+    defSite (DefinitionSite mdl position _ _) = object
+      [ "filepath" .= filePath (Map.findWithDefault __IMPOSSIBLE__ mdl modFile)
+      , "position" .= position
+      ]
+
+instance EncodeTCM TokenBased where
+instance ToJSON TokenBased where
+    toJSON TokenBased = String "TokenBased"
+    toJSON NotOnlyTokenBased = String "NotOnlyTokenBased"
+
+-- | Turns syntax highlighting information into a JSON value
+jsonifyHighlightingInfo
+  :: HighlightingInfo
+  -> RemoveTokenBasedHighlighting
+  -> HighlightingMethod
+  -> ModuleToSource
+     -- ^ Must contain a mapping for every definition site's module.
+  -> IO Value
+jsonifyHighlightingInfo info remove method modFile =
+  case chooseHighlightingMethod info method of
+    Direct   -> direct
+    Indirect -> indirect
+  where
+    result :: Value
+    result = object
+      [ "remove" .= case remove of
+          RemoveHighlighting -> True
+          KeepHighlighting -> False
+      , "payload" .= map (showAspects modFile) (toList info)
+      ]
+
+    direct :: IO Value
+    direct = return $ object
+      [ "kind"   .= String "HighlightingInfo"
+      , "direct" .= True
+      , "info"   .= result
+      ]
+
+    indirect :: IO Value
+    indirect = do
+      filepath <- writeToTempFile (BS.unpack (encode result))
+      return $ object
+        [ "kind"     .= String "HighlightingInfo"
+        , "direct"   .= False
+        , "filepath" .= filepath
+        ]
diff --git a/src/full/Agda/Interaction/Highlighting/LaTeX.hs b/src/full/Agda/Interaction/Highlighting/LaTeX.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/LaTeX.hs
@@ -0,0 +1,11 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Generating highlighted and aligned LaTeX from literate Agda source.
+
+module Agda.Interaction.Highlighting.LaTeX
+  ( module Exports
+  ) where
+
+import Agda.Interaction.Highlighting.LaTeX.Backend as Exports
+  ( latexBackend
+  )
diff --git a/src/full/Agda/Interaction/Highlighting/LaTeX/Backend.hs b/src/full/Agda/Interaction/Highlighting/LaTeX/Backend.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/LaTeX/Backend.hs
@@ -0,0 +1,196 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Highlighting.LaTeX.Backend
+  ( latexBackend
+  ) where
+
+import Agda.Interaction.Highlighting.LaTeX.Base
+  ( LaTeXOptions(..)
+  , LogLaTeXT
+  , runLogLaTeXTWith
+  , logMsgToText
+  , generateLaTeXIO
+  , prepareCommonAssets
+  )
+
+import Control.DeepSeq
+import Control.Monad.Trans (MonadIO)
+
+import qualified Data.Map as Map
+import Data.Map (Map)
+
+import qualified Data.Text as T
+
+import GHC.Generics (Generic)
+
+import System.FilePath ( (</>) )
+
+import Agda.Compiler.Backend (Backend(..), Backend'(..), Definition, Recompile(..))
+import Agda.Compiler.Common (curIF, IsMain(IsMain, NotMain))
+
+import Agda.Interaction.Options
+  ( ArgDescr(NoArg, ReqArg)
+  , CommandLineOptions ( optGHCiInteraction, optPragmaOptions )
+  , optCountClusters
+  , Flag
+  , OptDescr(..)
+  )
+
+import Agda.Syntax.Position (mkRangeFile, rangeFilePath)
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName, projectRoot)
+
+import Agda.TypeChecking.Monad
+  ( HasOptions(commandLineOptions)
+  , MonadDebug
+  , stModuleToSource
+  , useTC
+  , ReadTCState
+  , reportS
+  )
+
+import Agda.Utils.FileName (filePath, mkAbsolute)
+
+------------------------------------------------------------------------
+-- * Main.
+
+-- Command-line flag options, prior to e.g. path resolution and validation.
+data LaTeXFlags = LaTeXFlags
+  { latexFlagOutDir        :: FilePath
+  , latexFlagSourceFile    :: Maybe FilePath
+  , latexFlagGenerateLaTeX :: Bool
+    -- ^ Are we going to try to generate LaTeX at all?
+  } deriving (Eq, Generic)
+
+instance NFData LaTeXFlags
+
+-- | The default output directory for LaTeX.
+
+defaultLaTeXDir :: FilePath
+defaultLaTeXDir = "latex"
+
+defaultLaTeXFlags :: LaTeXFlags
+defaultLaTeXFlags = LaTeXFlags
+  { latexFlagOutDir        = defaultLaTeXDir
+  , latexFlagSourceFile    = Nothing
+  , latexFlagGenerateLaTeX = False
+  }
+
+latexFlagsDescriptions :: [OptDescr (Flag LaTeXFlags)]
+latexFlagsDescriptions =
+  [ Option []     ["latex"] (NoArg latexFlag)
+                  "generate LaTeX with highlighted source code"
+  , Option []     ["latex-dir"] (ReqArg latexDirFlag "DIR")
+                  ("directory in which LaTeX files are placed (default: " ++
+                    defaultLaTeXDir ++ ")")
+  ]
+
+latexFlag :: Flag LaTeXFlags
+latexFlag o = return $ o { latexFlagGenerateLaTeX = True }
+
+latexDirFlag :: FilePath -> Flag LaTeXFlags
+latexDirFlag d o = return $ o { latexFlagOutDir = d }
+
+data LaTeXCompileEnv = LaTeXCompileEnv LaTeXFlags
+data LaTeXModuleEnv  = LaTeXModuleEnv LaTeXOptions
+data LaTeXModule     = LaTeXModule
+data LaTeXDef        = LaTeXDef
+
+latexBackend :: Backend
+latexBackend = Backend latexBackend'
+
+latexBackend' :: Backend' LaTeXFlags LaTeXCompileEnv LaTeXModuleEnv LaTeXModule LaTeXDef
+latexBackend' = Backend'
+  { backendName           = "LaTeX"
+  , backendVersion        = Nothing
+  , options               = defaultLaTeXFlags
+  , commandLineFlags      = latexFlagsDescriptions
+  , isEnabled             = latexFlagGenerateLaTeX
+  , preCompile            = preCompileLaTeX
+  , preModule             = preModuleLaTeX
+  , compileDef            = compileDefLaTeX
+  , postModule            = postModuleLaTeX
+  , postCompile           = postCompileLaTeX
+  , scopeCheckingSuffices = True
+  , mayEraseType          = const $ return False
+  }
+
+runLogLaTeXWithMonadDebug :: MonadDebug m => LogLaTeXT m a -> m a
+runLogLaTeXWithMonadDebug = runLogLaTeXTWith $ (reportS "compile.latex" 1) . T.unpack . logMsgToText
+
+-- Resolve the raw flags into usable LaTeX options.
+resolveLaTeXOptions :: (HasOptions m, ReadTCState m) => LaTeXFlags -> TopLevelModuleName -> m LaTeXOptions
+resolveLaTeXOptions flags moduleName = do
+  options <- commandLineOptions
+  modFiles <- useTC stModuleToSource
+  let
+    mSrcFileName =
+      (\f -> mkRangeFile (mkAbsolute (filePath f)) (Just moduleName)) <$>
+      Map.lookup moduleName modFiles
+    countClusters = optCountClusters . optPragmaOptions $ options
+    latexDir = latexFlagOutDir flags
+    -- FIXME: This reliance on emacs-mode to decide whether to interpret the output location as project-relative or
+    -- cwd-relative is gross. Also it currently behaves differently for JSON mode :-/
+    -- And it prevents us from doing a real "one-time" setup.
+    outDir = case (mSrcFileName, optGHCiInteraction options) of
+      (Just sourceFile, True) ->
+        filePath (projectRoot (rangeFilePath sourceFile) moduleName) </>
+        latexDir
+      _ -> latexDir
+  return LaTeXOptions
+    { latexOptOutDir         = outDir
+    , latexOptSourceFileName = mSrcFileName
+    , latexOptCountClusters  = countClusters
+    }
+
+preCompileLaTeX
+  :: Applicative m
+  => LaTeXFlags
+  -> m LaTeXCompileEnv
+preCompileLaTeX flags = pure $ LaTeXCompileEnv flags
+
+preModuleLaTeX
+  :: (HasOptions m, ReadTCState m)
+  => LaTeXCompileEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> Maybe FilePath
+  -> m (Recompile LaTeXModuleEnv LaTeXModule)
+preModuleLaTeX (LaTeXCompileEnv flags) isMain moduleName _ifacePath = case isMain of
+  IsMain  -> Recompile . LaTeXModuleEnv <$> resolveLaTeXOptions flags moduleName
+  NotMain -> return $ Skip LaTeXModule
+
+compileDefLaTeX
+  :: Applicative m
+  => LaTeXCompileEnv
+  -> LaTeXModuleEnv
+  -> IsMain
+  -> Definition
+  -> m LaTeXDef
+compileDefLaTeX _cenv _menv _main _def = pure LaTeXDef
+
+postModuleLaTeX
+  :: (MonadDebug m, ReadTCState m, MonadIO m)
+  => LaTeXCompileEnv
+  -> LaTeXModuleEnv
+  -> IsMain
+  -> TopLevelModuleName
+  -> [LaTeXDef]
+  -> m LaTeXModule
+postModuleLaTeX _cenv (LaTeXModuleEnv latexOpts) _main _moduleName _defs = do
+  i <- curIF
+  runLogLaTeXWithMonadDebug $ do
+    -- FIXME: It would be better to do "prepareCommonAssets" in @preCompileLaTeX@, but because
+    -- the output directory depends on the module-relative project root (when in emacs-mode),
+    -- we can't do that until we see the module.
+    -- However, for now that is OK because we only generate LaTeX for the main module.
+    prepareCommonAssets (latexOptOutDir latexOpts)
+    generateLaTeXIO latexOpts i
+  return LaTeXModule
+
+postCompileLaTeX
+  :: Applicative m
+  => LaTeXCompileEnv
+  -> IsMain
+  -> Map TopLevelModuleName LaTeXModule
+  -> m ()
+postCompileLaTeX _cenv _main _modulesByName = pure ()
diff --git a/src/full/Agda/Interaction/Highlighting/LaTeX/Base.hs b/src/full/Agda/Interaction/Highlighting/LaTeX/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/LaTeX/Base.hs
@@ -0,0 +1,857 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE ViewPatterns #-}
+
+-- | Function for generating highlighted and aligned LaTeX from literate
+-- Agda source.
+
+module Agda.Interaction.Highlighting.LaTeX.Base
+  ( generateLaTeXIO
+  , prepareCommonAssets
+  , runLogLaTeXTWith
+  , logMsgToText
+  , LogMessage(..)
+  , MonadLogLaTeX
+  , LogLaTeXT
+  , LaTeXOptions(..)
+  ) where
+
+import Prelude hiding (log)
+
+import Data.Bifunctor (second)
+import Data.Char
+import Data.Maybe
+import Data.Function (on)
+import Data.Foldable (toList)
+
+import Control.Exception.Base (IOException, try)
+import Control.Monad (forM_, mapM_, unless, when)
+import Control.Monad.Trans.Reader as R ( ReaderT(runReaderT))
+import Control.Monad.RWS.Strict
+  ( RWST(runRWST)
+  , MonadReader(..), asks
+  , MonadState(..), gets, modify
+  , lift, tell
+  )
+import Control.Monad.IO.Class
+  ( MonadIO(..)
+  )
+
+import System.Directory
+import System.FilePath
+import System.Process
+
+import Data.Text (Text)
+import qualified Data.Text               as T
+#ifdef COUNT_CLUSTERS
+import qualified Data.Text.ICU           as ICU
+#endif
+import qualified Data.Text.Lazy          as L
+import qualified Data.Text.Lazy.Encoding as E
+import qualified Data.ByteString.Lazy    as BS
+
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as Set
+import qualified Data.IntMap  as IntMap
+import qualified Data.List    as List
+
+import Paths_Agda
+
+import Agda.Syntax.Common
+import Agda.Syntax.Parser.Literate (literateTeX, LayerRole, atomizeLayers)
+import qualified Agda.Syntax.Parser.Literate as L
+import Agda.Syntax.Position (RangeFile, startPos)
+import Agda.Syntax.TopLevelModuleName
+  (TopLevelModuleName, moduleNameParts)
+
+import Agda.Interaction.Highlighting.Precise hiding (toList)
+
+import Agda.TypeChecking.Monad (Interface(..)) --, reportSLn)
+
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor  ((<&>))
+import Agda.Utils.List     (last1, updateHead, updateLast)
+import Agda.Utils.Maybe    (whenJust)
+import Agda.Utils.Monad
+import qualified Agda.Utils.List1 as List1
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- * Logging
+
+class Monad m => MonadLogLaTeX m where
+  logLaTeX :: LogMessage -> m ()
+
+-- | Log LaTeX messages using a provided action.
+--
+-- This could be accomplished by putting logs into the RWST output and splitting it
+-- into a WriterT, but that becomes slightly more complicated to reason about in
+-- the presence of IO exceptions.
+--
+-- We want the logging to be reasonably polymorphic, avoid space leaks that can occur
+-- with WriterT, and also be usable during outer phases such as directory preparation.
+--
+-- I'm not certain this is the best way to do it, but whatever.
+type LogLaTeXT m = ReaderT (LogMessage -> m ()) m
+
+instance Monad m => MonadLogLaTeX (LogLaTeXT m) where
+  logLaTeX message = do
+    doLog <- ask
+    lift $ doLog message
+
+runLogLaTeXTWith :: Monad m => (LogMessage -> m ()) -> LogLaTeXT m a -> m a
+runLogLaTeXTWith = flip runReaderT
+
+-- Not currently used, but for example:
+-- runLogLaTeXWithIO :: MonadIO m => LogLaTeXT m a -> m a
+-- runLogLaTeXWithIO = runLogLaTeXTWith $ liftIO . T.putStrLn . logMsgToText
+
+------------------------------------------------------------------------
+-- * Datatypes.
+
+-- | The @LaTeX@ monad is a combination of @ExceptT@, @RWST@ and
+-- a logger @m@. The error part is just used to keep track whether we finished or
+-- not, the reader part contains static options used, the writer is where the
+-- output goes and the state is for keeping track of the tokens and some
+-- other useful info, and the MonadLogLaTeX part is used for printing debugging info.
+
+type LaTeX a = forall m. MonadLogLaTeX m => RWST Env [Output] State m a
+
+-- | Output items.
+
+data LogMessage = LogMessage Debug Text [Text] deriving Show
+
+data Output
+  = Text !Text
+    -- ^ A piece of text.
+  | MaybeColumn !AlignmentColumn
+    -- ^ A column. If it turns out to be an indentation column that is
+    --   not used to indent or align something, then no column will be
+    --   generated, only whitespace ('agdaSpace').
+  deriving Show
+
+-- | Column kinds.
+
+data Kind
+  = Indentation
+    -- ^ Used only for indentation (the placement of the first token
+    -- on a line, relative to tokens on previous lines).
+  | Alignment
+    -- ^ Used both for indentation and for alignment.
+  deriving (Eq, Show)
+
+-- | Unique identifiers for indentation columns.
+
+type IndentationColumnId = Int
+
+-- | Alignment and indentation columns.
+
+data AlignmentColumn = AlignmentColumn
+  { columnCodeBlock :: !Int
+    -- ^ The column's code block.
+  , columnColumn :: !Int
+    -- ^ The column number.
+  , columnKind :: Maybe IndentationColumnId
+    -- ^ The column kind. 'Nothing' for alignment columns and @'Just'
+    -- i@ for indentation columns, where @i@ is the column's unique
+    -- identifier.
+  } deriving Show
+
+-- | Type of function for estimating column width of text.
+
+type TextWidthEstimator = Text -> Int
+
+data Env = Env
+  { estimateTextWidth :: !TextWidthEstimator
+    -- ^ How to estimate the column width of text (i.e. Count extended grapheme clusters vs. code points).
+  , debugs :: [Debug]
+    -- ^ Says what debug information should printed.
+  }
+
+data State = State
+  { codeBlock     :: !Int   -- ^ The number of the current code block.
+  , column        :: !Int   -- ^ The current column number.
+  , columns       :: [AlignmentColumn]
+                            -- ^ All alignment columns found on the
+                            --   current line (so far), in reverse
+                            --   order.
+  , columnsPrev   :: [AlignmentColumn]
+                            -- ^ All alignment columns found in
+                            --   previous lines (in any code block),
+                            --   with larger columns coming first.
+  , nextId        :: !IndentationColumnId
+                            -- ^ The next indentation column
+                            -- identifier.
+  , usedColumns   :: HashSet IndentationColumnId
+                            -- ^ Indentation columns that have
+                            -- actually
+                            --   been used.
+  }
+
+type Tokens = [Token]
+
+data Token = Token
+  { text     :: !Text
+  , info     :: Aspects
+  }
+  deriving Show
+
+withTokenText :: (Text -> Text) -> Token -> Token
+withTokenText f tok@Token{text = t} = tok{text = f t}
+
+data Debug = MoveColumn | NonCode | Code | Spaces | Output | FileSystem
+  deriving (Eq, Show)
+
+-- | Run function for the @LaTeX@ monad.
+runLaTeX :: MonadLogLaTeX m =>
+  LaTeX a -> Env -> State -> m (a, State, [Output])
+-- ASR (2021-02-07). The eta-expansion is required by GHC >= 9.0.1
+-- (see Issue #4955).
+runLaTeX l = runRWST l
+
+emptyState :: State
+emptyState = State
+  { codeBlock     = 0
+  , column        = 0
+  , columns       = []
+  , columnsPrev   = []
+  , nextId        = 0
+  , usedColumns   = Set.empty
+  }
+
+emptyEnv
+  :: TextWidthEstimator  -- ^ Count extended grapheme clusters?
+  -> Env
+emptyEnv twe = Env twe []
+
+
+------------------------------------------------------------------------
+-- * Some helpers.
+
+-- | Gives the size of the string. If cluster counting is enabled,
+-- then the number of extended grapheme clusters is computed (the root
+-- locale is used), and otherwise the number of code points.
+
+size :: Text -> LaTeX Int
+size t = asks estimateTextWidth <&> ($ t)
+
+-- | Does the string consist solely of whitespace?
+
+isSpaces :: Text -> Bool
+isSpaces = T.all isSpace
+
+-- | Is the character a whitespace character distinct from '\n'?
+
+isSpaceNotNewline :: Char -> Bool
+isSpaceNotNewline c = isSpace c && c /= '\n'
+
+-- | Replaces all forms of whitespace, except for new-line characters,
+-- with spaces.
+
+replaceSpaces :: Text -> Text
+replaceSpaces = T.map (\c -> if isSpaceNotNewline c then ' ' else c)
+
+
+-- | If the `Token` consists of spaces, the internal column counter is advanced
+--   by the length of the token. Otherwise, `moveColumnForToken` is a no-op.
+moveColumnForToken :: Token -> LaTeX ()
+moveColumnForToken Token{ text = t } = do
+  unless (isSpaces t) $ do
+    log MoveColumn t
+    -- ASR (2021-02-07). The eta-expansion is required by GHC >= 9.0.1
+    -- (see Issue #4955).
+    n <- size t
+    moveColumn n
+
+-- | Merges 'columns' into 'columnsPrev', resets 'column' and
+-- 'columns'
+
+resetColumn :: LaTeX ()
+resetColumn = modify $ \s ->
+  s { column      = 0
+    , columnsPrev = mergeCols (columns s) (columnsPrev s)
+    , columns     = []
+    }
+  where
+  -- Remove shadowed columns from old.
+  mergeCols []         old = old
+  mergeCols new@(n:ns) old = new ++ filter ((< leastNew) . columnColumn) old
+    where
+    leastNew = columnColumn (last1 n ns)
+
+moveColumn :: Int -> LaTeX ()
+moveColumn i = modify $ \s -> s { column = i + column s }
+
+-- | Registers a column of the given kind. The column is returned.
+
+registerColumn :: Kind -> LaTeX AlignmentColumn
+registerColumn kind = do
+  column    <- gets column
+  codeBlock <- gets codeBlock
+  colKind   <- case kind of
+                 Alignment   -> return Nothing
+                 Indentation -> do
+                   nextId <- gets nextId
+                   modify $ \s -> s { nextId = succ nextId }
+                   return (Just nextId)
+  let c = AlignmentColumn { columnColumn    = column
+                          , columnCodeBlock = codeBlock
+                          , columnKind      = colKind
+                          }
+  modify $ \s -> s { columns = c : columns s }
+  return c
+
+-- | Registers the given column as used (if it is an indentation
+-- column).
+
+useColumn :: AlignmentColumn -> LaTeX ()
+useColumn c = whenJust (columnKind c) $ \ i ->
+  modify $ \ s -> s { usedColumns = Set.insert i (usedColumns s) }
+
+-- | Alignment column zero in the current code block.
+
+columnZero :: LaTeX AlignmentColumn
+columnZero = do
+  codeBlock <- gets codeBlock
+  return $ AlignmentColumn { columnColumn    = 0
+                           , columnCodeBlock = codeBlock
+                           , columnKind      = Nothing
+                           }
+
+-- | Registers column zero as an alignment column.
+
+registerColumnZero :: LaTeX ()
+registerColumnZero = do
+  c <- columnZero
+  modify $ \s -> s { columns = [c] }
+
+-- | Changes to the state that are performed at the start of a code
+-- block.
+
+enterCode :: LaTeX ()
+enterCode = do
+  resetColumn
+  modify $ \s -> s { codeBlock = codeBlock s + 1 }
+
+-- | Changes to the state that are performed at the end of a code
+-- block.
+
+leaveCode :: LaTeX ()
+leaveCode = return ()
+
+tshow :: Show a => a -> Text
+tshow = T.pack . show
+
+logMsgToText :: LogMessage -> Text
+logMsgToText (LogMessage messageLabel text extra) = T.concat $
+  [ tshow messageLabel, ": '", text, "' "
+  ] ++ if null extra then [] else ["(", T.unwords extra, ")"]
+
+logHelper :: Debug -> Text -> [Text] -> LaTeX ()
+logHelper debug text extra = do
+  logLevels <- debugs <$> ask
+  when (debug `elem` logLevels) $ do
+    lift $ logLaTeX (LogMessage debug text extra)
+
+log :: Debug -> Text -> LaTeX ()
+log MoveColumn text = do
+  cols <- gets columns
+  logHelper MoveColumn text ["columns=", tshow cols]
+log Code text = do
+  cols <- gets columns
+  col <- gets column
+  logHelper Code text ["columns=", tshow cols, "col=", tshow col]
+log debug text = logHelper debug text []
+
+output :: Output -> LaTeX ()
+output item = do
+  log Output $ tshow item
+  tell [item]
+
+------------------------------------------------------------------------
+-- * LaTeX and polytable strings.
+
+-- Polytable, http://www.ctan.org/pkg/polytable, is used for code
+-- alignment, similar to lhs2TeX's approach.
+
+nl :: Text
+nl = "%\n"
+
+-- | A command that is used when two tokens are put next to each other
+-- in the same column.
+
+agdaSpace :: Text
+agdaSpace = cmdPrefix <> "Space" <> cmdArg T.empty <> nl
+
+-- | The column's name.
+--
+-- Indentation columns have unique names, distinct from all alignment
+-- column names.
+
+columnName :: AlignmentColumn -> Text
+columnName c = T.pack $ case columnKind c of
+  Nothing -> show (columnColumn c)
+  Just i  -> show i ++ "I"
+
+-- | Opens a column with the given name.
+
+ptOpen' :: Text -> Text
+ptOpen' name = "\\>[" <> name <> "]"
+
+-- | Opens the given column.
+
+ptOpen :: AlignmentColumn -> Text
+ptOpen c = ptOpen' (columnName c)
+
+-- | Opens a special column that is only used at the beginning of
+-- lines.
+
+ptOpenBeginningOfLine :: Text
+ptOpenBeginningOfLine = ptOpen' "." <> "[@{}l@{}]"
+
+-- | Opens the given column, and inserts an indentation instruction
+-- with the given argument at the end of it.
+
+ptOpenIndent
+  :: AlignmentColumn
+  -> Int              -- ^ Indentation instruction argument.
+  -> Text
+ptOpenIndent c delta =
+  ptOpen c <> "[@{}l@{"
+           <> cmdPrefix
+           <> "Indent"
+           <> cmdArg (T.pack $ show delta)
+           <> "}]"
+
+ptClose :: Text
+ptClose = "\\<"
+
+ptClose' :: AlignmentColumn -> Text
+ptClose' c =
+  ptClose <> "[" <> columnName c <> "]"
+
+ptNL :: Text
+ptNL = nl <> "\\\\\n"
+
+ptEmptyLine :: Text
+ptEmptyLine =
+  nl <> "\\\\["
+     <> cmdPrefix
+     <> "EmptyExtraSkip"
+     <> "]%\n"
+
+cmdPrefix :: Text
+cmdPrefix = "\\Agda"
+
+cmdArg :: Text -> Text
+cmdArg x = "{" <> x <> "}"
+
+------------------------------------------------------------------------
+-- * Output generation from a stream of labelled tokens.
+
+processLayers :: [(LayerRole, Tokens)] -> LaTeX ()
+-- ASR (2021-02-07). The eta-expansion on @lt@ is required by GHC >=
+-- 9.0.1 (see Issue #4955).
+processLayers lt = forM_ lt $ \ (layerRole,toks) -> do
+  case layerRole of
+    L.Markup  -> processMarkup  toks
+    L.Comment -> processComment toks
+    L.Code    -> processCode    toks
+
+-- | Deals with markup, which is output verbatim.
+processMarkup :: Tokens -> LaTeX ()
+-- ASR (2021-02-07). The eta-expansion on @ts@ is required by GHC >=
+-- 9.0.1 (see Issue #4955).
+processMarkup ts = forM_ ts $ \ t' -> do
+  moveColumnForToken t'
+  output (Text (text t'))
+
+-- | Deals with literate text, which is output verbatim
+processComment :: Tokens -> LaTeX ()
+-- ASR (2021-02-07). The eta-expansion with @ts@ is required by GHC >=
+-- 9.0.1 (see Issue #4955).
+processComment ts = forM_ ts $ \ t' -> do
+  unless ("%" == T.take 1 (T.stripStart (text t'))) $ do
+    moveColumnForToken t'
+  output (Text (text t'))
+
+-- | Deals with code blocks. Every token, except spaces, is pretty
+-- printed as a LaTeX command.
+processCode :: Tokens -> LaTeX ()
+processCode toks' = do
+  output $ Text nl
+  enterCode
+  mapM_ go toks'
+  ptOpenWhenColumnZero =<< gets column
+  output $ Text $ ptClose <> nl
+  leaveCode
+
+  where
+    go tok'@Token{ text = tok } = do
+      -- Get the column information before grabbing the token, since
+      -- grabbing (possibly) moves the column.
+      col  <- gets column
+
+      moveColumnForToken tok'
+      log Code tok
+
+      unless (T.null tok) $
+        if (isSpaces tok) then do
+            spaces $ T.group $ replaceSpaces tok
+        else do
+          ptOpenWhenColumnZero col
+          output $ Text $
+            -- we return the escaped token wrapped in commands corresponding
+            -- to its aspect (if any) and other aspects (e.g. error, unsolved meta)
+            foldr (\c t -> cmdPrefix <> T.pack c <> cmdArg t)
+                  (escape tok)
+                  $ map fromOtherAspect (toList $ otherAspects $ info tok') ++
+                    concatMap fromAspect (toList $ aspect $ info tok')
+
+    -- Non-whitespace tokens at the start of a line trigger an
+    -- alignment column.
+    ptOpenWhenColumnZero col =
+        when (col == 0) $ do
+          registerColumnZero
+          -- ASR (2021-02-07). The eta-expansion @\o -> output o@ is
+          -- required by GHC >= 9.0.1 (see Issue #4955).
+          (\o -> output o). Text . ptOpen =<< columnZero
+
+    -- Translation from OtherAspect to command strings. So far it happens
+    -- to correspond to @show@ but it does not have to (cf. fromAspect)
+    fromOtherAspect :: OtherAspect -> String
+    fromOtherAspect = show
+
+    fromAspect :: Aspect -> [String]
+    fromAspect a = let s = [show a] in case a of
+      Comment           -> s
+      Keyword           -> s
+      Hole              -> s
+      String            -> s
+      Number            -> s
+      Symbol            -> s
+      PrimitiveType     -> s
+      Pragma            -> s
+      Background        -> s
+      Markup            -> s
+      Name Nothing isOp -> fromAspect (Name (Just Postulate) isOp)
+        -- At the time of writing the case above can be encountered in
+        -- --only-scope-checking mode, for instance for the token "Size"
+        -- in the following code:
+        --
+        --   {-# BUILTIN SIZE Size #-}
+        --
+        -- The choice of "Postulate" works for this example, but might
+        -- be less appropriate for others.
+      Name (Just kind) isOp ->
+        (\c -> if isOp then ["Operator", c] else [c]) $
+        case kind of
+          Bound                     -> sk
+          Generalizable             -> sk
+          Constructor Inductive     -> "InductiveConstructor"
+          Constructor CoInductive   -> "CoinductiveConstructor"
+          Datatype                  -> sk
+          Field                     -> sk
+          Function                  -> sk
+          Module                    -> sk
+          Postulate                 -> sk
+          Primitive                 -> sk
+          Record                    -> sk
+          Argument                  -> sk
+          Macro                     -> sk
+        where
+        sk = show kind
+
+-- | Escapes special characters.
+escape :: Text -> Text
+escape (T.uncons -> Nothing)     = T.empty
+escape (T.uncons -> Just (c, s)) = T.pack (replace c) <> escape s
+  where
+  replace :: Char -> String
+  replace char = case char of
+    '_'  -> "\\AgdaUnderscore{}"
+    '{'  -> "\\{"
+    '}'  -> "\\}"
+    '#'  -> "\\#"
+    '$'  -> "\\$"
+    '&'  -> "\\&"
+    '%'  -> "\\%"
+    '~'  -> "\\textasciitilde{}"
+    '^'  -> "\\textasciicircum{}"
+    '\\' -> "\\textbackslash{}"
+    ' '  -> "\\ "
+    _    -> [ char ]
+#if __GLASGOW_HASKELL__ < 810
+escape _                         = __IMPOSSIBLE__
+#endif
+
+-- | Every element in the list should consist of either one or more
+-- newline characters, or one or more space characters. Two adjacent
+-- list elements must not contain the same character.
+--
+-- If the final element of the list consists of spaces, then these
+-- spaces are assumed to not be trailing whitespace.
+spaces :: [Text] -> LaTeX ()
+spaces [] = return ()
+
+-- Newlines.
+spaces (s@(T.uncons -> Just ('\n', _)) : ss) = do
+  col <- gets column
+  when (col == 0) $
+    -- ASR (2021-02-07). The eta-expansion @\o -> output o@ is
+    -- required by GHC >= 9.0.1 (see Issue #4955).
+    (\o -> output o) . Text . ptOpen =<< columnZero
+  output $ Text $ ptClose <> ptNL <>
+                  T.replicate (T.length s - 1) ptEmptyLine
+  resetColumn
+  spaces ss
+
+-- Spaces followed by a newline character.
+spaces (_ : ss@(_ : _)) = spaces ss
+
+-- Spaces that are not followed by a newline character.
+spaces [ s ] = do
+  col <- gets column
+
+  let len  = T.length s
+      kind = if col /= 0 && len == 1
+             then Indentation
+             else Alignment
+
+  moveColumn len
+  column <- registerColumn kind
+
+  if col /= 0
+  then log Spaces "col /= 0"
+  else do
+    columns    <- gets columnsPrev
+    codeBlock  <- gets codeBlock
+
+    log Spaces $
+      "col == 0: " <> T.pack (show (len, columns))
+
+    case filter ((<= len) . columnColumn) columns of
+      c : _ | columnColumn c == len, isJust (columnKind c) -> do
+        -- Align. (This happens automatically if the column is an
+        -- alignment column, but c is an indentation column.)
+        useColumn c
+        output $ Text $ ptOpenBeginningOfLine
+        output $ Text $ ptClose' c
+      c : _ | columnColumn c <  len -> do
+        -- Indent.
+        useColumn c
+        output $ Text $ ptOpenIndent c (codeBlock - columnCodeBlock c)
+      _ -> return ()
+
+  output $ MaybeColumn column
+
+-- | Split multi-lines string literals into multiple string literals
+-- Isolating leading spaces for the alignment machinery to work
+-- properly
+stringLiteral :: Token -> Tokens
+stringLiteral t | aspect (info t) == Just String =
+  map (\ x -> t { text = x })
+          $ concatMap leadingSpaces
+          $ List.intersperse "\n"
+          $ T.lines (text t)
+  where
+  leadingSpaces :: Text -> [Text]
+  leadingSpaces tok = [pre, suf]
+    where (pre , suf) = T.span isSpaceNotNewline tok
+
+stringLiteral t = [t]
+
+-- | Split multi-line comments into several tokens.
+-- See issue #5398.
+multiLineComment :: Token -> Tokens
+multiLineComment Token{ text = s, info = i } | aspect i == Just Comment =
+  map (`Token` i)
+    $ List.intersperse "\n"
+    $ T.lines s
+-- multiLineComment Token{ text = s, info = i } | aspect i == Just Comment =
+--   map emptyToPar
+--     $ List1.groupBy ((==) `on` T.null)
+--     $ T.lines s
+--   where
+--   emptyToPar :: List1 Text -> Token
+--   emptyToPar ts@(t :| _)
+--     | T.null t  = Token{ text = "\n", info = mempty }
+--     | otherwise = Token{ text = sconcat $ List1.intersperse "\n" ts, info = i }
+multiLineComment t = [t]
+
+------------------------------------------------------------------------
+-- * Main.
+
+-- | The Agda data directory containing the files for the LaTeX backend.
+
+latexDataDir :: FilePath
+latexDataDir = "latex"
+
+defaultStyFile :: String
+defaultStyFile = "agda.sty"
+
+data LaTeXOptions = LaTeXOptions
+  { latexOptOutDir         :: FilePath
+  , latexOptSourceFileName :: Maybe RangeFile
+    -- ^ The parser uses a @Position@ which includes a source filename for
+    -- error reporting and such. We don't actually get the source filename
+    -- with an @Interface@, and it isn't necessary to look it up.
+    -- This is a "nice-to-have" parameter.
+  , latexOptCountClusters  :: Bool
+    -- ^ Count extended grapheme clusters rather than code points when
+    -- generating LaTeX.
+  }
+
+getTextWidthEstimator :: Bool -> TextWidthEstimator
+getTextWidthEstimator _countClusters =
+#ifdef COUNT_CLUSTERS
+  if _countClusters
+    then length . (ICU.breaks (ICU.breakCharacter ICU.Root))
+    else T.length
+#else
+  T.length
+#endif
+
+-- | Create the common base output directory and check for/install the style file.
+prepareCommonAssets :: (MonadLogLaTeX m, MonadIO m) => FilePath -> m ()
+prepareCommonAssets dir = do
+  -- Make sure @dir@ will exist.
+  dirExisted <- liftIO $ doesDirectoryExist dir
+  unless dirExisted $
+    -- Create directory @dir@ and parent directories.
+    liftIO $ createDirectoryIfMissing True dir
+
+  -- Check whether TeX will find @agda.sty@.
+  texFindsSty <- liftIO $ try $
+      readProcess
+        "kpsewhich"
+        (applyWhen dirExisted (("--path=" ++ dir) :) [defaultStyFile])
+        ""
+  case texFindsSty of
+    Right _ -> return ()
+    Left (e :: IOException) -> do
+     -- -- we are lacking MonadDebug here, so no debug printing via reportSLn
+     -- reportSLn "compile.latex.sty" 70 $ unlines
+     --   [ unwords [ "Searching for", defaultStyFile, "in", dir, "returns:" ]
+     --   , show e
+     --   ]
+     let agdaSty = dir </> defaultStyFile
+     unlessM (pure dirExisted `and2M` liftIO (doesFileExist agdaSty)) $ do
+       -- It is safe now to create the default style file in @dir@ without overwriting
+       -- a possibly user-edited copy there.
+       logLaTeX $ LogMessage FileSystem
+         (T.pack $ unwords [defaultStyFile, "was not found. Copying a default version of", defaultStyFile, "into", dir])
+         []
+       liftIO $ do
+         styFile <- getDataFileName $
+           latexDataDir </> defaultStyFile
+         copyFile styFile agdaSty
+
+-- | Generates a LaTeX file for the given interface.
+generateLaTeXIO :: (MonadLogLaTeX m, MonadIO m) => LaTeXOptions -> Interface -> m ()
+generateLaTeXIO opts i = do
+  let textWidthEstimator = getTextWidthEstimator (latexOptCountClusters opts)
+  let baseDir = latexOptOutDir opts
+  let outPath = baseDir </>
+                latexOutRelativeFilePath (iTopLevelModuleName i)
+  latex <- E.encodeUtf8 <$> toLaTeX
+              (emptyEnv textWidthEstimator)
+              (latexOptSourceFileName opts)
+              (iSource i)
+              (iHighlighting i)
+  liftIO $ do
+    createDirectoryIfMissing True (takeDirectory outPath)
+    BS.writeFile outPath latex
+
+latexOutRelativeFilePath :: TopLevelModuleName -> FilePath
+latexOutRelativeFilePath m =
+  List.intercalate [pathSeparator]
+    (map T.unpack $ List1.toList $ moduleNameParts m) <.>
+  "tex"
+
+-- | Transforms the source code into LaTeX.
+toLaTeX
+  :: MonadLogLaTeX m
+  => Env
+  -> Maybe RangeFile
+  -> L.Text
+  -> HighlightingInfo
+  -> m L.Text
+toLaTeX env path source hi =
+
+  processTokens env
+
+    . map
+      ( ( \(role, tokens) ->
+            (role,) $
+              -- This bit fixes issue 954
+              ( applyWhen (L.isCode role) $
+                  -- Remove trailing whitespace from the
+                  -- final line; the function spaces
+                  -- expects trailing whitespace to be
+                  -- followed by a newline character.
+                    whenMoreThanOne
+                      ( updateLast
+                          $ withTokenText
+                          $ \suf ->
+                            maybe
+                              suf
+                              (T.dropWhileEnd isSpaceNotNewline)
+                              (T.stripSuffix "\n" suf)
+                      )
+                      . updateLast (withTokenText $ T.dropWhileEnd isSpaceNotNewline)
+                      . updateHead
+                        ( withTokenText $
+                            \pre ->
+                              fromMaybe pre $ T.stripPrefix "\n" $
+                                T.dropWhile
+                                  isSpaceNotNewline
+                                  pre
+                        )
+              )
+                tokens
+        ) . ( second
+                ( -- Split tokens at newlines
+                  concatMap stringLiteral
+                . concatMap multiLineComment
+                . List1.toList
+                . fmap (\ (mi, cs) -> Token
+                        { text = T.pack $ List1.toList cs
+                        , info = fromMaybe mempty mi
+                        }
+                      )
+                . List1.groupByFst1
+                )
+            )
+      )
+    . List1.groupByFst
+
+    -- Look up the meta info at each position in the highlighting info.
+    . zipWith (\pos (role, char) -> (role, (IntMap.lookup pos infoMap, char)))
+              [1..]
+    -- Map each character to its role
+    . atomizeLayers
+    . literateTeX (startPos path)
+    $ L.unpack source
+  where
+  infoMap = toMap hi
+
+  whenMoreThanOne :: ([a] -> [a]) -> [a] -> [a]
+  whenMoreThanOne f xs@(_:_:_) = f xs
+  whenMoreThanOne _ xs         = xs
+
+
+processTokens
+  :: MonadLogLaTeX m
+  => Env
+  -> [(LayerRole, Tokens)]
+  -> m L.Text
+processTokens env ts = do
+  ((), s, os) <- runLaTeX (processLayers ts) env emptyState
+  return $ L.fromChunks $ map (render s) os
+  where
+    render _ (Text s)        = s
+    render s (MaybeColumn c)
+      | Just i <- columnKind c,
+        not (i `Set.member` usedColumns s) = agdaSpace
+      | otherwise                          = nl <> ptOpen c
diff --git a/src/full/Agda/Interaction/Highlighting/Precise.hs b/src/full/Agda/Interaction/Highlighting/Precise.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Precise.hs
@@ -0,0 +1,323 @@
+-- | Types used for precise syntax highlighting.
+
+module Agda.Interaction.Highlighting.Precise
+  ( -- * Highlighting information
+    Aspect(..)
+  , NameKind(..)
+  , OtherAspect(..)
+  , Aspects(..)
+  , DefinitionSite(..)
+  , TokenBased(..)
+  , RangePair(..)
+  , rangePairInvariant
+  , PositionMap(..)
+  , DelayedMerge(..)
+  , delayedMergeInvariant
+  , HighlightingInfo
+  , highlightingInfoInvariant
+  , HighlightingInfoBuilder
+  , highlightingInfoBuilderInvariant
+    -- ** Operations
+  , parserBased
+  , kindOfNameToNameKind
+  , IsBasicRangeMap(..)
+  , RangeMap.several
+  , Convert(..)
+  , RangeMap.insideAndOutside
+  , RangeMap.restrictTo
+  ) where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import Data.Function (on)
+import Data.Semigroup
+
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import GHC.Generics (Generic)
+
+import qualified Agda.Syntax.Common   as Common
+import Agda.Syntax.TopLevelModuleName
+import Agda.Syntax.Scope.Base                   ( KindOfName(..) )
+
+import Agda.Interaction.Highlighting.Range
+
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.RangeMap (RangeMap, IsBasicRangeMap(..))
+import qualified Agda.Utils.RangeMap as RangeMap
+
+import Agda.Syntax.Common.Aspect
+import Agda.Utils.String
+
+import Agda.Utils.Impossible
+
+-- | A limited kind of syntax highlighting information: a pair
+-- consisting of 'Ranges' and 'Aspects'.
+--
+-- Note the invariant which 'RangePair's should satisfy
+-- ('rangePairInvariant').
+
+newtype RangePair = RangePair
+  { rangePair :: (Ranges, Aspects)
+  }
+  deriving (Show, NFData)
+
+-- | Invariant for 'RangePair'.
+
+rangePairInvariant :: RangePair -> Bool
+rangePairInvariant (RangePair (rs, _)) =
+  rangesInvariant rs
+
+-- | Syntax highlighting information, represented by maps from
+-- positions to 'Aspects'.
+--
+-- The first position in the file has number 1.
+
+newtype PositionMap = PositionMap
+  { positionMap :: IntMap Aspects
+  }
+  deriving (Show, NFData)
+
+-- | Highlighting info with delayed merging.
+--
+-- Merging large sets of highlighting info repeatedly might be costly.
+-- The idea of this type is to accumulate small pieces of highlighting
+-- information, and then to merge them all at the end.
+--
+-- Note the invariant which values of this type should satisfy
+-- ('delayedMergeInvariant').
+
+newtype DelayedMerge hl = DelayedMerge (Endo [hl])
+  deriving (Semigroup, Monoid)
+
+instance Show hl => Show (DelayedMerge hl) where
+  showsPrec _ (DelayedMerge f) =
+    showString "DelayedMerge (Endo (" .
+    shows (appEndo f []) .
+    showString " ++))"
+
+-- | Invariant for @'DelayedMerge' hl@, parametrised by the invariant
+-- for @hl@.
+--
+-- Additionally the endofunction should be extensionally equal to @(fs
+-- '++')@ for some list @fs@.
+
+delayedMergeInvariant :: (hl -> Bool) -> DelayedMerge hl -> Bool
+delayedMergeInvariant inv (DelayedMerge f) =
+  all inv (appEndo f [])
+
+-- | Highlighting information.
+--
+-- Note the invariant which values of this type should satisfy
+-- ('highlightingInfoInvariant').
+--
+-- This is a type synonym in order to make it easy to change to
+-- another representation.
+
+type HighlightingInfo = RangeMap Aspects
+
+-- | The invariant for 'HighlightingInfo'.
+
+highlightingInfoInvariant :: HighlightingInfo -> Bool
+highlightingInfoInvariant = RangeMap.rangeMapInvariant
+
+-- | A type that is intended to be used when constructing highlighting
+-- information.
+--
+-- Note the invariant which values of this type should satisfy
+-- ('highlightingInfoBuilderInvariant').
+--
+-- This is a type synonym in order to make it easy to change to
+-- another representation.
+--
+-- The type should be an instance of @'IsBasicRangeMap' 'Aspects'@,
+-- 'Semigroup' and 'Monoid', and there should be an instance of
+-- @'Convert' 'HighlightingInfoBuilder' 'HighlightingInfo'@.
+
+type HighlightingInfoBuilder = DelayedMerge RangePair
+
+-- | The invariant for 'HighlightingInfoBuilder'.
+--
+-- Additionally the endofunction should be extensionally equal to @(fs
+-- '++')@ for some list @fs@.
+
+highlightingInfoBuilderInvariant :: HighlightingInfoBuilder -> Bool
+highlightingInfoBuilderInvariant =
+  delayedMergeInvariant rangePairInvariant
+
+------------------------------------------------------------------------
+-- Creation and conversion
+
+-- | A variant of 'mempty' with 'tokenBased' set to
+-- 'NotOnlyTokenBased'.
+
+parserBased :: Aspects
+parserBased = mempty { tokenBased = NotOnlyTokenBased }
+
+-- | Conversion from classification of the scope checker.
+
+kindOfNameToNameKind :: KindOfName -> NameKind
+kindOfNameToNameKind = \case
+  -- Inductive is Constructor default, overwritten by CoInductive
+  ConName                  -> Constructor Common.Inductive
+  CoConName                -> Constructor Common.CoInductive
+  FldName                  -> Field
+  PatternSynName           -> Constructor Common.Inductive
+  GeneralizeName           -> Generalizable
+  DisallowedGeneralizeName -> Generalizable
+  MacroName                -> Macro
+  QuotableName             -> Function
+  DataName                 -> Datatype
+  RecName                  -> Record
+  FunName                  -> Function
+  AxiomName                -> Postulate
+  PrimName                 -> Primitive
+  OtherDefName             -> Function
+
+instance IsBasicRangeMap Aspects RangePair where
+  singleton rs m = RangePair (rs, m)
+
+  toList (RangePair (Ranges rs, m)) =
+    [ (r, m) | r <- rs, not (null r) ]
+
+  toMap f = toMap (convert (DelayedMerge (Endo (f :))) :: PositionMap)
+
+instance IsBasicRangeMap Aspects PositionMap where
+  singleton rs m = PositionMap
+    { positionMap =
+      IntMap.fromDistinctAscList [ (p, m) | p <- rangesToPositions rs ]
+    }
+
+  toList = map join . List1.groupBy' p . IntMap.toAscList . positionMap
+    where
+    p (pos1, m1) (pos2, m2) = pos2 == pos1 + 1 && m1 == m2
+    join pms = ( Range { from = List1.head ps, to = List1.last ps + 1 }
+               , List1.head ms
+               )
+      where (ps, ms) = List1.unzip pms
+
+  toMap = positionMap
+
+instance Semigroup a =>
+         IsBasicRangeMap a (DelayedMerge (RangeMap a)) where
+  singleton r m = DelayedMerge (Endo (singleton r m :))
+
+  toMap  f = toMap  (convert f :: RangeMap a)
+  toList f = toList (convert f :: RangeMap a)
+
+instance IsBasicRangeMap Aspects (DelayedMerge RangePair) where
+  singleton r m = DelayedMerge (Endo (singleton r m :))
+
+  toMap  f = toMap  (convert f :: PositionMap)
+  toList f = toList (convert f :: RangeMap Aspects)
+
+instance IsBasicRangeMap Aspects (DelayedMerge PositionMap) where
+  singleton r m = DelayedMerge (Endo (singleton r m :))
+
+  toMap  f = toMap  (convert f :: PositionMap)
+  toList f = toList (convert f :: PositionMap)
+
+-- | Conversion between different types.
+
+class Convert a b where
+  convert :: a -> b
+
+instance Monoid hl => Convert (DelayedMerge hl) hl where
+  convert (DelayedMerge f) = mconcat (appEndo f [])
+
+instance Convert (RangeMap Aspects) (RangeMap Aspects) where
+  convert = id
+
+instance Convert PositionMap (RangeMap Aspects) where
+  convert =
+    RangeMap.fromNonOverlappingNonEmptyAscendingList .
+    toList
+
+instance Convert (DelayedMerge PositionMap) (RangeMap Aspects) where
+  convert f = convert (convert f :: PositionMap)
+
+instance Convert (DelayedMerge RangePair) PositionMap where
+  convert (DelayedMerge f) =
+    PositionMap $
+    IntMap.fromListWith (flip (<>))
+      [ (p, m)
+      | RangePair (r, m) <- appEndo f []
+      , p                <- rangesToPositions r
+      ]
+
+instance Convert (DelayedMerge RangePair) (RangeMap Aspects) where
+  convert (DelayedMerge f) =
+    mconcat
+      [ singleton r m
+      | RangePair (r, m) <- appEndo f []
+      ]
+
+------------------------------------------------------------------------
+-- Merging
+
+instance Semigroup TokenBased where
+  b1@NotOnlyTokenBased <> b2 = b1
+  TokenBased           <> b2 = b2
+
+instance Monoid TokenBased where
+  mempty  = TokenBased
+  mappend = (<>)
+
+
+instance Semigroup DefinitionSite where
+  d1 <> d2 | d1 == d2  = d1
+           | otherwise = d1 -- TODO: __IMPOSSIBLE__
+
+-- | Merges meta information.
+
+mergeAspects :: Aspects -> Aspects -> Aspects
+mergeAspects m1 m2 = Aspects
+  { aspect       = (unionMaybeWith (<>) `on` aspect) m1 m2
+  , otherAspects = (Set.union `on` otherAspects) m1 m2
+  , note         = case (note m1, note m2) of
+      (n1, "") -> n1
+      ("", n2) -> n2
+      (n1, n2)
+        | n1 == n2  -> n1
+        | otherwise -> addFinalNewLine n1 ++ "----\n" ++ n2
+  , definitionSite = (unionMaybeWith (<>) `on` definitionSite) m1 m2
+  , tokenBased     = tokenBased m1 <> tokenBased m2
+  }
+
+instance Semigroup Aspects where
+  (<>) = mergeAspects
+
+instance Monoid Aspects where
+  mempty = Aspects
+    { aspect         = Nothing
+    , otherAspects   = Set.empty
+    , note           = []
+    , definitionSite = Nothing
+    , tokenBased     = mempty
+    }
+  mappend = (<>)
+
+instance Semigroup PositionMap where
+  f1 <> f2 = PositionMap
+    { positionMap = (IntMap.unionWith mappend `on` positionMap) f1 f2 }
+
+instance Monoid PositionMap where
+  mempty  = PositionMap { positionMap = IntMap.empty }
+  mappend = (<>)
+
+------------------------------------------------------------------------
+-- NFData instances
+
+instance NFData Aspect
+instance NFData OtherAspect
+instance NFData DefinitionSite
+
+instance NFData Aspects where
+  rnf (Aspects a b c d _) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
diff --git a/src/full/Agda/Interaction/Highlighting/Range.hs b/src/full/Agda/Interaction/Highlighting/Range.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Range.hs
@@ -0,0 +1,132 @@
+
+-- | Ranges.
+
+module Agda.Interaction.Highlighting.Range
+  ( Range(..)
+  , rangeInvariant
+  , Ranges(..)
+  , rangesInvariant
+  , overlapping
+  , overlappings
+  , empty
+  , rangeToPositions
+  , rangesToPositions
+  , rToR
+  , rangeToRange
+  , minus
+  ) where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import qualified Agda.Syntax.Position as P
+
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+
+-- | Character ranges. The first character in the file has position 1.
+-- Note that the 'to' position is considered to be outside of the
+-- range.
+--
+-- Invariant: @'from' '<=' 'to'@.
+
+data Range = Range { from, to :: !Int }
+             deriving (Eq, Ord, Show)
+
+instance Null Range where
+  empty  = Range 0 0
+  null r = to r <= from r
+
+instance NFData Range where
+  rnf (Range _ _) = ()
+
+-- | The 'Range' invariant.
+
+rangeInvariant :: Range -> Bool
+rangeInvariant r = from r <= to r
+
+-- | Zero or more consecutive and separated ranges.
+
+newtype Ranges = Ranges [Range]
+  deriving (Eq, Show, NFData)
+
+-- | The 'Ranges' invariant.
+
+rangesInvariant :: Ranges -> Bool
+rangesInvariant (Ranges rs) = allConsecutive (\ r s -> to r < from s) rs
+
+------------------------------------------------------------------------
+-- Queries
+
+-- | 'True' iff the ranges overlap.
+--
+-- The ranges are assumed to be well-formed.
+
+overlapping :: Range -> Range -> Bool
+overlapping r1 r2 = (not $ r1 `isLeftOf` r2) && (not $ r2 `isLeftOf` r1)
+
+isLeftOf :: Range -> Range -> Bool
+isLeftOf r1 r2 = to r1 <= from r2
+
+overlappings :: Ranges -> Ranges -> Bool
+-- specification: overlappings (Ranges r1s) (Ranges r2s) = or [ overlapping r1 r2 | r1 <- r1s, r2 <- r2s ]
+overlappings (Ranges r1s) (Ranges r2s) =
+  isNothing $ mergeStrictlyOrderedBy isLeftOf r1s r2s
+
+------------------------------------------------------------------------
+-- Conversion
+
+-- | Converts a range to a list of positions.
+
+rangeToPositions :: Range -> [Int]
+rangeToPositions r = [from r .. to r - 1]
+
+-- | Converts several ranges to a list of positions.
+
+rangesToPositions :: Ranges -> [Int]
+rangesToPositions (Ranges rs) = concatMap rangeToPositions rs
+
+-- | Converts a 'P.Range' to a 'Ranges'.
+
+rToR :: P.Range -> Ranges
+rToR r = Ranges (map iToR (P.rangeIntervals r))
+  where
+  iToR (P.Interval { P.iStart = P.Pn { P.posPos = pos1 }
+                   , P.iEnd   = P.Pn { P.posPos = pos2 }
+                   }) =
+    Range { from = fromIntegral pos1, to = fromIntegral pos2 }
+
+-- | Converts a 'P.Range', seen as a continuous range, to a 'Range'.
+
+rangeToRange :: P.Range -> Range
+rangeToRange r =
+  case P.rangeToInterval r of
+    Nothing -> Range { from = 0, to = 0 }
+    Just i  -> Range { from = fromIntegral $ P.posPos $ P.iStart i
+                     , to   = fromIntegral $ P.posPos $ P.iEnd i
+                     }
+
+------------------------------------------------------------------------
+-- Operations
+
+-- | @minus xs ys@ computes the difference between @xs@ and @ys@: the
+-- result contains those positions which are present in @xs@ but not
+-- in @ys@.
+--
+-- Linear in the lengths of the input ranges.
+
+minus :: Ranges -> Ranges -> Ranges
+minus (Ranges rs1) (Ranges rs2) = Ranges (m rs1 rs2)
+  where
+  m []     _      = []
+  m xs     []     = xs
+  m (x:xs) (y:ys)
+    | null y          = m (x:xs) ys
+    | to x < from y   = x : m xs (y:ys)
+    | to y < from x   = m (x:xs) ys
+    | from x < from y = Range { from = from x, to = from y } :
+                        m (Range { from = from y, to = to x } : xs) (y:ys)
+    | to y < to x     = m (Range { from = to y, to = to x } : xs) ys
+    | otherwise       = m xs (y:ys)
diff --git a/src/full/Agda/Interaction/Highlighting/Vim.hs b/src/full/Agda/Interaction/Highlighting/Vim.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Highlighting/Vim.hs
@@ -0,0 +1,95 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Highlighting.Vim where
+
+import Control.Monad.Trans
+
+import Data.Function ( on )
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Data.Maybe
+
+import System.FilePath
+
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Name as CName
+
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.List1             ( List1, pattern (:|) )
+import qualified Agda.Utils.List1   as List1
+import qualified Agda.Utils.IO.UTF8 as UTF8
+import Agda.Utils.Tuple
+import Agda.Syntax.Common.Pretty
+
+vimFile :: FilePath -> FilePath
+vimFile file =
+    case splitFileName file of
+        (path, name) -> path </> "" <.> name <.> "vim"
+
+escape :: String -> String
+escape = concatMap esc
+    where
+        escchars :: String
+        escchars = "$\\^.*~[]"
+        esc c   | c `elem` escchars = ['\\',c]
+                | otherwise         = [c]
+
+wordBounded :: String -> String
+wordBounded s0 = concat ["\\<", s0, "\\>"]
+
+keyword :: String -> [String] -> String
+keyword _ [] = ""
+keyword cat ws  = "syn keyword " ++ unwords (cat : ws)
+
+match :: String -> List1 String -> String
+match cat (w :| ws) =
+  "syn match "
+    ++ cat
+    ++ " \""
+    ++ List.intercalate "\\|" (map (wordBounded . escape) $ w:ws)
+    ++ "\""
+
+matches :: [String] -> [String] -> [String] -> [String] -> [String] -> [String] -> [String]
+matches cons icons defs idefs flds iflds =
+    map snd
+    $ List.sortBy (compare `on` fst)
+    $ cons' ++ defs' ++ icons' ++ idefs'
+    where
+        cons'  = foo "agdaConstructor"      $ classify length cons
+        icons' = foo "agdaInfixConstructor" $ classify length icons
+        defs'  = foo "agdaFunction"         $ classify length defs
+        idefs' = foo "agdaInfixFunction"    $ classify length idefs
+
+        classify f = List1.groupBy ((==) `on` f)
+                     . List.sortBy (compare `on` f)
+
+        foo :: String -> [List1 String] -> [(Int, String)]
+        foo cat = map (length . List1.head /\ match cat)
+
+toVim :: NamesInScope -> String
+toVim ns = unlines $ matches mcons micons mdefs midefs mflds miflds
+    where
+        cons = [ x | (x, con :| _) <- Map.toList ns, isJust $ isConName $ anameKind con ]
+        defs = [ x | (x, def :| _) <- Map.toList ns, isDefName (anameKind def) ]
+        flds = [ x | (x, fld :| _) <- Map.toList ns, anameKind fld == FldName  ]
+
+        mcons = map prettyShow cons
+        mdefs = map prettyShow defs
+        mflds = map prettyShow flds
+
+        micons = concatMap parts cons
+        midefs = concatMap parts defs
+        miflds = concatMap parts flds
+
+        parts n
+          | isOperator n = map rawNameToString $ nameStringParts n
+          | otherwise    = []
+
+generateVimFile :: FilePath -> TCM ()
+generateVimFile file = do
+    scope <- getScope
+    liftIO $ UTF8.writeFile (vimFile file) $ toVim $ names scope
+    where
+        names = nsNames . everythingInScope
diff --git a/src/full/Agda/Interaction/Imports.hs b/src/full/Agda/Interaction/Imports.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Imports.hs
@@ -0,0 +1,1324 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# LANGUAGE RecursiveDo #-}
+
+{-| This module deals with finding imported modules and loading their
+    interface files.
+-}
+module Agda.Interaction.Imports
+  ( Mode, pattern ScopeCheck, pattern TypeCheck
+
+  , CheckResult (CheckResult)
+  , crModuleInfo
+  , crInterface
+  , crWarnings
+  , crMode
+  , crSource
+
+  , Source(..)
+  , scopeCheckImport
+  , parseSource
+  , typeCheckMain
+
+  -- Currently only used by test/api/Issue1168.hs:
+  , readInterface
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad               ( forM, forM_, void )
+import Control.Monad.Except
+import Control.Monad.IO.Class      ( MonadIO(..) )
+import Control.Monad.State
+import Control.Monad.Trans.Maybe
+import qualified Control.Exception as E
+
+#if __GLASGOW_HASKELL__ < 808
+import Control.Monad.Fail (MonadFail)
+#endif
+
+import Data.Either
+import qualified Data.List as List
+import Data.Maybe
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.HashMap.Strict as HMap
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Text (Text)
+import qualified Data.Text.Lazy as TL
+
+import System.Directory (doesFileExist, removeFile)
+import System.FilePath  ( (</>) )
+
+import Agda.Benchmarking
+
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Attribute
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Parser
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.TopLevelModuleName
+import Agda.Syntax.Translation.ConcreteToAbstract as CToA
+
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Warnings hiding (warnings)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Rewriting.Confluence ( checkConfluenceOfRules )
+import Agda.TypeChecking.MetaVars ( openMetasToPostulates )
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Serialise
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Pretty as P
+import Agda.TypeChecking.DeadCode
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+import Agda.TheTypeChecker
+
+import Agda.Interaction.BasicOps ( getGoals, showGoals )
+import Agda.Interaction.FindFile
+import Agda.Interaction.Highlighting.Generate
+import Agda.Interaction.Highlighting.Precise  ( convert )
+import Agda.Interaction.Highlighting.Vim
+import Agda.Interaction.Library
+import Agda.Interaction.Options
+import qualified Agda.Interaction.Options.Lenses as Lens
+import Agda.Interaction.Options.Warnings (unsolvedWarnings)
+import Agda.Interaction.Response
+  (RemoveTokenBasedHighlighting(KeepHighlighting))
+
+import Agda.Utils.FileName
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.IO.Binary
+import Agda.Syntax.Common.Pretty hiding (Mode)
+import qualified Agda.Utils.ProfileOptions as Profile
+import Agda.Utils.Hash
+import qualified Agda.Utils.Trie as Trie
+
+import Agda.Utils.Impossible
+
+-- | Whether to ignore interfaces (@.agdai@) other than built-in modules
+
+ignoreInterfaces :: HasOptions m => m Bool
+ignoreInterfaces = optIgnoreInterfaces <$> commandLineOptions
+
+-- | Whether to ignore all interface files (@.agdai@)
+
+ignoreAllInterfaces :: HasOptions m => m Bool
+ignoreAllInterfaces = optIgnoreAllInterfaces <$> commandLineOptions
+
+-- | The decorated source code.
+
+data Source = Source
+  { srcText        :: TL.Text               -- ^ Source code.
+  , srcFileType    :: FileType              -- ^ Source file type
+  , srcOrigin      :: SourceFile            -- ^ Source location at the time of its parsing
+  , srcModule      :: C.Module              -- ^ The parsed module.
+  , srcModuleName  :: TopLevelModuleName    -- ^ The top-level module name.
+  , srcProjectLibs :: [AgdaLibFile]         -- ^ The .agda-lib file(s) of the project this file belongs to.
+  , srcAttributes  :: !Attributes
+    -- ^ Every encountered attribute.
+  }
+
+-- | Parses a source file and prepares the 'Source' record.
+
+parseSource :: SourceFile -> TCM Source
+parseSource sourceFile@(SourceFile f) = Bench.billTo [Bench.Parsing] $ do
+  (source, fileType, parsedMod, attrs, parsedModName) <- mdo
+    -- This piece of code uses mdo because the top-level module name
+    -- (parsedModName) is obtained from the parser's result, but it is
+    -- also used by the parser.
+    let rf = mkRangeFile f (Just parsedModName)
+    source                         <- runPM $ readFilePM rf
+    ((parsedMod, attrs), fileType) <- runPM $
+                                      parseFile moduleParser rf $
+                                      TL.unpack source
+    parsedModName                  <- moduleName f parsedMod
+    return (source, fileType, parsedMod, attrs, parsedModName)
+  libs <- getAgdaLibFiles f parsedModName
+  return Source
+    { srcText        = source
+    , srcFileType    = fileType
+    , srcOrigin      = sourceFile
+    , srcModule      = parsedMod
+    , srcModuleName  = parsedModName
+    , srcProjectLibs = libs
+    , srcAttributes  = attrs
+    }
+
+srcDefaultPragmas :: Source -> [OptionsPragma]
+srcDefaultPragmas src = map _libPragmas (srcProjectLibs src)
+
+srcFilePragmas :: Source -> [OptionsPragma]
+srcFilePragmas src = pragmas
+  where
+  cpragmas = C.modPragmas (srcModule src)
+  pragmas = [ OptionsPragma
+                { pragmaStrings = opts
+                , pragmaRange   = r
+                }
+            | C.OptionsPragma r opts <- cpragmas
+            ]
+
+-- | Set options from a 'Source' pragma, using the source
+--   ranges of the pragmas for error reporting.
+setOptionsFromSourcePragmas :: Source -> TCM ()
+setOptionsFromSourcePragmas src = do
+  mapM_ setOptionsFromPragma (srcDefaultPragmas src)
+  mapM_ setOptionsFromPragma (srcFilePragmas    src)
+
+-- | Is the aim to type-check the top-level module, or only to
+-- scope-check it?
+
+data Mode
+  = ScopeCheck
+  | TypeCheck
+  deriving (Eq, Show)
+
+-- | Are we loading the interface for the user-loaded file
+--   or for an import?
+data MainInterface
+  = MainInterface Mode -- ^ For the main file.
+                       --
+                       --   In this case state changes inflicted by
+                       --   'createInterface' are preserved.
+  | NotMainInterface   -- ^ For an imported file.
+                       --
+                       --   In this case state changes inflicted by
+                       --   'createInterface' are not preserved.
+  deriving (Eq, Show)
+
+-- | Should state changes inflicted by 'createInterface' be preserved?
+
+includeStateChanges :: MainInterface -> Bool
+includeStateChanges (MainInterface _) = True
+includeStateChanges NotMainInterface  = False
+
+-- | The kind of interface produced by 'createInterface'
+moduleCheckMode :: MainInterface -> ModuleCheckMode
+moduleCheckMode = \case
+    MainInterface TypeCheck                       -> ModuleTypeChecked
+    NotMainInterface                              -> ModuleTypeChecked
+    MainInterface ScopeCheck                      -> ModuleScopeChecked
+
+-- | Merge an interface into the current proof state.
+mergeInterface :: Interface -> TCM ()
+mergeInterface i = do
+    let sig     = iSignature i
+        builtin = Map.toAscList $ iBuiltin i
+        primOrBi = \case
+          (_, Prim x)                     -> Left x
+          (x, Builtin t)                  -> Right (x, Builtin t)
+          (x, BuiltinRewriteRelations xs) -> Right (x, BuiltinRewriteRelations xs)
+        (prim, bi') = partitionEithers $ map primOrBi builtin
+        bi      = Map.fromDistinctAscList bi'
+        warns   = iWarnings i
+    bs <- getsTC stBuiltinThings
+    reportSLn "import.iface.merge" 10 "Merging interface"
+    reportSLn "import.iface.merge" 20 $
+      "  Current builtins " ++ show (Map.keys bs) ++ "\n" ++
+      "  New builtins     " ++ show (Map.keys bi)
+    let check (BuiltinName b) (Builtin x) (Builtin y)
+              | x == y    = return ()
+              | otherwise = typeError $ DuplicateBuiltinBinding b x y
+        check _ (BuiltinRewriteRelations xs) (BuiltinRewriteRelations ys) = return ()
+        check _ _ _ = __IMPOSSIBLE__
+    sequence_ $ Map.intersectionWithKey check bs bi
+    addImportedThings
+      sig
+      (iMetaBindings i)
+      bi
+      (iPatternSyns i)
+      (iDisplayForms i)
+      (iUserWarnings i)
+      (iPartialDefs i)
+      warns
+      (iOpaqueBlocks i)
+      (iOpaqueNames i)
+    reportSLn "import.iface.merge" 20 $
+      "  Rebinding primitives " ++ show prim
+    mapM_ rebind prim
+    whenJustM (optConfluenceCheck <$> pragmaOptions) $ \confChk -> do
+      reportSLn "import.iface.confluence" 20 $ "  Checking confluence of imported rewrite rules"
+      checkConfluenceOfRules confChk $ concat $ HMap.elems $ sig ^. sigRewriteRules
+    where
+        rebind (x, q) = do
+            PrimImpl _ pf <- lookupPrimitiveFunction x
+            stImportedBuiltins `modifyTCLens` Map.insert (someBuiltin x) (Prim pf{ primFunName = q })
+
+addImportedThings
+  :: Signature
+  -> RemoteMetaStore
+  -> BuiltinThings PrimFun
+  -> A.PatternSynDefns
+  -> DisplayForms
+  -> Map A.QName Text      -- ^ Imported user warnings
+  -> Set QName             -- ^ Name of imported definitions which are partial
+  -> [TCWarning]
+  -> Map OpaqueId OpaqueBlock
+  -> Map QName OpaqueId
+  -> TCM ()
+addImportedThings isig metas ibuiltin patsyns display userwarn
+                  partialdefs warnings oblock oid = do
+  stImports              `modifyTCLens` \ imp -> unionSignatures [imp, isig]
+  stImportedMetaStore    `modifyTCLens` HMap.union metas
+  stImportedBuiltins     `modifyTCLens` \ imp -> Map.union imp ibuiltin
+  stImportedUserWarnings `modifyTCLens` \ imp -> Map.union imp userwarn
+  stImportedPartialDefs  `modifyTCLens` \ imp -> Set.union imp partialdefs
+  stPatternSynImports    `modifyTCLens` \ imp -> Map.union imp patsyns
+  stImportedDisplayForms `modifyTCLens` \ imp -> HMap.unionWith (++) imp display
+  stTCWarnings           `modifyTCLens` \ imp -> imp `List.union` warnings
+  stOpaqueBlocks         `modifyTCLens` \ imp -> imp `Map.union` oblock
+  stOpaqueIds            `modifyTCLens` \ imp -> imp `Map.union` oid
+  addImportedInstances isig
+
+-- | Scope checks the given module. A proper version of the module
+-- name (with correct definition sites) is returned.
+
+scopeCheckImport ::
+  TopLevelModuleName -> ModuleName ->
+  TCM (ModuleName, Map ModuleName Scope)
+scopeCheckImport top x = do
+    reportSLn "import.scope" 5 $ "Scope checking " ++ prettyShow x
+    verboseS "import.scope" 10 $ do
+      visited <- prettyShow <$> getPrettyVisitedModules
+      reportSLn "import.scope" 10 $ "  visited: " ++ visited
+    -- Since scopeCheckImport is called from the scope checker,
+    -- we need to reimburse her account.
+    i <- Bench.billTo [] $ getNonMainInterface top Nothing
+    addImport top
+
+    -- If that interface was supposed to raise a warning on import, do so.
+    whenJust (iImportWarning i) $ warning . UserWarning
+
+    -- let s = publicModules $ iInsideScope i
+    let s = iScope i
+    return (iModuleName i `withRangesOfQ` mnameToConcrete x, s)
+
+-- | If the module has already been visited (without warnings), then
+-- its interface is returned directly. Otherwise the computation is
+-- used to find the interface and the computed interface is stored for
+-- potential later use.
+
+alreadyVisited :: TopLevelModuleName ->
+                  MainInterface ->
+                  PragmaOptions ->
+                  TCM ModuleInfo ->
+                  TCM ModuleInfo
+alreadyVisited x isMain currentOptions getModule =
+  case isMain of
+    MainInterface TypeCheck                       -> useExistingOrLoadAndRecordVisited ModuleTypeChecked
+    NotMainInterface                              -> useExistingOrLoadAndRecordVisited ModuleTypeChecked
+    MainInterface ScopeCheck                      -> useExistingOrLoadAndRecordVisited ModuleScopeChecked
+  where
+  useExistingOrLoadAndRecordVisited :: ModuleCheckMode -> TCM ModuleInfo
+  useExistingOrLoadAndRecordVisited mode = fromMaybeM loadAndRecordVisited (existingWithoutWarnings mode)
+
+  -- Case: already visited.
+  --
+  -- A module with warnings should never be allowed to be
+  -- imported from another module.
+  existingWithoutWarnings :: ModuleCheckMode -> TCM (Maybe ModuleInfo)
+  existingWithoutWarnings mode = runMaybeT $ exceptToMaybeT $ do
+    mi <- maybeToExceptT "interface has not been visited in this context" $ MaybeT $
+      getVisitedModule x
+
+    when (miMode mi < mode) $
+      throwError "previously-visited interface was not sufficiently checked"
+
+    unless (null $ miWarnings mi) $
+      throwError "previously-visited interface had warnings"
+
+    reportSLn "import.visit" 10 $ "  Already visited " ++ prettyShow x
+
+    lift $ processResultingModule mi
+
+  processResultingModule :: ModuleInfo -> TCM ModuleInfo
+  processResultingModule mi = do
+    let ModuleInfo { miInterface = i, miPrimitive = isPrim, miWarnings = ws } = mi
+
+    -- Check that imported options are compatible with current ones (issue #2487),
+    -- but give primitive modules a pass
+    -- compute updated warnings if needed
+    wt <- fromMaybe ws <$> (getOptionsCompatibilityWarnings isMain isPrim currentOptions i)
+
+    return mi { miWarnings = wt }
+
+  loadAndRecordVisited :: TCM ModuleInfo
+  loadAndRecordVisited = do
+    reportSLn "import.visit" 5 $ "  Getting interface for " ++ prettyShow x
+    mi <- processResultingModule =<< getModule
+    reportSLn "import.visit" 5 $ "  Now we've looked at " ++ prettyShow x
+
+    -- Interfaces are not stored if we are only scope-checking, or
+    -- if any warnings were encountered.
+    case (isMain, miWarnings mi) of
+      (MainInterface ScopeCheck, _) -> return ()
+      (_, _:_)                      -> return ()
+      _                             -> storeDecodedModule mi
+
+    reportS "warning.import" 10
+      [ "module: " ++ show (moduleNameParts x)
+      , "WarningOnImport: " ++ show (iImportWarning (miInterface mi))
+      ]
+
+    visitModule mi
+    return mi
+
+
+-- | The result and associated parameters of a type-checked file,
+--   when invoked directly via interaction or a backend.
+--   Note that the constructor is not exported.
+
+data CheckResult = CheckResult'
+  { crModuleInfo :: ModuleInfo
+  , crSource'    :: Source
+  }
+
+-- | Flattened unidirectional pattern for 'CheckResult' for destructuring inside
+--   the 'ModuleInfo' field.
+pattern CheckResult :: Interface -> [TCWarning] -> ModuleCheckMode -> Source -> CheckResult
+pattern CheckResult { crInterface, crWarnings, crMode, crSource } <- CheckResult'
+    { crModuleInfo = ModuleInfo
+        { miInterface = crInterface
+        , miWarnings = crWarnings
+        , miMode = crMode
+        }
+    , crSource' = crSource
+    }
+
+-- | Type checks the main file of the interaction.
+--   This could be the file loaded in the interacting editor (emacs),
+--   or the file passed on the command line.
+--
+--   First, the primitive modules are imported.
+--   Then, @getInterface@ is called to do the main work.
+--
+--   If the 'Mode' is 'ScopeCheck', then type-checking is not
+--   performed, only scope-checking. (This may include type-checking
+--   of imported modules.) In this case the generated, partial
+--   interface is not stored in the state ('stDecodedModules'). Note,
+--   however, that if the file has already been type-checked, then a
+--   complete interface is returned.
+
+typeCheckMain
+  :: Mode
+     -- ^ Should the file be type-checked, or only scope-checked?
+  -> Source
+     -- ^ The decorated source code.
+  -> TCM CheckResult
+typeCheckMain mode src = do
+  -- liftIO $ putStrLn $ "This is typeCheckMain " ++ prettyShow f
+  -- liftIO . putStrLn . show =<< getVerbosity
+
+  -- For the main interface, we also remember the pragmas from the file
+  setOptionsFromSourcePragmas src
+  loadPrims <- optLoadPrimitives <$> pragmaOptions
+
+  when loadPrims $ do
+    reportSLn "import.main" 10 "Importing the primitive modules."
+    libdirPrim <- liftIO getPrimitiveLibDir
+    reportSLn "import.main" 20 $ "Library primitive dir = " ++ show libdirPrim
+    -- Turn off import-chasing messages.
+    -- We have to modify the persistent verbosity setting, since
+    -- getInterface resets the current verbosity settings to the persistent ones.
+
+    bracket_ (getsTC Lens.getPersistentVerbosity) Lens.putPersistentVerbosity $ do
+      Lens.modifyPersistentVerbosity
+        (Strict.Just . Trie.insert [] 0 . Strict.fromMaybe Trie.empty)
+        -- set root verbosity to 0
+
+      -- We don't want to generate highlighting information for Agda.Primitive.
+      withHighlightingLevel None $
+        forM_ (Set.map (libdirPrim </>) Lens.primitiveModules) $ \f -> do
+          primSource <- parseSource (SourceFile $ mkAbsolute f)
+          checkModuleName' (srcModuleName primSource) (srcOrigin primSource)
+          void $ getNonMainInterface (srcModuleName primSource) (Just primSource)
+
+    reportSLn "import.main" 10 $ "Done importing the primitive modules."
+
+  -- Now do the type checking via getInterface.
+  checkModuleName' (srcModuleName src) (srcOrigin src)
+
+  mi <- getInterface (srcModuleName src) (MainInterface mode) (Just src)
+
+  stCurrentModule `setTCLens'`
+    Just ( iModuleName (miInterface mi)
+         , iTopLevelModuleName (miInterface mi)
+         )
+
+  return $ CheckResult' mi src
+  where
+  checkModuleName' m f =
+    -- Andreas, 2016-07-11, issue 2092
+    -- The error range should be set to the file with the wrong module name
+    -- not the importing one (which would be the default).
+    setCurrentRange m $ checkModuleName m f Nothing
+
+-- | Tries to return the interface associated to the given (imported) module.
+--   The time stamp of the relevant interface file is also returned.
+--   Calls itself recursively for the imports of the given module.
+--   May type check the module.
+--   An error is raised if a warning is encountered.
+--
+--   Do not use this for the main file, use 'typeCheckMain' instead.
+
+getNonMainInterface
+  :: TopLevelModuleName
+  -> Maybe Source
+     -- ^ Optional: the source code and some information about the source code.
+  -> TCM Interface
+getNonMainInterface x msrc = do
+  -- Preserve/restore the current pragma options, which will be mutated when loading
+  -- and checking the interface.
+  mi <- bracket_ (useTC stPragmaOptions) (stPragmaOptions `setTCLens`) $
+          getInterface x NotMainInterface msrc
+  tcWarningsToError $ miWarnings mi
+  return (miInterface mi)
+
+-- | A more precise variant of 'getNonMainInterface'. If warnings are
+-- encountered then they are returned instead of being turned into
+-- errors.
+
+getInterface
+  :: TopLevelModuleName
+  -> MainInterface
+  -> Maybe Source
+     -- ^ Optional: the source code and some information about the source code.
+  -> TCM ModuleInfo
+getInterface x isMain msrc =
+  addImportCycleCheck x $ do
+     -- We remember but reset the pragma options locally
+     -- Issue #3644 (Abel 2020-05-08): Set approximate range for errors in options
+     currentOptions <- useTC stPragmaOptions
+     setCurrentRange (C.modPragmas . srcModule <$> msrc) $
+       -- Now reset the options
+       setCommandLineOptions . stPersistentOptions . stPersistentState =<< getTC
+
+     alreadyVisited x isMain currentOptions $ do
+      file <- case msrc of
+        Nothing  -> findFile x
+        Just src -> do
+          -- Andreas, 2021-08-17, issue #5508.
+          -- So it happened with @msrc == Just{}@ that the file was not added to @ModuleToSource@,
+          -- only with @msrc == Nothing@ (then @findFile@ does it).
+          -- As a consequence, the file was added later, but with a file name constructed
+          -- from a module name.  As #5508 shows, this can be fatal in case-insensitive file systems.
+          -- The file name (with case variant) then no longer maps to the module name.
+          -- To prevent this, we register the connection in @ModuleToSource@ here,
+          -- where we have the correct spelling of the file name.
+          let file = srcOrigin src
+          modifyTCLens stModuleToSource $ Map.insert x (srcFilePath file)
+          pure file
+      reportSLn "import.iface" 15 $ List.intercalate "\n" $ map ("  " ++)
+        [ "module: " ++ prettyShow x
+        , "file:   " ++ prettyShow file
+        ]
+
+      reportSLn "import.iface" 10 $ "  Check for cycle"
+      checkForImportCycle
+
+      -- -- Andreas, 2014-10-20 AIM XX:
+      -- -- Always retype-check the main file to get the iInsideScope
+      -- -- which is no longer serialized.
+      -- let maySkip = isMain == NotMainInterface
+      -- Andreas, 2015-07-13: Serialize iInsideScope again.
+      -- Andreas, 2020-05-13 issue #4647: don't skip if reload because of top-level command
+      stored <- runExceptT $ Bench.billTo [Bench.Import] $ do
+        getStoredInterface x file msrc
+
+      let recheck = \reason -> do
+            reportSLn "import.iface" 5 $ concat ["  ", prettyShow x, " is not up-to-date because ", reason, "."]
+            setCommandLineOptions . stPersistentOptions . stPersistentState =<< getTC
+            case isMain of
+              MainInterface _ -> createInterface x file isMain msrc
+              NotMainInterface -> createInterfaceIsolated x file msrc
+
+      either recheck pure stored
+
+-- | Check if the options used for checking an imported module are
+--   compatible with the current options. Raises Non-fatal errors if
+--   not.
+checkOptionsCompatible ::
+  PragmaOptions -> PragmaOptions -> TopLevelModuleName -> TCM Bool
+checkOptionsCompatible current imported importedModule = flip execStateT True $ do
+  reportSDoc "import.iface.options" 5 $ P.nest 2 $ "current options  =" P.<+> showOptions current
+  reportSDoc "import.iface.options" 5 $ P.nest 2 $ "imported options =" P.<+> showOptions imported
+  forM_ infectiveCoinfectiveOptions $ \opt -> do
+    unless (icOptionOK opt current imported) $ do
+      put False
+      warning $
+        (case icOptionKind opt of
+           Infective   -> InfectiveImport
+           Coinfective -> CoInfectiveImport)
+        (icOptionWarning opt importedModule)
+  where
+  showOptions opts =
+    P.prettyList $
+    map (\opt -> (P.text (icOptionDescription opt) <> ": ") P.<+>
+                 P.pretty (icOptionActive opt opts))
+      infectiveCoinfectiveOptions
+
+-- | Compare options and return collected warnings.
+-- | Returns `Nothing` if warning collection was skipped.
+
+getOptionsCompatibilityWarnings :: MainInterface -> Bool -> PragmaOptions -> Interface -> TCM (Maybe [TCWarning])
+getOptionsCompatibilityWarnings isMain isPrim currentOptions i = runMaybeT $ exceptToMaybeT $ do
+  -- We're just dropping these reasons-for-skipping messages for now.
+  -- They weren't logged before, but they're nice for documenting the early returns.
+  when isPrim $
+    throwError "Options consistency checking disabled for always-available primitive module"
+  whenM (lift $ checkOptionsCompatible currentOptions (iOptionsUsed i)
+                  (iTopLevelModuleName i)) $
+    throwError "No warnings to collect because options were compatible"
+  lift $ getAllWarnings' isMain ErrorWarnings
+
+-- | Try to get the interface from interface file or cache.
+
+getStoredInterface
+  :: TopLevelModuleName
+     -- ^ Module name of file we process.
+  -> SourceFile
+     -- ^ File we process.
+  -> Maybe Source
+  -> ExceptT String TCM ModuleInfo
+getStoredInterface x file msrc = do
+  -- Check whether interface file exists and is in cache
+  --  in the correct version (as testified by the interface file hash).
+  --
+  -- This is a lazy action which may be skipped if there is no cached interface
+  -- and we're ignoring interface files for some reason.
+  let getIFileHashesET = do
+        -- Check that the interface file exists and return its hash.
+        ifile <- maybeToExceptT "the interface file could not be found" $ MaybeT $
+          findInterfaceFile' file
+
+        -- Check that the interface file exists and return its hash.
+        hashes <- maybeToExceptT "the interface file hash could not be read" $ MaybeT $ liftIO $
+          getInterfaceFileHashes ifile
+
+        return (ifile, hashes)
+
+  -- Examine the hash of the interface file. If it is different from the
+  -- stored version (in stDecodedModules), or if there is no stored version,
+  -- read and decode it. Otherwise use the stored version.
+  --
+  -- This is a lazy action which may be skipped if the cached or on-disk interface
+  -- is invalid, missing, or skipped for some other reason.
+  let checkSourceHashET ifaceH = do
+        sourceH <- case msrc of
+                    Nothing -> liftIO $ hashTextFile (srcFilePath file)
+                    Just src -> return $ hashText (srcText src)
+
+        unless (sourceH == ifaceH) $
+          throwError $ concat
+            [ "the source hash (", show sourceH, ")"
+            , " does not match the source hash for the interface (", show ifaceH, ")"
+            ]
+
+        reportSLn "import.iface" 5 $ concat ["  ", prettyShow x, " is up-to-date."]
+
+  -- Check if we have cached the module.
+  cachedE <- runExceptT $ maybeToExceptT "the interface has not been decoded" $ MaybeT $
+      lift $ getDecodedModule x
+
+  case cachedE of
+    -- If it's cached ignoreInterfaces has no effect;
+    -- to avoid typechecking a file more than once.
+    Right mi -> do
+      (ifile, hashes) <- getIFileHashesET
+
+      let ifp = filePath $ intFilePath ifile
+      let i = miInterface mi
+
+      -- Make sure the hashes match.
+      let cachedIfaceHash = iFullHash i
+      let fileIfaceHash = snd hashes
+      unless (cachedIfaceHash == fileIfaceHash) $ do
+        lift $ dropDecodedModule x
+        reportSLn "import.iface" 50 $ "  cached hash = " ++ show cachedIfaceHash
+        reportSLn "import.iface" 50 $ "  stored hash = " ++ show fileIfaceHash
+        reportSLn "import.iface" 5 $ "  file is newer, re-reading " ++ ifp
+        throwError $ concat
+          [ "the cached interface hash (", show cachedIfaceHash, ")"
+          , " does not match interface file (", show fileIfaceHash, ")"
+          ]
+
+      Bench.billTo [Bench.Deserialization] $ do
+        checkSourceHashET (iSourceHash i)
+
+        reportSLn "import.iface" 5 $ "  using stored version of " ++ (filePath $ intFilePath ifile)
+        loadDecodedModule file mi
+
+    Left whyNotCached -> withExceptT (\e -> concat [whyNotCached, " and ", e]) $ do
+      whenM ignoreAllInterfaces $
+        throwError "we're ignoring all interface files"
+
+      whenM ignoreInterfaces $
+        unlessM (lift $ Lens.isBuiltinModule (filePath $ srcFilePath file)) $
+            throwError "we're ignoring non-builtin interface files"
+
+      (ifile, hashes) <- getIFileHashesET
+
+      let ifp = (filePath . intFilePath $ ifile)
+
+      Bench.billTo [Bench.Deserialization] $ do
+        checkSourceHashET (fst hashes)
+
+        reportSLn "import.iface" 5 $ "  no stored version, reading " ++ ifp
+
+        i <- maybeToExceptT "bad interface, re-type checking" $ MaybeT $
+          readInterface ifile
+
+        -- Ensure that the given module name matches the one in the file.
+        let topLevelName = iTopLevelModuleName i
+        unless (topLevelName == x) $
+          -- Andreas, 2014-03-27 This check is now done in the scope checker.
+          -- checkModuleName topLevelName file
+          lift $ typeError $ OverlappingProjects (srcFilePath file) topLevelName x
+
+        isPrimitiveModule <- lift $ Lens.isPrimitiveModule (filePath $ srcFilePath file)
+
+        lift $ chaseMsg "Loading " x $ Just ifp
+        -- print imported warnings
+        let ws = filter ((Strict.Just (Just x) ==) .
+                         fmap rangeFileName . tcWarningOrigin) $
+                 iWarnings i
+        unless (null ws) $ alwaysReportSDoc "warning" 1 $ P.vcat $ P.prettyTCM <$> ws
+
+        loadDecodedModule file $ ModuleInfo
+          { miInterface = i
+          , miWarnings = []
+          , miPrimitive = isPrimitiveModule
+          , miMode = ModuleTypeChecked
+          }
+
+
+loadDecodedModule
+  :: SourceFile
+     -- ^ File we process.
+  -> ModuleInfo
+  -> ExceptT String TCM ModuleInfo
+loadDecodedModule file mi = do
+  let fp = filePath $ srcFilePath file
+  let i = miInterface mi
+
+  -- Check that it's the right version
+  reportSLn "import.iface" 5 $ "  imports: " ++ prettyShow (iImportedModules i)
+
+  -- We set the pragma options of the skipped file here, so that
+  -- we can check that they are compatible with those of the
+  -- imported modules. Also, if the top-level file is skipped we
+  -- want the pragmas to apply to interactive commands in the UI.
+  -- Jesper, 2021-04-18: Check for changed options in library files!
+  -- (see #5250)
+  libOptions <- lift $ getLibraryOptions
+    (srcFilePath file)
+    (iTopLevelModuleName i)
+  lift $ mapM_ setOptionsFromPragma (libOptions ++ iFilePragmaOptions i)
+
+  -- Check that options that matter haven't changed compared to
+  -- current options (issue #2487)
+  unlessM (lift $ Lens.isBuiltinModule fp) $ do
+    current <- useTC stPragmaOptions
+    when (recheckBecausePragmaOptionsChanged (iOptionsUsed i) current) $
+      throwError "options changed"
+
+  -- If any of the imports are newer we need to retype check
+  badHashMessages <- fmap lefts $ forM (iImportedModules i) $ \(impName, impHash) -> runExceptT $ do
+    reportSLn "import.iface" 30 $ concat ["Checking that module hash of import ", prettyShow impName, " matches ", prettyShow impHash ]
+    latestImpHash <- lift $ lift $ setCurrentRange impName $ moduleHash impName
+    reportSLn "import.iface" 30 $ concat ["Done checking module hash of import ", prettyShow impName]
+    when (impHash /= latestImpHash) $
+      throwError $ concat
+        [ "module hash for imported module ", prettyShow impName, " is out of date"
+        , " (import cached=", prettyShow impHash, ", latest=", prettyShow latestImpHash, ")"
+        ]
+
+  unlessNull badHashMessages (throwError . unlines)
+
+  reportSLn "import.iface" 5 "  New module. Let's check it out."
+  lift $ mergeInterface i
+  Bench.billTo [Bench.Highlighting] $
+    lift $ ifTopLevelAndHighlightingLevelIs NonInteractive $
+      highlightFromInterface i file
+
+  return mi
+
+-- | Run the type checker on a file and create an interface.
+--
+--   Mostly, this function calls 'createInterface'.
+--   But if it is not the main module we check,
+--   we do it in a fresh state, suitably initialize,
+--   in order to forget some state changes after successful type checking.
+
+createInterfaceIsolated
+  :: TopLevelModuleName
+     -- ^ Module name of file we process.
+  -> SourceFile
+     -- ^ File we process.
+  -> Maybe Source
+     -- ^ Optional: the source code and some information about the source code.
+  -> TCM ModuleInfo
+createInterfaceIsolated x file msrc = do
+      cleanCachedLog
+
+      ms          <- getImportPath
+      range       <- asksTC envRange
+      call        <- asksTC envCall
+      mf          <- useTC stModuleToSource
+      vs          <- getVisitedModules
+      ds          <- getDecodedModules
+      opts        <- stPersistentOptions . stPersistentState <$> getTC
+      isig        <- useTC stImports
+      metas       <- useTC stImportedMetaStore
+      ibuiltin    <- useTC stImportedBuiltins
+      display     <- useTC stImportsDisplayForms
+      userwarn    <- useTC stImportedUserWarnings
+      partialdefs <- useTC stImportedPartialDefs
+      opaqueblk   <- useTC stOpaqueBlocks
+      opaqueid    <- useTC stOpaqueIds
+      ipatsyns <- getPatternSynImports
+      ho       <- getInteractionOutputCallback
+      -- Every interface is treated in isolation. Note: Some changes to
+      -- the persistent state may not be preserved if an error other
+      -- than a type error or an IO exception is encountered in an
+      -- imported module.
+      (mi, newModToSource, newDecodedModules) <- (either throwError pure =<<) $
+           withoutCache $
+           -- The cache should not be used for an imported module, and it
+           -- should be restored after the module has been type-checked
+           freshTCM $
+             withImportPath ms $
+             localTC (\e -> e
+                              -- Andreas, 2014-08-18:
+                              -- Preserve the range of import statement
+                              -- for reporting termination errors in
+                              -- imported modules:
+                            { envRange              = range
+                            , envCall               = call
+                            }) $ do
+               setDecodedModules ds
+               setCommandLineOptions opts
+               setInteractionOutputCallback ho
+               stModuleToSource `setTCLens` mf
+               setVisitedModules vs
+               addImportedThings isig metas ibuiltin ipatsyns display
+                 userwarn partialdefs [] opaqueblk opaqueid
+
+               r  <- createInterface x file NotMainInterface msrc
+               mf' <- useTC stModuleToSource
+               ds' <- getDecodedModules
+               return (r, mf', ds')
+
+      stModuleToSource `setTCLens` newModToSource
+      setDecodedModules newDecodedModules
+
+      -- We skip the file which has just been type-checked to
+      -- be able to forget some of the local state from
+      -- checking the module.
+      -- Note that this doesn't actually read the interface
+      -- file, only the cached interface. (This comment is not
+      -- correct, see
+      -- test/Fail/customised/NestedProjectRoots.err.)
+      validated <- runExceptT $ loadDecodedModule file mi
+
+      -- NOTE: This attempts to type-check FOREVER if for some
+      -- reason it continually fails to validate interface.
+      let recheckOnError = \msg -> do
+            alwaysReportSLn "import.iface" 1 $ "Failed to validate just-loaded interface: " ++ msg
+            createInterfaceIsolated x file msrc
+
+      either recheckOnError pure validated
+
+
+-- | Formats and outputs the "Checking", "Finished" and "Loading " messages.
+
+chaseMsg
+  :: String               -- ^ The prefix, like @Checking@, @Finished@, @Loading @.
+  -> TopLevelModuleName   -- ^ The module name.
+  -> Maybe String         -- ^ Optionally: the file name.
+  -> TCM ()
+chaseMsg kind x file = do
+  indentation <- (`replicate` ' ') <$> asksTC (pred . length . envImportPath)
+  traceImports <- optTraceImports <$> commandLineOptions
+  let maybeFile = caseMaybe file "." $ \ f -> " (" ++ f ++ ")."
+      vLvl | kind == "Checking"
+             && traceImports > 0 = 1
+           | kind == "Finished"
+             && traceImports > 1 = 1
+           | List.isPrefixOf "Loading" kind
+             && traceImports > 2 = 1
+           | otherwise = 2
+  alwaysReportSLn "import.chase" vLvl $ concat
+    [ indentation, kind, " ", prettyShow x, maybeFile ]
+
+-- | Print the highlighting information contained in the given interface.
+
+highlightFromInterface
+  :: Interface
+  -> SourceFile
+     -- ^ The corresponding file.
+  -> TCM ()
+highlightFromInterface i file = do
+  reportSLn "import.iface" 5 $
+    "Generating syntax info for " ++ filePath (srcFilePath file) ++
+    " (read from interface)."
+  printHighlightingInfo KeepHighlighting (iHighlighting i)
+
+-- | Read interface file corresponding to a module.
+
+readInterface :: InterfaceFile -> TCM (Maybe Interface)
+readInterface file = do
+    let ifp = filePath $ intFilePath file
+    -- Decode the interface file
+    (s, close) <- liftIO $ readBinaryFile' ifp
+    do  mi <- liftIO . E.evaluate =<< decodeInterface s
+
+        -- Close the file. Note
+        -- ⑴ that evaluate ensures that i is evaluated to WHNF (before
+        --   the next IO operation is executed), and
+        -- ⑵ that decode returns Nothing if an error is encountered,
+        -- so it is safe to close the file here.
+        liftIO close
+
+        return $ constructIScope <$> mi
+      -- Catch exceptions and close
+      `catchError` \e -> liftIO close >> handler e
+  -- Catch exceptions
+  `catchError` handler
+  where
+    handler = \case
+      IOException _ _ e -> do
+        alwaysReportSLn "" 0 $ "IO exception: " ++ show e
+        return Nothing   -- Work-around for file locking bug.
+                         -- TODO: What does this refer to? Please
+                         -- document.
+      e -> throwError e
+
+-- | Writes the given interface to the given file.
+--
+-- The written interface is decoded and returned.
+
+writeInterface :: AbsolutePath -> Interface -> TCM Interface
+writeInterface file i = let fp = filePath file in do
+    reportSLn "import.iface.write" 5  $
+      "Writing interface file " ++ fp ++ "."
+    -- Andreas, 2015-07-13
+    -- After QName memoization (AIM XXI), scope serialization might be cheap enough.
+    -- -- Andreas, Makoto, 2014-10-18 AIM XX:
+    -- -- iInsideScope is bloating the interface files, so we do not serialize it?
+    -- i <- return $
+    --   i { iInsideScope  = emptyScopeInfo
+    --     }
+    -- [Old: Andreas, 2016-02-02 this causes issue #1804, so don't do it:]
+    -- Andreas, 2020-05-13, #1804, #4647: removed private declarations
+    -- only when we actually write the interface.
+    let filteredIface = i { iInsideScope  = withoutPrivates $ iInsideScope i }
+    reportSLn "import.iface.write" 50 $
+      "Writing interface file with hash " ++ show (iFullHash filteredIface) ++ "."
+    encodedIface <- encodeFile fp filteredIface
+    reportSLn "import.iface.write" 5 "Wrote interface file."
+    fromMaybe __IMPOSSIBLE__ <$> (Bench.billTo [Bench.Deserialization] (decode encodedIface))
+  `catchError` \e -> do
+    alwaysReportSLn "" 1 $
+      "Failed to write interface " ++ fp ++ "."
+    liftIO $
+      whenM (doesFileExist fp) $ removeFile fp
+    throwError e
+
+-- | Tries to type check a module and write out its interface. The
+-- function only writes out an interface file if it does not encounter
+-- any warnings.
+--
+-- If appropriate this function writes out syntax highlighting
+-- information.
+
+createInterface
+  :: TopLevelModuleName    -- ^ The expected module name.
+  -> SourceFile            -- ^ The file to type check.
+  -> MainInterface         -- ^ Are we dealing with the main module?
+  -> Maybe Source      -- ^ Optional information about the source code.
+  -> TCM ModuleInfo
+createInterface mname file isMain msrc = do
+  let x = mname
+  let fp = filePath $ srcFilePath file
+  let checkMsg = case isMain of
+                   MainInterface ScopeCheck -> "Reading "
+                   _                        -> "Checking"
+      withMsgs = bracket_
+       (chaseMsg checkMsg x $ Just fp)
+       (const $ do ws <- getAllWarnings AllWarnings
+                   let classified = classifyWarnings ws
+                   let wa' = filter ((Strict.Just (Just mname) ==) .
+                                     fmap rangeFileName . tcWarningOrigin) $
+                             tcWarnings classified
+                   unless (null wa') $
+                     alwaysReportSDoc "warning" 1 $ P.vcat $ P.prettyTCM <$> wa'
+                   when (null (nonFatalErrors classified)) $ chaseMsg "Finished" x Nothing)
+
+  withMsgs $
+    Bench.billTo [Bench.TopModule mname] $
+    localTC (\e -> e { envCurrentPath = Just (srcFilePath file) }) $ do
+
+    let onlyScope = isMain == MainInterface ScopeCheck
+
+    reportSLn "import.iface.create" 5 $
+      "Creating interface for " ++ prettyShow mname ++ "."
+    verboseS "import.iface.create" 10 $ do
+      visited <- prettyShow <$> getPrettyVisitedModules
+      reportSLn "import.iface.create" 10 $ "  visited: " ++ visited
+
+    src <- maybe (parseSource file) pure msrc
+
+    let srcPath = srcFilePath $ srcOrigin src
+
+    fileTokenInfo <- Bench.billTo [Bench.Highlighting] $
+      generateTokenInfoFromSource
+        (let !top = srcModuleName src in
+         mkRangeFile srcPath (Just top))
+        (TL.unpack $ srcText src)
+    stTokens `modifyTCLens` (fileTokenInfo <>)
+
+    setOptionsFromSourcePragmas src
+    checkAttributes (srcAttributes src)
+    syntactic <- optSyntacticEquality <$> pragmaOptions
+    localTC (\env -> env { envSyntacticEqualityFuel = syntactic }) $ do
+
+    verboseS "import.iface.create" 15 $ do
+      nestingLevel      <- asksTC (pred . length . envImportPath)
+      highlightingLevel <- asksTC envHighlightingLevel
+      reportSLn "import.iface.create" 15 $ unlines
+        [ "  nesting      level: " ++ show nestingLevel
+        , "  highlighting level: " ++ show highlightingLevel
+        ]
+
+    -- Scope checking.
+    reportSLn "import.iface.create" 7 "Starting scope checking."
+    topLevel <- Bench.billTo [Bench.Scoping] $ do
+      let topDecls = C.modDecls $ srcModule src
+      concreteToAbstract_ (TopLevel srcPath mname topDecls)
+    reportSLn "import.iface.create" 7 "Finished scope checking."
+
+    let ds    = topLevelDecls topLevel
+        scope = topLevelScope topLevel
+
+    -- Highlighting from scope checker.
+    reportSLn "import.iface.create" 7 "Starting highlighting from scope."
+    Bench.billTo [Bench.Highlighting] $ do
+      -- Generate and print approximate syntax highlighting info.
+      ifTopLevelAndHighlightingLevelIs NonInteractive $
+        printHighlightingInfo KeepHighlighting fileTokenInfo
+      ifTopLevelAndHighlightingLevelIsOr NonInteractive onlyScope $
+        mapM_ (\ d -> generateAndPrintSyntaxInfo d Partial onlyScope) ds
+    reportSLn "import.iface.create" 7 "Finished highlighting from scope."
+
+
+    -- Type checking.
+
+    -- Now that all the options are in we can check if caching should
+    -- be on.
+    activateLoadedFileCache
+
+    -- invalidate cache if pragmas change, TODO move
+    cachingStarts
+    opts <- useTC stPragmaOptions
+    me <- readFromCachedLog
+    case me of
+      Just (Pragmas opts', _) | opts == opts'
+        -> return ()
+      _ -> do
+        reportSLn "cache" 10 $ "pragma changed: " ++ show (isJust me)
+        cleanCachedLog
+    writeToCurrentLog $ Pragmas opts
+
+    if onlyScope
+      then do
+        reportSLn "import.iface.create" 7 "Skipping type checking."
+        cacheCurrentLog
+      else do
+        reportSLn "import.iface.create" 7 "Starting type checking."
+        Bench.billTo [Bench.Typing] $ mapM_ checkDeclCached ds `finally_` cacheCurrentLog
+        reportSLn "import.iface.create" 7 "Finished type checking."
+
+    -- Ulf, 2013-11-09: Since we're rethrowing the error, leave it up to the
+    -- code that handles that error to reset the state.
+    -- Ulf, 2013-11-13: Errors are now caught and highlighted in InteractionTop.
+    -- catchError_ (checkDecls ds) $ \e -> do
+    --   ifTopLevelAndHighlightingLevelIs NonInteractive $
+    --     printErrorInfo e
+    --   throwError e
+
+    unfreezeMetas
+
+    -- Profiling: Count number of metas.
+    whenProfile Profile.Metas $ do
+      m <- fresh
+      tickN "metas" (fromIntegral (metaId m))
+
+    -- Highlighting from type checker.
+    reportSLn "import.iface.create" 7 "Starting highlighting from type info."
+    Bench.billTo [Bench.Highlighting] $ do
+
+      -- Move any remaining token highlighting to stSyntaxInfo.
+      toks <- useTC stTokens
+      ifTopLevelAndHighlightingLevelIs NonInteractive $
+        printHighlightingInfo KeepHighlighting toks
+      stTokens `setTCLens` mempty
+
+      -- Grabbing warnings and unsolved metas to highlight them
+      warnings <- getAllWarnings AllWarnings
+      unless (null warnings) $ reportSDoc "import.iface.create" 20 $
+        "collected warnings: " <> prettyTCM warnings
+      unsolved <- getAllUnsolvedWarnings
+      unless (null unsolved) $ reportSDoc "import.iface.create" 20 $
+        "collected unsolved: " <> prettyTCM unsolved
+      let warningInfo =
+            convert $ foldMap warningHighlighting $ unsolved ++ warnings
+
+      stSyntaxInfo `modifyTCLens` \inf -> (inf `mappend` toks) `mappend` warningInfo
+
+      whenM (optGenerateVimFile <$> commandLineOptions) $
+        -- Generate Vim file.
+        withScope_ scope $ generateVimFile $ filePath $ srcPath
+    reportSLn "import.iface.create" 7 "Finished highlighting from type info."
+
+    setScope scope
+    reportSLn "scope.top" 50 $ "SCOPE " ++ show scope
+
+    -- TODO: It would be nice if unsolved things were highlighted
+    -- after every mutual block.
+
+    openMetas           <- getOpenMetas
+    unless (null openMetas) $ do
+      reportSLn "import.metas" 10 "We have unsolved metas."
+      reportSLn "import.metas" 10 =<< showGoals =<< getGoals
+
+    ifTopLevelAndHighlightingLevelIs NonInteractive printUnsolvedInfo
+
+    -- Andreas, 2016-08-03, issue #964
+    -- When open metas are allowed,
+    -- permanently freeze them now by turning them into postulates.
+    -- This will enable serialization.
+    -- savedMetaStore <- useTC stMetaStore
+    unless (includeStateChanges isMain) $
+      -- Andreas, 2018-11-15, re issue #3393:
+      -- We do not get here when checking the main module
+      -- (then includeStateChanges is True).
+      whenM (optAllowUnsolved <$> pragmaOptions) $ do
+        reportSLn "import.iface.create" 7 "Turning unsolved metas (if any) into postulates."
+        withCurrentModule (scope ^. scopeCurrent) openMetasToPostulates
+        -- Clear constraints as they might refer to what
+        -- they think are open metas.
+        stAwakeConstraints    `setTCLens` []
+        stSleepingConstraints `setTCLens` []
+
+    -- Serialization.
+    reportSLn "import.iface.create" 7 "Starting serialization."
+    i <- Bench.billTo [Bench.Serialization, Bench.BuildInterface] $
+      buildInterface src topLevel
+
+    reportS "tc.top" 101 $
+      "Signature:" :
+      [ unlines
+          [ prettyShow q
+          , "  type: " ++ show (defType def)
+          , "  def:  " ++ show cc
+          ]
+      | (q, def) <- HMap.toList $ iSignature i ^. sigDefinitions,
+        Function{ funCompiled = cc } <- [theDef def]
+      ]
+    reportSLn "import.iface.create" 7 "Finished serialization."
+
+    mallWarnings <- getAllWarnings' isMain ErrorWarnings
+
+    reportSLn "import.iface.create" 7 "Considering writing to interface file."
+    finalIface <- constructIScope <$> case (mallWarnings, isMain) of
+      (_:_, _) -> do
+        -- Andreas, 2018-11-15, re issue #3393
+        -- The following is not sufficient to fix #3393
+        -- since the replacement of metas by postulates did not happen.
+        -- -- | not (allowUnsolved && all (isUnsolvedWarning . tcWarning) allWarnings) -> do
+        reportSLn "import.iface.create" 7 "We have warnings, skipping writing interface file."
+        return i
+      ([], MainInterface ScopeCheck) -> do
+        reportSLn "import.iface.create" 7 "We are just scope-checking, skipping writing interface file."
+        return i
+      ([], _) -> Bench.billTo [Bench.Serialization] $ do
+        reportSLn "import.iface.create" 7 "Actually calling writeInterface."
+        -- The file was successfully type-checked (and no warnings were
+        -- encountered), so the interface should be written out.
+        ifile <- toIFile file
+        serializedIface <- writeInterface ifile i
+        reportSLn "import.iface.create" 7 "Finished writing to interface file."
+        return serializedIface
+
+    -- -- Restore the open metas, as we might continue in interaction mode.
+    -- Actually, we do not serialize the metas if checking the MainInterface
+    -- stMetaStore `setTCLens` savedMetaStore
+
+    -- Profiling: Print statistics.
+    printStatistics (Just mname) =<< getStatistics
+
+    -- Get the statistics of the current module
+    -- and add it to the accumulated statistics.
+    localStatistics <- getStatistics
+    lensAccumStatistics `modifyTCLens` Map.unionWith (+) localStatistics
+    reportSLn "import.iface" 5 "Accumulated statistics."
+
+    isPrimitiveModule <- Lens.isPrimitiveModule (filePath srcPath)
+
+    return ModuleInfo
+      { miInterface = finalIface
+      , miWarnings = mallWarnings
+      , miPrimitive = isPrimitiveModule
+      , miMode = moduleCheckMode isMain
+      }
+
+-- | Expert version of 'getAllWarnings'; if 'isMain' is a
+-- 'MainInterface', the warnings definitely include also unsolved
+-- warnings.
+
+getAllWarnings' :: (MonadFail m, ReadTCState m, MonadWarning m, MonadTCM m) => MainInterface -> WhichWarnings -> m [TCWarning]
+getAllWarnings' (MainInterface _) = getAllWarningsPreserving unsolvedWarnings
+getAllWarnings' NotMainInterface  = getAllWarningsPreserving Set.empty
+
+-- Andreas, issue 964: not checking null interactionPoints
+-- anymore; we want to serialize with open interaction points now!
+
+-- | Reconstruct the 'iScope' (not serialized)
+--   from the 'iInsideScope' (serialized).
+
+constructIScope :: Interface -> Interface
+constructIScope i = billToPure [ Deserialization ] $
+  i{ iScope = publicModules $ iInsideScope i }
+
+-- | Builds an interface for the current module, which should already
+-- have been successfully type checked.
+
+buildInterface
+  :: Source
+     -- ^ 'Source' for the current module.
+  -> TopLevelInfo
+     -- ^ 'TopLevelInfo' scope information for the current module.
+  -> TCM Interface
+buildInterface src topLevel = do
+    reportSLn "import.iface" 5 "Building interface..."
+    let mname = CToA.topLevelModuleName topLevel
+        source   = srcText src
+        fileType = srcFileType src
+        defPragmas = srcDefaultPragmas src
+        filePragmas  = srcFilePragmas src
+    -- Andreas, 2014-05-03: killRange did not result in significant reduction
+    -- of .agdai file size, and lost a few seconds performance on library-test.
+    -- Andreas, Makoto, 2014-10-18 AIM XX: repeating the experiment
+    -- with discarding also the nameBindingSite in QName:
+    -- Saves 10% on serialization time (and file size)!
+    --
+    -- NOTE: We no longer discard all nameBindingSites (but the commit
+    -- that introduced this change seems to have made Agda a bit
+    -- faster and interface file sizes a bit smaller, at least for the
+    -- standard library).
+    builtin     <- useTC stLocalBuiltins
+    mhs         <- mapM (\top -> (top,) <$> moduleHash top) .
+                   Set.toAscList =<<
+                   useR stImportedModules
+    foreignCode <- useTC stForeignCode
+    -- Ulf, 2016-04-12:
+    -- Non-closed display forms are not applicable outside the module anyway,
+    -- and should be dead-code eliminated (#1928).
+    origDisplayForms <- HMap.filter (not . null) . HMap.map (filter isClosed) <$> useTC stImportsDisplayForms
+    -- TODO: Kill some ranges?
+    let scope = topLevelScope topLevel
+    -- Andreas, Oskar, 2023-10-19, issue #6931:
+    -- To not delete module telescopes of empty public modules,
+    -- we need to pass the public modules to the dead-code elimination
+    -- (to be mined for additional roots for the reachability analysis).
+    (display, sig, solvedMetas) <-
+      eliminateDeadCode (publicModules scope) builtin origDisplayForms ==<<
+        (getSignature, useR stSolvedMetaStore)
+    userwarns   <- useTC stLocalUserWarnings
+    importwarn  <- useTC stWarningOnImport
+    syntaxInfo  <- useTC stSyntaxInfo
+    optionsUsed <- useTC stPragmaOptions
+    partialDefs <- useTC stLocalPartialDefs
+
+    -- Only serialise the opaque blocks actually defined in this
+    -- top-level module.
+    opaqueBlocks' <- useTC stOpaqueBlocks
+    opaqueIds' <- useTC stOpaqueIds
+    let
+      mh = moduleNameId (srcModuleName src)
+      opaqueBlocks = Map.filterWithKey (\(OpaqueId _ mod) _ -> mod == mh) opaqueBlocks'
+      isLocal qnm = case nameId (qnameName qnm) of
+        NameId _ mh' -> mh' == mh
+      opaqueIds = Map.filterWithKey (\qnm (OpaqueId _ mod) -> isLocal qnm || mod == mh) opaqueIds'
+
+    -- Andreas, 2015-02-09 kill ranges in pattern synonyms before
+    -- serialization to avoid error locations pointing to external files
+    -- when expanding a pattern synonym.
+    patsyns <- killRange <$> getPatternSyns
+    let builtin' = Map.mapWithKey (\ x b -> primName x <$> b) builtin
+    warnings <- filter (isSourceCodeWarning . warningName . tcWarning) <$> getAllWarnings AllWarnings
+    let i = Interface
+          { iSourceHash      = hashText source
+          , iSource          = source
+          , iFileType        = fileType
+          , iImportedModules = mhs
+          , iModuleName      = mname
+          , iTopLevelModuleName = srcModuleName src
+          , iScope           = empty -- publicModules scope
+          , iInsideScope     = scope
+          , iSignature       = sig
+          , iMetaBindings    = solvedMetas
+          , iDisplayForms    = display
+          , iUserWarnings    = userwarns
+          , iImportWarning   = importwarn
+          , iBuiltin         = builtin'
+          , iForeignCode     = foreignCode
+          , iHighlighting    = syntaxInfo
+          , iDefaultPragmaOptions = defPragmas
+          , iFilePragmaOptions    = filePragmas
+          , iOptionsUsed     = optionsUsed
+          , iPatternSyns     = patsyns
+          , iWarnings        = warnings
+          , iPartialDefs     = partialDefs
+          , iOpaqueBlocks    = opaqueBlocks
+          , iOpaqueNames     = opaqueIds
+          }
+    i <-
+      ifM (optSaveMetas <$> pragmaOptions)
+        (return i)
+        (do reportSLn "import.iface" 7
+              "  instantiating all meta variables"
+            -- Note that the meta-variables in the definitions in
+            -- "sig" have already been instantiated (by
+            -- eliminateDeadCode).
+            instantiateFullExceptForDefinitions i)
+    reportSLn "import.iface" 7 "  interface complete"
+    return i
+
+    where
+      primName (PrimitiveName x) b = (x, primFunName b)
+      primName (BuiltinName x)   b = __IMPOSSIBLE__
+
+-- | Returns (iSourceHash, iFullHash)
+--   We do not need to check that the file exist because we only
+--   accept @InterfaceFile@ as an input and not arbitrary @AbsolutePath@!
+getInterfaceFileHashes :: InterfaceFile -> IO (Maybe (Hash, Hash))
+getInterfaceFileHashes fp = do
+  let ifile = filePath $ intFilePath fp
+  (s, close) <- readBinaryFile' ifile
+  let hs = decodeHashes s
+  maybe 0 (uncurry (+)) hs `seq` close
+  return hs
+
+moduleHash :: TopLevelModuleName -> TCM Hash
+moduleHash m = iFullHash <$> getNonMainInterface m Nothing
diff --git a/src/full/Agda/Interaction/Imports.hs-boot b/src/full/Agda/Interaction/Imports.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Imports.hs-boot
@@ -0,0 +1,14 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Imports where
+
+import Data.Map                     ( Map )
+
+import Agda.Syntax.Abstract.Name    ( ModuleName )
+import Agda.Syntax.Scope.Base       ( Scope )
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+import Agda.TypeChecking.Monad.Base ( TCM )
+
+scopeCheckImport ::
+  TopLevelModuleName -> ModuleName ->
+  TCM (ModuleName, Map ModuleName Scope)
diff --git a/src/full/Agda/Interaction/InteractionTop.hs b/src/full/Agda/Interaction/InteractionTop.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/InteractionTop.hs
@@ -0,0 +1,1215 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# OPTIONS_GHC -fno-cse #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.Interaction.InteractionTop
+  ( module Agda.Interaction.InteractionTop
+  )
+  where
+
+import Prelude hiding (null)
+
+import Control.Concurrent
+import Control.Concurrent.Async
+import Control.Concurrent.STM.TChan
+import Control.Concurrent.STM.TVar
+
+import qualified Control.Exception  as E
+
+import Control.Monad
+import Control.Monad.Except         ( MonadError(..), ExceptT(..), runExceptT )
+import Control.Monad.IO.Class       ( MonadIO(..) )
+import Control.Monad.Fail           ( MonadFail )
+import Control.Monad.State          ( MonadState(..), gets, modify, runStateT )
+import Control.Monad.STM
+import Control.Monad.Trans          ( lift )
+
+import qualified Data.Char as Char
+import Data.Function (on)
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Data.Maybe
+
+import System.Directory
+import System.FilePath
+
+import Agda.TypeChecking.Monad as TCM
+  hiding (initState, setCommandLineOptions)
+import qualified Agda.TypeChecking.Monad as TCM
+import qualified Agda.TypeChecking.Pretty as TCP
+import Agda.TypeChecking.Rules.Term (checkExpr, isType_)
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Warnings (runPM, warning)
+
+import Agda.Syntax.Fixity
+import Agda.Syntax.Position
+import Agda.Syntax.Parser
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Glyph
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pretty
+import Agda.Syntax.Info (mkDefInfo)
+import Agda.Syntax.Translation.ConcreteToAbstract
+import Agda.Syntax.Translation.AbstractToConcrete hiding (withScope)
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.Interaction.Base
+import Agda.Interaction.ExitCode
+import Agda.Interaction.FindFile
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Lenses as Lenses
+import Agda.Interaction.MakeCase
+import Agda.Interaction.SearchAbout
+import Agda.Interaction.Response hiding (Function, ExtendedLambda)
+import qualified Agda.Interaction.Response as R
+import qualified Agda.Interaction.BasicOps as B
+import Agda.Interaction.Highlighting.Precise hiding (Error, Postulate, singleton)
+import Agda.Interaction.Imports  ( Mode, pattern ScopeCheck, pattern TypeCheck )
+import qualified Agda.Interaction.Imports as Imp
+import Agda.Interaction.Highlighting.Generate
+
+import Agda.Compiler.Backend
+
+import Agda.Auto.Auto as Auto
+
+import Agda.Utils.Either
+import Agda.Utils.FileName
+import Agda.Utils.Function
+import Agda.Utils.Hash
+import Agda.Utils.Lens
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty hiding (Mode)
+import qualified Agda.Utils.ProfileOptions as Profile
+import Agda.Utils.Singleton
+import Agda.Utils.String
+import Agda.Utils.Time
+import Agda.Utils.Tuple
+import Agda.Utils.WithDefault (lensCollapseDefault, lensKeepDefault)
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- The CommandM monad
+
+-- | Restore both 'TCState' and 'CommandState'.
+
+localStateCommandM :: CommandM a -> CommandM a
+localStateCommandM m = do
+  cSt <- get
+  tcSt <- getTC
+  x <- m
+  putTC tcSt
+  put cSt
+  return x
+
+-- | Restore 'TCState', do not touch 'CommandState'.
+
+liftLocalState :: TCM a -> CommandM a
+liftLocalState = lift . localTCState
+
+-- | Build an opposite action to 'lift' for state monads.
+
+revLift
+    :: MonadState st m
+    => (forall c . m c -> st -> k (c, st))      -- ^ run
+    -> (forall b . k b -> m b)                  -- ^ lift
+    -> (forall x . (m a -> k x) -> k x) -> m a  -- ^ reverse lift in double negative position
+revLift run lift' f = do
+    st <- get
+    (a, st') <- lift' $ f (`run` st)
+    put st'
+    return a
+
+revLiftTC
+    :: MonadTCState m
+    => (forall c . m c -> TCState -> k (c, TCState))  -- ^ run
+    -> (forall b . k b -> m b)                        -- ^ lift
+    -> (forall x . (m a -> k x) -> k x) -> m a        -- ^ reverse lift in double negative position
+revLiftTC run lift' f = do
+    st <- getTC
+    (a, st') <- lift' $ f (`run` st)
+    putTC st'
+    return a
+
+-- | Opposite of 'liftIO' for 'CommandM'.
+--
+-- This function should only be applied to computations that are
+-- guaranteed not to raise any errors (except for 'IOException's).
+
+commandMToIO :: (forall x . (CommandM a -> IO x) -> IO x) -> CommandM a
+commandMToIO ci_i = revLift runStateT lift $ \ct -> revLiftTC runSafeTCM liftIO $ ci_i . (. ct)
+
+-- | Lift a TCM action transformer to a CommandM action transformer.
+
+liftCommandMT :: (forall x . TCM x -> TCM x) -> CommandM a -> CommandM a
+liftCommandMT f m = revLift runStateT lift $ f . ($ m)
+
+-- | Ditto, but restore state.
+
+liftCommandMTLocalState :: (forall x . TCM x -> TCM x) -> CommandM a -> CommandM a
+liftCommandMTLocalState f = liftCommandMT f . localStateCommandM
+
+-- | Put a response by the callback function given by 'stInteractionOutputCallback'.
+
+putResponse :: Response -> CommandM ()
+putResponse = lift . appInteractionOutputCallback
+
+
+-- | A Lens for 'theInteractionPoints'.
+
+modifyTheInteractionPoints :: ([InteractionId] -> [InteractionId]) -> CommandM ()
+modifyTheInteractionPoints f = modify $ \ s ->
+  s { theInteractionPoints = f (theInteractionPoints s) }
+
+
+-- * Operations for manipulating 'oldInteractionScopes'.
+
+-- | A Lens for 'oldInteractionScopes'.
+modifyOldInteractionScopes :: (OldInteractionScopes -> OldInteractionScopes) -> CommandM ()
+modifyOldInteractionScopes f = modify $ \ s ->
+  s { oldInteractionScopes = f $ oldInteractionScopes s }
+
+insertOldInteractionScope :: InteractionId -> ScopeInfo -> CommandM ()
+insertOldInteractionScope ii scope = do
+  lift $ reportSLn "interaction.scope" 20 $ "inserting old interaction scope " ++ show ii
+  modifyOldInteractionScopes $ Map.insert ii scope
+
+removeOldInteractionScope :: InteractionId -> CommandM ()
+removeOldInteractionScope ii = do
+  lift $ reportSLn "interaction.scope" 20 $ "removing old interaction scope " ++ show ii
+  modifyOldInteractionScopes $ Map.delete ii
+
+getOldInteractionScope :: InteractionId -> CommandM ScopeInfo
+getOldInteractionScope ii = do
+  ms <- gets $ Map.lookup ii . oldInteractionScopes
+  case ms of
+    Nothing    -> fail $ "not an old interaction point: " ++ show ii
+    Just scope -> return scope
+
+-- | Do setup and error handling for a command.
+
+handleCommand_ :: CommandM () -> CommandM ()
+handleCommand_ = handleCommand id (return ())
+
+handleCommand :: (forall a. CommandM a -> CommandM a) -> CommandM () -> CommandM () -> CommandM ()
+handleCommand wrap onFail cmd = handleNastyErrors $ wrap $ do
+    oldState <- getTC
+
+    -- -- Andreas, 2016-11-18 OLD CODE:
+    -- -- onFail and handleErr are executed in "new" command state (not TCState).
+    -- -- But it seems that if an exception is raised, it is identical to the old state,
+    -- -- see code for catchErr.
+    -- res <- (`catchErr` (return . Just)) $ Nothing <$ cmd
+    -- maybe (return ()) (\ e -> onFail >> handleErr e) res
+
+    -- Andreas, 2016-11-18 NEW CODE: execute onFail and handleErr in handler
+    -- which means (looking at catchErr) they run in state s rathern than s'.
+    -- Yet, it looks like s == s' in case the command failed.
+    cmd `catchErr` \ e -> do
+      onFail
+      handleErr Nothing e
+      -- Andreas, 2016-11-18, issue #2174
+      -- Reset TCState after error is handled, to get rid of metas created during failed command
+      lift $ do
+        newPersistentState <- useTC lensPersistentState
+        putTC oldState
+        lensPersistentState `setTCLens` newPersistentState
+
+  where
+    -- Preserves state so we can do unsolved meta highlighting
+    catchErr :: CommandM a -> (TCErr -> CommandM a) -> CommandM a
+    catchErr m h = do
+      s       <- get
+      (x, s') <- lift $ do runStateT m s
+         `catchError_` \ e ->
+           runStateT (h e) s
+      put s'
+      return x
+
+    -- Handle every possible kind of error (#637), except for
+    -- AsyncCancelled, which is used to abort Agda.
+    handleNastyErrors :: CommandM () -> CommandM ()
+    handleNastyErrors m = commandMToIO $ \ toIO -> do
+      let handle e =
+            Right <$>
+              toIO (handleErr (Just Direct) $
+                        Exception noRange $ text $ E.displayException e)
+
+          asyncHandler e@AsyncCancelled = return (Left e)
+
+          generalHandler (e :: E.SomeException) = handle e
+
+      r <- ((Right <$> toIO m) `E.catch` asyncHandler)
+             `E.catch` generalHandler
+      case r of
+        Right x -> return x
+        Left e  -> E.throwIO e
+
+    -- Displays an error and instructs Emacs to jump to the site of the
+    -- error. Because this function may switch the focus to another file
+    -- the status information is also updated.
+    handleErr method e = do
+        unsolved <- lift $ computeUnsolvedInfo
+        err     <- lift $ errorHighlighting e
+        modFile <- lift $ useTC stModuleToSource
+        method  <- case method of
+          Nothing -> lift $ viewTC eHighlightingMethod
+          Just m  -> return m
+        let info = convert $ err <> unsolved
+                     -- Errors take precedence over unsolved things.
+
+        -- TODO: make a better predicate for this
+        noError <- lift $ null <$> renderError e
+
+        showImpl <- lift $ optShowImplicit <$> useTC stPragmaOptions
+        showIrr <- lift $ optShowIrrelevant <$> useTC stPragmaOptions
+        unless noError $ do
+          mapM_ putResponse $
+            [ Resp_DisplayInfo $ Info_Error $ Info_GenericError e ] ++
+            tellEmacsToJumpToError (getRange e) ++
+            [ Resp_HighlightingInfo info KeepHighlighting
+                                    method modFile ] ++
+            [ Resp_Status $ Status { sChecked = False
+                                   , sShowImplicitArguments = showImpl
+                                   , sShowIrrelevantArguments = showIrr
+                                   } ]
+          whenM (optExitOnError <$> commandLineOptions) $
+            liftIO $ exitAgdaWith TCMError
+
+-- | Run an 'IOTCM' value, catch the exceptions, emit output
+--
+--   If an error happens the state of 'CommandM' does not change,
+--   but stPersistent may change (which contains successfully
+--   loaded interfaces for example).
+
+runInteraction :: IOTCM -> CommandM ()
+runInteraction iotcm =
+  handleCommand inEmacs onFail $ do
+    currentAbs <- liftIO $ absolute current
+    cf  <- gets theCurrentFile
+    cmd <- if independent cmd then return cmd else do
+      when (Just currentAbs /= (currentFilePath <$> cf)) $ do
+        let mode = TypeCheck
+        cmd_load' current [] True mode $ \_ -> return ()
+      cf <- fromMaybe __IMPOSSIBLE__ <$> gets theCurrentFile
+      return $ case iotcm (Just (currentFileModule cf)) of
+        IOTCM _ _ _ cmd -> cmd
+
+    withCurrentFile $ interpret cmd
+
+    cf' <- gets theCurrentFile
+    when (updateInteractionPointsAfter cmd
+            &&
+          Just currentAbs == (currentFilePath <$> cf')) $ do
+        putResponse . Resp_InteractionPoints =<< gets theInteractionPoints
+
+  where
+    -- The ranges in cmd might be incorrect because of the use of
+    -- Nothing here. That is taken care of above.
+    IOTCM current highlighting highlightingMethod cmd = iotcm Nothing
+
+    inEmacs :: forall a. CommandM a -> CommandM a
+    inEmacs = liftCommandMT $ withEnv $ initEnv
+            { envHighlightingLevel  = highlighting
+            , envHighlightingMethod = highlightingMethod
+            }
+
+    -- If an independent command fails we should reset theCurrentFile (Issue853).
+    onFail | independent cmd = modify $ \ s -> s { theCurrentFile = Nothing }
+           | otherwise       = return ()
+
+------------------------------------------------------------------------
+-- Command queues
+
+-- | If the next command from the command queue is anything but an
+-- actual command, then the command is returned.
+--
+-- If the command is an 'IOTCM' command, then the following happens:
+-- The given computation is applied to the command and executed. If an
+-- abort command is encountered (and acted upon), then the computation
+-- is interrupted, the persistent state and all options are restored,
+-- and some commands are sent to the frontend. If the computation was
+-- not interrupted, then its result is returned.
+
+-- TODO: It might be nice if some of the changes to the persistent
+-- state inflicted by the interrupted computation were preserved.
+
+maybeAbort :: (IOTCM -> CommandM a) -> CommandM (Command' (Maybe a))
+maybeAbort m = do
+  commandState <- get
+  let q = commandQueue commandState
+  (n, cmd) <- liftIO $ atomically $ readTChan (commands q)
+  case cmd of
+    Done      -> return Done
+    Error e   -> return (Error e)
+    Command c -> do
+      tcState <- getTC
+      tcEnv   <- askTC
+      result  <- liftIO $ race
+                   (runTCM tcEnv tcState $
+                    runStateT (m c) commandState)
+                   (waitForAbort n q)
+      case result of
+        Left ((x, commandState'), tcState') -> do
+          putTC tcState'
+          put commandState'
+          case c Nothing of
+            IOTCM _ _ _ Cmd_exit -> do
+              putResponse Resp_DoneExiting
+              return Done
+            _ -> return (Command (Just x))
+        Right a -> do
+          liftIO $ popAbortedCommands q a
+          putTC $ initState
+            { stPersistentState = stPersistentState tcState
+            , stPreScopeState   =
+                (stPreScopeState initState)
+                  { stPrePragmaOptions =
+                      stPrePragmaOptions
+                        (stPreScopeState tcState)
+                  }
+            }
+          put $ (initCommandState (commandQueue commandState))
+            { optionsOnReload = optionsOnReload commandState
+            }
+          putResponse Resp_DoneAborting
+          displayStatus
+          return (Command Nothing)
+  where
+
+  -- Returns if the currently executing command should be aborted.
+  -- The "abort number" is returned.
+
+  waitForAbort
+    :: Integer       -- The number of the currently executing command.
+    -> CommandQueue  -- The command queue.
+    -> IO Integer
+  waitForAbort n q = do
+    atomically $ do
+      a <- readTVar (abort q)
+      case a of
+        Just a' | n <= a' -> return a'
+        _                 -> retry
+
+  -- Removes every command for which the command number is at most
+  -- the given number (the "abort number") from the command queue.
+  --
+  -- New commands could be added to the end of the queue while this
+  -- computation is running. This does not lead to a race condition,
+  -- because those commands have higher command numbers, so they will
+  -- not be removed.
+
+  popAbortedCommands :: CommandQueue -> Integer -> IO ()
+  popAbortedCommands q n = do
+    done <- atomically $ do
+      cmd <- tryReadTChan (commands q)
+      case cmd of
+        Nothing -> return True
+        Just c  ->
+          if fst c <= n then
+            return False
+           else do
+            unGetTChan (commands q) c
+            return True
+    unless done $
+      popAbortedCommands q n
+
+-- | Creates a command queue, and forks a thread that writes commands
+-- to the queue. The queue is returned.
+
+initialiseCommandQueue
+  :: IO Command
+     -- ^ Returns the next command.
+  -> IO CommandQueue
+initialiseCommandQueue next = do
+  commands <- newTChanIO
+  abort    <- newTVarIO Nothing
+
+  let -- Read commands. The argument is the number of the previous
+      -- command (other than abort commands) that was read, if any.
+      readCommands n = do
+        c <- next
+        case c of
+          Command c | IOTCM _ _ _ Cmd_abort <- c Nothing -> do
+            atomically $ writeTVar abort (Just n)
+            readCommands n
+          _ -> do
+            let n' = (succ n)
+            atomically $ writeTChan commands (n', c)
+            case c of
+              Done -> return ()
+              _    -> readCommands n'
+
+  _ <- forkIO (readCommands 0)
+
+  return (CommandQueue { .. })
+
+---------------------------------------------------------
+
+-- | Can the command run even if the relevant file has not been loaded
+--   into the state?
+
+independent :: Interaction -> Bool
+independent (Cmd_load {})                   = True
+independent (Cmd_compile {})                = True
+independent (Cmd_load_highlighting_info {}) = True
+independent Cmd_tokenHighlighting {}        = True
+independent Cmd_show_version                = True
+independent _                               = False
+
+-- | Should 'Resp_InteractionPoints' be issued after the command has
+-- run?
+
+updateInteractionPointsAfter :: Interaction -> Bool
+updateInteractionPointsAfter Cmd_load{}                          = True
+updateInteractionPointsAfter Cmd_compile{}                       = True
+updateInteractionPointsAfter Cmd_constraints{}                   = False
+updateInteractionPointsAfter Cmd_metas{}                         = False
+updateInteractionPointsAfter Cmd_no_metas{}                      = False
+updateInteractionPointsAfter Cmd_show_module_contents_toplevel{} = False
+updateInteractionPointsAfter Cmd_search_about_toplevel{}         = False
+updateInteractionPointsAfter Cmd_solveAll{}                      = True
+updateInteractionPointsAfter Cmd_solveOne{}                      = True
+updateInteractionPointsAfter Cmd_infer_toplevel{}                = False
+updateInteractionPointsAfter Cmd_compute_toplevel{}              = False
+updateInteractionPointsAfter Cmd_load_highlighting_info{}        = False
+updateInteractionPointsAfter Cmd_tokenHighlighting{}             = False
+updateInteractionPointsAfter Cmd_highlight{}                     = True
+updateInteractionPointsAfter ShowImplicitArgs{}                  = False
+updateInteractionPointsAfter ToggleImplicitArgs{}                = False
+updateInteractionPointsAfter ShowIrrelevantArgs{}                = False
+updateInteractionPointsAfter ToggleIrrelevantArgs{}              = False
+updateInteractionPointsAfter Cmd_give{}                          = True
+updateInteractionPointsAfter Cmd_refine{}                        = True
+updateInteractionPointsAfter Cmd_intro{}                         = True
+updateInteractionPointsAfter Cmd_refine_or_intro{}               = True
+updateInteractionPointsAfter Cmd_autoOne{}                       = True
+updateInteractionPointsAfter Cmd_autoAll{}                       = True
+updateInteractionPointsAfter Cmd_context{}                       = False
+updateInteractionPointsAfter Cmd_helper_function{}               = False
+updateInteractionPointsAfter Cmd_infer{}                         = False
+updateInteractionPointsAfter Cmd_goal_type{}                     = False
+updateInteractionPointsAfter Cmd_elaborate_give{}                = True
+updateInteractionPointsAfter Cmd_goal_type_context{}             = False
+updateInteractionPointsAfter Cmd_goal_type_context_infer{}       = False
+updateInteractionPointsAfter Cmd_goal_type_context_check{}       = False
+updateInteractionPointsAfter Cmd_show_module_contents{}          = False
+updateInteractionPointsAfter Cmd_make_case{}                     = True
+updateInteractionPointsAfter Cmd_compute{}                       = False
+updateInteractionPointsAfter Cmd_why_in_scope{}                  = False
+updateInteractionPointsAfter Cmd_why_in_scope_toplevel{}         = False
+updateInteractionPointsAfter Cmd_show_version{}                  = False
+updateInteractionPointsAfter Cmd_abort{}                         = False
+updateInteractionPointsAfter Cmd_exit{}                          = False
+
+-- | Interpret an interaction
+
+interpret :: Interaction -> CommandM ()
+
+interpret (Cmd_load m argv) =
+  cmd_load' m argv True mode $ \_ -> interpret $ Cmd_metas AsIs
+  where
+  mode = TypeCheck
+
+interpret (Cmd_compile backend file argv) =
+  cmd_load' file argv allowUnsolved mode $ \ checkResult -> do
+    mw <- lift $ applyFlagsToTCWarnings $ crWarnings checkResult
+    case mw of
+      [] -> do
+        lift $ case backend of
+          LaTeX                    -> callBackend "LaTeX" IsMain checkResult
+          QuickLaTeX               -> callBackend "LaTeX" IsMain checkResult
+          OtherBackend "GHCNoMain" -> callBackend "GHC" NotMain checkResult   -- for backwards compatibility
+          OtherBackend b           -> callBackend b IsMain checkResult
+        display_info . Info_CompilationOk backend =<< lift B.getWarningsAndNonFatalErrors
+      w@(_:_) -> display_info $ Info_Error $ Info_CompilationError w
+  where
+  allowUnsolved = backend `elem` [LaTeX, QuickLaTeX]
+  mode | QuickLaTeX <- backend = ScopeCheck
+       | otherwise             = TypeCheck
+
+interpret Cmd_constraints =
+    display_info . Info_Constraints =<< lift B.getConstraints
+
+interpret (Cmd_metas norm) = do
+  ms <- lift $ B.getGoals' norm (max Simplified norm)
+  display_info . Info_AllGoalsWarnings ms =<< lift B.getWarningsAndNonFatalErrors
+
+interpret Cmd_no_metas = do
+  metas <- getOpenMetas
+  unless (null metas) $
+    typeError $ GenericError "Unsolved meta-variables"
+
+interpret (Cmd_show_module_contents_toplevel norm s) =
+  atTopLevel $ showModuleContents norm noRange s
+
+interpret (Cmd_search_about_toplevel norm s) =
+  atTopLevel $ searchAbout norm noRange s
+
+interpret (Cmd_solveAll norm)        = solveInstantiatedGoals norm Nothing
+interpret (Cmd_solveOne norm ii _ _) = solveInstantiatedGoals norm' (Just ii)
+  -- `solveOne` is called via `agda2-maybe-normalised` which does not use
+  -- AsIs < Simplified < Normalised but rather Simplified < Instantiated < Normalised
+  -- So we remap the Rewrite modifiers to match solveAll's behaviour.
+  -- NB: instantiate is called in getSolvedInteractionPoints no matter what.
+  where norm' = case norm of
+                  Simplified   -> AsIs
+                  Instantiated -> Simplified
+                  _            -> norm
+
+interpret (Cmd_infer_toplevel norm s) = do
+  (time, expr) <- parseAndDoAtToplevel (B.typeInCurrent norm) s
+  state <- get
+  display_info $ Info_InferredType state time expr
+
+interpret (Cmd_compute_toplevel cmode s) = do
+  (time, expr) <- parseAndDoAtToplevel action (B.computeWrapInput cmode s)
+  state <- get
+  display_info $ Info_NormalForm state cmode time expr
+    where
+    action = allowNonTerminatingReductions
+           . (if B.computeIgnoreAbstract cmode then ignoreAbstractMode else inConcreteMode)
+           . B.evalInCurrent cmode
+-- interpret (Cmd_compute_toplevel cmode s) =
+--   parseAndDoAtToplevel action Info_NormalForm $ computeWrapInput cmode s
+--   where
+--   action = allowNonTerminatingReductions
+--          . (if computeIgnoreAbstract cmode then ignoreAbstractMode else inConcreteMode)
+--          . (B.showComputed cmode <=< B.evalInCurrent)
+
+
+interpret (ShowImplicitArgs showImpl) = do
+  opts <- lift commandLineOptions
+  setCommandLineOpts $
+    set (lensPragmaOptions . lensOptShowImplicit . lensKeepDefault) showImpl opts
+
+interpret ToggleImplicitArgs = do
+  opts <- lift commandLineOptions
+  setCommandLineOpts $
+    over (lensPragmaOptions . lensOptShowImplicit . lensCollapseDefault) not opts
+
+interpret (ShowIrrelevantArgs showIrr) = do
+  opts <- lift commandLineOptions
+  setCommandLineOpts $
+    set (lensPragmaOptions . lensOptShowIrrelevant . lensKeepDefault) showIrr opts
+
+interpret ToggleIrrelevantArgs = do
+  opts <- lift commandLineOptions
+  setCommandLineOpts $
+    over (lensPragmaOptions . lensOptShowIrrelevant . lensCollapseDefault) not opts
+
+interpret (Cmd_load_highlighting_info source) = do
+  l <- asksTC envHighlightingLevel
+  when (l /= None) $ do
+    -- Make sure that the include directories have
+    -- been set.
+    setCommandLineOpts =<< lift commandLineOptions
+    resp <- lift $ liftIO . tellToUpdateHighlighting =<< do
+      ex        <- liftIO $ doesFileExist source
+      absSource <- liftIO $ SourceFile <$> absolute source
+      if ex
+        then
+           do
+              src <- Imp.parseSource absSource
+              let m = Imp.srcModuleName src
+              checkModuleName m absSource Nothing
+              mmi <- getVisitedModule m
+              case mmi of
+                Nothing -> return Nothing
+                Just mi ->
+                  if hashText (Imp.srcText src) == iSourceHash (miInterface mi)
+                    then do
+                      modFile <- useTC stModuleToSource
+                      method  <- viewTC eHighlightingMethod
+                      return $ Just (iHighlighting $ miInterface mi, method, modFile)
+                    else
+                      return Nothing
+            `catchError` \_ -> return Nothing
+        else
+          return Nothing
+    mapM_ putResponse resp
+
+interpret (Cmd_tokenHighlighting source remove) = do
+  info <- do l <- asksTC envHighlightingLevel
+             if l == None
+               then return Nothing
+               else do
+                 source' <- liftIO (absolute source)
+                 lift $ (Just <$> generateTokenInfo source')
+                           `catchError` \_ ->
+                        return Nothing
+      `finally`
+    case remove of
+      Remove -> liftIO $ removeFile source
+      Keep   -> return ()
+  case info of
+    Just info' -> lift $ printHighlightingInfo RemoveHighlighting info'
+    Nothing    -> return ()
+
+interpret (Cmd_highlight ii rng s) = do
+  l <- asksTC envHighlightingLevel
+  when (l /= None) $ do
+    scope <- getOldInteractionScope ii
+    removeOldInteractionScope ii
+    handle $ do
+      parsed <- try (Info_HighlightingParseError ii) $
+             B.parseExpr rng s
+      expr <- try (Info_HighlightingScopeCheckError ii) $
+             concreteToAbstract scope parsed
+      lift $ printHighlightingInfo KeepHighlighting =<<
+               generateTokenInfoFromString rng s
+      lift $ highlightExpr expr
+  where
+    handle :: ExceptT Info_Error TCM () -> CommandM ()
+    handle m = do
+      res <- lift $ runExceptT m
+      case res of
+        Left err -> display_info $ Info_Error err
+        Right _ -> return ()
+    try :: Info_Error -> TCM a -> ExceptT Info_Error TCM a
+    try err m = ExceptT $ do
+      (mapLeft (const err) <$> freshTCM m) `catchError` \ _ -> return (Left err)
+      -- freshTCM to avoid scope checking creating new interaction points
+
+interpret (Cmd_give   force ii rng s) = give_gen force ii rng s Give
+interpret (Cmd_refine ii rng s) = give_gen WithoutForce ii rng s Refine
+
+interpret (Cmd_intro pmLambda ii rng _) = do
+  ss <- lift $ B.introTactic pmLambda ii
+  liftCommandMT (withInteractionId ii) $ case ss of
+    []    -> do
+      display_info $ Info_Intro_NotFound
+    [s]   -> give_gen WithoutForce ii rng s Intro
+    _:_:_ -> do
+      display_info $ Info_Intro_ConstructorUnknown ss
+
+interpret (Cmd_refine_or_intro pmLambda ii r s) = interpret $
+  let s' = trim s
+  in (if null s' then Cmd_intro pmLambda else Cmd_refine) ii r s'
+
+interpret (Cmd_autoOne ii rng hint) = do
+  -- Andreas, 2014-07-05 Issue 1226:
+  -- Save the state to have access to even those interaction ids
+  -- that Auto solves (since Auto gives the solution right away).
+  st <- getTC
+  (time , res) <- maybeTimed $ Auto.auto ii rng hint
+  case autoProgress res of
+   Solutions sols -> do
+    lift $ reportSLn "auto" 10 $ "Auto produced the following solutions " ++ show sols
+    forM_ sols $ \(ii', sol) -> do
+      -- Andreas, 2014-07-05 Issue 1226:
+      -- For highlighting, Resp_GiveAction needs to access
+      -- the @oldInteractionScope@s of the interaction points solved by Auto.
+      -- We dig them out from the state before Auto was invoked.
+      insertOldInteractionScope ii' =<< liftLocalState (putTC st >> getInteractionScope ii')
+      -- Andreas, 2014-07-07: NOT TRUE:
+      -- -- Andreas, 2014-07-05: The following should be obsolete,
+      -- -- as Auto has removed the interaction points already:
+      -- modifyTheInteractionPoints $ filter (/= ii)
+      putResponse $ Resp_GiveAction ii' $ Give_String sol
+    -- Andreas, 2014-07-07: Remove the interaction points in one go.
+    modifyTheInteractionPoints (List.\\ (map fst sols))
+    case autoMessage res of
+     Nothing  -> interpret $ Cmd_metas AsIs
+     Just msg -> display_info $ Info_Auto msg
+   FunClauses cs -> do
+    case autoMessage res of
+     Nothing  -> return ()
+     Just msg -> display_info $ Info_Auto msg
+    putResponse $ Resp_MakeCase ii R.Function cs
+   Refinement s -> give_gen WithoutForce ii rng s Refine
+  maybe (return ()) (display_info . Info_Time) time
+
+interpret Cmd_autoAll = do
+  iis <- getInteractionPoints
+  unless (null iis) $ do
+    let time = 1000 `div` length iis
+    st <- getTC
+    solved <- forM iis $ \ ii -> do
+      rng <- getInteractionRange ii
+      res <- Auto.auto ii rng ("-t " ++ show time ++ "ms")
+      case autoProgress res of
+        Solutions sols -> forM sols $ \ (jj, s) -> do
+            oldInteractionScope <- liftLocalState (putTC st >> getInteractionScope jj)
+            insertOldInteractionScope jj oldInteractionScope
+            putResponse $ Resp_GiveAction ii $ Give_String s
+            return jj
+        _ -> return []
+    modifyTheInteractionPoints (List.\\ concat solved)
+
+interpret (Cmd_context norm ii _ _) =
+  display_info . Info_Context ii =<< liftLocalState (B.getResponseContext norm ii)
+
+interpret (Cmd_helper_function norm ii rng s) = do
+  -- Create type of application of new helper function that would solve the goal.
+  helperType <- liftLocalState $ withInteractionId ii $ inTopContext $ B.metaHelperType norm ii rng s
+  display_info $ Info_GoalSpecific ii (Goal_HelperFunction helperType)
+
+interpret (Cmd_infer norm ii rng s) = do
+  expr <- liftLocalState $ withInteractionId ii $ B.typeInMeta ii norm =<< B.parseExprIn ii rng s
+  display_info $ Info_GoalSpecific ii (Goal_InferredType expr)
+
+interpret (Cmd_goal_type norm ii _ _) =
+  display_info $ Info_GoalSpecific ii (Goal_CurrentGoal norm)
+
+interpret (Cmd_elaborate_give norm ii rng s) =
+  give_gen WithoutForce ii rng s $ ElaborateGive norm
+
+interpret (Cmd_goal_type_context norm ii rng s) =
+  cmd_goal_type_context_and GoalOnly norm ii rng s
+
+interpret (Cmd_goal_type_context_infer norm ii rng s) = do
+  -- In case of the empty expression to type, don't fail with
+  -- a stupid parse error, but just fall back to
+  -- Cmd_goal_type_context.
+  aux <- if all Char.isSpace s
+            then return GoalOnly
+            else do
+              liftLocalState $ withInteractionId ii $ do
+                parsed <- B.parseExprIn ii rng s
+                (typ, faces) <- B.typeAndFacesInMeta ii norm parsed
+                return (GoalAndHave typ faces)
+  cmd_goal_type_context_and aux norm ii rng s
+
+interpret (Cmd_goal_type_context_check norm ii rng s) = do
+  term <- liftLocalState $ withInteractionId ii $ do
+    expr <- B.parseExprIn ii rng s
+    goal <- B.typeOfMeta AsIs ii
+    term <- case goal of
+      OfType _ ty -> checkExpr expr =<< isType_ ty
+      _           -> __IMPOSSIBLE__
+    B.normalForm norm term
+  cmd_goal_type_context_and (GoalAndElaboration term) norm ii rng s
+
+interpret (Cmd_show_module_contents norm ii rng s) =
+  liftCommandMT (withInteractionId ii) $ showModuleContents norm rng s
+
+interpret (Cmd_why_in_scope_toplevel s) =
+  atTopLevel $ whyInScope s
+
+interpret (Cmd_why_in_scope ii _range s) =
+  liftCommandMT (withInteractionId ii) $ whyInScope s
+
+interpret (Cmd_make_case ii rng s) = do
+  (f, casectxt, cs) <- lift $ makeCase ii rng s
+  liftCommandMT (withInteractionId ii) $ do
+    tel <- lift $ lookupSection (qnameModule f) -- don't shadow the names in this telescope
+    unicode <- getsTC $ optUseUnicode . getPragmaOptions
+    pcs      :: [Doc]      <- lift $ inTopContext $ addContext tel $ mapM prettyA cs
+    let pcs' :: [String]    = List.map (extlam_dropName unicode casectxt . decorate) pcs
+    lift $ reportSDoc "interaction.case" 60 $ TCP.vcat
+      [ "InteractionTop.Cmd_make_case"
+      , TCP.nest 2 $ TCP.vcat
+        [ "cs   = " TCP.<+> TCP.vcat (map prettyA cs)
+        , "pcs  = " TCP.<+> TCP.vcat (map return pcs)
+        , "pcs' = " TCP.<+> TCP.vcat (map TCP.text pcs')
+        ]
+      ]
+    lift $ reportSDoc "interaction.case" 90 $ TCP.vcat
+      [ "InteractionTop.Cmd_make_case"
+      , TCP.nest 2 $ TCP.vcat
+        [ "cs   = " TCP.<+> TCP.text (show cs)
+        ]
+      ]
+    putResponse $ Resp_MakeCase ii (makeCaseVariant casectxt) pcs'
+  where
+    decorate = renderStyle (style { mode = OneLineMode })
+
+    makeCaseVariant :: CaseContext -> MakeCaseVariant
+    makeCaseVariant Nothing = R.Function
+    makeCaseVariant Just{}  = R.ExtendedLambda
+
+    -- very dirty hack, string manipulation by dropping the function name
+    -- and replacing the last " = " with " -> ". It's important not to replace
+    -- the equal sign in named implicit with an arrow!
+    extlam_dropName :: UnicodeOrAscii -> CaseContext -> String -> String
+    extlam_dropName _ Nothing x = x
+    extlam_dropName glyphMode Just{}  x
+        = unwords $ reverse $ replEquals $ reverse $ drop 1 $ words x
+      where
+        arrow = render $ _arrow $ specialCharactersForGlyphs glyphMode
+        replEquals ("=" : ws) = arrow : ws
+        replEquals (w   : ws) = w : replEquals ws
+        replEquals []         = []
+
+interpret (Cmd_compute cmode ii rng s) = do
+  expr <- liftLocalState $ do
+    e <- B.parseExprIn ii rng $ B.computeWrapInput cmode s
+    withInteractionId ii $ applyWhen (B.computeIgnoreAbstract cmode) ignoreAbstractMode $ B.evalInCurrent cmode e
+  display_info $ Info_GoalSpecific ii (Goal_NormalForm cmode expr)
+
+interpret Cmd_show_version = display_info Info_Version
+
+interpret Cmd_abort = return ()
+interpret Cmd_exit  = return ()
+
+-- | Solved goals already instantiated internally
+-- The second argument potentially limits it to one specific goal.
+solveInstantiatedGoals :: Rewrite -> Maybe InteractionId -> CommandM ()
+solveInstantiatedGoals norm mii = do
+  -- Andreas, 2016-10-23 issue #2280: throw away meta elims.
+  out <- lift $ localTC (\ e -> e { envPrintMetasBare = True }) $ do
+    sip <- B.getSolvedInteractionPoints False norm
+           -- only solve metas which have a proper instantiation, i.e., not another meta
+    let sip' = maybe id (\ ii -> filter ((ii ==) . fst3)) mii sip
+    mapM prt sip'
+  putResponse $ Resp_SolveAll out
+  where
+      prt (i, m, e) = do
+        mi <- getMetaInfo <$> lookupLocalMeta m
+        e' <- withMetaInfo mi $ abstractToConcreteCtx TopCtx e
+        return (i, e')
+
+-- | @cmd_load' file argv unsolvedOk cmd@
+--   loads the module in file @file@,
+--   using @argv@ as the command-line options.
+--
+-- If type checking completes without any exceptions having been
+-- encountered then the command @cmd r@ is executed, where @r@ is the
+-- result of 'Imp.typeCheckMain'.
+
+cmd_load'
+  :: FilePath  -- ^ File to load into interaction.
+  -> [String]  -- ^ Arguments to Agda for loading this file
+  -> Bool      -- ^ Allow unsolved meta-variables?
+  -> Mode      -- ^ Full type-checking, or only scope-checking?
+  -> (CheckResult -> CommandM a)
+               -- ^ Continuation after successful loading.
+  -> CommandM a
+cmd_load' file argv unsolvedOK mode cmd = do
+    fp <- liftIO $ absolute file
+    ex <- liftIO $ doesFileExist $ filePath fp
+    unless ex $ typeError $ GenericError $
+      "The file " ++ file ++ " was not found."
+
+    -- Forget the previous "current file" and interaction points.
+    modify $ \ st -> st { theInteractionPoints = []
+                        , theCurrentFile       = Nothing
+                        }
+
+    t <- liftIO $ getModificationTime file
+
+    -- Update the status. Because the "current file" is not set the
+    -- status is not "Checked".
+    displayStatus
+
+    -- Reset the state, preserving options and decoded modules. Note
+    -- that if the include directories have changed, then the decoded
+    -- modules are reset by TCM.setCommandLineOptions' below.
+    lift resetState
+
+    -- Clear the info buffer to make room for information about which
+    -- module is currently being type-checked.
+    putResponse Resp_ClearRunningInfo
+
+    -- Remove any prior syntax highlighting.
+    putResponse (Resp_ClearHighlighting NotOnlyTokenBased)
+
+    -- Parse the file.
+    --
+    -- Note that options are set below.
+    src <- lift $ Imp.parseSource (SourceFile fp)
+
+    -- Store the warnings.
+    warnings <- useTC stTCWarnings
+
+    -- All options are reset when a file is reloaded, including the
+    -- choice of whether or not to display implicit arguments.
+    opts0 <- gets optionsOnReload
+    backends <- useTC stBackends
+    let (z, warns) = runOptM $ parseBackendOptions backends argv opts0
+    mapM_ (lift . warning . OptionWarning) warns
+    case z of
+      Left err -> lift $ typeError $ GenericError err
+      Right (_, opts) -> do
+        opts <- lift $ addTrustedExecutables opts
+        let update = over (lensOptAllowUnsolved . lensKeepDefault) (unsolvedOK &&)
+            root   = projectRoot fp $ Imp.srcModuleName src
+        lift $ TCM.setCommandLineOptions' root $ mapPragmaOptions update opts
+
+    -- Restore the warnings that were saved above.
+    modifyTCLens stTCWarnings (++ warnings)
+
+    ok <- lift $ Imp.typeCheckMain mode src
+
+    -- The module type checked. If the file was not changed while the
+    -- type checker was running then the interaction points and the
+    -- "current file" are stored.
+    t' <- liftIO $ getModificationTime file
+    when (t == t') $ do
+      is <- lift $ sortInteractionPoints =<< getInteractionPoints
+      modify $ \st -> st { theInteractionPoints = is
+                         , theCurrentFile       = Just $ CurrentFile
+                             { currentFilePath   = fp
+                             , currentFileModule = Imp.srcModuleName src
+                             , currentFileArgs   = argv
+                             , currentFileStamp  = t
+                             }
+                         }
+
+    cmd ok
+
+-- | Set 'envCurrentPath' to 'theCurrentFile', if any.
+withCurrentFile :: CommandM a -> CommandM a
+withCurrentFile m = do
+  mfile <- gets $ fmap currentFilePath . theCurrentFile
+  localTC (\ e -> e { envCurrentPath = mfile }) m
+
+atTopLevel :: CommandM a -> CommandM a
+atTopLevel cmd = liftCommandMT B.atTopLevel cmd
+
+---------------------------------------------------------------------------
+-- Giving, refining.
+
+data GiveRefine = Give | Refine | Intro | ElaborateGive Rewrite
+  deriving (Eq, Show)
+
+-- | A "give"-like action (give, refine, etc).
+--
+--   @give_gen force ii rng s give_ref mk_newtxt@
+--   acts on interaction point @ii@
+--   occupying range @rng@,
+--   placing the new content given by string @s@,
+--   and replacing @ii@ by the newly created interaction points
+--   in the state if safety checks pass (unless @force@ is applied).
+give_gen
+  :: UseForce       -- ^ Should safety checks be skipped?
+  -> InteractionId
+  -> Range
+  -> String
+  -> GiveRefine
+  -> CommandM ()
+give_gen force ii rng s0 giveRefine = do
+  let s = trim s0
+  reportSLn "interaction.give" 20 $ "give_gen  " ++ s
+  -- Andreas, 2015-02-26 if string is empty do nothing rather
+  -- than giving a parse error.
+  unless (null s) $ do
+    let give_ref =
+          case giveRefine of
+            Give               -> B.give
+            Refine             -> B.refine
+            Intro              -> B.refine
+            ElaborateGive norm -> B.elaborate_give norm
+    -- save scope of the interaction point (for printing the given expr. later)
+    scope     <- getInteractionScope ii
+    -- parse string and "give", obtaining an abstract expression
+    -- and newly created interaction points
+    (time, (ae, ae0, iis)) <- maybeTimed $ do
+        -- Issue 3000: mark the current hole as solved before giving, to avoid confusing it with potential
+        -- new interaction points introduced by the give.
+        removeInteractionPoint ii
+        mis  <- getInteractionPoints
+        reportSLn "interaction.give" 30 $ "interaction points before = " ++ show mis
+        given <- lift $ B.parseExprIn ii rng s
+        ae    <- lift $ give_ref force ii Nothing given
+        mis' <- getInteractionPoints
+        reportSLn "interaction.give" 30 $ "interaction points after = " ++ show mis'
+        return (ae, given, mis' List.\\ mis)
+    -- favonia: backup the old scope for highlighting
+    insertOldInteractionScope ii scope
+    -- sort the new interaction points and put them into the state
+    -- in replacement of the old interaction point
+    iis' <- sortInteractionPoints iis
+    modifyTheInteractionPoints $ replace ii iis'
+    -- print abstract expr
+    ce        <- abstractToConcreteScope scope ae
+    reportS "interaction.give" 30
+      [ "ce = " ++ show ce
+      , "scopePrecedence = " ++ show (scope ^. scopePrecedence)
+      ]
+    -- if the command was @Give@, use the literal user input;
+    -- Andreas, 2014-01-15, see issue 1020:
+    -- Refine could solve a goal by introducing the sole constructor
+    -- without arguments.  Then there are no interaction metas, but
+    -- we still cannot just `give' the user string (which may be empty).
+    -- WRONG: also, if no interaction metas were created by @Refine@
+    -- WRONG: let literally = (giveRefine == Give || null iis) && rng /= noRange
+    -- Ulf, 2015-03-30, if we're doing intro we can't do literal give since
+    -- there is nothing in the hole (issue 1892).
+    let literally = (giveRefine == Give || giveRefine == Refine) && ae == ae0 && rng /= noRange
+    -- Ulf, 2014-01-24: This works for give since we're highlighting the string
+    -- that's already in the buffer. Doing it before the give action means that
+    -- the highlighting is moved together with the text when the hole goes away.
+    -- To make it work for refine we'd have to adjust the ranges.
+    when literally $ do
+      l <- asksTC envHighlightingLevel
+      when (l /= None) $ lift $ do
+        printHighlightingInfo KeepHighlighting =<<
+          generateTokenInfoFromString rng s
+        highlightExpr ae
+    putResponse $ Resp_GiveAction ii $ mkNewTxt literally ce
+    reportSLn "interaction.give" 30 $ "putResponse GiveAction passed"
+    -- display new goal set (if not measuring time)
+    maybe (interpret $ Cmd_metas AsIs) (display_info . Info_Time) time
+    reportSLn "interaction.give" 30 $ "interpret Cmd_metas passed"
+  where
+    -- Substitutes xs for x in ys.
+    replace x xs ys = concatMap (\ y -> if y == x then xs else [y]) ys
+    -- For @Give@ we can replace the ii by the user given input.
+    mkNewTxt True  C.Paren{} = Give_Paren
+    mkNewTxt True  _         = Give_NoParen
+    -- Otherwise, we replace it by the reified value Agda computed.
+    mkNewTxt False ce        = Give_String $ prettyShow ce
+
+highlightExpr :: A.Expr -> TCM ()
+highlightExpr e =
+  localTC (\st -> st { envImportPath         = []
+                     , envHighlightingLevel  = NonInteractive
+                     , envHighlightingMethod = Direct }) $
+    generateAndPrintSyntaxInfo decl Full True
+  where
+    dummy = mkName_ (NameId 0 noModuleNameHash) ("dummy" :: String)
+    info  = mkDefInfo (nameConcrete dummy) noFixity' PublicAccess ConcreteDef (getRange e)
+    decl  = A.Axiom OtherDefName info defaultArgInfo Nothing (qnameFromList $ singleton dummy) e
+
+-- | Sorts interaction points based on their ranges.
+
+sortInteractionPoints
+  :: (MonadInteractionPoints m, MonadError TCErr m, MonadFail m)
+  => [InteractionId] -> m [InteractionId]
+sortInteractionPoints is =
+  map fst . List.sortBy (compare `on` snd) <$> do
+    forM is $ \ i -> do
+      (i,) <$> getInteractionRange i
+
+-- | Displays the current goal, the given document, and the current
+--   context.
+--
+--   Should not modify the state.
+
+cmd_goal_type_context_and :: GoalTypeAux -> Rewrite -> InteractionId -> Range ->
+                             String -> CommandM ()
+cmd_goal_type_context_and aux norm ii _ _ = do
+  ctx <- lift $ B.getResponseContext norm ii
+  constr <- lift $ lookupInteractionId ii >>= B.getConstraintsMentioning norm
+  boundary <- lift $ B.getIPBoundary norm ii
+  display_info $ Info_GoalSpecific ii (Goal_GoalType norm aux ctx boundary constr)
+
+-- | Shows all the top-level names in the given module, along with
+-- their types.
+
+showModuleContents :: Rewrite -> Range -> String -> CommandM ()
+showModuleContents norm rng s = do
+  (modules, tel, types) <- lift $ B.moduleContents norm rng s
+  display_info $ Info_ModuleContents modules tel types
+
+-- | Shows all the top-level names in scope which mention all the given
+-- identifiers in their type.
+
+searchAbout :: Rewrite -> Range -> String -> CommandM ()
+searchAbout norm rg names = do
+  unlessNull (trim names) $ \ trimmedNames -> do
+    hits <- lift $ findMentions norm rg trimmedNames
+    display_info $ Info_SearchAbout hits trimmedNames
+
+-- | Explain why something is in scope.
+
+whyInScope :: String -> CommandM ()
+whyInScope s = do
+  Just file <- gets theCurrentFile
+  let cwd = takeDirectory (filePath $ currentFilePath file)
+  why <- liftLocalState $ B.whyInScope cwd s
+  display_info $ Info_WhyInScope why
+
+-- | Sets the command line options and updates the status information.
+
+setCommandLineOpts :: CommandLineOptions -> CommandM ()
+setCommandLineOpts opts = do
+    lift $ TCM.setCommandLineOptions opts
+    displayStatus
+
+
+-- | Computes some status information.
+--
+--   Does not change the state.
+
+status :: CommandM Status
+status = do
+  cf       <- gets theCurrentFile
+  showImpl <- lift showImplicitArguments
+  showIrr  <- lift showIrrelevantArguments
+
+  -- Check if the file was successfully type checked, and has not
+  -- changed since. Note: This code does not check if any dependencies
+  -- have changed, and uses a time stamp to check for changes.
+  checked  <- lift $ case cf of
+    Nothing -> return False
+    Just f  -> do
+      t <- liftIO $ getModificationTime $ filePath (currentFilePath f)
+      if currentFileStamp f == t
+        then
+          maybe False (null . miWarnings) <$>
+          getVisitedModule (currentFileModule f)
+        else
+            return False
+
+  return $ Status { sShowImplicitArguments   = showImpl,
+                    sShowIrrelevantArguments = showIrr,
+                    sChecked                 = checked }
+
+-- | Displays or updates status information.
+--
+--   Does not change the state.
+
+displayStatus :: CommandM ()
+displayStatus =
+  putResponse . Resp_Status  =<< status
+
+-- | @display_info@ does what @'display_info'' False@ does, but
+--   additionally displays some status information (see 'status' and
+--   'displayStatus').
+
+display_info :: DisplayInfo -> CommandM ()
+display_info info = do
+  displayStatus
+  putResponse $ Resp_DisplayInfo info
+
+-- | Parses and scope checks an expression (using the \"inside scope\"
+-- as the scope), performs the given command with the expression as
+-- input, and returns the result and the time it takes.
+
+parseAndDoAtToplevel
+  :: (A.Expr -> TCM a)
+     -- ^ The command to perform.
+  -> String
+     -- ^ The expression to parse.
+  -> CommandM (Maybe CPUTime, a)
+parseAndDoAtToplevel cmd s = do
+  localStateCommandM $ do
+    (e, attrs) <- lift $ runPM $ parse exprParser s
+    lift $ checkAttributes attrs
+    maybeTimed $ atTopLevel $ lift $
+      cmd =<< concreteToAbstract_ e
+
+maybeTimed :: CommandM a -> CommandM (Maybe CPUTime, a)
+maybeTimed work = do
+  doTime <- lift $ hasProfileOption Profile.Interactive
+  if not doTime
+    then (Nothing,) <$> work
+    else do
+      (r, time) <- measureTime work
+      return (Just time, r)
+
+-- | Tell to highlight the code using the given highlighting
+-- info (unless it is @Nothing@).
+
+tellToUpdateHighlighting
+  :: Maybe (HighlightingInfo, HighlightingMethod, ModuleToSource) -> IO [Response]
+tellToUpdateHighlighting Nothing                = return []
+tellToUpdateHighlighting (Just (info, method, modFile)) =
+  return [Resp_HighlightingInfo info KeepHighlighting method modFile]
+
+-- | Tells the Emacs mode to go to the first error position (if any).
+
+tellEmacsToJumpToError :: Range -> [Response]
+tellEmacsToJumpToError r =
+  case rStart r of
+    Nothing                                           -> []
+    Just (Pn { srcFile = Strict.Nothing })            -> []
+    Just (Pn { srcFile = Strict.Just f, posPos = p }) ->
+       [ Resp_JumpToError (filePath (rangeFilePath f)) p ]
diff --git a/src/full/Agda/Interaction/JSON.hs b/src/full/Agda/Interaction/JSON.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/JSON.hs
@@ -0,0 +1,147 @@
+{-# LANGUAGE CPP               #-}
+{-# LANGUAGE OverloadedStrings #-}
+
+-- | Encoding stuff into JSON values in TCM
+
+module Agda.Interaction.JSON
+  ( module Export
+  , EncodeTCM(..)
+  , obj, kind, kind'
+  , (.=)
+  , (@=), (#=)
+  ) where
+
+import Control.Monad as Export ((>=>), (<=<))
+import Data.Aeson    as Export hiding (Result(..), (.=))
+
+import qualified Data.Aeson
+import Data.Aeson.Types ( Pair )
+#if MIN_VERSION_aeson(2,0,0)
+import qualified Data.Aeson.Key as Key
+#endif
+
+import Data.Text (Text)
+import GHC.Int (Int32)
+
+-- import qualified Agda.Syntax.Translation.InternalToAbstract as I2A
+-- import qualified Agda.Syntax.Translation.AbstractToConcrete as A2C
+
+-- import qualified Agda.Syntax.Concrete as C
+-- import qualified Agda.Syntax.Internal as I
+import Agda.TypeChecking.Monad
+import Agda.Syntax.Common.Pretty
+import qualified Agda.Utils.FileName as File
+import qualified Agda.Utils.Maybe.Strict as Strict
+
+#if MIN_VERSION_aeson(2,0,0)
+toKey :: Text -> Key
+toKey = Key.fromText
+#else
+type Key = Text
+
+toKey :: Text -> Key
+toKey = id
+#endif
+
+---------------------------------------------------------------------------
+-- * The EncodeTCM class
+
+-- | The JSON version of`PrettyTCM`, for encoding JSON value in TCM
+class EncodeTCM a where
+  encodeTCM :: a -> TCM Value
+  default encodeTCM :: ToJSON a => a -> TCM Value
+  encodeTCM = pure . toJSON
+
+-- | TCM monadic version of object
+obj :: [TCM Pair] -> TCM Value
+obj = (object <$>) . sequence
+
+-- | A key-value pair for encoding a JSON object.
+(.=) :: ToJSON a => Text -> a -> Pair
+(.=) = (Data.Aeson..=) . toKey
+
+-- | Pairs a key with a value wrapped in TCM
+(#=) :: (ToJSON a) => Text -> TCM a -> TCM Pair
+(#=) key boxed = do
+  value <- boxed
+  pure $ key .= toJSON value
+
+-- | Abbreviation of `_ #= encodeTCM _`
+(@=) :: (EncodeTCM a) => Text -> a -> TCM Pair
+(@=) key value = do
+  encoded <- encodeTCM value
+  pure $ key .= encoded
+
+-- | A handy alternative of `obj` with kind specified
+kind :: Text -> [TCM Pair] -> TCM Value
+kind k = obj . (("kind" @= String k) :)
+
+-- | A handy alternative of `object` with kind specified
+kind' :: Text -> [Pair] -> Value
+kind' k = object . (("kind" .= String k) :)
+
+-- ---------------------------------------------------------------------------
+-- -- * The Rep & ToRep class
+--
+-- -- | Translates internal types to concrete types
+-- class ToRep i c | i -> c where
+--   toRep :: i -> TCM c
+--
+-- instance ToRep I.Term C.Expr where
+--   toRep internal = I2A.reify internal >>= A2C.abstractToConcrete_
+--
+-- instance ToRep I.Type C.Expr where
+--   toRep internal = I2A.reify internal >>= A2C.abstractToConcrete_
+--
+-- data Rep internal concrete = Rep
+--   { internalRep :: internal
+--   , concreteRep :: concrete
+--   }
+--
+-- instance (ToJSON i, ToJSON c) => ToJSON (Rep i c) where
+--   toJSON (Rep i c) = object
+--     [ "internal" .= i
+--     , "concrete" .= c
+--     ]
+--
+-- rep :: (ToRep i c) => i -> TCM (Rep i c)
+-- rep internal = do
+--   concrete <- toRep internal
+--   return $ Rep
+--     { internalRep = internal
+--     , concreteRep = concrete
+--     }
+
+--------------------------------------------------------------------------------
+-- Instances of ToJSON or EncodeTCM
+
+encodeListTCM :: EncodeTCM a => [a] -> TCM Value
+encodeListTCM = mapM encodeTCM >=> return . toJSONList
+
+instance EncodeTCM a => EncodeTCM [a] where
+  encodeTCM = mapM encodeTCM >=> return . toJSONList
+
+-- overlaps with the instance declared above
+instance {-# OVERLAPPING #-} EncodeTCM String
+
+instance EncodeTCM Bool where
+instance EncodeTCM Int where
+instance EncodeTCM Int32 where
+instance EncodeTCM Value where
+instance EncodeTCM Doc where
+
+instance ToJSON Doc where
+  toJSON = toJSON . render
+
+instance EncodeTCM a => EncodeTCM (Maybe a) where
+  encodeTCM Nothing   = return Null
+  encodeTCM (Just a)  = encodeTCM a
+
+instance ToJSON File.AbsolutePath where
+  toJSON (File.AbsolutePath path) = toJSON path
+
+#if !(MIN_VERSION_aeson(1,5,3))
+instance ToJSON a => ToJSON (Strict.Maybe a) where
+  toJSON (Strict.Just a) = toJSON a
+  toJSON Strict.Nothing  = Null
+#endif
diff --git a/src/full/Agda/Interaction/JSONTop.hs b/src/full/Agda/Interaction/JSONTop.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/JSONTop.hs
@@ -0,0 +1,465 @@
+module Agda.Interaction.JSONTop
+    ( jsonREPL
+    ) where
+
+import Control.Monad
+         ( (<=<), forM )
+import Control.Monad.IO.Class
+         ( MonadIO(..) )
+
+import Data.ByteString.Lazy (ByteString)
+import qualified Data.ByteString.Lazy.Char8 as BS
+import qualified Data.Text as T
+import qualified Data.Set as Set
+
+import Agda.Interaction.AgdaTop
+import Agda.Interaction.Base
+         ( CommandState(..), CurrentFile(..), ComputeMode(..), Rewrite(..), OutputForm(..), OutputConstraint(..) )
+import qualified Agda.Interaction.BasicOps as B
+import Agda.Interaction.EmacsTop
+import Agda.Interaction.JSON
+import Agda.Interaction.Response as R
+import Agda.Interaction.Highlighting.JSON
+
+import Agda.Syntax.Abstract.Pretty
+         ( prettyATop )
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Name
+         ( NameInScope(..), Name )
+import Agda.Syntax.Internal
+         ( telToList, Dom'(..), Dom, MetaId(..), ProblemId(..), Blocker(..), alwaysUnblock )
+import Agda.Syntax.Position
+         ( Range, rangeIntervals, Interval'(..), Position'(..), noRange )
+import Agda.Syntax.Scope.Base
+         ( WhyInScopeData(..) )
+
+import Agda.TypeChecking.Errors
+         ( getAllWarningsOfTCErr )
+import Agda.TypeChecking.Monad
+         ( Comparison(..), inTopContext, TCM, TCErr, TCWarning, NamedMeta(..), withInteractionId )
+import Agda.TypeChecking.Monad.MetaVars
+         ( getInteractionRange, getMetaRange, withMetaId )
+import Agda.TypeChecking.Pretty
+         ( PrettyTCM(..), prettyTCM )
+-- borrowed from EmacsTop, for temporarily serialising stuff
+import Agda.TypeChecking.Pretty.Warning
+         ( filterTCWarnings )
+import Agda.TypeChecking.Warnings
+         ( WarningsAndNonFatalErrors(..) )
+
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Syntax.Common.Pretty
+         ( Pretty(..), prettyShow )
+import Agda.Utils.Time
+         ( CPUTime(..) )
+
+import Agda.VersionCommit
+
+--------------------------------------------------------------------------------
+
+-- | 'jsonREPL' is a interpreter like 'mimicGHCi', but outputs JSON-encoded strings.
+--
+--   'jsonREPL' reads Haskell values (that starts from 'IOTCM' ...) from stdin,
+--   interprets them, and outputs JSON-encoded strings. into stdout.
+
+jsonREPL :: TCM () -> TCM ()
+jsonREPL = repl (liftIO . BS.putStrLn <=< jsonifyResponse) "JSON> "
+
+instance EncodeTCM NameInScope where
+instance ToJSON NameInScope where
+  toJSON InScope    = toJSON True
+  toJSON NotInScope = toJSON False
+
+instance EncodeTCM Status where
+instance ToJSON Status where
+  toJSON status = object
+    [ "showImplicitArguments"   .= sShowImplicitArguments status
+    , "showIrrelevantArguments" .= sShowIrrelevantArguments status
+    , "checked"                 .= sChecked status
+    ]
+
+instance EncodeTCM CommandState where
+instance ToJSON CommandState where
+  toJSON commandState = object
+    [ "interactionPoints" .= theInteractionPoints commandState
+    , "currentFile"       .= theCurrentFile commandState
+    -- more?
+    ]
+
+instance EncodeTCM CurrentFile where
+instance ToJSON CurrentFile where
+  toJSON (CurrentFile path _ _ time) = toJSON (path, time)  -- backwards compat.
+
+instance EncodeTCM ResponseContextEntry where
+  encodeTCM entry = obj
+    [ "originalName" @= encodePretty (respOrigName entry)
+    , "reifiedName"  @= encodePretty (respReifName entry)
+    , "binding"      #= prettyATop (unArg (respType entry))
+    , "inScope"      @= respInScope entry
+    ]
+
+instance EncodeTCM (Position' ()) where
+instance ToJSON (Position' ()) where
+  toJSON p = object
+    [ "pos"  .= toJSON (posPos p)
+    , "line" .= toJSON (posLine p)
+    , "col"  .= toJSON (posCol p)
+    ]
+
+instance EncodeTCM Range where
+instance ToJSON Range where
+  toJSON = toJSON . map prettyInterval . rangeIntervals
+    where prettyInterval i = object [ "start" .= iStart i, "end" .= iEnd i ]
+
+instance EncodeTCM ProblemId where
+instance EncodeTCM MetaId    where
+
+instance ToJSON ProblemId where toJSON (ProblemId i) = toJSON i
+
+instance ToJSON ModuleNameHash where
+  toJSON (ModuleNameHash h) = toJSON h
+
+instance ToJSON MetaId where
+  toJSON m = object
+    [ "id"     .= toJSON (metaId m)
+    , "module" .= toJSON (metaModule m)
+    ]
+
+instance EncodeTCM InteractionId where
+  encodeTCM ii@(InteractionId i) = obj
+    [ "id"    @= toJSON i
+    , "range" #= intervalsTCM
+    ]
+    where
+      intervalsTCM = toJSON <$> getInteractionRange ii
+instance ToJSON InteractionId where
+  toJSON (InteractionId i) = toJSON i
+
+instance EncodeTCM NamedMeta where
+  encodeTCM m = obj
+    [ "name"  #= nameTCM
+    , "range" #= intervalsTCM
+    ]
+    where
+      nameTCM = encodeShow <$> withMetaId (nmid m) (prettyATop m)
+      intervalsTCM = toJSON <$> getMetaRange (nmid m)
+
+instance EncodeTCM GiveResult where
+instance ToJSON GiveResult where
+  toJSON (Give_String s) = object [ "str" .= s ]
+  toJSON Give_Paren   = object [ "paren" .= True ]
+  toJSON Give_NoParen = object [ "paren" .= False ]
+
+instance EncodeTCM MakeCaseVariant where
+instance ToJSON MakeCaseVariant where
+  toJSON R.Function = String "Function"
+  toJSON R.ExtendedLambda = String "ExtendedLambda"
+
+encodePretty :: Pretty a => a -> Value
+encodePretty = encodeShow . pretty
+
+encodeShow :: Show a => a -> Value
+encodeShow = String . T.pack . show
+
+encodePrettyTCM :: PrettyTCM a => a -> TCM Value
+encodePrettyTCM = (encodeShow <$>) . prettyTCM
+
+instance EncodeTCM Rewrite where
+instance ToJSON Rewrite where toJSON = encodeShow
+
+instance EncodeTCM CPUTime where
+instance ToJSON CPUTime where toJSON = encodePretty
+
+instance EncodeTCM ComputeMode where
+instance ToJSON ComputeMode where toJSON = encodeShow
+
+encodeOCCmp :: (a -> TCM Value)
+  -> Comparison -> a -> a -> T.Text
+  -> TCM Value
+encodeOCCmp f c i j k = kind k
+  [ "comparison"     @= encodeShow c
+  , "constraintObjs" #= traverse f [i, j]
+  ]
+
+  -- Goals
+encodeOC :: (a -> TCM Value)
+  -> (b -> TCM Value)
+  -> OutputConstraint b a
+  -> TCM Value
+encodeOC f encPrettyTCM = \case
+ OfType i a -> kind "OfType"
+  [ "constraintObj" #= f i
+  , "type"          #= encPrettyTCM a
+  ]
+ CmpInType c a i j -> kind "CmpInType"
+  [ "comparison"     @= encodeShow c
+  , "type"           #= encPrettyTCM a
+  , "constraintObjs" #= traverse f [i, j]
+  ]
+ CmpElim ps a is js -> kind "CmpElim"
+  [ "polarities"     @= map encodeShow ps
+  , "type"           #= encPrettyTCM a
+  , "constraintObjs" #= traverse (traverse f) [is, js]
+  ]
+ JustType a -> kind "JustType"
+  [ "constraintObj"  #= f a
+  ]
+ JustSort a -> kind "JustSort"
+  [ "constraintObj"  #= f a
+  ]
+ CmpTypes  c i j -> encodeOCCmp f c i j "CmpTypes"
+ CmpLevels c i j -> encodeOCCmp f c i j "CmpLevels"
+ CmpTeles  c i j -> encodeOCCmp f c i j "CmpTeles"
+ CmpSorts  c i j -> encodeOCCmp f c i j "CmpSorts"
+ Assign i a -> kind "Assign"
+  [ "constraintObj"  #= f i
+  , "value"          #= encPrettyTCM a
+  ]
+ TypedAssign i v t -> kind "TypedAssign"
+  [ "constraintObj"  #= f i
+  , "value"          #= encPrettyTCM v
+  , "type"           #= encPrettyTCM t
+  ]
+ PostponedCheckArgs i es t0 t1 -> kind "PostponedCheckArgs"
+  [ "constraintObj"  #= f i
+  , "ofType"         #= encPrettyTCM t0
+  , "arguments"      #= forM es encPrettyTCM
+  , "type"           #= encPrettyTCM t1
+  ]
+ IsEmptyType a -> kind "IsEmptyType"
+  [ "type"           #= encPrettyTCM a
+  ]
+ SizeLtSat a -> kind "SizeLtSat"
+  [ "type"           #= encPrettyTCM a
+  ]
+ FindInstanceOF i t cs -> kind "FindInstanceOF"
+  [ "constraintObj"  #= f i
+  , "candidates"     #= forM cs encodeKVPairs
+  , "type"           #= encPrettyTCM t
+  ]
+  where encodeKVPairs (_, v, t) = obj -- TODO: encode kind
+          [ "value"  #= encPrettyTCM v
+          , "type"   #= encPrettyTCM t
+          ]
+ PTSInstance a b -> kind "PTSInstance"
+  [ "constraintObjs" #= traverse f [a, b]
+  ]
+ PostponedCheckFunDef name a err -> kind "PostponedCheckFunDef"
+  [ "name"           @= encodePretty name
+  , "type"           #= encPrettyTCM a
+  , "error"          #= encodeTCM err
+  ]
+ DataSort q s -> kind "DataSort"
+  [ "name"           @= encodePretty q
+  , "sort"           #= f s
+  ]
+ CheckLock t lk -> kind "CheckLock"
+  [ "head"           #= f t
+  , "lock"           #= f lk
+  ]
+ UsableAtMod mod t -> kind "UsableAtMod"
+  [ "mod"           @= encodePretty mod
+  , "term"          #= f t
+  ]
+
+encodeNamedPretty :: PrettyTCM a => (Name, a) -> TCM Value
+encodeNamedPretty (name, a) = obj
+  [ "name" @= encodePretty name
+  , "term" #= encodePrettyTCM a
+  ]
+
+instance EncodeTCM (OutputForm C.Expr C.Expr) where
+  encodeTCM (OutputForm range problems unblock oc) = obj
+    [ "range"      @= range
+    , "problems"   @= problems
+    , "unblocker"  @= unblock
+    , "constraint" #= encodeOC (pure . encodePretty) (pure . encodePretty) oc
+    ]
+
+instance EncodeTCM Blocker where
+  encodeTCM (UnblockOnMeta x)    = kind "UnblockOnMeta" [ "meta" @= x ]
+  encodeTCM (UnblockOnProblem p) = kind "UnblockOnProblem" [ "id" @= p ]
+  encodeTCM (UnblockOnDef q)     = kind "UnblockOnDef" [ "name" @= encodePretty q ]
+  encodeTCM (UnblockOnAll us)    = kind "UnblockOnAll" [ "blockers" @= Set.toList us ]
+  encodeTCM (UnblockOnAny us)    = kind "UnblockOnAny" [ "blockers" @= Set.toList us ]
+
+instance EncodeTCM DisplayInfo where
+  encodeTCM (Info_CompilationOk backend wes) = kind "CompilationOk"
+    [ "backend"           @= encodePretty backend
+    , "warnings"          #= encodeTCM (filterTCWarnings (tcWarnings wes))
+    , "errors"            #= encodeTCM (filterTCWarnings (nonFatalErrors wes))
+    ]
+  encodeTCM (Info_Constraints constraints) = kind "Constraints"
+    [ "constraints"       #= forM constraints encodeTCM
+    ]
+  encodeTCM (Info_AllGoalsWarnings (vis, invis) wes) = kind "AllGoalsWarnings"
+    [ "visibleGoals"      #= forM vis (\i -> withInteractionId (B.outputFormId $ OutputForm noRange [] alwaysUnblock i) $ encodeOC encodeTCM encodePrettyTCM i)
+    , "invisibleGoals"    #= forM invis (encodeOC encodeTCM encodePrettyTCM)
+    , "warnings"          #= encodeTCM (filterTCWarnings (tcWarnings wes))
+    , "errors"            #= encodeTCM (filterTCWarnings (nonFatalErrors wes))
+    ]
+  encodeTCM (Info_Time time) = kind "Time"
+    [ "time"              @= time
+    ]
+  encodeTCM (Info_Error err) = encodeTCM err
+  encodeTCM Info_Intro_NotFound = kind "IntroNotFound" []
+  encodeTCM (Info_Intro_ConstructorUnknown introductions) = kind "IntroConstructorUnknown"
+    [ "constructors"      @= map toJSON introductions
+    ]
+  encodeTCM (Info_Auto info) = kind "Auto"
+    [ "info"              @= toJSON info
+    ]
+  encodeTCM (Info_ModuleContents names tele contents) = kind "ModuleContents"
+    [ "contents"          #= forM contents encodeNamedPretty
+    , "telescope"         #= forM (telToList tele) encodeDomType
+    , "names"             @= map encodePretty names
+    ]
+    where
+      encodeDomType :: PrettyTCM a => Dom (ArgName, a) -> TCM Value
+      encodeDomType dom = obj
+        [ "dom"       #= encodePrettyTCM (unDom dom)
+        , "name"      @= fmap encodePretty (bareNameOf dom)
+        , "finite"    @= toJSON (domIsFinite dom)
+        , "cohesion"  @= encodeShow (modCohesion . argInfoModality $ domInfo dom)
+        , "relevance" @= encodeShow (modRelevance . argInfoModality $ domInfo dom)
+        , "hiding"    @= case argInfoHiding $ domInfo dom of
+          Instance o -> show o
+          o -> show o
+        ]
+  encodeTCM (Info_SearchAbout results search) = kind "SearchAbout"
+    [ "results"           #= forM results encodeNamedPretty
+    , "search"            @= toJSON search
+    ]
+  encodeTCM (Info_WhyInScope why@(WhyInScopeData y path _ _ _)) = kind "WhyInScope"
+    [ "thing"             @= prettyShow y
+    , "filepath"          @= toJSON path
+    -- use Emacs message first
+    , "message"           #= explainWhyInScope why
+    ]
+  encodeTCM (Info_NormalForm commandState computeMode time expr) = kind "NormalForm"
+    [ "commandState"      @= commandState
+    , "computeMode"       @= computeMode
+    , "time"              @= time
+    , "expr"              #= encodePrettyTCM expr
+    ]
+  encodeTCM (Info_InferredType commandState time expr) = kind "InferredType"
+    [ "commandState"      @= commandState
+    , "time"              @= time
+    , "expr"              #= encodePrettyTCM expr
+    ]
+  encodeTCM (Info_Context ii ctx) = kind "Context"
+    [ "interactionPoint"  @= ii
+    , "context"           @= ctx
+    ]
+  encodeTCM Info_Version = kind "Version"
+    [ "version"           @= (versionWithCommitInfo :: String)
+    ]
+  encodeTCM (Info_GoalSpecific ii info) = kind "GoalSpecific"
+    [ "interactionPoint"  @= ii
+    , "goalInfo"          #= withInteractionId ii (encodeGoalSpecific ii info)
+    ]
+
+instance EncodeTCM GoalTypeAux where
+  encodeTCM GoalOnly = kind "GoalOnly" []
+  encodeTCM (GoalAndHave expr _) = kind "GoalAndHave"
+    [ "expr" #= encodePrettyTCM expr ]
+  encodeTCM (GoalAndElaboration term) = kind "GoalAndElaboration"
+    [ "term" #= encodePrettyTCM term ]
+
+encodeGoalSpecific :: InteractionId -> GoalDisplayInfo -> TCM Value
+encodeGoalSpecific ii = go
+  where
+  go (Goal_HelperFunction helperType) = kind "HelperFunction"
+    [ "signature"   #= inTopContext (prettyATop helperType)
+    ]
+  go (Goal_NormalForm computeMode expr) = kind "NormalForm"
+    [ "computeMode" @= computeMode
+    , "expr"        #= B.showComputed computeMode expr
+    ]
+  go (Goal_GoalType rewrite goalType entries boundary outputForms) = kind "GoalType"
+    [ "rewrite"     @= rewrite
+    , "typeAux"     @= goalType
+    , "type"        #= prettyTypeOfMeta rewrite ii
+    , "entries"     @= entries
+    , "boundary"    @= map encodePretty boundary
+    , "outputForms" @= map encodePretty outputForms
+    ]
+  go (Goal_CurrentGoal rewrite) = kind "CurrentGoal"
+    [ "rewrite"     @= rewrite
+    , "type"        #= prettyTypeOfMeta rewrite ii
+    ]
+  go (Goal_InferredType expr) = kind "InferredType"
+    [ "expr"        #= prettyATop expr
+    ]
+
+instance EncodeTCM Info_Error where
+  encodeTCM (Info_GenericError err) = kind "Error"
+    [ "warnings"          #= (getAllWarningsOfTCErr err
+                            >>= encodeTCM . filterTCWarnings)
+    , "error"             #= encodeTCM err
+    ]
+  encodeTCM err = kind "Error"
+    [ "warnings"          @= ([] :: [String])
+    , "error"             #= obj
+      [ "message"           #= showInfoError err
+      ]
+    ]
+
+instance EncodeTCM TCErr where
+  encodeTCM err = obj
+    [ "message"     #= encodePrettyTCM err
+    ]
+
+instance EncodeTCM TCWarning where
+  encodeTCM w = obj
+    [ "message"     #= (P.render <$> prettyTCM w)
+    ]
+
+instance EncodeTCM Response where
+  encodeTCM (Resp_HighlightingInfo info remove method modFile) =
+    liftIO $ jsonifyHighlightingInfo info remove method modFile
+  encodeTCM (Resp_DisplayInfo info) = kind "DisplayInfo"
+    [ "info"          @= info
+    ]
+  encodeTCM (Resp_ClearHighlighting tokenBased) = kind "ClearHighlighting"
+    [ "tokenBased"    @= tokenBased
+    ]
+  encodeTCM Resp_DoneAborting = kind "DoneAborting" []
+  encodeTCM Resp_DoneExiting = kind "DoneExiting" []
+  encodeTCM Resp_ClearRunningInfo = kind "ClearRunningInfo" []
+  encodeTCM (Resp_RunningInfo debugLevel msg) = kind "RunningInfo"
+    [ "debugLevel"    @= debugLevel
+    , "message"       @= msg
+    ]
+  encodeTCM (Resp_Status status) = kind "Status"
+    [ "status"        @= status
+    ]
+  encodeTCM (Resp_JumpToError filepath position) = kind "JumpToError"
+    [ "filepath"      @= filepath
+    , "position"      @= position
+    ]
+  encodeTCM (Resp_InteractionPoints interactionPoints) = kind "InteractionPoints"
+    [ "interactionPoints" @= interactionPoints
+    ]
+  encodeTCM (Resp_GiveAction i giveResult) = kind "GiveAction"
+    [ "interactionPoint"  @= i
+    , "giveResult"        @= giveResult
+    ]
+  encodeTCM (Resp_MakeCase id variant clauses) = kind "MakeCase"
+    [ "interactionPoint"  @= id
+    , "variant"           @= variant
+    , "clauses"           @= clauses
+    ]
+  encodeTCM (Resp_SolveAll solutions) = kind "SolveAll"
+    [ "solutions"     @= map encodeSolution solutions
+    ]
+    where
+      encodeSolution (i, expr) = object
+        [ "interactionPoint"  .= i
+        , "expression"        .= P.prettyShow expr
+        ]
+
+-- | Convert Response to an JSON value for interactive editor frontends.
+jsonifyResponse :: Response -> TCM ByteString
+jsonifyResponse = pure . encode <=< encodeTCM
diff --git a/src/full/Agda/Interaction/Library.hs b/src/full/Agda/Interaction/Library.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Library.hs
@@ -0,0 +1,546 @@
+{-# LANGUAGE OverloadedLists #-}
+
+-- | Library management.
+--
+--   Sample use:
+--
+--   @
+--     -- Get libraries as listed in @.agda/libraries@ file.
+--     libs <- getInstalledLibraries Nothing
+--
+--     -- Get the libraries (and immediate paths) relevant for @projectRoot@.
+--     -- This involves locating and processing the @.agda-lib@ file for the project.
+--     (libNames, includePaths) <-  getDefaultLibraries projectRoot True
+--
+--     -- Get include paths of depended-on libraries.
+--     resolvedPaths <- libraryIncludePaths Nothing libs libNames
+--
+--     let allPaths = includePaths ++ resolvedPaths
+--   @
+--
+module Agda.Interaction.Library
+  ( findProjectRoot
+  , getAgdaAppDir
+  , getDefaultLibraries
+  , getInstalledLibraries
+  , getTrustedExecutables
+  , libraryIncludePaths
+  , getAgdaLibFiles'
+  , getPrimitiveLibDir
+  , LibName
+  , OptionsPragma(..)
+  , AgdaLibFile(..)
+  , ExeName
+  , LibM
+  , mkLibM
+  , LibWarning(..)
+  , LibPositionInfo(..)
+  , libraryWarningName
+  , ProjectConfig(..)
+  -- * Exported for testing
+  , VersionView(..), versionView, unVersionView
+  , findLib'
+  ) where
+
+import Control.Arrow          ( first , second )
+import qualified Control.Exception as E
+import Control.Monad          ( filterM, forM )
+import Control.Monad.Except
+import Control.Monad.State
+import Control.Monad.Writer   ( Writer, runWriterT, tell )
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+import Data.Char
+import Data.Either
+import Data.Function (on)
+import Data.Map ( Map )
+import qualified Data.Map as Map
+import qualified Data.List as List
+import qualified Data.Text as T
+
+import System.Directory
+import System.FilePath
+import System.Environment
+
+import Agda.Interaction.Library.Base
+import Agda.Interaction.Library.Parse
+
+import Agda.Utils.Environment
+import Agda.Utils.FileName
+import Agda.Utils.Functor ( (<&>) )
+import Agda.Utils.IO ( catchIO )
+import qualified Agda.Utils.IO.UTF8 as UTF8
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1             ( List1, pattern (:|) )
+import Agda.Utils.List2             ( List2 )
+import qualified Agda.Utils.List1   as List1
+import qualified Agda.Utils.List2   as List2
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.String ( trim )
+import Agda.Utils.Tuple ( mapSndM )
+
+import Agda.Version
+
+-- Paths_Agda.hs is in $(BUILD_DIR)/build/autogen/.
+import Paths_Agda ( getDataFileName )
+
+------------------------------------------------------------------------
+-- * Types and Monads
+------------------------------------------------------------------------
+
+-- | Library names are structured into the base name and a suffix of version
+--   numbers, e.g. @mylib-1.2.3@.  The version suffix is optional.
+data VersionView = VersionView
+  { vvBase    :: LibName
+      -- ^ Actual library name.
+  , vvNumbers :: [Integer]
+      -- ^ Major version, minor version, subminor version, etc., all non-negative.
+      --   Note: a priori, there is no reason why the version numbers should be @Int@s.
+  } deriving (Eq, Show)
+
+-- | Raise collected 'LibErrors' as exception.
+--
+mkLibM :: [AgdaLibFile] -> LibErrorIO a -> LibM a
+mkLibM libs m = do
+  (x, ews) <- lift $ lift $ runWriterT m
+  let (errs, warns) = partitionEithers ews
+  tell warns
+  unless (null errs) $ do
+    let doc = vcat $ map (formatLibError libs) errs
+    throwError doc
+  return x
+
+------------------------------------------------------------------------
+-- * Resources
+------------------------------------------------------------------------
+
+-- | Get the path to @~/.agda@ (system-specific).
+--   Can be overwritten by the @AGDA_DIR@ environment variable.
+--
+--   (This is not to be confused with the directory for the data files
+--   that Agda needs (e.g. the primitive modules).)
+--
+getAgdaAppDir :: IO FilePath
+getAgdaAppDir = do
+  -- System-specific command to build the path to ~/.agda (Unix) or %APPDATA%\agda (Win)
+  let agdaDir = getAppUserDataDirectory "agda" >>= \legacyAgdaDir ->
+        ifM (doesDirectoryExist legacyAgdaDir)
+            (pure legacyAgdaDir)
+            (getXdgDirectory XdgConfig "agda")
+  -- The default can be overwritten by setting the AGDA_DIR environment variable
+  caseMaybeM (lookupEnv "AGDA_DIR") agdaDir $ \ dir ->
+      ifM (doesDirectoryExist dir) (canonicalizePath dir) $ do
+        d <- agdaDir
+        putStrLn $ "Warning: Environment variable AGDA_DIR points to non-existing directory " ++ show dir ++ ", using " ++ show d ++ " instead."
+        return d
+
+-- | Returns the absolute default lib dir. This directory is used to
+-- store the Primitive.agda file.
+getPrimitiveLibDir :: IO FilePath
+getPrimitiveLibDir = do
+  libdir <- filePath <$> (absolute =<< getDataFileName "lib")
+  ifM (doesDirectoryExist libdir)
+      (return $ libdir </> "prim")
+      (error $ "The lib directory " ++ libdir ++ " does not exist")
+
+-- | The @~/.agda/libraries@ file lists the libraries Agda should know about.
+--   The content of @libraries@ is a list of paths to @.agda-lib@ files.
+--
+--   Agda honors also version-specific @libraries@ files, e.g. @libraries-2.6.0@.
+--
+--   @defaultLibraryFiles@ gives a list of all @libraries@ files Agda should process
+--   by default.  The first file in this list that exists is actually used.
+--
+defaultLibraryFiles :: List1 FilePath
+defaultLibraryFiles = ("libraries-" ++ version) :| "libraries" : []
+
+-- | The @defaultsFile@ contains a list of library names relevant for each Agda project.
+--
+defaultsFile :: FilePath
+defaultsFile = "defaults"
+
+-- | The @~/.agda/executables@ file lists the executables Agda should know about.
+--   The content of @executables@ is a list of paths to executables.
+--
+--   Agda honors also version-specific @executables@ files, e.g. @executables-2.6.0@.
+--
+--   @defaultExecutablesFiles@ gives a list of all @executables@ Agda should process
+--   by default.  The first file in this list that exists is actually used.
+--
+defaultExecutableFiles :: List1 FilePath
+defaultExecutableFiles = ("executables-" ++ version) :| "executables" : []
+
+------------------------------------------------------------------------
+-- * Get the libraries for the current project
+------------------------------------------------------------------------
+
+-- | Find project root by looking for @.agda-lib@ files.
+--
+--   If there are none, look in the parent directories until one is found.
+
+findProjectConfig
+  :: FilePath                          -- ^ Candidate (init: the directory Agda was called in)
+  -> LibM ProjectConfig                -- ^ Actual root and @.agda-lib@ files for this project
+findProjectConfig root = mkLibM [] $ findProjectConfig' root
+
+findProjectConfig'
+  :: FilePath                          -- ^ Candidate (init: the directory Agda was called in)
+  -> LibErrorIO ProjectConfig          -- ^ Actual root and @.agda-lib@ files for this project
+findProjectConfig' root = do
+  getCachedProjectConfig root >>= \case
+    Just conf -> return conf
+    Nothing   -> do
+      libFiles <- liftIO $ getDirectoryContents root >>=
+        filterM (\file -> and2M
+          (pure $ takeExtension file == ".agda-lib")
+          (doesFileExist (root </> file)))
+      case libFiles of
+        []     -> liftIO (upPath root) >>= \case
+          Just up -> do
+            conf <- findProjectConfig' up
+            conf <- return $ case conf of
+                  DefaultProjectConfig{} -> conf
+                  ProjectConfig{..}      ->
+                    ProjectConfig{ configAbove = configAbove + 1
+                                 , ..
+                                 }
+            storeCachedProjectConfig root conf
+            return conf
+          Nothing -> return DefaultProjectConfig
+        files -> do
+          let conf = ProjectConfig root files 0
+          storeCachedProjectConfig root conf
+          return conf
+
+  where
+    -- Note that "going up" one directory is OS dependent
+    -- if the directory is a symlink.
+    --
+    -- Quoting from https://hackage.haskell.org/package/directory-1.3.6.1/docs/System-Directory.html#v:canonicalizePath :
+    --
+    --   Note that on Windows parent directories .. are always fully
+    --   expanded before the symbolic links, as consistent with the
+    --   rest of the Windows API (such as GetFullPathName). In
+    --   contrast, on POSIX systems parent directories .. are
+    --   expanded alongside symbolic links from left to right. To
+    --   put this more concretely: if L is a symbolic link for R/P,
+    --   then on Windows L\.. refers to ., whereas on other
+    --   operating systems L/.. refers to R.
+    upPath :: FilePath -> IO (Maybe FilePath)
+    upPath root = do
+      up <- canonicalizePath $ root </> ".."
+      if up == root then return Nothing else return $ Just up
+
+
+-- | Get project root
+
+findProjectRoot :: FilePath -> LibM (Maybe FilePath)
+findProjectRoot root = findProjectConfig root <&> \case
+  ProjectConfig p _ _  -> Just p
+  DefaultProjectConfig -> Nothing
+
+
+-- | Get the contents of @.agda-lib@ files in the given project root.
+getAgdaLibFiles' :: FilePath -> LibErrorIO [AgdaLibFile]
+getAgdaLibFiles' path = findProjectConfig' path >>= \case
+  DefaultProjectConfig          -> return []
+  ProjectConfig root libs above ->
+    map (set libAbove above) <$>
+    parseLibFiles Nothing (map ((0,) . (root </>)) libs)
+
+-- | Get dependencies and include paths for given project root:
+--
+--   Look for @.agda-lib@ files according to 'findAgdaLibFiles'.
+--   If none are found, use default dependencies (according to @defaults@ file)
+--   and current directory (project root).
+--
+getDefaultLibraries
+  :: FilePath  -- ^ Project root.
+  -> Bool      -- ^ Use @defaults@ if no @.agda-lib@ file exists for this project?
+  -> LibM ([LibName], [FilePath])  -- ^ The returned @LibName@s are all non-empty strings.
+getDefaultLibraries root optDefaultLibs = mkLibM [] $ do
+  libs <- getAgdaLibFiles' root
+  if null libs
+    then (,[]) <$> if optDefaultLibs then (libNameForCurrentDir :) <$> readDefaultsFile else return []
+    else return $ libsAndPaths libs
+  where
+    libsAndPaths ls = ( concatMap _libDepends ls
+                      , nubOn id (concatMap _libIncludes ls)
+                      )
+
+-- | Return list of libraries to be used by default.
+--
+--   None if the @defaults@ file does not exist.
+--
+readDefaultsFile :: LibErrorIO [LibName]
+readDefaultsFile = do
+    agdaDir <- liftIO getAgdaAppDir
+    let file = agdaDir </> defaultsFile
+    ifNotM (liftIO $ doesFileExist file) (return []) $ {-else-} do
+      ls <- liftIO $ map snd . stripCommentLines <$> UTF8.readFile file
+      return $ concatMap splitCommas ls
+  `catchIO` \ e -> do
+    raiseErrors' [ ReadError e "Failed to read defaults file." ]
+    return []
+
+------------------------------------------------------------------------
+-- * Reading the installed libraries
+------------------------------------------------------------------------
+
+-- | Returns the path of the @libraries@ file which lists the libraries Agda knows about.
+--
+--   Note: file may not exist.
+--
+--   If the user specified an alternative @libraries@ file which does not exist,
+--   an exception is thrown containing the name of this file.
+getLibrariesFile
+  :: (MonadIO m, MonadError FilePath m)
+  => Maybe FilePath -- ^ Override the default @libraries@ file?
+  -> m LibrariesFile
+getLibrariesFile (Just overrideLibFile) = do
+  -- A user-specified override file must exist.
+  ifM (liftIO $ doesFileExist overrideLibFile)
+    {-then-} (return $ LibrariesFile overrideLibFile True)
+    {-else-} (throwError overrideLibFile)
+getLibrariesFile Nothing = do
+  agdaDir <- liftIO $ getAgdaAppDir
+  let defaults = List1.map (agdaDir </>) defaultLibraryFiles -- NB: very short list
+  files <- liftIO $ filterM doesFileExist (List1.toList defaults)
+  case files of
+    file : _ -> return $ LibrariesFile file True
+    []       -> return $ LibrariesFile (List1.last defaults) False -- doesn't exist, but that's ok
+
+-- | Parse the descriptions of the libraries Agda knows about.
+--
+--   Returns none if there is no @libraries@ file.
+--
+getInstalledLibraries
+  :: Maybe FilePath     -- ^ Override the default @libraries@ file?
+  -> LibM [AgdaLibFile] -- ^ Content of library files.  (Might have empty @LibName@s.)
+getInstalledLibraries overrideLibFile = mkLibM [] $ do
+    filem <- liftIO $ runExceptT $ getLibrariesFile overrideLibFile
+    case filem of
+      Left theOverrideLibFile -> do
+        raiseErrors' [ LibrariesFileNotFound theOverrideLibFile ]
+        return []
+      Right file -> do
+        if not (lfExists file) then return [] else do
+          ls    <- liftIO $ stripCommentLines <$> UTF8.readFile (lfPath file)
+          files <- liftIO $ sequence [ (i, ) <$> expandEnvironmentVariables s | (i, s) <- ls ]
+          parseLibFiles (Just file) $ nubOn snd files
+  `catchIO` \ e -> do
+    raiseErrors' [ ReadError e "Failed to read installed libraries." ]
+    return []
+
+-- | Parse the given library files.
+--
+parseLibFiles
+  :: Maybe LibrariesFile       -- ^ Name of @libraries@ file for error reporting.
+  -> [(LineNumber, FilePath)]  -- ^ Library files paired with their line number in @libraries@.
+  -> LibErrorIO [AgdaLibFile]  -- ^ Content of library files.  (Might have empty @LibName@s.)
+parseLibFiles mlibFile files = do
+
+  anns <- forM files $ \(ln, file) -> do
+    getCachedAgdaLibFile file >>= \case
+      Just lib -> return (Right lib, [])
+      Nothing  -> do
+        (e, ws) <- liftIO $ runP <$> parseLibFile file
+        let pos = LibPositionInfo (lfPath <$> mlibFile) ln file
+            ws' = map (LibWarning (Just pos)) ws
+        case e of
+          Left err -> do
+            return (Left (Just pos, err), ws')
+          Right lib -> do
+            storeCachedAgdaLibFile file lib
+            return (Right lib, ws')
+
+  let (xs, warns) = unzip anns
+      (errs, als) = partitionEithers xs
+
+  List1.unlessNull (concat warns) warnings
+  List1.unlessNull errs $ \ errs1 ->
+    raiseErrors $ fmap (\ (mc, err) -> LibError mc $ LibParseError err) errs1
+
+  return $ nubOn _libFile als
+
+-- | Remove trailing white space and line comments.
+--
+stripCommentLines :: String -> [(LineNumber, String)]
+stripCommentLines = concatMap strip . zip [1..] . lines
+  where
+    strip (i, s) = [ (i, s') | not $ null s' ]
+      where s' = trimLineComment s
+
+-- | Returns the path of the @executables@ file which lists the trusted executables Agda knows about.
+--
+--   Note: file may not exist.
+--
+getExecutablesFile
+  :: IO ExecutablesFile
+getExecutablesFile = do
+  agdaDir <- getAgdaAppDir
+  let defaults = List1.map (agdaDir </>) defaultExecutableFiles  -- NB: very short list
+  files <- filterM doesFileExist (List1.toList defaults)
+  case files of
+    file : _ -> return $ ExecutablesFile file True
+    []       -> return $ ExecutablesFile (List1.last defaults) False -- doesn't exist, but that's ok
+
+-- | Return the trusted executables Agda knows about.
+--
+--   Returns none if there is no @executables@ file.
+--
+getTrustedExecutables
+  :: LibM (Map ExeName FilePath)  -- ^ Content of @executables@ files.
+getTrustedExecutables = mkLibM [] $ do
+    file <- liftIO getExecutablesFile
+    if not (efExists file) then return Map.empty else do
+      es    <- liftIO $ stripCommentLines <$> UTF8.readFile (efPath file)
+      lines <- liftIO $ mapM (mapSndM expandEnvironmentVariables) es
+      parseExecutablesFile file lines
+  `catchIO` \ e -> do
+    raiseErrors' [ ReadError e "Failed to read trusted executables." ]
+    return Map.empty
+
+-- | Parse the @executables@ file.
+--
+parseExecutablesFile
+  :: ExecutablesFile
+  -> [(LineNumber, FilePath)]
+  -> LibErrorIO (Map ExeName FilePath)
+parseExecutablesFile ef files = do
+  executables <- forM files $ \(ln, fp) -> do
+    -- Compute canonical executable name and absolute filepath.
+    let strExeName  = takeFileName fp
+    let strExeName' = fromMaybe strExeName $ stripExtension exeExtension strExeName
+    let txtExeName  = T.pack strExeName'
+    exePath <- liftIO $ makeAbsolute fp
+    return (txtExeName, (ln, exePath))
+
+  -- Create a map from executable names to their location(s).
+  let exeMap1 :: Map ExeName (List1 (LineNumber, FilePath))
+      exeMap1 = Map.fromListWith (<>) $ map (second singleton) $ reverse executables
+
+  -- Separate non-ambiguous from ambiguous mappings.
+  let (exeMap, duplicates) = Map.mapEither List2.fromList1Either exeMap1
+
+  -- Report ambiguous mappings with line numbers.
+  List1.unlessNull (Map.toList duplicates) $ \ duplicates1 ->
+    raiseErrors' $ fmap (uncurry $ DuplicateExecutable $ efPath ef) duplicates1
+
+  -- Return non-ambiguous mappings without line numbers.
+  return $ fmap snd exeMap
+
+------------------------------------------------------------------------
+-- * Resolving library names to include pathes
+------------------------------------------------------------------------
+
+-- | Get all include pathes for a list of libraries to use.
+libraryIncludePaths
+  :: Maybe FilePath  -- ^ @libraries@ file (error reporting only).
+  -> [AgdaLibFile]   -- ^ Libraries Agda knows about.
+  -> [LibName]       -- ^ (Non-empty) library names to be resolved to (lists of) pathes.
+  -> LibM [FilePath] -- ^ Resolved pathes (no duplicates).  Contains "." if @[LibName]@ does.
+libraryIncludePaths overrideLibFile libs xs0 = mkLibM libs $ do
+    efile <- liftIO $ runExceptT $ getLibrariesFile overrideLibFile
+    case efile of
+      Left theOverrideLibFile -> do
+        raiseErrors' [ LibrariesFileNotFound theOverrideLibFile ]
+        return []
+      Right file -> embedWriter $ (dot ++) . incs <$> find file [] xs
+  where
+    (dots, xs) = List.partition (== libNameForCurrentDir) $ map trim xs0
+    incs       = nubOn id . concatMap _libIncludes
+    dot        = [ "." | not $ null dots ]
+
+    -- Due to library dependencies, the work list may grow temporarily.
+    find
+      :: LibrariesFile  -- Only for error reporting.
+      -> [LibName]      -- Already resolved libraries.
+      -> [LibName]      -- Work list: libraries left to be resolved.
+      -> Writer LibErrWarns [AgdaLibFile]
+    find _ _ [] = pure []
+    find file visited (x : xs)
+      | x `elem` visited = find file visited xs
+      | otherwise = do
+          -- May or may not find the library
+          ml <- case findLib x libs of
+            [l] -> pure (Just l)
+            []  -> Nothing <$ raiseErrors' [LibNotFound file x]
+            ls  -> Nothing <$ raiseErrors' [AmbiguousLib x ls]
+          -- If it is found, add its dependencies to work list
+          let xs' = foldMap _libDepends ml ++ xs
+          mcons ml <$> find file (x : visited) xs'
+
+-- | @findLib x libs@ retrieves the matches for @x@ from list @libs@.
+--
+--   1. Case @x@ is unversioned:
+--      If @x@ is contained in @libs@, then that match is returned.
+--      Otherwise, the matches with the highest version number are returned.
+--
+--   2. Case @x@ is versioned: the matches with the highest version number are returned.
+--
+--   Examples, see 'findLib''.
+--
+findLib :: LibName -> [AgdaLibFile] -> [AgdaLibFile]
+findLib = findLib' _libName
+
+-- | Generalized version of 'findLib' for testing.
+--
+--   > findLib' id "a"   [ "a-1", "a-02", "a-2", "b" ] == [ "a-02", "a-2" ]
+--
+--   > findLib' id "a"   [ "a", "a-1", "a-01", "a-2", "b" ] == [ "a" ]
+--   > findLib' id "a-1" [ "a", "a-1", "a-01", "a-2", "b" ] == [ "a-1", "a-01" ]
+--   > findLib' id "a-2" [ "a", "a-1", "a-01", "a-2", "b" ] == [ "a-2" ]
+--   > findLib' id "c"   [ "a", "a-1", "a-01", "a-2", "b" ] == []
+--
+findLib' :: (a -> LibName) -> LibName -> [a] -> [a]
+findLib' libName x libs =
+  case ls of
+    -- Take the first and all exact matches (modulo leading zeros in version numbers).
+    l : ls' -> l : takeWhile (((==) `on` versionMeasure) l) ls'
+    []      -> []
+  where
+    -- @LibName@s that match @x@, sorted descendingly.
+    -- The unversioned LibName, if any, will come first.
+    ls = List.sortBy (flip compare `on` versionMeasure)
+                     [ l | l <- libs, x `hasMatch` libName l ]
+
+    -- foo > foo-2.2 > foo-2.0.1 > foo-2 > foo-1.0
+    versionMeasure l = (rx, null vs, vs)
+      where
+        VersionView rx vs = versionView (libName l)
+
+-- | @x `hasMatch` y@ if @x@ and @y@ have the same @vvBase@ and
+--   either @x@ has no version qualifier or the versions also match.
+hasMatch :: LibName -> LibName -> Bool
+hasMatch x y = rx == ry && (vx == vy || null vx)
+  where
+    VersionView rx vx = versionView x
+    VersionView ry vy = versionView y
+
+-- | Split a library name into basename and a list of version numbers.
+--
+--   > versionView "foo-1.2.3"    == VersionView "foo" [1, 2, 3]
+--   > versionView "foo-01.002.3" == VersionView "foo" [1, 2, 3]
+--
+--   Note that because of leading zeros, @versionView@ is not injective.
+--   (@unVersionView . versionView@ would produce a normal form.)
+versionView :: LibName -> VersionView
+versionView s =
+  case span (\ c -> isDigit c || c == '.') (reverse s) of
+    (v, '-' : x) | valid vs ->
+      VersionView (reverse x) $ reverse $ map (read . reverse) vs
+      where vs = chopWhen (== '.') v
+            valid [] = False
+            valid vs = not $ any null vs
+    _ -> VersionView s []
+
+-- | Print a @VersionView@, inverse of @versionView@ (modulo leading zeros).
+unVersionView :: VersionView -> LibName
+unVersionView = \case
+  VersionView base [] -> base
+  VersionView base vs -> base ++ "-" ++ List.intercalate "." (map show vs)
diff --git a/src/full/Agda/Interaction/Library/Base.hs b/src/full/Agda/Interaction/Library/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Library/Base.hs
@@ -0,0 +1,458 @@
+-- | Basic data types for library management.
+
+module Agda.Interaction.Library.Base where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+import qualified Control.Exception as E
+
+import Control.Monad.Except
+import Control.Monad.State
+import Control.Monad.Writer        ( WriterT, MonadWriter, tell )
+import Control.Monad.IO.Class      ( MonadIO(..) )
+
+import Data.Bifunctor              ( first , second )
+import Data.Map                    ( Map )
+import qualified Data.Map          as Map
+import Data.Semigroup              ( Semigroup(..) )
+import Data.Text                   ( Text, unpack )
+
+import GHC.Generics                ( Generic )
+
+import System.Directory
+
+import Agda.Interaction.Options.Warnings
+
+import Agda.Syntax.Position
+
+import Agda.Utils.Lens
+import Agda.Utils.List1            ( List1, toList )
+import Agda.Utils.List2            ( List2, toList )
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+-- | A symbolic library name.
+--
+type LibName = String
+
+data LibrariesFile = LibrariesFile
+  { lfPath   :: FilePath
+      -- ^ E.g. @~/.agda/libraries@.
+  , lfExists :: Bool
+       -- ^ The libraries file might not exist,
+       --   but we may print its assumed location in error messages.
+  } deriving (Show)
+
+-- | A symbolic executable name.
+--
+type ExeName = Text
+
+data ExecutablesFile = ExecutablesFile
+  { efPath   :: FilePath
+      -- ^ E.g. @~/.agda/executables@.
+  , efExists :: Bool
+       -- ^ The executables file might not exist,
+       --   but we may print its assumed location in error messages.
+  } deriving (Show, Generic)
+
+-- | The special name @\".\"@ is used to indicated that the current directory
+--   should count as a project root.
+--
+libNameForCurrentDir :: LibName
+libNameForCurrentDir = "."
+
+-- | A file can either belong to a project located at a given root
+--   containing one or more .agda-lib files, or be part of the default
+--   project.
+data ProjectConfig
+  = ProjectConfig
+    { configRoot         :: FilePath
+    , configAgdaLibFiles :: [FilePath]
+    , configAbove        :: !Int
+      -- ^ How many directories above the Agda file is the @.agda-lib@
+      -- file located?
+    }
+  | DefaultProjectConfig
+  deriving Generic
+
+-- | The options from an @OPTIONS@ pragma (or a @.agda-lib@ file).
+--
+-- In the future it might be nice to switch to a more structured
+-- representation. Note that, currently, there is not a one-to-one
+-- correspondence between list elements and options.
+data OptionsPragma = OptionsPragma
+  { pragmaStrings :: [String]
+    -- ^ The options.
+  , pragmaRange :: Range
+    -- ^ The range of the options in the pragma (not including things
+    -- like an @OPTIONS@ keyword).
+  }
+  deriving Show
+
+instance Semigroup OptionsPragma where
+  OptionsPragma { pragmaStrings = ss1, pragmaRange = r1 } <>
+    OptionsPragma { pragmaStrings = ss2, pragmaRange = r2 } =
+    OptionsPragma
+      { pragmaStrings = ss1 ++ ss2
+      , pragmaRange   = fuseRanges r1 r2
+      }
+
+instance Monoid OptionsPragma where
+  mempty  = OptionsPragma { pragmaStrings = [], pragmaRange = noRange }
+  mappend = (<>)
+
+-- | Ranges are not forced.
+
+instance NFData OptionsPragma where
+  rnf (OptionsPragma a _) = rnf a
+
+-- | Content of a @.agda-lib@ file.
+--
+data AgdaLibFile = AgdaLibFile
+  { _libName     :: LibName     -- ^ The symbolic name of the library.
+  , _libFile     :: FilePath    -- ^ Path to this @.agda-lib@ file (not content of the file).
+  , _libAbove    :: !Int        -- ^ How many directories above the
+                                --   Agda file is the @.agda-lib@ file
+                                --   located?
+  , _libIncludes :: [FilePath]  -- ^ Roots where to look for the modules of the library.
+  , _libDepends  :: [LibName]   -- ^ Dependencies.
+  , _libPragmas  :: OptionsPragma
+                                -- ^ Default pragma options for all files in the library.
+  }
+  deriving (Show, Generic)
+
+emptyLibFile :: AgdaLibFile
+emptyLibFile = AgdaLibFile
+  { _libName     = ""
+  , _libFile     = ""
+  , _libAbove    = 0
+  , _libIncludes = []
+  , _libDepends  = []
+  , _libPragmas  = mempty
+  }
+
+-- | Lenses for AgdaLibFile
+
+libName :: Lens' AgdaLibFile LibName
+libName f a = f (_libName a) <&> \ x -> a { _libName = x }
+
+libFile :: Lens' AgdaLibFile FilePath
+libFile f a = f (_libFile a) <&> \ x -> a { _libFile = x }
+
+libAbove :: Lens' AgdaLibFile Int
+libAbove f a = f (_libAbove a) <&> \ x -> a { _libAbove = x }
+
+libIncludes :: Lens' AgdaLibFile [FilePath]
+libIncludes f a = f (_libIncludes a) <&> \ x -> a { _libIncludes = x }
+
+libDepends :: Lens' AgdaLibFile [LibName]
+libDepends f a = f (_libDepends a) <&> \ x -> a { _libDepends = x }
+
+libPragmas :: Lens' AgdaLibFile OptionsPragma
+libPragmas f a = f (_libPragmas a) <&> \ x -> a { _libPragmas = x }
+
+
+------------------------------------------------------------------------
+-- * Library warnings and errors
+------------------------------------------------------------------------
+
+-- ** Position information
+
+type LineNumber = Int
+
+-- | Information about which @.agda-lib@ file we are reading
+--   and from where in the @libraries@ file it came from.
+
+data LibPositionInfo = LibPositionInfo
+  { libFilePos :: Maybe FilePath -- ^ Name of @libraries@ file.
+  , lineNumPos :: LineNumber     -- ^ Line number in @libraries@ file.
+  , filePos    :: FilePath       -- ^ Library file.
+  }
+  deriving (Show, Generic)
+
+-- ** Warnings
+
+data LibWarning = LibWarning (Maybe LibPositionInfo) LibWarning'
+  deriving (Show, Generic)
+
+-- | Library Warnings.
+data LibWarning'
+  = UnknownField String
+  deriving (Show, Generic)
+
+libraryWarningName :: LibWarning -> WarningName
+libraryWarningName (LibWarning c (UnknownField{})) = LibUnknownField_
+
+-- * Errors
+
+data LibError = LibError (Maybe LibPositionInfo) LibError'
+
+-- | Collected errors while processing library files.
+--
+data LibError'
+  = LibrariesFileNotFound FilePath
+      -- ^ The user specified replacement for the default @libraries@ file does not exist.
+  | LibNotFound LibrariesFile LibName
+      -- ^ Raised when a library name could not successfully be resolved
+      --   to an @.agda-lib@ file.
+      --
+  | AmbiguousLib LibName [AgdaLibFile]
+      -- ^ Raised when a library name is defined in several @.agda-lib files@.
+  | LibParseError LibParseError
+      -- ^ The @.agda-lib@ file could not be parsed.
+  | ReadError
+      -- ^ An I/O Error occurred when reading a file.
+      E.IOException
+        -- ^ The caught exception
+      String
+        -- ^ Explanation when this error occurred.
+  | DuplicateExecutable
+      -- ^ The @executables@ file contains duplicate entries.
+      FilePath
+        -- ^ Name of the @executables@ file.
+      Text
+        -- ^ Name of the executable that is defined twice.
+      (List2 (LineNumber, FilePath))
+        -- ^ The resolutions of the executable.
+  -- deriving (Show)
+
+-- | Exceptions thrown by the @.agda-lib@ parser.
+--
+data LibParseError
+  = BadLibraryName String
+      -- ^ An invalid library name, e.g., containing spaces.
+  | ReadFailure FilePath E.IOException
+      -- ^ I/O error while reading file.
+  | MissingFields (List1 String)
+      -- ^ Missing these mandatory fields.
+  | DuplicateFields (List1 String)
+      -- ^ These fields occur each more than once.
+  | MissingFieldName LineNumber
+      -- ^ At the given line number, a field name is missing before the @:@.
+  | BadFieldName LineNumber String
+      -- ^ At the given line number, an invalid field name is encountered before the @:@.
+      --   (E.g., containing spaces.)
+  | MissingColonForField LineNumber String
+      -- ^ At the given line number, the given field is not followed by @:@.
+  | ContentWithoutField LineNumber
+      -- ^ At the given line number, indented text (content) is not preceded by a field.
+
+-- ** Raising warnings and errors
+
+-- | Collection of 'LibError's and 'LibWarning's.
+--
+type LibErrWarns = [Either LibError LibWarning]
+
+warnings :: MonadWriter LibErrWarns m => List1 LibWarning -> m ()
+warnings = tell . map Right . toList
+
+warnings' :: MonadWriter LibErrWarns m => List1 LibWarning' -> m ()
+warnings' = tell . map (Right . LibWarning Nothing) . toList
+
+raiseErrors' :: MonadWriter LibErrWarns m => List1 LibError' -> m ()
+raiseErrors' = tell . map (Left . (LibError Nothing)) . toList
+
+raiseErrors :: MonadWriter LibErrWarns m => List1 LibError -> m ()
+raiseErrors = tell . map Left . toList
+
+
+------------------------------------------------------------------------
+-- * Library Monad
+------------------------------------------------------------------------
+
+-- | Collects 'LibError's and 'LibWarning's.
+--
+type LibErrorIO = WriterT LibErrWarns (StateT LibState IO)
+
+-- | Throws 'Doc' exceptions, still collects 'LibWarning's.
+type LibM = ExceptT Doc (WriterT [LibWarning] (StateT LibState IO))
+
+-- | Cache locations of project configurations and parsed @.agda-lib@ files.
+type LibState =
+  ( Map FilePath ProjectConfig
+  , Map FilePath AgdaLibFile
+  )
+
+getCachedProjectConfig
+  :: (MonadState LibState m, MonadIO m)
+  => FilePath -> m (Maybe ProjectConfig)
+getCachedProjectConfig path = do
+  path <- liftIO $ canonicalizePath path
+  cache <- gets fst
+  return $ Map.lookup path cache
+
+storeCachedProjectConfig
+  :: (MonadState LibState m, MonadIO m)
+  => FilePath -> ProjectConfig -> m ()
+storeCachedProjectConfig path conf = do
+  path <- liftIO $ canonicalizePath path
+  modify $ first $ Map.insert path conf
+
+getCachedAgdaLibFile
+  :: (MonadState LibState m, MonadIO m)
+  => FilePath -> m (Maybe AgdaLibFile)
+getCachedAgdaLibFile path = do
+  path <- liftIO $ canonicalizePath path
+  gets $ Map.lookup path . snd
+
+storeCachedAgdaLibFile
+  :: (MonadState LibState m, MonadIO m)
+  => FilePath -> AgdaLibFile -> m ()
+storeCachedAgdaLibFile path lib = do
+  path <- liftIO $ canonicalizePath path
+  modify $ second $ Map.insert path lib
+
+------------------------------------------------------------------------
+-- * Prettyprinting errors and warnings
+------------------------------------------------------------------------
+
+-- | Pretty-print 'LibError'.
+formatLibError :: [AgdaLibFile] -> LibError -> Doc
+formatLibError installed (LibError mc e) =
+  case (mc, e) of
+    (Just c, LibParseError err) -> sep  [ formatLibPositionInfo c err, pretty e ]
+    (_     , LibNotFound{}    ) -> vcat [ pretty e, prettyInstalledLibraries installed ]
+    _ -> pretty e
+
+-- | Does a parse error contain a line number?
+hasLineNumber :: LibParseError -> Maybe LineNumber
+hasLineNumber = \case
+  BadLibraryName       _   -> Nothing
+  ReadFailure          _ _ -> Nothing
+  MissingFields        _   -> Nothing
+  DuplicateFields      _   -> Nothing
+  MissingFieldName     l   -> Just l
+  BadFieldName         l _ -> Just l
+  MissingColonForField l _ -> Just l
+  ContentWithoutField  l   -> Just l
+
+-- UNUSED:
+-- -- | Does a parse error contain the name of the parsed file?
+-- hasFilePath :: LibParseError -> Maybe FilePath
+-- hasFilePath = \case
+--   BadLibraryName       _   -> Nothing
+--   ReadFailure          f _ -> Just f
+--   MissingFields        _   -> Nothing
+--   DuplicateFields      _   -> Nothing
+--   MissingFieldName     _   -> Nothing
+--   BadFieldName         _ _ -> Nothing
+--   MissingColonForField _ _ -> Nothing
+--   ContentWithoutField  _   -> Nothing
+
+-- | Compute a position position prefix.
+--
+--   Depending on the error to be printed, it will
+--
+--   - either give the name of the @libraries@ file and a line inside it,
+--
+--   - or give the name of the @.agda-lib@ file.
+--
+formatLibPositionInfo :: LibPositionInfo -> LibParseError -> Doc
+formatLibPositionInfo (LibPositionInfo libFile lineNum file) = \case
+
+  -- If we couldn't even read the @.agda-lib@ file, report error in the @libraries@ file.
+  ReadFailure _ _
+    | Just lf <- libFile
+      -> hcat [ text lf, ":", pretty lineNum, ":" ]
+    | otherwise
+      -> empty
+
+  -- If the parse error comes with a line number, print it here.
+  e | Just l <- hasLineNumber e
+      -> hcat [ text file, ":", pretty l, ":" ]
+    | otherwise
+      -> hcat [ text file, ":" ]
+
+prettyInstalledLibraries :: [AgdaLibFile] -> Doc
+prettyInstalledLibraries installed =
+  vcat $ ("Installed libraries:" :) $
+    map (nest 2) $
+    if null installed then ["(none)"]
+    else [ sep [ text $ _libName l, nest 2 $ parens $ text $ _libFile l ]
+         | l <- installed
+         ]
+
+-- | Pretty-print library management error without position info.
+
+instance Pretty LibError' where
+  pretty = \case
+
+    LibrariesFileNotFound path -> sep
+      [ text "Libraries file not found:"
+      , text path
+      ]
+
+    LibNotFound file lib -> vcat $
+      [ text $ "Library '" ++ lib ++ "' not found."
+      , sep [ "Add the path to its .agda-lib file to"
+            , nest 2 $ text $ "'" ++ lfPath file ++ "'"
+            , "to install."
+            ]
+      ]
+
+    AmbiguousLib lib tgts -> vcat $
+      sep [ text $ "Ambiguous library '" ++ lib ++ "'."
+            , "Could refer to any one of"
+          ]
+        : [ nest 2 $ text (_libName l) <+> parens (text $ _libFile l) | l <- tgts ]
+
+    LibParseError err -> pretty err
+
+    ReadError e msg -> vcat
+      [ text $ msg
+      , text $ E.displayException e
+      ]
+
+    DuplicateExecutable exeFile exe paths -> vcat $
+      hcat [ "Duplicate entries for executable '", (text . unpack) exe, "' in ", text exeFile, ":" ] :
+      map (\ (ln, fp) -> nest 2 $ (pretty ln <> colon) <+> text fp) (toList paths)
+
+-- | Print library file parse error without position info.
+--
+instance Pretty LibParseError where
+  pretty = \case
+
+    BadLibraryName s -> sep
+      [ "Bad library name:", quotes (text s) ]
+    ReadFailure file e -> vcat
+      [ hsep [ "Failed to read library file", text file <> "." ]
+      , "Reason:" <+> text (E.displayException e)
+      ]
+
+    MissingFields   xs -> "Missing"   <+> listFields xs
+    DuplicateFields xs -> "Duplicate" <+> listFields xs
+
+    MissingFieldName     l   -> atLine l $ "Missing field name"
+    BadFieldName         l s -> atLine l $ "Bad field name" <+> text (show s)
+    MissingColonForField l s -> atLine l $ "Missing ':' for field " <+> text (show s)
+    ContentWithoutField  l   -> atLine l $ "Missing field"
+
+    where
+    listFields xs = hsep $ fieldS xs : list xs
+    fieldS xs     = singPlural xs "field:" "fields:"
+    list          = punctuate comma . map (quotes . text) . toList
+    atLine l      = id
+    -- The line number will be printed by 'formatLibPositionInfo'!
+    -- atLine l doc  = hsep [ text (show l) <> ":", doc ]
+
+
+instance Pretty LibWarning where
+  pretty (LibWarning mc w) =
+    case mc of
+      Nothing -> pretty w
+      Just (LibPositionInfo _ _ file) -> hcat [ text file, ":"] <+> pretty w
+
+instance Pretty LibWarning' where
+  pretty (UnknownField s) = text $ "Unknown field '" ++ s ++ "'"
+
+------------------------------------------------------------------------
+-- NFData instances
+------------------------------------------------------------------------
+
+instance NFData ExecutablesFile
+instance NFData ProjectConfig
+instance NFData AgdaLibFile
+instance NFData LibPositionInfo
+instance NFData LibWarning
+instance NFData LibWarning'
diff --git a/src/full/Agda/Interaction/Library/Parse.hs b/src/full/Agda/Interaction/Library/Parse.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Library/Parse.hs
@@ -0,0 +1,292 @@
+-- | Parser for @.agda-lib@ files.
+--
+--   Example file:
+--
+--   @
+--     name: Main
+--     depend:
+--       standard-library
+--     include: .
+--       src more-src
+--
+--   @
+--
+--   Should parse as:
+--
+--   @
+--     AgdaLib
+--       { libName     = "Main"
+--       , libFile     = path_to_this_file
+--       , libIncludes = [ "." , "src" , "more-src" ]
+--       , libDepends  = [ "standard-library" ]
+--       }
+--   @
+--
+module Agda.Interaction.Library.Parse
+  ( parseLibFile
+  , splitCommas
+  , trimLineComment
+  , runP
+  ) where
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Writer
+import Data.Char
+import qualified Data.List as List
+import System.FilePath
+
+import Agda.Interaction.Library.Base
+
+import Agda.Syntax.Position
+
+import Agda.Utils.Applicative
+import Agda.Utils.FileName
+import Agda.Utils.IO                ( catchIO )
+import qualified Agda.Utils.IO.UTF8 as UTF8
+import Agda.Utils.Lens
+import Agda.Utils.List              ( duplicates )
+import Agda.Utils.List1             ( List1, toList )
+import qualified Agda.Utils.List1   as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Singleton
+import Agda.Utils.String            ( ltrim )
+
+-- | Parser monad: Can throw @LibParseError@s, and collects
+-- @LibWarning'@s library warnings.
+type P = ExceptT LibParseError (Writer [LibWarning'])
+
+runP :: P a -> (Either LibParseError a, [LibWarning'])
+runP = runWriter . runExceptT
+
+warningP :: LibWarning' -> P ()
+warningP = tell . pure
+
+-- | The config files we parse have the generic structure of a sequence
+--   of @field : content@ entries.
+type GenericFile = [GenericEntry]
+
+data GenericEntry = GenericEntry
+  { geHeader   :: String   -- ^ E.g. field name.    @trim@med.
+  , _geContent :: [String] -- ^ E.g. field content. @trim@med.
+  }
+
+-- | Library file field format format [sic!].
+data Field = forall a. Field
+  { fName     :: String            -- ^ Name of the field.
+  , fOptional :: Bool              -- ^ Is it optional?
+  , fParse    :: Range -> [String] -> P a
+                 -- ^ Content parser for this field.
+                 --
+                 -- The range points to the start of the file.
+  , fSet      :: LensSet AgdaLibFile a
+    -- ^ Sets parsed content in 'AgdaLibFile' structure.
+  }
+
+optionalField ::
+  String -> (Range -> [String] -> P a) -> Lens' AgdaLibFile a -> Field
+optionalField str p l = Field str True p (set l)
+
+-- | @.agda-lib@ file format with parsers and setters.
+agdaLibFields :: [Field]
+agdaLibFields =
+  -- Andreas, 2017-08-23, issue #2708, field "name" is optional.
+  [ optionalField "name"    (\_ -> parseName)                     libName
+  , optionalField "include" (\_ -> pure . concatMap parsePaths)   libIncludes
+  , optionalField "depend"  (\_ -> pure . concatMap splitCommas)  libDepends
+  , optionalField "flags"   (\r -> pure . foldMap (parseFlags r)) libPragmas
+  ]
+  where
+    parseName :: [String] -> P LibName
+    parseName [s] | [name] <- words s = pure name
+    parseName ls = throwError $ BadLibraryName $ unwords ls
+
+    parsePaths :: String -> [FilePath]
+    parsePaths = go id where
+      fixup acc = let fp = acc [] in not (null fp) ?$> fp
+      go acc []           = fixup acc
+      go acc ('\\' : ' '  :cs) = go (acc . (' ':)) cs
+      go acc ('\\' : '\\' :cs) = go (acc . ('\\':)) cs
+      go acc (       ' '  :cs) = fixup acc ++ go id cs
+      go acc (c           :cs) = go (acc . (c:)) cs
+
+    parseFlags :: Range -> String -> OptionsPragma
+    parseFlags r s = OptionsPragma
+      { pragmaStrings = words s
+      , pragmaRange   = r
+      }
+
+-- | Parse @.agda-lib@ file.
+--
+-- Sets 'libFile' name and turn mentioned include directories into absolute
+-- pathes (provided the given 'FilePath' is absolute).
+--
+parseLibFile :: FilePath -> IO (P AgdaLibFile)
+parseLibFile file = do
+  abs <- absolute file
+  (fmap setPath . parseLib abs <$> UTF8.readFile file) `catchIO` \e ->
+    return $ throwError $ ReadFailure file e
+  where
+    setPath      lib = unrelativise (takeDirectory file) (set libFile file lib)
+    unrelativise dir = over libIncludes (map (dir </>))
+
+-- | Parse file contents.
+parseLib
+  :: AbsolutePath
+     -- ^ The parsed file.
+  -> String -> P AgdaLibFile
+parseLib file s = fromGeneric file =<< parseGeneric s
+
+-- | Parse 'GenericFile' with 'agdaLibFields' descriptors.
+fromGeneric
+  :: AbsolutePath
+     -- ^ The parsed file.
+  -> GenericFile -> P AgdaLibFile
+fromGeneric file = fromGeneric' file agdaLibFields
+
+-- | Given a list of 'Field' descriptors (with their custom parsers),
+--   parse a 'GenericFile' into the 'AgdaLibFile' structure.
+--
+--   Checks mandatory fields are present;
+--   no duplicate fields, no unknown fields.
+
+fromGeneric'
+  :: AbsolutePath
+     -- ^ The parsed file.
+  -> [Field] -> GenericFile -> P AgdaLibFile
+fromGeneric' file fields fs = do
+  checkFields fields (map geHeader fs)
+  foldM upd emptyLibFile fs
+  where
+    -- The range points to the start of the file.
+    r = Range
+          (Strict.Just $ mkRangeFile file Nothing)
+          (singleton (posToInterval () p p))
+      where
+      p = Pn { srcFile = ()
+             , posPos  = 1
+             , posLine = 1
+             , posCol  = 1
+             }
+
+    upd :: AgdaLibFile -> GenericEntry -> P AgdaLibFile
+    upd l (GenericEntry h cs) = do
+      mf <- findField h fields
+      case mf of
+        Just Field{..} -> do
+          x <- fParse r cs
+          return $ fSet x l
+        Nothing -> return l
+
+-- | Ensure that there are no duplicate fields and no mandatory fields are missing.
+checkFields :: [Field] -> [String] -> P ()
+checkFields fields fs = do
+  -- Report missing mandatory fields.
+  () <- List1.unlessNull missing $ throwError . MissingFields
+  -- Report duplicate fields.
+  List1.unlessNull (duplicates fs) $ throwError . DuplicateFields
+  where
+  mandatory :: [String]
+  mandatory = [ fName f | f <- fields, not $ fOptional f ]
+  missing   :: [String]
+  missing   = mandatory List.\\ fs
+
+-- | Find 'Field' with given 'fName', throw error if unknown.
+findField :: String -> [Field] -> P (Maybe Field)
+findField s fs = maybe err (return . Just) $ List.find ((s ==) . fName) fs
+  where err = warningP (UnknownField s) >> return Nothing
+
+-- Generic file parser ----------------------------------------------------
+
+-- | Example:
+--
+-- @
+--     parseGeneric "name:Main--BLA\ndepend:--BLA\n  standard-library--BLA\ninclude : . --BLA\n  src more-src   \n"
+--     == Right [("name",["Main"]),("depend",["standard-library"]),("include",[".","src more-src"])]
+-- @
+parseGeneric :: String -> P GenericFile
+parseGeneric s =
+  groupLines =<< concat <$> zipWithM parseLine [1..] (map stripComments $ lines s)
+
+-- | Lines with line numbers.
+data GenericLine
+  = Header  LineNumber String
+      -- ^ Header line, like a field name, e.g. "include :".  Cannot be indented.
+      --   @String@ is 'trim'med.
+  | Content LineNumber String
+      -- ^ Other line.  Must be indented.
+      --   @String@ is 'trim'med.
+  deriving (Show)
+
+-- | Parse line into 'Header' and 'Content' components.
+--
+--   Precondition: line comments and trailing whitespace have been stripped away.
+--
+--   Example file:
+--
+--   @
+--     name: Main
+--     depend:
+--       standard-library
+--     include: .
+--       src more-src
+--   @
+--
+--   This should give
+--
+--   @
+--     [ Header  1 "name"
+--     , Content 1 "Main"
+--     , Header  2 "depend"
+--     , Content 3 "standard-library"
+--     , Header  4 "include"
+--     , Content 4 "."
+--     , Content 5 "src more-src"
+--     ]
+--   @
+parseLine :: LineNumber -> String -> P [GenericLine]
+parseLine _ "" = pure []
+parseLine l s@(c:_)
+    -- Indented lines are 'Content'.
+  | isSpace c   = pure [Content l $ ltrim s]
+    -- Non-indented lines are 'Header'.
+  | otherwise   =
+    case break (== ':') s of
+      -- Headers are single words followed by a colon.
+      -- Anything after the colon that is not whitespace is 'Content'.
+      (h, ':' : r) ->
+        case words h of
+          [h] -> pure $ Header l h : [Content l r' | let r' = ltrim r, not (null r')]
+          []  -> throwError $ MissingFieldName l
+          hs  -> throwError $ BadFieldName l h
+      _ -> throwError $ MissingColonForField l (ltrim s)
+
+-- | Collect 'Header' and subsequent 'Content's into 'GenericEntry'.
+--
+--   Leading 'Content's?  That's an error.
+--
+groupLines :: [GenericLine] -> P GenericFile
+groupLines [] = pure []
+groupLines (Content l c : _) = throwError $ ContentWithoutField l
+groupLines (Header _ h : ls) = (GenericEntry h [ c | Content _ c <- cs ] :) <$> groupLines ls1
+  where
+    (cs, ls1) = span isContent ls
+    isContent Content{} = True
+    isContent Header{} = False
+
+-- | Remove leading whitespace and line comment.
+trimLineComment :: String -> String
+trimLineComment = stripComments . ltrim
+
+-- | Break a comma-separated string.  Result strings are @trim@med.
+splitCommas :: String -> [String]
+splitCommas = words . map (\c -> if c == ',' then ' ' else c)
+
+-- | ...and trailing, but not leading, whitespace.
+stripComments :: String -> String
+stripComments "" = ""
+stripComments ('-':'-':c:_) | isSpace c = ""
+stripComments (c : s) = cons c (stripComments s)
+  where
+    cons c "" | isSpace c = ""
+    cons c s = c : s
diff --git a/src/full/Agda/Interaction/MakeCase.hs b/src/full/Agda/Interaction/MakeCase.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/MakeCase.hs
@@ -0,0 +1,558 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.Interaction.MakeCase where
+
+import Prelude hiding ((!!), null)
+
+import Control.Monad
+
+import Data.Either
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Maybe
+import Data.Monoid
+
+import Agda.Syntax.Common
+import Agda.Syntax.Info
+import Agda.Syntax.Position
+import Agda.Syntax.Concrete (NameInScope(..))
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Concrete.Pattern as C
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Abstract.Pattern as A
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Scope.Base  ( ResolvedName(..), BindingSource(..), KindOfName(..), exceptKindsOfNames )
+import Agda.Syntax.Scope.Monad ( resolveName' )
+import Agda.Syntax.Translation.InternalToAbstract
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Coverage
+import Agda.TypeChecking.Coverage.Match ( SplitPatVar(..) , SplitPattern , applySplitPSubst , fromSplitPatterns )
+import Agda.TypeChecking.Empty ( isEmptyTel )
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Rules.Def (checkClauseLHS)
+import Agda.TypeChecking.Rules.LHS (LHSResult(..))
+import Agda.TypeChecking.Rules.LHS.Problem (AsBinding(..))
+
+import Agda.Interaction.Options
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens   (set)
+import Agda.Utils.List
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.WithDefault (lensKeepDefault)
+
+import Agda.Utils.Impossible
+
+type CaseContext = Maybe ExtLamInfo
+
+-- | Parse variables (visible or hidden), returning their de Bruijn indices.
+--   Used in 'makeCase'.
+
+parseVariables
+  :: QName           -- ^ The function name.
+  -> Context         -- ^ The context of the RHS of the clause we are splitting.
+  -> [AsBinding]     -- ^ The as-bindings of the clause we are splitting
+  -> InteractionId   -- ^ The hole of this function we are working on.
+  -> Range           -- ^ The range of this hole.
+  -> [String]        -- ^ The words the user entered in this hole (variable names).
+  -> TCM [(Int,NameInScope)] -- ^ The computed de Bruijn indices of the variables to split on,
+                             --   with information about whether each variable is in scope.
+parseVariables f cxt asb ii rng ss = do
+
+  -- We parse the variables in two steps:
+  -- (1) Convert the strings given by the user to abstract names,
+  --     using the scope information from the interaction meta.
+  -- (2) Convert the abstract names to de Bruijn indices,
+  --     using the context of the clause.
+
+  -- Get into the context of the meta.
+  mId <- lookupInteractionId ii
+  updateMetaVarRange mId rng
+  mi  <- getMetaInfo <$> lookupLocalMeta mId
+  enterClosure mi $ \ r -> do
+
+  reportSDoc "interaction.case" 20 $ do
+    m   <- currentModule
+    tel <- lookupSection m
+    vcat
+     [ "parseVariables:"
+     , "current module  =" <+> prettyTCM m
+     , "current section =" <+> inTopContext (prettyTCM tel)
+     , "clause context  =" <+> prettyTCM (PrettyContext cxt)
+     ]
+
+  -- Get printed representation of variables in context.  These are
+  -- used for recognizing when the user wants to make a hidden
+  -- variable (which is not in scope) visible.
+  n  <- getContextSize
+  xs <- forM (downFrom n) $ \ i ->
+    (,) <$> (P.render <$> prettyTCM (var i)) <*> nameOfBV i
+
+  -- Step 1: From strings to abstract names
+  abstractNames :: [(A.Name, Maybe BindingSource)] <- forM ss $ \s -> do
+
+    let cname = C.QName $ C.Name r C.InScope $ C.stringNameParts s
+    -- Note: the range in the concrete name is only approximate.
+    -- Jesper, 2018-12-19: Don't consider generalizable names since
+    -- they can be shadowed by hidden variables.
+    resolveName' (exceptKindsOfNames [GeneralizeName]) Nothing cname >>= \case
+
+      -- Fail if s is a name, but not of a variable.
+      DefinedName{}       -> failNotVar s
+      FieldName{}         -> failNotVar s
+      ConstructorName{}   -> failNotVar s
+      PatternSynResName{} -> failNotVar s
+
+      -- If s is a variable name, return it together with binding information.
+      VarName x b -> return (x, Just b)
+
+      -- If s is not a name, compare it to the printed variable representation.
+      UnknownName -> case (lookup s xs) of
+        Nothing -> failUnbound s
+        Just x  -> return (x, Nothing)
+
+  -- Step 2: Resolve each abstract name to a de Bruijn index.
+
+  -- First, get context names of the clause.
+  let clauseCxtNames = map (fst . unDom) cxt
+
+  -- Valid names to split on are pattern variables of the clause,
+  -- plus as-bindings that refer to a variable.
+  let clauseVars = zip clauseCxtNames (map var [0..]) ++
+                   map (\(AsB name v _ _) -> (name,v)) asb
+
+  -- We cannot split on module parameters or make them visible
+  params <- moduleParamsToApply $ qnameModule f
+  let isParam i = any ((== var i) . unArg) params
+
+  forM (zip ss abstractNames) $ \(s, (name, bound)) -> case bound of
+    -- Case 1: variable has a binding site. Check if it also exists in
+    -- the clause context so we can split on it.
+    Just bindingSource -> case (lookup name clauseVars, bindingSource) of
+      -- Case 1a: it is also known in the clause telescope and is
+      -- actually a variable. If a pattern variable (`PatternBound`)
+      -- has been refined to a module parameter we do allow splitting
+      -- on it, since the instantiation could as well have been the
+      -- other way around (see #2183).
+      (Just (Var i []), PatternBound) -> return (i, C.InScope)
+      -- Case 1b: the variable has been refined.
+      (Just v         , PatternBound) -> failInstantiatedVar s v
+      -- Case 1c: the variable is bound locally (e.g. a record let)
+      (Nothing        , PatternBound) -> failCaseLet s
+      -- Case 1d: module parameter
+      (Just (Var i []), LambdaBound ) -> failModuleBound s
+      -- Case 1e: locally lambda-bound variable
+      (_              , LambdaBound ) -> failLocal s
+      -- Case 1f: let-bound variable
+      (_              , LetBound    ) -> failLetBound s
+      -- Case 1g: with-bound variable (not used?)
+      (_              , WithBound   ) -> __IMPOSSIBLE__
+    -- Case 2: variable has no binding site, so we check if it can be
+    -- made visible.
+    Nothing -> case List.find (((==) `on` nameConcrete) name . fst) clauseVars of
+      -- Case 2a: there is a variable with that concrete name in the
+      -- clause context. If it is not a parameter, we can make it
+      -- visible.
+      Just (x, Var i []) | isParam i -> failHiddenModuleBound s
+                         | otherwise -> return (i, C.NotInScope)
+      -- Case 2b: there is a variable with that concrete name, but it
+      -- has been refined.
+      Just (x, v) -> failInstantiatedVar s v
+      -- Case 2c: there is no variable with that name. Since it was in
+      -- scope for the interaction meta, the only possibility is that
+      -- it is a hidden lambda-bound variable.
+      Nothing -> failHiddenLocal s
+
+  where
+
+  failNotVar s      = typeError $ GenericError $ "Not a variable: " ++ s
+  failUnbound s     = typeError $ GenericError $ "Unbound variable " ++ s
+  failAmbiguous s   = typeError $ GenericError $ "Ambiguous variable " ++ s
+  failLocal s       = typeError $ GenericError $
+    "Cannot split on local variable " ++ s
+  failHiddenLocal s = typeError $ GenericError $
+    "Cannot make hidden lambda-bound variable " ++ s ++ " visible"
+  failModuleBound s = typeError $ GenericError $
+    "Cannot split on module parameter " ++ s
+  failHiddenModuleBound s = typeError $ GenericError $
+    "Cannot make hidden module parameter " ++ s ++ " visible"
+  failLetBound s = typeError . GenericError $
+    "Cannot split on let-bound variable " ++ s
+  failInstantiatedVar s v = typeError . GenericDocError =<< sep
+      [ text $ "Cannot split on variable " ++ s ++ ", because it is bound to"
+      , prettyTCM v
+      ]
+  failCaseLet s     = typeError $ GenericError $
+    "Cannot split on variable " ++ s ++
+    ", because let-declarations may not be defined by pattern-matching"
+
+
+
+-- | Lookup the clause for an interaction point in the signature.
+--   Returns the CaseContext, the previous clauses, the clause itself,
+--   and a list of the remaining ones.
+
+type ClauseZipper =
+   ( [Clause] -- previous clauses
+   , Clause   -- clause of interest
+   , [Clause] -- other clauses
+   )
+
+getClauseZipperForIP :: QName -> Int -> TCM (CaseContext, ClauseZipper)
+getClauseZipperForIP f clauseNo = do
+  (theDef <$> getConstInfo f) >>= \case
+    Function{funClauses = cs, funExtLam = extlam} -> do
+      let (cs1,ccs2) = fromMaybe __IMPOSSIBLE__ $ splitExactlyAt clauseNo cs
+          (c,cs2)    = fromMaybe __IMPOSSIBLE__ $ uncons ccs2
+      return (extlam, (cs1, c, cs2))
+    d -> do
+      reportSDoc "impossible" 10 $ vcat
+        [ "getClauseZipperForIP" <+> prettyTCM f <+> text (show clauseNo)
+          <+> "received"
+        , text (show d)
+        ]
+      __IMPOSSIBLE__
+
+recheckAbstractClause :: Type -> Maybe Substitution -> A.SpineClause -> TCM (Clause, Context, [AsBinding])
+recheckAbstractClause t sub acl = checkClauseLHS t sub acl $ \ lhs -> do
+  let cl = Clause { clauseLHSRange    = getRange acl
+                  , clauseFullRange   = getRange acl
+                  , clauseTel         = lhsVarTele lhs
+                  , namedClausePats   = lhsPatterns lhs
+                  , clauseBody        = Nothing -- We don't need the body for make case
+                  , clauseType        = Just (lhsBodyType lhs)
+                  , clauseCatchall    = False
+                  , clauseExact       = Nothing
+                  , clauseRecursive   = Nothing
+                  , clauseUnreachable = Nothing
+                  , clauseEllipsis    = lhsEllipsis $ A.spLhsInfo $ A.clauseLHS acl
+                  , clauseWhereModule = A.whereModule $ A.clauseWhereDecls acl
+                  }
+  cxt <- getContext
+  let asb = lhsAsBindings lhs
+  return (cl, cxt, asb)
+
+
+-- | Entry point for case splitting tactic.
+
+makeCase :: InteractionId -> Range -> String -> TCM (QName, CaseContext, [A.Clause])
+makeCase hole rng s = withInteractionId hole $ locallyTC eMakeCase (const True) $ do
+
+  -- Jesper, 2018-12-10: print unsolved metas in dot patterns as _
+  localTC (\ e -> e { envPrintMetasBare = True }) $ do
+
+  -- Get function clause which contains the interaction point.
+  InteractionPoint { ipMeta = mm, ipClause = ipCl} <- lookupInteractionPoint hole
+  (f, clauseNo, clTy, clWithSub, absCl@A.Clause{ clauseRHS = rhs }, clClos) <- case ipCl of
+    IPClause f i t sub cl clo -> return (f, i, t, sub, cl, clo)
+    IPNoClause                -> typeError $ GenericError $
+      "Cannot split here, as we are not in a function definition"
+  (casectxt, (prevClauses0, _clause, follClauses0)) <- getClauseZipperForIP f clauseNo
+
+  -- Instead of using the actual internal clause, we retype check the abstract clause (with
+  -- eMakeCase = True). This disables the forcing translation in the unifier, which allows us to
+  -- split on forced variables.
+  (clause, clauseCxt, clauseAsBindings) <-
+    enterClosure clClos $ \ _ -> locallyTC eMakeCase (const True) $
+      recheckAbstractClause clTy clWithSub absCl
+
+  let (prevClauses, follClauses) = killRange (prevClauses0, follClauses0)
+    -- Andreas, 2019-08-08, issue #3966
+    -- Kill the ranges of the existing clauses to prevent wrong error
+    -- location to be set by the coverage checker (via isCovered)
+    -- for test/interaction/Issue191
+  let perm = fromMaybe __IMPOSSIBLE__ $ clausePerm clause
+      tel  = clauseTel  clause
+      ps   = namedClausePats clause
+      ell  = clauseEllipsis clause
+  reportSDoc "interaction.case" 100 $ vcat
+    [ "splitting clause:"
+    , nest 2 $ vcat
+      [ "f       =" <+> (text . show) f
+      , "context =" <+> ((inTopContext . (text . show)) =<< getContextTelescope)
+      , "tel     =" <+> (text . show) tel
+      , "perm    =" <+> text (show perm)
+      , "ps      =" <+> (text . show) ps
+      ]
+    ]
+  reportSDoc "interaction.case" 60 $ vcat
+    [ "splitting clause:"
+    , nest 2 $ vcat
+      [ "f       =" <+> pretty f
+      , "context =" <+> ((inTopContext . pretty) =<< getContextTelescope)
+      , "tel     =" <+> pretty tel
+      , "perm    =" <+> (text . show) perm
+      , "ps      =" <+> pretty ps
+      ]
+    ]
+  reportSDoc "interaction.case" 10 $ vcat
+    [ "splitting clause:"
+    , nest 2 $ vcat
+      [ "f       =" <+> prettyTCM f
+      , "context =" <+> ((inTopContext . prettyTCM) =<< getContextTelescope)
+      , "tel     =" <+> (inTopContext . prettyTCM) tel
+      , "perm    =" <+> text (show perm)
+      , "ps      =" <+> addContext tel (prettyTCMPatternList ps)
+      , "ell     =" <+> text (show ell)
+      , "type    =" <+> addContext tel (prettyTCM $ clauseType clause)
+      ]
+    ]
+
+  -- Check split variables.
+
+  let vars = words s
+
+  -- If the user just entered ".", do nothing.
+  -- This will expand an ellipsis, if present.
+
+  if concat vars == "." then do
+    cl <- makeAbstractClause f rhs NoEllipsis $ clauseToSplitClause clause
+    return (f, casectxt, [cl])
+
+  -- If we have no split variables, split on result.
+
+  else if null vars then do
+    -- Andreas, 2017-07-24, issue #2654:
+    -- When we introduce projection patterns in an extended lambda,
+    -- we need to print them postfix.
+    let postProjInExtLam = applyWhen (isJust casectxt) $
+          withPragmaOptions $ set (lensOptPostfixProjections . lensKeepDefault) True
+    (piTel, sc) <- insertTrailingArgs False $ clauseToSplitClause clause
+    -- Andreas, 2015-05-05 If we introduced new function arguments
+    -- do not split on result.  This might be more what the user wants.
+    -- To split on result, he can then C-c C-c again.
+    -- Andreas, 2015-05-21 Issue 1516:  However, if only hidden
+    -- arguments are introduced, C-c C-c virtually does nothing
+    -- (as they are not shown and get lost on the way to emacs and back).
+    newPats <- if null piTel then return False else do
+      -- If there were any pattern introduce, they will only have effect
+      -- if any of them is shown by the printer
+      imp <- optShowImplicit <$> pragmaOptions
+      return $ imp || any visible (telToList piTel)
+    scs <- if newPats then return [sc] else postProjInExtLam $ do
+      res <- splitResult f sc
+      case res of
+
+        Left err  -> do
+          -- Andreas, 2017-12-16, issue #2871
+          -- If there is nothing to split, introduce trailing hidden arguments.
+
+          -- Get trailing hidden pattern variables
+          let trailingPatVars :: [NamedArg DBPatVar]
+              trailingPatVars = takeWhileJust isVarP $ reverse ps
+              isVarP (Arg ai (Named n (VarP _ x))) = Just $ Arg ai $ Named n x
+              isVarP _ = Nothing
+          -- If all are already coming from the user, there is really nothing todo!
+          when (all ((UserWritten ==) . getOrigin) trailingPatVars) $ do
+            typeError $ SplitError err
+          -- Otherwise, we make these user-written
+          let xs = map (dbPatVarIndex . namedArg) trailingPatVars
+          return [makePatternVarsVisible xs sc]
+
+        Right cov -> ifNotM (optCopatterns <$> pragmaOptions) failNoCop $ {-else-} do
+          -- Andreas, 2016-05-03: do not introduce function arguments after projection.
+          -- This is sometimes annoying and can anyway be done by another C-c C-c.
+          -- mapM (snd <.> fixTarget) $ splitClauses cov
+          return cov
+    checkClauseIsClean ipCl
+    (f, casectxt,) <$> do
+      -- Andreas, 2020-05-18, issue #4536
+      -- When result splitting yields no clauses, replace rhs by @record{}@.
+      if null scs then
+        return [ A.spineToLhs $ absCl{ A.clauseRHS = makeRHSEmptyRecord rhs } ]
+      else mapM (makeAbstractClause f rhs ell) scs
+  else do
+    -- split on variables
+    xs <- parseVariables f clauseCxt clauseAsBindings hole rng vars
+    reportSLn "interaction.case" 30 $ "parsedVariables: " ++ show (zip xs vars)
+    -- Variables that are not in scope yet are brought into scope (@toShow@)
+    -- The other variables are split on (@toSplit@).
+    let (toShow, toSplit) = partitionEithers $ for (zip xs vars) $ \ ((x,nis), s) ->
+          if (nis == C.NotInScope) then Left x else Right x
+    let sc = makePatternVarsVisible toShow $ clauseToSplitClause clause
+    scs <- split f toSplit sc
+    reportSLn "interaction.case" 70 $ "makeCase: survived the splitting"
+
+    -- If any of the split variables is hidden by the ellipsis, we
+    -- should force the expansion of the ellipsis.
+    let splitNames = map (\i -> fst $ unDom $ clauseCxt !! i) toSplit
+    shouldExpandEllipsis <- return (not $ null toShow) `or2M` anyEllipsisVar f absCl splitNames
+    let ell' | shouldExpandEllipsis = NoEllipsis
+             | otherwise            = ell
+
+    -- CLEAN UP OF THE GENERATED CLAUSES
+    -- 1. filter out the generated clauses that are already covered
+    --    we consider a generated clause already covered if it is covered by:
+    --    a. a pre-existing clause defined before the one we splitted (prevClauses)
+    --    b. a pre-existing clause defined after the one we splitted (follClauses)
+    --       under the condition that it did not cover the one we splitted but was
+    --       covered by it (i.e. it was considered unreachable).
+    -- The key idea here is:
+    --       f m    zero = ?  ---- split on m --->  f (suc m) zero = ?
+    --       f zero zero = ?                        f zero    zero = ?
+    --       f _    _    = ?                        f _       _    = ?
+    -- because [f zero zero] is already defined.
+    -- However we ignore [f _ _]: [f m zero] was already a refinement of it,
+    -- hinting that we considered it more important than the catchall.
+    let sclause = clauseToSplitClause clause
+    fcs <- filterM (\ cl -> (isCovered f [clause] (clauseToSplitClause cl)) `and2M`
+                            (not <$> isCovered f [cl] sclause))
+                   follClauses
+    scs <- filterM (not <.> isCovered f (prevClauses ++ fcs) . fst) scs
+    reportSLn "interaction.case" 70 $ "makeCase: survived filtering out already covered clauses"
+    -- 2. filter out trivially impossible clauses not asked for by the user
+    cs <- catMaybes <$> do
+     forM scs $ \ (sc, isAbsurd) -> if isAbsurd
+      -- absurd clause coming from a split asked for by the user
+      then Just <$> makeAbsurdClause f ell' sc
+      -- trivially empty clause due to the refined patterns
+      else
+        ifM (liftTCM $ (optInferAbsurdClauses <$> pragmaOptions) `and2M` isEmptyTel (scTel sc))
+          {- then -} (pure Nothing)
+          {- else -} (Just <$> makeAbstractClause f rhs ell' sc)
+    reportSLn "interaction.case" 70 $ "makeCase: survived filtering out impossible clauses"
+    -- 3. If the cleanup removed everything then we know that none of the clauses where
+    --    absurd but that all of them were trivially empty. In this case we rewind and
+    --    insert all the clauses (garbage in, garbage out!)
+    cs <- if not (null cs) then pure cs
+          else mapM (makeAbstractClause f rhs ell' . fst) scs
+
+    reportSDoc "interaction.case" 65 $ vcat
+      [ "split result:"
+      , nest 2 $ vcat $ map prettyA cs
+      ]
+    checkClauseIsClean ipCl
+    return (f, casectxt, cs)
+
+  where
+  failNoCop = typeError $ GenericError $
+    "OPTION --copatterns needed to split on result here"
+
+  -- Split clause on given variables, return the resulting clauses together
+  -- with a bool indicating whether each clause is absurd
+  split :: QName -> [Nat] -> SplitClause -> TCM [(SplitClause, Bool)]
+  split f [] clause = return [(clause,False)]
+  split f (var : vars) clause = do
+    z <- dontAssignMetas $ splitClauseWithAbsurd clause var
+    case z of
+      Left err          -> typeError $ SplitError err
+      Right (Left cl)   -> return [(cl,True)]
+      Right (Right cov) -> concat <$> do
+            forM (splitClauses cov) $ \ cl ->
+              split f (mapMaybe (newVar cl) vars) cl
+
+  -- Finds the new variable corresponding to an old one, if any.
+  newVar :: SplitClause -> Nat -> Maybe Nat
+  newVar c x = case applySplitPSubst (scSubst c) (var x) of
+    Var y [] -> Just y
+    _        -> Nothing
+
+  -- Check whether clause has been refined after last load.
+  -- In this case, we refuse to split, as this might lose the refinements.
+  checkClauseIsClean :: IPClause -> TCM ()
+  checkClauseIsClean ipCl = do
+    sips <- filter ipSolved . BiMap.elems <$> useTC stInteractionPoints
+    when (List.any ((== ipCl) . ipClause) sips) $
+      typeError $ GenericError $ "Cannot split as clause rhs has been refined.  Please reload"
+
+-- | Make the given pattern variables visible by marking their origin as
+--   'CaseSplit' and pattern origin as 'PatOSplit' in the 'SplitClause'.
+makePatternVarsVisible :: [Nat] -> SplitClause -> SplitClause
+makePatternVarsVisible [] sc = sc
+makePatternVarsVisible is sc@SClause{ scPats = ps } =
+  sc{ scPats = mapNamedArgPattern mkVis ps }
+  where
+  mkVis :: NamedArg SplitPattern -> NamedArg SplitPattern
+  mkVis (Arg ai (Named n (VarP o (SplitPatVar x i ls))))
+    | i `elem` is =
+      -- We could introduce extra consistency checks, like
+      -- if visible ai then __IMPOSSIBLE__ else
+      -- or passing the parsed name along and comparing it with @x@
+      Arg (setOrigin CaseSplit ai) $ Named n $ VarP (PatternInfo PatOSplit []) $ SplitPatVar x i ls
+  mkVis np = np
+
+-- | If a copattern split yields no clauses, we must be at an empty record type.
+--   In this case, replace the rhs by @record{}@
+makeRHSEmptyRecord :: A.RHS -> A.RHS
+makeRHSEmptyRecord = \case
+  A.RHS{}            -> A.RHS{ rhsExpr = A.Rec empty empty, rhsConcrete = Nothing }
+  rhs@A.RewriteRHS{} -> rhs{ A.rewriteRHS = makeRHSEmptyRecord $ A.rewriteRHS rhs }
+  A.AbsurdRHS        -> __IMPOSSIBLE__
+  A.WithRHS{}        -> __IMPOSSIBLE__
+
+-- | Make clause with no rhs (because of absurd match).
+
+makeAbsurdClause :: QName -> ExpandedEllipsis -> SplitClause -> TCM A.Clause
+makeAbsurdClause f ell (SClause tel sps _ _ t) = do
+  let ps = fromSplitPatterns sps
+  reportSDoc "interaction.case" 10 $ vcat
+    [ "Interaction.MakeCase.makeAbsurdClause: split clause:"
+    , nest 2 $ vcat
+      [ "context =" <+> do (inTopContext . prettyTCM) =<< getContextTelescope
+      , "tel     =" <+> do inTopContext $ prettyTCM tel
+      , "ps      =" <+> do inTopContext $ addContext tel $ prettyTCMPatternList ps -- P.sep <$> prettyTCMPatterns ps
+      , "ell     =" <+> text (show ell)
+      ]
+    ]
+  withCurrentModule (qnameModule f) $
+    -- Andreas, 2015-05-29 Issue 635
+    -- Contract implicit record patterns before printing.
+    -- c <- translateRecordPatterns $ Clause noRange tel perm ps NoBody t False
+    -- Jesper, 2015-09-19 Don't contract, since we do on-demand splitting
+    inTopContext $ reify $ QNamed f $ Clause
+      { clauseLHSRange  = noRange
+      , clauseFullRange = noRange
+      , clauseTel       = tel
+      , namedClausePats = ps
+      , clauseBody      = Nothing
+      , clauseType      = argFromDom <$> t
+      , clauseCatchall    = False
+      , clauseExact       = Nothing
+      , clauseRecursive   = Nothing
+      , clauseUnreachable = Nothing
+      , clauseEllipsis    = ell
+      , clauseWhereModule = Nothing
+      }
+
+-- | Make a clause with a question mark as rhs.
+
+makeAbstractClause :: QName -> A.RHS -> ExpandedEllipsis -> SplitClause -> TCM A.Clause
+makeAbstractClause f rhs ell cl = do
+
+  lhs <- A.clauseLHS <$> makeAbsurdClause f ell cl
+  reportSDoc "interaction.case" 60 $ "reified lhs: " <+> prettyA lhs
+  return $ A.Clause lhs [] rhs A.noWhereDecls False
+  -- let ii = InteractionId (-1)  -- Dummy interaction point since we never type check this.
+  --                              -- Can end up in verbose output though (#1842), hence not __IMPOSSIBLE__.
+  -- let info = A.emptyMetaInfo   -- metaNumber = Nothing in order to print as ?, not ?n
+  -- return $ A.Clause lhs [] (A.RHS $ A.QuestionMark info ii) [] False
+
+anyEllipsisVar :: QName -> A.SpineClause -> [Name] -> TCM Bool
+anyEllipsisVar f cl xs = do
+  let lhs = A.clauseLHS cl
+      ps  = A.spLhsPats lhs
+      ell = lhsEllipsis $ A.spLhsInfo lhs
+      anyVar :: A.Pattern -> Any -> Any
+      anyVar p acc = Any $ getAny acc || case p of
+        A.VarP x -> A.unBind x `elem` xs
+        _        -> False
+  case ell of
+    NoEllipsis           -> return False
+    ExpandedEllipsis _ k -> do
+      ps' <- snd <$> reifyDisplayFormP f ps []
+      let ellipsisPats :: A.Patterns
+          ellipsisPats = fst $ C.splitEllipsis k ps'
+      reportSDoc "interaction.case.ellipsis" 40 $ vcat
+        [ "should we expand the ellipsis?"
+        , nest 2 $ "xs           =" <+> prettyList_ (map prettyA xs)
+        , nest 2 $ "ellipsisPats =" <+> prettyList_ (map prettyA ellipsisPats)
+        ]
+      return $ getAny $ A.foldrAPattern anyVar ellipsisPats
diff --git a/src/full/Agda/Interaction/Monad.hs b/src/full/Agda/Interaction/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Monad.hs
@@ -0,0 +1,49 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fwarn-orphans #-}
+{-# LANGUAGE CPP               #-}
+
+module Agda.Interaction.Monad
+  ( IM
+  , runIM
+  , readline
+  ) where
+
+import Agda.TypeChecking.Monad
+  ( HasOptions
+  , MonadTCEnv
+  , MonadTCM
+  , MonadTCState
+  , ReadTCState
+  , TCErr
+  , TCM, TCMT(..)
+  , mapTCMT
+  )
+import Control.Exception (throwIO)
+import Control.Monad.Except (MonadError (..))
+import Control.Monad.Trans (MonadIO, lift, liftIO)
+import qualified System.Console.Haskeline as Haskeline
+
+-- MonadException is replaced by MonadCatch in haskeline 0.8
+#if MIN_VERSION_haskeline(0,8,0)
+import qualified Control.Monad.Catch as Haskeline (catch)
+#endif
+
+-- | Interaction monad.
+newtype IM a = IM {unIM :: TCMT (Haskeline.InputT IO) a}
+  deriving
+  ( Functor, Applicative, Monad, MonadIO
+  , HasOptions, MonadTCEnv, ReadTCState, MonadTCState, MonadTCM )
+
+runIM :: IM a -> TCM a
+runIM = mapTCMT (Haskeline.runInputT Haskeline.defaultSettings) . unIM
+
+instance MonadError TCErr IM where
+  throwError                = liftIO . throwIO
+  catchError (IM (TCM m)) h = IM . TCM $ \s e ->
+    m s e `Haskeline.catch` \err -> unTCM (unIM (h err)) s e
+
+-- | Line reader. The line reader history is not stored between
+-- sessions.
+readline :: String -> IM (Maybe String)
+readline s = IM $ lift (Haskeline.getInputLine s)
diff --git a/src/full/Agda/Interaction/Options.hs b/src/full/Agda/Interaction/Options.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options.hs
@@ -0,0 +1,9 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Options
+    ( module Opts.Base
+    , module Opts.HasOptions
+    ) where
+
+import Agda.Interaction.Options.Base as Opts.Base
+import Agda.Interaction.Options.HasOptions as Opts.HasOptions
diff --git a/src/full/Agda/Interaction/Options/Base.hs b/src/full/Agda/Interaction/Options/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options/Base.hs
@@ -0,0 +1,1973 @@
+{-# LANGUAGE CPP       #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE PartialTypeSignatures #-}
+{-# OPTIONS_GHC -Wno-partial-type-signatures #-}
+
+{-# OPTIONS_GHC -Wno-missing-signatures #-}
+
+module Agda.Interaction.Options.Base
+    ( CommandLineOptions(..)
+    , PragmaOptions(..)
+    , OptionWarning(..), optionWarningName
+    , Flag, OptM, runOptM, OptDescr(..), ArgDescr(..)
+    , Verbosity, VerboseKey, VerboseLevel
+    , WarningMode(..)
+    , ConfluenceCheck(..)
+    , PrintAgdaVersion(..)
+    , UnicodeOrAscii(..)
+    , DiagnosticsColours(..)
+    , checkOpts
+    , parsePragmaOptions
+    , parsePluginOptions
+    , parseVerboseKey
+    , stripRTS
+    , defaultOptions
+    , defaultInteractionOptions
+    , defaultCutOff
+    , defaultPragmaOptions
+    , standardOptions_
+    , unsafePragmaOptions
+    , recheckBecausePragmaOptionsChanged
+    , InfectiveCoinfective(..)
+    , InfectiveCoinfectiveOption(..)
+    , infectiveCoinfectiveOptions
+    , safeFlag
+    , mapFlag
+    , usage
+    -- Reused by PandocAgda
+    , inputFlag
+    , standardOptions, deadStandardOptions
+    , getOptSimple
+    -- * Lenses for 'PragmaOptions'
+    , lensOptShowImplicit
+    , lensOptShowIrrelevant
+    , lensOptUseUnicode
+    , lensOptVerbose
+    , lensOptProfiling
+    , lensOptProp
+    , lensOptLevelUniverse
+    , lensOptTwoLevel
+    , lensOptAllowUnsolved
+    , lensOptAllowIncompleteMatch
+    , lensOptPositivityCheck
+    , lensOptTerminationCheck
+    , lensOptTerminationDepth
+    , lensOptUniverseCheck, lensOptNoUniverseCheck
+    , lensOptOmegaInOmega
+    , lensOptCumulativity
+    , lensOptSizedTypes
+    , lensOptGuardedness
+    , lensOptInjectiveTypeConstructors
+    , lensOptUniversePolymorphism
+    , lensOptIrrelevantProjections
+    , lensOptExperimentalIrrelevance
+    , lensOptWithoutK
+    , lensOptCubicalCompatible
+    , lensOptCopatterns
+    , lensOptPatternMatching
+    , lensOptExactSplit
+    , lensOptHiddenArgumentPuns
+    , lensOptEta
+    , lensOptForcing
+    , lensOptProjectionLike
+    , lensOptErasure
+    , lensOptErasedMatches
+    , lensOptEraseRecordParameters
+    , lensOptRewriting
+    , lensOptCubical
+    , lensOptGuarded
+    , lensOptFirstOrder
+    , lensOptPostfixProjections
+    , lensOptKeepPatternVariables
+    , lensOptInferAbsurdClauses
+    , lensOptInstanceSearchDepth
+    , lensOptOverlappingInstances
+    , lensOptQualifiedInstances
+    , lensOptInversionMaxDepth
+    , lensOptSafe
+    , lensOptDoubleCheck
+    , lensOptSyntacticEquality
+    , lensOptWarningMode
+    , lensOptCompileMain
+    , lensOptCaching
+    , lensOptCountClusters
+    , lensOptAutoInline
+    , lensOptPrintPatternSynonyms
+    , lensOptFastReduce
+    , lensOptCallByName
+    , lensOptConfluenceCheck
+    , lensOptCohesion
+    , lensOptFlatSplit
+    , lensOptImportSorts
+    , lensOptLoadPrimitives
+    , lensOptAllowExec
+    , lensOptSaveMetas
+    , lensOptShowIdentitySubstitutions
+    , lensOptKeepCoveringClauses
+    -- * Boolean accessors to 'PragmaOptions' collapsing default
+    , optShowImplicit
+    , optShowGeneralized
+    , optShowIrrelevant
+    , optProp
+    , optLevelUniverse
+    , optTwoLevel
+    , optAllowUnsolved
+    , optAllowIncompleteMatch
+    , optPositivityCheck
+    , optTerminationCheck
+    , optUniverseCheck
+    , optOmegaInOmega
+    , optCumulativity
+    , optSizedTypes
+    , optGuardedness
+    , optInjectiveTypeConstructors
+    , optUniversePolymorphism
+    , optIrrelevantProjections
+    , optExperimentalIrrelevance
+    , optWithoutK
+    , optCubicalCompatible
+    , optCopatterns
+    , optPatternMatching
+    , optHiddenArgumentPuns
+    , optEta
+    , optForcing
+    , optProjectionLike
+    , optErasure
+    , optErasedMatches
+    , optEraseRecordParameters
+    , optRewriting
+    , optGuarded
+    , optFirstOrder
+    , optPostfixProjections
+    , optKeepPatternVariables
+    , optInferAbsurdClauses
+    , optOverlappingInstances
+    , optQualifiedInstances
+    , optSafe
+    , optDoubleCheck
+    , optCompileNoMain
+    , optCaching
+    , optCountClusters
+    , optAutoInline
+    , optPrintPatternSynonyms
+    , optFastReduce
+    , optCallByName
+    , optCohesion
+    , optFlatSplit
+    , optImportSorts
+    , optLoadPrimitives
+    , optAllowExec
+    , optSaveMetas
+    , optShowIdentitySubstitutions
+    , optKeepCoveringClauses
+    , optLargeIndices
+    , optForcedArgumentRecursion
+    -- * Non-boolean accessors to 'PragmaOptions'
+    , optConfluenceCheck
+    , optCubical
+    , optInstanceSearchDepth
+    , optInversionMaxDepth
+    , optProfiling
+    , optSyntacticEquality
+    , optTerminationDepth
+    , optUseUnicode
+    , optVerbose
+    , optWarningMode
+    ) where
+
+import Prelude hiding ( null, not, (&&), (||) )
+
+import Control.DeepSeq
+import Control.Monad        ( (>=>), when, unless, void )
+import Control.Monad.Except ( ExceptT, MonadError(throwError), runExceptT )
+import Control.Monad.Writer ( Writer, runWriter, MonadWriter(..) )
+
+import Data.Function            ( (&) )
+import Data.List                ( intercalate )
+import Data.Maybe
+import Data.Map                 ( Map )
+import qualified Data.Map as Map
+import Data.Set                 ( Set )
+import qualified Data.Set as Set
+
+import GHC.Generics (Generic)
+
+import System.Console.GetOpt    ( getOpt', usageInfo, ArgOrder(ReturnInOrder)
+                                , OptDescr(..), ArgDescr(..)
+                                )
+import qualified System.IO.Unsafe as UNSAFE (unsafePerformIO)
+
+import Text.EditDistance
+import Text.Read                ( readMaybe )
+
+import Agda.Termination.CutOff  ( CutOff(..), defaultCutOff )
+
+import Agda.Interaction.Library ( ExeName, LibName, OptionsPragma(..) )
+import Agda.Interaction.Options.Help
+  ( Help(HelpFor, GeneralHelp)
+  , string2HelpTopic
+  , allHelpTopics
+  , helpTopicUsage
+  )
+import Agda.Interaction.Options.Warnings
+import Agda.Syntax.Concrete.Glyph ( unsafeSetUnicodeOrAscii, UnicodeOrAscii(..) )
+import Agda.Syntax.Common (Cubical(..))
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+
+import Agda.Utils.Boolean
+import Agda.Utils.FileName      ( AbsolutePath )
+import Agda.Utils.Function      ( applyWhen, applyUnless )
+import Agda.Utils.Functor       ( (<&>) )
+import Agda.Utils.Lens          ( Lens', (^.), over, set )
+import Agda.Utils.List          ( headWithDefault, initLast1 )
+import Agda.Utils.List1         ( List1, String1, pattern (:|), toList )
+import qualified Agda.Utils.List1        as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad         ( tell1 )
+import Agda.Utils.Null
+import Agda.Utils.ProfileOptions
+import Agda.Utils.String        ( unwords1 )
+import Agda.Utils.Trie          ( Trie )
+import qualified Agda.Utils.Trie as Trie
+import Agda.Utils.TypeLits
+import Agda.Utils.WithDefault
+
+import Agda.Utils.Impossible
+
+import Agda.Version
+
+-- OptDescr is a Functor --------------------------------------------------
+
+type VerboseKey     = String
+type VerboseKeyItem = String1
+type VerboseLevel   = Int
+-- | 'Strict.Nothing' is used if no verbosity options have been given,
+-- thus making it possible to handle the default case relatively
+-- quickly. Note that 'Strict.Nothing' corresponds to a trie with
+-- verbosity level 1 for the empty path.
+type Verbosity = Strict.Maybe (Trie VerboseKeyItem VerboseLevel)
+
+parseVerboseKey :: VerboseKey -> [VerboseKeyItem]
+parseVerboseKey = List1.wordsBy (`elem` ['.', ':'])
+
+data DiagnosticsColours
+  = AlwaysColour
+  | NeverColour
+  | AutoColour
+  deriving (Show, Generic)
+
+instance NFData DiagnosticsColours
+
+-- Don't forget to update
+--   doc/user-manual/tools/command-line-options.rst
+-- if you make changes to the command-line options!
+
+data CommandLineOptions = Options
+  { optProgramName           :: String
+  , optInputFile             :: Maybe FilePath
+  , optIncludePaths          :: [FilePath]
+  , optAbsoluteIncludePaths  :: [AbsolutePath]
+      -- ^ The list should not contain duplicates.
+  , optLibraries             :: [LibName]
+  , optOverrideLibrariesFile :: Maybe FilePath
+      -- ^ Use this (if 'Just') instead of @~\/.agda\/libraries@.
+  , optDefaultLibs           :: Bool
+       -- ^ Use @~\/.agda\/defaults@.
+  , optUseLibs               :: Bool
+       -- ^ look for @.agda-lib@ files.
+  , optTraceImports          :: Integer
+       -- ^ Configure notifications about imported modules.
+  , optTrustedExecutables    :: Map ExeName FilePath
+       -- ^ Map names of trusted executables to absolute paths.
+  , optPrintAgdaDataDir      :: Bool
+  , optPrintAgdaAppDir       :: Bool
+  , optPrintVersion          :: Maybe PrintAgdaVersion
+  , optPrintHelp             :: Maybe Help
+  , optInteractive           :: Bool
+      -- ^ Agda REPL (@-I@).
+  , optGHCiInteraction       :: Bool
+  , optJSONInteraction       :: Bool
+  , optExitOnError           :: !Bool
+      -- ^ Exit if an interactive command fails.
+  , optCompileDir            :: Maybe FilePath
+      -- ^ In the absence of a path the project root is used.
+  , optGenerateVimFile       :: Bool
+  , optIgnoreInterfaces      :: Bool
+  , optIgnoreAllInterfaces   :: Bool
+  , optLocalInterfaces       :: Bool
+  , optPragmaOptions         :: PragmaOptions
+  , optOnlyScopeChecking     :: Bool
+      -- ^ Should the top-level module only be scope-checked, and not type-checked?
+  , optTransliterate         :: Bool
+      -- ^ Should code points that are not supported by the locale be transliterated?
+  , optDiagnosticsColour     :: DiagnosticsColours
+      -- ^ Configure colour output.
+  }
+  deriving (Show, Generic)
+
+instance NFData CommandLineOptions
+
+-- | Options which can be set in a pragma.
+
+data PragmaOptions = PragmaOptions
+  { _optShowImplicit              :: WithDefault 'False
+  , _optShowGeneralized           :: WithDefault 'True
+      -- ^ Show generalized parameters in Pi types
+  , _optShowIrrelevant            :: WithDefault 'False
+  , _optUseUnicode                :: WithDefault' UnicodeOrAscii 'True -- Would like to write UnicodeOk instead of True here
+  , _optVerbose                   :: !Verbosity
+  , _optProfiling                 :: ProfileOptions
+  , _optProp                      :: WithDefault 'False
+  , _optLevelUniverse             :: WithDefault 'False
+  , _optTwoLevel                  :: WithDefault 'False
+  , _optAllowUnsolved             :: WithDefault 'False
+  , _optAllowIncompleteMatch      :: WithDefault 'False
+  , _optPositivityCheck           :: WithDefault 'True
+  , _optTerminationCheck          :: WithDefault 'True
+  , _optTerminationDepth          :: CutOff
+      -- ^ Cut off structural order comparison at some depth in termination checker?
+  , _optUniverseCheck             :: WithDefault 'True
+  , _optOmegaInOmega              :: WithDefault 'False
+  , _optCumulativity              :: WithDefault 'False
+  , _optSizedTypes                :: WithDefault 'False
+  , _optGuardedness               :: WithDefault 'False
+  , _optInjectiveTypeConstructors :: WithDefault 'False
+  , _optUniversePolymorphism      :: WithDefault 'True
+  , _optIrrelevantProjections     :: WithDefault 'False
+      -- off by default in > 2.5.4, see issue #2170
+  , _optExperimentalIrrelevance   :: WithDefault 'False
+      -- ^ irrelevant levels, irrelevant data matching
+  , _optWithoutK                  :: WithDefault 'False
+  , _optCubicalCompatible         :: WithDefault 'False
+  , _optCopatterns                :: WithDefault 'True
+      -- ^ Allow definitions by copattern matching?
+  , _optPatternMatching           :: WithDefault 'True
+      -- ^ Is pattern matching allowed in the current file?
+  , _optExactSplit                :: WithDefault 'False
+  , _optHiddenArgumentPuns        :: WithDefault 'False
+      -- ^ Should patterns of the form @{x}@ or @⦃ x ⦄@ be interpreted as puns?
+  , _optEta                       :: WithDefault 'True
+  , _optForcing                   :: WithDefault 'True
+      -- ^ Perform the forcing analysis on data constructors?
+  , _optProjectionLike            :: WithDefault 'True
+      -- ^ Perform the projection-likeness analysis on functions?
+  , _optErasure                   :: WithDefault 'False
+  , _optErasedMatches             :: WithDefault 'True
+      -- ^ Allow matching in erased positions for single-constructor,
+      -- non-indexed data/record types. (This kind of matching is always
+      -- allowed for record types with η-equality.)
+  , _optEraseRecordParameters     :: WithDefault 'False
+      -- ^ Mark parameters of record modules as erased?
+  , _optRewriting                 :: WithDefault 'False
+      -- ^ Can rewrite rules be added and used?
+  , _optCubical                   :: Maybe Cubical
+  , _optGuarded                   :: WithDefault 'False
+  , _optFirstOrder                :: WithDefault 'False
+      -- ^ Should we speculatively unify function applications as if they were injective?
+  , _optPostfixProjections        :: WithDefault 'False
+      -- ^ Should system generated projections 'ProjSystem' be printed
+      --   postfix (True) or prefix (False).
+  , _optKeepPatternVariables      :: WithDefault 'False
+      -- ^ Should case splitting replace variables with dot patterns
+      --   (False) or keep them as variables (True).
+  , _optInferAbsurdClauses        :: WithDefault 'True
+      -- ^ Should case splitting and coverage checking try to discharge absurd clauses?
+      --   Default: 'True', but 'False' might make coverage checking considerably faster in some cases.
+  , _optInstanceSearchDepth       :: Int
+  , _optOverlappingInstances      :: WithDefault 'False
+  , _optQualifiedInstances        :: WithDefault 'True
+      -- ^ Should instance search consider instances with qualified names?
+  , _optInversionMaxDepth         :: Int
+  , _optSafe                      :: WithDefault 'False
+  , _optDoubleCheck               :: WithDefault 'False
+  , _optSyntacticEquality         :: !(Strict.Maybe Int)
+    -- ^ Should the conversion checker use the syntactic equality
+    -- shortcut? 'Nothing' means that it should. @'Just' n@, for a
+    -- non-negative number @n@, means that syntactic equality checking
+    -- gets @n@ units of fuel. If the fuel becomes zero, then
+    -- syntactic equality checking is turned off. The fuel counter is
+    -- decreased in the failure continuation of
+    -- 'Agda.TypeChecking.SyntacticEquality.checkSyntacticEquality'.
+  , _optWarningMode               :: WarningMode
+  , _optCompileMain               :: WithDefault 'True
+    -- ^ Treat the module given at the command line or via interaction as main module in compilation?
+  , _optCaching                   :: WithDefault 'True
+  , _optCountClusters             :: WithDefault 'False
+    -- ^ Count extended grapheme clusters rather than code points
+    --   when generating LaTeX.
+  , _optAutoInline                :: WithDefault 'False
+    -- ^ Automatic compile-time inlining for simple definitions
+    --   (unless marked @NOINLINE@).
+  , _optPrintPatternSynonyms      :: WithDefault 'True
+  , _optFastReduce                :: WithDefault 'True
+      -- ^ Use the Agda abstract machine ('fastReduce')?
+  , _optCallByName                :: WithDefault 'False
+      -- ^ Use call-by-name instead of call-by-need.
+  , _optConfluenceCheck           :: Maybe ConfluenceCheck
+      -- ^ Check confluence of rewrite rules?
+  , _optCohesion                  :: WithDefault 'False
+      -- ^ Are the cohesion modalities available?
+  , _optFlatSplit                 :: WithDefault 'False
+      -- ^ Can we split on a @(\@flat x : A)@ argument?
+  , _optImportSorts               :: WithDefault 'True
+      -- ^ Should every top-level module start with an implicit statement
+      --   @open import Agda.Primitive using (Set; Prop)@?
+  , _optLoadPrimitives            :: WithDefault 'True
+      -- ^ Should we load the primitive modules at all?
+      --   This is a stronger form of 'optImportSorts'.
+  , _optAllowExec                 :: WithDefault 'False
+      -- ^ Allow running external @executables@ from meta programs.
+  , _optSaveMetas                 :: WithDefault 'False
+      -- ^ Save meta-variables to interface files.
+  , _optShowIdentitySubstitutions :: WithDefault 'False
+      -- ^ Show identity substitutions when pretty-printing terms
+      --   (i.e. always show all arguments of a metavariable).
+  , _optKeepCoveringClauses       :: WithDefault 'False
+      -- ^ Do not discard clauses constructed by the coverage checker
+      --   (needed for some external backends).
+  , _optLargeIndices              :: WithDefault 'False
+      -- ^ Allow large indices, and large forced arguments in
+      -- constructors.
+  , _optForcedArgumentRecursion   :: WithDefault 'True
+      -- ^ Allow recursion on forced constructor arguments.
+  }
+  deriving (Show, Eq, Generic)
+
+instance NFData PragmaOptions
+
+data ConfluenceCheck
+  = LocalConfluenceCheck
+  | GlobalConfluenceCheck
+  deriving (Show, Eq, Generic)
+
+instance NFData ConfluenceCheck
+
+-- | Options @--version@ and @--numeric-version@ (last wins).
+data PrintAgdaVersion
+  = PrintAgdaVersion
+      -- ^ Print Agda version information and exit.
+  | PrintAgdaNumericVersion
+      -- ^ Print Agda version number and exit.
+  deriving (Show, Generic)
+
+instance NFData PrintAgdaVersion
+
+-- collapse defaults
+optShowImplicit              :: PragmaOptions -> Bool
+optShowGeneralized           :: PragmaOptions -> Bool
+optShowIrrelevant            :: PragmaOptions -> Bool
+optProp                      :: PragmaOptions -> Bool
+optLevelUniverse             :: PragmaOptions -> Bool
+optTwoLevel                  :: PragmaOptions -> Bool
+optAllowUnsolved             :: PragmaOptions -> Bool
+optAllowIncompleteMatch      :: PragmaOptions -> Bool
+optPositivityCheck           :: PragmaOptions -> Bool
+optTerminationCheck          :: PragmaOptions -> Bool
+optUniverseCheck             :: PragmaOptions -> Bool
+optOmegaInOmega              :: PragmaOptions -> Bool
+optCumulativity              :: PragmaOptions -> Bool
+optSizedTypes                :: PragmaOptions -> Bool
+optGuardedness               :: PragmaOptions -> Bool
+optInjectiveTypeConstructors :: PragmaOptions -> Bool
+optUniversePolymorphism      :: PragmaOptions -> Bool
+optIrrelevantProjections     :: PragmaOptions -> Bool
+optExperimentalIrrelevance   :: PragmaOptions -> Bool
+optWithoutK                  :: PragmaOptions -> Bool
+optCubicalCompatible         :: PragmaOptions -> Bool
+optCopatterns                :: PragmaOptions -> Bool
+optPatternMatching           :: PragmaOptions -> Bool
+optHiddenArgumentPuns        :: PragmaOptions -> Bool
+optEta                       :: PragmaOptions -> Bool
+optForcing                   :: PragmaOptions -> Bool
+optProjectionLike            :: PragmaOptions -> Bool
+-- | 'optErasure' is implied by 'optEraseRecordParameters'.
+--   'optErasure' is also implied by an explicitly given `--erased-matches`.
+optErasure                   :: PragmaOptions -> Bool
+optErasedMatches             :: PragmaOptions -> Bool
+optEraseRecordParameters     :: PragmaOptions -> Bool
+optRewriting                 :: PragmaOptions -> Bool
+optGuarded                   :: PragmaOptions -> Bool
+optFirstOrder                :: PragmaOptions -> Bool
+optPostfixProjections        :: PragmaOptions -> Bool
+optKeepPatternVariables      :: PragmaOptions -> Bool
+optInferAbsurdClauses        :: PragmaOptions -> Bool
+optOverlappingInstances      :: PragmaOptions -> Bool
+optQualifiedInstances        :: PragmaOptions -> Bool
+optSafe                      :: PragmaOptions -> Bool
+optDoubleCheck               :: PragmaOptions -> Bool
+optCompileNoMain             :: PragmaOptions -> Bool
+optCaching                   :: PragmaOptions -> Bool
+optCountClusters             :: PragmaOptions -> Bool
+optAutoInline                :: PragmaOptions -> Bool
+optPrintPatternSynonyms      :: PragmaOptions -> Bool
+optFastReduce                :: PragmaOptions -> Bool
+optCallByName                :: PragmaOptions -> Bool
+-- | 'optCohesion' is implied by 'optFlatSplit'.
+optCohesion                  :: PragmaOptions -> Bool
+optFlatSplit                 :: PragmaOptions -> Bool
+-- | 'optImportSorts' requires 'optLoadPrimitives'.
+optImportSorts               :: PragmaOptions -> Bool
+optLoadPrimitives            :: PragmaOptions -> Bool
+optAllowExec                 :: PragmaOptions -> Bool
+optSaveMetas                 :: PragmaOptions -> Bool
+optShowIdentitySubstitutions :: PragmaOptions -> Bool
+optKeepCoveringClauses       :: PragmaOptions -> Bool
+optLargeIndices              :: PragmaOptions -> Bool
+optForcedArgumentRecursion   :: PragmaOptions -> Bool
+
+optShowImplicit              = collapseDefault . _optShowImplicit
+optShowGeneralized           = collapseDefault . _optShowGeneralized
+optShowIrrelevant            = collapseDefault . _optShowIrrelevant
+optProp                      = collapseDefault . _optProp
+optLevelUniverse             = collapseDefault . _optLevelUniverse
+optTwoLevel                  = collapseDefault . _optTwoLevel
+optAllowUnsolved             = collapseDefault . _optAllowUnsolved
+optAllowIncompleteMatch      = collapseDefault . _optAllowIncompleteMatch
+optPositivityCheck           = collapseDefault . _optPositivityCheck
+optTerminationCheck          = collapseDefault . _optTerminationCheck
+optUniverseCheck             = collapseDefault . _optUniverseCheck
+optOmegaInOmega              = collapseDefault . _optOmegaInOmega
+optCumulativity              = collapseDefault . _optCumulativity
+optSizedTypes                = collapseDefault . _optSizedTypes
+optGuardedness               = collapseDefault . _optGuardedness
+optInjectiveTypeConstructors = collapseDefault . _optInjectiveTypeConstructors
+optUniversePolymorphism      = collapseDefault . _optUniversePolymorphism
+optIrrelevantProjections     = collapseDefault . _optIrrelevantProjections
+optExperimentalIrrelevance   = collapseDefault . _optExperimentalIrrelevance
+optWithoutK                  = collapseDefault . _optWithoutK
+optCubicalCompatible         = collapseDefault . _optCubicalCompatible
+optCopatterns                = collapseDefault . _optCopatterns
+optPatternMatching           = collapseDefault . _optPatternMatching
+optHiddenArgumentPuns        = collapseDefault . _optHiddenArgumentPuns
+optEta                       = collapseDefault . _optEta
+optForcing                   = collapseDefault . _optForcing
+optProjectionLike            = collapseDefault . _optProjectionLike
+-- --erase-record-parameters implies --erasure
+optErasure                   = collapseDefault . _optErasure || optEraseRecordParameters || (Value True ==) . _optErasedMatches
+optErasedMatches             = collapseDefault . _optErasedMatches && optErasure
+optEraseRecordParameters     = collapseDefault . _optEraseRecordParameters
+optRewriting                 = collapseDefault . _optRewriting
+optGuarded                   = collapseDefault . _optGuarded
+optFirstOrder                = collapseDefault . _optFirstOrder
+optPostfixProjections        = collapseDefault . _optPostfixProjections
+optKeepPatternVariables      = collapseDefault . _optKeepPatternVariables
+optInferAbsurdClauses        = collapseDefault . _optInferAbsurdClauses
+optOverlappingInstances      = collapseDefault . _optOverlappingInstances
+optQualifiedInstances        = collapseDefault . _optQualifiedInstances
+optSafe                      = collapseDefault . _optSafe
+optDoubleCheck               = collapseDefault . _optDoubleCheck
+optCompileNoMain             = not . collapseDefault . _optCompileMain
+optCaching                   = collapseDefault . _optCaching
+optCountClusters             = collapseDefault . _optCountClusters
+optAutoInline                = collapseDefault . _optAutoInline
+optPrintPatternSynonyms      = collapseDefault . _optPrintPatternSynonyms
+optFastReduce                = collapseDefault . _optFastReduce
+optCallByName                = collapseDefault . _optCallByName
+-- --flat-split implies --cohesion
+optCohesion                  = collapseDefault . _optCohesion      || optFlatSplit
+optFlatSplit                 = collapseDefault . _optFlatSplit
+-- --no-load-primitives implies --no-import-sorts
+optImportSorts               = collapseDefault . _optImportSorts   && optLoadPrimitives
+optLoadPrimitives            = collapseDefault . _optLoadPrimitives
+optAllowExec                 = collapseDefault . _optAllowExec
+optSaveMetas                 = collapseDefault . _optSaveMetas
+optShowIdentitySubstitutions = collapseDefault . _optShowIdentitySubstitutions
+optKeepCoveringClauses       = collapseDefault . _optKeepCoveringClauses
+optLargeIndices              = collapseDefault . _optLargeIndices
+optForcedArgumentRecursion   = collapseDefault . _optForcedArgumentRecursion
+
+-- Collapse defaults (non-Bool)
+
+optUseUnicode                :: PragmaOptions -> UnicodeOrAscii
+optUseUnicode                = collapseDefault . _optUseUnicode
+
+-- Extra trivial accessors (keep in alphabetical order)
+
+optConfluenceCheck     :: PragmaOptions -> _
+optCubical             :: PragmaOptions -> _
+optInstanceSearchDepth :: PragmaOptions -> _
+optInversionMaxDepth   :: PragmaOptions -> _
+optProfiling           :: PragmaOptions -> _
+optSyntacticEquality   :: PragmaOptions -> _
+optTerminationDepth    :: PragmaOptions -> _
+optVerbose             :: PragmaOptions -> _
+optWarningMode         :: PragmaOptions -> _
+
+optConfluenceCheck     = _optConfluenceCheck
+optCubical             = _optCubical
+optInstanceSearchDepth = _optInstanceSearchDepth
+optInversionMaxDepth   = _optInversionMaxDepth
+optProfiling           = _optProfiling
+optSyntacticEquality   = _optSyntacticEquality
+optTerminationDepth    = _optTerminationDepth
+optVerbose             = _optVerbose
+optWarningMode         = _optWarningMode
+
+-- Lenses for PragmaOptions
+-- N.B.: We use PartialTypeSignatures here to not repeat default values (DRY!).
+
+lensOptShowImplicit :: Lens' PragmaOptions _
+lensOptShowImplicit f o = f (_optShowImplicit o) <&> \ i -> o{ _optShowImplicit = i }
+
+lensOptShowIrrelevant :: Lens' PragmaOptions _
+lensOptShowIrrelevant f o = f (_optShowIrrelevant o) <&> \ i -> o{ _optShowIrrelevant = i }
+
+lensOptUseUnicode :: Lens' PragmaOptions _
+lensOptUseUnicode f o = f (_optUseUnicode o) <&> \ i -> o{ _optUseUnicode = i }
+
+lensOptVerbose :: Lens' PragmaOptions _
+lensOptVerbose f o = f (_optVerbose o) <&> \ i -> o{ _optVerbose = i }
+
+lensOptProfiling :: Lens' PragmaOptions _
+lensOptProfiling f o = f (_optProfiling o) <&> \ i -> o{ _optProfiling = i }
+
+lensOptProp :: Lens' PragmaOptions _
+lensOptProp f o = f (_optProp o) <&> \ i -> o{ _optProp = i }
+
+lensOptLevelUniverse :: Lens' PragmaOptions _
+lensOptLevelUniverse f o = f (_optLevelUniverse o) <&> \ i -> o{ _optLevelUniverse = i }
+
+lensOptTwoLevel :: Lens' PragmaOptions _
+lensOptTwoLevel f o = f (_optTwoLevel o) <&> \ i -> o{ _optTwoLevel = i }
+
+lensOptAllowUnsolved :: Lens' PragmaOptions _
+lensOptAllowUnsolved f o = f (_optAllowUnsolved o) <&> \ i -> o{ _optAllowUnsolved = i }
+
+lensOptAllowIncompleteMatch :: Lens' PragmaOptions _
+lensOptAllowIncompleteMatch f o = f (_optAllowIncompleteMatch o) <&> \ i -> o{ _optAllowIncompleteMatch = i }
+
+lensOptPositivityCheck :: Lens' PragmaOptions _
+lensOptPositivityCheck f o = f (_optPositivityCheck o) <&> \ i -> o{ _optPositivityCheck = i }
+
+lensOptTerminationCheck :: Lens' PragmaOptions _
+lensOptTerminationCheck f o = f (_optTerminationCheck o) <&> \ i -> o{ _optTerminationCheck = i }
+
+lensOptTerminationDepth :: Lens' PragmaOptions _
+lensOptTerminationDepth f o = f (_optTerminationDepth o) <&> \ i -> o{ _optTerminationDepth = i }
+
+lensOptUniverseCheck :: Lens' PragmaOptions _
+lensOptUniverseCheck f o = f (_optUniverseCheck o) <&> \ i -> o{ _optUniverseCheck = i }
+
+lensOptNoUniverseCheck :: Lens' PragmaOptions _
+lensOptNoUniverseCheck f o = f (mapValue not $ _optUniverseCheck o) <&> \ i -> o{ _optUniverseCheck = mapValue not i }
+
+lensOptOmegaInOmega :: Lens' PragmaOptions _
+lensOptOmegaInOmega f o = f (_optOmegaInOmega o) <&> \ i -> o{ _optOmegaInOmega = i }
+
+lensOptCumulativity :: Lens' PragmaOptions _
+lensOptCumulativity f o = f (_optCumulativity o) <&> \ i -> o{ _optCumulativity = i }
+
+lensOptSizedTypes :: Lens' PragmaOptions _
+lensOptSizedTypes f o = f (_optSizedTypes o) <&> \ i -> o{ _optSizedTypes = i }
+
+lensOptGuardedness :: Lens' PragmaOptions _
+lensOptGuardedness f o = f (_optGuardedness o) <&> \ i -> o{ _optGuardedness = i }
+
+lensOptInjectiveTypeConstructors :: Lens' PragmaOptions _
+lensOptInjectiveTypeConstructors f o = f (_optInjectiveTypeConstructors o) <&> \ i -> o{ _optInjectiveTypeConstructors = i }
+
+lensOptUniversePolymorphism :: Lens' PragmaOptions _
+lensOptUniversePolymorphism f o = f (_optUniversePolymorphism o) <&> \ i -> o{ _optUniversePolymorphism = i }
+
+lensOptIrrelevantProjections :: Lens' PragmaOptions _
+lensOptIrrelevantProjections f o = f (_optIrrelevantProjections o) <&> \ i -> o{ _optIrrelevantProjections = i }
+
+lensOptExperimentalIrrelevance :: Lens' PragmaOptions _
+lensOptExperimentalIrrelevance f o = f (_optExperimentalIrrelevance o) <&> \ i -> o{ _optExperimentalIrrelevance = i }
+
+lensOptWithoutK :: Lens' PragmaOptions _
+lensOptWithoutK f o = f (_optWithoutK o) <&> \ i -> o{ _optWithoutK = i }
+
+lensOptCubicalCompatible :: Lens' PragmaOptions _
+lensOptCubicalCompatible f o = f (_optCubicalCompatible o) <&> \ i -> o{ _optCubicalCompatible = i }
+
+lensOptCopatterns :: Lens' PragmaOptions _
+lensOptCopatterns f o = f (_optCopatterns o) <&> \ i -> o{ _optCopatterns = i }
+
+lensOptPatternMatching :: Lens' PragmaOptions _
+lensOptPatternMatching f o = f (_optPatternMatching o) <&> \ i -> o{ _optPatternMatching = i }
+
+lensOptExactSplit :: Lens' PragmaOptions _
+lensOptExactSplit f o = f (_optExactSplit o) <&> \ i -> o{ _optExactSplit = i }
+
+lensOptHiddenArgumentPuns :: Lens' PragmaOptions _
+lensOptHiddenArgumentPuns f o = f (_optHiddenArgumentPuns o) <&> \ i -> o{ _optHiddenArgumentPuns = i }
+
+lensOptEta :: Lens' PragmaOptions _
+lensOptEta f o = f (_optEta o) <&> \ i -> o{ _optEta = i }
+
+lensOptForcing :: Lens' PragmaOptions _
+lensOptForcing f o = f (_optForcing o) <&> \ i -> o{ _optForcing = i }
+
+lensOptProjectionLike :: Lens' PragmaOptions _
+lensOptProjectionLike f o = f (_optProjectionLike o) <&> \ i -> o{ _optProjectionLike = i }
+
+lensOptErasure :: Lens' PragmaOptions _
+lensOptErasure f o = f (_optErasure o) <&> \ i -> o{ _optErasure = i }
+
+lensOptErasedMatches :: Lens' PragmaOptions _
+lensOptErasedMatches f o = f (_optErasedMatches o) <&> \ i -> o{ _optErasedMatches = i }
+
+lensOptEraseRecordParameters :: Lens' PragmaOptions _
+lensOptEraseRecordParameters f o = f (_optEraseRecordParameters o) <&> \ i -> o{ _optEraseRecordParameters = i }
+
+lensOptRewriting :: Lens' PragmaOptions _
+lensOptRewriting f o = f (_optRewriting o) <&> \ i -> o{ _optRewriting = i }
+
+lensOptCubical :: Lens' PragmaOptions _
+lensOptCubical f o = f (_optCubical o) <&> \ i -> o{ _optCubical = i }
+
+lensOptGuarded :: Lens' PragmaOptions _
+lensOptGuarded f o = f (_optGuarded o) <&> \ i -> o{ _optGuarded = i }
+
+lensOptFirstOrder :: Lens' PragmaOptions _
+lensOptFirstOrder f o = f (_optFirstOrder o) <&> \ i -> o{ _optFirstOrder = i }
+
+lensOptPostfixProjections :: Lens' PragmaOptions _
+lensOptPostfixProjections f o = f (_optPostfixProjections o) <&> \ i -> o{ _optPostfixProjections = i }
+
+lensOptKeepPatternVariables :: Lens' PragmaOptions _
+lensOptKeepPatternVariables f o = f (_optKeepPatternVariables o) <&> \ i -> o{ _optKeepPatternVariables = i }
+
+lensOptInferAbsurdClauses :: Lens' PragmaOptions _
+lensOptInferAbsurdClauses f o = f (_optInferAbsurdClauses o) <&> \ i -> o{ _optInferAbsurdClauses = i }
+
+lensOptInstanceSearchDepth :: Lens' PragmaOptions _
+lensOptInstanceSearchDepth f o = f (_optInstanceSearchDepth o) <&> \ i -> o{ _optInstanceSearchDepth = i }
+
+lensOptOverlappingInstances :: Lens' PragmaOptions _
+lensOptOverlappingInstances f o = f (_optOverlappingInstances o) <&> \ i -> o{ _optOverlappingInstances = i }
+
+lensOptQualifiedInstances :: Lens' PragmaOptions _
+lensOptQualifiedInstances f o = f (_optQualifiedInstances o) <&> \ i -> o{ _optQualifiedInstances = i }
+
+lensOptInversionMaxDepth :: Lens' PragmaOptions _
+lensOptInversionMaxDepth f o = f (_optInversionMaxDepth o) <&> \ i -> o{ _optInversionMaxDepth = i }
+
+lensOptSafe :: Lens' PragmaOptions _
+lensOptSafe f o = f (_optSafe o) <&> \ i -> o{ _optSafe = i }
+
+lensOptDoubleCheck :: Lens' PragmaOptions _
+lensOptDoubleCheck f o = f (_optDoubleCheck o) <&> \ i -> o{ _optDoubleCheck = i }
+
+lensOptSyntacticEquality :: Lens' PragmaOptions _
+lensOptSyntacticEquality f o = f (_optSyntacticEquality o) <&> \ i -> o{ _optSyntacticEquality = i }
+
+lensOptWarningMode :: Lens' PragmaOptions _
+lensOptWarningMode f o = f (_optWarningMode o) <&> \ i -> o{ _optWarningMode = i }
+
+lensOptCompileMain :: Lens' PragmaOptions _
+lensOptCompileMain f o = f (_optCompileMain o) <&> \ i -> o{ _optCompileMain = i }
+
+lensOptCaching :: Lens' PragmaOptions _
+lensOptCaching f o = f (_optCaching o) <&> \ i -> o{ _optCaching = i }
+
+lensOptCountClusters :: Lens' PragmaOptions _
+lensOptCountClusters f o = f (_optCountClusters o) <&> \ i -> o{ _optCountClusters = i }
+
+lensOptAutoInline :: Lens' PragmaOptions _
+lensOptAutoInline f o = f (_optAutoInline o) <&> \ i -> o{ _optAutoInline = i }
+
+lensOptPrintPatternSynonyms :: Lens' PragmaOptions _
+lensOptPrintPatternSynonyms f o = f (_optPrintPatternSynonyms o) <&> \ i -> o{ _optPrintPatternSynonyms = i }
+
+lensOptFastReduce :: Lens' PragmaOptions _
+lensOptFastReduce f o = f (_optFastReduce o) <&> \ i -> o{ _optFastReduce = i }
+
+lensOptCallByName :: Lens' PragmaOptions _
+lensOptCallByName f o = f (_optCallByName o) <&> \ i -> o{ _optCallByName = i }
+
+lensOptConfluenceCheck :: Lens' PragmaOptions _
+lensOptConfluenceCheck f o = f (_optConfluenceCheck o) <&> \ i -> o{ _optConfluenceCheck = i }
+
+lensOptCohesion :: Lens' PragmaOptions _
+lensOptCohesion f o = f (_optCohesion o) <&> \ i -> o{ _optCohesion = i }
+
+lensOptFlatSplit :: Lens' PragmaOptions _
+lensOptFlatSplit f o = f (_optFlatSplit o) <&> \ i -> o{ _optFlatSplit = i }
+
+lensOptImportSorts :: Lens' PragmaOptions _
+lensOptImportSorts f o = f (_optImportSorts o) <&> \ i -> o{ _optImportSorts = i }
+
+lensOptLoadPrimitives :: Lens' PragmaOptions _
+lensOptLoadPrimitives f o = f (_optLoadPrimitives o) <&> \ i -> o{ _optLoadPrimitives = i }
+
+lensOptAllowExec :: Lens' PragmaOptions _
+lensOptAllowExec f o = f (_optAllowExec o) <&> \ i -> o{ _optAllowExec = i }
+
+lensOptSaveMetas :: Lens' PragmaOptions _
+lensOptSaveMetas f o = f (_optSaveMetas o) <&> \ i -> o{ _optSaveMetas = i }
+
+lensOptShowIdentitySubstitutions :: Lens' PragmaOptions _
+lensOptShowIdentitySubstitutions f o = f (_optShowIdentitySubstitutions o) <&> \ i -> o{ _optShowIdentitySubstitutions = i }
+
+lensOptKeepCoveringClauses :: Lens' PragmaOptions _
+lensOptKeepCoveringClauses f o = f (_optKeepCoveringClauses o) <&> \ i -> o{ _optKeepCoveringClauses = i }
+
+lensOptLargeIndices :: Lens' PragmaOptions _
+lensOptLargeIndices f o = f (_optLargeIndices o) <&> \ i -> o{ _optLargeIndices = i }
+
+lensOptForcedArgumentRecursion :: Lens' PragmaOptions _
+lensOptForcedArgumentRecursion f o = f (_optForcedArgumentRecursion o) <&> \ i -> o{ _optForcedArgumentRecursion = i }
+
+
+-- | Map a function over the long options. Also removes the short options.
+--   Will be used to add the plugin name to the plugin options.
+mapFlag :: (String -> String) -> OptDescr a -> OptDescr a
+mapFlag f (Option _ long arg descr) = Option [] (map f long) arg descr
+
+defaultInteractionOptions :: PragmaOptions
+defaultInteractionOptions = defaultPragmaOptions
+
+defaultOptions :: CommandLineOptions
+defaultOptions = Options
+  { optProgramName      = "agda"
+  , optInputFile             = Nothing
+  , optIncludePaths          = []
+  , optAbsoluteIncludePaths  = []
+  , optLibraries             = []
+  , optOverrideLibrariesFile = Nothing
+  , optDefaultLibs           = True
+  , optUseLibs               = True
+  , optTraceImports          = 1
+  , optTrustedExecutables    = Map.empty
+  , optPrintAgdaDataDir      = False
+  , optPrintAgdaAppDir       = False
+  , optPrintVersion          = Nothing
+  , optPrintHelp             = Nothing
+  , optInteractive           = False
+  , optGHCiInteraction       = False
+  , optJSONInteraction       = False
+  , optExitOnError           = False
+  , optCompileDir            = Nothing
+  , optGenerateVimFile       = False
+  , optIgnoreInterfaces      = False
+  , optIgnoreAllInterfaces   = False
+  , optLocalInterfaces       = False
+  , optPragmaOptions         = defaultPragmaOptions
+  , optOnlyScopeChecking     = False
+  , optTransliterate         = False
+  , optDiagnosticsColour     = AutoColour
+  }
+
+defaultPragmaOptions :: PragmaOptions
+defaultPragmaOptions = PragmaOptions
+  { _optShowImplicit              = Default
+  , _optShowGeneralized           = Default
+  , _optShowIrrelevant            = Default
+  , _optUseUnicode                = Default -- UnicodeOk
+  , _optVerbose                   = Strict.Nothing
+  , _optProfiling                 = noProfileOptions
+  , _optProp                      = Default
+  , _optLevelUniverse             = Default
+  , _optTwoLevel                  = Default
+  , _optAllowUnsolved             = Default
+  , _optAllowIncompleteMatch      = Default
+  , _optPositivityCheck           = Default
+  , _optTerminationCheck          = Default
+  , _optTerminationDepth          = defaultCutOff
+  , _optUniverseCheck             = Default
+  , _optOmegaInOmega              = Default
+  , _optCumulativity              = Default
+  , _optSizedTypes                = Default
+  , _optGuardedness               = Default
+  , _optInjectiveTypeConstructors = Default
+  , _optUniversePolymorphism      = Default
+  , _optIrrelevantProjections     = Default
+  , _optExperimentalIrrelevance   = Default
+  , _optWithoutK                  = Default
+  , _optCubicalCompatible         = Default
+  , _optCopatterns                = Default
+  , _optPatternMatching           = Default
+  , _optExactSplit                = Default
+  , _optHiddenArgumentPuns        = Default
+  , _optEta                       = Default
+  , _optForcing                   = Default
+  , _optProjectionLike            = Default
+  , _optErasure                   = Default
+  , _optErasedMatches             = Default
+  , _optEraseRecordParameters     = Default
+  , _optRewriting                 = Default
+  , _optCubical                   = Nothing
+  , _optGuarded                   = Default
+  , _optFirstOrder                = Default
+  , _optPostfixProjections        = Default
+  , _optKeepPatternVariables      = Default
+  , _optInferAbsurdClauses        = Default
+  , _optInstanceSearchDepth       = 500
+  , _optOverlappingInstances      = Default
+  , _optQualifiedInstances        = Default
+  , _optInversionMaxDepth         = 50
+  , _optSafe                      = Default
+  , _optDoubleCheck               = Default
+  , _optSyntacticEquality         = Strict.Nothing
+  , _optWarningMode               = defaultWarningMode
+  , _optCompileMain               = Default
+  , _optCaching                   = Default
+  , _optCountClusters             = Default
+  , _optAutoInline                = Default
+  , _optPrintPatternSynonyms      = Default
+  , _optFastReduce                = Default
+  , _optCallByName                = Default
+  , _optConfluenceCheck           = Nothing
+  , _optCohesion                  = Default
+  , _optFlatSplit                 = Default
+  , _optImportSorts               = Default
+  , _optLoadPrimitives            = Default
+  , _optAllowExec                 = Default
+  , _optSaveMetas                 = Default
+  , _optShowIdentitySubstitutions = Default
+  , _optKeepCoveringClauses       = Default
+  , _optForcedArgumentRecursion   = Default
+  , _optLargeIndices              = Default
+  }
+
+-- | The options parse monad 'OptM' collects warnings that are not discarded
+--   when a fatal error occurrs
+newtype OptM a = OptM { unOptM :: ExceptT OptionError (Writer OptionWarnings) a }
+  deriving (Functor, Applicative, Monad, MonadError OptionError, MonadWriter OptionWarnings)
+
+type OptionError = String
+type OptionWarnings = [OptionWarning]
+
+runOptM :: OptM opts -> (Either OptionError opts, OptionWarnings)
+runOptM = runWriter . runExceptT . unOptM
+
+{- | @f :: Flag opts@  is an action on the option record that results from
+     parsing an option.  @f opts@ produces either an error message or an
+     updated options record
+-}
+type Flag opts = opts -> OptM opts
+
+-- | Warnings when parsing options.
+
+data OptionWarning
+  = OptionRenamed { oldOptionName :: String, newOptionName :: String }
+  deriving (Show, Generic)
+
+instance NFData OptionWarning
+
+instance Pretty OptionWarning where
+  pretty = \case
+    OptionRenamed old new -> hsep
+      [ "Option", name old, "is deprecated, please use", name new, "instead" ]
+    where
+    name = text . ("--" ++)
+
+optionWarningName :: OptionWarning -> WarningName
+optionWarningName = \case
+  OptionRenamed{} -> OptionRenamed_
+
+-- | Checks that the given options are consistent.
+--   Also makes adjustments (e.g. when one option implies another).
+
+checkOpts :: MonadError OptionError m => CommandLineOptions -> m CommandLineOptions
+checkOpts opts = do
+  -- NOTE: This is a temporary hold-out until --vim can be converted into a backend or plugin,
+  -- whose options compatibility currently is checked in `Agda.Compiler.Backend`.
+  --
+  -- Additionally, note that some options checking is performed in `Agda.Main`
+  -- in which the top-level frontend and backend interactors are selected.
+  --
+  -- Those checks are not represented here, because:
+  --   - They are used solely for selecting the initial executon mode; they
+  --     don't need to be checked on a per-module etc basis.
+  --   - I hope/expect that the presence of those specific flags will be eventually
+  --     abstracted out (like the Backends' internal flags), so that they are invisible
+  --     to the rest of the type-checking system.
+  when (optGenerateVimFile opts && optOnlyScopeChecking opts) $
+    throwError $ "The --only-scope-checking flag cannot be combined with --vim."
+
+  lensPragmaOptions checkPragmaOptions opts
+
+-- | Check for pragma option consistency and make adjustments.
+
+checkPragmaOptions :: MonadError OptionError m => PragmaOptions -> m PragmaOptions
+checkPragmaOptions opts = do
+
+  -- Check for errors in pragma options.
+
+  when ((optEraseRecordParameters `butNot` optErasure) opts) $
+    throwError
+      "The option --erase-record-parameters requires the use of --erasure"
+
+#ifndef COUNT_CLUSTERS
+  when (optCountClusters opts) $
+    throwError
+      "Cluster counting has not been enabled in this build of Agda."
+#endif
+
+  -- Perform corrections in pragma options.
+
+  return $ opts
+
+    -- -WTerminationIssue iff --termination-check
+    & conformWarningToOption TerminationIssue_ optTerminationCheck
+
+    -- -WNotStrictlyPositive iff --positivity-check
+    . conformWarningToOption NotStrictlyPositive_ optPositivityCheck
+
+    -- unsolvedWarnings iff --no-allow-unsolved-metas
+    . conformWarningsToOption unsolvedWarnings (not . optAllowUnsolved)
+
+    -- incompleteMatchWarnings iff --no-allow-incomplete-matches
+    . conformWarningsToOption incompleteMatchWarnings (not . optAllowIncompleteMatch)
+
+-- | Activate warning when and only when option is on.
+conformWarningToOption ::
+     WarningName
+       -- ^ Warning to toggle.
+  -> (PragmaOptions -> Bool)
+       -- ^ Which flag to conform to?
+  -> PragmaOptions
+       -- ^ Options to modify.
+  -> PragmaOptions
+       -- ^ Modified options.
+conformWarningToOption = conformWarningsToOption . Set.singleton
+
+-- | Activate warnings when option is on and deactivate them when option is off.
+conformWarningsToOption ::
+     Set WarningName
+       -- ^ Warnings to toggle.
+  -> (PragmaOptions -> Bool)
+       -- ^ Which flag to conform to?
+  -> PragmaOptions
+       -- ^ Options to modify.
+  -> PragmaOptions
+       -- ^ Modified options.
+conformWarningsToOption ws f opts =
+  over (lensOptWarningMode . warningSet) (if f opts then (`Set.union` ws) else (Set.\\ ws)) opts
+
+-- | Check for unsafe pragmas. Gives a list of used unsafe flags.
+
+unsafePragmaOptions :: PragmaOptions -> [String]
+unsafePragmaOptions opts =
+  [ "--allow-unsolved-metas"            | optAllowUnsolved opts                             ] ++
+  [ "--allow-incomplete-matches"        | optAllowIncompleteMatch opts                      ] ++
+  [ "--no-positivity-check"             | not (optPositivityCheck opts)                     ] ++
+  [ "--no-termination-check"            | not (optTerminationCheck opts)                    ] ++
+  [ "--type-in-type"                    | not (optUniverseCheck opts)                       ] ++
+  [ "--omega-in-omega"                  | optOmegaInOmega opts                              ] ++
+  [ "--sized-types"                     | optSizedTypes opts                                ] ++
+  [ "--injective-type-constructors"     | optInjectiveTypeConstructors opts                 ] ++
+  [ "--irrelevant-projections"          | optIrrelevantProjections opts                     ] ++
+  [ "--experimental-irrelevance"        | optExperimentalIrrelevance opts                   ] ++
+  [ "--rewriting"                       | optRewriting opts                                 ] ++
+  [ "--cubical-compatible and --with-K" | optCubicalCompatible opts, not (optWithoutK opts) ] ++
+  [ "--without-K and --flat-split"      | optWithoutK opts, optFlatSplit opts               ] ++
+  [ "--cumulativity"                    | optCumulativity opts                              ] ++
+  [ "--allow-exec"                      | optAllowExec opts                                 ] ++
+  [ "--no-load-primitives"              | not $ optLoadPrimitives opts                      ] ++
+  [ "--without-K and --large-indices"   | optWithoutK opts, optLargeIndices opts            ] ++
+  [ "--large-indices and --forced-argument-recursion"
+  | optLargeIndices opts, optForcedArgumentRecursion opts ] ++
+  []
+
+-- | This function returns 'True' if the file should be rechecked.
+
+recheckBecausePragmaOptionsChanged
+  :: PragmaOptions
+     -- ^ The options that were used to check the file.
+  -> PragmaOptions
+     -- ^ The options that are currently in effect.
+  -> Bool
+recheckBecausePragmaOptionsChanged used current =
+  blankOut used /= blankOut current
+  where
+  -- "Blank out" irrelevant options.
+  -- It does not matter what we replace them with, so we take the null value.
+  blankOut opts = opts
+    { _optShowImplicit              = empty
+    , _optShowIrrelevant            = empty
+    , _optVerbose                   = empty
+    , _optProfiling                 = empty
+    , _optPostfixProjections        = empty
+    , _optCompileMain               = empty
+    , _optCaching                   = empty
+    , _optCountClusters             = empty
+    , _optPrintPatternSynonyms      = empty
+    , _optShowIdentitySubstitutions = empty
+    , _optKeepPatternVariables      = empty
+    }
+
+-- | Infective or coinfective?
+
+data InfectiveCoinfective
+  = Infective
+  | Coinfective
+    deriving (Eq, Show, Generic)
+
+instance NFData InfectiveCoinfective
+
+-- | Descriptions of infective and coinfective options.
+
+data InfectiveCoinfectiveOption = ICOption
+  { icOptionActive :: PragmaOptions -> Bool
+    -- ^ Is the option active?
+  , icOptionDescription :: String
+    -- ^ A description of the option (typically a flag that activates
+    -- the option).
+  , icOptionKind :: InfectiveCoinfective
+    -- ^ Is the option (roughly speaking) infective or coinfective?
+  , icOptionOK :: PragmaOptions -> PragmaOptions -> Bool
+    -- ^ This function returns 'True' exactly when, from the
+    -- perspective of the option in question, the options in the
+    -- current module (the first argument) are compatible with the
+    -- options in a given imported module (the second argument).
+  , icOptionWarning :: TopLevelModuleName -> Doc
+    -- ^ A warning message that should be used if this option is not
+    -- used correctly. The given module name is the name of an
+    -- imported module for which 'icOptionOK' failed.
+  }
+
+-- | A standard infective option: If the option is active in an
+-- imported module, then it must be active in the current module.
+
+infectiveOption
+  :: (PragmaOptions -> Bool)
+     -- ^ Is the option active?
+  -> String
+    -- ^ A description of the option.
+  -> InfectiveCoinfectiveOption
+infectiveOption opt s = ICOption
+  { icOptionActive      = opt
+  , icOptionDescription = s
+  , icOptionKind        = Infective
+  , icOptionOK          = \current imported ->
+                           opt imported <= opt current
+  , icOptionWarning     = \m -> fsep $
+      pwords "Importing module" ++ [pretty m] ++ pwords "using the" ++
+      [text s] ++ pwords "flag from a module which does not."
+  }
+
+-- | A standard coinfective option: If the option is active in the
+-- current module, then it must be active in all imported modules.
+
+coinfectiveOption
+  :: (PragmaOptions -> Bool)
+     -- ^ Is the option active?
+  -> String
+    -- ^ A description of the option.
+  -> InfectiveCoinfectiveOption
+coinfectiveOption opt s = ICOption
+  { icOptionActive      = opt
+  , icOptionDescription = s
+  , icOptionKind        = Coinfective
+  , icOptionOK          = \current imported ->
+                           opt current <= opt imported
+  , icOptionWarning     = \m -> fsep $
+      pwords "Importing module" ++ [pretty m] ++
+      pwords "not using the" ++ [text s] ++
+      pwords "flag from a module which does."
+  }
+
+-- | Infective and coinfective options.
+--
+-- Note that @--cubical@ and @--erased-cubical@ are \"jointly
+-- infective\": if one of them is used in one module, then one or the
+-- other must be used in all modules that depend on this module.
+
+infectiveCoinfectiveOptions :: [InfectiveCoinfectiveOption]
+infectiveCoinfectiveOptions =
+  [ coinfectiveOption optSafe                 "--safe"
+  , coinfectiveOption optWithoutK             "--without-K"
+  , cubicalCompatible
+  , coinfectiveOption (not . optUniversePolymorphism)
+                                              "--no-universe-polymorphism"
+  , coinfectiveOption (not . optCumulativity) "--no-cumulativity"
+  , coinfectiveOption optLevelUniverse        "--level-universe"
+  , infectiveOption (isJust . optCubical)     "--cubical/--erased-cubical"
+  , infectiveOption optGuarded                "--guarded"
+  , infectiveOption optProp                   "--prop"
+  , infectiveOption optTwoLevel               "--two-level"
+  , infectiveOption optRewriting              "--rewriting"
+  , infectiveOption optSizedTypes             "--sized-types"
+  , infectiveOption optGuardedness            "--guardedness"
+  , infectiveOption optFlatSplit              "--flat-split"
+  , infectiveOption optCohesion               "--cohesion"
+  , infectiveOption optErasure                "--erasure"
+  , infectiveOption optErasedMatches          "--erased-matches"
+  ]
+  where
+  cubicalCompatible =
+    (coinfectiveOption optCubicalCompatible "--cubical-compatible")
+      { icOptionOK = \current imported ->
+        -- One must use --cubical-compatible in the imported module if
+        -- it is used in the current module, except if the current
+        -- module also uses --with-K and not --safe, and the imported
+        -- module uses --with-K.
+        if optCubicalCompatible current
+        then optCubicalCompatible imported
+               ||
+             not (optWithoutK imported)
+               &&
+             not (optWithoutK current)
+               &&
+             not (optSafe current)
+        else True
+      }
+
+inputFlag :: FilePath -> Flag CommandLineOptions
+inputFlag f o =
+    case optInputFile o of
+        Nothing  -> return $ o { optInputFile = Just f }
+        Just _   -> throwError "only one input file allowed"
+
+printAgdaDataDirFlag :: Flag CommandLineOptions
+printAgdaDataDirFlag o = return $ o { optPrintAgdaDataDir = True }
+
+printAgdaAppDirFlag :: Flag CommandLineOptions
+printAgdaAppDirFlag o = return $ o { optPrintAgdaAppDir = True }
+
+versionFlag :: Flag CommandLineOptions
+versionFlag o = return $ o { optPrintVersion = Just PrintAgdaVersion }
+
+numericVersionFlag :: Flag CommandLineOptions
+numericVersionFlag o = return $ o { optPrintVersion = Just PrintAgdaNumericVersion }
+
+helpFlag :: Maybe String -> Flag CommandLineOptions
+helpFlag Nothing    o = return $ o { optPrintHelp = Just GeneralHelp }
+helpFlag (Just str) o = case string2HelpTopic str of
+  Just hpt -> return $ o { optPrintHelp = Just (HelpFor hpt) }
+  Nothing -> throwError $ "unknown help topic " ++ str ++ " (available: " ++
+                           intercalate ", " (map fst allHelpTopics) ++ ")"
+
+safeFlag :: Flag PragmaOptions
+safeFlag o = do
+  return $ o { _optSafe        = Value True
+             , _optSizedTypes  = setDefault False (_optSizedTypes o)
+             }
+
+syntacticEqualityFlag :: Maybe String -> Flag PragmaOptions
+syntacticEqualityFlag s o =
+  case fuel of
+    Left err   -> throwError err
+    Right fuel -> return $ o { _optSyntacticEquality = fuel }
+  where
+  fuel = case s of
+    Nothing -> Right Strict.Nothing
+    Just s  -> case readMaybe s of
+      Just n | n >= 0 -> Right (Strict.Just n)
+      _               -> Left $ "Not a natural number: " ++ s
+
+ignoreInterfacesFlag :: Flag CommandLineOptions
+ignoreInterfacesFlag o = return $ o { optIgnoreInterfaces = True }
+
+ignoreAllInterfacesFlag :: Flag CommandLineOptions
+ignoreAllInterfacesFlag o = return $ o { optIgnoreAllInterfaces = True }
+
+localInterfacesFlag :: Flag CommandLineOptions
+localInterfacesFlag o = return $ o { optLocalInterfaces = True }
+
+traceImportsFlag :: Maybe String -> Flag CommandLineOptions
+traceImportsFlag arg o = do
+  mode <- case arg of
+            Nothing -> return 2
+            Just str -> case reads str :: [(Integer, String)] of
+                          [(n, "")] -> return n
+                          _ -> throwError $ "unknown printing option " ++ str ++ ". Please specify a number."
+  return $ o { optTraceImports = mode }
+
+diagnosticsColour :: Maybe String -> Flag CommandLineOptions
+diagnosticsColour arg o = case arg of
+  Just "auto"   -> pure o { optDiagnosticsColour = AutoColour }
+  Just "always" -> pure o { optDiagnosticsColour = AlwaysColour }
+  Just "never"  -> pure o { optDiagnosticsColour = NeverColour }
+  Just str -> throwError $ "unknown colour option " ++ str ++ ". Please specify one of auto, always, or never."
+  Nothing -> pure o { optDiagnosticsColour = AutoColour }
+
+-- | Side effect for setting '_optUseUnicode'.
+--
+unicodeOrAsciiEffect :: UnicodeOrAscii -> Flag PragmaOptions
+unicodeOrAsciiEffect a o = return $ UNSAFE.unsafePerformIO $ do
+  unsafeSetUnicodeOrAscii a
+  return o
+
+ghciInteractionFlag :: Flag CommandLineOptions
+ghciInteractionFlag o = return $ o { optGHCiInteraction = True }
+
+jsonInteractionFlag :: Flag CommandLineOptions
+jsonInteractionFlag o = return $ o { optJSONInteraction = True }
+
+interactionExitFlag :: Flag CommandLineOptions
+interactionExitFlag o = return $ o { optExitOnError = True }
+
+vimFlag :: Flag CommandLineOptions
+vimFlag o = return $ o { optGenerateVimFile = True }
+
+onlyScopeCheckingFlag :: Flag CommandLineOptions
+onlyScopeCheckingFlag o = return $ o { optOnlyScopeChecking = True }
+
+transliterateFlag :: Flag CommandLineOptions
+transliterateFlag o = return $ o { optTransliterate = True }
+
+withKFlag :: Flag PragmaOptions
+withKFlag =
+  -- with-K is the opposite of --without-K, so collapse default when disabling --without-K
+  (lensOptWithoutK $ lensCollapseDefault $ const $ pure False)
+  >=>
+  -- with-K only restores any unsetting of --erased-matches, so keep its default
+  (lensOptErasedMatches $ lensKeepDefault $ const $ pure True)
+
+
+withoutKFlag :: Flag PragmaOptions
+withoutKFlag o = return $ o
+  { _optWithoutK                = Value True
+  , _optFlatSplit               = setDefault False $ _optFlatSplit o
+  , _optErasedMatches           = setDefault False $ _optErasedMatches o
+  }
+
+cubicalCompatibleFlag :: Flag PragmaOptions
+cubicalCompatibleFlag o =
+  return $ o
+  { _optCubicalCompatible       = Value True
+  , _optWithoutK                = setDefault True  $ _optWithoutK o
+  , _optFlatSplit               = setDefault False $ _optFlatSplit o
+  , _optErasedMatches           = setDefault False $ _optErasedMatches o
+  }
+
+cubicalFlag
+  :: Cubical  -- ^ Which variant of Cubical Agda?
+  -> Flag PragmaOptions
+cubicalFlag variant o =
+  return $ o
+  { _optCubical                 = Just variant
+  , _optCubicalCompatible       = setDefault True  $ _optCubicalCompatible o
+  , _optWithoutK                = setDefault True  $ _optWithoutK o
+  , _optTwoLevel                = setDefault True  $ _optTwoLevel o
+  , _optFlatSplit               = setDefault False $ _optFlatSplit o
+  , _optErasedMatches           = setDefault False $ _optErasedMatches o
+  }
+
+instanceDepthFlag :: String -> Flag PragmaOptions
+instanceDepthFlag s o = do
+  d <- integerArgument "--instance-search-depth" s
+  return $ o { _optInstanceSearchDepth = d }
+
+inversionMaxDepthFlag :: String -> Flag PragmaOptions
+inversionMaxDepthFlag s o = do
+  d <- integerArgument "--inversion-max-depth" s
+  return $ o { _optInversionMaxDepth = d }
+
+interactiveFlag :: Flag CommandLineOptions
+interactiveFlag  o = return $ o { optInteractive = True }
+
+compileDirFlag :: FilePath -> Flag CommandLineOptions
+compileDirFlag f o = return $ o { optCompileDir = Just f }
+
+includeFlag :: FilePath -> Flag CommandLineOptions
+includeFlag d o = return $ o { optIncludePaths = d : optIncludePaths o }
+
+libraryFlag :: String -> Flag CommandLineOptions
+libraryFlag s o = return $ o { optLibraries = optLibraries o ++ [s] }
+
+overrideLibrariesFileFlag :: String -> Flag CommandLineOptions
+overrideLibrariesFileFlag s o =
+  return $ o
+    { optOverrideLibrariesFile = Just s
+    , optUseLibs = True
+    }
+
+noDefaultLibsFlag :: Flag CommandLineOptions
+noDefaultLibsFlag o = return $ o { optDefaultLibs = False }
+
+noLibsFlag :: Flag CommandLineOptions
+noLibsFlag o = return $ o { optUseLibs = False }
+
+verboseFlag :: String -> Flag PragmaOptions
+verboseFlag s o =
+    do  (k,n) <- parseVerbose s
+        return $
+          o { _optVerbose =
+                Strict.Just $ Trie.insert k n $
+                case _optVerbose o of
+                  Strict.Nothing -> Trie.singleton [] 1
+                  Strict.Just v  -> v
+            }
+  where
+    parseVerbose :: String -> OptM ([VerboseKeyItem], VerboseLevel)
+    parseVerbose s = case parseVerboseKey s of
+      []  -> usage
+      s0:ss0 -> do
+        let (ss, s) = initLast1 s0 ss0
+        -- The last entry must be a number.
+        n <- maybe usage return $ readMaybe $ toList s
+        return (ss, n)
+    usage = throwError "argument to verbose should be on the form x.y.z:N or N"
+
+profileFlag :: String -> Flag PragmaOptions
+profileFlag s o =
+  case addProfileOption s (_optProfiling o) of
+    Left err   -> throwError err
+    Right prof -> pure o{ _optProfiling = prof }
+
+warningModeFlag :: String -> Flag PragmaOptions
+warningModeFlag s o = case warningModeUpdate s of
+  Right upd -> return $ o { _optWarningMode = upd (_optWarningMode o) }
+  Left err  -> throwError $ prettyWarningModeError err ++ " See --help=warning."
+
+terminationDepthFlag :: String -> Flag PragmaOptions
+terminationDepthFlag s o =
+    do k <- maybe usage return $ readMaybe s
+       when (k < 1) $ usage -- or: turn termination checking off for 0
+       return $ o { _optTerminationDepth = CutOff $ k-1 }
+    where usage = throwError "argument to termination-depth should be >= 1"
+
+confluenceCheckFlag :: ConfluenceCheck -> Flag PragmaOptions
+confluenceCheckFlag f o = return $ o { _optConfluenceCheck = Just f }
+
+noConfluenceCheckFlag :: Flag PragmaOptions
+noConfluenceCheckFlag o = return $ o { _optConfluenceCheck = Nothing }
+
+exactSplitFlag :: Bool -> Flag PragmaOptions
+exactSplitFlag b o = do
+  return $ conformWarningsToOption exactSplitWarnings (const b)
+         $ o { _optExactSplit  = Value b }
+
+
+integerArgument :: String -> String -> OptM Int
+integerArgument flag s = maybe usage return $ readMaybe s
+  where
+  usage = throwError $ "option '" ++ flag ++ "' requires an integer argument"
+
+standardOptions :: [OptDescr (Flag CommandLineOptions)]
+standardOptions =
+    [ Option ['V']  ["version"] (NoArg versionFlag)
+                    ("print version information and exit")
+
+    , Option []     ["numeric-version"] (NoArg numericVersionFlag)
+                    ("print version number and exit")
+
+    , Option ['?']  ["help"]    (OptArg helpFlag "TOPIC") $ concat
+                    [ "print help and exit; available "
+                    , singPlural allHelpTopics "TOPIC" "TOPICs"
+                    , ": "
+                    , intercalate ", " $ map fst allHelpTopics
+                    ]
+
+    , Option []     ["print-agda-dir"] (NoArg printAgdaDataDirFlag)
+                    ("print the Agda data directory exit")
+
+    , Option []     ["print-agda-app-dir"] (NoArg printAgdaAppDirFlag)
+                    ("print $AGDA_DIR and exit")
+
+    , Option []     ["print-agda-data-dir"] (NoArg printAgdaDataDirFlag)
+                    ("print the Agda data directory exit")
+
+
+    , Option ['I']  ["interactive"] (NoArg interactiveFlag)
+                    "start in interactive mode"
+    , Option []     ["interaction"] (NoArg ghciInteractionFlag)
+                    "for use with the Emacs mode"
+    , Option []     ["interaction-json"] (NoArg jsonInteractionFlag)
+                    "for use with other editors such as Atom"
+    , Option []     ["interaction-exit-on-error"]
+                    (NoArg interactionExitFlag)
+                    "exit if a type error is encountered"
+
+    , Option []     ["compile-dir"] (ReqArg compileDirFlag "DIR")
+                    ("directory for compiler output (default: the project root)")
+
+    , Option []     ["trace-imports"] (OptArg traceImportsFlag "LEVEL")
+                    ("print information about accessed modules during type-checking (where LEVEL=0|1|2|3, default: 2)")
+
+    , Option []     ["vim"] (NoArg vimFlag)
+                    "generate Vim highlighting files"
+    , Option []     ["ignore-interfaces"] (NoArg ignoreInterfacesFlag)
+                    "ignore interface files (re-type check everything)"
+    , Option []     ["local-interfaces"] (NoArg localInterfacesFlag)
+                    "put new interface files next to the Agda files they correspond to"
+    , Option ['i']  ["include-path"] (ReqArg includeFlag "DIR")
+                    "look for imports in DIR"
+    , Option ['l']  ["library"] (ReqArg libraryFlag "LIB")
+                    "use library LIB"
+    , Option []     ["library-file"] (ReqArg overrideLibrariesFileFlag "FILE")
+                    "use FILE instead of the standard libraries file"
+    , Option []     ["no-libraries"] (NoArg noLibsFlag)
+                    "don't use any library files"
+    , Option []     ["no-default-libraries"] (NoArg noDefaultLibsFlag)
+                    "don't use default libraries"
+    , Option []     ["only-scope-checking"] (NoArg onlyScopeCheckingFlag)
+                    "only scope-check the top-level module, do not type-check it"
+    , Option []     ["transliterate"] (NoArg transliterateFlag)
+                    "transliterate unsupported code points when printing to stdout/stderr"
+    , Option []     ["colour", "color"] (OptArg diagnosticsColour "always|auto|never")
+                    ("whether or not to colour diagnostics output. The default is auto.")
+    ] ++ map (fmap lensPragmaOptions) pragmaOptions
+
+-- | Defined locally here since module ''Agda.Interaction.Options.Lenses''
+--   has cyclic dependency.
+lensPragmaOptions :: Lens' CommandLineOptions PragmaOptions
+lensPragmaOptions f st = f (optPragmaOptions st) <&> \ opts -> st { optPragmaOptions = opts }
+
+-- | Command line options of previous versions of Agda.
+--   Should not be listed in the usage info, put parsed by GetOpt for good error messaging.
+deadStandardOptions :: [OptDescr (Flag CommandLineOptions)]
+deadStandardOptions =
+    [ removedOption "sharing"    msgSharing
+    , removedOption "no-sharing" msgSharing
+    , Option []     ["ignore-all-interfaces"] (NoArg ignoreAllInterfacesFlag) -- not deprecated! Just hidden
+                    "ignore all interface files (re-type check everything, including builtin files)"
+      -- https://github.com/agda/agda/issues/3522#issuecomment-461010898
+      -- The option is "developer only", so it is hidden.
+      -- However, it is documented in the user manual.
+    ] ++ map (fmap lensPragmaOptions) deadPragmaOptions
+  where
+    msgSharing = "(in favor of the Agda abstract machine)"
+
+-- | Construct a flag of type @WithDefault _@
+--
+pragmaFlag :: (IsBool a, KnownBool b)
+  => String
+       -- ^ Long option name.  Prepended with @no-@ for negative version.
+  -> Lens' PragmaOptions (WithDefault' a b)
+       -- ^ Field to switch.
+  -> String
+       -- ^ Explanation for positive option.
+  -> String
+       -- ^ Additional info for positive option (not repeated for negative option).
+  -> Maybe String
+       -- ^ Explanation for negative option.
+  -> [OptDescr (Flag PragmaOptions)]
+pragmaFlag long field = pragmaFlag' long field (const return)
+
+-- | Construct a flag of type @WithDefault _@
+--
+pragmaFlag' :: (IsBool a, KnownBool b)
+  => String
+       -- ^ Long option name.  Prepended with @no-@ for negative version.
+  -> Lens' PragmaOptions (WithDefault' a b)
+       -- ^ Field to switch.
+  -> (a -> Flag PragmaOptions)
+       -- ^ Given the new value, perform additional effect (can override field setting).
+  -> String
+       -- ^ Explanation for positive option.
+  -> String
+       -- ^ Additional info for positive option (not repeated for negative option).
+  -> Maybe String
+       -- ^ Explanation for negative option.
+  -> [OptDescr (Flag PragmaOptions)]
+       -- ^ Pair of option descriptors (positive, negative)
+pragmaFlag' long field = pragmaFlagBool' long (field . lensCollapseDefault)
+
+-- | Construct a flag of type 'IsBool'.
+--
+pragmaFlagBool :: (IsBool a)
+  => String
+       -- ^ Long option name.  Prepended with @no-@ for negative version.
+  -> Lens' PragmaOptions a
+       -- ^ Field to switch.
+  -> String
+       -- ^ Explanation for positive option.
+  -> String
+       -- ^ Additional info for positive option (not repeated for negative option).
+  -> Maybe String
+       -- ^ Explanation for negative option.
+  -> [OptDescr (Flag PragmaOptions)]
+pragmaFlagBool long field = pragmaFlagBool' long field (const return)
+
+-- | Construct a flag of type 'IsBool' with extra effect.
+--
+pragmaFlagBool' :: IsBool a
+  => String
+       -- ^ Long option name.  Prepended with @no-@ for negative version.
+  -> Lens' PragmaOptions a
+       -- ^ Field to switch.
+  -> (a -> Flag PragmaOptions)
+       -- ^ Given the new value, perform additional effect (can override field setting).
+  -> String
+       -- ^ Explanation for positive option.
+  -> String
+       -- ^ Additional info for positive option (not repeated for negative option).
+  -> Maybe String
+       -- ^ Explanation for negative option.
+  -> [OptDescr (Flag PragmaOptions)]
+       -- ^ Pair of option descriptors (positive, negative)
+pragmaFlagBool' long field effect pos info neg =
+  [ Option [] [no b long] (flag b) (def b $ expl b) | b <- [True,False] ]
+  where
+  b0     = defaultPragmaOptions ^. field
+  no   b = applyUnless b ("no-" ++)
+  flag b = NoArg $ effect a . set field a
+    where a = fromBool b
+  def  b = applyWhen (fromBool b == b0) (++ " (default)")
+  expl b = if b then unwords1 [pos, info] else fromMaybe ("do not " ++ pos) neg
+
+
+pragmaOptions :: [OptDescr (Flag PragmaOptions)]
+pragmaOptions = concat
+  [ pragmaFlag      "show-implicit" lensOptShowImplicit
+                    "show implicit arguments when printing" ""
+                    Nothing
+  , pragmaFlag      "show-irrelevant" lensOptShowIrrelevant
+                    "show irrelevant arguments when printing" ""
+                    Nothing
+  , pragmaFlag      "show-identity-substitutions" lensOptShowIdentitySubstitutions
+                    "show all arguments of metavariables when printing terms" ""
+                    Nothing
+  , pragmaFlag'     "unicode" lensOptUseUnicode unicodeOrAsciiEffect
+                    "use unicode characters when printing terms" ""
+                    Nothing
+  , [ Option ['v']  ["verbose"] (ReqArg verboseFlag "N")
+                    "set verbosity level to N. Only has an effect if Agda was built with the \"debug\" flag."
+    , Option []     ["profile"] (ReqArg profileFlag "TYPE")
+                    ("turn on profiling for TYPE (where TYPE=" ++ intercalate "|" validProfileOptionStrings ++ ")")
+    ]
+  , pragmaFlag      "allow-unsolved-metas" lensOptAllowUnsolved
+                    "succeed and create interface file regardless of unsolved meta variables" ""
+                    Nothing
+  , pragmaFlag      "allow-incomplete-matches" lensOptAllowIncompleteMatch
+                    "succeed and create interface file regardless of incomplete pattern matches" ""
+                    Nothing
+  , pragmaFlag      "positivity-check" lensOptPositivityCheck
+                    "warn about not strictly positive data types" ""
+                    Nothing
+  , pragmaFlag      "termination-check" lensOptTerminationCheck
+                    "warn about possibly nonterminating code" ""
+                    Nothing
+  , [ Option []     ["termination-depth"] (ReqArg terminationDepthFlag "N")
+                    "allow termination checker to count decrease/increase upto N (default N=1)"
+    ]
+  , pragmaFlag      "type-in-type" lensOptNoUniverseCheck
+                    "ignore universe levels"  "(this makes Agda inconsistent)"
+                    Nothing
+  , pragmaFlag      "omega-in-omega" lensOptOmegaInOmega
+                    "enable typing rule Setω : Setω" "(this makes Agda inconsistent)"
+                    Nothing
+  , pragmaFlag      "cumulativity" lensOptCumulativity
+                    "enable subtyping of universes" "(e.g. Set =< Set₁)"
+                    $ Just "disable subtyping of universes"
+  , pragmaFlag      "prop" lensOptProp
+                    "enable the use of the Prop universe" ""
+                    $ Just "disable the use of the Prop universe"
+  , pragmaFlag      "level-universe" lensOptLevelUniverse
+                    "place type Level in a dedicated LevelUniv universe" ""
+                    Nothing
+  , pragmaFlag      "two-level" lensOptTwoLevel
+                    "enable the use of SSet* universes" ""
+                    Nothing
+  , pragmaFlag      "sized-types" lensOptSizedTypes
+                    "enable sized types" "(inconsistent with --guardedness)"
+                    $ Just "disable sized types"
+  , pragmaFlag      "cohesion" lensOptCohesion
+                    "enable the cohesion modalities" "(in particular @flat)"
+                    Nothing
+  , pragmaFlag      "flat-split" lensOptFlatSplit
+                    "allow splitting on `(@flat x : A)' arguments" "(implies --cohesion)"
+                    Nothing
+  , pragmaFlag      "guardedness" lensOptGuardedness
+                    "enable constructor-based guarded corecursion" "(inconsistent with --sized-types)"
+                    $ Just "disable constructor-based guarded corecursion"
+  , pragmaFlag      "injective-type-constructors" lensOptInjectiveTypeConstructors
+                    "enable injective type constructors" "(makes Agda anti-classical and possibly inconsistent)"
+                    $ Just "disable injective type constructors"
+  , pragmaFlag      "universe-polymorphism" lensOptUniversePolymorphism
+                    "enable universe polymorphism" ""
+                    $ Just "disable universe polymorphism"
+  , pragmaFlag      "irrelevant-projections" lensOptIrrelevantProjections
+                    "enable projection of irrelevant record fields and similar irrelevant definitions" "(inconsistent)"
+                    $ Just "disable projection of irrelevant record fields and similar irrelevant definitions"
+  , pragmaFlag      "experimental-irrelevance" lensOptExperimentalIrrelevance
+                    "enable potentially unsound irrelevance features" "(irrelevant levels, irrelevant data matching)"
+                    Nothing
+  , [ Option []     ["with-K"] (NoArg withKFlag)
+                    "enable the K rule in pattern matching (default)"
+    , Option []     ["cubical-compatible"] (NoArg cubicalCompatibleFlag)
+                    "turn on generation of auxiliary code required for --cubical, implies --without-K"
+    , Option []     ["without-K"] (NoArg withoutKFlag)
+                    "turn on checks to make code compatible with HoTT (e.g. disabling the K rule). Implies --no-flat-split."
+    ]
+  , pragmaFlag      "copatterns" lensOptCopatterns
+                    "enable definitions by copattern matching" ""
+                    $ Just "disable definitions by copattern matching"
+  , pragmaFlag      "pattern-matching" lensOptPatternMatching
+                    "enable pattern matching" ""
+                    $ Just "disable pattern matching completely"
+  , [ Option []     ["exact-split"] (NoArg $ exactSplitFlag True)
+                    "require all clauses in a definition to hold as definitional equalities (unless marked CATCHALL)"
+    , Option []     ["no-exact-split"] (NoArg $ exactSplitFlag False)
+                    "do not require all clauses in a definition to hold as definitional equalities (default)"
+    ]
+  , pragmaFlag      "hidden-argument-puns" lensOptHiddenArgumentPuns
+                    "interpret the patterns {x} and {{x}} as puns" ""
+                    Nothing
+  , pragmaFlag      "eta-equality" lensOptEta
+                    "default records to eta-equality" ""
+                    $ Just "default records to no-eta-equality"
+  , pragmaFlag      "forcing" lensOptForcing
+                    "enable the forcing analysis for data constructors" "(optimisation)"
+                    $ Just "disable the forcing analysis"
+  , pragmaFlag      "projection-like" lensOptProjectionLike
+                    "enable the analysis whether function signatures liken those of projections" "(optimisation)"
+                    $ Just "disable the projection-like analysis"
+  , pragmaFlag      "erasure" lensOptErasure
+                    "enable erasure" ""
+                    Nothing
+  , pragmaFlag      "erased-matches" lensOptErasedMatches
+                    "allow matching in erased positions for single-constructor types" "(implies --erasure if supplied explicitly)"
+                    Nothing
+  , pragmaFlag      "erase-record-parameters" lensOptEraseRecordParameters
+                    "mark all parameters of record modules as erased" "(implies --erasure)"
+                    Nothing
+  , pragmaFlag      "rewriting" lensOptRewriting
+                    "enable declaration and use of REWRITE rules" ""
+                    $ Just "disable declaration and use of REWRITE rules"
+  , [ Option []     ["local-confluence-check"] (NoArg $ confluenceCheckFlag LocalConfluenceCheck)
+                    "enable checking of local confluence of REWRITE rules"
+    , Option []     ["confluence-check"] (NoArg $ confluenceCheckFlag GlobalConfluenceCheck)
+                    "enable global confluence checking of REWRITE rules (more restrictive than --local-confluence-check)"
+    , Option []     ["no-confluence-check"] (NoArg noConfluenceCheckFlag)
+                    "disable confluence checking of REWRITE rules (default)"
+    , Option []     ["cubical"] (NoArg $ cubicalFlag CFull)
+                    "enable cubical features (e.g. overloads lambdas for paths), implies --cubical-compatible"
+    , Option []     ["erased-cubical"] (NoArg $ cubicalFlag CErased)
+                    "enable cubical features (some only in erased settings), implies --cubical-compatible"
+    ]
+  , pragmaFlag      "guarded" lensOptGuarded
+                    "enable @lock/@tick attributes" ""
+                    $ Just "disable @lock/@tick attributes"
+  , lossyUnificationOption
+  , pragmaFlag      "postfix-projections" lensOptPostfixProjections
+                    "prefer postfix projection notation" ""
+                    $ Just "prefer prefix projection notation"
+  , pragmaFlag      "keep-pattern-variables" lensOptKeepPatternVariables
+                    "don't replace variables with dot patterns during case splitting" ""
+                    $ Just "replace variables with dot patterns during case splitting"
+  , pragmaFlag      "infer-absurd-clauses" lensOptInferAbsurdClauses
+                    "eliminate absurd clauses in case splitting and coverage checking" ""
+                    $ Just "do not automatically eliminate absurd clauses in case splitting and coverage checking (can speed up type-checking)"
+  , [ Option []     ["instance-search-depth"] (ReqArg instanceDepthFlag "N")
+                    "set instance search depth to N (default: 500)"
+    ]
+  , pragmaFlag      "overlapping-instances" lensOptOverlappingInstances
+                    "consider recursive instance arguments during pruning of instance candidates" ""
+                    Nothing
+  , pragmaFlag      "qualified-instances" lensOptQualifiedInstances
+                    "use instances with qualified names" ""
+                    Nothing
+  , [ Option []     ["inversion-max-depth"] (ReqArg inversionMaxDepthFlag "N")
+                    "set maximum depth for pattern match inversion to N (default: 50)"
+    , Option []     ["safe"] (NoArg safeFlag)
+                    "disable postulates, unsafe OPTION pragmas and primEraseEquality, implies --no-sized-types"
+    ]
+  , pragmaFlag      "double-check" lensOptDoubleCheck
+                    "enable double-checking of all terms using the internal typechecker" ""
+                    $ Just "disable double-checking of terms"
+  , [ Option []     ["no-syntactic-equality"] (NoArg $ syntacticEqualityFlag (Just "0"))
+                    "disable the syntactic equality shortcut in the conversion checker"
+    , Option []     ["syntactic-equality"] (OptArg syntacticEqualityFlag "FUEL")
+                    "give the syntactic equality shortcut FUEL units of fuel (default: unlimited)"
+    , Option ['W']  ["warning"] (ReqArg warningModeFlag "FLAG")
+                    ("set warning flags. See --help=warning.")
+    ]
+  , pragmaFlag      "main" lensOptCompileMain
+                    "treat the requested module as the main module of a program when compiling" ""
+                    Nothing
+  , pragmaFlag      "caching" lensOptCaching
+                    "enable caching of typechecking" ""
+                    $ Just "disable caching of typechecking"
+  , pragmaFlag      "count-clusters" lensOptCountClusters
+                    "count extended grapheme clusters when generating LaTeX"
+                    ("(note that this flag " ++
+#ifdef COUNT_CLUSTERS
+                      "is not enabled in all builds"
+#else
+                      "has not been enabled in this build"
+#endif
+                      ++ " of Agda)")
+                    Nothing
+  , pragmaFlag      "auto-inline" lensOptAutoInline
+                    "enable automatic compile-time inlining" ""
+                    $ Just "disable automatic compile-time inlining, only definitions marked INLINE will be inlined"
+  , pragmaFlag      "print-pattern-synonyms" lensOptPrintPatternSynonyms
+                    "keep pattern synonyms when printing terms" ""
+                    $ Just "expand pattern synonyms when printing terms"
+  , pragmaFlag      "fast-reduce" lensOptFastReduce
+                    "enable reduction using the Agda Abstract Machine" ""
+                    $ Just "disable reduction using the Agda Abstract Machine"
+  , pragmaFlag      "call-by-name" lensOptCallByName
+                    "use call-by-name evaluation instead of call-by-need" ""
+                    $ Just "use call-by-need evaluation"
+
+  , pragmaFlag      "import-sorts" lensOptImportSorts
+                    "implicitly import Agda.Primitive using (Set; Prop) at the start of each top-level module" ""
+                    $ Just "disable the implicit import of Agda.Primitive using (Set; Prop) at the start of each top-level module"
+  , pragmaFlag      "load-primitives" lensOptLoadPrimitives
+                    "load primitives modules" ""
+                    $ Just "disable loading of primitive modules completely (implies --no-import-sorts)"
+  , pragmaFlag      "allow-exec" lensOptAllowExec
+                    "allow system calls to trusted executables with primExec" ""
+                    Nothing
+  , pragmaFlag      "save-metas" lensOptSaveMetas
+                    "save meta-variables" ""
+                    Nothing
+  , pragmaFlag      "keep-covering-clauses" lensOptKeepCoveringClauses
+                    "do not discard covering clauses" "(required for some external backends)"
+                    $ Just "discard covering clauses"
+  , pragmaFlag      "large-indices" lensOptLargeIndices
+                    "allow constructors with large indices" ""
+                    $ Just "always check that constructor arguments live in universes compatible with that of the datatype"
+  , pragmaFlag      "forced-argument-recursion" lensOptForcedArgumentRecursion
+                    "allow recursion on forced constructor arguments" ""
+                    Nothing
+  ]
+
+pragmaOptionDefault :: KnownBool b => (PragmaOptions -> WithDefault b) -> Bool -> String
+pragmaOptionDefault f b =
+  if b == collapseDefault (f defaultPragmaOptions) then " (default)" else ""
+
+lossyUnificationOption :: [OptDescr (Flag PragmaOptions)]
+lossyUnificationOption =
+  pragmaFlag "lossy-unification" lensOptFirstOrder
+    "enable heuristically unifying `f es = f es'` by unifying `es = es'`"
+    "even when it could lose solutions"
+    Nothing
+
+-- | Pragma options of previous versions of Agda.
+--   Should not be listed in the usage info, put parsed by GetOpt for good error messaging.
+deadPragmaOptions :: [OptDescr (Flag PragmaOptions)]
+deadPragmaOptions = concat
+  [ map (uncurry removedOption)
+    [ ("guardedness-preserving-type-constructors"
+      , "")
+    , ("no-coverage-check"
+      , inVersion "2.5.1") -- see issue #1918
+    , ("no-sort-comparison"
+      , "")
+    , ("subtyping"
+      , inVersion "2.6.3") -- see issue #5427
+    , ("no-subtyping"
+      , inVersion "2.6.3") -- see issue #5427
+    , ("no-flat-split", inVersion "2.6.3")  -- See issue #6263.
+    ]
+  , map (uncurry renamedNoArgOption)
+    [ ( "experimental-lossy-unification"
+      , headWithDefault __IMPOSSIBLE__ lossyUnificationOption
+      )
+    ]
+  ]
+  where
+    inVersion = ("in version " ++)
+
+-- | Generate a dead options that just error out saying this option has been removed.
+removedOption ::
+     String
+       -- ^ The name of the removed option.
+  -> String
+       -- ^ Optional: additional remark, like in which version the option was removed.
+  -> OptDescr (Flag a)
+removedOption name remark = Option [] [name] (NoArg $ const $ throwError msg) msg
+  where
+  msg = unwords ["Option", "--" ++ name, "has been removed", remark]
+
+-- | Generate a deprecated option that resolves to another option.
+renamedNoArgOption ::
+     String
+       -- ^ The deprecated long option name.
+  -> OptDescr (Flag a)
+       -- ^ The new option.
+  -> OptDescr (Flag a)
+       -- ^ The old option which additionally emits a 'RenamedOption' warning.
+renamedNoArgOption old = \case
+  Option _ [new] (NoArg flag) description ->
+    Option [] [old] (NoArg flag') $ concat [description, " (DEPRECATED, use --", new, ")"]
+    where
+    flag' o = tell1 (OptionRenamed old new) >> flag o
+  _ -> __IMPOSSIBLE__
+
+-- | Used for printing usage info.
+--   Does not include the dead options.
+standardOptions_ :: [OptDescr ()]
+standardOptions_ = map void standardOptions
+
+-- | Simple interface for System.Console.GetOpt
+--   Could be moved to Agda.Utils.Options (does not exist yet)
+getOptSimple
+  :: [String]               -- ^ command line argument words
+  -> [OptDescr (Flag opts)] -- ^ options handlers
+  -> (String -> Flag opts)  -- ^ handler of non-options (only one is allowed)
+  -> Flag opts              -- ^ combined opts data structure transformer
+getOptSimple argv opts fileArg = \ defaults ->
+  case getOpt' (ReturnInOrder fileArg) opts argv of
+    (o, _, []          , [] )  -> foldl (>>=) (return defaults) o
+    (_, _, unrecognized, errs) -> throwError $ umsg ++ emsg
+
+      where
+      ucap = "Unrecognized " ++ plural unrecognized "option" ++ ":"
+      ecap = plural errs "Option error" ++ ":"
+      umsg = if null unrecognized then "" else unlines $
+       ucap : map suggest unrecognized
+      emsg = if null errs then "" else unlines $
+       ecap : errs
+      plural [_] x = x
+      plural _   x = x ++ "s"
+
+      -- Suggest alternatives that are at most 3 typos away
+
+      longopts :: [String]
+      longopts = map ("--" ++) $ concatMap (\ (Option _ long _ _) -> long) opts
+
+      dist :: String -> String -> Int
+      dist s t = restrictedDamerauLevenshteinDistance defaultEditCosts s t
+
+      close :: String -> String -> Maybe (Int, String)
+      close s t = let d = dist s t in if d <= 3 then Just (d, t) else Nothing
+
+      closeopts :: String -> [(Int, String)]
+      closeopts s = mapMaybe (close s) longopts
+
+      alts :: String -> [List1 String]
+      alts s = map (fmap snd) $ List1.groupOn fst $ closeopts s
+
+      suggest :: String -> String
+      suggest s = case alts s of
+        []     -> s
+        as : _ -> s ++ " (did you mean " ++ sugs as ++ " ?)"
+
+      sugs :: List1 String -> String
+      sugs (a :| []) = a
+      sugs as  = "any of " ++ List1.unwords as
+
+-- | Parse options from an options pragma.
+parsePragmaOptions
+  :: OptionsPragma
+     -- ^ Pragma options.
+  -> CommandLineOptions
+     -- ^ Command-line options which should be updated.
+  -> OptM PragmaOptions
+parsePragmaOptions argv opts = do
+  ps <- getOptSimple
+          (pragmaStrings argv)
+          (deadPragmaOptions ++ pragmaOptions)
+          (\s _ -> throwError $ "Bad option in pragma: " ++ s)
+          (optPragmaOptions opts)
+  checkPragmaOptions ps
+
+-- | Parse options for a plugin.
+parsePluginOptions :: [String] -> [OptDescr (Flag opts)] -> Flag opts
+parsePluginOptions argv opts =
+  getOptSimple argv opts
+    (\s _ -> throwError $
+               "Internal error: Flag " ++ s ++ " passed to a plugin")
+
+-- | The usage info message. The argument is the program name (probably
+--   agda).
+usage :: [OptDescr ()] -> String -> Help -> String
+usage options progName GeneralHelp = usageInfo (header progName) options
+    where
+        header progName = unlines [ "Agda version " ++ version, ""
+                                  , "Usage: " ++ progName ++ " [OPTIONS...] [FILE]" ]
+
+usage options progName (HelpFor topic) = helpTopicUsage topic
+
+-- | Removes RTS options from a list of options.
+
+stripRTS :: [String] -> [String]
+stripRTS [] = []
+stripRTS ("--RTS" : argv) = argv
+stripRTS (arg : argv)
+  | is "+RTS" arg = stripRTS $ drop 1 $ dropWhile (not . is "-RTS") argv
+  | otherwise     = arg : stripRTS argv
+  where
+    is x arg = [x] == take 1 (words arg)
diff --git a/src/full/Agda/Interaction/Options/HasOptions.hs b/src/full/Agda/Interaction/Options/HasOptions.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options/HasOptions.hs
@@ -0,0 +1,41 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Options.HasOptions
+  ( HasOptions (pragmaOptions, commandLineOptions)
+  ) where
+
+import Control.Monad.Except (ExceptT)
+import Control.Monad.Reader (ReaderT)
+import Control.Monad.State (StateT)
+import Control.Monad.Trans ( MonadTrans, lift )
+import Control.Monad.Trans.Identity (IdentityT)
+import Control.Monad.Trans.Maybe (MaybeT)
+import Control.Monad.Writer (WriterT)
+
+import Agda.Interaction.Options.Base (PragmaOptions, CommandLineOptions)
+import Agda.Utils.Update (ChangeT)
+import Agda.Utils.ListT (ListT)
+
+class (Functor m, Applicative m, Monad m) => HasOptions m where
+  -- | Returns the pragma options which are currently in effect.
+  pragmaOptions      :: m PragmaOptions
+  -- | Returns the command line options which are currently in effect.
+  commandLineOptions :: m CommandLineOptions
+
+  default pragmaOptions :: (HasOptions n, MonadTrans t, m ~ t n) => m PragmaOptions
+  pragmaOptions      = lift pragmaOptions
+
+  default commandLineOptions :: (HasOptions n, MonadTrans t, m ~ t n) => m CommandLineOptions
+  commandLineOptions = lift commandLineOptions
+
+-- HasOptions lifts through monad transformers
+-- (see default signatures in the HasOptions class).
+
+instance HasOptions m => HasOptions (ChangeT m)
+instance HasOptions m => HasOptions (ExceptT e m)
+instance HasOptions m => HasOptions (IdentityT m)
+instance HasOptions m => HasOptions (ListT m)
+instance HasOptions m => HasOptions (MaybeT m)
+instance HasOptions m => HasOptions (ReaderT r m)
+instance HasOptions m => HasOptions (StateT s m)
+instance (HasOptions m, Monoid w) => HasOptions (WriterT w m)
diff --git a/src/full/Agda/Interaction/Options/Help.hs b/src/full/Agda/Interaction/Options/Help.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options/Help.hs
@@ -0,0 +1,54 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.Options.Help
+       (
+         Help (..)
+       , helpTopicUsage
+       , string2HelpTopic
+       , allHelpTopics
+       ) where
+
+import Control.DeepSeq
+
+import GHC.Generics (Generic)
+
+import Agda.Interaction.Options.Warnings
+
+-- | Interface to the @help@ function
+data Help
+  = GeneralHelp
+  -- ^ General usage information
+  | HelpFor HelpTopic
+  -- ^ Specialised usage information about TOPIC
+  deriving (Eq, Show, Generic)
+
+instance NFData Help
+
+-- | List of Help Topics
+-- NOTA BENE:
+-- You need to add each new topic together with its name to @allHelpTopics@
+
+data HelpTopic
+  = Warning
+  deriving (Eq, Show, Generic)
+
+instance NFData HelpTopic
+
+allHelpTopics :: [(String, HelpTopic)]
+allHelpTopics = [("warning", Warning)]
+
+-- | Usage information generation
+
+helpTopicUsage :: HelpTopic -> String
+helpTopicUsage tp = case tp of
+  Warning -> usageWarning
+
+-- | Conversion functions to strings
+
+string2HelpTopic :: String -> Maybe HelpTopic
+string2HelpTopic str = lookup str allHelpTopics
+
+-- UNUSED Liang-Ting Chen 2019-07-15
+--helpTopic2String :: HelpTopic -> String
+--helpTopic2String w = fromMaybe __IMPOSSIBLE__ $ lookup w (map swap allHelpTopics)
+--
diff --git a/src/full/Agda/Interaction/Options/Lenses.hs b/src/full/Agda/Interaction/Options/Lenses.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options/Lenses.hs
@@ -0,0 +1,301 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Lenses for 'CommandLineOptions' and 'PragmaOptions'.
+--
+--   Add as needed.
+--
+--   Nothing smart happening here.
+
+module Agda.Interaction.Options.Lenses where
+
+import Control.Monad.IO.Class   ( MonadIO(..) )
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import System.FilePath ((</>))
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.State
+import Agda.Interaction.Library (getPrimitiveLibDir)
+import Agda.Interaction.Options
+
+import Agda.Utils.Lens
+import Agda.Utils.FileName
+import Agda.Utils.WithDefault (pattern Value)
+
+---------------------------------------------------------------------------
+-- * Pragma options
+---------------------------------------------------------------------------
+
+class LensPragmaOptions a where
+  getPragmaOptions  :: a -> PragmaOptions
+  setPragmaOptions  :: PragmaOptions -> a -> a
+  mapPragmaOptions  :: (PragmaOptions -> PragmaOptions) -> a -> a
+  lensPragmaOptions :: Lens' a PragmaOptions
+  -- lensPragmaOptions :: forall f. Functor f => (PragmaOptions -> f PragmaOptions) -> a -> f a
+
+  -- default implementations
+  setPragmaOptions     = mapPragmaOptions . const
+  mapPragmaOptions f a = setPragmaOptions (f $ getPragmaOptions a) a
+
+instance LensPragmaOptions CommandLineOptions where
+  getPragmaOptions = optPragmaOptions
+  setPragmaOptions opts st = st { optPragmaOptions = opts }
+  lensPragmaOptions f st = f (optPragmaOptions st) <&> \ opts -> st { optPragmaOptions = opts }
+
+instance LensPragmaOptions TCState where
+  getPragmaOptions = (^. stPragmaOptions)
+  setPragmaOptions = set stPragmaOptions
+  lensPragmaOptions = stPragmaOptions
+
+modifyPragmaOptions :: MonadTCState m => (PragmaOptions -> PragmaOptions) -> m ()
+modifyPragmaOptions = modifyTC . mapPragmaOptions
+
+---------------------------------------------------------------------------
+-- ** Verbosity in the local pragma options
+---------------------------------------------------------------------------
+
+class LensVerbosity a where
+  getVerbosity :: a -> Verbosity
+  setVerbosity :: Verbosity -> a -> a
+  mapVerbosity :: (Verbosity -> Verbosity) -> a -> a
+
+  -- default implementations
+  setVerbosity     = mapVerbosity . const
+  mapVerbosity f a = setVerbosity (f $ getVerbosity a) a
+
+instance LensVerbosity PragmaOptions where
+  getVerbosity = _optVerbose
+  setVerbosity is opts = opts { _optVerbose = is }
+
+instance LensVerbosity TCState where
+  getVerbosity = getVerbosity . getPragmaOptions
+  mapVerbosity = mapPragmaOptions . mapVerbosity
+
+modifyVerbosity :: MonadTCState m => (Verbosity -> Verbosity) -> m ()
+modifyVerbosity = modifyTC . mapVerbosity
+
+putVerbosity :: MonadTCState m => Verbosity -> m ()
+putVerbosity = modifyTC . setVerbosity
+
+---------------------------------------------------------------------------
+-- * Command line options
+---------------------------------------------------------------------------
+
+class LensCommandLineOptions a where
+  getCommandLineOptions :: a -> CommandLineOptions
+  setCommandLineOptions :: CommandLineOptions -> a -> a
+  mapCommandLineOptions :: (CommandLineOptions -> CommandLineOptions) -> a -> a
+
+  -- default implementations
+  setCommandLineOptions     = mapCommandLineOptions . const
+  mapCommandLineOptions f a = setCommandLineOptions (f $ getCommandLineOptions a) a
+
+instance LensCommandLineOptions PersistentTCState where
+  getCommandLineOptions = stPersistentOptions
+  setCommandLineOptions opts st = st { stPersistentOptions = opts }
+
+instance LensCommandLineOptions TCState where
+  getCommandLineOptions = getCommandLineOptions . stPersistentState
+  mapCommandLineOptions = updatePersistentState . mapCommandLineOptions
+
+modifyCommandLineOptions :: MonadTCState m => (CommandLineOptions -> CommandLineOptions) -> m ()
+modifyCommandLineOptions = modifyTC . mapCommandLineOptions
+
+---------------------------------------------------------------------------
+-- ** Safe mode
+---------------------------------------------------------------------------
+
+type SafeMode = Bool
+
+class LensSafeMode a where
+  getSafeMode :: a -> SafeMode
+  setSafeMode :: SafeMode -> a -> a
+  mapSafeMode :: (SafeMode -> SafeMode) -> a -> a
+
+  -- default implementations
+  setSafeMode     = mapSafeMode . const
+  mapSafeMode f a = setSafeMode (f $ getSafeMode a) a
+
+instance LensSafeMode PragmaOptions where
+  getSafeMode = optSafe
+  setSafeMode is opts = opts { _optSafe = Value is } -- setSafeOption
+
+instance LensSafeMode CommandLineOptions where
+  getSafeMode = getSafeMode . getPragmaOptions
+  mapSafeMode = mapPragmaOptions . mapSafeMode
+
+instance LensSafeMode PersistentTCState where
+  getSafeMode = getSafeMode . getCommandLineOptions
+  mapSafeMode = mapCommandLineOptions . mapSafeMode
+
+instance LensSafeMode TCState where
+  getSafeMode = getSafeMode . getCommandLineOptions
+  mapSafeMode = mapCommandLineOptions . mapSafeMode
+
+modifySafeMode :: MonadTCState m => (SafeMode -> SafeMode) -> m ()
+modifySafeMode = modifyTC . mapSafeMode
+
+putSafeMode :: MonadTCState m => SafeMode -> m ()
+putSafeMode = modifyTC . setSafeMode
+
+-- | These builtins may use postulates, and are still considered --safe
+
+builtinModulesWithSafePostulates :: Set FilePath
+builtinModulesWithSafePostulates =
+  primitiveModules `Set.union` (Set.fromList
+  [ "Agda" </> "Builtin" </> "Bool.agda"
+  , "Agda" </> "Builtin" </> "Char.agda"
+  , "Agda" </> "Builtin" </> "Char" </> "Properties.agda"
+  , "Agda" </> "Builtin" </> "Coinduction.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "Equiv.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "Glue.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "HCompU.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "Id.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "Path.agda"
+  , "Agda" </> "Builtin" </> "Cubical" </> "Sub.agda"
+  , "Agda" </> "Builtin" </> "Equality" </> "Erase.agda"
+  , "Agda" </> "Builtin" </> "Equality.agda"
+  , "Agda" </> "Builtin" </> "Float.agda"
+  , "Agda" </> "Builtin" </> "Float" </> "Properties.agda"
+  , "Agda" </> "Builtin" </> "FromNat.agda"
+  , "Agda" </> "Builtin" </> "FromNeg.agda"
+  , "Agda" </> "Builtin" </> "FromString.agda"
+  , "Agda" </> "Builtin" </> "Int.agda"
+  , "Agda" </> "Builtin" </> "IO.agda"
+  , "Agda" </> "Builtin" </> "List.agda"
+  , "Agda" </> "Builtin" </> "Maybe.agda"
+  , "Agda" </> "Builtin" </> "Nat.agda"
+  , "Agda" </> "Builtin" </> "Reflection.agda"
+  , "Agda" </> "Builtin" </> "Reflection" </> "Properties.agda"
+  , "Agda" </> "Builtin" </> "Reflection" </> "External.agda"
+  , "Agda" </> "Builtin" </> "Sigma.agda"
+  , "Agda" </> "Builtin" </> "Size.agda"
+  , "Agda" </> "Builtin" </> "Strict.agda"
+  , "Agda" </> "Builtin" </> "String.agda"
+  , "Agda" </> "Builtin" </> "String" </> "Properties.agda"
+  , "Agda" </> "Builtin" </> "Unit.agda"
+  , "Agda" </> "Builtin" </> "Word.agda"
+  , "Agda" </> "Builtin" </> "Word" </> "Properties.agda"
+  ])
+
+-- | These builtins may not use postulates under --safe. They are not
+--   automatically unsafe, but will be if they use an unsafe feature.
+
+builtinModulesWithUnsafePostulates :: Set FilePath
+builtinModulesWithUnsafePostulates = Set.fromList
+  [ "Agda" </> "Builtin" </> "TrustMe.agda"
+  , "Agda" </> "Builtin" </> "Equality" </> "Rewrite.agda"
+  ]
+
+primitiveModules :: Set FilePath
+primitiveModules = Set.fromList
+  [ "Agda" </> "Primitive.agda"
+  , "Agda" </> "Primitive" </> "Cubical.agda"
+  ]
+
+builtinModules :: Set FilePath
+builtinModules = builtinModulesWithSafePostulates `Set.union`
+                 builtinModulesWithUnsafePostulates
+
+isPrimitiveModule :: MonadIO m => FilePath -> m Bool
+isPrimitiveModule file = do
+  libdirPrim <- liftIO getPrimitiveLibDir
+  return (file `Set.member` Set.map (libdirPrim </>) primitiveModules)
+
+isBuiltinModule :: MonadIO m => FilePath -> m Bool
+isBuiltinModule file = do
+  libdirPrim <- liftIO getPrimitiveLibDir
+  return (file `Set.member` Set.map (libdirPrim </>) builtinModules)
+
+isBuiltinModuleWithSafePostulates :: MonadIO m => FilePath -> m Bool
+isBuiltinModuleWithSafePostulates file = do
+  libdirPrim <- liftIO getPrimitiveLibDir
+  let safeBuiltins   = Set.map (libdirPrim </>) builtinModulesWithSafePostulates
+  return (file `Set.member` safeBuiltins)
+
+---------------------------------------------------------------------------
+-- ** Include directories
+---------------------------------------------------------------------------
+
+class LensIncludePaths a where
+  getIncludePaths :: a -> [FilePath]
+  setIncludePaths :: [FilePath] -> a -> a
+  mapIncludePaths :: ([FilePath] -> [FilePath]) -> a -> a
+
+  getAbsoluteIncludePaths :: a -> [AbsolutePath]
+  setAbsoluteIncludePaths :: [AbsolutePath] -> a -> a
+  mapAbsoluteIncludePaths :: ([AbsolutePath] -> [AbsolutePath]) -> a -> a
+
+  -- default implementations
+  setIncludePaths     = mapIncludePaths . const
+  mapIncludePaths f a = setIncludePaths (f $ getIncludePaths a) a
+  setAbsoluteIncludePaths     = mapAbsoluteIncludePaths . const
+  mapAbsoluteIncludePaths f a = setAbsoluteIncludePaths (f $ getAbsoluteIncludePaths a) a
+
+instance LensIncludePaths CommandLineOptions where
+  getIncludePaths = optIncludePaths
+  setIncludePaths is opts = opts { optIncludePaths = is }
+  getAbsoluteIncludePaths = optAbsoluteIncludePaths
+  setAbsoluteIncludePaths is opts = opts { optAbsoluteIncludePaths = is }
+
+instance LensIncludePaths PersistentTCState where
+  getIncludePaths = getIncludePaths . getCommandLineOptions
+  mapIncludePaths = mapCommandLineOptions . mapIncludePaths
+  getAbsoluteIncludePaths = getAbsoluteIncludePaths . getCommandLineOptions
+  mapAbsoluteIncludePaths = mapCommandLineOptions . mapAbsoluteIncludePaths
+
+instance LensIncludePaths TCState where
+  getIncludePaths = getIncludePaths . getCommandLineOptions
+  mapIncludePaths = mapCommandLineOptions . mapIncludePaths
+  getAbsoluteIncludePaths = getAbsoluteIncludePaths . getCommandLineOptions
+  mapAbsoluteIncludePaths = mapCommandLineOptions . mapAbsoluteIncludePaths
+
+modifyIncludePaths :: MonadTCState m => ([FilePath] -> [FilePath]) -> m ()
+modifyIncludePaths = modifyTC . mapIncludePaths
+
+putIncludePaths :: MonadTCState m => [FilePath] -> m ()
+putIncludePaths = modifyTC . setIncludePaths
+
+modifyAbsoluteIncludePaths :: MonadTCState m => ([AbsolutePath] -> [AbsolutePath]) -> m ()
+modifyAbsoluteIncludePaths = modifyTC . mapAbsoluteIncludePaths
+
+putAbsoluteIncludePaths :: MonadTCState m => [AbsolutePath] -> m ()
+putAbsoluteIncludePaths = modifyTC . setAbsoluteIncludePaths
+
+---------------------------------------------------------------------------
+-- ** Include directories
+---------------------------------------------------------------------------
+
+type PersistentVerbosity = Verbosity
+class LensPersistentVerbosity a where
+  getPersistentVerbosity :: a -> PersistentVerbosity
+  setPersistentVerbosity :: PersistentVerbosity -> a -> a
+  mapPersistentVerbosity :: (PersistentVerbosity -> PersistentVerbosity) -> a -> a
+
+  -- default implementations
+  setPersistentVerbosity     = mapPersistentVerbosity . const
+  mapPersistentVerbosity f a = setPersistentVerbosity (f $ getPersistentVerbosity a) a
+
+instance LensPersistentVerbosity PragmaOptions where
+  getPersistentVerbosity = getVerbosity
+  setPersistentVerbosity = setVerbosity
+
+instance LensPersistentVerbosity CommandLineOptions where
+  getPersistentVerbosity = getPersistentVerbosity . getPragmaOptions
+  mapPersistentVerbosity = mapPragmaOptions . mapPersistentVerbosity
+
+instance LensPersistentVerbosity PersistentTCState where
+  getPersistentVerbosity = getPersistentVerbosity . getCommandLineOptions
+  mapPersistentVerbosity = mapCommandLineOptions . mapPersistentVerbosity
+
+instance LensPersistentVerbosity TCState where
+  getPersistentVerbosity = getPersistentVerbosity . getCommandLineOptions
+  mapPersistentVerbosity = mapCommandLineOptions . mapPersistentVerbosity
+
+modifyPersistentVerbosity :: MonadTCState m => (PersistentVerbosity -> PersistentVerbosity) -> m ()
+modifyPersistentVerbosity = modifyTC . mapPersistentVerbosity
+
+putPersistentVerbosity :: MonadTCState m => PersistentVerbosity -> m ()
+putPersistentVerbosity = modifyTC . setPersistentVerbosity
diff --git a/src/full/Agda/Interaction/Options/Warnings.hs b/src/full/Agda/Interaction/Options/Warnings.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Options/Warnings.hs
@@ -0,0 +1,485 @@
+
+module Agda.Interaction.Options.Warnings
+       (
+         WarningMode (..)
+       , warningSet
+       , warn2Error
+       , lensSingleWarning
+       , defaultWarningSet
+       , allWarnings
+       , usualWarnings
+       , noWarnings
+       , unsolvedWarnings
+       , incompleteMatchWarnings
+       , errorWarnings
+       , exactSplitWarnings
+       , defaultWarningMode
+       , WarningModeError(..)
+       , prettyWarningModeError
+       , warningModeUpdate
+       , warningSets
+       , WarningName (..)
+       , warningName2String
+       , string2WarningName
+       , usageWarning
+       )
+where
+
+import Control.Arrow ( (&&&) )
+import Control.DeepSeq
+import Control.Monad ( guard, when )
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.HashMap.Strict as HMap
+import Data.List ( stripPrefix, intercalate, partition, sort )
+
+import GHC.Generics (Generic)
+
+import Agda.Utils.Either ( maybeToEither )
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+
+import Agda.Utils.Impossible
+
+
+-- | A @WarningMode@ has two components: a set of warnings to be displayed
+-- and a flag stating whether warnings should be turned into fatal errors.
+data WarningMode = WarningMode
+  { _warningSet :: Set WarningName
+  , _warn2Error :: Bool
+  } deriving (Eq, Show, Generic)
+
+instance NFData WarningMode
+
+-- Lenses
+
+warningSet :: Lens' WarningMode (Set WarningName)
+warningSet f o = (\ ws -> o { _warningSet = ws }) <$> f (_warningSet o)
+
+warn2Error :: Lens' WarningMode Bool
+warn2Error f o = (\ ws -> o { _warn2Error = ws }) <$> f (_warn2Error o)
+
+lensSingleWarning :: WarningName -> Lens' WarningMode Bool
+lensSingleWarning w = warningSet . contains w
+
+-- | The @defaultWarningMode@ is a curated set of warnings covering non-fatal
+-- errors and disabling style-related ones
+
+defaultWarningSet :: String
+defaultWarningSet = "warn"
+
+defaultWarningMode :: WarningMode
+defaultWarningMode = WarningMode ws False where
+  ws = fst $ fromMaybe __IMPOSSIBLE__ $ lookup defaultWarningSet warningSets
+
+-- | Some warnings are errors and cannot be turned off.
+data WarningModeError = Unknown String | NoNoError String
+
+prettyWarningModeError :: WarningModeError -> String
+prettyWarningModeError = \case
+  Unknown str -> concat [ "Unknown warning flag: ", str, "." ]
+  NoNoError str -> concat [ "You may only turn off benign warnings. The warning "
+                          , str
+                          ," is a non-fatal error and thus cannot be ignored." ]
+
+-- | From user-given directives we compute WarningMode updates
+type WarningModeUpdate = WarningMode -> WarningMode
+
+-- | @warningModeUpdate str@ computes the action of @str@ over the current
+-- @WarningMode@: it may reset the set of warnings, add or remove a specific
+-- flag or demand that any warning be turned into an error
+
+warningModeUpdate :: String -> Either WarningModeError WarningModeUpdate
+warningModeUpdate str = case str of
+  "error"   -> pure $ set warn2Error True
+  "noerror" -> pure $ set warn2Error False
+  _ | Just ws <- fst <$> lookup str warningSets
+            -> pure $ set warningSet ws
+  _ -> case stripPrefix "no" str of
+    Nothing   -> do
+      wname :: WarningName <- maybeToEither (Unknown str) $ string2WarningName str
+      pure (over warningSet $ Set.insert wname)
+    Just str' -> do
+      wname :: WarningName <- maybeToEither (Unknown str') $ string2WarningName str'
+      when (wname `elem` errorWarnings) (Left (NoNoError str'))
+      pure (over warningSet $ Set.delete wname)
+
+-- | Common sets of warnings
+
+warningSets :: [(String, (Set WarningName, String))]
+warningSets = [ ("all"   , (allWarnings, "All of the existing warnings"))
+              , ("warn"  , (usualWarnings, "Default warning level"))
+              , ("ignore", (errorWarnings, "Ignore all the benign warnings"))
+              ]
+
+noWarnings :: Set WarningName
+noWarnings = Set.empty
+
+unsolvedWarnings :: Set WarningName
+unsolvedWarnings = Set.fromList
+                 [ UnsolvedMetaVariables_
+                 , UnsolvedInteractionMetas_
+                 , UnsolvedConstraints_
+                 ]
+
+incompleteMatchWarnings :: Set WarningName
+incompleteMatchWarnings = Set.fromList [ CoverageIssue_ ]
+
+errorWarnings :: Set WarningName
+errorWarnings = Set.fromList
+  [ CoverageIssue_
+  , InvalidCharacterLiteral_
+  , MissingDefinitions_
+  , MissingDeclarations_
+  , NotAllowedInMutual_
+  , NotStrictlyPositive_
+  , OverlappingTokensWarning_
+  , PragmaCompiled_
+  , SafeFlagPostulate_
+  , SafeFlagPragma_
+  , SafeFlagNonTerminating_
+  , SafeFlagTerminating_
+  , SafeFlagWithoutKFlagPrimEraseEquality_
+  , SafeFlagNoPositivityCheck_
+  , SafeFlagPolarity_
+  , SafeFlagNoUniverseCheck_
+  , SafeFlagEta_
+  , SafeFlagInjective_
+  , SafeFlagNoCoverageCheck_
+  , TerminationIssue_
+  , UnsolvedMetaVariables_
+  , UnsolvedInteractionMetas_
+  , UnsolvedConstraints_
+  , InfectiveImport_
+  , CoInfectiveImport_
+  , RewriteNonConfluent_
+  , RewriteMaybeNonConfluent_
+  , RewriteAmbiguousRules_
+  , RewriteMissingRule_
+  ]
+
+allWarnings :: Set WarningName
+allWarnings = Set.fromList [minBound..maxBound]
+
+usualWarnings :: Set WarningName
+usualWarnings =
+  allWarnings Set.\\ exactSplitWarnings Set.\\ Set.fromList
+    [ UnknownFixityInMixfixDecl_
+    , ShadowingInTelescope_
+    ]
+
+-- | Warnings enabled by @--exact-split@.
+--
+exactSplitWarnings :: Set WarningName
+exactSplitWarnings = Set.fromList
+  [ CoverageNoExactSplit_
+  , InlineNoExactSplit_
+  ]
+
+-- | The @WarningName@ data enumeration is meant to have a one-to-one correspondance
+-- to existing warnings in the codebase.
+
+data WarningName
+  -- Option Warnings
+  = OptionRenamed_
+  -- Parser Warnings
+  | OverlappingTokensWarning_
+  | UnsupportedAttribute_
+  | MultipleAttributes_
+  -- Library Warnings
+  | LibUnknownField_
+  -- Nicifer Warnings
+  | EmptyAbstract_
+  | EmptyConstructor_
+  | EmptyField_
+  | EmptyGeneralize_
+  | EmptyInstance_
+  | EmptyMacro_
+  | EmptyMutual_
+  | EmptyPostulate_
+  | EmptyPrimitive_
+  | EmptyPrivate_
+  | EmptyRewritePragma_
+  | EmptyWhere_
+  | HiddenGeneralize_
+  | InvalidCatchallPragma_
+  | InvalidConstructor_
+  | InvalidConstructorBlock_
+  | InvalidCoverageCheckPragma_
+  | InvalidNoPositivityCheckPragma_
+  | InvalidNoUniverseCheckPragma_
+  | InvalidRecordDirective_
+  | InvalidTerminationCheckPragma_
+  | MissingDeclarations_
+  | MissingDefinitions_
+  | NotAllowedInMutual_
+  | OpenPublicAbstract_
+  | OpenPublicPrivate_
+  | PolarityPragmasButNotPostulates_
+  | PragmaCompiled_
+  | PragmaNoTerminationCheck_
+  | ShadowingInTelescope_
+  | UnknownFixityInMixfixDecl_
+  | UnknownNamesInFixityDecl_
+  | UnknownNamesInPolarityPragmas_
+  | UselessAbstract_
+  | UselessInstance_
+  | UselessPrivate_
+  -- Scope and Type Checking Warnings
+  | AbsurdPatternRequiresNoRHS_
+  | AsPatternShadowsConstructorOrPatternSynonym_
+  | PatternShadowsConstructor_
+  | CantGeneralizeOverSorts_
+  | ClashesViaRenaming_                -- issue #4154
+  | CoverageIssue_
+  | CoverageNoExactSplit_
+  | InlineNoExactSplit_
+  | DeprecationWarning_
+  | DuplicateUsing_
+  | FixityInRenamingModule_
+  | InvalidCharacterLiteral_
+  | UselessPragma_
+  | GenericWarning_
+  | IllformedAsClause_
+  | InstanceArgWithExplicitArg_
+  | InstanceWithExplicitArg_
+  | InstanceNoOutputTypeName_
+  | InteractionMetaBoundaries_
+  | InversionDepthReached_
+  | ModuleDoesntExport_
+  | NoGuardednessFlag_
+  | NotInScope_
+  | NotStrictlyPositive_
+  | UnsupportedIndexedMatch_
+  | OldBuiltin_
+  | PlentyInHardCompileTimeMode_
+  | PragmaCompileErased_
+  | RewriteMaybeNonConfluent_
+  | RewriteNonConfluent_
+  | RewriteAmbiguousRules_
+  | RewriteMissingRule_
+  | SafeFlagEta_
+  | SafeFlagInjective_
+  | SafeFlagNoCoverageCheck_
+  | SafeFlagNonTerminating_
+  | SafeFlagNoPositivityCheck_
+  | SafeFlagNoUniverseCheck_
+  | SafeFlagPolarity_
+  | SafeFlagPostulate_
+  | SafeFlagPragma_
+  | SafeFlagTerminating_
+  | SafeFlagWithoutKFlagPrimEraseEquality_
+  | TerminationIssue_
+  | UnreachableClauses_
+  | UnsolvedConstraints_
+  | UnsolvedInteractionMetas_
+  | UnsolvedMetaVariables_
+  | UselessHiding_
+  | UselessInline_
+  | UselessPatternDeclarationForRecord_
+  | UselessPublic_
+  | UserWarning_
+  | WithoutKFlagPrimEraseEquality_
+  | WrongInstanceDeclaration_
+  -- Checking consistency of options
+  | CoInfectiveImport_
+  | InfectiveImport_
+  -- Record field warnings
+  | DuplicateFields_
+  | TooManyFields_
+  -- Opaque/unfolding
+  | NotAffectedByOpaque_
+  | UnfoldTransparentName_
+  | UselessOpaque_
+  -- Cubical
+  | FaceConstraintCannotBeHidden_
+  | FaceConstraintCannotBeNamed_
+  -- Not source code related
+  | DuplicateInterfaceFiles_
+  deriving (Eq, Ord, Show, Read, Enum, Bounded, Generic)
+
+instance NFData WarningName
+
+-- | The flag corresponding to a warning is precisely the name of the constructor
+-- minus the trailing underscore.
+
+string2WarningName :: String -> Maybe WarningName
+string2WarningName = (`HMap.lookup` warnings) where
+  warnings = HMap.fromList $ map (\x -> (warningName2String x, x)) [minBound..maxBound]
+
+warningName2String :: WarningName -> String
+warningName2String = initWithDefault __IMPOSSIBLE__ . show
+
+-- | @warningUsage@ generated using @warningNameDescription@
+
+usageWarning :: String
+usageWarning = intercalate "\n"
+  [ "The -W or --warning option can be used to disable or enable\
+    \ different warnings. The flag -W error (or --warning=error)\
+    \ can be used to turn all warnings into errors, while -W noerror\
+    \ turns this off again."
+  , ""
+  , "A group of warnings can be enabled by -W group, where group is\
+    \ one of the following:"
+  , ""
+  , untable (fmap (fst &&& snd . snd) warningSets)
+
+  , "Individual benign warnings can be turned on and off by -W Name and\
+    \ -W noName, respectively, where Name comes from the following\
+    \ list (warnings marked with 'd' are turned on by default):"
+  , ""
+  , warningTable True benign
+
+  , "Error warnings are always on and cannot be turned off:"
+  , ""
+  , warningTable False severe
+  ]
+
+  where
+
+    (severe, benign) = partition (`Set.member` errorWarnings) [minBound..maxBound]
+
+    warningTable printD ws =
+      untable $ forMaybe ws $ \ w ->
+        let wnd = warningNameDescription w in
+        ( warningName2String w
+        , applyWhen printD ((if w `Set.member` usualWarnings then "d" else " ") ++)
+          " " ++
+          wnd
+        ) <$ guard (not $ null wnd)
+
+    untable :: [(String, String)] -> String
+    untable rows =
+      let len = maximum (map (length . fst) rows) in
+      unlines $ for (sort rows) $ \ (hdr, cnt) ->
+        concat [ hdr, replicate (1 + len - length hdr) ' ', cnt ]
+
+
+-- | @WarningName@ descriptions used for generating usage information
+-- Leave String empty to skip that name.
+--
+-- The description should be a completion of the sentence "This warning is about ...".
+-- So, typically the subject is in plural.
+--
+warningNameDescription :: WarningName -> String
+warningNameDescription = \case
+  -- Option Warnings
+  OptionRenamed_                   -> "Renamed options."
+  -- Parser Warnings
+  OverlappingTokensWarning_        -> "Multi-line comments spanning one or more literate text blocks."
+  UnsupportedAttribute_            -> "Unsupported attributes."
+  MultipleAttributes_              -> "Multiple attributes."
+  -- Library Warnings
+  LibUnknownField_                 -> "Unknown fields in library files."
+  -- Nicifer Warnings
+  EmptyAbstract_                   -> "Empty `abstract' blocks."
+  EmptyConstructor_                -> "Empty `constructor' blocks."
+  EmptyField_                      -> "Empty `field` blocks."
+  EmptyGeneralize_                 -> "Empty `variable' blocks."
+  EmptyInstance_                   -> "Empty `instance' blocks."
+  EmptyMacro_                      -> "Empty `macro' blocks."
+  EmptyMutual_                     -> "Empty `mutual' blocks."
+  EmptyPostulate_                  -> "Empty `postulate' blocks."
+  EmptyPrimitive_                  -> "Empty `primitive' blocks."
+  EmptyPrivate_                    -> "Empty `private' blocks."
+  EmptyRewritePragma_              -> "Empty `REWRITE' pragmas."
+  EmptyWhere_                      -> "Empty `where' blocks."
+  HiddenGeneralize_                -> "Hidden identifiers in variable blocks."
+  InvalidCatchallPragma_           -> "`CATCHALL' pragmas before a non-function clause."
+  InvalidConstructor_              -> "`constructor' blocks that contain declarations other than type signatures for constructors."
+  InvalidConstructorBlock_         -> "`constructor' blocks outside of `interleaved mutual' blocks."
+  InvalidCoverageCheckPragma_      -> "Coverage checking pragmas before non-function or `mutual' blocks."
+  InvalidNoPositivityCheckPragma_  -> "Positivity checking pragmas before non-`data', `record' or `mutual' blocks."
+  InvalidNoUniverseCheckPragma_    -> "Universe checking pragmas before non-`data' or `record' declaration."
+  InvalidRecordDirective_          -> "Record directives outside of record definitions or below field declarations."
+  InvalidTerminationCheckPragma_   -> "Termination checking pragmas before non-function or `mutual' blocks."
+  MissingDeclarations_             -> "Definitions not associated to a declaration."
+  MissingDefinitions_              -> "Declarations not associated to a definition."
+  NotAllowedInMutual_              -> "Declarations not allowed in a mutual block."
+  OpenPublicAbstract_              -> "'open public' directives in 'abstract' blocks."
+  OpenPublicPrivate_               -> "'open public' directives in 'private' blocks."
+  PolarityPragmasButNotPostulates_ -> "Polarity pragmas for non-postulates."
+  PragmaCompiled_                  -> "'COMPILE' pragmas in safe mode."
+  PragmaNoTerminationCheck_        -> "`NO_TERMINATION_CHECK' pragmas; such are deprecated."
+  ShadowingInTelescope_            -> "Repeated variable names in telescopes."
+  UnknownFixityInMixfixDecl_       -> "Mixfix names without an associated fixity declaration."
+  UnknownNamesInFixityDecl_        -> "Names not declared in the same scope as their syntax or fixity declaration."
+  UnknownNamesInPolarityPragmas_   -> "Names not declared in the same scope as their polarity pragmas."
+  UselessAbstract_                 -> "`abstract' blocks where they have no effect."
+  UselessHiding_                   -> "Names in `hiding' directive that are anyway not imported."
+  UselessInline_                   -> "`INLINE' pragmas where they have no effect."
+  UselessInstance_                 -> "`instance' blocks where they have no effect."
+  UselessPrivate_                  -> "`private' blocks where they have no effect."
+  UselessPublic_                   -> "`public' blocks where they have no effect."
+  UselessPatternDeclarationForRecord_ -> "`pattern' attributes where they have no effect."
+  -- Scope and Type Checking Warnings
+  AbsurdPatternRequiresNoRHS_      -> "Clauses with an absurd pattern that have a right hand side."
+  AsPatternShadowsConstructorOrPatternSynonym_ -> "@-patterns that shadow constructors or pattern synonyms."
+  PatternShadowsConstructor_       -> "Pattern variables that shadow constructors."
+  CantGeneralizeOverSorts_         -> "Attempts to generalize over sort metas in 'variable' declaration."
+  ClashesViaRenaming_              -> "Clashes introduced by `renaming'."  -- issue #4154
+  CoverageIssue_                   -> "Failed coverage checks."
+  CoverageNoExactSplit_            -> "Failed exact split checks."
+  InlineNoExactSplit_              -> "Failed exact split checks after inlining record constructors."
+  DeprecationWarning_              -> "Deprecated features."
+  InvalidCharacterLiteral_         -> "Illegal character literals."
+  UselessPragma_                   -> "Pragmas that get ignored."
+  GenericWarning_                  -> ""
+  IllformedAsClause_               -> "Illformed `as'-clauses in `import' statements."
+  InstanceNoOutputTypeName_        -> "Instance arguments whose type does not end in a named or variable type; those are never considered by instance search."
+  InstanceArgWithExplicitArg_      -> "Instance arguments with explicit arguments; those are never considered by instance search."
+  InstanceWithExplicitArg_         -> "`instance` declarations with explicit arguments; those are never considered by instance search."
+  InversionDepthReached_           -> "Inversions of pattern-matching failures due to exhausted inversion depth."
+  NoGuardednessFlag_               -> "Coinductive records without --guardedness flag."
+  ModuleDoesntExport_              -> "Imported names that are not actually exported."
+  DuplicateUsing_                  -> "Repeated names in using directive."
+  FixityInRenamingModule_          -> "Fixity annotations in `renaming' directive for `module'."
+  NotInScope_                      -> "Out of scope names."
+  NotStrictlyPositive_             -> "Failed strict positivity checks."
+  UnsupportedIndexedMatch_         -> "Failures to compute full equivalence when splitting on indexed family."
+  OldBuiltin_                      -> "Deprecated `BUILTIN' pragmas."
+  PlentyInHardCompileTimeMode_     -> "Uses of @ω or @plenty in hard compile-time mode."
+  PragmaCompileErased_             -> "`COMPILE' pragmas targeting an erased symbol."
+  RewriteMaybeNonConfluent_        -> "Failed local confluence checks while computing overlap."
+  RewriteNonConfluent_             -> "Failed local confluence checks while joining critical pairs."
+  RewriteAmbiguousRules_           -> "Failed global confluence checks because of overlapping rules."
+  RewriteMissingRule_              -> "Failed global confluence checks because of missing rule."
+  SafeFlagEta_                     -> "`ETA' pragmas with the safe flag."
+  SafeFlagInjective_               -> "`INJECTIVE' pragmas with the safe flag."
+  SafeFlagNoCoverageCheck_         -> "`NON_COVERING` pragmas with the safe flag."
+  SafeFlagNonTerminating_          -> "`NON_TERMINATING' pragmas with the safe flag."
+  SafeFlagNoPositivityCheck_       -> "`NO_POSITIVITY_CHECK' pragmas with the safe flag."
+  SafeFlagNoUniverseCheck_         -> "`NO_UNIVERSE_CHECK' pragmas with the safe flag."
+  SafeFlagPolarity_                -> "`POLARITY' pragmas with the safe flag."
+  SafeFlagPostulate_               -> "`postulate' blocks with the safe flag."
+  SafeFlagPragma_                  -> "Unsafe `OPTIONS' pragmas with the safe flag."
+  SafeFlagTerminating_             -> "`TERMINATING' pragmas with the safe flag."
+  SafeFlagWithoutKFlagPrimEraseEquality_ -> "`primEraseEquality' used with the safe and without-K flags."
+  TerminationIssue_                -> "Failed termination checks."
+  UnreachableClauses_              -> "Unreachable function clauses."
+  UnsolvedConstraints_             -> "Unsolved constraints."
+  UnsolvedInteractionMetas_        -> "Unsolved interaction meta variables."
+  InteractionMetaBoundaries_       -> "Interaction meta variables that have unsolved boundary constraints."
+  UnsolvedMetaVariables_           -> "Unsolved meta variables."
+  UserWarning_                     -> "User-defined warnings via one of the 'WARNING_ON_*' pragmas."
+  WithoutKFlagPrimEraseEquality_   -> "Uses of `primEraseEquality' with the without-K flags."
+  WrongInstanceDeclaration_        -> "Instances that do not adhere to the required format."
+  -- Checking consistency of options
+  CoInfectiveImport_               -> "Importing a file not using e.g. `--safe'  from one which does."
+  InfectiveImport_                 -> "Importing a file using e.g. `--cubical' into one which does not."
+  -- Record field warnings
+  DuplicateFields_                 -> "Record expressions with duplicate field names."
+  TooManyFields_                   -> "Record expressions with invalid field names."
+  -- Opaque/unfolding warnings
+  NotAffectedByOpaque_             -> "Declarations unaffected by enclosing `opaque` blocks."
+  UnfoldTransparentName_           -> "Non-`opaque` names mentioned in an `unfolding` clause."
+  UselessOpaque_                   -> "`opaque` blocks that have no effect."
+  -- Cubical
+  FaceConstraintCannotBeHidden_    -> "Face constraint patterns that are given as implicit arguments."
+  FaceConstraintCannotBeNamed_     -> "Face constraint patterns that are given as named arguments."
+  -- Not source code related
+  DuplicateInterfaceFiles_         -> "Duplicate interface files."
diff --git a/src/full/Agda/Interaction/Response.hs b/src/full/Agda/Interaction/Response.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Response.hs
@@ -0,0 +1,219 @@
+------------------------------------------------------------------------
+-- | Data type for all interactive responses
+------------------------------------------------------------------------
+
+module Agda.Interaction.Response
+  ( Response (..)
+  , RemoveTokenBasedHighlighting (..)
+  , MakeCaseVariant (..)
+  , DisplayInfo (..)
+  , GoalDisplayInfo(..)
+  , Goals
+  , WarningsAndNonFatalErrors
+  , Info_Error(..)
+  , GoalTypeAux(..)
+  , ResponseContextEntry(..)
+  , Status (..)
+  , GiveResult (..)
+  , InteractionOutputCallback
+  , defaultInteractionOutputCallback
+  ) where
+
+import Agda.Interaction.Base
+  ( CommandState
+  , CompilerBackend
+  , ComputeMode
+  , OutputConstraint
+  , OutputConstraint'
+  , OutputForm
+  , Rewrite
+  )
+import Agda.Interaction.Highlighting.Precise
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Common         (InteractionId(..), Arg)
+import Agda.Syntax.Concrete       (Expr)
+import Agda.Syntax.Concrete.Name  (Name, QName, NameInScope)
+import Agda.Syntax.Scope.Base     (WhyInScopeData)
+import qualified Agda.Syntax.Internal as I
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Base
+  (TCM, TCErr, TCWarning, HighlightingMethod, ModuleToSource, NamedMeta, TCWarning, IPFace')
+import Agda.TypeChecking.Warnings (WarningsAndNonFatalErrors)
+import Agda.Utils.Impossible
+import Agda.Utils.Time
+
+import Control.Monad.Trans ( MonadIO(liftIO) )
+import Data.Int
+import System.IO
+
+-- | Responses for any interactive interface
+--
+--   Note that the response is given in pieces and incrementally,
+--   so the user can have timely response even during long computations.
+
+data Response
+    = Resp_HighlightingInfo
+        HighlightingInfo
+        RemoveTokenBasedHighlighting
+        HighlightingMethod
+        ModuleToSource
+    | Resp_Status Status
+    | Resp_JumpToError FilePath Int32
+    | Resp_InteractionPoints [InteractionId]
+    | Resp_GiveAction InteractionId GiveResult
+    | Resp_MakeCase InteractionId MakeCaseVariant [String]
+      -- ^ Response is list of printed clauses.
+    | Resp_SolveAll [(InteractionId, Expr)]
+      -- ^ Solution for one or more meta-variables.
+    | Resp_DisplayInfo DisplayInfo
+    | Resp_RunningInfo Int String
+      -- ^ The integer is the message's debug level.
+    | Resp_ClearRunningInfo
+    | Resp_ClearHighlighting TokenBased
+      -- ^ Clear highlighting of the given kind.
+    | Resp_DoneAborting
+      -- ^ A command sent when an abort command has completed
+      -- successfully.
+    | Resp_DoneExiting
+      -- ^ A command sent when an exit command is about to be
+      -- completed.
+
+-- | Should token-based highlighting be removed in conjunction with
+-- the application of new highlighting (in order to reduce the risk of
+-- flicker)?
+
+data RemoveTokenBasedHighlighting
+  = RemoveHighlighting
+    -- ^ Yes, remove all token-based highlighting from the file.
+  | KeepHighlighting
+    -- ^ No.
+
+-- | There are two kinds of \"make case\" commands.
+
+data MakeCaseVariant = Function | ExtendedLambda
+
+-- | Info to display at the end of an interactive command
+
+data DisplayInfo
+    = Info_CompilationOk CompilerBackend WarningsAndNonFatalErrors
+    | Info_Constraints [OutputForm Expr Expr]
+    | Info_AllGoalsWarnings Goals WarningsAndNonFatalErrors
+    | Info_Time CPUTime
+    | Info_Error Info_Error
+        -- ^ When an error message is displayed this constructor should be
+        -- used, if appropriate.
+    | Info_Intro_NotFound
+    | Info_Intro_ConstructorUnknown [String]
+    | Info_Auto String
+        -- ^ 'Info_Auto' denotes either an error or a success (when 'Resp_GiveAction' is present)
+        --   TODO: split these into separate constructors
+    | Info_ModuleContents [Name] I.Telescope [(Name, I.Type)]
+    | Info_SearchAbout [(Name, I.Type)] String
+    | Info_WhyInScope WhyInScopeData
+    | Info_NormalForm CommandState ComputeMode (Maybe CPUTime) A.Expr
+    | Info_InferredType CommandState (Maybe CPUTime) A.Expr
+    | Info_Context InteractionId [ResponseContextEntry]
+    | Info_Version
+    | Info_GoalSpecific InteractionId GoalDisplayInfo
+
+data GoalDisplayInfo
+    = Goal_HelperFunction (OutputConstraint' A.Expr A.Expr)
+    | Goal_NormalForm ComputeMode A.Expr
+    | Goal_GoalType Rewrite GoalTypeAux [ResponseContextEntry] [IPFace' Expr] [OutputForm Expr Expr]
+    | Goal_CurrentGoal Rewrite
+    | Goal_InferredType A.Expr
+
+-- | Goals & Warnings
+type Goals = ( [OutputConstraint A.Expr InteractionId] -- visible metas (goals)
+             , [OutputConstraint A.Expr NamedMeta]     -- hidden (unsolved) metas
+             )
+
+-- | Errors that goes into Info_Error
+--
+--   When an error message is displayed this constructor should be
+--   used, if appropriate.
+data Info_Error
+    = Info_GenericError TCErr
+    | Info_CompilationError [TCWarning]
+    | Info_HighlightingParseError InteractionId
+    | Info_HighlightingScopeCheckError InteractionId
+
+-- | Auxiliary information that comes with Goal Type
+
+data GoalTypeAux
+    = GoalOnly
+    | GoalAndHave A.Expr [IPFace' Expr]
+    | GoalAndElaboration I.Term
+
+-- | Entry in context.
+
+data ResponseContextEntry = ResponseContextEntry
+  { respOrigName :: Name        -- ^ The original concrete name.
+  , respReifName :: Name        -- ^ The name reified from abstract syntax.
+  , respType     :: Arg A.Expr  -- ^ The type.
+  , respLetValue :: Maybe A.Expr -- ^ The value (if it is a let-bound variable)
+  , respInScope  :: NameInScope -- ^ Whether the 'respReifName' is in scope.
+  }
+
+
+-- | Status information.
+
+data Status = Status
+  { sShowImplicitArguments :: Bool
+    -- ^ Are implicit arguments displayed?
+  , sShowIrrelevantArguments :: Bool
+    -- ^ Are irrelevant arguments displayed?
+  , sChecked               :: Bool
+    -- ^ Has the module been successfully type checked?
+  }
+
+-- | Give action result
+--
+--   Comment derived from agda2-mode.el
+--
+--   If 'GiveResult' is 'Give_String s', then the goal is replaced by 's',
+--   and otherwise the text inside the goal is retained (parenthesised
+--   if 'GiveResult' is 'Give_Paren').
+
+data GiveResult
+    = Give_String String
+    | Give_Paren
+    | Give_NoParen
+
+-- | Callback fuction to call when there is a response
+--   to give to the interactive frontend.
+--
+--   Note that the response is given in pieces and incrementally,
+--   so the user can have timely response even during long computations.
+--
+--   Typical 'InteractionOutputCallback' functions:
+--
+--    * Convert the response into a 'String' representation and
+--      print it on standard output
+--      (suitable for inter-process communication).
+--
+--    * Put the response into a mutable variable stored in the
+--      closure of the 'InteractionOutputCallback' function.
+--      (suitable for intra-process communication).
+
+type InteractionOutputCallback = Response -> TCM ()
+
+-- | The default 'InteractionOutputCallback' function prints certain
+-- things to stdout (other things generate internal errors).
+
+defaultInteractionOutputCallback :: InteractionOutputCallback
+defaultInteractionOutputCallback = \case
+  Resp_HighlightingInfo {}  -> __IMPOSSIBLE__
+  Resp_Status {}            -> __IMPOSSIBLE__
+  Resp_JumpToError {}       -> __IMPOSSIBLE__
+  Resp_InteractionPoints {} -> __IMPOSSIBLE__
+  Resp_GiveAction {}        -> __IMPOSSIBLE__
+  Resp_MakeCase {}          -> __IMPOSSIBLE__
+  Resp_SolveAll {}          -> __IMPOSSIBLE__
+  Resp_DisplayInfo {}       -> __IMPOSSIBLE__
+  Resp_RunningInfo _ s      -> liftIO $ do
+                                 putStr s
+                                 hFlush stdout
+  Resp_ClearRunningInfo {}  -> __IMPOSSIBLE__
+  Resp_ClearHighlighting {} -> __IMPOSSIBLE__
+  Resp_DoneAborting {}      -> __IMPOSSIBLE__
+  Resp_DoneExiting {}       -> __IMPOSSIBLE__
diff --git a/src/full/Agda/Interaction/Response.hs-boot b/src/full/Agda/Interaction/Response.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/Response.hs-boot
@@ -0,0 +1,40 @@
+module Agda.Interaction.Response where
+
+import Data.Int (Int32)
+
+import Agda.Syntax.Common   (InteractionId)
+import Agda.Syntax.Concrete (Expr)
+
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Base
+    (TCM, ModuleToSource, HighlightingMethod)
+
+import Agda.Interaction.Highlighting.Precise
+    (TokenBased, HighlightingInfo)
+
+data Response
+    = Resp_HighlightingInfo
+        HighlightingInfo
+        RemoveTokenBasedHighlighting
+        HighlightingMethod
+        ModuleToSource
+    | Resp_Status Status
+    | Resp_JumpToError FilePath Int32
+    | Resp_InteractionPoints [InteractionId]
+    | Resp_GiveAction InteractionId GiveResult
+    | Resp_MakeCase InteractionId MakeCaseVariant [String]
+    | Resp_SolveAll [(InteractionId, Expr)]
+    | Resp_DisplayInfo DisplayInfo
+    | Resp_RunningInfo Int String
+    | Resp_ClearRunningInfo
+    | Resp_ClearHighlighting TokenBased
+    | Resp_DoneAborting
+    | Resp_DoneExiting
+
+data MakeCaseVariant
+data DisplayInfo
+data RemoveTokenBasedHighlighting
+data GiveResult
+data Status
+
+type InteractionOutputCallback = Response -> TCM ()
+defaultInteractionOutputCallback :: InteractionOutputCallback
diff --git a/src/full/Agda/Interaction/SearchAbout.hs b/src/full/Agda/Interaction/SearchAbout.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Interaction/SearchAbout.hs
@@ -0,0 +1,77 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Interaction.SearchAbout (findMentions) where
+
+import Control.Monad
+
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.List (isInfixOf)
+import Data.Either (partitionEithers)
+import Data.Foldable (toList)
+
+import Agda.Syntax.Position (Range)
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad
+import Agda.TypeChecking.Monad.Signature
+import Agda.TypeChecking.Monad.Env
+import Agda.Syntax.Internal.Names (namesIn)
+import Agda.Interaction.Base (Rewrite)
+import Agda.Interaction.BasicOps (normalForm, parseName)
+
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Internal as I
+
+import Agda.Utils.List   ( initLast1  )
+import qualified Agda.Utils.List1 as List1
+import Agda.Syntax.Common.Pretty ( prettyShow )
+
+findMentions :: Rewrite -> Range -> String -> ScopeM [(C.Name, I.Type)]
+findMentions norm rg nm = do
+  -- We start by dealing with the user's input
+
+  -- The users passes in `nm`, a list of identifiers and strings
+  -- to match against definitions in scope. `findMentions` will
+  -- select all of the definitions such that:
+  -- - all of the specified identifiers appear in their type
+  --   (which has been normalised according to `norm`)
+  -- - all of the specified strings are substrings of their name
+
+  -- We separate the strings from the names by a rough analysis
+  -- and then parse and resolve the names in the current scope
+  let (userSubStrings, nms) = partitionEithers $ isString <$> words nm
+  rnms <- mapM (resolveName <=< parseName rg) nms
+  let userIdentifiers = fmap (fmap anameName . anames) rnms
+
+  -- We then collect all the things in scope, by name.
+  -- Issue #2381: We explicitly filter out pattern synonyms because they
+  -- don't have a type. Looking it up makes Agda panic!
+  snms <- fmap (nsNames . allThingsInScope) $ getNamedScope =<< currentModule
+  let namesInScope = filter ((PatternSynName /=) . anameKind . snd)
+                   $ List1.concat $ map (\ (c, as) -> fmap (c,) as) $ Map.toList snms
+
+  -- Once we have the user-provided names and the names of all the
+  -- thing in scope we can start the search: for each name in scope,
+  -- we grab its type, normalise it according to `norm` and collect
+  -- the identifiers in it. We then check whether it meets the user's
+  -- criteria.
+  ress <- forM namesInScope $ \ (x, n) -> do
+    t <- normalForm norm =<< typeOfConst (anameName n)
+    return $ do
+      guard $ all (`isInfixOf` prettyShow x) userSubStrings
+      guard $ all (any (`Set.member` namesIn t)) userIdentifiers
+      return (x, t)
+  return $ concat ress
+
+  where
+    isString :: String -> Either String String
+    isString ('"' : c : cs)
+      | (str, '"') <- initLast1 c cs
+      = Left $ filter (/= '"') str
+    isString str
+      = Right str
+
+    anames (DefinedName _ an _)   = [an]
+    anames (FieldName     ans)    = toList ans
+    anames (ConstructorName _ ans)= toList ans
+    anames _                      = []
diff --git a/src/full/Agda/Main.hs b/src/full/Agda/Main.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Main.hs
@@ -0,0 +1,392 @@
+{-# LANGUAGE CPP #-}
+
+{-| Agda main module.
+-}
+module Agda.Main where
+
+import Prelude hiding (null)
+
+import qualified Control.Exception as E
+import Control.Monad          ( void )
+import Control.Monad.Except   ( MonadError(..), ExceptT(..), runExceptT )
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+import qualified Data.List as List
+import Data.Maybe
+
+import System.Environment
+import System.Exit
+import System.Console.GetOpt
+import qualified System.IO as IO
+
+import Paths_Agda            ( getDataDir )
+
+import Agda.Interaction.CommandLine
+import Agda.Interaction.ExitCode (AgdaError(..), exitSuccess, exitAgdaWith)
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Help (Help (..))
+import Agda.Interaction.EmacsTop (mimicGHCi)
+import Agda.Interaction.JSONTop (jsonREPL)
+import Agda.Interaction.FindFile ( SourceFile(SourceFile) )
+import qualified Agda.Interaction.Imports as Imp
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Errors
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Warnings
+import Agda.TypeChecking.Pretty
+
+import Agda.Compiler.Backend
+import Agda.Compiler.Builtin
+
+import Agda.VersionCommit
+
+import qualified Agda.Utils.Benchmark as UtilsBench
+import qualified Agda.Syntax.Common.Pretty.ANSI as ANSI
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.FileName (absolute, filePath, AbsolutePath)
+import Agda.Utils.String
+import Agda.Utils.Monad
+import Agda.Utils.Null
+
+import Agda.Utils.Impossible
+import Agda.Interaction.Library (getAgdaAppDir)
+
+-- | The main function
+runAgda :: [Backend] -> IO ()
+runAgda backends = runAgda' $ builtinBackends ++ backends
+
+-- | The main function without importing built-in backends
+runAgda' :: [Backend] -> IO ()
+runAgda' backends = runTCMPrettyErrors $ do
+  progName <- liftIO getProgName
+  argv     <- liftIO getArgs
+  let (z, warns) = runOptM $ parseBackendOptions backends argv defaultOptions
+  mapM_ (warning . OptionWarning) warns
+  conf     <- liftIO $ runExceptT $ do
+    (bs, opts) <- ExceptT $ pure z
+    -- The absolute path of the input file, if provided
+    inputFile <- liftIO $ mapM absolute $ optInputFile opts
+    mode      <- getMainMode bs inputFile opts
+    return (bs, opts, mode)
+
+  case conf of
+    Left err -> liftIO $ optionError err
+    Right (bs, opts, mode) -> do
+
+      when (optTransliterate opts) $ liftIO $ do
+        -- When --interaction or --interaction-json is used, then we
+        -- use UTF-8 when writing to stdout (and when reading from
+        -- stdin).
+        if optGHCiInteraction opts || optJSONInteraction opts
+        then optionError $
+               "The option --transliterate must not be combined with " ++
+               "--interaction or --interaction-json"
+        else do
+          -- Transliterate unsupported code points.
+          enc <- IO.mkTextEncoding
+                   (show IO.localeEncoding ++ "//TRANSLIT")
+          IO.hSetEncoding IO.stdout enc
+          IO.hSetEncoding IO.stderr enc
+
+      case mode of
+        MainModePrintHelp hp     -> liftIO $ printUsage bs hp
+        MainModePrintVersion o   -> liftIO $ printVersion bs o
+        MainModePrintAgdaDataDir -> liftIO $ printAgdaDataDir
+        MainModePrintAgdaAppDir  -> liftIO $ printAgdaAppDir
+        MainModeRun interactor   -> do
+          setTCLens stBackends bs
+          runAgdaWithOptions interactor progName opts
+
+-- | Main execution mode
+data MainMode
+  = MainModeRun (Interactor ())
+  | MainModePrintHelp Help
+  | MainModePrintVersion PrintAgdaVersion
+  | MainModePrintAgdaDataDir
+  | MainModePrintAgdaAppDir
+
+-- | Determine the main execution mode to run, based on the configured backends and command line options.
+-- | This is pure.
+getMainMode :: MonadError String m => [Backend] -> Maybe AbsolutePath -> CommandLineOptions -> m MainMode
+getMainMode configuredBackends maybeInputFile opts
+  | Just hp <- optPrintHelp opts    = return $ MainModePrintHelp hp
+  | Just o  <- optPrintVersion opts = return $ MainModePrintVersion o
+  | optPrintAgdaDataDir opts        = return $ MainModePrintAgdaDataDir
+  | optPrintAgdaAppDir opts         = return $ MainModePrintAgdaAppDir
+  | otherwise = do
+      mi <- getInteractor configuredBackends maybeInputFile opts
+      -- If there was no selection whatsoever (e.g. just invoked "agda"), we just show help and exit.
+      return $ maybe (MainModePrintHelp GeneralHelp) MainModeRun mi
+
+type Interactor a
+    -- Setup/initialization action.
+    -- This is separated so that errors can be reported in the appropriate format.
+    = TCM ()
+    -- Type-checking action
+    -> (AbsolutePath -> TCM CheckResult)
+    -- Main transformed action.
+    -> TCM a
+
+data FrontendType
+  = FrontEndEmacs
+  | FrontEndJson
+  | FrontEndRepl
+
+-- Emacs mode. Note that it ignores the "check" action because it calls typeCheck directly.
+emacsModeInteractor :: Interactor ()
+emacsModeInteractor setup _check = mimicGHCi setup
+
+-- JSON mode. Note that it ignores the "check" action because it calls typeCheck directly.
+jsonModeInteractor :: Interactor ()
+jsonModeInteractor setup _check = jsonREPL setup
+
+-- The deprecated repl mode.
+replInteractor :: Maybe AbsolutePath -> Interactor ()
+replInteractor = runInteractionLoop
+
+-- The interactor to use when there are no frontends or backends specified.
+defaultInteractor :: AbsolutePath -> Interactor ()
+defaultInteractor file setup check = do setup; void $ check file
+
+getInteractor :: MonadError String m => [Backend] -> Maybe AbsolutePath -> CommandLineOptions -> m (Maybe (Interactor ()))
+getInteractor configuredBackends maybeInputFile opts =
+  case (maybeInputFile, enabledFrontends, enabledBackends) of
+    (Just inputFile, [],             _:_) -> return $ Just $ backendInteraction inputFile enabledBackends
+    (Just inputFile, [],              []) -> return $ Just $ defaultInteractor inputFile
+    (Nothing,        [],              []) -> return Nothing -- No backends, frontends, or input files specified.
+    (Nothing,        [],             _:_) -> throwError $ concat ["No input file specified for ", enabledBackendNames]
+    (_,              _:_,            _:_) -> throwError $ concat ["Cannot mix ", enabledFrontendNames, " with ", enabledBackendNames]
+    (_,              _:_:_,           []) -> throwError $ concat ["Must not specify multiple ", enabledFrontendNames]
+    (_,              [fe],            []) | optOnlyScopeChecking opts -> errorFrontendScopeChecking fe
+    (_,              [FrontEndRepl],  []) -> return $ Just $ replInteractor maybeInputFile
+    (Nothing,        [FrontEndEmacs], []) -> return $ Just $ emacsModeInteractor
+    (Nothing,        [FrontEndJson],  []) -> return $ Just $ jsonModeInteractor
+    (Just inputFile, [FrontEndEmacs], []) -> errorFrontendFileDisallowed inputFile FrontEndEmacs
+    (Just inputFile, [FrontEndJson],  []) -> errorFrontendFileDisallowed inputFile FrontEndJson
+  where
+    -- NOTE: The notion of a backend being "enabled" *just* refers to this top-level interaction mode selection. The
+    -- interaction/interactive front-ends may still invoke available backends even if they are not "enabled".
+    isBackendEnabled (Backend b) = isEnabled b (options b)
+    enabledBackends = filter isBackendEnabled configuredBackends
+    enabledFrontends = concat
+      [ [ FrontEndRepl  | optInteractive     opts ]
+      , [ FrontEndEmacs | optGHCiInteraction opts ]
+      , [ FrontEndJson  | optJSONInteraction opts ]
+      ]
+    -- Constructs messages like "(no backend)", "backend ghc", "backends (ghc, ocaml)"
+    pluralize w []  = concat ["(no ", w, ")"]
+    pluralize w [x] = concat [w, " ", x]
+    pluralize w xs  = concat [w, "s (", List.intercalate ", " xs, ")"]
+    enabledBackendNames  = pluralize "backend" [ backendName b | Backend b <- enabledBackends ]
+    enabledFrontendNames = pluralize "frontend" (frontendFlagName <$> enabledFrontends)
+    frontendFlagName = ("--" ++) . \case
+      FrontEndEmacs -> "interaction"
+      FrontEndJson -> "interaction-json"
+      FrontEndRepl -> "interactive"
+    errorFrontendScopeChecking fe = throwError $
+      concat ["The --only-scope-checking flag cannot be combined with ", frontendFlagName fe]
+    errorFrontendFileDisallowed inputFile fe = throwError $
+      concat ["Must not specify an input file (", filePath inputFile, ") with ", frontendFlagName fe]
+
+-- | Run Agda with parsed command line options
+runAgdaWithOptions
+  :: Interactor a       -- ^ Backend interaction
+  -> String             -- ^ program name
+  -> CommandLineOptions -- ^ parsed command line options
+  -> TCM a
+runAgdaWithOptions interactor progName opts = do
+          -- Main function.
+          -- Bill everything to root of Benchmark trie.
+          UtilsBench.setBenchmarking UtilsBench.BenchmarkOn
+            -- Andreas, Nisse, 2016-10-11 AIM XXIV
+            -- Turn benchmarking on provisionally, otherwise we lose track of time spent
+            -- on e.g. LaTeX-code generation.
+            -- Benchmarking might be turned off later by setCommandlineOptions
+
+          Bench.billTo [] $
+            interactor initialSetup checkFile
+          `finally_` do
+            -- Print benchmarks.
+            Bench.print
+
+            -- Print accumulated statistics.
+            printStatistics Nothing =<< useTC lensAccumStatistics
+  where
+    -- Options are fleshed out here so that (most) errors like
+    -- "bad library path" are validated within the interactor,
+    -- so that they are reported with the appropriate protocol/formatting.
+    initialSetup :: TCM ()
+    initialSetup = do
+      opts <- addTrustedExecutables opts
+      setCommandLineOptions opts
+
+    checkFile :: AbsolutePath -> TCM CheckResult
+    checkFile inputFile = do
+        -- Andreas, 2013-10-30 The following 'resetState' kills the
+        -- verbosity options.  That does not make sense (see fail/Issue641).
+        -- 'resetState' here does not seem to serve any purpose,
+        -- thus, I am removing it.
+        -- resetState
+          let mode = if optOnlyScopeChecking opts
+                     then Imp.ScopeCheck
+                     else Imp.TypeCheck
+
+          result <- Imp.typeCheckMain mode =<< Imp.parseSource (SourceFile inputFile)
+
+          unless (crMode result == ModuleScopeChecked) $
+            unlessNullM (applyFlagsToTCWarnings (crWarnings result)) $ \ ws ->
+              typeError $ NonFatalErrors ws
+
+          let i = crInterface result
+          reportSDoc "main" 50 $ pretty i
+
+          -- Print accumulated warnings
+          unlessNullM (tcWarnings . classifyWarnings <$> getAllWarnings AllWarnings) $ \ ws -> do
+            let banner = text $ "\n" ++ delimiter "All done; warnings encountered"
+            alwaysReportSDoc "warning" 1 $
+              vcat $ punctuate "\n" $ banner : (prettyTCM <$> ws)
+
+          return result
+
+
+
+-- | Print usage information.
+printUsage :: [Backend] -> Help -> IO ()
+printUsage backends hp = do
+  progName <- getProgName
+  putStr $ usage standardOptions_ progName hp
+  when (hp == GeneralHelp) $ mapM_ (putStr . backendUsage) backends
+
+backendUsage :: Backend -> String
+backendUsage (Backend b) =
+  usageInfo ("\n" ++ backendName b ++ " backend options") $
+    map void (commandLineFlags b)
+
+-- | Print version information.
+printVersion :: [Backend] -> PrintAgdaVersion -> IO ()
+printVersion _ PrintAgdaNumericVersion = putStrLn versionWithCommitInfo
+printVersion backends PrintAgdaVersion = do
+  putStrLn $ "Agda version " ++ versionWithCommitInfo
+  unless (null flags) $
+    mapM_ putStrLn $ ("Built with flags (cabal -f)" :) $ map bullet flags
+  mapM_ putStrLn
+    [ bullet $ name ++ " backend version " ++ ver
+    | Backend Backend'{ backendName = name, backendVersion = Just ver } <- backends ]
+  where
+  bullet = (" - " ++)
+  -- Print cabal flags that were involved in compilation.
+  flags =
+#ifdef COUNT_CLUSTERS
+    "enable-cluster-counting: unicode cluster counting in LaTeX backend using the ICU library" :
+#endif
+#ifdef OPTIMISE_HEAVILY
+    "optimise-heavily: extra optimisations" :
+#endif
+#ifdef DEBUG
+    "debug: enable debug printing ('-v' verbosity flags)" :
+#endif
+#ifdef DEBUG_PARSING
+    "debug-parsing: enable printing grammars for operator parsing via '-v scope.grammar:10'" :
+#endif
+#ifdef DEBUG_SERIALISATION
+    "debug-serialisation: extra debug info during serialisation into '.agdai' files" :
+#endif
+    []
+
+printAgdaDataDir :: IO ()
+printAgdaDataDir = putStrLn =<< getDataDir
+
+printAgdaAppDir :: IO ()
+printAgdaAppDir = putStrLn =<< getAgdaAppDir
+
+-- | What to do for bad options.
+optionError :: String -> IO ()
+optionError err = do
+  prog <- getProgName
+  putStrLn $ "Error: " ++ err ++ "\nRun '" ++ prog ++ " --help' for help on command line options."
+  exitAgdaWith OptionError
+
+-- | Run a TCM action in IO; catch and pretty print errors.
+
+-- If some error message cannot be printed due to locale issues, then
+-- one may get the "Error when handling error" error message. There is
+-- currently no test case for this error, but on some systems one can
+-- (at the time of writing) trigger it by running @LC_CTYPE=C agda
+-- --no-libraries Bug.agda@, where @Bug.agda@ contains the following
+-- code (if there is some other file in the same directory, for
+-- instance @Bug.lagda@, then the error message may be different):
+--
+-- @
+-- _ : Set
+-- _ = Set
+-- @
+
+runTCMPrettyErrors :: TCM () -> IO ()
+runTCMPrettyErrors tcm = do
+  r <- runTCMTop
+    ( ( (Nothing <$ tcm)
+          `catchError` \err -> do
+            s2s <- prettyTCWarnings' =<< getAllWarningsOfTCErr err
+            s1  <- prettyError err
+            ANSI.putDoc (P.vcat s2s P.$+$ s1)
+            liftIO $ do
+              helpForLocaleError err
+            return (Just TCMError)
+      ) `catchImpossible` \e -> do
+          liftIO $ putStr $ E.displayException e
+          return (Just ImpossibleError)
+    ) `E.catches`
+        -- Catch all exceptions except for those of type ExitCode
+        -- (which are thrown by exitWith) and asynchronous exceptions
+        -- (which are for instance raised when Ctrl-C is used, or if
+        -- the program runs out of heap or stack space).
+        [ E.Handler $ \(e :: ExitCode)         -> E.throw e
+        , E.Handler $ \(e :: E.AsyncException) -> E.throw e
+        , E.Handler $ \(e :: E.SomeException)  -> do
+            liftIO $ putStr $ E.displayException e
+            return $ Right (Just UnknownError)
+        ]
+  case r of
+    Right Nothing       -> exitSuccess
+    Right (Just reason) -> exitAgdaWith reason
+    Left err            -> do
+      liftIO $ do
+        putStrLn "\n\nError when handling error:"
+        putStrLn $ tcErrString err
+        helpForLocaleError err
+      exitAgdaWith UnknownError
+
+-- | If the error is an IO error, and the error message suggests that
+-- the problem is related to locales or code pages, print out some
+-- extra information.
+
+helpForLocaleError :: TCErr -> IO ()
+helpForLocaleError e = case e of
+  (IOException _ _ e)
+    | "invalid argument" `List.isInfixOf` show e -> msg
+  _                                              -> return ()
+  where
+  msg = putStr $ unlines
+    [ ""
+    , "This error may be due to the use of a locale or code page that does not"
+    , "support some character used in the program being type-checked."
+    , ""
+    , "If it is, then one option is to use the option --transliterate, in which"
+    , "case unsupported characters are (hopefully) replaced with something else,"
+    , "perhaps question marks. However, that could make the output harder to"
+    , "read."
+    , ""
+    , "If you want to fix the problem \"properly\", then you could try one of the"
+    , "following suggestions:"
+    , ""
+    , "* If you are using Windows, try switching to a different code page (for"
+    , "  instance by running the command 'CHCP 65001')."
+    , ""
+    , "* If you are using a Unix-like system, try using a different locale. The"
+    , "  installed locales are perhaps printed by the command 'locale -a'. If"
+    , "  you have a UTF-8 locale installed (for instance sv_SE.UTF-8), then you"
+    , "  can perhaps make Agda use this locale by running something like"
+    , "  'LC_ALL=sv_SE.UTF-8 agda <...>'."
+    ]
diff --git a/src/full/Agda/Syntax/Abstract.hs b/src/full/Agda/Syntax/Abstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract.hs
@@ -0,0 +1,1207 @@
+
+{-| The abstract syntax. This is what you get after desugaring and scope
+    analysis of the concrete syntax. The type checker works on abstract syntax,
+    producing internal syntax ("Agda.Syntax.Internal").
+-}
+module Agda.Syntax.Abstract
+    ( module Agda.Syntax.Abstract
+    , module Agda.Syntax.Abstract.Name
+    ) where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import Data.Bifunctor
+import qualified Data.Foldable as Fold
+import Data.Function (on)
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Maybe
+import qualified Data.Set as Set
+import Data.Set (Set)
+import Data.Void
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Concrete (FieldAssignment'(..))
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Abstract.Name
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Common
+import Agda.Syntax.Info
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+
+import Agda.TypeChecking.Positivity.Occurrence
+
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+-- | A name in a binding position: we also compare the nameConcrete
+-- when comparing the binders for equality.
+--
+-- With @--caching@ on we compare abstract syntax to determine if we can
+-- reuse previous typechecking results: during that comparison two
+-- names can have the same nameId but be semantically different,
+-- e.g. in @{_ : A} -> ..@ vs. @{r : A} -> ..@.
+
+newtype BindName = BindName { unBind :: Name }
+  deriving (Show, HasRange, KillRange, SetRange, NFData)
+
+mkBindName :: Name -> BindName
+mkBindName x = BindName x
+
+instance Eq BindName where
+  BindName n == BindName m
+    = ((==) `on` nameId) n m
+      && ((==) `on` nameConcrete) n m
+
+instance Ord BindName where
+  BindName n `compare` BindName m
+    = (compare `on` nameId) n m
+      `mappend` (compare `on` nameConcrete) n m
+
+type Args = [NamedArg Expr]
+
+-- | Types are just expressions.
+-- Use this type synonym for hinting that an expression should be a type.
+type Type = Expr
+
+-- | Expressions after scope checking (operators parsed, names resolved).
+data Expr
+  = Var  Name                          -- ^ Bound variable.
+  | Def'  QName Suffix                 -- ^ Constant: axiom, function, data or record type,
+                                       --   with a possible suffix.
+  | Proj ProjOrigin AmbiguousQName     -- ^ Projection (overloaded).
+  | Con  AmbiguousQName                -- ^ Constructor (overloaded).
+  | PatternSyn AmbiguousQName          -- ^ Pattern synonym.
+  | Macro QName                        -- ^ Macro.
+  | Lit ExprInfo Literal               -- ^ Literal.
+  | QuestionMark MetaInfo InteractionId
+    -- ^ Meta variable for interaction.
+    --   The 'InteractionId' is usually identical with the
+    --   'metaNumber' of 'MetaInfo'.
+    --   However, if you want to print an interaction meta as
+    --   just @?@ instead of @?n@, you should set the
+    --   'metaNumber' to 'Nothing' while keeping the 'InteractionId'.
+  | Underscore   MetaInfo
+    -- ^ Meta variable for hidden argument (must be inferred locally).
+  | Dot ExprInfo Expr                  -- ^ @.e@, for postfix projection.
+  | App  AppInfo Expr (NamedArg Expr)  -- ^ Ordinary (binary) application.
+  | WithApp ExprInfo Expr [Expr]       -- ^ With application.
+  | Lam  ExprInfo LamBinding Expr      -- ^ @λ bs → e@.
+  | AbsurdLam ExprInfo Hiding          -- ^ @λ()@ or @λ{}@.
+  | ExtendedLam ExprInfo DefInfo Erased QName (List1 Clause)
+  | Pi   ExprInfo Telescope1 Type      -- ^ Dependent function space @Γ → A@.
+  | Generalized (Set QName) Type       -- ^ Like a Pi, but the ordering is not known
+  | Fun  ExprInfo (Arg Type) Type      -- ^ Non-dependent function space.
+  | Let  ExprInfo (List1 LetBinding) Expr
+                                       -- ^ @let bs in e@.
+  | Rec  ExprInfo RecordAssigns        -- ^ Record construction.
+  | RecUpdate ExprInfo Expr Assigns    -- ^ Record update.
+  | ScopedExpr ScopeInfo Expr          -- ^ Scope annotation.
+  | Quote ExprInfo                     -- ^ Quote an identifier 'QName'.
+  | QuoteTerm ExprInfo                 -- ^ Quote a term.
+  | Unquote ExprInfo                   -- ^ The splicing construct: unquote ...
+  | DontCare Expr                      -- ^ For printing @DontCare@ from @Syntax.Internal@.
+  deriving (Show, Generic)
+
+-- | Pattern synonym for regular 'Def'.
+pattern Def :: QName -> Expr
+pattern Def x = Def' x NoSuffix
+
+-- | Smart constructor for 'Generalized'.
+generalized :: Set QName -> Type -> Type
+generalized s e
+    | null s    = e
+    | otherwise = Generalized s e
+
+-- | Record field assignment @f = e@.
+type Assign  = FieldAssignment' Expr
+type Assigns = [Assign]
+type RecordAssign  = Either Assign ModuleName
+type RecordAssigns = [RecordAssign]
+
+-- | Renaming (generic).
+type Ren a = Map a (List1 a)
+
+data ScopeCopyInfo = ScopeCopyInfo
+  { renModules :: Ren ModuleName
+  , renNames   :: Ren QName }
+  deriving (Eq, Show, Generic)
+
+initCopyInfo :: ScopeCopyInfo
+initCopyInfo = ScopeCopyInfo
+  { renModules = mempty
+  , renNames   = mempty
+  }
+
+instance Pretty ScopeCopyInfo where
+  pretty i = vcat [ prRen "renModules =" (renModules i)
+                  , prRen "renNames   =" (renNames i) ]
+    where
+      prRen s r = sep [ text s, nest 2 $ vcat (map pr xs) ]
+        where
+          xs = [ (k, v) | (k, vs) <- Map.toList r, v <- List1.toList vs ]
+      pr (x, y) = pretty x <+> "->" <+> pretty y
+
+type RecordDirectives = RecordDirectives' QName
+
+data Declaration
+  = Axiom      KindOfName DefInfo ArgInfo (Maybe [Occurrence]) QName Type
+    -- ^ Type signature (can be irrelevant, but not hidden).
+    --
+    -- The fourth argument contains an optional assignment of
+    -- polarities to arguments.
+  | Generalize (Set QName) DefInfo ArgInfo QName Type
+    -- ^ First argument is set of generalizable variables used in the type.
+  | Field      DefInfo QName (Arg Type)              -- ^ record field
+  | Primitive  DefInfo QName (Arg Type)              -- ^ primitive function
+  | Mutual     MutualInfo [Declaration]              -- ^ a bunch of mutually recursive definitions
+  | Section    Range Erased ModuleName GeneralizeTelescope [Declaration]
+  | Apply      ModuleInfo Erased ModuleName ModuleApplication
+               ScopeCopyInfo ImportDirective
+    -- ^ The @ImportDirective@ is for highlighting purposes.
+  | Import     ModuleInfo ModuleName ImportDirective
+    -- ^ The @ImportDirective@ is for highlighting purposes.
+  | Pragma     Range      Pragma
+  | Open       ModuleInfo ModuleName ImportDirective
+  | FunDef     DefInfo QName [Clause] -- ^ sequence of function clauses
+  | DataSig    DefInfo Erased QName GeneralizeTelescope Type -- ^ lone data signature
+  | DataDef    DefInfo QName UniverseCheck DataDefParams [Constructor]
+  | RecSig     DefInfo Erased QName GeneralizeTelescope Type -- ^ lone record signature
+  | RecDef     DefInfo QName UniverseCheck RecordDirectives DataDefParams Type [Declaration]
+      -- ^ The 'Type' gives the constructor type telescope, @(x1 : A1)..(xn : An) -> Dummy@,
+      --   and the optional name is the constructor's name.
+      --   The optional 'Range' is for the @pattern@ attribute.
+  | PatternSynDef QName [Arg BindName] (Pattern' Void)
+      -- ^ Only for highlighting purposes
+  | UnquoteDecl MutualInfo [DefInfo] [QName] Expr
+  | UnquoteDef  [DefInfo] [QName] Expr
+  | UnquoteData [DefInfo] QName UniverseCheck [DefInfo] [QName] Expr
+  | ScopedDecl ScopeInfo [Declaration]  -- ^ scope annotation
+  | UnfoldingDecl Range [QName]
+    -- ^ Only for highlighting the unfolded names
+  deriving (Show, Generic)
+
+type DefInfo = DefInfo' Expr
+
+type ImportDirective = ImportDirective' QName ModuleName
+type Renaming        = Renaming'        QName ModuleName
+type ImportedName    = ImportedName'    QName ModuleName
+
+data ModuleApplication
+    = SectionApp Telescope ModuleName [NamedArg Expr]
+      -- ^ @tel. M args@:  applies @M@ to @args@ and abstracts @tel@.
+    | RecordModuleInstance ModuleName
+      -- ^ @M {{...}}@
+  deriving (Show, Eq, Generic)
+
+data Pragma
+  = OptionsPragma [String]
+  | BuiltinPragma RString ResolvedName
+    -- ^ 'ResolvedName' is not 'UnknownName'.
+    --   Name can be ambiguous e.g. for built-in constructors.
+  | BuiltinNoDefPragma RString KindOfName QName
+    -- ^ Builtins that do not come with a definition,
+    --   but declare a name for an Agda concept.
+  | RewritePragma Range [QName]
+    -- ^ Range is range of REWRITE keyword.
+  | CompilePragma RString QName String
+  | StaticPragma QName
+  | EtaPragma QName
+    -- ^ For coinductive records, use pragma instead of regular
+    --   @eta-equality@ definition (as it is might make Agda loop).
+  | InjectivePragma QName
+  | InlinePragma Bool QName -- INLINE or NOINLINE
+  | NotProjectionLikePragma QName
+    -- Mark the definition as not being projection-like
+  | DisplayPragma QName [NamedArg Pattern] Expr
+  deriving (Show, Eq, Generic)
+
+-- | Bindings that are valid in a @let@.
+data LetBinding
+  = LetBind LetInfo ArgInfo BindName Type Expr
+    -- ^ @LetBind info rel name type defn@
+  | LetPatBind LetInfo Pattern Expr
+    -- ^ Irrefutable pattern binding.
+  | LetApply ModuleInfo Erased ModuleName ModuleApplication
+      ScopeCopyInfo ImportDirective
+    -- ^ @LetApply mi newM (oldM args) renamings dir@.
+    -- The @ImportDirective@ is for highlighting purposes.
+  | LetOpen ModuleInfo ModuleName ImportDirective
+    -- ^ only for highlighting and abstractToConcrete
+  | LetDeclaredVariable BindName
+    -- ^ Only used for highlighting. Refers to the first occurrence of
+    -- @x@ in @let x : A; x = e@.
+  deriving (Show, Eq, Generic)
+
+-- | Only 'Axiom's.
+type TypeSignature  = Declaration
+type Constructor    = TypeSignature
+type Field          = TypeSignature
+
+type TacticAttr = Maybe (Ranged Expr)
+
+-- A Binder @x\@p@, the pattern is optional
+data Binder' a = Binder
+  { binderPattern :: Maybe Pattern
+  , binderName    :: a
+  } deriving (Show, Eq, Functor, Foldable, Traversable, Generic)
+
+type Binder = Binder' BindName
+
+mkBinder :: a -> Binder' a
+mkBinder = Binder Nothing
+
+mkBinder_ :: Name -> Binder
+mkBinder_ = mkBinder . mkBindName
+
+extractPattern :: Binder' a -> Maybe (Pattern, a)
+extractPattern (Binder p a) = (,a) <$> p
+
+-- | A lambda binding is either domain free or typed.
+data LamBinding
+  = DomainFree TacticAttr (NamedArg Binder)
+    -- ^ . @x@ or @{x}@ or @.x@ or @{x = y}@ or @x\@p@ or @(p)@
+  | DomainFull TypedBinding
+    -- ^ . @(xs:e)@ or @{xs:e}@ or @(let Ds)@
+  deriving (Show, Eq, Generic)
+
+mkDomainFree :: NamedArg Binder -> LamBinding
+mkDomainFree = DomainFree Nothing
+
+-- | Extra information that is attached to a typed binding, that plays a
+-- role during type checking but strictly speaking is not part of the
+-- @name : type@" relation which a makes up a binding.
+data TypedBindingInfo
+  = TypedBindingInfo
+    { tbTacticAttr :: TacticAttr
+      -- ^ Does this binding have a tactic annotation?
+    , tbFinite     :: Bool
+      -- ^ Does this binding correspond to a Partial binder, rather than
+      -- to a Pi binder? Must be present here to be reflected into
+      -- abstract syntax later (and to be printed to the user later).
+    }
+  deriving (Show, Eq, Generic)
+
+defaultTbInfo :: TypedBindingInfo
+defaultTbInfo = TypedBindingInfo
+  { tbTacticAttr = Nothing
+  , tbFinite = False
+  }
+
+-- | A typed binding.  Appears in dependent function spaces, typed lambdas, and
+--   telescopes.  It might be tempting to simplify this to only bind a single
+--   name at a time, and translate, say, @(x y : A)@ to @(x : A)(y : A)@
+--   before type-checking.  However, this would be slightly problematic:
+--
+--     1. We would have to typecheck the type @A@ several times.
+--
+--     2. If @A@ contains a meta variable or hole, it would be duplicated
+--        by such a translation.
+--
+--   While 1. is only slightly inefficient, 2. would be an outright bug.
+--   Duplicating @A@ could not be done naively, we would have to make sure
+--   that the metas of the copy are aliases of the metas of the original.
+
+data TypedBinding
+  = TBind Range TypedBindingInfo (List1 (NamedArg Binder)) Type
+    -- ^ As in telescope @(x y z : A)@ or type @(x y z : A) -> B@.
+  | TLet Range (List1 LetBinding)
+    -- ^ E.g. @(let x = e)@ or @(let open M)@.
+  deriving (Show, Eq, Generic)
+
+mkTBind :: Range -> List1 (NamedArg Binder) -> Type -> TypedBinding
+mkTBind r = TBind r defaultTbInfo
+
+mkTLet :: Range -> [LetBinding] -> Maybe TypedBinding
+mkTLet _ []     = Nothing
+mkTLet r (d:ds) = Just $ TLet r (d :| ds)
+
+type Telescope1 = List1 TypedBinding
+type Telescope  = [TypedBinding]
+
+mkPi :: ExprInfo -> Telescope -> Type -> Type
+mkPi i []     e = e
+mkPi i (x:xs) e = Pi i (x :| xs) e
+
+data GeneralizeTelescope = GeneralizeTel
+  { generalizeTelVars :: Map QName Name
+    -- ^ Maps generalize variables to the corresponding bound variable (to be
+    --   introduced by the generalisation).
+  , generalizeTel     :: Telescope }
+  deriving (Show, Eq, Generic)
+
+data DataDefParams = DataDefParams
+  { dataDefGeneralizedParams :: Set Name
+    -- ^ We don't yet know the position of generalized parameters from the data
+    --   sig, so we keep these in a set on the side.
+  , dataDefParams :: [LamBinding]
+  }
+  deriving (Show, Eq, Generic)
+
+noDataDefParams :: DataDefParams
+noDataDefParams = DataDefParams Set.empty []
+
+-- | A user pattern together with an internal term that it should be equal to
+--   after splitting is complete.
+--   Special cases:
+--    * User pattern is a variable but internal term isn't:
+--      this will be turned into an as pattern.
+--    * User pattern is a dot pattern:
+--      this pattern won't trigger any splitting but will be checked
+--      for equality after all splitting is complete and as patterns have
+--      been bound.
+--    * User pattern is an absurd pattern:
+--      emptiness of the type will be checked after splitting is complete.
+--    * User pattern is an annotated wildcard:
+--      type annotation will be checked after splitting is complete.
+data ProblemEq = ProblemEq
+  { problemInPat :: Pattern
+  , problemInst  :: I.Term
+  , problemType  :: I.Dom I.Type
+  } deriving (Show, Generic)
+
+-- These are not relevant for caching purposes
+instance Eq ProblemEq where _ == _ = True
+
+-- | We could throw away @where@ clauses at this point and translate them to
+--   @let@. It's not obvious how to remember that the @let@ was really a
+--   @where@ clause though, so for the time being we keep it here.
+data Clause' lhs = Clause
+  { clauseLHS        :: lhs
+  , clauseStrippedPats :: [ProblemEq]
+      -- ^ Only in with-clauses where we inherit some already checked patterns from the parent.
+      --   These live in the context of the parent clause left-hand side.
+  , clauseRHS        :: RHS
+  , clauseWhereDecls :: WhereDeclarations
+  , clauseCatchall   :: Bool
+  } deriving (Show, Functor, Foldable, Traversable, Eq, Generic)
+
+data WhereDeclarations = WhereDecls
+  { whereModule :: Maybe ModuleName
+      -- #2897: we need to restrict named where modules in refined contexts,
+      --        so remember whether it was named here
+  , whereAnywhere :: Bool
+      -- ^ is it an ordinary unnamed @where@?
+  , whereDecls :: Maybe Declaration
+      -- ^ The declaration is a 'Section'.
+  } deriving (Show, Eq, Generic)
+
+instance Null WhereDeclarations where
+  empty = WhereDecls empty False empty
+
+noWhereDecls :: WhereDeclarations
+noWhereDecls = empty
+
+type Clause = Clause' LHS
+type SpineClause = Clause' SpineLHS
+type RewriteEqn  = RewriteEqn' QName BindName Pattern Expr
+type WithExpr' e = Named BindName (Arg e)
+type WithExpr    = WithExpr' Expr
+
+data RHS
+  = RHS
+    { rhsExpr     :: Expr
+    , rhsConcrete :: Maybe C.Expr
+      -- ^ We store the original concrete expression in case
+      --   we have to reproduce it during interactive case splitting.
+      --   'Nothing' for internally generated rhss.
+    }
+  | AbsurdRHS
+  | WithRHS QName [WithExpr] (List1 Clause)
+      -- ^ The 'QName' is the name of the with function.
+  | RewriteRHS
+    { rewriteExprs      :: [RewriteEqn]
+      -- ^ The 'QName's are the names of the generated with functions,
+      --   one for each 'Expr'.
+    , rewriteStrippedPats :: [ProblemEq]
+      -- ^ The patterns stripped by with-desugaring. These are only present
+      --   if this rewrite follows a with.
+    , rewriteRHS        :: RHS
+      -- ^ The RHS should not be another @RewriteRHS@.
+    , rewriteWhereDecls :: WhereDeclarations
+      -- ^ The where clauses are attached to the @RewriteRHS@ by
+      ---  the scope checker (instead of to the clause).
+    }
+  deriving (Show, Generic)
+
+-- | Ignore 'rhsConcrete' when comparing 'RHS's.
+instance Eq RHS where
+  RHS e _          == RHS e' _            = e == e'
+  AbsurdRHS        == AbsurdRHS           = True
+  WithRHS a b c    == WithRHS a' b' c'    = (a == a') && (b == b') && (c == c')
+  RewriteRHS a b c d == RewriteRHS a' b' c' d' = and [ a == a', b == b', c == c' , d == d' ]
+  _                == _                   = False
+
+-- | The lhs of a clause in spine view (inside-out).
+--   Projection patterns are contained in @spLhsPats@,
+--   represented as @ProjP d@.
+data SpineLHS = SpineLHS
+  { spLhsInfo     :: LHSInfo             -- ^ Range.
+  , spLhsDefName  :: QName               -- ^ Name of function we are defining.
+  , spLhsPats     :: [NamedArg Pattern]  -- ^ Elimination by pattern, projections, with-patterns.
+  }
+  deriving (Show, Eq, Generic)
+
+-- | Ignore 'Range' when comparing 'LHS's.
+instance Eq LHS where
+  LHS _ core == LHS _ core' = core == core'
+
+-- | The lhs of a clause in focused (projection-application) view (outside-in).
+--   Projection patters are represented as 'LHSProj's.
+data LHS = LHS
+  { lhsInfo     :: LHSInfo               -- ^ Range.
+  , lhsCore     :: LHSCore               -- ^ Copatterns.
+  }
+  deriving (Show, Generic)
+
+-- | The lhs in projection-application and with-pattern view.
+--   Parameterised over the type @e@ of dot patterns.
+data LHSCore' e
+    -- | The head applied to ordinary patterns.
+  = LHSHead  { lhsDefName  :: QName
+                 -- ^ Head @f@.
+             , lhsPats     :: [NamedArg (Pattern' e)]
+                 -- ^ Applied to patterns @ps@.
+             }
+    -- | Projection.
+  | LHSProj  { lhsDestructor :: AmbiguousQName
+                 -- ^ Record projection identifier.
+             , lhsFocus      :: NamedArg (LHSCore' e)
+                 -- ^ Main argument of projection.
+             , lhsPats       :: [NamedArg (Pattern' e)]
+                 -- ^ Further applied to patterns.
+             }
+    -- | With patterns.
+  | LHSWith  { lhsHead         :: LHSCore' e
+                 -- ^ E.g. the 'LHSHead'.
+             , lhsWithPatterns :: [Arg (Pattern' e)]
+                 -- ^ Applied to with patterns @| p1 | ... | pn@.
+                 --   These patterns are not prefixed with @WithP@!
+             , lhsPats         :: [NamedArg (Pattern' e)]
+                 -- ^ Further applied to patterns.
+             }
+  deriving (Show, Functor, Foldable, Traversable, Eq, Generic)
+
+type LHSCore = LHSCore' Expr
+
+---------------------------------------------------------------------------
+-- * Patterns
+---------------------------------------------------------------------------
+
+-- | Parameterised over the type of dot patterns.
+data Pattern' e
+  = VarP BindName
+  | ConP ConPatInfo AmbiguousQName (NAPs e)
+  | ProjP PatInfo ProjOrigin AmbiguousQName
+    -- ^ Destructor pattern @d@.
+  | DefP PatInfo AmbiguousQName (NAPs e)
+    -- ^ Defined pattern: function definition @f ps@.
+    --   It is also abused to convert destructor patterns into concrete syntax
+    --   thus, we put AmbiguousQName here as well.
+  | WildP PatInfo
+    -- ^ Underscore pattern entered by user.
+    --   Or generated at type checking for implicit arguments.
+  | AsP PatInfo BindName (Pattern' e)
+  | DotP PatInfo e
+    -- ^ Dot pattern @.e@
+  | AbsurdP PatInfo
+  | LitP PatInfo Literal
+  | PatternSynP PatInfo AmbiguousQName (NAPs e)
+  | RecP PatInfo [FieldAssignment' (Pattern' e)]
+  | EqualP PatInfo [(e, e)]
+  | WithP PatInfo (Pattern' e)  -- ^ @| p@, for with-patterns.
+  | AnnP PatInfo e (Pattern' e) -- ^ Pattern with type annotation
+  deriving (Show, Functor, Foldable, Traversable, Eq, Generic)
+
+type NAPs e   = [NamedArg (Pattern' e)]
+type NAPs1 e  = List1 (NamedArg (Pattern' e))
+type Pattern  = Pattern' Expr
+type Patterns = [NamedArg Pattern]
+
+instance IsProjP (Pattern' e) where
+  -- Andreas, 2018-06-19, issue #3130
+  -- Do not interpret things like .(p) as projection pattern any more.
+  -- maybePostfixProjP (DotP _ e)    = isProjP e <&> \ (_o, d) -> (ProjPostfix, d)
+  isProjP (ProjP _ o d) = Just (o, d)
+  isProjP _ = Nothing
+
+instance IsProjP Expr where
+  isProjP (Proj o ds)      = Just (o, ds)
+  isProjP (ScopedExpr _ e) = isProjP e
+  isProjP _ = Nothing
+
+{--------------------------------------------------------------------------
+    Things we parse but are not part of the Agda file syntax
+ --------------------------------------------------------------------------}
+
+type HoleContent = C.HoleContent' () BindName Pattern Expr
+
+{--------------------------------------------------------------------------
+    Instances
+ --------------------------------------------------------------------------}
+
+-- | Does not compare 'ScopeInfo' fields.
+--   Does not distinguish between prefix and postfix projections.
+
+instance Eq Expr where
+  ScopedExpr _ a1            == ScopedExpr _ a2            = a1 == a2
+
+  Var a1                     == Var a2                     = a1 == a2
+  Def' a1 s1                 == Def' a2 s2                 = (a1, s1) == (a2, s2)
+  Proj _ a1                  == Proj _ a2                  = a1 == a2
+  Con a1                     == Con a2                     = a1 == a2
+  PatternSyn a1              == PatternSyn a2              = a1 == a2
+  Macro a1                   == Macro a2                   = a1 == a2
+  Lit r1 a1                  == Lit r2 a2                  = (r1, a1) == (r2, a2)
+  QuestionMark a1 b1         == QuestionMark a2 b2         = (a1, b1) == (a2, b2)
+  Underscore a1              == Underscore a2              = a1 == a2
+  Dot r1 e1                  == Dot r2 e2                  = (r1, e1) == (r2, e2)
+  App a1 b1 c1               == App a2 b2 c2               = (a1, b1, c1) == (a2, b2, c2)
+  WithApp a1 b1 c1           == WithApp a2 b2 c2           = (a1, b1, c1) == (a2, b2, c2)
+  Lam a1 b1 c1               == Lam a2 b2 c2               = (a1, b1, c1) == (a2, b2, c2)
+  AbsurdLam a1 b1            == AbsurdLam a2 b2            = (a1, b1) == (a2, b2)
+  ExtendedLam a1 b1 c1 d1 e1 == ExtendedLam a2 b2 c2 d2 e2 = (a1, b1, c1, d1, e1) ==
+                                                             (a2, b2, c2, d2, e2)
+  Pi a1 b1 c1                == Pi a2 b2 c2                = (a1, b1, c1) == (a2, b2, c2)
+  Generalized a1 b1          == Generalized a2 b2          = (a1, b1) == (a2, b2)
+  Fun a1 b1 c1               == Fun a2 b2 c2               = (a1, b1, c1) == (a2, b2, c2)
+  Let a1 b1 c1               == Let a2 b2 c2               = (a1, b1, c1) == (a2, b2, c2)
+  Rec a1 b1                  == Rec a2 b2                  = (a1, b1) == (a2, b2)
+  RecUpdate a1 b1 c1         == RecUpdate a2 b2 c2         = (a1, b1, c1) == (a2, b2, c2)
+  Quote a1                   == Quote a2                   = a1 == a2
+  QuoteTerm a1               == QuoteTerm a2               = a1 == a2
+  Unquote a1                 == Unquote a2                 = a1 == a2
+  DontCare a1                == DontCare a2                = a1 == a2
+
+  _                          == _                          = False
+
+-- | Does not compare 'ScopeInfo' fields.
+
+instance Eq Declaration where
+  ScopedDecl _ a1                == ScopedDecl _ a2                = a1 == a2
+
+  Axiom a1 b1 c1 d1 e1 f1        == Axiom a2 b2 c2 d2 e2 f2        = (a1, b1, c1, d1, e1, f1) == (a2, b2, c2, d2, e2, f2)
+  Generalize a1 b1 c1 d1 e1      == Generalize a2 b2 c2 d2 e2      = (a1, b1, c1, d1, e1) == (a2, b2, c2, d2, e2)
+  Field a1 b1 c1                 == Field a2 b2 c2                 = (a1, b1, c1) == (a2, b2, c2)
+  Primitive a1 b1 c1             == Primitive a2 b2 c2             = (a1, b1, c1) == (a2, b2, c2)
+  Mutual a1 b1                   == Mutual a2 b2                   = (a1, b1) == (a2, b2)
+  Section a1 b1 c1 d1 e1         == Section a2 b2 c2 d2 e2         = (a1, b1, c1, d1, e1) == (a2, b2, c2, d2, e2)
+  Apply a1 b1 c1 d1 e1 f1        == Apply a2 b2 c2 d2 e2 f2        = (a1, b1, c1, d1, e1, f1) == (a2, b2, c2, d2, e2, f2)
+  Import a1 b1 c1                == Import a2 b2 c2                = (a1, b1, c1) == (a2, b2, c2)
+  Pragma a1 b1                   == Pragma a2 b2                   = (a1, b1) == (a2, b2)
+  Open a1 b1 c1                  == Open a2 b2 c2                  = (a1, b1, c1) == (a2, b2, c2)
+  FunDef a1 b1 c1                == FunDef a2 b2 c2                = (a1, b1, c1) == (a2, b2, c2)
+  DataSig a1 b1 c1 d1 e1         == DataSig a2 b2 c2 d2 e2         = (a1, b1, c1, d1, e1) == (a2, b2, c2, d2, e2)
+  DataDef a1 b1 c1 d1 e1         == DataDef a2 b2 c2 d2 e2         = (a1, b1, c1, d1, e1) == (a2, b2, c2, d2, e2)
+  RecSig a1 b1 c1 d1 e1          == RecSig a2 b2 c2 d2 e2          = (a1, b1, c1, d1, e1) == (a2, b2, c2, d2, e2)
+  RecDef a1 b1 c1 d1 e1 f1 g1    == RecDef a2 b2 c2 d2 e2 f2 g2    = (a1, b1, c1, d1, e1, f1, g1) == (a2, b2, c2, d2, e2, f2, g2)
+  PatternSynDef a1 b1 c1         == PatternSynDef a2 b2 c2         = (a1, b1, c1) == (a2, b2, c2)
+  UnquoteDecl a1 b1 c1 d1        == UnquoteDecl a2 b2 c2 d2        = (a1, b1, c1, d1) == (a2, b2, c2, d2)
+  UnquoteDef a1 b1 c1            == UnquoteDef a2 b2 c2            = (a1, b1, c1) == (a2, b2, c2)
+  UnfoldingDecl a1 b1            == UnfoldingDecl a2 b2            = (a1,b1) == (a2,b2)
+
+  _                              == _                              = False
+
+instance Underscore Expr where
+  underscore   = Underscore emptyMetaInfo
+  isUnderscore = __IMPOSSIBLE__
+
+instance LensHiding LamBinding where
+  getHiding   (DomainFree _ x) = getHiding x
+  getHiding   (DomainFull tb)  = getHiding tb
+  mapHiding f (DomainFree t x) = DomainFree t $ mapHiding f x
+  mapHiding f (DomainFull tb)  = DomainFull $ mapHiding f tb
+
+instance LensHiding TypedBinding where
+  getHiding (TBind _ _ (x :| _) _) = getHiding x   -- Slightly dubious
+  getHiding TLet{}                 = mempty
+  mapHiding f (TBind r t xs e)     = TBind r t ((fmap . mapHiding) f xs) e
+  mapHiding f b@TLet{}             = b
+
+instance HasRange a => HasRange (Binder' a) where
+  getRange (Binder p n) = fuseRange p n
+
+instance HasRange LamBinding where
+    getRange (DomainFree _ x) = getRange x
+    getRange (DomainFull b)   = getRange b
+
+instance HasRange TypedBinding where
+    getRange (TBind r _ _ _) = r
+    getRange (TLet r _)    = r
+
+instance HasRange Expr where
+    getRange (Var x)                 = getRange x
+    getRange (Def' x _)              = getRange x
+    getRange (Proj _ x)              = getRange x
+    getRange (Con x)                 = getRange x
+    getRange (Lit i _)               = getRange i
+    getRange (QuestionMark i _)      = getRange i
+    getRange (Underscore  i)         = getRange i
+    getRange (Dot i _)               = getRange i
+    getRange (App i _ _)             = getRange i
+    getRange (WithApp i _ _)         = getRange i
+    getRange (Lam i _ _)             = getRange i
+    getRange (AbsurdLam i _)         = getRange i
+    getRange (ExtendedLam i _ _ _ _) = getRange i
+    getRange (Pi i _ _)              = getRange i
+    getRange (Generalized _ x)       = getRange x
+    getRange (Fun i _ _)             = getRange i
+    getRange (Let i _ _)             = getRange i
+    getRange (Rec i _)               = getRange i
+    getRange (RecUpdate i _ _)       = getRange i
+    getRange (ScopedExpr _ e)        = getRange e
+    getRange (Quote i)               = getRange i
+    getRange (QuoteTerm i)           = getRange i
+    getRange (Unquote i)             = getRange i
+    getRange (DontCare{})            = noRange
+    getRange (PatternSyn x)          = getRange x
+    getRange (Macro x)               = getRange x
+
+instance HasRange Declaration where
+    getRange (Axiom    _ i _ _ _ _  )  = getRange i
+    getRange (Generalize _ i _ _ _)    = getRange i
+    getRange (Field      i _ _      )  = getRange i
+    getRange (Mutual     i _        )  = getRange i
+    getRange (Section    i _ _ _ _  )  = getRange i
+    getRange (Apply      i _ _ _ _ _)  = getRange i
+    getRange (Import     i _ _      )  = getRange i
+    getRange (Primitive  i _ _      )  = getRange i
+    getRange (Pragma     i _        )  = getRange i
+    getRange (Open       i _ _      )  = getRange i
+    getRange (ScopedDecl _ d        )  = getRange d
+    getRange (FunDef     i _ _      )  = getRange i
+    getRange (DataSig    i _ _ _ _  )  = getRange i
+    getRange (DataDef    i _ _ _ _  )  = getRange i
+    getRange (RecSig     i _ _ _ _  )  = getRange i
+    getRange (RecDef i _ _ _ _ _ _)    = getRange i
+    getRange (PatternSynDef x _ _   )  = getRange x
+    getRange (UnquoteDecl _ i _ _)     = getRange i
+    getRange (UnquoteDef i _ _)        = getRange i
+    getRange (UnquoteData i _ _ j _ _) = getRange (i, j)
+    getRange (UnfoldingDecl r _)       = r
+
+instance HasRange (Pattern' e) where
+    getRange (VarP x)            = getRange x
+    getRange (ConP i _ _)        = getRange i
+    getRange (ProjP i _ _)       = getRange i
+    getRange (DefP i _ _)        = getRange i
+    getRange (WildP i)           = getRange i
+    getRange (AsP i _ _)         = getRange i
+    getRange (DotP i _)          = getRange i
+    getRange (AbsurdP i)         = getRange i
+    getRange (LitP i l)          = getRange i
+    getRange (PatternSynP i _ _) = getRange i
+    getRange (RecP i _)          = getRange i
+    getRange (EqualP i _)        = getRange i
+    getRange (WithP i _)         = getRange i
+    getRange (AnnP i _ _)        = getRange i
+
+instance HasRange SpineLHS where
+    getRange (SpineLHS i _ _)  = getRange i
+
+instance HasRange LHS where
+    getRange (LHS i _)   = getRange i
+
+instance HasRange (LHSCore' e) where
+    getRange (LHSHead f ps)         = fuseRange f ps
+    getRange (LHSProj d lhscore ps) = d `fuseRange` lhscore `fuseRange` ps
+    getRange (LHSWith h wps ps)     = h `fuseRange` wps `fuseRange` ps
+
+instance HasRange a => HasRange (Clause' a) where
+    getRange (Clause lhs _ rhs ds catchall) = getRange (lhs, rhs, ds)
+
+instance HasRange RHS where
+    getRange AbsurdRHS                 = noRange
+    getRange (RHS e _)                 = getRange e
+    getRange (WithRHS _ e cs)          = fuseRange e cs
+    getRange (RewriteRHS xes _ rhs wh) = getRange (xes, rhs, wh)
+
+instance HasRange WhereDeclarations where
+  getRange (WhereDecls _ _ ds) = getRange ds
+
+instance HasRange LetBinding where
+    getRange (LetBind i _ _ _ _     ) = getRange i
+    getRange (LetPatBind  i _ _      ) = getRange i
+    getRange (LetApply i _ _ _ _ _   ) = getRange i
+    getRange (LetOpen  i _ _         ) = getRange i
+    getRange (LetDeclaredVariable x)  = getRange x
+
+-- setRange for patterns applies the range to the outermost pattern constructor
+instance SetRange (Pattern' a) where
+    setRange r (VarP x)            = VarP (setRange r x)
+    setRange r (ConP i ns as)       = ConP (setRange r i) ns as
+    setRange r (ProjP _ o ns)       = ProjP (PatRange r) o ns
+    setRange r (DefP _ ns as)       = DefP (PatRange r) ns as -- (setRange r n) as
+    setRange r (WildP _)            = WildP (PatRange r)
+    setRange r (AsP _ n p)          = AsP (PatRange r) (setRange r n) p
+    setRange r (DotP _ e)           = DotP (PatRange r) e
+    setRange r (AbsurdP _)          = AbsurdP (PatRange r)
+    setRange r (LitP _ l)           = LitP (PatRange r) l
+    setRange r (PatternSynP _ n as) = PatternSynP (PatRange r) n as
+    setRange r (RecP i as)          = RecP (PatRange r) as
+    setRange r (EqualP _ es)        = EqualP (PatRange r) es
+    setRange r (WithP i p)          = WithP (setRange r i) p
+    setRange r (AnnP i a p)         = AnnP (setRange r i) a p
+
+instance KillRange a => KillRange (Binder' a) where
+  killRange (Binder a b) = killRangeN Binder a b
+
+instance KillRange LamBinding where
+  killRange (DomainFree t x) = killRangeN DomainFree t x
+  killRange (DomainFull b)   = killRangeN DomainFull b
+
+instance KillRange GeneralizeTelescope where
+  killRange (GeneralizeTel s tel) = GeneralizeTel s (killRange tel)
+
+instance KillRange DataDefParams where
+  killRange (DataDefParams s tel) = DataDefParams s (killRange tel)
+
+instance KillRange TypedBindingInfo where
+  killRange (TypedBindingInfo a b) = killRangeN TypedBindingInfo a b
+
+instance KillRange TypedBinding where
+  killRange (TBind r t xs e) = killRangeN TBind r t xs e
+  killRange (TLet r lbs)     = killRangeN TLet r lbs
+
+instance KillRange Expr where
+  killRange (Var x)                  = killRangeN Var x
+  killRange (Def' x v)               = killRangeN Def' x v
+  killRange (Proj o x)               = killRangeN (Proj o) x
+  killRange (Con x)                  = killRangeN Con x
+  killRange (Lit i l)                = killRangeN Lit i l
+  killRange (QuestionMark i ii)      = killRangeN QuestionMark i ii
+  killRange (Underscore  i)          = killRangeN Underscore i
+  killRange (Dot i e)                = killRangeN Dot i e
+  killRange (App i e1 e2)            = killRangeN App i e1 e2
+  killRange (WithApp i e es)         = killRangeN WithApp i e es
+  killRange (Lam i b e)              = killRangeN Lam i b e
+  killRange (AbsurdLam i h)          = killRangeN AbsurdLam i h
+  killRange (ExtendedLam i n e d ps) = killRangeN ExtendedLam i n e d ps
+  killRange (Pi i a b)               = killRangeN Pi i a b
+  killRange (Generalized s x)        = killRangeN (Generalized s) x
+  killRange (Fun i a b)              = killRangeN Fun i a b
+  killRange (Let i ds e)             = killRangeN Let i ds e
+  killRange (Rec i fs)               = killRangeN Rec i fs
+  killRange (RecUpdate i e fs)       = killRangeN RecUpdate i e fs
+  killRange (ScopedExpr s e)         = killRangeN (ScopedExpr s) e
+  killRange (Quote i)                = killRangeN Quote i
+  killRange (QuoteTerm i)            = killRangeN QuoteTerm i
+  killRange (Unquote i)              = killRangeN Unquote i
+  killRange (DontCare e)             = killRangeN DontCare e
+  killRange (PatternSyn x)           = killRangeN PatternSyn x
+  killRange (Macro x)                = killRangeN Macro x
+
+instance KillRange Suffix where
+  killRange = id
+
+instance KillRange Declaration where
+  killRange (Axiom    p i a b c d     ) = killRangeN (\i a c d -> Axiom p i a b c d) i a c d
+  killRange (Generalize s i j x e     ) = killRangeN (Generalize s) i j x e
+  killRange (Field      i a b         ) = killRangeN Field      i a b
+  killRange (Mutual     i a           ) = killRangeN Mutual     i a
+  killRange (Section    i a b c d     ) = killRangeN Section    i a b c d
+  killRange (Apply      i a b c d e   ) = killRangeN Apply      i a b c d e
+  killRange (Import     i a b         ) = killRangeN Import     i a b
+  killRange (Primitive  i a b         ) = killRangeN Primitive  i a b
+  killRange (Pragma     i a           ) = Pragma (killRange i) a
+  killRange (Open       i x dir       ) = killRangeN Open       i x dir
+  killRange (ScopedDecl a d           ) = killRangeN (ScopedDecl a) d
+  killRange (FunDef  i a b            ) = killRangeN FunDef  i a b
+  killRange (DataSig i a b c d        ) = killRangeN DataSig i a b c d
+  killRange (DataDef i a b c d        ) = killRangeN DataDef i a b c d
+  killRange (RecSig  i a b c d        ) = killRangeN RecSig  i a b c d
+  killRange (RecDef  i a b c d e f    ) = killRangeN RecDef  i a b c d e f
+  killRange (PatternSynDef x xs p     ) = killRangeN PatternSynDef x xs p
+  killRange (UnquoteDecl mi i x e     ) = killRangeN UnquoteDecl mi i x e
+  killRange (UnquoteDef i x e         ) = killRangeN UnquoteDef i x e
+  killRange (UnquoteData i xs uc j cs e) = killRangeN UnquoteData i xs uc j cs e
+  killRange (UnfoldingDecl r xs)         = killRangeN UnfoldingDecl r xs
+
+instance KillRange ModuleApplication where
+  killRange (SectionApp a b c  ) = killRangeN SectionApp a b c
+  killRange (RecordModuleInstance a) = killRangeN RecordModuleInstance a
+
+instance KillRange ScopeCopyInfo where
+  killRange (ScopeCopyInfo a b) = killRangeN ScopeCopyInfo a b
+
+instance KillRange e => KillRange (Pattern' e) where
+  killRange (VarP x)           = killRangeN VarP x
+  killRange (ConP i a b)        = killRangeN ConP i a b
+  killRange (ProjP i o a)       = killRangeN ProjP i o a
+  killRange (DefP i a b)        = killRangeN DefP i a b
+  killRange (WildP i)           = killRangeN WildP i
+  killRange (AsP i a b)         = killRangeN AsP i a b
+  killRange (DotP i a)          = killRangeN DotP i a
+  killRange (AbsurdP i)         = killRangeN AbsurdP i
+  killRange (LitP i l)          = killRangeN LitP i l
+  killRange (PatternSynP i a p) = killRangeN PatternSynP i a p
+  killRange (RecP i as)         = killRangeN RecP i as
+  killRange (EqualP i es)       = killRangeN EqualP i es
+  killRange (WithP i p)         = killRangeN WithP i p
+  killRange (AnnP i a p)        = killRangeN AnnP i a p
+
+instance KillRange SpineLHS where
+  killRange (SpineLHS i a b)  = killRangeN SpineLHS i a b
+
+instance KillRange LHS where
+  killRange (LHS i a)   = killRangeN LHS i a
+
+instance KillRange e => KillRange (LHSCore' e) where
+  killRange (LHSHead a b)   = killRangeN LHSHead a b
+  killRange (LHSProj a b c) = killRangeN LHSProj a b c
+  killRange (LHSWith a b c) = killRangeN LHSWith a b c
+
+instance KillRange a => KillRange (Clause' a) where
+  killRange (Clause lhs spats rhs ds catchall) = killRangeN Clause lhs spats rhs ds catchall
+
+instance KillRange ProblemEq where
+  killRange (ProblemEq p v a) = killRangeN ProblemEq p v a
+
+instance KillRange RHS where
+  killRange AbsurdRHS                = AbsurdRHS
+  killRange (RHS e c)                = killRangeN RHS e c
+  killRange (WithRHS q e cs)         = killRangeN WithRHS q e cs
+  killRange (RewriteRHS xes spats rhs wh) = killRangeN RewriteRHS xes spats rhs wh
+
+instance KillRange WhereDeclarations where
+  killRange (WhereDecls a b c) = killRangeN WhereDecls a b c
+
+instance KillRange LetBinding where
+  killRange (LetBind   i info a b c) = killRangeN LetBind i info a b c
+  killRange (LetPatBind i a b       ) = killRangeN LetPatBind i a b
+  killRange (LetApply   i a b c d e ) = killRangeN LetApply i a b c d e
+  killRange (LetOpen    i x dir     ) = killRangeN LetOpen  i x dir
+  killRange (LetDeclaredVariable x)  = killRangeN LetDeclaredVariable x
+
+instance NFData Expr
+instance NFData ScopeCopyInfo
+instance NFData Declaration
+instance NFData ModuleApplication
+instance NFData Pragma
+instance NFData LetBinding
+instance NFData a => NFData (Binder' a)
+instance NFData LamBinding
+instance NFData TypedBinding
+instance NFData TypedBindingInfo
+instance NFData GeneralizeTelescope
+instance NFData DataDefParams
+instance NFData ProblemEq
+instance NFData lhs => NFData (Clause' lhs)
+instance NFData WhereDeclarations
+instance NFData RHS
+instance NFData SpineLHS
+instance NFData LHS
+instance NFData e => NFData (LHSCore' e)
+instance NFData e => NFData (Pattern' e)
+
+------------------------------------------------------------------------
+-- Queries
+------------------------------------------------------------------------
+
+-- class AllNames moved to Abstract.Views.DeclaredNames
+
+-- | The name defined by the given axiom.
+--
+-- Precondition: The declaration has to be a (scoped) 'Axiom'.
+
+axiomName :: Declaration -> QName
+axiomName (Axiom _ _ _ _ q _)  = q
+axiomName (ScopedDecl _ (d:_)) = axiomName d
+axiomName _                    = __IMPOSSIBLE__
+
+-- | Are we in an abstract block?
+--
+--   In that case some definition is abstract.
+class AnyAbstract a where
+  anyAbstract :: a -> Bool
+
+instance AnyAbstract a => AnyAbstract [a] where
+  anyAbstract = Fold.any anyAbstract
+
+instance AnyAbstract Declaration where
+  anyAbstract (Axiom _ i _ _ _ _)    = defAbstract i == AbstractDef
+  anyAbstract (Field i _ _)          = defAbstract i == AbstractDef
+  anyAbstract (Mutual     _ ds)      = anyAbstract ds
+  anyAbstract (ScopedDecl _ ds)      = anyAbstract ds
+  anyAbstract (Section _ _ _ _ ds)   = anyAbstract ds
+  anyAbstract (FunDef i _ _)         = defAbstract i == AbstractDef
+  anyAbstract (DataDef i _ _ _ _)    = defAbstract i == AbstractDef
+  anyAbstract (RecDef i _ _ _ _ _ _) = defAbstract i == AbstractDef
+  anyAbstract (DataSig i _ _ _ _)    = defAbstract i == AbstractDef
+  anyAbstract (RecSig i _ _ _ _)     = defAbstract i == AbstractDef
+  anyAbstract _                      = __IMPOSSIBLE__
+
+-- | Turn a name into an expression.
+
+class NameToExpr a where
+  nameToExpr :: a -> Expr
+
+-- | Turn an 'AbstractName' into an expression.
+
+instance NameToExpr AbstractName where
+  nameToExpr d =
+    case anameKind d of
+      DataName                 -> Def x
+      RecName                  -> Def x
+      AxiomName                -> Def x
+      PrimName                 -> Def x
+      FunName                  -> Def x
+      OtherDefName             -> Def x
+      GeneralizeName           -> Def x
+      DisallowedGeneralizeName -> Def x
+      FldName                  -> Proj ProjSystem ux
+      ConName                  -> Con ux
+      CoConName                -> Con ux
+      PatternSynName           -> PatternSyn ux
+      MacroName                -> Macro x
+      QuotableName             -> App (defaultAppInfo r) (Quote i) (defaultNamedArg $ Def x)
+    where
+    x  = anameName d
+    ux = unambiguous x
+    r  = getRange x
+    i  = ExprRange r
+
+-- | Turn a 'ResolvedName' into an expression.
+--
+--   Assumes name is not 'UnknownName'.
+
+instance NameToExpr ResolvedName where
+  nameToExpr = \case
+    VarName x _          -> Var x
+    DefinedName _ x s    -> withSuffix s $ nameToExpr x  -- Can be 'isDefName', 'MacroName', 'QuotableName'.
+    FieldName xs         -> Proj ProjSystem . AmbQ . fmap anameName $ xs
+    ConstructorName _ xs -> Con . AmbQ . fmap anameName $ xs
+    PatternSynResName xs -> PatternSyn . AmbQ . fmap anameName $ xs
+    UnknownName          -> __IMPOSSIBLE__
+    where
+      withSuffix NoSuffix   e       = e
+      withSuffix s@Suffix{} (Def x) = Def' x s
+      withSuffix _          _       = __IMPOSSIBLE__
+
+app :: Expr -> [NamedArg Expr] -> Expr
+app = foldl (App defaultAppInfo_)
+
+mkLet :: ExprInfo -> [LetBinding] -> Expr -> Expr
+mkLet _ []     e = e
+mkLet i (d:ds) e = Let i (d :| ds) e
+
+patternToExpr :: Pattern -> Expr
+patternToExpr = \case
+  VarP x             -> Var (unBind x)
+  ConP _ c ps        -> Con c `app` map (fmap (fmap patternToExpr)) ps
+  ProjP _ o ds       -> Proj o ds
+  DefP _ fs ps       -> Def (headAmbQ fs) `app` map (fmap (fmap patternToExpr)) ps
+  WildP _            -> Underscore emptyMetaInfo
+  AsP _ _ p          -> patternToExpr p
+  DotP _ e           -> e
+  AbsurdP _          -> Underscore emptyMetaInfo  -- TODO: could this happen?
+  LitP (PatRange r) l-> Lit (ExprRange r) l
+  PatternSynP _ c ps -> PatternSyn c `app` (map . fmap . fmap) patternToExpr ps
+  RecP _ as          -> Rec exprNoRange $ map (Left . fmap patternToExpr) as
+  EqualP{}           -> __IMPOSSIBLE__  -- Andrea TODO: where is this used?
+  WithP r p          -> __IMPOSSIBLE__
+  AnnP _ _ p         -> patternToExpr p
+
+type PatternSynDefn = ([Arg Name], Pattern' Void)
+type PatternSynDefns = Map QName PatternSynDefn
+
+lambdaLiftExpr :: [Name] -> Expr -> Expr
+lambdaLiftExpr ns e
+  = foldr
+      (\ n -> Lam exprNoRange (mkDomainFree $ defaultNamedArg $ mkBinder_ n))
+      e
+      ns
+
+-- NOTE: This is only used on expressions that come from right-hand sides of pattern synonyms, and
+-- thus does not have to handle all forms of expressions.
+class SubstExpr a where
+  substExpr :: [(Name, Expr)] -> a -> a
+
+  default substExpr
+    :: (Functor t, SubstExpr b, t b ~ a)
+    => [(Name, Expr)] -> a -> a
+  substExpr = fmap . substExpr
+
+instance SubstExpr a => SubstExpr (Maybe a)
+instance SubstExpr a => SubstExpr [a]
+instance SubstExpr a => SubstExpr (List1 a)
+instance SubstExpr a => SubstExpr (Arg a)
+instance SubstExpr a => SubstExpr (Named name a)
+instance SubstExpr a => SubstExpr (FieldAssignment' a)
+
+instance (SubstExpr a, SubstExpr b) => SubstExpr (a, b) where
+  substExpr s (x, y) = (substExpr s x, substExpr s y)
+
+instance (SubstExpr a, SubstExpr b) => SubstExpr (Either a b) where
+  substExpr s (Left x)  = Left (substExpr s x)
+  substExpr s (Right y) = Right (substExpr s y)
+
+instance SubstExpr C.Name where
+  substExpr _ = id
+
+instance SubstExpr ModuleName where
+  substExpr _ = id
+
+instance SubstExpr Expr where
+  substExpr s e = case e of
+    Var n           -> fromMaybe e (lookup n s)
+    Con _           -> e
+    Proj{}          -> e
+    Def' _ _        -> e
+    PatternSyn{}    -> e
+    Lit _ _         -> e
+    Underscore   _  -> e
+    App  i e e'     -> App i (substExpr s e) (substExpr s e')
+    Rec  i nes      -> Rec i (substExpr s nes)
+    ScopedExpr si e -> ScopedExpr si (substExpr s e)
+    -- The below cannot appear in pattern synonym right-hand sides
+    QuestionMark{}  -> __IMPOSSIBLE__
+    Dot{}           -> __IMPOSSIBLE__
+    WithApp{}       -> __IMPOSSIBLE__
+    Lam{}           -> __IMPOSSIBLE__
+    AbsurdLam{}     -> __IMPOSSIBLE__
+    ExtendedLam{}   -> __IMPOSSIBLE__
+    Pi{}            -> __IMPOSSIBLE__
+    Generalized{}   -> __IMPOSSIBLE__
+    Fun{}           -> __IMPOSSIBLE__
+    Let{}           -> __IMPOSSIBLE__
+    RecUpdate{}     -> __IMPOSSIBLE__
+    Quote{}         -> __IMPOSSIBLE__
+    QuoteTerm{}     -> __IMPOSSIBLE__
+    Unquote{}       -> __IMPOSSIBLE__
+    DontCare{}      -> __IMPOSSIBLE__
+    Macro{}         -> __IMPOSSIBLE__
+
+-- TODO: more informative failure
+insertImplicitPatSynArgs
+  :: HasRange a
+  => (Range -> a)
+  -> Range
+  -> [Arg Name]
+  -> [NamedArg a]
+  -> Maybe ([(Name, a)], [Arg Name])
+insertImplicitPatSynArgs wild r ns as = matchArgs r ns as
+  where
+    matchNextArg r n as@(~(a : as'))
+      | matchNext n as = return (namedArg a, as')
+      | visible n      = Nothing
+      | otherwise      = return (wild r, as)
+
+    matchNext _ [] = False
+    matchNext n (a:as) = sameHiding n a && maybe True (x ==) (bareNameOf a)
+      where
+        x = C.nameToRawName $ nameConcrete $ unArg n
+
+    matchArgs r [] []     = return ([], [])
+    matchArgs r [] as     = Nothing
+    matchArgs r (n:ns) [] | visible n = return ([], n : ns)    -- under-applied
+    matchArgs r (n:ns) as = do
+      (p, as) <- matchNextArg r n as
+      first ((unArg n, p) :) <$> matchArgs (getRange p) ns as
+
+------------------------------------------------------------------------
+-- Declaration spines
+------------------------------------------------------------------------
+
+-- | Declaration spines. Used in debugging to make it easy to see
+-- where constructors such as 'ScopedDecl' and 'Mutual' are placed.
+
+data DeclarationSpine
+  = AxiomS
+  | GeneralizeS
+  | FieldS
+  | PrimitiveS
+  | MutualS [DeclarationSpine]
+  | SectionS [DeclarationSpine]
+  | ApplyS
+  | ImportS
+  | PragmaS
+  | OpenS
+  | FunDefS [ClauseSpine]
+  | DataSigS
+  | DataDefS
+  | RecSigS
+  | RecDefS [DeclarationSpine]
+  | PatternSynDefS
+  | UnquoteDeclS
+  | UnquoteDefS
+  | UnquoteDataS
+  | ScopedDeclS [DeclarationSpine]
+  | UnfoldingDeclS
+  deriving Show
+
+-- | Clause spines.
+
+data ClauseSpine = ClauseS RHSSpine WhereDeclarationsSpine
+  deriving Show
+
+-- | Right-hand side spines.
+
+data RHSSpine
+  = RHSS
+  | AbsurdRHSS
+  | WithRHSS (List1 ClauseSpine)
+  | RewriteRHSS RHSSpine WhereDeclarationsSpine
+  deriving Show
+
+-- | Spines corresponding to 'WhereDeclarations' values.
+
+data WhereDeclarationsSpine = WhereDeclsS (Maybe DeclarationSpine)
+  deriving Show
+
+-- | The declaration spine corresponding to a declaration.
+
+declarationSpine :: Declaration -> DeclarationSpine
+declarationSpine = \case
+  Axiom _ _ _ _ _ _       -> AxiomS
+  Generalize _ _ _ _ _    -> GeneralizeS
+  Field _ _ _             -> FieldS
+  Primitive _ _ _         -> PrimitiveS
+  Mutual _ ds             -> MutualS (map declarationSpine ds)
+  Section _ _ _ _ ds      -> SectionS (map declarationSpine ds)
+  Apply _ _ _ _ _ _       -> ApplyS
+  Import _ _ _            -> ImportS
+  Pragma _ _              -> PragmaS
+  Open _ _ _              -> OpenS
+  FunDef _ _ cs           -> FunDefS (map clauseSpine cs)
+  DataSig _ _ _ _ _       -> DataSigS
+  DataDef _ _ _ _ _       -> DataDefS
+  RecSig _ _ _ _ _        -> RecSigS
+  RecDef _ _ _ _ _ _ ds   -> RecDefS (map declarationSpine ds)
+  PatternSynDef _ _ _     -> PatternSynDefS
+  UnquoteDecl _ _ _ _     -> UnquoteDeclS
+  UnquoteDef _ _ _        -> UnquoteDefS
+  UnquoteData _ _ _ _ _ _ -> UnquoteDataS
+  ScopedDecl _ ds         -> ScopedDeclS (map declarationSpine ds)
+  UnfoldingDecl _ _       -> UnquoteDeclS
+
+-- | The clause spine corresponding to a clause.
+
+clauseSpine :: Clause -> ClauseSpine
+clauseSpine (Clause _ _ rhs ws _) =
+  ClauseS (rhsSpine rhs) (whereDeclarationsSpine ws)
+
+-- | The right-hand side spine corresponding to a right-hand side.
+
+rhsSpine :: RHS -> RHSSpine
+rhsSpine = \case
+  RHS _ _               -> RHSS
+  AbsurdRHS             -> AbsurdRHSS
+  WithRHS _ _ cs        -> WithRHSS $ fmap clauseSpine cs
+  RewriteRHS _ _ rhs ws ->
+    RewriteRHSS (rhsSpine rhs) (whereDeclarationsSpine ws)
+
+-- | The spine corresponding to a 'WhereDeclarations' value.
+
+whereDeclarationsSpine :: WhereDeclarations -> WhereDeclarationsSpine
+whereDeclarationsSpine (WhereDecls _ _ md) =
+  WhereDeclsS (fmap declarationSpine md)
diff --git a/src/full/Agda/Syntax/Abstract/Name.hs b/src/full/Agda/Syntax/Abstract/Name.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/Name.hs
@@ -0,0 +1,489 @@
+
+{-| Abstract names carry unique identifiers and stuff.
+-}
+module Agda.Syntax.Abstract.Name
+  ( module Agda.Syntax.Abstract.Name
+  , IsNoName(..)
+  , FreshNameMode(..)
+  ) where
+
+import Prelude hiding (length)
+
+import Control.DeepSeq
+
+import Data.Foldable (length)
+import Data.Function (on)
+import Data.Hashable (Hashable(..))
+import qualified Data.List as List
+import Data.Maybe
+import Data.Void
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Name (IsNoName(..), NumHoles(..), NameInScope(..), LensInScope(..), FreshNameMode(..))
+import qualified Agda.Syntax.Concrete.Name as C
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import qualified Agda.Utils.List as L
+import Agda.Utils.List1 (List1, pattern (:|), (<|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- | A name is a unique identifier and a suggestion for a concrete name. The
+--   concrete name contains the source location (if any) of the name. The
+--   source location of the binding site is also recorded.
+data Name = Name
+  { nameId           :: !NameId
+  , nameConcrete     :: C.Name  -- ^ The concrete name used for this instance
+  , nameCanonical    :: C.Name  -- ^ The concrete name in the original definition (needed by primShowQName, see #4735)
+  , nameBindingSite  :: Range
+  , nameFixity       :: Fixity'
+  , nameIsRecordName :: Bool
+      -- ^ Is this the name of the invisible record variable `self`?
+      --   Should not be printed or displayed in the context, see issue #3584.
+  }
+
+-- | Useful for debugging scoping problems
+uglyShowName :: Name -> String
+uglyShowName x = show (nameId x, nameConcrete x)
+
+-- | Qualified names are non-empty lists of names. Equality on qualified names
+--   are just equality on the last name, i.e. the module part is just
+--   for show.
+--
+-- The 'SetRange' instance for qualified names sets all individual
+-- ranges (including those of the module prefix) to the given one.
+data QName = QName { qnameModule :: ModuleName
+                   , qnameName   :: Name
+                   }
+
+-- | Something preceeded by a qualified name.
+data QNamed a = QNamed
+  { qname  :: QName
+  , qnamed :: a
+  }
+  deriving (Functor, Foldable, Traversable)
+
+-- | A module name is just a qualified name.
+--
+-- The 'SetRange' instance for module names sets all individual ranges
+-- to the given one.
+newtype ModuleName = MName { mnameToList :: [Name] }
+  deriving (Eq, Ord)
+
+-- | Ambiguous qualified names. Used for overloaded constructors.
+--
+-- Invariant: All the names in the list must have the same concrete,
+-- unqualified name.  (This implies that they all have the same 'Range').
+newtype AmbiguousQName = AmbQ { unAmbQ :: List1 QName }
+  deriving (Eq, Ord, NFData)
+
+-- | A singleton "ambiguous" name.
+unambiguous :: QName -> AmbiguousQName
+unambiguous x = AmbQ (x :| [])
+
+-- | Get the first of the ambiguous names.
+headAmbQ :: AmbiguousQName -> QName
+headAmbQ (AmbQ xs) = List1.head xs
+
+-- | Is a name ambiguous.
+isAmbiguous :: AmbiguousQName -> Bool
+isAmbiguous (AmbQ (_ :| xs)) = not (null xs)
+
+-- | Get the name if unambiguous.
+getUnambiguous :: AmbiguousQName -> Maybe QName
+getUnambiguous (AmbQ (x :| [])) = Just x
+getUnambiguous _                = Nothing
+
+-- | A name suffix
+data Suffix
+  = NoSuffix
+  | Suffix !Integer
+  deriving (Show, Eq, Ord)
+
+instance NFData Suffix where
+  rnf NoSuffix   = ()
+  rnf (Suffix _) = ()
+
+-- | Check whether we are a projection pattern.
+class IsProjP a where
+  isProjP :: a -> Maybe (ProjOrigin, AmbiguousQName)
+
+instance IsProjP a => IsProjP (Arg a) where
+  isProjP p = case isProjP $ unArg p of
+    Just (ProjPostfix , f)
+     | getHiding p /= NotHidden -> Nothing
+    x -> x
+
+instance IsProjP a => IsProjP (Named n a) where
+  isProjP = isProjP . namedThing
+
+instance IsProjP Void where
+  isProjP _ = __IMPOSSIBLE__
+
+-- | A module is anonymous if the qualification path ends in an underscore.
+isAnonymousModuleName :: ModuleName -> Bool
+isAnonymousModuleName (MName mms) = maybe False isNoName $ L.lastMaybe mms
+
+-- | Sets the ranges of the individual names in the module name to
+-- match those of the corresponding concrete names. If the concrete
+-- names are fewer than the number of module name name parts, then the
+-- initial name parts get the range 'noRange'.
+--
+-- @C.D.E \`withRangesOf\` [A, B]@ returns @C.D.E@ but with ranges set
+-- as follows:
+--
+-- * @C@: 'noRange'.
+--
+-- * @D@: the range of @A@.
+--
+-- * @E@: the range of @B@.
+--
+-- Precondition: The number of module name name parts has to be at
+-- least as large as the length of the list.
+
+withRangesOf :: ModuleName -> List1 C.Name -> ModuleName
+MName ms `withRangesOf` ns = if m < n then __IMPOSSIBLE__ else MName $
+      zipWith setRange (replicate (m - n) noRange ++ map getRange (List1.toList ns)) ms
+  where
+    m = length ms
+    n = length ns
+
+-- | Like 'withRangesOf', but uses the name parts (qualifier + name)
+-- of the qualified name as the list of concrete names.
+
+withRangesOfQ :: ModuleName -> C.QName -> ModuleName
+m `withRangesOfQ` q = m `withRangesOf` C.qnameParts q
+
+mnameFromList :: [Name] -> ModuleName
+mnameFromList = MName
+
+mnameFromList1 :: List1 Name -> ModuleName
+mnameFromList1 = MName . List1.toList
+
+mnameToList1 :: ModuleName -> List1 Name
+mnameToList1 (MName ns) = List1.ifNull ns __IMPOSSIBLE__ id
+
+noModuleName :: ModuleName
+noModuleName = mnameFromList []
+
+commonParentModule :: ModuleName -> ModuleName -> ModuleName
+commonParentModule m1 m2 =
+  mnameFromList $ L.commonPrefix (mnameToList m1) (mnameToList m2)
+
+-- | Make a 'Name' from some kind of string.
+class MkName a where
+  -- | The 'Range' sets the /definition site/ of the name, not the use site.
+  mkName :: Range -> NameId -> a -> Name
+
+  mkName_ :: NameId -> a -> Name
+  mkName_ = mkName noRange
+
+instance MkName String where
+  mkName r i s = makeName i (C.Name noRange InScope (C.stringNameParts s)) r noFixity' False
+
+makeName :: NameId -> C.Name -> Range -> Fixity' -> Bool -> Name
+makeName i c r f rec = Name i c c r f rec
+
+qnameToList0 :: QName -> [Name]
+qnameToList0 = List1.toList . qnameToList
+
+qnameToList :: QName -> List1 Name
+qnameToList (QName m x) = mnameToList m `List1.snoc` x
+
+qnameFromList :: List1 Name -> QName
+qnameFromList xs = QName (mnameFromList $ List1.init xs) (List1.last xs)
+
+qnameToMName :: QName -> ModuleName
+qnameToMName = mnameFromList1 . qnameToList
+
+mnameToQName :: ModuleName -> QName
+mnameToQName = qnameFromList . mnameToList1
+
+showQNameId :: QName -> String
+showQNameId q = show (List1.toList ns) ++ "@" ++ show (List1.head ms)
+  where
+    (ns, ms) = List1.unzip $ fmap (unNameId . nameId) $ List1.snoc (mnameToList $ qnameModule q) (qnameName q)
+    unNameId (NameId n m) = (n, m)
+
+-- | Turn a qualified name into a concrete name. This should only be used as a
+--   fallback when looking up the right concrete name in the scope fails.
+qnameToConcrete :: QName -> C.QName
+qnameToConcrete (QName m x) =       -- Use the canonical name here (#5048)
+   foldr (C.Qual . nameConcrete) (C.QName $ nameCanonical x) (mnameToList m)
+
+mnameToConcrete :: ModuleName -> C.QName
+mnameToConcrete (MName []) = __IMPOSSIBLE__ -- C.QName C.noName_  -- should never happen?
+mnameToConcrete (MName (x:xs)) = foldr C.Qual (C.QName $ List1.last cs) $ List1.init cs
+  where
+    cs = fmap nameConcrete (x :| xs)
+
+qualifyM :: ModuleName -> ModuleName -> ModuleName
+qualifyM m1 m2 = mnameFromList $ mnameToList m1 ++ mnameToList m2
+
+qualifyQ :: ModuleName -> QName -> QName
+qualifyQ m x = qnameFromList $ mnameToList m `List1.prependList` qnameToList x
+
+qualify :: ModuleName -> Name -> QName
+qualify = QName
+
+-- | Convert a 'Name' to a 'QName' (add no module name).
+qualify_ :: Name -> QName
+qualify_ = qualify noModuleName
+
+-- | Is the name an operator?
+
+isOperator :: QName -> Bool
+isOperator = C.isOperator . nameConcrete . qnameName
+
+-- | Is the first module a weak parent of the second?
+isLeParentModuleOf :: ModuleName -> ModuleName -> Bool
+isLeParentModuleOf = List.isPrefixOf `on` mnameToList
+
+-- | Is the first module a proper parent of the second?
+isLtParentModuleOf :: ModuleName -> ModuleName -> Bool
+isLtParentModuleOf x y =
+  isJust $ (L.stripPrefixBy (==) `on` mnameToList) x y
+
+-- | Is the first module a weak child of the second?
+isLeChildModuleOf :: ModuleName -> ModuleName -> Bool
+isLeChildModuleOf = flip isLeParentModuleOf
+
+-- | Is the first module a proper child of the second?
+isLtChildModuleOf :: ModuleName -> ModuleName -> Bool
+isLtChildModuleOf = flip isLtParentModuleOf
+
+isInModule :: QName -> ModuleName -> Bool
+isInModule q m = mnameToList m `List.isPrefixOf` qnameToList0 q
+
+-- | Get the next version of the concrete name. For instance, @nextName "x" = "x₁"@.
+--   The name must not be a 'NoName'.
+nextName :: C.FreshNameMode -> Name -> Name
+nextName freshNameMode x = x { nameConcrete = C.nextName freshNameMode (nameConcrete x) }
+
+sameRoot :: Name -> Name -> Bool
+sameRoot = C.sameRoot `on` nameConcrete
+
+------------------------------------------------------------------------
+-- * Important instances: Eq, Ord, Hashable
+--
+--   For the identity and comparing of names, only the 'NameId' matters!
+------------------------------------------------------------------------
+
+instance Eq Name where
+  (==) = (==) `on` nameId
+
+instance Ord Name where
+  compare = compare `on` nameId
+
+instance Hashable Name where
+  {-# INLINE hashWithSalt #-}
+  hashWithSalt salt = hashWithSalt salt . nameId
+
+instance Eq QName where
+  (==) = (==) `on` qnameName
+
+instance Ord QName where
+  compare = compare `on` qnameName
+
+instance Hashable QName where
+  {-# INLINE hashWithSalt #-}
+  hashWithSalt salt = hashWithSalt salt . qnameName
+
+------------------------------------------------------------------------
+-- * IsNoName instances (checking for "_")
+------------------------------------------------------------------------
+
+-- | An abstract name is empty if its concrete name is empty.
+instance IsNoName Name where
+  isNoName = isNoName . nameConcrete
+
+instance NumHoles Name where
+  numHoles = numHoles . nameConcrete
+
+instance NumHoles QName where
+  numHoles = numHoles . qnameName
+
+-- | We can have an instance for ambiguous names as all share a common concrete name.
+instance NumHoles AmbiguousQName where
+  numHoles = numHoles . headAmbQ
+
+------------------------------------------------------------------------
+-- * name lenses
+------------------------------------------------------------------------
+
+lensQNameName :: Lens' QName Name
+lensQNameName f (QName m n) = QName m <$> f n
+
+------------------------------------------------------------------------
+-- * LensFixity' instances
+------------------------------------------------------------------------
+
+instance LensFixity' Name where
+  lensFixity' f n = f (nameFixity n) <&> \ fix' -> n { nameFixity = fix' }
+
+instance LensFixity' QName where
+  lensFixity' = lensQNameName . lensFixity'
+
+------------------------------------------------------------------------
+-- * LensFixity instances
+------------------------------------------------------------------------
+
+instance LensFixity Name where
+  lensFixity = lensFixity' . lensFixity
+
+instance LensFixity QName where
+  lensFixity = lensFixity' . lensFixity
+
+------------------------------------------------------------------------
+-- * LensInScope instances
+------------------------------------------------------------------------
+
+instance LensInScope Name where
+  lensInScope f n@Name{ nameConcrete = x } =
+    (\y -> n { nameConcrete = y }) <$> lensInScope f x
+
+instance LensInScope QName where
+  lensInScope f q@QName{ qnameName = n } =
+    (\n' -> q { qnameName = n' }) <$> lensInScope f n
+
+------------------------------------------------------------------------
+-- * Show instances (only for debug printing!)
+--
+-- | Use 'prettyShow' to print names to the user.
+------------------------------------------------------------------------
+
+deriving instance Show Name
+deriving instance Show ModuleName
+deriving instance Show QName
+deriving instance Show a => Show (QNamed a)
+deriving instance Show AmbiguousQName
+
+nameToArgName :: Name -> ArgName
+nameToArgName = stringToArgName . prettyShow
+
+namedArgName :: NamedArg Name -> ArgName
+namedArgName x = fromMaybe (nameToArgName $ namedArg x) $ bareNameOf x
+
+------------------------------------------------------------------------
+-- * Pretty instances
+------------------------------------------------------------------------
+
+instance Pretty Name where
+  pretty = pretty . nameConcrete
+
+instance Pretty ModuleName where
+  pretty = hcat . punctuate "." . map pretty . mnameToList
+
+instance Pretty QName where
+  pretty = hcat . punctuate "." . map pretty . qnameToList0 . useCanonical
+    where
+      -- #4735: When printing a fully qualified name (as done by primShowQName) we need to
+      -- use the origincal concrete name, not the possibly renamed concrete name in 'nameConcrete'.
+      useCanonical q = q { qnameName = (qnameName q) { nameConcrete = nameCanonical (qnameName q) } }
+
+instance Pretty AmbiguousQName where
+  pretty (AmbQ qs) = hcat $ punctuate " | " $ map pretty $ List1.toList qs
+
+instance Pretty a => Pretty (QNamed a) where
+  pretty (QNamed a b) = pretty a <> "." <> pretty b
+
+------------------------------------------------------------------------
+-- * Range instances
+------------------------------------------------------------------------
+
+-- ** HasRange
+
+instance HasRange Name where
+  getRange = getRange . nameConcrete
+
+instance HasRange ModuleName where
+  getRange (MName []) = noRange
+  getRange (MName xs) = getRange xs
+
+instance HasRange QName where
+  getRange q = getRange (qnameModule q, qnameName q)
+
+-- | The range of an @AmbiguousQName@ is the range of any of its
+--   disambiguations (they are the same concrete name).
+instance HasRange AmbiguousQName where
+  getRange (AmbQ (c :| _)) = getRange c
+
+-- ** SetRange
+
+instance SetRange Name where
+  setRange r x = x { nameConcrete = setRange r $ nameConcrete x }
+
+instance SetRange QName where
+  setRange r q = q { qnameModule = setRange r $ qnameModule q
+                   , qnameName   = setRange r $ qnameName   q
+                   }
+
+instance SetRange ModuleName where
+  setRange r (MName ns) = MName (zipWith setRange rs ns)
+    where
+      -- Put the range only on the last name. Otherwise
+      -- we get overlapping jump-to-definition links for all
+      -- the parts (See #2666).
+      rs = replicate (length ns - 1) noRange ++ [r]
+
+-- ** KillRange
+
+instance KillRange Name where
+  killRange (Name a b c d e f) =
+    (killRangeN Name a b c d e f) { nameBindingSite = d }
+    -- Andreas, 2017-07-25, issue #2649
+    -- Preserve the nameBindingSite for error message.
+    --
+    -- Older remarks:
+    --
+    -- Andreas, 2014-03-30
+    -- An experiment: what happens if we preserve
+    -- the range of the binding site, but kill all
+    -- other ranges before serialization?
+    --
+    -- Andreas, Makoto, 2014-10-18 AIM XX
+    -- Kill all ranges in signature, including nameBindingSite.
+
+instance KillRange ModuleName where
+  killRange (MName xs) = MName $ killRange xs
+
+instance KillRange QName where
+  killRange (QName a b) = killRangeN QName a b
+  -- killRange q = q { qnameModule = killRange $ qnameModule q
+  --                 , qnameName   = killRange $ qnameName   q
+  --                 }
+
+instance KillRange AmbiguousQName where
+  killRange (AmbQ xs) = AmbQ $ killRange xs
+
+------------------------------------------------------------------------
+-- * Sized instances
+------------------------------------------------------------------------
+
+instance Sized QName where
+  size = size . qnameToList
+  natSize = natSize . qnameToList
+
+instance Sized ModuleName where
+  size = size . mnameToList
+  natSize = natSize . mnameToList
+
+------------------------------------------------------------------------
+-- * NFData instances
+------------------------------------------------------------------------
+
+-- | The range is not forced.
+
+instance NFData Name where
+  rnf (Name _ a b _ c d) = rnf (a, b, c, d)
+
+instance NFData QName where
+  rnf (QName a b) = rnf a `seq` rnf b
+
+instance NFData ModuleName where
+  rnf (MName a) = rnf a
diff --git a/src/full/Agda/Syntax/Abstract/Pattern.hs b/src/full/Agda/Syntax/Abstract/Pattern.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/Pattern.hs
@@ -0,0 +1,441 @@
+
+-- | Auxiliary functions to handle patterns in the abstract syntax.
+--
+--   Generic and specific traversals.
+
+module Agda.Syntax.Abstract.Pattern where
+
+import Prelude hiding (null)
+
+import Control.Arrow           ( (***), second )
+import Control.Monad           ( (>=>) )
+import Control.Monad.Identity  ( Identity(..), runIdentity )
+import Control.Applicative     ( liftA2 )
+
+
+import Data.Maybe
+import Data.Monoid
+
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete (FieldAssignment')
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Pattern (IsWithP(..))
+import Agda.Syntax.Info
+import Agda.Syntax.Position
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Null
+
+import Agda.Utils.Impossible
+
+-- * Generic traversals
+------------------------------------------------------------------------
+
+type NAP = NamedArg Pattern
+
+class MapNamedArgPattern a  where
+  mapNamedArgPattern :: (NAP -> NAP) -> a -> a
+
+  default mapNamedArgPattern
+     :: (Functor f, MapNamedArgPattern a', a ~ f a') => (NAP -> NAP) -> a -> a
+  mapNamedArgPattern = fmap . mapNamedArgPattern
+
+instance MapNamedArgPattern NAP where
+  mapNamedArgPattern f p =
+    case namedArg p of
+      -- no sub patterns:
+      VarP{}    -> f p
+      WildP{}   -> f p
+      DotP{}    -> f p
+      EqualP{}  -> f p
+      LitP{}    -> f p
+      AbsurdP{} -> f p
+      ProjP{}   -> f p
+      -- list of NamedArg subpatterns:
+      ConP i qs ps       -> f $ setNamedArg p $ ConP i qs $ mapNamedArgPattern f ps
+      DefP i qs ps       -> f $ setNamedArg p $ DefP i qs $ mapNamedArgPattern f ps
+      PatternSynP i x ps -> f $ setNamedArg p $ PatternSynP i x $ mapNamedArgPattern f ps
+      -- Pattern subpattern(s):
+      -- RecP: we copy the NamedArg info to the subpatterns but discard it after recursion
+      RecP i fs          -> f $ setNamedArg p $ RecP i $ map (fmap namedArg) $ mapNamedArgPattern f $ map (fmap (setNamedArg p)) fs
+      -- AsP: we hand the NamedArg info to the subpattern
+      AsP i x p0         -> f $ updateNamedArg (AsP i x) $ mapNamedArgPattern f $ setNamedArg p p0
+      -- WithP: like AsP
+      WithP i p0         -> f $ updateNamedArg (WithP i) $ mapNamedArgPattern f $ setNamedArg p p0
+      AnnP i a p0        -> f $ updateNamedArg (AnnP i a) $ mapNamedArgPattern f $ setNamedArg p p0
+
+instance MapNamedArgPattern a => MapNamedArgPattern [a]                  where
+instance MapNamedArgPattern a => MapNamedArgPattern (FieldAssignment' a) where
+instance MapNamedArgPattern a => MapNamedArgPattern (Maybe a)            where
+
+instance (MapNamedArgPattern a, MapNamedArgPattern b) => MapNamedArgPattern (a,b) where
+  mapNamedArgPattern f (a, b) = (mapNamedArgPattern f a, mapNamedArgPattern f b)
+
+-- | Generic pattern traversal.
+
+class APatternLike p where
+  type ADotT p
+
+  -- | Fold pattern.
+  foldrAPattern
+    :: Monoid m
+    => (Pattern' (ADotT p) -> m -> m)
+         -- ^ Combine a pattern and the value computed from its subpatterns.
+    -> p -> m
+
+  default foldrAPattern
+    :: (Monoid m, Foldable f, APatternLike b, (ADotT p) ~ (ADotT b), f b ~ p)
+    => (Pattern' (ADotT p) -> m -> m) -> p -> m
+  foldrAPattern = foldMap . foldrAPattern
+
+  -- | Traverse pattern.
+  traverseAPatternM
+    :: Monad m
+    => (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))  -- ^ @pre@: Modification before recursion.
+    -> (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))  -- ^ @post@: Modification after recursion.
+    -> p -> m p
+
+  default traverseAPatternM
+    :: (Traversable f, APatternLike q, (ADotT p) ~ (ADotT q), f q ~ p, Monad m)
+    => (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))
+    -> (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))
+    -> p -> m p
+  traverseAPatternM pre post = traverse $ traverseAPatternM pre post
+
+-- | Compute from each subpattern a value and collect them all in a monoid.
+
+foldAPattern :: (APatternLike p, Monoid m) => (Pattern' (ADotT p) -> m) -> p -> m
+foldAPattern f = foldrAPattern $ \ p m -> f p `mappend` m
+
+-- | Traverse pattern(s) with a modification before the recursive descent.
+
+preTraverseAPatternM
+  :: (APatternLike p, Monad m )
+  => (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))  -- ^ @pre@: Modification before recursion.
+  -> p -> m p
+preTraverseAPatternM pre p = traverseAPatternM pre return p
+
+-- | Traverse pattern(s) with a modification after the recursive descent.
+
+postTraverseAPatternM
+  :: (APatternLike p, Monad m )
+  => (Pattern' (ADotT p) -> m (Pattern' (ADotT p)))  -- ^ @post@: Modification after recursion.
+  -> p -> m p
+postTraverseAPatternM post p = traverseAPatternM return post p
+
+-- | Map pattern(s) with a modification after the recursive descent.
+
+mapAPattern :: APatternLike p => (Pattern' (ADotT p) -> Pattern' (ADotT p)) -> p -> p
+mapAPattern f = runIdentity . postTraverseAPatternM (Identity . f)
+
+-- Interesting instance:
+
+instance APatternLike (Pattern' a) where
+  type ADotT (Pattern' a) = a
+
+  foldrAPattern f p = f p $
+    case p of
+      AsP _ _ p          -> foldrAPattern f p
+      ConP _ _ ps        -> foldrAPattern f ps
+      DefP _ _ ps        -> foldrAPattern f ps
+      RecP _ ps          -> foldrAPattern f ps
+      PatternSynP _ _ ps -> foldrAPattern f ps
+      WithP _ p          -> foldrAPattern f p
+      VarP _             -> mempty
+      ProjP _ _ _        -> mempty
+      WildP _            -> mempty
+      DotP _ _           -> mempty
+      AbsurdP _          -> mempty
+      LitP _ _           -> mempty
+      EqualP _ _         -> mempty
+      AnnP _ _ p         -> foldrAPattern f p
+
+  traverseAPatternM pre post = pre >=> recurse >=> post
+    where
+    recurse = \case
+      -- Non-recursive cases:
+      p@A.VarP{}            -> return p
+      p@A.WildP{}           -> return p
+      p@A.DotP{}            -> return p
+      p@A.LitP{}            -> return p
+      p@A.AbsurdP{}         -> return p
+      p@A.ProjP{}           -> return p
+      p@A.EqualP{}          -> return p
+      -- Recursive cases:
+      A.ConP        i ds ps -> A.ConP        i ds <$> traverseAPatternM pre post ps
+      A.DefP        i q  ps -> A.DefP        i q  <$> traverseAPatternM pre post ps
+      A.AsP         i x  p  -> A.AsP         i x  <$> traverseAPatternM pre post p
+      A.RecP        i    ps -> A.RecP        i    <$> traverseAPatternM pre post ps
+      A.PatternSynP i x  ps -> A.PatternSynP i x  <$> traverseAPatternM pre post ps
+      A.WithP       i p     -> A.WithP       i    <$> traverseAPatternM pre post p
+      A.AnnP        i a  p  -> A.AnnP        i a  <$> traverseAPatternM pre post p
+
+instance APatternLike a => APatternLike (Arg a) where
+  type ADotT (Arg a) = ADotT a
+
+instance APatternLike a => APatternLike (Named n a) where
+  type ADotT (Named n a) = ADotT a
+
+instance APatternLike a => APatternLike [a] where
+  type ADotT [a] = ADotT a
+
+instance APatternLike a => APatternLike (Maybe a) where
+  type ADotT (Maybe a) = ADotT a
+
+instance APatternLike a => APatternLike (FieldAssignment' a) where
+  type ADotT (FieldAssignment' a) = ADotT a
+
+instance (APatternLike a, APatternLike b, ADotT a ~ ADotT b) => APatternLike (a, b) where
+  type ADotT (a, b) = ADotT a
+
+  foldrAPattern f (p, p') =
+    foldrAPattern f p `mappend` foldrAPattern f p'
+
+  traverseAPatternM pre post (p, p') =
+    liftA2 (,)
+      (traverseAPatternM pre post p)
+      (traverseAPatternM pre post p')
+
+
+-- * Specific folds
+------------------------------------------------------------------------
+
+-- | Collect pattern variables in left-to-right textual order.
+
+patternVars :: APatternLike p => p -> [A.Name]
+patternVars p = foldAPattern f p `appEndo` []
+  where
+  -- We use difference lists @[A.Name] -> [A.Name]@ to avoid reconcatenation.
+  f :: Pattern' a -> Endo [A.Name]
+  f = \case
+    A.VarP x         -> Endo (unBind x :)
+    A.AsP _ x _      -> Endo (unBind x :)
+    A.LitP        {} -> mempty
+    A.ConP        {} -> mempty
+    A.RecP        {} -> mempty
+    A.DefP        {} -> mempty
+    A.ProjP       {} -> mempty
+    A.WildP       {} -> mempty
+    A.DotP        {} -> mempty
+    A.AbsurdP     {} -> mempty
+    A.EqualP      {} -> mempty
+    A.PatternSynP {} -> mempty
+    A.WithP _ _      -> mempty
+    A.AnnP        {} -> mempty
+
+-- | Check if a pattern contains a specific (sub)pattern.
+
+containsAPattern :: APatternLike p => (Pattern' (ADotT p) -> Bool) -> p -> Bool
+containsAPattern f = getAny . foldAPattern (Any . f)
+
+-- | Check if a pattern contains an absurd pattern.
+--   For instance, @suc ()@, does so.
+--
+--   Precondition: contains no pattern synonyms.
+
+containsAbsurdPattern :: APatternLike p => p -> Bool
+containsAbsurdPattern = containsAPattern $ \case
+    A.PatternSynP{} -> __IMPOSSIBLE__
+    A.AbsurdP{}     -> True
+    _               -> False
+
+-- | Check if a pattern contains an @-pattern.
+--
+containsAsPattern :: APatternLike p => p -> Bool
+containsAsPattern = containsAPattern $ \case
+    A.AsP{}         -> True
+    _               -> False
+
+-- | Check if any user-written pattern variables occur more than once,
+--   and throw the given error if they do.
+checkPatternLinearity :: (Monad m, APatternLike p)
+                      => p -> ([C.Name] -> m ()) -> m ()
+checkPatternLinearity ps err =
+  unlessNull (duplicates $ map nameConcrete $ patternVars ps) $ \ys -> err ys
+
+
+-- * Specific traversals
+------------------------------------------------------------------------
+
+-- | Pattern substitution.
+--
+-- For the embedded expression, the given pattern substitution is turned into
+-- an expression substitution.
+
+substPattern :: [(Name, Pattern)] -> Pattern -> Pattern
+substPattern s = substPattern' (substExpr $ map (second patternToExpr) s) s
+
+-- | Pattern substitution, parametrized by substitution function for embedded expressions.
+
+substPattern'
+  :: (e -> e)              -- ^ Substitution function for expressions.
+  -> [(Name, Pattern' e)]  -- ^ (Parallel) substitution.
+  -> Pattern' e            -- ^ Input pattern.
+  -> Pattern' e
+substPattern' subE s = mapAPattern $ \ p -> case p of
+  VarP x            -> fromMaybe p $ lookup (A.unBind x) s
+  DotP i e          -> DotP i $ subE e
+  EqualP i es       -> EqualP i $ map (subE *** subE) es
+  AnnP i a p        -> AnnP i (subE a) p
+  -- No action on the other patterns (besides the recursion):
+  ConP _ _ _        -> p
+  RecP _ _          -> p
+  ProjP _ _ _       -> p
+  WildP _           -> p
+  AbsurdP _         -> p
+  LitP _ _          -> p
+  DefP _ _ _        -> p
+  AsP _ _ _         -> p -- Note: cannot substitute into as-variable
+  PatternSynP _ _ _ -> p
+  WithP _ _         -> p
+
+
+-- * Other pattern utilities
+------------------------------------------------------------------------
+
+-- | Check for with-pattern.
+instance IsWithP (Pattern' e) where
+  isWithP = \case
+    WithP _ p -> Just p
+    _ -> Nothing
+
+-- | Split patterns into (patterns, trailing with-patterns).
+splitOffTrailingWithPatterns :: A.Patterns -> (A.Patterns, A.Patterns)
+splitOffTrailingWithPatterns = spanEnd (isJust . isWithP)
+
+-- | Get the tail of with-patterns of a pattern spine.
+trailingWithPatterns :: Patterns -> Patterns
+trailingWithPatterns = snd . splitOffTrailingWithPatterns
+
+-- | The next patterns are ...
+--
+-- (This view discards 'PatInfo'.)
+data LHSPatternView e
+  = LHSAppP  (NAPs e)
+      -- ^ Application patterns (non-empty list).
+  | LHSProjP ProjOrigin AmbiguousQName (NamedArg (Pattern' e))
+      -- ^ A projection pattern.  Is also stored unmodified here.
+  | LHSWithP [Pattern' e]
+      -- ^ With patterns (non-empty list).
+      --   These patterns are not prefixed with 'WithP'.
+  deriving (Show)
+
+-- | Construct the 'LHSPatternView' of the given list (if not empty).
+--
+-- Return the view and the remaining patterns.
+
+lhsPatternView :: IsProjP e => NAPs e -> Maybe (LHSPatternView e, NAPs e)
+lhsPatternView [] = Nothing
+lhsPatternView (p0 : ps) =
+  case namedArg p0 of
+    ProjP _i o d -> Just (LHSProjP o d p0, ps)
+    -- If the next pattern is a with-pattern, collect more with-patterns
+    WithP _i p   -> Just (LHSWithP (p : map namedArg ps1), ps2)
+      where
+      (ps1, ps2) = spanJust isWithP ps
+    -- If the next pattern is an application pattern, collect more of these
+    _ -> Just (LHSAppP (p0 : ps1), ps2)
+      where
+      (ps1, ps2) = span (\ p -> isNothing (isProjP p) && isNothing (isWithP p)) ps
+
+-- * Left-hand-side manipulation
+------------------------------------------------------------------------
+
+-- | Convert a focused lhs to spine view and back.
+class LHSToSpine a b where
+  lhsToSpine :: a -> b
+  spineToLhs :: b -> a
+
+-- | Clause instance.
+instance LHSToSpine Clause SpineClause where
+  lhsToSpine = fmap lhsToSpine
+  spineToLhs = fmap spineToLhs
+
+-- | List instance (for clauses).
+instance LHSToSpine a b => LHSToSpine [a] [b] where
+  lhsToSpine = map lhsToSpine
+  spineToLhs = map spineToLhs
+
+-- | LHS instance.
+instance LHSToSpine LHS SpineLHS where
+  lhsToSpine (LHS i core) = SpineLHS i f ps
+    where QNamed f ps = lhsCoreToSpine core
+  spineToLhs (SpineLHS i f ps) = LHS i (spineToLhsCore $ QNamed f ps)
+
+lhsCoreToSpine :: LHSCore' e -> A.QNamed [NamedArg (Pattern' e)]
+lhsCoreToSpine = \case
+  LHSHead f ps     -> QNamed f ps
+  LHSProj d h ps   -> lhsCoreToSpine (namedArg h) <&> (++ (p : ps))
+    where p = updateNamedArg (const $ ProjP empty ProjPrefix d) h
+  LHSWith h wps ps -> lhsCoreToSpine h <&> (++ map fromWithPat wps ++ ps)
+    where
+      fromWithPat :: Arg (Pattern' e) -> NamedArg (Pattern' e)
+      fromWithPat = fmap (unnamed . mkWithP)
+      mkWithP p   = WithP (PatRange $ getRange p) p
+
+spineToLhsCore :: IsProjP e => QNamed [NamedArg (Pattern' e)] -> LHSCore' e
+spineToLhsCore (QNamed f ps) = lhsCoreAddSpine (LHSHead f []) ps
+
+-- | Add applicative patterns (non-projection / non-with patterns) to the right.
+lhsCoreApp :: LHSCore' e -> [NamedArg (Pattern' e)] -> LHSCore' e
+lhsCoreApp core ps = core { lhsPats = lhsPats core ++ ps }
+
+-- | Add with-patterns to the right.
+lhsCoreWith :: LHSCore' e -> [Arg (Pattern' e)] -> LHSCore' e
+lhsCoreWith (LHSWith core wps []) wps' = LHSWith core (wps ++ wps') []
+lhsCoreWith core                  wps' = LHSWith core wps' []
+
+lhsCoreAddChunk :: IsProjP e => LHSCore' e -> LHSPatternView e -> LHSCore' e
+lhsCoreAddChunk core = \case
+  LHSAppP ps               -> lhsCoreApp core ps
+  LHSWithP wps             -> lhsCoreWith core (defaultArg <$> wps)
+  LHSProjP ProjPrefix d np -> LHSProj d (setNamedArg np core) []  -- Prefix projection pattern.
+  LHSProjP _          _ np -> lhsCoreApp core [np]       -- Postfix projection pattern.
+
+-- | Add projection, with, and applicative patterns to the right.
+lhsCoreAddSpine :: IsProjP e => LHSCore' e -> [NamedArg (Pattern' e)] -> LHSCore' e
+lhsCoreAddSpine core ps =
+  -- Recurse on lhsPatternView until no patterns left.
+  case lhsPatternView ps of
+    Nothing       -> core
+    Just (v, ps') -> lhsCoreAddChunk core chunk `lhsCoreAddSpine` ps'
+      where
+      -- Andreas, 2016-06-13
+      -- If the projection was written prefix by the user
+      -- or it is a fully applied operator
+      -- we turn it to prefix projection form.
+      chunk = case v of
+        LHSProjP ProjPrefix _ _
+          -> v
+        LHSProjP _ d np | let nh = C.numHoles d, nh > 0, nh <= 1 + length ps'
+          -> LHSProjP ProjPrefix d np
+        _ -> v
+
+-- | Used for checking pattern linearity.
+lhsCoreAllPatterns :: LHSCore' e -> [Pattern' e]
+lhsCoreAllPatterns = map namedArg . qnamed . lhsCoreToSpine
+
+-- | Used in ''Agda.Syntax.Translation.AbstractToConcrete''.
+--   Returns a 'DefP'.
+lhsCoreToPattern :: LHSCore -> Pattern
+lhsCoreToPattern lc =
+  case lc of
+    LHSHead f aps         -> DefP noInfo (unambiguous f) aps
+    LHSProj d lhscore aps -> DefP noInfo d $
+      fmap (fmap lhsCoreToPattern) lhscore : aps
+    LHSWith h wps aps     -> case lhsCoreToPattern h of
+      DefP r q ps         -> DefP r q $ ps ++ map fromWithPat wps ++ aps
+        where
+          fromWithPat :: Arg Pattern -> NamedArg Pattern
+          fromWithPat = fmap (unnamed . mkWithP)
+          mkWithP p   = WithP (PatRange $ getRange p) p
+      _ -> __IMPOSSIBLE__
+  where noInfo = empty -- TODO, preserve range!
+
+mapLHSHead :: (QName -> [NamedArg Pattern] -> LHSCore) -> LHSCore -> LHSCore
+mapLHSHead f = \case
+  LHSHead x ps     -> f x ps
+  LHSProj d h ps   -> LHSProj d (fmap (fmap (mapLHSHead f)) h) ps
+  LHSWith h wps ps -> LHSWith (mapLHSHead f h) wps ps
diff --git a/src/full/Agda/Syntax/Abstract/PatternSynonyms.hs b/src/full/Agda/Syntax/Abstract/PatternSynonyms.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/PatternSynonyms.hs
@@ -0,0 +1,84 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Pattern synonym utilities: folding pattern synonym definitions for
+--   printing and merging pattern synonym definitions to handle overloaded
+--   pattern synonyms.
+module Agda.Syntax.Abstract.PatternSynonyms
+  ( matchPatternSyn
+  , matchPatternSynP
+  , mergePatternSynDefs
+  ) where
+
+import Control.Applicative  ( Alternative(empty) )
+import Control.Monad        ( foldM, guard, zipWithM, zipWithM_ )
+import Control.Monad.Writer ( MonadWriter(..), WriterT, execWriterT )
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Traversable (forM)
+import Data.Void
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract
+import Agda.Syntax.Abstract.Views
+
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+
+-- | Merge a list of pattern synonym definitions. Fails unless all definitions
+--   have the same shape (i.e. equal up to renaming of variables and constructor
+--   names).
+mergePatternSynDefs :: List1 PatternSynDefn -> Maybe PatternSynDefn
+mergePatternSynDefs (def :| defs) = foldM mergeDef def defs
+
+mergeDef :: PatternSynDefn -> PatternSynDefn -> Maybe PatternSynDefn
+mergeDef (xs, p) (ys, q) = do
+  guard $ map getArgInfo xs == map getArgInfo ys
+  let ren = zip (map unArg xs) (map unArg ys)
+  (xs,) <$> merge ren p q
+  where
+    merge ren p@(VarP x) (VarP y)   = p <$ guard ((unBind x, unBind y) `elem` ren)
+    merge ren p@(LitP _ l) (LitP _ l') = p <$ guard (l == l')
+    merge ren p@(WildP _) (WildP _) = return p
+    merge ren (ConP i (AmbQ cs) ps) (ConP _ (AmbQ cs') qs) = do
+      guard $ map getArgInfo ps == map getArgInfo qs
+      ConP i (AmbQ $ List1.union cs cs') <$> zipWithM (mergeArg ren) ps qs
+    merge _ _ _ = empty
+
+    mergeArg ren p q = setNamedArg p <$> merge ren (namedArg p) (namedArg q)
+
+-- | Match an expression against a pattern synonym.
+matchPatternSyn :: PatternSynDefn -> Expr -> Maybe [Arg Expr]
+matchPatternSyn = runMatch match
+  where
+    match (VarP x) e = unBind x ==> e
+    match (LitP _ l) (Lit _ l') = guard (l == l')
+    match (ConP _ (AmbQ cs) ps) e = do
+      Application (Con (AmbQ cs')) args <- return (appView e)
+      guard $ all (`elem` cs) cs'                       -- check all possible constructors appear in the synonym
+      guard $ map getArgInfo ps == map getArgInfo args  -- check that we agree on the hiding (TODO: too strict?)
+      zipWithM_ match (map namedArg ps) (map namedArg args)
+    match _ _ = empty
+
+-- | Match a pattern against a pattern synonym.
+matchPatternSynP :: PatternSynDefn -> Pattern' e -> Maybe [Arg (Pattern' e)]
+matchPatternSynP = runMatch match
+  where
+    match (VarP x) q = unBind x ==> q
+    match (LitP _ l) (LitP _ l') = guard (l == l')
+    match (WildP _) (WildP _) = return ()
+    match (ConP _ (AmbQ cs) ps) (ConP _ (AmbQ cs') qs) = do
+      guard $ all (`elem` cs) cs'
+      guard $ map getArgInfo ps == map getArgInfo qs
+      zipWithM_ match (map namedArg ps) (map namedArg qs)
+    match _ _ = empty
+
+type Match e = WriterT (Map Name e) Maybe
+
+(==>) :: Name -> e -> Match e ()
+x ==> e = tell (Map.singleton x e)
+
+runMatch :: (Pattern' Void -> e -> Match e ()) -> PatternSynDefn -> e -> Maybe [Arg e]
+runMatch match (xs, pat) e = do
+  sub <- execWriterT (match pat e)
+  forM xs $ \ x -> (<$ x) <$> Map.lookup (unArg x) sub
diff --git a/src/full/Agda/Syntax/Abstract/Pretty.hs b/src/full/Agda/Syntax/Abstract/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/Pretty.hs
@@ -0,0 +1,26 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Abstract.Pretty where
+
+import Agda.Syntax.Fixity
+import Agda.Syntax.Translation.AbstractToConcrete
+import Agda.Syntax.Common.Pretty
+
+showA :: (ToConcrete a, Show (ConOfAbs a), MonadAbsToCon m) => a -> m String
+showA x = show <$> abstractToConcrete_ x
+
+prettyA :: (ToConcrete a, Pretty (ConOfAbs a), MonadAbsToCon m) => a -> m Doc
+prettyA x = pretty <$> abstractToConcrete_ x
+
+prettyAs :: (ToConcrete a, ConOfAbs a ~ [ce], Pretty ce, MonadAbsToCon m) => a -> m Doc
+prettyAs x = fsep . map pretty <$> abstractToConcrete_ x
+
+-- | Variant of 'showA' which does not insert outermost parentheses.
+
+showATop :: (ToConcrete a, Show (ConOfAbs a), MonadAbsToCon m) => a -> m String
+showATop x = show <$> abstractToConcreteCtx TopCtx x
+
+-- | Variant of 'prettyA' which does not insert outermost parentheses.
+
+prettyATop :: (ToConcrete a, Pretty (ConOfAbs a),  MonadAbsToCon m) => a -> m Doc
+prettyATop x = pretty <$> abstractToConcreteCtx TopCtx x
diff --git a/src/full/Agda/Syntax/Abstract/UsedNames.hs b/src/full/Agda/Syntax/Abstract/UsedNames.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/UsedNames.hs
@@ -0,0 +1,182 @@
+
+module Agda.Syntax.Abstract.UsedNames
+  ( allUsedNames
+  ) where
+
+import Data.Foldable (foldMap)
+import Data.Semigroup (Semigroup, (<>))
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract
+import Agda.Syntax.Concrete (FieldAssignment'(..))
+import Agda.Utils.List1 (List1)
+
+import Agda.Utils.Impossible
+
+-- | All names used in an abstract expression. This is used when rendering clauses to figure out
+--   which (implicit) pattern variables must be preserved. For example, the for @f : Nat → Nat@, the
+--   clause @f {n} = 0@ can be printed as @f = 0@ (dropping the @n@), but @f {n} = n@ must preserve
+--   the @n@.
+allUsedNames :: Expr -> Set Name
+allUsedNames = usedNames . boundAndUsed
+
+data BoundAndUsedNames = BoundAndUsedNames
+  { boundNames :: Set Name
+  , usedNames  :: Set Name }
+
+-- | Bound names in first argument scope over second argument.
+instance Semigroup BoundAndUsedNames where
+  BoundAndUsedNames bound1 used1 <> BoundAndUsedNames bound2 used2 =
+    BoundAndUsedNames (bound1 <> bound2) (used1 <> Set.difference used2 bound1)
+
+instance Monoid BoundAndUsedNames where
+  mempty  = BoundAndUsedNames mempty mempty
+  mappend = (<>)
+
+singleUse :: Name -> BoundAndUsedNames
+singleUse x = BoundAndUsedNames mempty (Set.singleton x)
+
+singleBind :: Name -> BoundAndUsedNames
+singleBind x = BoundAndUsedNames (Set.singleton x) mempty
+
+noBindings :: BoundAndUsedNames -> BoundAndUsedNames
+noBindings names = names{ boundNames = mempty }
+
+-- | Bound names in first argument do *not* scope over second argument.
+parB :: BoundAndUsedNames -> BoundAndUsedNames -> BoundAndUsedNames
+parB (BoundAndUsedNames bound1 used1) (BoundAndUsedNames bound2 used2) =
+  BoundAndUsedNames (bound1 <> bound2) (used1 <> used2)
+
+parBindings :: (BoundAndUsed a, BoundAndUsed b) => a -> b -> BoundAndUsedNames
+parBindings a b = boundAndUsed a `parB` boundAndUsed b
+
+parBoundAndUsed :: (Foldable f, BoundAndUsed a) => f a -> BoundAndUsedNames
+parBoundAndUsed = foldr parBindings mempty
+
+class BoundAndUsed a where
+  boundAndUsed :: a -> BoundAndUsedNames
+
+  default boundAndUsed :: (a ~ f b, Foldable f, BoundAndUsed b) => a -> BoundAndUsedNames
+  boundAndUsed = foldMap boundAndUsed
+
+instance BoundAndUsed BoundAndUsedNames where
+  boundAndUsed = id
+
+instance BoundAndUsed a => BoundAndUsed (Arg a)
+instance BoundAndUsed a => BoundAndUsed (Named n a)
+instance BoundAndUsed a => BoundAndUsed (List1 a)
+instance BoundAndUsed a => BoundAndUsed [a]
+instance BoundAndUsed a => BoundAndUsed (Maybe a)
+
+instance (BoundAndUsed a, BoundAndUsed b) => BoundAndUsed (Either a b) where
+  boundAndUsed = either boundAndUsed boundAndUsed
+
+instance BoundAndUsed ModuleName where
+  boundAndUsed _ = mempty
+
+instance (BoundAndUsed a, BoundAndUsed b) => BoundAndUsed (a, b) where
+  boundAndUsed (a, b) = boundAndUsed a <> boundAndUsed b
+
+instance BoundAndUsed Expr where
+  boundAndUsed = noBindings . \ case
+    Var x                  -> singleUse x
+    Def'{}                 -> mempty
+    Proj{}                 -> mempty
+    Con{}                  -> mempty
+    PatternSyn{}           -> mempty
+    Macro{}                -> mempty
+    Lit{}                  -> mempty
+    QuestionMark{}         -> mempty
+    Underscore{}           -> mempty
+    Dot _ expr             -> boundAndUsed expr
+    App _ expr arg         -> boundAndUsed (expr, arg)
+    WithApp _ expr exprs   -> boundAndUsed (expr, exprs)
+    Lam _ bind expr        -> boundAndUsed (bind, expr)
+    AbsurdLam{}            -> mempty
+    ExtendedLam _ _ _ _ cs -> boundAndUsed cs
+    Pi _ tel expr          -> boundAndUsed (tel, expr)
+    Generalized _ expr     -> boundAndUsed expr
+    Fun _ arg expr         -> boundAndUsed (arg, expr)
+    Let _ binds expr       -> boundAndUsed (binds, expr)
+    Rec _ as               -> boundAndUsed as
+    RecUpdate _ expr as    -> boundAndUsed expr <> boundAndUsed as
+    ScopedExpr _ expr      -> boundAndUsed expr
+    Quote{}                -> mempty
+    QuoteTerm{}            -> mempty
+    Unquote{}              -> mempty
+    DontCare expr          -> boundAndUsed expr
+
+instance BoundAndUsed lhs => BoundAndUsed (Clause' lhs) where
+  -- Note: where declarations are ignored. We use this only on expressions coming from
+  --       InternalToAbstract where there are no where decls.
+  boundAndUsed Clause{ clauseLHS = lhs, clauseRHS = rhs } = boundAndUsed (lhs, rhs)
+
+instance BoundAndUsed RHS where
+  boundAndUsed = \ case
+    RHS body _              -> boundAndUsed body
+    AbsurdRHS               -> mempty
+    WithRHS _ es cs         -> boundAndUsed (es, cs)
+    RewriteRHS eqns _ rhs _ -> boundAndUsed (eqns, rhs)
+
+instance BoundAndUsed LHS where
+  boundAndUsed = boundAndUsed . lhsCore
+
+instance BoundAndUsed e => BoundAndUsed (LHSCore' e) where
+  boundAndUsed = \ case
+    LHSHead _ ps       -> parBoundAndUsed ps
+    LHSProj _ lhs ps   -> lhs `parBindings` parBoundAndUsed ps
+    LHSWith lhs wps ps -> lhs `parBindings` parBoundAndUsed wps
+                              `parBindings` parBoundAndUsed ps
+
+instance (BoundAndUsed x, BoundAndUsed p, BoundAndUsed e) => BoundAndUsed (RewriteEqn' q x p e) where
+  boundAndUsed (Rewrite es)  = boundAndUsed $ snd <$> es
+  boundAndUsed (Invert _ bs) = parBoundAndUsed (namedThing <$> bs) <> boundAndUsed (nameOf <$> bs)
+
+instance BoundAndUsed LetBinding where
+  boundAndUsed = \ case   -- Note: binder last since it's not recursive
+    LetBind _ _ x ty e     -> boundAndUsed ((ty, e), x)
+    LetPatBind _ p e       -> boundAndUsed (e, p)
+    LetApply _ _ _ app _ _ -> boundAndUsed app
+    LetOpen{}              -> mempty
+    LetDeclaredVariable{}  -> mempty   -- Only used for highlighting
+
+instance BoundAndUsed LamBinding where
+  boundAndUsed (DomainFree _ b) = boundAndUsed b
+  boundAndUsed (DomainFull b)   = boundAndUsed b
+
+instance BoundAndUsed TypedBinding where
+  boundAndUsed (TBind _ _ bs ty) = boundAndUsed (ty, bs)
+  boundAndUsed (TLet _ bs)       = boundAndUsed bs
+
+instance BoundAndUsed name => BoundAndUsed (Binder' name) where
+  boundAndUsed (Binder p x) = parBindings p x
+
+instance BoundAndUsed BindName where
+  boundAndUsed x = singleBind (unBind x)
+
+instance BoundAndUsed e => BoundAndUsed (Pattern' e) where
+  boundAndUsed = \ case
+    VarP x             -> boundAndUsed x
+    ConP _ _ ps        -> parBoundAndUsed ps
+    ProjP{}            -> mempty
+    DefP _ _ ps        -> parBoundAndUsed ps
+    WildP{}            -> mempty
+    AsP _ x p          -> parBindings x p
+    DotP _ e           -> boundAndUsed e
+    AbsurdP{}          -> mempty
+    LitP{}             -> mempty
+    PatternSynP _ _ ps -> parBoundAndUsed ps
+    RecP _ as          -> parBoundAndUsed as
+    EqualP _ eqs       -> parBoundAndUsed eqs
+    WithP _ p          -> boundAndUsed p
+    AnnP _ ty p        -> boundAndUsed (ty, p)
+
+instance BoundAndUsed e => BoundAndUsed (FieldAssignment' e) where
+  boundAndUsed (FieldAssignment _ e) = boundAndUsed e
+
+instance BoundAndUsed ModuleApplication where
+  boundAndUsed (SectionApp tel _ es)  = noBindings $ boundAndUsed (tel, es)
+  boundAndUsed RecordModuleInstance{} = mempty
+
diff --git a/src/full/Agda/Syntax/Abstract/Views.hs b/src/full/Agda/Syntax/Abstract/Views.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Abstract/Views.hs
@@ -0,0 +1,631 @@
+
+module Agda.Syntax.Abstract.Views where
+
+import Prelude hiding (null)
+
+import Control.Applicative ( Const(Const), getConst )
+import Control.Monad.Identity
+
+import Data.Foldable (foldMap)
+import qualified Data.DList as DL
+import Data.Semigroup ((<>))
+import Data.Void
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Concrete (FieldAssignment', exprFieldA)
+import Agda.Syntax.Info
+import Agda.Syntax.Scope.Base (KindOfName(..), conKindOfName, WithKind(..))
+
+import Agda.Utils.Either
+import Agda.Utils.List1 (List1)
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+
+data AppView' arg = Application Expr [NamedArg arg]
+  deriving (Functor)
+
+type AppView = AppView' Expr
+
+-- | Gather applications to expose head and spine.
+--
+--   Note: everything is an application, possibly of itself to 0 arguments
+appView :: Expr -> AppView
+appView = fmap snd . appView'
+
+appView' :: Expr -> AppView' (AppInfo, Expr)
+appView' e = f (DL.toList es)
+  where
+  (f, es) = appView'' e
+
+  appView'' e = case e of
+    App i e1 e2
+      | Dot _ e2' <- unScope $ namedArg e2
+      , Just f <- maybeProjTurnPostfix e2'
+      , getHiding e2 == NotHidden -- Jesper, 2018-12-13: postfix projections shouldn't be hidden
+      -> (Application f, singleton (defaultNamedArg (i, e1)))
+    App i e1 arg | (f, es) <- appView'' e1 ->
+      (f, es `DL.snoc` (fmap . fmap) (i,) arg)
+    ScopedExpr _ e -> appView'' e
+    _              -> (Application e, mempty)
+
+maybeProjTurnPostfix :: Expr -> Maybe Expr
+maybeProjTurnPostfix e =
+  case e of
+    ScopedExpr i e' -> ScopedExpr i <$> maybeProjTurnPostfix e'
+    Proj _ x        -> return $ Proj ProjPostfix x
+    _               -> Nothing
+
+unAppView :: AppView -> Expr
+unAppView (Application h es) =
+  foldl (App defaultAppInfo_) h es
+
+-- | Collects plain lambdas.
+data LamView = LamView [LamBinding] Expr
+
+lamView :: Expr -> LamView
+lamView (Lam i b e) = cons b $ lamView e
+  where cons b (LamView bs e) = LamView (b : bs) e
+lamView (ScopedExpr _ e) = lamView e
+lamView e = LamView [] e
+
+-- | Collect @A.Pi@s.
+data PiView = PiView [(ExprInfo, Telescope1)] Type
+
+piView :: Expr -> PiView
+piView = \case
+   Pi i tel b -> cons $ piView b
+     where cons (PiView tels t) = PiView ((i,tel) : tels) t
+   e -> PiView [] e
+
+unPiView :: PiView -> Expr
+unPiView (PiView tels t) = foldr (uncurry Pi) t tels
+
+-- | Gather top-level 'AsP'atterns and 'AnnP'atterns to expose underlying pattern.
+asView :: A.Pattern -> ([Name], [A.Expr], A.Pattern)
+asView (A.AsP _ x p)  = (\(asb, ann, p) -> (unBind x : asb, ann, p)) $ asView p
+asView (A.AnnP _ a p) = (\(asb, ann, p) -> (asb, a : ann, p))        $ asView p
+asView p              = ([], [], p)
+
+-- | Remove top 'ScopedExpr' wrappers.
+unScope :: Expr -> Expr
+unScope (ScopedExpr scope e) = unScope e
+unScope (QuestionMark i ii)  = QuestionMark (i {metaScope = empty}) ii
+unScope (Underscore i)       = Underscore (i {metaScope = empty})
+unScope e                    = e
+
+-- | Remove 'ScopedExpr' wrappers everywhere.
+--
+--   NB: Unless the implementation of 'ExprLike' for clauses
+--   has been finished, this does not work for clauses yet.
+deepUnscope :: ExprLike a => a -> a
+deepUnscope = mapExpr unScope
+
+deepUnscopeDecls :: [A.Declaration] -> [A.Declaration]
+deepUnscopeDecls = concatMap deepUnscopeDecl
+
+deepUnscopeDecl :: A.Declaration -> [A.Declaration]
+deepUnscopeDecl = \case
+  A.ScopedDecl _ ds           -> deepUnscopeDecls ds
+  A.Mutual i ds               -> [A.Mutual i (deepUnscopeDecls ds)]
+  A.Section i e m tel ds      -> [A.Section i e m (deepUnscope tel)
+                                   (deepUnscopeDecls ds)]
+  A.RecDef i x uc dir bs e ds -> [ A.RecDef i x uc dir (deepUnscope bs)
+                                     (deepUnscope e)
+                                     (deepUnscopeDecls ds) ]
+  d                           -> [deepUnscope d]
+
+-- * Traversal
+---------------------------------------------------------------------------
+
+-- Type aliases to abbreviate the quantified foralls which we use to avoid
+-- giving in to NoMonoLocalBinds.
+type RecurseExprFn m a = Applicative m => (Expr -> m Expr -> m Expr) -> a -> m a
+type RecurseExprRecFn m = forall a. ExprLike a => a -> m a
+
+type FoldExprFn m a = Monoid m => (Expr -> m) -> a -> m
+type FoldExprRecFn m = forall a. ExprLike a => a -> m
+
+type TraverseExprFn m a = (Applicative m, Monad m) => (Expr -> m Expr) -> a -> m a
+type TraverseExprRecFn m = forall a. ExprLike a => a -> m a
+
+-- | Apply an expression rewriting to every subexpression, inside-out.
+--   See "Agda.Syntax.Internal.Generic".
+class ExprLike a where
+  -- | The first expression is pre-traversal, the second one post-traversal.
+  recurseExpr :: RecurseExprFn m a
+  default recurseExpr :: (Traversable f, ExprLike a', a ~ f a', Applicative m)
+                      => (Expr -> m Expr -> m Expr) -> a -> m a
+  recurseExpr = traverse . recurseExpr
+
+  foldExpr :: FoldExprFn m a
+  foldExpr f = getConst . recurseExpr (\ pre post -> Const (f pre) <* post)
+
+  traverseExpr :: TraverseExprFn m a
+  traverseExpr f = recurseExpr (\ pre post -> f =<< post)
+
+  mapExpr :: (Expr -> Expr) -> (a -> a)
+  mapExpr f = runIdentity . traverseExpr (Identity . f)
+
+instance ExprLike Expr where
+  recurseExpr :: forall m. RecurseExprFn m Expr
+  recurseExpr f e0 = f e0 $ do
+    let
+      recurse :: RecurseExprRecFn m
+      recurse e = recurseExpr f e
+    case e0 of
+      Var{}                      -> pure e0
+      Def'{}                     -> pure e0
+      Proj{}                     -> pure e0
+      Con{}                      -> pure e0
+      Lit{}                      -> pure e0
+      QuestionMark{}             -> pure e0
+      Underscore{}               -> pure e0
+      Dot ei e                   -> Dot ei <$> recurse e
+      App ei e arg               -> App ei <$> recurse e <*> recurse arg
+      WithApp ei e es            -> WithApp ei <$> recurse e <*> recurse es
+      Lam ei b e                 -> Lam ei <$> recurse b <*> recurse e
+      AbsurdLam{}                -> pure e0
+      ExtendedLam ei di er x cls -> ExtendedLam ei di er x <$> recurse cls
+      Pi ei tel e                -> Pi ei <$> recurse tel <*> recurse e
+      Generalized  s e           -> Generalized s <$> recurse e
+      Fun ei arg e               -> Fun ei <$> recurse arg <*> recurse e
+      Let ei bs e                -> Let ei <$> recurse bs <*> recurse e
+      Rec ei bs                  -> Rec ei <$> recurse bs
+      RecUpdate ei e bs          -> RecUpdate ei <$> recurse e <*> recurse bs
+      ScopedExpr sc e            -> ScopedExpr sc <$> recurse e
+      Quote{}                    -> pure e0
+      QuoteTerm{}                -> pure e0
+      Unquote{}                  -> pure e0
+      DontCare e                 -> DontCare <$> recurse e
+      PatternSyn{}               -> pure e0
+      Macro{}                    -> pure e0
+
+  foldExpr :: forall m. FoldExprFn m Expr
+  foldExpr f e =
+    case e of
+      Var{}                  -> m
+      Def'{}                 -> m
+      Proj{}                 -> m
+      Con{}                  -> m
+      PatternSyn{}           -> m
+      Macro{}                -> m
+      Lit{}                  -> m
+      QuestionMark{}         -> m
+      Underscore{}           -> m
+      Dot _ e                -> m `mappend` fold e
+      App _ e e'             -> m `mappend` fold e `mappend` fold e'
+      WithApp _ e es         -> m `mappend` fold e `mappend` fold es
+      Lam _ b e              -> m `mappend` fold b `mappend` fold e
+      AbsurdLam{}            -> m
+      ExtendedLam _ _ _ _ cs -> m `mappend` fold cs
+      Pi _ tel e             -> m `mappend` fold tel `mappend` fold e
+      Generalized _ e        -> m `mappend` fold e
+      Fun _ e e'             -> m `mappend` fold e `mappend` fold e'
+      Let _ bs e             -> m `mappend` fold bs `mappend` fold e
+      Rec _ as               -> m `mappend` fold as
+      RecUpdate _ e as       -> m `mappend` fold e `mappend` fold as
+      ScopedExpr _ e         -> m `mappend` fold e
+      Quote{}                -> m
+      QuoteTerm{}            -> m
+      Unquote{}              -> m
+      DontCare e             -> m `mappend` fold e
+   where
+     m = f e
+     fold :: FoldExprRecFn m
+     fold = foldExpr f
+
+  traverseExpr :: forall m. TraverseExprFn m Expr
+  traverseExpr f e = do
+    let
+      trav :: TraverseExprRecFn m
+      trav e = traverseExpr f e
+    case e of
+      Var{}                      -> f e
+      Def'{}                     -> f e
+      Proj{}                     -> f e
+      Con{}                      -> f e
+      Lit{}                      -> f e
+      QuestionMark{}             -> f e
+      Underscore{}               -> f e
+      Dot ei e                   -> f =<< Dot ei <$> trav e
+      App ei e arg               -> f =<< App ei <$> trav e <*> trav arg
+      WithApp ei e es            -> f =<< WithApp ei <$> trav e <*> trav es
+      Lam ei b e                 -> f =<< Lam ei <$> trav b <*> trav e
+      AbsurdLam{}                -> f e
+      ExtendedLam ei di re x cls -> f =<< ExtendedLam ei di re x <$> trav cls
+      Pi ei tel e                -> f =<< Pi ei <$> trav tel <*> trav e
+      Generalized s e            -> f =<< Generalized s <$> trav e
+      Fun ei arg e               -> f =<< Fun ei <$> trav arg <*> trav e
+      Let ei bs e                -> f =<< Let ei <$> trav bs <*> trav e
+      Rec ei bs                  -> f =<< Rec ei <$> trav bs
+      RecUpdate ei e bs          -> f =<< RecUpdate ei <$> trav e <*> trav bs
+      ScopedExpr sc e            -> f =<< ScopedExpr sc <$> trav e
+      Quote{}                    -> f e
+      QuoteTerm{}                -> f e
+      Unquote{}                  -> f e
+      DontCare e                 -> f =<< DontCare <$> trav e
+      PatternSyn{}               -> f e
+      Macro{}                    -> f e
+
+instance ExprLike a => ExprLike (Arg a)
+instance ExprLike a => ExprLike (Maybe a)
+instance ExprLike a => ExprLike (Named x a)
+instance ExprLike a => ExprLike (Ranged a)
+instance ExprLike a => ExprLike [a]
+instance ExprLike a => ExprLike (List1 a)
+
+instance (ExprLike a, ExprLike b) => ExprLike (a, b) where
+  recurseExpr f (x, y) = (,) <$> recurseExpr f x <*> recurseExpr f y
+
+instance ExprLike Void where
+  recurseExpr f = absurd
+
+instance ExprLike a => ExprLike (FieldAssignment' a) where
+  recurseExpr = exprFieldA . recurseExpr
+
+instance (ExprLike a, ExprLike b) => ExprLike (Either a b) where
+  recurseExpr f = traverseEither (recurseExpr f)
+                                 (recurseExpr f)
+
+instance ExprLike BindName where
+  recurseExpr f = pure
+
+instance ExprLike ModuleName where
+  recurseExpr f = pure
+
+instance ExprLike QName where
+  recurseExpr _ = pure
+
+instance ExprLike LamBinding where
+  recurseExpr f e =
+    case e of
+      DomainFree t x -> DomainFree <$> recurseExpr f t <*> pure x
+      DomainFull bs  -> DomainFull <$> recurseExpr f bs
+  foldExpr f e =
+    case e of
+      DomainFree t _ -> foldExpr f t
+      DomainFull bs -> foldExpr f bs
+  traverseExpr f e =
+    case e of
+      DomainFree t x -> DomainFree <$> traverseExpr f t <*> pure x
+      DomainFull bs  -> DomainFull <$> traverseExpr f bs
+
+instance ExprLike GeneralizeTelescope where
+  recurseExpr  f (GeneralizeTel s tel) = GeneralizeTel s <$> recurseExpr f tel
+  foldExpr     f (GeneralizeTel s tel) = foldExpr f tel
+  traverseExpr f (GeneralizeTel s tel) = GeneralizeTel s <$> traverseExpr f tel
+
+instance ExprLike DataDefParams where
+  recurseExpr  f (DataDefParams s tel) = DataDefParams s <$> recurseExpr f tel
+  foldExpr     f (DataDefParams s tel) = foldExpr f tel
+  traverseExpr f (DataDefParams s tel) = DataDefParams s <$> traverseExpr f tel
+
+instance ExprLike TypedBindingInfo where
+  recurseExpr f (TypedBindingInfo s t)  = TypedBindingInfo <$> recurseExpr f s <*> pure t
+  foldExpr f (TypedBindingInfo s t)     = foldExpr f s
+  traverseExpr f (TypedBindingInfo s t) = TypedBindingInfo <$> traverseExpr f s <*> pure t
+
+instance ExprLike TypedBinding where
+  recurseExpr f e =
+    case e of
+      TBind r t xs e -> TBind r <$> recurseExpr f t <*> pure xs <*> recurseExpr f e
+      TLet r ds      -> TLet r <$> recurseExpr f ds
+  foldExpr f e =
+    case e of
+      TBind _ t _ e -> foldExpr f t `mappend` foldExpr f e
+      TLet _ ds     -> foldExpr f ds
+  traverseExpr f e =
+    case e of
+      TBind r t xs e -> TBind r <$> traverseExpr f t <*> pure xs <*> traverseExpr f e
+      TLet r ds      -> TLet r <$> traverseExpr f ds
+
+instance ExprLike LetBinding where
+  recurseExpr :: forall m. RecurseExprFn m LetBinding
+  recurseExpr f e = do
+    let
+      recurse :: RecurseExprRecFn m
+      recurse e = recurseExpr f e
+    case e of
+      LetBind li ai x e e'  -> LetBind li ai x <$> recurse e <*> recurse e'
+      LetPatBind li p e     -> LetPatBind li <$> recurse p <*> recurse e
+      LetApply{}            -> pure e
+      LetOpen{}             -> pure e
+      LetDeclaredVariable _ -> pure e
+
+  foldExpr :: forall m. FoldExprFn m LetBinding
+  foldExpr f e =
+    case e of
+      LetBind _ _ _ e e'    -> fold e `mappend` fold e'
+      LetPatBind _ p e      -> fold p `mappend` fold e
+      LetApply{}            -> mempty
+      LetOpen{}             -> mempty
+      LetDeclaredVariable _ -> mempty
+    where
+      fold :: FoldExprRecFn m
+      fold e = foldExpr f e
+
+  traverseExpr :: forall m. TraverseExprFn m LetBinding
+  traverseExpr f e = do
+    let
+      trav :: TraverseExprRecFn m
+      trav e = traverseExpr f e
+    case e of
+      LetBind li ai x e e'  -> LetBind li ai x <$> trav e <*> trav e'
+      LetPatBind li p e     -> LetPatBind li <$> trav p <*> trav e
+      LetApply{}            -> pure e
+      LetOpen{}             -> pure e
+      LetDeclaredVariable _ -> pure e
+
+instance ExprLike a => ExprLike (Pattern' a) where
+
+instance ExprLike a => ExprLike (Clause' a) where
+  recurseExpr :: forall m. RecurseExprFn m (Clause' a)
+  recurseExpr f (Clause lhs spats rhs ds ca) = Clause <$> rec lhs <*> pure spats <*> rec rhs <*> rec ds <*> pure ca
+    where
+      rec :: RecurseExprRecFn m
+      rec = recurseExpr f
+
+instance ExprLike RHS where
+  recurseExpr :: forall m. RecurseExprFn m RHS
+  recurseExpr f rhs =
+    case rhs of
+      RHS e c                 -> RHS <$> rec e <*> pure c
+      AbsurdRHS{}             -> pure rhs
+      WithRHS x es cs         -> WithRHS x <$> rec es <*> rec cs
+      RewriteRHS xes spats rhs ds -> RewriteRHS <$> rec xes <*> pure spats <*> rec rhs <*> rec ds
+    where
+      rec :: RecurseExprRecFn m
+      rec e = recurseExpr f e
+
+instance (ExprLike qn, ExprLike nm, ExprLike p, ExprLike e) => ExprLike (RewriteEqn' qn nm p e) where
+  recurseExpr f = \case
+    Rewrite es    -> Rewrite <$> recurseExpr f es
+    Invert qn pes -> Invert <$> recurseExpr f qn <*> recurseExpr f pes
+
+instance ExprLike WhereDeclarations where
+  recurseExpr f (WhereDecls a b c) = WhereDecls a b <$> recurseExpr f c
+
+instance ExprLike ModuleApplication where
+  recurseExpr :: forall m. RecurseExprFn m ModuleApplication
+  recurseExpr f a =
+    case a of
+      SectionApp tel m es -> SectionApp <$> rec tel <*> rec m <*> rec es
+      RecordModuleInstance{} -> pure a
+    where
+      rec :: RecurseExprRecFn m
+      rec e = recurseExpr f e
+
+instance ExprLike Pragma where
+  recurseExpr :: forall m. RecurseExprFn m Pragma
+  recurseExpr f p =
+    case p of
+      BuiltinPragma s x           -> pure p
+      OptionsPragma{}             -> pure p
+      BuiltinNoDefPragma{}        -> pure p
+      RewritePragma{}             -> pure p
+      CompilePragma{}             -> pure p
+      StaticPragma{}              -> pure p
+      InjectivePragma{}           -> pure p
+      InlinePragma{}              -> pure p
+      EtaPragma{}                 -> pure p
+      NotProjectionLikePragma{}   -> pure p
+      DisplayPragma f xs e        -> DisplayPragma f <$> rec xs <*> rec e
+    where
+      rec :: RecurseExprRecFn m
+      rec e = recurseExpr f e
+
+instance ExprLike LHS where
+  recurseExpr f (LHS i p) = LHS i <$> recurseExpr f p
+
+instance ExprLike a => ExprLike (LHSCore' a)   where
+instance ExprLike a => ExprLike (WithHiding a) where
+
+instance ExprLike SpineLHS where
+  recurseExpr f (SpineLHS i x ps) = SpineLHS i x <$> recurseExpr f ps
+
+instance ExprLike Declaration where
+  recurseExpr :: forall m. RecurseExprFn m Declaration
+  recurseExpr f d =
+    case d of
+      Axiom a d i mp x e        -> Axiom a d i mp x <$> rec e
+      Generalize s i j x e      -> Generalize s i j x <$> rec e
+      Field i x e               -> Field i x <$> rec e
+      Primitive i x e           -> Primitive i x <$> rec e
+      Mutual i ds               -> Mutual i <$> rec ds
+      Section i e m tel ds      -> Section i e m <$> rec tel <*> rec ds
+      Apply i e m a ci d        -> (\a -> Apply i e m a ci d) <$> rec a
+      Import{}                  -> pure d
+      Pragma i p                -> Pragma i <$> rec p
+      Open{}                    -> pure d
+      FunDef i f cs             -> FunDef i f <$> rec cs
+      DataSig i er d tel e      -> DataSig i er d <$> rec tel <*> rec e
+      DataDef i d uc bs cs      -> DataDef i d uc <$> rec bs <*> rec cs
+      RecSig i er r tel e       -> RecSig i er r <$> rec tel <*> rec e
+      RecDef i r uc dir bs e ds -> RecDef i r uc dir <$> rec bs <*> rec e <*> rec ds
+      PatternSynDef f xs p      -> PatternSynDef f xs <$> rec p
+      UnquoteDecl i is xs e     -> UnquoteDecl i is xs <$> rec e
+      UnquoteDef i xs e         -> UnquoteDef i xs <$> rec e
+      UnquoteData i xs uc j cs e -> UnquoteData i xs uc j cs <$> rec e
+      ScopedDecl s ds           -> ScopedDecl s <$> rec ds
+      UnfoldingDecl r ds        -> UnfoldingDecl r <$> rec ds
+    where
+      rec :: RecurseExprRecFn m
+      rec e = recurseExpr f e
+
+
+-- * Getting all declared names
+---------------------------------------------------------------------------
+
+type KName = WithKind QName
+
+-- | Extracts "all" names which are declared in a 'Declaration'.
+--
+-- Includes: local modules and @where@ clauses.
+-- Excludes: @open public@, @let@, @with@ function names, extended lambdas.
+
+class DeclaredNames a where
+  declaredNames :: Collection KName m => a -> m
+
+  default declaredNames
+     :: (Foldable t, DeclaredNames b, t b ~ a)
+     => Collection KName m => a -> m
+  declaredNames = foldMap declaredNames
+
+instance DeclaredNames a => DeclaredNames [a]
+instance DeclaredNames a => DeclaredNames (List1 a)
+instance DeclaredNames a => DeclaredNames (Maybe a)
+instance DeclaredNames a => DeclaredNames (Arg a)
+instance DeclaredNames a => DeclaredNames (Named name a)
+instance DeclaredNames a => DeclaredNames (FieldAssignment' a)
+
+instance (DeclaredNames a, DeclaredNames b) => DeclaredNames (Either a b) where
+  declaredNames = either declaredNames declaredNames
+
+instance (DeclaredNames a, DeclaredNames b) => DeclaredNames (a,b) where
+  declaredNames (a,b) = declaredNames a <> declaredNames b
+
+instance DeclaredNames KName where
+  declaredNames = singleton
+
+instance DeclaredNames RecordDirectives where
+  declaredNames (RecordDirectives i _ _ c) = kc where
+    kc = maybe mempty (singleton . WithKind k) c
+    k  = maybe ConName (conKindOfName . rangedThing) i
+
+instance DeclaredNames Declaration where
+  declaredNames = \case
+      Axiom _ di _ _ q _           -> singleton . (`WithKind` q) $
+                                      case defMacro di of
+                                        MacroDef    -> MacroName
+                                        NotMacroDef -> AxiomName
+      Generalize _ _ _ q _         -> singleton (WithKind GeneralizeName q)
+      Field _ q _                  -> singleton (WithKind FldName q)
+      Primitive _ q _              -> singleton (WithKind PrimName q)
+      Mutual _ decls               -> declaredNames decls
+      DataSig _ _ q _ _            -> singleton (WithKind DataName q)
+      DataDef _ q _ _ decls        -> singleton (WithKind DataName q) <> foldMap con decls
+      RecSig _ _ q _ _             -> singleton (WithKind RecName q)
+      RecDef _ q _ dir _ _ decls   -> singleton (WithKind RecName q) <> declaredNames dir <> declaredNames decls
+      PatternSynDef q _ _          -> singleton (WithKind PatternSynName q)
+      UnquoteDecl _ _ qs _         -> fromList $ map (WithKind OtherDefName) qs  -- could be Fun or Axiom
+      UnquoteDef _ qs _            -> fromList $ map (WithKind FunName) qs       -- cannot be Axiom
+      UnquoteData _ d _ _ cs _     -> singleton (WithKind DataName d) <> (fromList $ map (WithKind ConName) cs) -- singleton _ <> map (WithKind ConName) cs
+      FunDef _ q cls               -> singleton (WithKind FunName q) <> declaredNames cls
+      ScopedDecl _ decls           -> declaredNames decls
+      Section _ _ _ _ decls        -> declaredNames decls
+      Pragma _ pragma              -> declaredNames pragma
+      Apply{}                      -> mempty
+      Import{}                     -> mempty
+      Open{}                       -> mempty
+      UnfoldingDecl{}              -> mempty
+    where
+    con = \case
+      Axiom _ _ _ _ q _ -> singleton $ WithKind ConName q
+      _ -> __IMPOSSIBLE__
+
+instance DeclaredNames Pragma where
+  declaredNames = \case
+    BuiltinNoDefPragma _b kind x -> singleton $ WithKind kind x
+    BuiltinPragma{}           -> mempty
+    CompilePragma{}           -> mempty
+    RewritePragma{}           -> mempty
+    StaticPragma{}            -> mempty
+    EtaPragma{}               -> mempty
+    InjectivePragma{}         -> mempty
+    InlinePragma{}            -> mempty
+    NotProjectionLikePragma{} -> mempty
+    DisplayPragma{}           -> mempty
+    OptionsPragma{}           -> mempty
+
+instance DeclaredNames Clause where
+  declaredNames (Clause _ _ rhs decls _) = declaredNames rhs <> declaredNames decls
+
+instance DeclaredNames WhereDeclarations where
+  declaredNames (WhereDecls _ _ ds) = declaredNames ds
+
+instance DeclaredNames RHS where
+  declaredNames = \case
+    RHS _ _                   -> mempty
+    AbsurdRHS                 -> mempty
+    WithRHS _q _es cls        -> declaredNames cls
+    RewriteRHS _qes _ rhs cls -> declaredNames rhs <> declaredNames cls
+
+-- Andreas, 2020-04-13: Migration from Agda.Syntax.Abstract.AllNames
+--
+-- Since we are not interested in names of extended lambdas, we do not
+-- traverse into expression.
+--
+-- However, we keep this code (originally Agda.Syntax.Abstract.AllNames) around
+-- should arise a need to collect extended lambda names.
+
+-- instance (DeclaredNames a, DeclaredNames b, DeclaredNames c) => DeclaredNames (a,b,c) where
+--   declaredNames (a,b,c) = declaredNames a <> declaredNames b <> declaredNames c
+
+-- instance DeclaredNames RHS where
+--   declaredNames = \case
+--     RHS e _                  -> declaredNames e
+--     AbsurdRHS{}              -> mempty
+--     WithRHS q _ cls          -> singleton (WithKind FunName q) <> declaredNames cls
+--     RewriteRHS qes _ rhs cls -> declaredNames (qes, rhs, cls)
+
+-- instance DeclaredNames ModuleName where
+--   declaredNames _ = mempty
+
+-- instance (DeclaredNames qn, DeclaredNames e) => DeclaredNames (RewriteEqn' qn p e) where
+--   declaredNames = \case
+--     Rewrite es    -> declaredNames es
+--     Invert qn pes -> declaredNames qn <> declaredNames pes
+
+-- instance DeclaredNames Expr where
+--   declaredNames = \case
+--     Var{}                 -> mempty
+--     Def{}                 -> mempty
+--     Proj{}                -> mempty
+--     Con{}                 -> mempty
+--     Lit{}                 -> mempty
+--     QuestionMark{}        -> mempty
+--     Underscore{}          -> mempty
+--     Dot _ e               -> declaredNames e
+--     App _ e1 e2           -> declaredNames e1 <> declaredNames e2
+--     WithApp _ e es        -> declaredNames e <> declaredNames es
+--     Lam _ b e             -> declaredNames b <> declaredNames e
+--     AbsurdLam{}           -> mempty
+--     ExtendedLam _ _ q cls -> singleton (WithKind FunName q) <> declaredNames cls
+--     Pi _ tel e            -> declaredNames tel <> declaredNames e
+--     Generalized s e       -> declaredNames e  -- NOT: fromList (map (WithKind GeneralizeName) $ Set.toList s) <> declaredNames e
+--     Fun _ e1 e2           -> declaredNames e1 <> declaredNames e2
+--     Set{}                 -> mempty
+--     Prop{}                -> mempty
+--     Let _ lbs e           -> declaredNames lbs <> declaredNames e
+--     Rec _ fields          -> declaredNames fields
+--     RecUpdate _ e fs      -> declaredNames e <> declaredNames fs
+--     ScopedExpr _ e        -> declaredNames e
+--     Quote{}               -> mempty
+--     QuoteTerm{}           -> mempty
+--     Unquote{}             -> mempty
+--     DontCare{}            -> mempty
+--     PatternSyn{}          -> mempty
+--     Macro{}               -> mempty
+
+-- instance DeclaredNames LamBinding where
+--   declaredNames DomainFree{}       = mempty
+--   declaredNames (DomainFull binds) = declaredNames binds
+
+-- instance DeclaredNames TypedBinding where
+--   declaredNames (TBind _ t _ e) = declaredNames (t, e)
+--   declaredNames (TLet _ lbs)    = declaredNames lbs
+
+-- instance DeclaredNames LetBinding where
+--   declaredNames (LetBind _ _ _ e1 e2)   = declaredNames e1 <> declaredNames e2
+--   declaredNames (LetPatBind _ _ e)      = declaredNames e
+--   declaredNames (LetApply _ _ app _ _)  = declaredNames app
+--   declaredNames LetOpen{}               = mempty
+--   declaredNames (LetDeclaredVariable _) = mempty
+
+-- instance DeclaredNames ModuleApplication where
+--   declaredNames (SectionApp bindss _ es) = declaredNames bindss <> declaredNames es
+--   declaredNames RecordModuleInstance{}   = mempty
diff --git a/src/full/Agda/Syntax/Builtin.hs b/src/full/Agda/Syntax/Builtin.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Builtin.hs
@@ -0,0 +1,1100 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | This module defines the names of all builtin and primitives used in Agda.
+--
+-- See "Agda.TypeChecking.Monad.Builtin"
+module Agda.Syntax.Builtin where
+
+import GHC.Generics (Generic)
+
+import Control.DeepSeq (NFData)
+
+import qualified Data.Map as M
+import Data.Hashable
+
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.Position
+
+import Agda.Utils.List
+
+-- | Either a 'BuiltinId' or 'PrimitiveId', used for some lookups.
+data SomeBuiltin
+  = BuiltinName !BuiltinId
+  | PrimitiveName !PrimitiveId
+  deriving (Show, Eq, Ord, Generic)
+
+instance Hashable SomeBuiltin
+instance NFData SomeBuiltin
+
+-- | The class of types which can be converted to 'SomeBuiltin'.
+class IsBuiltin a where
+  -- | Convert this value to a builtin.
+  someBuiltin :: a -> SomeBuiltin
+
+  -- | Get the identifier for this builtin, generally used for error messages.
+  getBuiltinId :: a -> String
+
+instance IsBuiltin SomeBuiltin where
+  someBuiltin = id
+
+  getBuiltinId (BuiltinName x) = getBuiltinId x
+  getBuiltinId (PrimitiveName x) = getBuiltinId x
+
+-- * Builtins
+
+-- | A builtin name, defined by the @BUILTIN@ pragma.
+data BuiltinId
+  = BuiltinNat
+  | BuiltinSuc
+  | BuiltinZero
+  | BuiltinNatPlus
+  | BuiltinNatMinus
+  | BuiltinNatTimes
+  | BuiltinNatDivSucAux
+  | BuiltinNatModSucAux
+  | BuiltinNatEquals
+  | BuiltinNatLess
+  | BuiltinWord64
+  | BuiltinInteger
+  | BuiltinIntegerPos
+  | BuiltinIntegerNegSuc
+  | BuiltinFloat
+  | BuiltinChar
+  | BuiltinString
+  | BuiltinUnit
+  | BuiltinUnitUnit
+  | BuiltinSigma
+  | BuiltinSigmaCon
+  | BuiltinBool
+  | BuiltinTrue
+  | BuiltinFalse
+  | BuiltinList
+  | BuiltinNil
+  | BuiltinCons
+  | BuiltinMaybe
+  | BuiltinNothing
+  | BuiltinJust
+  | BuiltinIO
+  | BuiltinId
+  | BuiltinReflId
+  | BuiltinPath
+  | BuiltinPathP
+  | BuiltinIntervalUniv
+  | BuiltinInterval
+  | BuiltinIZero
+  | BuiltinIOne
+  | BuiltinPartial
+  | BuiltinPartialP
+  | BuiltinIsOne
+  | BuiltinItIsOne
+  | BuiltinEquiv
+  | BuiltinEquivFun
+  | BuiltinEquivProof
+  | BuiltinTranspProof
+  | BuiltinIsOne1
+  | BuiltinIsOne2
+  | BuiltinIsOneEmpty
+  | BuiltinSub
+  | BuiltinSubIn
+  | BuiltinSizeUniv
+  | BuiltinSize
+  | BuiltinSizeLt
+  | BuiltinSizeSuc
+  | BuiltinSizeInf
+  | BuiltinSizeMax
+  | BuiltinInf
+  | BuiltinSharp
+  | BuiltinFlat
+  | BuiltinEquality
+  | BuiltinRefl
+  | BuiltinRewrite
+  | BuiltinLevelMax
+  | BuiltinLevel
+  | BuiltinLevelZero
+  | BuiltinLevelSuc
+  | BuiltinProp
+  | BuiltinSet
+  | BuiltinStrictSet
+  | BuiltinPropOmega
+  | BuiltinSetOmega
+  | BuiltinSSetOmega
+  | BuiltinLevelUniv
+  | BuiltinFromNat
+  | BuiltinFromNeg
+  | BuiltinFromString
+  | BuiltinQName
+  | BuiltinAgdaSort
+  | BuiltinAgdaSortSet
+  | BuiltinAgdaSortLit
+  | BuiltinAgdaSortProp
+  | BuiltinAgdaSortPropLit
+  | BuiltinAgdaSortInf
+  | BuiltinAgdaSortUnsupported
+  | BuiltinHiding
+  | BuiltinHidden
+  | BuiltinInstance
+  | BuiltinVisible
+  | BuiltinRelevance
+  | BuiltinRelevant
+  | BuiltinIrrelevant
+  | BuiltinQuantity
+  | BuiltinQuantity0
+  | BuiltinQuantityω
+  | BuiltinModality
+  | BuiltinModalityConstructor
+  | BuiltinAssoc
+  | BuiltinAssocLeft
+  | BuiltinAssocRight
+  | BuiltinAssocNon
+  | BuiltinPrecedence
+  | BuiltinPrecRelated
+  | BuiltinPrecUnrelated
+  | BuiltinFixity
+  | BuiltinFixityFixity
+  | BuiltinArg
+  | BuiltinArgInfo
+  | BuiltinArgArgInfo
+  | BuiltinArgArg
+  | BuiltinAbs
+  | BuiltinAbsAbs
+  | BuiltinAgdaTerm
+  | BuiltinAgdaTermVar
+  | BuiltinAgdaTermLam
+  | BuiltinAgdaTermExtLam
+  | BuiltinAgdaTermDef
+  | BuiltinAgdaTermCon
+  | BuiltinAgdaTermPi
+  | BuiltinAgdaTermSort
+  | BuiltinAgdaTermLit
+  | BuiltinAgdaTermUnsupported
+  | BuiltinAgdaTermMeta
+  | BuiltinAgdaErrorPart
+  | BuiltinAgdaErrorPartString
+  | BuiltinAgdaErrorPartTerm
+  | BuiltinAgdaErrorPartPatt
+  | BuiltinAgdaErrorPartName
+  | BuiltinAgdaLiteral
+  | BuiltinAgdaLitNat
+  | BuiltinAgdaLitWord64
+  | BuiltinAgdaLitFloat
+  | BuiltinAgdaLitChar
+  | BuiltinAgdaLitString
+  | BuiltinAgdaLitQName
+  | BuiltinAgdaLitMeta
+  | BuiltinAgdaClause
+  | BuiltinAgdaClauseClause
+  | BuiltinAgdaClauseAbsurd
+  | BuiltinAgdaPattern
+  | BuiltinAgdaPatVar
+  | BuiltinAgdaPatCon
+  | BuiltinAgdaPatDot
+  | BuiltinAgdaPatLit
+  | BuiltinAgdaPatProj
+  | BuiltinAgdaPatAbsurd
+  | BuiltinAgdaDefinitionFunDef
+  | BuiltinAgdaDefinitionDataDef
+  | BuiltinAgdaDefinitionRecordDef
+  | BuiltinAgdaDefinitionDataConstructor
+  | BuiltinAgdaDefinitionPostulate
+  | BuiltinAgdaDefinitionPrimitive
+  | BuiltinAgdaDefinition
+  | BuiltinAgdaMeta
+  | BuiltinAgdaTCM
+  | BuiltinAgdaTCMReturn
+  | BuiltinAgdaTCMBind
+  | BuiltinAgdaTCMUnify
+  | BuiltinAgdaTCMTypeError
+  | BuiltinAgdaTCMInferType
+  | BuiltinAgdaTCMCheckType
+  | BuiltinAgdaTCMNormalise
+  | BuiltinAgdaTCMReduce
+  | BuiltinAgdaTCMCatchError
+  | BuiltinAgdaTCMGetContext
+  | BuiltinAgdaTCMExtendContext
+  | BuiltinAgdaTCMInContext
+  | BuiltinAgdaTCMFreshName
+  | BuiltinAgdaTCMDeclareDef
+  | BuiltinAgdaTCMDeclarePostulate
+  | BuiltinAgdaTCMDeclareData
+  | BuiltinAgdaTCMDefineData
+  | BuiltinAgdaTCMDefineFun
+  | BuiltinAgdaTCMGetType
+  | BuiltinAgdaTCMGetDefinition
+  | BuiltinAgdaTCMBlock
+  | BuiltinAgdaTCMCommit
+  | BuiltinAgdaTCMQuoteTerm
+  | BuiltinAgdaTCMUnquoteTerm
+  | BuiltinAgdaTCMQuoteOmegaTerm
+  | BuiltinAgdaTCMIsMacro
+  | BuiltinAgdaTCMWithNormalisation
+  | BuiltinAgdaTCMWithReconstructed
+  | BuiltinAgdaTCMWithExpandLast
+  | BuiltinAgdaTCMWithReduceDefs
+  | BuiltinAgdaTCMAskNormalisation
+  | BuiltinAgdaTCMAskReconstructed
+  | BuiltinAgdaTCMAskExpandLast
+  | BuiltinAgdaTCMAskReduceDefs
+  | BuiltinAgdaTCMFormatErrorParts
+  | BuiltinAgdaTCMDebugPrint
+  | BuiltinAgdaTCMNoConstraints
+  | BuiltinAgdaTCMRunSpeculative
+  | BuiltinAgdaTCMExec
+  | BuiltinAgdaTCMGetInstances
+  | BuiltinAgdaTCMPragmaForeign
+  | BuiltinAgdaTCMPragmaCompile
+  | BuiltinAgdaBlocker
+  | BuiltinAgdaBlockerAny
+  | BuiltinAgdaBlockerAll
+  | BuiltinAgdaBlockerMeta
+  deriving (Show, Eq, Ord, Bounded, Enum, Generic)
+
+instance NFData BuiltinId
+
+instance Hashable BuiltinId where
+  s `hashWithSalt` b = s `hashWithSalt` fromEnum b
+
+instance KillRange BuiltinId where
+  killRange = id
+
+instance Pretty BuiltinId where
+  pretty = text . getBuiltinId
+
+instance IsBuiltin BuiltinId where
+  someBuiltin = BuiltinName
+
+  getBuiltinId = \case
+    BuiltinNat                               -> "NATURAL"
+    BuiltinSuc                               -> "SUC"
+    BuiltinZero                              -> "ZERO"
+    BuiltinNatPlus                           -> "NATPLUS"
+    BuiltinNatMinus                          -> "NATMINUS"
+    BuiltinNatTimes                          -> "NATTIMES"
+    BuiltinNatDivSucAux                      -> "NATDIVSUCAUX"
+    BuiltinNatModSucAux                      -> "NATMODSUCAUX"
+    BuiltinNatEquals                         -> "NATEQUALS"
+    BuiltinNatLess                           -> "NATLESS"
+    BuiltinWord64                            -> "WORD64"
+    BuiltinInteger                           -> "INTEGER"
+    BuiltinIntegerPos                        -> "INTEGERPOS"
+    BuiltinIntegerNegSuc                     -> "INTEGERNEGSUC"
+    BuiltinFloat                             -> "FLOAT"
+    BuiltinChar                              -> "CHAR"
+    BuiltinString                            -> "STRING"
+    BuiltinUnit                              -> "UNIT"
+    BuiltinUnitUnit                          -> "UNITUNIT"
+    BuiltinSigma                             -> "SIGMA"
+    BuiltinSigmaCon                          -> "SIGMACON"
+    BuiltinBool                              -> "BOOL"
+    BuiltinTrue                              -> "TRUE"
+    BuiltinFalse                             -> "FALSE"
+    BuiltinList                              -> "LIST"
+    BuiltinNil                               -> "NIL"
+    BuiltinCons                              -> "CONS"
+    BuiltinMaybe                             -> "MAYBE"
+    BuiltinNothing                           -> "NOTHING"
+    BuiltinJust                              -> "JUST"
+    BuiltinIO                                -> "IO"
+    BuiltinId                                -> "ID"
+    BuiltinReflId                            -> "REFLID"
+    BuiltinPath                              -> "PATH"
+    BuiltinPathP                             -> "PATHP"
+    BuiltinIntervalUniv                      -> "CUBEINTERVALUNIV"
+    BuiltinInterval                          -> "INTERVAL"
+    BuiltinIZero                             -> "IZERO"
+    BuiltinIOne                              -> "IONE"
+    BuiltinPartial                           -> "PARTIAL"
+    BuiltinPartialP                          -> "PARTIALP"
+    BuiltinIsOne                             -> "ISONE"
+    BuiltinItIsOne                           -> "ITISONE"
+    BuiltinEquiv                             -> "EQUIV"
+    BuiltinEquivFun                          -> "EQUIVFUN"
+    BuiltinEquivProof                        -> "EQUIVPROOF"
+    BuiltinTranspProof                       -> "TRANSPPROOF"
+    BuiltinIsOne1                            -> "ISONE1"
+    BuiltinIsOne2                            -> "ISONE2"
+    BuiltinIsOneEmpty                        -> "ISONEEMPTY"
+    BuiltinSub                               -> "SUB"
+    BuiltinSubIn                             -> "SUBIN"
+    BuiltinSizeUniv                          -> "SIZEUNIV"
+    BuiltinSize                              -> "SIZE"
+    BuiltinSizeLt                            -> "SIZELT"
+    BuiltinSizeSuc                           -> "SIZESUC"
+    BuiltinSizeInf                           -> "SIZEINF"
+    BuiltinSizeMax                           -> "SIZEMAX"
+    BuiltinInf                               -> "INFINITY"
+    BuiltinSharp                             -> "SHARP"
+    BuiltinFlat                              -> "FLAT"
+    BuiltinEquality                          -> "EQUALITY"
+    BuiltinRefl                              -> "REFL"
+    BuiltinRewrite                           -> "REWRITE"
+    BuiltinLevelMax                          -> "LEVELMAX"
+    BuiltinLevel                             -> "LEVEL"
+    BuiltinLevelZero                         -> "LEVELZERO"
+    BuiltinLevelSuc                          -> "LEVELSUC"
+    BuiltinProp                              -> "PROP"
+    BuiltinSet                               -> "TYPE"
+    BuiltinStrictSet                         -> "STRICTSET"
+    BuiltinPropOmega                         -> "PROPOMEGA"
+    BuiltinSetOmega                          -> "SETOMEGA"
+    BuiltinSSetOmega                         -> "STRICTSETOMEGA"
+    BuiltinLevelUniv                         -> "LEVELUNIV"
+    BuiltinFromNat                           -> "FROMNAT"
+    BuiltinFromNeg                           -> "FROMNEG"
+    BuiltinFromString                        -> "FROMSTRING"
+    BuiltinQName                             -> "QNAME"
+    BuiltinAgdaSort                          -> "AGDASORT"
+    BuiltinAgdaSortSet                       -> "AGDASORTSET"
+    BuiltinAgdaSortLit                       -> "AGDASORTLIT"
+    BuiltinAgdaSortProp                      -> "AGDASORTPROP"
+    BuiltinAgdaSortPropLit                   -> "AGDASORTPROPLIT"
+    BuiltinAgdaSortInf                       -> "AGDASORTINF"
+    BuiltinAgdaSortUnsupported               -> "AGDASORTUNSUPPORTED"
+    BuiltinHiding                            -> "HIDING"
+    BuiltinHidden                            -> "HIDDEN"
+    BuiltinInstance                          -> "INSTANCE"
+    BuiltinVisible                           -> "VISIBLE"
+    BuiltinRelevance                         -> "RELEVANCE"
+    BuiltinRelevant                          -> "RELEVANT"
+    BuiltinIrrelevant                        -> "IRRELEVANT"
+    BuiltinQuantity                          -> "QUANTITY"
+    BuiltinQuantity0                         -> "QUANTITY-0"
+    BuiltinQuantityω                         -> "QUANTITY-ω"
+    BuiltinModality                          -> "MODALITY"
+    BuiltinModalityConstructor               -> "MODALITY-CONSTRUCTOR"
+    BuiltinAssoc                             -> "ASSOC"
+    BuiltinAssocLeft                         -> "ASSOCLEFT"
+    BuiltinAssocRight                        -> "ASSOCRIGHT"
+    BuiltinAssocNon                          -> "ASSOCNON"
+    BuiltinPrecedence                        -> "PRECEDENCE"
+    BuiltinPrecRelated                       -> "PRECRELATED"
+    BuiltinPrecUnrelated                     -> "PRECUNRELATED"
+    BuiltinFixity                            -> "FIXITY"
+    BuiltinFixityFixity                      -> "FIXITYFIXITY"
+    BuiltinArg                               -> "ARG"
+    BuiltinArgInfo                           -> "ARGINFO"
+    BuiltinArgArgInfo                        -> "ARGARGINFO"
+    BuiltinArgArg                            -> "ARGARG"
+    BuiltinAbs                               -> "ABS"
+    BuiltinAbsAbs                            -> "ABSABS"
+    BuiltinAgdaTerm                          -> "AGDATERM"
+    BuiltinAgdaTermVar                       -> "AGDATERMVAR"
+    BuiltinAgdaTermLam                       -> "AGDATERMLAM"
+    BuiltinAgdaTermExtLam                    -> "AGDATERMEXTLAM"
+    BuiltinAgdaTermDef                       -> "AGDATERMDEF"
+    BuiltinAgdaTermCon                       -> "AGDATERMCON"
+    BuiltinAgdaTermPi                        -> "AGDATERMPI"
+    BuiltinAgdaTermSort                      -> "AGDATERMSORT"
+    BuiltinAgdaTermLit                       -> "AGDATERMLIT"
+    BuiltinAgdaTermUnsupported               -> "AGDATERMUNSUPPORTED"
+    BuiltinAgdaTermMeta                      -> "AGDATERMMETA"
+    BuiltinAgdaErrorPart                     -> "AGDAERRORPART"
+    BuiltinAgdaErrorPartString               -> "AGDAERRORPARTSTRING"
+    BuiltinAgdaErrorPartTerm                 -> "AGDAERRORPARTTERM"
+    BuiltinAgdaErrorPartPatt                 -> "AGDAERRORPARTPATT"
+    BuiltinAgdaErrorPartName                 -> "AGDAERRORPARTNAME"
+    BuiltinAgdaLiteral                       -> "AGDALITERAL"
+    BuiltinAgdaLitNat                        -> "AGDALITNAT"
+    BuiltinAgdaLitWord64                     -> "AGDALITWORD64"
+    BuiltinAgdaLitFloat                      -> "AGDALITFLOAT"
+    BuiltinAgdaLitChar                       -> "AGDALITCHAR"
+    BuiltinAgdaLitString                     -> "AGDALITSTRING"
+    BuiltinAgdaLitQName                      -> "AGDALITQNAME"
+    BuiltinAgdaLitMeta                       -> "AGDALITMETA"
+    BuiltinAgdaClause                        -> "AGDACLAUSE"
+    BuiltinAgdaClauseClause                  -> "AGDACLAUSECLAUSE"
+    BuiltinAgdaClauseAbsurd                  -> "AGDACLAUSEABSURD"
+    BuiltinAgdaPattern                       -> "AGDAPATTERN"
+    BuiltinAgdaPatVar                        -> "AGDAPATVAR"
+    BuiltinAgdaPatCon                        -> "AGDAPATCON"
+    BuiltinAgdaPatDot                        -> "AGDAPATDOT"
+    BuiltinAgdaPatLit                        -> "AGDAPATLIT"
+    BuiltinAgdaPatProj                       -> "AGDAPATPROJ"
+    BuiltinAgdaPatAbsurd                     -> "AGDAPATABSURD"
+    BuiltinAgdaDefinitionFunDef              -> "AGDADEFINITIONFUNDEF"
+    BuiltinAgdaDefinitionDataDef             -> "AGDADEFINITIONDATADEF"
+    BuiltinAgdaDefinitionRecordDef           -> "AGDADEFINITIONRECORDDEF"
+    BuiltinAgdaDefinitionDataConstructor     -> "AGDADEFINITIONDATACONSTRUCTOR"
+    BuiltinAgdaDefinitionPostulate           -> "AGDADEFINITIONPOSTULATE"
+    BuiltinAgdaDefinitionPrimitive           -> "AGDADEFINITIONPRIMITIVE"
+    BuiltinAgdaDefinition                    -> "AGDADEFINITION"
+    BuiltinAgdaMeta                          -> "AGDAMETA"
+    BuiltinAgdaTCM                           -> "AGDATCM"
+    BuiltinAgdaTCMReturn                     -> "AGDATCMRETURN"
+    BuiltinAgdaTCMBind                       -> "AGDATCMBIND"
+    BuiltinAgdaTCMUnify                      -> "AGDATCMUNIFY"
+    BuiltinAgdaTCMTypeError                  -> "AGDATCMTYPEERROR"
+    BuiltinAgdaTCMInferType                  -> "AGDATCMINFERTYPE"
+    BuiltinAgdaTCMCheckType                  -> "AGDATCMCHECKTYPE"
+    BuiltinAgdaTCMNormalise                  -> "AGDATCMNORMALISE"
+    BuiltinAgdaTCMReduce                     -> "AGDATCMREDUCE"
+    BuiltinAgdaTCMCatchError                 -> "AGDATCMCATCHERROR"
+    BuiltinAgdaTCMGetContext                 -> "AGDATCMGETCONTEXT"
+    BuiltinAgdaTCMExtendContext              -> "AGDATCMEXTENDCONTEXT"
+    BuiltinAgdaTCMInContext                  -> "AGDATCMINCONTEXT"
+    BuiltinAgdaTCMFreshName                  -> "AGDATCMFRESHNAME"
+    BuiltinAgdaTCMDeclareDef                 -> "AGDATCMDECLAREDEF"
+    BuiltinAgdaTCMDeclarePostulate           -> "AGDATCMDECLAREPOSTULATE"
+    BuiltinAgdaTCMDeclareData                -> "AGDATCMDECLAREDATA"
+    BuiltinAgdaTCMDefineData                 -> "AGDATCMDEFINEDATA"
+    BuiltinAgdaTCMDefineFun                  -> "AGDATCMDEFINEFUN"
+    BuiltinAgdaTCMGetType                    -> "AGDATCMGETTYPE"
+    BuiltinAgdaTCMGetDefinition              -> "AGDATCMGETDEFINITION"
+    BuiltinAgdaTCMBlock                      -> "AGDATCMBLOCK"
+    BuiltinAgdaTCMCommit                     -> "AGDATCMCOMMIT"
+    BuiltinAgdaTCMQuoteTerm                  -> "AGDATCMQUOTETERM"
+    BuiltinAgdaTCMUnquoteTerm                -> "AGDATCMUNQUOTETERM"
+    BuiltinAgdaTCMQuoteOmegaTerm             -> "AGDATCMQUOTEOMEGATERM"
+    BuiltinAgdaTCMIsMacro                    -> "AGDATCMISMACRO"
+    BuiltinAgdaTCMWithNormalisation          -> "AGDATCMWITHNORMALISATION"
+    BuiltinAgdaTCMWithReconstructed          -> "AGDATCMWITHRECONSTRUCTED"
+    BuiltinAgdaTCMWithExpandLast             -> "AGDATCMWITHEXPANDLAST"
+    BuiltinAgdaTCMWithReduceDefs             -> "AGDATCMWITHREDUCEDEFS"
+    BuiltinAgdaTCMAskNormalisation           -> "AGDATCMASKNORMALISATION"
+    BuiltinAgdaTCMAskReconstructed           -> "AGDATCMASKRECONSTRUCTED"
+    BuiltinAgdaTCMAskExpandLast              -> "AGDATCMASKEXPANDLAST"
+    BuiltinAgdaTCMAskReduceDefs              -> "AGDATCMASKREDUCEDEFS"
+    BuiltinAgdaTCMFormatErrorParts           -> "AGDATCMFORMATERRORPARTS"
+    BuiltinAgdaTCMDebugPrint                 -> "AGDATCMDEBUGPRINT"
+    BuiltinAgdaTCMNoConstraints              -> "AGDATCMNOCONSTRAINTS"
+    BuiltinAgdaTCMRunSpeculative             -> "AGDATCMRUNSPECULATIVE"
+    BuiltinAgdaTCMExec                       -> "AGDATCMEXEC"
+    BuiltinAgdaTCMGetInstances               -> "AGDATCMGETINSTANCES"
+    BuiltinAgdaTCMPragmaForeign              -> "AGDATCMPRAGMAFOREIGN"
+    BuiltinAgdaTCMPragmaCompile              -> "AGDATCMPRAGMACOMPILE"
+    BuiltinAgdaBlocker                       -> "AGDABLOCKER"
+    BuiltinAgdaBlockerAny                    -> "AGDABLOCKERANY"
+    BuiltinAgdaBlockerAll                    -> "AGDABLOCKERALL"
+    BuiltinAgdaBlockerMeta                   -> "AGDABLOCKERMETA"
+
+-- | Builtins that come without a definition in Agda syntax.
+--   These are giving names to Agda internal concepts which
+--   cannot be assigned an Agda type.
+--
+--   An example would be a user-defined name for @Set@.
+--
+--     {-# BUILTIN TYPE Type #-}
+--
+--   The type of @Type@ would be @Type : Level → Setω@
+--   which is not valid Agda.
+isBuiltinNoDef :: BuiltinId -> Bool
+isBuiltinNoDef = hasElem builtinsNoDef
+
+builtinsNoDef :: [BuiltinId]
+builtinsNoDef =
+  sizeBuiltins ++
+   -- builtinConId,
+  [ builtinIntervalUniv
+  , builtinId
+  , builtinReflId
+  , builtinInterval
+  , builtinPartial
+  , builtinPartialP
+  , builtinIsOne
+  , builtinSub
+  , builtinIZero
+  , builtinIOne
+  , builtinProp
+  , builtinSet
+  , builtinStrictSet
+  , builtinPropOmega
+  , builtinSetOmega
+  , builtinSSetOmega
+  , builtinLevelUniv
+  ]
+
+sizeBuiltins :: [BuiltinId]
+sizeBuiltins =
+  [ builtinSizeUniv
+  , builtinSize
+  , builtinSizeLt
+  , builtinSizeSuc
+  , builtinSizeInf
+  , builtinSizeMax
+  ]
+
+builtinNat, builtinSuc, builtinZero, builtinNatPlus, builtinNatMinus,
+  builtinNatTimes, builtinNatDivSucAux, builtinNatModSucAux, builtinNatEquals,
+  builtinNatLess, builtinInteger, builtinIntegerPos, builtinIntegerNegSuc,
+  builtinWord64,
+  builtinFloat, builtinChar, builtinString, builtinUnit, builtinUnitUnit,
+  builtinSigma,
+  builtinBool, builtinTrue, builtinFalse,
+  builtinList, builtinNil, builtinCons, builtinIO,
+  builtinMaybe, builtinNothing, builtinJust,
+  builtinPath, builtinPathP, builtinInterval, builtinIZero, builtinIOne, builtinPartial, builtinPartialP,
+  builtinIsOne,  builtinItIsOne, builtinIsOne1, builtinIsOne2, builtinIsOneEmpty,
+  builtinSub, builtinSubIn,
+  builtinEquiv, builtinEquivFun, builtinEquivProof,
+  builtinTranspProof,
+  builtinId, builtinReflId,
+  builtinSizeUniv, builtinSize, builtinSizeLt,
+  builtinSizeSuc, builtinSizeInf, builtinSizeMax,
+  builtinInf, builtinSharp, builtinFlat,
+  builtinEquality, builtinRefl, builtinRewrite, builtinLevelMax,
+  builtinLevel, builtinLevelZero, builtinLevelSuc,
+  builtinProp, builtinSet, builtinStrictSet,
+  builtinPropOmega, builtinSetOmega, builtinSSetOmega,
+  builtinLevelUniv,
+  builtinIntervalUniv,
+  builtinFromNat, builtinFromNeg, builtinFromString,
+  builtinQName, builtinAgdaSort, builtinAgdaSortSet, builtinAgdaSortLit,
+  builtinAgdaSortProp, builtinAgdaSortPropLit, builtinAgdaSortInf,
+  builtinAgdaSortUnsupported,
+  builtinHiding, builtinHidden, builtinInstance, builtinVisible,
+  builtinRelevance, builtinRelevant, builtinIrrelevant,
+  builtinQuantity, builtinQuantity0, builtinQuantityω,
+  builtinModality, builtinModalityConstructor,
+  builtinAssoc, builtinAssocLeft, builtinAssocRight, builtinAssocNon,
+  builtinPrecedence, builtinPrecRelated, builtinPrecUnrelated,
+  builtinFixity, builtinFixityFixity,
+  builtinArgInfo, builtinArgArgInfo,
+  builtinArg, builtinArgArg,
+  builtinAbs, builtinAbsAbs, builtinAgdaTerm,
+  builtinAgdaTermVar, builtinAgdaTermLam, builtinAgdaTermExtLam,
+  builtinAgdaTermDef, builtinAgdaTermCon, builtinAgdaTermPi,
+  builtinAgdaTermSort, builtinAgdaTermLit, builtinAgdaTermUnsupported, builtinAgdaTermMeta,
+  builtinAgdaErrorPart, builtinAgdaErrorPartString, builtinAgdaErrorPartTerm, builtinAgdaErrorPartPatt, builtinAgdaErrorPartName,
+  builtinAgdaLiteral, builtinAgdaLitNat, builtinAgdaLitWord64, builtinAgdaLitFloat,
+  builtinAgdaLitChar, builtinAgdaLitString, builtinAgdaLitQName, builtinAgdaLitMeta,
+  builtinAgdaClause, builtinAgdaClauseClause, builtinAgdaClauseAbsurd, builtinAgdaPattern,
+  builtinAgdaPatVar, builtinAgdaPatCon, builtinAgdaPatDot, builtinAgdaPatLit,
+  builtinAgdaPatProj, builtinAgdaPatAbsurd,
+  builtinAgdaDefinitionFunDef,
+  builtinAgdaDefinitionDataDef, builtinAgdaDefinitionRecordDef,
+  builtinAgdaDefinitionDataConstructor, builtinAgdaDefinitionPostulate,
+  builtinAgdaDefinitionPrimitive, builtinAgdaDefinition,
+  builtinAgdaMeta,
+  builtinAgdaTCM, builtinAgdaTCMReturn, builtinAgdaTCMBind, builtinAgdaTCMUnify,
+  builtinAgdaTCMTypeError, builtinAgdaTCMInferType,
+  builtinAgdaTCMCheckType, builtinAgdaTCMNormalise, builtinAgdaTCMReduce,
+  builtinAgdaTCMCatchError,
+  builtinAgdaTCMGetContext, builtinAgdaTCMExtendContext, builtinAgdaTCMInContext,
+  builtinAgdaTCMFreshName, builtinAgdaTCMDeclareDef, builtinAgdaTCMDeclarePostulate, builtinAgdaTCMDeclareData, builtinAgdaTCMDefineData, builtinAgdaTCMDefineFun,
+  builtinAgdaTCMGetType, builtinAgdaTCMGetDefinition,
+  builtinAgdaTCMQuoteTerm, builtinAgdaTCMUnquoteTerm, builtinAgdaTCMQuoteOmegaTerm,
+  builtinAgdaTCMCommit, builtinAgdaTCMIsMacro, builtinAgdaTCMBlock,
+  builtinAgdaBlocker, builtinAgdaBlockerAll, builtinAgdaBlockerAny, builtinAgdaBlockerMeta,
+  builtinAgdaTCMFormatErrorParts, builtinAgdaTCMDebugPrint,
+  builtinAgdaTCMWithNormalisation, builtinAgdaTCMWithReconstructed,
+  builtinAgdaTCMWithExpandLast, builtinAgdaTCMWithReduceDefs,
+  builtinAgdaTCMAskNormalisation, builtinAgdaTCMAskReconstructed,
+  builtinAgdaTCMAskExpandLast, builtinAgdaTCMAskReduceDefs,
+  builtinAgdaTCMNoConstraints,
+  builtinAgdaTCMRunSpeculative,
+  builtinAgdaTCMExec,
+  builtinAgdaTCMGetInstances,
+  builtinAgdaTCMPragmaForeign,
+  builtinAgdaTCMPragmaCompile
+  :: BuiltinId
+
+builtinNat                               = BuiltinNat
+builtinSuc                               = BuiltinSuc
+builtinZero                              = BuiltinZero
+builtinNatPlus                           = BuiltinNatPlus
+builtinNatMinus                          = BuiltinNatMinus
+builtinNatTimes                          = BuiltinNatTimes
+builtinNatDivSucAux                      = BuiltinNatDivSucAux
+builtinNatModSucAux                      = BuiltinNatModSucAux
+builtinNatEquals                         = BuiltinNatEquals
+builtinNatLess                           = BuiltinNatLess
+builtinWord64                            = BuiltinWord64
+builtinInteger                           = BuiltinInteger
+builtinIntegerPos                        = BuiltinIntegerPos
+builtinIntegerNegSuc                     = BuiltinIntegerNegSuc
+builtinFloat                             = BuiltinFloat
+builtinChar                              = BuiltinChar
+builtinString                            = BuiltinString
+builtinUnit                              = BuiltinUnit
+builtinUnitUnit                          = BuiltinUnitUnit
+builtinSigma                             = BuiltinSigma
+builtinBool                              = BuiltinBool
+builtinTrue                              = BuiltinTrue
+builtinFalse                             = BuiltinFalse
+builtinList                              = BuiltinList
+builtinNil                               = BuiltinNil
+builtinCons                              = BuiltinCons
+builtinMaybe                             = BuiltinMaybe
+builtinNothing                           = BuiltinNothing
+builtinJust                              = BuiltinJust
+builtinIO                                = BuiltinIO
+builtinId                                = BuiltinId
+builtinReflId                            = BuiltinReflId
+builtinPath                              = BuiltinPath
+builtinPathP                             = BuiltinPathP
+builtinIntervalUniv                      = BuiltinIntervalUniv
+builtinInterval                          = BuiltinInterval
+builtinIZero                             = BuiltinIZero
+builtinIOne                              = BuiltinIOne
+builtinPartial                           = BuiltinPartial
+builtinPartialP                          = BuiltinPartialP
+builtinIsOne                             = BuiltinIsOne
+builtinItIsOne                           = BuiltinItIsOne
+builtinEquiv                             = BuiltinEquiv
+builtinEquivFun                          = BuiltinEquivFun
+builtinEquivProof                        = BuiltinEquivProof
+builtinTranspProof                       = BuiltinTranspProof
+builtinIsOne1                            = BuiltinIsOne1
+builtinIsOne2                            = BuiltinIsOne2
+builtinIsOneEmpty                        = BuiltinIsOneEmpty
+builtinSub                               = BuiltinSub
+builtinSubIn                             = BuiltinSubIn
+builtinSizeUniv                          = BuiltinSizeUniv
+builtinSize                              = BuiltinSize
+builtinSizeLt                            = BuiltinSizeLt
+builtinSizeSuc                           = BuiltinSizeSuc
+builtinSizeInf                           = BuiltinSizeInf
+builtinSizeMax                           = BuiltinSizeMax
+builtinInf                               = BuiltinInf
+builtinSharp                             = BuiltinSharp
+builtinFlat                              = BuiltinFlat
+builtinEquality                          = BuiltinEquality
+builtinRefl                              = BuiltinRefl
+builtinRewrite                           = BuiltinRewrite
+builtinLevelMax                          = BuiltinLevelMax
+builtinLevel                             = BuiltinLevel
+builtinLevelZero                         = BuiltinLevelZero
+builtinLevelSuc                          = BuiltinLevelSuc
+builtinProp                              = BuiltinProp
+builtinSet                               = BuiltinSet
+builtinStrictSet                         = BuiltinStrictSet
+builtinPropOmega                         = BuiltinPropOmega
+builtinSetOmega                          = BuiltinSetOmega
+builtinSSetOmega                         = BuiltinSSetOmega
+builtinLevelUniv                         = BuiltinLevelUniv
+builtinFromNat                           = BuiltinFromNat
+builtinFromNeg                           = BuiltinFromNeg
+builtinFromString                        = BuiltinFromString
+builtinQName                             = BuiltinQName
+builtinAgdaSort                          = BuiltinAgdaSort
+builtinAgdaSortSet                       = BuiltinAgdaSortSet
+builtinAgdaSortLit                       = BuiltinAgdaSortLit
+builtinAgdaSortProp                      = BuiltinAgdaSortProp
+builtinAgdaSortPropLit                   = BuiltinAgdaSortPropLit
+builtinAgdaSortInf                       = BuiltinAgdaSortInf
+builtinAgdaSortUnsupported               = BuiltinAgdaSortUnsupported
+builtinHiding                            = BuiltinHiding
+builtinHidden                            = BuiltinHidden
+builtinInstance                          = BuiltinInstance
+builtinVisible                           = BuiltinVisible
+builtinRelevance                         = BuiltinRelevance
+builtinRelevant                          = BuiltinRelevant
+builtinIrrelevant                        = BuiltinIrrelevant
+builtinQuantity                          = BuiltinQuantity
+builtinQuantity0                         = BuiltinQuantity0
+builtinQuantityω                         = BuiltinQuantityω
+builtinModality                          = BuiltinModality
+builtinModalityConstructor               = BuiltinModalityConstructor
+builtinAssoc                             = BuiltinAssoc
+builtinAssocLeft                         = BuiltinAssocLeft
+builtinAssocRight                        = BuiltinAssocRight
+builtinAssocNon                          = BuiltinAssocNon
+builtinPrecedence                        = BuiltinPrecedence
+builtinPrecRelated                       = BuiltinPrecRelated
+builtinPrecUnrelated                     = BuiltinPrecUnrelated
+builtinFixity                            = BuiltinFixity
+builtinFixityFixity                      = BuiltinFixityFixity
+builtinArg                               = BuiltinArg
+builtinArgInfo                           = BuiltinArgInfo
+builtinArgArgInfo                        = BuiltinArgArgInfo
+builtinArgArg                            = BuiltinArgArg
+builtinAbs                               = BuiltinAbs
+builtinAbsAbs                            = BuiltinAbsAbs
+builtinAgdaTerm                          = BuiltinAgdaTerm
+builtinAgdaTermVar                       = BuiltinAgdaTermVar
+builtinAgdaTermLam                       = BuiltinAgdaTermLam
+builtinAgdaTermExtLam                    = BuiltinAgdaTermExtLam
+builtinAgdaTermDef                       = BuiltinAgdaTermDef
+builtinAgdaTermCon                       = BuiltinAgdaTermCon
+builtinAgdaTermPi                        = BuiltinAgdaTermPi
+builtinAgdaTermSort                      = BuiltinAgdaTermSort
+builtinAgdaTermLit                       = BuiltinAgdaTermLit
+builtinAgdaTermUnsupported               = BuiltinAgdaTermUnsupported
+builtinAgdaTermMeta                      = BuiltinAgdaTermMeta
+builtinAgdaErrorPart                     = BuiltinAgdaErrorPart
+builtinAgdaErrorPartString               = BuiltinAgdaErrorPartString
+builtinAgdaErrorPartTerm                 = BuiltinAgdaErrorPartTerm
+builtinAgdaErrorPartPatt                 = BuiltinAgdaErrorPartPatt
+builtinAgdaErrorPartName                 = BuiltinAgdaErrorPartName
+builtinAgdaLiteral                       = BuiltinAgdaLiteral
+builtinAgdaLitNat                        = BuiltinAgdaLitNat
+builtinAgdaLitWord64                     = BuiltinAgdaLitWord64
+builtinAgdaLitFloat                      = BuiltinAgdaLitFloat
+builtinAgdaLitChar                       = BuiltinAgdaLitChar
+builtinAgdaLitString                     = BuiltinAgdaLitString
+builtinAgdaLitQName                      = BuiltinAgdaLitQName
+builtinAgdaLitMeta                       = BuiltinAgdaLitMeta
+builtinAgdaClause                        = BuiltinAgdaClause
+builtinAgdaClauseClause                  = BuiltinAgdaClauseClause
+builtinAgdaClauseAbsurd                  = BuiltinAgdaClauseAbsurd
+builtinAgdaPattern                       = BuiltinAgdaPattern
+builtinAgdaPatVar                        = BuiltinAgdaPatVar
+builtinAgdaPatCon                        = BuiltinAgdaPatCon
+builtinAgdaPatDot                        = BuiltinAgdaPatDot
+builtinAgdaPatLit                        = BuiltinAgdaPatLit
+builtinAgdaPatProj                       = BuiltinAgdaPatProj
+builtinAgdaPatAbsurd                     = BuiltinAgdaPatAbsurd
+builtinAgdaDefinitionFunDef              = BuiltinAgdaDefinitionFunDef
+builtinAgdaDefinitionDataDef             = BuiltinAgdaDefinitionDataDef
+builtinAgdaDefinitionRecordDef           = BuiltinAgdaDefinitionRecordDef
+builtinAgdaDefinitionDataConstructor     = BuiltinAgdaDefinitionDataConstructor
+builtinAgdaDefinitionPostulate           = BuiltinAgdaDefinitionPostulate
+builtinAgdaDefinitionPrimitive           = BuiltinAgdaDefinitionPrimitive
+builtinAgdaDefinition                    = BuiltinAgdaDefinition
+builtinAgdaMeta                          = BuiltinAgdaMeta
+builtinAgdaTCM                           = BuiltinAgdaTCM
+builtinAgdaTCMReturn                     = BuiltinAgdaTCMReturn
+builtinAgdaTCMBind                       = BuiltinAgdaTCMBind
+builtinAgdaTCMUnify                      = BuiltinAgdaTCMUnify
+builtinAgdaTCMTypeError                  = BuiltinAgdaTCMTypeError
+builtinAgdaTCMInferType                  = BuiltinAgdaTCMInferType
+builtinAgdaTCMCheckType                  = BuiltinAgdaTCMCheckType
+builtinAgdaTCMNormalise                  = BuiltinAgdaTCMNormalise
+builtinAgdaTCMReduce                     = BuiltinAgdaTCMReduce
+builtinAgdaTCMCatchError                 = BuiltinAgdaTCMCatchError
+builtinAgdaTCMGetContext                 = BuiltinAgdaTCMGetContext
+builtinAgdaTCMExtendContext              = BuiltinAgdaTCMExtendContext
+builtinAgdaTCMInContext                  = BuiltinAgdaTCMInContext
+builtinAgdaTCMFreshName                  = BuiltinAgdaTCMFreshName
+builtinAgdaTCMDeclareDef                 = BuiltinAgdaTCMDeclareDef
+builtinAgdaTCMDeclarePostulate           = BuiltinAgdaTCMDeclarePostulate
+builtinAgdaTCMDeclareData                = BuiltinAgdaTCMDeclareData
+builtinAgdaTCMDefineData                 = BuiltinAgdaTCMDefineData
+builtinAgdaTCMDefineFun                  = BuiltinAgdaTCMDefineFun
+builtinAgdaTCMGetType                    = BuiltinAgdaTCMGetType
+builtinAgdaTCMGetDefinition              = BuiltinAgdaTCMGetDefinition
+builtinAgdaTCMBlock                      = BuiltinAgdaTCMBlock
+builtinAgdaTCMCommit                     = BuiltinAgdaTCMCommit
+builtinAgdaTCMQuoteTerm                  = BuiltinAgdaTCMQuoteTerm
+builtinAgdaTCMUnquoteTerm                = BuiltinAgdaTCMUnquoteTerm
+builtinAgdaTCMQuoteOmegaTerm             = BuiltinAgdaTCMQuoteOmegaTerm
+builtinAgdaTCMIsMacro                    = BuiltinAgdaTCMIsMacro
+builtinAgdaTCMWithNormalisation          = BuiltinAgdaTCMWithNormalisation
+builtinAgdaTCMWithReconstructed          = BuiltinAgdaTCMWithReconstructed
+builtinAgdaTCMWithExpandLast             = BuiltinAgdaTCMWithExpandLast
+builtinAgdaTCMWithReduceDefs             = BuiltinAgdaTCMWithReduceDefs
+builtinAgdaTCMAskNormalisation           = BuiltinAgdaTCMAskNormalisation
+builtinAgdaTCMAskReconstructed           = BuiltinAgdaTCMAskReconstructed
+builtinAgdaTCMAskExpandLast              = BuiltinAgdaTCMAskExpandLast
+builtinAgdaTCMAskReduceDefs              = BuiltinAgdaTCMAskReduceDefs
+builtinAgdaTCMFormatErrorParts           = BuiltinAgdaTCMFormatErrorParts
+builtinAgdaTCMDebugPrint                 = BuiltinAgdaTCMDebugPrint
+builtinAgdaTCMNoConstraints              = BuiltinAgdaTCMNoConstraints
+builtinAgdaTCMRunSpeculative             = BuiltinAgdaTCMRunSpeculative
+builtinAgdaTCMExec                       = BuiltinAgdaTCMExec
+builtinAgdaTCMGetInstances               = BuiltinAgdaTCMGetInstances
+builtinAgdaTCMPragmaForeign              = BuiltinAgdaTCMPragmaForeign
+builtinAgdaTCMPragmaCompile              = BuiltinAgdaTCMPragmaCompile
+builtinAgdaBlocker                       = BuiltinAgdaBlocker
+builtinAgdaBlockerAny                    = BuiltinAgdaBlockerAny
+builtinAgdaBlockerAll                    = BuiltinAgdaBlockerAll
+builtinAgdaBlockerMeta                   = BuiltinAgdaBlockerMeta
+
+-- | Lookup a builtin by the string used in the @BUILTIN@ pragma.
+builtinById :: String -> Maybe BuiltinId
+builtinById = flip M.lookup m where
+  m = M.fromList [(getBuiltinId x, x) | x <- [(minBound :: BuiltinId)..]]
+
+-- * Primitives
+
+-- | A primitive name, defined by the @primitive@ block.
+data PrimitiveId
+  -- Cubical
+  = PrimConId
+  | PrimIdElim
+  | PrimIMin
+  | PrimIMax
+  | PrimINeg
+  | PrimPartial
+  | PrimPartialP
+  | PrimSubOut
+  | PrimGlue
+  | Prim_glue
+  | Prim_unglue
+  | Prim_glueU
+  | Prim_unglueU
+  | PrimFaceForall
+  | PrimComp
+  | PrimPOr
+  | PrimTrans
+  | PrimDepIMin
+  | PrimIdFace
+  | PrimIdPath
+  | PrimHComp
+  --  Integer
+  | PrimShowInteger
+  -- Natural
+  | PrimNatPlus
+  | PrimNatMinus
+  | PrimNatTimes
+  | PrimNatDivSucAux
+  | PrimNatModSucAux
+  | PrimNatEquality
+  | PrimNatLess
+  | PrimShowNat
+  -- Word64
+  | PrimWord64FromNat
+  | PrimWord64ToNat
+  | PrimWord64ToNatInjective
+  -- Level
+  | PrimLevelZero
+  | PrimLevelSuc
+  | PrimLevelMax
+  -- Float
+  | PrimFloatEquality
+  | PrimFloatInequality
+  | PrimFloatLess
+  | PrimFloatIsInfinite
+  | PrimFloatIsNaN
+  | PrimFloatIsNegativeZero
+  | PrimFloatIsSafeInteger
+  | PrimFloatToWord64
+  | PrimFloatToWord64Injective
+  | PrimNatToFloat
+  | PrimIntToFloat
+  | PrimFloatRound
+  | PrimFloatFloor
+  | PrimFloatCeiling
+  | PrimFloatToRatio
+  | PrimRatioToFloat
+  | PrimFloatDecode
+  | PrimFloatEncode
+  | PrimShowFloat
+  | PrimFloatPlus
+  | PrimFloatMinus
+  | PrimFloatTimes
+  | PrimFloatNegate
+  | PrimFloatDiv
+  | PrimFloatPow
+  | PrimFloatSqrt
+  | PrimFloatExp
+  | PrimFloatLog
+  | PrimFloatSin
+  | PrimFloatCos
+  | PrimFloatTan
+  | PrimFloatASin
+  | PrimFloatACos
+  | PrimFloatATan
+  | PrimFloatATan2
+  | PrimFloatSinh
+  | PrimFloatCosh
+  | PrimFloatTanh
+  | PrimFloatASinh
+  | PrimFloatACosh
+  | PrimFloatATanh
+  -- Character
+  | PrimCharEquality
+  | PrimIsLower
+  | PrimIsDigit
+  | PrimIsAlpha
+  | PrimIsSpace
+  | PrimIsAscii
+  | PrimIsLatin1
+  | PrimIsPrint
+  | PrimIsHexDigit
+  | PrimToUpper
+  | PrimToLower
+  | PrimCharToNat
+  | PrimCharToNatInjective
+  | PrimNatToChar
+  | PrimShowChar
+  -- String
+  | PrimStringToList
+  | PrimStringToListInjective
+  | PrimStringFromList
+  | PrimStringFromListInjective
+  | PrimStringAppend
+  | PrimStringEquality
+  | PrimShowString
+  | PrimStringUncons
+  -- "Other stuff"
+  | PrimErase
+  | PrimEraseEquality
+  | PrimForce
+  | PrimForceLemma
+  | PrimQNameEquality
+  | PrimQNameLess
+  | PrimShowQName
+  | PrimQNameFixity
+  | PrimQNameToWord64s
+  | PrimQNameToWord64sInjective
+  | PrimMetaEquality
+  | PrimMetaLess
+  | PrimShowMeta
+  | PrimMetaToNat
+  | PrimMetaToNatInjective
+  | PrimLockUniv
+  deriving (Show, Eq, Ord, Bounded, Enum, Generic)
+
+instance NFData PrimitiveId
+
+instance Hashable PrimitiveId where
+  s `hashWithSalt` b = s `hashWithSalt` fromEnum b
+
+instance KillRange PrimitiveId where
+  killRange = id
+
+instance Pretty PrimitiveId where
+  pretty = text . getBuiltinId
+
+instance IsBuiltin PrimitiveId where
+  someBuiltin = PrimitiveName
+
+  getBuiltinId = \case
+    -- Cubical
+    PrimConId                             -> "primConId"
+    PrimIdElim                            -> "primIdElim"
+    PrimIMin                              -> "primIMin"
+    PrimIMax                              -> "primIMax"
+    PrimINeg                              -> "primINeg"
+    PrimPartial                           -> "primPartial"
+    PrimPartialP                          -> "primPartialP"
+    PrimSubOut                            -> "primSubOut"
+    PrimGlue                              -> "primGlue"
+    Prim_glue                             -> "prim^glue"
+    Prim_unglue                           -> "prim^unglue"
+    Prim_glueU                            -> "prim^glueU"
+    Prim_unglueU                          -> "prim^unglueU"
+    PrimFaceForall                        -> "primFaceForall"
+    PrimComp                              -> "primComp"
+    PrimPOr                               -> "primPOr"
+    PrimTrans                             -> "primTransp"
+    PrimDepIMin                           -> "primDepIMin"
+    PrimIdFace                            -> "primIdFace"
+    PrimIdPath                            -> "primIdPath"
+    PrimHComp                             -> "primHComp"
+    --  Integer
+    PrimShowInteger                       -> "primShowInteger"
+    -- Natural
+    PrimNatPlus                           -> "primNatPlus"
+    PrimNatMinus                          -> "primNatMinus"
+    PrimNatTimes                          -> "primNatTimes"
+    PrimNatDivSucAux                      -> "primNatDivSucAux"
+    PrimNatModSucAux                      -> "primNatModSucAux"
+    PrimNatEquality                       -> "primNatEquality"
+    PrimNatLess                           -> "primNatLess"
+    PrimShowNat                           -> "primShowNat"
+    -- Word64
+    PrimWord64FromNat                     -> "primWord64FromNat"
+    PrimWord64ToNat                       -> "primWord64ToNat"
+    PrimWord64ToNatInjective              -> "primWord64ToNatInjective"
+    -- Level
+    PrimLevelZero                         -> "primLevelZero"
+    PrimLevelSuc                          -> "primLevelSuc"
+    PrimLevelMax                          -> "primLevelMax"
+    -- Float
+    PrimFloatEquality                     -> "primFloatEquality"
+    PrimFloatInequality                   -> "primFloatInequality"
+    PrimFloatLess                         -> "primFloatLess"
+    PrimFloatIsInfinite                   -> "primFloatIsInfinite"
+    PrimFloatIsNaN                        -> "primFloatIsNaN"
+    PrimFloatIsNegativeZero               -> "primFloatIsNegativeZero"
+    PrimFloatIsSafeInteger                -> "primFloatIsSafeInteger"
+    PrimFloatToWord64                     -> "primFloatToWord64"
+    PrimFloatToWord64Injective            -> "primFloatToWord64Injective"
+    PrimNatToFloat                        -> "primNatToFloat"
+    PrimIntToFloat                        -> "primIntToFloat"
+    PrimFloatRound                        -> "primFloatRound"
+    PrimFloatFloor                        -> "primFloatFloor"
+    PrimFloatCeiling                      -> "primFloatCeiling"
+    PrimFloatToRatio                      -> "primFloatToRatio"
+    PrimRatioToFloat                      -> "primRatioToFloat"
+    PrimFloatDecode                       -> "primFloatDecode"
+    PrimFloatEncode                       -> "primFloatEncode"
+    PrimShowFloat                         -> "primShowFloat"
+    PrimFloatPlus                         -> "primFloatPlus"
+    PrimFloatMinus                        -> "primFloatMinus"
+    PrimFloatTimes                        -> "primFloatTimes"
+    PrimFloatNegate                       -> "primFloatNegate"
+    PrimFloatDiv                          -> "primFloatDiv"
+    PrimFloatPow                          -> "primFloatPow"
+    PrimFloatSqrt                         -> "primFloatSqrt"
+    PrimFloatExp                          -> "primFloatExp"
+    PrimFloatLog                          -> "primFloatLog"
+    PrimFloatSin                          -> "primFloatSin"
+    PrimFloatCos                          -> "primFloatCos"
+    PrimFloatTan                          -> "primFloatTan"
+    PrimFloatASin                         -> "primFloatASin"
+    PrimFloatACos                         -> "primFloatACos"
+    PrimFloatATan                         -> "primFloatATan"
+    PrimFloatATan2                        -> "primFloatATan2"
+    PrimFloatSinh                         -> "primFloatSinh"
+    PrimFloatCosh                         -> "primFloatCosh"
+    PrimFloatTanh                         -> "primFloatTanh"
+    PrimFloatASinh                        -> "primFloatASinh"
+    PrimFloatACosh                        -> "primFloatACosh"
+    PrimFloatATanh                        -> "primFloatATanh"
+    -- Character
+    PrimCharEquality                      -> "primCharEquality"
+    PrimIsLower                           -> "primIsLower"
+    PrimIsDigit                           -> "primIsDigit"
+    PrimIsAlpha                           -> "primIsAlpha"
+    PrimIsSpace                           -> "primIsSpace"
+    PrimIsAscii                           -> "primIsAscii"
+    PrimIsLatin1                          -> "primIsLatin1"
+    PrimIsPrint                           -> "primIsPrint"
+    PrimIsHexDigit                        -> "primIsHexDigit"
+    PrimToUpper                           -> "primToUpper"
+    PrimToLower                           -> "primToLower"
+    PrimCharToNat                         -> "primCharToNat"
+    PrimCharToNatInjective                -> "primCharToNatInjective"
+    PrimNatToChar                         -> "primNatToChar"
+    PrimShowChar                          -> "primShowChar"
+    -- String
+    PrimStringToList                      -> "primStringToList"
+    PrimStringToListInjective             -> "primStringToListInjective"
+    PrimStringFromList                    -> "primStringFromList"
+    PrimStringFromListInjective           -> "primStringFromListInjective"
+    PrimStringAppend                      -> "primStringAppend"
+    PrimStringEquality                    -> "primStringEquality"
+    PrimShowString                        -> "primShowString"
+    PrimStringUncons                      -> "primStringUncons"
+    -- "Other stuff"
+    PrimErase                             -> "primErase"
+    PrimEraseEquality                     -> "primEraseEquality"
+    PrimForce                             -> "primForce"
+    PrimForceLemma                        -> "primForceLemma"
+    PrimQNameEquality                     -> "primQNameEquality"
+    PrimQNameLess                         -> "primQNameLess"
+    PrimShowQName                         -> "primShowQName"
+    PrimQNameFixity                       -> "primQNameFixity"
+    PrimQNameToWord64s                    -> "primQNameToWord64s"
+    PrimQNameToWord64sInjective           -> "primQNameToWord64sInjective"
+    PrimMetaEquality                      -> "primMetaEquality"
+    PrimMetaLess                          -> "primMetaLess"
+    PrimShowMeta                          -> "primShowMeta"
+    PrimMetaToNat                         -> "primMetaToNat"
+    PrimMetaToNatInjective                -> "primMetaToNatInjective"
+    PrimLockUniv                          -> "primLockUniv"
+
+builtinConId, builtinIdElim, builtinSubOut,
+  builtinIMin, builtinIMax, builtinINeg,
+  builtinGlue, builtin_glue, builtin_unglue, builtin_glueU, builtin_unglueU,
+  builtinFaceForall, builtinComp, builtinPOr,
+  builtinTrans,  builtinDepIMin,
+  builtinIdFace, builtinIdPath, builtinHComp, builtinLockUniv
+  :: PrimitiveId
+builtinConId                             = PrimConId
+builtinIdElim                            = PrimIdElim
+builtinIMin                              = PrimIMin
+builtinIMax                              = PrimIMax
+builtinINeg                              = PrimINeg
+builtinSubOut                            = PrimSubOut
+builtinGlue                              = PrimGlue
+builtin_glue                             = Prim_glue
+builtin_unglue                           = Prim_unglue
+builtin_glueU                            = Prim_glueU
+builtin_unglueU                          = Prim_unglueU
+builtinFaceForall                        = PrimFaceForall
+builtinComp                              = PrimComp
+builtinPOr                               = PrimPOr
+builtinTrans                             = PrimTrans
+builtinDepIMin                           = PrimDepIMin
+builtinIdFace                            = PrimIdFace
+builtinIdPath                            = PrimIdPath
+builtinHComp                             = PrimHComp
+builtinLockUniv                          = PrimLockUniv
+
+-- | Lookup a primitive by its identifier.
+primitiveById :: String -> Maybe PrimitiveId
+primitiveById = flip M.lookup m where
+  m = M.fromList [(getBuiltinId x, x) | x <- [(minBound :: PrimitiveId)..]]
diff --git a/src/full/Agda/Syntax/Common.hs b/src/full/Agda/Syntax/Common.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Common.hs
@@ -0,0 +1,3114 @@
+{-| Some common syntactic entities are defined in this module.
+-}
+module Agda.Syntax.Common
+  ( module Agda.Syntax.Common
+  , module Agda.Syntax.TopLevelModuleName.Boot
+  , Induction(..)
+  )
+  where
+
+import Agda.Syntax.TopLevelModuleName.Boot
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+import Control.Arrow ((&&&))
+import Control.Applicative ((<|>), liftA2)
+
+import Data.Bifunctor
+import Data.ByteString.Char8 (ByteString)
+import qualified Data.ByteString.Char8 as ByteString
+import qualified Data.Foldable as Fold
+import Data.Function (on)
+import Data.Hashable (Hashable(..))
+import qualified Data.Strict.Maybe as Strict
+import Data.Word
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as HashSet
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+
+import Agda.Utils.BiMap (HasTag(..))
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List1  ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.PartialOrd
+import Agda.Utils.POMonoid
+import Agda.Syntax.Common.Aspect (Induction(..))
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+type Nat    = Int
+type Arity  = Nat
+
+---------------------------------------------------------------------------
+-- * File
+---------------------------------------------------------------------------
+
+data FileType = AgdaFileType | MdFileType | RstFileType | TexFileType | OrgFileType | TypstFileType
+  deriving (Eq, Ord, Show, Generic)
+
+instance Pretty FileType where
+  pretty = \case
+    AgdaFileType -> "Agda"
+    MdFileType   -> "Markdown"
+    RstFileType  -> "ReStructedText"
+    TexFileType  -> "LaTeX"
+    OrgFileType  -> "org-mode"
+    TypstFileType -> "Typst"
+
+instance NFData FileType
+
+---------------------------------------------------------------------------
+-- * Agda variants
+---------------------------------------------------------------------------
+
+-- | Variants of Cubical Agda.
+
+data Cubical = CErased | CFull
+    deriving (Eq, Show, Generic)
+
+instance NFData Cubical
+
+-- | Agda variants.
+--
+-- Only some variants are tracked.
+
+data Language
+  = WithoutK
+  | WithK
+  | Cubical Cubical
+    deriving (Eq, Show, Generic)
+
+instance KillRange Language where
+  killRange = id
+
+instance NFData Language
+
+---------------------------------------------------------------------------
+-- * Record Directives
+---------------------------------------------------------------------------
+
+data RecordDirectives' a = RecordDirectives
+  { recInductive   :: Maybe (Ranged Induction)
+  , recHasEta      :: Maybe HasEta0
+  , recPattern     :: Maybe Range
+  , recConstructor :: Maybe a
+  } deriving (Functor, Show, Eq)
+
+emptyRecordDirectives :: RecordDirectives' a
+emptyRecordDirectives = RecordDirectives empty empty empty empty
+
+instance HasRange a => HasRange (RecordDirectives' a) where
+  getRange (RecordDirectives a b c d) = getRange (a,b,c,d)
+
+instance KillRange a => KillRange (RecordDirectives' a) where
+  killRange (RecordDirectives a b c d) = killRangeN RecordDirectives a b c d
+
+instance NFData a => NFData (RecordDirectives' a) where
+  rnf (RecordDirectives a b c d) = c `seq` rnf (a, b, d)
+
+---------------------------------------------------------------------------
+-- * Eta-equality
+---------------------------------------------------------------------------
+
+-- | Does a record come with eta-equality?
+data HasEta' a
+  = YesEta
+  | NoEta a
+  deriving (Show, Eq, Ord, Functor, Foldable, Traversable)
+
+instance HasRange a => HasRange (HasEta' a) where
+  getRange = foldMap getRange
+
+instance KillRange a => KillRange (HasEta' a) where
+  killRange = fmap killRange
+
+instance NFData a => NFData (HasEta' a) where
+  rnf YesEta    = ()
+  rnf (NoEta p) = rnf p
+
+-- | Pattern and copattern matching is allowed in the presence of eta.
+--
+--   In the absence of eta, we have to choose whether we want to allow
+--   matching on the constructor or copattern matching with the projections.
+--   Having both leads to breakage of subject reduction (issue #4560).
+
+type HasEta  = HasEta' PatternOrCopattern
+type HasEta0 = HasEta' ()
+
+-- | For a record without eta, which type of matching do we allow?
+data PatternOrCopattern
+  = PatternMatching
+      -- ^ Can match on the record constructor.
+  | CopatternMatching
+      -- ^ Can copattern match using the projections. (Default.)
+  deriving (Show, Eq, Ord, Enum, Bounded)
+
+instance NFData PatternOrCopattern where
+  rnf PatternMatching   = ()
+  rnf CopatternMatching = ()
+
+instance HasRange PatternOrCopattern where
+  getRange _ = noRange
+
+instance KillRange PatternOrCopattern where
+  killRange = id
+
+-- | Can we pattern match on the record constructor?
+class PatternMatchingAllowed a where
+  patternMatchingAllowed :: a -> Bool
+
+instance PatternMatchingAllowed PatternOrCopattern where
+  patternMatchingAllowed = (== PatternMatching)
+
+instance PatternMatchingAllowed HasEta where
+  patternMatchingAllowed = \case
+    YesEta -> True
+    NoEta p -> patternMatchingAllowed p
+
+
+-- | Can we construct a record by copattern matching?
+class CopatternMatchingAllowed a where
+  copatternMatchingAllowed :: a -> Bool
+
+instance CopatternMatchingAllowed PatternOrCopattern where
+  copatternMatchingAllowed = (== CopatternMatching)
+
+instance CopatternMatchingAllowed HasEta where
+  copatternMatchingAllowed = \case
+    YesEta -> True
+    NoEta p -> copatternMatchingAllowed p
+
+---------------------------------------------------------------------------
+-- * Induction
+---------------------------------------------------------------------------
+
+instance Pretty Induction where
+  pretty Inductive   = "inductive"
+  pretty CoInductive = "coinductive"
+
+instance HasRange Induction where
+  getRange _ = noRange
+
+instance KillRange Induction where
+  killRange = id
+
+instance PatternMatchingAllowed Induction where
+  patternMatchingAllowed = (== Inductive)
+
+---------------------------------------------------------------------------
+-- * Hiding
+---------------------------------------------------------------------------
+
+data Overlappable = YesOverlap | NoOverlap
+  deriving (Show, Eq, Ord)
+
+data Hiding  = Hidden | Instance Overlappable | NotHidden
+  deriving (Show, Eq, Ord)
+
+instance Pretty Hiding where
+  pretty = text . hidingToString
+
+hidingToString :: Hiding -> String
+hidingToString = \case
+  Hidden     -> "hidden"
+  NotHidden  -> "visible"
+  Instance{} -> "instance"
+
+-- | Just for the 'Hiding' instance. Should never combine different
+--   overlapping.
+instance Semigroup Overlappable where
+  NoOverlap  <> NoOverlap  = NoOverlap
+  YesOverlap <> YesOverlap = YesOverlap
+  _          <> _          = __IMPOSSIBLE__
+
+-- | 'Hiding' is an idempotent partial monoid, with unit 'NotHidden'.
+--   'Instance' and 'NotHidden' are incompatible.
+instance Semigroup Hiding where
+  NotHidden  <> h           = h
+  h          <> NotHidden   = h
+  Hidden     <> Hidden      = Hidden
+  Instance o <> Instance o' = Instance (o <> o')
+  _          <> _           = __IMPOSSIBLE__
+
+instance Monoid Overlappable where
+  mempty  = NoOverlap
+  mappend = (<>)
+
+instance Monoid Hiding where
+  mempty = NotHidden
+  mappend = (<>)
+
+instance HasRange Hiding where
+  getRange _ = noRange
+
+instance KillRange Hiding where
+  killRange = id
+
+instance NFData Overlappable where
+  rnf NoOverlap  = ()
+  rnf YesOverlap = ()
+
+instance NFData Hiding where
+  rnf Hidden       = ()
+  rnf (Instance o) = rnf o
+  rnf NotHidden    = ()
+
+-- | Decorating something with 'Hiding' information.
+data WithHiding a = WithHiding
+  { whHiding :: !Hiding
+  , whThing  :: a
+  }
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+instance Decoration WithHiding where
+  traverseF f (WithHiding h a) = WithHiding h <$> f a
+
+instance Applicative WithHiding where
+  pure = WithHiding mempty
+  WithHiding h f <*> WithHiding h' a = WithHiding (mappend h h') (f a)
+
+instance HasRange a => HasRange (WithHiding a) where
+  getRange = getRange . dget
+
+instance SetRange a => SetRange (WithHiding a) where
+  setRange = fmap . setRange
+
+instance KillRange a => KillRange (WithHiding a) where
+  killRange = fmap killRange
+
+instance NFData a => NFData (WithHiding a) where
+  rnf (WithHiding _ a) = rnf a
+
+-- | A lens to access the 'Hiding' attribute in data structures.
+--   Minimal implementation: @getHiding@ and @mapHiding@ or @LensArgInfo@.
+class LensHiding a where
+
+  getHiding :: a -> Hiding
+
+  setHiding :: Hiding -> a -> a
+  setHiding h = mapHiding (const h)
+
+  mapHiding :: (Hiding -> Hiding) -> a -> a
+
+  default getHiding :: LensArgInfo a => a -> Hiding
+  getHiding = argInfoHiding . getArgInfo
+
+  default mapHiding :: LensArgInfo a => (Hiding -> Hiding) -> a -> a
+  mapHiding f = mapArgInfo $ \ ai -> ai { argInfoHiding = f $ argInfoHiding ai }
+
+instance LensHiding Hiding where
+  getHiding = id
+  setHiding = const
+  mapHiding = id
+
+instance LensHiding (WithHiding a) where
+  getHiding   (WithHiding h _) = h
+  setHiding h (WithHiding _ a) = WithHiding h a
+  mapHiding f (WithHiding h a) = WithHiding (f h) a
+
+instance LensHiding a => LensHiding (Named nm a) where
+  getHiding = getHiding . namedThing
+  setHiding = fmap . setHiding
+  mapHiding = fmap . mapHiding
+
+-- | Monoidal composition of 'Hiding' information in some data.
+mergeHiding :: LensHiding a => WithHiding a -> a
+mergeHiding (WithHiding h a) = mapHiding (mappend h) a
+
+-- | 'NotHidden' arguments are @visible@.
+visible :: LensHiding a => a -> Bool
+visible a = getHiding a == NotHidden
+
+-- | 'Instance' and 'Hidden' arguments are @notVisible@.
+notVisible :: LensHiding a => a -> Bool
+notVisible a = getHiding a /= NotHidden
+
+-- | 'Hidden' arguments are @hidden@.
+hidden :: LensHiding a => a -> Bool
+hidden a = getHiding a == Hidden
+
+hide :: LensHiding a => a -> a
+hide = setHiding Hidden
+
+hideOrKeepInstance :: LensHiding a => a -> a
+hideOrKeepInstance x =
+  case getHiding x of
+    Hidden     -> x
+    Instance{} -> x
+    NotHidden  -> setHiding Hidden x
+
+makeInstance :: LensHiding a => a -> a
+makeInstance = makeInstance' NoOverlap
+
+makeInstance' :: LensHiding a => Overlappable -> a -> a
+makeInstance' o = setHiding (Instance o)
+
+isOverlappable :: LensHiding a => a -> Bool
+isOverlappable x =
+  case getHiding x of
+    Instance YesOverlap -> True
+    _ -> False
+
+isInstance :: LensHiding a => a -> Bool
+isInstance x =
+  case getHiding x of
+    Instance{} -> True
+    _          -> False
+
+-- | Ignores 'Overlappable'.
+sameHiding :: (LensHiding a, LensHiding b) => a -> b -> Bool
+sameHiding x y =
+  case (getHiding x, getHiding y) of
+    (Instance{}, Instance{}) -> True
+    (hx, hy)                 -> hx == hy
+
+---------------------------------------------------------------------------
+-- * Modalities
+---------------------------------------------------------------------------
+
+-- | Type wrapper to indicate additive monoid/semigroup context.
+newtype UnderAddition t = UnderAddition t deriving (Show, Functor, Eq, Ord, PartialOrd)
+
+instance Applicative UnderAddition where
+  pure = UnderAddition
+  (<*>) (UnderAddition f) (UnderAddition a) = pure (f a)
+
+-- | Type wrapper to indicate composition or multiplicative monoid/semigroup context.
+newtype UnderComposition t = UnderComposition t deriving (Show, Functor, Eq, Ord, PartialOrd)
+
+instance Applicative UnderComposition where
+  pure = UnderComposition
+  (<*>) (UnderComposition f) (UnderComposition a) = pure (f a)
+
+-- | We have a tuple of modalities, which might not be fully orthogonal.
+--   For example, irrelevant stuff is also run-time irrelevant.
+data Modality = Modality
+  { modRelevance :: Relevance
+      -- ^ Legacy irrelevance.
+      --   See Pfenning, LiCS 2001; Abel, Vezzosi and Winterhalter, ICFP 2017.
+  , modQuantity  :: Quantity
+      -- ^ Cardinality / runtime erasure.
+      --   See Conor McBride, I got plenty o' nutting, Wadlerfest 2016.
+      --   See Bob Atkey, Syntax and Semantics of Quantitative Type Theory, LiCS 2018.
+  , modCohesion :: Cohesion
+      -- ^ Cohesion/what was in Agda-flat.
+      --   see "Brouwer's fixed-point theorem in real-cohesive homotopy type theory" (arXiv:1509.07584)
+      --   Currently only the comonad is implemented.
+  } deriving (Eq, Ord, Show, Generic)
+
+-- | Dominance ordering.
+instance PartialOrd Modality where
+  comparable (Modality r q c) (Modality r' q' c') = comparable (r, (q, c)) (r', (q', c'))
+
+-- | Pointwise composition.
+instance Semigroup (UnderComposition Modality) where
+  (<>) = liftA2 composeModality
+
+-- | Pointwise composition unit.
+instance Monoid (UnderComposition Modality) where
+  mempty  = pure unitModality
+  mappend = (<>)
+
+instance POSemigroup (UnderComposition Modality) where
+instance POMonoid (UnderComposition Modality) where
+
+instance LeftClosedPOMonoid (UnderComposition Modality) where
+  inverseCompose = liftA2 inverseComposeModality
+
+-- | Pointwise addition.
+instance Semigroup (UnderAddition Modality) where
+  (<>) = liftA2 addModality
+
+-- | Pointwise additive unit.
+instance Monoid (UnderAddition Modality) where
+  mempty  = pure zeroModality
+  mappend = (<>)
+
+instance POSemigroup (UnderAddition Modality) where
+instance POMonoid (UnderAddition Modality) where
+
+-- | @m `moreUsableModality` m'@ means that an @m@ can be used
+--   where ever an @m'@ is required.
+
+moreUsableModality :: Modality -> Modality -> Bool
+moreUsableModality m m' = related m POLE m'
+
+usableModality :: LensModality a => a -> Bool
+usableModality a = usableRelevance m && usableQuantity m && usableCohesion m
+  where m = getModality a
+
+-- | Multiplicative monoid (standard monoid).
+composeModality :: Modality -> Modality -> Modality
+composeModality (Modality r q c) (Modality r' q' c') =
+    Modality (r `composeRelevance` r')
+             (q `composeQuantity` q')
+             (c `composeCohesion` c')
+
+-- | Compose with modality flag from the left.
+--   This function is e.g. used to update the modality information
+--   on pattern variables @a@ after a match against something of modality @q@.
+applyModality :: LensModality a => Modality -> a -> a
+applyModality m = mapModality (m `composeModality`)
+
+-- | @inverseComposeModality r x@ returns the least modality @y@
+--   such that forall @x@, @y@ we have
+--   @x \`moreUsableModality\` (r \`composeModality\` y)@
+--   iff
+--   @(r \`inverseComposeModality\` x) \`moreUsableModality\` y@ (Galois connection).
+inverseComposeModality :: Modality -> Modality -> Modality
+inverseComposeModality (Modality r q c) (Modality r' q' c') =
+  Modality (r `inverseComposeRelevance` r')
+           (q `inverseComposeQuantity`  q')
+           (c `inverseComposeCohesion`  c')
+
+-- | Left division by a 'Modality'.
+--   Used e.g. to modify context when going into a @m@ argument.
+--
+-- Note that this function does not change quantities.
+inverseApplyModalityButNotQuantity :: LensModality a => Modality -> a -> a
+inverseApplyModalityButNotQuantity m =
+  mapModality (m' `inverseComposeModality`)
+  where
+  m' = setQuantity (Quantity1 Q1Inferred) m
+
+-- | 'Modality' forms a pointwise additive monoid.
+addModality :: Modality -> Modality -> Modality
+addModality (Modality r q c) (Modality r' q' c') = Modality (addRelevance r r') (addQuantity q q') (addCohesion c c')
+
+-- | Identity under addition
+zeroModality :: Modality
+zeroModality = Modality zeroRelevance zeroQuantity zeroCohesion
+
+-- | Identity under composition
+unitModality :: Modality
+unitModality = Modality unitRelevance unitQuantity unitCohesion
+
+-- | Absorptive element under addition.
+topModality :: Modality
+topModality = Modality topRelevance topQuantity topCohesion
+
+-- | The default Modality
+--   Beware that this is neither the additive unit nor the unit under
+--   composition, because the default quantity is ω.
+defaultModality :: Modality
+defaultModality = Modality defaultRelevance defaultQuantity defaultCohesion
+
+-- | Equality ignoring origin.
+
+sameModality :: (LensModality a, LensModality b) => a -> b -> Bool
+sameModality x y = case (getModality x , getModality y) of
+  (Modality r q c , Modality r' q' c') -> sameRelevance r r' && sameQuantity q q' && sameCohesion c c'
+
+-- boilerplate instances
+
+instance HasRange Modality where
+  getRange (Modality r q c) = getRange (r, q, c)
+
+instance KillRange Modality where
+  killRange (Modality r q c) = killRangeN Modality r q c
+
+instance NFData Modality where
+
+-- Lens stuff
+
+lModRelevance :: Lens' Modality Relevance
+lModRelevance f m = f (modRelevance m) <&> \ r -> m { modRelevance = r }
+
+lModQuantity :: Lens' Modality Quantity
+lModQuantity f m = f (modQuantity m) <&> \ q -> m { modQuantity = q }
+
+lModCohesion :: Lens' Modality Cohesion
+lModCohesion f m = f (modCohesion m) <&> \ q -> m { modCohesion = q }
+
+class LensModality a where
+
+  getModality :: a -> Modality
+
+  setModality :: Modality -> a -> a
+  setModality = mapModality . const
+
+  mapModality :: (Modality -> Modality) -> a -> a
+
+  default getModality :: LensArgInfo a => a -> Modality
+  getModality = argInfoModality . getArgInfo
+
+  default mapModality :: LensArgInfo a => (Modality -> Modality) -> a -> a
+  mapModality f = mapArgInfo $ \ ai -> ai { argInfoModality = f $ argInfoModality ai }
+
+instance LensModality Modality where
+  getModality = id
+  setModality = const
+  mapModality = id
+
+instance LensRelevance Modality where
+  getRelevance = modRelevance
+  setRelevance h m = m { modRelevance = h }
+  mapRelevance f m = m { modRelevance = f (modRelevance m) }
+
+instance LensQuantity Modality where
+  getQuantity = modQuantity
+  setQuantity h m = m { modQuantity = h }
+  mapQuantity f m = m { modQuantity = f (modQuantity m) }
+
+instance LensCohesion Modality where
+  getCohesion = modCohesion
+  setCohesion h m = m { modCohesion = h }
+  mapCohesion f m = m { modCohesion = f (modCohesion m) }
+
+-- default accessors for Relevance
+
+getRelevanceMod :: LensModality a => LensGet a Relevance
+getRelevanceMod = getRelevance . getModality
+
+setRelevanceMod :: LensModality a => LensSet a Relevance
+setRelevanceMod = mapModality . setRelevance
+
+mapRelevanceMod :: LensModality a => LensMap a Relevance
+mapRelevanceMod = mapModality . mapRelevance
+
+-- default accessors for Quantity
+
+getQuantityMod :: LensModality a => LensGet a Quantity
+getQuantityMod = getQuantity . getModality
+
+setQuantityMod :: LensModality a => LensSet a Quantity
+setQuantityMod = mapModality . setQuantity
+
+mapQuantityMod :: LensModality a => LensMap a Quantity
+mapQuantityMod = mapModality . mapQuantity
+
+-- default accessors for Cohesion
+
+getCohesionMod :: LensModality a => LensGet a Cohesion
+getCohesionMod = getCohesion . getModality
+
+setCohesionMod :: LensModality a => LensSet a Cohesion
+setCohesionMod = mapModality . setCohesion
+
+mapCohesionMod :: LensModality a => LensMap a Cohesion
+mapCohesionMod = mapModality . mapCohesion
+
+---------------------------------------------------------------------------
+-- * Quantities
+---------------------------------------------------------------------------
+
+-- ** Quantity origin.
+
+-- | Origin of 'Quantity0'.
+data Q0Origin
+  = Q0Inferred       -- ^ User wrote nothing.
+  | Q0       Range   -- ^ User wrote "@0".
+  | Q0Erased Range   -- ^ User wrote "@erased".
+  deriving (Show, Generic, Eq, Ord)
+
+-- | Origin of 'Quantity1'.
+data Q1Origin
+  = Q1Inferred       -- ^ User wrote nothing.
+  | Q1       Range   -- ^ User wrote "@1".
+  | Q1Linear Range   -- ^ User wrote "@linear".
+  deriving (Show, Generic, Eq, Ord)
+
+-- | Origin of 'Quantityω'.
+data QωOrigin
+  = QωInferred       -- ^ User wrote nothing.
+  | Qω       Range   -- ^ User wrote "@ω".
+  | QωPlenty Range   -- ^ User wrote "@plenty".
+  deriving (Show, Generic, Eq, Ord)
+
+-- *** Instances for 'Q0Origin'.
+
+-- | Right-biased composition, because the left quantity
+--   acts as context, and the right one as occurrence.
+instance Semigroup Q0Origin where
+  (<>) = curry $ \case
+    (Q0Inferred, o) -> o
+    (o, Q0Inferred) -> o
+    (o, Q0       r) -> Q0 $ fuseRange o r
+    (o, Q0Erased r) -> Q0 $ fuseRange o r
+
+instance Monoid Q0Origin where
+  mempty = Q0Inferred
+  mappend = (<>)
+
+instance Null Q0Origin where
+  empty = mempty
+
+instance HasRange Q0Origin where
+  getRange = \case
+    Q0Inferred -> noRange
+    Q0       r -> r
+    Q0Erased r -> r
+
+instance SetRange Q0Origin where
+  setRange r = \case
+    Q0Inferred -> Q0Inferred
+    Q0       _ -> Q0       r
+    Q0Erased _ -> Q0Erased r
+
+instance KillRange Q0Origin where
+  killRange = \case
+    Q0Inferred -> Q0Inferred
+    Q0       _ -> Q0       noRange
+    Q0Erased _ -> Q0Erased noRange
+
+instance NFData Q0Origin where
+  rnf = \case
+    Q0Inferred -> ()
+    Q0       _ -> ()
+    Q0Erased _ -> ()
+
+-- *** Instances for 'Q1Origin'.
+
+-- | Right-biased composition, because the left quantity
+--   acts as context, and the right one as occurrence.
+instance Semigroup Q1Origin where
+  (<>) = curry $ \case
+    (Q1Inferred, o) -> o
+    (o, Q1Inferred) -> o
+    (o, Q1       r) -> Q1 $ fuseRange o r
+    (o, Q1Linear r) -> Q1 $ fuseRange o r
+
+instance Monoid Q1Origin where
+  mempty = Q1Inferred
+  mappend = (<>)
+
+instance Null Q1Origin where
+  empty = mempty
+
+instance HasRange Q1Origin where
+  getRange = \case
+    Q1Inferred -> noRange
+    Q1       r -> r
+    Q1Linear r -> r
+
+instance SetRange Q1Origin where
+  setRange r = \case
+    Q1Inferred -> Q1Inferred
+    Q1       _ -> Q1       r
+    Q1Linear _ -> Q1Linear r
+
+instance KillRange Q1Origin where
+  killRange = \case
+    Q1Inferred -> Q1Inferred
+    Q1       _ -> Q1       noRange
+    Q1Linear _ -> Q1Linear noRange
+
+instance NFData Q1Origin where
+  rnf = \case
+    Q1Inferred -> ()
+    Q1       _ -> ()
+    Q1Linear _ -> ()
+
+-- *** Instances for 'QωOrigin'.
+
+-- | Right-biased composition, because the left quantity
+--   acts as context, and the right one as occurrence.
+instance Semigroup QωOrigin where
+  (<>) = curry $ \case
+    (QωInferred, o) -> o
+    (o, QωInferred) -> o
+    (o, Qω       r) -> Qω $ fuseRange o r
+    (o, QωPlenty r) -> Qω $ fuseRange o r
+
+instance Monoid QωOrigin where
+  mempty = QωInferred
+  mappend = (<>)
+
+instance Null QωOrigin where
+  empty = mempty
+
+instance HasRange QωOrigin where
+  getRange = \case
+    QωInferred -> noRange
+    Qω       r -> r
+    QωPlenty r -> r
+
+instance SetRange QωOrigin where
+  setRange r = \case
+    QωInferred -> QωInferred
+    Qω       _ -> Qω       r
+    QωPlenty _ -> QωPlenty r
+
+instance KillRange QωOrigin where
+  killRange = \case
+    QωInferred -> QωInferred
+    Qω       _ -> Qω       noRange
+    QωPlenty _ -> QωPlenty noRange
+
+instance NFData QωOrigin where
+  rnf = \case
+    QωInferred -> ()
+    Qω       _ -> ()
+    QωPlenty _ -> ()
+
+-- ** Quantity.
+
+-- | Quantity for linearity.
+--
+--   A quantity is a set of natural numbers, indicating possible semantic
+--   uses of a variable.  A singleton set @{n}@ requires that the
+--   corresponding variable is used exactly @n@ times.
+--
+data Quantity
+  = Quantity0 Q0Origin -- ^ Zero uses @{0}@, erased at runtime.
+  | Quantity1 Q1Origin -- ^ Linear use @{1}@ (could be updated destructively).
+    -- Mostly TODO (needs postponable constraints between quantities to compute uses).
+  | Quantityω QωOrigin -- ^ Unrestricted use @ℕ@.
+  deriving (Show, Generic, Eq, Ord)
+    -- @Ord@ instance in case @Quantity@ is used in keys for maps etc.
+
+-- | Equality ignoring origin.
+
+sameQuantity :: Quantity -> Quantity -> Bool
+sameQuantity = curry $ \case
+  (Quantity0{}, Quantity0{}) -> True
+  (Quantity1{}, Quantity1{}) -> True
+  (Quantityω{}, Quantityω{}) -> True
+  _ -> False
+
+-- | Composition of quantities (multiplication).
+--
+-- 'Quantity0' is dominant.
+-- 'Quantity1' is neutral.
+--
+-- Right-biased for origin.
+--
+instance Semigroup (UnderComposition Quantity) where
+  (<>) = liftA2 composeQuantity
+
+-- | In the absense of finite quantities besides 0, ω is the unit.
+--   Otherwise, 1 is the unit.
+instance Monoid (UnderComposition Quantity) where
+  mempty  = pure unitQuantity
+  mappend = (<>)
+
+instance POSemigroup (UnderComposition Quantity) where
+instance POMonoid (UnderComposition Quantity) where
+
+instance LeftClosedPOMonoid (UnderComposition Quantity) where
+  inverseCompose = liftA2 inverseComposeQuantity
+
+instance Semigroup (UnderAddition Quantity) where
+  (<>) = liftA2 addQuantity
+
+instance Monoid (UnderAddition Quantity) where
+  mempty  = pure zeroQuantity
+  mappend = (<>)
+
+instance POSemigroup (UnderAddition Quantity) where
+instance POMonoid (UnderAddition Quantity) where
+
+-- | Note that the order is @ω ≤ 0,1@, more options is smaller.
+instance PartialOrd Quantity where
+  comparable = curry $ \case
+    (q, q') | sameQuantity q q' -> POEQ
+    -- ω is least
+    (Quantityω{}, _)  -> POLT
+    (_, Quantityω{})  -> POGT
+    -- others are uncomparable
+    _ -> POAny
+
+-- | 'Quantity' forms an additive monoid with zero Quantity0.
+addQuantity :: Quantity -> Quantity -> Quantity
+addQuantity = curry $ \case
+  -- ω is absorptive
+  (q@Quantityω{}, _) -> q
+  (_, q@Quantityω{}) -> q
+  -- 0 is neutral
+  (Quantity0{}, q) -> q
+  (q, Quantity0{}) -> q
+  -- 1 + 1 = ω
+  (Quantity1 _, Quantity1 _) -> topQuantity
+
+-- | Identity element under addition
+zeroQuantity :: Quantity
+zeroQuantity = Quantity0 mempty
+
+-- | Absorptive element!
+--   This differs from Relevance and Cohesion whose default
+--   is the multiplicative unit.
+defaultQuantity :: Quantity
+defaultQuantity = topQuantity
+
+-- | Identity element under composition
+unitQuantity :: Quantity
+unitQuantity = Quantityω mempty
+
+-- | Absorptive element is ω.
+topQuantity :: Quantity
+topQuantity = Quantityω mempty
+
+-- | @m `moreUsableQuantity` m'@ means that an @m@ can be used
+--   where ever an @m'@ is required.
+
+moreQuantity :: Quantity -> Quantity -> Bool
+moreQuantity m m' = related m POLE m'
+
+-- | Composition of quantities (multiplication).
+--
+-- 'Quantity0' is dominant.
+-- 'Quantity1' is neutral.
+--
+-- Right-biased for origin.
+--
+composeQuantity :: Quantity -> Quantity -> Quantity
+composeQuantity = curry $ \case
+  (Quantity1 o, Quantity1 o') -> Quantity1 (o <> o')
+  (Quantity1{}, q           ) -> q
+  (q          , Quantity1{} ) -> q
+  (Quantity0 o, Quantity0 o') -> Quantity0 (o <> o')
+  (_          , Quantity0 o ) -> Quantity0 o
+  (Quantity0 o, _           ) -> Quantity0 o
+  (Quantityω o, Quantityω o') -> Quantityω (o <> o')
+
+-- | Compose with quantity flag from the left.
+--   This function is e.g. used to update the quantity information
+--   on pattern variables @a@ after a match against something of quantity @q@.
+
+applyQuantity :: LensQuantity a => Quantity -> a -> a
+applyQuantity q = mapQuantity (q `composeQuantity`)
+
+-- | @inverseComposeQuantity r x@ returns the least quantity @y@
+--   such that forall @x@, @y@ we have
+--   @x \`moreQuantity\` (r \`composeQuantity\` y)@
+--   iff
+--   @(r \`inverseComposeQuantity\` x) \`moreQuantity\` y@ (Galois connection).
+
+inverseComposeQuantity :: Quantity -> Quantity -> Quantity
+inverseComposeQuantity = curry $ \case
+    (Quantity1{} , x)              -> x             -- going to linear arg: nothing changes
+    (Quantity0{} , x)              -> topQuantity   -- going to erased arg: every thing usable
+    (Quantityω{} , x@Quantityω{})  -> x
+    (Quantityω{} , _)              -> zeroQuantity  -- linear resources are unusable as arguments to unrestricted functions
+
+-- | Left division by a 'Quantity'.
+--   Used e.g. to modify context when going into a @q@ argument.
+
+inverseApplyQuantity :: LensQuantity a => Quantity -> a -> a
+inverseApplyQuantity q = mapQuantity (q `inverseComposeQuantity`)
+
+-- | Check for 'Quantity0'.
+
+hasQuantity0 :: LensQuantity a => a -> Bool
+hasQuantity0 a
+  | Quantity0{} <- getQuantity a = True
+  | otherwise = False
+
+-- | Check for 'Quantity1'.
+
+hasQuantity1 :: LensQuantity a => a -> Bool
+hasQuantity1 a
+  | Quantity1{} <- getQuantity a = True
+  | otherwise = False
+
+-- | Check for 'Quantityω'.
+
+hasQuantityω :: LensQuantity a => a -> Bool
+hasQuantityω a
+  | Quantityω{} <- getQuantity a = True
+  | otherwise = False
+
+-- | Did the user supply a quantity annotation?
+
+noUserQuantity :: LensQuantity a => a -> Bool
+noUserQuantity a = case getQuantity a of
+  Quantity0 o -> null o
+  Quantity1 o -> null o
+  Quantityω o -> null o
+
+-- | A thing of quantity 0 is unusable, all others are usable.
+
+usableQuantity :: LensQuantity a => a -> Bool
+usableQuantity = not . hasQuantity0
+
+-- boilerplate instances
+
+class LensQuantity a where
+
+  getQuantity :: a -> Quantity
+
+  setQuantity :: Quantity -> a -> a
+  setQuantity = mapQuantity . const
+
+  mapQuantity :: (Quantity -> Quantity) -> a -> a
+
+  default getQuantity :: LensModality a => a -> Quantity
+  getQuantity = modQuantity . getModality
+
+  default mapQuantity :: LensModality a => (Quantity -> Quantity) -> a -> a
+  mapQuantity f = mapModality $ \ ai -> ai { modQuantity = f $ modQuantity ai }
+
+instance LensQuantity Quantity where
+  getQuantity = id
+  setQuantity = const
+  mapQuantity = id
+
+instance HasRange Quantity where
+  getRange = \case
+    Quantity0 o -> getRange o
+    Quantity1 o -> getRange o
+    Quantityω o -> getRange o
+
+instance SetRange Quantity where
+  setRange r = \case
+    Quantity0 o -> Quantity0 $ setRange r o
+    Quantity1 o -> Quantity1 $ setRange r o
+    Quantityω o -> Quantityω $ setRange r o
+
+instance KillRange Quantity where
+  killRange = \case
+    Quantity0 o -> Quantity0 $ killRange o
+    Quantity1 o -> Quantity1 $ killRange o
+    Quantityω o -> Quantityω $ killRange o
+
+instance NFData Quantity where
+  rnf (Quantity0 o) = rnf o
+  rnf (Quantity1 o) = rnf o
+  rnf (Quantityω o) = rnf o
+
+-- ** Erased.
+
+-- | A special case of 'Quantity': erased or not.
+--
+-- Note that the 'Ord' instance does *not* ignore the origin
+-- arguments.
+
+data Erased
+  = Erased Q0Origin
+  | NotErased QωOrigin
+  deriving (Show, Eq, Ord, Generic)
+
+-- | The default value of type 'Erased': not erased.
+
+defaultErased :: Erased
+defaultErased = NotErased QωInferred
+
+-- | 'Erased' can be embedded into 'Quantity'.
+
+asQuantity :: Erased -> Quantity
+asQuantity (Erased    o) = Quantity0 o
+asQuantity (NotErased o) = Quantityω o
+
+-- | 'Quantity' can be projected onto 'Erased'.
+
+erasedFromQuantity :: Quantity -> Maybe Erased
+erasedFromQuantity = \case
+  Quantity1{} -> Nothing
+  Quantity0 o -> Just $ Erased    o
+  Quantityω o -> Just $ NotErased o
+
+-- | Equality ignoring origin.
+
+sameErased :: Erased -> Erased -> Bool
+sameErased = sameQuantity `on` asQuantity
+
+-- | Is the value \"erased\"?
+
+isErased :: Erased -> Bool
+isErased = hasQuantity0 . asQuantity
+
+instance NFData Erased
+
+instance HasRange Erased where
+  getRange = getRange . asQuantity
+
+instance KillRange Erased where
+  killRange = \case
+    Erased o    -> Erased $ killRange o
+    NotErased o -> NotErased $ killRange o
+
+-- | Composition of values of type 'Erased'.
+--
+-- 'Erased' is dominant.
+-- 'NotErased' is neutral.
+--
+-- Right-biased for the origin.
+
+composeErased :: Erased -> Erased -> Erased
+composeErased = curry $ \case
+  (Erased o,    Erased o')    -> Erased (o <> o')
+  (NotErased _, Erased o)     -> Erased o
+  (Erased o,    NotErased _)  -> Erased o
+  (NotErased o, NotErased o') -> NotErased (o <> o')
+
+instance Semigroup (UnderComposition Erased) where
+  (<>) = liftA2 composeErased
+
+---------------------------------------------------------------------------
+-- * Relevance
+---------------------------------------------------------------------------
+
+-- | A function argument can be relevant or irrelevant.
+--   See "Agda.TypeChecking.Irrelevance".
+data Relevance
+  = Relevant    -- ^ The argument is (possibly) relevant at compile-time.
+  | NonStrict   -- ^ The argument may never flow into evaluation position.
+                --   Therefore, it is irrelevant at run-time.
+                --   It is treated relevantly during equality checking.
+                --
+                --   The above comment is probably obsolete, as we currently have
+                --   erasure (/at/0, @Quantity0@) for that. What's described here is probably
+                --   shape-irrelevance (..). If you enable @--experimental-irrelevance@,
+                --   then the type of an irrelevant function is forced to be shape-irrelevant.
+                --   See:
+                --   - <https://doi.org/10.2168/LMCS-8(1:29)2012> example 2.8
+                --     (Not enforcing shape-irrelevant codomains can break subject reduction!)
+                --   - <https://dl.acm.org/doi/10.1145/3110277>
+                --   - <https://doi.org/10.1145/3209108.3209119>
+  | Irrelevant  -- ^ The argument is irrelevant at compile- and runtime.
+    deriving (Show, Eq, Enum, Bounded, Generic)
+
+allRelevances :: [Relevance]
+allRelevances = [minBound..maxBound]
+
+instance HasRange Relevance where
+  getRange _ = noRange
+
+instance SetRange Relevance where
+  setRange _ = id
+
+instance KillRange Relevance where
+  killRange rel = rel -- no range to kill
+
+instance NFData Relevance where
+  rnf Relevant   = ()
+  rnf NonStrict  = ()
+  rnf Irrelevant = ()
+
+-- | A lens to access the 'Relevance' attribute in data structures.
+--   Minimal implementation: @getRelevance@ and @mapRelevance@ or @LensModality@.
+class LensRelevance a where
+
+  getRelevance :: a -> Relevance
+
+  setRelevance :: Relevance -> a -> a
+  setRelevance h = mapRelevance (const h)
+
+  mapRelevance :: (Relevance -> Relevance) -> a -> a
+
+  default getRelevance :: LensModality a => a -> Relevance
+  getRelevance = modRelevance . getModality
+
+  default mapRelevance :: LensModality a => (Relevance -> Relevance) -> a -> a
+  mapRelevance f = mapModality $ \ ai -> ai { modRelevance = f $ modRelevance ai }
+
+instance LensRelevance Relevance where
+  getRelevance = id
+  setRelevance = const
+  mapRelevance = id
+
+isRelevant :: LensRelevance a => a -> Bool
+isRelevant a = getRelevance a == Relevant
+
+isIrrelevant :: LensRelevance a => a -> Bool
+isIrrelevant a = getRelevance a == Irrelevant
+
+isNonStrict :: LensRelevance a => a -> Bool
+isNonStrict a = getRelevance a == NonStrict
+
+-- | Information ordering.
+-- @Relevant  \`moreRelevant\`
+--  NonStrict \`moreRelevant\`
+--  Irrelevant@
+moreRelevant :: Relevance -> Relevance -> Bool
+moreRelevant = (<=)
+
+-- | Equality ignoring origin.
+sameRelevance :: Relevance -> Relevance -> Bool
+sameRelevance = (==)
+
+-- | More relevant is smaller.
+instance Ord Relevance where
+  compare = curry $ \case
+    (r, r') | r == r' -> EQ
+    -- top
+    (_, Irrelevant) -> LT
+    (Irrelevant, _) -> GT
+    -- bottom
+    (Relevant, _) -> LT
+    (_, Relevant) -> GT
+    -- redundant case
+    (NonStrict,NonStrict) -> EQ
+
+-- | More relevant is smaller.
+instance PartialOrd Relevance where
+  comparable = comparableOrd
+
+-- | @usableRelevance rel == False@ iff we cannot use a variable of @rel@.
+usableRelevance :: LensRelevance a => a -> Bool
+usableRelevance = isRelevant
+
+-- | 'Relevance' composition.
+--   'Irrelevant' is dominant, 'Relevant' is neutral.
+--   Composition coincides with 'max'.
+composeRelevance :: Relevance -> Relevance -> Relevance
+composeRelevance r r' =
+  case (r, r') of
+    (Irrelevant, _) -> Irrelevant
+    (_, Irrelevant) -> Irrelevant
+    (NonStrict, _)  -> NonStrict
+    (_, NonStrict)  -> NonStrict
+    (Relevant, Relevant) -> Relevant
+
+-- | Compose with relevance flag from the left.
+--   This function is e.g. used to update the relevance information
+--   on pattern variables @a@ after a match against something @rel@.
+applyRelevance :: LensRelevance a => Relevance -> a -> a
+applyRelevance rel = mapRelevance (rel `composeRelevance`)
+
+-- | @inverseComposeRelevance r x@ returns the most irrelevant @y@
+--   such that forall @x@, @y@ we have
+--   @x \`moreRelevant\` (r \`composeRelevance\` y)@
+--   iff
+--   @(r \`inverseComposeRelevance\` x) \`moreRelevant\` y@ (Galois connection).
+inverseComposeRelevance :: Relevance -> Relevance -> Relevance
+inverseComposeRelevance r x =
+  case (r, x) of
+    (Relevant  , x)          -> x          -- going to relevant arg.: nothing changes
+                                           -- because Relevant is comp.-neutral
+    (Irrelevant, x)          -> Relevant   -- going irrelevant: every thing usable
+    (NonStrict , Irrelevant) -> Irrelevant -- otherwise: irrelevant things remain unusable
+    (NonStrict , _)          -> Relevant   -- but @NonStrict@s become usable
+
+-- | Left division by a 'Relevance'.
+--   Used e.g. to modify context when going into a @rel@ argument.
+inverseApplyRelevance :: LensRelevance a => Relevance -> a -> a
+inverseApplyRelevance rel = mapRelevance (rel `inverseComposeRelevance`)
+
+-- | 'Relevance' forms a semigroup under composition.
+instance Semigroup (UnderComposition Relevance) where
+  (<>) = liftA2 composeRelevance
+
+-- | 'Relevant' is the unit under composition.
+instance Monoid (UnderComposition Relevance) where
+  mempty  = pure unitRelevance
+  mappend = (<>)
+
+instance POSemigroup (UnderComposition Relevance) where
+instance POMonoid (UnderComposition Relevance) where
+
+instance LeftClosedPOMonoid (UnderComposition Relevance) where
+  inverseCompose = liftA2 inverseComposeRelevance
+
+instance Semigroup (UnderAddition Relevance) where
+  (<>) = liftA2 addRelevance
+
+instance Monoid (UnderAddition Relevance) where
+  mempty  = pure zeroRelevance
+  mappend = (<>)
+
+instance POSemigroup (UnderAddition Relevance) where
+instance POMonoid (UnderAddition Relevance) where
+
+-- | Combine inferred 'Relevance'.
+--   The unit is 'Irrelevant'.
+addRelevance :: Relevance -> Relevance -> Relevance
+addRelevance = min
+
+-- | 'Relevance' forms a monoid under addition, and even a semiring.
+zeroRelevance :: Relevance
+zeroRelevance = Irrelevant
+
+-- | Identity element under composition
+unitRelevance :: Relevance
+unitRelevance = Relevant
+
+-- | Absorptive element under addition.
+topRelevance :: Relevance
+topRelevance = Relevant
+
+-- | Default Relevance is the identity element under composition
+defaultRelevance :: Relevance
+defaultRelevance = unitRelevance
+
+-- | Irrelevant function arguments may appear non-strictly in the codomain type.
+irrToNonStrict :: Relevance -> Relevance
+irrToNonStrict Irrelevant = NonStrict
+irrToNonStrict rel        = rel
+
+-- | Applied when working on types (unless --experimental-irrelevance).
+nonStrictToRel :: Relevance -> Relevance
+nonStrictToRel NonStrict = Relevant
+nonStrictToRel rel       = rel
+
+nonStrictToIrr :: Relevance -> Relevance
+nonStrictToIrr NonStrict = Irrelevant
+nonStrictToIrr rel       = rel
+
+---------------------------------------------------------------------------
+-- * Annotations
+---------------------------------------------------------------------------
+
+-- | We have a tuple of annotations, which might not be fully orthogonal.
+data Annotation = Annotation
+  { annLock :: Lock
+    -- ^ Fitch-style dependent right adjoints.
+    --   See Modal Dependent Type Theory and Dependent Right Adjoints, arXiv:1804.05236.
+  } deriving (Eq, Ord, Show, Generic)
+
+instance HasRange Annotation where
+  getRange _ = noRange
+
+instance KillRange Annotation where
+  killRange = id
+
+defaultAnnotation :: Annotation
+defaultAnnotation = Annotation defaultLock
+
+instance NFData Annotation where
+  rnf (Annotation l) = rnf l
+
+class LensAnnotation a where
+
+  getAnnotation :: a -> Annotation
+
+  setAnnotation :: Annotation -> a -> a
+
+  mapAnnotation :: (Annotation -> Annotation) -> a -> a
+  mapAnnotation f a = setAnnotation (f $ getAnnotation a) a
+
+  default getAnnotation :: LensArgInfo a => a -> Annotation
+  getAnnotation = argInfoAnnotation . getArgInfo
+
+  default setAnnotation :: LensArgInfo a => Annotation -> a -> a
+  setAnnotation a = mapArgInfo $ \ ai -> ai { argInfoAnnotation = a }
+
+instance LensAnnotation Annotation where
+  getAnnotation = id
+  setAnnotation = const
+  mapAnnotation = id
+
+instance LensAnnotation (Arg t) where
+  getAnnotation = getAnnotation . getArgInfo
+  setAnnotation = mapArgInfo . setAnnotation
+
+
+---------------------------------------------------------------------------
+-- * Locks
+---------------------------------------------------------------------------
+
+data LockOrigin
+  = LockOLock -- ^ The user wrote @lock.
+  | LockOTick -- ^ The user wrote @tick.
+  deriving (Show, Generic, Eq, Enum, Bounded, Ord)
+
+data Lock
+  = IsNotLock
+  | IsLock LockOrigin
+  -- ^ In the future there might be different kinds of them.
+  --   For now we assume lock weakening.
+  deriving (Show, Generic, Eq, Ord)
+
+defaultLock :: Lock
+defaultLock = IsNotLock
+
+instance NFData Lock where
+  rnf IsNotLock          = ()
+  rnf (IsLock LockOLock) = ()
+  rnf (IsLock LockOTick) = ()
+
+class LensLock a where
+
+  getLock :: a -> Lock
+
+  setLock :: Lock -> a -> a
+  setLock = mapLock . const
+
+  mapLock :: (Lock -> Lock) -> a -> a
+  mapLock f a = setLock (f $ getLock a) a
+
+instance LensLock Lock where
+  getLock = id
+  setLock = const
+  mapLock = id
+
+instance LensLock ArgInfo where
+  getLock = annLock . argInfoAnnotation
+  setLock l info = info { argInfoAnnotation = (argInfoAnnotation info){ annLock = l } }
+
+instance LensLock (Arg t) where
+  getLock = getLock . getArgInfo
+  setLock = mapArgInfo . setLock
+
+---------------------------------------------------------------------------
+-- * Cohesion
+---------------------------------------------------------------------------
+
+-- | Cohesion modalities
+--   see "Brouwer's fixed-point theorem in real-cohesive homotopy type theory" (arXiv:1509.07584)
+--   types are now given an additional topological layer which the modalities interact with.
+data Cohesion
+  = Flat        -- ^ same points, discrete topology, idempotent comonad, box-like.
+  | Continuous  -- ^ identity modality.
+  -- | Sharp    -- ^ same points, codiscrete topology, idempotent monad, diamond-like.
+  | Squash      -- ^ single point space, artificially added for Flat left-composition.
+    deriving (Show, Eq, Enum, Bounded, Generic)
+
+allCohesions :: [Cohesion]
+allCohesions = [minBound..maxBound]
+
+instance HasRange Cohesion where
+  getRange _ = noRange
+
+instance SetRange Cohesion where
+  setRange _ = id
+
+instance KillRange Cohesion where
+  killRange rel = rel -- no range to kill
+
+instance NFData Cohesion where
+  rnf Flat       = ()
+  rnf Continuous = ()
+  rnf Squash     = ()
+
+-- | A lens to access the 'Cohesion' attribute in data structures.
+--   Minimal implementation: @getCohesion@ and @mapCohesion@ or @LensModality@.
+class LensCohesion a where
+
+  getCohesion :: a -> Cohesion
+
+  setCohesion :: Cohesion -> a -> a
+  setCohesion h = mapCohesion (const h)
+
+  mapCohesion :: (Cohesion -> Cohesion) -> a -> a
+
+  default getCohesion :: LensModality a => a -> Cohesion
+  getCohesion = modCohesion . getModality
+
+  default mapCohesion :: LensModality a => (Cohesion -> Cohesion) -> a -> a
+  mapCohesion f = mapModality $ \ ai -> ai { modCohesion = f $ modCohesion ai }
+
+instance LensCohesion Cohesion where
+  getCohesion = id
+  setCohesion = const
+  mapCohesion = id
+
+-- | Information ordering.
+-- @Flat  \`moreCohesion\`
+--  Continuous \`moreCohesion\`
+--  Sharp \`moreCohesion\`
+--  Squash@
+moreCohesion :: Cohesion -> Cohesion -> Bool
+moreCohesion = (<=)
+
+-- | Equality ignoring origin.
+sameCohesion :: Cohesion -> Cohesion -> Bool
+sameCohesion = (==)
+
+-- | Order is given by implication: flatter is smaller.
+instance Ord Cohesion where
+  compare = curry $ \case
+    (r, r') | r == r' -> EQ
+    -- top
+    (_, Squash) -> LT
+    (Squash, _) -> GT
+    -- bottom
+    (Flat, _) -> LT
+    (_, Flat) -> GT
+    -- redundant case
+    (Continuous,Continuous) -> EQ
+
+-- | Flatter is smaller.
+instance PartialOrd Cohesion where
+  comparable = comparableOrd
+
+-- | @usableCohesion rel == False@ iff we cannot use a variable of @rel@.
+usableCohesion :: LensCohesion a => a -> Bool
+usableCohesion a = getCohesion a `moreCohesion` Continuous
+
+-- | 'Cohesion' composition.
+--   'Squash' is dominant, 'Continuous' is neutral.
+composeCohesion :: Cohesion -> Cohesion -> Cohesion
+composeCohesion r r' =
+  case (r, r') of
+    (Squash, _) -> Squash
+    (_, Squash) -> Squash
+    (Flat, _)  -> Flat
+    (_, Flat)  -> Flat
+    (Continuous, Continuous) -> Continuous
+
+-- | Compose with cohesion flag from the left.
+--   This function is e.g. used to update the cohesion information
+--   on pattern variables @a@ after a match against something of cohesion @rel@.
+applyCohesion :: LensCohesion a => Cohesion -> a -> a
+applyCohesion rel = mapCohesion (rel `composeCohesion`)
+
+-- | @inverseComposeCohesion r x@ returns the least @y@
+--   such that forall @x@, @y@ we have
+--   @x \`moreCohesion\` (r \`composeCohesion\` y)@
+--   iff
+--   @(r \`inverseComposeCohesion\` x) \`moreCohesion\` y@ (Galois connection).
+--   The above law fails for @r = Squash@.
+inverseComposeCohesion :: Cohesion -> Cohesion -> Cohesion
+inverseComposeCohesion r x =
+  case (r, x) of
+    (Continuous  , x) -> x          -- going to continous arg.: nothing changes
+                                    -- because Continuous is comp.-neutral
+    (Squash, x)       -> Flat       -- in squash position everything is usable
+    (Flat , Flat)     -> Flat       -- otherwise: Flat things remain Flat
+    (Flat , _)        -> Squash     -- but everything else becomes unusable.
+
+-- | Left division by a 'Cohesion'.
+--   Used e.g. to modify context when going into a @rel@ argument.
+inverseApplyCohesion :: LensCohesion a => Cohesion -> a -> a
+inverseApplyCohesion rel = mapCohesion (rel `inverseComposeCohesion`)
+
+-- | 'Cohesion' forms a semigroup under composition.
+instance Semigroup (UnderComposition Cohesion) where
+  (<>) = liftA2 composeCohesion
+
+-- | 'Continous' is the multiplicative unit.
+instance Monoid (UnderComposition Cohesion) where
+  mempty  = pure unitCohesion
+  mappend = (<>)
+
+instance POSemigroup (UnderComposition Cohesion) where
+instance POMonoid (UnderComposition Cohesion) where
+
+instance LeftClosedPOMonoid (UnderComposition Cohesion) where
+  inverseCompose = liftA2 inverseComposeCohesion
+
+-- | 'Cohesion' forms a semigroup under addition.
+instance Semigroup (UnderAddition Cohesion) where
+  (<>) = liftA2 addCohesion
+
+-- | 'Squash' is the additive unit.
+instance Monoid (UnderAddition Cohesion) where
+  mempty  = pure zeroCohesion
+  mappend = (<>)
+
+instance POSemigroup (UnderAddition Cohesion) where
+instance POMonoid (UnderAddition Cohesion) where
+
+-- | Combine inferred 'Cohesion'.
+--   The unit is 'Squash'.
+addCohesion :: Cohesion -> Cohesion -> Cohesion
+addCohesion = min
+
+-- | 'Cohesion' forms a monoid under addition, and even a semiring.
+zeroCohesion :: Cohesion
+zeroCohesion = Squash
+
+-- | Identity under composition
+unitCohesion :: Cohesion
+unitCohesion = Continuous
+
+-- | Absorptive element under addition.
+topCohesion :: Cohesion
+topCohesion = Flat
+
+-- | Default Cohesion is the identity element under composition
+defaultCohesion :: Cohesion
+defaultCohesion = unitCohesion
+
+---------------------------------------------------------------------------
+-- * Origin of arguments (user-written, inserted or reflected)
+---------------------------------------------------------------------------
+
+-- | Origin of arguments.
+data Origin
+  = UserWritten     -- ^ From the source file / user input.  (Preserve!)
+  | Inserted        -- ^ E.g. inserted hidden arguments.
+  | Reflected       -- ^ Produced by the reflection machinery.
+  | CaseSplit       -- ^ Produced by an interactive case split.
+  | Substitution    -- ^ Named application produced to represent a substitution. E.g. "?0 (x = n)" instead of "?0 n"
+  | ExpandedPun     -- ^ An expanded hidden argument pun.
+  | Generalization  -- ^ Inserted by the generalization process
+  deriving (Show, Eq, Ord)
+
+instance HasRange Origin where
+  getRange _ = noRange
+
+instance KillRange Origin where
+  killRange = id
+
+instance NFData Origin where
+  rnf UserWritten = ()
+  rnf Inserted = ()
+  rnf Reflected = ()
+  rnf CaseSplit = ()
+  rnf Substitution = ()
+  rnf ExpandedPun = ()
+  rnf Generalization = ()
+
+-- | Decorating something with 'Origin' information.
+data WithOrigin a = WithOrigin
+  { woOrigin :: !Origin
+  , woThing  :: a
+  }
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+instance Decoration WithOrigin where
+  traverseF f (WithOrigin h a) = WithOrigin h <$> f a
+
+instance Pretty a => Pretty (WithOrigin a) where
+  prettyPrec p = prettyPrec p . woThing
+
+instance HasRange a => HasRange (WithOrigin a) where
+  getRange = getRange . dget
+
+instance SetRange a => SetRange (WithOrigin a) where
+  setRange = fmap . setRange
+
+instance KillRange a => KillRange (WithOrigin a) where
+  killRange = fmap killRange
+
+instance NFData a => NFData (WithOrigin a) where
+  rnf (WithOrigin _ a) = rnf a
+
+-- | A lens to access the 'Origin' attribute in data structures.
+--   Minimal implementation: @getOrigin@ and @mapOrigin@ or @LensArgInfo@.
+
+class LensOrigin a where
+
+  getOrigin :: a -> Origin
+
+  setOrigin :: Origin -> a -> a
+  setOrigin o = mapOrigin (const o)
+
+  mapOrigin :: (Origin -> Origin) -> a -> a
+
+  default getOrigin :: LensArgInfo a => a -> Origin
+  getOrigin = argInfoOrigin . getArgInfo
+
+  default mapOrigin :: LensArgInfo a => (Origin -> Origin) -> a -> a
+  mapOrigin f = mapArgInfo $ \ ai -> ai { argInfoOrigin = f $ argInfoOrigin ai }
+
+instance LensOrigin Origin where
+  getOrigin = id
+  setOrigin = const
+  mapOrigin = id
+
+instance LensOrigin (WithOrigin a) where
+  getOrigin   (WithOrigin h _) = h
+  setOrigin h (WithOrigin _ a) = WithOrigin h a
+  mapOrigin f (WithOrigin h a) = WithOrigin (f h) a
+
+-----------------------------------------------------------------------------
+-- * Free variable annotations
+-----------------------------------------------------------------------------
+
+data FreeVariables = UnknownFVs | KnownFVs IntSet
+  deriving (Eq, Ord, Show)
+
+instance Semigroup FreeVariables where
+  UnknownFVs   <> _            = UnknownFVs
+  _            <> UnknownFVs   = UnknownFVs
+  KnownFVs vs1 <> KnownFVs vs2 = KnownFVs (IntSet.union vs1 vs2)
+
+instance Monoid FreeVariables where
+  mempty  = KnownFVs IntSet.empty
+  mappend = (<>)
+
+instance KillRange FreeVariables where
+  killRange = id
+
+instance NFData FreeVariables where
+  rnf UnknownFVs    = ()
+  rnf (KnownFVs fv) = rnf fv
+
+unknownFreeVariables :: FreeVariables
+unknownFreeVariables = UnknownFVs
+
+noFreeVariables :: FreeVariables
+noFreeVariables = mempty
+
+oneFreeVariable :: Int -> FreeVariables
+oneFreeVariable = KnownFVs . IntSet.singleton
+
+freeVariablesFromList :: [Int] -> FreeVariables
+freeVariablesFromList = mconcat . map oneFreeVariable
+
+-- | A lens to access the 'FreeVariables' attribute in data structures.
+--   Minimal implementation: @getFreeVariables@ and @mapFreeVariables@ or @LensArgInfo@.
+class LensFreeVariables a where
+
+  getFreeVariables :: a -> FreeVariables
+
+  setFreeVariables :: FreeVariables -> a -> a
+  setFreeVariables o = mapFreeVariables (const o)
+
+  mapFreeVariables :: (FreeVariables -> FreeVariables) -> a -> a
+
+  default getFreeVariables :: LensArgInfo a => a -> FreeVariables
+  getFreeVariables = argInfoFreeVariables . getArgInfo
+
+  default mapFreeVariables :: LensArgInfo a => (FreeVariables -> FreeVariables) -> a -> a
+  mapFreeVariables f = mapArgInfo $ \ ai -> ai { argInfoFreeVariables = f $ argInfoFreeVariables ai }
+
+instance LensFreeVariables FreeVariables where
+  getFreeVariables = id
+  setFreeVariables = const
+  mapFreeVariables = id
+
+hasNoFreeVariables :: LensFreeVariables a => a -> Bool
+hasNoFreeVariables x =
+  case getFreeVariables x of
+    UnknownFVs  -> False
+    KnownFVs fv -> IntSet.null fv
+
+---------------------------------------------------------------------------
+-- * Argument decoration
+---------------------------------------------------------------------------
+
+-- | A function argument can be hidden and/or irrelevant.
+
+data ArgInfo = ArgInfo
+  { argInfoHiding        :: Hiding
+  , argInfoModality      :: Modality
+  , argInfoOrigin        :: Origin
+  , argInfoFreeVariables :: FreeVariables
+  , argInfoAnnotation    :: Annotation
+    -- ^ Sometimes we want a different kind of binder/pi-type, without it
+    --   supporting any of the @Modality@ interface.
+  } deriving (Eq, Ord, Show)
+
+instance HasRange ArgInfo where
+  getRange (ArgInfo h m o _fv a) = getRange (h, m, o, a)
+
+instance KillRange ArgInfo where
+  killRange (ArgInfo h m o fv a) = killRangeN ArgInfo h m o fv a
+
+class LensArgInfo a where
+  getArgInfo :: a -> ArgInfo
+  setArgInfo :: ArgInfo -> a -> a
+  setArgInfo ai = mapArgInfo (const ai)
+  mapArgInfo :: (ArgInfo -> ArgInfo) -> a -> a
+  mapArgInfo f a = setArgInfo (f $ getArgInfo a) a
+
+instance LensArgInfo ArgInfo where
+  getArgInfo = id
+  setArgInfo = const
+  mapArgInfo = id
+
+instance NFData ArgInfo where
+  rnf (ArgInfo a b c d e) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d `seq` rnf e
+
+instance LensHiding ArgInfo where
+  getHiding = argInfoHiding
+  setHiding h ai = ai { argInfoHiding = h }
+  mapHiding f ai = ai { argInfoHiding = f (argInfoHiding ai) }
+
+instance LensModality ArgInfo where
+  getModality = argInfoModality
+  setModality m ai = ai { argInfoModality = m }
+  mapModality f ai = ai { argInfoModality = f (argInfoModality ai) }
+
+instance LensOrigin ArgInfo where
+  getOrigin = argInfoOrigin
+  setOrigin o ai = ai { argInfoOrigin = o }
+  mapOrigin f ai = ai { argInfoOrigin = f (argInfoOrigin ai) }
+
+instance LensFreeVariables ArgInfo where
+  getFreeVariables = argInfoFreeVariables
+  setFreeVariables o ai = ai { argInfoFreeVariables = o }
+  mapFreeVariables f ai = ai { argInfoFreeVariables = f (argInfoFreeVariables ai) }
+
+instance LensAnnotation ArgInfo where
+  getAnnotation = argInfoAnnotation
+  setAnnotation m ai = ai { argInfoAnnotation = m }
+  mapAnnotation f ai = ai { argInfoAnnotation = f (argInfoAnnotation ai) }
+
+-- inherited instances
+
+instance LensRelevance ArgInfo where
+  getRelevance = getRelevanceMod
+  setRelevance = setRelevanceMod
+  mapRelevance = mapRelevanceMod
+
+instance LensQuantity ArgInfo where
+  getQuantity = getQuantityMod
+  setQuantity = setQuantityMod
+  mapQuantity = mapQuantityMod
+
+instance LensCohesion ArgInfo where
+  getCohesion = getCohesionMod
+  setCohesion = setCohesionMod
+  mapCohesion = mapCohesionMod
+
+defaultArgInfo :: ArgInfo
+defaultArgInfo =  ArgInfo
+  { argInfoHiding        = NotHidden
+  , argInfoModality      = defaultModality
+  , argInfoOrigin        = UserWritten
+  , argInfoFreeVariables = UnknownFVs
+  , argInfoAnnotation    = defaultAnnotation
+  }
+
+-- Accessing through ArgInfo
+
+-- default accessors for Hiding
+
+getHidingArgInfo :: LensArgInfo a => LensGet a Hiding
+getHidingArgInfo = getHiding . getArgInfo
+
+setHidingArgInfo :: LensArgInfo a => LensSet a Hiding
+setHidingArgInfo = mapArgInfo . setHiding
+
+mapHidingArgInfo :: LensArgInfo a => LensMap a Hiding
+mapHidingArgInfo = mapArgInfo . mapHiding
+
+-- default accessors for Modality
+
+getModalityArgInfo :: LensArgInfo a => LensGet a Modality
+getModalityArgInfo = getModality . getArgInfo
+
+setModalityArgInfo :: LensArgInfo a => LensSet a Modality
+setModalityArgInfo = mapArgInfo . setModality
+
+mapModalityArgInfo :: LensArgInfo a => LensMap a Modality
+mapModalityArgInfo = mapArgInfo . mapModality
+
+-- default accessors for Origin
+
+getOriginArgInfo :: LensArgInfo a => LensGet a Origin
+getOriginArgInfo = getOrigin . getArgInfo
+
+setOriginArgInfo :: LensArgInfo a => LensSet a Origin
+setOriginArgInfo = mapArgInfo . setOrigin
+
+mapOriginArgInfo :: LensArgInfo a => LensMap a Origin
+mapOriginArgInfo = mapArgInfo . mapOrigin
+
+-- default accessors for FreeVariables
+
+getFreeVariablesArgInfo :: LensArgInfo a => LensGet a FreeVariables
+getFreeVariablesArgInfo = getFreeVariables . getArgInfo
+
+setFreeVariablesArgInfo :: LensArgInfo a => LensSet a FreeVariables
+setFreeVariablesArgInfo = mapArgInfo . setFreeVariables
+
+mapFreeVariablesArgInfo :: LensArgInfo a => LensMap a FreeVariables
+mapFreeVariablesArgInfo = mapArgInfo . mapFreeVariables
+
+-- inserted hidden arguments
+
+isInsertedHidden :: (LensHiding a, LensOrigin a) => a -> Bool
+isInsertedHidden a = getHiding a == Hidden && getOrigin a == Inserted
+
+---------------------------------------------------------------------------
+-- * Arguments
+---------------------------------------------------------------------------
+
+data Arg e  = Arg
+  { argInfo :: ArgInfo
+  , unArg :: e
+  } deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+instance Decoration Arg where
+  traverseF f (Arg ai a) = Arg ai <$> f a
+
+instance HasRange a => HasRange (Arg a) where
+    getRange = getRange . unArg
+
+instance SetRange a => SetRange (Arg a) where
+  setRange r = fmap $ setRange r
+
+instance KillRange a => KillRange (Arg a) where
+  killRange (Arg info a) = killRangeN Arg info a
+
+-- Andreas, 2019-07-05, issue #3889
+-- A dedicated equality for with-abstraction now exists,
+-- thus, we can use intensional equality for Arg.
+--
+-- -- | Ignores 'Quantity', 'Relevance', 'Origin', and 'FreeVariables'.
+-- --   Ignores content of argument if 'Irrelevant'.
+-- --
+-- instance Eq a => Eq (Arg a) where
+--   Arg (ArgInfo h1 m1 _ _) x1 == Arg (ArgInfo h2 m2 _ _) x2 =
+--     h1 == h2 && (isIrrelevant m1 || isIrrelevant m2 || x1 == x2)
+--     -- Andreas, 2017-10-04, issue #2775, ignore irrelevant arguments during with-abstraction.
+--     -- This is a hack, we should not use '(==)' in with-abstraction
+--     -- and more generally not use it on Syntax.
+--     -- Andrea: except for caching.
+
+-- instance Show a => Show (Arg a) where
+--     show (Arg (ArgInfo h (Modality r q) o fv) a) = showFVs fv $ showQ q $ showR r $ showO o $ showH h $ show a
+--       where
+--         showH Hidden       s = "{" ++ s ++ "}"
+--         showH NotHidden    s = "(" ++ s ++ ")"
+--         showH (Instance o) s = showOv o ++ "{{" ++ s ++ "}}"
+--           where showOv YesOverlap = "overlap "
+--                 showOv NoOverlap  = ""
+--         showR r s = case r of
+--           Irrelevant   -> "." ++ s
+--           NonStrict    -> "?" ++ s
+--           Relevant     -> "r" ++ s -- Andreas: I want to see it explicitly
+--         showQ q s = case q of
+--           Quantity0   -> "0" ++ s
+--           Quantity1   -> "1" ++ s
+--           Quantityω   -> "ω" ++ s
+--         showO o s = case o of
+--           UserWritten -> "u" ++ s
+--           Inserted    -> "i" ++ s
+--           Reflected   -> "g" ++ s -- generated by reflection
+--           CaseSplit   -> "c" ++ s -- generated by case split
+--           Substitution -> "s" ++ s
+--         showFVs UnknownFVs    s = s
+--         showFVs (KnownFVs fv) s = "fv" ++ show (IntSet.toList fv) ++ s
+
+-- -- defined in Concrete.Pretty
+-- instance Pretty a => Pretty (Arg a) where
+--     pretty (Arg (ArgInfo h (Modality r q) o fv) a) = prettyFVs fv $ prettyQ q $ prettyR r $ prettyO o $ prettyH h $ pretty a
+--       where
+--         prettyH Hidden       s = "{" <> s <> "}"
+--         prettyH NotHidden    s = "(" <> s <> ")"
+--         prettyH (Instance o) s = prettyOv o <> "{{" <> s <> "}}"
+--           where prettyOv YesOverlap = "overlap "
+--                 prettyOv NoOverlap  = ""
+--         prettyR r s = case r of
+--           Irrelevant   -> "." <> s
+--           NonStrict    -> "?" <> s
+--           Relevant     -> "r" <> s -- Andreas: I want to see it explicitly
+--         prettyQ q s = case q of
+--           Quantity0   -> "0" <> s
+--           Quantity1   -> "1" <> s
+--           Quantityω   -> "ω" <> s
+--         prettyO o s = case o of
+--           UserWritten -> "u" <> s
+--           Inserted    -> "i" <> s
+--           Reflected   -> "g" <> s -- generated by reflection
+--           CaseSplit   -> "c" <> s -- generated by case split
+--           Substitution -> "s" <> s
+--         prettyFVs UnknownFVs    s = s
+--         prettyFVs (KnownFVs fv) s = "fv" <> pretty (IntSet.toList fv) <> s
+
+instance NFData e => NFData (Arg e) where
+  rnf (Arg a b) = rnf a `seq` rnf b
+
+instance LensArgInfo (Arg a) where
+  getArgInfo        = argInfo
+  setArgInfo ai arg = arg { argInfo = ai }
+  mapArgInfo f arg  = arg { argInfo = f $ argInfo arg }
+
+-- The other lenses are defined through LensArgInfo
+
+instance LensHiding (Arg e) where
+  getHiding = getHidingArgInfo
+  setHiding = setHidingArgInfo
+  mapHiding = mapHidingArgInfo
+
+instance LensModality (Arg e) where
+  getModality = getModalityArgInfo
+  setModality = setModalityArgInfo
+  mapModality = mapModalityArgInfo
+
+instance LensOrigin (Arg e) where
+  getOrigin = getOriginArgInfo
+  setOrigin = setOriginArgInfo
+  mapOrigin = mapOriginArgInfo
+
+instance LensFreeVariables (Arg e) where
+  getFreeVariables = getFreeVariablesArgInfo
+  setFreeVariables = setFreeVariablesArgInfo
+  mapFreeVariables = mapFreeVariablesArgInfo
+
+-- Since we have LensModality, we get relevance and quantity by default
+
+instance LensRelevance (Arg e) where
+  getRelevance = getRelevanceMod
+  setRelevance = setRelevanceMod
+  mapRelevance = mapRelevanceMod
+
+instance LensQuantity (Arg e) where
+  getQuantity = getQuantityMod
+  setQuantity = setQuantityMod
+  mapQuantity = mapQuantityMod
+
+instance LensCohesion (Arg e) where
+  getCohesion = getCohesionMod
+  setCohesion = setCohesionMod
+  mapCohesion = mapCohesionMod
+
+defaultArg :: a -> Arg a
+defaultArg = Arg defaultArgInfo
+
+-- | @xs \`withArgsFrom\` args@ translates @xs@ into a list of 'Arg's,
+-- using the elements in @args@ to fill in the non-'unArg' fields.
+--
+-- Precondition: The two lists should have equal length.
+
+withArgsFrom :: [a] -> [Arg b] -> [Arg a]
+xs `withArgsFrom` args =
+  zipWith (\x arg -> fmap (const x) arg) xs args
+
+withNamedArgsFrom :: [a] -> [NamedArg b] -> [NamedArg a]
+xs `withNamedArgsFrom` args =
+  zipWith (\x -> fmap (x <$)) xs args
+
+---------------------------------------------------------------------------
+-- * Names
+---------------------------------------------------------------------------
+
+class Eq a => Underscore a where
+  underscore   :: a
+  isUnderscore :: a -> Bool
+  isUnderscore = (== underscore)
+
+instance Underscore String where
+  underscore = "_"
+
+instance Underscore ByteString where
+  underscore = ByteString.pack underscore
+
+instance Underscore Doc where
+  underscore = text underscore
+
+---------------------------------------------------------------------------
+-- * Named arguments
+---------------------------------------------------------------------------
+
+-- | Something potentially carrying a name.
+data Named name a =
+    Named { nameOf     :: Maybe name
+          , namedThing :: a
+          }
+    deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+-- | Standard naming.
+type Named_ = Named NamedName
+
+-- | Standard argument names.
+type NamedName = WithOrigin (Ranged ArgName)
+
+-- | Equality of argument names of things modulo 'Range' and 'Origin'.
+sameName :: NamedName -> NamedName -> Bool
+sameName = (==) `on` (rangedThing . woThing)
+
+unnamed :: a -> Named name a
+unnamed = Named Nothing
+
+isUnnamed :: Named name a -> Maybe a
+isUnnamed = \case
+  Named Nothing a -> Just a
+  Named Just{}  a -> Nothing
+
+named :: name -> a -> Named name a
+named = Named . Just
+
+userNamed :: Ranged ArgName -> a -> Named_ a
+userNamed = Named . Just . WithOrigin UserWritten
+
+-- | Accessor/editor for the 'nameOf' component.
+class LensNamed a where
+  -- | The type of the name
+  type NameOf a
+  lensNamed :: Lens' a (Maybe (NameOf a))
+
+  -- Lenses lift through decorations:
+  default lensNamed :: (Decoration f, LensNamed b, NameOf b ~ NameOf a, f b ~ a) => Lens' a (Maybe (NameOf a))
+  lensNamed = traverseF . lensNamed
+
+instance LensNamed a => LensNamed (Arg a) where
+  type NameOf (Arg a) = NameOf a
+
+instance LensNamed (Maybe a) where
+  type NameOf (Maybe a) = a
+  lensNamed = id
+
+instance LensNamed (Named name a) where
+  type NameOf (Named name a) = name
+
+  lensNamed f (Named mn a) = f mn <&> \ mn' -> Named mn' a
+
+getNameOf :: LensNamed a => a -> Maybe (NameOf a)
+getNameOf a = a ^. lensNamed
+
+setNameOf :: LensNamed a => Maybe (NameOf a) -> a -> a
+setNameOf = set lensNamed
+
+mapNameOf :: LensNamed a => (Maybe (NameOf a) -> Maybe (NameOf a)) -> a -> a
+mapNameOf = over lensNamed
+bareNameOf :: (LensNamed a, NameOf a ~ NamedName) => a -> Maybe ArgName
+bareNameOf a = rangedThing . woThing <$> getNameOf a
+
+bareNameWithDefault :: (LensNamed a, NameOf a ~ NamedName) => ArgName -> a -> ArgName
+bareNameWithDefault x a = maybe x (rangedThing . woThing) $ getNameOf a
+
+-- | Equality of argument names of things modulo 'Range' and 'Origin'.
+namedSame :: (LensNamed a, LensNamed b, NameOf a ~ NamedName, NameOf b ~ NamedName) => a -> b -> Bool
+namedSame a b = case (getNameOf a, getNameOf b) of
+  (Nothing, Nothing) -> True
+  (Just x , Just y ) -> sameName x y
+  _ -> False
+
+-- | Does an argument @arg@ fit the shape @dom@ of the next expected argument?
+--
+--   The hiding has to match, and if the argument has a name, it should match
+--   the name of the domain.
+--
+--   'Nothing' should be '__IMPOSSIBLE__', so use as
+--   @@
+--     fromMaybe __IMPOSSIBLE__ $ fittingNamedArg arg dom
+--   @@
+--
+fittingNamedArg
+  :: ( LensNamed arg, NameOf arg ~ NamedName, LensHiding arg
+     , LensNamed dom, NameOf dom ~ NamedName, LensHiding dom )
+  => arg -> dom -> Maybe Bool
+fittingNamedArg arg dom
+    | not $ sameHiding arg dom = no
+    | visible arg              = yes
+    | otherwise =
+        caseMaybe (bareNameOf arg) yes        $ \ x ->
+        caseMaybe (bareNameOf dom) impossible $ \ y ->
+        return $ x == y
+  where
+    yes = return True
+    no  = return False
+    impossible = Nothing
+
+-- Standard instances for 'Named':
+
+instance Decoration (Named name) where
+  traverseF f (Named n a) = Named n <$> f a
+
+instance HasRange a => HasRange (Named name a) where
+    getRange = getRange . namedThing
+
+instance SetRange a => SetRange (Named name a) where
+  setRange r = fmap $ setRange r
+
+instance (KillRange name, KillRange a) => KillRange (Named name a) where
+  killRange (Named n a) = Named (killRange n) (killRange a)
+
+-- instance Show a => Show (Named_ a) where
+--     show (Named Nothing a)  = show a
+--     show (Named (Just n) a) = rawNameToString (rangedThing n) ++ " = " ++ show a
+
+-- -- Defined in Concrete.Pretty
+-- instance Pretty a => Pretty (Named_ a) where
+--     pretty (Named Nothing a)  = pretty a
+--     pretty (Named (Just n) a) = text (rawNameToString (rangedThing n)) <+> "=" <+> pretty a
+
+instance (NFData name, NFData a) => NFData (Named name a) where
+  rnf (Named a b) = rnf a `seq` rnf b
+
+-- | Only 'Hidden' arguments can have names.
+type NamedArg a = Arg (Named_ a)
+
+-- | Get the content of a 'NamedArg'.
+namedArg :: NamedArg a -> a
+namedArg = namedThing . unArg
+
+defaultNamedArg :: a -> NamedArg a
+defaultNamedArg = unnamedArg defaultArgInfo
+
+unnamedArg :: ArgInfo -> a -> NamedArg a
+unnamedArg info = Arg info . unnamed
+
+-- | The functor instance for 'NamedArg' would be ambiguous,
+--   so we give it another name here.
+updateNamedArg :: (a -> b) -> NamedArg a -> NamedArg b
+updateNamedArg = fmap . fmap
+
+updateNamedArgA :: Applicative f => (a -> f b) -> NamedArg a -> f (NamedArg b)
+updateNamedArgA = traverse . traverse
+
+-- | @setNamedArg a b = updateNamedArg (const b) a@
+setNamedArg :: NamedArg a -> b -> NamedArg b
+setNamedArg a b = (b <$) <$> a
+
+-- ** ArgName
+
+-- | Names in binders and arguments.
+type ArgName = String
+
+argNameToString :: ArgName -> String
+argNameToString = id
+
+stringToArgName :: String -> ArgName
+stringToArgName = id
+
+appendArgNames :: ArgName -> ArgName -> ArgName
+appendArgNames = (++)
+
+---------------------------------------------------------------------------
+-- * Range decoration.
+---------------------------------------------------------------------------
+
+-- | Thing with range info.
+data Ranged a = Ranged
+  { rangeOf     :: Range
+  , rangedThing :: a
+  }
+  deriving (Show, Functor, Foldable, Traversable)
+
+-- | Thing with no range info.
+unranged :: a -> Ranged a
+unranged = Ranged noRange
+
+-- | Ignores range.
+instance Pretty a => Pretty (Ranged a) where
+  pretty = pretty . rangedThing
+
+-- | Ignores range.
+instance Eq a => Eq (Ranged a) where
+  (==) = (==) `on` rangedThing
+
+-- | Ignores range.
+instance Ord a => Ord (Ranged a) where
+  compare = compare `on` rangedThing
+
+instance HasRange (Ranged a) where
+  getRange = rangeOf
+
+instance KillRange (Ranged a) where
+  killRange (Ranged _ x) = Ranged noRange x
+
+instance Decoration Ranged where
+  traverseF f (Ranged r x) = Ranged r <$> f x
+
+-- | Ranges are not forced.
+
+instance NFData a => NFData (Ranged a) where
+  rnf (Ranged _ a) = rnf a
+
+---------------------------------------------------------------------------
+-- * Raw names (before parsing into name parts).
+---------------------------------------------------------------------------
+
+-- | A @RawName@ is some sort of string.
+type RawName = String
+
+rawNameToString :: RawName -> String
+rawNameToString = id
+
+stringToRawName :: String -> RawName
+stringToRawName = id
+
+-- | String with range info.
+type RString = Ranged RawName
+
+---------------------------------------------------------------------------
+-- * Further constructor and projection info
+---------------------------------------------------------------------------
+
+-- | Where does the 'ConP' or 'Con' come from?
+data ConOrigin
+  = ConOSystem  -- ^ Inserted by system or expanded from an implicit pattern.
+  | ConOCon     -- ^ User wrote a constructor (pattern).
+  | ConORec     -- ^ User wrote a record (pattern).
+  | ConOSplit   -- ^ Generated by interactive case splitting.
+  deriving (Show, Eq, Ord, Enum, Bounded, Generic)
+
+instance NFData ConOrigin
+
+instance KillRange ConOrigin where
+  killRange = id
+
+-- | Prefer user-written over system-inserted.
+bestConInfo :: ConOrigin -> ConOrigin -> ConOrigin
+bestConInfo ConOSystem o = o
+bestConInfo o _ = o
+
+-- | Where does a projection come from?
+data ProjOrigin
+  = ProjPrefix    -- ^ User wrote a prefix projection.
+  | ProjPostfix   -- ^ User wrote a postfix projection.
+  | ProjSystem    -- ^ Projection was generated by the system.
+  deriving (Show, Eq, Ord, Enum, Bounded, Generic)
+
+instance NFData ProjOrigin
+
+instance KillRange ProjOrigin where
+  killRange = id
+
+---------------------------------------------------------------------------
+-- * Infixity, access, abstract, etc.
+---------------------------------------------------------------------------
+
+-- | Functions can be defined in both infix and prefix style. See
+--   'Agda.Syntax.Concrete.LHS'.
+data IsInfix = InfixDef | PrefixDef
+    deriving (Show, Eq, Ord)
+
+-- ** private blocks, public imports
+
+-- | Access modifier.
+data Access
+  = PrivateAccess Origin
+      -- ^ Store the 'Origin' of the private block that lead to this qualifier.
+      --   This is needed for more faithful printing of declarations.
+  | PublicAccess
+    deriving (Show, Eq, Ord)
+
+instance Pretty Access where
+  pretty = text . \case
+    PrivateAccess _ -> "private"
+    PublicAccess    -> "public"
+
+instance NFData Access where
+  rnf _ = ()
+
+instance HasRange Access where
+  getRange _ = noRange
+
+instance KillRange Access where
+  killRange = id
+
+-- ** abstract blocks
+
+-- | Abstract or concrete.
+data IsAbstract = AbstractDef | ConcreteDef
+    deriving (Show, Eq, Ord, Generic)
+
+-- | Semigroup computes if any of several is an 'AbstractDef'.
+instance Semigroup IsAbstract where
+  AbstractDef <> _ = AbstractDef
+  ConcreteDef <> a = a
+
+-- | Default is 'ConcreteDef'.
+instance Monoid IsAbstract where
+  mempty  = ConcreteDef
+  mappend = (<>)
+
+instance KillRange IsAbstract where
+  killRange = id
+
+instance NFData IsAbstract
+
+class LensIsAbstract a where
+  lensIsAbstract :: Lens' a IsAbstract
+
+instance LensIsAbstract IsAbstract where
+  lensIsAbstract = id
+
+-- | Is any element of a collection an 'AbstractDef'.
+class AnyIsAbstract a where
+  anyIsAbstract :: a -> IsAbstract
+
+  default anyIsAbstract :: (Foldable t, AnyIsAbstract b, t b ~ a) => a -> IsAbstract
+  anyIsAbstract = Fold.foldMap anyIsAbstract
+
+instance AnyIsAbstract IsAbstract where
+  anyIsAbstract = id
+
+instance AnyIsAbstract a => AnyIsAbstract [a] where
+instance AnyIsAbstract a => AnyIsAbstract (Maybe a) where
+
+-- ** instance blocks
+
+-- | Is this definition eligible for instance search?
+data IsInstance
+  = InstanceDef Range  -- ^ Range of the @instance@ keyword.
+  | NotInstanceDef
+    deriving (Show, Eq, Ord)
+
+instance KillRange IsInstance where
+  killRange = \case
+    InstanceDef _    -> InstanceDef noRange
+    i@NotInstanceDef -> i
+
+instance HasRange IsInstance where
+  getRange = \case
+    InstanceDef r  -> r
+    NotInstanceDef -> noRange
+
+instance NFData IsInstance where
+  rnf (InstanceDef _) = ()
+  rnf NotInstanceDef  = ()
+
+-- ** macro blocks
+
+-- | Is this a macro definition?
+data IsMacro = MacroDef | NotMacroDef
+  deriving (Show, Eq, Ord, Generic)
+
+instance KillRange IsMacro where killRange = id
+instance HasRange  IsMacro where getRange _ = noRange
+
+instance NFData IsMacro
+
+-- ** opaque blocks
+
+-- | Opaque or transparent.
+data IsOpaque
+  = OpaqueDef {-# UNPACK #-} !OpaqueId
+    -- ^ This definition is opaque, and it is guarded by the given
+    -- opaque block.
+  | TransparentDef
+  deriving (Show, Eq, Ord, Generic)
+
+instance KillRange IsOpaque where
+  killRange = id
+
+instance NFData IsOpaque
+
+class LensIsOpaque a where
+  lensIsOpaque :: Lens' a IsOpaque
+
+instance LensIsOpaque IsOpaque where
+  lensIsOpaque = id
+
+-- | Monoid representing the combined opaque blocks of a 'Foldable'
+-- containing possibly-opaque declarations.
+data JointOpacity
+  = UniqueOpaque    {-# UNPACK #-} !OpaqueId
+  -- ^ Every definition agrees on what opaque block they belong to.
+  | DifferentOpaque !(HashSet OpaqueId)
+  -- ^ More than one opaque block was found.
+  | NoOpaque
+  -- ^ Nothing here is opaque.
+
+instance Semigroup JointOpacity where
+  UniqueOpaque i <> UniqueOpaque j
+    | i == j    = UniqueOpaque i
+    | otherwise = DifferentOpaque (HashSet.fromList [i, j])
+
+  DifferentOpaque is <> UniqueOpaque j     = DifferentOpaque (HashSet.insert j is)
+  UniqueOpaque i     <> DifferentOpaque js = DifferentOpaque (HashSet.insert i js)
+  DifferentOpaque is <> DifferentOpaque js = DifferentOpaque (HashSet.union is js)
+
+  NoOpaque <> x = x
+  x <> NoOpaque = x
+
+instance Monoid JointOpacity where
+  mappend = (<>)
+  mempty = NoOpaque
+
+class AllAreOpaque a where
+  jointOpacity :: a -> JointOpacity
+
+  default jointOpacity :: (Foldable t, AllAreOpaque b, t b ~ a) => a -> JointOpacity
+  jointOpacity = Fold.foldMap jointOpacity
+
+instance AllAreOpaque IsOpaque where
+  jointOpacity = \case
+    TransparentDef -> NoOpaque
+    OpaqueDef i    -> UniqueOpaque i
+
+instance AllAreOpaque a => AllAreOpaque [a] where
+instance AllAreOpaque a => AllAreOpaque (Maybe a) where
+
+---------------------------------------------------------------------------
+-- * NameId
+---------------------------------------------------------------------------
+
+-- | The unique identifier of a name. Second argument is the top-level module
+--   identifier.
+data NameId = NameId {-# UNPACK #-} !Word64 {-# UNPACK #-} !ModuleNameHash
+    deriving (Eq, Ord, Generic, Show)
+
+instance KillRange NameId where
+  killRange = id
+
+instance Pretty NameId where
+  pretty (NameId n m) = text $ show n ++ "@" ++ show m
+
+instance Enum NameId where
+  succ (NameId n m)     = NameId (n + 1) m
+  pred (NameId n m)     = NameId (n - 1) m
+  toEnum n              = __IMPOSSIBLE__  -- should not be used
+  fromEnum (NameId n _) = fromIntegral n
+
+instance NFData NameId where
+  rnf (NameId _ _) = ()
+
+instance Hashable NameId where
+  {-# INLINE hashWithSalt #-}
+  hashWithSalt salt (NameId n (ModuleNameHash m)) = hashWithSalt salt (n, m)
+
+---------------------------------------------------------------------------
+-- * Meta variables
+---------------------------------------------------------------------------
+
+-- | Meta-variable identifiers use the same structure as 'NameId's.
+
+data MetaId = MetaId
+  { metaId     :: {-# UNPACK #-} !Word64
+  , metaModule :: {-# UNPACK #-} !ModuleNameHash
+  }
+  deriving (Eq, Ord, Generic)
+
+instance Pretty MetaId where
+  pretty (MetaId n m) =
+    text $ "_" ++ show n ++ "@" ++ show (moduleNameHash m)
+
+instance Enum MetaId where
+  succ MetaId{..} = MetaId { metaId = succ metaId, .. }
+  pred MetaId{..} = MetaId { metaId = pred metaId, .. }
+
+  -- The following functions should not be used.
+  toEnum   = __IMPOSSIBLE__
+  fromEnum = __IMPOSSIBLE__
+
+-- | The record selectors are not included in the resulting strings.
+
+instance Show MetaId where
+  showsPrec p (MetaId n m) = showParen (p > 0) $
+    showString "MetaId " .
+    showsPrec 11 n .
+    showString " " .
+    showsPrec 11 m
+
+instance NFData MetaId where
+  rnf (MetaId x y) = rnf x `seq` rnf y
+
+instance Hashable MetaId where
+  {-# INLINE hashWithSalt #-}
+  hashWithSalt salt (MetaId n m) = hashWithSalt salt (n, m)
+
+newtype Constr a = Constr a
+
+-----------------------------------------------------------------------------
+-- * Problems
+-----------------------------------------------------------------------------
+
+-- | A "problem" consists of a set of constraints and the same constraint can be part of multiple
+--   problems.
+newtype ProblemId = ProblemId Nat
+  deriving (Eq, Ord, Enum, Real, Integral, Num, NFData)
+
+-- This particular Show instance is ok because of the Num instance.
+instance Show   ProblemId where show   (ProblemId n) = show n
+instance Pretty ProblemId where pretty (ProblemId n) = pretty n
+
+-- | The unique identifier of an opaque block. Second argument is the
+-- top-level module identifier.
+data OpaqueId = OpaqueId {-# UNPACK #-} !Word64 {-# UNPACK #-} !ModuleNameHash
+    deriving (Eq, Ord, Generic, Show)
+
+instance KillRange OpaqueId where
+  killRange = id
+
+instance Pretty OpaqueId where
+  pretty (OpaqueId n m) = text $ show n ++ "@" ++ show m
+
+instance Enum OpaqueId where
+  succ (OpaqueId n m)     = OpaqueId (n + 1) m
+  pred (OpaqueId n m)     = OpaqueId (n - 1) m
+  toEnum n                = __IMPOSSIBLE__  -- should not be used
+  fromEnum (OpaqueId n _) = fromIntegral n
+
+instance NFData OpaqueId where
+  rnf (OpaqueId _ _) = ()
+
+instance Hashable OpaqueId where
+  {-# INLINE hashWithSalt #-}
+  hashWithSalt salt (OpaqueId n (ModuleNameHash m)) = hashWithSalt salt (n, m)
+
+------------------------------------------------------------------------
+-- * Placeholders (used to parse sections)
+------------------------------------------------------------------------
+
+-- | The position of a name part or underscore in a name.
+
+data PositionInName
+  = Beginning
+    -- ^ The following underscore is at the beginning of the name:
+    -- @_foo@.
+  | Middle
+    -- ^ The following underscore is in the middle of the name:
+    -- @foo_bar@.
+  | End
+    -- ^ The following underscore is at the end of the name: @foo_@.
+  deriving (Show, Eq, Ord)
+
+-- | Placeholders are used to represent the underscores in a section.
+
+data MaybePlaceholder e
+  = Placeholder !PositionInName
+  | NoPlaceholder !(Strict.Maybe PositionInName) e
+    -- ^ The second argument is used only (but not always) for name
+    -- parts other than underscores.
+  deriving (Eq, Ord, Functor, Foldable, Traversable, Show)
+
+-- | An abbreviation: @noPlaceholder = 'NoPlaceholder'
+-- 'Strict.Nothing'@.
+
+noPlaceholder :: e -> MaybePlaceholder e
+noPlaceholder = NoPlaceholder Strict.Nothing
+
+instance HasRange a => HasRange (MaybePlaceholder a) where
+  getRange Placeholder{}       = noRange
+  getRange (NoPlaceholder _ e) = getRange e
+
+instance KillRange a => KillRange (MaybePlaceholder a) where
+  killRange p@Placeholder{}     = p
+  killRange (NoPlaceholder p e) = killRangeN (NoPlaceholder p) e
+
+instance NFData a => NFData (MaybePlaceholder a) where
+  rnf (Placeholder _)     = ()
+  rnf (NoPlaceholder _ a) = rnf a
+
+---------------------------------------------------------------------------
+-- * Interaction meta variables
+---------------------------------------------------------------------------
+
+newtype InteractionId = InteractionId { interactionId :: Nat }
+    deriving ( Eq
+             , Ord
+             , Show
+             , Num
+             , Integral
+             , Real
+             , Enum
+             , NFData
+             )
+
+instance Pretty InteractionId where
+    pretty (InteractionId i) = text $ "?" ++ show i
+
+instance KillRange InteractionId where killRange = id
+
+---------------------------------------------------------------------------
+-- * Fixity
+---------------------------------------------------------------------------
+
+-- | Precedence levels for operators.
+
+type PrecedenceLevel = Double
+
+data FixityLevel
+  = Unrelated
+    -- ^ No fixity declared.
+  | Related !PrecedenceLevel
+    -- ^ Fixity level declared as the number.
+  deriving (Eq, Ord, Show)
+
+instance Null FixityLevel where
+  null Unrelated = True
+  null Related{} = False
+  empty = Unrelated
+
+instance NFData FixityLevel where
+  rnf Unrelated   = ()
+  rnf (Related _) = ()
+
+-- | Associativity.
+
+data Associativity = NonAssoc | LeftAssoc | RightAssoc
+   deriving (Eq, Ord, Show)
+
+-- | Fixity of operators.
+
+data Fixity = Fixity
+  { fixityRange :: Range
+    -- ^ Range of the whole fixity declaration.
+  , fixityLevel :: !FixityLevel
+  , fixityAssoc :: !Associativity
+  }
+  deriving Show
+
+noFixity :: Fixity
+noFixity = Fixity noRange Unrelated NonAssoc
+
+defaultFixity :: Fixity
+defaultFixity = Fixity noRange (Related 20) NonAssoc
+
+-- For @instance Pretty Fixity@, see Agda.Syntax.Concrete.Pretty
+
+instance Eq Fixity where
+  f1 == f2 = compare f1 f2 == EQ
+
+instance Ord Fixity where
+  compare = compare `on` (fixityLevel &&& fixityAssoc)
+
+instance Null Fixity where
+  null  = null . fixityLevel
+  empty = noFixity
+
+instance HasRange Fixity where
+  getRange = fixityRange
+
+instance KillRange Fixity where
+  killRange f = f { fixityRange = noRange }
+
+instance NFData Fixity where
+  rnf (Fixity _ _ _) = ()     -- Ranges are not forced, the other fields are strict.
+
+-- * Notation coupled with 'Fixity'
+
+-- | The notation is handled as the fixity in the renamer.
+--   Hence, they are grouped together in this type.
+data Fixity' = Fixity'
+    { theFixity   :: !Fixity
+    , theNotation :: Notation
+    , theNameRange :: Range
+      -- ^ Range of the name in the fixity declaration
+      --   (used for correct highlighting, see issue #2140).
+    }
+  deriving Show
+
+noFixity' :: Fixity'
+noFixity' = Fixity' noFixity noNotation noRange
+
+instance Eq Fixity' where
+  Fixity' f n _ == Fixity' f' n' _ = f == f' && n == n'
+
+instance Null Fixity' where
+  null (Fixity' f n _) = null f && null n
+  empty = noFixity'
+
+instance NFData Fixity' where
+  rnf (Fixity' _ a _) = rnf a
+
+instance KillRange Fixity' where
+  killRange (Fixity' f n r) = killRangeN Fixity' f n r
+
+-- lenses
+
+_fixityAssoc :: Lens' Fixity Associativity
+_fixityAssoc f r = f (fixityAssoc r) <&> \x -> r { fixityAssoc = x }
+
+_fixityLevel :: Lens' Fixity FixityLevel
+_fixityLevel f r = f (fixityLevel r) <&> \x -> r { fixityLevel = x }
+
+-- Lens focusing on Fixity
+
+class LensFixity a where
+  lensFixity :: Lens' a Fixity
+
+instance LensFixity Fixity where
+  lensFixity = id
+
+instance LensFixity Fixity' where
+  lensFixity f fix' = f (theFixity fix') <&> \ fx -> fix' { theFixity = fx }
+
+-- Lens focusing on Fixity'
+
+class LensFixity' a where
+  lensFixity' :: Lens' a Fixity'
+
+instance LensFixity' Fixity' where
+  lensFixity' = id
+---------------------------------------------------------------------------
+-- * Import directive
+---------------------------------------------------------------------------
+
+-- | The things you are allowed to say when you shuffle names between name
+--   spaces (i.e. in @import@, @namespace@, or @open@ declarations).
+data ImportDirective' n m = ImportDirective
+  { importDirRange :: Range
+  , using          :: Using' n m
+  , hiding         :: HidingDirective' n m
+  , impRenaming    :: RenamingDirective' n m
+  , publicOpen     :: Maybe Range -- ^ Only for @open@. Exports the opened names from the current module.
+  }
+  deriving Eq
+
+type HidingDirective'   n m = [ImportedName' n m]
+type RenamingDirective' n m = [Renaming' n m]
+
+-- | @null@ for import directives holds when everything is imported unchanged
+--   (no names are hidden or renamed).
+instance Null (ImportDirective' n m) where
+  null = \case
+    ImportDirective _ UseEverything [] [] _ -> True
+    _ -> False
+  empty = defaultImportDir
+
+instance (HasRange n, HasRange m) => Semigroup (ImportDirective' n m) where
+  i1 <> i2 = ImportDirective
+    { importDirRange = fuseRange i1 i2
+    , using          = using i1 <> using i2
+    , hiding         = hiding i1 ++ hiding i2
+    , impRenaming    = impRenaming i1 ++ impRenaming i2
+    , publicOpen     = publicOpen i1 <|> publicOpen i2
+    }
+
+instance (HasRange n, HasRange m) => Monoid (ImportDirective' n m) where
+  mempty  = empty
+  mappend = (<>)
+
+-- | Default is directive is @private@ (use everything, but do not export).
+defaultImportDir :: ImportDirective' n m
+defaultImportDir = ImportDirective noRange UseEverything [] [] Nothing
+
+-- | @isDefaultImportDir@ implies @null@, but not the other way round.
+isDefaultImportDir :: ImportDirective' n m -> Bool
+isDefaultImportDir dir = null dir && null (publicOpen dir)
+
+-- | The @using@ clause of import directive.
+data Using' n m
+  = UseEverything              -- ^ No @using@ clause given.
+  | Using [ImportedName' n m]  -- ^ @using@ the specified names.
+  deriving Eq
+
+instance Semigroup (Using' n m) where
+  UseEverything <> u             = u
+  u             <> UseEverything = u
+  Using xs      <> Using ys      = Using (xs ++ ys)
+
+instance Monoid (Using' n m) where
+  mempty  = UseEverything
+  mappend = (<>)
+
+instance Null (Using' n m) where
+  null UseEverything = True
+  null Using{}       = False
+  empty = mempty
+
+mapUsing :: ([ImportedName' n1 m1] -> [ImportedName' n2 m2]) -> Using' n1 m1 -> Using' n2 m2
+mapUsing f = \case
+  UseEverything -> UseEverything
+  Using xs      -> Using $ f xs
+
+-- | An imported name can be a module or a defined name.
+data ImportedName' n m
+  = ImportedModule  m  -- ^ Imported module name of type @m@.
+  | ImportedName    n  -- ^ Imported name of type @n@.
+  deriving (Eq, Ord, Show)
+
+fromImportedName :: ImportedName' a a -> a
+fromImportedName = \case
+  ImportedModule x -> x
+  ImportedName   x -> x
+
+setImportedName :: ImportedName' a a -> a -> ImportedName' a a
+setImportedName (ImportedName   x) y = ImportedName   y
+setImportedName (ImportedModule x) y = ImportedModule y
+
+-- | Like 'partitionEithers'.
+partitionImportedNames :: [ImportedName' n m] -> ([n], [m])
+partitionImportedNames = flip foldr ([], []) $ \case
+  ImportedName   n -> first  (n:)
+  ImportedModule m -> second (m:)
+
+-- -- Defined in Concrete.Pretty
+-- instance (Pretty n, Pretty m) => Pretty (ImportedName' n m) where
+--   pretty (ImportedModule x) = "module" <+> pretty x
+--   pretty (ImportedName   x) = pretty x
+
+-- instance (Show n, Show m) => Show (ImportedName' n m) where
+--   show (ImportedModule x) = "module " ++ show x
+--   show (ImportedName   x) = show x
+
+data Renaming' n m = Renaming
+  { renFrom    :: ImportedName' n m
+    -- ^ Rename from this name.
+  , renTo      :: ImportedName' n m
+    -- ^ To this one.  Must be same kind as 'renFrom'.
+  , renFixity  :: Maybe Fixity
+    -- ^ New fixity of 'renTo' (optional).
+  , renToRange :: Range
+    -- ^ The range of the \"to\" keyword.  Retained for highlighting purposes.
+  }
+  deriving Eq
+
+-- ** HasRange instances
+
+instance (HasRange a, HasRange b) => HasRange (ImportDirective' a b) where
+  getRange = importDirRange
+
+instance (HasRange a, HasRange b) => HasRange (Using' a b) where
+  getRange (Using  xs) = getRange xs
+  getRange UseEverything = noRange
+
+instance (HasRange a, HasRange b) => HasRange (Renaming' a b) where
+  getRange r = getRange (renFrom r, renTo r)
+
+instance (HasRange a, HasRange b) => HasRange (ImportedName' a b) where
+  getRange (ImportedName   x) = getRange x
+  getRange (ImportedModule x) = getRange x
+
+-- ** KillRange instances
+
+instance (KillRange a, KillRange b) => KillRange (ImportDirective' a b) where
+  killRange (ImportDirective _ u h r p) =
+    killRangeN (\u h r -> ImportDirective noRange u h r p) u h r
+
+instance (KillRange a, KillRange b) => KillRange (Using' a b) where
+  killRange (Using  i) = killRangeN Using  i
+  killRange UseEverything = UseEverything
+
+instance (KillRange a, KillRange b) => KillRange (Renaming' a b) where
+  killRange (Renaming i n mf _to) = killRangeN (\ i n mf -> Renaming i n mf noRange) i n mf
+
+instance (KillRange a, KillRange b) => KillRange (ImportedName' a b) where
+  killRange (ImportedModule n) = killRangeN ImportedModule n
+  killRange (ImportedName   n) = killRangeN ImportedName   n
+
+-- ** NFData instances
+
+-- | Ranges are not forced.
+
+instance (NFData a, NFData b) => NFData (ImportDirective' a b) where
+  rnf (ImportDirective _ a b c _) = rnf a `seq` rnf b `seq` rnf c
+
+instance (NFData a, NFData b) => NFData (Using' a b) where
+  rnf UseEverything = ()
+  rnf (Using a)     = rnf a
+
+-- | Ranges are not forced.
+
+instance (NFData a, NFData b) => NFData (Renaming' a b) where
+  rnf (Renaming a b c _) = rnf a `seq` rnf b `seq` rnf c
+
+instance (NFData a, NFData b) => NFData (ImportedName' a b) where
+  rnf (ImportedModule a) = rnf a
+  rnf (ImportedName a)   = rnf a
+
+-----------------------------------------------------------------------------
+-- * Termination
+-----------------------------------------------------------------------------
+
+-- | Termination check? (Default = TerminationCheck).
+data TerminationCheck m
+  = TerminationCheck
+    -- ^ Run the termination checker.
+  | NoTerminationCheck
+    -- ^ Skip termination checking (unsafe).
+  | NonTerminating
+    -- ^ Treat as non-terminating.
+  | Terminating
+    -- ^ Treat as terminating (unsafe).  Same effect as 'NoTerminationCheck'.
+  | TerminationMeasure Range m
+    -- ^ Skip termination checking but use measure instead.
+    deriving (Show, Eq, Functor)
+
+instance KillRange m => KillRange (TerminationCheck m) where
+  killRange (TerminationMeasure _ m) = TerminationMeasure noRange (killRange m)
+  killRange t                        = t
+
+instance NFData a => NFData (TerminationCheck a) where
+  rnf TerminationCheck         = ()
+  rnf NoTerminationCheck       = ()
+  rnf NonTerminating           = ()
+  rnf Terminating              = ()
+  rnf (TerminationMeasure _ a) = rnf a
+
+-----------------------------------------------------------------------------
+-- * Positivity
+-----------------------------------------------------------------------------
+
+-- | Positivity check? (Default = True).
+data PositivityCheck = YesPositivityCheck | NoPositivityCheck
+  deriving (Eq, Ord, Show, Bounded, Enum, Generic)
+
+instance KillRange PositivityCheck where
+  killRange = id
+
+-- Semigroup and Monoid via conjunction
+instance Semigroup PositivityCheck where
+  NoPositivityCheck <> _ = NoPositivityCheck
+  _ <> NoPositivityCheck = NoPositivityCheck
+  _ <> _ = YesPositivityCheck
+
+instance Monoid PositivityCheck where
+  mempty  = YesPositivityCheck
+  mappend = (<>)
+
+instance NFData PositivityCheck
+
+-----------------------------------------------------------------------------
+-- * Universe checking
+-----------------------------------------------------------------------------
+
+-- | Universe check? (Default is yes).
+data UniverseCheck = YesUniverseCheck | NoUniverseCheck
+  deriving (Eq, Ord, Show, Bounded, Enum, Generic)
+
+instance KillRange UniverseCheck where
+  killRange = id
+
+instance NFData UniverseCheck
+
+-----------------------------------------------------------------------------
+-- * Universe checking
+-----------------------------------------------------------------------------
+
+-- | Coverage check? (Default is yes).
+data CoverageCheck = YesCoverageCheck | NoCoverageCheck
+  deriving (Eq, Ord, Show, Bounded, Enum, Generic)
+
+instance KillRange CoverageCheck where
+  killRange = id
+
+-- Semigroup and Monoid via conjunction
+instance Semigroup CoverageCheck where
+  NoCoverageCheck <> _ = NoCoverageCheck
+  _ <> NoCoverageCheck = NoCoverageCheck
+  _ <> _ = YesCoverageCheck
+
+instance Monoid CoverageCheck where
+  mempty  = YesCoverageCheck
+  mappend = (<>)
+
+instance NFData CoverageCheck
+
+-----------------------------------------------------------------------------
+-- * Rewrite Directives on the LHS
+-----------------------------------------------------------------------------
+
+-- | @RewriteEqn' qn p e@ represents the @rewrite@ and irrefutable @with@
+--   clauses of the LHS.
+--   @qn@ stands for the QName of the auxiliary function generated to implement the feature
+--   @nm@ is the type of names for pattern variables
+--   @p@  is the type of patterns
+--   @e@  is the type of expressions
+
+data RewriteEqn' qn nm p e
+  = Rewrite (List1 (qn, e))             -- ^ @rewrite e@
+  | Invert qn (List1 (Named nm (p, e))) -- ^ @with p <- e in eq@
+  deriving (Eq, Show, Functor, Foldable, Traversable)
+
+instance (NFData qn, NFData nm, NFData p, NFData e) => NFData (RewriteEqn' qn nm p e) where
+  rnf = \case
+    Rewrite es    -> rnf es
+    Invert qn pes -> rnf (qn, pes)
+
+instance (Pretty nm, Pretty p, Pretty e) => Pretty (RewriteEqn' qn nm p e) where
+  pretty = \case
+    Rewrite es   -> prefixedThings (text "rewrite") $ List1.toList (pretty . snd <$> es)
+    Invert _ pes -> prefixedThings (text "invert") $ List1.toList (namedWith <$> pes) where
+
+      namedWith (Named nm (p, e)) =
+        let patexp = pretty p <+> "<-" <+> pretty e in
+        case nm of
+          Nothing -> patexp
+          Just nm -> pretty nm <+> ":" <+> patexp
+
+instance (HasRange qn, HasRange nm, HasRange p, HasRange e) => HasRange (RewriteEqn' qn nm p e) where
+  getRange = \case
+    Rewrite es    -> getRange es
+    Invert qn pes -> getRange (qn, pes)
+
+instance (KillRange qn, KillRange nm, KillRange e, KillRange p) => KillRange (RewriteEqn' qn nm p e) where
+  killRange = \case
+    Rewrite es    -> killRangeN Rewrite es
+    Invert qn pes -> killRangeN Invert qn pes
+
+-----------------------------------------------------------------------------
+-- * Information on expanded ellipsis (@...@)
+-----------------------------------------------------------------------------
+
+-- ^ When the ellipsis in a clause is expanded, we remember that we
+--   did so. We also store the number of with-arguments that are
+--   included in the expanded ellipsis.
+data ExpandedEllipsis
+  = ExpandedEllipsis
+  { ellipsisRange :: Range
+  , ellipsisWithArgs :: Int
+  }
+  | NoEllipsis
+  deriving (Show, Eq)
+
+instance Null ExpandedEllipsis where
+  null  = (== NoEllipsis)
+  empty = NoEllipsis
+
+instance Semigroup ExpandedEllipsis where
+  NoEllipsis <> e          = e
+  e          <> NoEllipsis = e
+  (ExpandedEllipsis r1 k1) <> (ExpandedEllipsis r2 k2) = ExpandedEllipsis (r1 <> r2) (k1 + k2)
+
+instance Monoid ExpandedEllipsis where
+  mempty  = NoEllipsis
+  mappend = (<>)
+
+instance KillRange ExpandedEllipsis where
+  killRange (ExpandedEllipsis _ k) = ExpandedEllipsis noRange k
+  killRange NoEllipsis             = NoEllipsis
+
+instance NFData ExpandedEllipsis where
+  rnf (ExpandedEllipsis _ a) = rnf a
+  rnf NoEllipsis             = ()
+
+-- | Notation as provided by the @syntax@ declaration.
+type Notation = [NotationPart]
+
+noNotation :: Notation
+noNotation = []
+
+-- | Positions of variables in syntax declarations.
+
+data BoundVariablePosition = BoundVariablePosition
+  { holeNumber :: !Int
+    -- ^ The position (in the left-hand side of the syntax
+    -- declaration) of the hole in which the variable is bound,
+    -- counting from zero (and excluding parts that are not holes).
+    -- For instance, for @syntax Σ A (λ x → B) = B , A , x@ the number
+    -- for @x@ is @1@, corresponding to @B@ (@0@ would correspond to
+    -- @A@).
+  , varNumber :: !Int
+    -- ^ The position in the list of variables for this particular
+    -- variable, counting from zero, and including wildcards. For
+    -- instance, for @syntax F (λ x _ y → A) = y ! A ! x@ the number
+    -- for @x@ is @0@, the number for @_@ is @1@, and the number for
+    -- @y@ is @2@.
+  }
+  deriving (Eq, Ord, Show)
+
+-- | Notation parts.
+
+data NotationPart
+  = IdPart RString
+    -- ^ An identifier part. For instance, for @_+_@ the only
+    -- identifier part is @+@.
+  | HolePart Range (NamedArg (Ranged Int))
+    -- ^ A hole: a place where argument expressions can be written.
+    -- For instance, for @_+_@ the two underscores are holes, and for
+    -- @syntax Σ A (λ x → B) = B , A , x@ the variables @A@ and @B@
+    -- are holes. The number is the position of the hole, counting
+    -- from zero. For instance, the number for @A@ is @0@, and the
+    -- number for @B@ is @1@.
+  | VarPart Range (Ranged BoundVariablePosition)
+    -- ^ A bound variable.
+    --
+    -- The first range is the range of the variable in the right-hand
+    -- side of the syntax declaration, and the second range is the
+    -- range of the variable in the left-hand side.
+  | WildPart (Ranged BoundVariablePosition)
+    -- ^ A wildcard (an underscore in binding position).
+  deriving Show
+
+instance Eq NotationPart where
+  VarPart _ i  == VarPart _ j  = i == j
+  HolePart _ x == HolePart _ y = x == y
+  WildPart i   == WildPart j   = i == j
+  IdPart x     == IdPart y     = x == y
+  _            == _            = False
+
+instance Ord NotationPart where
+  VarPart _ i  `compare` VarPart _ j  = i `compare` j
+  HolePart _ x `compare` HolePart _ y = x `compare` y
+  WildPart i   `compare` WildPart j   = i `compare` j
+  IdPart x     `compare` IdPart y     = x `compare` y
+  VarPart{}    `compare` _            = LT
+  _            `compare` VarPart{}    = GT
+  HolePart{}   `compare` _            = LT
+  _            `compare` HolePart{}   = GT
+  WildPart{}   `compare` _            = LT
+  _            `compare` WildPart{}   = GT
+
+instance HasRange NotationPart where
+  getRange = \case
+    IdPart x     -> getRange x
+    VarPart r _  -> r
+    WildPart i   -> getRange i
+    HolePart r _ -> r
+
+instance SetRange NotationPart where
+  setRange r = \case
+    IdPart x     -> IdPart x
+    VarPart _ i  -> VarPart r i
+    WildPart i   -> WildPart i
+    HolePart _ i -> HolePart r i
+
+instance KillRange NotationPart where
+  killRange = \case
+    IdPart x     -> IdPart $ killRange x
+    VarPart _ i  -> VarPart noRange $ killRange i
+    WildPart i   -> WildPart $ killRange i
+    HolePart _ x -> HolePart noRange $ killRange x
+
+instance NFData BoundVariablePosition where
+  rnf = (`seq` ())
+
+instance NFData NotationPart where
+  rnf (VarPart _ a)  = rnf a
+  rnf (HolePart _ a) = rnf a
+  rnf (WildPart a)   = rnf a
+  rnf (IdPart a)     = rnf a
diff --git a/src/full/Agda/Syntax/Common/Aspect.hs b/src/full/Agda/Syntax/Common/Aspect.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Common/Aspect.hs
@@ -0,0 +1,175 @@
+module Agda.Syntax.Common.Aspect where
+
+import Agda.Syntax.TopLevelModuleName.Boot (TopLevelModuleName')
+import Agda.Syntax.Position (Range)
+import Agda.Utils.Maybe
+import GHC.Generics
+
+import Data.Set (Set)
+
+import Control.DeepSeq
+
+data Induction = Inductive | CoInductive  -- Keep in this order!
+  deriving (Eq, Ord, Show)
+
+data Aspect
+  = Comment
+  | Keyword
+  | String
+  | Number
+  | Hole
+  | Symbol                     -- ^ Symbols like forall, =, ->, etc.
+  | PrimitiveType              -- ^ Things like Set and Prop.
+  | Name (Maybe NameKind) Bool -- ^ Is the name an operator part?
+  | Pragma                     -- ^ Text occurring in pragmas that
+                               --   does not have a more specific
+                               --   aspect.
+  | Background                 -- ^ Non-code contents in literate Agda
+  | Markup
+    -- ^ Delimiters used to separate the Agda code blocks from the
+    -- other contents in literate Agda
+    deriving (Eq, Show, Generic)
+
+-- | @NameKind@s are figured out during scope checking.
+
+data NameKind
+  = Bound                         -- ^ Bound variable.
+  | Generalizable                 -- ^ Generalizable variable.
+                                  --   (This includes generalizable
+                                  --   variables that have been
+                                  --   generalized).
+  | Constructor Induction         -- ^ Inductive or coinductive constructor.
+  | Datatype
+  | Field                         -- ^ Record field.
+  | Function
+  | Module                        -- ^ Module name.
+  | Postulate
+  | Primitive                     -- ^ Primitive.
+  | Record                        -- ^ Record type.
+  | Argument                      -- ^ Named argument, like x in {x = v}
+  | Macro                         -- ^ Macro.
+    deriving (Eq, Show, Generic)
+
+-- | Other aspects, generated by type checking.
+--   (These can overlap with each other and with 'Aspect's.)
+
+data OtherAspect
+  = Error
+  | ErrorWarning
+    -- ^ A warning that is considered fatal in the end.
+  | DottedPattern
+  | UnsolvedMeta
+  | UnsolvedConstraint
+    -- ^ Unsolved constraint not connected to meta-variable. This
+    -- could for instance be an emptyness constraint.
+  | TerminationProblem
+  | PositivityProblem
+  | Deadcode
+    -- ^ Used for highlighting unreachable clauses, unreachable RHS
+    -- (because of an absurd pattern), etc.
+  | ShadowingInTelescope
+    -- ^ Used for shadowed repeated variable names in telescopes.
+  | CoverageProblem
+  | IncompletePattern
+    -- ^ When this constructor is used it is probably a good idea to
+    -- include a 'note' explaining why the pattern is incomplete.
+  | TypeChecks
+    -- ^ Code which is being type-checked.
+  | MissingDefinition
+    -- ^ Function declaration without matching definition
+  -- NB: We put CatchallClause last so that it is overwritten by other,
+  -- more important, aspects in the emacs mode.
+  | CatchallClause
+  | ConfluenceProblem
+    deriving (Eq, Ord, Show, Enum, Bounded, Generic)
+
+-- | Some 'NameKind's are more informative than others.
+instance Semigroup NameKind where
+  -- During scope-checking of record, we build a constructor
+  -- whose arguments (@Bound@ variables) are the fields.
+  -- Later, we process them as @Field@s proper.
+  Field    <> Bound    = Field
+  Bound    <> Field    = Field
+  -- -- Projections are special functions.
+  -- -- TODO necessary?
+  -- Field    <> Function = Field
+  -- Function <> Field    = Field
+  -- TODO: more overwrites?
+  k1 <> k2 | k1 == k2  = k1
+           | otherwise = k1 -- TODO: __IMPOSSIBLE__
+
+-- | @NameKind@ in @Name@ can get more precise.
+instance Semigroup Aspect where
+  Name mk1 op1 <> Name mk2 op2 = Name (unionMaybeWith (<>) mk1 mk2) op1
+    -- (op1 || op2) breaks associativity
+  a1 <> a2 | a1 == a2  = a1
+           | otherwise = a1 -- TODO: __IMPOSSIBLE__
+
+------------------------------------------------------------------------
+-- Highlighting information
+
+-- | Syntactic aspects of the code. (These cannot overlap.)
+
+-- | Meta information which can be associated with a
+-- character\/character range.
+
+data Aspects = Aspects
+  { aspect       :: Maybe Aspect
+  , otherAspects :: Set OtherAspect
+  , note         :: String
+    -- ^ This note, if not null, can be displayed as a tool-tip or
+    -- something like that. It should contain useful information about
+    -- the range (like the module containing a certain identifier, or
+    -- the fixity of an operator).
+  , definitionSite :: Maybe DefinitionSite
+    -- ^ The definition site of the annotated thing, if applicable and
+    --   known.
+  , tokenBased :: !TokenBased
+    -- ^ Is this entry token-based?
+  }
+  deriving (Show, Generic)
+
+data DefinitionSite = DefinitionSite
+  { defSiteModule :: (TopLevelModuleName' Range)
+      -- ^ The defining module.
+  , defSitePos    :: Int
+      -- ^ The file position in that module. File positions are
+      -- counted from 1.
+  , defSiteHere   :: Bool
+      -- ^ Has this @DefinitionSite@ been created at the defining site of the name?
+  , defSiteAnchor :: Maybe String
+      -- ^ A pretty name for the HTML linking.
+  }
+  deriving (Show, Generic)
+
+instance Eq DefinitionSite where
+  DefinitionSite m p _ _ == DefinitionSite m' p' _ _ = m == m' && p == p'
+
+-- | Is the highlighting \"token-based\", i.e. based only on
+-- information from the lexer?
+
+data TokenBased = TokenBased | NotOnlyTokenBased
+  deriving (Eq, Show)
+
+instance Eq Aspects where
+  Aspects a o _ d t == Aspects a' o' _ d' t' =
+    (a, o, d, t) == (a', o', d', t')
+
+instance NFData Induction where
+  rnf Inductive   = ()
+  rnf CoInductive = ()
+
+instance NFData NameKind where
+  rnf = \case
+    Bound         -> ()
+    Generalizable -> ()
+    Constructor c -> rnf c
+    Datatype      -> ()
+    Field         -> ()
+    Function      -> ()
+    Module        -> ()
+    Postulate     -> ()
+    Primitive     -> ()
+    Record        -> ()
+    Argument      -> ()
+    Macro         -> ()
diff --git a/src/full/Agda/Syntax/Common/Pretty.hs b/src/full/Agda/Syntax/Common/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Common/Pretty.hs
@@ -0,0 +1,316 @@
+
+{-| Pretty printing functions.
+-}
+module Agda.Syntax.Common.Pretty
+    ( module Agda.Syntax.Common.Pretty
+    , module Text.PrettyPrint.Annotated
+    -- This re-export can be removed once <GHC-8.4 is dropped.
+    , module Data.Semigroup
+    ) where
+
+import Prelude hiding (null)
+
+import qualified Data.Foldable as Fold
+import qualified Data.IntSet as IntSet
+import qualified Data.IntMap as IntMap
+import qualified Data.Text as T
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.IntSet (IntSet)
+import Data.IntMap (IntMap)
+import Data.Word (Word64)
+import Data.Text (Text)
+import Data.Int (Int32)
+import Data.Map (Map)
+import Data.Set (Set)
+
+import qualified Text.PrettyPrint.Annotated as P
+import Text.PrettyPrint.Annotated hiding
+  ( Doc, TextDetails(Str), empty, (<>), sep, fsep, hsep, hcat, vcat, punctuate
+
+  , parens, brackets, braces, quotes, doubleQuotes
+
+  , semi, comma, colon, space, equals, lparen, rparen, lbrack, rbrack
+  , lbrace, rbrace
+  )
+
+import Data.Semigroup ((<>))
+
+import Agda.Utils.Float
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Null
+import Agda.Utils.Size
+
+import Agda.Syntax.Common.Aspect
+import Agda.Syntax.Position
+import Agda.Utils.Impossible
+import Agda.Utils.FileName
+
+
+-- * Pretty class
+
+-- | The type of documents. We use documents annotated by 'Aspects' to
+-- record syntactic highlighting information that is generated during
+-- pretty-printing.
+type Doc = P.Doc Aspects
+
+-- | While 'Show' is for rendering data in Haskell syntax,
+--   'Pretty' is for displaying data to the world, i.e., the
+--   user and the environment.
+--
+--   Atomic data has no inner document structure, so just
+--   implement 'pretty' as @pretty a = text $ ... a ...@.
+
+class Pretty a where
+  pretty      :: a -> Doc
+  prettyPrec  :: Int -> a -> Doc
+  prettyList  :: [a] -> Doc
+
+  pretty      = prettyPrec 0
+  prettyPrec  = const pretty
+  prettyList  = brackets . prettyList_
+
+-- | Use instead of 'show' when printing to world.
+
+prettyShow :: Pretty a => a -> String
+prettyShow = render . pretty
+
+-- * Pretty instances
+
+instance Pretty Bool    where pretty = text . show
+instance Pretty Int     where pretty = text . show
+instance Pretty Int32   where pretty = text . show
+instance Pretty Integer where pretty = text . show
+instance Pretty Word64  where pretty = text . show
+instance Pretty Double  where pretty = text . toStringWithoutDotZero
+instance Pretty Text    where pretty = text . T.unpack
+
+instance Pretty Char where
+  pretty c = text [c]
+  prettyList = text
+
+
+-- The equational constraint forces GHC to pick this instance and unify
+-- the type variable, instead of deferring selection to when the type of
+-- annotations is solved.
+instance a ~ Aspects => Pretty (P.Doc a) where
+  pretty = id
+
+instance Pretty () where
+  pretty _ = P.empty
+
+instance Pretty a => Pretty (Maybe a) where
+  prettyPrec p Nothing  = "(nothing)"
+  prettyPrec p (Just x) = prettyPrec p x
+
+instance Pretty a => Pretty [a] where
+  pretty = prettyList
+
+instance Pretty a => Pretty (List1 a) where
+  pretty = prettyList . List1.toList
+
+instance Pretty IntSet where
+  pretty = prettySet . IntSet.toList
+
+instance Pretty a => Pretty (Set a) where
+  pretty = prettySet . Set.toList
+
+instance Pretty a => Pretty (IntMap a) where
+  pretty = prettyMap . IntMap.toList
+
+instance (Pretty k, Pretty v) => Pretty (Map k v) where
+  pretty = prettyMap . Map.toList
+
+-- Pretty instances for dependencies of this module (to avoid dependency cycles)
+
+instance Pretty AbsolutePath where
+  pretty = text . filePath
+
+instance Pretty RangeFile where
+  pretty = pretty . rangeFilePath
+
+instance Pretty a => Pretty (Position' (Strict.Maybe a)) where
+  pretty (Pn Strict.Nothing  _ l c) = pretty l <> "," <> pretty c
+  pretty (Pn (Strict.Just f) _ l c) =
+    pretty f <> ":" <> pretty l <> "," <> pretty c
+
+instance Pretty PositionWithoutFile where
+  pretty p = pretty (p { srcFile = Strict.Nothing } :: Position)
+
+instance Pretty IntervalWithoutFile where
+  pretty (Interval s e) = start <> "-" <> end
+    where
+      sl = posLine s
+      el = posLine e
+      sc = posCol s
+      ec = posCol e
+
+      start :: Doc
+      start = pretty sl <> comma <> pretty sc
+
+      end :: Doc
+        | sl == el  = pretty ec
+        | otherwise = pretty el <> comma <> pretty ec
+
+instance Pretty a => Pretty (Interval' (Strict.Maybe a)) where
+  pretty i@(Interval s _) = file <> pretty (setIntervalFile () i)
+    where
+      file :: Doc
+      file = case srcFile s of
+               Strict.Nothing -> empty
+               Strict.Just f  -> pretty f <> colon
+
+instance Pretty a => Pretty (Range' (Strict.Maybe a)) where
+  pretty r = maybe empty pretty (rangeToIntervalWithFile r)
+
+instance (Pretty a, HasRange a) => Pretty (PrintRange a) where
+  pretty (PrintRange a) = pretty a <+> parens ("at" <+> pretty (getRange a))
+
+
+-- * Generalizing the original type from list to Foldable
+
+sep, fsep, hsep, hcat, vcat :: Foldable t => t Doc -> Doc
+sep  = P.sep  . Fold.toList
+fsep = P.fsep . Fold.toList
+hsep = P.hsep . Fold.toList
+hcat = P.hcat . Fold.toList
+vcat = P.vcat . Fold.toList
+
+punctuate :: Foldable t => Doc -> t Doc -> [Doc]
+punctuate d = P.punctuate d . Fold.toList
+
+-- * 'Doc' utilities
+
+pwords :: String -> [Doc]
+pwords = map text . words
+
+fwords :: String -> Doc
+fwords = fsep . pwords
+
+-- | Separate, but only if both separees are not null.
+
+hsepWith :: Doc -> Doc -> Doc -> Doc
+hsepWith sep d1 d2
+  | null d2   = d1
+  | null d1   = d2
+  | otherwise = d1 <+> sep <+> d2
+
+-- | Comma separated list, without the brackets.
+prettyList_ :: Pretty a => [a] -> Doc
+prettyList_ = fsep . punctuate comma . map pretty
+
+-- | Pretty print a set.
+prettySet :: Pretty a => [a] -> Doc
+prettySet = braces . prettyList_
+
+-- | Pretty print an association list.
+prettyMap :: (Pretty k, Pretty v) => [(k,v)] -> Doc
+prettyMap = braces . fsep . punctuate comma . map prettyAssign
+
+-- | Pretty print a single association.
+prettyAssign :: (Pretty k, Pretty v) => (k,v) -> Doc
+prettyAssign (k, v) = sep [ prettyPrec 1 k <+> hlSymbol "->", nest 2 $ pretty v ]
+
+-- ASR (2016-12-13): In pretty >= 1.1.2.0 the below function 'mparens'
+-- is called 'maybeParens'. I didn't use that name due to the issue
+-- https://github.com/haskell/pretty/issues/40.
+
+-- | Apply 'parens' to 'Doc' if boolean is true.
+mparens :: Bool -> Doc -> Doc
+mparens True  = parens
+mparens False = id
+
+-- | Only wrap in parens if not 'empty'
+parensNonEmpty :: Doc -> Doc
+parensNonEmpty d = if null d then empty else parens d
+
+-- | @align max rows@ lays out the elements of @rows@ in two columns,
+-- with the second components aligned. The alignment column of the
+-- second components is at most @max@ characters to the right of the
+-- left-most column.
+--
+-- Precondition: @max > 0@.
+
+align :: Int -> [(String, Doc)] -> Doc
+align max rows =
+  vcat $ map (\(s, d) -> text s $$ nest (maxLen + 1) d) $ rows
+  where maxLen = maximum $ 0 : filter (< max) (map (length . fst) rows)
+
+-- | Handles strings with newlines properly (preserving indentation)
+multiLineText :: String -> Doc
+multiLineText = vcat . map text . lines
+
+infixl 6 <?>
+-- | @a <?> b = hang a 2 b@
+(<?>) :: Doc -> Doc -> Doc
+a <?> b = hang a 2 b
+
+-- | @pshow = text . show@
+pshow :: Show a => a -> Doc
+pshow = text . show
+
+singPlural :: Sized a => a -> c -> c -> c
+singPlural xs singular plural = if natSize xs == 1 then singular else plural
+
+-- | Used for with-like 'telescopes'
+
+prefixedThings :: Doc -> [Doc] -> Doc
+prefixedThings kw = \case
+  []           -> P.empty
+  (doc : docs) -> fsep $ (kw <+> doc) : map (hlSymbol "|" <+>) docs
+
+-- | Attach a simple 'Aspect', rather than a full set of 'Aspects', to a
+-- document.
+annotateAspect :: Aspect -> Doc -> Doc
+annotateAspect a = annotate a' where
+  a' = Aspects
+    { aspect         = Just a
+    , otherAspects   = mempty
+    , note           = ""
+    , definitionSite = Nothing
+    , tokenBased     = TokenBased
+    }
+
+-- * Syntax highlighting helpers
+
+hlComment, hlSymbol, hlKeyword, hlString, hlNumber, hlHole, hlPrimitiveType, hlPragma
+  :: Doc -> Doc
+
+hlComment       = annotateAspect Comment
+hlSymbol        = annotateAspect Symbol
+hlKeyword       = annotateAspect Keyword
+hlString        = annotateAspect String
+hlNumber        = annotateAspect Number
+hlHole          = annotateAspect Hole
+hlPrimitiveType = annotateAspect PrimitiveType
+hlPragma        = annotateAspect Pragma
+
+-- * Delimiter wrappers
+--
+-- These use the 'Symbol' highlight for the punctuation characters.
+
+parens       :: Doc -> Doc -- ^ Wrap document in @(...)@
+brackets     :: Doc -> Doc -- ^ Wrap document in @[...]@
+braces       :: Doc -> Doc -- ^ Wrap document in @{...}@
+quotes       :: Doc -> Doc -- ^ Wrap document in @\'...\'@
+doubleQuotes :: Doc -> Doc -- ^ Wrap document in @\"...\"@
+quotes p       = hlSymbol (char '\'') <> p <> hlSymbol (char '\'')
+doubleQuotes p = hlSymbol (char '"') <> p <> hlSymbol (char '"')
+parens p       = lparen <> p <> rparen
+brackets p     = lbrack <> p <> rbrack
+braces p       = lbrace <> p <> rbrace
+
+semi, comma, colon, space, equals, lparen, rparen, lbrack, rbrack, lbrace, rbrace :: Doc
+semi   = hlSymbol $ char ';'
+comma  = hlSymbol $ char ','
+colon  = hlSymbol $ char ':'
+space  = hlSymbol $ char ' '
+equals = hlSymbol $ char '='
+lparen = hlSymbol $ char '('
+rparen = hlSymbol $ char ')'
+lbrack = hlSymbol $ char '['
+rbrack = hlSymbol $ char ']'
+lbrace = hlSymbol $ char '{'
+rbrace = hlSymbol $ char '}'
diff --git a/src/full/Agda/Syntax/Common/Pretty/ANSI.hs b/src/full/Agda/Syntax/Common/Pretty/ANSI.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Common/Pretty/ANSI.hs
@@ -0,0 +1,60 @@
+module Agda.Syntax.Common.Pretty.ANSI where
+import Control.Monad.IO.Class
+import Control.Monad
+
+import Text.PrettyPrint.Annotated.HughesPJ (renderDecoratedM)
+
+import Agda.Interaction.Options.HasOptions
+import Agda.Interaction.Options.Base
+import Agda.Syntax.Common.Aspect
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Monad
+
+import System.Console.ANSI
+import System.IO
+
+-- | Render an annotated, pretty-printing 'Doc'ument into a string
+-- suitable for printing on VT100-compatible terminals.
+renderAnsiIO :: Doc -> IO ()
+renderAnsiIO = renderDecoratedM start end putStr (putStr "\n") where
+  start = maybe mempty (setSGR . aspSGR) . aspect
+  end _ = setSGR [Reset]
+
+  aspSGR :: Aspect -> [SGR]
+  aspSGR String        = [SetColor Foreground Dull Red]
+  aspSGR Number        = [SetColor Foreground Dull Magenta]
+  aspSGR PrimitiveType = [SetColor Foreground Dull Blue]
+  aspSGR (Name (Just nk) _) = case nk of
+    Bound                   -> []
+    Generalizable           -> []
+    Argument                -> []
+
+    Constructor Inductive   -> [SetColor Foreground Dull Green]
+    Constructor CoInductive -> [SetColor Foreground Dull Green]
+
+    Field                   -> [SetColor Foreground Vivid Magenta]
+
+    Module                  -> [SetColor Foreground Vivid Magenta]
+
+    Function                -> [SetColor Foreground Dull Blue]
+    Postulate               -> [SetColor Foreground Dull Blue]
+    Datatype                -> [SetColor Foreground Dull Blue]
+    Record                  -> [SetColor Foreground Dull Blue]
+    Primitive               -> [SetColor Foreground Dull Blue]
+
+    Macro                   -> [SetColor Foreground Dull Cyan]
+  aspSGR _ = []
+
+putDoc :: (MonadIO m, HasOptions m) => Doc -> m ()
+putDoc doc = do
+  outputcol <- liftIO (hSupportsANSI stdout)
+  wantscol <- commandLineOptions
+  let
+    col = case optDiagnosticsColour wantscol of
+      AutoColour   -> outputcol
+      AlwaysColour -> True
+      NeverColour  -> False
+
+  liftIO $ if col
+    then renderAnsiIO doc
+    else putStrLn (render doc)
diff --git a/src/full/Agda/Syntax/Concrete.hs b/src/full/Agda/Syntax/Concrete.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete.hs
@@ -0,0 +1,1440 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE ApplicativeDo #-}  -- see exprToPattern
+
+{-| The concrete syntax is a raw representation of the program text
+    without any desugaring at all.  This is what the parser produces.
+    The idea is that if we figure out how to keep the concrete syntax
+    around, it can be printed exactly as the user wrote it.
+-}
+module Agda.Syntax.Concrete
+  ( -- * Expressions
+    Expr(..)
+  , OpApp(..), fromOrdinary
+  , OpAppArgs, OpAppArgs'
+  , module Agda.Syntax.Concrete.Name
+  , AppView(..), appView, unAppView
+  , rawApp, rawAppP
+  , isSingleIdentifierP, removeParenP
+  , isPattern, isAbsurdP, isBinderP
+  , observeHiding
+  , observeRelevance
+  , observeModifiers
+  , exprToPatternWithHoles
+  , returnExpr
+    -- * Bindings
+  , Binder'(..)
+  , Binder
+  , mkBinder_
+  , mkBinder
+  , LamBinding
+  , LamBinding'(..)
+  , dropTypeAndModality
+  , TypedBinding
+  , TypedBinding'(..)
+  , RecordAssignment
+  , RecordAssignments
+  , FieldAssignment, FieldAssignment'(..), nameFieldA, exprFieldA
+  , ModuleAssignment(..)
+  , BoundName(..), mkBoundName_, mkBoundName
+  , TacticAttribute
+  , Telescope, Telescope1
+  , lamBindingsToTelescope
+  , makePi
+  , mkLam, mkLet, mkTLet
+    -- * Declarations
+  , Declaration(..)
+  , isPragma
+  , isRecordDirective
+  , RecordDirective(..)
+  , RecordDirectives
+  , ModuleApplication(..)
+  , TypeSignature
+  , TypeSignatureOrInstanceBlock
+  , ImportDirective, Using, ImportedName
+  , Renaming, RenamingDirective, HidingDirective
+  , AsName'(..), AsName
+  , OpenShortHand(..), RewriteEqn, WithExpr
+  , LHS(..), Pattern(..), LHSCore(..)
+  , LamClause(..)
+  , RHS, RHS'(..), WhereClause, WhereClause'(..), ExprWhere(..)
+  , DoStmt(..)
+  , Pragma(..)
+  , Module(..)
+  , ThingWithFixity(..)
+  , HoleContent, HoleContent'(..)
+  , spanAllowedBeforeModule
+  )
+  where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import qualified Data.DList as DL
+import Data.Functor.Identity
+import Data.Set         ( Set  )
+import Data.Text        ( Text )
+-- import Data.Traversable ( forM )
+
+import GHC.Generics     ( Generic )
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Fixity
+import Agda.Syntax.Literal
+
+import Agda.Syntax.Concrete.Name
+import qualified Agda.Syntax.Abstract.Name as A
+
+import Agda.TypeChecking.Positivity.Occurrence
+
+import Agda.Utils.Applicative ( forA )
+import Agda.Utils.Either      ( maybeLeft )
+import Agda.Utils.Lens
+import Agda.Utils.List1       ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.List2       ( List2, pattern List2 )
+import Agda.Syntax.Common.Aspect (NameKind)
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+data OpApp e
+  = SyntaxBindingLambda Range (List1 LamBinding) e
+    -- ^ An abstraction inside a special syntax declaration
+    --   (see Issue 358 why we introduce this).
+  | Ordinary e
+  deriving (Functor, Foldable, Traversable, Eq)
+
+fromOrdinary :: e -> OpApp e -> e
+fromOrdinary d (Ordinary e) = e
+fromOrdinary d _            = d
+
+data FieldAssignment' a = FieldAssignment { _nameFieldA :: Name, _exprFieldA :: a }
+  deriving (Functor, Foldable, Traversable, Show, Eq)
+
+type FieldAssignment = FieldAssignment' Expr
+
+data ModuleAssignment  = ModuleAssignment
+                           { _qnameModA     :: QName
+                           , _exprModA      :: [Expr]
+                           , _importDirModA :: ImportDirective
+                           }
+  deriving Eq
+
+type RecordAssignment  = Either FieldAssignment ModuleAssignment
+type RecordAssignments = [RecordAssignment]
+
+nameFieldA :: Lens' (FieldAssignment' a) Name
+nameFieldA f r = f (_nameFieldA r) <&> \x -> r { _nameFieldA = x }
+
+exprFieldA :: Lens' (FieldAssignment' a) a
+exprFieldA f r = f (_exprFieldA r) <&> \x -> r { _exprFieldA = x }
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+--qnameModA :: Lens' ModuleAssignment QName
+--qnameModA f r = f (_qnameModA r) <&> \x -> r { _qnameModA = x }
+--
+--exprModA :: Lens' [Expr] ModuleAssignment
+--exprModA f r = f (_exprModA r) <&> \x -> r { _exprModA = x }
+--
+--importDirModA :: Lens' ModuleAssignment ImportDirective
+--importDirModA f r = f (_importDirModA r) <&> \x -> r { _importDirModA = x }
+
+-- | Concrete expressions. Should represent exactly what the user wrote.
+data Expr
+  = Ident QName                                -- ^ ex: @x@
+  | Lit Range Literal                          -- ^ ex: @1@ or @\"foo\"@
+  | QuestionMark Range (Maybe Nat)             -- ^ ex: @?@ or @{! ... !}@
+  | Underscore Range (Maybe String)            -- ^ ex: @_@ or @_A_5@
+  | RawApp Range (List2 Expr)                  -- ^ before parsing operators
+  | App Range Expr (NamedArg Expr)             -- ^ ex: @e e@, @e {e}@, or @e {x = e}@
+  | OpApp Range QName (Set A.Name) OpAppArgs   -- ^ ex: @e + e@
+                                               -- The 'QName' is possibly ambiguous,
+                                               -- but it must correspond to one of the names in the set.
+  | WithApp Range Expr [Expr]                  -- ^ ex: @e | e1 | .. | en@
+  | HiddenArg Range (Named_ Expr)              -- ^ ex: @{e}@ or @{x=e}@
+  | InstanceArg Range (Named_ Expr)            -- ^ ex: @{{e}}@ or @{{x=e}}@
+  | Lam Range (List1 LamBinding) Expr          -- ^ ex: @\\x {y} -> e@ or @\\(x:A){y:B} -> e@
+  | AbsurdLam Range Hiding                     -- ^ ex: @\\ ()@
+  | ExtendedLam Range Erased
+      (List1 LamClause)                        -- ^ ex: @\\ { p11 .. p1a -> e1 ; .. ; pn1 .. pnz -> en }@
+  | Fun Range (Arg Expr) Expr                  -- ^ ex: @e -> e@ or @.e -> e@ (NYI: @{e} -> e@)
+  | Pi Telescope1 Expr                         -- ^ ex: @(xs:e) -> e@ or @{xs:e} -> e@
+  | Rec Range RecordAssignments                -- ^ ex: @record {x = a; y = b}@, or @record { x = a; M1; M2 }@
+  | RecUpdate Range Expr [FieldAssignment]     -- ^ ex: @record e {x = a; y = b}@
+  | Let Range (List1 Declaration) (Maybe Expr) -- ^ ex: @let Ds in e@, missing body when parsing do-notation let
+  | Paren Range Expr                           -- ^ ex: @(e)@
+  | IdiomBrackets Range [Expr]                 -- ^ ex: @(| e1 | e2 | .. | en |)@ or @(|)@
+  | DoBlock Range (List1 DoStmt)               -- ^ ex: @do x <- m1; m2@
+  | Absurd Range                               -- ^ ex: @()@ or @{}@, only in patterns
+  | As Range Name Expr                         -- ^ ex: @x\@p@, only in patterns
+  | Dot Range Expr                             -- ^ ex: @.p@, only in patterns
+  | DoubleDot Range Expr                       -- ^ ex: @..A@, used for parsing @..A -> B@
+  | Quote Range                                -- ^ ex: @quote@, should be applied to a name
+  | QuoteTerm Range                            -- ^ ex: @quoteTerm@, should be applied to a term
+  | Tactic Range Expr                          -- ^ ex: @\@(tactic t)@, used to declare tactic arguments
+  | Unquote Range                              -- ^ ex: @unquote@, should be applied to a term of type @Term@
+  | DontCare Expr                              -- ^ to print irrelevant things
+  | Equal Range Expr Expr                      -- ^ ex: @a = b@, used internally in the parser
+  | Ellipsis Range                             -- ^ @...@, used internally to parse patterns.
+  | KnownIdent NameKind QName
+    -- ^ An identifier coming from abstract syntax, for which we know a
+    -- precise syntactic highlighting class (used in printing).
+  | KnownOpApp NameKind Range QName (Set A.Name) OpAppArgs
+    -- ^ An operator application coming from abstract syntax, for which
+    -- we know a precise syntactic highlighting class (used in
+    -- printing).
+  | Generalized Expr
+  deriving Eq
+
+type OpAppArgs = OpAppArgs' Expr
+type OpAppArgs' e = [NamedArg (MaybePlaceholder (OpApp e))]
+
+-- | Concrete patterns. No literals in patterns at the moment.
+data Pattern
+  = IdentP Bool QName                      -- ^ @c@ or @x@
+                                           --
+                                           -- If the boolean is
+                                           -- 'False', then the
+                                           -- 'QName' must not refer
+                                           -- to a constructor or a
+                                           -- pattern synonym. The
+                                           -- value 'False' is used
+                                           -- when a hidden argument
+                                           -- pun is expanded.
+  | QuoteP Range                           -- ^ @quote@
+  | AppP Pattern (NamedArg Pattern)        -- ^ @p p'@ or @p {x = p'}@
+  | RawAppP Range (List2 Pattern)          -- ^ @p1..pn@ before parsing operators
+  | OpAppP Range QName (Set A.Name)
+           [NamedArg Pattern]              -- ^ eg: @p => p'@ for operator @_=>_@
+                                           -- The 'QName' is possibly
+                                           -- ambiguous, but it must
+                                           -- correspond to one of
+                                           -- the names in the set.
+  | HiddenP Range (Named_ Pattern)         -- ^ @{p}@ or @{x = p}@
+  | InstanceP Range (Named_ Pattern)       -- ^ @{{p}}@ or @{{x = p}}@
+  | ParenP Range Pattern                   -- ^ @(p)@
+  | WildP Range                            -- ^ @_@
+  | AbsurdP Range                          -- ^ @()@
+  | AsP Range Name Pattern                 -- ^ @x\@p@ unused
+  | DotP Range Expr                        -- ^ @.e@
+  | LitP Range Literal                     -- ^ @0@, @1@, etc.
+  | RecP Range [FieldAssignment' Pattern]  -- ^ @record {x = p; y = q}@
+  | EqualP Range [(Expr,Expr)]             -- ^ @i = i1@ i.e. cubical face lattice generator
+  | EllipsisP Range (Maybe Pattern)        -- ^ @...@, only as left-most pattern.
+                                           --   Second arg is @Nothing@ before expansion, and
+                                           --   @Just p@ after expanding ellipsis to @p@.
+  | WithP Range Pattern                    -- ^ @| p@, for with-patterns.
+  deriving Eq
+
+data DoStmt
+  = DoBind Range Pattern Expr [LamClause]   -- ^ @p ← e where cs@
+  | DoThen Expr
+  | DoLet Range (List1 Declaration)
+  deriving Eq
+
+-- | A Binder @x\@p@, the pattern is optional
+data Binder' a = Binder
+  { binderPattern :: Maybe Pattern
+  , binderName    :: a
+  } deriving (Eq, Functor, Foldable, Traversable)
+
+type Binder = Binder' BoundName
+
+mkBinder_ :: Name -> Binder
+mkBinder_ = mkBinder . mkBoundName_
+
+mkBinder :: a -> Binder' a
+mkBinder = Binder Nothing
+
+-- | A lambda binding is either domain free or typed.
+
+type LamBinding = LamBinding' TypedBinding
+data LamBinding' a
+  = DomainFree (NamedArg Binder)
+    -- ^ . @x@ or @{x}@ or @.x@ or @.{x}@ or @{.x}@ or @x\@p@ or @(p)@
+  | DomainFull a
+    -- ^ . @(xs : e)@ or @{xs : e}@
+  deriving (Functor, Foldable, Traversable, Eq)
+
+-- | Drop type annotations and lets from bindings.
+dropTypeAndModality :: LamBinding -> [LamBinding]
+dropTypeAndModality (DomainFull (TBind _ xs _)) =
+  map (DomainFree . setModality defaultModality) $ List1.toList xs
+dropTypeAndModality (DomainFull TLet{}) = []
+dropTypeAndModality (DomainFree x) = [DomainFree $ setModality defaultModality x]
+
+data BoundName = BName
+  { boundName       :: Name
+  , bnameFixity     :: Fixity'
+  , bnameTactic     :: TacticAttribute -- From @tactic attribute
+  , bnameIsFinite   :: Bool
+  }
+  deriving Eq
+
+type TacticAttribute = Maybe (Ranged Expr)
+
+mkBoundName_ :: Name -> BoundName
+mkBoundName_ x = mkBoundName x noFixity'
+
+mkBoundName :: Name -> Fixity' -> BoundName
+mkBoundName x f = BName x f Nothing False
+
+-- | A typed binding.
+
+type TypedBinding = TypedBinding' Expr
+
+data TypedBinding' e
+  = TBind Range (List1 (NamedArg Binder)) e
+    -- ^ Binding @(x1\@p1 ... xn\@pn : A)@.
+  | TLet  Range (List1 Declaration)
+    -- ^ Let binding @(let Ds)@ or @(open M args)@.
+  deriving (Functor, Foldable, Traversable, Eq)
+
+-- | A telescope is a sequence of typed bindings. Bound variables are in scope
+--   in later types.
+type Telescope1 = List1 TypedBinding
+type Telescope  = [TypedBinding]
+
+-- | We can try to get a @Telescope@ from a @[LamBinding]@.
+--   If we have a type annotation already, we're happy.
+--   Otherwise we manufacture a binder with an underscore for the type.
+lamBindingsToTelescope :: Range -> [LamBinding] -> Telescope
+lamBindingsToTelescope r = fmap $ \case
+  DomainFull ty -> ty
+  DomainFree nm -> TBind r (List1.singleton nm) $ Underscore r Nothing
+
+-- | Smart constructor for @Pi@: check whether the @Telescope@ is empty
+
+makePi :: Telescope -> Expr -> Expr
+makePi []     = id
+makePi (b:bs) = Pi (b :| bs)
+
+-- | Smart constructor for @Lam@: check for non-zero bindings.
+
+mkLam :: Range -> [LamBinding] -> Expr -> Expr
+mkLam r []     e = e
+mkLam r (x:xs) e = Lam r (x :| xs) e
+
+-- | Smart constructor for @Let@: check for non-zero let bindings.
+
+mkLet :: Range -> [Declaration] -> Expr -> Expr
+mkLet r []     e = e
+mkLet r (d:ds) e = Let r (d :| ds) (Just e)
+
+-- | Smart constructor for @TLet@: check for non-zero let bindings.
+
+mkTLet :: Range -> [Declaration] -> Maybe (TypedBinding' e)
+mkTLet r []     = Nothing
+mkTLet r (d:ds) = Just $ TLet r (d :| ds)
+
+{-| Left hand sides can be written in infix style. For example:
+
+    > n + suc m = suc (n + m)
+    > (f ∘ g) x = f (g x)
+
+   We use fixity information to see which name is actually defined.
+-}
+data LHS = LHS  -- ^ Original pattern (including with-patterns), rewrite equations and with-expressions.
+  { lhsOriginalPattern :: Pattern
+    -- ^ e.g. @f ps | wps@
+  , lhsRewriteEqn      :: [RewriteEqn]
+    -- ^ @(rewrite e | with p <- e in eq)@ (many)
+  , lhsWithExpr        :: [WithExpr]
+    -- ^ @with e1 in eq | {e2} | ...@ (many)
+  }
+  deriving Eq
+
+type RewriteEqn = RewriteEqn' () Name Pattern Expr
+type WithExpr   = Named Name (Arg Expr)
+
+-- | Processed (operator-parsed) intermediate form of the core @f ps@ of 'LHS'.
+--   Corresponds to 'lhsOriginalPattern'.
+data LHSCore
+  = LHSHead  { lhsDefName      :: QName               -- ^ @f@
+             , lhsPats         :: [NamedArg Pattern]  -- ^ @ps@
+             }
+  | LHSProj  { lhsDestructor   :: QName               -- ^ Record projection.
+             , lhsPatsLeft     :: [NamedArg Pattern]  -- ^ Patterns for record indices (currently none).
+             , lhsFocus        :: NamedArg LHSCore    -- ^ Main argument.
+             , lhsPats         :: [NamedArg Pattern]  -- ^ More application patterns.
+             }
+  | LHSWith  { lhsHead         :: LHSCore
+             , lhsWithPatterns :: [Pattern]          -- ^ Non-empty; at least one @(| p)@.
+             , lhsPats         :: [NamedArg Pattern] -- ^ More application patterns.
+             }
+  | LHSEllipsis
+             { lhsEllipsisRange :: Range
+             , lhsEllipsisPat   :: LHSCore           -- ^ Pattern that was expanded from an ellipsis @...@.
+             }
+  deriving Eq
+
+type RHS = RHS' Expr
+data RHS' e
+  = AbsurdRHS -- ^ No right hand side because of absurd match.
+  | RHS e
+  deriving (Functor, Foldable, Traversable, Eq)
+
+-- | @where@ block following a clause.
+type WhereClause = WhereClause' [Declaration]
+
+-- The generalization @WhereClause'@ is for the sake of Concrete.Generic.
+data WhereClause' decls
+  = NoWhere
+      -- ^ No @where@ clauses.
+  | AnyWhere Range decls
+      -- ^ Ordinary @where@.  'Range' of the @where@ keyword.
+      --   List of declarations can be empty.
+  | SomeWhere Range Erased Name Access decls
+      -- ^ Named where: @module M where ds@.
+      --   'Range' of the keywords @module@ and @where@.
+      --   The 'Access' flag applies to the 'Name' (not the module contents!)
+      --   and is propagated from the parent function.
+      --   List of declarations can be empty.
+  deriving (Eq, Functor, Foldable, Traversable)
+
+data LamClause = LamClause
+  { lamLHS      :: [Pattern]   -- ^ Possibly empty sequence.
+  , lamRHS      :: RHS
+  , lamCatchAll :: Bool
+  }
+  deriving Eq
+
+-- | An expression followed by a where clause.
+--   Currently only used to give better a better error message in interaction.
+data ExprWhere = ExprWhere Expr WhereClause
+
+-- | The things you are allowed to say when you shuffle names between name
+--   spaces (i.e. in @import@, @namespace@, or @open@ declarations).
+type ImportDirective = ImportDirective' Name Name
+type Using           = Using'           Name Name
+type Renaming        = Renaming'        Name Name
+type RenamingDirective = RenamingDirective' Name Name
+type HidingDirective   = HidingDirective'   Name Name  -- 'Hiding' is already taken
+
+-- | An imported name can be a module or a defined name.
+type ImportedName = ImportedName' Name Name
+
+-- | The content of the @as@-clause of the import statement.
+data AsName' a = AsName
+  { asName  :: a
+    -- ^ The \"as\" name.
+  , asRange :: Range
+    -- ^ The range of the \"as\" keyword.  Retained for highlighting purposes.
+  }
+  deriving (Show, Functor, Foldable, Traversable, Eq)
+
+-- | From the parser, we get an expression for the @as@-'Name', which
+--   we have to parse into a 'Name'.
+type AsName = AsName' (Either Expr Name)
+
+{--------------------------------------------------------------------------
+    Declarations
+ --------------------------------------------------------------------------}
+
+-- | Just type signatures.
+type TypeSignature = Declaration
+
+-- | Just field signatures
+type FieldSignature = Declaration
+
+-- | Just type signatures or instance blocks.
+type TypeSignatureOrInstanceBlock = Declaration
+
+-- | Isolated record directives parsed as Declarations
+data RecordDirective
+   = Induction (Ranged Induction)
+       -- ^ Range of keyword @[co]inductive@.
+   | Constructor Name IsInstance
+   | Eta         (Ranged HasEta0)
+       -- ^ Range of @[no-]eta-equality@ keyword.
+   | PatternOrCopattern Range
+       -- ^ If declaration @pattern@ is present, give its range.
+   deriving (Eq, Show)
+
+type RecordDirectives = RecordDirectives' (Name, IsInstance)
+
+{-| The representation type of a declaration. The comments indicate
+    which type in the intended family the constructor targets.
+-}
+
+data Declaration
+  = TypeSig ArgInfo TacticAttribute Name Expr
+      -- ^ Axioms and functions can be irrelevant. (Hiding should be NotHidden)
+  | FieldSig IsInstance TacticAttribute Name (Arg Expr)
+  | Generalize Range [TypeSignature] -- ^ Variables to be generalized, can be hidden and/or irrelevant.
+  | Field Range [FieldSignature]
+  | FunClause LHS RHS WhereClause Bool
+  | DataSig     Range Erased Name [LamBinding] Expr -- ^ lone data signature in mutual block
+  | Data        Range Erased Name [LamBinding] Expr
+                [TypeSignatureOrInstanceBlock]
+  | DataDef     Range Name [LamBinding] [TypeSignatureOrInstanceBlock]
+  | RecordSig   Range Erased Name [LamBinding] Expr -- ^ lone record signature in mutual block
+  | RecordDef   Range Name RecordDirectives [LamBinding] [Declaration]
+  | Record      Range Erased Name RecordDirectives [LamBinding] Expr
+                [Declaration]
+  | RecordDirective RecordDirective -- ^ Should not survive beyond the parser
+  | Infix Fixity (List1 Name)
+  | Syntax      Name Notation -- ^ notation declaration for a name
+  | PatternSyn  Range Name [Arg Name] Pattern
+  | Mutual      Range [Declaration]  -- @Range@ of the whole @mutual@ block.
+  | InterleavedMutual Range [Declaration]
+  | Abstract    Range [Declaration]
+  | Private     Range Origin [Declaration]
+    -- ^ In "Agda.Syntax.Concrete.Definitions" we generate private blocks
+    --   temporarily, which should be treated different that user-declared
+    --   private blocks.  Thus the 'Origin'.
+  | InstanceB   Range [Declaration]
+    -- ^ The 'Range' here (exceptionally) only refers to the range of the
+    --   @instance@ keyword.  The range of the whole block @InstanceB r ds@
+    --   is @fuseRange r ds@.
+  | LoneConstructor Range [Declaration]
+  | Macro       Range [Declaration]
+  | Postulate   Range [TypeSignatureOrInstanceBlock]
+  | Primitive   Range [TypeSignature]
+  | Open        Range QName ImportDirective
+  | Import      Range QName (Maybe AsName) !OpenShortHand ImportDirective
+  | ModuleMacro Range Erased  Name ModuleApplication !OpenShortHand
+                ImportDirective
+  | Module      Range Erased QName Telescope [Declaration]
+  | UnquoteDecl Range [Name] Expr
+      -- ^ @unquoteDecl xs = e@
+  | UnquoteDef  Range [Name] Expr
+      -- ^ @unquoteDef xs = e@
+  | UnquoteData Range Name [Name] Expr
+      -- ^ @unquoteDecl data d constructor xs = e@
+  | Pragma      Pragma
+  | Opaque      Range [Declaration]
+    -- ^ @opaque ...@
+  | Unfolding   Range [QName]
+    -- ^ @unfolding ...@
+  deriving Eq
+
+-- | Extract a record directive
+isRecordDirective :: Declaration -> Maybe RecordDirective
+isRecordDirective (RecordDirective r) = Just r
+isRecordDirective (InstanceB r [RecordDirective (Constructor n p)]) = Just (Constructor n (InstanceDef r))
+isRecordDirective _ = Nothing
+
+-- | Return 'Pragma' if 'Declaration' is 'Pragma'.
+{-# SPECIALIZE isPragma :: Declaration -> Maybe Pragma #-}
+{-# SPECIALIZE isPragma :: Declaration -> [Pragma] #-}
+isPragma :: CMaybe Pragma m => Declaration -> m
+isPragma = \case
+    Pragma p                -> singleton p
+    Private  _ _ _          -> empty
+    Abstract _ _            -> empty
+    InstanceB _ _           -> empty
+    Mutual _ _              -> empty
+    Module _ _ _ _ _        -> empty
+    Macro _ _               -> empty
+    Record _ _ _ _ _ _ _    -> empty
+    RecordDef _ _ _ _ _     -> empty
+    TypeSig _ _ _ _         -> empty
+    FieldSig _ _ _ _        -> empty
+    Generalize _ _          -> empty
+    Field _ _               -> empty
+    FunClause _ _ _ _       -> empty
+    DataSig _ _ _ _ _       -> empty
+    Data _ _ _ _ _ _        -> empty
+    DataDef _ _ _ _         -> empty
+    RecordSig _ _ _ _ _     -> empty
+    RecordDirective _       -> empty
+    Infix _ _               -> empty
+    Syntax _ _              -> empty
+    PatternSyn _ _ _ _      -> empty
+    InterleavedMutual _ _   -> empty
+    LoneConstructor _ _     -> empty
+    Postulate _ _           -> empty
+    Primitive _ _           -> empty
+    Open _ _ _              -> empty
+    Import _ _ _ _ _        -> empty
+    ModuleMacro _ _ _ _ _ _ -> empty
+    UnquoteDecl _ _ _       -> empty
+    UnquoteDef _ _ _        -> empty
+    UnquoteData _ _ _ _     -> empty
+    Opaque _ _              -> empty
+    Unfolding _ _           -> empty
+
+data ModuleApplication
+  = SectionApp Range Telescope Expr
+    -- ^ @tel. M args@
+  | RecordModuleInstance Range QName
+    -- ^ @M {{...}}@
+  deriving Eq
+
+data OpenShortHand = DoOpen | DontOpen
+  deriving (Eq, Show, Generic)
+
+-- Pragmas ----------------------------------------------------------------
+
+data Pragma
+  = OptionsPragma             Range [String]
+  | BuiltinPragma             Range RString QName
+  | RewritePragma             Range Range [QName]        -- ^ Second Range is for REWRITE keyword.
+  | ForeignPragma             Range RString String       -- ^ first string is backend name
+  | CompilePragma             Range RString QName String -- ^ first string is backend name
+  | StaticPragma              Range QName
+  | InlinePragma              Range Bool QName  -- ^ INLINE or NOINLINE
+
+  | ImpossiblePragma          Range [String]
+    -- ^ Throws an internal error in the scope checker.
+    --   The 'String's are words to be displayed with the error.
+  | EtaPragma                 Range QName
+    -- ^ For coinductive records, use pragma instead of regular
+    --   @eta-equality@ definition (as it is might make Agda loop).
+  | WarningOnUsage            Range QName Text
+    -- ^ Applies to the named function
+  | WarningOnImport           Range Text
+    -- ^ Applies to the current module
+  | InjectivePragma           Range QName
+    -- ^ Mark a definition as injective for the pattern matching unifier.
+  | DisplayPragma             Range Pattern Expr
+    -- ^ Display lhs as rhs (modifies the printer).
+
+  -- Attached (more or less) pragmas handled in the nicifier (Concrete.Definitions):
+  | CatchallPragma            Range
+    -- ^ Applies to the following function clause.
+  | TerminationCheckPragma    Range (TerminationCheck Name)
+    -- ^ Applies to the following function (and all that are mutually recursive with it)
+    --   or to the functions in the following mutual block.
+  | NoCoverageCheckPragma     Range
+    -- ^ Applies to the following function (and all that are mutually recursive with it)
+    --   or to the functions in the following mutual block.
+  | NoPositivityCheckPragma   Range
+    -- ^ Applies to the following data/record type or mutual block.
+  | PolarityPragma            Range Name [Occurrence]
+  | NoUniverseCheckPragma     Range
+    -- ^ Applies to the following data/record type.
+  | NotProjectionLikePragma   Range QName
+    -- ^ Applies to the stated function
+  deriving Eq
+
+---------------------------------------------------------------------------
+
+-- | Modules: Top-level pragmas plus other top-level declarations.
+
+data Module = Mod
+  { modPragmas :: [Pragma]
+  , modDecls   :: [Declaration]
+  }
+
+-- | Splits off allowed (= import) declarations before the first
+--   non-allowed declaration.
+--   After successful parsing, the first non-allowed declaration
+--   should be a module declaration.
+spanAllowedBeforeModule :: [Declaration] -> ([Declaration], [Declaration])
+spanAllowedBeforeModule = span isAllowedBeforeModule
+  where
+    isAllowedBeforeModule (Pragma OptionsPragma{}) = True
+    isAllowedBeforeModule (Pragma BuiltinPragma{}) = True
+    isAllowedBeforeModule (Private _ _ ds) = all isAllowedBeforeModule ds
+    isAllowedBeforeModule Import{}       = True
+    isAllowedBeforeModule ModuleMacro{}  = True
+    isAllowedBeforeModule Open{}         = True
+    isAllowedBeforeModule _              = False
+
+{--------------------------------------------------------------------------
+    Things we parse but are not part of the Agda file syntax
+ --------------------------------------------------------------------------}
+
+-- | Extended content of an interaction hole.
+data HoleContent' qn nm p e
+  = HoleContentExpr    e                       -- ^ @e@
+  | HoleContentRewrite [RewriteEqn' qn nm p e] -- ^ @(rewrite | invert) e0 | ... | en@
+  deriving (Functor, Foldable, Traversable)
+
+type HoleContent = HoleContent' () Name Pattern Expr
+
+---------------------------------------------------------------------------
+-- * Smart constructors
+---------------------------------------------------------------------------
+
+rawApp :: List1 Expr -> Expr
+rawApp es@(e1 :| e2 : rest) = RawApp (getRange es) $ List2 e1 e2 rest
+rawApp (e :| []) = e
+
+rawAppP :: List1 Pattern -> Pattern
+rawAppP ps@(p1 :| p2 : rest) = RawAppP (getRange ps) $ List2 p1 p2 rest
+rawAppP (p :| []) = p
+
+{--------------------------------------------------------------------------
+    Views
+ --------------------------------------------------------------------------}
+
+-- | The 'Expr' is not an application.
+data AppView = AppView Expr [NamedArg Expr]
+
+appView :: Expr -> AppView
+appView e = f (DL.toList ess)
+  where
+    (f, ess) = appView' e
+
+    appView' = \case
+      App r e1 e2      -> vApp (appView' e1) e2
+      RawApp _ (List2 e1 e2 es)
+                       -> (AppView e1, DL.fromList (map arg (e2 : es)))
+      e                -> (AppView e, mempty)
+
+    vApp (f, es) arg = (f, es `DL.snoc` arg)
+
+    arg (HiddenArg   _ e) = hide         $ defaultArg e
+    arg (InstanceArg _ e) = makeInstance $ defaultArg e
+    arg e                 = defaultArg (unnamed e)
+
+unAppView :: AppView -> Expr
+unAppView (AppView e nargs) = rawApp (e :| map unNamedArg nargs)
+
+  where
+    unNamedArg narg = ($ unArg narg) $ case getHiding narg of
+      Hidden     -> HiddenArg (getRange narg)
+      NotHidden  -> namedThing
+      Instance{} -> InstanceArg (getRange narg)
+
+isSingleIdentifierP :: Pattern -> Maybe Name
+isSingleIdentifierP = \case
+  IdentP _ (QName x) -> Just x
+  WildP r            -> Just $ noName r
+  ParenP _ p         -> isSingleIdentifierP p
+  _                  -> Nothing
+
+removeParenP :: Pattern -> Pattern
+removeParenP = \case
+    ParenP _ p -> removeParenP p
+    p -> p
+
+-- | Observe the hiding status of an expression
+observeHiding :: Expr -> WithHiding Expr
+observeHiding = \case
+  HiddenArg _   (Named Nothing e) -> WithHiding Hidden e
+  InstanceArg _ (Named Nothing e) -> WithHiding (Instance NoOverlap) e
+  e                               -> WithHiding NotHidden e
+
+-- | Observe the relevance status of an expression
+observeRelevance :: Expr -> (Relevance, Expr)
+observeRelevance = \case
+  Dot _ e       -> (Irrelevant, e)
+  DoubleDot _ e -> (NonStrict, e)
+  e             -> (Relevant, e)
+
+-- | Observe various modifiers applied to an expression
+observeModifiers :: Expr -> Arg Expr
+observeModifiers e =
+  let (rel, WithHiding hid e') = fmap observeHiding (observeRelevance e) in
+  setRelevance rel $ setHiding hid $ defaultArg e'
+
+returnExpr :: Expr -> Maybe Expr
+returnExpr (Pi _ e)        = returnExpr e
+returnExpr (Fun _ _  e)    = returnExpr e
+returnExpr (Let _ _ e)     = returnExpr =<< e
+returnExpr (Paren _ e)     = returnExpr e
+returnExpr (Generalized e) = returnExpr e
+returnExpr e               = pure e
+
+-- | Turn an expression into a pattern. Fails if the expression is not a
+--   valid pattern.
+
+isPattern :: Expr -> Maybe Pattern
+isPattern = exprToPattern (const Nothing)
+
+-- | Turn an expression into a pattern, turning non-pattern subexpressions into 'WildP'.
+
+exprToPatternWithHoles :: Expr -> Pattern
+exprToPatternWithHoles = runIdentity . exprToPattern (Identity . WildP . getRange)
+
+-- | Generic expression to pattern conversion.
+
+exprToPattern :: Applicative m
+  => (Expr -> m Pattern)  -- ^ Default result for non-pattern things.
+  -> Expr                 -- ^ The expression to translate.
+  -> m Pattern            -- ^ The translated pattern (maybe).
+exprToPattern fallback = loop
+  where
+  loop = \case
+    Ident       x        -> pure $ IdentP True x
+    App         _ e1 e2  -> AppP <$> loop e1 <*> traverse (traverse loop) e2
+    Paren       r e      -> ParenP r <$> loop e
+    Underscore  r _      -> pure $ WildP r
+    Absurd      r        -> pure $ AbsurdP r
+    As          r x e    -> pushUnderBracesP r (AsP r x) <$> loop e
+    Dot         r e      -> pure $ pushUnderBracesE r (DotP r) e
+    -- Wen, 2020-08-27: We disallow Float patterns, since equality for floating
+    -- point numbers is not stable across architectures and with different
+    -- compiler flags.
+    e@(Lit _ LitFloat{}) -> fallback e
+    Lit         r l      -> pure $ LitP r l
+    HiddenArg   r e      -> HiddenP   r <$> traverse loop e
+    InstanceArg r e      -> InstanceP r <$> traverse loop e
+    RawApp      r es     -> RawAppP   r <$> traverse loop es
+    Quote       r        -> pure $ QuoteP r
+    Equal       r e1 e2  -> pure $ EqualP r [(e1, e2)]
+    Ellipsis    r        -> pure $ EllipsisP r Nothing
+    e@(Rec r es)
+        -- We cannot translate record expressions with module parts.
+      | Just fs <- mapM maybeLeft es -> RecP r <$> traverse (traverse loop) fs
+      | otherwise -> fallback e
+    -- WithApp has already lost the range information of the bars '|'
+    WithApp     r e es   -> do -- ApplicativeDo
+      p  <- loop e
+      ps <- forA es $ \ e -> do -- ApplicativeDo
+        p <- loop e
+        pure $ defaultNamedArg $ WithP (getRange e) p   -- TODO #2822: Range!
+      pure $ foldl AppP p ps
+    e -> fallback e
+
+  pushUnderBracesP :: Range -> (Pattern -> Pattern) -> (Pattern -> Pattern)
+  pushUnderBracesP r f = \case
+    HiddenP   _ p   -> HiddenP   r $ fmap f p
+    InstanceP _ p   -> InstanceP r $ fmap f p
+    p               -> f p
+
+  pushUnderBracesE :: Range -> (Expr -> Pattern) -> (Expr -> Pattern)
+  pushUnderBracesE r f = \case
+    HiddenArg   _ p -> HiddenP   r $ fmap f p
+    InstanceArg _ p -> InstanceP r $ fmap f p
+    p               -> f p
+
+isAbsurdP :: Pattern -> Maybe (Range, Hiding)
+isAbsurdP = \case
+  AbsurdP r      -> pure (r, NotHidden)
+  AsP _ _      p -> isAbsurdP p
+  ParenP _     p -> isAbsurdP p
+  HiddenP   _ np -> (Hidden <$)              <$> isAbsurdP (namedThing np)
+  InstanceP _ np -> (Instance YesOverlap <$) <$> isAbsurdP (namedThing np)
+  _ -> Nothing
+
+isBinderP :: Pattern -> Maybe Binder
+isBinderP = \case
+  IdentP _ qn
+             -> mkBinder_ <$> isUnqualified qn
+  WildP r    -> pure $ mkBinder_ $ setRange r simpleHole
+  AsP r n p  -> pure $ Binder (Just p) $ mkBoundName_ n
+  ParenP r p -> pure $ Binder (Just p) $ mkBoundName_ $ setRange r simpleHole
+  _ -> Nothing
+
+{--------------------------------------------------------------------------
+    Instances
+ --------------------------------------------------------------------------}
+
+-- Null
+------------------------------------------------------------------------
+
+-- | A 'WhereClause' is 'null' when the @where@ keyword is absent.
+--   An empty list of declarations does not count as 'null' here.
+
+instance Null (WhereClause' a) where
+  empty = NoWhere
+  null NoWhere = True
+  null AnyWhere{} = False
+  null SomeWhere{} = False
+
+-- Lenses
+------------------------------------------------------------------------
+
+instance LensHiding LamBinding where
+  getHiding   (DomainFree x) = getHiding x
+  getHiding   (DomainFull a) = getHiding a
+  mapHiding f (DomainFree x) = DomainFree $ mapHiding f x
+  mapHiding f (DomainFull a) = DomainFull $ mapHiding f a
+
+instance LensHiding TypedBinding where
+  getHiding (TBind _ (x :| _) _) = getHiding x   -- Slightly dubious
+  getHiding TLet{}               = mempty
+  mapHiding f (TBind r xs e) = TBind r (fmap (mapHiding f) xs) e
+  mapHiding f b@TLet{}       = b
+
+instance LensRelevance TypedBinding where
+  getRelevance (TBind _ (x :| _) _) = getRelevance x   -- Slightly dubious
+  getRelevance TLet{}               = unitRelevance
+  mapRelevance f (TBind r xs e) = TBind r (fmap (mapRelevance f) xs) e
+  mapRelevance f b@TLet{}       = b
+
+-- HasRange instances
+------------------------------------------------------------------------
+
+instance HasRange e => HasRange (OpApp e) where
+  getRange = \case
+    Ordinary e -> getRange e
+    SyntaxBindingLambda r _ _ -> r
+
+instance HasRange Expr where
+  getRange = \case
+      Ident x            -> getRange x
+      Lit r _            -> r
+      QuestionMark r _   -> r
+      Underscore r _     -> r
+      App r _ _          -> r
+      RawApp r _         -> r
+      OpApp r _ _ _      -> r
+      WithApp r _ _      -> r
+      Lam r _ _          -> r
+      AbsurdLam r _      -> r
+      ExtendedLam r _ _  -> r
+      Fun r _ _          -> r
+      Pi b e             -> fuseRange b e
+      Let r _ _          -> r
+      Paren r _          -> r
+      IdiomBrackets r _  -> r
+      DoBlock r _        -> r
+      As r _ _           -> r
+      Dot r _            -> r
+      DoubleDot r _      -> r
+      Absurd r           -> r
+      HiddenArg r _      -> r
+      InstanceArg r _    -> r
+      Rec r _            -> r
+      RecUpdate r _ _    -> r
+      Quote r            -> r
+      QuoteTerm r        -> r
+      Unquote r          -> r
+      Tactic r _         -> r
+      DontCare{}         -> noRange
+      Equal r _ _        -> r
+      Ellipsis r         -> r
+      Generalized e      -> getRange e
+      KnownIdent _ q     -> getRange q
+      KnownOpApp _ r _ _ _ -> r
+
+-- instance HasRange Telescope where
+--     getRange (TeleBind bs) = getRange bs
+--     getRange (TeleFun x y) = fuseRange x y
+
+instance HasRange Binder where
+  getRange (Binder a b) = fuseRange a b
+
+instance HasRange TypedBinding where
+  getRange (TBind r _ _) = r
+  getRange (TLet r _)    = r
+
+instance HasRange LamBinding where
+  getRange (DomainFree x) = getRange x
+  getRange (DomainFull b) = getRange b
+
+instance HasRange BoundName where
+  getRange = getRange . boundName
+
+instance HasRange WhereClause where
+  getRange  NoWhere               = noRange
+  getRange (AnyWhere r ds)        = getRange (r, ds)
+  getRange (SomeWhere r e x _ ds) = getRange (r, e, x, ds)
+
+instance HasRange ModuleApplication where
+  getRange (SectionApp r _ _) = r
+  getRange (RecordModuleInstance r _) = r
+
+instance HasRange a => HasRange (FieldAssignment' a) where
+  getRange (FieldAssignment a b) = fuseRange a b
+
+instance HasRange ModuleAssignment where
+  getRange (ModuleAssignment a b c) = fuseRange a b `fuseRange` c
+
+instance HasRange RecordDirective where
+  getRange (Induction a)          = getRange a
+  getRange (Eta a    )            = getRange a
+  getRange (Constructor a b)      = getRange (a, b)
+  getRange (PatternOrCopattern r) = r
+
+instance HasRange Declaration where
+  getRange (TypeSig _ _ x t)       = fuseRange x t
+  getRange (FieldSig _ _ x t)      = fuseRange x t
+  getRange (Field r _)             = r
+  getRange (FunClause lhs rhs wh _) = fuseRange lhs rhs `fuseRange` wh
+  getRange (DataSig r _ _ _ _)     = r
+  getRange (Data r _ _ _ _ _)      = r
+  getRange (DataDef r _ _ _)       = r
+  getRange (RecordSig r _ _ _ _)   = r
+  getRange (RecordDef r _ _ _ _)   = r
+  getRange (Record r _ _ _ _ _ _)  = r
+  getRange (RecordDirective r)     = getRange r
+  getRange (Mutual r _)            = r
+  getRange (InterleavedMutual r _) = r
+  getRange (LoneConstructor r _)   = r
+  getRange (Abstract r _)          = r
+  getRange (Generalize r _)        = r
+  getRange (Open r _ _)            = r
+  getRange (ModuleMacro r _ _ _ _ _)
+                                   = r
+  getRange (Import r _ _ _ _)      = r
+  getRange (InstanceB r _)         = r
+  getRange (Macro r _)             = r
+  getRange (Private r _ _)         = r
+  getRange (Postulate r _)         = r
+  getRange (Primitive r _)         = r
+  getRange (Module r _ _ _ _)      = r
+  getRange (Infix f _)             = getRange f
+  getRange (Syntax n _)            = getRange n
+  getRange (PatternSyn r _ _ _)    = r
+  getRange (UnquoteDecl r _ _)     = r
+  getRange (UnquoteDef r _ _)      = r
+  getRange (UnquoteData r _ _ _)   = r
+  getRange (Pragma p)              = getRange p
+  getRange (Opaque r _)            = r
+  getRange (Unfolding r _)         = r
+
+instance HasRange LHS where
+  getRange (LHS p eqns ws) = p `fuseRange` eqns `fuseRange` ws
+
+instance HasRange LHSCore where
+  getRange (LHSHead f ps)              = fuseRange f ps
+  getRange (LHSProj d ps1 lhscore ps2) = d `fuseRange` ps1 `fuseRange` lhscore `fuseRange` ps2
+  getRange (LHSWith f wps ps)          = f `fuseRange` wps `fuseRange` ps
+  getRange (LHSEllipsis r p)           = r
+
+instance HasRange RHS where
+  getRange AbsurdRHS = noRange
+  getRange (RHS e)   = getRange e
+
+instance HasRange LamClause where
+  getRange (LamClause lhs rhs _) = getRange (lhs, rhs)
+
+instance HasRange DoStmt where
+  getRange (DoBind r _ _ _) = r
+  getRange (DoThen e)       = getRange e
+  getRange (DoLet r _)      = r
+
+instance HasRange Pragma where
+  getRange (OptionsPragma r _)               = r
+  getRange (BuiltinPragma r _ _)             = r
+  getRange (RewritePragma r _ _)             = r
+  getRange (CompilePragma r _ _ _)           = r
+  getRange (ForeignPragma r _ _)             = r
+  getRange (StaticPragma r _)                = r
+  getRange (InjectivePragma r _)             = r
+  getRange (InlinePragma r _ _)              = r
+  getRange (ImpossiblePragma r _)            = r
+  getRange (EtaPragma r _)                   = r
+  getRange (TerminationCheckPragma r _)      = r
+  getRange (NoCoverageCheckPragma r)         = r
+  getRange (WarningOnUsage r _ _)            = r
+  getRange (WarningOnImport r _)             = r
+  getRange (CatchallPragma r)                = r
+  getRange (DisplayPragma r _ _)             = r
+  getRange (NoPositivityCheckPragma r)       = r
+  getRange (PolarityPragma r _ _)            = r
+  getRange (NoUniverseCheckPragma r)         = r
+  getRange (NotProjectionLikePragma r _)     = r
+
+instance HasRange AsName where
+  getRange a = getRange (asRange a, asName a)
+
+instance HasRange Pattern where
+  getRange (IdentP _ x)       = getRange x
+  getRange (AppP p q)         = fuseRange p q
+  getRange (OpAppP r _ _ _)   = r
+  getRange (RawAppP r _)      = r
+  getRange (ParenP r _)       = r
+  getRange (WildP r)          = r
+  getRange (AsP r _ _)        = r
+  getRange (AbsurdP r)        = r
+  getRange (LitP r _)         = r
+  getRange (QuoteP r)         = r
+  getRange (HiddenP r _)      = r
+  getRange (InstanceP r _)    = r
+  getRange (DotP r _)         = r
+  getRange (RecP r _)         = r
+  getRange (EqualP r _)       = r
+  getRange (EllipsisP r _)    = r
+  getRange (WithP r _)        = r
+
+-- SetRange instances
+------------------------------------------------------------------------
+
+instance SetRange Pattern where
+  setRange r (IdentP c x)       = IdentP c (setRange r x)
+  setRange r (AppP p q)         = AppP (setRange r p) (setRange r q)
+  setRange r (OpAppP _ x ns ps) = OpAppP r x ns ps
+  setRange r (RawAppP _ ps)     = RawAppP r ps
+  setRange r (ParenP _ p)       = ParenP r p
+  setRange r (WildP _)          = WildP r
+  setRange r (AsP _ x p)        = AsP r (setRange r x) p
+  setRange r (AbsurdP _)        = AbsurdP r
+  setRange r (LitP _ l)         = LitP r l
+  setRange r (QuoteP _)         = QuoteP r
+  setRange r (HiddenP _ p)      = HiddenP r p
+  setRange r (InstanceP _ p)    = InstanceP r p
+  setRange r (DotP _ e)         = DotP r e
+  setRange r (RecP _ fs)        = RecP r fs
+  setRange r (EqualP _ es)      = EqualP r es
+  setRange r (EllipsisP _ mp)   = EllipsisP r mp
+  setRange r (WithP _ p)        = WithP r p
+
+instance SetRange TypedBinding where
+  setRange r (TBind _ xs e) = TBind r xs e
+  setRange r (TLet _ ds)    = TLet r ds
+
+-- KillRange instances
+------------------------------------------------------------------------
+
+instance KillRange a => KillRange (FieldAssignment' a) where
+  killRange (FieldAssignment a b) = killRangeN FieldAssignment a b
+
+instance KillRange ModuleAssignment where
+  killRange (ModuleAssignment a b c) = killRangeN ModuleAssignment a b c
+
+instance KillRange AsName where
+  killRange (AsName n _) = killRangeN (flip AsName noRange) n
+
+instance KillRange Binder where
+  killRange (Binder a b) = killRangeN Binder a b
+
+instance KillRange BoundName where
+  killRange (BName n f t b) = killRangeN BName n f t b
+
+instance KillRange RecordDirective where
+  killRange (Induction a)          = killRangeN Induction a
+  killRange (Eta a    )            = killRangeN Eta a
+  killRange (Constructor a b)      = killRangeN Constructor a b
+  killRange (PatternOrCopattern _) = PatternOrCopattern noRange
+
+instance KillRange Declaration where
+  killRange (TypeSig i t n e)       = killRangeN (TypeSig i) t n e
+  killRange (FieldSig i t n e)      = killRangeN FieldSig i t n e
+  killRange (Generalize r ds )      = killRangeN (Generalize noRange) ds
+  killRange (Field r fs)            = killRangeN (Field noRange) fs
+  killRange (FunClause l r w ca)    = killRangeN FunClause l r w ca
+  killRange (DataSig _ er n l e)    = killRangeN (DataSig noRange) er n l e
+  killRange (Data _ er n l e c)     = killRangeN (Data noRange) er n l e c
+  killRange (DataDef _ n l c)       = killRangeN (DataDef noRange) n l c
+  killRange (RecordSig _ er n l e)  = killRangeN (RecordSig noRange) er n l e
+  killRange (RecordDef _ n dir k d) = killRangeN (RecordDef noRange) n dir k d
+  killRange (RecordDirective a)     = killRangeN RecordDirective a
+  killRange (Record _ er n dir k e d)
+                                    = killRangeN (Record noRange) er n dir k e d
+  killRange (Infix f n)             = killRangeN Infix f n
+  killRange (Syntax n no)           = killRangeN (\n -> Syntax n no) n
+  killRange (PatternSyn _ n ns p)   = killRangeN (PatternSyn noRange) n ns p
+  killRange (Mutual _ d)            = killRangeN (Mutual noRange) d
+  killRange (InterleavedMutual _ d) = killRangeN (InterleavedMutual noRange) d
+  killRange (LoneConstructor _ d)   = killRangeN (LoneConstructor noRange) d
+  killRange (Abstract _ d)          = killRangeN (Abstract noRange) d
+  killRange (Private _ o d)         = killRangeN (Private noRange) o d
+  killRange (InstanceB _ d)         = killRangeN (InstanceB noRange) d
+  killRange (Macro _ d)             = killRangeN (Macro noRange) d
+  killRange (Postulate _ t)         = killRangeN (Postulate noRange) t
+  killRange (Primitive _ t)         = killRangeN (Primitive noRange) t
+  killRange (Open _ q i)            = killRangeN (Open noRange) q i
+  killRange (Import _ q a o i)      = killRangeN (\q a -> Import noRange q a o) q a i
+  killRange (ModuleMacro _ e n m o i)
+                                    = killRangeN
+                                        (\e n m -> ModuleMacro noRange e n m o)
+                                        e n m i
+  killRange (Module _ e q t d)      = killRangeN (Module noRange) e q t d
+  killRange (UnquoteDecl _ x t)     = killRangeN (UnquoteDecl noRange) x t
+  killRange (UnquoteDef _ x t)      = killRangeN (UnquoteDef noRange) x t
+  killRange (UnquoteData _ xs cs t) = killRangeN (UnquoteData noRange) xs cs t
+  killRange (Pragma p)              = killRangeN Pragma p
+  killRange (Opaque r xs)           = killRangeN Opaque r xs
+  killRange (Unfolding r xs)        = killRangeN Unfolding r xs
+
+instance KillRange Expr where
+  killRange (Ident q)              = killRangeN Ident q
+  killRange (Lit _ l)              = killRangeN (Lit noRange) l
+  killRange (QuestionMark _ n)     = QuestionMark noRange n
+  killRange (Underscore _ n)       = Underscore noRange n
+  killRange (RawApp _ e)           = killRangeN (RawApp noRange) e
+  killRange (App _ e a)            = killRangeN (App noRange) e a
+  killRange (OpApp _ n ns o)       = killRangeN (OpApp noRange) n ns o
+  killRange (WithApp _ e es)       = killRangeN (WithApp noRange) e es
+  killRange (HiddenArg _ n)        = killRangeN (HiddenArg noRange) n
+  killRange (InstanceArg _ n)      = killRangeN (InstanceArg noRange) n
+  killRange (Lam _ l e)            = killRangeN (Lam noRange) l e
+  killRange (AbsurdLam _ h)        = killRangeN (AbsurdLam noRange) h
+  killRange (ExtendedLam _ e lrw)  = killRangeN (ExtendedLam noRange) e lrw
+  killRange (Fun _ e1 e2)          = killRangeN (Fun noRange) e1 e2
+  killRange (Pi t e)               = killRangeN Pi t e
+  killRange (Rec _ ne)             = killRangeN (Rec noRange) ne
+  killRange (RecUpdate _ e ne)     = killRangeN (RecUpdate noRange) e ne
+  killRange (Let _ d e)            = killRangeN (Let noRange) d e
+  killRange (Paren _ e)            = killRangeN (Paren noRange) e
+  killRange (IdiomBrackets _ es)   = killRangeN (IdiomBrackets noRange) es
+  killRange (DoBlock _ ss)         = killRangeN (DoBlock noRange) ss
+  killRange (Absurd _)             = Absurd noRange
+  killRange (As _ n e)             = killRangeN (As noRange) n e
+  killRange (Dot _ e)              = killRangeN (Dot noRange) e
+  killRange (DoubleDot _ e)        = killRangeN (DoubleDot noRange) e
+  killRange (Quote _)              = Quote noRange
+  killRange (QuoteTerm _)          = QuoteTerm noRange
+  killRange (Unquote _)            = Unquote noRange
+  killRange (Tactic _ t)           = killRangeN (Tactic noRange) t
+  killRange (DontCare e)           = killRangeN DontCare e
+  killRange (Equal _ x y)          = Equal noRange x y
+  killRange (Ellipsis _)           = Ellipsis noRange
+  killRange (Generalized e)        = killRangeN Generalized e
+  killRange (KnownIdent a b)       = killRangeN (KnownIdent a) b
+  killRange (KnownOpApp a b c d e) = killRangeN (KnownOpApp a) b c d e
+
+instance KillRange LamBinding where
+  killRange (DomainFree b) = killRangeN DomainFree b
+  killRange (DomainFull t) = killRangeN DomainFull t
+
+instance KillRange LHS where
+  killRange (LHS p r w)  = killRangeN LHS p r w
+
+instance KillRange LamClause where
+  killRange (LamClause a b c) = killRangeN LamClause a b c
+
+instance KillRange DoStmt where
+  killRange (DoBind r p e w) = killRangeN DoBind r p e w
+  killRange (DoThen e)       = killRangeN DoThen e
+  killRange (DoLet r ds)     = killRangeN DoLet r ds
+
+instance KillRange ModuleApplication where
+  killRange (SectionApp _ t e)    = killRangeN (SectionApp noRange) t e
+  killRange (RecordModuleInstance _ q) = killRangeN (RecordModuleInstance noRange) q
+
+instance KillRange e => KillRange (OpApp e) where
+  killRange (SyntaxBindingLambda _ l e) = killRangeN (SyntaxBindingLambda noRange) l e
+  killRange (Ordinary e)                = killRangeN Ordinary e
+
+instance KillRange Pattern where
+  killRange (IdentP c q)      = killRangeN IdentP c q
+  killRange (AppP p ps)       = killRangeN AppP p ps
+  killRange (RawAppP _ p)     = killRangeN (RawAppP noRange) p
+  killRange (OpAppP _ n ns p) = killRangeN (OpAppP noRange) n ns p
+  killRange (HiddenP _ n)     = killRangeN (HiddenP noRange) n
+  killRange (InstanceP _ n)   = killRangeN (InstanceP noRange) n
+  killRange (ParenP _ p)      = killRangeN (ParenP noRange) p
+  killRange (WildP _)         = WildP noRange
+  killRange (AbsurdP _)       = AbsurdP noRange
+  killRange (AsP _ n p)       = killRangeN (AsP noRange) n p
+  killRange (DotP _ e)        = killRangeN (DotP noRange) e
+  killRange (LitP _ l)        = killRangeN (LitP noRange) l
+  killRange (QuoteP _)        = QuoteP noRange
+  killRange (RecP _ fs)       = killRangeN (RecP noRange) fs
+  killRange (EqualP _ es)     = killRangeN (EqualP noRange) es
+  killRange (EllipsisP _ mp)  = killRangeN (EllipsisP noRange) mp
+  killRange (WithP _ p)       = killRangeN (WithP noRange) p
+
+instance KillRange Pragma where
+  killRange (OptionsPragma _ s)               = OptionsPragma noRange s
+  killRange (BuiltinPragma _ s e)             = killRangeN (BuiltinPragma noRange s) e
+  killRange (RewritePragma _ _ qs)            = killRangeN (RewritePragma noRange noRange) qs
+  killRange (StaticPragma _ q)                = killRangeN (StaticPragma noRange) q
+  killRange (InjectivePragma _ q)             = killRangeN (InjectivePragma noRange) q
+  killRange (InlinePragma _ b q)              = killRangeN (InlinePragma noRange b) q
+  killRange (CompilePragma _ b q s)           = killRangeN (\ q -> CompilePragma noRange b q s) q
+  killRange (ForeignPragma _ b s)             = ForeignPragma noRange b s
+  killRange (ImpossiblePragma _ strs)         = ImpossiblePragma noRange strs
+  killRange (TerminationCheckPragma _ t)      = TerminationCheckPragma noRange (killRange t)
+  killRange (NoCoverageCheckPragma _)         = NoCoverageCheckPragma noRange
+  killRange (WarningOnUsage _ nm str)         = WarningOnUsage noRange (killRange nm) str
+  killRange (WarningOnImport _ str)           = WarningOnImport noRange str
+  killRange (CatchallPragma _)                = CatchallPragma noRange
+  killRange (DisplayPragma _ lhs rhs)         = killRangeN (DisplayPragma noRange) lhs rhs
+  killRange (EtaPragma _ q)                   = killRangeN (EtaPragma noRange) q
+  killRange (NoPositivityCheckPragma _)       = NoPositivityCheckPragma noRange
+  killRange (PolarityPragma _ q occs)         = killRangeN (\q -> PolarityPragma noRange q occs) q
+  killRange (NoUniverseCheckPragma _)         = NoUniverseCheckPragma noRange
+  killRange (NotProjectionLikePragma _ q)     = NotProjectionLikePragma noRange q
+
+instance KillRange RHS where
+  killRange AbsurdRHS = AbsurdRHS
+  killRange (RHS e)   = killRangeN RHS e
+
+instance KillRange TypedBinding where
+  killRange (TBind _ b e) = killRangeN (TBind noRange) b e
+  killRange (TLet r ds)   = killRangeN TLet r ds
+
+instance KillRange WhereClause where
+  killRange NoWhere               = NoWhere
+  killRange (AnyWhere r d)        = killRangeN (AnyWhere noRange) d
+  killRange (SomeWhere r e n a d) =
+    killRangeN (SomeWhere noRange) e n a d
+
+------------------------------------------------------------------------
+-- NFData instances
+
+-- | Ranges are not forced.
+
+instance NFData Expr where
+  rnf (Ident a)           = rnf a
+  rnf (Lit _ a)           = rnf a
+  rnf (QuestionMark _ a)  = rnf a
+  rnf (Underscore _ a)    = rnf a
+  rnf (RawApp _ a)        = rnf a
+  rnf (App _ a b)         = rnf a `seq` rnf b
+  rnf (OpApp _ a b c)     = rnf a `seq` rnf b `seq` rnf c
+  rnf (WithApp _ a b)     = rnf a `seq` rnf b
+  rnf (HiddenArg _ a)     = rnf a
+  rnf (InstanceArg _ a)   = rnf a
+  rnf (Lam _ a b)         = rnf a `seq` rnf b
+  rnf (AbsurdLam _ a)     = rnf a
+  rnf (ExtendedLam _ a b) = rnf a `seq` rnf b
+  rnf (Fun _ a b)         = rnf a `seq` rnf b
+  rnf (Pi a b)            = rnf a `seq` rnf b
+  rnf (Rec _ a)           = rnf a
+  rnf (RecUpdate _ a b)   = rnf a `seq` rnf b
+  rnf (Let _ a b)         = rnf a `seq` rnf b
+  rnf (Paren _ a)         = rnf a
+  rnf (IdiomBrackets _ a) = rnf a
+  rnf (DoBlock _ a)       = rnf a
+  rnf (Absurd _)          = ()
+  rnf (As _ a b)          = rnf a `seq` rnf b
+  rnf (Dot _ a)           = rnf a
+  rnf (DoubleDot _ a)     = rnf a
+  rnf (Quote _)           = ()
+  rnf (QuoteTerm _)       = ()
+  rnf (Tactic _ a)        = rnf a
+  rnf (Unquote _)         = ()
+  rnf (DontCare a)        = rnf a
+  rnf (Equal _ a b)       = rnf a `seq` rnf b
+  rnf (Ellipsis _)        = ()
+  rnf (Generalized e)     = rnf e
+  rnf (KnownIdent a b)    = rnf b
+  rnf (KnownOpApp a b c d e) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d `seq` rnf c
+
+-- | Ranges are not forced.
+
+instance NFData Pattern where
+  rnf (IdentP a b)     = rnf a `seq` rnf b
+  rnf (QuoteP _)       = ()
+  rnf (AppP a b)       = rnf a `seq` rnf b
+  rnf (RawAppP _ a)    = rnf a
+  rnf (OpAppP _ a b c) = rnf a `seq` rnf b `seq` rnf c
+  rnf (HiddenP _ a)    = rnf a
+  rnf (InstanceP _ a)  = rnf a
+  rnf (ParenP _ a)     = rnf a
+  rnf (WildP _)        = ()
+  rnf (AbsurdP _)      = ()
+  rnf (AsP _ a b)      = rnf a `seq` rnf b
+  rnf (DotP _ a)       = rnf a
+  rnf (LitP _ a)       = rnf a
+  rnf (RecP _ a)       = rnf a
+  rnf (EqualP _ es)    = rnf es
+  rnf (EllipsisP _ mp) = rnf mp
+  rnf (WithP _ a)      = rnf a
+
+-- | Ranges are not forced.
+
+instance NFData RecordDirective where
+  rnf (Induction a)          = rnf a
+  rnf (Eta a    )            = rnf a
+  rnf (Constructor a b)      = rnf (a, b)
+  rnf (PatternOrCopattern _) = ()
+
+instance NFData Declaration where
+  rnf (TypeSig a b c d)       = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (FieldSig a b c d)      = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (Generalize _ a)        = rnf a
+  rnf (Field _ fs)            = rnf fs
+  rnf (FunClause a b c d)     = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (DataSig _ a b c d)     = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (Data _ a b c d e)      = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+                                      `seq` rnf e
+  rnf (DataDef _ a b c)       = rnf a `seq` rnf b `seq` rnf c
+  rnf (RecordSig _ a b c d)   = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (RecordDef _ a b c d)   = rnf (a, b, c, d)
+  rnf (Record _ a b c d e f)  = rnf (a, b, c, d, e, f)
+  rnf (RecordDirective a)     = rnf a
+  rnf (Infix a b)             = rnf a `seq` rnf b
+  rnf (Syntax a b)            = rnf a `seq` rnf b
+  rnf (PatternSyn _ a b c)    = rnf a `seq` rnf b `seq` rnf c
+  rnf (Mutual _ a)            = rnf a
+  rnf (InterleavedMutual _ a) = rnf a
+  rnf (LoneConstructor _ a)   = rnf a
+  rnf (Abstract _ a)          = rnf a
+  rnf (Private _ _ a)         = rnf a
+  rnf (InstanceB _ a)         = rnf a
+  rnf (Macro _ a)             = rnf a
+  rnf (Postulate _ a)         = rnf a
+  rnf (Primitive _ a)         = rnf a
+  rnf (Open _ a b)            = rnf a `seq` rnf b
+  rnf (Import _ a b _ c)      = rnf a `seq` rnf b `seq` rnf c
+  rnf (ModuleMacro _ a b c _ d)
+                              = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (Module _ a b c d)      = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+  rnf (UnquoteDecl _ a b)     = rnf a `seq` rnf b
+  rnf (UnquoteDef _ a b)      = rnf a `seq` rnf b
+  rnf (UnquoteData _ a b c)   = rnf a `seq` rnf b `seq` rnf c
+  rnf (Pragma a)              = rnf a
+  rnf (Opaque r xs)           = rnf r `seq` rnf xs
+  rnf (Unfolding r xs)        = rnf r `seq` rnf xs
+
+instance NFData OpenShortHand
+
+-- | Ranges are not forced.
+
+instance NFData Pragma where
+  rnf (OptionsPragma _ a)               = rnf a
+  rnf (BuiltinPragma _ a b)             = rnf a `seq` rnf b
+  rnf (RewritePragma _ _ a)             = rnf a
+  rnf (CompilePragma _ a b c)           = rnf a `seq` rnf b `seq` rnf c
+  rnf (ForeignPragma _ b s)             = rnf b `seq` rnf s
+  rnf (StaticPragma _ a)                = rnf a
+  rnf (InjectivePragma _ a)             = rnf a
+  rnf (InlinePragma _ _ a)              = rnf a
+  rnf (ImpossiblePragma _ a)            = rnf a
+  rnf (EtaPragma _ a)                   = rnf a
+  rnf (TerminationCheckPragma _ a)      = rnf a
+  rnf (NoCoverageCheckPragma _)         = ()
+  rnf (WarningOnUsage _ a b)            = rnf a `seq` rnf b
+  rnf (WarningOnImport _ a)             = rnf a
+  rnf (CatchallPragma _)                = ()
+  rnf (DisplayPragma _ a b)             = rnf a `seq` rnf b
+  rnf (NoPositivityCheckPragma _)       = ()
+  rnf (PolarityPragma _ a b)            = rnf a `seq` rnf b
+  rnf (NoUniverseCheckPragma _)         = ()
+  rnf (NotProjectionLikePragma _ q)     = rnf q
+
+-- | Ranges are not forced.
+
+instance NFData AsName where
+  rnf (AsName a _) = rnf a
+
+-- | Ranges are not forced.
+
+instance NFData a => NFData (TypedBinding' a) where
+  rnf (TBind _ a b) = rnf a `seq` rnf b
+  rnf (TLet _ a)    = rnf a
+
+-- | Ranges are not forced.
+
+instance NFData ModuleApplication where
+  rnf (SectionApp _ a b)    = rnf a `seq` rnf b
+  rnf (RecordModuleInstance _ a) = rnf a
+
+-- | Ranges are not forced.
+
+instance NFData a => NFData (OpApp a) where
+  rnf (SyntaxBindingLambda _ a b) = rnf a `seq` rnf b
+  rnf (Ordinary a)                = rnf a
+
+-- | Ranges are not forced.
+
+instance NFData LHS where
+  rnf (LHS a b c) = rnf a `seq` rnf b `seq` rnf c
+
+instance NFData a => NFData (FieldAssignment' a) where
+  rnf (FieldAssignment a b) = rnf a `seq` rnf b
+
+instance NFData ModuleAssignment where
+  rnf (ModuleAssignment a b c) = rnf a `seq` rnf b `seq` rnf c
+
+instance NFData a => NFData (WhereClause' a) where
+  rnf NoWhere               = ()
+  rnf (AnyWhere _ a)        = rnf a
+  rnf (SomeWhere _ a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+
+instance NFData LamClause where
+  rnf (LamClause a b c) = rnf (a, b, c)
+
+instance NFData a => NFData (LamBinding' a) where
+  rnf (DomainFree a) = rnf a
+  rnf (DomainFull a) = rnf a
+
+instance NFData Binder where
+  rnf (Binder a b) = rnf a `seq` rnf b
+
+instance NFData BoundName where
+  rnf (BName a b c d) = rnf a `seq` rnf b `seq` rnf c `seq` rnf d
+
+instance NFData a => NFData (RHS' a) where
+  rnf AbsurdRHS = ()
+  rnf (RHS a)   = rnf a
+
+instance NFData DoStmt where
+  rnf (DoBind _ p e w) = rnf (p, e, w)
+  rnf (DoThen e)       = rnf e
+  rnf (DoLet _ ds)     = rnf ds
diff --git a/src/full/Agda/Syntax/Concrete/Attribute.hs b/src/full/Agda/Syntax/Concrete/Attribute.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Attribute.hs
@@ -0,0 +1,229 @@
+
+-- | Attributes: concrete syntax for ArgInfo, esp. modalities.
+
+module Agda.Syntax.Concrete.Attribute where
+
+import Control.Arrow (second)
+import Control.Monad (foldM)
+
+import Data.List (foldl')
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Maybe
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete (Expr(..), TacticAttribute)
+import Agda.Syntax.Concrete.Pretty () --instance only
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Syntax.Position
+
+import Agda.Utils.List1 (List1, pattern (:|))
+
+import Agda.Utils.Impossible
+
+-- | An attribute is a modifier for `ArgInfo`.
+
+data Attribute
+  = RelevanceAttribute Relevance
+  | QuantityAttribute  Quantity
+  | TacticAttribute (Ranged Expr)
+  | CohesionAttribute Cohesion
+  | LockAttribute      Lock
+  deriving (Show)
+
+instance HasRange Attribute where
+  getRange = \case
+    RelevanceAttribute r -> getRange r
+    QuantityAttribute q  -> getRange q
+    CohesionAttribute c  -> getRange c
+    TacticAttribute e    -> getRange e
+    LockAttribute l      -> NoRange
+
+instance SetRange Attribute where
+  setRange r = \case
+    RelevanceAttribute a -> RelevanceAttribute $ setRange r a
+    QuantityAttribute q  -> QuantityAttribute  $ setRange r q
+    CohesionAttribute c  -> CohesionAttribute  $ setRange r c
+    TacticAttribute e    -> TacticAttribute e  -- -- $ setRange r e -- SetRange Expr not yet implemented
+    LockAttribute l      -> LockAttribute l
+
+instance KillRange Attribute where
+  killRange = \case
+    RelevanceAttribute a -> RelevanceAttribute $ killRange a
+    QuantityAttribute q  -> QuantityAttribute  $ killRange q
+    CohesionAttribute c  -> CohesionAttribute  $ killRange c
+    TacticAttribute e    -> TacticAttribute    $ killRange e
+    LockAttribute l      -> LockAttribute l
+
+-- | (Conjunctive constraint.)
+
+type LensAttribute a = (LensRelevance a, LensQuantity a, LensCohesion a, LensLock a)
+
+-- | Modifiers for 'Relevance'.
+
+relevanceAttributeTable :: [(String, Relevance)]
+relevanceAttributeTable = concat
+  [ map (, Irrelevant)  [ "irr", "irrelevant" ]
+  , map (, NonStrict)   [ "shirr", "shape-irrelevant" ]
+  , map (, Relevant)    [ "relevant" ]
+  ]
+
+-- | Modifiers for 'Quantity'.
+
+quantityAttributeTable :: [(String, Quantity)]
+quantityAttributeTable =
+  [ ("0"      , Quantity0 $ Q0       noRange)
+  , ("erased" , Quantity0 $ Q0Erased noRange)
+  -- TODO: linearity
+  -- , ("1"      , Quantity1 $ Q1       noRange)
+  -- , ("linear" , Quantity1 $ Q1Linear noRange)
+  , ("ω"      , Quantityω $ Qω       noRange)
+  , ("plenty" , Quantityω $ QωPlenty noRange)
+  ]
+-- quantityAttributeTable = concat
+--   [ map (, Quantity0) [ "0", "erased" ] -- , "static", "compile-time" ]
+--   , map (, Quantityω) [ "ω", "plenty" ] -- , "dynamic", "runtime", "unrestricted", "abundant" ]
+--   -- , map (, Quantity1)  [ "1", "linear" ]
+--   -- , map (, Quantity01) [ "01", "affine" ]
+--   ]
+
+cohesionAttributeTable :: [(String, Cohesion)]
+cohesionAttributeTable =
+  [ ("♭"    , Flat)
+  , ("flat" , Flat)
+  ]
+
+-- | Information about attributes (attribute, range, printed
+-- representation).
+--
+-- This information is returned by the parser. Code that calls the
+-- parser should, if appropriate, complain if support for the given
+-- attributes has not been enabled. This can be taken care of by
+-- 'Agda.Syntax.Translation.ConcreteToAbstract.checkAttributes', which
+-- should not be called until after pragma options have been set.
+
+type Attributes = [(Attribute, Range, String)]
+
+-- | Modifiers for 'Quantity'.
+
+lockAttributeTable :: [(String, Lock)]
+lockAttributeTable = concat
+  [ map (, IsNotLock) [ "notlock" ] -- default, shouldn't be used much
+  , map (, IsLock LockOTick) [ "tick" ] -- @tick
+  , map (, IsLock LockOLock) [ "lock" ] -- @lock
+  ]
+
+
+-- | Concrete syntax for all attributes.
+
+attributesMap :: Map String Attribute
+attributesMap = Map.fromListWith __IMPOSSIBLE__ $ concat
+  [ map (second RelevanceAttribute) relevanceAttributeTable
+  , map (second QuantityAttribute)  quantityAttributeTable
+  , map (second CohesionAttribute)  cohesionAttributeTable
+  , map (second LockAttribute)      lockAttributeTable
+  ]
+
+-- | Parsing a string into an attribute.
+
+stringToAttribute :: String -> Maybe Attribute
+stringToAttribute = (`Map.lookup` attributesMap)
+
+-- | Parsing an expression into an attribute.
+
+exprToAttribute :: Expr -> Maybe Attribute
+exprToAttribute = \case
+  e@(Paren _ (Tactic _ t)) -> Just $ TacticAttribute $ Ranged (getRange e) t
+  e -> setRange (getRange e) $ stringToAttribute $ prettyShow e
+
+-- | Setting an attribute (in e.g. an 'Arg').  Overwrites previous value.
+
+setAttribute :: (LensAttribute a) => Attribute -> a -> a
+setAttribute = \case
+  RelevanceAttribute r -> setRelevance r
+  QuantityAttribute  q -> setQuantity  q
+  CohesionAttribute  c -> setCohesion  c
+  LockAttribute      l -> setLock      l
+  TacticAttribute t    -> id
+
+
+-- | Setting some attributes in left-to-right order.
+--   Blindly overwrites previous settings.
+
+setAttributes :: (LensAttribute a) => [Attribute] -> a -> a
+setAttributes attrs arg = foldl' (flip setAttribute) arg attrs
+
+---------------------------------------------------------------------------
+-- * Applying attributes only if they have not been set already.
+--   No overwriting.
+---------------------------------------------------------------------------
+
+-- | Setting 'Relevance' if unset.
+
+setPristineRelevance :: (LensRelevance a) => Relevance -> a -> Maybe a
+setPristineRelevance r a
+  | getRelevance a == defaultRelevance = Just $ setRelevance r a
+  | otherwise = Nothing
+
+-- | Setting 'Quantity' if unset.
+
+setPristineQuantity :: (LensQuantity a) => Quantity -> a -> Maybe a
+setPristineQuantity q a
+  | noUserQuantity a = Just $ setQuantity q a
+  | otherwise = Nothing
+
+-- | Setting 'Cohesion' if unset.
+
+setPristineCohesion :: (LensCohesion a) => Cohesion -> a -> Maybe a
+setPristineCohesion c a
+  | getCohesion a == defaultCohesion = Just $ setCohesion c a
+  | otherwise = Nothing
+
+-- | Setting 'Lock' if unset.
+
+setPristineLock :: (LensLock a) => Lock -> a -> Maybe a
+setPristineLock q a
+  | getLock a == defaultLock = Just $ setLock q a
+  | otherwise = Nothing
+
+-- | Setting an unset attribute (to e.g. an 'Arg').
+
+setPristineAttribute :: (LensAttribute a) => Attribute -> a -> Maybe a
+setPristineAttribute = \case
+  RelevanceAttribute r -> setPristineRelevance r
+  QuantityAttribute  q -> setPristineQuantity  q
+  CohesionAttribute  c -> setPristineCohesion  c
+  LockAttribute      l -> setPristineLock      l
+  TacticAttribute{}    -> Just
+
+-- | Setting a list of unset attributes.
+
+setPristineAttributes :: (LensAttribute a) => [Attribute] -> a -> Maybe a
+setPristineAttributes attrs arg = foldM (flip setPristineAttribute) arg attrs
+
+---------------------------------------------------------------------------
+-- * Filtering attributes
+---------------------------------------------------------------------------
+
+isRelevanceAttribute :: Attribute -> Maybe Relevance
+isRelevanceAttribute = \case
+  RelevanceAttribute q -> Just q
+  _ -> Nothing
+
+isQuantityAttribute :: Attribute -> Maybe Quantity
+isQuantityAttribute = \case
+  QuantityAttribute q -> Just q
+  _ -> Nothing
+
+isTacticAttribute :: Attribute -> TacticAttribute
+isTacticAttribute (TacticAttribute t) = Just t
+isTacticAttribute _                   = Nothing
+
+relevanceAttributes :: [Attribute] -> [Attribute]
+relevanceAttributes = filter $ isJust . isRelevanceAttribute
+
+quantityAttributes :: [Attribute] -> [Attribute]
+quantityAttributes = filter $ isJust . isQuantityAttribute
+
+tacticAttributes :: [Attribute] -> [Attribute]
+tacticAttributes = filter $ isJust . isTacticAttribute
diff --git a/src/full/Agda/Syntax/Concrete/Definitions.hs b/src/full/Agda/Syntax/Concrete/Definitions.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Definitions.hs
@@ -0,0 +1,1522 @@
+{-# LANGUAGE GADTs              #-}
+
+-- | Preprocess 'Agda.Syntax.Concrete.Declaration's, producing 'NiceDeclaration's.
+--
+--   * Attach fixity and syntax declarations to the definition they refer to.
+--
+--   * Distribute the following attributes to the individual definitions:
+--       @abstract@,
+--       @instance@,
+--       @postulate@,
+--       @primitive@,
+--       @private@,
+--       termination pragmas.
+--
+--   * Gather the function clauses belonging to one function definition.
+--
+--   * Expand ellipsis @...@ in function clauses following @with@.
+--
+--   * Infer mutual blocks.
+--     A block starts when a lone signature is encountered, and ends when
+--     all lone signatures have seen their definition.
+--
+--   * Handle interleaved mutual blocks.
+--     In an `interleaved mutual' block we:
+--     * leave the data and fun sigs in place
+--     * classify signatures in `constructor' block based on their return type
+--       and group them all as a data def at the position in the block where the
+--       first constructor for the data sig in question occured
+--     * classify fun clauses based on the declared function used and group them
+--       all as a fundef at the position in the block where the first such fun
+--       clause appeared
+--
+--   * Report basic well-formedness error,
+--     when one of the above transformation fails.
+--     When possible, errors should be deferred to the scope checking phase
+--     (ConcreteToAbstract), where we are in the TCM and can produce more
+--     informative error messages.
+
+
+module Agda.Syntax.Concrete.Definitions
+    ( NiceDeclaration(..)
+    , NiceConstructor, NiceTypeSignature
+    , Clause(..)
+    , DeclarationException(..)
+    , DeclarationWarning(..), DeclarationWarning'(..), unsafeDeclarationWarning
+    , Nice, NiceEnv(..), runNice
+    , niceDeclarations
+    , notSoNiceDeclarations
+    , niceHasAbstract
+    , Measure
+    , declarationWarningName
+    ) where
+
+
+import Prelude hiding (null)
+
+import Control.Monad         ( forM, guard, unless, void, when )
+import Control.Monad.Except  ( )
+import Control.Monad.Reader  ( asks )
+import Control.Monad.State   ( MonadState(..), gets, StateT, runStateT )
+import Control.Monad.Trans   ( lift )
+
+import Data.Bifunctor
+import Data.Either (isLeft, isRight)
+import Data.Function (on)
+import qualified Data.Map as Map
+import Data.Map (Map)
+import Data.Maybe
+import Data.Semigroup ( Semigroup(..) )
+import qualified Data.List as List
+import qualified Data.Foldable as Fold
+import qualified Data.Traversable as Trav
+
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Pattern
+import Agda.Syntax.Common hiding (TerminationCheck())
+import qualified Agda.Syntax.Common as Common
+import Agda.Syntax.Position
+import Agda.Syntax.Notation
+import Agda.Syntax.Concrete.Pretty () --instance only
+import Agda.Syntax.Concrete.Fixity
+import Agda.Syntax.Common.Pretty
+
+import Agda.Syntax.Concrete.Definitions.Errors
+import Agda.Syntax.Concrete.Definitions.Monad
+import Agda.Syntax.Concrete.Definitions.Types
+
+import Agda.Utils.AffineHole
+import Agda.Utils.CallStack ( CallStack, HasCallStack, withCallerCallStack )
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List (isSublistOf, spanJust)
+import Agda.Utils.List1 (List1, pattern (:|), (<|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+import Agda.Utils.Three
+import Agda.Utils.Tuple
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+{--------------------------------------------------------------------------
+    The niceifier
+ --------------------------------------------------------------------------}
+
+-- | Check that declarations in a mutual block are consistently
+--   equipped with MEASURE pragmas, or whether there is a
+--   NO_TERMINATION_CHECK pragma.
+combineTerminationChecks :: Range -> [TerminationCheck] -> Nice TerminationCheck
+combineTerminationChecks r tcs = loop tcs where
+  loop :: [TerminationCheck] -> Nice TerminationCheck
+  loop []         = return TerminationCheck
+  loop (tc : tcs) = do
+    let failure r = declarationException $ InvalidMeasureMutual r
+    tc' <- loop tcs
+    case (tc, tc') of
+      (TerminationCheck      , tc'                   ) -> return tc'
+      (tc                    , TerminationCheck      ) -> return tc
+      (NonTerminating        , NonTerminating        ) -> return NonTerminating
+      (NoTerminationCheck    , NoTerminationCheck    ) -> return NoTerminationCheck
+      (NoTerminationCheck    , Terminating           ) -> return Terminating
+      (Terminating           , NoTerminationCheck    ) -> return Terminating
+      (Terminating           , Terminating           ) -> return Terminating
+      (TerminationMeasure{}  , TerminationMeasure{}  ) -> return tc
+      (TerminationMeasure r _, NoTerminationCheck    ) -> failure r
+      (TerminationMeasure r _, Terminating           ) -> failure r
+      (NoTerminationCheck    , TerminationMeasure r _) -> failure r
+      (Terminating           , TerminationMeasure r _) -> failure r
+      (TerminationMeasure r _, NonTerminating        ) -> failure r
+      (NonTerminating        , TerminationMeasure r _) -> failure r
+      (NoTerminationCheck    , NonTerminating        ) -> failure r
+      (Terminating           , NonTerminating        ) -> failure r
+      (NonTerminating        , NoTerminationCheck    ) -> failure r
+      (NonTerminating        , Terminating           ) -> failure r
+
+combineCoverageChecks :: [CoverageCheck] -> CoverageCheck
+combineCoverageChecks = Fold.fold
+
+combinePositivityChecks :: [PositivityCheck] -> PositivityCheck
+combinePositivityChecks = Fold.fold
+
+data DeclKind
+    = LoneSigDecl Range DataRecOrFun Name
+    | LoneDefs DataRecOrFun [Name]
+    | OtherDecl
+  deriving (Eq, Show)
+
+declKind :: NiceDeclaration -> DeclKind
+declKind (FunSig r _ _ _ _ _ tc cc x _)      = LoneSigDecl r (FunName tc cc) x
+declKind (NiceRecSig r _ _ _ pc uc x _ _)    = LoneSigDecl r (RecName pc uc) x
+declKind (NiceDataSig r _ _ _ pc uc x _ _)   = LoneSigDecl r (DataName pc uc) x
+declKind (FunDef r _ abs ins tc cc x _)      = LoneDefs (FunName tc cc) [x]
+declKind (NiceDataDef _ _ _ pc uc x pars _)  = LoneDefs (DataName pc uc) [x]
+declKind (NiceUnquoteData _ _ _ pc uc x _ _) = LoneDefs (DataName pc uc) [x]
+declKind (NiceRecDef _ _ _ pc uc x _ pars _) = LoneDefs (RecName pc uc) [x]
+declKind (NiceUnquoteDef _ _ _ tc cc xs _)   = LoneDefs (FunName tc cc) xs
+declKind Axiom{}                             = OtherDecl
+declKind NiceField{}                         = OtherDecl
+declKind PrimitiveFunction{}                 = OtherDecl
+declKind NiceMutual{}                        = OtherDecl
+declKind NiceModule{}                        = OtherDecl
+declKind NiceModuleMacro{}                   = OtherDecl
+declKind NiceOpen{}                          = OtherDecl
+declKind NiceImport{}                        = OtherDecl
+declKind NicePragma{}                        = OtherDecl
+declKind NiceFunClause{}                     = OtherDecl
+declKind NicePatternSyn{}                    = OtherDecl
+declKind NiceGeneralize{}                    = OtherDecl
+declKind NiceUnquoteDecl{}                   = OtherDecl
+declKind NiceLoneConstructor{}               = OtherDecl
+declKind NiceOpaque{}                        = OtherDecl
+
+-- | Replace (Data/Rec/Fun)Sigs with Axioms for postulated names
+--   The first argument is a list of axioms only.
+replaceSigs
+  :: LoneSigs               -- ^ Lone signatures to be turned into Axioms
+  -> [NiceDeclaration]      -- ^ Declarations containing them
+  -> [NiceDeclaration]      -- ^ In the output, everything should be defined
+replaceSigs ps = if Map.null ps then id else \case
+  []     -> __IMPOSSIBLE__
+  (d:ds) ->
+    case replaceable d of
+      -- If declaration d of x is mentioned in the map of lone signatures then replace
+      -- it with an axiom
+      Just (x, axiom)
+        | (Just (LoneSig _ x' _), ps') <- Map.updateLookupWithKey (\ _ _ -> Nothing) x ps
+        , getRange x == getRange x'
+            -- Use the range as UID to ensure we do not replace the wrong signature.
+            -- This could happen if the user wrote a duplicate definition.
+        -> axiom : replaceSigs ps' ds
+      _ -> d     : replaceSigs ps  ds
+
+  where
+
+    -- A @replaceable@ declaration is a signature. It has a name and we can make an
+    -- @Axiom@ out of it.
+    replaceable :: NiceDeclaration -> Maybe (Name, NiceDeclaration)
+    replaceable = \case
+      FunSig r acc abst inst _ argi _ _ x' e ->
+        -- #4881: Don't use the unique NameId for NoName lookups.
+        let x = if isNoName x' then noName (nameRange x') else x' in
+        Just (x, Axiom r acc abst inst argi x' e)
+      NiceRecSig r erased acc abst _ _ x pars t ->
+        let e = Generalized $ makePi (lamBindingsToTelescope r pars) t in
+        Just (x, Axiom r acc abst NotInstanceDef
+                   (setQuantity (asQuantity erased) defaultArgInfo) x e)
+      NiceDataSig r erased acc abst _ _ x pars t ->
+        let e = Generalized $ makePi (lamBindingsToTelescope r pars) t in
+        Just (x, Axiom r acc abst NotInstanceDef
+                   (setQuantity (asQuantity erased) defaultArgInfo) x e)
+      _ -> Nothing
+
+-- | Main. Fixities (or more precisely syntax declarations) are needed when
+--   grouping function clauses.
+niceDeclarations :: Fixities -> [Declaration] -> Nice [NiceDeclaration]
+niceDeclarations fixs ds = do
+
+  -- Run the nicifier in an initial environment. But keep the warnings.
+  st <- get
+  put $ initNiceState { niceWarn = niceWarn st }
+  nds <- nice ds
+
+  -- Check that every signature got its definition.
+  ps <- use loneSigs
+  checkLoneSigs ps
+  -- We postulate the missing ones and insert them in place of the corresponding @FunSig@
+  let ds = replaceSigs ps nds
+
+  -- Note that loneSigs is ensured to be empty.
+  -- (Important, since inferMutualBlocks also uses loneSigs state).
+  res <- inferMutualBlocks ds
+
+  -- Restore the old state, but keep the warnings.
+  warns <- gets niceWarn
+  put $ st { niceWarn = warns }
+  return res
+
+  where
+
+    inferMutualBlocks :: [NiceDeclaration] -> Nice [NiceDeclaration]
+    inferMutualBlocks [] = return []
+    inferMutualBlocks (d : ds) =
+      case declKind d of
+        OtherDecl    -> (d :) <$> inferMutualBlocks ds
+        LoneDefs{}   -> (d :) <$> inferMutualBlocks ds  -- Andreas, 2017-10-09, issue #2576: report error in ConcreteToAbstract
+        LoneSigDecl r k x  -> do
+          _ <- addLoneSig r x k
+          InferredMutual checks nds0 ds1 <- untilAllDefined (mutualChecks k) ds
+          -- If we still have lone signatures without any accompanying definition,
+          -- we postulate the definition and substitute the axiom for the lone signature
+          ps <- use loneSigs
+          checkLoneSigs ps
+          let ds0 = replaceSigs ps (d : nds0) -- NB: don't forget the LoneSig the block started with!
+          -- We then keep processing the rest of the block
+          tc <- combineTerminationChecks (getRange d) (mutualTermination checks)
+          let cc = combineCoverageChecks              (mutualCoverage checks)
+          let pc = combinePositivityChecks            (mutualPositivity checks)
+          (NiceMutual (getRange ds0) tc cc pc ds0 :) <$> inferMutualBlocks ds1
+      where
+        untilAllDefined :: MutualChecks -> [NiceDeclaration] -> Nice InferredMutual
+        untilAllDefined checks ds = do
+          done <- noLoneSigs
+          if done then return (InferredMutual checks [] ds) else
+            case ds of
+              []     -> return (InferredMutual checks [] ds)
+              d : ds -> case declKind d of
+                LoneSigDecl r k x -> do
+                  void $ addLoneSig r x k
+                  extendInferredBlock  d <$> untilAllDefined (mutualChecks k <> checks) ds
+                LoneDefs k xs -> do
+                  mapM_ removeLoneSig xs
+                  extendInferredBlock  d <$> untilAllDefined (mutualChecks k <> checks) ds
+                OtherDecl -> extendInferredBlock d <$> untilAllDefined checks ds
+
+    nice :: [Declaration] -> Nice [NiceDeclaration]
+    nice [] = return []
+    nice ds = do
+      (xs , ys) <- nice1 ds
+      (xs ++) <$> nice ys
+
+    nice1 :: [Declaration] -> Nice ([NiceDeclaration], [Declaration])
+    nice1 []     = return ([], []) -- Andreas, 2017-09-16, issue #2759: no longer __IMPOSSIBLE__
+    nice1 (d:ds) = do
+      let justWarning :: HasCallStack => DeclarationWarning' -> Nice ([NiceDeclaration], [Declaration])
+          justWarning w = do
+            -- NOTE: This is the location of the invoker of justWarning, not here.
+            withCallerCallStack $ declarationWarning' w
+            nice1 ds
+
+      case d of
+
+        TypeSig info _tac x t -> do
+          termCheck <- use terminationCheckPragma
+          covCheck  <- use coverageCheckPragma
+          -- Andreas, 2020-09-28, issue #4950: take only range of identifier,
+          -- since parser expands type signatures with several identifiers
+          -- (like @x y z : A@) into several type signatures (with imprecise ranges).
+          let r = getRange x
+          -- register x as lone type signature, to recognize clauses later
+          x' <- addLoneSig r x $ FunName termCheck covCheck
+          return ([FunSig r PublicAccess ConcreteDef NotInstanceDef NotMacroDef info termCheck covCheck x' t] , ds)
+
+        -- Should not show up: all FieldSig are part of a Field block
+        FieldSig{} -> __IMPOSSIBLE__
+
+        Generalize r [] -> justWarning $ EmptyGeneralize r
+        Generalize r sigs -> do
+          gs <- forM sigs $ \case
+            sig@(TypeSig info tac x t) -> do
+              -- Andreas, 2022-03-25, issue #5850:
+              -- Warn about @variable {x} : A@ which is equivalent to @variable x : A@.
+              when (getHiding info == Hidden) $
+                declarationWarning $ HiddenGeneralize $ getRange x
+              return $ NiceGeneralize (getRange sig) PublicAccess info tac x t
+            _ -> __IMPOSSIBLE__
+          return (gs, ds)
+
+        (FunClause lhs _ _ _)         -> do
+          termCheck <- use terminationCheckPragma
+          covCheck  <- use coverageCheckPragma
+          catchall  <- popCatchallPragma
+          xs <- loneFuns <$> use loneSigs
+          -- for each type signature 'x' waiting for clauses, we try
+          -- if we have some clauses for 'x'
+          case [ (x, (x', fits, rest))
+               | (x, x') <- xs
+               , let (fits, rest) =
+                      -- Anonymous declarations only have 1 clause each!
+                      if isNoName x then ([d], ds)
+                      else span (couldBeFunClauseOf (Map.lookup x fixs) x) (d : ds)
+               , not (null fits)
+               ] of
+
+            -- case: clauses match none of the sigs
+            [] -> case lhs of
+              -- Subcase: The lhs is single identifier (potentially anonymous).
+              -- Treat it as a function clause without a type signature.
+              LHS p [] [] | Just x <- isSingleIdentifierP p -> do
+                d  <- mkFunDef (setOrigin Inserted defaultArgInfo) termCheck covCheck x Nothing [d] -- fun def without type signature is relevant
+                return (d , ds)
+              -- Subcase: The lhs is a proper pattern.
+              -- This could be a let-pattern binding. Pass it on.
+              -- A missing type signature error might be raise in ConcreteToAbstract
+              _ -> do
+                return ([NiceFunClause (getRange d) PublicAccess ConcreteDef termCheck covCheck catchall d] , ds)
+
+            -- case: clauses match exactly one of the sigs
+            [(x,(x',fits,rest))] -> do
+               -- The x'@NoName{} is the unique version of x@NoName{}.
+               removeLoneSig x
+               ds  <- expandEllipsis fits
+               cs  <- mkClauses x' ds False
+               return ([FunDef (getRange fits) fits ConcreteDef NotInstanceDef termCheck covCheck x' cs] , rest)
+
+            -- case: clauses match more than one sigs (ambiguity)
+            xf:xfs -> declarationException $ AmbiguousFunClauses lhs $ List1.reverse $ fmap fst $ xf :| xfs
+                 -- "ambiguous function clause; cannot assign it uniquely to one type signature"
+
+        Field r [] -> justWarning $ EmptyField r
+        Field _ fs -> (,ds) <$> niceAxioms FieldBlock fs
+
+        DataSig r erased x tel t -> do
+          pc <- use positivityCheckPragma
+          uc <- use universeCheckPragma
+          _ <- addLoneSig r x $ DataName pc uc
+          (,ds) <$> dataOrRec pc uc NiceDataDef
+                      (flip NiceDataSig erased) (niceAxioms DataBlock) r
+                      x (Just (tel, t)) Nothing
+
+        Data r erased x tel t cs -> do
+          pc <- use positivityCheckPragma
+          -- Andreas, 2018-10-27, issue #3327
+          -- Propagate {-# NO_UNIVERSE_CHECK #-} pragma from signature to definition.
+          -- Universe check is performed if both the current value of
+          -- 'universeCheckPragma' AND the one from the signature say so.
+          uc <- use universeCheckPragma
+          uc <- if uc == NoUniverseCheck then return uc else getUniverseCheckFromSig x
+          mt <- defaultTypeSig (DataName pc uc) x (Just t)
+          (,ds) <$> dataOrRec pc uc NiceDataDef
+                      (flip NiceDataSig erased) (niceAxioms DataBlock) r
+                      x ((tel,) <$> mt) (Just (tel, cs))
+
+        DataDef r x tel cs -> do
+          pc <- use positivityCheckPragma
+          -- Andreas, 2018-10-27, issue #3327
+          -- Propagate {-# NO_UNIVERSE_CHECK #-} pragma from signature to definition.
+          -- Universe check is performed if both the current value of
+          -- 'universeCheckPragma' AND the one from the signature say so.
+          uc <- use universeCheckPragma
+          uc <- if uc == NoUniverseCheck then return uc else getUniverseCheckFromSig x
+          mt <- defaultTypeSig (DataName pc uc) x Nothing
+          (,ds) <$> dataOrRec pc uc NiceDataDef
+                      (flip NiceDataSig defaultErased)
+                      (niceAxioms DataBlock) r x ((tel,) <$> mt)
+                      (Just (tel, cs))
+
+        RecordSig r erased x tel t -> do
+          pc <- use positivityCheckPragma
+          uc <- use universeCheckPragma
+          _ <- addLoneSig r x $ RecName pc uc
+          return ( [NiceRecSig r erased PublicAccess ConcreteDef pc uc x
+                      tel t]
+                 , ds
+                 )
+
+        Record r erased x dir tel t cs -> do
+          pc <- use positivityCheckPragma
+          -- Andreas, 2018-10-27, issue #3327
+          -- Propagate {-# NO_UNIVERSE_CHECK #-} pragma from signature to definition.
+          -- Universe check is performed if both the current value of
+          -- 'universeCheckPragma' AND the one from the signature say so.
+          uc <- use universeCheckPragma
+          uc <- if uc == NoUniverseCheck then return uc else getUniverseCheckFromSig x
+          mt <- defaultTypeSig (RecName pc uc) x (Just t)
+          (,ds) <$> dataOrRec pc uc
+                      (\r o a pc uc x tel cs ->
+                        NiceRecDef r o a pc uc x dir tel cs)
+                      (flip NiceRecSig erased) return r x
+                      ((tel,) <$> mt) (Just (tel, cs))
+
+        RecordDef r x dir tel cs   -> do
+          pc <- use positivityCheckPragma
+          -- Andreas, 2018-10-27, issue #3327
+          -- Propagate {-# NO_UNIVERSE_CHECK #-} pragma from signature to definition.
+          -- Universe check is performed if both the current value of
+          -- 'universeCheckPragma' AND the one from the signature say so.
+          uc <- use universeCheckPragma
+          uc <- if uc == NoUniverseCheck then return uc else getUniverseCheckFromSig x
+          mt <- defaultTypeSig (RecName pc uc) x Nothing
+          (,ds) <$> dataOrRec pc uc
+                      (\r o a pc uc x tel cs ->
+                        NiceRecDef r o a pc uc x dir tel cs)
+                      (flip NiceRecSig defaultErased) return r x
+                      ((tel,) <$> mt) (Just (tel, cs))
+
+        RecordDirective r -> justWarning $ InvalidRecordDirective (getRange r)
+
+        Mutual r ds' -> do
+          -- The lone signatures encountered so far are not in scope
+          -- for the mutual definition
+          breakImplicitMutualBlock r "`mutual` blocks"
+          case ds' of
+            [] -> justWarning $ EmptyMutual r
+            _  -> (,ds) <$> (singleton <$> (mkOldMutual r =<< nice ds'))
+
+        InterleavedMutual r ds' -> do
+          -- The lone signatures encountered so far are not in scope
+          -- for the mutual definition
+          breakImplicitMutualBlock r "`interleaved mutual` blocks"
+          case ds' of
+            [] -> justWarning $ EmptyMutual r
+            _  -> (,ds) <$> (singleton <$> (mkInterleavedMutual r =<< nice ds'))
+
+        LoneConstructor r [] -> justWarning $ EmptyConstructor r
+        LoneConstructor r ds' ->
+          ((,ds) . singleton . NiceLoneConstructor r) <$> niceAxioms ConstructorBlock ds'
+
+
+        Abstract r []  -> justWarning $ EmptyAbstract r
+        Abstract r ds' ->
+          (,ds) <$> (abstractBlock r =<< nice ds')
+
+        Private r UserWritten []  -> justWarning $ EmptyPrivate r
+        Private r o ds' ->
+          (,ds) <$> (privateBlock r o =<< nice ds')
+
+        InstanceB r []  -> justWarning $ EmptyInstance r
+        InstanceB r ds' ->
+          (,ds) <$> (instanceBlock r =<< nice ds')
+
+        Macro r []  -> justWarning $ EmptyMacro r
+        Macro r ds' ->
+          (,ds) <$> (macroBlock r =<< nice ds')
+
+        Postulate r []  -> justWarning $ EmptyPostulate r
+        Postulate _ ds' ->
+          (,ds) <$> niceAxioms PostulateBlock ds'
+
+        Primitive r []  -> justWarning $ EmptyPrimitive r
+        Primitive _ ds' -> (,ds) <$> (map toPrim <$> niceAxioms PrimitiveBlock ds')
+
+        Module r erased x tel ds' -> return $
+          ([NiceModule r PublicAccess ConcreteDef erased x tel ds'], ds)
+
+        ModuleMacro r erased x modapp op is -> return $
+          ([NiceModuleMacro r PublicAccess erased x modapp op is], ds)
+
+        -- Fixity and syntax declarations and polarity pragmas have
+        -- already been processed.
+        Infix _ _  -> return ([], ds)
+        Syntax _ _ -> return ([], ds)
+
+        PatternSyn r n as p -> do
+          return ([NicePatternSyn r PublicAccess n as p] , ds)
+        Open r x is         -> return ([NiceOpen r x is] , ds)
+        Import r x as op is -> return ([NiceImport r x as op is] , ds)
+
+        UnquoteDecl r xs e -> do
+          tc <- use terminationCheckPragma
+          cc <- use coverageCheckPragma
+          return ([NiceUnquoteDecl r PublicAccess ConcreteDef NotInstanceDef tc cc xs e] , ds)
+
+        UnquoteDef r xs e -> do
+          sigs <- map fst . loneFuns <$> use loneSigs
+          List1.ifNotNull (filter (`notElem` sigs) xs)
+            {-then-} (declarationException . UnquoteDefRequiresSignature)
+            {-else-} $ do
+              mapM_ removeLoneSig xs
+              return ([NiceUnquoteDef r PublicAccess ConcreteDef TerminationCheck YesCoverageCheck xs e] , ds)
+
+        UnquoteData r xs cs e -> do
+          pc <- use positivityCheckPragma
+          uc <- use universeCheckPragma
+          return ([NiceUnquoteData r PublicAccess ConcreteDef pc uc xs cs e], ds)
+
+        Pragma p -> do
+          -- Warn about unsafe pragmas unless we are in a builtin module.
+          whenM (asks safeButNotBuiltin) $
+            whenJust (unsafePragma p) $ \ w ->
+              declarationWarning w
+          nicePragma p ds
+
+        Opaque r ds' -> do
+          breakImplicitMutualBlock r "`opaque` blocks"
+
+          -- Split the enclosed declarations into an initial run of
+          -- 'unfolding' statements and the rest of the body.
+          let
+            (unfoldings, body) = flip spanMaybe ds' $ \case
+              Unfolding _ ns -> pure ns
+              _ -> Nothing
+
+          -- The body of an 'opaque' definition can have mutual
+          -- recursion by interleaving type signatures and definitions,
+          -- just like the body of a module.
+          decls0 <- nice body
+          ps <- use loneSigs
+          checkLoneSigs ps
+          let decls = replaceSigs ps decls0
+          body <- inferMutualBlocks decls
+          pure ([NiceOpaque r (concat unfoldings) body], ds)
+
+        Unfolding r _ -> declarationException $ UnfoldingOutsideOpaque r
+
+    nicePragma :: Pragma -> [Declaration] -> Nice ([NiceDeclaration], [Declaration])
+
+    nicePragma (TerminationCheckPragma r (TerminationMeasure _ x)) ds =
+      if canHaveTerminationMeasure ds then
+        withTerminationCheckPragma (TerminationMeasure r x) $ nice1 ds
+      else do
+        declarationWarning $ InvalidTerminationCheckPragma r
+        nice1 ds
+
+    nicePragma (TerminationCheckPragma r NoTerminationCheck) ds = do
+      -- This PRAGMA has been deprecated in favour of (NON_)TERMINATING
+      -- We warn the user about it and then assume the function is NON_TERMINATING.
+      declarationWarning $ PragmaNoTerminationCheck r
+      nicePragma (TerminationCheckPragma r NonTerminating) ds
+
+    nicePragma (TerminationCheckPragma r tc) ds =
+      if canHaveTerminationCheckPragma ds then
+        withTerminationCheckPragma tc $ nice1 ds
+      else do
+        declarationWarning $ InvalidTerminationCheckPragma r
+        nice1 ds
+
+    nicePragma (NoCoverageCheckPragma r) ds =
+      if canHaveCoverageCheckPragma ds then
+        withCoverageCheckPragma NoCoverageCheck $ nice1 ds
+      else do
+        declarationWarning $ InvalidCoverageCheckPragma r
+        nice1 ds
+
+    nicePragma (CatchallPragma r) ds =
+      if canHaveCatchallPragma ds then
+        withCatchallPragma True $ nice1 ds
+      else do
+        declarationWarning $ InvalidCatchallPragma r
+        nice1 ds
+
+    nicePragma (NoPositivityCheckPragma r) ds =
+      if canHaveNoPositivityCheckPragma ds then
+        withPositivityCheckPragma NoPositivityCheck $ nice1 ds
+      else do
+        declarationWarning $ InvalidNoPositivityCheckPragma r
+        nice1 ds
+
+    nicePragma (NoUniverseCheckPragma r) ds =
+      if canHaveNoUniverseCheckPragma ds then
+        withUniverseCheckPragma NoUniverseCheck $ nice1 ds
+      else do
+        declarationWarning $ InvalidNoUniverseCheckPragma r
+        nice1 ds
+
+    nicePragma p@CompilePragma{} ds = do
+      return ([NicePragma (getRange p) p], ds)
+
+    nicePragma (PolarityPragma{}) ds = return ([], ds)
+
+    nicePragma (BuiltinPragma r str qn@(QName x)) ds = do
+      return ([NicePragma r (BuiltinPragma r str qn)], ds)
+
+    nicePragma p@RewritePragma{} ds = return ([NicePragma (getRange p) p], ds)
+    nicePragma p ds = return ([NicePragma (getRange p) p], ds)
+
+    canHaveTerminationMeasure :: [Declaration] -> Bool
+    canHaveTerminationMeasure [] = False
+    canHaveTerminationMeasure (d:ds) = case d of
+      TypeSig{} -> True
+      (Pragma p) | isAttachedPragma p -> canHaveTerminationMeasure ds
+      _         -> False
+
+    canHaveTerminationCheckPragma :: [Declaration] -> Bool
+    canHaveTerminationCheckPragma []     = False
+    canHaveTerminationCheckPragma (d:ds) = case d of
+      Mutual _ ds   -> any (canHaveTerminationCheckPragma . singleton) ds
+      TypeSig{}     -> True
+      FunClause{}   -> True
+      UnquoteDecl{} -> True
+      (Pragma p) | isAttachedPragma p -> canHaveTerminationCheckPragma ds
+      _             -> False
+
+    canHaveCoverageCheckPragma :: [Declaration] -> Bool
+    canHaveCoverageCheckPragma = canHaveTerminationCheckPragma
+
+    canHaveCatchallPragma :: [Declaration] -> Bool
+    canHaveCatchallPragma []     = False
+    canHaveCatchallPragma (d:ds) = case d of
+      FunClause{} -> True
+      (Pragma p) | isAttachedPragma p -> canHaveCatchallPragma ds
+      _           -> False
+
+    canHaveNoPositivityCheckPragma :: [Declaration] -> Bool
+    canHaveNoPositivityCheckPragma []     = False
+    canHaveNoPositivityCheckPragma (d:ds) = case d of
+      Mutual _ ds                   -> any (canHaveNoPositivityCheckPragma . singleton) ds
+      Data{}                        -> True
+      DataSig{}                     -> True
+      DataDef{}                     -> True
+      Record{}                      -> True
+      RecordSig{}                   -> True
+      RecordDef{}                   -> True
+      Pragma p | isAttachedPragma p -> canHaveNoPositivityCheckPragma ds
+      _                             -> False
+
+    canHaveNoUniverseCheckPragma :: [Declaration] -> Bool
+    canHaveNoUniverseCheckPragma []     = False
+    canHaveNoUniverseCheckPragma (d:ds) = case d of
+      Data{}                        -> True
+      DataSig{}                     -> True
+      DataDef{}                     -> True
+      Record{}                      -> True
+      RecordSig{}                   -> True
+      RecordDef{}                   -> True
+      Pragma p | isAttachedPragma p -> canHaveNoPositivityCheckPragma ds
+      _                             -> False
+
+    -- Pragma that attaches to the following declaration.
+    isAttachedPragma :: Pragma -> Bool
+    isAttachedPragma = \case
+      TerminationCheckPragma{}  -> True
+      CatchallPragma{}          -> True
+      NoPositivityCheckPragma{} -> True
+      NoUniverseCheckPragma{}   -> True
+      _                         -> False
+
+    -- We could add a default type signature here, but at the moment we can't
+    -- infer the type of a record or datatype, so better to just fail here.
+    defaultTypeSig :: DataRecOrFun -> Name -> Maybe Expr -> Nice (Maybe Expr)
+    defaultTypeSig k x t@Just{} = return t
+    defaultTypeSig k x Nothing  = do
+      caseMaybeM (getSig x) (return Nothing) $ \ k' -> do
+        unless (sameKind k k') $ declarationException $ WrongDefinition x k' k
+        Nothing <$ removeLoneSig x
+
+    dataOrRec
+      :: forall a decl
+      .  PositivityCheck
+      -> UniverseCheck
+      -> (Range -> Origin -> IsAbstract -> PositivityCheck -> UniverseCheck -> Name -> [LamBinding] -> [decl] -> NiceDeclaration)
+         -- Construct definition.
+      -> (Range -> Access -> IsAbstract -> PositivityCheck -> UniverseCheck -> Name -> [LamBinding] -> Expr -> NiceDeclaration)
+         -- Construct signature.
+      -> ([a] -> Nice [decl])        -- Constructor checking.
+      -> Range
+      -> Name                        -- Data/record type name.
+      -> Maybe ([LamBinding], Expr)  -- Parameters and type.  If not @Nothing@ a signature is created.
+      -> Maybe ([LamBinding], [a])   -- Parameters and constructors.  If not @Nothing@, a definition body is created.
+      -> Nice [NiceDeclaration]
+    dataOrRec pc uc mkDef mkSig niceD r x mt mcs = do
+      mds <- Trav.forM mcs $ \ (tel, cs) -> (tel,) <$> niceD cs
+      -- We set origin to UserWritten if the user split the data/rec herself,
+      -- and to Inserted if the she wrote a single declaration that we're
+      -- splitting up here. We distinguish these because the scoping rules for
+      -- generalizable variables differ in these cases.
+      let o | isJust mt && isJust mcs = Inserted
+            | otherwise               = UserWritten
+      return $ catMaybes $
+        [ mt  <&> \ (tel, t)  -> mkSig (fuseRange x t) PublicAccess ConcreteDef pc uc x tel t
+        , mds <&> \ (tel, ds) -> mkDef r o ConcreteDef pc uc x (caseMaybe mt tel $ const $ concatMap dropTypeAndModality tel) ds
+          -- If a type is given (mt /= Nothing), we have to delete the types in @tel@
+          -- for the data definition, lest we duplicate them. And also drop modalities (#1886).
+        ]
+    -- Translate axioms
+    niceAxioms :: KindOfBlock -> [TypeSignatureOrInstanceBlock] -> Nice [NiceDeclaration]
+    niceAxioms b ds = List.concat <$> mapM (niceAxiom b) ds
+
+    niceAxiom :: KindOfBlock -> TypeSignatureOrInstanceBlock -> Nice [NiceDeclaration]
+    niceAxiom b = \case
+      d@(TypeSig rel _tac x t) -> do
+        return [ Axiom (getRange d) PublicAccess ConcreteDef NotInstanceDef rel x t ]
+      d@(FieldSig i tac x argt) | b == FieldBlock -> do
+        return [ NiceField (getRange d) PublicAccess ConcreteDef i tac x argt ]
+      InstanceB r decls -> do
+        instanceBlock r =<< niceAxioms InstanceBlock decls
+      Private r o decls | PostulateBlock <- b -> do
+        privateBlock r o =<< niceAxioms b decls
+      Pragma p@(RewritePragma r _ _) -> do
+        return [ NicePragma r p ]
+      d -> declarationException $ WrongContentBlock b $ getRange d
+
+    toPrim :: NiceDeclaration -> NiceDeclaration
+    toPrim (Axiom r p a i rel x t) = PrimitiveFunction r p a x (Arg rel t)
+    toPrim _                       = __IMPOSSIBLE__
+
+    -- Create a function definition.
+    mkFunDef info termCheck covCheck x mt ds0 = do
+      ds <- expandEllipsis ds0
+      cs <- mkClauses x ds False
+      return [ FunSig (fuseRange x t) PublicAccess ConcreteDef NotInstanceDef NotMacroDef info termCheck covCheck x t
+             , FunDef (getRange ds0) ds0 ConcreteDef NotInstanceDef termCheck covCheck x cs ]
+        where
+          t = fromMaybe (underscore (getRange x)) mt
+
+    underscore r = Underscore r Nothing
+
+
+    expandEllipsis :: [Declaration] -> Nice [Declaration]
+    expandEllipsis [] = return []
+    expandEllipsis (d@(FunClause lhs@(LHS p _ _) _ _ _) : ds)
+      | hasEllipsis p = (d :) <$> expandEllipsis ds
+      | otherwise     = (d :) <$> expand (killRange p) ds
+      where
+        expand :: Pattern -> [Declaration] -> Nice [Declaration]
+        expand _ [] = return []
+        expand p (d : ds) = do
+          case d of
+            Pragma (CatchallPragma _) -> do
+                  (d :) <$> expand p ds
+            FunClause (LHS p0 eqs es) rhs wh ca -> do
+              case hasEllipsis' p0 of
+                ManyHoles -> declarationException $ MultipleEllipses p0
+                OneHole cxt ~(EllipsisP r Nothing) -> do
+                  -- Replace the ellipsis by @p@.
+                  let p1 = cxt $ EllipsisP r $ Just $ setRange r p
+                  let d' = FunClause (LHS p1 eqs es) rhs wh ca
+                  -- If we have with-expressions (es /= []) then the following
+                  -- ellipses also get the additional patterns in p0.
+                  (d' :) <$> expand (if null es then p else killRange p1) ds
+                ZeroHoles _ -> do
+                  -- We can have ellipses after a fun clause without.
+                  -- They refer to the last clause that introduced new with-expressions.
+                  -- Same here: If we have new with-expressions, the next ellipses will
+                  -- refer to us.
+                  -- Andreas, Jesper, 2017-05-13, issue #2578
+                  -- Need to update the range also on the next with-patterns.
+                  (d :) <$> expand (if null es then p else killRange p0) ds
+            _ -> __IMPOSSIBLE__
+    expandEllipsis _ = __IMPOSSIBLE__
+
+    -- Turn function clauses into nice function clauses.
+    mkClauses :: Name -> [Declaration] -> Catchall -> Nice [Clause]
+    mkClauses _ [] _ = return []
+    mkClauses x (Pragma (CatchallPragma r) : cs) True  = do
+      declarationWarning $ InvalidCatchallPragma r
+      mkClauses x cs True
+    mkClauses x (Pragma (CatchallPragma r) : cs) False = do
+      when (null cs) $ declarationWarning $ InvalidCatchallPragma r
+      mkClauses x cs True
+
+    mkClauses x (FunClause lhs rhs wh ca : cs) catchall
+      | null (lhsWithExpr lhs) || hasEllipsis lhs  =
+      (Clause x (ca || catchall) lhs rhs wh [] :) <$> mkClauses x cs False   -- Will result in an error later.
+
+    mkClauses x (FunClause lhs rhs wh ca : cs) catchall = do
+      when (null withClauses) $ declarationException $ MissingWithClauses x lhs
+      wcs <- mkClauses x withClauses False
+      (Clause x (ca || catchall) lhs rhs wh wcs :) <$> mkClauses x cs' False
+      where
+        (withClauses, cs') = subClauses cs
+
+        -- A clause is a subclause if the number of with-patterns is
+        -- greater or equal to the current number of with-patterns plus the
+        -- number of with arguments.
+        numWith = numberOfWithPatterns p + length (filter visible es) where LHS p _ es = lhs
+
+        subClauses :: [Declaration] -> ([Declaration],[Declaration])
+        subClauses (c@(FunClause (LHS p0 _ _) _ _ _) : cs)
+         | isEllipsis p0 ||
+           numberOfWithPatterns p0 >= numWith = mapFst (c:) (subClauses cs)
+         | otherwise                           = ([], c:cs)
+        subClauses (c@(Pragma (CatchallPragma r)) : cs) = case subClauses cs of
+          ([], cs') -> ([], c:cs')
+          (cs, cs') -> (c:cs, cs')
+        subClauses [] = ([],[])
+        subClauses _  = __IMPOSSIBLE__
+    mkClauses _ _ _ = __IMPOSSIBLE__
+
+    couldBeCallOf :: Maybe Fixity' -> Name -> Pattern -> Bool
+    couldBeCallOf mFixity x p =
+      let
+      pns        = patternNames p
+      xStrings   = nameStringParts x
+      patStrings = concatMap nameStringParts pns
+      in
+--          trace ("x = " ++ prettyShow x) $
+--          trace ("pns = " ++ show pns) $
+--          trace ("xStrings = " ++ show xStrings) $
+--          trace ("patStrings = " ++ show patStrings) $
+--          trace ("mFixity = " ++ show mFixity) $
+      case (listToMaybe pns, mFixity) of
+        -- first identifier in the patterns is the fun.symbol?
+        (Just y, _) | x == y -> True -- trace ("couldBe since y = " ++ prettyShow y) $ True
+        -- are the parts of x contained in p
+        _ | xStrings `isSublistOf` patStrings -> True -- trace ("couldBe since isSublistOf") $ True
+        -- looking for a mixfix fun.symb
+        (_, Just fix) ->  -- also matches in case of a postfix
+           let notStrings = stringParts (theNotation fix)
+           in  -- trace ("notStrings = " ++ show notStrings) $
+               -- trace ("patStrings = " ++ show patStrings) $
+               not (null notStrings) && (notStrings `isSublistOf` patStrings)
+        -- not a notation, not first id: give up
+        _ -> False -- trace ("couldBe not (case default)") $ False
+
+
+    -- for finding nice clauses for a type sig in mutual blocks
+    couldBeNiceFunClauseOf :: Maybe Fixity' -> Name -> NiceDeclaration
+                           -> Maybe (MutualChecks, Declaration)
+    couldBeNiceFunClauseOf mf n (NiceFunClause _ _ _ tc cc _ d)
+      = (MutualChecks [tc] [cc] [], d) <$ guard (couldBeFunClauseOf mf n d)
+    couldBeNiceFunClauseOf _ _ _ = Nothing
+
+    -- for finding clauses for a type sig in mutual blocks
+    couldBeFunClauseOf :: Maybe Fixity' -> Name -> Declaration -> Bool
+    couldBeFunClauseOf mFixity x (Pragma (CatchallPragma{})) = True
+    couldBeFunClauseOf mFixity x (FunClause (LHS p _ _) _ _ _) =
+       hasEllipsis p || couldBeCallOf mFixity x p
+    couldBeFunClauseOf _ _ _ = False -- trace ("couldBe not (fun default)") $ False
+
+    -- Turn a new style `interleaved mutual' block into a new style mutual block
+    -- by grouping the declarations in blocks.
+    mkInterleavedMutual
+      :: Range                 -- Range of the whole @mutual@ block.
+      -> [NiceDeclaration]     -- Declarations inside the block.
+      -> Nice NiceDeclaration  -- Returns a 'NiceMutual'.
+    mkInterleavedMutual r ds' = do
+      (other, (m, checks, _)) <- runStateT (groupByBlocks r ds') (empty, mempty, 0)
+      let idecls = other ++ concatMap (uncurry interleavedDecl) (Map.toList m)
+      let decls0 = map snd $ List.sortBy (compare `on` fst) idecls
+      ps <- use loneSigs
+      checkLoneSigs ps
+      let decls = replaceSigs ps decls0
+      -- process the checks
+      tc <- combineTerminationChecks r (mutualTermination checks)
+      let cc = combineCoverageChecks   (mutualCoverage checks)
+      let pc = combinePositivityChecks (mutualPositivity checks)
+      pure $ NiceMutual r tc cc pc decls
+
+      where
+
+        ------------------------------------------------------------------------------
+        -- Adding Signatures
+        addType :: Name -> (DeclNum -> a) -> MutualChecks
+                -> StateT (Map Name a, MutualChecks, DeclNum) Nice ()
+        addType n c mc = do
+          (m, checks, i) <- get
+          when (isJust $ Map.lookup n m) $ lift $ declarationException $ DuplicateDefinition n
+          put (Map.insert n (c i) m, mc <> checks, i + 1)
+
+        addFunType d@(FunSig _ _ _ _ _ _ tc cc n _) = do
+           let checks = MutualChecks [tc] [cc] []
+           addType n (\ i -> InterleavedFun i d Nothing) checks
+        addFunType _ = __IMPOSSIBLE__
+
+        addDataType d@(NiceDataSig _ _ _ _ pc uc n _ _) = do
+          let checks = MutualChecks [] [] [pc]
+          addType n (\ i -> InterleavedData i d Nothing) checks
+        addDataType _ = __IMPOSSIBLE__
+
+        ------------------------------------------------------------------------------
+        -- Adding constructors & clauses
+
+        addDataConstructors :: Maybe Range        -- Range of the `data A where` (if any)
+                            -> Maybe Name         -- Data type the constructors belong to
+                            -> [NiceConstructor]  -- Constructors to add
+                            -> StateT (InterleavedMutual, MutualChecks, DeclNum) Nice ()
+        -- if we know the type's name, we can go ahead
+        addDataConstructors mr (Just n) ds = do
+          (m, checks, i) <- get
+          case Map.lookup n m of
+            Just (InterleavedData i0 sig cs) -> do
+              lift $ removeLoneSig n
+              -- add the constructors to the existing ones (if any)
+              let (cs', i') = case cs of
+                    Nothing        -> ((i , ds :| [] ), i + 1)
+                    Just (i1, ds1) -> ((i1, ds <| ds1), i)
+              put (Map.insert n (InterleavedData i0 sig (Just cs')) m, checks, i')
+            _ -> lift $ declarationWarning $ MissingDeclarations $ case mr of
+                   Just r -> [(n, r)]
+                   Nothing -> flip foldMap ds $ \case
+                     Axiom r _ _ _ _ n _ -> [(n, r)]
+                     _ -> __IMPOSSIBLE__
+
+        addDataConstructors mr Nothing [] = pure ()
+
+        -- Otherwise we try to guess which datasig the constructor is referring to
+        addDataConstructors mr Nothing (d : ds) = do
+          -- get the candidate data types that are in this interleaved mutual block
+          (m, _, _) <- get
+          let sigs = mapMaybe (\ (n, d) -> n <$ isInterleavedData d) $ Map.toList m
+          -- check whether this constructor matches any of them
+          case isConstructor sigs d of
+            Right n -> do
+              -- if so grab the whole block that may work and add them
+              let (ds0, ds1) = span (isRight . isConstructor [n]) ds
+              addDataConstructors Nothing (Just n) (d : ds0)
+              -- and then repeat the process for the rest of the block
+              addDataConstructors Nothing Nothing ds1
+            Left (n, ns) -> lift $ declarationException $ AmbiguousConstructor (getRange d) n ns
+
+        addFunDef :: NiceDeclaration -> StateT (InterleavedMutual, MutualChecks, DeclNum) Nice ()
+        addFunDef (FunDef _ ds _ _ tc cc n cs) = do
+          let check = MutualChecks [tc] [cc] []
+          (m, checks, i) <- get
+          case Map.lookup n m of
+            Just (InterleavedFun i0 sig cs0) -> do
+              let (cs', i') = case cs0 of
+                    Nothing        -> ((i,  (ds, cs) :| [] ), i + 1)
+                    Just (i1, cs1) -> ((i1, (ds, cs) <| cs1), i)
+              put (Map.insert n (InterleavedFun i0 sig (Just cs')) m, check <> checks, i')
+            _ -> __IMPOSSIBLE__ -- A FunDef always come after an existing FunSig!
+        addFunDef _ = __IMPOSSIBLE__
+
+        addFunClauses :: Range -> [NiceDeclaration]
+                      -> StateT (InterleavedMutual, MutualChecks, DeclNum) Nice [(DeclNum, NiceDeclaration)]
+        addFunClauses r (nd@(NiceFunClause _ _ _ tc cc _ d@(FunClause lhs _ _ _)) : ds) = do
+          -- get the candidate functions that are in this interleaved mutual block
+          (m, checks, i) <- get
+          let sigs = mapMaybe (\ (n, d) -> n <$ isInterleavedFun d) $ Map.toList m
+          -- find the funsig candidates for the funclause of interest
+          case [ (x, fits, rest)
+               | x <- sigs
+               , let (fits, rest) = spanJust (couldBeNiceFunClauseOf (Map.lookup x fixs) x) (nd : ds)
+               , not (null fits)
+               ] of
+            -- no candidate: keep the isolated fun clause, we'll complain about it later
+            [] -> do
+              let check = MutualChecks [tc] [cc] []
+              put (m, check <> checks, i + 1)
+              ((i,nd) :) <$> groupByBlocks r ds
+            -- exactly one candidate: attach the funclause to the definition
+            [(n, fits0, rest)] -> do
+              let (checkss, fits) = unzip fits0
+              ds <- lift $ expandEllipsis fits
+              cs <- lift $ mkClauses n ds False
+              case Map.lookup n m of
+                Just (InterleavedFun i0 sig cs0) -> do
+                  let (cs', i') = case cs0 of
+                        Nothing        -> ((i,  (fits,cs) :| [] ), i + 1)
+                        Just (i1, cs1) -> ((i1, (fits,cs) <| cs1), i)
+                  let checks' = Fold.fold checkss
+                  put (Map.insert n (InterleavedFun i0 sig (Just cs')) m, checks' <> checks, i')
+                _ -> __IMPOSSIBLE__
+              groupByBlocks r rest
+            -- more than one candidate: fail, complaining about the ambiguity!
+            xf:xfs -> lift $ declarationException
+                           $ AmbiguousFunClauses lhs
+                           $ List1.reverse $ fmap (\ (a,_,_) -> a) $ xf :| xfs
+        addFunClauses _ _ = __IMPOSSIBLE__
+
+        groupByBlocks :: Range -> [NiceDeclaration]
+                      -> StateT (InterleavedMutual, MutualChecks, DeclNum) Nice [(DeclNum, NiceDeclaration)]
+        groupByBlocks r []       = pure []
+        groupByBlocks r (d : ds) = do
+          -- for most branches we deal with the one declaration and move on
+          let oneOff act = act >>= \ ns -> (ns ++) <$> groupByBlocks r ds
+          case d of
+            NiceDataSig{}                -> oneOff $ [] <$ addDataType d
+            NiceDataDef r _ _ _ _ n _ ds -> oneOff $ [] <$ addDataConstructors (Just r) (Just n) ds
+            NiceLoneConstructor r ds     -> oneOff $ [] <$ addDataConstructors Nothing Nothing ds
+            FunSig{}                     -> oneOff $ [] <$ addFunType d
+            FunDef _ _ _  _ _ _ n cs
+                      | not (isNoName n) -> oneOff $ [] <$ addFunDef d
+            -- It's a bit different for fun clauses because we may need to grab a lot
+            -- of clauses to handle ellipses properly.
+            NiceFunClause{}              -> addFunClauses r (d:ds)
+            -- We do not need to worry about RecSig vs. RecDef: we know there's exactly one
+            -- of each for record definitions and leaving them in place should be enough!
+            _ -> oneOff $ do
+              (m, c, i) <- get -- TODO: grab checks from c?
+              put (m, c, i + 1)
+              pure [(i,d)]
+
+    -- Extract the name of the return type (if any) of a potential constructor.
+    -- In case of failure return the name of the constructor and the list of candidates
+    -- for the return type.
+    -- A `constructor' block should only contain NiceConstructors so we crash with
+    -- an IMPOSSIBLE otherwise
+    isConstructor :: [Name] -> NiceDeclaration -> Either (Name, [Name]) Name
+    isConstructor ns (Axiom _ _ _ _ _ n e)
+       -- extract the return type & see it as an LHS-style pattern
+       | Just p <- exprToPatternWithHoles <$> returnExpr e =
+         case [ x | x <- ns
+                  , couldBeCallOf (Map.lookup x fixs) x p
+                  ] of
+           [x] -> Right x
+           xs  -> Left (n, xs)
+       -- which may fail (e.g. if the "return type" is a hole
+       | otherwise = Left (n, [])
+    isConstructor _ _ = __IMPOSSIBLE__
+
+    -- Turn an old-style mutual block into a new style mutual block
+    -- by pushing the definitions to the end.
+    mkOldMutual
+      :: Range                 -- Range of the whole @mutual@ block.
+      -> [NiceDeclaration]     -- Declarations inside the block.
+      -> Nice NiceDeclaration  -- Returns a 'NiceMutual'.
+    mkOldMutual r ds' = do
+        -- Postulate the missing definitions
+        let ps = loneSigsFromLoneNames loneNames
+        checkLoneSigs ps
+        let ds = replaceSigs ps ds'
+
+        -- -- Remove the declarations that aren't allowed in old style mutual blocks
+        -- ds <- fmap catMaybes $ forM ds $ \ d -> let success = pure (Just d) in case d of
+        --   -- Andreas, 2013-11-23 allow postulates in mutual blocks
+        --   Axiom{}          -> success
+        --   -- Andreas, 2017-10-09, issue #2576, raise error about missing type signature
+        --   -- in ConcreteToAbstract rather than here.
+        --   NiceFunClause{}  -> success
+        --   -- Andreas, 2018-05-11, issue #3052, allow pat.syn.s in mutual blocks
+        --   NicePatternSyn{} -> success
+        --   -- Otherwise, only categorized signatures and definitions are allowed:
+        --   -- Data, Record, Fun
+        --   _ -> if (declKind d /= OtherDecl) then success
+        --        else Nothing <$ declarationWarning (NotAllowedInMutual (getRange d) $ declName d)
+        -- Sort the declarations in the mutual block.
+        -- Declarations of names go to the top.  (Includes module definitions.)
+        -- Definitions of names go to the bottom.
+        -- Some declarations are forbidden, as their positioning could confuse
+        -- the user.
+        (top, bottom, invalid) <- forEither3M ds $ \ d -> do
+          let top       = return (In1 d)
+              bottom    = return (In2 d)
+              invalid s = In3 d <$ do declarationWarning $ NotAllowedInMutual (getRange d) s
+          case d of
+            -- Andreas, 2013-11-23 allow postulates in mutual blocks
+            Axiom{}             -> top
+            NiceField{}         -> top
+            PrimitiveFunction{} -> top
+            -- Andreas, 2019-07-23 issue #3932:
+            -- Nested mutual blocks are not supported.
+            NiceMutual{}        -> invalid "mutual blocks"
+            -- Andreas, 2018-10-29, issue #3246
+            -- We could allow modules (top), but this is potentially confusing.
+            NiceModule{}        -> invalid "Module definitions"
+            -- Lone constructors are only allowed in new-style mutual blocks
+            NiceLoneConstructor{} -> invalid "Lone constructors"
+            NiceModuleMacro{}   -> top
+            NiceOpen{}          -> top
+            NiceImport{}        -> top
+            NiceRecSig{}        -> top
+            NiceDataSig{}       -> top
+            -- Andreas, 2017-10-09, issue #2576, raise error about missing type signature
+            -- in ConcreteToAbstract rather than here.
+            NiceFunClause{}     -> bottom
+            FunSig{}            -> top
+            FunDef{}            -> bottom
+            NiceDataDef{}       -> bottom
+            NiceRecDef{}        -> bottom
+            -- Andreas, 2018-05-11, issue #3051, allow pat.syn.s in mutual blocks
+            -- Andreas, 2018-10-29: We shift pattern synonyms to the bottom
+            -- since they might refer to constructors defined in a data types
+            -- just above them.
+            NicePatternSyn{}    -> bottom
+            NiceGeneralize{}    -> top
+            NiceUnquoteDecl{}   -> top
+            NiceUnquoteDef{}    -> bottom
+            NiceUnquoteData{}   -> top
+
+            -- Opaque blocks can not participate in old-style mutual
+            -- recursion. If some of the definitions are opaque then
+            -- they all need to be.
+            NiceOpaque{}        ->
+              In3 d <$ do declarationException $ OpaqueInMutual (getRange d)
+            NicePragma r pragma -> case pragma of
+
+              OptionsPragma{}           -> top     -- error thrown in the type checker
+
+              -- Some builtins require a definition, and they affect type checking
+              -- Thus, we do not handle BUILTINs in mutual blocks (at least for now).
+              BuiltinPragma{}           -> invalid "BUILTIN pragmas"
+
+              -- The REWRITE pragma behaves differently before or after the def.
+              -- and affects type checking.  Thus, we refuse it here.
+              RewritePragma{}           -> invalid "REWRITE pragmas"
+
+              -- Compiler pragmas are not needed for type checking, thus,
+              -- can go to the bottom.
+              ForeignPragma{}           -> bottom
+              CompilePragma{}           -> bottom
+
+              StaticPragma{}            -> bottom
+              InlinePragma{}            -> bottom
+              NotProjectionLikePragma{} -> bottom
+
+              ImpossiblePragma{}        -> top     -- error thrown in scope checker
+              EtaPragma{}               -> bottom  -- needs record definition
+              WarningOnUsage{}          -> top
+              WarningOnImport{}         -> top
+              InjectivePragma{}         -> top     -- only needs name, not definition
+              DisplayPragma{}           -> top     -- only for printing
+
+              -- The attached pragmas have already been handled at this point.
+              CatchallPragma{}          -> __IMPOSSIBLE__
+              TerminationCheckPragma{}  -> __IMPOSSIBLE__
+              NoPositivityCheckPragma{} -> __IMPOSSIBLE__
+              PolarityPragma{}          -> __IMPOSSIBLE__
+              NoUniverseCheckPragma{}   -> __IMPOSSIBLE__
+              NoCoverageCheckPragma{}   -> __IMPOSSIBLE__
+
+
+        -- -- Pull type signatures to the top
+        -- let (sigs, other) = List.partition isTypeSig ds
+
+        -- -- Push definitions to the bottom
+        -- let (other, defs) = flip List.partition ds $ \case
+        --       FunDef{}         -> False
+        --       NiceDataDef{}    -> False
+        --       NiceRecDef{}         -> False
+        --       NiceFunClause{}  -> False
+        --       NicePatternSyn{} -> False
+        --       NiceUnquoteDef{} -> False
+        --       _ -> True
+
+        -- Compute termination checking flag for mutual block
+        tc0 <- use terminationCheckPragma
+        let tcs = map termCheck ds
+        tc <- combineTerminationChecks r (tc0:tcs)
+
+        -- Compute coverage checking flag for mutual block
+        cc0 <- use coverageCheckPragma
+        let ccs = map covCheck ds
+        let cc = combineCoverageChecks (cc0:ccs)
+
+        -- Compute positivity checking flag for mutual block
+        pc0 <- use positivityCheckPragma
+        let pcs = map positivityCheckOldMutual ds
+        let pc = combinePositivityChecks (pc0:pcs)
+
+        return $ NiceMutual r tc cc pc $ top ++ bottom
+        -- return $ NiceMutual r tc pc $ other ++ defs
+        -- return $ NiceMutual r tc pc $ sigs ++ other
+      where
+
+        -- isTypeSig Axiom{}                     = True
+        -- isTypeSig d | LoneSig{} <- declKind d = True
+        -- isTypeSig _                           = False
+
+        sigNames  = [ (r, x, k) | LoneSigDecl r k x <- map declKind ds' ]
+        defNames  = [ (x, k) | LoneDefs k xs <- map declKind ds', x <- xs ]
+        -- compute the set difference with equality just on names
+        loneNames = [ (r, x, k) | (r, x, k) <- sigNames, List.all ((x /=) . fst) defNames ]
+
+        termCheck :: NiceDeclaration -> TerminationCheck
+        -- Andreas, 2013-02-28 (issue 804):
+        -- do not termination check a mutual block if any of its
+        -- inner declarations comes with a {-# NO_TERMINATION_CHECK #-}
+        termCheck (FunSig _ _ _ _ _ _ tc _ _ _)      = tc
+        termCheck (FunDef _ _ _ _ tc _ _ _)          = tc
+        -- ASR (28 December 2015): Is this equation necessary?
+        termCheck (NiceMutual _ tc _ _ _)            = tc
+        termCheck (NiceUnquoteDecl _ _ _ _ tc _ _ _) = tc
+        termCheck (NiceUnquoteDef _ _ _ tc _ _ _)    = tc
+        termCheck Axiom{}               = TerminationCheck
+        termCheck NiceField{}           = TerminationCheck
+        termCheck PrimitiveFunction{}   = TerminationCheck
+        termCheck NiceModule{}          = TerminationCheck
+        termCheck NiceModuleMacro{}     = TerminationCheck
+        termCheck NiceOpen{}            = TerminationCheck
+        termCheck NiceImport{}          = TerminationCheck
+        termCheck NicePragma{}          = TerminationCheck
+        termCheck NiceRecSig{}          = TerminationCheck
+        termCheck NiceDataSig{}         = TerminationCheck
+        termCheck NiceFunClause{}       = TerminationCheck
+        termCheck NiceDataDef{}         = TerminationCheck
+        termCheck NiceRecDef{}          = TerminationCheck
+        termCheck NicePatternSyn{}      = TerminationCheck
+        termCheck NiceGeneralize{}      = TerminationCheck
+        termCheck NiceLoneConstructor{} = TerminationCheck
+        termCheck NiceUnquoteData{}     = TerminationCheck
+        termCheck NiceOpaque{}          = TerminationCheck
+
+        covCheck :: NiceDeclaration -> CoverageCheck
+        covCheck (FunSig _ _ _ _ _ _ _ cc _ _)      = cc
+        covCheck (FunDef _ _ _ _ _ cc _ _)          = cc
+        -- ASR (28 December 2015): Is this equation necessary?
+        covCheck (NiceMutual _ _ cc _ _)            = cc
+        covCheck (NiceUnquoteDecl _ _ _ _ _ cc _ _) = cc
+        covCheck (NiceUnquoteDef _ _ _ _ cc _ _)    = cc
+        covCheck Axiom{}               = YesCoverageCheck
+        covCheck NiceField{}           = YesCoverageCheck
+        covCheck PrimitiveFunction{}   = YesCoverageCheck
+        covCheck NiceModule{}          = YesCoverageCheck
+        covCheck NiceModuleMacro{}     = YesCoverageCheck
+        covCheck NiceOpen{}            = YesCoverageCheck
+        covCheck NiceImport{}          = YesCoverageCheck
+        covCheck NicePragma{}          = YesCoverageCheck
+        covCheck NiceRecSig{}          = YesCoverageCheck
+        covCheck NiceDataSig{}         = YesCoverageCheck
+        covCheck NiceFunClause{}       = YesCoverageCheck
+        covCheck NiceDataDef{}         = YesCoverageCheck
+        covCheck NiceRecDef{}          = YesCoverageCheck
+        covCheck NicePatternSyn{}      = YesCoverageCheck
+        covCheck NiceGeneralize{}      = YesCoverageCheck
+        covCheck NiceLoneConstructor{} = YesCoverageCheck
+        covCheck NiceUnquoteData{}     = YesCoverageCheck
+        covCheck NiceOpaque{}          = YesCoverageCheck
+
+        -- ASR (26 December 2015): Do not positivity check a mutual
+        -- block if any of its inner declarations comes with a
+        -- NO_POSITIVITY_CHECK pragma. See Issue 1614.
+        positivityCheckOldMutual :: NiceDeclaration -> PositivityCheck
+        positivityCheckOldMutual (NiceDataDef _ _ _ pc _ _ _ _) = pc
+        positivityCheckOldMutual (NiceDataSig _ _ _ _ pc _ _ _ _) = pc
+        positivityCheckOldMutual (NiceMutual _ _ _ pc _)        = pc
+        positivityCheckOldMutual (NiceRecSig _ _ _ _ pc _ _ _ _) = pc
+        positivityCheckOldMutual (NiceRecDef _ _ _ pc _ _ _ _ _) = pc
+        positivityCheckOldMutual _                              = YesPositivityCheck
+
+        -- A mutual block cannot have a measure,
+        -- but it can skip termination check.
+
+    abstractBlock _ [] = return []
+    abstractBlock r ds = do
+      (ds', anyChange) <- runChangeT $ mkAbstract ds
+      let inherited = r == noRange
+      if anyChange then return ds' else do
+        -- hack to avoid failing on inherited abstract blocks in where clauses
+        unless inherited $ declarationWarning $ UselessAbstract r
+        return ds -- no change!
+
+    privateBlock _ _ [] = return []
+    privateBlock r o ds = do
+      (ds', anyChange) <- runChangeT $ mkPrivate o ds
+      if anyChange then return ds' else do
+        when (o == UserWritten) $ declarationWarning $ UselessPrivate r
+        return ds -- no change!
+
+    instanceBlock
+      :: Range  -- Range of @instance@ keyword.
+      -> [NiceDeclaration]
+      -> Nice [NiceDeclaration]
+    instanceBlock _ [] = return []
+    instanceBlock r ds = do
+      let (ds', anyChange) = runChange $ mapM (mkInstance r) ds
+      if anyChange then return ds' else do
+        declarationWarning $ UselessInstance r
+        return ds -- no change!
+
+    -- Make a declaration eligible for instance search.
+    mkInstance
+      :: Range  -- Range of @instance@ keyword.
+      -> Updater NiceDeclaration
+    mkInstance r0 = \case
+        Axiom r p a i rel x e          -> (\ i -> Axiom r p a i rel x e) <$> setInstance r0 i
+        FunSig r p a i m rel tc cc x e -> (\ i -> FunSig r p a i m rel tc cc x e) <$> setInstance r0 i
+        NiceUnquoteDecl r p a i tc cc x e -> (\ i -> NiceUnquoteDecl r p a i tc cc x e) <$> setInstance r0 i
+        NiceMutual r tc cc pc ds       -> NiceMutual r tc cc pc <$> mapM (mkInstance r0) ds
+        NiceLoneConstructor r ds       -> NiceLoneConstructor r <$> mapM (mkInstance r0) ds
+        d@NiceFunClause{}              -> return d
+        FunDef r ds a i tc cc x cs     -> (\ i -> FunDef r ds a i tc cc x cs) <$> setInstance r0 i
+        NiceOpaque r ns i              -> (\ i -> NiceOpaque r ns i) <$> traverse (mkInstance r0) i
+        d@NiceField{}                  -> return d  -- Field instance are handled by the parser
+        d@PrimitiveFunction{}          -> return d
+        d@NiceUnquoteDef{}             -> return d
+        d@NiceRecSig{}                 -> return d
+        d@NiceDataSig{}                -> return d
+        d@NiceModuleMacro{}            -> return d
+        d@NiceModule{}                 -> return d
+        d@NicePragma{}                 -> return d
+        d@NiceOpen{}                   -> return d
+        d@NiceImport{}                 -> return d
+        d@NiceDataDef{}                -> return d
+        d@NiceRecDef{}                 -> return d
+        d@NicePatternSyn{}             -> return d
+        d@NiceGeneralize{}             -> return d
+        d@NiceUnquoteData{}            -> return d
+
+    setInstance
+      :: Range  -- Range of @instance@ keyword.
+      -> Updater IsInstance
+    setInstance r0 = \case
+      i@InstanceDef{} -> return i
+      _               -> dirty $ InstanceDef r0
+
+    macroBlock r ds = mapM mkMacro ds
+
+    mkMacro :: NiceDeclaration -> Nice NiceDeclaration
+    mkMacro = \case
+        FunSig r p a i _ rel tc cc x e -> return $ FunSig r p a i MacroDef rel tc cc x e
+        d@FunDef{}                     -> return d
+        d                              -> declarationException (BadMacroDef d)
+
+-- | Make a declaration abstract.
+--
+-- Mark computation as 'dirty' if there was a declaration that could be made abstract.
+-- If no abstraction is taking place, we want to complain about 'UselessAbstract'.
+--
+-- Alternatively, we could only flag 'dirty' if a non-abstract thing was abstracted.
+-- Then, nested @abstract@s would sometimes also be complained about.
+
+class MakeAbstract a where
+  mkAbstract :: UpdaterT Nice a
+
+  default mkAbstract :: (Traversable f, MakeAbstract a', a ~ f a') => UpdaterT Nice a
+  mkAbstract = traverse mkAbstract
+
+instance MakeAbstract a => MakeAbstract [a]
+
+-- Leads to overlap with 'WhereClause':
+-- instance (Traversable f, MakeAbstract a) => MakeAbstract (f a) where
+--   mkAbstract = traverse mkAbstract
+
+instance MakeAbstract IsAbstract where
+  mkAbstract = \case
+    a@AbstractDef -> return a
+    ConcreteDef -> dirty $ AbstractDef
+
+instance MakeAbstract NiceDeclaration where
+  mkAbstract = \case
+      NiceMutual r termCheck cc pc ds  -> NiceMutual r termCheck cc pc <$> mkAbstract ds
+      NiceLoneConstructor r ds         -> NiceLoneConstructor r <$> mkAbstract ds
+      FunDef r ds a i tc cc x cs       -> (\ a -> FunDef r ds a i tc cc x) <$> mkAbstract a <*> mkAbstract cs
+      NiceDataDef r o a pc uc x ps cs  -> (\ a -> NiceDataDef r o a pc uc x ps) <$> mkAbstract a <*> mkAbstract cs
+      NiceRecDef r o a pc uc x dir ps cs -> (\ a -> NiceRecDef r o a pc uc x dir ps cs) <$> mkAbstract a
+      NiceFunClause r p a tc cc catchall d  -> (\ a -> NiceFunClause r p a tc cc catchall d) <$> mkAbstract a
+      -- The following declarations have an @InAbstract@ field
+      -- but are not really definitions, so we do count them into
+      -- the declarations which can be made abstract
+      -- (thus, do not notify progress with @dirty@).
+      Axiom r p a i rel x e          -> return $ Axiom             r p AbstractDef i rel x e
+      FunSig r p a i m rel tc cc x e -> return $ FunSig            r p AbstractDef i m rel tc cc x e
+      NiceRecSig  r er p a pc uc x ls t -> return $ NiceRecSig  r er p AbstractDef pc uc x ls t
+      NiceDataSig r er p a pc uc x ls t -> return $ NiceDataSig r er p AbstractDef pc uc x ls t
+      NiceField r p _ i tac x e      -> return $ NiceField         r p AbstractDef i tac x e
+      PrimitiveFunction r p _ x e    -> return $ PrimitiveFunction r p AbstractDef x e
+      -- Andreas, 2016-07-17 it does have effect on unquoted defs.
+      -- Need to set updater state to dirty!
+      NiceUnquoteDecl r p _ i tc cc x e -> tellDirty $> NiceUnquoteDecl r p AbstractDef i tc cc x e
+      NiceUnquoteDef r p _ tc cc x e    -> tellDirty $> NiceUnquoteDef r p AbstractDef tc cc x e
+      NiceUnquoteData r p _ tc cc x xs e -> tellDirty $> NiceUnquoteData r p AbstractDef tc cc x xs e
+      d@NiceModule{}                 -> return d
+      d@NiceModuleMacro{}            -> return d
+      d@NicePragma{}                 -> return d
+      d@(NiceOpen _ _ directives)              -> do
+        whenJust (publicOpen directives) $ lift . declarationWarning . OpenPublicAbstract
+        return d
+      d@NiceImport{}                 -> return d
+      d@NicePatternSyn{}             -> return d
+      d@NiceGeneralize{}             -> return d
+      NiceOpaque r ns ds             -> NiceOpaque r ns <$> mkAbstract ds
+
+instance MakeAbstract Clause where
+  mkAbstract (Clause x catchall lhs rhs wh with) = do
+    Clause x catchall lhs rhs <$> mkAbstract wh <*> mkAbstract with
+
+-- | Contents of a @where@ clause are abstract if the parent is.
+instance MakeAbstract WhereClause where
+  mkAbstract  NoWhere               = return $ NoWhere
+  mkAbstract (AnyWhere r ds)        = dirty $ AnyWhere r
+                                                [Abstract noRange ds]
+  mkAbstract (SomeWhere r e m a ds) = dirty $ SomeWhere r e m a
+                                                [Abstract noRange ds]
+
+-- | Make a declaration private.
+--
+-- Andreas, 2012-11-17:
+-- Mark computation as 'dirty' if there was a declaration that could be privatized.
+-- If no privatization is taking place, we want to complain about 'UselessPrivate'.
+--
+-- Alternatively, we could only flag 'dirty' if a non-private thing was privatized.
+-- Then, nested @private@s would sometimes also be complained about.
+
+class MakePrivate a where
+  mkPrivate :: Origin -> UpdaterT Nice a
+
+  default mkPrivate :: (Traversable f, MakePrivate a', a ~ f a') => Origin -> UpdaterT Nice a
+  mkPrivate o = traverse $ mkPrivate o
+
+instance MakePrivate a => MakePrivate [a]
+
+-- Leads to overlap with 'WhereClause':
+-- instance (Traversable f, MakePrivate a) => MakePrivate (f a) where
+--   mkPrivate = traverse mkPrivate
+
+instance MakePrivate Access where
+  mkPrivate o = \case
+    p@PrivateAccess{} -> return p  -- OR? return $ PrivateAccess o
+    _                 -> dirty $ PrivateAccess o
+
+instance MakePrivate NiceDeclaration where
+  mkPrivate o = \case
+      Axiom r p a i rel x e                    -> (\ p -> Axiom r p a i rel x e)                <$> mkPrivate o p
+      NiceField r p a i tac x e                -> (\ p -> NiceField r p a i tac x e)            <$> mkPrivate o p
+      PrimitiveFunction r p a x e              -> (\ p -> PrimitiveFunction r p a x e)          <$> mkPrivate o p
+      NiceMutual r tc cc pc ds                 -> (\ ds-> NiceMutual r tc cc pc ds)             <$> mkPrivate o ds
+      NiceLoneConstructor r ds                 -> NiceLoneConstructor r                         <$> mkPrivate o ds
+      NiceModule r p a e x tel ds              -> (\ p -> NiceModule r p a e x tel ds)          <$> mkPrivate o p
+      NiceModuleMacro r p e x ma op is         -> (\ p -> NiceModuleMacro r p e x ma op is)     <$> mkPrivate o p
+      FunSig r p a i m rel tc cc x e           -> (\ p -> FunSig r p a i m rel tc cc x e)       <$> mkPrivate o p
+      NiceRecSig r er p a pc uc x ls t         -> (\ p -> NiceRecSig r er p a pc uc x ls t)     <$> mkPrivate o p
+      NiceDataSig r er p a pc uc x ls t        -> (\ p -> NiceDataSig r er p a pc uc x ls t)    <$> mkPrivate o p
+      NiceFunClause r p a tc cc catchall d     -> (\ p -> NiceFunClause r p a tc cc catchall d) <$> mkPrivate o p
+      NiceUnquoteDecl r p a i tc cc x e        -> (\ p -> NiceUnquoteDecl r p a i tc cc x e)    <$> mkPrivate o p
+      NiceUnquoteDef r p a tc cc x e           -> (\ p -> NiceUnquoteDef r p a tc cc x e)       <$> mkPrivate o p
+      NicePatternSyn r p x xs p'               -> (\ p -> NicePatternSyn r p x xs p')           <$> mkPrivate o p
+      NiceGeneralize r p i tac x t             -> (\ p -> NiceGeneralize r p i tac x t)         <$> mkPrivate o p
+      NiceOpaque r ns ds                       -> (\ p -> NiceOpaque r ns p)                    <$> mkPrivate o ds
+      d@NicePragma{}                           -> return d
+      d@(NiceOpen _ _ directives)              -> do
+        whenJust (publicOpen directives) $ lift . declarationWarning . OpenPublicPrivate
+        return d
+      d@NiceImport{}                           -> return d
+      -- Andreas, 2016-07-08, issue #2089
+      -- we need to propagate 'private' to the named where modules
+      FunDef r ds a i tc cc x cls              -> FunDef r ds a i tc cc x <$> mkPrivate o cls
+      d@NiceDataDef{}                          -> return d
+      d@NiceRecDef{}                           -> return d
+      d@NiceUnquoteData{}                      -> return d
+
+instance MakePrivate Clause where
+  mkPrivate o (Clause x catchall lhs rhs wh with) = do
+    Clause x catchall lhs rhs <$> mkPrivate o wh <*> mkPrivate o with
+
+instance MakePrivate WhereClause where
+  mkPrivate o = \case
+    d@NoWhere    -> return d
+    -- @where@-declarations are protected behind an anonymous module,
+    -- thus, they are effectively private by default.
+    d@AnyWhere{} -> return d
+    -- Andreas, 2016-07-08
+    -- A @where@-module is private if the parent function is private.
+    -- The contents of this module are not private, unless declared so!
+    -- Thus, we do not recurse into the @ds@ (could not anyway).
+    SomeWhere r e m a ds ->
+      mkPrivate o a <&> \a' -> SomeWhere r e m a' ds
+
+-- The following function is (at the time of writing) only used three
+-- times: for building Lets, and for printing error messages.
+
+-- | (Approximately) convert a 'NiceDeclaration' back to a list of
+-- 'Declaration's.
+notSoNiceDeclarations :: NiceDeclaration -> [Declaration]
+notSoNiceDeclarations = \case
+    Axiom _ _ _ i rel x e          -> inst i [TypeSig rel Nothing x e]
+    NiceField _ _ _ i tac x argt   -> [FieldSig i tac x argt]
+    PrimitiveFunction r _ _ x e    -> [Primitive r [TypeSig (argInfo e) Nothing x (unArg e)]]
+    NiceMutual r _ _ _ ds          -> [Mutual r $ concatMap notSoNiceDeclarations ds]
+    NiceLoneConstructor r ds       -> [LoneConstructor r $ concatMap notSoNiceDeclarations ds]
+    NiceModule r _ _ e x tel ds    -> [Module r e x tel ds]
+    NiceModuleMacro r _ e x ma o dir
+                                   -> [ModuleMacro r e x ma o dir]
+    NiceOpen r x dir               -> [Open r x dir]
+    NiceImport r x as o dir        -> [Import r x as o dir]
+    NicePragma _ p                 -> [Pragma p]
+    NiceRecSig r er _ _ _ _ x bs e -> [RecordSig r er x bs e]
+    NiceDataSig r er _ _ _ _ x bs e -> [DataSig r er x bs e]
+    NiceFunClause _ _ _ _ _ _ d    -> [d]
+    FunSig _ _ _ i _ rel _ _ x e   -> inst i [TypeSig rel Nothing x e]
+    FunDef _ ds _ _ _ _ _ _        -> ds
+    NiceDataDef r _ _ _ _ x bs cs  -> [DataDef r x bs $ concatMap notSoNiceDeclarations cs]
+    NiceRecDef r _ _ _ _ x dir bs ds -> [RecordDef r x dir bs ds]
+    NicePatternSyn r _ n as p      -> [PatternSyn r n as p]
+    NiceGeneralize r _ i tac n e   -> [Generalize r [TypeSig i tac n e]]
+    NiceUnquoteDecl r _ _ i _ _ x e -> inst i [UnquoteDecl r x e]
+    NiceUnquoteDef r _ _ _ _ x e    -> [UnquoteDef r x e]
+    NiceUnquoteData r _ _ _ _ x xs e  -> [UnquoteData r x xs e]
+    NiceOpaque r ns ds                -> [Opaque r (Unfolding r ns:concatMap notSoNiceDeclarations ds)]
+  where
+    inst (InstanceDef r) ds = [InstanceB r ds]
+    inst NotInstanceDef  ds = ds
+
+-- | Has the 'NiceDeclaration' a field of type 'IsAbstract'?
+niceHasAbstract :: NiceDeclaration -> Maybe IsAbstract
+niceHasAbstract = \case
+    Axiom{}                       -> Nothing
+    NiceField _ _ a _ _ _ _       -> Just a
+    PrimitiveFunction _ _ a _ _   -> Just a
+    NiceMutual{}                  -> Nothing
+    NiceLoneConstructor{}         -> Nothing
+    NiceModule _ _ a _ _ _ _      -> Just a
+    NiceModuleMacro{}             -> Nothing
+    NiceOpen{}                    -> Nothing
+    NiceImport{}                  -> Nothing
+    NicePragma{}                  -> Nothing
+    NiceRecSig{}                  -> Nothing
+    NiceDataSig{}                 -> Nothing
+    NiceFunClause _ _ a _ _ _ _   -> Just a
+    FunSig{}                      -> Nothing
+    FunDef _ _ a _ _ _ _ _        -> Just a
+    NiceDataDef _ _ a _ _ _ _ _   -> Just a
+    NiceRecDef _ _ a _ _ _ _ _ _ -> Just a
+    NicePatternSyn{}              -> Nothing
+    NiceGeneralize{}              -> Nothing
+    NiceUnquoteDecl _ _ a _ _ _ _ _ -> Just a
+    NiceUnquoteDef _ _ a _ _ _ _    -> Just a
+    NiceUnquoteData _ _ a _ _ _ _ _ -> Just a
+    NiceOpaque{}                    -> Nothing
diff --git a/src/full/Agda/Syntax/Concrete/Definitions/Errors.hs b/src/full/Agda/Syntax/Concrete/Definitions/Errors.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Definitions/Errors.hs
@@ -0,0 +1,522 @@
+module Agda.Syntax.Concrete.Definitions.Errors where
+
+import Control.DeepSeq
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Definitions.Types
+
+import Agda.Interaction.Options.Warnings
+
+import Agda.Utils.Null ( empty )
+import Agda.Utils.CallStack ( CallStack )
+import Agda.Utils.List1 (List1, pattern (:|))
+import Agda.Utils.List2 (List2, pattern List2)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Singleton
+
+------------------------------------------------------------------------
+-- Errors
+
+-- | Exception with internal source code callstack
+data DeclarationException = DeclarationException
+  { deLocation  :: CallStack
+  , deException :: DeclarationException'
+  }
+
+-- | The exception type.
+data DeclarationException'
+  = MultipleEllipses Pattern
+  | InvalidName Name
+  | DuplicateDefinition Name
+  | DuplicateAnonDeclaration Range
+  | MissingWithClauses Name LHS
+  | WrongDefinition Name DataRecOrFun DataRecOrFun
+  | DeclarationPanic String
+  | WrongContentBlock KindOfBlock Range
+  | AmbiguousFunClauses LHS (List1 Name)
+      -- ^ In a mutual block, a clause could belong to any of the ≥2 type signatures ('Name').
+  | AmbiguousConstructor Range Name [Name]
+      -- ^ In an interleaved mutual block, a constructor could belong to any of the data signatures ('Name')
+  | InvalidMeasureMutual Range
+      -- ^ In a mutual block, all or none need a MEASURE pragma.
+      --   Range is of mutual block.
+  | UnquoteDefRequiresSignature (List1 Name)
+  | BadMacroDef NiceDeclaration
+  | UnfoldingOutsideOpaque Range
+    -- ^ An unfolding declaration was not the first declaration
+    -- contained in an opaque block.
+  | OpaqueInMutual Range
+      -- ^ @opaque@ block nested in a @mutual@ block. This can never
+      -- happen, even with reordering.
+  | DisallowedInterleavedMutual Range String (List1 Name)
+      -- ^ A declaration that breaks an implicit mutual block (named by
+      -- the String argument) was present while the given lone type
+      -- signatures were still without their definitions.
+    deriving Show
+
+------------------------------------------------------------------------
+-- Warnings
+
+data DeclarationWarning = DeclarationWarning
+  { dwLocation :: CallStack
+  , dwWarning  :: DeclarationWarning'
+  } deriving (Show, Generic)
+
+-- | Non-fatal errors encountered in the Nicifier.
+data DeclarationWarning'
+  -- Please keep in alphabetical order.
+  = EmptyAbstract Range    -- ^ Empty @abstract@  block.
+  | EmptyConstructor Range -- ^ Empty @constructor@ block.
+  | EmptyField Range       -- ^ Empty @field@     block.
+  | EmptyGeneralize Range  -- ^ Empty @variable@  block.
+  | EmptyInstance Range    -- ^ Empty @instance@  block
+  | EmptyMacro Range       -- ^ Empty @macro@     block.
+  | EmptyMutual Range      -- ^ Empty @mutual@    block.
+  | EmptyPostulate Range   -- ^ Empty @postulate@ block.
+  | EmptyPrivate Range     -- ^ Empty @private@   block.
+  | EmptyPrimitive Range   -- ^ Empty @primitive@ block.
+  | HiddenGeneralize Range
+      -- ^ A 'Hidden' identifier in a @variable@ declaration.
+      --   Hiding has no effect there as generalized variables are always hidden
+      --   (or instance variables).
+  | InvalidCatchallPragma Range
+      -- ^ A {-\# CATCHALL \#-} pragma
+      --   that does not precede a function clause.
+  | InvalidConstructor Range
+      -- ^ Invalid definition in a constructor block
+  | InvalidConstructorBlock Range
+      -- ^ Invalid constructor block (not inside an interleaved mutual block)
+  | InvalidCoverageCheckPragma Range
+      -- ^ A {-\# NON_COVERING \#-} pragma that does not apply to any function.
+  | InvalidNoPositivityCheckPragma Range
+      -- ^ A {-\# NO_POSITIVITY_CHECK \#-} pragma
+      --   that does not apply to any data or record type.
+  | InvalidNoUniverseCheckPragma Range
+      -- ^ A {-\# NO_UNIVERSE_CHECK \#-} pragma
+      --   that does not apply to a data or record type.
+  | InvalidRecordDirective Range
+      -- ^ A record directive outside of a record / below existing fields.
+  | InvalidTerminationCheckPragma Range
+      -- ^ A {-\# TERMINATING \#-} and {-\# NON_TERMINATING \#-} pragma
+      --   that does not apply to any function.
+  | MissingDeclarations [(Name, Range)]
+      -- ^ Definitions (e.g. constructors or functions) without a declaration.
+  | MissingDefinitions [(Name, Range)]
+      -- ^ Declarations (e.g. type signatures) without a definition.
+  | NotAllowedInMutual Range String
+  | OpenPublicPrivate Range
+      -- ^ @private@ has no effect on @open public@.  (But the user might think so.)
+  | OpenPublicAbstract Range
+      -- ^ @abstract@ has no effect on @open public@.  (But the user might think so.)
+  | PolarityPragmasButNotPostulates [Name]
+  | PragmaNoTerminationCheck Range
+      -- ^ Pragma @{-\# NO_TERMINATION_CHECK \#-}@ has been replaced
+      --   by @{-\# TERMINATING \#-}@ and @{-\# NON_TERMINATING \#-}@.
+  | PragmaCompiled Range
+      -- ^ @COMPILE@ pragmas are not allowed in safe mode.
+  | SafeFlagEta               Range -- ^ @ETA@                 pragma is unsafe.
+  | SafeFlagInjective         Range -- ^ @INJECTIVE@           pragma is unsafe.
+  | SafeFlagNoCoverageCheck   Range -- ^ @NON_COVERING@        pragma is unsafe.
+  | SafeFlagNoPositivityCheck Range -- ^ @NO_POSITIVITY_CHECK@ pragma is unsafe.
+  | SafeFlagNoUniverseCheck   Range -- ^ @NO_UNIVERSE_CHECK@   pragma is unsafe.
+  | SafeFlagNonTerminating    Range -- ^ @NON_TERMINATING@     pragma is unsafe.
+  | SafeFlagPolarity          Range -- ^ @POLARITY@            pragma is unsafe.
+  | SafeFlagTerminating       Range -- ^ @TERMINATING@         pragma is unsafe.
+  | ShadowingInTelescope (List1 (Name, List2 Range))
+  | UnknownFixityInMixfixDecl [Name]
+  | UnknownNamesInFixityDecl [Name]
+  | UnknownNamesInPolarityPragmas [Name]
+  | UselessAbstract Range
+      -- ^ @abstract@ block with nothing that can (newly) be made abstract.
+  | UselessInstance Range
+      -- ^ @instance@ block with nothing that can (newly) become an instance.
+  | UselessPrivate Range
+      -- ^ @private@ block with nothing that can (newly) be made private.
+  deriving (Show, Generic)
+
+declarationWarningName :: DeclarationWarning -> WarningName
+declarationWarningName = declarationWarningName' . dwWarning
+
+declarationWarningName' :: DeclarationWarning' -> WarningName
+declarationWarningName' = \case
+  -- Please keep in alphabetical order.
+  EmptyAbstract{}                   -> EmptyAbstract_
+  EmptyConstructor{}                -> EmptyConstructor_
+  EmptyField{}                      -> EmptyField_
+  EmptyGeneralize{}                 -> EmptyGeneralize_
+  EmptyInstance{}                   -> EmptyInstance_
+  EmptyMacro{}                      -> EmptyMacro_
+  EmptyMutual{}                     -> EmptyMutual_
+  EmptyPrivate{}                    -> EmptyPrivate_
+  EmptyPostulate{}                  -> EmptyPostulate_
+  EmptyPrimitive{}                  -> EmptyPrimitive_
+  HiddenGeneralize{}                -> HiddenGeneralize_
+  InvalidCatchallPragma{}           -> InvalidCatchallPragma_
+  InvalidConstructor{}              -> InvalidConstructor_
+  InvalidConstructorBlock{}         -> InvalidConstructorBlock_
+  InvalidNoPositivityCheckPragma{}  -> InvalidNoPositivityCheckPragma_
+  InvalidNoUniverseCheckPragma{}    -> InvalidNoUniverseCheckPragma_
+  InvalidRecordDirective{}          -> InvalidRecordDirective_
+  InvalidTerminationCheckPragma{}   -> InvalidTerminationCheckPragma_
+  InvalidCoverageCheckPragma{}      -> InvalidCoverageCheckPragma_
+  MissingDeclarations{}             -> MissingDeclarations_
+  MissingDefinitions{}              -> MissingDefinitions_
+  NotAllowedInMutual{}              -> NotAllowedInMutual_
+  OpenPublicPrivate{}               -> OpenPublicPrivate_
+  OpenPublicAbstract{}              -> OpenPublicAbstract_
+  PolarityPragmasButNotPostulates{} -> PolarityPragmasButNotPostulates_
+  PragmaNoTerminationCheck{}        -> PragmaNoTerminationCheck_
+  PragmaCompiled{}                  -> PragmaCompiled_
+  SafeFlagEta                    {} -> SafeFlagEta_
+  SafeFlagInjective              {} -> SafeFlagInjective_
+  SafeFlagNoCoverageCheck        {} -> SafeFlagNoCoverageCheck_
+  SafeFlagNoPositivityCheck      {} -> SafeFlagNoPositivityCheck_
+  SafeFlagNoUniverseCheck        {} -> SafeFlagNoUniverseCheck_
+  SafeFlagNonTerminating         {} -> SafeFlagNonTerminating_
+  SafeFlagPolarity               {} -> SafeFlagPolarity_
+  SafeFlagTerminating            {} -> SafeFlagTerminating_
+  ShadowingInTelescope{}            -> ShadowingInTelescope_
+  UnknownFixityInMixfixDecl{}       -> UnknownFixityInMixfixDecl_
+  UnknownNamesInFixityDecl{}        -> UnknownNamesInFixityDecl_
+  UnknownNamesInPolarityPragmas{}   -> UnknownNamesInPolarityPragmas_
+  UselessAbstract{}                 -> UselessAbstract_
+  UselessInstance{}                 -> UselessInstance_
+  UselessPrivate{}                  -> UselessPrivate_
+
+-- | Nicifier warnings turned into errors in @--safe@ mode.
+unsafeDeclarationWarning :: DeclarationWarning -> Bool
+unsafeDeclarationWarning = unsafeDeclarationWarning' . dwWarning
+
+unsafeDeclarationWarning' :: DeclarationWarning' -> Bool
+unsafeDeclarationWarning' = \case
+  -- Please keep in alphabetical order.
+  EmptyAbstract{}                   -> False
+  EmptyConstructor{}                -> False
+  EmptyField{}                      -> False
+  EmptyGeneralize{}                 -> False
+  EmptyInstance{}                   -> False
+  EmptyMacro{}                      -> False
+  EmptyMutual{}                     -> False
+  EmptyPrivate{}                    -> False
+  EmptyPostulate{}                  -> False
+  EmptyPrimitive{}                  -> False
+  HiddenGeneralize{}                -> False
+  InvalidCatchallPragma{}           -> False
+  InvalidConstructor{}              -> False
+  InvalidConstructorBlock{}         -> False
+  InvalidNoPositivityCheckPragma{}  -> False
+  InvalidNoUniverseCheckPragma{}    -> False
+  InvalidRecordDirective{}          -> False
+  InvalidTerminationCheckPragma{}   -> False
+  InvalidCoverageCheckPragma{}      -> False
+  MissingDeclarations{}             -> True  -- not safe
+  MissingDefinitions{}              -> True  -- not safe
+  NotAllowedInMutual{}              -> False -- really safe?
+  OpenPublicPrivate{}               -> False
+  OpenPublicAbstract{}              -> False
+  PolarityPragmasButNotPostulates{} -> False
+  PragmaNoTerminationCheck{}        -> True  -- not safe
+  PragmaCompiled{}                  -> True  -- not safe
+  SafeFlagEta                    {} -> True
+  SafeFlagInjective              {} -> True
+  SafeFlagNoCoverageCheck        {} -> True
+  SafeFlagNoPositivityCheck      {} -> True
+  SafeFlagNoUniverseCheck        {} -> True
+  SafeFlagNonTerminating         {} -> True
+  SafeFlagPolarity               {} -> True
+  SafeFlagTerminating            {} -> True
+  ShadowingInTelescope{}            -> False
+  UnknownFixityInMixfixDecl{}       -> False
+  UnknownNamesInFixityDecl{}        -> False
+  UnknownNamesInPolarityPragmas{}   -> False
+  UselessAbstract{}                 -> False
+  UselessInstance{}                 -> False
+  UselessPrivate{}                  -> False
+
+-- | Pragmas not allowed in @--safe@ mode produce an 'unsafeDeclarationWarning'.
+--
+unsafePragma :: CMaybe DeclarationWarning' m => Pragma -> m
+unsafePragma p =
+  case p of
+    BuiltinPragma{}            -> empty
+    CatchallPragma{}           -> empty
+    CompilePragma{}            -> singleton $ PragmaCompiled r
+    DisplayPragma{}            -> empty
+    EtaPragma{}                -> singleton $ SafeFlagEta r
+    ForeignPragma{}            -> empty
+    ImpossiblePragma{}         -> empty
+    InjectivePragma{}          -> singleton $ SafeFlagInjective r
+    InlinePragma{}             -> empty
+    NoCoverageCheckPragma{}    -> singleton $ SafeFlagNoCoverageCheck r
+    NoPositivityCheckPragma{}  -> singleton $ SafeFlagNoPositivityCheck r
+    NoUniverseCheckPragma{}    -> singleton $ SafeFlagNoUniverseCheck r
+    NotProjectionLikePragma{}  -> empty
+    OptionsPragma{}            -> empty
+    PolarityPragma{}           -> singleton $ SafeFlagPolarity r
+    RewritePragma{}            -> empty
+      -- @RewritePragma@ already requires --rewriting which is incompatible with --safe
+    StaticPragma{}             -> empty
+    TerminationCheckPragma _ m ->
+      case m of
+        NonTerminating         -> singleton $ SafeFlagNonTerminating r
+        Terminating            -> singleton $ SafeFlagTerminating r
+        TerminationCheck       -> empty
+        TerminationMeasure{}   -> empty
+        -- @NO_TERMINATION_CHECK@ pragma was removed, but still parses. See Issue #1763.
+        -- There is the unsafe @'PragmaNoTerminationCheck'@ warning thrown already,
+        -- so we need not throw anything here.
+        NoTerminationCheck     -> empty
+    WarningOnImport{}          -> empty
+    WarningOnUsage{}           -> empty
+  where
+    r = getRange p
+
+------------------------------------------------------------------------
+-- Instances
+
+instance HasRange DeclarationException where
+  getRange (DeclarationException _ err) = getRange err
+
+instance HasRange DeclarationException' where
+  getRange (MultipleEllipses d)                 = getRange d
+  getRange (InvalidName x)                      = getRange x
+  getRange (DuplicateDefinition x)              = getRange x
+  getRange (DuplicateAnonDeclaration r)         = r
+  getRange (MissingWithClauses x lhs)           = getRange lhs
+  getRange (WrongDefinition x k k')             = getRange x
+  getRange (AmbiguousFunClauses lhs xs)         = getRange lhs
+  getRange (AmbiguousConstructor r _ _)         = r
+  getRange (DeclarationPanic _)                 = noRange
+  getRange (WrongContentBlock _ r)              = r
+  getRange (InvalidMeasureMutual r)             = r
+  getRange (UnquoteDefRequiresSignature x)      = getRange x
+  getRange (BadMacroDef d)                      = getRange d
+  getRange (UnfoldingOutsideOpaque r)           = r
+  getRange (OpaqueInMutual r)                   = r
+  getRange (DisallowedInterleavedMutual r _ _)  = r
+
+instance HasRange DeclarationWarning where
+  getRange (DeclarationWarning _ w) = getRange w
+
+instance HasRange DeclarationWarning' where
+  getRange = \case
+    EmptyAbstract r                    -> r
+    EmptyConstructor r                 -> r
+    EmptyField r                       -> r
+    EmptyGeneralize r                  -> r
+    EmptyInstance r                    -> r
+    EmptyMacro r                       -> r
+    EmptyMutual r                      -> r
+    EmptyPostulate r                   -> r
+    EmptyPrimitive r                   -> r
+    EmptyPrivate r                     -> r
+    HiddenGeneralize r                 -> r
+    InvalidCatchallPragma r            -> r
+    InvalidConstructor r               -> r
+    InvalidConstructorBlock r          -> r
+    InvalidCoverageCheckPragma r       -> r
+    InvalidNoPositivityCheckPragma r   -> r
+    InvalidNoUniverseCheckPragma r     -> r
+    InvalidRecordDirective r           -> r
+    InvalidTerminationCheckPragma r    -> r
+    MissingDeclarations xs             -> getRange xs
+    MissingDefinitions xs              -> getRange xs
+    NotAllowedInMutual r x             -> r
+    OpenPublicAbstract r               -> r
+    OpenPublicPrivate r                -> r
+    PolarityPragmasButNotPostulates xs -> getRange xs
+    PragmaCompiled r                   -> r
+    PragmaNoTerminationCheck r         -> r
+    SafeFlagEta r                      -> r
+    SafeFlagInjective r                -> r
+    SafeFlagNoCoverageCheck r          -> r
+    SafeFlagNoPositivityCheck r        -> r
+    SafeFlagNoUniverseCheck r          -> r
+    SafeFlagNonTerminating r           -> r
+    SafeFlagPolarity r                 -> r
+    SafeFlagTerminating r              -> r
+    ShadowingInTelescope ns            -> getRange ns
+    UnknownFixityInMixfixDecl xs       -> getRange xs
+    UnknownNamesInFixityDecl xs        -> getRange xs
+    UnknownNamesInPolarityPragmas xs   -> getRange xs
+    UselessAbstract r                  -> r
+    UselessInstance r                  -> r
+    UselessPrivate r                   -> r
+
+-- These error messages can (should) be terminated by a dot ".",
+-- there is no error context printed after them.
+instance Pretty DeclarationException' where
+  pretty (MultipleEllipses p) = fsep $
+    pwords "Multiple ellipses in left-hand side" ++ [pretty p]
+  pretty (InvalidName x) = fsep $
+    pwords "Invalid name:" ++ [pretty x]
+  pretty (DuplicateDefinition x) = fsep $
+    pwords "Duplicate definition of" ++ [pretty x]
+  pretty (DuplicateAnonDeclaration _) = fsep $
+    pwords "Duplicate declaration of _"
+  pretty (MissingWithClauses x lhs) = fsep $
+    pwords "Missing with-clauses for function" ++ [pretty x]
+
+  pretty (WrongDefinition x k k') = fsep $ pretty x :
+    pwords ("has been declared as a " ++ prettyShow k ++
+      ", but is being defined as a " ++ prettyShow k')
+  pretty (AmbiguousFunClauses lhs xs) = sep
+    [ fsep $
+        pwords "More than one matching type signature for left hand side " ++ [pretty lhs] ++
+        pwords "it could belong to any of:"
+    , vcat $ fmap (pretty . PrintRange) xs
+    ]
+  pretty (AmbiguousConstructor _ n ns) = sep
+    [ fsep (pwords "Could not find a matching data signature for constructor " ++ [pretty n])
+    , vcat (case ns of
+              [] -> [fsep $ pwords "There was no candidate."]
+              _  -> fsep (pwords "It could be any of:") : fmap (pretty . PrintRange) ns
+           )
+    ]
+  pretty (WrongContentBlock b _)      = fsep . pwords $
+    case b of
+      PostulateBlock -> "A `postulate` block can only contain type signatures, possibly under keywords `instance` and `private`"
+      DataBlock -> "A data definition can only contain type signatures, possibly under keyword instance"
+      _ -> "Unexpected declaration"
+  pretty (InvalidMeasureMutual _) = fsep $
+    pwords "In a mutual block, either all functions must have the same (or no) termination checking pragma."
+  pretty (UnquoteDefRequiresSignature xs) = fsep $
+    pwords "Missing type signatures for unquoteDef" ++ map pretty (List1.toList xs)
+  pretty (BadMacroDef nd) = fsep $
+    text (declName nd) : pwords "are not allowed in macro blocks"
+  pretty (DeclarationPanic s) = text s
+  pretty (UnfoldingOutsideOpaque _) = fsep . pwords $
+    "Unfolding declarations can only appear as the first declaration immediately contained in an opaque block."
+  pretty (OpaqueInMutual _) = fsep $
+    pwords "Opaque blocks can not participate in mutual recursion. If the opaque definitions are to be mutually recursive, move the `mutual` block inside the `opaque` block."
+  pretty (DisallowedInterleavedMutual _ what xs) = vcat $ List1.concat
+    [ singleton $ fsep $ pwords "The following names are declared, but not accompanied by a definition:"
+      -- Andreas, 2023-09-07, issue #6823: print also the range.
+      -- Print a bullet list; thus, the plural version of this error message is sufficient.
+    , fmap (("-" <+>) . pretty . PrintRange) xs
+    , singleton $ fwords $ "Since " ++ what ++ " can not participate in mutual recursion, their definition must be given before this point."
+    ]
+
+instance Pretty DeclarationWarning where
+  pretty (DeclarationWarning _ w) = pretty w
+
+instance Pretty DeclarationWarning' where
+  pretty = \case
+
+    UnknownNamesInFixityDecl xs -> fsep $
+      pwords "The following names are not declared in the same scope as their syntax or fixity declaration (i.e., either not in scope at all, imported from another module, or declared in a super module):"
+      ++ punctuate comma (map pretty xs)
+
+    UnknownFixityInMixfixDecl xs -> fsep $
+      pwords "The following mixfix names do not have an associated fixity declaration:"
+      ++ punctuate comma (map pretty xs)
+
+    UnknownNamesInPolarityPragmas xs -> fsep $
+      pwords "The following names are not declared in the same scope as their polarity pragmas (they could for instance be out of scope, imported from another module, or declared in a super module):"
+      ++ punctuate comma  (map pretty xs)
+
+    MissingDeclarations xs -> fsep $
+     pwords "The following names are defined but not accompanied by a declaration:"
+     ++ punctuate comma (map (pretty . fst) xs)
+
+    MissingDefinitions xs -> fsep $
+     pwords "The following names are declared but not accompanied by a definition:"
+     ++ punctuate comma (map (pretty . fst) xs)
+
+    NotAllowedInMutual r nd -> fsep $
+      text nd : pwords "in mutual blocks are not supported.  Suggestion: get rid of the mutual block by manually ordering declarations"
+
+    PolarityPragmasButNotPostulates xs -> fsep $
+      pwords "Polarity pragmas have been given for the following identifiers which are not postulates:"
+      ++ punctuate comma (map pretty xs)
+
+    UselessPrivate _ -> fsep $
+      pwords "Using private here has no effect. Private applies only to declarations that introduce new identifiers into the module, like type signatures and data, record, and module declarations."
+
+    UselessAbstract _ -> fsep $
+      pwords "Using abstract here has no effect. Abstract applies to only definitions like data definitions, record type definitions and function clauses."
+
+    UselessInstance _ -> fsep $
+      pwords "Using instance here has no effect. Instance applies only to declarations that introduce new identifiers into the module, like type signatures and axioms."
+
+    EmptyMutual    _ -> fsep $ pwords "Empty mutual block."
+
+    EmptyConstructor{}  -> fsep $ pwords "Empty constructor block."
+
+    EmptyAbstract  _ -> fsep $ pwords "Empty abstract block."
+
+    EmptyPrivate   _ -> fsep $ pwords "Empty private block."
+
+    EmptyInstance  _ -> fsep $ pwords "Empty instance block."
+
+    EmptyMacro     _ -> fsep $ pwords "Empty macro block."
+
+    EmptyPostulate _ -> fsep $ pwords "Empty postulate block."
+
+    EmptyGeneralize _ -> fsep $ pwords "Empty variable block."
+
+    EmptyPrimitive _ -> fsep $ pwords "Empty primitive block."
+
+    EmptyField _ -> fsep $ pwords "Empty field block."
+
+    HiddenGeneralize _ -> fsep $ pwords "Declaring a variable as hidden has no effect in a variable block. Generalization never introduces visible arguments."
+
+    InvalidRecordDirective{} -> fsep $
+      pwords "Record directives can only be used inside record definitions and before field declarations."
+
+    InvalidTerminationCheckPragma _ -> fsep $
+      pwords "Termination checking pragmas can only precede a function definition or a mutual block (that contains a function definition)."
+
+    InvalidConstructor{} -> fsep $
+      pwords "`constructor' blocks may only contain type signatures for constructors."
+
+    InvalidConstructorBlock{} -> fsep $
+      pwords "No `constructor' blocks outside of `interleaved mutual' blocks."
+
+    InvalidCoverageCheckPragma _ -> fsep $
+      pwords "Coverage checking pragmas can only precede a function definition or a mutual block (that contains a function definition)."
+
+    InvalidNoPositivityCheckPragma _ -> fsep $
+      pwords "NO_POSITIVITY_CHECKING pragmas can only precede a data/record definition or a mutual block (that contains a data/record definition)."
+
+    InvalidCatchallPragma _ -> fsep $
+      pwords "The CATCHALL pragma can only precede a function clause."
+
+    InvalidNoUniverseCheckPragma _ -> fsep $
+      pwords "NO_UNIVERSE_CHECKING pragmas can only precede a data/record definition."
+
+    PragmaNoTerminationCheck _ -> fsep $
+      pwords "Pragma {-# NO_TERMINATION_CHECK #-} has been removed.  To skip the termination check, label your definitions either as {-# TERMINATING #-} or {-# NON_TERMINATING #-}."
+
+    PragmaCompiled _ -> fsep $
+      pwords "COMPILE pragma not allowed in safe mode."
+
+    OpenPublicAbstract _ -> fsep $
+      pwords "public does not have any effect in an abstract block."
+
+    OpenPublicPrivate _ -> fsep $
+      pwords "public does not have any effect in a private block."
+
+    ShadowingInTelescope nrs -> fsep $
+      pwords "Shadowing in telescope, repeated variable names:"
+      ++ punctuate comma (fmap (pretty . fst) nrs)
+
+    SafeFlagEta               _ -> unsafePragma "ETA"
+    SafeFlagInjective         _ -> unsafePragma "INJECTIVE"
+    SafeFlagNoCoverageCheck   _ -> unsafePragma "NON_COVERING"
+    SafeFlagNoPositivityCheck _ -> unsafePragma "NO_POSITIVITY_CHECK"
+    SafeFlagNoUniverseCheck   _ -> unsafePragma "NO_UNIVERSE_CHECK"
+    SafeFlagNonTerminating    _ -> unsafePragma "NON_TERMINATING"
+    SafeFlagPolarity          _ -> unsafePragma "POLARITY"
+    SafeFlagTerminating       _ -> unsafePragma "TERMINATING"
+
+    where
+      unsafePragma s = fsep $ ["Cannot", "use", s] ++ pwords "pragma with safe flag."
+
+instance NFData DeclarationWarning
+instance NFData DeclarationWarning'
diff --git a/src/full/Agda/Syntax/Concrete/Definitions/Monad.hs b/src/full/Agda/Syntax/Concrete/Definitions/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Definitions/Monad.hs
@@ -0,0 +1,280 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Concrete.Definitions.Monad where
+
+import Prelude hiding ( null )
+
+import Control.Monad        ( unless )
+import Control.Monad.Except ( MonadError(..), ExceptT, runExceptT )
+import Control.Monad.Reader ( MonadReader, ReaderT, runReaderT )
+import Control.Monad.State  ( MonadState(..), modify, State, runState )
+
+import Data.Bifunctor (second)
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common hiding (TerminationCheck())
+import Agda.Syntax.Concrete.Name
+import Agda.Syntax.Concrete.Definitions.Types
+import Agda.Syntax.Concrete.Definitions.Errors
+
+import Agda.Utils.CallStack ( CallStack, HasCallStack, withCallerCallStack )
+import Agda.Utils.Lens
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null (Null(..))
+
+import Agda.Utils.Impossible
+
+-- | Nicifier monad.
+--   Preserve the state when throwing an exception.
+
+newtype Nice a = Nice { unNice :: ReaderT NiceEnv (ExceptT DeclarationException (State NiceState)) a }
+  deriving ( Functor, Applicative, Monad
+           , MonadReader NiceEnv, MonadState NiceState, MonadError DeclarationException
+           )
+
+-- | Run a Nicifier computation, return result and warnings
+--   (in chronological order).
+runNice :: NiceEnv -> Nice a -> (Either DeclarationException a, NiceWarnings)
+runNice env m = second (reverse . niceWarn) $
+  runExceptT (unNice m `runReaderT` env) `runState` initNiceState
+
+instance Null a => Null (Nice a) where
+  empty = pure empty
+  null _ = __IMPOSSIBLE__
+
+-- | Nicifier parameters.
+
+data NiceEnv = NiceEnv
+  { safeButNotBuiltin :: Bool
+       -- ^ We are in a module declared @--safe@ which is not a builtin module.
+  }
+
+-- | Nicifier state.
+
+data NiceState = NiceState
+  { _loneSigs :: LoneSigs
+    -- ^ Lone type signatures that wait for their definition.
+  , _termChk  :: TerminationCheck
+    -- ^ Termination checking pragma waiting for a definition.
+  , _posChk   :: PositivityCheck
+    -- ^ Positivity checking pragma waiting for a definition.
+  , _uniChk   :: UniverseCheck
+    -- ^ Universe checking pragma waiting for a data/rec signature or definition.
+  , _catchall :: Catchall
+    -- ^ Catchall pragma waiting for a function clause.
+  , _covChk  :: CoverageCheck
+    -- ^ Coverage pragma waiting for a definition.
+  , niceWarn :: NiceWarnings
+    -- ^ Stack of warnings. Head is last warning.
+  , _nameId  :: NameId
+    -- ^ We distinguish different 'NoName's (anonymous definitions) by a unique 'NameId'.
+  }
+
+data LoneSig = LoneSig
+  { loneSigRange :: Range
+  , loneSigName  :: Name
+      -- ^ If 'isNoName', this name can have a different 'NameId'
+      --   than the key of 'LoneSigs' pointing to it.
+  , loneSigKind  :: DataRecOrFun
+  }
+  deriving Show
+
+type LoneSigs     = Map Name LoneSig
+     -- ^ We retain the 'Name' also in the codomain since
+     --   'Name' as a key is up to @Eq Name@ which ignores the range.
+     --   However, without range names are not unique in case the
+     --   user gives a second definition of the same name.
+     --   This causes then problems in 'replaceSigs' which might
+     --   replace the wrong signature.
+     --
+     --   Another reason is that we want to distinguish different
+     --   occurrences of 'NoName' in a mutual block (issue #4157).
+     --   The 'NoName' in the codomain will have a unique 'NameId'.
+
+type NiceWarnings = [DeclarationWarning]
+     -- ^ Stack of warnings. Head is last warning.
+
+-- | Initial nicifier state.
+
+initNiceState :: NiceState
+initNiceState = NiceState
+  { _loneSigs = Map.empty
+  , _termChk  = TerminationCheck
+  , _posChk   = YesPositivityCheck
+  , _uniChk   = YesUniverseCheck
+  , _catchall = False
+  , _covChk   = YesCoverageCheck
+  , niceWarn  = []
+  , _nameId   = NameId 1 noModuleNameHash
+  }
+
+lensNameId :: Lens' NiceState NameId
+lensNameId f e = f (_nameId e) <&> \ i -> e { _nameId = i }
+
+nextNameId :: Nice NameId
+nextNameId = do
+  i <- use lensNameId
+  lensNameId %= succ
+  return i
+
+-- * Handling the lone signatures, stored to infer mutual blocks.
+
+-- | Lens for field '_loneSigs'.
+
+loneSigs :: Lens' NiceState LoneSigs
+loneSigs f e = f (_loneSigs e) <&> \ s -> e { _loneSigs = s }
+
+-- | Adding a lone signature to the state.
+--   Return the name (which is made unique if 'isNoName').
+
+addLoneSig :: Range -> Name -> DataRecOrFun -> Nice Name
+addLoneSig r x k = do
+  -- Andreas, 2020-05-19, issue #4157, make '_' unique.
+  x' <- case x of
+    Name{}     -> pure x
+    NoName r _ -> NoName r <$> nextNameId
+  loneSigs %== \ s -> do
+    let (mr, s') = Map.insertLookupWithKey (\ _k new _old -> new) x (LoneSig r x' k) s
+    case mr of
+      Nothing -> return s'
+      Just{}  -> declarationException $
+        if not $ isNoName x then DuplicateDefinition x else DuplicateAnonDeclaration r
+  return x'
+
+-- | Remove a lone signature from the state.
+
+removeLoneSig :: Name -> Nice ()
+removeLoneSig x = loneSigs %= Map.delete x
+
+-- | Search for forward type signature.
+
+getSig :: Name -> Nice (Maybe DataRecOrFun)
+getSig x = fmap loneSigKind . Map.lookup x <$> use loneSigs
+
+-- | Check that no lone signatures are left in the state.
+
+noLoneSigs :: Nice Bool
+noLoneSigs = null <$> use loneSigs
+
+forgetLoneSigs :: Nice ()
+forgetLoneSigs = loneSigs .= Map.empty
+
+-- | Ensure that all forward declarations have been given a definition.
+checkLoneSigs :: LoneSigs -> Nice ()
+checkLoneSigs xs = do
+  forgetLoneSigs
+  unless (Map.null xs) $ declarationWarning $ MissingDefinitions $
+    map (\s -> (loneSigName s , loneSigRange s)) $ Map.elems xs
+
+-- | Ensure that all forward declarations have been given a definition,
+-- raising an error indicating *why* they would have had to have been
+-- defined.
+breakImplicitMutualBlock :: Range -> String -> Nice ()
+breakImplicitMutualBlock r why = do
+  m <- use loneSigs
+  List1.unlessNull (Map.elems m) $ \ xs ->
+    declarationException $ DisallowedInterleavedMutual r why $
+      -- Andreas, 2023-09-07: We discard the 'loneSigRange's because the 'Name' already has a range.
+      fmap loneSigName xs
+
+-- | Get names of lone function signatures, plus their unique names.
+
+loneFuns :: LoneSigs -> [(Name,Name)]
+loneFuns = map (second loneSigName) . filter (isFunName . loneSigKind . snd) . Map.toList
+
+-- | Create a 'LoneSigs' map from an association list.
+
+loneSigsFromLoneNames :: [(Range, Name, DataRecOrFun)] -> LoneSigs
+loneSigsFromLoneNames = Map.fromListWith __IMPOSSIBLE__ . map (\(r,x,k) -> (x, LoneSig r x k))
+
+-- | Lens for field '_termChk'.
+
+terminationCheckPragma :: Lens' NiceState TerminationCheck
+terminationCheckPragma f e = f (_termChk e) <&> \ s -> e { _termChk = s }
+
+withTerminationCheckPragma :: TerminationCheck -> Nice a -> Nice a
+withTerminationCheckPragma tc f = do
+  tc_old <- use terminationCheckPragma
+  terminationCheckPragma .= tc
+  result <- f
+  terminationCheckPragma .= tc_old
+  return result
+
+coverageCheckPragma :: Lens' NiceState CoverageCheck
+coverageCheckPragma f e = f (_covChk e) <&> \ s -> e { _covChk = s }
+
+withCoverageCheckPragma :: CoverageCheck -> Nice a -> Nice a
+withCoverageCheckPragma tc f = do
+  tc_old <- use coverageCheckPragma
+  coverageCheckPragma .= tc
+  result <- f
+  coverageCheckPragma .= tc_old
+  return result
+
+-- | Lens for field '_posChk'.
+
+positivityCheckPragma :: Lens' NiceState PositivityCheck
+positivityCheckPragma f e = f (_posChk e) <&> \ s -> e { _posChk = s }
+
+withPositivityCheckPragma :: PositivityCheck -> Nice a -> Nice a
+withPositivityCheckPragma pc f = do
+  pc_old <- use positivityCheckPragma
+  positivityCheckPragma .= pc
+  result <- f
+  positivityCheckPragma .= pc_old
+  return result
+
+-- | Lens for field '_uniChk'.
+
+universeCheckPragma :: Lens' NiceState UniverseCheck
+universeCheckPragma f e = f (_uniChk e) <&> \ s -> e { _uniChk = s }
+
+withUniverseCheckPragma :: UniverseCheck -> Nice a -> Nice a
+withUniverseCheckPragma uc f = do
+  uc_old <- use universeCheckPragma
+  universeCheckPragma .= uc
+  result <- f
+  universeCheckPragma .= uc_old
+  return result
+
+-- | Get universe check pragma from a data/rec signature.
+--   Defaults to 'YesUniverseCheck'.
+
+getUniverseCheckFromSig :: Name -> Nice UniverseCheck
+getUniverseCheckFromSig x = maybe YesUniverseCheck universeCheck <$> getSig x
+
+-- | Lens for field '_catchall'.
+
+catchallPragma :: Lens' NiceState Catchall
+catchallPragma f e = f (_catchall e) <&> \ s -> e { _catchall = s }
+
+-- | Get current catchall pragma, and reset it for the next clause.
+
+popCatchallPragma :: Nice Catchall
+popCatchallPragma = do
+  ca <- use catchallPragma
+  catchallPragma .= False
+  return ca
+
+withCatchallPragma :: Catchall -> Nice a -> Nice a
+withCatchallPragma ca f = do
+  ca_old <- use catchallPragma
+  catchallPragma .= ca
+  result <- f
+  catchallPragma .= ca_old
+  return result
+
+-- | Add a new warning.
+niceWarning :: DeclarationWarning -> Nice ()
+niceWarning w = modify $ \ st -> st { niceWarn = w : niceWarn st }
+
+declarationException :: HasCallStack => DeclarationException' -> Nice a
+declarationException e = withCallerCallStack $ throwError . flip DeclarationException e
+
+declarationWarning' :: DeclarationWarning' -> CallStack -> Nice ()
+declarationWarning' w loc = niceWarning $ DeclarationWarning loc w
+
+declarationWarning :: HasCallStack => DeclarationWarning' -> Nice ()
+declarationWarning = withCallerCallStack . declarationWarning'
diff --git a/src/full/Agda/Syntax/Concrete/Definitions/Types.hs b/src/full/Agda/Syntax/Concrete/Definitions/Types.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Definitions/Types.hs
@@ -0,0 +1,341 @@
+module Agda.Syntax.Concrete.Definitions.Types where
+
+import Control.DeepSeq
+
+import Data.Map (Map)
+import Data.Semigroup ( Semigroup(..) )
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common hiding (TerminationCheck())
+import qualified Agda.Syntax.Common as Common
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Name   ()
+import Agda.Syntax.Concrete.Pretty ()
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Impossible
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.List1 as List1
+
+{--------------------------------------------------------------------------
+    Types
+ --------------------------------------------------------------------------}
+
+{-| The nice declarations. No fixity declarations and function definitions are
+    contained in a single constructor instead of spread out between type
+    signatures and clauses. The @private@, @postulate@, @abstract@ and @instance@
+    modifiers have been distributed to the individual declarations.
+
+    Observe the order of components:
+
+      Range
+      Fixity'
+      Access
+      IsAbstract
+      IsInstance
+      TerminationCheck
+      PositivityCheck
+
+      further attributes
+
+      (Q)Name
+
+      content (Expr, Declaration ...)
+-}
+data NiceDeclaration
+  = Axiom Range Access IsAbstract IsInstance ArgInfo Name Expr
+      -- ^ 'IsAbstract' argument: We record whether a declaration was made in an @abstract@ block.
+      --
+      --   'ArgInfo' argument: Axioms and functions can be declared irrelevant.
+      --   ('Hiding' should be 'NotHidden'.)
+  | NiceField Range Access IsAbstract IsInstance TacticAttribute Name (Arg Expr)
+  | PrimitiveFunction Range Access IsAbstract Name (Arg Expr)
+  | NiceMutual Range TerminationCheck CoverageCheck PositivityCheck [NiceDeclaration]
+  | NiceModule Range Access IsAbstract Erased QName Telescope
+      [Declaration]
+  | NiceModuleMacro Range Access Erased Name ModuleApplication
+      OpenShortHand ImportDirective
+  | NiceOpen Range QName ImportDirective
+  | NiceImport Range QName (Maybe AsName) OpenShortHand ImportDirective
+  | NicePragma Range Pragma
+  | NiceRecSig Range Erased Access IsAbstract PositivityCheck
+      UniverseCheck Name [LamBinding] Expr
+  | NiceDataSig Range Erased Access IsAbstract PositivityCheck
+      UniverseCheck Name [LamBinding] Expr
+  | NiceFunClause Range Access IsAbstract TerminationCheck CoverageCheck Catchall Declaration
+    -- ^ An uncategorized function clause, could be a function clause
+    --   without type signature or a pattern lhs (e.g. for irrefutable let).
+    --   The 'Declaration' is the actual 'FunClause'.
+  | FunSig Range Access IsAbstract IsInstance IsMacro ArgInfo TerminationCheck CoverageCheck Name Expr
+  | FunDef Range [Declaration] IsAbstract IsInstance TerminationCheck CoverageCheck Name [Clause]
+      -- ^ Block of function clauses (we have seen the type signature before).
+      --   The 'Declaration's are the original declarations that were processed
+      --   into this 'FunDef' and are only used in 'notSoNiceDeclaration'.
+      --   Andreas, 2017-01-01: Because of issue #2372, we add 'IsInstance' here.
+      --   An alias should know that it is an instance.
+  | NiceDataDef Range Origin IsAbstract PositivityCheck UniverseCheck Name [LamBinding] [NiceConstructor]
+  | NiceLoneConstructor Range [NiceConstructor]
+  | NiceRecDef Range Origin IsAbstract PositivityCheck UniverseCheck Name RecordDirectives [LamBinding] [Declaration]
+      -- ^ @(Maybe Range)@ gives range of the 'pattern' declaration.
+  | NicePatternSyn Range Access Name [Arg Name] Pattern
+  | NiceGeneralize Range Access ArgInfo TacticAttribute Name Expr
+  | NiceUnquoteDecl Range Access IsAbstract IsInstance TerminationCheck CoverageCheck [Name] Expr
+  | NiceUnquoteDef Range Access IsAbstract TerminationCheck CoverageCheck [Name] Expr
+  | NiceUnquoteData Range Access IsAbstract PositivityCheck UniverseCheck Name [Name] Expr
+  | NiceOpaque Range [QName] [NiceDeclaration]
+  deriving (Show, Generic)
+
+instance NFData NiceDeclaration
+
+type TerminationCheck = Common.TerminationCheck Measure
+
+-- | Termination measure is, for now, a variable name.
+type Measure = Name
+
+type Catchall = Bool
+
+-- | Only 'Axiom's.
+type NiceConstructor = NiceTypeSignature
+
+-- | Only 'Axiom's.
+type NiceTypeSignature  = NiceDeclaration
+
+-- | One clause in a function definition. There is no guarantee that the 'LHS'
+--   actually declares the 'Name'. We will have to check that later.
+data Clause = Clause Name Catchall LHS RHS WhereClause [Clause]
+    deriving (Show, Generic)
+
+instance NFData Clause
+
+-- | When processing a mutual block we collect the various checks present in the block
+--   before combining them.
+
+data MutualChecks = MutualChecks
+  { mutualTermination :: [TerminationCheck]
+  , mutualCoverage    :: [CoverageCheck]
+  , mutualPositivity  :: [PositivityCheck]
+  }
+
+instance Semigroup MutualChecks where
+  MutualChecks a b c <> MutualChecks a' b' c'
+    = MutualChecks (a <> a') (b <> b') (c <> c')
+
+instance Monoid MutualChecks where
+  mempty = MutualChecks [] [] []
+  mappend = (<>)
+
+-- | In an inferred `mutual' block we keep accumulating nice declarations until all
+--   of the lone signatures have an attached definition. The type is therefore a bit
+--   span-like: we return an initial segment (the inferred mutual block) together
+--   with leftovers.
+
+data InferredMutual = InferredMutual
+  { inferredChecks    :: MutualChecks       -- checks for this block
+  , inferredBlock     :: [NiceDeclaration]  -- mutual block
+  , inferredLeftovers :: [NiceDeclaration]  -- leftovers
+  }
+
+extendInferredBlock :: NiceDeclaration -> InferredMutual -> InferredMutual
+extendInferredBlock d (InferredMutual cs ds left) = InferredMutual cs (d : ds) left
+
+-- | In an `interleaved mutual' block we collect the data signatures, function signatures,
+--   as well as their associated constructors and function clauses respectively.
+--   Each signature is given a position in the block (from 0 onwards) and each set
+--   of constructor / clauses is given a *distinct* one. This allows for interleaved
+--   forward declarations similar to what one gets in a new-style mutual block.
+type InterleavedMutual = Map Name InterleavedDecl
+
+data InterleavedDecl
+  = InterleavedData
+    { interleavedDeclNum  :: DeclNum
+        -- ^ Internal number of the data signature.
+    , interleavedDeclSig  :: NiceDeclaration
+        -- ^ The data signature.
+    , interleavedDataCons :: Maybe (DeclNum, List1 [NiceConstructor])
+        -- ^ Constructors associated to the data signature.
+    }
+  | InterleavedFun
+    { interleavedDeclNum  :: DeclNum
+        -- ^ Internal number of the function signature.
+    , interleavedDeclSig  :: NiceDeclaration
+        -- ^ The function signature.
+    , interleavedFunClauses :: Maybe (DeclNum, List1 ([Declaration],[Clause]))
+        -- ^ Function clauses associated to the function signature.
+    }
+
+-- | Numbering declarations in an @interleaved mutual@ block.
+type DeclNum = Int
+
+isInterleavedFun :: InterleavedDecl -> Maybe ()
+isInterleavedFun InterleavedFun{} = Just ()
+isInterleavedFun _ = Nothing
+
+isInterleavedData :: InterleavedDecl -> Maybe ()
+isInterleavedData InterleavedData{} = Just ()
+isInterleavedData _ = Nothing
+
+interleavedDecl :: Name -> InterleavedDecl -> [(DeclNum, NiceDeclaration)]
+interleavedDecl k = \case
+  InterleavedData i d@(NiceDataSig _ _ acc abs pc uc _ pars _) ds ->
+    let fpars   = concatMap dropTypeAndModality pars
+        r       = getRange (k, fpars)
+        ddef cs = NiceDataDef (getRange (r, cs)) UserWritten
+                    abs pc uc k fpars cs
+    in (i,d) : maybe [] (\ (j, dss) -> [(j, ddef (sconcat (List1.reverse dss)))]) ds
+  InterleavedFun i d@(FunSig r acc abs inst mac info tc cc n e) dcs ->
+    let fdef dcss = let (dss, css) = List1.unzip dcss in
+                    FunDef r (sconcat dss) abs inst tc cc n (sconcat css)
+    in (i,d) : maybe [] (\ (j, dcss) -> [(j, fdef (List1.reverse dcss))]) dcs
+  _ -> __IMPOSSIBLE__ -- someone messed up and broke the invariant
+
+-- | Several declarations expect only type signatures as sub-declarations.  These are:
+data KindOfBlock
+  = PostulateBlock  -- ^ @postulate@
+  | PrimitiveBlock  -- ^ @primitive@.  Ensured by parser.
+  | InstanceBlock   -- ^ @instance@.  Actually, here all kinds of sub-declarations are allowed a priori.
+  | FieldBlock      -- ^ @field@.  Ensured by parser.
+  | DataBlock       -- ^ @data ... where@.  Here we got a bad error message for Agda-2.5 (Issue 1698).
+  | ConstructorBlock  -- ^ @constructor@, in @interleaved mutual@.
+  deriving (Eq, Ord, Show)
+
+
+instance HasRange NiceDeclaration where
+  getRange (Axiom r _ _ _ _ _ _)           = r
+  getRange (NiceField r _ _ _ _ _ _)       = r
+  getRange (NiceMutual r _ _ _ _)          = r
+  getRange (NiceModule r _ _ _ _ _ _ )     = r
+  getRange (NiceModuleMacro r _ _ _ _ _ _) = r
+  getRange (NiceOpen r _ _)                = r
+  getRange (NiceImport r _ _ _ _)          = r
+  getRange (NicePragma r _)                = r
+  getRange (PrimitiveFunction r _ _ _ _)   = r
+  getRange (FunSig r _ _ _ _ _ _ _ _ _)    = r
+  getRange (FunDef r _ _ _ _ _ _ _)        = r
+  getRange (NiceDataDef r _ _ _ _ _ _ _)   = r
+  getRange (NiceLoneConstructor r _)       = r
+  getRange (NiceRecDef r _ _ _ _ _ _ _ _)  = r
+  getRange (NiceRecSig r _ _ _ _ _ _ _ _)  = r
+  getRange (NiceDataSig r _ _ _ _ _ _ _ _) = r
+  getRange (NicePatternSyn r _ _ _ _)      = r
+  getRange (NiceGeneralize r _ _ _ _ _)    = r
+  getRange (NiceFunClause r _ _ _ _ _ _)   = r
+  getRange (NiceUnquoteDecl r _ _ _ _ _ _ _) = r
+  getRange (NiceUnquoteDef r _ _ _ _ _ _)  = r
+  getRange (NiceUnquoteData r _ _ _ _ _ _ _) = r
+  getRange (NiceOpaque r _ _)                = r
+
+instance Pretty NiceDeclaration where
+  pretty = \case
+    Axiom _ _ _ _ _ x _            -> text "postulate" <+> pretty x <+> colon <+> text "_"
+    NiceField _ _ _ _ _ x _        -> text "field" <+> pretty x
+    PrimitiveFunction _ _ _ x _    -> text "primitive" <+> pretty x
+    NiceMutual{}                   -> text "mutual"
+    NiceOpaque _ _ ds              -> text "opaque" <+> nest 2 (vcat (map pretty ds))
+    NiceModule _ _ _ _ x _ _       -> text "module" <+> pretty x <+> text "where"
+    NiceModuleMacro _ _ _ x _ _ _  -> text "module" <+> pretty x <+> text "= ..."
+    NiceOpen _ x _                 -> text "open" <+> pretty x
+    NiceImport _ x _ _ _           -> text "import" <+> pretty x
+    NicePragma{}                   -> text "{-# ... #-}"
+    NiceRecSig _ _ _ _ _ _ x _ _   -> text "record" <+> pretty x
+    NiceDataSig _ _ _ _ _ _ x _ _  -> text "data" <+> pretty x
+    NiceFunClause{}                -> text "<function clause>"
+    FunSig _ _ _ _ _ _ _ _ x _     -> pretty x <+> colon <+> text "_"
+    FunDef _ _ _ _ _ _ x _         -> pretty x <+> text "= _"
+    NiceDataDef _ _ _ _ _ x _ _    -> text "data" <+> pretty x <+> text "where"
+    NiceLoneConstructor _ ds       -> text "constructor"
+    NiceRecDef _ _ _ _ _ x  _ _ _  -> text "record" <+> pretty x <+> text "where"
+    NicePatternSyn _ _ x _ _       -> text "pattern" <+> pretty x
+    NiceGeneralize _ _ _ _ x _     -> text "variable" <+> pretty x
+    NiceUnquoteDecl _ _ _ _ _ _ xs _ -> text "<unquote declarations>"
+    NiceUnquoteDef _ _ _ _ _ xs _    -> text "<unquote definitions>"
+    NiceUnquoteData _ _ _ _ _ x xs _ -> text "<unquote data types>"
+
+declName :: NiceDeclaration -> String
+declName Axiom{}             = "Postulates"
+declName NiceField{}         = "Fields"
+declName NiceMutual{}        = "Mutual blocks"
+declName NiceModule{}        = "Modules"
+declName NiceModuleMacro{}   = "Modules"
+declName NiceOpen{}          = "Open declarations"
+declName NiceImport{}        = "Import statements"
+declName NicePragma{}        = "Pragmas"
+declName PrimitiveFunction{} = "Primitive declarations"
+declName NicePatternSyn{}    = "Pattern synonyms"
+declName NiceGeneralize{}    = "Generalized variables"
+declName NiceUnquoteDecl{}   = "Unquoted declarations"
+declName NiceUnquoteDef{}    = "Unquoted definitions"
+declName NiceUnquoteData{}   = "Unquoted data types"
+declName NiceRecSig{}        = "Records"
+declName NiceDataSig{}       = "Data types"
+declName NiceFunClause{}     = "Functions without a type signature"
+declName FunSig{}            = "Type signatures"
+declName FunDef{}            = "Function definitions"
+declName NiceRecDef{}        = "Records"
+declName NiceDataDef{}       = "Data types"
+declName NiceLoneConstructor{} = "Constructors"
+declName NiceOpaque{}          = "Opaque blocks"
+
+
+data InMutual
+  = InMutual    -- ^ we are nicifying a mutual block
+  | NotInMutual -- ^ we are nicifying decls not in a mutual block
+    deriving (Eq, Show)
+
+-- | The kind of the forward declaration.
+
+data DataRecOrFun
+  = DataName
+    { _kindPosCheck :: PositivityCheck
+    , _kindUniCheck :: UniverseCheck
+    }
+    -- ^ Name of a data type
+  | RecName
+    { _kindPosCheck :: PositivityCheck
+    , _kindUniCheck :: UniverseCheck
+    }
+    -- ^ Name of a record type
+  | FunName TerminationCheck CoverageCheck
+    -- ^ Name of a function.
+  deriving Show
+
+-- Ignore pragmas when checking equality
+instance Eq DataRecOrFun where
+  DataName{} == DataName{} = True
+  RecName{}  == RecName{}  = True
+  FunName{}  == FunName{}  = True
+  _          == _          = False
+
+instance Pretty DataRecOrFun where
+  pretty DataName{} = "data type"
+  pretty RecName{}  = "record type"
+  pretty FunName{}  = "function"
+
+isFunName :: DataRecOrFun -> Bool
+isFunName (FunName{}) = True
+isFunName _           = False
+
+sameKind :: DataRecOrFun -> DataRecOrFun -> Bool
+sameKind = (==)
+
+terminationCheck :: DataRecOrFun -> TerminationCheck
+terminationCheck (FunName tc _) = tc
+terminationCheck _ = TerminationCheck
+
+coverageCheck :: DataRecOrFun -> CoverageCheck
+coverageCheck (FunName _ cc) = cc
+coverageCheck _ = YesCoverageCheck
+
+positivityCheck :: DataRecOrFun -> PositivityCheck
+positivityCheck (DataName pc _) = pc
+positivityCheck (RecName pc _)  = pc
+positivityCheck (FunName _ _)   = YesPositivityCheck
+
+mutualChecks :: DataRecOrFun -> MutualChecks
+mutualChecks k = MutualChecks [terminationCheck k] [coverageCheck k] [positivityCheck k]
+
+universeCheck :: DataRecOrFun -> UniverseCheck
+universeCheck (DataName _ uc) = uc
+universeCheck (RecName _ uc)  = uc
+universeCheck (FunName _ _)   = YesUniverseCheck
diff --git a/src/full/Agda/Syntax/Concrete/Fixity.hs b/src/full/Agda/Syntax/Concrete/Fixity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Fixity.hs
@@ -0,0 +1,255 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Collecting fixity declarations (and polarity pragmas) for concrete
+--   declarations.
+
+module Agda.Syntax.Concrete.Fixity
+  ( Fixities, Polarities, MonadFixityError(..)
+  , DoWarn(..)
+  , fixitiesAndPolarities
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Syntax.Builtin (builtinById, isBuiltinNoDef)
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete
+import Agda.Syntax.Position
+import Agda.TypeChecking.Positivity.Occurrence (Occurrence)
+
+import Agda.Utils.CallStack (HasCallStack)
+import Agda.Utils.Functor
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null
+import Agda.Utils.Impossible
+
+
+type Fixities   = Map Name Fixity'
+type Polarities = Map Name [Occurrence]
+
+class Monad m => MonadFixityError m where
+  throwMultipleFixityDecls            :: [(Name, [Fixity'])] -> m a
+  throwMultiplePolarityPragmas        :: [Name] -> m a
+  warnUnknownNamesInFixityDecl        :: HasCallStack => [Name] -> m ()
+  warnUnknownNamesInPolarityPragmas   :: HasCallStack => [Name] -> m ()
+  warnUnknownFixityInMixfixDecl       :: HasCallStack => [Name] -> m ()
+  warnPolarityPragmasButNotPostulates :: HasCallStack => [Name] -> m ()
+
+-- | Add more fixities. Throw an exception for multiple fixity declarations.
+--   OR:  Disjoint union of fixity maps.  Throws exception if not disjoint.
+
+plusFixities :: MonadFixityError m => Fixities -> Fixities -> m Fixities
+plusFixities m1 m2
+    -- If maps are not disjoint, report conflicts as exception.
+    | not (null isect) = throwMultipleFixityDecls isect
+    -- Otherwise, do the union.
+    | otherwise        = return $ Map.unionWithKey mergeFixites m1 m2
+  where
+    --  Merge two fixities, assuming there is no conflict
+    mergeFixites name (Fixity' f1 s1 r1) (Fixity' f2 s2 r2) = Fixity' f s $ fuseRange r1 r2
+              where f | null f1 = f2
+                      | null f2 = f1
+                      | otherwise = __IMPOSSIBLE__
+                    s | null s1 = s2
+                      | null s2 = s1
+                      | otherwise = __IMPOSSIBLE__
+
+    -- Compute a list of conflicts in a format suitable for error reporting.
+    isect = [ (x, map (Map.findWithDefault __IMPOSSIBLE__ x) [m1,m2])
+            | (x, False) <- Map.assocs $ Map.intersectionWith compatible m1 m2 ]
+
+    -- Check for no conflict.
+    compatible (Fixity' f1 s1 _) (Fixity' f2 s2 _) =
+      (null f1 || null f2) &&
+      (null s1 || null s2)
+
+-- | While 'Fixities' and Polarities are not semigroups under disjoint
+--   union (which might fail), we get a semigroup instance for the
+--   monadic @m (Fixities, Polarities)@ which propagates the first
+--   error.
+newtype MonadicFixPol m = MonadicFixPol { runMonadicFixPol :: m (Fixities, Polarities) }
+
+returnFix :: Monad m => Fixities -> MonadicFixPol m
+returnFix fx = MonadicFixPol $ return (fx, Map.empty)
+
+returnPol :: Monad m => Polarities -> MonadicFixPol m
+returnPol pol = MonadicFixPol $ return (Map.empty, pol)
+
+instance MonadFixityError m => Semigroup (MonadicFixPol m) where
+  c1 <> c2 = MonadicFixPol $ do
+    (f1, p1) <- runMonadicFixPol c1
+    (f2, p2) <- runMonadicFixPol c2
+    f <- plusFixities f1 f2
+    p <- mergePolarities p1 p2
+    return (f, p)
+    where
+    mergePolarities p1 p2
+      | Map.null i = return (Map.union p1 p2)
+      | otherwise  = throwMultiplePolarityPragmas $
+                     map fst $ Map.toList i
+      where
+      -- Only the keys are used.
+      i = Map.intersection p1 p2
+
+instance MonadFixityError m => Monoid (MonadicFixPol m) where
+  mempty  = MonadicFixPol $ return (Map.empty, Map.empty)
+  mappend = (<>)
+
+data DoWarn = NoWarn | DoWarn
+  deriving (Eq, Show)
+
+-- | Get the fixities and polarity pragmas from the current block.
+--   Doesn't go inside modules and where blocks.
+--   The reason for this is that these declarations have to appear at the same
+--   level (or possibly outside an abstract or mutual block) as their target
+--   declaration.
+fixitiesAndPolarities :: MonadFixityError m => DoWarn -> [Declaration] -> m (Fixities, Polarities)
+fixitiesAndPolarities doWarn ds = do
+  (fixs, pols) <- runMonadicFixPol $ fixitiesAndPolarities' ds
+  let DeclaredNames declared postulates privateNames = foldMap declaredNames ds
+  let publicNames = declared Set.\\ privateNames
+
+  -- If we have names in fixity declarations which are not defined in the
+  -- appropriate scope, raise a warning and delete them from fixs.
+  fixs <- ifNull (Map.keysSet fixs Set.\\ declared) (return fixs) $ \ unknownFixs -> do
+    when (doWarn == DoWarn) $ warnUnknownNamesInFixityDecl $ Set.toList unknownFixs
+    -- Note: Data.Map.restrictKeys requires containers >= 0.5.8.2
+    -- return $ Map.restrictKeys fixs declared
+    return $ Map.filterWithKey (\ k _ -> Set.member k declared) fixs
+
+  -- Same for undefined names in polarity declarations.
+  pols <- ifNull (Map.keysSet pols Set.\\ declared) (return pols) $
+    \ unknownPols -> do
+      when (doWarn == DoWarn) $ warnUnknownNamesInPolarityPragmas $ Set.toList unknownPols
+      -- Note: Data.Map.restrictKeys requires containers >= 0.5.8.2
+      -- return $ Map.restrictKeys polarities declared
+      return $ Map.filterWithKey (\ k _ -> Set.member k declared) pols
+
+  -- If we have public mixfix identifiers without a corresponding fixity
+  -- declaration, we raise a warning
+  ifNull (Set.filter isOpenMixfix publicNames Set.\\ Map.keysSet fixs) (return ()) $
+    when (doWarn == DoWarn) . warnUnknownFixityInMixfixDecl . Set.toList
+
+  -- Check that every polarity pragma is used for a postulate.
+  ifNull (Map.keysSet pols Set.\\ postulates) (return ()) $
+    when (doWarn == DoWarn) . warnPolarityPragmasButNotPostulates . Set.toList
+
+  return (fixs, pols)
+
+fixitiesAndPolarities' :: MonadFixityError m => [Declaration] -> MonadicFixPol m
+fixitiesAndPolarities' = foldMap $ \case
+  -- These declarations define polarities:
+  Pragma (PolarityPragma _ x occs) -> returnPol $ Map.singleton x occs
+  -- These declarations define fixities:
+  Syntax x syn    -> returnFix $ Map.singleton x (Fixity' noFixity syn $ getRange x)
+  Infix  f xs     -> returnFix $ Map.fromList $ for (List1.toList xs) $ \ x -> (x, Fixity' f noNotation $ getRange x)
+  -- We look into these blocks:
+  Mutual    _ ds' -> fixitiesAndPolarities' ds'
+  InterleavedMutual _ ds' -> fixitiesAndPolarities' ds'
+  Abstract  _ ds' -> fixitiesAndPolarities' ds'
+  Private _ _ ds' -> fixitiesAndPolarities' ds'
+  InstanceB _ ds' -> fixitiesAndPolarities' ds'
+  Macro     _ ds' -> fixitiesAndPolarities' ds'
+  Opaque    _ ds' -> fixitiesAndPolarities' ds'
+  -- All other declarations are ignored.
+  -- We expand these boring cases to trigger a revisit
+  -- in case the @Declaration@ type is extended in the future.
+  TypeSig         {}  -> mempty
+  FieldSig        {}  -> mempty
+  Generalize      {}  -> mempty
+  Field           {}  -> mempty
+  FunClause       {}  -> mempty
+  DataSig         {}  -> mempty
+  DataDef         {}  -> mempty
+  Data            {}  -> mempty
+  RecordSig       {}  -> mempty
+  RecordDef       {}  -> mempty
+  Record          {}  -> mempty
+  RecordDirective {}  -> mempty
+  LoneConstructor {}  -> mempty
+  PatternSyn      {}  -> mempty
+  Postulate       {}  -> mempty
+  Primitive       {}  -> mempty
+  Open            {}  -> mempty
+  Import          {}  -> mempty
+  ModuleMacro     {}  -> mempty
+  Module          {}  -> mempty
+  UnquoteDecl     {}  -> mempty
+  UnquoteDef      {}  -> mempty
+  UnquoteData     {}  -> mempty
+  Pragma          {}  -> mempty
+  Unfolding       {}  -> mempty
+
+data DeclaredNames = DeclaredNames { _allNames, _postulates, _privateNames :: Set Name }
+
+instance Semigroup DeclaredNames where
+  DeclaredNames xs ps as <> DeclaredNames ys qs bs =
+    DeclaredNames (xs <> ys) (ps <> qs) (as <> bs)
+
+instance Monoid DeclaredNames where
+  mempty  = DeclaredNames Set.empty Set.empty Set.empty
+  mappend = (<>)
+
+allPostulates :: DeclaredNames -> DeclaredNames
+allPostulates (DeclaredNames xs ps as) = DeclaredNames xs (xs <> ps) as
+
+allPrivateNames :: DeclaredNames -> DeclaredNames
+allPrivateNames (DeclaredNames xs ps as) = DeclaredNames xs ps (xs <> as)
+
+declaresNames :: [Name] -> DeclaredNames
+declaresNames xs = DeclaredNames (Set.fromList xs) Set.empty Set.empty
+
+declaresName :: Name -> DeclaredNames
+declaresName x = declaresNames [x]
+
+-- | Compute the names defined in a declaration. We stay in the current scope,
+--   i.e., do not go into modules.
+declaredNames :: Declaration -> DeclaredNames
+declaredNames = \case
+  TypeSig _ _ x _       -> declaresName x
+  FieldSig _ _ x _      -> declaresName x
+  Field _ fs            -> foldMap declaredNames fs
+  FunClause (LHS p [] []) _ _ _
+    | IdentP _ (QName x) <- removeParenP p
+                        -> declaresName x
+  FunClause{}           -> mempty
+  DataSig _ _ x _ _     -> declaresName x
+  DataDef _ _ _ cs      -> foldMap declaredNames cs
+  Data _ _ x _ _ cs     -> declaresName x <> foldMap declaredNames cs
+  RecordSig _ _ x _ _   -> declaresName x
+  RecordDef _ x d _ _   -> declaresNames $     foldMap (:[]) (fst <$> recConstructor d)
+  Record _ _ x d _ _ _  -> declaresNames $ x : foldMap (:[]) (fst <$> recConstructor d)
+  RecordDirective _     -> mempty
+  Infix _ _             -> mempty
+  Syntax _ _            -> mempty
+  PatternSyn _ x _ _    -> declaresName x
+  Mutual    _ ds        -> foldMap declaredNames ds
+  InterleavedMutual    _ ds -> foldMap declaredNames ds
+  LoneConstructor _ ds  -> foldMap declaredNames ds
+  Abstract  _ ds        -> foldMap declaredNames ds
+  Private _ _ ds        -> allPrivateNames $ foldMap declaredNames ds
+  InstanceB _ ds        -> foldMap declaredNames ds
+  Macro     _ ds        -> foldMap declaredNames ds
+  Postulate _ ds        -> allPostulates $ foldMap declaredNames ds
+  Primitive _ ds        -> foldMap declaredNames ds
+  Generalize _ ds       -> foldMap declaredNames ds
+  Opaque _ ds           -> foldMap declaredNames ds
+  Open{}                -> mempty
+  Unfolding{}           -> mempty
+  Import{}              -> mempty
+  ModuleMacro{}         -> mempty
+  Module{}              -> mempty
+  UnquoteDecl _ xs _    -> declaresNames xs
+  UnquoteDef{}          -> mempty
+  UnquoteData _ x cs _  -> declaresNames (x:cs)
+  -- BUILTIN pragmas which do not require an accompanying definition declare
+  -- the (unqualified) name they mention.
+  Pragma (BuiltinPragma _ b (QName x))
+    | any isBuiltinNoDef . builtinById $ rangedThing b -> declaresName x
+  Pragma{}             -> mempty
diff --git a/src/full/Agda/Syntax/Concrete/Generic.hs b/src/full/Agda/Syntax/Concrete/Generic.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Generic.hs
@@ -0,0 +1,392 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Generic traversal and reduce for concrete syntax,
+--   in the style of "Agda.Syntax.Internal.Generic".
+--
+--   However, here we use the terminology of 'Data.Traversable'.
+
+module Agda.Syntax.Concrete.Generic where
+
+import Data.Bifunctor
+import Data.Functor
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete
+
+import Agda.Utils.Either
+import Agda.Utils.List1 (List1)
+import Agda.Utils.List2 (List2)
+
+import Agda.Utils.Impossible
+
+-- Generic traversals for concrete expressions.
+-- ========================================================================
+
+-- | Generic traversals for concrete expressions.
+--
+--   Note: does not go into patterns!
+class ExprLike a where
+  mapExpr :: (Expr -> Expr) -> a -> a
+  -- ^ This corresponds to 'map'.
+
+  foldExpr :: Monoid m => (Expr -> m) -> a -> m
+  -- ^ This corresponds to 'foldMap'.
+
+  traverseExpr :: Monad m => (Expr -> m Expr) -> a -> m a
+  -- ^ This corresponds to 'mapM'.
+
+  default mapExpr :: (Functor t, ExprLike b, t b ~ a) => (Expr -> Expr) -> a -> a
+  mapExpr = fmap . mapExpr
+
+  default foldExpr
+    :: (Monoid m, Foldable t, ExprLike b, t b ~ a)
+    => (Expr -> m) -> a -> m
+  foldExpr = foldMap . foldExpr
+
+  default traverseExpr
+    :: (Monad m, Traversable t, ExprLike b, t b ~ a)
+    => (Expr -> m Expr) -> a -> m a
+  traverseExpr = traverse . traverseExpr
+
+
+-- Instances for things that do not contain expressions.
+---------------------------------------------------------------------------
+
+instance ExprLike () where
+  mapExpr _      = id
+  foldExpr _ _   = mempty
+  traverseExpr _ = return
+
+instance ExprLike Name where
+  mapExpr _      = id
+  foldExpr _ _   = mempty
+  traverseExpr _ = return
+
+instance ExprLike QName where
+  mapExpr _      = id
+  foldExpr _ _   = mempty
+  traverseExpr _ = return
+
+instance ExprLike Bool where
+  mapExpr _      = id
+  foldExpr _ _   = mempty
+  traverseExpr _ = return
+
+-- Instances for collections and decorations.
+---------------------------------------------------------------------------
+
+instance ExprLike a => ExprLike [a]
+instance ExprLike a => ExprLike (List1 a)
+instance ExprLike a => ExprLike (List2 a)
+instance ExprLike a => ExprLike (Maybe a)
+
+instance ExprLike a => ExprLike (Arg a)
+instance ExprLike a => ExprLike (Named name a)
+instance ExprLike a => ExprLike (Ranged a)
+instance ExprLike a => ExprLike (WithHiding a)
+
+instance ExprLike a => ExprLike (MaybePlaceholder a)
+instance ExprLike a => ExprLike (RHS' a)
+instance ExprLike a => ExprLike (TypedBinding' a)
+instance ExprLike a => ExprLike (WhereClause' a)
+
+instance (ExprLike a, ExprLike b) => ExprLike (Either a b) where
+  mapExpr f      = bimap (mapExpr f) (mapExpr f)
+  traverseExpr f = traverseEither (traverseExpr f) (traverseExpr f)
+  foldExpr f     = either (foldExpr f) (foldExpr f)
+
+instance (ExprLike a, ExprLike b) => ExprLike (a, b) where
+  mapExpr      f (x, y) = (mapExpr f x, mapExpr f y)
+  traverseExpr f (x, y) = (,) <$> traverseExpr f x <*> traverseExpr f y
+  foldExpr     f (x, y) = foldExpr f x `mappend` foldExpr f y
+
+instance (ExprLike a, ExprLike b, ExprLike c) => ExprLike (a, b, c) where
+  mapExpr      f (x, y, z) = (mapExpr f x, mapExpr f y, mapExpr f z)
+  traverseExpr f (x, y, z) = (,,) <$> traverseExpr f x <*> traverseExpr f y <*> traverseExpr f z
+  foldExpr     f (x, y, z) = foldExpr f x `mappend` foldExpr f y `mappend` foldExpr f z
+
+instance (ExprLike a, ExprLike b, ExprLike c, ExprLike d) => ExprLike (a, b, c, d) where
+  mapExpr      f (x, y, z, w) = (mapExpr f x, mapExpr f y, mapExpr f z, mapExpr f w)
+  traverseExpr f (x, y, z, w) = (,,,) <$> traverseExpr f x <*> traverseExpr f y <*> traverseExpr f z <*> traverseExpr f w
+  foldExpr     f (x, y, z, w) = foldExpr f x `mappend` foldExpr f y `mappend` foldExpr f z `mappend` foldExpr f w
+
+-- Interesting instances
+---------------------------------------------------------------------------
+
+instance ExprLike Expr where
+  mapExpr f e0 = case e0 of
+     Ident{}                 -> f $ e0
+     Lit{}                   -> f $ e0
+     QuestionMark{}          -> f $ e0
+     Underscore{}            -> f $ e0
+     RawApp r es             -> f $ RawApp r               $ mapE es
+     App r e es              -> f $ App r       (mapE e)   $ mapE es
+     OpApp r q ns es         -> f $ OpApp r q ns           $ mapE es
+     WithApp r e es          -> f $ WithApp r   (mapE e)   $ mapE es
+     HiddenArg r e           -> f $ HiddenArg r            $ mapE e
+     InstanceArg r e         -> f $ InstanceArg r          $ mapE e
+     Lam r bs e              -> f $ Lam r       (mapE bs)  $ mapE e
+     AbsurdLam{}             -> f $ e0
+     ExtendedLam r e cs      -> f $ ExtendedLam r e        $ mapE cs
+     Fun r a b               -> f $ Fun r     (mapE <$> a) $ mapE b
+     Pi tel e                -> f $ Pi          (mapE tel) $ mapE e
+     Rec r es                -> f $ Rec r                  $ mapE es
+     RecUpdate r e es        -> f $ RecUpdate r (mapE e)   $ mapE es
+     Let r ds e              -> f $ Let r       (mapE ds)  $ mapE e
+     Paren r e               -> f $ Paren r                $ mapE e
+     IdiomBrackets r es      -> f $ IdiomBrackets r        $ mapE es
+     DoBlock r ss            -> f $ DoBlock r              $ mapE ss
+     Absurd{}                -> f $ e0
+     As r x e                -> f $ As r x                 $ mapE e
+     Dot r e                 -> f $ Dot r                  $ mapE e
+     DoubleDot r e           -> f $ DoubleDot r            $ mapE e
+     Tactic r e              -> f $ Tactic r     (mapE e)
+     Quote{}                 -> f $ e0
+     QuoteTerm{}             -> f $ e0
+     Unquote{}               -> f $ e0
+     DontCare e              -> f $ DontCare               $ mapE e
+     Equal{}                 -> f $ e0
+     Ellipsis{}              -> f $ e0
+     Generalized e           -> f $ Generalized            $ mapE e
+     KnownIdent{}            -> f $ e0
+     KnownOpApp nk r q ns es -> f $ KnownOpApp nk r q ns   $ mapE es
+   where
+     mapE :: ExprLike e => e -> e
+     mapE = mapExpr f
+
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike FieldAssignment where
+  mapExpr      f (FieldAssignment x e) = FieldAssignment x (mapExpr f e)
+  traverseExpr f (FieldAssignment x e) = (\e' -> FieldAssignment x e') <$> traverseExpr f e
+  foldExpr     f (FieldAssignment _ e) = foldExpr f e
+
+instance ExprLike ModuleAssignment where
+  mapExpr      f (ModuleAssignment m es i) = ModuleAssignment m (mapExpr f es) i
+  traverseExpr f (ModuleAssignment m es i) = (\es' -> ModuleAssignment m es' i) <$> traverseExpr f es
+  foldExpr     f (ModuleAssignment m es i) = foldExpr f es
+
+instance ExprLike a => ExprLike (OpApp a) where
+  mapExpr f = \case
+     SyntaxBindingLambda r bs e -> SyntaxBindingLambda r (mapE bs) $ mapE e
+     Ordinary                 e -> Ordinary                        $ mapE e
+   where
+     mapE :: ExprLike e => e -> e
+     mapE = mapExpr f
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike LamBinding where
+  mapExpr f = \case
+     e@DomainFree{}-> e
+     DomainFull bs -> DomainFull $ mapE bs
+   where mapE e = mapExpr f e
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike LHS where
+  mapExpr f = \case
+     LHS ps res wes -> LHS ps (mapE res) (mapE wes)
+   where
+     mapE :: ExprLike a => a -> a
+     mapE = mapExpr f
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance (ExprLike qn, ExprLike e) => ExprLike (RewriteEqn' qn nm p e) where
+  mapExpr f = \case
+    Rewrite es    -> Rewrite (mapExpr f es)
+    Invert qn pes -> Invert qn (fmap (fmap $ fmap $ mapExpr f) pes)
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike LamClause where
+  mapExpr f (LamClause ps rhs ca) = LamClause ps (mapExpr f rhs) ca
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike DoStmt where
+  mapExpr f (DoBind r p e cs) = DoBind r p (mapExpr f e) (mapExpr f cs)
+  mapExpr f (DoThen e)        = DoThen (mapExpr f e)
+  mapExpr f (DoLet r ds)      = DoLet r (mapExpr f ds)
+
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike ModuleApplication where
+  mapExpr f = \case
+     SectionApp r bs e -> SectionApp r (mapE bs) $ mapE e
+     e@RecordModuleInstance{} -> e
+   where
+     mapE :: ExprLike e => e -> e
+     mapE = mapExpr f
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+instance ExprLike Declaration where
+  mapExpr f = \case
+     TypeSig ai t x e          -> TypeSig ai (mapE t) x (mapE e)
+     FieldSig i t n e          -> FieldSig i (mapE t) n (mapE e)
+     Field r fs                -> Field r                              $ map (mapExpr f) fs
+     FunClause lhs rhs wh ca   -> FunClause (mapE lhs) (mapE rhs) (mapE wh) (mapE ca)
+     DataSig r er x bs e       -> DataSig r er x (mapE bs)             $ mapE e
+     DataDef r n bs cs         -> DataDef r n (mapE bs)                $ mapE cs
+     Data r er n bs e cs       -> Data r er n (mapE bs) (mapE e)       $ mapE cs
+     RecordSig r er ind bs e   -> RecordSig r er ind (mapE bs)         $ mapE e
+     RecordDef r n dir tel ds  -> RecordDef r n dir (mapE tel)         $ mapE ds
+     Record r er n dir tel e ds
+                               -> Record r er n dir (mapE tel) (mapE e)
+                                                                       $ mapE ds
+     e@RecordDirective{}       -> e
+     e@Infix{}                 -> e
+     e@Syntax{}                -> e
+     e@PatternSyn{}            -> e
+     Mutual    r ds            -> Mutual    r                          $ mapE ds
+     InterleavedMutual r ds    -> InterleavedMutual r                  $ mapE ds
+     LoneConstructor r ds      -> LoneConstructor r                    $ mapE ds
+     Abstract  r ds            -> Abstract  r                          $ mapE ds
+     Private   r o ds          -> Private   r o                        $ mapE ds
+     InstanceB r ds            -> InstanceB r                          $ mapE ds
+     Macro     r ds            -> Macro     r                          $ mapE ds
+     Postulate r ds            -> Postulate r                          $ mapE ds
+     Primitive r ds            -> Primitive r                          $ mapE ds
+     Generalize r ds           -> Generalize r                         $ mapE ds
+     Opaque  r ds              -> Opaque r                             $ mapE ds
+     e@Open{}                  -> e
+     e@Import{}                -> e
+     ModuleMacro r e n es op dir
+                               -> ModuleMacro r e n (mapE es) op dir
+     Module r e n tel ds       -> Module r e n (mapE tel)              $ mapE ds
+     UnquoteDecl r x e         -> UnquoteDecl r x (mapE e)
+     UnquoteDef r x e          -> UnquoteDef r x (mapE e)
+     UnquoteData r x xs e      -> UnquoteData r x xs (mapE e)
+     e@Pragma{}                -> e
+     e@Unfolding{}             -> e
+   where
+     mapE :: ExprLike e => e -> e
+     mapE = mapExpr f
+
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+
+{- Template
+
+instance ExprLike a where
+  mapExpr f = \case
+    where mapE e = mapExpr f e
+  foldExpr     = __IMPOSSIBLE__
+  traverseExpr = __IMPOSSIBLE__
+
+-}
+
+-- Generic traversals for concrete declarations.
+-- ========================================================================
+
+class FoldDecl a where
+
+  -- | Collect declarations and subdeclarations, transitively.
+  -- Prefix-order tree traversal.
+  foldDecl :: Monoid m => (Declaration -> m) -> a -> m
+
+  default foldDecl :: (Monoid m, Foldable t, FoldDecl b, t b ~ a)
+    => (Declaration -> m) -> a -> m
+  foldDecl = foldMap . foldDecl
+
+instance FoldDecl a => FoldDecl [a]
+instance FoldDecl a => FoldDecl (List1 a)
+instance FoldDecl a => FoldDecl (List2 a)
+instance FoldDecl a => FoldDecl (WhereClause' a)
+
+instance FoldDecl Declaration where
+  foldDecl f d = f d <> case d of
+    Private  _ _        ds  -> foldDecl f ds
+    Abstract _          ds  -> foldDecl f ds
+    InstanceB _         ds  -> foldDecl f ds
+    InterleavedMutual _ ds  -> foldDecl f ds
+    LoneConstructor _   ds  -> foldDecl f ds
+    Mutual _            ds  -> foldDecl f ds
+    Module _ _ _ _      ds  -> foldDecl f ds
+    Macro _             ds  -> foldDecl f ds
+    Record _ _ _ _ _ _  ds  -> foldDecl f ds
+    RecordDef _ _ _ _   ds  -> foldDecl f ds
+    TypeSig _ _ _ _         -> mempty
+    FieldSig _ _ _ _        -> mempty
+    Generalize _ _          -> mempty
+    Field _ _               -> mempty
+    FunClause _ _ wh _      -> foldDecl f wh
+    DataSig _ _ _ _ _       -> mempty
+    Data _ _ _ _ _ _        -> mempty
+    DataDef _ _ _ _         -> mempty
+    RecordSig _ _ _ _ _     -> mempty
+    RecordDirective _       -> mempty
+    Infix _ _               -> mempty
+    Syntax _ _              -> mempty
+    PatternSyn _ _ _ _      -> mempty
+    Postulate _ _           -> mempty
+    Primitive _ _           -> mempty
+    Open _ _ _              -> mempty
+    Import _ _ _ _ _        -> mempty
+    ModuleMacro _ _ _ _ _ _ -> mempty
+    UnquoteDecl _ _ _       -> mempty
+    UnquoteDef _ _ _        -> mempty
+    UnquoteData _ _ _ _     -> mempty
+    Pragma _                -> mempty
+    Opaque _ ds             -> foldDecl f ds
+    Unfolding _ _           -> mempty
+
+class TraverseDecl a where
+
+  -- | Update declarations and their subdeclarations.
+  -- Prefix-order traversal: traverses subdeclarations of updated declaration.
+  --
+  preTraverseDecl :: Monad m => (Declaration -> m Declaration) -> a -> m a
+
+  default preTraverseDecl :: (Monad m, Traversable t, TraverseDecl b, t b ~ a)
+    => (Declaration -> m Declaration) -> a -> m a
+  preTraverseDecl = traverse . preTraverseDecl
+
+instance TraverseDecl a => TraverseDecl [a]
+instance TraverseDecl a => TraverseDecl (List1 a)
+instance TraverseDecl a => TraverseDecl (List2 a)
+instance TraverseDecl a => TraverseDecl (WhereClause' a)
+
+instance TraverseDecl Declaration where
+  preTraverseDecl f d0 = do
+    d <- f d0
+    case d of
+      Private  r o        ds     -> Private r o             <$> preTraverseDecl f ds
+      Abstract r          ds     -> Abstract r              <$> preTraverseDecl f ds
+      InstanceB r         ds     -> InstanceB r             <$> preTraverseDecl f ds
+      InterleavedMutual r ds     -> InterleavedMutual r     <$> preTraverseDecl f ds
+      LoneConstructor r   ds     -> LoneConstructor r       <$> preTraverseDecl f ds
+      Mutual r            ds     -> Mutual r                <$> preTraverseDecl f ds
+      Module r er n tel   ds     -> Module r er n tel       <$> preTraverseDecl f ds
+      Macro r             ds     -> Macro r                 <$> preTraverseDecl f ds
+      Opaque r ds                -> Opaque r                <$> preTraverseDecl f ds
+      Record r er n dir tel t ds -> Record r er n dir tel t <$> preTraverseDecl f ds
+      RecordDef r n dir tel   ds -> RecordDef r n dir tel   <$> preTraverseDecl f ds
+      TypeSig _ _ _ _            -> return d
+      FieldSig _ _ _ _           -> return d
+      Generalize _ _             -> return d
+      Field _ _                  -> return d
+      FunClause lhs rhs wh ca    -> preTraverseDecl f wh <&> \ wh' -> FunClause lhs rhs wh' ca
+      DataSig _ _ _ _ _          -> return d
+      Data _ _ _ _ _ _           -> return d
+      DataDef _ _ _ _            -> return d
+      RecordSig _ _ _ _ _        -> return d
+      RecordDirective _          -> return d
+      Infix _ _                  -> return d
+      Syntax _ _                 -> return d
+      PatternSyn _ _ _ _         -> return d
+      Postulate _ _              -> return d
+      Primitive _ _              -> return d
+      Open _ _ _                 -> return d
+      Import _ _ _ _ _           -> return d
+      ModuleMacro _ _ _ _ _ _    -> return d
+      UnquoteDecl _ _ _          -> return d
+      UnquoteDef _ _ _           -> return d
+      UnquoteData _ _ _ _        -> return d
+      Pragma _                   -> return d
+      Unfolding _ _              -> return d
diff --git a/src/full/Agda/Syntax/Concrete/Glyph.hs b/src/full/Agda/Syntax/Concrete/Glyph.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Glyph.hs
@@ -0,0 +1,129 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| Choice of Unicode or ASCII glyphs.
+-}
+module Agda.Syntax.Concrete.Glyph
+  ( UnicodeOrAscii(..)
+  , unsafeSetUnicodeOrAscii
+  , specialCharactersForGlyphs
+  , braces', dbraces
+  , forallQ
+  , leftIdiomBrkt, rightIdiomBrkt, emptyIdiomBrkt
+  , arrow, lambda
+  , SpecialCharacters(..)
+  ) where
+
+import Control.DeepSeq
+
+import Data.IORef (IORef, newIORef, readIORef, writeIORef)
+import qualified System.IO.Unsafe as UNSAFE (unsafePerformIO)
+
+import GHC.Generics (Generic)
+
+import Agda.Utils.Boolean
+import Agda.Utils.List
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+-- | We want to know whether we are allowed to insert unicode characters or not.
+data UnicodeOrAscii
+  = UnicodeOk  -- ^ 'true': Unicode characters are allowed.
+  | AsciiOnly  -- ^ 'false: Stick to ASCII.
+  deriving (Show, Eq, Enum, Bounded, Generic)
+
+instance NFData UnicodeOrAscii
+
+instance Boolean UnicodeOrAscii where
+  fromBool = \case
+    True -> UnicodeOk
+    False -> AsciiOnly
+
+instance IsBool UnicodeOrAscii where
+  toBool = \case
+    UnicodeOk -> True
+    AsciiOnly -> False
+
+{-# NOINLINE unsafeUnicodeOrAsciiIORef #-}
+unsafeUnicodeOrAsciiIORef :: IORef UnicodeOrAscii
+unsafeUnicodeOrAsciiIORef = UNSAFE.unsafePerformIO $ newIORef UnicodeOk
+
+{-# NOINLINE unsafeSetUnicodeOrAscii #-}
+unsafeSetUnicodeOrAscii :: UnicodeOrAscii -> IO ()
+unsafeSetUnicodeOrAscii = writeIORef unsafeUnicodeOrAsciiIORef
+
+-- | Are we allowed to use unicode supscript characters?
+unsafeUnicodeOrAscii :: UnicodeOrAscii
+unsafeUnicodeOrAscii = UNSAFE.unsafePerformIO (readIORef unsafeUnicodeOrAsciiIORef)
+
+-- | Picking the appropriate set of special characters depending on
+-- whether we are allowed to use unicode or have to limit ourselves
+-- to ascii.
+
+data SpecialCharacters = SpecialCharacters
+  { _dbraces :: Doc -> Doc
+  , _lambda  :: Doc
+  , _arrow   :: Doc
+  , _forallQ :: Doc
+  , _leftIdiomBrkt  :: Doc
+  , _rightIdiomBrkt :: Doc
+  , _emptyIdiomBrkt :: Doc
+  }
+
+specialCharactersUnicode :: SpecialCharacters
+specialCharactersUnicode = SpecialCharacters
+  { _dbraces        = ((hlSymbol "\x2983 " <>) . (<> hlSymbol " \x2984"))
+  , _lambda         = hlSymbol "\x03bb"
+  , _arrow          = hlSymbol "\x2192"
+  , _forallQ        = hlSymbol "\x2200"
+  , _leftIdiomBrkt  = hlSymbol "\x2987"
+  , _rightIdiomBrkt = hlSymbol "\x2988"
+  , _emptyIdiomBrkt = hlSymbol "\x2987\x2988"
+  }
+
+specialCharactersAscii :: SpecialCharacters
+specialCharactersAscii = SpecialCharacters
+  { _dbraces        = braces . braces'
+  , _lambda         = hlSymbol "\\"
+  , _arrow          = hlSymbol "->"
+  , _forallQ        = hlSymbol "forall"
+  , _leftIdiomBrkt  = hlSymbol "(|"
+  , _rightIdiomBrkt = hlSymbol "|)"
+  , _emptyIdiomBrkt = hlSymbol "(|)"
+  }
+
+-- | Return the glyph set based on a given (unicode or ascii) glyph mode
+specialCharactersForGlyphs :: UnicodeOrAscii -> SpecialCharacters
+specialCharactersForGlyphs UnicodeOk = specialCharactersUnicode
+specialCharactersForGlyphs AsciiOnly = specialCharactersAscii
+
+-- | Choose the glyph set based on the unsafe IORef.
+{-# NOINLINE specialCharacters #-}
+specialCharacters :: SpecialCharacters
+specialCharacters = specialCharactersForGlyphs unsafeUnicodeOrAscii
+
+braces' :: Doc -> Doc
+braces' d = caseList (render d) (braces d) {-else-} $ \ c cs ->
+  braces (spaceIfDash c <> d <> spaceIfDash (last1 c cs))
+  -- Add space to avoid starting a comment (Ulf, 2010-09-13, #269)
+  -- Andreas, 2018-07-21, #3161: Also avoid ending a comment
+  where
+  spaceIfDash '-' = " "
+  spaceIfDash _   = empty
+
+-- double braces...
+dbraces :: Doc -> Doc
+dbraces = _dbraces specialCharacters
+
+-- forall quantifier
+forallQ :: Doc
+forallQ = hlSymbol $ _forallQ specialCharacters
+
+-- left, right, and empty idiom bracket
+leftIdiomBrkt, rightIdiomBrkt, emptyIdiomBrkt :: Doc
+leftIdiomBrkt  = _leftIdiomBrkt  specialCharacters
+rightIdiomBrkt = _rightIdiomBrkt specialCharacters
+emptyIdiomBrkt = _emptyIdiomBrkt specialCharacters
+
+arrow, lambda :: Doc
+arrow  = _arrow specialCharacters
+lambda = _lambda specialCharacters
diff --git a/src/full/Agda/Syntax/Concrete/Name.hs b/src/full/Agda/Syntax/Concrete/Name.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Name.hs
@@ -0,0 +1,469 @@
+{-| Names in the concrete syntax are just strings (or lists of strings for
+    qualified names).
+-}
+module Agda.Syntax.Concrete.Name where
+
+import Control.DeepSeq
+
+import Data.ByteString.Char8 (ByteString)
+import Data.Function (on)
+import qualified Data.Foldable as Fold
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+
+import Agda.Utils.Lens
+import Agda.Utils.List  (last1)
+import Agda.Utils.List1 (List1, pattern (:|), (<|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Suffix
+
+import Agda.Utils.Impossible
+
+{-| A name is a non-empty list of alternating 'Id's and 'Hole's. A normal name
+    is represented by a singleton list, and operators are represented by a list
+    with 'Hole's where the arguments should go. For instance: @[Hole,Id "+",Hole]@
+    is infix addition.
+
+    Equality and ordering on @Name@s are defined to ignore range so same names
+    in different locations are equal.
+-}
+data Name
+  = Name -- ^ A (mixfix) identifier.
+    { nameRange     :: Range
+    , nameInScope   :: NameInScope
+    , nameNameParts :: NameParts
+    }
+  | NoName -- ^ @_@.
+    { nameRange     :: Range
+    , nameId        :: NameId
+    }
+
+type NameParts = List1 NamePart
+
+-- | An open mixfix identifier is either prefix, infix, or suffix.
+--   That is to say: at least one of its extremities is a @Hole@
+
+isOpenMixfix :: Name -> Bool
+isOpenMixfix = \case
+  Name _ _ (x :| x' : xs) -> x == Hole || last1 x' xs == Hole
+  _ -> False
+
+instance Underscore Name where
+  underscore = NoName noRange __IMPOSSIBLE__
+  isUnderscore NoName{} = True
+  isUnderscore (Name {nameNameParts = Id x :| []}) = isUnderscore x
+  isUnderscore _ = False
+
+-- | Mixfix identifiers are composed of words and holes,
+--   e.g. @_+_@ or @if_then_else_@ or @[_/_]@.
+data NamePart
+  = Hole       -- ^ @_@ part.
+  | Id RawName  -- ^ Identifier part.
+  deriving Generic
+
+-- | Define equality on @Name@ to ignore range so same names in different
+--   locations are equal.
+--
+--   Is there a reason not to do this? -Jeff
+--
+--   No. But there are tons of reasons to do it. For instance, when using
+--   names as keys in maps you really don't want to have to get the range
+--   right to be able to do a lookup. -Ulf
+
+instance Eq Name where
+    Name _ _ xs    == Name _ _ ys    = xs == ys
+    NoName _ i     == NoName _ j     = i == j
+    _              == _              = False
+
+instance Ord Name where
+    compare (Name _ _ xs)  (Name _ _ ys)      = compare xs ys
+    compare (NoName _ i)   (NoName _ j)       = compare i j
+    compare (NoName {})    (Name {})          = LT
+    compare (Name {})      (NoName {})        = GT
+
+instance Eq NamePart where
+  Hole  == Hole  = True
+  Id s1 == Id s2 = s1 == s2
+  _     == _     = False
+
+instance Ord NamePart where
+  compare Hole    Hole    = EQ
+  compare Hole    (Id {}) = LT
+  compare (Id {}) Hole    = GT
+  compare (Id s1) (Id s2) = compare s1 s2
+
+-- | @QName@ is a list of namespaces and the name of the constant.
+--   For the moment assumes namespaces are just @Name@s and not
+--     explicitly applied modules.
+--   Also assumes namespaces are generative by just using derived
+--     equality. We will have to define an equality instance to
+--     non-generative namespaces (as well as having some sort of
+--     lookup table for namespace names).
+data QName
+  = Qual  Name QName -- ^ @A.rest@.
+  | QName Name       -- ^ @x@.
+  deriving (Eq, Ord)
+
+instance Underscore QName where
+  underscore = QName underscore
+  isUnderscore (QName x) = isUnderscore x
+  isUnderscore Qual{}    = False
+
+------------------------------------------------------------------------
+-- * Constructing simple 'Name's.
+------------------------------------------------------------------------
+
+-- | Create an ordinary 'InScope' name.
+simpleName :: RawName -> Name
+simpleName = Name noRange InScope . singleton . Id
+
+-- | Create a binary operator name in scope.
+simpleBinaryOperator :: RawName -> Name
+simpleBinaryOperator s = Name noRange InScope $ Hole :| Id s : Hole : []
+
+-- | Create an ordinary 'InScope' name containing a single 'Hole'.
+simpleHole :: Name
+simpleHole = Name noRange InScope $ singleton Hole
+
+------------------------------------------------------------------------
+-- * Operations on 'Name' and 'NamePart'
+------------------------------------------------------------------------
+
+-- | Don't use on 'NoName{}'.
+lensNameParts :: Lens' Name NameParts
+lensNameParts f = \case
+  n@Name{} -> f (nameNameParts n) <&> \ ps -> n { nameNameParts = ps }
+  NoName{} -> __IMPOSSIBLE__
+
+nameToRawName :: Name -> RawName
+nameToRawName = prettyShow
+
+nameParts :: Name -> NameParts
+nameParts (Name _ _ ps)    = ps
+nameParts (NoName _ _)     = singleton $ Id "_" -- To not return an empty list
+
+nameStringParts :: Name -> [RawName]
+nameStringParts n = [ s | Id s <- List1.toList $ nameParts n ]
+
+-- | Parse a string to parts of a concrete name.
+--
+--   Note: @stringNameParts "_" == [Id "_"] == nameParts NoName{}@
+
+stringNameParts :: String -> NameParts
+stringNameParts ""  = singleton $ Id "_"  -- NoName
+stringNameParts "_" = singleton $ Id "_"  -- NoName
+stringNameParts s = List1.fromListSafe __IMPOSSIBLE__ $ loop s
+  where
+  loop ""                              = []
+  loop ('_':s)                         = Hole : loop s
+  loop s | (x, s') <- break (== '_') s = Id (stringToRawName x) : loop s'
+
+-- | Number of holes in a 'Name' (i.e., arity of a mixfix-operator).
+class NumHoles a where
+  numHoles :: a -> Int
+
+instance NumHoles NameParts where
+  numHoles = length . List1.filter (== Hole)
+
+instance NumHoles Name where
+  numHoles NoName{}         = 0
+  numHoles (Name { nameNameParts = parts }) = numHoles parts
+
+instance NumHoles QName where
+  numHoles (QName x)  = numHoles x
+  numHoles (Qual _ x) = numHoles x
+
+-- | Is the name an operator?
+--   Needs at least 2 'NamePart's.
+isOperator :: Name -> Bool
+isOperator = \case
+  Name _ _ (_ :| _ : _) -> True
+  _ -> False
+
+isHole :: NamePart -> Bool
+isHole Hole = True
+isHole _    = False
+
+isPrefix, isPostfix, isInfix, isNonfix :: Name -> Bool
+isPrefix  x = not (isHole (List1.head xs)) &&      isHole (List1.last xs)  where xs = nameParts x
+isPostfix x =      isHole (List1.head xs)  && not (isHole (List1.last xs)) where xs = nameParts x
+isInfix   x =      isHole (List1.head xs)  &&      isHole (List1.last xs)  where xs = nameParts x
+isNonfix  x = not (isHole (List1.head xs)) && not (isHole (List1.last xs)) where xs = nameParts x
+
+
+------------------------------------------------------------------------
+-- * Keeping track of which names are (not) in scope
+------------------------------------------------------------------------
+
+data NameInScope = InScope | NotInScope
+  deriving (Eq, Show)
+
+class LensInScope a where
+  lensInScope :: Lens' a NameInScope
+
+  isInScope :: a -> NameInScope
+  isInScope x = x ^. lensInScope
+
+  mapInScope :: (NameInScope -> NameInScope) -> a -> a
+  mapInScope = over lensInScope
+
+  setInScope :: a -> a
+  setInScope = mapInScope $ const InScope
+
+  setNotInScope :: a -> a
+  setNotInScope = mapInScope $ const NotInScope
+
+instance LensInScope NameInScope where
+  lensInScope = id
+
+instance LensInScope Name where
+  lensInScope f = \case
+    n@Name{ nameInScope = nis } -> (\nis' -> n { nameInScope = nis' }) <$> f nis
+    n@NoName{} -> n <$ f InScope
+
+instance LensInScope QName where
+  lensInScope f = \case
+    Qual x xs -> (`Qual` xs) <$> lensInScope f x
+    QName x   -> QName <$> lensInScope f x
+
+------------------------------------------------------------------------
+-- * Generating fresh names
+------------------------------------------------------------------------
+
+-- | Method by which to generate fresh unshadowed names.
+data FreshNameMode
+  = UnicodeSubscript
+  -- ^ Append an integer Unicode subscript: x, x₁, x₂, …
+  | AsciiCounter
+  -- ^ Append an integer ASCII counter: x, x1, x2, …
+
+  -- Note that @Agda.Utils.Suffix@ supports an additional style, @Prime@, but
+  -- we currently only encounter it when extending an existing name of that
+  -- format, (x', x'', …), not for an initially-generated permutation. There's
+  -- no reason we couldn't, except that we currently choose between
+  -- subscript/counter styles based on the --no-unicode mode rather than any
+  -- finer-grained option.
+  --   | PrimeTickCount
+  --   ^ Append an ASCII prime/apostrophe: x, x', x'', …
+
+nextRawName :: FreshNameMode -> RawName -> RawName
+nextRawName freshNameMode s = addSuffix root (maybe initialSuffix nextSuffix suffix)
+  where
+  (root, suffix) = suffixView s
+  initialSuffix = case freshNameMode of
+    UnicodeSubscript -> Subscript 1
+    AsciiCounter -> Index 1
+
+-- | Get the next version of the concrete name. For instance,
+--   @nextName "x" = "x₁"@.  The name must not be a 'NoName'.
+nextName :: FreshNameMode -> Name -> Name
+nextName freshNameMode x@Name{} = setNotInScope $ over (lensNameParts . lastIdPart) (nextRawName freshNameMode) x
+nextName             _ NoName{} = __IMPOSSIBLE__
+
+-- | Zoom on the last non-hole in a name.
+lastIdPart :: Lens' NameParts RawName
+lastIdPart f = loop
+  where
+  loop = \case
+    Id s :| []     -> f s <&> \ s -> Id s :| []
+    Id s :| [Hole] -> f s <&> \ s -> Id s :| [Hole]
+    p1 :| p2 : ps  -> (p1 <|) <$> loop (p2 :| ps)
+    Hole :| []     -> __IMPOSSIBLE__
+
+-- | Get the first version of the concrete name that does not satisfy
+--   the given predicate.
+firstNonTakenName :: FreshNameMode -> (Name -> Bool) -> Name -> Name
+firstNonTakenName freshNameMode taken x =
+  if taken x
+  then firstNonTakenName freshNameMode taken (nextName freshNameMode x)
+  else x
+
+-- | Lens for accessing and modifying the suffix of a name.
+--   The suffix of a @NoName@ is always @Nothing@, and should not be
+--   changed.
+nameSuffix :: Lens' Name (Maybe Suffix)
+nameSuffix (f :: Maybe Suffix -> f (Maybe Suffix)) = \case
+
+  n@NoName{} -> f Nothing <&> \case
+    Nothing -> n
+    Just {} -> __IMPOSSIBLE__
+
+  n@Name{} -> lensNameParts (lastIdPart idSuf) n
+    where
+    idSuf s =
+      let (root, suffix) = suffixView s
+      in maybe root (addSuffix root) <$> (f suffix)
+
+-- | Split a name into a base name plus a suffix.
+nameSuffixView :: Name -> (Maybe Suffix, Name)
+nameSuffixView = nameSuffix (,Nothing)
+
+-- | Replaces the suffix of a name. Unless the suffix is @Nothing@,
+--   the name should not be @NoName@.
+setNameSuffix :: Maybe Suffix -> Name -> Name
+setNameSuffix = set nameSuffix
+
+-- | Get a raw version of the name with all suffixes removed. For
+--   instance, @nameRoot "x₁₂₃" = "x"@.
+nameRoot :: Name -> RawName
+nameRoot x = nameToRawName $ snd $ nameSuffixView x
+
+sameRoot :: Name -> Name -> Bool
+sameRoot = (==) `on` nameRoot
+
+------------------------------------------------------------------------
+-- * Operations on qualified names
+------------------------------------------------------------------------
+
+-- | Lens for the unqualified part of a QName
+lensQNameName :: Lens' QName Name
+lensQNameName f (QName n)  = QName <$> f n
+lensQNameName f (Qual m n) = Qual m <$> lensQNameName f n
+
+-- | @qualify A.B x == A.B.x@
+qualify :: QName -> Name -> QName
+qualify (QName m) x     = Qual m (QName x)
+qualify (Qual m m') x   = Qual m $ qualify m' x
+
+-- | @unqualify A.B.x == x@
+--
+-- The range is preserved.
+unqualify :: QName -> Name
+unqualify q = unqualify' q `withRangeOf` q
+  where
+  unqualify' (QName x)  = x
+  unqualify' (Qual _ x) = unqualify' x
+
+-- | @qnameParts A.B.x = [A, B, x]@
+qnameParts :: QName -> List1 Name
+qnameParts (Qual x q) = x <| qnameParts q
+qnameParts (QName x)  = singleton x
+
+-- | Is the name (un)qualified?
+
+isQualified :: QName -> Bool
+isQualified Qual{}  = True
+isQualified QName{} = False
+
+isUnqualified :: QName -> Maybe Name
+isUnqualified Qual{}    = Nothing
+isUnqualified (QName n) = Just n
+
+------------------------------------------------------------------------
+-- * No name stuff
+------------------------------------------------------------------------
+
+-- | @noName_ = 'noName' 'noRange'@
+noName_ :: Name
+noName_ = noName noRange
+
+noName :: Range -> Name
+noName r = NoName r (NameId 0 noModuleNameHash)
+
+-- | Check whether a name is the empty name "_".
+class IsNoName a where
+  isNoName :: a -> Bool
+
+  default isNoName :: (Foldable t, IsNoName b, t b ~ a) => a -> Bool
+  isNoName = Fold.all isNoName
+
+instance IsNoName String where
+  isNoName = isUnderscore
+
+instance IsNoName ByteString where
+  isNoName = isUnderscore
+
+instance IsNoName Name where
+  isNoName = \case
+    NoName{}              -> True
+    Name _ _ (Hole :| []) -> True
+    Name _ _ (Id x :| []) -> isNoName x
+    _ -> False
+
+instance IsNoName QName where
+  isNoName (QName x) = isNoName x
+  isNoName Qual{}    = False        -- M.A._ does not qualify as empty name
+
+instance IsNoName a => IsNoName (Ranged a) where
+instance IsNoName a => IsNoName (WithOrigin a) where
+
+------------------------------------------------------------------------
+-- * Showing names
+------------------------------------------------------------------------
+
+deriving instance Show Name
+deriving instance Show NamePart
+deriving instance Show QName
+
+------------------------------------------------------------------------
+-- * Printing names
+------------------------------------------------------------------------
+
+instance Pretty Name where
+  pretty (Name _ _ xs)    = hcat $ fmap pretty xs
+  pretty (NoName _ _)     = "_"
+
+instance Pretty NamePart where
+  pretty Hole   = "_"
+  pretty (Id s) = text $ rawNameToString s
+
+instance Pretty QName where
+  pretty (Qual m x)
+    | isUnderscore m = pretty x -- don't print anonymous modules
+    | otherwise      = pretty m <> "." <> pretty x
+  pretty (QName x)  = pretty x
+
+------------------------------------------------------------------------
+-- * Range instances
+------------------------------------------------------------------------
+
+instance HasRange Name where
+    getRange (Name r _ _ps) = r
+    getRange (NoName r _)   = r
+
+instance HasRange QName where
+    getRange (QName  x) = getRange x
+    getRange (Qual n x) = fuseRange n x
+
+instance SetRange Name where
+  setRange r (Name _ nis ps) = Name r nis ps
+  setRange r (NoName _ i)  = NoName r i
+
+instance SetRange QName where
+  setRange r (QName x)  = QName (setRange r x)
+  setRange r (Qual n x) = Qual (setRange r n) (setRange r x)
+
+instance KillRange QName where
+  killRange (QName x) = QName $ killRange x
+  killRange (Qual n x) = killRange n `Qual` killRange x
+
+instance KillRange Name where
+  killRange (Name r nis ps)  = Name (killRange r) nis ps
+  killRange (NoName r i)     = NoName (killRange r) i
+
+------------------------------------------------------------------------
+-- * NFData instances
+------------------------------------------------------------------------
+
+instance NFData NameInScope where
+  rnf InScope    = ()
+  rnf NotInScope = ()
+
+-- | Ranges are not forced.
+
+instance NFData Name where
+  rnf (Name _ nis ns) = rnf nis `seq` rnf ns
+  rnf (NoName _ n)  = rnf n
+
+instance NFData NamePart where
+  rnf Hole   = ()
+  rnf (Id s) = rnf s
+
+instance NFData QName where
+  rnf (Qual a b) = rnf a `seq` rnf b
+  rnf (QName a)  = rnf a
diff --git a/src/full/Agda/Syntax/Concrete/Operators.hs b/src/full/Agda/Syntax/Concrete/Operators.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Operators.hs
@@ -0,0 +1,855 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PatternSynonyms #-}
+
+{-| The parser doesn't know about operators and parses everything as normal
+    function application. This module contains the functions that parses the
+    operators properly. For a stand-alone implementation of this see
+    @src\/prototyping\/mixfix\/old@.
+
+    It also contains the function that puts parenthesis back given the
+    precedence of the context.
+-}
+
+module Agda.Syntax.Concrete.Operators
+    ( parseApplication
+    , parseModuleApplication
+    , parseLHS
+    , parsePattern
+    , parsePatternSyn
+    ) where
+
+import Control.Applicative ( Alternative((<|>)))
+import Control.Monad.Except (throwError)
+
+import Data.Either (partitionEithers)
+import qualified Data.Foldable as Fold
+import qualified Data.Function
+import qualified Data.List as List
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Traversable as Trav
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete hiding (appView)
+import Agda.Syntax.Concrete.Operators.Parser
+import Agda.Syntax.Concrete.Operators.Parser.Monad hiding (parse)
+import Agda.Syntax.Concrete.Pattern
+import Agda.Syntax.Position
+import Agda.Syntax.Notation
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Flat
+import Agda.Syntax.Scope.Monad
+
+import Agda.TypeChecking.Monad.Base (typeError, TypeError(..), LHSOrPatSyn(..))
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.State (getScope)
+
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Either
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import Agda.Utils.List2 (List2, pattern List2)
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.List2 as List2
+import Agda.Utils.Maybe
+import Agda.Utils.Monad (guardWithError)
+import Agda.Utils.Trie (Trie)
+import qualified Agda.Utils.Trie as Trie
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Billing
+---------------------------------------------------------------------------
+
+-- | Bills the operator parser.
+
+billToParser :: ExprKind -> ScopeM a -> ScopeM a
+billToParser k = Bench.billTo
+  [ Bench.Parsing
+  , case k of
+      IsExpr    -> Bench.OperatorsExpr
+      IsPattern -> Bench.OperatorsPattern
+  ]
+
+---------------------------------------------------------------------------
+-- * Building the parser
+---------------------------------------------------------------------------
+
+-- | A data structure used internally by 'buildParsers'.
+data InternalParsers e = InternalParsers
+  { pTop    :: Parser e e
+  , pApp    :: Parser e e
+  , pArgs   :: Parser e [NamedArg e]
+  , pNonfix :: Parser e e
+  , pAtom   :: Parser e e
+  }
+
+-- | Expression kinds: Expressions or patterns.
+data ExprKind = IsExpr | IsPattern
+  deriving (Eq, Show)
+
+-- | The data returned by 'buildParsers'.
+
+data Parsers e = Parsers
+  { parser :: [e] -> [e]
+    -- ^ A parser for expressions or patterns (depending on the
+    -- 'ExprKind' argument given to 'buildParsers').
+  , argsParser :: [e] -> [[NamedArg e]]
+    -- ^ A parser for sequences of arguments.
+  , operators :: [NotationSection]
+    -- ^ All operators/notations/sections that were used to generate
+    -- the grammar.
+  , flattenedScope :: FlatScope
+    -- ^ A flattened scope that only contains those names that are
+    -- unqualified or qualified by qualifiers that occur in the list
+    -- of names given to 'buildParsers'.
+  }
+
+-- | Builds parsers for operator applications from all the operators
+-- and function symbols in scope.
+--
+-- When parsing a pattern we do not use bound names. The effect is
+-- that unqualified operator parts (that are not constructor parts)
+-- can be used as atomic names in the pattern (so they can be
+-- rebound). See @test/succeed/OpBind.agda@ for an example.
+--
+-- When parsing a pattern we also disallow the use of sections, mainly
+-- because there is little need for sections in patterns. Note that
+-- sections are parsed by splitting up names into multiple tokens
+-- (@_+_@ is replaced by @_@, @+@ and @_@), and if we were to support
+-- sections in patterns, then we would have to accept certain such
+-- sequences of tokens as single pattern variables.
+
+buildParsers
+  :: forall e. IsExpr e
+  => ExprKind
+     -- ^ Should expressions or patterns be parsed?
+  -> [QName]
+     -- ^ This list must include every name part in the
+     -- expression/pattern to be parsed (excluding name parts inside
+     -- things like parenthesised subexpressions that are treated as
+     -- atoms). The list is used to optimise the parser. For
+     -- instance, a given notation is only included in the generated
+     -- grammar if all of the notation's name parts are present in
+     -- the list of names.
+  -> ScopeM (Parsers e)
+buildParsers kind exprNames = do
+    flat         <- flattenScope (qualifierModules exprNames) <$>
+                      getScope
+    (names, ops0) <- localNames flat
+    let ops | kind == IsPattern = filter (not . isLambdaNotation) ops0
+            | otherwise         = ops0
+
+    let -- All names.
+        namesInExpr :: Set QName
+        namesInExpr = Set.fromList exprNames
+
+        partListsInExpr' = map (List1.toList . nameParts . unqualify) $
+                           Set.toList namesInExpr
+
+        partListTrie f =
+          foldr (\ps -> Trie.union (Trie.everyPrefix ps ()))
+                Trie.empty
+                (f partListsInExpr')
+
+        -- All names.
+        partListsInExpr :: Trie NamePart ()
+        partListsInExpr = partListTrie id
+
+        -- All names, with the name parts in reverse order.
+        reversedPartListsInExpr :: Trie NamePart ()
+        reversedPartListsInExpr = partListTrie (map reverse)
+
+        -- Every regular name part (not holes etc.).
+        partsInExpr :: Set RawName
+        partsInExpr =
+          Set.fromList [ s | Id s <- concat partListsInExpr' ]
+
+        -- Are all name parts present in the expression?
+        partsPresent n =
+          [ Set.member p partsInExpr
+          | p <- stringParts (notation n)
+          ]
+
+        addHole True  p = [Hole, Id p]
+        addHole False p = [Id p]
+
+        -- Is the first identifier part present in n present in the
+        -- expression, without any preceding name parts, except for a
+        -- leading underscore iff withHole is True?
+        firstPartPresent withHole n =
+          Trie.member (addHole withHole p) partListsInExpr
+          where
+          p = case n of
+            HolePart{} : IdPart p : _ -> rangedThing p
+            IdPart p : _              -> rangedThing p
+            _                         -> __IMPOSSIBLE__
+
+        -- Is the last identifier part present in n present in the
+        -- expression, without any succeeding name parts, except for a
+        -- trailing underscore iff withHole is True?
+        lastPartPresent withHole n =
+          Trie.member (addHole withHole p) reversedPartListsInExpr
+          where
+          p = case reverse n of
+            HolePart{} : IdPart p : _ -> rangedThing p
+            IdPart p : _              -> rangedThing p
+            _                         -> __IMPOSSIBLE__
+
+        -- Are the initial and final identifier parts present with
+        -- the right mix of leading and trailing underscores?
+        correctUnderscores :: Bool -> Bool -> Notation -> Bool
+        correctUnderscores withInitialHole withFinalHole n =
+          firstPartPresent withInitialHole n
+            &&
+          lastPartPresent  withFinalHole   n
+
+        -- Should be used with operators (not sections) and notations
+        -- coming from syntax declarations.
+        filterCorrectUnderscoresOp :: [NewNotation] -> [NotationSection]
+        filterCorrectUnderscoresOp ns =
+          [ noSection n
+          | n <- ns
+          , if notaIsOperator n
+            then correctUnderscores False False (notation n)
+            else all (\s -> Trie.member [Id s] partListsInExpr)
+                     (stringParts $ notation n)
+          ]
+
+        -- Should be used with sections.
+        correctUnderscoresSect :: NotationKind -> Notation -> Bool
+        correctUnderscoresSect k n = case (k, notationKind n) of
+          (PrefixNotation,  InfixNotation)   -> correctUnderscores True False n
+          (PostfixNotation, InfixNotation)   -> correctUnderscores False True n
+          (NonfixNotation,  InfixNotation)   -> correctUnderscores True True n
+          (NonfixNotation,  PrefixNotation)  -> correctUnderscores False True n
+          (NonfixNotation,  PostfixNotation) -> correctUnderscores True False n
+          _                                  -> __IMPOSSIBLE__
+
+        -- If "or" is replaced by "and" in conParts/allParts below,
+        -- then the misspelled operator application "if x thenn x else
+        -- x" can be parsed as "if" applied to five arguments,
+        -- resulting in a confusing error message claiming that "if"
+        -- is not in scope.
+
+        (non, fix) = List.partition nonfix (filter (and . partsPresent) ops)
+
+        cons       = getDefinedNames
+                       (someKindsOfNames [ConName, CoConName, FldName, PatternSynName]) flat
+        conNames   = Set.fromList $
+                       filter (flip Set.member namesInExpr) $
+                       map (notaName . List1.head) cons
+        conParts   = Set.fromList $
+                       concatMap notationNames $
+                       filter (or . partsPresent) $
+                       List1.concat cons
+
+        allNames   = Set.fromList $
+                       filter (flip Set.member namesInExpr) names
+        allParts   = Set.union conParts
+                       (Set.fromList $
+                        concatMap notationNames $
+                        filter (or . partsPresent) ops)
+
+        isAtom x
+          | kind == IsPattern && not (isQualified x) =
+            not (Set.member x conParts) || Set.member x conNames
+          | otherwise =
+            not (Set.member x allParts) || Set.member x allNames
+        -- If string is a part of notation, it cannot be used as an identifier,
+        -- unless it is also used as an identifier. See issue 307.
+
+        parseSections = case kind of
+          IsPattern -> DoNotParseSections
+          IsExpr    -> ParseSections
+
+    let nonClosedSections l ns =
+          case parseSections of
+            DoNotParseSections -> []
+            ParseSections      ->
+              [ NotationSection n k (Just l) True
+              | n <- ns
+              , isinfix n && notaIsOperator n
+              , k <- [PrefixNotation, PostfixNotation]
+              , correctUnderscoresSect k (notation n)
+              ]
+
+        unrelatedOperators :: [NotationSection]
+        unrelatedOperators =
+          filterCorrectUnderscoresOp unrelated
+            ++
+          nonClosedSections Unrelated unrelated
+          where
+          unrelated = filter ((== Unrelated) . level) fix
+
+        nonWithSections :: [NotationSection]
+        nonWithSections =
+          map (\s -> s { sectLevel = Nothing })
+              (filterCorrectUnderscoresOp non)
+            ++
+          case parseSections of
+            DoNotParseSections -> []
+            ParseSections      ->
+              [ NotationSection n NonfixNotation Nothing True
+              | n <- fix
+              , notaIsOperator n
+              , correctUnderscoresSect NonfixNotation (notation n)
+              ]
+
+        -- The triples have the form (level, operators). The lowest
+        -- level comes first.
+        relatedOperators :: [(PrecedenceLevel, [NotationSection])]
+        relatedOperators =
+          map (\((l, ns) :| rest) -> (l, ns ++ concatMap snd rest)) .
+          List1.groupOn fst .
+          mapMaybe (\n -> case level n of
+                            Unrelated     -> Nothing
+                            r@(Related l) ->
+                              Just (l, filterCorrectUnderscoresOp [n] ++
+                                       nonClosedSections r [n])) $
+          fix
+
+        everything :: [NotationSection]
+        everything =
+          concatMap snd relatedOperators ++
+          unrelatedOperators ++
+          nonWithSections
+
+    reportS "scope.operators" 50
+      [ "unrelatedOperators = " ++ prettyShow unrelatedOperators
+      , "nonWithSections    = " ++ prettyShow nonWithSections
+      , "relatedOperators   = " ++ prettyShow relatedOperators
+      ]
+
+    let g = Data.Function.fix $ \p -> InternalParsers
+              { pTop    = memoise TopK $
+                          Fold.asum $
+                            foldr (\(l, ns) higher ->
+                                       mkP (Right l) parseSections
+                                           (pTop p) ns higher True) (pApp p)
+                                   relatedOperators :
+                            zipWith (\ k n ->
+                                    mkP (Left k) parseSections
+                                        (pTop p) [n] (pApp p) False) [0..] unrelatedOperators
+              , pApp    = memoise AppK $ appP (pNonfix p) (pArgs p)
+              , pArgs   = argsP (pNonfix p)
+              , pNonfix = memoise NonfixK $
+                          Fold.asum $
+                            pAtom p :
+                            map (\sect ->
+                              let n = sectNotation sect
+
+                                  inner :: forall k. NK k ->
+                                           Parser e (OperatorType k e)
+                                  inner = opP parseSections (pTop p) n
+                              in
+                              case notationKind (notation n) of
+                                InfixNotation ->
+                                  flip ($) <$> placeholder Beginning
+                                           <*> inner In
+                                           <*> placeholder End
+                                PrefixNotation ->
+                                  inner Pre <*> placeholder End
+                                PostfixNotation ->
+                                  flip ($) <$> placeholder Beginning
+                                           <*> inner Post
+                                NonfixNotation -> inner Non
+                                NoNotation     -> __IMPOSSIBLE__) nonWithSections
+              , pAtom   = atomP isAtom
+              }
+
+    -- Andreas, 2020-06-03 #4712
+    -- Note: needs Agda to be compiled with DEBUG_PARSING to print the grammar.
+    reportSDoc "scope.grammar" 10 $ return $
+      "Operator grammar:" $$ nest 2 (grammar (pTop g))
+
+    return $ Parsers
+      { parser         = parse (parseSections, pTop  g)
+      , argsParser     = parse (parseSections, pArgs g)
+      , operators      = everything
+      , flattenedScope = flat
+      }
+    where
+        level :: NewNotation -> FixityLevel
+        level = fixityLevel . notaFixity
+
+        nonfix, isinfix, isprefix, ispostfix :: NewNotation -> Bool
+        nonfix    = (== NonfixNotation)  . notationKind . notation
+        isinfix   = (== InfixNotation)   . notationKind . notation
+        isprefix  = (== PrefixNotation)  . notationKind . notation
+        ispostfix = (== PostfixNotation) . notationKind . notation
+
+        isPrefix, isPostfix :: NotationSection -> Bool
+        isPrefix  = (== PrefixNotation)  . sectKind
+        isPostfix = (== PostfixNotation) . sectKind
+
+        isInfix :: Associativity -> NotationSection -> Bool
+        isInfix ass s =
+          sectKind s == InfixNotation
+             &&
+          fixityAssoc (notaFixity (sectNotation s)) == ass
+
+        mkP :: PrecedenceKey  -- Memoisation key.
+            -> ParseSections
+            -> Parser e e
+            -> [NotationSection]
+            -> Parser e e  -- A parser for an expression of higher precedence.
+            -> Bool  -- Include the \"expression of higher precedence\"
+                     -- parser as one of the choices?
+            -> Parser e e
+        mkP key parseSections p0 ops higher includeHigher =
+            memoise (NodeK key) $
+              Fold.asum $
+                applyWhen includeHigher (higher :) $
+                catMaybes [nonAssoc, preRights, postLefts]
+            where
+            choice :: forall k.
+                      NK k -> [NotationSection] ->
+                      Parser e (OperatorType k e)
+            choice k =
+              Fold.asum .
+              map (\sect ->
+                let n = sectNotation sect
+
+                    inner :: forall k.
+                             NK k -> Parser e (OperatorType k e)
+                    inner = opP parseSections p0 n
+                in
+                case k of
+                  In   -> inner In
+
+                  Pre  -> if isinfix n || ispostfix n
+                          then flip ($) <$> placeholder Beginning
+                                        <*> inner In
+                          else inner Pre
+
+                  Post -> if isinfix n || isprefix n
+                          then flip <$> inner In
+                                    <*> placeholder End
+                          else inner Post
+
+                  Non  -> __IMPOSSIBLE__)
+
+            nonAssoc :: Maybe (Parser e e)
+            nonAssoc = case filter (isInfix NonAssoc) ops of
+              []  -> Nothing
+              ops -> Just $
+                (\x f y -> f (noPlaceholder x) (noPlaceholder y))
+                  <$> higher
+                  <*> choice In ops
+                  <*> higher
+
+            or p1 []   p2 []   = Nothing
+            or p1 []   p2 ops2 = Just (p2 ops2)
+            or p1 ops1 p2 []   = Just (p1 ops1)
+            or p1 ops1 p2 ops2 = Just (p1 ops1 <|> p2 ops2)
+
+            preRight :: Maybe (Parser e (MaybePlaceholder e -> e))
+            preRight =
+              or (choice Pre)
+                 (filter isPrefix ops)
+                 (\ops -> flip ($) <$> (noPlaceholder <$> higher)
+                                   <*> choice In ops)
+                 (filter (isInfix RightAssoc) ops)
+
+            preRights :: Maybe (Parser e e)
+            preRights = do
+              preRight <- preRight
+              return $ Data.Function.fix $ \preRights ->
+                memoiseIfPrinting (PreRightsK key) $
+                  preRight <*> (noPlaceholder <$> (preRights <|> higher))
+
+            postLeft :: Maybe (Parser e (MaybePlaceholder e -> e))
+            postLeft =
+              or (choice Post)
+                 (filter isPostfix ops)
+                 (\ops -> flip <$> choice In ops
+                               <*> (noPlaceholder <$> higher))
+                 (filter (isInfix LeftAssoc) ops)
+
+            postLefts :: Maybe (Parser e e)
+            postLefts = do
+              postLeft <- postLeft
+              return $ Data.Function.fix $ \postLefts ->
+                memoise (PostLeftsK key) $
+                  flip ($) <$> (noPlaceholder <$> (postLefts <|> higher))
+                           <*> postLeft
+
+
+---------------------------------------------------------------------------
+-- * Parse functions
+---------------------------------------------------------------------------
+
+-- | Returns the list of possible parses.
+parsePat
+  :: ([Pattern] -> [Pattern]) -- ^ Turns a 'RawAppP' into possible parses.
+  -> Pattern                  -- ^ Pattern possibly containing 'RawAppP's.
+  -> [Pattern]                -- ^ Possible parses, not containing 'RawAppP's.
+parsePat prs = \case
+    AppP p (Arg info q) ->
+        fullParen' <$> (AppP <$> parsePat prs p <*> (Arg info <$> traverse (parsePat prs) q))
+    RawAppP _ ps     -> fullParen' <$> (parsePat prs =<< prs (List2.toList ps))
+    OpAppP r d ns ps -> fullParen' . OpAppP r d ns <$> (mapM . traverse . traverse) (parsePat prs) ps
+    HiddenP _ _      -> fail "bad hidden argument"
+    InstanceP _ _    -> fail "bad instance argument"
+    AsP r x p        -> AsP r x <$> parsePat prs p
+    p@DotP{}         -> return p
+    ParenP r p       -> fullParen' <$> parsePat prs p
+    p@WildP{}        -> return p
+    p@AbsurdP{}      -> return p
+    p@LitP{}         -> return p
+    p@QuoteP{}       -> return p
+    p@IdentP{}       -> return p
+    RecP r fs        -> RecP r <$> mapM (traverse (parsePat prs)) fs
+    p@EqualP{}       -> return p -- Andrea: cargo culted from DotP
+    EllipsisP r mp   -> caseMaybe mp (fail "bad ellipsis") $ \p ->
+                          EllipsisP r . Just <$> parsePat prs p
+    WithP r p        -> WithP r <$> parsePat prs p
+
+
+{- Implement parsing of copattern left hand sides, e.g.
+
+  record Tree (A : Set) : Set where
+    field
+      label : A
+      child : Bool -> Tree A
+
+  -- corecursive function defined by copattern matching
+  alternate : {A : Set}(a b : A) -> Tree A
+  -- shallow copatterns
+         label (alternate a b)              = a
+         child (alternate a b) True         = alternate b a
+  -- deep copatterns:
+  label (child (alternate a b) False)       = b
+  child (child (alternate a b) False) True  = alternate a b
+  child (child (alternate a b) False) False = alternate a b
+
+  Delivers an infinite tree
+
+                   a
+              b        b
+            a   a    a   a
+           b b b b  b b b b
+                 ...
+
+  Each lhs is a pattern tree with a distinct path of destructors
+  ("child", "label") from the root to the defined symbol ("alternate").
+  All branches besides this distinct path are patterns.
+
+  Syntax.Concrete.LHSCore represents a lhs
+   - the destructor path
+   - the side patterns
+   - the defined function symbol
+   - the applied patterns
+-}
+
+-- | The result of 'parseLHS'.
+data ParseLHS
+  = ParsePattern Pattern    -- ^ We parsed a pattern.
+  | ParseLHS QName LHSCore  -- ^ We parsed a lhs.
+
+instance Pretty ParseLHS where
+  pretty = \case
+    ParsePattern p  -> pretty p
+    ParseLHS _f lhs -> pretty lhs
+
+-- | Parses a left-hand side, workhorse for 'parseLHS'.
+--
+parseLHS'
+  :: LHSOrPatSyn
+       -- ^ Are we trying to parse a lhs or a pattern synonym?
+       --   For error reporting only!
+  -> Maybe QName
+       -- ^ Name of the function/patSyn definition if we parse a lhs.
+       --   'Nothing' if we parse a pattern.
+  -> Pattern
+       -- ^ Thing to parse.
+  -> ScopeM (ParseLHS, [NotationSection])
+       -- ^ The returned list contains all operators/notations/sections that
+       -- were used to generate the grammar.
+
+parseLHS' IsLHS (Just qn) WildP{} =
+    return (ParseLHS qn $ LHSHead qn [], [])
+
+parseLHS' lhsOrPatSyn top p = do
+
+    -- Build parser.
+    patP <- buildParsers IsPattern (patternQNames p)
+
+    -- Run parser, forcing result.
+    let ps   = let result = parsePat (parser patP) p
+               in  foldr seq () result `seq` result
+
+    -- Classify parse results.
+    let cons = getNames (someKindsOfNames [ConName, CoConName, PatternSynName])
+                        (flattenedScope patP)
+    let flds = getNames (someKindsOfNames [FldName])
+                        (flattenedScope patP)
+    let conf = PatternCheckConfig top (hasElem cons) (hasElem flds)
+
+    let (errs, results) = partitionEithers $ map (validPattern conf) ps
+    reportS "scope.operators" 60 $ vcat $
+      [ "Possible parses for lhs:" ] ++ map (nest 2 . pretty . snd) results
+    case results of
+        -- Unique result.
+        [(_,lhs)] -> do reportS "scope.operators" 50 $ "Parsed lhs:" <+> pretty lhs
+                        return (lhs, operators patP)
+        -- No result.
+        []        -> typeError $ OperatorInformation (operators patP)
+                               $ NoParseForLHS lhsOrPatSyn (catMaybes errs) p
+        -- Ambiguous result.
+        rs        -> typeError $ OperatorInformation (operators patP)
+                               $ AmbiguousParseForLHS lhsOrPatSyn p $
+                       map (fullParen . fst) rs
+    where
+        getNames kinds flat =
+          map (notaName . List1.head) $ getDefinedNames kinds flat
+
+        -- The pattern is retained for error reporting in case of ambiguous parses.
+        validPattern :: PatternCheckConfig -> Pattern -> PM (Pattern, ParseLHS)
+        validPattern conf p = do
+          res <- classifyPattern conf p
+          case (res, top) of
+            (ParsePattern{}, Nothing) -> return (p, res)  -- expect pattern
+            (ParseLHS{}    , Just{} ) -> return (p, res)  -- expect lhs
+            _ -> throwError Nothing
+
+-- | Name sets for classifying a pattern.
+data PatternCheckConfig = PatternCheckConfig
+  { topName :: Maybe QName    -- ^ Name of defined symbol.
+  , conName :: QName -> Bool  -- ^ Valid constructor name?
+  , fldName :: QName -> Bool  -- ^ Valid field name?
+  }
+
+-- | The monad for pattern checking and classification.
+--
+--   The error message is either empty or a subpattern that was found to be invalid.
+type PM = Either (Maybe Pattern)
+
+-- | Returns zero or one classified patterns.
+--   In case of zero, return the offending subpattern.
+classifyPattern :: PatternCheckConfig -> Pattern -> PM ParseLHS
+classifyPattern conf p =
+  case patternAppView p of
+
+    -- case @f ps@
+    Arg _ (Named _ (IdentP _ x)) :| ps | Just x == topName conf -> do
+      mapM_ (valid . namedArg) ps
+      return $ ParseLHS x $ lhsCoreAddSpine (LHSHead x []) ps
+
+    -- case @d ps@
+    Arg _ (Named _ (IdentP _ x)) :| ps | fldName conf x -> do
+
+      -- Step 1: check for valid copattern lhs.
+      ps0 :: [NamedArg ParseLHS] <- mapM classPat ps
+      let (ps1, rest) = span (isParsePattern . namedArg) ps0
+      (p2, ps3) <- maybeToEither Nothing $ uncons rest
+          -- when (null rest): no field pattern or def pattern found
+
+      -- Ensure that the @ps3@ are patterns rather than lhss.
+      mapM_ (guardWithError Nothing . isParsePattern . namedArg) ps3
+
+      -- Step 2: construct the lhs.
+      let (f, lhs0)     = fromParseLHS $ namedArg p2
+          lhs           = setNamedArg p2 lhs0
+          (ps', _:ps'') = splitAt (length ps1) ps
+      return $ ParseLHS f $ lhsCoreAddSpine (LHSProj x ps' lhs []) ps''
+
+    -- case @...@
+    Arg _ (Named _ (EllipsisP r (Just p))) :| ps -> do
+      classifyPattern conf p >>= \case  -- TODO: avoid re-parsing
+        ParsePattern{}    -> throwError Nothing
+        (ParseLHS f core) -> do
+          mapM_ (valid . namedArg) ps
+          let ellcore = LHSEllipsis r core
+          return $ ParseLHS f $ lhsCoreAddSpine ellcore ps
+
+    -- case: ordinary pattern
+    _ -> ParsePattern p <$ valid p
+
+  where
+  valid = validConPattern $ conName conf
+
+  classPat :: NamedArg Pattern -> PM (NamedArg ParseLHS)
+  classPat = Trav.mapM (Trav.mapM (classifyPattern conf))
+
+  isParsePattern = \case
+    ParsePattern{} -> True
+    ParseLHS{}     -> False
+
+  fromParseLHS :: ParseLHS -> (QName, LHSCore)
+  fromParseLHS = \case
+    ParseLHS f lhs -> (f, lhs)
+    ParsePattern{} -> __IMPOSSIBLE__
+
+
+-- | Parses a left-hand side, and makes sure that it defined the expected name.
+parseLHS :: QName -> Pattern -> ScopeM LHSCore
+parseLHS top p = billToParser IsPattern $ do
+  (res, ops) <- parseLHS' IsLHS (Just top) p
+  case res of
+    ParseLHS f lhs -> return lhs
+    _ -> typeError $ OperatorInformation ops
+                   $ NoParseForLHS IsLHS [] p
+
+-- | Parses a pattern.
+parsePattern :: Pattern -> ScopeM Pattern
+parsePattern = parsePatternOrSyn IsLHS
+
+parsePatternSyn :: Pattern -> ScopeM Pattern
+parsePatternSyn = parsePatternOrSyn IsPatSyn
+
+parsePatternOrSyn :: LHSOrPatSyn -> Pattern -> ScopeM Pattern
+parsePatternOrSyn lhsOrPatSyn p = billToParser IsPattern $ do
+  (res, ops) <- parseLHS' lhsOrPatSyn Nothing p
+  case res of
+    ParsePattern p -> return p
+    _ -> typeError $ OperatorInformation ops
+                   $ NoParseForLHS lhsOrPatSyn [] p
+
+-- | Helper function for 'parseLHS' and 'parsePattern'.
+--
+--   Returns a subpattern that is not a valid constructor pattern
+--   or nothing if the whole pattern is a valid constructor pattern.
+validConPattern
+  :: (QName -> Bool)     -- ^ Test for constructor name.
+  -> Pattern             -- ^ Supposedly a constructor pattern.
+  -> PM ()   -- ^ Offending subpattern or nothing.
+validConPattern cons = loop
+  where
+  loop p = case appView p of
+      WithP _ p :| [] -> loop p
+      _ :| []         -> ok
+      IdentP _ x :| ps
+        | cons x      -> mapM_ loop ps
+        | otherwise   -> failure
+      QuoteP _ :| [_] -> ok
+      DotP _ e :| ps  -> mapM_ loop ps
+      _               -> failure
+    where
+    ok      = return ()
+    failure = throwError $ Just p
+
+
+-- | Helper function for 'parseLHS' and 'parsePattern'.
+appView :: Pattern -> List1 Pattern
+appView = loop []
+  where
+  loop acc = \case
+    AppP p a         -> loop (namedArg a : acc) p
+    OpAppP _ op _ ps -> (IdentP True op :| fmap namedArg ps)
+                          `List1.appendList`
+                        reverse acc
+    ParenP _ p       -> loop acc p
+    RawAppP _ _      -> __IMPOSSIBLE__
+    HiddenP _ _      -> __IMPOSSIBLE__
+    InstanceP _ _    -> __IMPOSSIBLE__
+    p@IdentP{}       -> ret p
+    p@WildP{}        -> ret p
+    p@AsP{}          -> ret p
+    p@AbsurdP{}      -> ret p
+    p@LitP{}         -> ret p
+    p@QuoteP{}       -> ret p
+    p@DotP{}         -> ret p
+    p@RecP{}         -> ret p
+    p@EqualP{}       -> ret p
+    p@EllipsisP{}    -> ret p
+    p@WithP{}        -> ret p
+   where
+   ret p = p :| reverse acc
+
+-- | Return all qualifiers occuring in a list of 'QName's.
+--   Each qualifier is returned as a list of names, e.g.
+--   for @Data.Nat._+_@ we return the list @[Data,Nat]@.
+qualifierModules :: [QName] -> [[Name]]
+qualifierModules qs =
+  nubOn id $ filter (not . null) $ map (List1.init . qnameParts) qs
+
+-- | Parse a list of expressions (typically from a 'RawApp') into an application.
+parseApplication :: List2 Expr -> ScopeM Expr
+parseApplication es  = billToParser IsExpr $ do
+    let es0 = List2.toList es
+    -- Build the parser
+    p <- buildParsers IsExpr [ q | Ident q <- es0 ]
+
+    -- Parse
+    let result = parser p es0
+    case foldr seq () result `seq` result of
+      [e]   -> do
+          reportSDoc "scope.operators" 50 $ return $
+            "Parsed an operator application:" <+> pretty e
+          return e
+      []    -> typeError $ OperatorInformation (operators p)
+                         $ NoParseForApplication es
+      e:es' -> typeError $ OperatorInformation (operators p)
+                         $ AmbiguousParseForApplication es
+                         $ fmap fullParen (e :| es')
+
+parseModuleIdentifier :: Expr -> ScopeM QName
+parseModuleIdentifier (Ident m) = return m
+parseModuleIdentifier e = typeError $ NotAModuleExpr e
+
+parseRawModuleApplication :: List2 Expr -> ScopeM (QName, [NamedArg Expr])
+parseRawModuleApplication es@(List2 e e2 rest) = billToParser IsExpr $ do
+    let es_args = e2:rest
+    m <- parseModuleIdentifier e
+
+    -- Build the arguments parser
+    p <- buildParsers IsExpr [ q | Ident q <- es_args ]
+
+    -- Parse
+    -- TODO: not sure about forcing
+    case {-force $-} argsParser p es_args of
+        [as] -> return (m, as)
+        []   -> typeError $ OperatorInformation (operators p)
+                          $ NoParseForApplication es
+        as : ass -> do
+          let f = fullParen . foldl (App noRange) (Ident m)
+          typeError $ OperatorInformation (operators p)
+                    $ AmbiguousParseForApplication es
+                    $ fmap f (as :| ass)
+
+-- | Parse an expression into a module application
+--   (an identifier plus a list of arguments).
+parseModuleApplication :: Expr -> ScopeM (QName, [NamedArg Expr])
+parseModuleApplication (RawApp _ es) = parseRawModuleApplication es
+parseModuleApplication (App r e1 e2) = do -- TODO: do we need this case?
+    (m, args) <- parseModuleApplication e1
+    return (m, args ++ [e2])
+parseModuleApplication e = do
+    m <- parseModuleIdentifier e
+    return (m, [])
+
+---------------------------------------------------------------------------
+-- * Inserting parenthesis
+---------------------------------------------------------------------------
+
+fullParen :: IsExpr e => e -> e
+fullParen e = case exprView $ fullParen' e of
+    ParenV e    -> e
+    e'          -> unExprView e'
+
+fullParen' :: IsExpr e => e -> e
+fullParen' e = case exprView e of
+    LocalV _     -> e
+    WildV _      -> e
+    OtherV _     -> e
+    HiddenArgV _ -> e
+    InstanceArgV _ -> e
+    ParenV _     -> e
+    AppV e1 (Arg info e2) -> par $ unExprView $ AppV (fullParen' e1) (Arg info e2')
+        where
+            e2' = case argInfoHiding info of
+                Hidden     -> e2
+                Instance{} -> e2
+                NotHidden  -> fullParen' <$> e2
+    OpAppV x ns es -> par $ unExprView $ OpAppV x ns $ (fmap . fmap . fmap . fmap . fmap) fullParen' es
+    LamV bs e -> par $ unExprView $ LamV bs (fullParen e)
+    where
+        par = unExprView . ParenV
diff --git a/src/full/Agda/Syntax/Concrete/Operators/Parser.hs b/src/full/Agda/Syntax/Concrete/Operators/Parser.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Operators/Parser.hs
@@ -0,0 +1,372 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs        #-}
+{-# LANGUAGE DataKinds    #-}
+
+module Agda.Syntax.Concrete.Operators.Parser where
+
+import Control.Applicative ( Alternative((<|>), many) )
+import Control.Monad ((<=<))
+
+import Data.Either
+import Data.Function (on)
+import Data.Kind ( Type )
+import qualified Data.List as List
+import Data.Maybe
+import qualified Data.Strict.Maybe as Strict
+import Data.Set (Set)
+
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Common
+import Agda.Syntax.Notation
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Operators.Parser.Monad hiding (parse)
+import qualified Agda.Syntax.Concrete.Operators.Parser.Monad as P
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.List  ( spanEnd )
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+placeholder :: PositionInName -> Parser e (MaybePlaceholder e)
+placeholder p =
+  doc (text ("_" ++ show p)) $
+  sat $ \case
+    Placeholder p' | p' == p -> True
+    _                        -> False
+
+maybePlaceholder ::
+  Maybe PositionInName -> Parser e e -> Parser e (MaybePlaceholder e)
+maybePlaceholder mp p = case mp of
+  Nothing -> p'
+  Just h  -> placeholder h <|> p'
+  where
+  p' = noPlaceholder <$> p
+
+satNoPlaceholder :: (e -> Maybe a) -> Parser e a
+satNoPlaceholder p = sat' $ \case
+    NoPlaceholder _ e -> p e
+    Placeholder _     -> Nothing
+
+data ExprView e
+    = LocalV QName
+    | WildV e
+    | OtherV e
+    | AppV e (NamedArg e)
+    | OpAppV QName (Set A.Name) (OpAppArgs' e)
+      -- ^ The 'QName' is possibly ambiguous, but it must correspond
+      -- to one of the names in the set.
+    | HiddenArgV (Named_ e)
+    | InstanceArgV (Named_ e)
+    | LamV (List1 LamBinding) e
+    | ParenV e
+--    deriving (Show)
+
+class HasRange e => IsExpr e where
+  exprView    :: e -> ExprView e
+  unExprView  :: ExprView e -> e
+  patternView :: e -> Maybe Pattern
+
+instance IsExpr e => HasRange (ExprView e) where
+  getRange = getRange . unExprView
+
+instance IsExpr Expr where
+    exprView = \case
+        Ident x         -> LocalV x
+        App _ e1 e2     -> AppV e1 e2
+        OpApp r d ns es -> OpAppV d ns es
+        HiddenArg _ e   -> HiddenArgV e
+        InstanceArg _ e -> InstanceArgV e
+        Paren _ e       -> ParenV e
+        Lam _ bs    e   -> LamV bs e
+        e@Underscore{}  -> WildV e
+        e               -> OtherV e
+    unExprView = \case
+        LocalV x       -> Ident x
+        AppV e1 e2     -> App (fuseRange e1 e2) e1 e2
+        OpAppV d ns es -> OpApp (fuseRange d es) d ns es
+        HiddenArgV e   -> HiddenArg (getRange e) e
+        InstanceArgV e -> InstanceArg (getRange e) e
+        ParenV e       -> Paren (getRange e) e
+        LamV bs e      -> Lam (fuseRange bs e) bs e
+        WildV e        -> e
+        OtherV e       -> e
+
+    patternView = isPattern
+
+instance IsExpr Pattern where
+    exprView = \case
+        IdentP True x    -> LocalV x
+        IdentP False _   -> __IMPOSSIBLE__
+        AppP e1 e2       -> AppV e1 e2
+        OpAppP r d ns es -> OpAppV d ns $ (fmap . fmap . fmap) (noPlaceholder . Ordinary) es
+        HiddenP _ e      -> HiddenArgV e
+        InstanceP _ e    -> InstanceArgV e
+        ParenP _ e       -> ParenV e
+        e@WildP{}        -> WildV e
+        e                -> OtherV e
+    unExprView = \case
+        LocalV x       -> IdentP True x
+        AppV e1 e2     -> AppP e1 e2
+        OpAppV d ns es -> let ess :: [NamedArg Pattern]
+                              ess = (fmap . fmap . fmap)
+                                      (\case
+                                          Placeholder{}     -> __IMPOSSIBLE__
+                                          NoPlaceholder _ x -> fromOrdinary __IMPOSSIBLE__ x)
+                                      es
+                          in OpAppP (fuseRange d ess) d ns ess
+        HiddenArgV e   -> HiddenP (getRange e) e
+        InstanceArgV e -> InstanceP (getRange e) e
+        ParenV e       -> ParenP (getRange e) e
+        LamV _ _       -> __IMPOSSIBLE__
+        WildV e        -> e
+        OtherV e       -> e
+
+    patternView = pure
+
+-- | Should sections be parsed?
+data ParseSections = ParseSections | DoNotParseSections
+  deriving (Eq, Show)
+
+-- | Runs a parser. If sections should be parsed, then identifiers
+-- with at least two name parts are split up into multiple tokens,
+-- using 'PositionInName' to record the tokens' original positions
+-- within their respective identifiers.
+
+parse :: IsExpr e => (ParseSections, Parser e a) -> [e] -> [a]
+parse (DoNotParseSections, p) es = P.parse p (map noPlaceholder es)
+parse (ParseSections,      p) es = P.parse p (List1.concat $ map splitExpr es)
+  where
+  splitExpr :: IsExpr e => e -> List1 (MaybePlaceholder e)
+  splitExpr e = case exprView e of
+    LocalV n -> splitName n
+    _        -> noSplit
+    where
+    noSplit = singleton $ noPlaceholder e
+
+    splitName n = case List1.last ns of
+      Name r nis ps@(_ :| _ : _) -> splitParts r nis (List1.init ns) Beginning ps
+      _                          -> noSplit
+      where
+      ns = qnameParts n
+
+      -- Note that the same range is used for every name part. This is
+      -- not entirely correct, but will hopefully not lead to any
+      -- problems.
+
+      -- Note also that the module qualifier, if any, is only applied
+      -- to the first name part.
+
+      splitParts _ _   _ _ (Hole :| [])     = singleton $ Placeholder End
+      splitParts r nis m _ (Id s :| [])     = singleton $ part r nis m End s
+      splitParts r nis m w (Hole :| p : ps) = Placeholder w    <| splitParts r nis m  Middle (p :| ps)
+      splitParts r nis m w (Id s :| p : ps) = part r nis m w s <| splitParts r nis [] Middle (p :| ps)
+
+      part r nis m w s =
+        NoPlaceholder (Strict.Just w)
+                      (unExprView $ LocalV $
+                         foldr Qual (QName $ Name r nis $ singleton $ Id s) m)
+
+---------------------------------------------------------------------------
+-- * Parser combinators
+---------------------------------------------------------------------------
+
+----------------------------
+-- Specific combinators
+
+-- | Parse a specific identifier as a NamePart
+partP :: IsExpr e => [Name] -> RawName -> Parser e Range
+partP ms s =
+  doc (text (show str)) $
+  satNoPlaceholder isLocal
+  where
+  str = prettyShow $ foldr Qual (QName $ simpleName s) ms
+  isLocal e = case exprView e of
+      LocalV y | str == prettyShow y -> Just $ getRange y
+      _ -> Nothing
+
+-- | Parses a split-up, unqualified name consisting of at least two
+-- name parts.
+--
+-- The parser does not check that underscores and other name parts
+-- alternate. The range of the resulting name is the range of the
+-- first name part that is not an underscore.
+
+atLeastTwoParts :: IsExpr e => Parser e Name
+atLeastTwoParts =
+  (\p1 ps p2 ->
+      let all = p1 :| ps ++ [p2] in
+      case List1.mapMaybe fst all of
+        (r,nis) : _ -> Name r nis (fmap snd all)
+        []          -> __IMPOSSIBLE__)
+  <$> part Beginning
+  <*> many (part Middle)
+  <*> part End
+  where
+  part pos = sat' $ \case
+    Placeholder pos'                   | pos == pos' -> Just ( Nothing
+                                                             , Hole
+                                                             )
+    NoPlaceholder (Strict.Just pos') e | pos == pos' ->
+      case exprView e of
+        LocalV (QName (Name r nis (Id s :| []))) -> Just (Just (r, nis), Id s)
+        _ -> Nothing
+    _ -> Nothing
+
+-- | Parses a potentially pattern-matching binder
+
+patternBinder :: IsExpr e => Parser e Binder
+patternBinder = inOnePart <|> mkBinder_ <$> atLeastTwoParts
+  where inOnePart = satNoPlaceholder $ isBinderP <=< patternView
+
+-- | Used to define the return type of 'opP'.
+
+type family OperatorType (k :: NotationKind) (e :: Type) :: Type
+type instance OperatorType 'InfixNotation   e = MaybePlaceholder e -> MaybePlaceholder e -> e
+type instance OperatorType 'PrefixNotation  e = MaybePlaceholder e -> e
+type instance OperatorType 'PostfixNotation e = MaybePlaceholder e -> e
+type instance OperatorType 'NonfixNotation  e = e
+
+-- | A singleton type for 'NotationKind' (except for the constructor
+-- 'NoNotation').
+
+data NK (k :: NotationKind) :: Type where
+  In   :: NK 'InfixNotation
+  Pre  :: NK 'PrefixNotation
+  Post :: NK 'PostfixNotation
+  Non  :: NK 'NonfixNotation
+
+-- | Parse the \"operator part\" of the given notation.
+--
+-- Normal holes (but not binders) at the beginning and end are
+-- ignored.
+--
+-- If the notation does not contain any binders, then a section
+-- notation is allowed.
+opP :: forall e k. IsExpr e
+    => ParseSections
+    -> Parser e e -> NewNotation -> NK k -> Parser e (OperatorType k e)
+opP parseSections p (NewNotation q names _ syn isOp) kind =
+  flip fmap (worker (List1.init $ qnameParts q)
+                    withoutExternalHoles) $ \(range, hs) ->
+
+  let (normal, binders) = partitionEithers hs
+      lastHole          = maximum $ (-1) : mapMaybe holeTarget syn
+
+      app :: ([(MaybePlaceholder e, NamedArg (Ranged Int))] ->
+              [(MaybePlaceholder e, NamedArg (Ranged Int))]) -> e
+      app f =
+        -- If we have an operator and there is exactly one
+        -- placeholder for every hole, then we only return
+        -- the operator.
+        if isOp && noPlaceholders args == lastHole + 1 then
+          -- Note that the information in the set "names" is thrown
+          -- away here.
+          unExprView (LocalV q')
+        else
+          unExprView (OpAppV q' names args)
+        where
+        args = map (findExprFor (f normal) binders) [0..lastHole]
+        q'   = setRange range q
+  in
+
+  case kind of
+    In   -> \x y -> app (\es -> (x, leadingHole) : es ++ [(y, trailingHole)])
+    Pre  -> \  y -> app (\es ->                    es ++ [(y, trailingHole)])
+    Post -> \x   -> app (\es -> (x, leadingHole) : es)
+    Non  ->         app (\es ->                    es)
+
+  where
+
+  (leadingHoles, syn1)                  = span    isAHole syn
+  (withoutExternalHoles, trailingHoles) = spanEnd isAHole syn1
+
+  leadingHole = case leadingHoles of
+    [HolePart _ h] -> h
+    _              -> __IMPOSSIBLE__
+
+  trailingHole = case trailingHoles of
+    [HolePart _ h] -> h
+    _              -> __IMPOSSIBLE__
+
+  worker ::
+    [Name] -> Notation ->
+    Parser e (Range, [Either (MaybePlaceholder e, NamedArg (Ranged Int))
+                             (LamBinding, Ranged BoundVariablePosition)])
+  worker ms []              = pure (noRange, [])
+  worker ms (IdPart x : xs) =
+    (\r1 (r2, es) -> (fuseRanges r1 r2, es))
+      <$> partP ms (rangedThing x)
+      <*> worker [] xs
+          -- Only the first part is qualified.
+  worker ms (HolePart _ h : xs) =
+    (\e (r, es) -> (r, Left (e, h) : es))
+      <$> maybePlaceholder
+            (if isOp && parseSections == ParseSections
+             then Just Middle else Nothing)
+            p
+      <*> worker ms xs
+  worker ms (WildPart h : xs) =
+    (\(r, es) -> let anon = mkBinder_ simpleHole
+                 in (r, Right (mkBinding h anon) : es))
+      <$> worker ms xs
+  worker ms (VarPart _ h : xs) = do
+    (\ b (r, es) -> (r, Right (mkBinding h b) : es))
+           -- Andreas, 2011-04-07 put just 'Relevant' here, is this
+           -- correct?
+      <$> patternBinder
+      <*> worker ms xs
+
+  mkBinding h b = (DomainFree $ defaultNamedArg b, h)
+
+  set x arg = fmap (fmap (const x)) arg
+
+  findExprFor ::
+    [(MaybePlaceholder e, NamedArg (Ranged Int))] ->
+    [(LamBinding, Ranged BoundVariablePosition)] -> Int ->
+    NamedArg (MaybePlaceholder (OpApp e))
+  findExprFor normalHoles binders n =
+    case [ h | h@(_, m) <- normalHoles, rangedThing (namedArg m) == n ] of
+      [(Placeholder p,     arg)] -> set (Placeholder p) arg
+      [(NoPlaceholder _ e, arg)] ->
+        List1.ifNull
+          (map snd $
+           List.sortBy (compare `on` fst)
+             [ (varNumber (rangedThing m), b)
+             | (b, m) <- binders
+             , holeNumber (rangedThing m) == n
+             ])
+        {-then-} (set (noPlaceholder (Ordinary e)) arg) -- no variable to bind
+        {-else-} $ \ bs -> set (noPlaceholder (SyntaxBindingLambda (fuseRange bs e) bs e)) arg
+      _ -> __IMPOSSIBLE__
+
+  noPlaceholders :: OpAppArgs' e -> Int
+  noPlaceholders = sum . fmap (isPlaceholder . namedArg)
+    where
+    isPlaceholder NoPlaceholder{} = 0
+    isPlaceholder Placeholder{}   = 1
+
+argsP :: IsExpr e => Parser e e -> Parser e [NamedArg e]
+argsP p = many (mkArg <$> p)
+  where
+  mkArg e = case exprView e of
+    HiddenArgV   e -> hide (defaultArg e)
+    InstanceArgV e -> makeInstance (defaultArg e)
+    _              -> defaultArg (unnamed e)
+
+appP :: IsExpr e => Parser e e -> Parser e [NamedArg e] -> Parser e e
+appP p pa = foldl app <$> p <*> pa
+    where
+        app e = unExprView . AppV e
+
+atomP :: IsExpr e => (QName -> Bool) -> Parser e e
+atomP p =
+  doc "<atom>" $
+  satNoPlaceholder $ \e ->
+  case exprView e of
+    LocalV x | not (p x) -> Nothing
+    _                    -> Just e
diff --git a/src/full/Agda/Syntax/Concrete/Operators/Parser/Monad.hs b/src/full/Agda/Syntax/Concrete/Operators/Parser/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Operators/Parser/Monad.hs
@@ -0,0 +1,96 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | The parser monad used by the operator parser
+------------------------------------------------------------------------
+
+{-# LANGUAGE CPP #-}
+
+module Agda.Syntax.Concrete.Operators.Parser.Monad
+  ( MemoKey(..), PrecedenceKey
+  , Parser
+  , parse
+  , sat'
+  , sat
+  , doc
+  , memoise
+  , memoiseIfPrinting
+  , grammar
+  ) where
+
+import Data.Hashable
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty
+
+import qualified Agda.Utils.Parser.MemoisedCPS as Parser
+
+-- | Memoisation keys.
+
+data MemoKey = NodeK      PrecedenceKey
+             | PostLeftsK PrecedenceKey
+             | PreRightsK PrecedenceKey
+             | TopK
+             | AppK
+             | NonfixK
+  deriving (Eq, Show, Generic)
+
+type PrecedenceKey = Either PrecedenceLevel PrecedenceLevel
+
+instance Hashable MemoKey
+
+-- | The parser monad.
+
+type Parser tok a =
+#ifdef DEBUG_PARSING
+  Parser.ParserWithGrammar
+#else
+  Parser.Parser
+#endif
+    MemoKey tok (MaybePlaceholder tok) a
+
+-- | Runs the parser.
+
+parse :: forall tok a. Parser tok a -> [MaybePlaceholder tok] -> [a]
+parse = Parser.parse
+
+-- | Parses a token satisfying the given predicate. The computed value
+-- is returned.
+
+sat' :: (MaybePlaceholder tok -> Maybe a) -> Parser tok a
+sat' = Parser.sat'
+
+-- | Parses a token satisfying the given predicate.
+
+sat :: (MaybePlaceholder tok -> Bool) ->
+       Parser tok (MaybePlaceholder tok)
+sat = Parser.sat
+
+-- | Uses the given document as the printed representation of the
+-- given parser. The document's precedence is taken to be 'atomP'.
+
+doc :: Doc -> Parser tok a -> Parser tok a
+doc = Parser.doc
+
+-- | Memoises the given parser.
+--
+-- Every memoised parser must be annotated with a /unique/ key.
+-- (Parametrised parsers must use distinct keys for distinct inputs.)
+
+memoise :: MemoKey -> Parser tok tok -> Parser tok tok
+memoise = Parser.memoise
+
+-- | Memoises the given parser, but only if printing, not if parsing.
+--
+-- Every memoised parser must be annotated with a /unique/ key.
+-- (Parametrised parsers must use distinct keys for distinct inputs.)
+
+memoiseIfPrinting :: MemoKey -> Parser tok tok -> Parser tok tok
+memoiseIfPrinting = Parser.memoiseIfPrinting
+
+-- | Tries to print the parser, or returns 'empty', depending on the
+-- implementation. This function might not terminate.
+
+grammar :: Parser tok a -> Doc
+grammar = Parser.grammar
diff --git a/src/full/Agda/Syntax/Concrete/Pattern.hs b/src/full/Agda/Syntax/Concrete/Pattern.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Pattern.hs
@@ -0,0 +1,387 @@
+
+-- | Tools for patterns in concrete syntax.
+
+module Agda.Syntax.Concrete.Pattern where
+
+import Control.Applicative ( liftA2 )
+import Control.Arrow ( first )
+import Control.Monad ( (>=>) )
+import Control.Monad.Identity
+
+import Data.Monoid ( Any(..), Endo(..), Sum(..) )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete
+
+import Agda.Utils.AffineHole
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.List
+import Agda.Utils.List1  ( List1, pattern (:|) )
+import Agda.Utils.List2  ( List2 )
+import Agda.Utils.Maybe
+import Agda.Utils.Singleton
+import qualified Agda.Utils.List1 as List1
+
+
+-- | Check for ellipsis @...@.
+
+class IsEllipsis a where
+  isEllipsis :: a -> Bool
+
+-- | Is the pattern just @...@?
+instance IsEllipsis Pattern where
+  isEllipsis = \case
+    EllipsisP{}         -> True
+    ParenP _ p          -> isEllipsis p
+    _ -> False
+
+-- | Has the lhs an occurrence of the ellipsis @...@?
+
+class HasEllipsis a where
+  hasEllipsis :: a -> Bool
+
+instance HasEllipsis Pattern where
+  hasEllipsis p =
+    case hasEllipsis' p of
+      ZeroHoles _ -> False
+      OneHole _ _ -> True
+      ManyHoles   -> True
+
+-- | Does the lhs contain an ellipsis?
+instance HasEllipsis LHS where
+  hasEllipsis (LHS p _ _) = hasEllipsis p
+  -- clauses that are already expanded don't have an ellipsis
+
+-- | Check for with-pattern @| p@.
+
+class IsWithP p where
+  isWithP :: p -> Maybe p
+
+  default isWithP :: (IsWithP q, Decoration f, f q ~ p) => p -> Maybe p
+  isWithP = traverseF isWithP
+
+instance IsWithP Pattern where
+  isWithP = \case
+    WithP _ p           -> Just p
+    ParenP _ p          -> isWithP p
+    _ -> Nothing
+
+instance IsWithP p => IsWithP (Arg p) where
+instance IsWithP p => IsWithP (Named n p) where
+
+
+-- * LHS manipulation (see also ''Agda.Syntax.Abstract.Pattern'')
+
+-- | The next patterns are ...
+--
+-- (This view discards 'PatInfo'.)
+data LHSPatternView
+  = LHSAppP  [NamedArg Pattern]
+      -- ^ Application patterns (non-empty list).
+  | LHSWithP [Pattern]
+      -- ^ With patterns (non-empty list).
+      --   These patterns are not prefixed with 'WithP'.
+
+-- | Construct the 'LHSPatternView' of the given list (if not empty).
+--
+-- Return the view and the remaining patterns.
+
+lhsPatternView :: [NamedArg Pattern] -> Maybe (LHSPatternView, [NamedArg Pattern])
+lhsPatternView [] = Nothing
+lhsPatternView (p0 : ps) =
+  case namedArg p0 of
+    WithP _i p   -> Just (LHSWithP (p : map namedArg ps1), ps2)
+      where
+      (ps1, ps2) = spanJust isWithP ps
+    -- If the next pattern is an application pattern, collect more of these
+    _ -> Just (LHSAppP (p0 : ps1), ps2)
+      where
+      (ps1, ps2) = span (isNothing . isWithP) ps
+
+-- | Add applicative patterns (non-projection / non-with patterns) to the right.
+lhsCoreApp :: LHSCore -> [NamedArg Pattern] -> LHSCore
+lhsCoreApp (LHSEllipsis r core) ps = LHSEllipsis r $ lhsCoreApp core ps
+lhsCoreApp core ps = core { lhsPats = lhsPats core ++ ps }
+
+-- | Add with-patterns to the right.
+lhsCoreWith :: LHSCore -> [Pattern] -> LHSCore
+lhsCoreWith (LHSWith core wps []) wps' = LHSWith core (wps ++ wps') []
+lhsCoreWith core                  wps' = LHSWith core wps' []
+
+-- | Append patterns to 'LHSCore', separating with patterns from the rest.
+lhsCoreAddSpine :: LHSCore -> [NamedArg Pattern] -> LHSCore
+lhsCoreAddSpine core ps0 =
+  -- Recurse on lhsPatternView until no patterns left.
+  case lhsPatternView ps0 of
+    Nothing       -> core
+    Just (LHSAppP  ps , ps') -> lhsCoreApp  core ps  `lhsCoreAddSpine` ps'
+    Just (LHSWithP wps, ps') -> lhsCoreWith core wps `lhsCoreAddSpine` ps'
+
+
+-- | Modify the 'Pattern' component in 'LHS'.
+mapLhsOriginalPattern :: (Pattern -> Pattern) -> LHS -> LHS
+mapLhsOriginalPattern f lhs@LHS{ lhsOriginalPattern = p } =
+  lhs { lhsOriginalPattern = f p }
+
+-- | Effectfully modify the 'Pattern' component in 'LHS'.
+mapLhsOriginalPatternM :: (Functor m, Applicative m) => (Pattern -> m Pattern) -> LHS -> m LHS
+mapLhsOriginalPatternM f lhs@LHS{ lhsOriginalPattern = p } = f p <&> \ p' ->
+  lhs { lhsOriginalPattern = p' }
+
+-- | Does the LHS contain projection patterns?
+hasCopatterns :: LHSCore -> Bool
+hasCopatterns = \case
+  LHSHead{}     -> False
+  LHSProj{}     -> True
+  LHSWith h _ _ -> hasCopatterns h
+  LHSEllipsis{} -> False
+
+-- * Generic fold
+
+-- | Generic pattern traversal.
+--
+-- See 'Agda.Syntax.Abstract.Pattern.APatternLike'.
+
+class CPatternLike p where
+
+  -- | Fold pattern.
+  foldrCPattern
+    :: Monoid m
+    => (Pattern -> m -> m)
+         -- ^ Combine a pattern and the value computed from its subpatterns.
+    -> p -> m
+
+  default foldrCPattern
+    :: (Monoid m, Foldable f, CPatternLike q, f q ~ p)
+    => (Pattern -> m -> m) -> p -> m
+  foldrCPattern = foldMap . foldrCPattern
+
+  -- | Traverse pattern with option of post-traversal modification.
+  traverseCPatternA :: (Applicative m, Functor m)
+      => (Pattern -> m Pattern -> m Pattern)
+         -- ^ Combine a pattern and the its recursively computed version.
+      -> p -> m p
+
+  default traverseCPatternA :: (Traversable f, CPatternLike q, f q ~ p, Applicative m, Functor m)
+      => (Pattern -> m Pattern -> m Pattern)
+      -> p -> m p
+  traverseCPatternA = traverse . traverseCPatternA
+
+  -- | Traverse pattern.
+  traverseCPatternM
+    :: Monad m => (Pattern -> m Pattern)  -- ^ @pre@: Modification before recursion.
+    -> (Pattern -> m Pattern)  -- ^ @post@: Modification after recursion.
+    -> p -> m p
+
+  default traverseCPatternM
+    :: (Traversable f, CPatternLike q, f q ~ p, Monad m)
+    => (Pattern -> m Pattern)
+    -> (Pattern -> m Pattern)
+    -> p -> m p
+  traverseCPatternM pre post = traverse $ traverseCPatternM pre post
+
+instance CPatternLike Pattern where
+  foldrCPattern f p0 = f p0 $
+    case p0 of
+      -- Recursive cases:
+      AppP p ps       -> foldrCPattern f (p, ps)
+      RawAppP _ ps    -> foldrCPattern f ps
+      OpAppP _ _ _ ps -> foldrCPattern f ps
+      HiddenP _ ps    -> foldrCPattern f ps
+      InstanceP _ ps  -> foldrCPattern f ps
+      ParenP _ p      -> foldrCPattern f p
+      AsP _ _ p       -> foldrCPattern f p
+      WithP _ p       -> foldrCPattern f p
+      RecP _ ps       -> foldrCPattern f ps
+      EllipsisP _ mp  -> foldrCPattern f mp
+      -- Nonrecursive cases:
+      IdentP _ _      -> mempty
+      WildP _         -> mempty
+      DotP _ _        -> mempty
+      AbsurdP _       -> mempty
+      LitP _ _        -> mempty
+      QuoteP _        -> mempty
+      EqualP _ _      -> mempty
+
+  traverseCPatternA f p0 = f p0 $ case p0 of
+      -- Recursive cases:
+      AppP        p ps    -> liftA2 AppP (traverseCPatternA f p) (traverseCPatternA f ps)
+      RawAppP   r ps      -> RawAppP r     <$> traverseCPatternA f ps
+      OpAppP    r x xs ps -> OpAppP r x xs <$> traverseCPatternA f ps
+      HiddenP   r p       -> HiddenP r     <$> traverseCPatternA f p
+      InstanceP r p       -> InstanceP r   <$> traverseCPatternA f p
+      ParenP    r p       -> ParenP r      <$> traverseCPatternA f p
+      AsP       r x p     -> AsP r x       <$> traverseCPatternA f p
+      WithP     r p       -> WithP r       <$> traverseCPatternA f p
+      RecP      r ps      -> RecP r        <$> traverseCPatternA f ps
+      EllipsisP r mp      -> EllipsisP r   <$> traverseCPatternA f mp
+      -- Nonrecursive cases:
+      IdentP _ _      -> pure p0
+      WildP _         -> pure p0
+      DotP _ _        -> pure p0
+      AbsurdP _       -> pure p0
+      LitP _ _        -> pure p0
+      QuoteP _        -> pure p0
+      EqualP _ _      -> pure p0
+
+  traverseCPatternM pre post = pre >=> recurse >=> post
+    where
+    recurse p0 = case p0 of
+      -- Recursive cases:
+      AppP        p ps    -> uncurry AppP  <$> traverseCPatternM pre post (p, ps)
+      RawAppP   r ps      -> RawAppP r     <$> traverseCPatternM pre post ps
+      OpAppP    r x xs ps -> OpAppP r x xs <$> traverseCPatternM pre post ps
+      HiddenP   r p       -> HiddenP r     <$> traverseCPatternM pre post p
+      InstanceP r p       -> InstanceP r   <$> traverseCPatternM pre post p
+      ParenP    r p       -> ParenP r      <$> traverseCPatternM pre post p
+      AsP       r x p     -> AsP r x       <$> traverseCPatternM pre post p
+      WithP     r p       -> WithP r       <$> traverseCPatternM pre post p
+      RecP      r ps      -> RecP r        <$> traverseCPatternM pre post ps
+      EllipsisP r mp      -> EllipsisP r   <$> traverseCPatternM pre post mp
+      -- Nonrecursive cases:
+      IdentP _ _      -> return p0
+      WildP _         -> return p0
+      DotP _ _        -> return p0
+      AbsurdP _       -> return p0
+      LitP _ _        -> return p0
+      QuoteP _        -> return p0
+      EqualP _ _      -> return p0
+
+instance (CPatternLike a, CPatternLike b) => CPatternLike (a,b) where
+  foldrCPattern f (p, p') =
+    foldrCPattern f p `mappend` foldrCPattern f p'
+
+  traverseCPatternA f (p, p') =
+    liftA2 (,)
+      (traverseCPatternA f p)
+      (traverseCPatternA f p')
+
+  traverseCPatternM pre post (p, p') =
+    liftA2 (,)
+      (traverseCPatternM pre post p)
+      (traverseCPatternM pre post p')
+
+instance CPatternLike p => CPatternLike (Arg p)
+instance CPatternLike p => CPatternLike (Named n p)
+instance CPatternLike p => CPatternLike [p]
+instance CPatternLike p => CPatternLike (List1 p)
+instance CPatternLike p => CPatternLike (List2 p)
+instance CPatternLike p => CPatternLike (Maybe p)
+instance CPatternLike p => CPatternLike (FieldAssignment' p)
+
+-- | Compute a value from each subpattern and collect all values in a monoid.
+
+foldCPattern :: (CPatternLike p, Monoid m) => (Pattern -> m) -> p -> m
+foldCPattern f = foldrCPattern $ \ p m -> f p `mappend` m
+
+-- | Traverse pattern(s) with a modification before the recursive descent.
+
+preTraverseCPatternM
+  :: (CPatternLike p, Monad m)
+  => (Pattern -> m Pattern)  -- ^ @pre@: Modification before recursion.
+  -> p -> m p
+preTraverseCPatternM pre p = traverseCPatternM pre return p
+
+-- | Traverse pattern(s) with a modification after the recursive descent.
+
+postTraverseCPatternM
+  :: (CPatternLike p, Monad m)
+  => (Pattern -> m Pattern)  -- ^ @post@: Modification after recursion.
+  -> p -> m p
+postTraverseCPatternM post p = traverseCPatternM return post p
+
+-- | Map pattern(s) with a modification after the recursive descent.
+
+mapCPattern :: CPatternLike p => (Pattern -> Pattern) -> p -> p
+mapCPattern f = runIdentity . postTraverseCPatternM (Identity . f)
+
+
+-- * Specific folds.
+
+-- | Get all the identifiers in a pattern in left-to-right order.
+--
+-- Implemented using difference lists.
+patternQNames :: CPatternLike p => p -> [QName]
+patternQNames p = foldCPattern f p `appEndo` []
+  where
+  f :: Pattern -> Endo [QName]
+  f = \case
+    IdentP _ x     -> Endo (x :)
+    OpAppP _ x _ _ -> Endo (x :)
+    AsP _ x _      -> mempty  -- x must be a bound name, can't be a constructor!
+    AppP _ _       -> mempty
+    WithP _ _      -> mempty
+    RawAppP _ _    -> mempty
+    HiddenP _ _    -> mempty
+    ParenP _ _     -> mempty
+    WildP _        -> mempty
+    AbsurdP _      -> mempty
+    DotP _ _       -> mempty
+    LitP _ _       -> mempty
+    QuoteP _       -> mempty
+    InstanceP _ _  -> mempty
+    RecP _ _       -> mempty
+    EqualP _ _     -> mempty
+    EllipsisP _ _  -> mempty
+
+-- | Get all the identifiers in a pattern in left-to-right order.
+patternNames :: Pattern -> [Name]
+patternNames = map unqualify . patternQNames
+
+-- | Does the pattern contain a with-pattern?
+-- (Shortcutting.)
+hasWithPatterns :: CPatternLike p => p -> Bool
+hasWithPatterns = getAny . foldCPattern (Any . isWithPattern)
+
+-- | Is 'WithP'?
+isWithPattern :: Pattern -> Bool
+isWithPattern = \case
+  WithP{} -> True
+  _ -> False
+
+-- | Count the number of with-subpatterns in a pattern?
+numberOfWithPatterns :: CPatternLike p => p -> Int
+numberOfWithPatterns = getSum . foldCPattern (Sum . f)
+  where f p = if isWithPattern p then 1 else 0
+
+-- | Compute the context in which the ellipsis occurs, if at all.
+--   If there are several occurrences, this is an error.
+--   This only counts ellipsis that haven't already been expanded.
+hasEllipsis' :: CPatternLike p => p -> AffineHole Pattern p
+hasEllipsis' = traverseCPatternA $ \ p mp ->
+  case p of
+    EllipsisP _ Nothing -> OneHole id p
+    _                   -> mp
+
+reintroduceEllipsis :: ExpandedEllipsis -> Pattern -> Pattern
+reintroduceEllipsis (ExpandedEllipsis r k) p | hasWithPatterns p =
+  let (args, wargs) = splitEllipsis k $ List1.toList $ patternAppView p
+      (hd,args') = fromMaybe __IMPOSSIBLE__ $ uncons args
+      core = foldl AppP (namedArg hd) args
+  in foldl AppP (EllipsisP r $ Just $ core) wargs
+reintroduceEllipsis _ p = p
+
+splitEllipsis :: (IsWithP p) => Int -> [p] -> ([p],[p])
+splitEllipsis k [] = ([] , [])
+splitEllipsis k (p:ps)
+  | isJust (isWithP p) = if
+      | k == 0    -> ([] , p:ps)
+      | otherwise -> first (p:) $ splitEllipsis (k-1) ps
+  | otherwise = first (p:) $ splitEllipsis k ps
+
+---------------------------------------------------------------------------
+-- * Helpers for pattern and lhs parsing
+---------------------------------------------------------------------------
+
+-- | View a pattern @p@ as a list @p0 .. pn@ where @p0@ is the identifier
+--   (in most cases a constructor).
+--
+--  Pattern needs to be parsed already (operators resolved).
+patternAppView :: Pattern -> List1 (NamedArg Pattern)
+patternAppView = \case
+    AppP p arg      -> patternAppView p `List1.appendList` [arg]
+    OpAppP _ x _ ps -> defaultNamedArg (IdentP True x) :| ps
+    ParenP _ p      -> patternAppView p
+    RawAppP _ _     -> __IMPOSSIBLE__
+    p               -> singleton $ defaultNamedArg p
diff --git a/src/full/Agda/Syntax/Concrete/Pretty.hs b/src/full/Agda/Syntax/Concrete/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Concrete/Pretty.hs
@@ -0,0 +1,798 @@
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+{-| Pretty printer for the concrete syntax.
+-}
+module Agda.Syntax.Concrete.Pretty
+  ( module Agda.Syntax.Concrete.Pretty
+  , module Agda.Syntax.Concrete.Glyph
+  ) where
+
+import Prelude hiding ( null )
+
+import Data.Maybe
+import qualified Data.Foldable  as Fold
+import qualified Data.Semigroup as Semigroup
+import qualified Data.Strict.Maybe as Strict
+import qualified Data.Text as T
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Glyph
+
+import Agda.Utils.Float (toStringWithoutDotZero)
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.List2 as List2
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Aspect as Asp
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+deriving instance Show Expr
+deriving instance (Show a) => Show (OpApp a)
+deriving instance Show Declaration
+deriving instance Show Pattern
+deriving instance Show a => Show (Binder' a)
+deriving instance Show TypedBinding
+deriving instance Show LamBinding
+deriving instance Show BoundName
+deriving instance Show ModuleAssignment
+deriving instance (Show a, Show b) => Show (ImportDirective' a b)
+deriving instance (Show a, Show b) => Show (Using' a b)
+deriving instance (Show a, Show b) => Show (Renaming' a b)
+deriving instance Show Pragma
+deriving instance Show RHS
+deriving instance Show LHS
+deriving instance Show LHSCore
+deriving instance Show LamClause
+deriving instance Show WhereClause
+deriving instance Show ModuleApplication
+deriving instance Show DoStmt
+deriving instance Show Module
+
+-- Lays out a list of documents [d₁, d₂, …] in the following way:
+-- @
+--   { d₁
+--   ; d₂
+--   ⋮
+--   }
+-- @
+-- If the list is empty, then the notation @{}@ is used.
+
+bracesAndSemicolons :: Foldable t => t Doc -> Doc
+bracesAndSemicolons ts = case Fold.toList ts of
+  []       -> "{}"
+  (d : ds) -> sep (["{" <+> d] ++ map (";" <+>) ds ++ ["}"])
+
+-- | @prettyHiding info visible doc@ puts the correct braces
+--   around @doc@ according to info @info@ and returns
+--   @visible doc@ if the we deal with a visible thing.
+prettyHiding :: LensHiding a => a -> (Doc -> Doc) -> Doc -> Doc
+prettyHiding a parens =
+  case getHiding a of
+    Hidden     -> braces'
+    Instance{} -> dbraces
+    NotHidden  -> parens
+
+prettyRelevance :: LensRelevance a => a -> Doc -> Doc
+prettyRelevance a = (pretty (getRelevance a) <>)
+
+prettyQuantity :: LensQuantity a => a -> Doc -> Doc
+prettyQuantity a = (pretty (getQuantity a) <+>)
+
+prettyLock :: LensLock a => a -> Doc -> Doc
+prettyLock a doc = case getLock a of
+  IsLock LockOLock -> "@lock" <+> doc
+  IsLock LockOTick -> "@tick" <+> doc
+  IsNotLock -> doc
+
+prettyErased :: Erased -> Doc -> Doc
+prettyErased = prettyQuantity . asQuantity
+
+prettyCohesion :: LensCohesion a => a -> Doc -> Doc
+prettyCohesion a = (pretty (getCohesion a) <+>)
+
+prettyTactic :: BoundName -> Doc -> Doc
+prettyTactic = prettyTactic' . bnameTactic
+
+prettyFiniteness :: BoundName -> Doc -> Doc
+prettyFiniteness name
+  | bnameIsFinite name = ("@finite" <+>)
+  | otherwise = id
+
+prettyTactic' :: TacticAttribute -> Doc -> Doc
+prettyTactic' Nothing  d = d
+prettyTactic' (Just t) d = "@" <> (parens ("tactic" <+> pretty t) <+> d)
+
+instance (Pretty a, Pretty b) => Pretty (a, b) where
+    pretty (a, b) = parens $ (pretty a <> comma) <+> pretty b
+
+instance Pretty (ThingWithFixity Name) where
+    pretty (ThingWithFixity n _) = pretty n
+
+instance Pretty a => Pretty (WithHiding a) where
+  pretty w = prettyHiding w id $ pretty $ dget w
+
+instance Pretty Relevance where
+  pretty Relevant   = empty
+  pretty Irrelevant = "."
+  pretty NonStrict  = ".."
+
+instance Pretty Q0Origin where
+  pretty = \case
+    Q0Inferred -> empty
+    Q0{}       -> "@0"
+    Q0Erased{} -> "@erased"
+
+instance Pretty Q1Origin where
+  pretty = \case
+    Q1Inferred -> empty
+    Q1{}       -> "@1"
+    Q1Linear{} -> "@linear"
+
+instance Pretty QωOrigin where
+  pretty = \case
+    QωInferred -> empty
+    Qω{}       -> "@ω"
+    QωPlenty{} -> "@plenty"
+
+instance Pretty Quantity where
+  pretty = \case
+    Quantity0 o -> ifNull (pretty o) "@0" id
+    Quantity1 o -> ifNull (pretty o) "@1" id
+    Quantityω o -> pretty o
+
+instance Pretty Erased where
+  pretty = pretty . asQuantity
+
+instance Pretty Cohesion where
+  pretty Flat   = "@♭"
+  pretty Continuous = mempty
+  pretty Squash  = "@⊤"
+
+instance Pretty Modality where
+  pretty mod = hsep
+    [ pretty (getRelevance mod)
+    , pretty (getQuantity mod)
+    , pretty (getCohesion mod)
+    ]
+
+-- | Show the attributes necessary to recover a modality, in long-form
+-- (e.g. using at-syntax rather than dots). For the default modality,
+-- the result is at-ω (rather than the empty document). Suitable for
+-- showing modalities outside of binders.
+attributesForModality :: Modality -> Doc
+attributesForModality mod
+  | mod == defaultModality = text "@ω"
+  | otherwise = fsep $ catMaybes [relevance, quantity, cohesion]
+  where
+    relevance = case getRelevance mod of
+      Relevant   -> Nothing
+      Irrelevant -> Just "@irrelevant"
+      NonStrict  -> Just "@shape-irrelevant"
+    quantity = case getQuantity mod of
+      Quantity0{} -> Just "@0"
+      Quantity1{} -> Just "@1"
+      Quantityω{} -> Nothing
+    cohesion = case getCohesion mod of
+      Flat{}       -> Just "@♭"
+      Continuous{} -> Nothing
+      Squash{}     -> Just "@⊤"
+
+instance Pretty (OpApp Expr) where
+  pretty (Ordinary e) = pretty e
+  pretty (SyntaxBindingLambda r bs e) = pretty (Lam r bs e)
+
+instance Pretty a => Pretty (MaybePlaceholder a) where
+  pretty Placeholder{}       = "_"
+  pretty (NoPlaceholder _ e) = pretty e
+
+instance Pretty Expr where
+    pretty e =
+        case e of
+            Ident x          -> pretty x
+            KnownIdent nk x  -> annotateAspect (Asp.Name (Just nk) False) (pretty x)
+            Lit _ l          -> pretty l
+            QuestionMark _ n -> hlSymbol "?" <> maybe empty (text . show) n
+            Underscore _ n   -> maybe underscore text n
+            App _ _ _        ->
+                case appView e of
+                    AppView e1 args     ->
+                        fsep $ pretty e1 : map pretty args
+--                      sep [ pretty e1
+--                          , nest 2 $ fsep $ map pretty args
+--                          ]
+            RawApp _ es    -> fsep $ map pretty $ List2.toList es
+            OpApp _ q _ es         -> fsep $ prettyOpApp (Asp.Name Nothing True) q es
+            KnownOpApp nk _ q _ es -> fsep $ prettyOpApp (Asp.Name (Just nk) True) q es
+
+            WithApp _ e es -> fsep $
+              pretty e : map ((hlSymbol "|" <+>) . pretty) es
+
+            HiddenArg _ e -> braces' $ pretty e
+            InstanceArg _ e -> dbraces $ pretty e
+            Lam _ bs (AbsurdLam _ h) -> lambda <+> fsep (fmap pretty bs) <+> absurd h
+            Lam _ bs e ->
+                sep [ lambda <+> fsep (fmap pretty bs) <+> arrow
+                    , nest 2 $ pretty e
+                    ]
+            AbsurdLam _ h -> lambda <+> absurd h
+            ExtendedLam _ e pes ->
+              lambda <+>
+              prettyErased e (bracesAndSemicolons (fmap pretty pes))
+            Fun _ e1 e2 ->
+                sep [ prettyCohesion e1 (prettyQuantity e1 (pretty e1)) <+> arrow
+                    , pretty e2
+                    ]
+            Pi tel e ->
+                sep [ pretty (Tel $ smashTel $ List1.toList tel) <+> arrow
+                    , pretty e
+                    ]
+            Let _ ds me  ->
+                sep [ hlKeyword "let" <+> vcat (fmap pretty ds)
+                    , maybe empty (\ e -> hlKeyword "in" <+> pretty e) me
+                    ]
+            Paren _ e -> parens $ pretty e
+            IdiomBrackets _ es ->
+              case es of
+                []   -> emptyIdiomBrkt
+                [e]  -> leftIdiomBrkt <+> pretty e <+> rightIdiomBrkt
+                e:es -> leftIdiomBrkt <+> pretty e <+> fsep (map (("|" <+>) . pretty) es) <+> rightIdiomBrkt
+            DoBlock _ ss -> hlKeyword "do" <+> vcat (fmap pretty ss)
+            As _ x e  -> pretty x <> hlSymbol "@" <> pretty e
+            Dot _ e   -> hlSymbol "." <> pretty e
+            DoubleDot _ e  -> hlSymbol ".." <> pretty e
+            Absurd _  -> hlSymbol "()"
+            Rec _ xs  -> sep [hlKeyword "record", bracesAndSemicolons (map pretty xs)]
+            RecUpdate _ e xs ->
+              sep [hlKeyword "record" <+> pretty e, bracesAndSemicolons (map pretty xs)]
+            Quote _ -> hlKeyword "quote"
+            QuoteTerm _ -> hlKeyword "quoteTerm"
+            Unquote _  -> hlKeyword "unquote"
+            Tactic _ t -> hlKeyword "tactic" <+> pretty t
+            -- Andreas, 2011-10-03 print irrelevant things as .(e)
+            DontCare e -> hlSymbol "." <> parens (pretty e)
+            Equal _ a b -> pretty a <+> equals <+> pretty b
+            Ellipsis _  -> hlSymbol "..."
+            Generalized e -> pretty e
+        where
+          absurd NotHidden  = parens mempty
+          absurd Instance{} = dbraces mempty
+          absurd Hidden     = braces mempty
+
+instance (Pretty a, Pretty b) => Pretty (Either a b) where
+  pretty = either pretty pretty
+
+instance Pretty a => Pretty (FieldAssignment' a) where
+  pretty (FieldAssignment x e) = sep [ pretty x <+> "=" , nest 2 $ pretty e ]
+
+instance Pretty ModuleAssignment where
+  pretty (ModuleAssignment m es i) = fsep (pretty m : map pretty es) <+> pretty i
+
+instance Pretty LamClause where
+  pretty (LamClause ps rhs _) =
+    sep [ fsep (map pretty ps)
+        , nest 2 $ pretty' rhs
+        ]
+    where
+      pretty' (RHS e)   = arrow <+> pretty e
+      pretty' AbsurdRHS = empty
+
+instance Pretty BoundName where
+  pretty BName{ boundName = x } = pretty x
+
+data NamedBinding = NamedBinding
+  { withHiding   :: Bool
+  , namedBinding :: NamedArg Binder
+  }
+
+isLabeled :: NamedArg Binder -> Maybe ArgName
+isLabeled x
+  | visible x              = Nothing  -- Ignore labels on visible arguments
+  | Just l <- bareNameOf x = boolToMaybe (l /= nameToRawName (boundName $ binderName $ namedArg x)) l
+  | otherwise              = Nothing
+
+instance Pretty a => Pretty (Binder' a) where
+  pretty (Binder mpat n) = let d = pretty n in case mpat of
+    Nothing  -> d
+    Just pat -> d <+> "@" <+> parens (pretty pat)
+
+instance Pretty NamedBinding where
+  pretty (NamedBinding withH x) = prH $
+    if | Just l <- isLabeled x -> text l <+> "=" <+> pretty xb
+       | otherwise             -> pretty xb
+
+    where
+
+    xb = namedArg x
+    bn = binderName xb
+    prH | withH     = prettyRelevance x
+                    . prettyHiding x mparens
+                    . prettyCohesion x
+                    . prettyQuantity x
+                    . prettyTactic bn
+        | otherwise = id
+    -- Parentheses are needed when an attribute @... is present
+    mparens
+      | noUserQuantity x, Nothing <- bnameTactic bn = id
+      | otherwise = parens
+
+instance Pretty LamBinding where
+    pretty (DomainFree x) = pretty (NamedBinding True x)
+    pretty (DomainFull b) = pretty b
+
+instance Pretty TypedBinding where
+    pretty (TLet _ ds) = parens $ "let" <+> vcat (fmap pretty ds)
+    pretty (TBind _ xs (Underscore _ Nothing)) =
+      fsep (fmap (pretty . NamedBinding True) xs)
+    pretty (TBind _ xs e) = fsep
+      [ prettyRelevance y
+        $ prettyHiding y parens
+        $ prettyFiniteness (binderName $ namedArg y)
+        $ prettyCohesion y
+        $ prettyQuantity y
+        $ prettyLock y
+        $ prettyTactic (binderName $ namedArg y) $
+        sep [ fsep (map (pretty . NamedBinding False) ys)
+            , ":" <+> pretty e ]
+      | ys@(y : _) <- groupBinds $ List1.toList xs ]
+      where
+        groupBinds [] = []
+        groupBinds (x : xs)
+          | Just{} <- isLabeled x = [x] : groupBinds xs
+          | otherwise   = (x : ys) : groupBinds zs
+          where (ys, zs) = span (same x) xs
+                same x y = getArgInfo x == getArgInfo y && isNothing (isLabeled y)
+
+newtype Tel = Tel Telescope
+
+instance Pretty Tel where
+    pretty (Tel tel)
+      | any isMeta tel = forallQ <+> fsep (map pretty tel)
+      | otherwise      = fsep (map pretty tel)
+      where
+        isMeta (TBind _ _ (Underscore _ Nothing)) = True
+        isMeta _ = False
+
+smashTel :: Telescope -> Telescope
+smashTel (TBind r xs e  :
+          TBind _ ys e' : tel)
+  | prettyShow e == prettyShow e' = smashTel (TBind r (xs Semigroup.<> ys) e : tel)
+smashTel (b : tel) = b : smashTel tel
+smashTel [] = []
+
+
+instance Pretty RHS where
+    pretty (RHS e)   = "=" <+> pretty e
+    pretty AbsurdRHS = empty
+
+instance Pretty WhereClause where
+  pretty  NoWhere = empty
+  pretty (AnyWhere _ [Module _ NotErased{} x [] ds])
+    | isNoName (unqualify x)
+                       = vcat [ "where", nest 2 (vcat $ map pretty ds) ]
+  pretty (AnyWhere _ ds) = vcat [ "where", nest 2 (vcat $ map pretty ds) ]
+  pretty (SomeWhere _ erased m a ds) =
+    vcat [ hsep $ applyWhen (a == PrivateAccess UserWritten) ("private" :)
+             [ "module", prettyErased erased (pretty m), "where" ]
+         , nest 2 (vcat $ map pretty ds)
+         ]
+
+instance Pretty LHS where
+  pretty (LHS p eqs es) = sep
+    [ pretty p
+    , nest 2 $ if null eqs then empty else fsep $ map pretty eqs
+    , nest 2 $ prefixedThings "with" (map prettyWithd es)
+    ] where
+
+    prettyWithd :: WithExpr -> Doc
+    prettyWithd (Named nm wh) =
+      let e = pretty wh in
+      case nm of
+        Nothing -> e
+        Just n  -> pretty n <+> ":" <+> e
+
+instance Pretty LHSCore where
+  pretty (LHSHead f ps) = sep $ pretty f : map (parens . pretty) ps
+  pretty (LHSProj d ps lhscore ps') = sep $
+    pretty d : map (parens . pretty) ps ++
+    parens (pretty lhscore) : map (parens . pretty) ps'
+  pretty (LHSWith h wps ps) = if null ps then doc else
+      sep $ parens doc : map (parens . pretty) ps
+    where
+    doc = sep $ pretty h : map (("|" <+>) . pretty) wps
+  pretty (LHSEllipsis r p) = "..."
+
+instance Pretty ModuleApplication where
+  pretty (SectionApp _ bs e) = fsep (map pretty bs) <+> "=" <+> pretty e
+  pretty (RecordModuleInstance _ rec) = "=" <+> pretty rec <+> "{{...}}"
+
+instance Pretty DoStmt where
+  pretty (DoBind _ p e cs) =
+    ((pretty p <+> "←") <?> pretty e) <?> prCs cs
+    where
+      prCs [] = empty
+      prCs cs = "where" <?> vcat (map pretty cs)
+  pretty (DoThen e) = pretty e
+  pretty (DoLet _ ds) = "let" <+> vcat (fmap pretty ds)
+
+instance Pretty Declaration where
+  prettyList = vcat . map pretty
+  pretty = \case
+    TypeSig i tac x e ->
+      sep [ prettyTactic' tac $ prettyRelevance i $ prettyCohesion i $ prettyQuantity i $ pretty x <+> ":"
+          , nest 2 $ pretty e
+          ]
+    FieldSig inst tac x (Arg i e) ->
+      mkInst inst $ mkOverlap i $
+      prettyRelevance i $ prettyHiding i id $ prettyCohesion i $ prettyQuantity i $
+      pretty $ TypeSig (setRelevance Relevant i) tac x e
+      where
+        mkInst (InstanceDef _) d = sep [ "instance", nest 2 d ]
+        mkInst NotInstanceDef  d = d
+
+        mkOverlap i d | isOverlappable i = "overlap" <+> d
+                      | otherwise        = d
+    Field _ fs ->
+      sep [ "field"
+          , nest 2 $ vcat (map pretty fs)
+          ]
+    FunClause lhs rhs wh _ ->
+      sep [ pretty lhs
+          , nest 2 $ pretty rhs
+          ] $$ nest 2 (pretty wh)
+    DataSig _ erased x tel e ->
+      sep [ hsep  [ "data"
+                  , prettyErased erased (pretty x)
+                  , fsep (map pretty tel)
+                  ]
+          , nest 2 $ hsep
+                  [ ":"
+                  , pretty e
+                  ]
+          ]
+    Data _ erased x tel e cs ->
+      sep [ hsep  [ "data"
+                  , prettyErased erased (pretty x)
+                  , fsep (map pretty tel)
+                  ]
+          , nest 2 $ hsep
+                  [ ":"
+                  , pretty e
+                  , "where"
+                  ]
+          ] $$ nest 2 (vcat $ map pretty cs)
+    DataDef _ x tel cs ->
+      sep [ hsep  [ "data"
+                  , pretty x
+                  , fsep (map pretty tel)
+                  ]
+          , nest 2 $ "where"
+          ] $$ nest 2 (vcat $ map pretty cs)
+    RecordSig _ erased x tel e ->
+      sep [ hsep  [ "record"
+                  , prettyErased erased (pretty x)
+                  , fsep (map pretty tel)
+                  ]
+          , nest 2 $ hsep
+                  [ ":"
+                  , pretty e
+                  ]
+          ]
+    Record _ erased x dir tel e cs ->
+      pRecord erased x dir tel (Just e) cs
+    RecordDef _ x dir tel cs ->
+      pRecord defaultErased x dir tel Nothing cs
+    RecordDirective r -> pRecordDirective r
+    Infix f xs  ->
+      pretty f <+> fsep (punctuate comma $ fmap pretty xs)
+    Syntax n xs -> "syntax" <+> pretty n <+> "..."
+    PatternSyn _ n as p -> "pattern" <+> pretty n <+> fsep (map pretty as)
+                             <+> "=" <+> pretty p
+    Mutual _ ds     -> namedBlock "mutual" ds
+    InterleavedMutual _ ds  -> namedBlock "interleaved mutual" ds
+    LoneConstructor _ ds -> namedBlock "constructor" ds
+    Abstract _ ds   -> namedBlock "abstract" ds
+    Private _ _ ds  -> namedBlock "private" ds
+    InstanceB _ ds  -> namedBlock "instance" ds
+    Macro _ ds      -> namedBlock "macro" ds
+    Postulate _ ds  -> namedBlock "postulate" ds
+    Primitive _ ds  -> namedBlock "primitive" ds
+    Generalize _ ds -> namedBlock "variable" ds
+    Opaque _ ds     -> namedBlock "opaque" ds
+    Unfolding _ rs  -> "unfolding" <+> braces (fsep (punctuate semi (pretty <$> rs)))
+    Module _ erased x tel ds ->
+      hsep [ "module"
+           , prettyErased erased (pretty x)
+           , fsep (map pretty tel)
+           , "where"
+           ] $$ nest 2 (vcat $ map pretty ds)
+    ModuleMacro _ NotErased{} x (SectionApp _ [] e) DoOpen i
+      | isNoName x ->
+      sep [ pretty DoOpen
+          , nest 2 $ pretty e
+          , nest 4 $ pretty i
+          ]
+    ModuleMacro _ erased x (SectionApp _ tel e) open i ->
+      sep [ pretty open <+> "module" <+>
+            prettyErased erased (pretty x) <+> fsep (map pretty tel)
+          , nest 2 $ "=" <+> pretty e <+> pretty i
+          ]
+    ModuleMacro _ erased x (RecordModuleInstance _ rec) open i ->
+      sep [ pretty open <+> "module" <+> prettyErased erased (pretty x)
+          , nest 2 $ "=" <+> pretty rec <+> "{{...}}"
+          ]
+    Open _ x i  -> hsep [ "open", pretty x, pretty i ]
+    Import _ x rn open i   ->
+      hsep [ pretty open, "import", pretty x, as rn, pretty i ]
+      where
+        as Nothing  = empty
+        as (Just x) = "as" <+> pretty (asName x)
+    UnquoteDecl _ xs t ->
+      sep [ "unquoteDecl" <+> fsep (map pretty xs) <+> "=", nest 2 $ pretty t ]
+    UnquoteDef _ xs t ->
+      sep [ "unquoteDef" <+> fsep (map pretty xs) <+> "=", nest 2 $ pretty t ]
+    UnquoteData _ x xs t ->
+      sep [ "unquoteData" <+> pretty x <+> fsep (map pretty xs) <+> "=", nest 2 $ pretty t ]
+    Pragma pr   -> sep [ "{-#" <+> pretty pr, "#-}" ]
+    where
+      namedBlock s ds =
+          sep [ text s
+              , nest 2 $ vcat $ map pretty ds
+              ]
+
+pHasEta0 :: HasEta0 -> Doc
+pHasEta0 = \case
+  YesEta   -> "eta-equality"
+  NoEta () -> "no-eta-equality"
+
+pRecordDirective :: RecordDirective -> Doc
+pRecordDirective = \case
+  Induction ind -> pretty (rangedThing ind)
+  Constructor n inst -> hsep [ pInst, "constructor", pretty n ] where
+    pInst = case inst of
+      InstanceDef{} -> "instance"
+      NotInstanceDef{} -> empty
+  Eta eta -> pHasEta0 (rangedThing eta)
+  PatternOrCopattern{} -> "pattern"
+
+pRecord
+  :: Erased
+  -> Name
+  -> RecordDirectives
+  -> [LamBinding]
+  -> Maybe Expr
+  -> [Declaration]
+  -> Doc
+pRecord erased x (RecordDirectives ind eta pat con) tel me ds = vcat
+    [ sep
+      [ hsep  [ "record"
+              , prettyErased erased (pretty x)
+              , fsep (map pretty tel)
+              ]
+      , nest 2 $ pType me
+      ]
+    , nest 2 $ vcat $ concat
+      [ pInd
+      , pEta
+      , pPat
+      , pCon
+      , map pretty ds
+      ]
+    ]
+  where pType (Just e) = hsep
+                [ ":"
+                , pretty e
+                , "where"
+                ]
+        pType Nothing  =
+                  "where"
+        pInd = maybeToList $ pretty . rangedThing <$> ind
+        pEta = maybeToList $ eta <&> pHasEta0
+        pPat = maybeToList $ "pattern" <$ pat
+        -- pEta = caseMaybe eta [] $ \case
+        --   YesEta -> [ "eta-equality" ]
+        --   NoEta  -> "no-eta-equality" : pPat
+        -- pPat = \case
+        --   PatternMatching   -> [ "pattern" ]
+        --   CopatternMatching -> []
+        pCon = maybeToList $ (("constructor" <+>) . pretty) . fst <$> con
+
+instance Pretty OpenShortHand where
+    pretty DoOpen = "open"
+    pretty DontOpen = empty
+
+instance Pretty Pragma where
+    pretty (OptionsPragma _ opts)  = fsep $ map text $ "OPTIONS" : opts
+    pretty (BuiltinPragma _ b x)   = hsep [ "BUILTIN", text (rangedThing b), pretty x ]
+    pretty (RewritePragma _ _ xs)    =
+      hsep [ "REWRITE", hsep $ map pretty xs ]
+    pretty (CompilePragma _ b x e) =
+      hsep [ "COMPILE", text (rangedThing b), pretty x, text e ]
+    pretty (ForeignPragma _ b s) =
+      vcat $ text ("FOREIGN " ++ rangedThing b) : map text (lines s)
+    pretty (StaticPragma _ i) =
+      hsep $ ["STATIC", pretty i]
+    pretty (InjectivePragma _ i) =
+      hsep $ ["INJECTIVE", pretty i]
+    pretty (InlinePragma _ True i) =
+      hsep $ ["INLINE", pretty i]
+    pretty (NotProjectionLikePragma _ i) =
+      hsep $ ["NOT_PROJECTION_LIKE", pretty i]
+    pretty (InlinePragma _ False i) =
+      hsep $ ["NOINLINE", pretty i]
+    pretty (ImpossiblePragma _ strs) =
+      hsep $ ["IMPOSSIBLE"] ++ map text strs
+    pretty (EtaPragma _ x) =
+      hsep $ ["ETA", pretty x]
+    pretty (TerminationCheckPragma _ tc) =
+      case tc of
+        TerminationCheck       -> __IMPOSSIBLE__
+        NoTerminationCheck     -> "NO_TERMINATION_CHECK"
+        NonTerminating         -> "NON_TERMINATING"
+        Terminating            -> "TERMINATING"
+        TerminationMeasure _ x -> hsep $ ["MEASURE", pretty x]
+    pretty (NoCoverageCheckPragma _) = "NON_COVERING"
+    pretty (WarningOnUsage _ nm str) = hsep [ "WARNING_ON_USAGE", pretty nm, text (T.unpack str) ]
+    pretty (WarningOnImport _ str)   = hsep [ "WARNING_ON_IMPORT", text (T.unpack str) ]
+    pretty (CatchallPragma _) = "CATCHALL"
+    pretty (DisplayPragma _ lhs rhs) = "DISPLAY" <+> sep [ pretty lhs <+> "=", nest 2 $ pretty rhs ]
+    pretty (NoPositivityCheckPragma _) = "NO_POSITIVITY_CHECK"
+    pretty (PolarityPragma _ q occs) =
+      hsep ("POLARITY" : pretty q : map pretty occs)
+    pretty (NoUniverseCheckPragma _) = "NO_UNIVERSE_CHECK"
+
+instance Pretty Associativity where
+  pretty = \case
+    LeftAssoc  -> "infixl"
+    RightAssoc -> "infixr"
+    NonAssoc   -> "infix"
+
+instance Pretty FixityLevel where
+  pretty = \case
+    Unrelated  -> empty
+    Related d  -> text $ toStringWithoutDotZero d
+
+instance Pretty Fixity where
+  pretty (Fixity _ level ass) = case level of
+    Unrelated  -> empty
+    Related{}  -> pretty ass <+> pretty level
+
+instance Pretty NotationPart where
+    pretty (IdPart x) = text $ rangedThing x
+    pretty HolePart{} = underscore
+    pretty VarPart{}  = underscore
+    pretty WildPart{} = underscore
+
+    prettyList = hcat . map pretty
+
+instance Pretty Fixity' where
+    pretty (Fixity' fix nota _range)
+      | null nota = pretty fix
+      | otherwise = "syntax" <+> pretty nota
+
+ -- Andreas 2010-09-21: do not print relevance in general, only in function types!
+ -- Andreas 2010-09-24: and in record fields
+instance Pretty a => Pretty (Arg a) where
+  prettyPrec p (Arg ai e) = prettyHiding ai localParens $ prettyPrec p' e
+      where p' | visible ai = p
+               | otherwise  = 0
+            localParens | getOrigin ai == Substitution = parens
+                        | otherwise = id
+
+instance Pretty e => Pretty (Named_ e) where
+  prettyPrec p (Named nm e)
+    | Just s <- bareNameOf nm = mparens (p > 0) $ sep [ text s <+> "=", pretty e ]
+    | otherwise               = prettyPrec p e
+
+instance Pretty Pattern where
+    prettyList = fsep . map pretty
+    pretty = \case
+            IdentP _ x      -> pretty x
+            AppP p1 p2      -> sep [ pretty p1, nest 2 $ pretty p2 ]
+            RawAppP _ ps    -> fsep $ map pretty $ List2.toList ps
+            OpAppP _ q _ ps -> fsep $ prettyOpApp (Asp.Name Nothing True) q $ fmap (fmap (fmap (NoPlaceholder Strict.Nothing))) ps
+            HiddenP _ p     -> braces' $ pretty p
+            InstanceP _ p   -> dbraces $ pretty p
+            ParenP _ p      -> parens $ pretty p
+            WildP _         -> underscore
+            AsP _ x p       -> pretty x <> "@" <> pretty p
+            DotP _ p        -> "." <> pretty p
+            AbsurdP _       -> "()"
+            LitP _ l        -> pretty l
+            QuoteP _        -> "quote"
+            RecP _ fs       -> sep [ "record", bracesAndSemicolons (map pretty fs) ]
+            EqualP _ es     -> sep $ [ parens (sep [pretty e1, "=", pretty e2]) | (e1,e2) <- es ]
+            EllipsisP _ mp  -> "..."
+            WithP _ p       -> "|" <+> pretty p
+
+prettyOpApp :: forall a .
+  Pretty a => Asp.Aspect -> QName -> [NamedArg (MaybePlaceholder a)] -> [Doc]
+prettyOpApp asp q es = merge [] $ prOp ms xs es
+  where
+    -- ms: the module part of the name.
+    ms = List1.init (qnameParts q)
+    -- xs: the concrete name (alternation of @Id@ and @Hole@)
+    xs = case unqualify q of
+           Name _ _ xs    -> List1.toList xs
+           NoName{}       -> __IMPOSSIBLE__
+
+    prOp :: [Name] -> [NamePart] -> [NamedArg (MaybePlaceholder a)] -> [(Doc, Maybe PositionInName)]
+    prOp ms (Hole : xs) (e : es) =
+      case namedArg e of
+        Placeholder p   -> (qual ms $ pretty e, Just p) : prOp [] xs es
+        NoPlaceholder{} -> (pretty e, Nothing) : prOp ms xs es
+          -- Module qualifier needs to go on section holes (#3072)
+    prOp _  (Hole : _)  []       = __IMPOSSIBLE__
+    prOp ms (Id x : xs) es       = ( qual ms $ annotateAspect asp $ pretty $ simpleName x
+                                   , Nothing
+                                   ) : prOp [] xs es
+      -- Qualify the name part with the module.
+      -- We then clear @ms@ such that the following name parts will not be qualified.
+
+    prOp _  []       es          = map (\e -> (pretty e, Nothing)) es
+
+    qual ms doc = hcat $ punctuate "." $ map pretty ms ++ [doc]
+
+    -- Section underscores should be printed without surrounding
+    -- whitespace. This function takes care of that.
+    merge :: [Doc] -> [(Doc, Maybe PositionInName)] -> [Doc]
+    merge before []                            = reverse before
+    merge before ((d, Nothing) : after)        = merge (d : before) after
+    merge before ((d, Just Beginning) : after) = mergeRight before d after
+    merge before ((d, Just End)       : after) = case mergeLeft d before of
+                                                   (d, bs) -> merge (d : bs) after
+    merge before ((d, Just Middle)    : after) = case mergeLeft d before of
+                                                   (d, bs) -> mergeRight bs d after
+
+    mergeRight before d after =
+      reverse before ++
+      case merge [] after of
+        []     -> [d]
+        a : as -> (d <> a) : as
+
+    mergeLeft d before = case before of
+      []     -> (d,      [])
+      b : bs -> (b <> d, bs)
+
+instance (Pretty a, Pretty b) => Pretty (ImportDirective' a b) where
+    pretty i =
+        sep [ public (publicOpen i)
+            , pretty $ using i
+            , prettyHiding $ hiding i
+            , rename $ impRenaming i
+            ]
+        where
+            public Just{}  = "public"
+            public Nothing = empty
+
+            prettyHiding [] = empty
+            prettyHiding xs = "hiding" <+> parens (fsep $ punctuate ";" $ map pretty xs)
+
+            rename [] = empty
+            rename xs = hsep [ "renaming"
+                             , parens $ fsep $ punctuate ";" $ map pretty xs
+                             ]
+
+instance (Pretty a, Pretty b) => Pretty (Using' a b) where
+    pretty UseEverything = empty
+    pretty (Using xs)    =
+        "using" <+> parens (fsep $ punctuate ";" $ map pretty xs)
+
+instance (Pretty a, Pretty b) => Pretty (Renaming' a b) where
+    pretty (Renaming from to mfx _r) = hsep
+      [ pretty from
+      , "to"
+      , maybe empty pretty mfx
+      , case to of
+          ImportedName a   -> pretty a
+          ImportedModule b -> pretty b   -- don't print "module" here
+      ]
+
+instance (Pretty a, Pretty b) => Pretty (ImportedName' a b) where
+    pretty (ImportedName   a) = pretty a
+    pretty (ImportedModule b) = "module" <+> pretty b
diff --git a/src/full/Agda/Syntax/DoNotation.hs b/src/full/Agda/Syntax/DoNotation.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/DoNotation.hs
@@ -0,0 +1,144 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-|
+    Desugaring for do-notation. Uses whatever `_>>=_` and `_>>_` happen to be
+    in scope.
+
+    Example:
+
+    ```
+      foo = do
+        x ← m₁
+        m₂
+        just y ← m₃
+          where nothing → m₄
+        let z = t
+        m₅
+    ```
+    desugars to
+    ```
+      foo =
+        m₁ >>= λ x →
+        m₂ >>
+        m₃ >>= λ where
+          just y → let z = t in m₅
+          nothing → m₄
+    ```
+ -}
+module Agda.Syntax.DoNotation (desugarDoNotation) where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Concrete
+
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.List1  ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+desugarDoNotation :: Range -> List1 DoStmt -> ScopeM Expr
+desugarDoNotation r ss = do
+  let qBind = QName $ simpleBinaryOperator ">>="
+      qThen = QName $ simpleBinaryOperator ">>"
+      isBind DoBind{} = True
+      isBind _        = False
+      isThen DoThen{} = True
+      isThen _        = False
+  -- Only check the operation we actually need. One could imagine to fall back
+  -- on _>>=_ if _>>_ is not in scope, but if we are desugaring to _>>_ at all
+  -- I think we should throw an error rather than silently switching to _>>=_.
+  -- / Ulf
+  mapM_ ensureInScope $ [qBind | any isBind ss] ++
+                        [qThen | any isThen $ List1.init ss] -- ignore the last 'DoThen'
+  desugarDo qBind qThen ss
+
+desugarDo :: QName -> QName -> List1 DoStmt -> ScopeM Expr
+desugarDo qBind qThen = \case
+
+  -- The last statement must be a DoThen.
+  DoThen e        :| [] -> return e
+
+  -- Or an absurd bind.
+  DoBind r p e [] :| [] | Just (r', NotHidden) <- isAbsurdP p ->
+    return $ appOp (setRange r qBind) e $ AbsurdLam r' NotHidden
+
+  -- Otherwise, sorry.
+  _ :| [] -> failure
+
+  -- `DoThen` and `DoLet` are easy.
+  DoThen e   :| ss -> appOp qThen e   <$> desugarDo0 ss
+  DoLet r ds :| ss -> Let r ds . Just <$> desugarDo0 ss
+
+  -- `DoBind` requires more work since we want to generate plain lambdas when possible.
+  DoBind r p e [] :| ss | Just x <- singleName p -> do
+    -- In this case we have a single name in the bind pattern and no where clauses.
+    -- It could still be a pattern bind though (for instance, `refl ← pure eq`), so
+    -- to figure out which one to use we look up the name in the scope; if it's a
+    -- constructor or pattern synonym we desugar to a pattern lambda.
+    res <- resolveName (QName x)
+    let isMatch = case res of
+          ConstructorName{}   -> True
+          PatternSynResName{} -> True
+          _                   -> False
+    rest <- desugarDo0 ss
+    if isMatch then return $ matchingBind qBind r p e rest []
+               else return $ nonMatchingBind qBind r x e rest
+
+  -- If there are @where@ clauses we have to desugar to a pattern lambda.
+  DoBind r p e cs :| ss -> do
+    rest <- desugarDo0 ss
+    return $ matchingBind qBind r p e rest cs
+
+  where
+  desugarDo0 :: [DoStmt] -> ScopeM Expr
+  desugarDo0 ss = List1.ifNull ss failure $ desugarDo qBind qThen
+
+  failure = genericError
+    "The last statement in a 'do' block must be an expression or an absurd match."
+
+singleName :: Pattern -> Maybe Name
+singleName = \case
+  IdentP _ (QName x) -> Just x
+  _ -> Nothing
+
+matchingBind :: QName -> Range -> Pattern -> Expr -> Expr -> [LamClause] -> Expr
+matchingBind qBind r p e body cs =
+  appOp (setRange r qBind) e             -- Set the range of the lambda to that of the
+    $ ExtendedLam (getRange cs)          -- where-clauses to make highlighting of overlapping
+        defaultErased                    -- patterns not highlight the rest of the do-block.
+    $ fmap addParens (mainClause :| cs)
+  where
+    mainClause = LamClause { lamLHS      = [p]
+                           , lamRHS      = RHS body
+                           , lamCatchAll = False }
+
+    -- Add parens to left-hand sides.
+    addParens c = c { lamLHS = addP (lamLHS c) }
+      where
+      addP []           = __IMPOSSIBLE__
+      addP pps@(p : ps) = [ParenP (getRange pps) $ rawAppP $ p :| ps ]
+
+nonMatchingBind :: QName -> Range -> Name -> Expr -> Expr -> Expr
+nonMatchingBind qBind r x e body =
+    appOp (setRange r qBind) e $ Lam (getRange (x, body)) (singleton bx) body
+  where bx = DomainFree $ defaultNamedArg $ mkBinder_ x
+
+appOp :: QName -> Expr -> Expr -> Expr
+appOp q e1 e2 = app (Ident q) [par e1, par e2]
+  where
+    par e = Paren (getRange e) e  -- Add parens to get the right precedence context (#3152)
+    app e es = foldl (\ e1 e2 -> App (getRange (e1, e2)) e1 (defaultNamedArg e2)) e es
+
+ensureInScope :: QName -> ScopeM ()
+ensureInScope q = do
+  r <- resolveName q
+  case r of
+    UnknownName -> genericError $
+      prettyShow q ++ " needs to be in scope to desugar 'do' block"
+    _ -> return ()
diff --git a/src/full/Agda/Syntax/Fixity.hs b/src/full/Agda/Syntax/Fixity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Fixity.hs
@@ -0,0 +1,154 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| Definitions for fixity, precedence levels, and declared syntax.
+-}
+module Agda.Syntax.Fixity where
+
+import Control.DeepSeq
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+-- The Fixity data type is now defined in Agda.Syntax.Common.
+-- Andreas, 2019-08-16, issue #1346
+
+-- | Decorating something with @Fixity'@.
+data ThingWithFixity x = ThingWithFixity x Fixity'
+  deriving (Functor, Foldable, Traversable, Show)
+
+instance LensFixity' (ThingWithFixity a) where
+  lensFixity' f (ThingWithFixity a fix') = ThingWithFixity a <$> f fix'
+
+instance LensFixity (ThingWithFixity a) where
+  lensFixity = lensFixity' . lensFixity
+
+-- | Do we prefer parens around arguments like @λ x → x@ or not?
+--   See 'lamBrackets'.
+data ParenPreference = PreferParen | PreferParenless
+  deriving (Eq, Ord, Show, Generic)
+
+instance NFData ParenPreference
+
+preferParen :: ParenPreference -> Bool
+preferParen p = PreferParen == p
+
+preferParenless :: ParenPreference -> Bool
+preferParenless p = PreferParenless == p
+
+-- * Precendence
+
+-- | Precedence is associated with a context.
+data Precedence = TopCtx | FunctionSpaceDomainCtx
+                | LeftOperandCtx Fixity | RightOperandCtx Fixity ParenPreference
+                | FunctionCtx | ArgumentCtx ParenPreference | InsideOperandCtx
+                | WithFunCtx | WithArgCtx | DotPatternCtx
+    deriving (Show, Eq, Generic)
+
+instance NFData Precedence
+
+instance Pretty Precedence where
+  pretty = text . show
+
+-- | When printing we keep track of a stack of precedences in order to be able
+--   to decide whether it's safe to leave out parens around lambdas. An empty
+--   stack is equivalent to `TopCtx`. Invariant: `notElem TopCtx`.
+type PrecedenceStack = [Precedence]
+
+pushPrecedence :: Precedence -> PrecedenceStack -> PrecedenceStack
+pushPrecedence TopCtx _  = []
+pushPrecedence p      ps = p : ps
+
+headPrecedence :: PrecedenceStack -> Precedence
+headPrecedence []      = TopCtx
+headPrecedence (p : _) = p
+
+-- | Argument context preferring parens.
+argumentCtx_ :: Precedence
+argumentCtx_ = ArgumentCtx PreferParen
+
+-- | Do we need to bracket an operator application of the given fixity
+--   in a context with the given precedence.
+opBrackets :: Fixity -> PrecedenceStack -> Bool
+opBrackets = opBrackets' False
+
+-- | Do we need to bracket an operator application of the given fixity
+--   in a context with the given precedence.
+opBrackets' :: Bool ->   -- Is the last argument a parenless lambda?
+               Fixity -> PrecedenceStack -> Bool
+opBrackets' isLam f ps = brack f (headPrecedence ps)
+  where
+    false = isLam && lamBrackets ps -- require more parens for `e >>= λ x → e₁` than `e >>= e₁`
+    brack                        (Fixity _ (Related n1) LeftAssoc)
+               (LeftOperandCtx   (Fixity _ (Related n2) LeftAssoc))  | n1 >= n2 = false
+    brack                        (Fixity _ (Related n1) RightAssoc)
+               (RightOperandCtx  (Fixity _ (Related n2) RightAssoc) _) | n1 >= n2 = false
+    brack f1   (LeftOperandCtx  f2) | Related f1 <- fixityLevel f1
+                                    , Related f2 <- fixityLevel f2
+                                    , f1 > f2 = false
+    brack f1   (RightOperandCtx f2 _) | Related f1 <- fixityLevel f1
+                                    , Related f2 <- fixityLevel f2
+                                    , f1 > f2 = false
+    brack _ TopCtx                 = false
+    brack _ FunctionSpaceDomainCtx = false
+    brack _ InsideOperandCtx       = false
+    brack _ WithArgCtx             = false
+    brack _ WithFunCtx             = false
+    brack _ _                      = True
+
+-- | Does a lambda-like thing (lambda, let or pi) need brackets in the
+-- given context? A peculiar thing with lambdas is that they don't
+-- need brackets in certain right operand contexts. To decide we need to look
+-- at the stack of precedences and not just the current precedence.
+-- Example: @m₁ >>= (λ x → x) >>= m₂@ (for @_>>=_@ left associative).
+lamBrackets :: PrecedenceStack -> Bool
+lamBrackets []       = False
+lamBrackets (p : ps) = case p of
+  TopCtx                 -> __IMPOSSIBLE__
+  ArgumentCtx pref       -> preferParen pref || lamBrackets ps
+  RightOperandCtx _ pref -> preferParen pref || lamBrackets ps
+  FunctionSpaceDomainCtx -> True
+  LeftOperandCtx{}       -> True
+  FunctionCtx            -> True
+  InsideOperandCtx       -> True
+  WithFunCtx             -> True
+  WithArgCtx             -> True
+  DotPatternCtx          -> True
+
+-- | Does a function application need brackets?
+appBrackets :: PrecedenceStack -> Bool
+appBrackets = appBrackets' False
+
+-- | Does a function application need brackets?
+appBrackets' :: Bool ->   -- Is the argument of the application a parenless lambda?
+                PrecedenceStack -> Bool
+appBrackets' isLam ps = brack (headPrecedence ps)
+  where
+    brack ArgumentCtx{} = True
+    brack DotPatternCtx = True
+    brack _             = isLam && lamBrackets ps -- allow e + e₁ λ x → e₂
+
+-- | Does a with application need brackets?
+withAppBrackets :: PrecedenceStack -> Bool
+withAppBrackets = brack . headPrecedence
+  where
+    brack TopCtx                 = False
+    brack FunctionSpaceDomainCtx = False
+    brack WithFunCtx             = False
+    brack _                      = True
+
+-- | Does a function space need brackets?
+piBrackets :: PrecedenceStack -> Bool
+piBrackets [] = False
+piBrackets _  = True
+
+roundFixBrackets :: PrecedenceStack -> Bool
+roundFixBrackets ps = DotPatternCtx == headPrecedence ps
+
+instance KillRange x => KillRange (ThingWithFixity x) where
+  killRange (ThingWithFixity c f) = ThingWithFixity (killRange c) f
diff --git a/src/full/Agda/Syntax/IdiomBrackets.hs b/src/full/Agda/Syntax/IdiomBrackets.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/IdiomBrackets.hs
@@ -0,0 +1,66 @@
+module Agda.Syntax.IdiomBrackets (parseIdiomBracketsSeq) where
+
+import Control.Monad
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Operators
+import Agda.Syntax.Concrete.Pretty ( leftIdiomBrkt, rightIdiomBrkt )
+
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.List1  ( List1, pattern (:|), (<|) )
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Singleton
+
+parseIdiomBracketsSeq :: Range -> [Expr] -> ScopeM Expr
+parseIdiomBracketsSeq r es = do
+  let qEmpty = QName $ simpleName "empty"
+      qPlus  = QName $ simpleBinaryOperator "<|>"
+      ePlus a b = App r (App r (Ident qPlus) (defaultNamedArg a)) (defaultNamedArg b)
+  case es of
+    []       -> ensureInScope qEmpty >> return (Ident qEmpty)
+    [e]      -> parseIdiomBrackets r e
+    es@(_:_) -> do
+      ensureInScope qPlus
+      es' <- mapM (parseIdiomBrackets r) es
+      return $ foldr1 ePlus es'
+
+parseIdiomBrackets :: Range -> Expr -> ScopeM Expr
+parseIdiomBrackets r e = do
+  let qPure = QName $ simpleName "pure"
+      qAp   = QName $ simpleBinaryOperator "<*>"
+      ePure   = App r (Ident qPure) . defaultNamedArg
+      eAp a b = App r (App r (Ident qAp) (defaultNamedArg a)) (defaultNamedArg b)
+  mapM_ ensureInScope [qPure, qAp]
+  case e of
+    RawApp _ es -> do
+      e :| es <- appViewM =<< parseApplication es
+      return $ foldl eAp (ePure e) es
+    _ -> return $ ePure e
+
+appViewM :: Expr -> ScopeM (List1 Expr)
+appViewM = \case
+    e@App{}         -> let AppView e' es = appView e in (e' :|) <$> mapM onlyVisible es
+    OpApp _ op _ es -> (Ident op :|) <$> mapM (ordinary <=< noPlaceholder <=< onlyVisible) es
+    e               -> return $ singleton e
+  where
+    onlyVisible a
+      | defaultNamedArg () == fmap (() <$) a = return $ namedArg a
+      | otherwise = genericError "Only regular arguments are allowed in idiom brackets (no implicit or instance arguments)"
+    noPlaceholder Placeholder{}       = genericError "Naked sections are not allowed in idiom brackets"
+    noPlaceholder (NoPlaceholder _ x) = return x
+
+    ordinary (Ordinary a) = return a
+    ordinary _ = genericError "Binding syntax is not allowed in idiom brackets"
+
+ensureInScope :: QName -> ScopeM ()
+ensureInScope q = do
+  r <- resolveName q
+  case r of
+    UnknownName -> genericError $
+      prettyShow q ++ " needs to be in scope to use idiom brackets " ++ prettyShow leftIdiomBrkt ++ " ... " ++ prettyShow rightIdiomBrkt
+    _ -> return ()
diff --git a/src/full/Agda/Syntax/Info.hs b/src/full/Agda/Syntax/Info.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Info.hs
@@ -0,0 +1,299 @@
+
+{-| An info object contains additional information about a piece of abstract
+    syntax that isn't part of the actual syntax. For instance, it might contain
+    the source code position of an expression or the concrete syntax that
+    an internal expression originates from.
+-}
+
+module Agda.Syntax.Info where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import Data.Semigroup (Semigroup)
+
+import GHC.Generics (Generic)
+
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Concrete
+import Agda.Syntax.Fixity
+import Agda.Syntax.Scope.Base (ScopeInfo, emptyScopeInfo)
+
+import Agda.Utils.Functor
+import Agda.Utils.Null
+
+{--------------------------------------------------------------------------
+    Meta information
+ --------------------------------------------------------------------------}
+
+data MetaInfo = MetaInfo
+  { metaRange          :: Range
+  , metaScope          :: ScopeInfo
+  , metaNumber         :: Maybe MetaId
+  , metaNameSuggestion :: String
+  }
+  deriving (Show, Eq, Generic)
+
+emptyMetaInfo :: MetaInfo
+emptyMetaInfo = MetaInfo
+  { metaRange          = noRange
+  , metaScope          = emptyScopeInfo
+  , metaNumber         = Nothing
+  , metaNameSuggestion = ""
+  }
+
+instance HasRange MetaInfo where
+  getRange = metaRange
+
+instance KillRange MetaInfo where
+  killRange m = m { metaRange = noRange }
+
+instance NFData MetaInfo
+
+{--------------------------------------------------------------------------
+    General expression information
+ --------------------------------------------------------------------------}
+
+newtype ExprInfo = ExprRange Range
+  deriving (Show, Eq, Null, NFData)
+
+exprNoRange :: ExprInfo
+exprNoRange = ExprRange noRange
+
+instance HasRange ExprInfo where
+  getRange (ExprRange r) = r
+
+instance KillRange ExprInfo where
+  killRange (ExprRange r) = exprNoRange
+
+{--------------------------------------------------------------------------
+    Application information
+ --------------------------------------------------------------------------}
+
+-- | Information about application
+data AppInfo = AppInfo
+  { appRange  :: Range
+  , appOrigin :: Origin
+  , appParens :: ParenPreference -- ^ Do we prefer a lambda argument with or without parens?
+  }
+  deriving (Show, Eq, Ord, Generic)
+
+-- | Default is system inserted and prefer parens.
+defaultAppInfo :: Range -> AppInfo
+defaultAppInfo r = AppInfo{ appRange = r, appOrigin = Inserted, appParens = PreferParen }
+
+-- | `AppInfo` with no range information.
+defaultAppInfo_ :: AppInfo
+defaultAppInfo_ = defaultAppInfo noRange
+
+instance HasRange AppInfo where
+  getRange = appRange
+
+instance KillRange AppInfo where
+  killRange (AppInfo r o p) = AppInfo (killRange r) o p
+
+instance LensOrigin AppInfo where
+  getOrigin = appOrigin
+  mapOrigin f i = i { appOrigin = f (appOrigin i) }
+
+instance NFData AppInfo
+
+{--------------------------------------------------------------------------
+    Module information
+ --------------------------------------------------------------------------}
+
+data ModuleInfo = ModuleInfo
+  { minfoRange    :: Range
+  , minfoAsTo     :: Range
+    -- ^ The range of the \"as\" and \"to\" keywords,
+    -- if any. Retained for highlighting purposes.
+  , minfoAsName   :: Maybe C.Name
+    -- ^ The \"as\" module name, if any. Retained for highlighting purposes.
+  , minfoOpenShort :: Maybe OpenShortHand
+  , minfoDirective :: Maybe ImportDirective
+    -- ^ Retained for @abstractToConcrete@ of 'ModuleMacro'.
+  }
+  deriving (Eq, Show, Generic)
+
+instance HasRange ModuleInfo where
+  getRange = minfoRange
+
+instance SetRange ModuleInfo where
+  setRange r i = i { minfoRange = r }
+
+instance KillRange ModuleInfo where
+  killRange m = m { minfoRange = noRange }
+
+instance NFData ModuleInfo
+
+---------------------------------------------------------------------------
+-- Let info
+---------------------------------------------------------------------------
+
+newtype LetInfo = LetRange Range
+  deriving (Show, Eq, Null, NFData)
+
+instance HasRange LetInfo where
+  getRange (LetRange r)   = r
+
+instance KillRange LetInfo where
+  killRange (LetRange r) = LetRange noRange
+
+{--------------------------------------------------------------------------
+    Definition information (declarations that actually define something)
+ --------------------------------------------------------------------------}
+
+data DefInfo' t = DefInfo
+  { defFixity   :: Fixity'
+  , defAccess   :: Access
+  , defAbstract :: IsAbstract
+  , defOpaque   :: IsOpaque
+  , defInstance :: IsInstance
+  , defMacro    :: IsMacro
+  , defInfo     :: DeclInfo
+  , defTactic   :: Maybe (Ranged t)
+  }
+  deriving (Show, Eq, Generic)
+
+mkDefInfo :: Name -> Fixity' -> Access -> IsAbstract -> Range -> DefInfo' t
+mkDefInfo x f a ab r = mkDefInfoInstance x f a ab NotInstanceDef NotMacroDef r
+
+-- | Same as @mkDefInfo@ but where we can also give the @IsInstance@
+mkDefInfoInstance :: Name -> Fixity' -> Access -> IsAbstract -> IsInstance -> IsMacro -> Range -> DefInfo' t
+mkDefInfoInstance x f a ab i m r = DefInfo f a ab TransparentDef i m (DeclInfo x r) Nothing
+
+instance HasRange (DefInfo' t) where
+  getRange = getRange . defInfo
+
+instance SetRange (DefInfo' t) where
+  setRange r i = i { defInfo = setRange r (defInfo i) }
+
+instance KillRange t => KillRange (DefInfo' t) where
+  killRange i = i { defInfo   = killRange $ defInfo i,
+                    defTactic = killRange $ defTactic i }
+
+instance LensIsAbstract (DefInfo' t) where
+  lensIsAbstract f i = (f $! defAbstract i) <&> \ a -> i { defAbstract = a }
+
+instance LensIsOpaque (DefInfo' t) where
+  lensIsOpaque f i = (f $! defOpaque i) <&> \ a -> i { defOpaque = a }
+
+instance AnyIsAbstract (DefInfo' t) where
+  anyIsAbstract = defAbstract
+
+instance AllAreOpaque (DefInfo' t) where
+  jointOpacity = jointOpacity . defOpaque
+
+instance NFData t => NFData (DefInfo' t)
+
+{--------------------------------------------------------------------------
+    General declaration information
+ --------------------------------------------------------------------------}
+
+data DeclInfo = DeclInfo
+  { declName  :: Name
+  , declRange :: Range
+  }
+  deriving (Show, Eq, Generic)
+
+instance HasRange DeclInfo where
+  getRange = declRange
+
+instance SetRange DeclInfo where
+  setRange r i = i { declRange = r }
+
+instance KillRange DeclInfo where
+  killRange i = i { declRange = noRange }
+
+instance NFData DeclInfo
+
+{--------------------------------------------------------------------------
+    Mutual block information
+ --------------------------------------------------------------------------}
+
+data MutualInfo = MutualInfo
+  { mutualTerminationCheck :: TerminationCheck Name
+  , mutualCoverageCheck    :: CoverageCheck
+  , mutualPositivityCheck  :: PositivityCheck
+  , mutualRange            :: Range
+  }
+  deriving (Show, Eq, Generic)
+
+-- | Default value for 'MutualInfo'.
+instance Null MutualInfo where
+  empty = MutualInfo TerminationCheck YesCoverageCheck YesPositivityCheck noRange
+
+instance HasRange MutualInfo where
+  getRange = mutualRange
+
+instance KillRange MutualInfo where
+  killRange i = i { mutualRange = noRange }
+
+instance NFData MutualInfo
+
+{--------------------------------------------------------------------------
+    Left hand side information
+ --------------------------------------------------------------------------}
+
+data LHSInfo = LHSInfo
+  { lhsRange    :: Range
+  , lhsEllipsis :: ExpandedEllipsis
+  } deriving (Show, Eq, Generic)
+
+instance HasRange LHSInfo where
+  getRange (LHSInfo r _) = r
+
+instance KillRange LHSInfo where
+  killRange (LHSInfo r ell) = LHSInfo noRange ell
+
+instance Null LHSInfo where
+  null i = null (lhsRange i) && null (lhsEllipsis i)
+  empty  = LHSInfo empty empty
+
+instance NFData LHSInfo
+
+{--------------------------------------------------------------------------
+    Pattern information
+ --------------------------------------------------------------------------}
+
+-- | For a general pattern we remember the source code position.
+newtype PatInfo
+  = PatRange Range
+  deriving (Eq, Null, Semigroup, Monoid, Show, SetRange, HasRange,
+            KillRange, NFData)
+
+-- | Empty range for patterns.
+patNoRange :: PatInfo
+patNoRange = PatRange noRange
+
+-- | Constructor pattern info.
+data ConPatInfo = ConPatInfo
+  { conPatOrigin   :: ConOrigin
+    -- ^ Does this pattern come form the eta-expansion of an implicit pattern?
+    ---  Or from a user written constructor or record pattern?
+  , conPatInfo     :: PatInfo
+  , conPatLazy     :: ConPatLazy
+  }
+  deriving (Eq, Show, Generic)
+
+instance HasRange ConPatInfo where
+  getRange = getRange . conPatInfo
+
+instance KillRange ConPatInfo where
+  killRange (ConPatInfo b i l) = ConPatInfo b (killRange i) l
+
+instance SetRange ConPatInfo where
+  setRange r (ConPatInfo b i l) = ConPatInfo b (PatRange r) l
+
+instance NFData ConPatInfo
+
+-- | Has the constructor pattern a dotted (forced) constructor?
+data ConPatLazy
+  = ConPatLazy   -- ^ Dotted constructor.
+  | ConPatEager  -- ^ Ordinary constructor.
+  deriving (Eq, Ord, Show, Bounded, Enum, Generic)
+
+instance NFData ConPatLazy
diff --git a/src/full/Agda/Syntax/Internal.hs b/src/full/Agda/Syntax/Internal.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal.hs
@@ -0,0 +1,1524 @@
+
+module Agda.Syntax.Internal
+    ( module Agda.Syntax.Internal
+    , module Agda.Syntax.Internal.Blockers
+    , module Agda.Syntax.Internal.Elim
+    , module Agda.Syntax.Internal.Univ
+    , module Agda.Syntax.Abstract.Name
+    , MetaId(..), ProblemId(..)
+    ) where
+
+import Prelude hiding (null)
+
+import Control.Monad.Identity
+import Control.DeepSeq
+
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Maybe
+import Data.Semigroup ( Semigroup, (<>), Sum(..) )
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Literal
+import Agda.Syntax.Concrete.Pretty (prettyHiding)
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Internal.Blockers
+import Agda.Syntax.Internal.Elim
+import Agda.Syntax.Internal.Univ
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.CallStack
+    ( CallStack
+    , HasCallStack
+    , prettyCallSite
+    , headCallSite
+    , withCallerCallStack
+    )
+
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.Null
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Function type domain
+---------------------------------------------------------------------------
+
+-- | Similar to 'Arg', but we need to distinguish
+--   an irrelevance annotation in a function domain
+--   (the domain itself is not irrelevant!)
+--   from an irrelevant argument.
+--
+--   @Dom@ is used in 'Pi' of internal syntax, in 'Context' and 'Telescope'.
+--   'Arg' is used for actual arguments ('Var', 'Con', 'Def' etc.)
+--   and in 'Abstract' syntax and other situations.
+--
+--   [ cubical ] When @annFinite (argInfoAnnotation domInfo) = True@ for
+--   the domain of a 'Pi' type, the elements should be compared by
+--   tabulating the domain type.  Only supported in case the domain type
+--   is primIsOne, to obtain the correct equality for partial elements.
+--
+data Dom' t e = Dom
+  { domInfo   :: ArgInfo
+  , domName   :: Maybe NamedName  -- ^ e.g. @x@ in @{x = y : A} -> B@.
+  , domIsFinite :: Bool
+    -- ^ Is this a Π-type (False), or a partial type (True)?
+  , domTactic :: Maybe t        -- ^ "@tactic e".
+  , unDom     :: e
+  } deriving (Show, Functor, Foldable, Traversable)
+
+type Dom = Dom' Term
+
+instance Decoration (Dom' t) where
+  traverseF f (Dom ai x t b a) = Dom ai x t b <$> f a
+
+instance HasRange a => HasRange (Dom' t a) where
+  getRange = getRange . unDom
+
+instance (KillRange t, KillRange a) => KillRange (Dom' t a) where
+  killRange (Dom info x t b a) = killRangeN Dom info x t b a
+
+-- | Ignores 'Origin' and 'FreeVariables' and tactic.
+instance Eq a => Eq (Dom' t a) where
+  Dom (ArgInfo h1 m1 _ _ a1) s1 f1 _ x1 == Dom (ArgInfo h2 m2 _ _ a2) s2 f2 _ x2 =
+    (h1, m1, a1, s1, f1, x1) == (h2, m2, a2, s2, f2, x2)
+
+instance LensNamed (Dom' t e) where
+  type NameOf (Dom' t e) = NamedName
+  lensNamed f dom = f (domName dom) <&> \ nm -> dom { domName = nm }
+
+instance LensArgInfo (Dom' t e) where
+  getArgInfo        = domInfo
+  setArgInfo ai dom = dom { domInfo = ai }
+  mapArgInfo f  dom = dom { domInfo = f $ domInfo dom }
+
+instance LensLock (Dom' t e) where
+  getLock = getLock . getArgInfo
+  setLock = mapArgInfo . setLock
+
+-- The other lenses are defined through LensArgInfo
+
+instance LensHiding        (Dom' t e) where
+instance LensModality      (Dom' t e) where
+instance LensOrigin        (Dom' t e) where
+instance LensFreeVariables (Dom' t e) where
+instance LensAnnotation    (Dom' t e) where
+
+-- Since we have LensModality, we get relevance and quantity by default
+
+instance LensRelevance (Dom' t e) where
+instance LensQuantity  (Dom' t e) where
+instance LensCohesion  (Dom' t e) where
+
+argFromDom :: Dom' t a -> Arg a
+argFromDom Dom{domInfo = i, unDom = a} = Arg i a
+
+namedArgFromDom :: Dom' t a -> NamedArg a
+namedArgFromDom Dom{domInfo = i, domName = s, unDom = a} = Arg i $ Named s a
+
+-- The following functions are less general than they could be:
+-- @Dom@ could be replaced by @Dom' t@.
+-- However, this causes problems with instance resolution in several places.
+-- often for class AddContext.
+
+domFromArg :: Arg a -> Dom a
+domFromArg (Arg i a) = Dom i Nothing False Nothing a
+
+domFromNamedArg :: NamedArg a -> Dom a
+domFromNamedArg (Arg i a) = Dom i (nameOf a) False Nothing (namedThing a)
+
+defaultDom :: a -> Dom a
+defaultDom = defaultArgDom defaultArgInfo
+
+defaultArgDom :: ArgInfo -> a -> Dom a
+defaultArgDom info x = domFromArg (Arg info x)
+
+defaultNamedArgDom :: ArgInfo -> String -> a -> Dom a
+defaultNamedArgDom info s x = (defaultArgDom info x) { domName = Just $ WithOrigin Inserted $ unranged s }
+
+-- | Type of argument lists.
+--
+type Args       = [Arg Term]
+type NamedArgs  = [NamedArg Term]
+
+data DataOrRecord' p
+  = IsData
+  | IsRecord p
+  deriving (Show, Eq, Generic)
+
+type DataOrRecord = DataOrRecord' PatternOrCopattern
+
+instance PatternMatchingAllowed DataOrRecord where
+  patternMatchingAllowed = \case
+    IsData -> True
+    IsRecord patCopat -> patternMatchingAllowed patCopat
+
+instance CopatternMatchingAllowed DataOrRecord where
+  copatternMatchingAllowed = \case
+    IsData -> False
+    IsRecord patCopat -> copatternMatchingAllowed patCopat
+
+-- | Store the names of the record fields in the constructor.
+--   This allows reduction of projection redexes outside of TCM.
+--   For instance, during substitution and application.
+data ConHead = ConHead
+  { conName       :: QName         -- ^ The name of the constructor.
+  , conDataRecord :: DataOrRecord  -- ^ Data or record constructor?
+  , conInductive  :: Induction     -- ^ Record constructors can be coinductive.
+  , conFields     :: [Arg QName]   -- ^ The name of the record fields.
+      --   'Arg' is stored since the info in the constructor args
+      --   might not be accurate because of subtyping (issue #2170).
+  } deriving (Show, Generic)
+
+instance Eq ConHead where
+  (==) = (==) `on` conName
+
+instance Ord ConHead where
+  (<=) = (<=) `on` conName
+
+instance Pretty ConHead where
+  pretty = pretty . conName
+
+instance HasRange ConHead where
+  getRange = getRange . conName
+
+instance SetRange ConHead where
+  setRange r = mapConName (setRange r)
+
+instance CopatternMatchingAllowed ConHead where
+  copatternMatchingAllowed = copatternMatchingAllowed . conDataRecord
+
+class LensConName a where
+  getConName :: a -> QName
+  setConName :: QName -> a -> a
+  setConName = mapConName . const
+  mapConName :: (QName -> QName) -> a -> a
+  mapConName f a = setConName (f (getConName a)) a
+
+instance LensConName ConHead where
+  getConName = conName
+  setConName c con = con { conName = c }
+
+
+-- | Raw values.
+--
+--   @Def@ is used for both defined and undefined constants.
+--   Assume there is a type declaration and a definition for
+--     every constant, even if the definition is an empty
+--     list of clauses.
+--
+data Term = Var {-# UNPACK #-} !Int Elims -- ^ @x es@ neutral
+          | Lam ArgInfo (Abs Term)        -- ^ Terms are beta normal. Relevance is ignored
+          | Lit Literal
+          | Def QName Elims               -- ^ @f es@, possibly a delta/iota-redex
+          | Con ConHead ConInfo Elims
+          -- ^ @c es@ or @record { fs = es }@
+          --   @es@ allows only Apply and IApply eliminations,
+          --   and IApply only for data constructors.
+          | Pi (Dom Type) (Abs Type)      -- ^ dependent or non-dependent function space
+          | Sort Sort
+          | Level Level
+          | MetaV {-# UNPACK #-} !MetaId Elims
+          | DontCare Term
+            -- ^ Irrelevant stuff in relevant position, but created
+            --   in an irrelevant context.  Basically, an internal
+            --   version of the irrelevance axiom @.irrAx : .A -> A@.
+          | Dummy String Elims
+            -- ^ A (part of a) term or type which is only used for internal purposes.
+            --   Replaces the @Sort Prop@ hack.
+            --   The @String@ typically describes the location where we create this dummy,
+            --   but can contain other information as well.
+            --   The second field accumulates eliminations in case we
+            --   apply a dummy term to more of them. Dummy terms should never be used in places
+            --   where they can affect type checking, so syntactic checks are free to ignore the
+            --   eliminators, which are only there to ease debugging when a dummy term incorrectly
+            --   leaks into a relevant position.
+  deriving Show
+
+type ConInfo = ConOrigin
+
+type Elim = Elim' Term
+type Elims = [Elim]  -- ^ eliminations ordered left-to-right.
+
+-- | Binder.
+--
+--   'Abs': The bound variable might appear in the body.
+--   'NoAbs' is pseudo-binder, it does not introduce a fresh variable,
+--      similar to the @const@ of Haskell.
+--
+data Abs a = Abs   { absName :: ArgName, unAbs :: a }
+               -- ^ The body has (at least) one free variable.
+               --   Danger: 'unAbs' doesn't shift variables properly
+           | NoAbs { absName :: ArgName, unAbs :: a }
+  deriving (Functor, Foldable, Traversable, Generic)
+
+instance Decoration Abs where
+  traverseF f (Abs   x a) = Abs   x <$> f a
+  traverseF f (NoAbs x a) = NoAbs x <$> f a
+
+-- | Types are terms with a sort annotation.
+--
+data Type'' t a = El { _getSort :: Sort' t, unEl :: a }
+  deriving (Show, Functor, Foldable, Traversable)
+
+type Type' a = Type'' Term a
+
+type Type = Type' Term
+
+instance Decoration (Type'' t) where
+  traverseF f (El s a) = El s <$> f a
+
+class LensSort a where
+  lensSort ::  Lens' a Sort
+  getSort  :: a -> Sort
+  getSort a = a ^. lensSort
+
+instance LensSort Sort where
+  lensSort f s = f s <&> \ s' -> s'
+
+instance LensSort (Type' a) where
+  lensSort f (El s a) = f s <&> \ s' -> El s' a
+
+-- General instance leads to overlapping instances.
+-- instance (Decoration f, LensSort a) => LensSort (f a) where
+instance LensSort a => LensSort (Dom a) where
+  lensSort = traverseF . lensSort
+
+instance LensSort a => LensSort (Arg a) where
+  lensSort = traverseF . lensSort
+
+
+-- | Sequence of types. An argument of the first type is bound in later types
+--   and so on.
+data Tele a = EmptyTel
+            | ExtendTel a (Abs (Tele a))  -- ^ 'Abs' is never 'NoAbs'.
+  deriving (Show, Functor, Foldable, Traversable, Generic)
+
+type Telescope = Tele (Dom Type)
+
+data UnivSize
+  = USmall  -- ^ @Prop/Set/SSet ℓ@.
+  | ULarge  -- ^ @(Prop/Set/SSet)ωᵢ@.
+  deriving stock (Eq, Show)
+
+-- | Sorts.
+--
+data Sort' t
+  = Univ Univ (Level' t)
+      -- ^ @Prop ℓ@, @Set ℓ@, @SSet ℓ@.
+  | Inf Univ !Integer
+      -- ^ @Propωᵢ@, @(S)Setωᵢ@.
+  | SizeUniv    -- ^ @SizeUniv@, a sort inhabited by type @Size@.
+  | LockUniv    -- ^ @LockUniv@, a sort for locks.
+  | LevelUniv   -- ^ @LevelUniv@, a sort inhabited by type @Level@. When --level-universe isn't on, this universe reduces to @Set 0@
+  | IntervalUniv -- ^ @IntervalUniv@, a sort inhabited by the cubical interval.
+  | PiSort (Dom' t t) (Sort' t) (Abs (Sort' t)) -- ^ Sort of the pi type.
+  | FunSort (Sort' t) (Sort' t) -- ^ Sort of a (non-dependent) function type.
+  | UnivSort (Sort' t) -- ^ Sort of another sort.
+  | MetaS {-# UNPACK #-} !MetaId [Elim' t]
+  | DefS QName [Elim' t] -- ^ A postulated sort.
+  | DummyS String
+    -- ^ A (part of a) term or type which is only used for internal purposes.
+    --   Replaces the abuse of @Prop@ for a dummy sort.
+    --   The @String@ typically describes the location where we create this dummy,
+    --   but can contain other information as well.
+  deriving Show
+
+pattern Prop, Type, SSet :: Level' t -> Sort' t
+pattern Prop l = Univ UProp l
+pattern Type l = Univ UType l
+pattern SSet l = Univ USSet l
+
+{-# COMPLETE
+  Prop, Type, SSet, Inf,
+  SizeUniv, LockUniv, LevelUniv, IntervalUniv,
+  PiSort, FunSort, UnivSort, MetaS, DefS, DummyS #-}
+
+type Sort = Sort' Term
+
+-- | Is this a strict universe inhabitable by data types?
+isStrictDataSort :: Sort' t -> Bool
+isStrictDataSort = \case
+  Univ u _ -> univFibrancy u == IsStrict
+  Inf  u _ -> univFibrancy u == IsStrict
+  _ -> False
+
+
+-- | A level is a maximum expression of a closed level and 0..n
+--   'PlusLevel' expressions each of which is an atom plus a number.
+data Level' t = Max !Integer [PlusLevel' t]
+  deriving (Show, Functor, Foldable, Traversable)
+
+type Level = Level' Term
+
+data PlusLevel' t = Plus !Integer t
+  deriving (Show, Functor, Foldable, Traversable)
+
+type PlusLevel = PlusLevel' Term
+type LevelAtom = Term
+
+---------------------------------------------------------------------------
+-- * Brave Terms
+---------------------------------------------------------------------------
+
+-- | Newtypes for terms that produce a dummy, rather than crash, when
+--   applied to incompatible eliminations.
+newtype BraveTerm = BraveTerm { unBrave :: Term } deriving Show
+
+---------------------------------------------------------------------------
+-- * Blocked Terms
+---------------------------------------------------------------------------
+
+type Blocked    = Blocked' Term
+type NotBlocked = NotBlocked' Term
+--
+-- | @'Blocked a@ without the @a@.
+type Blocked_ = Blocked ()
+
+---------------------------------------------------------------------------
+-- * Definitions
+---------------------------------------------------------------------------
+
+-- | Named pattern arguments.
+type NAPs = [NamedArg DeBruijnPattern]
+
+-- | A clause is a list of patterns and the clause body.
+--
+--  The telescope contains the types of the pattern variables and the
+--  de Bruijn indices say how to get from the order the variables occur in
+--  the patterns to the order they occur in the telescope. The body
+--  binds the variables in the order they appear in the telescope.
+--
+--  @clauseTel ~ permute clausePerm (patternVars namedClausePats)@
+--
+--  Terms in dot patterns are valid in the clause telescope.
+--
+--  For the purpose of the permutation and the body dot patterns count
+--  as variables. TODO: Change this!
+data Clause = Clause
+    { clauseLHSRange    :: Range
+    , clauseFullRange   :: Range
+    , clauseTel         :: Telescope
+      -- ^ @Δ@: The types of the pattern variables in dependency order.
+    , namedClausePats   :: NAPs
+      -- ^ @Δ ⊢ ps@.  The de Bruijn indices refer to @Δ@.
+    , clauseBody        :: Maybe Term
+      -- ^ @Just v@ with @Δ ⊢ v@ for a regular clause, or @Nothing@ for an
+      --   absurd one.
+    , clauseType        :: Maybe (Arg Type)
+      -- ^ @Δ ⊢ t@.  The type of the rhs under @clauseTel@.
+      --   Used, e.g., by @TermCheck@.
+      --   Can be 'Irrelevant' if we encountered an irrelevant projection
+      --   pattern on the lhs.
+    , clauseCatchall    :: Bool
+      -- ^ Clause has been labelled as CATCHALL.
+    , clauseExact       :: Maybe Bool
+      -- ^ Pattern matching of this clause is exact, no catch-all case.
+      --   Computed by the coverage checker.
+      --   @Nothing@ means coverage checker has not run yet (clause may be inexact).
+      --   @Just False@ means clause is not exact.
+      --   @Just True@ means clause is exact.
+    , clauseRecursive   :: Maybe Bool
+      -- ^ @clauseBody@ contains recursive calls; computed by termination checker.
+      --   @Nothing@ means that termination checker has not run yet,
+      --   or that @clauseBody@ contains meta-variables;
+      --   these could be filled with recursive calls later!
+      --   @Just False@ means definitely no recursive call.
+      --   @Just True@ means definitely a recursive call.
+    , clauseUnreachable :: Maybe Bool
+      -- ^ Clause has been labelled as unreachable by the coverage checker.
+      --   @Nothing@ means coverage checker has not run yet (clause may be unreachable).
+      --   @Just False@ means clause is not unreachable.
+      --   @Just True@ means clause is unreachable.
+    , clauseEllipsis    :: ExpandedEllipsis
+      -- ^ Was this clause created by expansion of an ellipsis?
+    , clauseWhereModule :: Maybe ModuleName
+      -- ^ Keeps track of the module name associate with the clause's where clause.
+    }
+  deriving (Show, Generic)
+
+clausePats :: Clause -> [Arg DeBruijnPattern]
+clausePats = map (fmap namedThing) . namedClausePats
+
+instance HasRange Clause where
+  getRange = clauseLHSRange
+
+-- | Pattern variables.
+type PatVarName = ArgName
+
+patVarNameToString :: PatVarName -> String
+patVarNameToString = argNameToString
+
+nameToPatVarName :: Name -> PatVarName
+nameToPatVarName = nameToArgName
+
+data PatternInfo = PatternInfo
+  { patOrigin :: PatOrigin
+  , patAsNames :: [Name]
+  } deriving (Show, Eq, Generic)
+
+defaultPatternInfo :: PatternInfo
+defaultPatternInfo = PatternInfo PatOSystem []
+
+-- | Origin of the pattern: what did the user write in this position?
+data PatOrigin
+  = PatOSystem         -- ^ Pattern inserted by the system
+  | PatOSplit          -- ^ Pattern generated by case split
+  | PatOVar Name       -- ^ User wrote a variable pattern
+  | PatODot            -- ^ User wrote a dot pattern
+  | PatOWild           -- ^ User wrote a wildcard pattern
+  | PatOCon            -- ^ User wrote a constructor pattern
+  | PatORec            -- ^ User wrote a record pattern
+  | PatOLit            -- ^ User wrote a literal pattern
+  | PatOAbsurd         -- ^ User wrote an absurd pattern
+  deriving (Show, Eq, Generic)
+
+-- | Patterns are variables, constructors, or wildcards.
+--   @QName@ is used in @ConP@ rather than @Name@ since
+--     a constructor might come from a particular namespace.
+--     This also meshes well with the fact that values (i.e.
+--     the arguments we are matching with) use @QName@.
+--
+data Pattern' x
+  = VarP PatternInfo x
+    -- ^ @x@
+  | DotP PatternInfo Term
+    -- ^ @.t@
+  | ConP ConHead ConPatternInfo [NamedArg (Pattern' x)]
+    -- ^ @c ps@
+    --   The subpatterns do not contain any projection copatterns.
+  | LitP PatternInfo Literal
+    -- ^ E.g. @5@, @"hello"@.
+  | ProjP ProjOrigin QName
+    -- ^ Projection copattern.  Can only appear by itself.
+  | IApplyP PatternInfo Term Term x
+    -- ^ Path elimination pattern, like @VarP@ but keeps track of endpoints.
+  | DefP PatternInfo QName [NamedArg (Pattern' x)]
+    -- ^ Used for HITs, the QName should be the one from primHComp.
+  deriving (Show, Functor, Foldable, Traversable, Generic)
+
+type Pattern = Pattern' PatVarName
+    -- ^ The @PatVarName@ is a name suggestion.
+
+varP :: a -> Pattern' a
+varP = VarP defaultPatternInfo
+
+dotP :: Term -> Pattern' a
+dotP = DotP defaultPatternInfo
+
+litP :: Literal -> Pattern' a
+litP = LitP defaultPatternInfo
+
+-- | Type used when numbering pattern variables.
+data DBPatVar = DBPatVar
+  { dbPatVarName  :: PatVarName
+  , dbPatVarIndex :: !Int
+  } deriving (Show, Eq, Generic)
+
+type DeBruijnPattern = Pattern' DBPatVar
+
+namedVarP :: PatVarName -> Named_ Pattern
+namedVarP x = Named named $ varP x
+  where named = if isUnderscore x then Nothing else Just $ WithOrigin Inserted $ unranged x
+
+namedDBVarP :: Int -> PatVarName -> Named_ DeBruijnPattern
+namedDBVarP m = (fmap . fmap) (\x -> DBPatVar x m) . namedVarP
+
+-- | Make an absurd pattern with the given de Bruijn index.
+absurdP :: Int -> DeBruijnPattern
+absurdP = VarP (PatternInfo PatOAbsurd []) . DBPatVar absurdPatternName
+
+-- | The @ConPatternInfo@ states whether the constructor belongs to
+--   a record type (@True@) or data type (@False@).
+--   In the former case, the @PatOrigin@ of the @conPInfo@ says
+--   whether the record pattern orginates from the expansion of an
+--   implicit pattern.
+--   The @Type@ is the type of the whole record pattern.
+--   The scope used for the type is given by any outer scope
+--   plus the clause's telescope ('clauseTel').
+data ConPatternInfo = ConPatternInfo
+  { conPInfo   :: PatternInfo
+    -- ^ Information on the origin of the pattern.
+  , conPRecord :: Bool
+    -- ^ @False@ if data constructor.
+    --   @True@ if record constructor.
+  , conPFallThrough :: Bool
+    -- ^ Should the match block on non-canonical terms or can it
+    --   proceed to the catch-all clause?
+  , conPType   :: Maybe (Arg Type)
+    -- ^ The type of the whole constructor pattern.
+    --   Should be present (@Just@) if constructor pattern is
+    --   is generated ordinarily by type-checking.
+    --   Could be absent (@Nothing@) if pattern comes from some
+    --   plugin (like Agsy).
+    --   Needed e.g. for with-clause stripping.
+  , conPLazy :: Bool
+    -- ^ Lazy patterns are generated by the forcing translation in the unifier
+    --   ('Agda.TypeChecking.Rules.LHS.Unify.unifyStep') and are dropped by
+    --   the clause compiler (TODO: not yet)
+    --   ('Agda.TypeChecking.CompiledClause.Compile.compileClauses') when the
+    --   variables they bind are unused. The GHC backend compiles lazy matches
+    --   to lazy patterns in Haskell (TODO: not yet).
+  }
+  deriving (Show, Generic)
+
+noConPatternInfo :: ConPatternInfo
+noConPatternInfo = ConPatternInfo defaultPatternInfo False False Nothing False
+
+-- | Build partial 'ConPatternInfo' from 'ConInfo'
+toConPatternInfo :: ConInfo -> ConPatternInfo
+toConPatternInfo ConORec = noConPatternInfo{ conPInfo = PatternInfo PatORec [] , conPRecord = True }
+toConPatternInfo _ = noConPatternInfo
+
+-- | Build 'ConInfo' from 'ConPatternInfo'.
+fromConPatternInfo :: ConPatternInfo -> ConInfo
+fromConPatternInfo i = patToConO $ patOrigin $ conPInfo i
+  where
+    patToConO :: PatOrigin -> ConOrigin
+    patToConO = \case
+      PatOSystem -> ConOSystem
+      PatOSplit  -> ConOSplit
+      PatOVar{}  -> ConOSystem
+      PatODot    -> ConOSystem
+      PatOWild   -> ConOSystem
+      PatOCon    -> ConOCon
+      PatORec    -> ConORec
+      PatOLit    -> ConOCon
+      PatOAbsurd -> ConOSystem
+
+-- | Extract pattern variables in left-to-right order.
+--   A 'DotP' is also treated as variable (see docu for 'Clause').
+class PatternVars a where
+  type PatternVarOut a
+  patternVars :: a -> [Arg (Either (PatternVarOut a) Term)]
+
+instance PatternVars (Arg (Pattern' a)) where
+  type PatternVarOut (Arg (Pattern' a)) = a
+
+  -- patternVars :: Arg (Pattern' a) -> [Arg (Either a Term)]
+  patternVars (Arg i (VarP _ x)   ) = [Arg i $ Left x]
+  patternVars (Arg i (DotP _ t)   ) = [Arg i $ Right t]
+  patternVars (Arg _ (ConP _ _ ps)) = patternVars ps
+  patternVars (Arg _ (DefP _ _ ps)) = patternVars ps
+  patternVars (Arg _ (LitP _ _)   ) = []
+  patternVars (Arg _ ProjP{}      ) = []
+  patternVars (Arg i (IApplyP _ _ _ x)) = [Arg i $ Left x]
+
+
+instance PatternVars (NamedArg (Pattern' a)) where
+  type PatternVarOut (NamedArg (Pattern' a)) = a
+
+  patternVars = patternVars . fmap namedThing
+
+instance PatternVars a => PatternVars [a] where
+  type PatternVarOut [a] = PatternVarOut a
+
+  patternVars = concatMap patternVars
+
+-- | Retrieve the PatternInfo from a pattern
+patternInfo :: Pattern' x -> Maybe PatternInfo
+patternInfo (VarP i _)        = Just i
+patternInfo (DotP i _)        = Just i
+patternInfo (LitP i _)        = Just i
+patternInfo (ConP _ ci _)     = Just $ conPInfo ci
+patternInfo ProjP{}           = Nothing
+patternInfo (IApplyP i _ _ _) = Just i
+patternInfo (DefP i _ _)      = Just i
+
+-- | Retrieve the origin of a pattern
+patternOrigin :: Pattern' x -> Maybe PatOrigin
+patternOrigin = fmap patOrigin . patternInfo
+
+-- | Does the pattern perform a match that could fail?
+properlyMatching :: Pattern' a -> Bool
+properlyMatching = properlyMatching' True True
+
+properlyMatching'
+  :: Bool       -- ^ Should absurd patterns count as proper match?
+  -> Bool       -- ^ Should projection patterns count as proper match?
+  -> Pattern' a -- ^ The pattern.
+  -> Bool
+properlyMatching' absP projP = \case
+  p | absP && patternOrigin p == Just PatOAbsurd -> True
+  ConP _ ci ps    -- record constructors do not count as proper matches themselves
+    | conPRecord ci -> List.any (properlyMatching . namedArg) ps
+    | otherwise     -> True
+  LitP{}    -> True
+  DefP{}    -> True
+  ProjP{}   -> projP
+  VarP{}    -> False
+  DotP{}    -> False
+  IApplyP{} -> False
+
+instance IsProjP (Pattern' a) where
+  isProjP = \case
+    ProjP o d -> Just (o, unambiguous d)
+    _ -> Nothing
+
+-----------------------------------------------------------------------------
+-- * Explicit substitutions
+-----------------------------------------------------------------------------
+
+-- | Substitutions.
+
+data Substitution' a
+
+  = IdS
+    -- ^ Identity substitution.
+    --   @Γ ⊢ IdS : Γ@
+
+  | EmptyS Impossible
+    -- ^ Empty substitution, lifts from the empty context. First argument is @__IMPOSSIBLE__@.
+    --   Apply this to closed terms you want to use in a non-empty context.
+    --   @Γ ⊢ EmptyS : ()@
+
+  | a :# Substitution' a
+    -- ^ Substitution extension, ``cons''.
+    --   @
+    --     Γ ⊢ u : Aρ   Γ ⊢ ρ : Δ
+    --     ----------------------
+    --     Γ ⊢ u :# ρ : Δ, A
+    --   @
+
+  | Strengthen Impossible !Int (Substitution' a)
+    -- ^ Strengthening substitution.  First argument is @__IMPOSSIBLE__@.
+    --   In @'Strengthen err n ρ@ the number @n@ must be non-negative.
+    --   This substitution should only be applied to values @t@ for
+    --   which none of the variables @0@ up to @n - 1@ are free in
+    --   @t[ρ]@, and in that case @n@ is subtracted from all free de
+    --   Bruijn indices in @t[ρ]@.
+    --        Γ ⊢ ρ : Δ    |Θ| = n
+    --     ---------------------------
+    --     Γ ⊢ Strengthen n ρ : Δ, Θ
+    --   @
+
+  | Wk !Int (Substitution' a)
+    -- ^ Weakening substitution, lifts to an extended context.
+    --   @
+    --         Γ ⊢ ρ : Δ
+    --     -------------------
+    --     Γ, Ψ ⊢ Wk |Ψ| ρ : Δ
+    --   @
+
+
+  | Lift !Int (Substitution' a)
+    -- ^ Lifting substitution.  Use this to go under a binder.
+    --   @Lift 1 ρ == var 0 :# Wk 1 ρ@.
+    --   @
+    --            Γ ⊢ ρ : Δ
+    --     -------------------------
+    --     Γ, Ψρ ⊢ Lift |Ψ| ρ : Δ, Ψ
+    --   @
+
+  deriving ( Show
+           , Functor
+           , Foldable
+           , Traversable
+           , Generic
+           )
+
+type Substitution = Substitution' Term
+type PatternSubstitution = Substitution' DeBruijnPattern
+
+infixr 4 :#
+
+instance Null (Substitution' a) where
+  empty = IdS
+  null IdS = True
+  null _   = False
+
+
+---------------------------------------------------------------------------
+-- * Views
+---------------------------------------------------------------------------
+
+-- | View type as equality type.
+
+data EqualityView
+  = EqualityViewType EqualityTypeData
+  | OtherType Type -- ^ reduced
+  | IdiomType Type -- ^ reduced
+
+data EqualityTypeData = EqualityTypeData
+    { _eqtSort   :: Sort        -- ^ Sort of this type.
+    , _eqtName   :: QName       -- ^ Builtin EQUALITY.
+    , _eqtParams :: Args        -- ^ Hidden.  Empty or @Level@.
+    , _eqtType   :: Arg Term    -- ^ Hidden.
+    , _eqtLhs    :: Arg Term    -- ^ NotHidden.
+    , _eqtRhs    :: Arg Term    -- ^ NotHidden.
+    }
+
+pattern EqualityType
+  :: Sort
+  -> QName
+  -> Args
+  -> Arg Term
+  -> Arg Term
+  -> Arg Term
+  -> EqualityView
+pattern EqualityType{ eqtSort, eqtName, eqtParams, eqtType, eqtLhs, eqtRhs } =
+  EqualityViewType (EqualityTypeData eqtSort eqtName eqtParams eqtType eqtLhs eqtRhs)
+
+{-# COMPLETE EqualityType, OtherType, IdiomType #-}
+
+isEqualityType :: EqualityView -> Bool
+isEqualityType EqualityType{} = True
+isEqualityType OtherType{}    = False
+isEqualityType IdiomType{}    = False
+
+-- | View type as path type.
+
+data PathView
+  = PathType
+    { pathSort  :: Sort     -- ^ Sort of this type.
+    , pathName  :: QName    -- ^ Builtin PATH.
+    , pathLevel :: Arg Term -- ^ Hidden
+    , pathType  :: Arg Term -- ^ Hidden
+    , pathLhs   :: Arg Term -- ^ NotHidden
+    , pathRhs   :: Arg Term -- ^ NotHidden
+    }
+  | OType Type -- ^ reduced
+
+isPathType :: PathView -> Bool
+isPathType PathType{} = True
+isPathType OType{}    = False
+
+data IntervalView
+      = IZero
+      | IOne
+      | IMin (Arg Term) (Arg Term)
+      | IMax (Arg Term) (Arg Term)
+      | INeg (Arg Term)
+      | OTerm Term
+      deriving Show
+
+isIOne :: IntervalView -> Bool
+isIOne IOne = True
+isIOne _ = False
+
+---------------------------------------------------------------------------
+-- * Absurd Lambda
+---------------------------------------------------------------------------
+
+-- | Absurd lambdas are internally represented as identity
+--   with variable name "()".
+absurdBody :: Abs Term
+absurdBody = Abs absurdPatternName $ Var 0 []
+
+isAbsurdBody :: Abs Term -> Bool
+isAbsurdBody (Abs x (Var 0 [])) = isAbsurdPatternName x
+isAbsurdBody _                  = False
+
+absurdPatternName :: PatVarName
+absurdPatternName = "()"
+
+isAbsurdPatternName :: PatVarName -> Bool
+isAbsurdPatternName x = x == absurdPatternName
+
+---------------------------------------------------------------------------
+-- * Smart constructors
+---------------------------------------------------------------------------
+
+-- | An unapplied variable.
+var :: Nat -> Term
+var i | i >= 0    = Var i []
+      | otherwise = __IMPOSSIBLE__
+
+-- | Add 'DontCare' is it is not already a @DontCare@.
+dontCare :: Term -> Term
+dontCare v =
+  case v of
+    DontCare{} -> v
+    _          -> DontCare v
+
+type DummyTermKind = String
+
+-- | Construct a string representing the call-site that created the dummy thing.
+dummyLocName :: CallStack -> String
+dummyLocName cs = maybe __IMPOSSIBLE__ prettyCallSite (headCallSite cs)
+
+-- | Aux: A dummy term to constitute a dummy term/level/sort/type.
+dummyTermWith :: DummyTermKind -> CallStack -> Term
+dummyTermWith kind cs = flip Dummy [] $ concat [kind, ": ", dummyLocName cs]
+
+-- | A dummy level to constitute a level/sort created at location.
+--   Note: use macro __DUMMY_LEVEL__ !
+dummyLevel :: CallStack -> Level
+dummyLevel = atomicLevel . dummyTermWith "dummyLevel"
+
+-- | A dummy term created at location.
+--   Note: use macro __DUMMY_TERM__ !
+dummyTerm :: CallStack -> Term
+dummyTerm = dummyTermWith "dummyTerm"
+
+__DUMMY_TERM__ :: HasCallStack => Term
+__DUMMY_TERM__ = withCallerCallStack dummyTerm
+
+__DUMMY_LEVEL__ :: HasCallStack => Level
+__DUMMY_LEVEL__ = withCallerCallStack dummyLevel
+
+-- | A dummy sort created at location.
+--   Note: use macro __DUMMY_SORT__ !
+dummySort :: CallStack -> Sort
+dummySort = DummyS . dummyLocName
+
+__DUMMY_SORT__ :: HasCallStack => Sort
+__DUMMY_SORT__ = withCallerCallStack dummySort
+
+-- | A dummy type created at location.
+--   Note: use macro __DUMMY_TYPE__ !
+dummyType :: CallStack -> Type
+dummyType cs = El (dummySort cs) $ dummyTermWith "dummyType" cs
+
+__DUMMY_TYPE__ :: HasCallStack => Type
+__DUMMY_TYPE__ = withCallerCallStack dummyType
+
+-- | Context entries without a type have this dummy type.
+--   Note: use macro __DUMMY_DOM__ !
+dummyDom :: CallStack -> Dom Type
+dummyDom = defaultDom . dummyType
+
+__DUMMY_DOM__ :: HasCallStack => Dom Type
+__DUMMY_DOM__ = withCallerCallStack dummyDom
+
+-- | Constant level @n@
+pattern ClosedLevel :: Integer -> Level
+pattern ClosedLevel n = Max n []
+
+atomicLevel :: t -> Level' t
+atomicLevel a = Max 0 [ Plus 0 a ]
+
+varSort :: Int -> Sort
+varSort n = Type $ atomicLevel $ var n
+
+tmSort :: Term -> Sort
+tmSort t = Type $ atomicLevel t
+
+tmSSort :: Term -> Sort
+tmSSort t = SSet $ atomicLevel t
+
+-- | Given a constant @m@ and level @l@, compute @m + l@
+levelPlus :: Integer -> Level -> Level
+levelPlus m (Max n as) = Max (m + n) $ map pplus as
+  where pplus (Plus n l) = Plus (m + n) l
+
+levelSuc :: Level -> Level
+levelSuc = levelPlus 1
+
+mkType :: Integer -> Sort
+mkType n = Type $ ClosedLevel n
+
+mkProp :: Integer -> Sort
+mkProp n = Prop $ ClosedLevel n
+
+mkSSet :: Integer -> Sort
+mkSSet n = SSet $ ClosedLevel n
+
+isSort :: Term -> Maybe Sort
+isSort = \case
+  Sort s -> Just s
+  _      -> Nothing
+
+impossibleTerm :: CallStack -> Term
+impossibleTerm = flip Dummy [] . show . Impossible
+
+---------------------------------------------------------------------------
+-- * Telescopes.
+---------------------------------------------------------------------------
+
+-- | A traversal for the names in a telescope.
+mapAbsNamesM :: Applicative m => (ArgName -> m ArgName) -> Tele a -> m (Tele a)
+mapAbsNamesM f EmptyTel                  = pure EmptyTel
+mapAbsNamesM f (ExtendTel a (  Abs x b)) = ExtendTel a <$> (  Abs <$> f x <*> mapAbsNamesM f b)
+mapAbsNamesM f (ExtendTel a (NoAbs x b)) = ExtendTel a <$> (NoAbs <$> f x <*> mapAbsNamesM f b)
+  -- Ulf, 2013-11-06: Last case is really impossible but I'd rather find out we
+  --                  violated that invariant somewhere other than here.
+
+mapAbsNames :: (ArgName -> ArgName) -> Tele a -> Tele a
+mapAbsNames f = runIdentity . mapAbsNamesM (Identity . f)
+
+-- Ulf, 2013-11-06
+-- The record parameter is named "" inside the record module so we can avoid
+-- printing it (issue 208), but we don't want that to show up in the type of
+-- the functions in the module (issue 892). This function is used on the record
+-- module telescope before adding it to a type in
+-- TypeChecking.Monad.Signature.addConstant (to handle functions defined in
+-- record modules) and TypeChecking.Rules.Record.checkProjection (to handle
+-- record projections).
+replaceEmptyName :: ArgName -> Tele a -> Tele a
+replaceEmptyName x = mapAbsNames $ \ y -> if null y then x else y
+
+-- | Telescope as list.
+type ListTel' a = [Dom (a, Type)]
+type ListTel = ListTel' ArgName
+
+telFromList' :: (a -> ArgName) -> ListTel' a -> Telescope
+telFromList' f = List.foldr extTel EmptyTel
+  where
+    extTel dom@Dom{unDom = (x, a)} = ExtendTel (dom{unDom = a}) . Abs (f x)
+
+-- | Convert a list telescope to a telescope.
+telFromList :: ListTel -> Telescope
+telFromList = telFromList' id
+
+-- | Convert a telescope to its list form.
+telToList :: Tele (Dom t) -> [Dom (ArgName,t)]
+telToList EmptyTel                    = []
+telToList (ExtendTel arg (Abs x tel)) = fmap (x,) arg : telToList tel
+telToList (ExtendTel _    NoAbs{}   ) = __IMPOSSIBLE__
+
+-- | Lens to edit a 'Telescope' as a list.
+listTel :: Lens' Telescope ListTel
+listTel f = fmap telFromList . f . telToList
+
+-- | Drop the types from a telescope.
+class TelToArgs a where
+  telToArgs :: a -> [Arg ArgName]
+
+instance TelToArgs ListTel where
+  telToArgs = map $ \ dom -> Arg (domInfo dom) (fst $ unDom dom)
+
+instance TelToArgs Telescope where
+  telToArgs = telToArgs . telToList
+
+-- | Constructing a singleton telescope.
+class SgTel a where
+  sgTel :: a -> Telescope
+
+instance SgTel (ArgName, Dom Type) where
+  sgTel (x, !dom) = ExtendTel dom $ Abs x EmptyTel
+
+instance SgTel (Dom (ArgName, Type)) where
+  sgTel dom = ExtendTel (snd <$> dom) $ Abs (fst $ unDom dom) EmptyTel
+
+instance SgTel (Dom Type) where
+  sgTel dom = sgTel (stringToArgName "_", dom)
+
+---------------------------------------------------------------------------
+-- * Simple operations on terms and types.
+---------------------------------------------------------------------------
+
+-- | Removing a topmost 'DontCare' constructor.
+stripDontCare :: Term -> Term
+stripDontCare = \case
+  DontCare v -> v
+  v          -> v
+
+-- | Doesn't do any reduction.
+arity :: Type -> Nat
+arity t = case unEl t of
+  Pi  _ b -> 1 + arity (unAbs b)
+  _       -> 0
+
+-- | Suggest a name if available (i.e. name is not "_")
+class Suggest a where
+  suggestName :: a -> Maybe String
+
+instance Suggest String where
+  suggestName "_" = Nothing
+  suggestName  x  = Just x
+
+instance Suggest (Abs b) where
+  suggestName = suggestName . absName
+
+instance Suggest Name where
+  suggestName = suggestName . nameToArgName
+
+instance Suggest Term where
+  suggestName (Lam _ v) = suggestName v
+  suggestName _         = Nothing
+
+-- Wrapping @forall a. (Suggest a) => a@ into a datatype because
+-- GHC doesn't support impredicative polymorphism
+data Suggestion = forall a. Suggest a => Suggestion a
+
+suggests :: [Suggestion] -> String
+suggests []     = "x"
+suggests (Suggestion x : xs) = fromMaybe (suggests xs) $ suggestName x
+
+---------------------------------------------------------------------------
+-- * Eliminations.
+---------------------------------------------------------------------------
+
+-- | Convert top-level postfix projections into prefix projections.
+unSpine :: Term -> Term
+unSpine = unSpine' $ const True
+
+-- | Convert 'Proj' projection eliminations
+--   according to their 'ProjOrigin' into
+--   'Def' projection applications.
+unSpine' :: (ProjOrigin -> Bool) -> Term -> Term
+unSpine' p v =
+  case hasElims v of
+    Just (h, es) -> loop h [] es
+    Nothing      -> v
+  where
+    loop :: (Elims -> Term) -> Elims -> Elims -> Term
+    loop h res es =
+      case es of
+        []                   -> v
+        Proj o f : es' | p o -> loop (Def f) [Apply (defaultArg v)] es'
+        e        : es'       -> loop h (e : res) es'
+      where v = h $ reverse res
+
+-- | A view distinguishing the neutrals @Var@, @Def@, and @MetaV@ which
+--   can be projected.
+hasElims :: Term -> Maybe (Elims -> Term, Elims)
+hasElims v =
+  case v of
+    Var   i es -> Just (Var   i, es)
+    Def   f es -> Just (Def   f, es)
+    MetaV x es -> Just (MetaV x, es)
+    Con{}      -> Nothing
+    Lit{}      -> Nothing
+    Lam{}      -> Nothing
+    Pi{}       -> Nothing
+    Sort{}     -> Nothing
+    Level{}    -> Nothing
+    DontCare{} -> Nothing
+    Dummy{}    -> Nothing
+
+---------------------------------------------------------------------------
+-- * Type family for type-directed operations.
+---------------------------------------------------------------------------
+
+-- @TypeOf a@ contains sufficient type information to do
+-- a type-directed traversal of @a@.
+type family TypeOf a
+
+type instance TypeOf Term        = Type                  -- Type of the term
+type instance TypeOf Elims       = (Type, Elims -> Term) -- Head symbol type + constructor
+type instance TypeOf (Abs Term)  = (Dom Type, Abs Type)  -- Domain type + codomain type
+type instance TypeOf (Abs Type)  = Dom Type              -- Domain type
+type instance TypeOf (Arg a)     = Dom (TypeOf a)
+type instance TypeOf (Dom a)     = TypeOf a
+type instance TypeOf Type        = ()
+type instance TypeOf Sort        = ()
+type instance TypeOf Level       = ()
+type instance TypeOf [PlusLevel] = ()
+type instance TypeOf PlusLevel   = ()
+
+---------------------------------------------------------------------------
+-- * Null instances.
+---------------------------------------------------------------------------
+
+instance Null (Tele a) where
+  empty = EmptyTel
+  null EmptyTel    = True
+  null ExtendTel{} = False
+
+-- | A 'null' clause is one with no patterns and no rhs.
+--   Should not exist in practice.
+instance Null Clause where
+  empty = Clause empty empty empty empty empty empty False Nothing Nothing Nothing empty empty
+  null (Clause _ _ tel pats body _ _ _ _ _ _ wm)
+    =  null tel
+    && null pats
+    && null body
+    && null wm
+
+
+---------------------------------------------------------------------------
+-- * Show instances.
+---------------------------------------------------------------------------
+
+instance Show a => Show (Abs a) where
+  showsPrec p (Abs x a) = showParen (p > 0) $
+    showString "Abs " . shows x . showString " " . showsPrec 10 a
+  showsPrec p (NoAbs x a) = showParen (p > 0) $
+    showString "NoAbs " . shows x . showString " " . showsPrec 10 a
+
+-- instance Show t => Show (Blocked t) where
+--   showsPrec p (Blocked m x) = showParen (p > 0) $
+--     showString "Blocked " . shows m . showString " " . showsPrec 10 x
+--   showsPrec p (NotBlocked x) = showsPrec p x
+
+---------------------------------------------------------------------------
+-- * Sized instances and TermSize.
+---------------------------------------------------------------------------
+
+-- | The size of a telescope is its length (as a list).
+instance Sized (Tele a) where
+  size  EmptyTel         = 0
+  size (ExtendTel _ tel) = 1 + size tel
+
+  natSize EmptyTel          = Zero
+  natSize (ExtendTel _ tel) = Succ $ natSize tel
+
+instance Sized a => Sized (Abs a) where
+  size    = size    . unAbs
+  natSize = natSize . unAbs
+
+-- | The size of a term is roughly the number of nodes in its
+--   syntax tree.  This number need not be precise for logical
+--   correctness of Agda, it is only used for reporting
+--   (and maybe decisions regarding performance).
+--
+--   Not counting towards the term size are:
+--
+--     * sort and color annotations,
+--     * projections.
+--
+class TermSize a where
+  termSize :: a -> Int
+  termSize = getSum . tsize
+
+  tsize :: a -> Sum Int
+
+instance {-# OVERLAPPABLE #-} (Foldable t, TermSize a) => TermSize (t a) where
+  tsize = foldMap tsize
+
+instance TermSize Term where
+  tsize = \case
+    Var _ vs    -> 1 + tsize vs
+    Def _ vs    -> 1 + tsize vs
+    Con _ _ vs    -> 1 + tsize vs
+    MetaV _ vs  -> 1 + tsize vs
+    Level l     -> tsize l
+    Lam _ f     -> 1 + tsize f
+    Lit _       -> 1
+    Pi a b      -> 1 + tsize a + tsize b
+    Sort s      -> tsize s
+    DontCare mv -> tsize mv
+    Dummy{}     -> 1
+
+instance TermSize Sort where
+  tsize = \case
+    Univ _ l  -> 1 + tsize l
+    Inf _ _   -> 1
+    SizeUniv  -> 1
+    LockUniv  -> 1
+    LevelUniv -> 1
+    IntervalUniv -> 1
+    PiSort a s1 s2 -> 1 + tsize a + tsize s1 + tsize s2
+    FunSort s1 s2 -> 1 + tsize s1 + tsize s2
+    UnivSort s -> 1 + tsize s
+    MetaS _ es -> 1 + tsize es
+    DefS _ es  -> 1 + tsize es
+    DummyS{}   -> 1
+
+instance TermSize Level where
+  tsize (Max _ as) = 1 + tsize as
+
+instance TermSize PlusLevel where
+  tsize (Plus _ a)      = tsize a
+
+instance TermSize a => TermSize (Substitution' a) where
+  tsize IdS                  = 1
+  tsize (EmptyS _)           = 1
+  tsize (Wk _ rho)           = 1 + tsize rho
+  tsize (t :# rho)           = 1 + tsize t + tsize rho
+  tsize (Strengthen _ _ rho) = 1 + tsize rho
+  tsize (Lift _ rho)         = 1 + tsize rho
+
+---------------------------------------------------------------------------
+-- * KillRange instances.
+---------------------------------------------------------------------------
+
+instance KillRange DataOrRecord where
+  killRange = id
+
+instance KillRange ConHead where
+  killRange (ConHead c d i fs) = killRangeN ConHead c d i fs
+
+instance KillRange Term where
+  killRange = \case
+    Var i vs    -> killRangeN (Var i) vs
+    Def c vs    -> killRangeN Def c vs
+    Con c ci vs -> killRangeN Con c ci vs
+    MetaV m vs  -> killRangeN (MetaV m) vs
+    Lam i f     -> killRangeN Lam i f
+    Lit l       -> killRangeN Lit l
+    Level l     -> killRangeN Level l
+    Pi a b      -> killRangeN Pi a b
+    Sort s      -> killRangeN Sort s
+    DontCare mv -> killRangeN DontCare mv
+    v@Dummy{}   -> v
+
+instance KillRange Level where
+  killRange (Max n as) = killRangeN (Max n) as
+
+instance KillRange PlusLevel where
+  killRange (Plus n l) = killRangeN (Plus n) l
+
+instance (KillRange a) => KillRange (Type' a) where
+  killRange (El s v) = killRangeN El s v
+
+instance KillRange Sort where
+  killRange = \case
+    Inf u n    -> Inf u n
+    SizeUniv   -> SizeUniv
+    LockUniv   -> LockUniv
+    LevelUniv  -> LevelUniv
+    IntervalUniv -> IntervalUniv
+    Univ u a   -> killRangeN (Univ u) a
+    PiSort a s1 s2 -> killRangeN PiSort a s1 s2
+    FunSort s1 s2 -> killRangeN FunSort s1 s2
+    UnivSort s -> killRangeN UnivSort s
+    MetaS x es -> killRangeN (MetaS x) es
+    DefS d es  -> killRangeN DefS d es
+    s@DummyS{} -> s
+
+instance KillRange Substitution where
+  killRange IdS                    = IdS
+  killRange (EmptyS err)           = EmptyS err
+  killRange (Wk n rho)             = killRangeN (Wk n) rho
+  killRange (t :# rho)             = killRangeN (:#) t rho
+  killRange (Strengthen err n rho) = killRangeN (Strengthen err n) rho
+  killRange (Lift n rho)           = killRangeN (Lift n) rho
+
+instance KillRange PatOrigin where
+  killRange = id
+
+instance KillRange PatternInfo where
+  killRange (PatternInfo o xs) = killRangeN PatternInfo o xs
+
+instance KillRange ConPatternInfo where
+  killRange (ConPatternInfo i mr b mt lz) = killRangeN (ConPatternInfo i mr b) mt lz
+
+instance KillRange DBPatVar where
+  killRange (DBPatVar x i) = killRangeN DBPatVar x i
+
+instance KillRange a => KillRange (Pattern' a) where
+  killRange p =
+    case p of
+      VarP o x         -> killRangeN VarP o x
+      DotP o v         -> killRangeN DotP o v
+      ConP con info ps -> killRangeN ConP con info ps
+      LitP o l         -> killRangeN LitP o l
+      ProjP o q        -> killRangeN (ProjP o) q
+      IApplyP o u t x  -> killRangeN (IApplyP o) u t x
+      DefP o q ps      -> killRangeN (DefP o) q ps
+
+instance KillRange Clause where
+  killRange (Clause rl rf tel ps body t catchall exact recursive unreachable ell wm) =
+    killRangeN Clause rl rf tel ps body t catchall exact recursive unreachable ell wm
+
+instance KillRange a => KillRange (Tele a) where
+  killRange = fmap killRange
+
+instance KillRange a => KillRange (Blocked a) where
+  killRange = fmap killRange
+
+instance KillRange a => KillRange (Abs a) where
+  killRange = fmap killRange
+
+-----------------------------------------------------------------------------
+-- * Simple pretty printing
+-----------------------------------------------------------------------------
+
+instance Pretty a => Pretty (Substitution' a) where
+  prettyPrec = pr
+    where
+    pr p rho = case rho of
+      IdS                -> "idS"
+      EmptyS err         -> "emptyS"
+      t :# rho           -> mparens (p > 2) $
+                            sep [ pr 2 rho <> ",", prettyPrec 3 t ]
+      Strengthen _ n rho -> mparens (p > 9) $
+                            text ("strS " ++ show n) <+> pr 10 rho
+      Wk n rho           -> mparens (p > 9) $
+                            text ("wkS " ++ show n) <+> pr 10 rho
+      Lift n rho         -> mparens (p > 9) $
+                            text ("liftS " ++ show n) <+> pr 10 rho
+
+instance Pretty Term where
+  prettyPrec p v =
+    case v of
+      Var x els -> text ("@" ++ show x) `pApp` els
+      Lam ai b   ->
+        mparens (p > 0) $
+        sep [ "λ" <+> prettyHiding ai id (text . absName $ b) <+> "->"
+            , nest 2 $ pretty (unAbs b) ]
+      Lit l                -> pretty l
+      Def q els            -> pretty q `pApp` els
+      Con c ci vs          -> pretty (conName c) `pApp` vs
+      Pi a (NoAbs _ b)     -> mparens (p > 0) $
+        sep [ prettyPrec 1 (unDom a) <+> "->"
+            , nest 2 $ pretty b ]
+      Pi a b               -> mparens (p > 0) $
+        sep [ pDom (domInfo a) (text (absName b) <+> ":" <+> pretty (unDom a)) <+> "->"
+            , nest 2 $ pretty (unAbs b) ]
+      Sort s      -> prettyPrec p s
+      Level l     -> prettyPrec p l
+      MetaV x els -> pretty x `pApp` els
+      DontCare v  -> prettyPrec p v
+      Dummy s es  -> parens (text s) `pApp` es
+    where
+      pApp d els = mparens (not (null els) && p > 9) $
+                   sep [d, nest 2 $ fsep (map (prettyPrec 10) els)]
+
+instance Pretty t => Pretty (Abs t) where
+  pretty (Abs   x t) = "Abs"   <+> (text x <> ".") <+> pretty t
+  pretty (NoAbs x t) = "NoAbs" <+> (text x <> ".") <+> pretty t
+
+instance (Pretty t, Pretty e) => Pretty (Dom' t e) where
+  pretty dom = pLock <+> pTac <+> pDom dom (pretty $ unDom dom)
+    where
+      pTac | Just t <- domTactic dom = "@" <> parens ("tactic" <+> pretty t)
+           | otherwise               = empty
+      pLock | IsLock{} <- getLock dom = "@lock"
+            | otherwise = empty
+
+pDom :: LensHiding a => a -> Doc -> Doc
+pDom i =
+  case getHiding i of
+    NotHidden  -> parens
+    Hidden     -> braces
+    Instance{} -> braces . braces
+
+instance Pretty Clause where
+  pretty Clause{clauseTel = tel, namedClausePats = ps, clauseBody = b, clauseType = t} =
+    sep [ pretty tel <+> "|-"
+        , nest 2 $ sep [ fsep (map (prettyPrec 10) ps) <+> "="
+                       , nest 2 $ pBody b t ] ]
+    where
+      pBody Nothing _ = "(absurd)"
+      pBody (Just b) Nothing  = pretty b
+      pBody (Just b) (Just t) = sep [ pretty b <+> ":", nest 2 $ pretty t ]
+
+instance Pretty a => Pretty (Tele (Dom a)) where
+  pretty tel = fsep [ pDom a (text x <+> ":" <+> pretty (unDom a)) | (x, a) <- telToList tel ]
+    where
+      telToList EmptyTel = []
+      telToList (ExtendTel a tel) = (absName tel, a) : telToList (unAbs tel)
+
+prettyPrecLevelSucs :: Int -> Integer -> (Int -> Doc) -> Doc
+prettyPrecLevelSucs p 0 d = d p
+prettyPrecLevelSucs p n d = mparens (p > 9) $ "lsuc" <+> prettyPrecLevelSucs 10 (n - 1) d
+
+instance Pretty Level where
+  prettyPrec p (Max n as) =
+    case as of
+      []  -> prettyN
+      [a] | n == 0 -> prettyPrec p a
+      _   -> mparens (p > 9) $ List.foldr1 (\a b -> "lub" <+> a <+> b) $
+        [ prettyN | n > 0 ] ++ map (prettyPrec 10) as
+    where
+      prettyN = prettyPrecLevelSucs p n (const "lzero")
+
+instance Pretty PlusLevel where
+  prettyPrec p (Plus n a) = prettyPrecLevelSucs p n $ \p -> prettyPrec p a
+
+instance Pretty Sort where
+  prettyPrec p s =
+    case s of
+      Univ u (ClosedLevel n) -> text $ suffix n $ showUniv u
+      Univ u l -> mparens (p > 9) $ text (showUniv u) <+> prettyPrec 10 l
+      Inf u n -> text $ suffix n $ showUniv u ++ "ω"
+      SizeUniv -> "SizeUniv"
+      LockUniv -> "LockUniv"
+      LevelUniv -> "LevelUniv"
+      IntervalUniv -> "IntervalUniv"
+      PiSort a s1 s2 -> mparens (p > 9) $
+        "piSort" <+> pDom (domInfo a) (text (absName s2) <+> ":" <+> pretty (unDom a) <+> ":" <+> pretty s1)
+                      <+> parens (pretty (unAbs s2))
+      FunSort a b -> mparens (p > 9) $
+        "funSort" <+> prettyPrec 10 a <+> prettyPrec 10 b
+      UnivSort s -> mparens (p > 9) $ "univSort" <+> prettyPrec 10 s
+      MetaS x es -> prettyPrec p $ MetaV x es
+      DefS d es  -> prettyPrec p $ Def d es
+      DummyS s   -> parens $ text s
+   where
+     suffix n = applyWhen (n /= 0) (++ show n)
+
+instance Pretty Type where
+  prettyPrec p (El _ a) = prettyPrec p a
+
+instance Pretty DBPatVar where
+  prettyPrec _ x = text $ patVarNameToString (dbPatVarName x) ++ "@" ++ show (dbPatVarIndex x)
+
+instance Pretty a => Pretty (Pattern' a) where
+  prettyPrec n (VarP _o x)   = prettyPrec n x
+  prettyPrec _ (DotP _o t)   = "." <> prettyPrec 10 t
+  prettyPrec n (ConP c i nps)= mparens (n > 0 && not (null nps)) $
+    (lazy <> pretty (conName c)) <+> fsep (map (prettyPrec 10) ps)
+    where ps = map (fmap namedThing) nps
+          lazy | conPLazy i = "~"
+               | otherwise  = empty
+  prettyPrec n (DefP o q nps)= mparens (n > 0 && not (null nps)) $
+    pretty q <+> fsep (map (prettyPrec 10) ps)
+    where ps = map (fmap namedThing) nps
+  -- -- Version with printing record type:
+  -- prettyPrec _ (ConP c i ps) = (if b then braces else parens) $ prTy $
+  --   text (show $ conName c) <+> fsep (map (pretty . namedArg) ps)
+  --   where
+  --     b = maybe False (== ConOSystem) $ conPRecord i
+  --     prTy d = caseMaybe (conPType i) d $ \ t -> d  <+> ":" <+> pretty t
+  prettyPrec _ (LitP _ l)    = pretty l
+  prettyPrec _ (ProjP _o q)  = text ("." ++ prettyShow q)
+  prettyPrec n (IApplyP _o _ _ x) = prettyPrec n x
+--  prettyPrec n (IApplyP _o u0 u1 x) = text "@[" <> prettyPrec 0 u0 <> text ", " <> prettyPrec 0 u1 <> text "]" <> prettyPrec n x
+
+instance Pretty a => Pretty (Blocked a) where
+  pretty = \case
+    NotBlocked ReallyNotBlocked a -> pretty a
+    NotBlocked nb a -> pretty a <+> ("[ blocked on" <+> pretty nb <+> "]")
+    Blocked     b a -> pretty a <+> ("[ stuck on" <+> pretty  b <+> "]")
+
+-----------------------------------------------------------------------------
+-- * NFData instances
+-----------------------------------------------------------------------------
+
+-- Note: only strict in the shape of the terms.
+
+instance NFData Term where
+  rnf = \case
+    Var _ es   -> rnf es
+    Lam _ b    -> rnf (unAbs b)
+    Lit l      -> rnf l
+    Def _ es   -> rnf es
+    Con _ _ vs -> rnf vs
+    Pi a b     -> rnf (unDom a, unAbs b)
+    Sort s     -> rnf s
+    Level l    -> rnf l
+    MetaV _ es -> rnf es
+    DontCare v -> rnf v
+    Dummy _ es -> rnf es
+
+instance NFData Type where
+  rnf (El s v) = rnf (s, v)
+
+instance NFData Sort where
+  rnf = \case
+    Univ _ l   -> rnf l
+    Inf _ _  -> ()
+    SizeUniv -> ()
+    LockUniv -> ()
+    LevelUniv -> ()
+    IntervalUniv -> ()
+    PiSort a b c -> rnf (a, b, unAbs c)
+    FunSort a b -> rnf (a, b)
+    UnivSort a -> rnf a
+    MetaS _ es -> rnf es
+    DefS _ es  -> rnf es
+    DummyS _   -> ()
+
+instance NFData Level where
+  rnf (Max n as) = rnf (n, as)
+
+instance NFData PlusLevel where
+  rnf (Plus n l) = rnf (n, l)
+
+instance NFData e => NFData (Dom e) where
+  rnf (Dom a c d e f) = rnf a `seq` rnf c `seq` rnf d `seq` rnf e `seq` rnf f
+
+instance NFData DataOrRecord
+instance NFData ConHead
+instance NFData a => NFData (Abs a)
+instance NFData a => NFData (Tele a)
+instance NFData IsFibrant
+instance NFData Clause
+instance NFData PatternInfo
+instance NFData PatOrigin
+instance NFData x => NFData (Pattern' x)
+instance NFData DBPatVar
+instance NFData ConPatternInfo
+instance NFData a => NFData (Substitution' a)
diff --git a/src/full/Agda/Syntax/Internal/Blockers.hs b/src/full/Agda/Syntax/Internal/Blockers.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Blockers.hs
@@ -0,0 +1,319 @@
+
+module Agda.Syntax.Internal.Blockers where
+
+import Control.DeepSeq
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Semigroup
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract.Name (QName)
+import Agda.Syntax.Internal.Elim
+
+import Agda.Syntax.Common.Pretty hiding ((<>))
+import Agda.Utils.Functor
+
+---------------------------------------------------------------------------
+-- * Blocked Terms
+---------------------------------------------------------------------------
+
+-- | Even if we are not stuck on a meta during reduction
+--   we can fail to reduce a definition by pattern matching
+--   for another reason.
+data NotBlocked' t
+  = StuckOn (Elim' t)
+    -- ^ The 'Elim' is neutral and blocks a pattern match.
+  | Underapplied
+    -- ^ Not enough arguments were supplied to complete the matching.
+  | AbsurdMatch
+    -- ^ We matched an absurd clause, results in a neutral 'Def'.
+  | MissingClauses QName
+    -- ^ We ran out of clauses for 'QName', all considered clauses
+    --   produced an actual mismatch.
+    --   This can happen when try to reduce a function application
+    --   but we are still missing some function clauses.
+    --   See "Agda.TypeChecking.Patterns.Match".
+  | ReallyNotBlocked
+    -- ^ Reduction was not blocked, we reached a whnf
+    --   which can be anything but a stuck @'Def'@.
+  deriving (Show, Generic)
+
+-- | 'ReallyNotBlocked' is the unit.
+--   'MissingClauses' is dominant.
+--   @'StuckOn'{}@ should be propagated, if tied, we take the left.
+instance Semigroup (NotBlocked' t) where
+  ReallyNotBlocked <> b = b
+  -- MissingClauses is dominant (absorptive)
+  b@MissingClauses{} <> _ = b
+  _ <> b@MissingClauses{} = b
+  -- StuckOn is second strongest
+  b@StuckOn{}      <> _ = b
+  _ <> b@StuckOn{}      = b
+  b <> _                = b
+
+instance Monoid (NotBlocked' t) where
+  -- ReallyNotBlocked is neutral
+  mempty  = ReallyNotBlocked
+  mappend = (<>)
+
+instance NFData t => NFData (NotBlocked' t)
+
+instance Pretty t => Pretty (NotBlocked' t) where
+  pretty = \case
+    StuckOn e        -> "elimination" <+> pretty e
+    Underapplied     -> "missing elimination (underapplied)"
+    AbsurdMatch      -> "absurd match"
+    MissingClauses x -> "missing clause for" <+> pretty x
+    ReallyNotBlocked -> "(not stuck)"
+
+-- | What is causing the blocking? Or in other words which metas or problems need to be solved to
+--   unblock the blocked computation/constraint.
+data Blocker = UnblockOnAll (Set Blocker)
+             | UnblockOnAny (Set Blocker)
+             | UnblockOnMeta MetaId     -- ^ Unblock if meta is instantiated
+             | UnblockOnProblem ProblemId
+             | UnblockOnDef QName       -- ^ Unblock when function is defined
+  deriving (Show, Eq, Ord, Generic)
+
+instance NFData Blocker
+
+alwaysUnblock :: Blocker
+alwaysUnblock = UnblockOnAll Set.empty
+
+neverUnblock :: Blocker
+neverUnblock = UnblockOnAny Set.empty
+
+unblockOnAll :: Set Blocker -> Blocker
+unblockOnAll us =
+  case allViewS us of
+    us | [u] <- Set.toList us -> u
+    us                        -> UnblockOnAll us
+  where
+    allViewS = Set.unions . map allView . Set.toList
+    allView (UnblockOnAll us) = allViewS us
+    allView u                 = Set.singleton u
+
+unblockOnAny :: Set Blocker -> Blocker
+unblockOnAny us =
+  case anyViewS us of
+    us | [u] <- Set.toList us        -> u
+    us | Set.member alwaysUnblock us -> alwaysUnblock
+       | otherwise                   -> UnblockOnAny us
+  where
+    anyViewS = Set.unions . map anyView . Set.toList
+    anyView (UnblockOnAny us) = anyViewS us
+    anyView u                 = Set.singleton u
+
+unblockOnEither :: Blocker -> Blocker -> Blocker
+unblockOnEither a b = unblockOnAny $ Set.fromList [a, b]
+
+unblockOnBoth :: Blocker -> Blocker -> Blocker
+unblockOnBoth a b = unblockOnAll $ Set.fromList [a, b]
+
+unblockOnMeta :: MetaId -> Blocker
+unblockOnMeta = UnblockOnMeta
+
+unblockOnProblem :: ProblemId -> Blocker
+unblockOnProblem = UnblockOnProblem
+
+unblockOnDef :: QName -> Blocker
+unblockOnDef = UnblockOnDef
+
+unblockOnAllMetas :: Set MetaId -> Blocker
+unblockOnAllMetas = unblockOnAll . Set.mapMonotonic unblockOnMeta
+
+unblockOnAnyMeta :: Set MetaId -> Blocker
+unblockOnAnyMeta = unblockOnAny . Set.mapMonotonic unblockOnMeta
+
+onBlockingMetasM :: Monad m => (MetaId -> m Blocker) -> Blocker -> m Blocker
+onBlockingMetasM f (UnblockOnAll bs)    = unblockOnAll . Set.fromList <$> mapM (onBlockingMetasM f) (Set.toList bs)
+onBlockingMetasM f (UnblockOnAny bs)    = unblockOnAny . Set.fromList <$> mapM (onBlockingMetasM f) (Set.toList bs)
+onBlockingMetasM f (UnblockOnMeta x)    = f x
+onBlockingMetasM f b@UnblockOnProblem{} = pure b
+onBlockingMetasM f b@UnblockOnDef{}     = pure b
+
+allBlockingMetas :: Blocker -> Set MetaId
+allBlockingMetas (UnblockOnAll us)  = Set.unions $ map allBlockingMetas $ Set.toList us
+allBlockingMetas (UnblockOnAny us)  = Set.unions $ map allBlockingMetas $ Set.toList us
+allBlockingMetas (UnblockOnMeta x)  = Set.singleton x
+allBlockingMetas UnblockOnProblem{} = Set.empty
+allBlockingMetas UnblockOnDef{}     = Set.empty
+
+allBlockingProblems :: Blocker -> Set ProblemId
+allBlockingProblems (UnblockOnAll us)    = Set.unions $ map allBlockingProblems $ Set.toList us
+allBlockingProblems (UnblockOnAny us)    = Set.unions $ map allBlockingProblems $ Set.toList us
+allBlockingProblems UnblockOnMeta{}      = Set.empty
+allBlockingProblems (UnblockOnProblem p) = Set.singleton p
+allBlockingProblems UnblockOnDef{}       = Set.empty
+
+allBlockingDefs :: Blocker -> Set QName
+allBlockingDefs (UnblockOnAll us)  = Set.unions $ map allBlockingDefs $ Set.toList us
+allBlockingDefs (UnblockOnAny us)  = Set.unions $ map allBlockingDefs $ Set.toList us
+allBlockingDefs UnblockOnMeta{}    = Set.empty
+allBlockingDefs UnblockOnProblem{} = Set.empty
+allBlockingDefs (UnblockOnDef q)   = Set.singleton q
+
+{- There are two possible instances of Semigroup, so we don't commit
+   to either one.
+instance Semigroup Blocker where
+  x <> y = unblockOnAll $ Set.fromList [x, y]
+
+instance Monoid Blocker where
+  mempty = alwaysUnblock
+  mappend = (<>)
+-}
+
+instance Pretty Blocker where
+  pretty (UnblockOnAll us)      = "all" <> parens (fsep $ punctuate "," $ map pretty $ Set.toList us)
+  pretty (UnblockOnAny us)      = "any" <> parens (fsep $ punctuate "," $ map pretty $ Set.toList us)
+  pretty (UnblockOnMeta m)      = pretty m
+  pretty (UnblockOnProblem pid) = "problem" <+> pretty pid
+  pretty (UnblockOnDef q)       = "definition" <+> pretty q
+
+-- | Something where a meta variable may block reduction. Notably a top-level meta is considered
+--   blocking. This did not use to be the case (pre Aug 2020).
+data Blocked' t a
+  = Blocked    { theBlocker      :: Blocker,       ignoreBlocking :: a }
+  | NotBlocked { blockingStatus  :: NotBlocked' t, ignoreBlocking :: a }
+  deriving (Show, Functor, Foldable, Traversable, Generic)
+
+instance Decoration (Blocked' t) where
+  traverseF f (Blocked b x)     = Blocked b <$> f x
+  traverseF f (NotBlocked nb x) = NotBlocked nb <$> f x
+
+-- | Blocking on _all_ blockers.
+instance Applicative (Blocked' t) where
+  pure = notBlocked
+  f <*> e = ((f $> ()) `mappend` (e $> ())) $> ignoreBlocking f (ignoreBlocking e)
+
+instance Semigroup a => Semigroup (Blocked' t a) where
+  Blocked x a    <> Blocked y b    = Blocked (unblockOnBoth x y) (a <> b)
+  b@Blocked{}    <> NotBlocked{}   = b
+  NotBlocked{}   <> b@Blocked{}    = b
+  NotBlocked x a <> NotBlocked y b = NotBlocked (x <> y) (a <> b)
+
+instance (Semigroup a, Monoid a) => Monoid (Blocked' t a) where
+  mempty = notBlocked mempty
+  mappend = (<>)
+
+instance (NFData t, NFData a) => NFData (Blocked' t a)
+
+-- | When trying to reduce @f es@, on match failed on one
+--   elimination @e ∈ es@ that came with info @r :: NotBlocked@.
+--   @stuckOn e r@ produces the new @NotBlocked@ info.
+--
+--   'MissingClauses' must be propagated, as this is blockage
+--   that can be lifted in the future (as more clauses are added).
+--
+--   @'StuckOn' e0@ is also propagated, since it provides more
+--   precise information as @StuckOn e@ (as @e0@ is the original
+--   reason why reduction got stuck and usually a subterm of @e@).
+--   An information like @StuckOn (Apply (Arg info (Var i [])))@
+--   (stuck on a variable) could be used by the lhs/coverage checker
+--   to trigger a split on that (pattern) variable.
+--
+--   In the remaining cases for @r@, we are terminally stuck
+--   due to @StuckOn e@.  Propagating @'AbsurdMatch'@ does not
+--   seem useful.
+--
+--   'Underapplied' must not be propagated, as this would mean
+--   that @f es@ is underapplied, which is not the case (it is stuck).
+--   Note that 'Underapplied' can only arise when projection patterns were
+--   missing to complete the original match (in @e@).
+--   (Missing ordinary pattern would mean the @e@ is of function type,
+--   but we cannot match against something of function type.)
+stuckOn :: Elim' t -> NotBlocked' t -> NotBlocked' t
+stuckOn e = \case
+    r@MissingClauses{} -> r
+    r@StuckOn{}        -> r
+    Underapplied     -> r'
+    AbsurdMatch      -> r'
+    ReallyNotBlocked -> r'
+  where r' = StuckOn e
+
+---------------------------------------------------------------------------
+-- * Handling blocked terms.
+---------------------------------------------------------------------------
+
+blockedOn :: Blocker -> a -> Blocked' t a
+blockedOn b | alwaysUnblock == b = notBlocked
+            | otherwise          = Blocked b
+
+blocked :: MetaId -> a -> Blocked' t a
+blocked = Blocked . unblockOnMeta
+
+notBlocked :: a -> Blocked' t a
+notBlocked = NotBlocked ReallyNotBlocked
+
+blocked_ :: MetaId -> Blocked' t ()
+blocked_ x = blocked x ()
+
+notBlocked_ :: Blocked' t ()
+notBlocked_ = notBlocked ()
+
+getBlocker :: Blocked' t a -> Blocker
+getBlocker (Blocked b _) = b
+getBlocker NotBlocked{}  = neverUnblock
+
+-----------------------------------------------------------------------------
+-- * Waking up logic
+-----------------------------------------------------------------------------
+
+-- | Should a constraint wake up or not? If not, we might refine the unblocker.
+data WakeUp = WakeUp | DontWakeUp (Maybe Blocker)
+  deriving (Show, Eq)
+
+wakeUpWhen :: (constr -> Bool) -> (constr -> WakeUp) -> constr -> WakeUp
+wakeUpWhen guard wake c | guard c   = wake c
+                        | otherwise = DontWakeUp Nothing
+
+wakeUpWhen_ :: (constr -> Bool) -> constr -> WakeUp
+wakeUpWhen_ p = wakeUpWhen p (const WakeUp)
+
+wakeIfBlockedOnProblem :: ProblemId -> Blocker -> WakeUp
+wakeIfBlockedOnProblem pid u
+  | u' == alwaysUnblock = WakeUp
+  | otherwise           = DontWakeUp (Just u')
+  where
+    u' = unblockProblem pid u
+
+wakeIfBlockedOnMeta :: MetaId -> Blocker -> WakeUp
+wakeIfBlockedOnMeta x u
+  | u' == alwaysUnblock = WakeUp
+  | otherwise           = DontWakeUp (Just u')
+  where
+    u' = unblockMeta x u
+
+wakeIfBlockedOnDef :: QName -> Blocker -> WakeUp
+wakeIfBlockedOnDef q u
+  | u' == alwaysUnblock = WakeUp
+  | otherwise           = DontWakeUp (Just u')
+  where
+    u' = unblockDef q u
+
+unblockMeta :: MetaId -> Blocker -> Blocker
+unblockMeta x u@(UnblockOnMeta y) | x == y    = alwaysUnblock
+                                  | otherwise = u
+unblockMeta _ u@UnblockOnProblem{} = u
+unblockMeta _ u@UnblockOnDef{}     = u
+unblockMeta x (UnblockOnAll us)    = unblockOnAll $ Set.map (unblockMeta x) us
+unblockMeta x (UnblockOnAny us)    = unblockOnAny $ Set.map (unblockMeta x) us
+
+unblockProblem :: ProblemId -> Blocker -> Blocker
+unblockProblem p u@(UnblockOnProblem q) | p == q    = alwaysUnblock
+                                        | otherwise = u
+unblockProblem _ u@UnblockOnMeta{} = u
+unblockProblem _ u@UnblockOnDef{}  = u
+unblockProblem p (UnblockOnAll us) = unblockOnAll $ Set.map (unblockProblem p) us
+unblockProblem p (UnblockOnAny us) = unblockOnAny $ Set.map (unblockProblem p) us
+
+unblockDef :: QName -> Blocker -> Blocker
+unblockDef q u@(UnblockOnDef q') | q == q'   = alwaysUnblock
+                                 | otherwise = u
+unblockDef q u@UnblockOnMeta{} = u
+unblockDef q u@UnblockOnProblem{} = u
+unblockDef q (UnblockOnAll us) = unblockOnAll $ Set.map (unblockDef q) us
+unblockDef q (UnblockOnAny us) = unblockOnAny $ Set.map (unblockDef q) us
diff --git a/src/full/Agda/Syntax/Internal/Defs.hs b/src/full/Agda/Syntax/Internal/Defs.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Defs.hs
@@ -0,0 +1,116 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Extract used definitions from terms.
+
+module Agda.Syntax.Internal.Defs where
+
+import Control.Monad.Reader
+import Control.Monad.Writer
+
+import qualified Data.Foldable as Fold
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+-- | @getDefs' lookup emb a@ extracts all used definitions
+--   (functions, data/record types) from @a@, embedded into a monoid via @emb@.
+--   Instantiations of meta variables are obtained via @lookup@.
+--
+--   Typical monoid instances would be @[QName]@ or @Set QName@.
+--   Note that @emb@ can also choose to discard a used definition
+--   by mapping to the unit of the monoid.
+getDefs' :: (GetDefs a, Monoid b) => (MetaId -> Maybe Term) -> (QName -> b) -> a -> b
+getDefs' lookup emb = execWriter . (`runReaderT` GetDefsEnv lookup emb) . getDefs
+
+-- | Inputs to and outputs of @getDefs'@ are organized as a monad.
+type GetDefsM b = ReaderT (GetDefsEnv b) (Writer b)
+
+data GetDefsEnv b = GetDefsEnv
+  { lookupMeta :: MetaId -> Maybe Term
+  , embDef     :: QName -> b
+  }
+
+-- | What it takes to get the used definitions.
+class Monad m => MonadGetDefs m where
+  doDef  :: QName -> m ()
+  doMeta :: MetaId -> m ()
+
+instance Monoid b => MonadGetDefs (GetDefsM b) where
+  doDef  d = tell . ($ d) =<< asks embDef
+  doMeta x = getDefs . ($ x) =<< asks lookupMeta
+
+-- | Getting the used definitions.
+--
+-- Note: in contrast to 'Agda.Syntax.Internal.Generic.foldTerm'
+-- @getDefs@ also collects from sorts in terms.
+-- Thus, this is not an instance of @foldTerm@.
+
+class GetDefs a where
+  getDefs :: MonadGetDefs m => a -> m ()
+
+  default getDefs :: (MonadGetDefs m, Foldable f, GetDefs b, f b ~ a) => a -> m ()
+  getDefs = Fold.mapM_ getDefs
+
+instance GetDefs Clause where
+  getDefs = getDefs . clauseBody
+
+instance GetDefs Term where
+  getDefs = \case
+    Def d vs   -> doDef d >> getDefs vs
+    Con _ _ vs -> getDefs vs
+    Lit l      -> return ()
+    Var i vs   -> getDefs vs
+    Lam _ v    -> getDefs v
+    Pi a b     -> getDefs a >> getDefs b
+    Sort s     -> getDefs s
+    Level l    -> getDefs l
+    MetaV x vs -> getDefs x >> getDefs vs
+    DontCare v -> getDefs v
+    Dummy{}    -> return ()
+
+instance GetDefs MetaId where
+  getDefs x = doMeta x
+
+instance GetDefs Type where
+  getDefs (El s t) = getDefs s >> getDefs t
+
+instance GetDefs Sort where
+  getDefs = \case
+    Univ _ l  -> getDefs l
+    Inf _ _   -> return ()
+    SizeUniv  -> return ()
+    LockUniv  -> return ()
+    LevelUniv -> return ()
+    IntervalUniv -> return ()
+    PiSort a s1 s2 -> getDefs a >> getDefs s1 >> getDefs s2
+    FunSort s1 s2 -> getDefs s1 >> getDefs s2
+    UnivSort s  -> getDefs s
+    MetaS x es  -> getDefs x >> getDefs es
+    DefS d es   -> doDef d >> getDefs es
+    DummyS{}    -> return ()
+
+instance GetDefs Level where
+  getDefs (Max _ ls) = getDefs ls
+
+instance GetDefs PlusLevel where
+  getDefs (Plus _ l)    = getDefs l
+
+-- collection instances
+
+instance GetDefs a => GetDefs (Maybe a) where
+instance GetDefs a => GetDefs [a]       where
+instance GetDefs a => GetDefs (Elim' a) where
+instance GetDefs a => GetDefs (Arg a)   where
+instance GetDefs a => GetDefs (Dom a)   where
+instance GetDefs a => GetDefs (Abs a)   where
+
+instance (GetDefs a, GetDefs b) => GetDefs (a,b) where
+  getDefs (a,b) = getDefs a >> getDefs b
+
+instance GetDefs Telescope where
+  getDefs = getDefs . telToList
+
+-- no defs here
+
+instance {-# OVERLAPPING #-} GetDefs String where
+  getDefs _ = return ()
diff --git a/src/full/Agda/Syntax/Internal/Elim.hs b/src/full/Agda/Syntax/Internal/Elim.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Elim.hs
@@ -0,0 +1,89 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Internal.Elim where
+
+import Control.DeepSeq
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Pretty () -- Pretty Arg instance
+import Agda.Syntax.Position
+import Agda.Syntax.Abstract.Name
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Empty
+import Agda.Utils.Maybe
+import Agda.Utils.Tuple
+
+-- | Eliminations, subsuming applications and projections.
+--
+data Elim' a
+  = Apply (Arg a)         -- ^ Application.
+  | Proj ProjOrigin QName -- ^ Projection.  'QName' is name of a record projection.
+  | IApply a a a -- ^ IApply x y r, x and y are the endpoints
+  deriving (Show, Functor, Foldable, Traversable)
+
+-- | This instance cheats on 'Proj', use with care.
+--   'Proj's are always assumed to be 'UserWritten', since they have no 'ArgInfo'.
+--   Same for IApply
+instance LensOrigin (Elim' a) where
+  getOrigin (Apply a)   = getOrigin a
+  getOrigin Proj{}      = UserWritten
+  getOrigin IApply{}    = UserWritten
+  mapOrigin f (Apply a) = Apply $ mapOrigin f a
+  mapOrigin f e@Proj{}  = e
+  mapOrigin f e@IApply{} = e
+
+-- | Drop 'Apply' constructor. (Safe)
+isApplyElim :: Elim' a -> Maybe (Arg a)
+isApplyElim (Apply u) = Just u
+isApplyElim Proj{}    = Nothing
+isApplyElim (IApply _ _ r) = Just (defaultArg r)
+
+isApplyElim' :: Empty -> Elim' a -> Arg a
+isApplyElim' e = fromMaybe (absurd e) . isApplyElim
+
+-- | Only 'Apply' variant.
+isProperApplyElim :: Elim' a -> Bool
+isProperApplyElim = \case
+  Apply _  -> True
+  IApply{} -> False
+  Proj{}   -> False
+
+-- | Drop 'Apply' constructors. (Safe)
+allApplyElims :: [Elim' a] -> Maybe [Arg a]
+allApplyElims = mapM isApplyElim
+
+-- | Split at first non-'Apply'
+splitApplyElims :: [Elim' a] -> ([Arg a], [Elim' a])
+splitApplyElims (Apply u : es) = mapFst (u :) $ splitApplyElims es
+splitApplyElims es             = ([], es)
+
+class IsProjElim e where
+  isProjElim  :: e -> Maybe (ProjOrigin, QName)
+
+instance IsProjElim (Elim' a) where
+  isProjElim (Proj o d) = Just (o, d)
+  isProjElim Apply{}    = Nothing
+  isProjElim IApply{} = Nothing
+
+-- | Discards @Proj f@ entries.
+argsFromElims :: [Elim' t] -> [Arg t]
+argsFromElims = mapMaybe isApplyElim
+
+-- | Drop 'Proj' constructors. (Safe)
+allProjElims :: [Elim' t] -> Maybe [(ProjOrigin, QName)]
+allProjElims = mapM isProjElim
+
+instance KillRange a => KillRange (Elim' a) where
+  killRange = fmap killRange
+
+instance Pretty tm => Pretty (Elim' tm) where
+  prettyPrec p (Apply v)    = prettyPrec p v
+  prettyPrec _ (Proj _o x)  = text ("." ++ prettyShow x)
+  prettyPrec p (IApply x y r) = prettyPrec p r
+--  prettyPrec p (IApply x y r) = text "@[" <> prettyPrec 0 x <> text ", " <> prettyPrec 0 y <> text "]" <> prettyPrec p r
+
+instance NFData a => NFData (Elim' a) where
+  rnf (Apply x) = rnf x
+  rnf Proj{}    = ()
+  rnf (IApply x y r) = rnf x `seq` rnf y `seq` rnf r
diff --git a/src/full/Agda/Syntax/Internal/Generic.hs b/src/full/Agda/Syntax/Internal/Generic.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Generic.hs
@@ -0,0 +1,171 @@
+
+-- | Tree traversal for internal syntax.
+
+module Agda.Syntax.Internal.Generic where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Utils.Functor
+
+-- | Generic term traversal.
+--
+--   Note: ignores sorts in terms!
+--   (Does not traverse into or collect from them.)
+
+class TermLike a where
+
+  -- | Generic traversal with post-traversal action.
+  --   Ignores sorts.
+  traverseTermM :: Monad m => (Term -> m Term) -> a -> m a
+
+  default traverseTermM :: (Monad m, Traversable f, TermLike b, f b ~ a)
+                        => (Term -> m Term) -> a -> m a
+  traverseTermM = traverse . traverseTermM
+
+  -- | Generic fold, ignoring sorts.
+  foldTerm :: Monoid m => (Term -> m) -> a -> m
+
+  default foldTerm
+    :: (Monoid m, Foldable f, TermLike b, f b ~ a) => (Term -> m) -> a -> m
+  foldTerm = foldMap . foldTerm
+
+-- Constants
+
+instance TermLike Bool where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+instance TermLike Int where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+instance TermLike Integer where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+instance TermLike Char where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+instance TermLike QName where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+-- Functors
+
+instance TermLike a => TermLike (Elim' a)      where
+instance TermLike a => TermLike (Arg a)        where
+instance TermLike a => TermLike (Dom a)        where
+instance TermLike a => TermLike [a]            where
+instance TermLike a => TermLike (Maybe a)      where
+instance TermLike a => TermLike (Blocked a)    where
+instance TermLike a => TermLike (Abs a)        where
+instance TermLike a => TermLike (Tele a)       where
+instance TermLike a => TermLike (WithHiding a) where
+
+-- Tuples
+
+instance (TermLike a, TermLike b) => TermLike (a, b) where
+  traverseTermM f (x, y) = (,) <$> traverseTermM f x <*> traverseTermM f y
+  foldTerm f (x, y) = foldTerm f x `mappend` foldTerm f y
+
+instance (TermLike a, TermLike b, TermLike c) => TermLike (a, b, c) where
+  traverseTermM f (x, y, z) = (,,) <$> traverseTermM f x <*> traverseTermM f y <*> traverseTermM f z
+  foldTerm f (x, y, z) = mconcat [foldTerm f x, foldTerm f y, foldTerm f z]
+
+instance (TermLike a, TermLike b, TermLike c, TermLike d) => TermLike (a, b, c, d) where
+  traverseTermM f (x, y, z, u) = (,,,) <$> traverseTermM f x <*> traverseTermM f y <*> traverseTermM f z <*> traverseTermM f u
+  foldTerm f (x, y, z, u) = mconcat [foldTerm f x, foldTerm f y, foldTerm f z, foldTerm f u]
+
+-- Real terms
+
+instance TermLike Term where
+
+  traverseTermM f = \case
+    Var i xs    -> f =<< Var i <$> traverseTermM f xs
+    Def c xs    -> f =<< Def c <$> traverseTermM f xs
+    Con c ci xs -> f =<< Con c ci <$> traverseTermM f xs
+    Lam h b     -> f =<< Lam h <$> traverseTermM f b
+    Pi a b      -> f =<< uncurry Pi <$> traverseTermM f (a, b)
+    MetaV m xs  -> f =<< MetaV m <$> traverseTermM f xs
+    Level l     -> f =<< Level <$> traverseTermM f l
+    t@Lit{}     -> f t
+    Sort s      -> f =<< Sort <$> traverseTermM f s
+    DontCare mv -> f =<< DontCare <$> traverseTermM f mv
+    Dummy s xs  -> f =<< Dummy s <$> traverseTermM f xs
+
+  foldTerm f t = f t `mappend` case t of
+    Var i xs    -> foldTerm f xs
+    Def c xs    -> foldTerm f xs
+    Con c ci xs -> foldTerm f xs
+    Lam h b     -> foldTerm f b
+    Pi a b      -> foldTerm f (a, b)
+    MetaV m xs  -> foldTerm f xs
+    Level l     -> foldTerm f l
+    Lit _       -> mempty
+    Sort s      -> foldTerm f s
+    DontCare mv -> foldTerm f mv
+    Dummy _ xs  -> foldTerm f xs
+
+instance TermLike Level where
+  traverseTermM f (Max n as) = Max n <$> traverseTermM f as
+  foldTerm f      (Max n as) = foldTerm f as
+
+instance TermLike PlusLevel where
+  traverseTermM f (Plus n l) = Plus n <$> traverseTermM f l
+  foldTerm f (Plus _ l)      = foldTerm f l
+
+instance TermLike Type where
+  traverseTermM f (El s t) = El s <$> traverseTermM f t
+  foldTerm f (El s t) = foldTerm f t
+
+instance TermLike Sort where
+  traverseTermM f = \case
+    Univ u l   -> Univ u <$> traverseTermM f l
+    s@(Inf _ _)-> pure s
+    s@SizeUniv -> pure s
+    s@LockUniv -> pure s
+    s@LevelUniv -> pure s
+    s@IntervalUniv -> pure s
+    PiSort a b c -> PiSort   <$> traverseTermM f a <*> traverseTermM f b <*> traverseTermM f c
+    FunSort a b -> FunSort   <$> traverseTermM f a <*> traverseTermM f b
+    UnivSort a -> UnivSort <$> traverseTermM f a
+    MetaS x es -> MetaS x  <$> traverseTermM f es
+    DefS q es  -> DefS q   <$> traverseTermM f es
+    s@(DummyS _) -> pure s
+
+  foldTerm f = \case
+    Univ _ l   -> foldTerm f l
+    Inf _ _    -> mempty
+    SizeUniv   -> mempty
+    LockUniv   -> mempty
+    LevelUniv  -> mempty
+    IntervalUniv -> mempty
+    PiSort a b c -> foldTerm f a <> foldTerm f b <> foldTerm f c
+    FunSort a b -> foldTerm f a <> foldTerm f b
+    UnivSort a -> foldTerm f a
+    MetaS _ es -> foldTerm f es
+    DefS _ es  -> foldTerm f es
+    DummyS _   -> mempty
+
+instance TermLike EqualityView where
+
+  traverseTermM f = \case
+    OtherType t -> OtherType
+      <$> traverseTermM f t
+    IdiomType t -> IdiomType
+      <$> traverseTermM f t
+    EqualityType s eq l t a b -> EqualityType s eq
+      <$> traverse (traverseTermM f) l
+      <*> traverseTermM f t
+      <*> traverseTermM f a
+      <*> traverseTermM f b
+
+  foldTerm f = \case
+    OtherType t -> foldTerm f t
+    IdiomType t -> foldTerm f t
+    EqualityType s eq l t a b -> foldTerm f (l ++ [t, a, b])
+
+-- | Put it in a monad to make it possible to do strictly.
+copyTerm :: (TermLike a, Monad m) => a -> m a
+copyTerm = traverseTermM return
diff --git a/src/full/Agda/Syntax/Internal/MetaVars.hs b/src/full/Agda/Syntax/Internal/MetaVars.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/MetaVars.hs
@@ -0,0 +1,98 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Internal.MetaVars where
+
+import Data.Monoid
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+
+import Agda.Utils.Singleton
+
+-- | Returns every meta-variable occurrence in the given type, except
+-- for those in sort annotations on types.
+class AllMetas t where
+  allMetas :: Monoid m => (MetaId -> m) -> t -> m
+
+  default allMetas :: (TermLike t, Monoid m) => (MetaId -> m) -> t -> m
+  allMetas = allMetas'
+
+-- Default instances
+instance AllMetas Term
+instance AllMetas Type
+instance TermLike a => AllMetas (Elim' a)
+instance TermLike a => AllMetas (Tele a)
+
+instance (AllMetas a, AllMetas b) => AllMetas (Dom' a b) where
+  allMetas f (Dom _ _ _ t e) = allMetas f t <> allMetas f e
+
+-- These types need to be packed up as a Term to get the metas.
+instance AllMetas Sort      where allMetas f   = allMetas f . Sort
+instance AllMetas Level     where allMetas f   = allMetas f . Level
+instance AllMetas PlusLevel where allMetas f l = allMetas f (Max 0 [l])
+
+instance {-# OVERLAPPING #-} AllMetas String where
+  allMetas f _ = mempty
+
+-- Generic instances
+instance (AllMetas a, AllMetas b) => AllMetas (a, b) where
+  allMetas f (x, y) = allMetas f x <> allMetas f y
+
+instance (AllMetas a, AllMetas b, AllMetas c) => AllMetas (a, b, c) where
+  allMetas f (x, y, z) = allMetas f (x, (y, z))
+
+instance (AllMetas a, AllMetas b, AllMetas c, AllMetas d) => AllMetas (a, b, c, d) where
+  allMetas f (x, y, z, w) = allMetas f (x, (y, (z, w)))
+
+instance AllMetas a => AllMetas [a]       where allMetas f xs = foldMap (allMetas f) xs
+instance AllMetas a => AllMetas (Maybe a) where allMetas f xs = foldMap (allMetas f) xs
+instance AllMetas a => AllMetas (Arg a)   where allMetas f xs = foldMap (allMetas f) xs
+
+allMetas' :: (TermLike a, Monoid m) => (MetaId -> m) -> a -> m
+allMetas' singl = foldTerm metas
+  where
+  metas (MetaV m _) = singl m
+  metas (Sort s)    = sortMetas s
+  metas _           = mempty
+
+  sortMetas Univ{}        = mempty
+  sortMetas Inf{}         = mempty
+  sortMetas SizeUniv{}    = mempty
+  sortMetas LockUniv{}    = mempty
+  sortMetas LevelUniv     = mempty
+  sortMetas IntervalUniv{} = mempty
+  sortMetas (PiSort _ s1 s2)  = sortMetas s1 <> sortMetas (unAbs s2)  -- the domain is a term so is covered by the fold
+  sortMetas (FunSort a b) = sortMetas a <> sortMetas b
+  sortMetas (UnivSort s)  = sortMetas s
+  sortMetas (MetaS x _)   = singl x
+  sortMetas DefS{}        = mempty
+  sortMetas DummyS{}      = mempty
+
+-- | Returns 'allMetas' in a list.
+--   @allMetasList = allMetas (:[])@.
+--
+--   Note: this resulting list is computed via difference lists.
+--   Thus, use this function if you actually need the whole list of metas.
+--   Otherwise, use 'allMetas' with a suitable monoid.
+allMetasList :: AllMetas a => a -> [MetaId]
+allMetasList t = allMetas singleton t `appEndo` []
+
+-- | 'True' if thing contains no metas.
+--   @noMetas = null . allMetasList@.
+noMetas :: AllMetas a => a -> Bool
+noMetas = getAll . allMetas (\ _m -> All False)
+
+-- | Returns the first meta it find in the thing, if any.
+--   @firstMeta == listToMaybe . allMetasList@.
+firstMeta :: AllMetas a => a -> Maybe MetaId
+firstMeta = getFirst . allMetas (First . Just)
+
+-- | A blocker that unblocks if any of the metas in a term are solved.
+unblockOnAnyMetaIn :: AllMetas t => t -> Blocker
+unblockOnAnyMetaIn t = unblockOnAnyMeta $ allMetas Set.singleton t
+
+-- | A blocker that unblocks if any of the metas in a term are solved.
+unblockOnAllMetasIn :: AllMetas t => t -> Blocker
+unblockOnAllMetasIn t = unblockOnAllMetas $ allMetas Set.singleton t
diff --git a/src/full/Agda/Syntax/Internal/Names.hs b/src/full/Agda/Syntax/Internal/Names.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Names.hs
@@ -0,0 +1,394 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Extract all names and meta-variables from things.
+
+module Agda.Syntax.Internal.Names where
+
+import Data.HashMap.Strict (HashMap)
+import Data.Map (Map)
+import Data.Set (Set)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Literal
+import Agda.Syntax.Internal
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Treeless
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.CompiledClause
+
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Singleton
+import Agda.Utils.Impossible
+
+-- | Some or all of the 'QName's that can be found in the given thing.
+
+namesIn :: (NamesIn a, Collection QName m) => a -> m
+namesIn = namesIn' singleton
+
+-- | Some or all of the 'QName's that can be found in the given thing.
+
+namesIn' :: (NamesIn a, Monoid m) => (QName -> m) -> a -> m
+namesIn' f = namesAndMetasIn' (either f mempty)
+
+-- | Some or all of the meta-variables that can be found in the given
+-- thing.
+
+metasIn :: (NamesIn a, Collection MetaId m) => a -> m
+metasIn = metasIn' singleton
+
+-- | Some or all of the meta-variables that can be found in the given
+-- thing.
+
+-- TODO: Does this function make
+-- Agda.Syntax.Internal.MetaVars.allMetas superfluous? Maybe not,
+-- allMetas ignores the first argument of PiSort.
+
+metasIn' :: (NamesIn a, Monoid m) => (MetaId -> m) -> a -> m
+metasIn' f = namesAndMetasIn' (either mempty f)
+
+-- | Some or all of the names and meta-variables that can be found in
+-- the given thing.
+
+namesAndMetasIn ::
+  (NamesIn a, Collection QName m1, Collection MetaId m2) =>
+  a -> (m1, m2)
+namesAndMetasIn =
+  namesAndMetasIn'
+    (either (\x -> (singleton x, mempty))
+            (\m -> (mempty, singleton m)))
+
+class NamesIn a where
+  -- | Some or all of the names and meta-variables that can be found
+  -- in the given thing.
+  namesAndMetasIn' :: Monoid m => (Either QName MetaId -> m) -> a -> m
+
+  default namesAndMetasIn' ::
+    (Monoid m, Foldable f, NamesIn b, f b ~ a) =>
+    (Either QName MetaId -> m) -> a -> m
+  namesAndMetasIn' = foldMap . namesAndMetasIn'
+
+-- Generic collections
+instance NamesIn a => NamesIn (Maybe a)
+instance NamesIn a => NamesIn (Strict.Maybe a)
+instance NamesIn a => NamesIn [a]
+instance NamesIn a => NamesIn (List1 a)
+instance NamesIn a => NamesIn (Set a)
+instance NamesIn a => NamesIn (Map k a)
+
+-- Decorations
+instance NamesIn a => NamesIn (Arg a)
+instance NamesIn a => NamesIn (Named n a)
+instance NamesIn a => NamesIn (Abs a)
+instance NamesIn a => NamesIn (WithArity a)
+instance NamesIn a => NamesIn (Open a)
+instance NamesIn a => NamesIn (C.FieldAssignment' a)
+
+instance (NamesIn a, NamesIn b) => NamesIn (Dom' a b) where
+  namesAndMetasIn' sg (Dom _ _ _ t e) =
+    mappend (namesAndMetasIn' sg t) (namesAndMetasIn' sg e)
+
+
+-- Specific collections
+instance NamesIn a => NamesIn (Tele a)
+
+-- Tuples
+
+instance (NamesIn a, NamesIn b) => NamesIn (a, b) where
+  namesAndMetasIn' sg (x, y) =
+    namesAndMetasIn' sg x <> namesAndMetasIn' sg y
+  {-# INLINE namesAndMetasIn' #-}
+
+instance (NamesIn a, NamesIn b, NamesIn c) => NamesIn (a, b, c) where
+  namesAndMetasIn' sg (x, y, z) =
+    namesAndMetasIn' sg x <> namesAndMetasIn' sg y <> namesAndMetasIn' sg z
+  {-# INLINE namesAndMetasIn' #-}
+
+instance (NamesIn a, NamesIn b, NamesIn c, NamesIn d) => NamesIn (a, b, c, d) where
+  namesAndMetasIn' sg (x, y, z, u) =
+    namesAndMetasIn' sg x <> namesAndMetasIn' sg y <> namesAndMetasIn' sg z <> namesAndMetasIn' sg u
+  {-# INLINE namesAndMetasIn' #-}
+
+instance
+  (NamesIn a, NamesIn b, NamesIn c, NamesIn d, NamesIn e) =>
+  NamesIn (a, b, c, d, e) where
+  namesAndMetasIn' sg (x, y, z, u, v) =
+    namesAndMetasIn' sg x <> namesAndMetasIn' sg y <> namesAndMetasIn' sg z <> namesAndMetasIn' sg u
+    <> namesAndMetasIn' sg v
+  {-# INLINE namesAndMetasIn' #-}
+
+instance
+  (NamesIn a, NamesIn b, NamesIn c, NamesIn d, NamesIn e, NamesIn f) =>
+  NamesIn (a, b, c, d, e, f) where
+  namesAndMetasIn' sg (x, y, z, u, v, w) =
+    namesAndMetasIn' sg x <> namesAndMetasIn' sg y <> namesAndMetasIn' sg z <> namesAndMetasIn' sg u
+    <> namesAndMetasIn' sg v <> namesAndMetasIn' sg w
+  {-# INLINE namesAndMetasIn' #-}
+
+instance NamesIn CompKit where
+  namesAndMetasIn' sg (CompKit a b) = namesAndMetasIn' sg (a,b)
+
+-- Base cases
+
+instance NamesIn QName where
+  namesAndMetasIn' sg x = sg (Left x)  -- interesting case!
+
+instance NamesIn MetaId where
+  namesAndMetasIn' sg x = sg (Right x)
+
+instance NamesIn ConHead where
+  namesAndMetasIn' sg h = namesAndMetasIn' sg (conName h)
+
+instance NamesIn Bool where
+  namesAndMetasIn' _ _ = mempty
+
+-- Andreas, 2017-07-27
+-- In the following clauses, the choice of fields is not obvious
+-- to the reader.  Please comment on the choices.
+
+instance NamesIn Definition where
+  namesAndMetasIn' sg
+    (Defn _ _ t _ _ _ _ disp _ _ _ _ _ _ _ _ _ _ def) =
+    namesAndMetasIn' sg (t, def, disp)
+
+instance NamesIn Defn where
+  namesAndMetasIn' sg = \case
+    Axiom _            -> mempty
+    DataOrRecSig _     -> mempty
+    GeneralizableVar   -> mempty
+    PrimitiveSort _ s  -> namesAndMetasIn' sg s
+    AbstractDefn{}     -> __IMPOSSIBLE__
+    -- Andreas 2017-07-27, Q: which names can be in @cc@ which are not already in @cl@?
+    Function cl cc _ _ _ _ _ _ _ _ _ _ el _ _ _
+      -> namesAndMetasIn' sg (cl, cc, el)
+    Datatype _ _ cl cs s _ _ _ trX trD
+      -> namesAndMetasIn' sg (cl, cs, s, trX, trD)
+    Record _ cl c _ fs recTel _ _ _ _ _ _ comp
+      -> namesAndMetasIn' sg (cl, c, fs, recTel, comp)
+    Constructor _ _ c d _ kit fs _ _ _ _
+      -> namesAndMetasIn' sg (c, d, kit, fs)
+    Primitive _ _ cl _ cc _
+      -> namesAndMetasIn' sg (cl, cc)
+
+instance NamesIn Clause where
+  namesAndMetasIn' sg (Clause _ _ tel ps b t _ _ _ _ _ _) =
+    namesAndMetasIn' sg (tel, ps, b, t)
+
+instance NamesIn CompiledClauses where
+  namesAndMetasIn' sg (Case _ c) = namesAndMetasIn' sg c
+  namesAndMetasIn' sg (Done _ v) = namesAndMetasIn' sg v
+  namesAndMetasIn' sg (Fail _)   = mempty
+
+-- Andreas, 2017-07-27
+-- Why ignoring the litBranches?
+instance NamesIn a => NamesIn (Case a) where
+  namesAndMetasIn' sg (Branches _ bs _ _ c _ _) =
+    namesAndMetasIn' sg (bs, c)
+
+instance NamesIn (Pattern' a) where
+  namesAndMetasIn' sg = \case
+    VarP _ _        -> mempty
+    LitP _ l        -> namesAndMetasIn' sg l
+    DotP _ v        -> namesAndMetasIn' sg v
+    ConP c _ args   -> namesAndMetasIn' sg (c, args)
+    DefP o q args   -> namesAndMetasIn' sg (q, args)
+    ProjP _ f       -> namesAndMetasIn' sg f
+    IApplyP _ t u _ -> namesAndMetasIn' sg (t, u)
+
+instance NamesIn a => NamesIn (Type' a) where
+  namesAndMetasIn' sg (El s t) = namesAndMetasIn' sg (s, t)
+
+instance NamesIn Sort where
+  namesAndMetasIn' sg = \case
+    Univ _ l    -> namesAndMetasIn' sg l
+    Inf _ _     -> mempty
+    SizeUniv    -> mempty
+    LockUniv    -> mempty
+    LevelUniv   -> mempty
+    IntervalUniv -> mempty
+    PiSort a b c  -> namesAndMetasIn' sg (a, b, c)
+    FunSort a b -> namesAndMetasIn' sg (a, b)
+    UnivSort a  -> namesAndMetasIn' sg a
+    MetaS x es  -> namesAndMetasIn' sg (x, es)
+    DefS d es   -> namesAndMetasIn' sg (d, es)
+    DummyS _    -> mempty
+
+instance NamesIn Term where
+  namesAndMetasIn' sg = \case
+    Var _ args   -> namesAndMetasIn' sg args
+    Lam _ b      -> namesAndMetasIn' sg b
+    Lit l        -> namesAndMetasIn' sg l
+    Def f args   -> namesAndMetasIn' sg (f, args)
+    Con c _ args -> namesAndMetasIn' sg (c, args)
+    Pi a b       -> namesAndMetasIn' sg (a, b)
+    Sort s       -> namesAndMetasIn' sg s
+    Level l      -> namesAndMetasIn' sg l
+    MetaV x args -> namesAndMetasIn' sg (x, args)
+    DontCare v   -> namesAndMetasIn' sg v
+    Dummy _ args -> namesAndMetasIn' sg args
+
+instance NamesIn Level where
+  namesAndMetasIn' sg (Max _ ls) = namesAndMetasIn' sg ls
+
+instance NamesIn PlusLevel where
+  namesAndMetasIn' sg (Plus _ l) = namesAndMetasIn' sg l
+
+-- For QName and Meta literals!
+instance NamesIn Literal where
+  namesAndMetasIn' sg = \case
+    LitNat _    -> mempty
+    LitWord64 _ -> mempty
+    LitString _ -> mempty
+    LitChar _   -> mempty
+    LitFloat _  -> mempty
+    LitQName x  -> namesAndMetasIn' sg x
+    LitMeta _ m -> namesAndMetasIn' sg m
+
+instance NamesIn a => NamesIn (Elim' a) where
+  namesAndMetasIn' sg (Apply arg)      = namesAndMetasIn' sg arg
+  namesAndMetasIn' sg (Proj _ f)       = namesAndMetasIn' sg f
+  namesAndMetasIn' sg (IApply x y arg) = namesAndMetasIn' sg (x, y, arg)
+
+instance NamesIn a => NamesIn (Substitution' a) where
+  namesAndMetasIn' sg = \case
+    IdS              -> mempty
+    EmptyS _         -> mempty
+    t :# s           -> namesAndMetasIn' sg (t, s)
+    Strengthen _ _ s -> namesAndMetasIn' sg s
+    Wk _ s           -> namesAndMetasIn' sg s
+    Lift _ s         -> namesAndMetasIn' sg s
+
+instance NamesIn DisplayForm where
+  namesAndMetasIn' sg (Display _ ps v) = namesAndMetasIn' sg (ps, v)
+
+instance NamesIn DisplayTerm where
+  namesAndMetasIn' sg = \case
+    DWithApp v us es -> namesAndMetasIn' sg (v, us, es)
+    DCon c _ vs      -> namesAndMetasIn' sg (c, vs)
+    DDef f es        -> namesAndMetasIn' sg (f, es)
+    DDot' v es       -> namesAndMetasIn' sg (v, es)
+    DTerm' v es      -> namesAndMetasIn' sg (v, es)
+
+instance NamesIn a => NamesIn (Builtin a) where
+  namesAndMetasIn' sg = \case
+    Builtin t -> namesAndMetasIn' sg t
+    Prim x    -> namesAndMetasIn' sg x
+    BuiltinRewriteRelations xs -> namesAndMetasIn' sg xs
+
+-- | Note that the 'primFunImplementation' is skipped.
+instance NamesIn PrimFun where
+  namesAndMetasIn' sg = \case
+    PrimFun x _ _ _ -> namesAndMetasIn' sg x
+
+instance NamesIn Section where
+  namesAndMetasIn' sg = \case
+    Section tel -> namesAndMetasIn' sg tel
+
+instance NamesIn NLPat where
+  namesAndMetasIn' sg = \case
+    PVar _ _      -> mempty
+    PDef a b      -> namesAndMetasIn' sg (a, b)
+    PLam _ a      -> namesAndMetasIn' sg a
+    PPi a b       -> namesAndMetasIn' sg (a, b)
+    PSort a       -> namesAndMetasIn' sg a
+    PBoundVar _ a -> namesAndMetasIn' sg a
+    PTerm a       -> namesAndMetasIn' sg a
+
+instance NamesIn NLPType where
+  namesAndMetasIn' sg = \case
+    NLPType a b -> namesAndMetasIn' sg (a, b)
+
+instance NamesIn NLPSort where
+  namesAndMetasIn' sg = \case
+    PUniv _ a     -> namesAndMetasIn' sg a
+    PInf _ _      -> mempty
+    PSizeUniv     -> mempty
+    PLockUniv     -> mempty
+    PLevelUniv    -> mempty
+    PIntervalUniv -> mempty
+
+instance NamesIn RewriteRule where
+  namesAndMetasIn' sg = \case
+    RewriteRule a b c d e f _ ->
+      namesAndMetasIn' sg (a, b, c, d, e, f)
+
+instance (NamesIn a, NamesIn b) => NamesIn (HashMap a b) where
+  namesAndMetasIn' sg map = foldMap (namesAndMetasIn' sg) map
+
+instance NamesIn System where
+  namesAndMetasIn' sg (System tel cs) = namesAndMetasIn' sg (tel, cs)
+
+instance NamesIn ExtLamInfo where
+  namesAndMetasIn' sg (ExtLamInfo _ _ s) = namesAndMetasIn' sg s
+
+instance NamesIn a => NamesIn (FunctionInverse' a) where
+  namesAndMetasIn' sg = \case
+    NotInjective -> mempty
+    Inverse m  -> namesAndMetasIn' sg m
+
+instance NamesIn TTerm where
+  namesAndMetasIn' sg = \case
+    TVar _         -> mempty
+    TPrim _        -> mempty
+    TDef x         -> namesAndMetasIn' sg x
+    TApp t xs      -> namesAndMetasIn' sg (t, xs)
+    TLam t         -> namesAndMetasIn' sg t
+    TLit l         -> namesAndMetasIn' sg l
+    TCon x         -> namesAndMetasIn' sg x
+    TLet t1 t2     -> namesAndMetasIn' sg (t1, t2)
+    TCase _ c t ts -> namesAndMetasIn' sg (c, t, ts)
+    TUnit          -> mempty
+    TSort          -> mempty
+    TErased        -> mempty
+    TCoerce t      -> namesAndMetasIn' sg t
+    TError _       -> mempty
+
+instance NamesIn TAlt where
+  namesAndMetasIn' sg = \case
+    TACon x _ t   -> namesAndMetasIn' sg (x, t)
+    TAGuard t1 t2 -> namesAndMetasIn' sg (t1, t2)
+    TALit l t     -> namesAndMetasIn' sg (l, t)
+
+instance NamesIn CaseType where
+  namesAndMetasIn' sg = \case
+    CTData x   -> namesAndMetasIn' sg x
+    CTNat      -> mempty
+    CTInt      -> mempty
+    CTChar     -> mempty
+    CTString   -> mempty
+    CTFloat    -> mempty
+    CTQName    -> mempty
+
+instance NamesIn CaseInfo where
+  namesAndMetasIn' sg (CaseInfo _ _ t) = namesAndMetasIn' sg t
+
+instance NamesIn Compiled where
+  namesAndMetasIn' sg (Compiled t _) = namesAndMetasIn' sg t
+
+-- Pattern synonym stuff --
+
+newtype PSyn = PSyn A.PatternSynDefn
+instance NamesIn PSyn where
+  namesAndMetasIn' sg (PSyn (_args, p)) = namesAndMetasIn' sg p
+
+instance NamesIn (A.Pattern' a) where
+  namesAndMetasIn' sg = \case
+    A.VarP _               -> mempty
+    A.ConP _ c args        -> namesAndMetasIn' sg (c, args)
+    A.ProjP _ _ d          -> namesAndMetasIn' sg d
+    A.DefP _ f args        -> namesAndMetasIn' sg (f, args)
+    A.WildP _              -> mempty
+    A.AsP _ _ p            -> namesAndMetasIn' sg p
+    A.AbsurdP _            -> mempty
+    A.LitP _ l             -> namesAndMetasIn' sg l
+    A.PatternSynP _ c args -> namesAndMetasIn' sg (c, args)
+    A.RecP _ fs            -> namesAndMetasIn' sg fs
+    A.DotP{}               -> __IMPOSSIBLE__    -- Dot patterns are not allowed in pattern synonyms
+    A.EqualP{}             -> __IMPOSSIBLE__    -- Andrea: should we allow these in pattern synonyms?
+    A.WithP _ p            -> namesAndMetasIn' sg p
+    A.AnnP _ a p           -> __IMPOSSIBLE__    -- Type annotations are not (yet) allowed in pattern synonyms
+
+instance NamesIn AmbiguousQName where
+  namesAndMetasIn' sg (AmbQ cs) = namesAndMetasIn' sg cs
diff --git a/src/full/Agda/Syntax/Internal/Pattern.hs b/src/full/Agda/Syntax/Internal/Pattern.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Pattern.hs
@@ -0,0 +1,365 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Internal.Pattern where
+
+import Control.Arrow       ( second )
+import Control.Monad       ( (>=>), forM )
+import Control.Monad.State ( MonadState(..), State, evalState )
+
+import Data.Maybe
+import Data.Monoid
+import qualified Data.List as List
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.Utils.List
+import Agda.Utils.Permutation
+import Agda.Utils.Size (size)
+
+import Agda.Utils.Impossible
+
+-- * Tools for clauses
+
+-- | Translate the clause patterns to terms with free variables bound by the
+--   clause telescope.
+--
+--   Precondition: no projection patterns.
+clauseArgs :: Clause -> Args
+clauseArgs cl = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ clauseElims cl
+
+-- | Translate the clause patterns to an elimination spine
+--   with free variables bound by the clause telescope.
+clauseElims :: Clause -> Elims
+clauseElims cl = patternsToElims $ namedClausePats cl
+
+-- | Arity of a function, computed from clauses.
+class FunArity a where
+  funArity :: a -> Int
+
+-- | Get the number of initial 'Apply' patterns.
+
+instance {-# OVERLAPPABLE #-} IsProjP p => FunArity [p] where
+  funArity = length . takeWhile (isNothing . isProjP)
+
+-- | Get the number of initial 'Apply' patterns in a clause.
+instance FunArity Clause where
+  funArity = funArity . namedClausePats
+
+-- | Get the number of common initial 'Apply' patterns in a list of clauses.
+instance {-# OVERLAPPING #-} FunArity [Clause] where
+  funArity []  = 0
+  funArity cls = minimum $ map funArity cls
+
+-- * Tools for patterns
+
+-- | Label the pattern variables from left to right
+--   using one label for each variable pattern and one for each dot pattern.
+class LabelPatVars a b where
+  type PatVarLabel b
+  labelPatVars :: a -> State [PatVarLabel b] b
+  unlabelPatVars :: b -> a
+  -- ^ Intended, but unpractical due to the absence of type-level lambda, is:
+  --   @labelPatVars :: f (Pattern' x) -> State [i] (f (Pattern' (i,x)))@
+
+  default labelPatVars
+    :: (Traversable f
+      , LabelPatVars a' b'
+      , PatVarLabel b ~  PatVarLabel b'
+      , f a' ~ a, f b' ~ b)
+    => a -> State [PatVarLabel b] b
+  labelPatVars = traverse labelPatVars
+
+  default unlabelPatVars
+    :: (Traversable f, LabelPatVars a' b', f a' ~ a, f b' ~ b)
+    => b -> a
+  unlabelPatVars = fmap unlabelPatVars
+
+instance LabelPatVars a b => LabelPatVars (Arg a) (Arg b) where
+  type PatVarLabel (Arg b) = PatVarLabel b
+
+instance LabelPatVars a b => LabelPatVars (Named x a) (Named x b) where
+  type PatVarLabel (Named x b) = PatVarLabel b
+
+instance LabelPatVars a b => LabelPatVars [a] [b] where
+  type PatVarLabel [b] = PatVarLabel b
+
+instance LabelPatVars Pattern DeBruijnPattern where
+  type PatVarLabel DeBruijnPattern = Int
+
+  labelPatVars = \case
+    VarP o x        -> VarP o . DBPatVar x <$> next
+    DotP o t        -> DotP o t <$ next
+    ConP c mt ps    -> ConP c mt <$> labelPatVars ps
+    DefP o q  ps    -> DefP o q <$> labelPatVars ps
+    LitP  o l       -> return $ LitP o l
+    ProjP o q       -> return $ ProjP o q
+    IApplyP o u t x -> IApplyP o u t . DBPatVar x <$> next
+   where
+    next = caseListM get __IMPOSSIBLE__ $ \x xs -> do
+      put xs
+      return x
+  unlabelPatVars = fmap dbPatVarName
+
+-- | Augment pattern variables with their de Bruijn index.
+{-# SPECIALIZE numberPatVars :: Int -> Permutation -> [NamedArg Pattern] -> [NamedArg DeBruijnPattern] #-}
+--
+--  Example:
+--  @
+--    f : (A : Set) (n : Nat) (v : Vec A n) -> ...
+--    f A .(suc n) (cons n x xs)
+--
+--    clauseTel = (A : Set) (n : Nat) (x : A) (xs : Vec A n)
+--    perm      = Perm 5 [0,2,3,4]
+--    invertP __IMPOSSIBLE__ perm = Perm 4 [0,__IMPOSSIBLE__,1,2,3]
+--    flipP ... = Perm 4 [3,__IMPOSSIBLE__,2,1,0]
+--    pats      = A .(suc 2) (cons n x xs)
+--    dBpats    = 3 .(suc 2) (cons 2 1 0 )
+--  @
+--
+numberPatVars :: (LabelPatVars a b, PatVarLabel b ~ Int) => Int -> Permutation -> a -> b
+numberPatVars err perm ps = evalState (labelPatVars ps) $
+  permPicks $ flipP $ invertP err perm
+
+unnumberPatVars :: LabelPatVars a b => b -> a
+unnumberPatVars = unlabelPatVars
+
+dbPatPerm :: [NamedArg DeBruijnPattern] -> Maybe Permutation
+dbPatPerm = dbPatPerm' True
+
+-- | Computes the permutation from the clause telescope
+--   to the pattern variables.
+--
+--   Use as @fromMaybe __IMPOSSIBLE__ . dbPatPerm@ to crash
+--   in a controlled way if a de Bruijn index is out of scope here.
+--
+--   The first argument controls whether dot patterns counts as variables or
+--   not.
+dbPatPerm' :: Bool -> [NamedArg DeBruijnPattern] -> Maybe Permutation
+dbPatPerm' countDots ps = Perm (size ixs) <$> picks
+  where
+    ixs   = concatMap (getIndices . namedThing . unArg) ps
+    n     = size $ catMaybes ixs
+    picks = forM (downFrom n) $ \ i -> List.elemIndex (Just i) ixs
+
+    getIndices :: DeBruijnPattern -> [Maybe Int]
+    getIndices (VarP _ x)    = [Just $ dbPatVarIndex x]
+    getIndices (ConP c _ ps) = concatMap (getIndices . namedThing . unArg) ps
+    getIndices (DefP _ _ ps) = concatMap (getIndices . namedThing . unArg) ps
+    getIndices (DotP _ _)    = [Nothing | countDots]
+    getIndices (LitP _ _)    = []
+    getIndices ProjP{}       = []
+    getIndices (IApplyP _ _ _ x) = [Just $ dbPatVarIndex x]
+
+-- | Computes the permutation from the clause telescope
+--   to the pattern variables.
+--
+--   Use as @fromMaybe __IMPOSSIBLE__ . clausePerm@ to crash
+--   in a controlled way if a de Bruijn index is out of scope here.
+clausePerm :: Clause -> Maybe Permutation
+clausePerm = dbPatPerm . namedClausePats
+
+-- | Turn a pattern into a term.
+--   Projection patterns are turned into projection eliminations,
+--   other patterns into apply elimination.
+patternToElim :: Arg DeBruijnPattern -> Elim
+patternToElim (Arg ai (VarP o x)) = Apply $ Arg ai $ var $ dbPatVarIndex x
+patternToElim (Arg ai (ConP c cpi ps)) = Apply $ Arg ai $ Con c ci $
+      map (patternToElim . fmap namedThing) ps
+  where ci = fromConPatternInfo cpi
+patternToElim (Arg ai (DefP o q ps)) = Apply $ Arg ai $ Def q $
+      map (patternToElim . fmap namedThing) ps
+patternToElim (Arg ai (DotP o t)   ) = Apply $ Arg ai t
+patternToElim (Arg ai (LitP o l)    ) = Apply $ Arg ai $ Lit l
+patternToElim (Arg ai (ProjP o dest)) = Proj o dest
+patternToElim (Arg ai (IApplyP o t u x)) = IApply t u $ var $ dbPatVarIndex x
+
+patternsToElims :: [NamedArg DeBruijnPattern] -> [Elim]
+patternsToElims ps = map build ps
+  where
+    build :: NamedArg DeBruijnPattern -> Elim
+    build = patternToElim . fmap namedThing
+
+patternToTerm :: DeBruijnPattern -> Term
+patternToTerm p = case patternToElim (defaultArg p) of
+  Apply x -> unArg x
+  Proj{}  -> __IMPOSSIBLE__
+  IApply _ _ x -> x
+
+
+class MapNamedArgPattern a p where
+  mapNamedArgPattern :: (NamedArg (Pattern' a) -> NamedArg (Pattern' a)) -> p -> p
+
+  default mapNamedArgPattern
+    :: (Functor f, MapNamedArgPattern a p', p ~ f p')
+    => (NamedArg (Pattern' a) -> NamedArg (Pattern' a)) -> p -> p
+  mapNamedArgPattern = fmap . mapNamedArgPattern
+
+-- | Modify the content of @VarP@, and the closest surrounding @NamedArg@.
+--
+--   Note: the @mapNamedArg@ for @Pattern'@ is not expressible simply
+--   by @fmap@ or @traverse@ etc., since @ConP@ has @NamedArg@ subpatterns,
+--   which are taken into account by @mapNamedArg@.
+
+instance MapNamedArgPattern a (NamedArg (Pattern' a)) where
+  mapNamedArgPattern f np =
+    case namedArg np of
+      VarP o x    -> f np
+      DotP  o t   -> f np
+      LitP o l    -> f np
+      ProjP o q   -> f np
+      ConP c i ps -> f $ setNamedArg np $ ConP c i $ mapNamedArgPattern f ps
+      DefP o q ps -> f $ setNamedArg np $ DefP o q $ mapNamedArgPattern f ps
+      IApplyP o u t x -> f np
+
+instance MapNamedArgPattern a p => MapNamedArgPattern a [p] where
+
+
+-- | Generic pattern traversal.
+--
+--   Pre-applies a pattern modification, recurses, and post-applies another one.
+
+class PatternLike a b where
+
+  -- | Fold pattern.
+  foldrPattern
+    :: Monoid m
+    => (Pattern' a -> m -> m)
+         -- ^ Combine a pattern and the value computed from its subpatterns.
+    -> b -> m
+
+  default foldrPattern
+    :: (Monoid m, Foldable f, PatternLike a p, f p ~ b)
+    => (Pattern' a -> m -> m) -> b -> m
+  foldrPattern = foldMap . foldrPattern
+
+  -- | Traverse pattern.
+  traversePatternM
+    :: Monad m
+    => (Pattern' a -> m (Pattern' a))  -- ^ @pre@: Modification before recursion.
+    -> (Pattern' a -> m (Pattern' a))  -- ^ @post@: Modification after recursion.
+    -> b -> m b
+
+  default traversePatternM
+    :: (Traversable f, PatternLike a p, f p ~ b, Monad m)
+    => (Pattern' a -> m (Pattern' a))
+    -> (Pattern' a -> m (Pattern' a))
+    -> b -> m b
+
+  traversePatternM pre post = traverse $ traversePatternM pre post
+
+-- | Compute from each subpattern a value and collect them all in a monoid.
+
+foldPattern :: (PatternLike a b, Monoid m) => (Pattern' a -> m) -> b -> m
+foldPattern f = foldrPattern $ \ p m -> f p `mappend` m
+
+-- | Traverse pattern(s) with a modification before the recursive descent.
+
+preTraversePatternM
+  :: (PatternLike a b, Monad m)
+  => (Pattern' a -> m (Pattern' a))  -- ^ @pre@: Modification before recursion.
+  -> b -> m b
+preTraversePatternM pre = traversePatternM pre return
+
+-- | Traverse pattern(s) with a modification after the recursive descent.
+
+postTraversePatternM :: (PatternLike a b, Monad m)
+                     => (Pattern' a -> m (Pattern' a))  -- ^ @post@: Modification after recursion.
+                     -> b -> m b
+postTraversePatternM = traversePatternM return
+
+-- This is where the action is:
+
+instance PatternLike a (Pattern' a) where
+
+  foldrPattern f p = f p $ case p of
+    ConP _ _ ps -> foldrPattern f ps
+    DefP _ _ ps -> foldrPattern f ps
+    VarP _ _    -> mempty
+    LitP _ _    -> mempty
+    DotP _ _    -> mempty
+    ProjP _ _   -> mempty
+    IApplyP{}   -> mempty
+
+  traversePatternM pre post = pre >=> recurse >=> post
+    where
+    recurse p = case p of
+      ConP c ci ps -> ConP c ci <$> traversePatternM pre post ps
+      DefP o q ps  -> DefP o q <$> traversePatternM pre post ps
+      VarP  _ _    -> return p
+      LitP  _ _    -> return p
+      DotP  _ _    -> return p
+      ProjP _ _    -> return p
+      IApplyP{}    -> return p
+
+-- Boilerplate instances:
+
+instance PatternLike a b => PatternLike a [b]         where
+instance PatternLike a b => PatternLike a (Arg b)     where
+instance PatternLike a b => PatternLike a (Named x b) where
+
+-- Counting pattern variables ---------------------------------------------
+
+class CountPatternVars a where
+  countPatternVars :: a -> Int
+
+  default countPatternVars :: (Foldable f, CountPatternVars b, f b ~ a) =>
+                              a -> Int
+  countPatternVars = getSum . foldMap (Sum . countPatternVars)
+
+instance CountPatternVars a => CountPatternVars [a] where
+instance CountPatternVars a => CountPatternVars (Arg a) where
+instance CountPatternVars a => CountPatternVars (Named x a) where
+
+instance CountPatternVars (Pattern' x) where
+  countPatternVars p =
+    case p of
+      VarP{}      -> 1
+      ConP _ _ ps -> countPatternVars ps
+      DotP{}      -> 1   -- dot patterns are treated as variables in the clauses
+      _           -> 0
+
+-- Computing modalities of pattern variables ------------------------------
+
+class PatternVarModalities p where
+  type PatVar p
+  -- | Get the list of pattern variables annotated with modalities.
+  patternVarModalities :: p -> [(PatVar p, Modality)]
+
+instance PatternVarModalities a => PatternVarModalities [a] where
+  type PatVar [a] = PatVar a
+  patternVarModalities = foldMap patternVarModalities
+
+instance PatternVarModalities a => PatternVarModalities (Named s a) where
+  type PatVar (Named s a) = PatVar a
+  patternVarModalities = foldMap patternVarModalities
+
+instance PatternVarModalities a => PatternVarModalities (Arg a) where
+  type PatVar (Arg a) = PatVar a
+  patternVarModalities arg = map (second (composeModality m)) (patternVarModalities $ unArg arg)
+    where m = getModality arg
+
+-- UNUSED:
+-- instance PatternVarModalities a x => PatternVarModalities (Elim' a) x where
+--   patternVarModalities (Apply x) = patternVarModalities x -- Note: x :: Arg a
+--   patternVarModalities (IApply x y p) = patternVarModalities [x, y, p]
+--   patternVarModalities Proj{}    = []
+
+instance PatternVarModalities (Pattern' x) where
+  type PatVar (Pattern' x) = x
+  patternVarModalities p =
+    case p of
+      VarP _ x    -> [(x, defaultModality)]
+      ConP _ _ ps -> patternVarModalities ps
+      DefP _ _ ps -> patternVarModalities ps
+      DotP{}      -> []
+      LitP{}      -> []
+      ProjP{}     -> []
+      IApplyP _ _ _ x -> [(x, defaultModality)]
+
+
+hasDefP :: [NamedArg DeBruijnPattern] -> Bool
+hasDefP ps = getAny $ flip foldPattern ps $ \ (x :: DeBruijnPattern) ->
+                  case x of
+                    DefP{} -> Any True
+                    _      -> Any False
diff --git a/src/full/Agda/Syntax/Internal/SanityCheck.hs b/src/full/Agda/Syntax/Internal/SanityCheck.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/SanityCheck.hs
@@ -0,0 +1,79 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Sanity checking for internal syntax. Mostly checking variable scoping.
+module Agda.Syntax.Internal.SanityCheck where
+
+import Control.Monad
+import qualified Data.IntSet as Set
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.List ( dropEnd, initWithDefault )
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+import Agda.Utils.Impossible
+
+
+sanityCheckVars :: (Pretty a, Free a) => Telescope -> a -> TCM ()
+sanityCheckVars tel v =
+  case filter bad (Set.toList $ allFreeVars v) of
+    [] -> return ()
+    xs -> do
+      alwaysReportSDoc "impossible" 1 . return $
+        sep [ hang "Sanity check failed for" 2
+                   (hang (pretty tel <+> "|-") 2 (pretty v))
+            , text $ "out of scope: " ++ show xs ]
+      __IMPOSSIBLE__
+  where
+    n     = size tel
+    bad x = x < 0 || x >= n
+
+-- | Check that @Γ ⊢ ρ : Δ@.
+sanityCheckSubst :: (Pretty a, Free a) => Telescope -> Substitution' a -> Telescope -> TCM ()
+sanityCheckSubst gamma rho delta = go gamma rho delta
+  where
+    go gamma rho delta =
+      case rho of
+
+        IdS      -> do
+          unless (size gamma == size delta) $ err $
+            "idS:" <+> hang (pretty gamma <+> "/=") 2 (pretty delta)
+
+        EmptyS _ -> do
+          unless (null delta) $ err $
+            "emptyS:" <+> pretty delta <+> "is not empty"
+
+        v :# rho -> do
+          when (null delta) $ err $ "consS: empty target"
+          sanityCheckVars gamma v
+          sanityCheckSubst gamma rho (dropLast delta)
+
+        Strengthen _ n rho -> do
+          unless (natSize delta >= toEnum n) $ err $ "strS: empty target"
+          sanityCheckSubst gamma rho (dropLastN n delta)
+
+        Wk n rho -> do
+          unless (natSize gamma >= toEnum n) $ err $
+            "wkS:" <+> sep [ "|" <> pretty gamma <> "|" , text $ "< " ++ show n ]
+          sanityCheckSubst (dropLastN n gamma) rho delta
+
+        Lift n rho -> do
+          unless (natSize gamma >= toEnum n) $ err $
+            "liftS: source" <+> sep [ "|" <> pretty gamma <> "|" , text $ "< " ++ show n ]
+          unless (natSize delta >= toEnum n) $ err $
+            "liftS: target" <+> sep [ "|" <> pretty delta <> "|" , text $ "< " ++ show n ]
+          sanityCheckSubst (dropLastN n gamma) rho (dropLastN n delta)
+
+    dropLast = telFromList . initWithDefault __IMPOSSIBLE__ . telToList
+    dropLastN n = telFromList . dropEnd n . telToList
+
+    err reason = do
+      alwaysReportSDoc "impossible" 1 . return $
+        sep [ hang "Sanity check failed for" 2 $
+              hang (pretty gamma <+> "|-") 2 $
+              hang (pretty rho <+> ":") 2 $
+                    pretty delta
+            , reason ]
+      __IMPOSSIBLE__
diff --git a/src/full/Agda/Syntax/Internal/Univ.hs b/src/full/Agda/Syntax/Internal/Univ.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Internal/Univ.hs
@@ -0,0 +1,103 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE DeriveAnyClass             #-}
+
+-- | Kinds of standard universes: @Prop@, @Type@, @SSet@.
+
+module Agda.Syntax.Internal.Univ where
+
+import Control.DeepSeq ( NFData  )
+import GHC.Generics    ( Generic )
+
+import Agda.Utils.Boolean
+
+-- * Types
+---------------------------------------------------------------------------
+
+-- | Flavor of standard universe (@Prop < Type < SSet@,).
+data Univ
+  = UProp  -- ^ Fibrant universe of propositions.
+  | UType  -- ^ Fibrant universe.
+  | USSet  -- ^ Non-fibrant universe.
+  deriving stock (Eq, Ord, Show, Bounded, Enum, Generic)
+  deriving anyclass NFData
+    -- NB: for deriving Ord, keep ordering UProp < UType < USSet!
+
+-- | We have @IsFibrant < IsStrict@.
+data IsFibrant
+  = IsFibrant  -- ^ Fibrant universe.
+  | IsStrict   -- ^ Non-fibrant universe.
+  deriving (Show, Eq, Ord, Generic)
+    -- NB: for deriving Ord, keep ordering IsFibrant < IsStrict!
+
+instance Boolean IsFibrant where
+  fromBool = \case
+    True -> IsFibrant
+    False -> IsStrict
+
+instance IsBool IsFibrant where
+  toBool = \case
+    IsFibrant -> True
+    IsStrict -> False
+
+-- * Universe kind arithmetic
+---------------------------------------------------------------------------
+
+-- | The successor universe type of a universe.
+univUniv :: Univ -> Univ
+univUniv = \case
+  UProp -> UType
+  UType -> UType
+  USSet -> USSet
+
+-- | Compute the universe type of a function space from the universe types of domain and codomain.
+funUniv :: Univ -> Univ -> Univ
+funUniv = curry $ \case
+  (USSet, _) -> USSet
+  (_, USSet) -> USSet
+  (_, u)     -> u
+
+-- ** Inverting 'funUniv'
+
+-- | Conclude @u1@ from @funUniv u1 u2@ and @u2@.
+
+domainUniv ::
+      Bool       -- ^ Have 'UProp'?
+   -> Univ       -- ^ 'Univ' kind of the 'funSort'.
+   -> Univ       -- ^ 'Univ' kind of the codomain.
+   -> Maybe Univ -- ^ 'Univ' kind of the domain, if unique.
+domainUniv propEnabled u = \case
+  USSet -> Nothing
+  _  | u == USSet  -> Just USSet
+     | propEnabled -> Nothing
+     | otherwise   -> Just UType
+
+-- | Conclude @u2@ from @funUniv u1 u2@ and @u1@.
+
+codomainUniv ::
+      Univ       -- ^ 'Univ' kind of the 'funSort'.
+   -> Univ       -- ^ 'Univ' kind of the domain.
+   -> Maybe Univ -- ^ 'Univ' kind of the codomain, if uniquely exists.
+codomainUniv u = \case
+  USSet -> Nothing
+  _ -> Just u
+
+-- * Fibrancy
+
+-- | Fibrancy of standard universes.
+
+univFibrancy :: Univ -> IsFibrant
+univFibrancy = \case
+  UProp -> IsFibrant
+  UType -> IsFibrant
+  USSet -> IsStrict
+
+-- * Printing
+
+-- | Hacky showing of standard universes, does not take actual names into account.
+
+showUniv :: Univ -> String
+showUniv = \case
+  UProp -> "Prop"
+  UType -> "Set"
+  USSet -> "SSet"
diff --git a/src/full/Agda/Syntax/Literal.hs b/src/full/Agda/Syntax/Literal.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Literal.hs
@@ -0,0 +1,106 @@
+
+module Agda.Syntax.Literal where
+
+import Control.DeepSeq
+import Data.Char
+import Data.Word
+
+import Data.Text (Text)
+import qualified Data.Text as T
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.TopLevelModuleName.Boot (TopLevelModuleName')
+import Agda.Syntax.Position (Range)
+import Agda.Utils.Float ( doubleDenotEq, doubleDenotOrd )
+import Agda.Syntax.Common.Pretty
+
+type RLiteral = Ranged Literal
+data Literal
+  = LitNat    !Integer
+  | LitWord64 !Word64
+  | LitFloat  !Double
+  | LitString !Text
+  | LitChar   !Char
+  | LitQName  !QName
+  | LitMeta   !(TopLevelModuleName' Range) !MetaId
+  deriving Show
+
+instance Pretty Literal where
+    pretty (LitNat n)     = hlNumber $ pretty n
+    pretty (LitWord64 n)  = hlNumber $ pretty n
+    pretty (LitFloat d)   = hlNumber $ pretty d
+    pretty (LitString s)  = hlString . text $ showText s ""
+    pretty (LitChar c)    = hlString . text $ "'" ++ showChar' c "'"
+    pretty (LitQName x)   = pretty x
+    pretty (LitMeta _ x)  = pretty x
+
+showText :: Text -> ShowS
+showText s = showString "\""
+           . T.foldr (\ c -> (showChar' c .)) id s
+           . showString "\""
+
+showChar' :: Char -> ShowS
+showChar' '"'   = showString "\\\""
+showChar' c
+    | escapeMe c = showLitChar c
+    | otherwise  = showString [c]
+    where
+        escapeMe c = not (isPrint c) || c == '\\'
+
+instance Eq Literal where
+  LitNat n    == LitNat m    = n == m
+  -- ASR (2016-09-29). We use bitwise equality for comparing Double
+  -- because Haskell's Eq, which equates 0.0 and -0.0, allows to prove
+  -- a contradiction (see Issue #2169).
+  LitWord64 n == LitWord64 m = n == m
+  LitFloat x  == LitFloat y  = doubleDenotEq x y
+  LitString s == LitString t = s == t
+  LitChar c   == LitChar d   = c == d
+  LitQName x  == LitQName y  = x == y
+  LitMeta f x == LitMeta g y = (f, x) == (g, y)
+  _           == _             = False
+
+instance Ord Literal where
+  LitNat n    `compare` LitNat m    = n `compare` m
+  LitWord64 n `compare` LitWord64 m = n `compare` m
+  LitFloat x  `compare` LitFloat y  = doubleDenotOrd x y
+  LitString s `compare` LitString t = s `compare` t
+  LitChar c   `compare` LitChar d   = c `compare` d
+  LitQName x  `compare` LitQName y  = x `compare` y
+  LitMeta f x `compare` LitMeta g y = (f, x) `compare` (g, y)
+  compare LitNat{}    _ = LT
+  compare _ LitNat{}    = GT
+  compare LitWord64{} _ = LT
+  compare _ LitWord64{} = GT
+  compare LitFloat{}  _ = LT
+  compare _ LitFloat{}  = GT
+  compare LitString{} _ = LT
+  compare _ LitString{} = GT
+  compare LitChar{} _   = LT
+  compare _ LitChar{}   = GT
+  compare LitQName{} _  = LT
+  compare _ LitQName{}  = GT
+  -- compare LitMeta{} _   = LT
+  -- compare _ LitMeta{}   = GT
+
+instance KillRange Literal where
+  killRange (LitNat    x) = LitNat    x
+  killRange (LitWord64 x) = LitWord64 x
+  killRange (LitFloat  x) = LitFloat  x
+  killRange (LitString x) = LitString x
+  killRange (LitChar   x) = LitChar   x
+  killRange (LitQName  x) = killRangeN LitQName x
+  killRange (LitMeta m x) = LitMeta (killRange m) x
+
+-- | Ranges are not forced.
+
+instance NFData Literal where
+  rnf (LitNat _     ) = ()
+  rnf (LitWord64 _  ) = ()
+  rnf (LitFloat _   ) = ()
+  rnf (LitString _  ) = ()
+  rnf (LitChar _    ) = ()
+  rnf (LitQName a   ) = rnf a
+  rnf (LitMeta m _  ) = rnf m
diff --git a/src/full/Agda/Syntax/Notation.hs b/src/full/Agda/Syntax/Notation.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Notation.hs
@@ -0,0 +1,430 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| As a concrete name, a notation is a non-empty list of alternating 'IdPart's and holes.
+    In contrast to concrete names, holes can be binders.
+
+    Example:
+    @
+       syntax fmap (λ x → e) xs = for x ∈ xs return e
+    @
+
+    The declared notation for @fmap@ is @for_∈_return_@ where the first hole is a binder.
+-}
+
+module Agda.Syntax.Notation where
+
+import Prelude hiding (null)
+
+import Control.Arrow ( (&&&) )
+import Control.DeepSeq
+import Control.Monad
+import Control.Monad.Except
+
+import qualified Data.List as List
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import GHC.Generics (Generic)
+
+import qualified Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty
+import Agda.Syntax.Concrete.Name
+import Agda.Syntax.Concrete.Pretty()
+import Agda.Syntax.Position
+
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1           ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+-- | Data type constructed in the Happy parser; converted to
+-- 'NotationPart' before it leaves the Happy code.
+data HoleName
+  = LambdaHole { _bindHoleNames :: List1 RString
+               , holeName       :: RString
+               }
+    -- ^ @λ x₁ … xₙ → y@: The first argument contains the bound names.
+  | ExprHole   { holeName      :: RString }
+    -- ^ Simple named hole with hiding.
+
+-- | Is the hole a binder?
+isLambdaHole :: HoleName -> Bool
+isLambdaHole (LambdaHole _ _) = True
+isLambdaHole _ = False
+
+-- | Get a flat list of identifier parts of a notation.
+stringParts :: Notation -> [String]
+stringParts gs = [ rangedThing x | IdPart x <- gs ]
+
+-- | Target argument position of a part (Nothing if it is not a hole).
+holeTarget :: NotationPart -> Maybe Int
+holeTarget (VarPart _ n)  = Just $ holeNumber $ rangedThing n
+holeTarget (WildPart n)   = Just $ holeNumber $ rangedThing n
+holeTarget (HolePart _ n) = Just $ rangedThing $ namedArg n
+holeTarget IdPart{}       = Nothing
+
+-- | Is the part a hole?
+isAHole :: NotationPart -> Bool
+isAHole HolePart{} = True
+isAHole VarPart{}  = False
+isAHole WildPart{} = False
+isAHole IdPart{}   = False
+
+-- | Is the part a binder?
+isBinder :: NotationPart -> Bool
+isBinder HolePart{} = False
+isBinder VarPart{}  = True
+isBinder WildPart{} = True
+isBinder IdPart{}   = False
+
+-- | Classification of notations.
+
+data NotationKind
+  = InfixNotation   -- ^ Ex: @_bla_blub_@.
+  | PrefixNotation  -- ^ Ex: @_bla_blub@.
+  | PostfixNotation -- ^ Ex: @bla_blub_@.
+  | NonfixNotation  -- ^ Ex: @bla_blub@.
+  | NoNotation
+   deriving (Eq, Show, Generic)
+
+-- | Classify a notation by presence of leading and/or trailing
+-- /normal/ holes.
+notationKind :: Notation -> NotationKind
+notationKind []  = NoNotation
+notationKind (h:syn) =
+  case (isAHole h, isAHole $ last1 h syn) of
+    (True , True ) -> InfixNotation
+    (True , False) -> PostfixNotation
+    (False, True ) -> PrefixNotation
+    (False, False) -> NonfixNotation
+
+-- | From notation with names to notation with indices.
+--
+--   An example (with some parts of the code omitted):
+--   The lists
+--   @["for", "x", "∈", "xs", "return", "e"]@
+--   and
+--   @['LambdaHole' ("x" :| []) "e", 'ExprHole' "xs"]@
+--   are mapped to the following notation:
+--   @
+--      [ 'IdPart' "for"    , 'VarPart' ('BoundVariablePosition' 0 0)
+--      , 'IdPart' "∈"      , 'HolePart' 1
+--      , 'IdPart' "return" , 'HolePart' 0
+--      ]
+--   @
+mkNotation :: [NamedArg HoleName] -> [RString] -> Either String Notation
+mkNotation _ [] = throwError "empty notation is disallowed"
+mkNotation holes ids = do
+  unless uniqueHoleNames     $ throwError "syntax must use unique argument names"
+  let xs :: Notation = map mkPart ids
+  unless (noAdjacentHoles xs)  $ throwError $ concat
+     [ "syntax must not contain adjacent holes ("
+     , prettyHoles
+     , ")"
+     ]
+  unless (isExprLinear xs)   $ throwError "syntax must use holes exactly once"
+  unless (isLambdaLinear xs) $ throwError "syntax must use binding holes exactly once"
+  -- Andreas, 2018-10-18, issue #3285:
+  -- syntax that is just a single hole is ill-formed and crashes the operator parser
+  when   (isSingleHole xs)   $ throwError "syntax cannot be a single hole"
+  return $ insertWildParts xs
+    where
+      holeNames :: [RString]
+      holeNames = map namedArg holes >>= \case
+        LambdaHole _ y -> [y]
+        ExprHole y     -> [y]
+
+      prettyHoles :: String
+      prettyHoles = List.unwords $ map (rawNameToString . rangedThing) holeNames
+
+      mkPart ident = maybe (IdPart ident) (`withRangeOf` ident) $ lookup ident holeMap
+
+      holeNumbers   = [0 .. length holes - 1]
+
+      numberedHoles :: [(Int, NamedArg HoleName)]
+      numberedHoles = zip holeNumbers holes
+
+      -- The WildParts don't correspond to anything in the right-hand side so
+      -- we add them next to their corresponding body. Slightly subtle: due to
+      -- the way the operator parsing works they can't be added first or last.
+      insertWildParts :: [NotationPart] -> [NotationPart]
+      insertWildParts xs = foldr ins xs wilds
+        where
+          wilds = [ i | (_, WildPart i) <- holeMap ]
+
+          ins w (HolePart r h : hs)
+            | namedArg h == fmap holeNumber w =
+              HolePart r h : WildPart w : hs
+          ins w (h : hs) = h : insBefore w hs
+          ins _ [] = __IMPOSSIBLE__
+
+          insBefore w (HolePart r h : hs)
+            | namedArg h == fmap holeNumber w =
+              WildPart w : HolePart r h : hs
+          insBefore w (h : hs) = h : insBefore w hs
+          insBefore _ [] = __IMPOSSIBLE__
+
+      -- A map (association list) from hole names to notation parts. A
+      -- @LambdaHole@ contributes one or more entries, one @HolePart@
+      -- and zero or more @VarPart@s or @WildParts@, all mapped to the
+      -- same number.
+      holeMap :: [(RString, NotationPart)]
+      holeMap = do
+        (i, h) <- numberedHoles
+        let ri x   = Ranged (getRange x) i
+            rp x n = Ranged (getRange x) $
+                     BoundVariablePosition
+                       { holeNumber = i
+                       , varNumber  = n
+                       }
+            hole y = HolePart noRange $ fmap (ri y <$) h
+                              -- This range is filled in by mkPart.
+        case namedArg h of
+          ExprHole y      -> [(y, hole y)]
+          LambdaHole xs y -> [(y, hole y)] ++
+            zipWith
+              (\ n x -> case rangedThing x of
+                "_" -> (x, WildPart (rp x n))
+                _   -> (x, VarPart noRange (rp x n)))
+                                   -- Filled in by mkPart.
+              [0..]
+              (List1.toList xs)
+
+      -- Check whether all hole names are distinct.
+      -- The hole names are the keys of the @holeMap@.
+      uniqueHoleNames = distinct [ x | (x, _) <- holeMap, rangedThing x /= "_" ]
+
+      isExprLinear xs =
+        List.sort [ i | x <- xs, isAHole x, let Just i = holeTarget x ]
+          ==
+        holeNumbers
+
+      isLambdaLinear xs =
+        List.sort [ rangedThing x | VarPart _ x <- xs ]
+          ==
+        [ BoundVariablePosition { holeNumber = i, varNumber = v }
+        | (i, h) <- numberedHoles
+        , LambdaHole vs _ <- [namedArg h]
+        , (v, x) <- zip [0..] $ map rangedThing $ List1.toList vs
+        , x /= "_"
+        ]
+
+      noAdjacentHoles :: [NotationPart] -> Bool
+      noAdjacentHoles =
+        noAdj .
+        filter (\h -> case h of
+                   HolePart{} -> True
+                   IdPart{}   -> True
+                   _          -> False)
+        where
+        noAdj []       = __IMPOSSIBLE__
+        noAdj [x]      = True
+        noAdj (x:y:xs) =
+          not (isAHole x && isAHole y) &&
+          noAdj (y:xs)
+
+      isSingleHole :: [NotationPart] -> Bool
+      isSingleHole = \case
+        [ IdPart{} ] -> False
+        [ _hole ]    -> True
+        _            -> False
+
+-- | All the notation information related to a name.
+data NewNotation = NewNotation
+  { notaName  :: QName
+  , notaNames :: Set A.Name
+    -- ^ The names the syntax and/or fixity belong to.
+    --
+    -- Invariant: The set is non-empty. Every name in the list matches
+    -- 'notaName'.
+  , notaFixity :: Fixity
+    -- ^ Associativity and precedence (fixity) of the names.
+  , notation :: Notation
+    -- ^ Syntax associated with the names.
+  , notaIsOperator :: Bool
+    -- ^ True if the notation comes from an operator (rather than a
+    -- syntax declaration).
+  } deriving (Show, Generic)
+
+instance LensFixity NewNotation where
+  lensFixity f nota = f (notaFixity nota) <&> \ fx -> nota { notaFixity = fx }
+
+-- | If an operator has no specific notation, then it is computed from
+-- its name.
+namesToNotation :: QName -> A.Name -> NewNotation
+namesToNotation q n = NewNotation
+  { notaName       = q
+  , notaNames      = Set.singleton n
+  , notaFixity     = f
+  , notation       = if null syn then syntaxOf (unqualify q) else syn
+  , notaIsOperator = null syn
+  }
+  where Fixity' f syn _ = A.nameFixity n
+
+-- | Replace 'noFixity' by 'defaultFixity'.
+useDefaultFixity :: NewNotation -> NewNotation
+useDefaultFixity n
+  | notaFixity n == noFixity = n { notaFixity = defaultFixity }
+  | otherwise                = n
+
+-- | Return the 'IdPart's of a notation, the first part qualified,
+--   the other parts unqualified.
+--   This allows for qualified use of operators, e.g.,
+--   @M.for x ∈ xs return e@, or @x ℕ.+ y@.
+notationNames :: NewNotation -> [QName]
+notationNames (NewNotation q _ _ parts _) =
+  zipWith ($) (reQualify : repeat QName) [simpleName $ rangedThing x | IdPart x <- parts ]
+  where
+    -- The qualification of @q@.
+    modules     = List1.init (qnameParts q)
+    -- Putting the qualification onto @x@.
+    reQualify x = List.foldr Qual (QName x) modules
+
+-- | Create a 'Notation' (without binders) from a concrete 'Name'.
+--   Does the obvious thing:
+--   'Hole's become 'HolePart's, 'Id's become 'IdParts'.
+--   If 'Name' has no 'Hole's, it returns 'noNotation'.
+syntaxOf :: Name -> Notation
+syntaxOf y
+  | isOperator y = mkSyn 0 $ List1.toList $ nameNameParts y
+  | otherwise    = noNotation
+  where
+    -- Turn a concrete name into a Notation,
+    -- numbering the holes from left to right.
+    -- Result will have no 'BindingHole's.
+    mkSyn :: Int -> [NamePart] -> Notation
+    mkSyn n []          = []
+    mkSyn n (Hole : xs) = HolePart noRange (defaultNamedArg $ unranged n) : mkSyn (1 + n) xs
+    mkSyn n (Id x : xs) = IdPart (unranged x) : mkSyn n xs
+
+-- | Merges 'NewNotation's that have the same precedence level and
+-- notation, with two exceptions:
+--
+-- * Operators and notations coming from syntax declarations are kept
+--   separate.
+--
+-- * If /all/ instances of a given 'NewNotation' have the same
+--   precedence level or are \"unrelated\", then they are merged. They
+--   get the given precedence level, if any, and otherwise they become
+--   unrelated (but related to each other).
+--
+-- If 'NewNotation's that are merged have distinct associativities,
+-- then they get 'NonAssoc' as their associativity.
+--
+-- Precondition: No 'A.Name' may occur in more than one list element.
+-- Every 'NewNotation' must have the same 'notaName'.
+--
+-- Postcondition: No 'A.Name' occurs in more than one list element.
+mergeNotations :: List1 NewNotation -> List1 NewNotation
+mergeNotations =
+  fmap merge
+  . List1.concatMap1 groupIfLevelsMatch
+  . List1.groupOn1 (notation &&& notaIsOperator)
+  where
+  groupIfLevelsMatch :: List1 NewNotation -> List1 (List1 NewNotation)
+  groupIfLevelsMatch ns =
+    if allEqual (map fixityLevel related)
+    then singleton $ sameAssoc $ sameLevel ns
+    else fmap singleton ns
+    where
+    -- Fixities of operators whose precedence level is not Unrelated.
+    related = List1.mapMaybe (maybeRelated . notaFixity) ns
+      where
+        maybeRelated f =
+          case fixityLevel f of
+            Unrelated  -> Nothing
+            Related {} -> Just f
+
+    -- Precondition: All related operators have the same precedence
+    -- level.
+    --
+    -- Gives all unrelated operators the same level.
+    sameLevel = fmap (set (_notaFixity . _fixityLevel) level)
+      where
+      level = case related of
+        f : _ -> fixityLevel f
+        []    -> Unrelated
+
+    -- If all related operators have the same associativity, then the
+    -- unrelated operators get the same associativity, and otherwise
+    -- all operators get the associativity NonAssoc.
+    sameAssoc = fmap (set (_notaFixity . _fixityAssoc) assoc)
+      where
+      assoc = case related of
+        f : _ | allEqual (map fixityAssoc related) -> fixityAssoc f
+        _                                          -> NonAssoc
+
+  merge :: List1 NewNotation -> NewNotation
+  merge (n :| ns) = n { notaNames = Set.unions $ map notaNames $ n:ns }
+
+-- | Check if a notation contains any lambdas (in which case it cannot be used in a pattern).
+isLambdaNotation :: NewNotation -> Bool
+isLambdaNotation n = any isBinder (notation n)
+  where
+    isBinder VarPart{}  = True
+    isBinder WildPart{} = True
+    isBinder IdPart{}   = False
+    isBinder HolePart{} = False
+
+-- | Lens for 'Fixity' in 'NewNotation'.
+
+_notaFixity :: Lens' NewNotation Fixity
+_notaFixity f r = f (notaFixity r) <&> \x -> r { notaFixity = x }
+
+-- * Sections
+
+-- | Sections, as well as non-sectioned operators.
+
+data NotationSection = NotationSection
+  { sectNotation  :: NewNotation
+  , sectKind      :: NotationKind
+    -- ^ For non-sectioned operators this should match the notation's
+    -- 'notationKind'.
+  , sectLevel     :: Maybe FixityLevel
+    -- ^ Effective precedence level. 'Nothing' for closed notations.
+  , sectIsSection :: Bool
+    -- ^ 'False' for non-sectioned operators.
+  }
+  deriving (Show, Generic)
+
+-- | Converts a notation to a (non-)section.
+
+noSection :: NewNotation -> NotationSection
+noSection n = NotationSection
+  { sectNotation  = n
+  , sectKind      = notationKind (notation n)
+  , sectLevel     = Just (fixityLevel (notaFixity n))
+  , sectIsSection = False
+  }
+
+
+-- * Pretty printing
+
+instance Pretty NewNotation where
+  pretty (NewNotation x _xs fx nota isOp) = hsepWith "=" px pn
+    where
+    px = fsep [ if isOp then empty else "syntax" , pretty fx , pretty x ]
+    pn = if isOp then empty else pretty nota
+
+instance Pretty NotationKind where pretty = pshow
+
+instance Pretty NotationSection where
+  pretty (NotationSection nota kind mlevel isSection)
+    | isSection = fsep
+        [ "section"
+        , pretty kind
+        , maybe empty pretty mlevel
+        , pretty nota
+        ]
+    | otherwise = pretty nota
+
+-- NFData instances
+
+instance NFData NotationKind
+instance NFData NewNotation
+instance NFData NotationSection
diff --git a/src/full/Agda/Syntax/Parser.hs b/src/full/Agda/Syntax/Parser.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser.hs
@@ -0,0 +1,270 @@
+
+module Agda.Syntax.Parser
+    ( -- * Types
+      Parser
+      -- * Parse functions
+    , Agda.Syntax.Parser.parse
+    , Agda.Syntax.Parser.parsePosString
+    , parseFile
+      -- * Parsers
+    , moduleParser
+    , moduleNameParser
+    , acceptableFileExts
+    , exprParser
+    , exprWhereParser
+    , holeContentParser
+    , tokensParser
+      -- * Reading files.
+    , readFilePM
+      -- * Parse errors
+    , ParseError(..)
+    , ParseWarning(..)
+    , PM(..)
+    , runPMIO
+    ) where
+
+import Control.Exception
+import Control.Monad          ( forM_ )
+import Control.Monad.Except
+import Control.Monad.State
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+import Data.Bifunctor
+import qualified Data.List as List
+import Data.Text.Lazy (Text)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Parser.Monad as M hiding (Parser, parseFlags)
+import qualified Agda.Syntax.Parser.Monad as M
+import qualified Agda.Syntax.Parser.Parser as P
+import Agda.Syntax.Parser.Lexer
+import Agda.Syntax.Parser.Literate
+import Agda.Syntax.Concrete
+import Agda.Syntax.Concrete.Attribute
+import Agda.Syntax.Parser.Tokens
+
+import Agda.Utils.FileName
+import Agda.Utils.IO.UTF8 (readTextFile)
+import Agda.Utils.Maybe   (forMaybe)
+import qualified Agda.Utils.Maybe.Strict as Strict
+
+------------------------------------------------------------------------
+-- Wrapping parse results
+
+-- | A monad for handling parse errors and warnings.
+
+newtype PM a = PM { unPM :: ExceptT ParseError (StateT [ParseWarning] IO) a }
+  deriving ( Functor, Applicative, Monad, MonadIO
+           , MonadError ParseError, MonadState [ParseWarning]
+           )
+
+-- | Run a 'PM' computation, returning a list of warnings in first-to-last order
+--   and either a parse error or the parsed thing.
+
+runPMIO :: (MonadIO m) => PM a -> m (Either ParseError a, [ParseWarning])
+runPMIO = liftIO . fmap (second reverse) . flip runStateT [] . runExceptT . unPM
+
+-- | Add a 'ParseWarning'.
+
+warning :: ParseWarning -> PM ()
+warning w = PM (modify (w:))
+
+-- | Embed a 'ParseResult' as 'PM' computation.
+
+wrap :: ParseResult a -> PM (a, Attributes)
+wrap (ParseFailed err)  = throwError err
+wrap (ParseOk s x)      = do
+  modify' (parseWarnings s ++)
+  return (x, parseAttributes s)
+
+wrapM :: IO (ParseResult a) -> PM (a, Attributes)
+wrapM m = liftIO m >>= wrap
+
+-- | Returns the contents of the given file.
+
+readFilePM :: RangeFile -> PM Text
+readFilePM file =
+  wrapIOM (ReadFileError file) $
+  readTextFile (filePath $ rangeFilePath file)
+
+wrapIOM :: (MonadError e m, MonadIO m) => (IOError -> e) -> IO a -> m a
+wrapIOM f m = do
+  a <- liftIO $ (Right <$> m) `catch` (\ err -> return $ Left (err :: IOError))
+  case a of
+    Right x  -> return x
+    Left err -> throwError (f err)
+
+------------------------------------------------------------------------
+-- Parse functions
+
+-- | Wrapped Parser type.
+
+data Parser a = Parser
+  { parser         :: M.Parser a
+  , parseFlags     :: ParseFlags
+  , parseLiterate  :: LiterateParser a
+  }
+
+type LiterateParser a =
+  Parser a -> [Layer] -> PM (a, Attributes)
+
+-- | Initial state for lexing.
+
+normalLexState :: [LexState]
+normalLexState = [normal]
+
+-- | Initial state for lexing with top-level layout.
+
+layoutLexState :: [LexState]
+layoutLexState = [layout, normal]
+
+-- | Parse without top-level layout.
+
+parse :: Parser a -> String -> PM (a, Attributes)
+parse p = wrapM . return . M.parse (parseFlags p) normalLexState (parser p)
+
+-- | Parse with top-level layout.
+
+parseFileFromString
+  :: SrcFile   -- ^ Name of source file.
+  -> Parser a  -- ^ Parser to use.
+  -> String    -- ^ Contents of source file.
+  -> PM (a, Attributes)
+parseFileFromString src p = wrapM . return . M.parseFromSrc (parseFlags p) layoutLexState (parser p) src
+
+-- | Parse with top-level layout.
+
+parseLiterateWithoutComments :: LiterateParser a
+parseLiterateWithoutComments p layers = parseFileFromString (literateSrcFile layers) p $ illiterate layers
+
+-- | Parse with top-level layout.
+
+parseLiterateWithComments :: LiterateParser [Token]
+parseLiterateWithComments p layers = do
+  (code, coh) <- parseLiterateWithoutComments p layers
+  let literate = filter (not . isCodeLayer) layers
+  let (terms, overlaps) = interleaveRanges (map Left code) (map Right literate)
+
+  forM_ (map fst overlaps) $ \c ->
+    warning $ OverlappingTokensWarning { warnRange = getRange c }
+
+  (, coh) <$> (return $ forMaybe terms $ \case
+    Left t                           -> Just t
+    Right (Layer Comment interval s) -> Just $ TokTeX    (interval, s)
+    Right (Layer Markup  interval s) -> Just $ TokMarkup (interval, s)
+    Right (Layer Code _ _)           -> Nothing)
+
+
+parseLiterateFile
+  :: Processor
+  -> Parser a
+  -> RangeFile
+     -- ^ The file.
+  -> String
+     -- ^ The file contents. Note that the file is /not/ read from
+     -- disk.
+  -> PM (a, Attributes)
+parseLiterateFile po p path = parseLiterate p p . po (startPos (Just path))
+
+parsePosString ::
+  Parser a -> Position -> String -> PM (a, Attributes)
+parsePosString p pos = wrapM . return . M.parsePosString pos (parseFlags p) normalLexState (parser p)
+
+-- | Extensions supported by `parseFile`.
+
+acceptableFileExts :: [String]
+acceptableFileExts = ".agda" : (fst <$> literateProcessors)
+
+parseFile
+  :: Show a
+  => Parser a
+  -> RangeFile
+     -- ^ The file.
+  -> String
+     -- ^ The file contents. Note that the file is /not/ read from
+     -- disk.
+  -> PM ((a, Attributes), FileType)
+parseFile p file input =
+  if ".agda" `List.isSuffixOf` path then
+    (, AgdaFileType) <$> parseFileFromString (Strict.Just file) p input
+  else
+    go literateProcessors
+  where
+    path = filePath (rangeFilePath file)
+
+    go [] = throwError InvalidExtensionError
+                   { errPath = file
+                   , errValidExts = acceptableFileExts
+                   }
+    go ((ext, (po, ft)) : pos)
+      | ext `List.isSuffixOf` path =
+          (, ft) <$> parseLiterateFile po p file input
+      | otherwise = go pos
+
+------------------------------------------------------------------------
+-- Specific parsers
+
+-- | Parses a module.
+
+moduleParser :: Parser Module
+moduleParser = Parser
+  { parser        = P.moduleParser
+  , parseFlags    = withoutComments
+  , parseLiterate = parseLiterateWithoutComments
+  }
+
+-- | Parses a module name.
+
+moduleNameParser :: Parser QName
+moduleNameParser = Parser
+  { parser        = P.moduleNameParser
+  , parseFlags    = withoutComments
+  , parseLiterate = parseLiterateWithoutComments
+  }
+
+-- | Parses an expression.
+
+exprParser :: Parser Expr
+exprParser = Parser
+  { parser        = P.exprParser
+  , parseFlags    = withoutComments
+  , parseLiterate = parseLiterateWithoutComments
+  }
+
+-- | Parses an expression followed by a where clause.
+
+exprWhereParser :: Parser ExprWhere
+exprWhereParser = Parser
+  { parser        = P.exprWhereParser
+  , parseFlags    = withoutComments
+  , parseLiterate = parseLiterateWithoutComments
+  }
+
+-- | Parses an expression or some other content of an interaction hole.
+
+holeContentParser :: Parser HoleContent
+holeContentParser = Parser
+  { parser        = P.holeContentParser
+  , parseFlags    = withoutComments
+  , parseLiterate = parseLiterateWithoutComments
+  }
+
+-- | Gives the parsed token stream (including comments).
+
+tokensParser :: Parser [Token]
+tokensParser = Parser
+  { parser        = P.tokensParser
+  , parseFlags    = withComments
+  , parseLiterate = parseLiterateWithComments
+  }
+
+-- | Keep comments in the token stream generated by the lexer.
+
+withComments :: ParseFlags
+withComments = defaultParseFlags { parseKeepComments = True }
+
+-- | Do not keep comments in the token stream generated by the lexer.
+
+withoutComments :: ParseFlags
+withoutComments = defaultParseFlags { parseKeepComments = False }
diff --git a/src/full/Agda/Syntax/Parser/Alex.hs b/src/full/Agda/Syntax/Parser/Alex.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Alex.hs
@@ -0,0 +1,157 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| This module defines the things required by Alex and some other
+    Alex related things.
+-}
+module Agda.Syntax.Parser.Alex
+    ( -- * Alex requirements
+      AlexInput(..)
+    , lensLexInput
+    , alexInputPrevChar
+    , alexGetChar, alexGetByte
+      -- * Lex actions
+    , LexAction(..), LexPredicate
+    , (.&&.), (.||.), not'
+    , PreviousInput, CurrentInput, TokenLength
+      -- * Monad operations
+    , getLexInput, setLexInput
+    )
+    where
+
+import Control.Monad.State
+import Data.Char
+import Data.Word
+
+import Agda.Syntax.Position
+import Agda.Syntax.Parser.Monad
+
+import Agda.Utils.Lens
+import Agda.Utils.Tuple
+
+-- | This is what the lexer manipulates.
+data AlexInput = AlexInput
+  { lexSrcFile  :: !SrcFile              -- ^ File.
+  , lexPos      :: !PositionWithoutFile  -- ^ Current position.
+  , lexInput    :: String                -- ^ Current input.
+  , lexPrevChar :: !Char                 -- ^ Previously read character.
+  }
+
+-- | A lens for 'lexInput'.
+lensLexInput :: Lens' AlexInput String
+lensLexInput f r = f (lexInput r) <&> \ s -> r { lexInput = s }
+
+-- | Get the previously lexed character. Same as 'lexPrevChar'. Alex needs this
+--   to be defined to handle \"patterns with a left-context\".
+alexInputPrevChar :: AlexInput -> Char
+alexInputPrevChar = lexPrevChar
+
+-- | Returns the next character, and updates the 'AlexInput' value.
+--
+-- This function is not suitable for use by Alex 2, because it can
+-- return non-ASCII characters.
+alexGetChar :: AlexInput -> Maybe (Char, AlexInput)
+alexGetChar     (AlexInput { lexInput = []              }) = Nothing
+alexGetChar inp@(AlexInput { lexInput = c:s, lexPos = p }) =
+    Just (c, AlexInput
+                 { lexSrcFile   = lexSrcFile inp
+                 , lexInput     = s
+                 , lexPos       = movePos p c
+                 , lexPrevChar  = c
+                 }
+         )
+
+-- | Returns the next byte, and updates the 'AlexInput' value.
+--
+-- A trick is used to handle the fact that there are more than 256
+-- Unicode code points. The function translates characters to bytes in
+-- the following way:
+--
+-- * Whitespace characters other than \'\\t\' and \'\\n\' are
+--   translated to \' \'.
+-- * Non-ASCII alphabetical characters are translated to \'z\'.
+-- * Other non-ASCII printable characters are translated to \'+\'.
+-- * Everything else is translated to \'\\1\'.
+--
+-- Note that it is important that there are no keywords containing
+-- \'z\', \'+\', \' \' or \'\\1\'.
+--
+-- This function is used by Alex (version 3).
+
+alexGetByte :: AlexInput -> Maybe (Word8, AlexInput)
+alexGetByte ai =
+  mapFst (fromIntegral . fromEnum . toASCII) <$> alexGetChar ai
+  where
+  toASCII c
+    | isSpace c && c /= '\t' && c /= '\n' = ' '
+    | isAscii c                           = c
+    | isPrint c                           = if isAlpha c then 'z'
+                                                         else '+'
+    | otherwise                           = '\1'
+
+{--------------------------------------------------------------------------
+    Monad operations
+ --------------------------------------------------------------------------}
+
+getLexInput :: Parser AlexInput
+getLexInput = gets getInp
+    where
+        getInp s = AlexInput
+                    { lexSrcFile    = parseSrcFile s
+                    , lexPos        = parsePos s
+                    , lexInput      = parseInp s
+                    , lexPrevChar   = parsePrevChar s
+                    }
+
+setLexInput :: AlexInput -> Parser ()
+setLexInput inp = modify upd
+    where
+        upd s = s { parseSrcFile    = lexSrcFile inp
+                  , parsePos        = lexPos inp
+                  , parseInp        = lexInput inp
+                  , parsePrevChar   = lexPrevChar inp
+                  }
+
+{--------------------------------------------------------------------------
+    Lex actions
+ --------------------------------------------------------------------------}
+
+type PreviousInput  = AlexInput
+type CurrentInput   = AlexInput
+type TokenLength    = Int
+
+-- | In the lexer, regular expressions are associated with lex actions who's
+--   task it is to construct the tokens.
+newtype LexAction r
+  = LexAction { runLexAction :: PreviousInput -> CurrentInput -> TokenLength -> Parser r }
+  deriving (Functor)
+
+instance Applicative LexAction where
+  pure r    = LexAction $ \ _ _ _ -> pure r
+  mf <*> mr = LexAction $ \ a b c -> runLexAction mf a b c <*> runLexAction mr a b c
+
+instance Monad LexAction where
+  return = pure
+  m >>= k  = LexAction $ \ a b c -> do
+    r <- runLexAction m a b c
+    runLexAction (k r) a b c
+
+instance MonadState ParseState LexAction where
+  get   = LexAction $ \ _ _ _ -> get
+  put s = LexAction $ \ _ _ _ -> put s
+
+-- | Sometimes regular expressions aren't enough. Alex provides a way to do
+--   arbitrary computations to see if the input matches. This is done with a
+--   lex predicate.
+type LexPredicate   = ([LexState], ParseFlags) -> PreviousInput -> TokenLength -> CurrentInput -> Bool
+
+-- | Conjunction of 'LexPredicate's.
+(.&&.) :: LexPredicate -> LexPredicate -> LexPredicate
+p1 .&&. p2 = \x y z u -> p1 x y z u && p2 x y z u
+
+-- | Disjunction of 'LexPredicate's.
+(.||.) :: LexPredicate -> LexPredicate -> LexPredicate
+p1 .||. p2 = \x y z u -> p1 x y z u || p2 x y z u
+
+-- | Negation of 'LexPredicate's.
+not' :: LexPredicate -> LexPredicate
+not' p = \x y z u -> not (p x y z u)
diff --git a/src/full/Agda/Syntax/Parser/Comments.hs b/src/full/Agda/Syntax/Parser/Comments.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Comments.hs
@@ -0,0 +1,78 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| This module defines the lex action to lex nested comments. As is well-known
+    this cannot be done by regular expressions (which, incidently, is probably
+    the reason why C-comments don't nest).
+
+    When scanning nested comments we simply keep track of the nesting level,
+    counting up for /open comments/ and down for /close comments/.
+-}
+module Agda.Syntax.Parser.Comments
+    where
+
+import qualified Data.List as List
+
+import {-# SOURCE #-} Agda.Syntax.Parser.LexActions
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.LookAhead
+import Agda.Syntax.Position
+
+-- | Should comment tokens be output?
+
+keepComments :: LexPredicate
+keepComments (_, s) _ _ _ = parseKeepComments s
+
+-- | Should comment tokens be output?
+
+keepCommentsM :: Parser Bool
+keepCommentsM = fmap parseKeepComments getParseFlags
+
+-- | Manually lexing a block comment. Assumes an /open comment/ has been lexed.
+--   In the end the comment is discarded and 'lexToken' is called to lex a real
+--   token.
+nestedComment :: LexAction Token
+nestedComment = LexAction $ \ inp inp' _ ->
+    do  setLexInput inp'
+        let err :: forall a. String -> LookAhead a
+            err _ = liftP $ parseErrorAt (lexPos inp) "Unterminated '{-'"
+        runLookAhead err $ skipBlock "{-" "-}"
+        keep <- keepCommentsM
+        if keep then do
+          inp'' <- getLexInput
+          let p1 = lexPos inp; p2 = lexPos inp''
+              i = posToInterval (lexSrcFile inp) p1 p2
+              s = case (p1, p2) of
+                    (Pn { posPos = p1 }, Pn { posPos = p2 }) ->
+                      List.genericTake (p2 - p1) $ lexInput inp
+          return $ TokComment (i, s)
+         else
+          lexToken
+
+
+-- | Lex a hole (@{! ... !}@). Holes can be nested.
+--   Returns @'TokSymbol' 'SymQuestionMark'@.
+hole :: LexAction Token
+hole = LexAction $ \ inp inp' _ ->
+    do  setLexInput inp'
+        let err :: forall a. String -> LookAhead a
+            err _ = liftP $ parseErrorAt (lexPos inp) "Unterminated '{!'"
+        runLookAhead err $ skipBlock "{!" "!}"
+        p <- lexPos <$> getLexInput
+        return $
+          TokSymbol SymQuestionMark $
+          posToInterval (lexSrcFile inp) (lexPos inp) p
+
+-- | Skip a block of text enclosed by the given open and close strings. Assumes
+--   the first open string has been consumed. Open-close pairs may be nested.
+skipBlock :: String -> String -> LookAhead ()
+skipBlock open close = scan 1
+    where
+        scan 0 = sync
+        scan n = match [ open   ==>  scan (n + 1)
+                       , close  ==>  scan (n - 1)
+                       ] `other` scan n
+            where
+                (==>) = (,)
+                other = ($)
diff --git a/src/full/Agda/Syntax/Parser/Layout.hs b/src/full/Agda/Syntax/Parser/Layout.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Layout.hs
@@ -0,0 +1,255 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| This module contains the lex actions that handle the layout rules. The way
+    it works is that the 'Parser' monad keeps track of a stack of
+    'LayoutContext's specifying the indentation of the layout blocks in scope.
+    For instance, consider the following incomplete (Haskell) program:
+
+    > f x = x'
+    >   where
+    >     x' = do y <- foo x; bar ...
+
+    At the @...@ the layout context would be
+
+    > [Layout 12, Layout 4, Layout 0]
+
+    The closest layout block is the one following @do@ which is
+    started by token @y@ at column 12.  The second closest block is the
+    @where@ clause started by the @x'@ token which has indentation 4.
+    Finally, there is a top-level layout block with indentation 0.
+
+    In April 2021 we changed layout handling in the lexer to allow
+    stacking of layout keywords on the same line, e.g.:
+
+    > private module M where
+    >    postulate A : Set
+    >              private
+    >                B : Set
+
+    The layout columns in the layout context (stack of layout blocks) can
+    have 'LayoutStatus' either 'Tentative' or 'Confirmed'. New layout
+    columns following a layout keyword are tentative until we see a new
+    line. E.g.
+
+      - The first @private@ block (column 8) is 'Tentative' when we
+        encounter the layout keyword @where@.
+
+      - The @postulate@ block (column 12) is 'Tentative' until the newline
+        after @A : Set@.
+
+    In contrast,
+
+      - The @module@ block (column 2) is 'Confirmed' from the beginning
+        since the first token (@postulate@) after the layout keyword @where@
+        is on a new line.
+
+      - The second @private@ block (column 14) is also 'Confirmed' from the
+        beginning (for the same reason).
+
+    A new layout column has to be strictly above the last __confirmed__
+    column only. E.g., when encountering @postulate@ at column 2 after
+    @where@, the confirmed column is still 0, so this is a valid start of
+    the block following @where@.
+
+    The column 8 of the @private@ block never enters the 'Confirmed' status
+    but remains 'Tentative'. Also, this block can never get more than the
+    one declaration it has (@module...@), because when the @module@ block
+    closes due to a column \< 2, it closes as well. One could say that
+    tentative blocks buried under confirmed blocks are passive, the only
+    wait for their closing.
+
+    To implement the process of block confirmation (function
+    'confirmLayout'), the lexer has to act on newline characters (except for
+    those in a block comment).
+
+      - In ordinary mode, when encountering a newline, we confirm the top
+        unconfirmed blocks. Example: The newline after @A : Set@ confirms
+        the column 12 after @postulate@. Function: 'confirmLayoutAtNewLine',
+        state @bol@.
+
+      - In the @layout@ state following a layout keyword, a newline does not
+        confirm any block, but announces that the next block should be
+        confirmed from the start. Function: 'confirmedLayoutComing'.
+
+    In order to implement 'confirmedLayoutComing' we have a 'LayoutStatus'
+    flag in the parse state (field 'stateLayStatus'). By default, for a new
+    layout block, the status is 'Tentative' (unless we saw a newline).
+
+    New layout blocks are created as follows. When a layout keyword is
+    encountered, we enter lexer state 'layout' via function 'withLayout'.
+    When we exit the 'layout' state via 'newLayoutBlock' with a token that
+    marks the new layout column, we push a new 'LayoutBlock' onto the
+    'LayoutContext' using the given column and the current 'parseLayStatus'
+    which is then reset to 'Tentative'.
+
+    The new block is actually only pushed if the column is above the last
+    confirmed layout column ('confirmedLayoutColumn'). If this check fails,
+    we instead enter the 'empty_layout' state. This state produces the
+    closing brace and is immediately left for 'bol' (beginning of line).
+
+    (Remark: In 'bol' we might confirm some tentative top blocks, but this
+    is irrelevant, since they will be closed immediately, given that the
+    current token is left of the confirmed column, and tentative columns
+    above it must be to the right of this column.)
+
+    The 'offsideRule' (state 'bol') is unchanged. It checks how the first
+    token on a new line relates to the top layout column, be it tentative or
+    confirmed. (Since we are on a new line, 'Tentative' can only happen when
+    we popped some 'Confirmed' columns and continue popping the top
+    'Tentative' columns here.) While the token is to the left of the layout
+    column, we keep closing blocks.
+
+-}
+module Agda.Syntax.Parser.Layout
+    ( withLayout
+    , offsideRule
+    , newLayoutBlock
+    , emptyLayout
+    , confirmLayout
+    ) where
+
+import Control.Monad        ( when )
+import Control.Monad.State  ( gets, modify )
+
+import Agda.Syntax.Parser.Lexer
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Parser.LexActions
+import Agda.Syntax.Position
+
+import Agda.Utils.Functor ((<&>))
+
+{-| Executed for the first token in each line (see 'Agda.Syntax.Parser.Lexer.bol'),
+    except when the last token was a layout keyword.
+
+    Checks the position of the token relative to the current layout context.
+    If the token is
+
+    - /to the left/ :
+        Exit the current block and a return virtual close brace (stay in the
+        'Agda.Syntax.Parser.Lexer.bol' state).
+
+    - /same column/ :
+        Exit the 'Agda.Syntax.Parser.Lexer.bol' state and return a virtual semi
+        colon.
+
+    - /to the right/ :
+        Exit the 'Agda.Syntax.Parser.Lexer.bol' state and continue lexing.
+
+-}
+offsideRule :: LexAction Token
+offsideRule = LexAction $ \ inp _ _ -> do
+    let p = lexPos inp
+        i = posToInterval (lexSrcFile inp) p p
+    getOffside p >>= \case
+        LT  -> do   popBlock
+                    return (TokSymbol SymCloseVirtualBrace i)
+        EQ  -> do   popLexState
+                    return (TokSymbol SymVirtualSemi i)
+        GT  -> do   popLexState
+                    lexToken
+
+
+{-| This action is only executed from the 'Agda.Syntax.Parser.Lexer.empty_layout'
+    state. It will exit this state, enter the 'Agda.Syntax.Parser.Lexer.bol' state,
+    and return a virtual close brace (closing the empty layout block started
+    by 'newLayoutBlock').
+-}
+emptyLayout :: LexAction Token
+emptyLayout = LexAction $ \ inp _ _ -> do
+    let p = lexPos inp
+        i = posToInterval (lexSrcFile inp) p p
+    popLexState
+    pushLexState bol
+    return (TokSymbol SymCloseVirtualBrace i)
+
+
+{-| Start a new layout block. This is how to get out of the
+    'Agda.Syntax.Parser.Lexer.layout' state. There are
+    two possibilities:
+
+    - The current token is to the right of the confirmed layout column.
+
+    - The current token is to the left of or in the same column as the confirmed
+      layout column.
+
+    In the first case everything is fine and we enter a new layout block at
+    the column of the current token. In the second case we have an empty layout
+    block so we enter the 'Agda.Syntax.Parser.Lexer.empty_layout' state. In both
+    cases we return a virtual open brace without consuming any input.
+
+    Entering a new state when we know we want to generate a virtual @{}@ may
+    seem a bit roundabout. The thing is that we can only generate one token at
+    a time, so the way to generate two tokens is to generate the first one and
+    then enter a state in which the only thing you can do is generate the
+    second one.
+-}
+newLayoutBlock :: LexAction Token
+newLayoutBlock = LexAction $ \ inp _ _ -> do
+    let p = lexPos inp
+        i = posToInterval (lexSrcFile inp) p p
+        offset = posCol p
+    status   <- popPendingLayout
+    kw       <- gets parseLayKw
+    prevOffs <- confirmedLayoutColumn <$> getContext
+    if prevOffs >= offset
+        then pushLexState empty_layout
+        else do
+            when (status == Confirmed) $
+              modifyContext $ confirmTentativeBlocks $ Just offset
+            pushBlock $ Layout kw status offset
+    return $ TokSymbol SymOpenVirtualBrace i
+  where
+
+    -- Get and reset the status of the coming layout block.
+    popPendingLayout :: Parser LayoutStatus
+    popPendingLayout = do
+        status <- gets parseLayStatus
+        resetLayoutStatus
+        return status
+
+    -- The confirmed layout column, or 0 if there is none.
+    confirmedLayoutColumn :: LayoutContext -> Column
+    confirmedLayoutColumn = \case
+       Layout _ Confirmed c : _   -> c
+       Layout _ Tentative _ : cxt -> confirmedLayoutColumn cxt
+       [] -> 0 -- should only happen when looking at the first token (top-level layout)
+
+-- | Compute the relative position of a location to the
+--   current layout context.
+getOffside :: Position' a -> Parser Ordering
+getOffside loc =
+    getContext <&> \case
+        Layout _ _ n : _ -> compare (posCol loc) n
+        _                -> GT
+
+-- | At a new line, we confirm either existing tentative layout
+--   columns, or, if the last token was a layout keyword, the expected
+--   new layout column.
+confirmLayout :: Parser ()
+confirmLayout = getLexState >>= \ case
+  s : _ | s == layout -> confirmedLayoutComing
+  _                   -> confirmLayoutAtNewLine
+  where
+
+  -- Mark the pending layout block as 'Confirmed'.
+  confirmedLayoutComing :: Parser ()
+  confirmedLayoutComing = modify $ \ s -> s { parseLayStatus = Confirmed }
+
+  -- Encountering a newline outside of a 'layout' state we confirm top
+  -- tentative layout columns.
+  confirmLayoutAtNewLine :: Parser ()
+  confirmLayoutAtNewLine = modifyContext $ confirmTentativeBlocks Nothing
+
+-- | Confirm all top 'Tentative' layout columns.
+-- If a column is given, only those below the given column.
+--
+-- The code ensures that the newly created 'Definitive' columns
+-- are strictly decreasing.
+--
+confirmTentativeBlocks :: Maybe Column -> LayoutContext -> LayoutContext
+confirmTentativeBlocks mcol = \case
+    Layout kw Tentative col : cxt | maybe True (col <) mcol
+            -> Layout kw Confirmed col : confirmTentativeBlocks (Just col) cxt
+    cxt  -> cxt
diff --git a/src/full/Agda/Syntax/Parser/Layout.hs-boot b/src/full/Agda/Syntax/Parser/Layout.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Layout.hs-boot
@@ -0,0 +1,15 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Parser.Layout where
+
+import Agda.Syntax.Parser.Alex   (LexAction)
+import Agda.Syntax.Parser.Monad  (Parser)
+import Agda.Syntax.Parser.Tokens (Token)
+
+offsideRule      :: LexAction Token
+newLayoutBlock   :: LexAction Token
+emptyLayout      :: LexAction Token
+
+confirmLayout    :: Parser ()
+-- confirmLayoutAtNewLine :: Parser ()
+-- confirmedLayoutComing  :: Parser ()
diff --git a/src/full/Agda/Syntax/Parser/LexActions.hs b/src/full/Agda/Syntax/Parser/LexActions.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/LexActions.hs
@@ -0,0 +1,302 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| This module contains the building blocks used to construct the lexer.
+-}
+module Agda.Syntax.Parser.LexActions
+    ( -- * Main function
+      lexToken
+      -- * Lex actions
+      -- ** General actions
+    , token
+    , withInterval, withInterval', withInterval_
+    , withLayout
+    , andThen, skip
+    , begin, end, beginWith, endWith
+    , begin_, end_
+    , lexError
+      -- ** Specialized actions
+    , keyword, symbol, identifier, literal, literal', integer
+      -- * Lex predicates
+    , followedBy, eof, inState
+    ) where
+
+import Control.Monad.State (modify)
+
+import Data.Bifunctor
+import Data.Char
+import Data.Foldable (foldl')
+import Data.Maybe
+
+import Agda.Syntax.Common (pattern Ranged)
+import Agda.Syntax.Parser.Lexer
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+
+import Agda.Utils.List
+import Agda.Utils.List1 (String1, toList)
+import qualified Agda.Utils.List1 as List1
+
+import Agda.Utils.Impossible
+
+{--------------------------------------------------------------------------
+    Scan functions
+ --------------------------------------------------------------------------}
+
+-- | Called at the end of a file. Returns 'TokEOF'.
+returnEOF :: AlexInput -> Parser Token
+returnEOF AlexInput{ lexSrcFile, lexPos } = do
+  -- Andreas, 2018-12-30, issue #3480
+  -- The following setLastPos leads to parse error reporting
+  -- far away from the interesting position, in particular
+  -- if there is a long comment before the EOF.
+  -- (Such a long comment is frequent in interactive programming, as
+  -- commenting out until the end of the file is a common habit.)
+  -- -- setLastPos lexPos
+  -- Without it, we get much more useful error locations.
+  setPrevToken "<EOF>"
+  return $ TokEOF $ posToInterval lexSrcFile lexPos lexPos
+
+-- | Set the current input and lex a new token (calls 'lexToken').
+skipTo :: AlexInput -> Parser Token
+skipTo inp = do
+  setLexInput inp
+  lexToken
+
+{-| Scan the input to find the next token. Calls
+'Agda.Syntax.Parser.Lexer.alexScanUser'. This is the main lexing function
+where all the work happens. The function 'Agda.Syntax.Parser.Lexer.lexer',
+used by the parser is the continuation version of this function.
+-}
+lexToken :: Parser Token
+lexToken =
+    do  inp <- getLexInput
+        lss <- getLexState
+        flags <- getParseFlags
+        case alexScanUser (lss, flags) inp (headWithDefault __IMPOSSIBLE__ lss) of
+            AlexEOF                     -> returnEOF inp
+            AlexSkip inp' len           -> skipTo inp'
+            AlexToken inp' len action   -> postToken <$> runLexAction action inp inp' len
+            AlexError i                 -> parseError $ concat
+              [ "Lexical error"
+              , case listToMaybe $ lexInput i of
+                  Just '\t'                -> " (you may want to replace tabs with spaces)"
+                  Just c | not (isPrint c) -> " (unprintable character)"
+                  _ -> ""
+              , ":"
+              ]
+
+isSub :: Char -> Bool
+isSub c = '\x2080' <= c && c <= '\x2089'
+
+readSubscript :: [Char] -> Integer
+readSubscript = read . map (\c -> toEnum (fromEnum c - 0x2080 + fromEnum '0'))
+
+postToken :: Token -> Token
+postToken (TokId (r, "\x03bb")) = TokSymbol SymLambda r
+postToken (TokId (r, "\x2026")) = TokSymbol SymEllipsis r
+postToken (TokId (r, "\x2192")) = TokSymbol SymArrow r
+postToken (TokId (r, "\x2983")) = TokSymbol SymDoubleOpenBrace r
+postToken (TokId (r, "\x2984")) = TokSymbol SymDoubleCloseBrace r
+postToken (TokId (r, "\x2987")) = TokSymbol SymOpenIdiomBracket r
+postToken (TokId (r, "\x2988")) = TokSymbol SymCloseIdiomBracket r
+postToken (TokId (r, "\x2987\x2988")) = TokSymbol SymEmptyIdiomBracket r
+postToken (TokId (r, "\x2200")) = TokKeyword KwForall r
+postToken t = t
+
+{--------------------------------------------------------------------------
+    Lex actions
+ --------------------------------------------------------------------------}
+
+-- | The most general way of parsing a token.
+token :: (String -> Parser tok) -> LexAction tok
+token action = LexAction $ \ inp inp' len ->
+    do  setLexInput inp'
+        let t = take len $ lexInput inp
+        setPrevToken t
+        setLastPos $ lexPos inp
+        action t
+
+-- | Parse a token from an 'Interval' and the lexed string.
+withInterval :: ((Interval, String) -> tok) -> LexAction tok
+withInterval f = token $ \s -> do
+                   r <- getParseInterval
+                   return $ f (r,s)
+
+-- | Like 'withInterval', but applies a function to the string.
+withInterval' :: (String -> a) -> ((Interval, a) -> tok) -> LexAction tok
+withInterval' f t = withInterval (t . second f)
+
+-- | Return a token without looking at the lexed string.
+withInterval_ :: (Interval -> r) -> LexAction r
+withInterval_ f = withInterval (f . fst)
+
+
+-- | Executed for layout keywords. Enters the 'Agda.Syntax.Parser.Lexer.layout'
+--   state and performs the given action.
+withLayout :: Keyword -> LexAction r -> LexAction r
+withLayout kw a = pushLexState layout `andThen` setLayoutKw `andThen` a
+  where
+  setLayoutKw = modify $ \ st -> st { parseLayKw = kw }
+
+infixr 1 `andThen`
+
+-- | Prepend some parser manipulation to an action.
+andThen :: Parser () -> LexAction r -> LexAction r
+andThen cmd a = LexAction $ \ inp inp' n -> do
+  cmd
+  runLexAction a inp inp' n
+
+-- | Visit the current lexeme again.
+revisit :: LexAction Token
+revisit = LexAction $ \ _ _ _ -> lexToken
+
+-- | Throw away the current lexeme.
+skip :: LexAction Token
+skip = LexAction $ \ _ inp' _ -> skipTo inp'
+
+-- | Enter a new state without consuming any input.
+begin :: LexState -> LexAction Token
+begin code = beginWith code revisit
+
+-- | Exit the current state without consuming any input.
+end :: LexAction Token
+end = endWith revisit
+
+-- | Enter a new state throwing away the current lexeme.
+begin_ :: LexState -> LexAction Token
+begin_ code = beginWith code skip
+
+-- | Exit the current state throwing away the current lexeme.
+end_ :: LexAction Token
+end_ = endWith skip
+
+-- | Enter a new state and perform the given action.
+beginWith :: LexState -> LexAction a -> LexAction a
+beginWith code a = pushLexState code `andThen` a
+
+-- | Exit the current state and perform the given action.
+endWith :: LexAction a -> LexAction a
+endWith a = popLexState `andThen` a
+
+
+-- | Parse a 'Keyword' token, triggers layout for 'layoutKeywords'.
+keyword :: Keyword -> LexAction Token
+keyword k =
+    case k of
+
+        -- Unconditional layout keyword.
+        _ | k `elem` layoutKeywords ->
+            withLayout k cont
+
+        -- Andreas, 2021-05-06, issue #5356:
+        -- @constructor@ is not a layout keyword after all, replaced by @data _ where@.
+        -- -- @constructor@ is not a layout keyword in @record ... where@ blocks,
+        -- -- only in @interleaved mutual@ blocks.
+        -- KwConstructor -> do
+        --     cxt <- getContext
+        --     if inMutualAndNotInWhereBlock cxt
+        --       then withLayout k cont
+        --       else cont
+
+        _ -> cont
+    where
+    cont = withInterval_ (TokKeyword k)
+
+    -- Andreas, 2021-05-06, issue #5356:
+    -- @constructor@ is not a layout keyword after all, replaced by @data _ where@.
+    -- -- Most recent block decides ...
+    -- inMutualAndNotInWhereBlock = \case
+    --   Layout KwMutual _ _ : _ -> True
+    --   Layout KwWhere  _ _ : _ -> False
+    --   _ : bs                  -> inMutualAndNotInWhereBlock bs
+    --   []                      -> True  -- For better errors on stray @constructor@ decls.
+
+
+-- | Parse a 'Symbol' token.
+symbol :: Symbol -> LexAction Token
+symbol s = withInterval_ (TokSymbol s)
+
+
+-- | Parse a number.
+
+number :: String -> Integer
+number str = case str of
+    '0' : 'x' : num -> parseNumber 16 num
+    '0' : 'b' : num -> parseNumber 2  num
+    num             -> parseNumber 10 num
+    where
+        parseNumber :: Integer -> String -> Integer
+        parseNumber radix = foldl' (addDigit radix) 0
+
+        -- We rely on Agda.Syntax.Parser.Lexer to enforce that the digits are
+        -- in the correct range (so e.g. the digit 'E' cannot appear in a
+        -- binary number).
+        addDigit :: Integer -> Integer -> Char -> Integer
+        addDigit radix n '_' = n
+        addDigit radix n c   = n * radix + fromIntegral (digitToInt c)
+
+integer :: String -> Integer
+integer = \case
+  '-' : str -> - (number str)
+  str       -> number str
+
+-- | Parse a literal.
+literal' :: (String -> a) -> (a -> Literal) -> LexAction Token
+literal' read lit = withInterval' read $ \ (r, a) ->
+  TokLiteral $ Ranged (getRange r) $ lit a
+
+literal :: Read a => (a -> Literal) -> LexAction Token
+literal = literal' read
+
+-- | Parse an identifier. Identifiers can be qualified (see 'Name').
+--   Example: @Foo.Bar.f@
+identifier :: LexAction Token
+identifier = qualified $ either (TokId . second toList) (TokQId . map (second toList))
+
+
+-- | Parse a possibly qualified name.
+qualified :: (Either (Interval, String1) [(Interval, String1)] -> a) -> LexAction a
+qualified tok =
+    token $ \s ->
+    do  i <- getParseInterval
+        case mkName i $ List1.wordsBy (== '.') s of
+            []  -> lexError "lex error on .."
+            [x] -> return $ tok $ Left  x
+            xs  -> return $ tok $ Right xs
+    where
+        -- Compute the ranges for the substrings (separated by '.') of
+        -- a name. Dots are included: the intervals generated for
+        -- "A.B.x" correspond to "A.", "B." and "x".
+        mkName :: Interval -> [String1] -> [(Interval, String1)]
+        mkName _ []     = []
+        mkName i [x]    = [(i, x)]
+        mkName i (x:xs) = (i0, x) : mkName i1 xs
+            where
+                p0 = iStart i
+                p1 = iEnd i
+                p' = movePos (movePosByString p0 x) '.'
+                i0 = Interval p0 p'
+                i1 = Interval p' p1
+
+
+{--------------------------------------------------------------------------
+    Predicates
+ --------------------------------------------------------------------------}
+
+-- | True when the given character is the next character of the input string.
+followedBy :: Char -> LexPredicate
+followedBy c' _ _ _ inp =
+    case lexInput inp of
+        []  -> False
+        c:_ -> c == c'
+
+-- | True if we are at the end of the file.
+eof :: LexPredicate
+eof _ _ _ inp = null $ lexInput inp
+
+-- | True if the given state appears somewhere on the state stack
+inState :: LexState -> LexPredicate
+inState s (ls, _) _ _ _ = s `elem` ls
diff --git a/src/full/Agda/Syntax/Parser/LexActions.hs-boot b/src/full/Agda/Syntax/Parser/LexActions.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/LexActions.hs-boot
@@ -0,0 +1,37 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Parser.LexActions where
+
+import Agda.Syntax.Literal
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Position
+
+lexToken :: Parser Token
+
+token :: (String -> Parser tok) -> LexAction tok
+
+withInterval  :: ((Interval, String) -> tok) -> LexAction tok
+withInterval' :: (String -> a) -> ((Interval, a) -> tok) -> LexAction tok
+withLayout :: Keyword -> LexAction r -> LexAction r
+
+andThen   :: Parser () -> LexAction r -> LexAction r
+skip      :: LexAction Token
+
+begin     :: LexState -> LexAction Token
+beginWith :: LexState -> LexAction a -> LexAction a
+endWith   :: LexAction a -> LexAction a
+begin_    :: LexState -> LexAction Token
+end_      :: LexAction Token
+
+keyword    :: Keyword -> LexAction Token
+symbol     :: Symbol -> LexAction Token
+identifier :: LexAction Token
+literal    :: Read a => (a -> Literal) -> LexAction Token
+literal'   :: (String -> a) -> (a -> Literal) -> LexAction Token
+integer    :: String -> Integer
+
+followedBy    :: Char -> LexPredicate
+eof           :: LexPredicate
+inState       :: LexState -> LexPredicate
diff --git a/src/full/Agda/Syntax/Parser/Lexer.x b/src/full/Agda/Syntax/Parser/Lexer.x
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Lexer.x
@@ -0,0 +1,325 @@
+{
+#if  __GLASGOW_HASKELL__ > 800
+{-# OPTIONS_GHC -Wno-error=deprecated-flags   #-}
+{-# OPTIONS_GHC -Wno-error=missing-signatures #-}
+{-# OPTIONS_GHC -Wno-error=tabs               #-}
+{-# OPTIONS_GHC -Wno-error=unused-imports     #-}
+#endif
+{-# OPTIONS_GHC -fno-warn-deprecated-flags   #-}
+{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
+{-# OPTIONS_GHC -fno-warn-tabs               #-}
+{-# OPTIONS_GHC -fno-warn-unused-imports     #-}
+
+{-| The lexer is generated by Alex (<http://www.haskell.org/alex>) and is an
+    adaptation of GHC's lexer. The main lexing function 'lexer' is called by
+    the "Agda.Syntax.Parser.Parser" to get the next token from the input.
+-}
+module Agda.Syntax.Parser.Lexer
+    ( -- * The main function
+      lexer
+      -- * Lex states
+    , normal, code
+    , layout, empty_layout, bol, imp_dir
+      -- * Alex generated functions
+    , AlexReturn(..), alexScanUser
+    ) where
+
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Comments
+#ifndef __HADDOCK__
+import {-# SOURCE #-} Agda.Syntax.Parser.Layout
+import {-# SOURCE #-} Agda.Syntax.Parser.LexActions
+#endif
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.StringLiterals
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Literal
+
+}
+
+-- Note that the regular expressions should not use non-ASCII
+-- characters, see Agda.Syntax.Parser.Alex.alexGetByte.
+
+$digit       = 0-9
+$hexdigit    = [ $digit a-f A-F ]
+$binarydigit = 0-1
+$alpha       = [ A-Z a-z _ ]
+$op          = [ \- \! \# \$ \% \& \* \+ \/ \< \= \> \^ \| \~ \? \` \[ \] \, \: ]
+$idstart     = [ $digit $alpha $op ]
+$idchar      = [ $idstart ' \\ ]
+$nonalpha    = $idchar # $alpha
+$white_notab = $white # \t
+$white_nonl  = $white_notab # \n
+
+@prettynumber = $digit+ ([_] $digit+)*
+              | "0x" $hexdigit+ ([_] $hexdigit+)*
+              | "0b" $binarydigit+ ([_] $binarydigit+)*
+@integer      = [\-]? @prettynumber
+@decimal      = $digit+
+@exponent     = [eE] [\-\+]? @decimal
+@float        = [\-]? @decimal \. @decimal @exponent?
+              | [\-]? @decimal @exponent
+
+-- A name can't start with \x (to allow \x -> x).
+-- Bug in alex: [ _ op ]+ doesn't seem to work!
+@start = ($idstart # [_]) | \\ [ $nonalpha ]
+@ident = @start $idchar* | [_] $idchar+
+
+@namespace  = (@ident \.)*
+@q_ident    = @namespace @ident
+
+tokens :-
+
+-- White space
+<0,code,bol_,layout_,empty_layout_,imp_dir_>
+    $white_nonl+    ;
+
+<pragma_,fpragma_> $white_notab ;
+
+-- Pragmas
+<0,code,pragma_>   "{-#"               { beginWith pragma  $ symbol SymOpenPragma }
+<fpragma_>         "{-#"               { beginWith fpragma $ symbol SymOpenPragma }
+<pragma_,fpragma_> "#-}"               { endWith $ symbol SymClosePragma }
+<pragma_>   "BUILTIN"                  { keyword KwBUILTIN }
+<pragma_>   "CATCHALL"                 { keyword KwCATCHALL }
+<pragma_>   "COMPILE"                  { endWith $ beginWith fpragma $ keyword KwCOMPILE }
+<pragma_>   "FOREIGN"                  { endWith $ beginWith fpragma $ keyword KwFOREIGN }
+<pragma_>   "DISPLAY"                  { keyword KwDISPLAY }
+<pragma_>   "ETA"                      { keyword KwETA }
+<pragma_>   "IMPOSSIBLE"               { keyword KwIMPOSSIBLE }
+<pragma_>   "INJECTIVE"                { keyword KwINJECTIVE }
+<pragma_>   "INLINE"                   { keyword KwINLINE }
+<pragma_>   "NOINLINE"                 { keyword KwNOINLINE }
+<pragma_>   "NOT_PROJECTION_LIKE"      { keyword KwNOT_PROJECTION_LIKE }
+<pragma_>   "LINE"                     { keyword KwLINE }
+<pragma_>   "MEASURE"                  { keyword KwMEASURE }
+<pragma_>   "NO_POSITIVITY_CHECK"      { keyword KwNO_POSITIVITY_CHECK }
+<pragma_>   "NO_TERMINATION_CHECK"     { keyword KwNO_TERMINATION_CHECK }
+<pragma_>   "NO_UNIVERSE_CHECK"        { keyword KwNO_UNIVERSE_CHECK }
+<pragma_>   "NON_COVERING"             { keyword KwNON_COVERING }
+<pragma_>   "NON_TERMINATING"          { keyword KwNON_TERMINATING }
+<pragma_>   "OPTIONS"                  { keyword KwOPTIONS }
+<pragma_>   "POLARITY"                 { keyword KwPOLARITY }
+<pragma_>   "REWRITE"                  { keyword KwREWRITE }
+<pragma_>   "STATIC"                   { keyword KwSTATIC }
+<pragma_>   "TERMINATING"              { keyword KwTERMINATING }
+<pragma_>   "WARNING_ON_USAGE"         { keyword KwWARNING_ON_USAGE }
+<pragma_>   "WARNING_ON_IMPORT"        { keyword KwWARNING_ON_IMPORT }
+<pragma_>   . # [ $white \" ] +        { withInterval $ TokString } -- we recognise string literals in pragmas
+<fpragma_>  . # [ $white ] +           { withInterval $ TokString }
+
+-- Comments
+    -- We need to rule out pragmas here. Usually longest match would take
+    -- precedence, but in some states pragmas aren't valid but comments are.
+<0,code,bol_,layout_,empty_layout_,imp_dir_>
+    "{-" / { not' (followedBy '#') }    { nestedComment }
+    -- A misplaced end-comment, like in @f {x-} = x-@ gives a parse error.
+    "-}"                                { symbol SymEndComment }
+    @ident "-}"                         { symbol SymEndComment }
+
+-- Dashes followed by a name symbol should be parsed as a name.
+<0,code,bol_,layout_,empty_layout_,imp_dir_>
+    "--" .* / { keepComments .&&. (followedBy '\n' .||. eof) }
+              { confirmLayout `andThen` withInterval TokComment }
+<0,code,bol_,layout_,empty_layout_,imp_dir_>
+    "--" .* / { followedBy '\n' .||. eof }
+              { confirmLayout `andThen` skip }
+
+-- Note: we need to confirm tentative layout columns whenever we meet
+-- a newline character ('\n').
+-- The exception is the newline after a layout keyword.
+
+-- We need to check the offside rule for the first token on each line.  We
+-- should not check the offside rule for the end of file token or an
+-- '\end{code}'
+<0,code,imp_dir_> \n    { begin bol_ }  -- Note that @begin@ revisits '\n' in the new state!
+<bol_>
+    {
+        \n                      { confirmLayout `andThen` skip }
+--      ^ \\ "end{code}"    { end }
+        () / { not' eof }       { offsideRule }
+    }
+
+-- After a layout keyword the
+-- indentation of the first token decides the column of the layout block.
+<layout_>
+    {   \n      { confirmLayout `andThen` skip}
+        ()      { endWith newLayoutBlock }
+    }
+
+-- The only rule for the empty_layout state. Generates a close brace.
+<empty_layout_> ()              { emptyLayout }
+
+-- Keywords
+<0,code> abstract          { keyword KwAbstract }
+<0,code> codata            { keyword KwCoData }
+<0,code> coinductive       { keyword KwCoInductive }
+<0,code> constructor       { keyword KwConstructor }
+<0,code> data              { keyword KwData }
+<0,code> do                { keyword KwDo }
+<0,code> "eta-equality"    { keyword KwEta }
+<0,code> field             { keyword KwField }
+<0,code> forall            { keyword KwForall }
+<0,code> import            { keyword KwImport }
+<0,code> in                { keyword KwIn }
+<0,code> inductive         { keyword KwInductive }
+<0,code> infix             { keyword KwInfix }
+<0,code> infixl            { keyword KwInfixL }
+<0,code> infixr            { keyword KwInfixR }
+<0,code> instance          { keyword KwInstance }
+<0,code> interleaved       { keyword KwInterleaved }
+<0,code> let               { keyword KwLet }
+<0,code> macro             { keyword KwMacro }
+<0,code> module            { keyword KwModule }
+<0,code> mutual            { keyword KwMutual }
+<0,code> "no-eta-equality" { keyword KwNoEta }
+<0,code> open              { keyword KwOpen }
+<0,code> overlap           { keyword KwOverlap }
+<0,code> pattern           { keyword KwPatternSyn }
+<0,code> postulate         { keyword KwPostulate }
+<0,code> primitive         { keyword KwPrimitive }
+<0,code> private           { keyword KwPrivate }
+<0,code> quote             { keyword KwQuote }
+<0,code> quoteTerm         { keyword KwQuoteTerm }
+<0,code> record            { keyword KwRecord }
+<0,code> rewrite           { keyword KwRewrite }
+<0,code> syntax            { keyword KwSyntax }
+<0,code> tactic            { keyword KwTactic }
+<0,code> unquote           { keyword KwUnquote }
+<0,code> unquoteDecl       { keyword KwUnquoteDecl }
+<0,code> unquoteDef        { keyword KwUnquoteDef  }
+<0,code> variable          { keyword KwVariable }
+<0,code> where             { keyword KwWhere }
+<0,code> with              { keyword KwWith }
+<0,code> opaque            { keyword KwOpaque }
+<0,code> unfolding         { keyword KwUnfolding }
+
+-- The parser is responsible to put the lexer in the imp_dir_ state when it
+-- expects an import directive keyword. This means that if you run the
+-- tokensParser you will never see these keywords.
+<0,code> using      { keyword KwUsing }
+<0,code> hiding     { keyword KwHiding }
+<0,code> renaming   { keyword KwRenaming }
+<imp_dir_> to       { endWith $ keyword KwTo }
+<0,code> public     { keyword KwPublic }
+
+-- Holes
+<0,code> "{!"           { hole }
+
+-- Special symbols
+<0,code> "..."          { symbol SymEllipsis }
+<0,code> ".."           { symbol SymDotDot }
+<0,code> "."            { symbol SymDot }
+<0,code> ";"            { symbol SymSemi }
+<0,code> ":"            { symbol SymColon }
+<0,code> "="            { symbol SymEqual }
+<0,code> "_"            { symbol SymUnderscore }
+<0,code> "?"            { symbol SymQuestionMark }
+<0,code> "|"            { symbol SymBar }
+<0,code> "(|" /[$white] { symbol SymOpenIdiomBracket }
+<0,code> "|)"           { symbol SymCloseIdiomBracket }
+<0,code> "(|)"          { symbol SymEmptyIdiomBracket }
+<0,code> "("            { symbol SymOpenParen }
+<0,code> ")"            { symbol SymCloseParen }
+<0,code> "->"           { symbol SymArrow }
+<0,code> "\"            { symbol SymLambda } -- "
+<0,code> "@"            { symbol SymAs }
+<0,code> "{{" /[^[!\-]] { symbol SymDoubleOpenBrace }
+-- Andreas, 2019-08-08, issue #3962, don't lex '{{' if followed by '-'
+-- since this will be confused with '{-' (start of comment) by Emacs.
+
+-- We don't lex '}}' into a SymDoubleCloseBrace. Instead, we lex it as
+-- two SymCloseBrace's. When the parser is looking for a double
+-- closing brace, it will also accept two SymCloseBrace's, after
+-- verifying that they are immediately next to each other.
+-- This trick allows us to keep "record { a = record {}}" working
+-- properly.
+-- <0,code> "}}"                { symbol SymDoubleCloseBrace }
+
+<0,code> "{"            { symbol SymOpenBrace }     -- you can't use braces for layout
+<0,code> "}"            { symbol SymCloseBrace }
+
+-- Literals
+<0,code> \'             { litChar }
+<0,code,pragma_> \"     { litString }
+<0,code> @integer       { literal' integer LitNat }
+<0,code> @float         { literal LitFloat }
+
+-- Identifiers
+<0,code,imp_dir_> @q_ident      { identifier }
+-- Andreas, 2013-02-21, added identifiers to the 'imp_dir_' state.
+-- This is to fix issue 782: 'toz' should not be lexed as 'to'
+-- (followed by 'z' after leaving imp_dir_).
+-- With identifiers in state imp_dir_, 'toz' should be lexed as
+-- identifier 'toz' in imp_dir_ state, leading to a parse error later.
+
+{
+
+-- | This is the initial state for parsing a regular, non-literate file.
+normal :: LexState
+normal = 0
+
+
+{-| The layout state. Entered when we see a layout keyword ('withLayout') and
+    exited at the next token ('newLayoutBlock').
+-}
+layout :: LexState
+layout = layout_
+
+
+{-| The state inside a pragma.
+-}
+pragma :: LexState
+pragma = pragma_
+
+-- | The state inside a FOREIGN pragma. This needs to be different so that we don't
+--   lex further strings as pragma keywords.
+fpragma :: LexState
+fpragma = fpragma_
+
+{-| We enter this state from 'newLayoutBlock' when the token following a
+    layout keyword is to the left of (or at the same column as) the current
+    layout context. Example:
+
+    > data Empty : Set where
+    > foo : Empty -> Nat
+
+    Here the second line is not part of the @where@ clause since it is has the
+    same indentation as the @data@ definition. What we have to do is insert an
+    empty layout block @{}@ after the @where@. The only thing that can happen
+    in this state is that 'emptyLayout' is executed, generating the closing
+    brace. The open brace is generated when entering by 'newLayoutBlock'.
+-}
+empty_layout :: LexState
+empty_layout = empty_layout_
+
+
+-- | This state is entered at the beginning of each line. You can't lex
+--   anything in this state, and to exit you have to check the layout rule.
+--   Done with 'offsideRule'.
+bol :: LexState
+bol = bol_
+
+
+-- | This state can only be entered by the parser. In this state you can only
+--   lex the keywords @using@, @hiding@, @renaming@ and @to@. Moreover they are
+--   only keywords in this particular state. The lexer will never enter this
+--   state by itself, that has to be done in the parser.
+imp_dir :: LexState
+imp_dir = imp_dir_
+
+
+-- | Return the next token. This is the function used by Happy in the parser.
+--
+--   @lexer k = 'lexToken' >>= k@
+lexer :: (Token -> Parser a) -> Parser a
+lexer k = lexToken >>= k
+
+-- | Do not use this function; it sets the 'ParseFlags' to
+-- 'undefined'.
+alexScan :: AlexInput -> Int -> AlexReturn (LexAction Token)
+
+-- | This is the main lexing function generated by Alex.
+alexScanUser :: ([LexState], ParseFlags) -> AlexInput -> Int -> AlexReturn (LexAction Token)
+
+}
diff --git a/src/full/Agda/Syntax/Parser/Literate.hs b/src/full/Agda/Syntax/Parser/Literate.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Literate.hs
@@ -0,0 +1,316 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ViewPatterns #-}
+
+-- | Preprocessors for literate code formats.
+
+module Agda.Syntax.Parser.Literate
+  ( literateProcessors
+  , literateExtsShortList
+  , literateSrcFile
+  , literateTeX
+  , literateRsT
+  , literateMd
+  , literateOrg
+  , illiterate
+  , atomizeLayers
+  , Processor
+  , Layers
+  , Layer(..)
+  , LayerRole(..)
+  , isCode
+  , isCodeLayer
+  )
+  where
+
+import Control.Monad ((<=<))
+import Data.Char (isSpace)
+import Data.List (isPrefixOf)
+import Text.Regex.TDFA
+  ( Regex, getAllTextSubmatches, match, matchM
+  , makeRegexOpts, blankCompOpt, blankExecOpt, newSyntax, caseSensitive
+  )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+
+import Agda.Utils.List
+import qualified Agda.Utils.List1 as List1
+
+import Agda.Utils.Impossible
+
+-- | Role of a character in the file.
+
+data LayerRole = Markup | Comment | Code
+  deriving (Show, Eq)
+
+-- | A sequence of characters in a file playing the same role.
+
+data Layer = Layer
+  { layerRole    :: LayerRole
+  , interval     :: Interval
+  , layerContent :: String
+  } deriving Show
+
+-- | A list of contiguous layers.
+
+type Layers = [Layer]
+
+instance HasRange Layer where
+  getRange = getRange . interval
+
+-- | Annotates a tokenized string with position information.
+
+mkLayers :: Position -> [(LayerRole, String)] -> Layers
+mkLayers pos []            = emptyLiterate pos
+mkLayers pos ((_,"") : xs) = mkLayers pos xs
+                             -- Empty layers are ignored.
+mkLayers pos ((ty,s) : xs) =
+  Layer ty (Interval pos next) s : mkLayers next xs
+  where
+  next = movePosByString pos s
+
+unMkLayers :: Layers -> [(LayerRole, String)]
+unMkLayers = map ((,) <$> layerRole <*> layerContent)
+
+atomizeLayers :: Layers -> [(LayerRole, Char)]
+atomizeLayers = (fmap <$> ((,) . fst) <*> snd) <=< unMkLayers
+
+-- | Type of a literate preprocessor:
+--   Invariants:
+--
+--   > f : Processor
+--
+--   proposition> f pos s /= []
+--
+--   proposition> f pos s >>= layerContent == s
+
+type Processor = Position -> String -> [Layer]
+
+literateSrcFile :: [Layer] -> SrcFile
+literateSrcFile []                    = __IMPOSSIBLE__
+literateSrcFile (Layer{interval} : _) = getIntervalFile interval
+
+-- | List of valid extensions for literate Agda files, and their
+--   corresponding preprocessors.
+--
+--   If you add new extensions, remember to update test/Utils.hs so
+--   that test cases ending in the new extensions are found.
+
+literateProcessors :: [(String, (Processor, FileType))]
+literateProcessors =
+  ((,) <$> (".lagda" ++) . fst <*> snd) <$>
+    [ (""    , (literateTeX, TexFileType))
+    , (".rst", (literateRsT, RstFileType))
+    , (".tex", (literateTeX, TexFileType))
+    , (".md",  (literateMd,  MdFileType ))
+    , (".org", (literateOrg, OrgFileType))
+    -- For now, treat typst as markdown because they use the same
+    -- syntax for code blocks.
+    , (".typ", (literateMd,  TypstFileType))
+    ]
+
+-- | Returns @True@ if the role corresponds to Agda code.
+
+isCode :: LayerRole -> Bool
+isCode Code    = True
+isCode Markup  = False
+isCode Comment = False
+
+-- | Returns @True@ if the layer contains Agda code.
+
+isCodeLayer :: Layer -> Bool
+isCodeLayer = isCode . layerRole
+
+-- | Blanks the non-code parts of a given file, preserving positions of
+--   characters corresponding to code. This way, there is a direct
+--   correspondence between source positions and positions in the
+--   processed result.
+
+illiterate :: [Layer] -> String
+illiterate xs = concat
+  [ (if isCode layerRole then id else bleach) layerContent
+  | Layer{layerRole, layerContent} <- xs
+  ]
+
+-- | Replaces non-space characters in a string with spaces.
+
+bleach :: String -> String
+bleach = map $ \ c -> if isSpace c && c /= '\t' then c else ' '
+
+-- | Check if a character is a blank character.
+
+isBlank :: Char -> Bool
+isBlank = (&&) <$> isSpace <*> (/= '\n')
+
+-- | Short list of extensions for literate Agda files.
+--   For display purposes.
+
+literateExtsShortList :: [String]
+literateExtsShortList = [".lagda"]
+
+-- | Returns a tuple consisting of the first line of the input, and the rest
+--   of the input.
+
+caseLine :: a -> (String -> String -> a) -> String -> a
+caseLine a k = \case
+  []   -> a
+  x:xs -> k (List1.toList line) rest
+    where
+    (line, rest) = breakAfter1 (== '\n') x xs
+
+-- | Canonical decomposition of an empty literate file.
+
+emptyLiterate :: Position -> [Layer]
+emptyLiterate pos = [Layer Markup (Interval pos pos) ""]
+
+-- | Create a regular expression that:
+--   - Must match the whole string
+--   - Works across line boundaries
+
+rex :: String -> Regex
+rex s =
+  makeRegexOpts blankCompOpt{newSyntax = True} blankExecOpt $
+    "\\`" ++ s ++ "\\'"
+
+-- | Preprocessor for literate TeX.
+
+literateTeX :: Position -> String -> [Layer]
+literateTeX pos s = mkLayers pos (tex s)
+  where
+  tex :: String -> [(LayerRole, String)]
+  tex = caseLine [] $ \ line rest ->
+    case r_begin `matchM` line of
+      Just (getAllTextSubmatches -> [_, pre, _, markup, whitespace]) ->
+        (Comment, pre) : (Markup, markup) :
+        (Code, whitespace) : code rest
+      Just _  -> __IMPOSSIBLE__
+      Nothing -> (Comment, line) : tex rest
+
+  r_begin = rex "(([^\\%]|\\\\.)*)(\\\\begin\\{code\\}[^\n]*)(\n)?"
+
+  code :: String -> [(LayerRole, String)]
+  code = caseLine [] $ \ line rest ->
+    case r_end `matchM` line of
+      Just (getAllTextSubmatches -> [_, code, markup, post]) ->
+        (Code, code) : (Markup, markup) : (Comment, post) : tex rest
+      Just _  -> __IMPOSSIBLE__
+      Nothing -> (Code, line) : code rest
+
+  r_end = rex "([[:blank:]]*)(\\\\end\\{code\\})(.*)"
+
+-- | Preprocessor for Markdown.
+
+literateMd :: Position -> String -> [Layer]
+literateMd pos s = mkLayers pos $ md s
+  where
+  md :: String -> [(LayerRole, String)]
+  md = caseLine [] $ \ line rest ->
+    case md_begin `matchM` line of
+      Just (getAllTextSubmatches -> [_, pre, markup, _]) ->
+        (Comment, pre) : (Markup, markup) : code rest
+      Just _  -> __IMPOSSIBLE__
+      Nothing ->
+        (Comment, line) :
+        if md_begin_other `match` line
+        then code_other rest
+        else md rest
+
+  md_begin       = rex "(.*)([[:space:]]*```(agda)?[[:space:]]*)"
+  md_begin_other = rex "[[:space:]]*```[a-zA-Z0-9-]*[[:space:]]*"
+
+  code :: String -> [(LayerRole, String)]
+  code = caseLine [] $ \ line rest ->
+    case md_end `matchM` line of
+      Just (getAllTextSubmatches -> [_, markup]) ->
+        (Markup, markup) : md rest
+      Just _  -> __IMPOSSIBLE__
+      Nothing -> (Code, line) : code rest
+
+  -- A non-Agda code block.
+  code_other :: String -> [(LayerRole, String)]
+  code_other = caseLine [] $ \ line rest ->
+    (Comment, line) :
+    if md_end `match` line
+    then md rest
+    else code_other rest
+
+  md_end = rex "([[:space:]]*```[[:space:]]*)"
+
+-- | Preprocessor for reStructuredText.
+
+literateRsT :: Position -> String -> [Layer]
+literateRsT pos s = mkLayers pos $ rst s
+  where
+  rst :: String -> [(LayerRole, String)]
+  rst = caseLine [] maybe_code
+
+  maybe_code line rest =
+    if r_comment `match` line then
+      not_code
+    else case r_code `match` line of
+      []                         -> not_code
+      [[_, before, "::", after]] ->
+        -- Code starts
+        if maybe True isBlank $ lastMaybe before then
+          (Markup, line) : code rest
+        else
+          (Comment, before ++ ":") : (Markup, ":" ++ after) : code rest
+      _ -> __IMPOSSIBLE__
+    where
+    not_code     = (Comment, line) : rst rest
+
+  -- Finds the next indented block in the input.
+  code :: String -> [(LayerRole, String)]
+  code = caseLine [] $ \ line rest ->
+    if all isSpace line then
+      (Markup, line) : code rest
+    else
+      let xs = takeWhile isBlank line in
+      if null xs
+      then maybe_code line rest
+      else (Code, line) : indented xs rest
+
+  -- Process an indented block.
+  indented :: String -> String -> [(LayerRole, String)]
+  indented ind = caseLine [] $ \ line rest ->
+    if all isSpace line || (ind `isPrefixOf` line)
+          then (Code, line) : indented ind rest
+          else maybe_code line rest
+
+  -- Beginning of a code block.
+  r_code = rex "(.*)(::)([[:space:]]*)"
+
+  -- Beginning of a comment block.
+  r_comment = rex "[[:space:]]*\\.\\.([[:space:]].*)?"
+
+-- | Preprocessor for Org mode documents.
+
+literateOrg :: Position -> String -> [Layer]
+literateOrg pos s = mkLayers pos $ org s
+  where
+  org :: String -> [(LayerRole, String)]
+  org = caseLine [] $ \ line rest ->
+    if org_begin `match` line then
+      (Markup, line) : code rest
+    else
+      (Comment, line) : org rest
+
+  -- Valid: #+begin_src agda2 :tangle yes
+  -- Valid: #+begin_src agda2
+  -- Invalid: #+begin_src adga2-foo
+  org_begin = rex' "\\`(.*)([[:space:]]*\\#\\+begin_src agda2[[:space:]]+)"
+
+  code :: String -> [(LayerRole, String)]
+  code = caseLine [] $ \ line rest ->
+    if org_end `match` line then
+      (Markup, line) : org rest
+    else
+      (Code, line) : code rest
+
+  org_end = rex' "\\`([[:space:]]*\\#\\+end_src[[:space:]]*)(.*)"
+
+  -- Explicit type annotation required to disambiguate source.
+  rex' :: String -> Regex
+  -- Source blocks start with `#+begin_src` but the casing does not matter.
+  rex' = makeRegexOpts blankCompOpt{newSyntax = True, caseSensitive = False} blankExecOpt
diff --git a/src/full/Agda/Syntax/Parser/LookAhead.hs b/src/full/Agda/Syntax/Parser/LookAhead.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/LookAhead.hs
@@ -0,0 +1,164 @@
+
+{-| When lexing by hand (for instance string literals) we need to do some
+    looking ahead. The 'LookAhead' monad keeps track of the position we are
+    currently looking at, and provides facilities to synchronise the look-ahead
+    position with the actual position of the 'Parser' monad (see 'sync' and
+    'rollback').
+-}
+module Agda.Syntax.Parser.LookAhead
+    ( -- * The LookAhead monad
+      LookAhead
+    , runLookAhead
+      -- * Operations
+    , lookAheadError
+    , getInput, setInput, liftP
+    , nextChar, eatNextChar
+    , sync, rollback
+    , match, match'
+    )
+    where
+
+import Control.Monad.Reader
+import Control.Monad.State
+
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Monad
+
+import Agda.Utils.Null (ifNull)
+import Agda.Utils.Maybe (fromMaybeM)
+
+{--------------------------------------------------------------------------
+    The look-ahead monad
+ --------------------------------------------------------------------------}
+
+{-| The LookAhead monad is basically a state monad keeping with an extra
+    'AlexInput', wrapped around the 'Parser' monad.
+-}
+newtype LookAhead a =
+    LookAhead { _unLookAhead :: ReaderT ErrorFunction
+                                       (StateT AlexInput Parser) a
+              }
+    deriving (Functor, Applicative, Monad)
+
+newtype ErrorFunction =
+    ErrorFun { throwError :: forall a. String -> LookAhead a }
+
+-- | Throw an error message according to the supplied method.
+lookAheadError :: String -> LookAhead a
+-- ASR (2021-02-07). The eta-expansion @\e -> throwError e@ is
+-- required GHC >= 9.0.1 ((see Issue #4955).
+lookAheadError s = ($ s) =<< do LookAhead $ asks (\e -> throwError e)
+
+{--------------------------------------------------------------------------
+    Operations
+ --------------------------------------------------------------------------}
+
+-- | Get the current look-ahead position.
+getInput :: LookAhead AlexInput
+getInput = LookAhead get
+
+
+-- | Set the look-ahead position.
+setInput :: AlexInput -> LookAhead ()
+setInput = LookAhead . put
+
+
+-- | Lift a computation in the 'Parser' monad to the 'LookAhead' monad.
+liftP :: Parser a -> LookAhead a
+liftP = LookAhead . lift . lift
+
+
+-- | Look at the next character. Fails if there are no more characters.
+nextChar :: LookAhead Char
+nextChar = fromMaybeM (lookAheadError "unexpected end of file") nextCharMaybe
+
+-- | Look at the next character. Return 'Nothing' if there are no more characters.
+nextCharMaybe :: LookAhead (Maybe Char)
+nextCharMaybe =
+    do  inp <- getInput
+        case alexGetChar inp of
+            Nothing         -> return Nothing
+            Just (c,inp')   ->
+                do  setInput inp'
+                    return $ Just c
+
+
+-- | Consume all the characters up to the current look-ahead position.
+sync :: LookAhead ()
+sync =
+    do  inp <- getInput
+        liftP $ setLexInput inp
+
+
+-- | Undo look-ahead. Restores the input from the 'ParseState'.
+rollback :: LookAhead ()
+rollback =
+    do  inp <- liftP getLexInput
+        setInput inp
+
+
+-- | Consume the next character. Does 'nextChar' followed by 'sync'.
+eatNextChar :: LookAhead Char
+eatNextChar =
+    do  c <- nextChar
+        sync
+        return c
+
+
+{-| Do a case on the current input string. If any of the given strings match we
+    move past it and execute the corresponding action. If no string matches, we
+    execute a default action, advancing the input one character. This function
+    only affects the look-ahead position.
+-}
+match :: [(String, LookAhead a)] -> LookAhead a -> LookAhead a
+match xs def =
+    do  c <- nextChar
+        match' c xs def
+
+{-| Same as 'match' but takes the initial character from the first argument
+    instead of reading it from the input.  Consequently, in the default case
+    the input is not advanced.
+-}
+match' :: Char -> [(String, LookAhead a)] -> LookAhead a -> LookAhead a
+match' c xs def = do
+
+  -- Set the error continuation to the default @def@, but make sure we reset
+  -- the input to where we started speculative matching.
+  inp <- getInput
+  let fallback = setInput inp >> def
+
+  -- Find the longest match from the table.
+  match'' fallback xs c
+
+  where
+  match'' fallback bs c =
+
+    -- Match the first character, dropping entries that do not match.
+    ifNull [ (s, p) | (c':s, p) <- bs, c == c' ]
+
+      -- If no alternatives are left, fall back to the failure continuation.
+      {-then-} fallback
+
+      -- Otherwise:
+      {-else-} $ \ bs' -> do
+
+        -- If we have a successful match, store it in the failure continuation.
+        fallback' <- do
+          case lookup "" bs' of
+
+            -- No match yet.
+            Nothing -> pure fallback
+
+            -- Match found!  Remember it, and the state of the input where we found it.
+            Just p  -> do
+              inp <- getInput
+              pure $ setInput inp >> p
+
+        -- Keep trying to find a (longer) match.
+        maybe fallback' (match'' fallback' bs') =<< nextCharMaybe
+
+-- | Run a 'LookAhead' computation. The first argument is the error function.
+runLookAhead :: (forall b. String -> LookAhead b) -> LookAhead a -> Parser a
+runLookAhead err (LookAhead m) =
+    do  inp <- getLexInput
+        evalStateT (runReaderT m (ErrorFun err)) inp
diff --git a/src/full/Agda/Syntax/Parser/Monad.hs b/src/full/Agda/Syntax/Parser/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Monad.hs
@@ -0,0 +1,430 @@
+
+module Agda.Syntax.Parser.Monad
+    ( -- * The parser monad
+      Parser
+    , ParseResult(..)
+    , ParseState(..)
+    , ParseError(..), ParseWarning(..)
+    , LexState
+    , LayoutBlock(..), LayoutContext, LayoutStatus(..)
+    , Column
+    , ParseFlags (..)
+      -- * Running the parser
+    , initState
+    , defaultParseFlags
+    , parse
+    , parsePosString
+    , parseFromSrc
+      -- * Manipulating the state
+    , setParsePos, setLastPos, getParseInterval
+    , setPrevToken
+    , getParseFlags
+    , getLexState, pushLexState, popLexState
+      -- ** Layout
+    , topBlock, popBlock, pushBlock
+    , getContext, setContext, modifyContext
+    , resetLayoutStatus
+      -- ** Errors
+    , parseWarning, parseWarningName
+    , parseError, parseErrorAt, parseError', parseErrorRange
+    , lexError
+    )
+    where
+
+import Control.DeepSeq
+import Control.Exception ( displayException )
+import Control.Monad.Except
+import Control.Monad.State
+
+import Data.Int
+import Data.Maybe ( listToMaybe )
+
+import Agda.Interaction.Options.Warnings
+
+import Agda.Syntax.Concrete.Attribute
+import Agda.Syntax.Position
+import Agda.Syntax.Parser.Tokens ( Keyword( KwMutual ) )
+
+import Agda.Utils.List ( tailWithDefault )
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+{--------------------------------------------------------------------------
+    The parse monad
+ --------------------------------------------------------------------------}
+
+-- | The parse monad.
+newtype Parser a = P { _runP :: StateT ParseState (Either ParseError) a }
+  deriving (Functor, Applicative, Monad, MonadState ParseState, MonadError ParseError)
+
+-- | The parser state. Contains everything the parser and the lexer could ever
+--   need.
+data ParseState = PState
+    { parseSrcFile  :: !SrcFile
+    , parsePos      :: !PositionWithoutFile  -- ^ position at current input location
+    , parseLastPos  :: !PositionWithoutFile  -- ^ position of last token
+    , parseInp      :: String                -- ^ the current input
+    , parsePrevChar :: !Char                 -- ^ the character before the input
+    , parsePrevToken:: String                -- ^ the previous token
+    , parseLayout   :: LayoutContext         -- ^ the stack of layout blocks
+    , parseLayStatus:: LayoutStatus          -- ^ the status of the coming layout block
+    , parseLayKw    :: Keyword               -- ^ the keyword for the coming layout block
+    , parseLexState :: [LexState]            -- ^ the state of the lexer
+                                             --   (states can be nested so we need a stack)
+    , parseFlags    :: ParseFlags            -- ^ parametrization of the parser
+    , parseWarnings :: ![ParseWarning]       -- ^ In reverse order.
+    , parseAttributes
+                    :: !Attributes
+      -- ^ Every encountered attribute.
+    }
+    deriving Show
+
+{-| For context sensitive lexing alex provides what is called /start codes/
+    in the Alex documentation.  It is really an integer representing the state
+    of the lexer, so we call it @LexState@ instead.
+-}
+type LexState = Int
+
+-- | The stack of layout blocks.
+--
+--   When we encounter a layout keyword, we push a 'Tentative' block
+--   with 'noColumn'.  This is replaced by aproper column once we
+--   reach the next token.
+type LayoutContext = [LayoutBlock]
+
+-- | We need to keep track of the context to do layout. The context
+--   specifies the indentation columns of the open layout blocks. See
+--   "Agda.Syntax.Parser.Layout" for more informaton.
+data LayoutBlock
+  = Layout Keyword LayoutStatus Column
+      -- ^ Layout at specified 'Column', introduced by 'Keyword'.
+    deriving Show
+
+-- | A (layout) column.
+type Column = Int32
+
+-- | Status of a layout column (see #1145).
+--   A layout column is 'Tentative' until we encounter a new line.
+--   This allows stacking of layout keywords.
+--
+--   Inside a @LayoutContext@ the sequence of 'Confirmed' columns
+--   needs to be strictly increasing.
+--   'Tentative columns between 'Confirmed' columns need to be
+--   strictly increasing as well.
+data LayoutStatus
+  = Tentative  -- ^ The token defining the layout column was on the same line
+               --   as the layout keyword and we have not seen a new line yet.
+  | Confirmed  -- ^ We have seen a new line since the layout keyword
+               --   and the layout column has not been superseded by
+               --   a smaller column.
+    deriving (Eq, Show)
+
+-- | Parser flags.
+data ParseFlags = ParseFlags
+  { parseKeepComments :: Bool
+    -- ^ Should comment tokens be returned by the lexer?
+  }
+  deriving Show
+
+-- | Parse errors: what you get if parsing fails.
+data ParseError
+
+  -- | Errors that arise at a specific position in the file
+  = ParseError
+    { errSrcFile   :: !SrcFile
+                      -- ^ The file in which the error occurred.
+    , errPos       :: !PositionWithoutFile
+                      -- ^ Where the error occurred.
+    , errInput     :: String
+                      -- ^ The remaining input.
+    , errPrevToken :: String
+                      -- ^ The previous token.
+    , errMsg       :: String
+                      -- ^ Hopefully an explanation of what happened.
+    }
+
+  -- | Parse errors that concern a range in a file.
+  | OverlappingTokensError
+    { errRange     :: !(Range' SrcFile)
+                      -- ^ The range of the bigger overlapping token
+    }
+
+  -- | Parse errors that concern a whole file.
+  | InvalidExtensionError
+    { errPath      :: !RangeFile
+                      -- ^ The file which the error concerns.
+    , errValidExts :: [String]
+    }
+  | ReadFileError
+    { errPath      :: !RangeFile
+    , errIOError   :: IOError
+    }
+  deriving Show
+
+-- | Warnings for parsing.
+data ParseWarning
+  -- | Parse errors that concern a range in a file.
+  = OverlappingTokensWarning
+    { warnRange    :: !(Range' SrcFile)
+                      -- ^ The range of the bigger overlapping token
+    }
+  | UnsupportedAttribute Range !(Maybe String)
+    -- ^ Unsupported attribute.
+  | MultipleAttributes Range !(Maybe String)
+    -- ^ Multiple attributes.
+  deriving Show
+
+instance NFData ParseWarning where
+  rnf (OverlappingTokensWarning _) = ()
+  rnf (UnsupportedAttribute _ s)   = rnf s
+  rnf (MultipleAttributes _ s)     = rnf s
+
+parseWarningName :: ParseWarning -> WarningName
+parseWarningName = \case
+  OverlappingTokensWarning{} -> OverlappingTokensWarning_
+  UnsupportedAttribute{}     -> UnsupportedAttribute_
+  MultipleAttributes{}       -> MultipleAttributes_
+
+-- | The result of parsing something.
+data ParseResult a
+  = ParseOk ParseState a
+  | ParseFailed ParseError
+  deriving Show
+
+-- | Old interface to parser.
+unP :: Parser a -> ParseState -> ParseResult a
+unP (P m) s = case runStateT m s of
+  Left err     -> ParseFailed err
+  Right (a, s) -> ParseOk s a
+
+-- | Throw a parse error at the current position.
+parseError :: String -> Parser a
+parseError msg = do
+  s <- get
+  throwError $ ParseError
+    { errSrcFile   = parseSrcFile s
+    , errPos       = parseLastPos s
+    , errInput     = parseInp s
+    , errPrevToken = parsePrevToken s
+    , errMsg       = msg
+    }
+
+-- | Records a warning.
+
+parseWarning :: ParseWarning -> Parser ()
+parseWarning w =
+  modify' $ \s -> s { parseWarnings = w : parseWarnings s }
+
+{--------------------------------------------------------------------------
+    Instances
+ --------------------------------------------------------------------------}
+
+instance Pretty ParseError where
+  pretty ParseError{errPos,errSrcFile,errMsg,errPrevToken,errInput} = vcat
+      [ (pretty (errPos { srcFile = errSrcFile }) <> colon) <+>
+        text errMsg
+      , text $ errPrevToken ++ "<ERROR>"
+      , text $ take 30 errInput ++ "..."
+      ]
+  pretty OverlappingTokensError{errRange} = vcat
+      [ (pretty errRange <> colon) <+>
+        "Multi-line comment spans one or more literate text blocks."
+      ]
+  pretty InvalidExtensionError{errPath,errValidExts} = vcat
+      [ (pretty errPath <> colon) <+>
+        "Unsupported extension."
+      , "Supported extensions are:" <+> prettyList_ errValidExts
+      ]
+  pretty ReadFileError{errPath,errIOError} = vcat
+      [ "Cannot read file" <+> pretty errPath
+      , "Error:" <+> text (displayException errIOError)
+      ]
+
+instance HasRange ParseError where
+  getRange err = case err of
+      ParseError{ errSrcFile, errPos = p } -> posToRange' errSrcFile p p
+      OverlappingTokensError{ errRange }   -> errRange
+      InvalidExtensionError{}              -> errPathRange
+      ReadFileError{}                      -> errPathRange
+    where
+    errPathRange = posToRange p p
+      where p = startPos $ Just $ errPath err
+
+instance Pretty ParseWarning where
+  pretty OverlappingTokensWarning{warnRange} = vcat
+      [ (pretty warnRange <> colon) <+>
+        "Multi-line comment spans one or more literate text blocks."
+      ]
+  pretty (UnsupportedAttribute r s) = vcat
+    [ (pretty r <> colon) <+>
+      (case s of
+         Nothing -> "Attributes"
+         Just s  -> text s <+> "attributes") <+>
+      "are not supported here."
+    ]
+  pretty (MultipleAttributes r s) = vcat
+    [ (pretty r <> colon) <+>
+      "Multiple" <+>
+      maybe id (\s -> (text s <+>)) s "attributes (ignored)."
+    ]
+
+instance HasRange ParseWarning where
+  getRange OverlappingTokensWarning{warnRange} = warnRange
+  getRange (UnsupportedAttribute r _)          = r
+  getRange (MultipleAttributes r _)            = r
+
+{--------------------------------------------------------------------------
+    Running the parser
+ --------------------------------------------------------------------------}
+
+initStatePos :: Position -> ParseFlags -> String -> [LexState] -> ParseState
+initStatePos pos flags inp st =
+        PState  { parseSrcFile      = srcFile pos
+                , parsePos          = pos'
+                , parseLastPos      = pos'
+                , parseInp          = inp
+                , parsePrevChar     = '\n'
+                , parsePrevToken    = ""
+                , parseLexState     = st
+                , parseLayout       = []        -- the first block will be from the top-level layout
+                , parseLayStatus    = Confirmed -- for the to-be-determined column of the top-level layout
+                , parseLayKw        = KwMutual  -- Layout keyword for the top-level layout.
+                                                -- Does not mean that the top-level block is a mutual block.
+                                                -- Just for better errors on stray @constructor@ decls.
+                , parseFlags        = flags
+                , parseWarnings     = []
+                , parseAttributes   = []
+                }
+  where
+  pos' = pos { srcFile = () }
+
+-- | Constructs the initial state of the parser. The string argument
+--   is the input string, the file path is only there because it's part
+--   of a position.
+initState ::
+  Maybe RangeFile -> ParseFlags -> String -> [LexState] -> ParseState
+initState file = initStatePos (startPos file)
+
+-- | The default flags.
+defaultParseFlags :: ParseFlags
+defaultParseFlags = ParseFlags { parseKeepComments = False }
+
+-- | The most general way of parsing a string. The "Agda.Syntax.Parser" will define
+--   more specialised functions that supply the 'ParseFlags' and the
+--   'LexState'.
+parse :: ParseFlags -> [LexState] -> Parser a -> String -> ParseResult a
+parse flags st p input = parseFromSrc flags st p Strict.Nothing input
+
+-- | The even more general way of parsing a string.
+parsePosString :: Position -> ParseFlags -> [LexState] -> Parser a -> String ->
+                  ParseResult a
+parsePosString pos flags st p input = unP p (initStatePos pos flags input st)
+
+-- | Parses a string as if it were the contents of the given file
+--   Useful for integrating preprocessors.
+parseFromSrc :: ParseFlags -> [LexState] -> Parser a -> SrcFile -> String
+              -> ParseResult a
+parseFromSrc flags st p src input = unP p (initState (Strict.toLazy src) flags input st)
+
+
+{--------------------------------------------------------------------------
+    Manipulating the state
+ --------------------------------------------------------------------------}
+
+setParsePos :: PositionWithoutFile -> Parser ()
+setParsePos p = modify $ \s -> s { parsePos = p }
+
+setLastPos :: PositionWithoutFile -> Parser ()
+setLastPos p = modify $ \s -> s { parseLastPos = p }
+
+setPrevToken :: String -> Parser ()
+setPrevToken t = modify $ \s -> s { parsePrevToken = t }
+
+getLastPos :: Parser PositionWithoutFile
+getLastPos = gets parseLastPos
+
+-- | The parse interval is between the last position and the current position.
+getParseInterval :: Parser Interval
+getParseInterval = do
+  s <- get
+  return $ posToInterval (parseSrcFile s) (parseLastPos s) (parsePos s)
+
+getLexState :: Parser [LexState]
+getLexState = gets parseLexState
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+--setLexState :: [LexState] -> Parser ()
+--setLexState ls = modify $ \ s -> s { parseLexState = ls }
+
+modifyLexState :: ([LexState] -> [LexState]) -> Parser ()
+modifyLexState f = modify $ \ s -> s { parseLexState = f (parseLexState s) }
+
+pushLexState :: LexState -> Parser ()
+pushLexState l = modifyLexState (l:)
+
+popLexState :: Parser ()
+popLexState = modifyLexState $ tailWithDefault __IMPOSSIBLE__
+
+getParseFlags :: Parser ParseFlags
+getParseFlags = gets parseFlags
+
+
+-- | Fake a parse error at the specified position. Used, for instance, when
+--   lexing nested comments, which when failing will always fail at the end
+--   of the file. A more informative position is the beginning of the failing
+--   comment.
+parseErrorAt :: PositionWithoutFile -> String -> Parser a
+parseErrorAt p msg =
+    do  setLastPos p
+        parseError msg
+
+-- | Use 'parseErrorAt' or 'parseError' as appropriate.
+parseError' :: Maybe PositionWithoutFile -> String -> Parser a
+parseError' = maybe parseError parseErrorAt
+
+-- | Report a parse error at the beginning of the given 'Range'.
+parseErrorRange :: HasRange r => r -> String -> Parser a
+parseErrorRange = parseError' . rStart' . getRange
+
+
+-- | For lexical errors we want to report the current position as the site of
+--   the error, whereas for parse errors the previous position is the one
+--   we're interested in (since this will be the position of the token we just
+--   lexed). This function does 'parseErrorAt' the current position.
+lexError :: String -> Parser a
+lexError msg =
+    do  p <- gets parsePos
+        parseErrorAt p msg
+
+{--------------------------------------------------------------------------
+    Layout
+ --------------------------------------------------------------------------}
+
+getContext :: MonadState ParseState m => m LayoutContext
+getContext = gets parseLayout
+
+setContext :: LayoutContext -> Parser ()
+setContext = modifyContext . const
+
+modifyContext :: (LayoutContext -> LayoutContext) -> Parser ()
+modifyContext f = modify $ \ s -> s { parseLayout = f (parseLayout s) }
+
+-- | Return the current layout block.
+topBlock :: Parser (Maybe LayoutBlock)
+topBlock = listToMaybe <$> getContext
+
+popBlock :: Parser ()
+popBlock =
+    do  ctx <- getContext
+        case ctx of
+            []      -> parseError "There is no layout block to close at this point."
+            _:ctx   -> setContext ctx
+
+pushBlock :: LayoutBlock -> Parser ()
+pushBlock l = modifyContext (l :)
+
+-- | When we see a layout keyword, by default we expect a 'Tentative' block.
+resetLayoutStatus :: Parser ()
+resetLayoutStatus = modify $ \ s -> s { parseLayStatus = Tentative }
diff --git a/src/full/Agda/Syntax/Parser/Parser.y b/src/full/Agda/Syntax/Parser/Parser.y
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Parser.y
@@ -0,0 +1,2526 @@
+{
+#if  __GLASGOW_HASKELL__ > 800
+{-# OPTIONS_GHC -Wno-error=missing-signatures #-}
+#endif
+{-# LANGUAGE PatternGuards #-}
+
+{-| The parser is generated by Happy (<http://www.haskell.org/happy>).
+ -
+ - Ideally, ranges should be as precise as possible, to get messages that
+ - emphasize precisely the faulting term(s) upon error.
+ -
+ - However, interactive highlighting is only applied at the end of each
+ - mutual block, keywords are only highlighted once (see
+ - `TypeChecking.Rules.Decl'). So if the ranges of two declarations
+ - interleave, one must ensure that keyword ranges are not included in
+ - the intersection. (Otherwise they are uncolored by the interactive
+ - highlighting.)
+ -
+ -}
+module Agda.Syntax.Parser.Parser (
+      moduleParser
+    , moduleNameParser
+    , exprParser
+    , exprWhereParser
+    , tokensParser
+    , holeContentParser
+    , splitOnDots  -- only used by the internal test-suite
+    ) where
+
+import Prelude hiding ( null )
+
+import Control.Applicative ( (<|>) )
+import Control.Monad
+import Control.Monad.State
+
+import Data.Bifunctor (first, second)
+import Data.Char
+import Data.DList (DList)
+import qualified Data.DList as DL
+import qualified Data.List as List
+import Data.Maybe
+import Data.Semigroup ((<>), sconcat)
+import qualified Data.Traversable as T
+
+import Agda.Syntax.Position hiding (tests)
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Lexer
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Attribute
+import Agda.Syntax.Concrete.Pattern
+import Agda.Syntax.Common
+import Agda.Syntax.Notation
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Positivity.Occurrence hiding (tests)
+
+import Agda.Utils.Either hiding (tests)
+import Agda.Utils.Functor
+import Agda.Utils.Hash
+import Agda.Utils.List ( spanJust, chopWhen )
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty hiding ((<>))
+import Agda.Utils.Singleton
+import qualified Agda.Utils.Maybe.Strict as Strict
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.List2 as List2
+
+import Agda.Utils.Impossible
+
+}
+
+%name tokensParser Tokens
+%name exprParser Expr
+%name exprWhereParser ExprWhere
+%name moduleParser File
+%name moduleNameParser ModuleName
+%name funclauseParser FunClause
+%name holeContentParser HoleContent
+
+%tokentype { Token }
+%monad { Parser }
+%lexer { lexer } { TokEOF{} }
+
+%expect 8
+-- * shift/reduce for \ x y z -> foo = bar
+--   shifting means it'll parse as \ x y z -> (foo = bar) rather than
+--   (\ x y z -> foo) = bar
+--
+-- * Telescope let and do-notation let.
+--      Expr2 -> 'let' Declarations . LetBody
+--      TypedBinding -> '(' 'let' Declarations . ')'
+--        ')'   shift, and enter state 486
+--              (reduce using rule 189)
+--   A do-block cannot end in a 'let' so committing to TypedBinding with a
+--   shift is the right thing to do here.
+--
+-- * Named implicits in TypedBinding {x = y}. When encountering the '=' shift
+--   treats this as a named implicit and reducing would fail later.
+
+-- This is a trick to get rid of shift/reduce conflicts arising because we want
+-- to parse things like "m >>= \x -> k x". See the Expr rule for more
+-- information.
+%nonassoc LOWEST
+%nonassoc '->'
+
+%token
+    'abstract'                { TokKeyword KwAbstract $$ }
+    'codata'                  { TokKeyword KwCoData $$ }
+    'coinductive'             { TokKeyword KwCoInductive $$ }
+    'constructor'             { TokKeyword KwConstructor $$ }
+    'data'                    { TokKeyword KwData $$ }
+    'eta-equality'            { TokKeyword KwEta $$ }
+    'field'                   { TokKeyword KwField $$ }
+    'forall'                  { TokKeyword KwForall $$ }
+    'variable'                { TokKeyword KwVariable $$ }
+    'hiding'                  { TokKeyword KwHiding $$ }
+    'import'                  { TokKeyword KwImport $$ }
+    'in'                      { TokKeyword KwIn $$ }
+    'inductive'               { TokKeyword KwInductive $$ }
+    'infix'                   { TokKeyword KwInfix $$ }
+    'infixl'                  { TokKeyword KwInfixL $$ }
+    'infixr'                  { TokKeyword KwInfixR $$ }
+    'instance'                { TokKeyword KwInstance $$ }
+    'overlap'                 { TokKeyword KwOverlap $$ }
+    'let'                     { TokKeyword KwLet $$ }
+    'macro'                   { TokKeyword KwMacro $$ }
+    'module'                  { TokKeyword KwModule $$ }
+    'interleaved'             { TokKeyword KwInterleaved $$ }
+    'mutual'                  { TokKeyword KwMutual $$ }
+    'no-eta-equality'         { TokKeyword KwNoEta $$ }
+    'open'                    { TokKeyword KwOpen $$ }
+    'pattern'                 { TokKeyword KwPatternSyn $$ }
+    'postulate'               { TokKeyword KwPostulate $$ }
+    'primitive'               { TokKeyword KwPrimitive $$ }
+    'private'                 { TokKeyword KwPrivate $$ }
+    'public'                  { TokKeyword KwPublic $$ }
+    'quote'                   { TokKeyword KwQuote $$ }
+    'quoteTerm'               { TokKeyword KwQuoteTerm $$ }
+    'record'                  { TokKeyword KwRecord $$ }
+    'renaming'                { TokKeyword KwRenaming $$ }
+    'rewrite'                 { TokKeyword KwRewrite $$ }
+    'syntax'                  { TokKeyword KwSyntax $$ }
+    'tactic'                  { TokKeyword KwTactic $$ }
+    'to'                      { TokKeyword KwTo $$ }
+    'unquote'                 { TokKeyword KwUnquote $$ }
+    'unquoteDecl'             { TokKeyword KwUnquoteDecl $$ }
+    'unquoteDef'              { TokKeyword KwUnquoteDef $$ }
+    'using'                   { TokKeyword KwUsing $$ }
+    'where'                   { TokKeyword KwWhere $$ }
+    'do'                      { TokKeyword KwDo $$ }
+    'with'                    { TokKeyword KwWith $$ }
+    'opaque'                  { TokKeyword KwOpaque $$ }
+    'unfolding'               { TokKeyword KwUnfolding $$ }
+
+    'BUILTIN'                 { TokKeyword KwBUILTIN $$ }
+    'CATCHALL'                { TokKeyword KwCATCHALL $$ }
+    'DISPLAY'                 { TokKeyword KwDISPLAY $$ }
+    'ETA'                     { TokKeyword KwETA $$ }
+    'FOREIGN'                 { TokKeyword KwFOREIGN $$ }
+    'COMPILE'                 { TokKeyword KwCOMPILE $$ }
+    'IMPOSSIBLE'              { TokKeyword KwIMPOSSIBLE $$ }
+    'INJECTIVE'               { TokKeyword KwINJECTIVE $$ }
+    'INLINE'                  { TokKeyword KwINLINE $$ }
+    'NOINLINE'                { TokKeyword KwNOINLINE $$ }
+    'MEASURE'                 { TokKeyword KwMEASURE $$ }
+    'NO_TERMINATION_CHECK'    { TokKeyword KwNO_TERMINATION_CHECK $$ }
+    'NO_POSITIVITY_CHECK'     { TokKeyword KwNO_POSITIVITY_CHECK $$ }
+    'NO_UNIVERSE_CHECK'       { TokKeyword KwNO_UNIVERSE_CHECK $$ }
+    'NON_TERMINATING'         { TokKeyword KwNON_TERMINATING $$ }
+    'NON_COVERING'            { TokKeyword KwNON_COVERING $$ }
+    'NOT_PROJECTION_LIKE'     { TokKeyword KwNOT_PROJECTION_LIKE $$ }
+    'OPTIONS'                 { TokKeyword KwOPTIONS $$ }
+    'POLARITY'                { TokKeyword KwPOLARITY $$ }
+    'WARNING_ON_USAGE'        { TokKeyword KwWARNING_ON_USAGE $$ }
+    'WARNING_ON_IMPORT'       { TokKeyword KwWARNING_ON_IMPORT $$ }
+    'REWRITE'                 { TokKeyword KwREWRITE $$ }
+    'STATIC'                  { TokKeyword KwSTATIC $$ }
+    'TERMINATING'             { TokKeyword KwTERMINATING $$ }
+
+    tex                       { TokTeX $$ }
+    comment                   { TokComment $$ }
+
+    '...'                     { TokSymbol SymEllipsis $$ }
+    '..'                      { TokSymbol SymDotDot $$ }
+    '.'                       { TokSymbol SymDot $$ }
+    ';'                       { TokSymbol SymSemi $$ }
+    ':'                       { TokSymbol SymColon $$ }
+    '='                       { TokSymbol SymEqual $$ }
+    '_'                       { TokSymbol SymUnderscore $$ }
+    '?'                       { TokSymbol SymQuestionMark $$ }
+    '->'                      { TokSymbol SymArrow $$ }
+    '\\'                      { TokSymbol SymLambda $$ }
+    '@'                       { TokSymbol SymAs $$ }
+    '|'                       { TokSymbol SymBar $$ }
+    '('                       { TokSymbol SymOpenParen $$ }
+    ')'                       { TokSymbol SymCloseParen $$ }
+    '(|'                      { TokSymbol SymOpenIdiomBracket $$ }
+    '|)'                      { TokSymbol SymCloseIdiomBracket $$ }
+    '(|)'                     { TokSymbol SymEmptyIdiomBracket $$ }
+    '{{'                      { TokSymbol SymDoubleOpenBrace $$ }
+    '}}'                      { TokSymbol SymDoubleCloseBrace $$ }
+    '{'                       { TokSymbol SymOpenBrace $$ }
+    '}'                       { TokSymbol SymCloseBrace $$ }
+--    ':{'                      { TokSymbol SymColonBrace $$ }
+    vopen                     { TokSymbol SymOpenVirtualBrace $$ }
+    vclose                    { TokSymbol SymCloseVirtualBrace $$ }
+    vsemi                     { TokSymbol SymVirtualSemi $$ }
+    '{-#'                     { TokSymbol SymOpenPragma $$ }
+    '#-}'                     { TokSymbol SymClosePragma $$ }
+
+    id                        { TokId $$ }
+    q_id                      { TokQId $$ }
+
+    string                    { TokString $$ }
+    literal                   { TokLiteral $$ }
+
+%%
+
+{--------------------------------------------------------------------------
+    Parsing the token stream. Used by the TeX compiler.
+ --------------------------------------------------------------------------}
+
+-- Parse a list of tokens.
+Tokens :: { [Token] }
+Tokens : TokensR        { reverse $1 }
+
+-- Happy is much better at parsing left recursive grammars (constant
+-- stack size vs. linear stack size for right recursive).
+TokensR :: { [Token] }
+TokensR : TokensR Token { $2 : $1 }
+        |               { [] }
+
+-- Parse single token.
+Token :: { Token }
+Token
+      -- Please keep these keywords in alphabetical order!
+    : 'abstract'                { TokKeyword KwAbstract $1 }
+    | 'codata'                  { TokKeyword KwCoData $1 }
+    | 'coinductive'             { TokKeyword KwCoInductive $1 }
+    | 'constructor'             { TokKeyword KwConstructor $1 }
+    | 'data'                    { TokKeyword KwData $1 }
+    | 'do'                      { TokKeyword KwDo $1 }
+    | 'eta-equality'            { TokKeyword KwEta $1 }
+    | 'field'                   { TokKeyword KwField $1 }
+    | 'forall'                  { TokKeyword KwForall $1 }
+    | 'hiding'                  { TokKeyword KwHiding $1 }
+    | 'import'                  { TokKeyword KwImport $1 }
+    | 'in'                      { TokKeyword KwIn $1 }
+    | 'inductive'               { TokKeyword KwInductive $1 }
+    | 'infix'                   { TokKeyword KwInfix $1 }
+    | 'infixl'                  { TokKeyword KwInfixL $1 }
+    | 'infixr'                  { TokKeyword KwInfixR $1 }
+    | 'instance'                { TokKeyword KwInstance $1 }
+    | 'let'                     { TokKeyword KwLet $1 }
+    | 'macro'                   { TokKeyword KwMacro $1 }
+    | 'module'                  { TokKeyword KwModule $1 }
+    | 'interleaved'             { TokKeyword KwInterleaved $1 }
+    | 'mutual'                  { TokKeyword KwMutual $1 }
+    | 'no-eta-equality'         { TokKeyword KwNoEta $1 }
+    | 'opaque'                  { TokKeyword KwOpaque $1 }
+    | 'open'                    { TokKeyword KwOpen $1 }
+    | 'overlap'                 { TokKeyword KwOverlap $1 }
+    | 'pattern'                 { TokKeyword KwPatternSyn $1 }
+    | 'postulate'               { TokKeyword KwPostulate $1 }
+    | 'primitive'               { TokKeyword KwPrimitive $1 }
+    | 'private'                 { TokKeyword KwPrivate $1 }
+    | 'public'                  { TokKeyword KwPublic $1 }
+    | 'quote'                   { TokKeyword KwQuote $1 }
+    | 'quoteTerm'               { TokKeyword KwQuoteTerm $1 }
+    | 'record'                  { TokKeyword KwRecord $1 }
+    | 'renaming'                { TokKeyword KwRenaming $1 }
+    | 'rewrite'                 { TokKeyword KwRewrite $1 }
+    | 'syntax'                  { TokKeyword KwSyntax $1 }
+    | 'tactic'                  { TokKeyword KwTactic $1 }
+    | 'to'                      { TokKeyword KwTo $1 }
+    | 'unfolding'               { TokKeyword KwUnfolding $1 }
+    | 'unquote'                 { TokKeyword KwUnquote $1 }
+    | 'unquoteDecl'             { TokKeyword KwUnquoteDecl $1 }
+    | 'unquoteDef'              { TokKeyword KwUnquoteDef $1 }
+    | 'using'                   { TokKeyword KwUsing $1 }
+    | 'variable'                { TokKeyword KwVariable $1 }
+    | 'where'                   { TokKeyword KwWhere $1 }
+    | 'with'                    { TokKeyword KwWith $1 }
+
+      -- Please keep these pragmas in alphabetical order!
+    | 'BUILTIN'                 { TokKeyword KwBUILTIN $1 }
+    | 'CATCHALL'                { TokKeyword KwCATCHALL $1 }
+    | 'COMPILE'                 { TokKeyword KwCOMPILE $1 }
+    | 'DISPLAY'                 { TokKeyword KwDISPLAY $1 }
+    | 'ETA'                     { TokKeyword KwETA $1 }
+    | 'FOREIGN'                 { TokKeyword KwFOREIGN $1 }
+    | 'IMPOSSIBLE'              { TokKeyword KwIMPOSSIBLE $1 }
+    | 'INJECTIVE'               { TokKeyword KwINJECTIVE $1 }
+    | 'INLINE'                  { TokKeyword KwINLINE $1 }
+    | 'MEASURE'                 { TokKeyword KwMEASURE $1 }
+    | 'NOINLINE'                { TokKeyword KwNOINLINE $1 }
+    | 'NO_POSITIVITY_CHECK'     { TokKeyword KwNO_POSITIVITY_CHECK $1 }
+    | 'NO_TERMINATION_CHECK'    { TokKeyword KwNO_TERMINATION_CHECK $1 }
+    | 'NO_UNIVERSE_CHECK'       { TokKeyword KwNO_UNIVERSE_CHECK $1 }
+    | 'NON_TERMINATING'         { TokKeyword KwNON_TERMINATING $1 }
+    | 'NON_COVERING'            { TokKeyword KwNON_COVERING $1 }
+    | 'NOT_PROJECTION_LIKE'     { TokKeyword KwNOT_PROJECTION_LIKE $1 }
+    | 'OPTIONS'                 { TokKeyword KwOPTIONS $1 }
+    | 'POLARITY'                { TokKeyword KwPOLARITY $1 }
+    | 'REWRITE'                 { TokKeyword KwREWRITE $1 }
+    | 'STATIC'                  { TokKeyword KwSTATIC $1 }
+    | 'TERMINATING'             { TokKeyword KwTERMINATING $1 }
+    | 'WARNING_ON_IMPORT'       { TokKeyword KwWARNING_ON_IMPORT $1 }
+    | 'WARNING_ON_USAGE'        { TokKeyword KwWARNING_ON_USAGE $1 }
+
+    | tex                       { TokTeX $1 }
+    | comment                   { TokComment $1 }
+
+    | '...'                     { TokSymbol SymEllipsis $1 }
+    | '..'                      { TokSymbol SymDotDot $1 }
+    | '.'                       { TokSymbol SymDot $1 }
+    | ';'                       { TokSymbol SymSemi $1 }
+    | ':'                       { TokSymbol SymColon $1 }
+    | '='                       { TokSymbol SymEqual $1 }
+    | '_'                       { TokSymbol SymUnderscore $1 }
+    | '?'                       { TokSymbol SymQuestionMark $1 }
+    | '->'                      { TokSymbol SymArrow $1 }
+    | '\\'                      { TokSymbol SymLambda $1 }
+    | '@'                       { TokSymbol SymAs $1 }
+    | '|'                       { TokSymbol SymBar $1 }
+    | '('                       { TokSymbol SymOpenParen $1 }
+    | ')'                       { TokSymbol SymCloseParen $1 }
+    | '(|'                      { TokSymbol SymOpenIdiomBracket $1 }
+    | '|)'                      { TokSymbol SymCloseIdiomBracket $1 }
+    | '(|)'                     { TokSymbol SymEmptyIdiomBracket $1 }
+    | '{{'                      { TokSymbol SymDoubleOpenBrace $1 }
+    | '}}'                      { TokSymbol SymDoubleCloseBrace $1 }
+    | '{'                       { TokSymbol SymOpenBrace $1 }
+    | '}'                       { TokSymbol SymCloseBrace $1 }
+    | vopen                     { TokSymbol SymOpenVirtualBrace $1 }
+    | vclose                    { TokSymbol SymCloseVirtualBrace $1 }
+    | vsemi                     { TokSymbol SymVirtualSemi $1 }
+    | '{-#'                     { TokSymbol SymOpenPragma $1 }
+    | '#-}'                     { TokSymbol SymClosePragma $1 }
+
+    | id                        { TokId $1 }
+    | q_id                      { TokQId $1 }
+    | string                    { TokString $1 }
+
+    | literal                   { TokLiteral $1 }
+
+{--------------------------------------------------------------------------
+    Top level
+ --------------------------------------------------------------------------}
+
+File :: { Module }
+File : vopen TopLevel maybe_vclose { takeOptionsPragmas $2 }
+
+maybe_vclose :: { () }
+maybe_vclose : {- empty -} { () }
+             | vclose      { () }
+
+{--------------------------------------------------------------------------
+    Meta rules
+ --------------------------------------------------------------------------}
+
+{-  A layout block might have to be closed by a parse error. Example:
+        let x = e in e'
+    Here the 'let' starts a layout block which should end before the 'in'.  The
+    problem is that the lexer doesn't know this, so there is no virtual close
+    brace. However when the parser sees the 'in' there will be a parse error.
+    This is our cue to close the layout block.
+-}
+close :: { () }
+close : vclose  { () }
+      | error   {% popBlock }
+
+
+-- You can use concrete semi colons in a layout block started with a virtual
+-- brace, so we don't have to distinguish between the two semi colons. You can't
+-- use a virtual semi colon in a block started by a concrete brace, but this is
+-- simply because the lexer will not generate virtual semis in this case.
+semi :: { Interval }
+semi : ';'    { $1 }
+     | vsemi  { $1 }
+
+
+-- Enter the 'imp_dir' lex state, where we can parse the keyword 'to'.
+beginImpDir :: { () }
+beginImpDir : {- empty -}   {% pushLexState imp_dir }
+
+{--------------------------------------------------------------------------
+    Helper rules
+ --------------------------------------------------------------------------}
+
+-- A float. Used in fixity declarations.
+Float :: { Ranged Double }
+Float : literal {% forM $1 $ \case
+                   { LitNat   i -> return $ fromInteger i
+                   ; LitFloat d -> return d
+                   ; _          -> parseError $ "Expected floating point number"
+                   }
+                }
+
+
+{--------------------------------------------------------------------------
+    Names
+ --------------------------------------------------------------------------}
+
+-- A name is really a sequence of parts, but the lexer just sees it as a
+-- string, so we have to do the translation here.
+Id :: { Name }
+Id : id     {% mkName $1 }
+
+-- Space separated list of one or more identifiers.
+SpaceIds :: { List1 Name }
+SpaceIds
+    : Id SpaceIds { $1 <| $2 }
+    | Id          { singleton $1 }
+
+-- When looking for a double closed brace, we accept either a single token '}}'
+-- (which is what the unicode character "RIGHT WHITE CURLY BRACKET" is
+-- postprocessed into in LexActions.hs), but also two consecutive tokens '}'
+-- (which a string '}}' is lexed to).  This small hack allows us to keep
+-- "record { a = record { }}" working. In the second case, we check that the two
+-- tokens '}' are immediately consecutive.
+DoubleCloseBrace :: { Range }
+DoubleCloseBrace
+  : '}}' { getRange $1 }
+  | '}' '}' {%
+      if posPos (fromJust (rEnd' (getRange $2))) -
+         posPos (fromJust (rStart' (getRange $1))) > 2
+      then parseErrorRange $2 "Expecting '}}', found separated '}'s."
+      else return $ getRange ($1, $2)
+    }
+
+-- A possibly dotted identifier.
+MaybeDottedId :: { Arg Name }
+MaybeDottedId
+  : '..' Id { setRelevance NonStrict $ defaultArg $2 }
+  | '.'  Id { setRelevance Irrelevant $ defaultArg $2 }
+  | Id      { defaultArg $1 }
+
+-- Space separated list of one or more possibly dotted identifiers.
+MaybeDottedIds :: { List1 (Arg Name) }
+MaybeDottedIds
+    : MaybeDottedId MaybeDottedIds { $1 <| $2 }
+    | MaybeDottedId                { singleton $1 }
+
+-- Space separated list of one or more identifiers, some of which may
+-- be surrounded by braces or dotted.
+ArgIds :: { List1 (Arg Name) }
+ArgIds
+    : MaybeDottedId ArgIds            { $1 <| $2 }
+    | MaybeDottedId                   { singleton $1 }
+    | '{{' MaybeDottedIds DoubleCloseBrace ArgIds { fmap makeInstance $2 <> $4 }
+    | '{{' MaybeDottedIds DoubleCloseBrace        { fmap makeInstance $2 }
+    | '{' MaybeDottedIds '}' ArgIds   { fmap hide $2 <> $4 }
+    | '{' MaybeDottedIds '}'          { fmap hide $2 }
+    | '.' '{' SpaceIds '}' ArgIds     { fmap (hide . setRelevance Irrelevant . defaultArg) $3 <> $5 }
+    | '.' '{' SpaceIds '}'            { fmap (hide . setRelevance Irrelevant . defaultArg) $3 }
+    | '.' '{{' SpaceIds DoubleCloseBrace ArgIds   { fmap (makeInstance . setRelevance Irrelevant . defaultArg) $3 <> $5 }
+    | '.' '{{' SpaceIds DoubleCloseBrace          { fmap (makeInstance . setRelevance Irrelevant . defaultArg) $3 }
+    | '..' '{' SpaceIds '}' ArgIds    { fmap (hide . setRelevance NonStrict . defaultArg) $3 <> $5 }
+    | '..' '{' SpaceIds '}'           { fmap (hide . setRelevance NonStrict . defaultArg) $3 }
+    | '..' '{{' SpaceIds DoubleCloseBrace ArgIds  { fmap (makeInstance . setRelevance NonStrict . defaultArg) $3 <> $5 }
+    | '..' '{{' SpaceIds DoubleCloseBrace         { fmap (makeInstance . setRelevance NonStrict . defaultArg) $3 }
+
+-- Modalities preceeding identifiers
+
+ModalArgIds :: { ([Attr], List1 (Arg Name)) }
+ModalArgIds : Attributes ArgIds  {% ($1,) `fmap` mapM (applyAttrs $1) $2 }
+
+-- Attributes are parsed as '@' followed by an atomic expression.
+
+Attribute :: { Attr }
+Attribute : '@' ExprOrAttr  {% toAttribute (getRange ($1,$2)) $2 }
+
+-- Parse a reverse list of modalities
+
+Attributes :: { [Attr] }
+Attributes : {- empty -}  { [] }
+  | Attributes Attribute { $2 : $1 }
+
+Attributes1 :: { List1 Attr }
+Attributes1 : Attribute  { singleton $1 }
+  | Attributes1 Attribute { $2 <| $1 }
+
+QId :: { QName }
+QId : q_id  {% mkQName $1 }
+    | Id    { QName $1 }
+
+
+-- A module name is just a qualified name
+ModuleName :: { QName }
+ModuleName : QId { $1 }
+
+
+-- A binding variable. Can be '_'
+BId :: { Name }
+BId : Id    { $1 }
+    | '_'   { setRange (getRange $1) simpleHole }
+
+{- UNUSED
+-- A binding variable. Can be '_'
+MaybeDottedBId :: { (Relevance, Name) }
+MaybeDottedBId
+    : BId        { (Relevant  , $1) }
+    | '.' BId    { (Irrelevant, $2) }
+    | '..' BId   { (NonStrict, $2) }
+-}
+
+
+-- Space separated list of binding identifiers. Used in fixity
+-- declarations infixl 100 + -
+SpaceBIds :: { List1 Name }
+SpaceBIds
+    : BId SpaceBIds { $1 <| $2 }
+    | BId           { singleton $1 }
+
+{- DOES PRODUCE REDUCE/REDUCE CONFLICTS!
+-- Space-separated list of binding identifiers. Used in dependent
+-- function spaces: (x y z : Nat) -> ...
+-- (Used to be comma-separated; hence the name)
+-- QUESTION: Should this be replaced by SpaceBIds above?
+--CommaBIds :: { [(Relevance,Name)] }
+CommaBIds :: { [Name] }
+CommaBIds
+    : CommaBIds BId { $1 ++ [$2] }  -- SWITCHING DOES NOT HELP
+    | BId           { [$1] }
+-}
+
+-- Space-separated list of binding identifiers. Used in dependent
+-- function spaces: (x y z : Nat) -> ...
+-- (Used to be comma-separated; hence the name)
+-- QUESTION: Should this be replaced by SpaceBIds above?
+-- Andreas, 2011-04-07 the trick avoids reduce/reduce conflicts
+-- when parsing  (x y z : A) -> B
+-- at point (x y  it is not clear whether x y is an application or
+-- a variable list. We could be parsing (x y z) -> B
+-- with ((x y) z) being a type.
+CommaBIds :: { List1 (NamedArg Binder) }
+CommaBIds : CommaBIdAndAbsurds {%
+    case $1 of
+      Left ns -> return ns
+      Right _ -> parseError $ "expected sequence of bound identifiers, not absurd pattern"
+    }
+
+CommaBIdAndAbsurds :: { Either (List1 (NamedArg Binder)) (List1 Expr) }
+CommaBIdAndAbsurds
+  : Application {% boundNamesOrAbsurd $1 }
+  | QId '=' QId {% (Left . singleton . updateNamedArg mkBinder) `fmap` mkNamedArg (Just $1) (Left $3) }
+  | '_' '=' QId {% (Left . singleton . updateNamedArg mkBinder) `fmap` mkNamedArg Nothing   (Left $3) }
+  | QId '=' '_' {% (Left . singleton . updateNamedArg mkBinder) `fmap` mkNamedArg (Just $1) (Right $ getRange $3) }
+  | '_' '=' '_' {% (Left . singleton . updateNamedArg mkBinder) `fmap` mkNamedArg Nothing   (Right $ getRange $3) }
+
+-- Parse a sequence of identifiers, including hiding info.
+-- Does not include instance arguments.
+-- E.g. x {y z} _ {v}
+-- To be used in typed bindings, like (x {y z} _ {v} : Nat).
+BIdsWithHiding :: { List1 (NamedArg Binder) }
+BIdsWithHiding : Application {%
+  -- interpret an expression as a name and maybe a pattern
+  case mapM exprAsNameOrHiddenNames $1 of
+    Nothing   -> parseError "Expected sequence of possibly hidden bound identifiers"
+    Just good -> forM (sconcat good) $ updateNamedArgA $ \ (n, me) -> do
+                   p <- traverse exprToPattern me
+                   pure $ Binder p (mkBoundName_ n)
+    }
+
+
+-- Space separated list of strings in a pragma.
+PragmaStrings :: { [(Interval, String)] }
+PragmaStrings
+    : {- empty -}           { [] }
+    | string PragmaStrings  { $1 : $2 }
+{- Unused
+PragmaString :: { String }
+PragmaString
+    : string { snd $1 }
+-}
+Strings :: { [(Interval, String)] }
+Strings : {- empty -}    { [] }
+        | string Strings { $1 : $2 }
+
+ForeignCode :: { DList (Interval, String) }
+ForeignCode
+  : {- empty -} { mempty }
+  | string ForeignCode { $1 `DL.cons` $2 }
+  | '{-#' ForeignCode '#-}' ForeignCode
+    { (($1, "{-#") `DL.cons` $2) <> (($3, "#-}") `DL.cons` $4) }
+
+PragmaName :: { Name }
+PragmaName : string {% mkName $1 }
+
+PragmaQName :: { QName }
+PragmaQName : string {% pragmaQName $1 }  -- Issue 2125. WAS: string {% fmap QName (mkName $1) }
+
+PragmaQNames :: { [QName] }
+PragmaQNames : Strings {% mapM pragmaQName $1 }
+
+{--------------------------------------------------------------------------
+    Expressions (terms and types)
+ --------------------------------------------------------------------------}
+
+{-  Expressions. You might expect lambdas and lets to appear in the first
+    expression category (lowest precedence). The reason they don't is that we
+    want to parse things like
+
+        m >>= \x -> k x
+
+    This will leads to a conflict in the following case
+
+        m >>= \x -> k x >>= \y -> k' y
+
+    At the second '>>=' we can either shift or reduce. We solve this problem
+    using Happy's precedence directives. The rule 'Expr -> Expr1' (which is the
+    rule you shouldn't use to reduce when seeing '>>=') is given LOWEST
+    precedence.  The terminals '->' and op (which is what you should shift)
+    is given higher precedence.
+-}
+
+-- Top level: Function types.
+Expr :: { Expr }
+Expr
+  : TeleArrow Expr                      { Pi $1 $2 }
+  | Application3 '->' Expr              { Fun (getRange ($1,$2,$3))
+                                              (defaultArg $ rawApp $1)
+                                              $3 }
+  | Attributes1 Application3 '->' Expr  {% applyAttrs1 $1 (defaultArg $ rawApp $2) <&> \ dom ->
+                                             Fun (getRange ($1,$2,$3,$4)) dom $4 }
+  | Expr1 %prec LOWEST                  { $1 }
+
+-- Level 1: Application
+Expr1 :: { Expr }
+Expr1
+  : UnnamedWithExprs
+      {% case $1 of
+           { e :| [] -> return e
+           ; e :| es -> return $ WithApp (fuseRange e es) e es
+           }
+      }
+
+WithExprs :: { List1 (Named Name Expr) }
+WithExprs
+  : Application3 'in' Id     '|' WithExprs { named $3  (rawApp $1) <| $5 }
+  | Application3 {- empty -} '|' WithExprs { unnamed   (rawApp $1) <| $3 }
+  | Application3 'in' Id                   { singleton (named $3 (rawApp $1)) }
+  | Application3 {- empty -}               { singleton (unnamed  (rawApp $1)) }
+
+UnnamedWithExprs :: { List1 Expr }
+UnnamedWithExprs
+  :  Application3 '|' UnnamedWithExprs { (rawApp $1) <| $3 }
+  | {- empty -} Application            { singleton (rawApp $1) }
+
+Application :: { List1 Expr }
+Application
+    : Expr2             { singleton $1 }
+    | Expr3 Application { $1 <| $2 }
+
+-- Level 2: Lambdas and lets
+Expr2 :: { Expr }
+Expr2
+    : '\\' LamBindings Expr        { Lam (getRange ($1,$2,$3)) $2 $3 }
+    | ExtendedOrAbsurdLam          { $1 }
+    | 'forall' ForallBindings Expr { forallPi $2 $3 }
+    | 'let' Declarations LetBody   { Let (getRange ($1,$2,$3)) $2 $3 }
+    | 'do' vopen DoStmts close     { DoBlock (getRange ($1, $3)) $3 }
+    | Expr3                        { $1 }
+    | 'tactic' Application3        { Tactic (getRange ($1, $2)) (rawApp $2) }
+
+LetBody :: { Maybe Expr }
+LetBody : 'in' Expr   { Just $2 }
+        | {- empty -} { Nothing }
+
+ExtendedOrAbsurdLam :: { Expr }
+ExtendedOrAbsurdLam
+    : '\\'             '{' LamClauses '}'                  {% extLam (getRange ($1, $2, $4))     []                $3 }
+    | '\\' Attributes1 '{' LamClauses '}'                  {% extLam (getRange ($1, $3, $5))     (List1.toList $2) $4 }
+    | '\\'             'where' vopen LamWhereClauses close {% extLam (getRange ($1, $2, $3, $5)) []                $4 }
+    | '\\' Attributes1 'where' vopen LamWhereClauses close {% extLam (getRange ($1, $3, $4, $6)) (List1.toList $2) $5 }
+    | '\\'             AbsurdLamBindings                   {% extOrAbsLam (getRange $1) []                $2 }
+    | '\\' Attributes1 AbsurdLamBindings                   {% extOrAbsLam (getRange $1) (List1.toList $2) $3 }
+
+Application3 :: { List1 Expr }
+Application3
+    : Expr3              { singleton $1 }
+    | Expr3 Application3 { $1 <| $2 }
+
+-- Christian Sattler, 2017-08-04, issue #2671
+-- We allow empty lists of expressions for the LHS of extended lambda clauses.
+-- I am not sure what Application3 is otherwise used for, so I keep the
+-- original type and create this copy solely for extended lambda clauses.
+Application3PossiblyEmpty :: { [Expr] }
+Application3PossiblyEmpty
+    :                                 { [] }
+    | Expr3 Application3PossiblyEmpty { $1 : $2 }
+
+-- Level 3: Atoms
+Expr3Curly :: { Expr }
+Expr3Curly
+    : '{' Expr4 '}'               {% HiddenArg (getRange ($1,$2,$3)) `fmap` maybeNamed $2 }
+    | '{' '}'                     { let r = fuseRange $1 $2 in HiddenArg r $ unnamed $ Absurd r }
+    | '{{' Expr4 DoubleCloseBrace {% InstanceArg (getRange ($1,$2,$3)) `fmap` maybeNamed $2 }
+    | '{{' DoubleCloseBrace       { let r = fuseRange $1 $2 in InstanceArg r $ unnamed $ Absurd r }
+
+Expr3NoCurly :: { Expr }
+Expr3NoCurly
+    : '?'                               { QuestionMark (getRange $1) Nothing }
+    | '_'                               { Underscore (getRange $1) Nothing }
+    | 'quote'                           { Quote (getRange $1) }
+    | 'quoteTerm'                       { QuoteTerm (getRange $1) }
+    | 'unquote'                         { Unquote (getRange $1) }
+    | '(|' UnnamedWithExprs '|)'        { IdiomBrackets (getRange ($1,$2,$3)) (List1.toList $2) }
+    | '(|)'                             { IdiomBrackets (getRange $1) [] }
+    | '(' ')'                           { Absurd (fuseRange $1 $2) }
+    | Id '@' Expr3                      { As (getRange ($1,$2,$3)) $1 $3 }
+    | '.' Expr3                         { Dot (fuseRange $1 $2) $2 }
+    | '..' Expr3                        { DoubleDot (fuseRange $1 $2) $2 }
+    | 'record' '{' RecordAssignments '}' { Rec (getRange ($1,$2,$3,$4)) $3 }
+    | 'record' Expr3NoCurly '{' FieldAssignments '}' { RecUpdate (getRange ($1,$2,$3,$4,$5)) $2 $4 }
+    | '...'                             { Ellipsis (getRange $1) }
+    | ExprOrAttr                       { $1 }
+
+-- Level 4: Maybe named, or cubical faces
+Expr4 :: { Expr }
+Expr4 : Expr1 '=' Expr { Equal (getRange ($1, $2, $3)) $1 $3 }
+      | Expr           { $1 }
+
+ExprOrAttr :: { Expr }
+ExprOrAttr
+    : QId           { Ident $1 }
+    | literal       { Lit (getRange $1) (rangedThing $1) }
+    | '(' Expr4 ')' { Paren (getRange ($1,$2,$3)) $2 }
+    -- ^ this is needed for cubical stuff
+
+Expr3 :: { Expr }
+Expr3
+    : Expr3Curly   { $1 }
+    | Expr3NoCurly { $1 }
+
+RecordAssignments :: { RecordAssignments }
+RecordAssignments
+  : {- empty -}        { [] }
+  | RecordAssignments1 { List1.toList $1 }
+
+RecordAssignments1 :: { List1 RecordAssignment }
+RecordAssignments1
+  : RecordAssignment                        { singleton $1 }
+  | RecordAssignment ';' RecordAssignments1 { $1 <| $3 }
+
+RecordAssignment :: { RecordAssignment }
+RecordAssignment
+  : FieldAssignment  { Left  $1 }
+  | ModuleAssignment { Right $1 }
+
+ModuleAssignment :: { ModuleAssignment }
+ModuleAssignment
+  : ModuleName OpenArgs ImportDirective  { ModuleAssignment $1 $2 $3 }
+
+FieldAssignments :: { [FieldAssignment] }
+FieldAssignments
+  : {- empty -}       { [] }
+  | FieldAssignments1 { List1.toList $1 }
+
+FieldAssignments1 :: { List1 FieldAssignment }
+FieldAssignments1
+  : FieldAssignment                       { singleton $1 }
+  | FieldAssignment ';' FieldAssignments1 { $1 <| $3 }
+
+FieldAssignment :: { FieldAssignment }
+FieldAssignment
+  : Id '=' Expr   { FieldAssignment $1 $3 }
+
+{--------------------------------------------------------------------------
+    Bindings
+ --------------------------------------------------------------------------}
+
+-- "Delta ->" to avoid conflict between Delta -> Gamma and Delta -> A.
+TeleArrow :: { Telescope1 }
+TeleArrow : Telescope1 '->' { $1 }
+
+Telescope1 :: { Telescope1 }
+Telescope1 : TypedBindings { $1 }
+
+TypedBindings :: { List1 TypedBinding }
+TypedBindings
+    : TypedBinding TypedBindings { $1 <| $2 }
+    | TypedBinding               { singleton $1 }
+
+
+-- A typed binding is either (x1 .. xn : A) or   {y1 .. ym : B}
+-- Andreas, 2011-04-07: or  .(x1 .. xn : A) or  .{y1 .. ym : B}
+-- Andreas, 2011-04-27: or ..(x1 .. xn : A) or ..{y1 .. ym : B}
+TypedBinding :: { TypedBinding }
+TypedBinding
+    : '.' '(' TBindWithHiding ')'    { setRange (getRange ($2,$3,$4)) $
+                             setRelevance Irrelevant $3 }
+    | '.' '{' TBind '}'    { setRange (getRange ($2,$3,$4)) $
+                             setHiding Hidden $
+                             setRelevance Irrelevant $3 }
+    | '.' '{{' TBind DoubleCloseBrace
+                           { setRange (getRange ($2,$3,$4)) $
+                             makeInstance $
+                             setRelevance Irrelevant $3 }
+    | '..' '(' TBindWithHiding ')'   { setRange (getRange ($2,$3,$4)) $
+                             setRelevance NonStrict $3 }
+    | '..' '{' TBind '}'   { setRange (getRange ($2,$3,$4)) $
+                             setHiding Hidden $
+                             setRelevance NonStrict $3 }
+    | '..' '{{' TBind DoubleCloseBrace
+                           { setRange (getRange ($2,$3,$4)) $
+                             makeInstance $
+                             setRelevance NonStrict $3 }
+    | '(' TBindWithHiding ')'        { setRange (getRange ($1,$2,$3)) $2 }
+    | '(' ModalTBindWithHiding ')'        { setRange (getRange ($1,$2,$3)) $2 }
+    | '{{' TBind DoubleCloseBrace
+                           { setRange (getRange ($1,$2,$3)) $
+                             makeInstance $2 }
+    | '{{' ModalTBind DoubleCloseBrace
+                           { setRange (getRange ($1,$2,$3)) $
+                             makeInstance $2 }
+    | '{' TBind '}'        { setRange (getRange ($1,$2,$3)) $
+                             setHiding Hidden $2 }
+    | '{' ModalTBind '}'   { setRange (getRange ($1,$2,$3)) $
+                             setHiding Hidden $2 }
+    | '(' Open ')'               { TLet (getRange ($1,$3)) $2 }
+    | '(' 'let' Declarations ')' { TLet (getRange ($1,$4)) $3 }
+
+
+-- x1 .. xn : A
+-- x1 .. xn :{i1 i2 ..} A
+TBind :: { TypedBinding }
+TBind : CommaBIds ':' Expr  {
+    let r = getRange ($1,$2,$3) -- the range is approximate only for TypedBindings
+    in TBind r $1 $3
+  }
+
+ModalTBind :: { TypedBinding }
+ModalTBind : Attributes1 CommaBIds ':' Expr  {% do
+    let r = getRange ($1,$2,$3,$4) -- the range is approximate only for TypedBindings
+    xs <- mapM (applyAttrs1 $1 . setTacticAttr $1) $2
+    return $ TBind r xs $4
+  }
+
+-- x {y z} _ {v} : A
+TBindWithHiding :: { TypedBinding }
+TBindWithHiding : BIdsWithHiding ':' Expr  {
+    let r = getRange ($1,$2,$3) -- the range is approximate only for TypedBindings
+    in TBind r $1 $3
+  }
+
+ModalTBindWithHiding :: { TypedBinding }
+ModalTBindWithHiding : Attributes1 BIdsWithHiding ':' Expr  {% do
+    let r = getRange ($1,$2,$3,$4) -- the range is approximate only for TypedBindings
+    xs <- mapM (applyAttrs1 $1 . setTacticAttr $1) $2
+    return $ TBind r xs $4
+  }
+
+-- A non-empty sequence of lambda bindings.
+LamBindings :: { List1 LamBinding }
+LamBindings
+  : LamBinds '->' {%
+      case absurdBinding $1 of
+        Just{}  -> parseError "Absurd lambda cannot have a body."
+        Nothing -> return $ List1.fromListSafe __IMPOSSIBLE__ $ lamBindings $1
+      }
+
+AbsurdLamBindings :: { Either ([LamBinding], Hiding) (List1 Expr) }
+AbsurdLamBindings
+  : LamBindsAbsurd {%
+    case $1 of
+      Left lb -> case absurdBinding lb of
+                   Nothing -> parseError "Missing body for lambda"
+                   Just h  -> return $ Left (lamBindings lb, h)
+      Right es -> return $ Right es
+    }
+
+-- absurd lambda is represented by @Left hiding@
+LamBinds :: { LamBinds }
+LamBinds
+  : DomainFreeBinding LamBinds  { fmap (map DomainFree (List1.toList $1) ++) $2 }
+  | TypedBinding LamBinds       { fmap (DomainFull $1 :) $2 }
+  | DomainFreeBinding           { mkLamBinds $ map DomainFree $ List1.toList $1 }
+  | TypedBinding                { mkLamBinds [DomainFull $1] }
+  | '(' ')'                     { mkAbsurdBinding NotHidden }
+  | '{' '}'                     { mkAbsurdBinding Hidden }
+  | '{{' DoubleCloseBrace       { mkAbsurdBinding (Instance NoOverlap) }
+
+-- Like LamBinds, but could also parse an absurd LHS of an extended lambda @{ p1 ... () }@
+LamBindsAbsurd :: { Either LamBinds (List1 Expr) }
+LamBindsAbsurd
+  : DomainFreeBinding LamBinds  { Left $ fmap (map DomainFree (List1.toList $1) ++) $2 }
+  | TypedBinding LamBinds       { Left $ fmap (DomainFull $1 :) $2 }
+  | DomainFreeBindingAbsurd     { case $1 of
+                                    Left lb -> Left $ mkLamBinds (map DomainFree $ List1.toList lb)
+                                    Right es -> Right es }
+  | TypedBinding                { Left $ mkLamBinds [DomainFull $1] }
+  | '(' ')'                     { Left $ mkAbsurdBinding NotHidden }
+  | '{' '}'                     { Left $ mkAbsurdBinding Hidden }
+  | '{{' DoubleCloseBrace       { Left $ mkAbsurdBinding (Instance NoOverlap) }
+
+-- FNF, 2011-05-05: No where-clauses in extended lambdas for now.
+-- Andreas, 2020-03-28: And also not in sight either nine years later.
+NonAbsurdLamClause :: { LamClause }
+NonAbsurdLamClause
+  : Application3PossiblyEmpty '->' Expr {% mkLamClause False $1 (RHS $3) }
+  | CatchallPragma
+    Application3PossiblyEmpty '->' Expr {% mkLamClause True  $2 (RHS $4) }
+
+AbsurdLamClause :: { LamClause }
+AbsurdLamClause
+-- FNF, 2011-05-09: By being more liberal here, we avoid shift/reduce and reduce/reduce errors.
+-- Later stages such as scope checking will complain if we let something through which we should not
+  : Application                {% mkAbsurdLamClause False $1 }
+  | CatchallPragma Application {% mkAbsurdLamClause True  $2 }
+
+LamClause :: { LamClause }
+LamClause
+  : NonAbsurdLamClause { $1 }
+  | AbsurdLamClause { $1 }
+
+-- Parses all extended lambda clauses except for a single absurd clause, which is taken care of
+-- in AbsurdLambda
+LamClauses :: { List1 LamClause }
+LamClauses
+   : LamClauses semi LamClause { $3 <| $1 }
+   | AbsurdLamClause semi LamClause { $3 <| singleton $1 }
+   | NonAbsurdLamClause { singleton $1 }
+
+-- Parses all extended lambda clauses including a single absurd clause.
+-- For lambda-where this is not[sic!, now?] taken care of in AbsurdLambda.
+LamWhereClauses :: { List1 LamClause }
+LamWhereClauses
+   : LamWhereClauses semi LamClause { $3 <| $1 }
+   | LamClause { singleton $1 }
+
+ForallBindings :: { List1 LamBinding }
+ForallBindings
+  : TypedUntypedBindings1 '->' { $1 }
+
+-- A non-empty sequence of possibly untyped bindings.
+TypedUntypedBindings1 :: { List1 LamBinding }
+TypedUntypedBindings1
+  : DomainFreeBinding TypedUntypedBindings1 { fmap DomainFree $1 <> $2 }
+  | TypedBinding TypedUntypedBindings1      { DomainFull $1 <| $2 }
+  | DomainFreeBinding                       { fmap DomainFree $1 }
+  | TypedBinding                            { singleton $ DomainFull $1 }
+
+-- A possibly empty sequence of possibly untyped bindings.
+-- This is used as telescope in data and record decls.
+TypedUntypedBindings :: { [LamBinding] }
+TypedUntypedBindings
+  : DomainFreeBinding TypedUntypedBindings { map DomainFree (List1.toList $1) ++ $2 }
+  | TypedBinding TypedUntypedBindings      { DomainFull $1 : $2 }
+  |                                        { [] }
+
+DomainFreeBindings :: { [NamedArg Binder] }
+DomainFreeBindings
+  : {- empty -}                          { [] }
+  | DomainFreeBinding DomainFreeBindings { List1.toList $1 ++ $2 }
+
+-- A domain free binding is either x or {x1 .. xn}
+DomainFreeBinding :: { List1 (NamedArg Binder) }
+DomainFreeBinding
+  : DomainFreeBindingAbsurd {% case $1 of
+                             Left lbs -> return lbs
+                             Right _ -> parseError "expected sequence of bound identifiers, not absurd pattern"
+                          }
+
+MaybeAsPattern :: { Maybe Pattern }
+MaybeAsPattern
+  : '@' Expr3   {% fmap Just (exprToPattern $2) }
+  | {- empty -} { Nothing }
+
+-- A domain free binding is either x or {x1 .. xn}
+DomainFreeBindingAbsurd :: { Either (List1 (NamedArg Binder)) (List1 Expr)}
+DomainFreeBindingAbsurd
+    : BId      MaybeAsPattern { Left . singleton $ mkDomainFree_ id $2 $1 }
+    | '.' BId  MaybeAsPattern { Left . singleton $ mkDomainFree_ (setRelevance Irrelevant) $3 $2 }
+    | '..' BId MaybeAsPattern { Left . singleton $ mkDomainFree_ (setRelevance NonStrict) $3 $2 }
+    | '(' Application ')'     {% exprToPattern (rawApp $2) >>= \ p ->
+                                 pure . Left . singleton $ mkDomainFree_ id (Just p) $ simpleHole }
+    | '(' Attributes1 CommaBIdAndAbsurds ')'
+         {% applyAttrs1 $2 defaultArgInfo <&> \ ai ->
+              first (fmap (setTacticAttr $2 . setArgInfo ai)) $3 }
+    | '{' CommaBIdAndAbsurds '}'
+         { first (fmap hide) $2 }
+    | '{' Attributes1 CommaBIdAndAbsurds '}'
+         {% applyAttrs1 $2 defaultArgInfo <&> \ ai ->
+              first (fmap (hide . setTacticAttr $2 . setArgInfo ai)) $3 }
+    | '{{' CommaBIds DoubleCloseBrace { Left $ fmap makeInstance $2 }
+    | '{{' Attributes1 CommaBIds DoubleCloseBrace
+         {% applyAttrs1 $2 defaultArgInfo <&> \ ai ->
+              Left $ fmap (makeInstance . setTacticAttr $2 . setArgInfo ai) $3 }
+    | '.' '{' CommaBIds '}' { Left $ fmap (hide . setRelevance Irrelevant) $3 }
+    | '.' '{{' CommaBIds DoubleCloseBrace { Left $ fmap (makeInstance . setRelevance Irrelevant) $3 }
+    | '..' '{' CommaBIds '}' { Left $ fmap (hide . setRelevance NonStrict) $3 }
+    | '..' '{{' CommaBIds DoubleCloseBrace { Left $ fmap (makeInstance . setRelevance NonStrict) $3 }
+
+
+{--------------------------------------------------------------------------
+    Do-notation
+ --------------------------------------------------------------------------}
+
+DoStmts :: { List1 DoStmt }
+DoStmts : DoStmt              { singleton $1 }
+        | DoStmt vsemi        { singleton $1 }    -- #3046
+        | DoStmt semi DoStmts { $1 <| $3 }
+
+DoStmt :: { DoStmt }
+DoStmt : Expr DoWhere {% buildDoStmt $1 $2 }
+
+DoWhere :: { [LamClause] }
+DoWhere
+  : {- empty -} { [] }
+  | 'where' vopen LamWhereClauses close { reverse (List1.toList $3) }
+
+{--------------------------------------------------------------------------
+    Modules and imports
+ --------------------------------------------------------------------------}
+
+-- Import directives
+ImportDirective :: { ImportDirective }
+ImportDirective
+  : ImportDirective1 ImportDirective { $1 <> $2 }
+  | {- empty -}                      { mempty }
+
+ImportDirective1 :: { ImportDirective }
+  : 'public'      { defaultImportDir { importDirRange = getRange $1, publicOpen = Just (getRange $1) } }
+  | Using         { defaultImportDir { importDirRange = snd $1, using    = fst $1 } }
+  | Hiding        { defaultImportDir { importDirRange = snd $1, hiding   = fst $1 } }
+  | RenamingDir   { defaultImportDir { importDirRange = snd $1, impRenaming = fst $1 } }
+
+Using :: { (Using, Range) }
+Using
+    : 'using' '(' CommaImportNames ')'   { (Using $3 , getRange ($1,$2,$3,$4)) }
+        -- using can have an empty list
+
+Hiding :: { ([ImportedName], Range) }
+Hiding
+    : 'hiding' '(' CommaImportNames ')'  { ($3 , getRange ($1,$2,$3,$4)) }
+        -- if you want to hide nothing that's fine, isn't it?
+
+RenamingDir :: { ([Renaming] , Range) }
+RenamingDir
+    : 'renaming' '(' Renamings ')'      { ($3 , getRange ($1,$2,$3,$4)) }
+    | 'renaming' '(' ')'                { ([] , getRange ($1,$2,$3)) }
+
+-- Renamings of the form 'x to y'
+Renamings :: { [Renaming] }
+Renamings
+    : Renaming ';' Renamings    { $1 : $3 }
+    | Renaming                  { [$1] }
+
+Renaming :: { Renaming }
+Renaming
+    : ImportName_ 'to' RenamingTarget { Renaming $1 (setImportedName $1 (snd $3)) (fst $3) (getRange $2) }
+
+RenamingTarget :: { (Maybe Fixity, Name) }
+RenamingTarget
+    : Id                 { (Nothing, $1) }
+    | 'infix'  Float Id  { (Just (Fixity (getRange ($1,$2)) (Related $ rangedThing $2) NonAssoc)  , $3) }
+    | 'infixl' Float Id  { (Just (Fixity (getRange ($1,$2)) (Related $ rangedThing $2) LeftAssoc) , $3) }
+    | 'infixr' Float Id  { (Just (Fixity (getRange ($1,$2)) (Related $ rangedThing $2) RightAssoc), $3) }
+
+-- We need a special imported name here, since we have to trigger
+-- the imp_dir state exactly one token before the 'to'
+ImportName_ :: { ImportedName }
+ImportName_
+    : beginImpDir Id          { ImportedName $2 }
+    | 'module' beginImpDir Id { ImportedModule $3 }
+
+ImportName :: { ImportedName }
+ImportName : Id          { ImportedName $1 }
+           | 'module' Id { ImportedModule $2 }
+
+-- Actually semi-colon separated, possibly empty list of ImportName.
+CommaImportNames :: { [ImportedName] }
+CommaImportNames
+    : {- empty -}       { [] }
+    | CommaImportNames1 { List1.toList $1 }
+
+CommaImportNames1 :: { List1 ImportedName }
+CommaImportNames1
+    : ImportName                        { singleton $1 }
+    | ImportName ';' CommaImportNames1  { $1 <| $3 }
+
+{--------------------------------------------------------------------------
+    Function clauses
+ --------------------------------------------------------------------------}
+
+-- A left hand side of a function clause. We parse it as an expression, and
+-- then check that it is a valid left hand side.
+LHS :: { [RewriteEqn] -> [WithExpr] -> LHS }
+LHS : Expr1 {% exprToLHS $1 }
+
+WithClause :: { [Either RewriteEqn (List1 (Named Name Expr))] }
+WithClause
+  : 'with' WithExprs WithClause
+    {% fmap (++ $3) (buildWithStmt $2)  }
+  | 'rewrite' UnnamedWithExprs WithClause
+    { Left (Rewrite $ fmap ((),) $2) : $3 }
+  | {- empty -} { [] }
+
+-- Parsing either an expression @e@ or a @(rewrite | with p <-) e1 | ... | en@.
+HoleContent :: { HoleContent }
+HoleContent
+  : Expr                   {  HoleContentExpr    $1 }
+  | WithClause
+    {% fmap HoleContentRewrite $ forM $1 $ \case
+         Left r  -> pure r
+         Right{} -> parseError "Cannot declare a 'with' abstraction from inside a hole."
+      }
+
+-- Where clauses are optional.
+WhereClause :: { WhereClause }
+WhereClause
+    : {- empty -} { NoWhere }
+    |                                'where' Declarations0
+        { AnyWhere  (getRange $1) $2 }
+    | 'module' Attributes Id         'where' Declarations0
+         {% onlyErased $2 >>= \erased ->
+            return $ SomeWhere (getRange ($1,$4)) erased
+                       $3 PublicAccess $5 }
+    | 'module' Attributes Underscore 'where' Declarations0
+         {% onlyErased $2 >>= \erased ->
+            return $ SomeWhere (getRange ($1,$4)) erased
+                       $3 PublicAccess $5 }
+  -- Note: The access modifier is a dummy, it is computed in the nicifier.
+
+ExprWhere :: { ExprWhere }
+ExprWhere : Expr WhereClause { ExprWhere $1 $2 }
+
+{--------------------------------------------------------------------------
+    Different kinds of declarations
+ --------------------------------------------------------------------------}
+
+-- Top-level definitions.
+Declaration :: { List1 Declaration }
+Declaration
+    : Fields          { singleton $1 }
+    | FunClause       { $1 }            -- includes type signatures
+    | Data            { singleton $1 }
+    | DataSig         { singleton $1 }  -- lone data type signature in mutual block
+    | Record          { singleton $1 }
+    | RecordSig       { singleton $1 }  -- lone record signature in mutual block
+    | Infix           { singleton $1 }
+    | Generalize      { singleton $1 }
+    | Mutual          { singleton $1 }
+    | Abstract        { singleton $1 }
+    | Private         { singleton $1 }
+    | Instance        { singleton $1 }
+    | Macro           { singleton $1 }
+    | Postulate       { singleton $1 }
+    | Primitive       { singleton $1 }
+    | Open            { $1 }
+    | ModuleMacro     { singleton $1 }
+    | Module          { singleton $1 }
+    | Pragma          { singleton $1 }
+    | Syntax          { singleton $1 }
+    | PatternSyn      { singleton $1 }
+    | UnquoteDecl     { singleton $1 }
+    | Constructor     { singleton $1 }
+    | Opaque          { singleton $1 }
+    | Unfolding       { singleton $1 }
+
+{--------------------------------------------------------------------------
+    Individual declarations
+ --------------------------------------------------------------------------}
+
+-- A variant of TypeSigs where any sub-sequence of names can be marked
+-- as hidden or irrelevant using braces and dots:
+-- {n1 .n2} n3 .n4 {n5} .{n6 n7} ... : Type.
+ArgTypeSigs :: { List1 (Arg Declaration) }
+ArgTypeSigs
+  : ModalArgIds ':' Expr { let (attrs, xs) = $1 in
+                           fmap (fmap (\ x -> typeSig defaultArgInfo (getTacticAttr attrs) x $3)) xs }
+  | 'overlap' ModalArgIds ':' Expr {%
+      let (attrs, xs) = $2
+          setOverlap x =
+            case getHiding x of
+              Instance _ -> return $ makeInstance' YesOverlap x
+              _          -> parseErrorRange $1
+                             "The 'overlap' keyword only applies to instance fields (fields marked with {{ }})"
+      in T.traverse (setOverlap . fmap (\ x -> typeSig defaultArgInfo (getTacticAttr attrs) x $4)) xs }
+  | 'instance' ArgTypeSignatures {
+    let
+      setInstance (TypeSig info tac x t) = TypeSig (makeInstance info) tac x t
+      setInstance _ = __IMPOSSIBLE__ in
+    fmap (fmap setInstance) $2 }
+
+-- Function declarations. The left hand side is parsed as an expression to allow
+-- declarations like 'x::xs ++ ys = e', when '::' has higher precedence than '++'.
+-- FunClause also handle possibly dotted type signatures.
+FunClause :: { List1 Declaration }
+FunClause
+  : {- emptyb -} LHS WHS RHS WhereClause {% funClauseOrTypeSigs [] $1 $2 $3 $4 }
+  | Attributes1  LHS WHS RHS WhereClause {% funClauseOrTypeSigs (List1.toList $1) $2 $3 $4 $5 }
+
+-- "With Hand Side", in between the Left & the Right hand ones
+WHS :: { [Either RewriteEqn (List1 (Named Name Expr))] }
+WHS
+  : {- empty -}                           { [] }
+  | 'with'    WithExprs        WithClause {% fmap (++ $3) (buildWithStmt $2) }
+  | 'rewrite' UnnamedWithExprs WithClause { Left (Rewrite $ fmap ((),) $2) : $3 }
+
+RHS :: { RHSOrTypeSigs }
+RHS
+  : {- empty -}    { JustRHS AbsurdRHS }
+  | '='       Expr { JustRHS (RHS $2) }
+  | ':'       Expr { TypeSigsRHS $2 }
+
+-- Data declaration. Can be local.
+Data :: { Declaration }
+Data : 'data' Id TypedUntypedBindings ':' Expr 'where'
+            Declarations0
+       { Data (getRange ($1,$2,$3,$4,$5,$6,$7))
+           defaultErased $2 $3 $5 $7 }
+     | 'data' Attributes1 Id TypedUntypedBindings ':' Expr 'where'
+            Declarations0
+       {% onlyErased (List1.toList $2) >>= \e ->
+          return $ Data (getRange (($1,$2,$3,$4),($5,$6,$7,$8)))
+                     e $3 $4 $6 $8 }
+
+  -- New cases when we already had a DataSig.  Then one can omit the sort.
+     | 'data' Id TypedUntypedBindings 'where'
+            Declarations0       { DataDef (getRange ($1,$2,$3,$4,$5)) $2 $3 $5 }
+
+-- Data type signature. Found in mutual blocks.
+DataSig :: { Declaration }
+DataSig
+  : 'data' Id TypedUntypedBindings ':' Expr
+    { DataSig (getRange ($1,$2,$3,$4,$5)) defaultErased $2 $3 $5 }
+  | 'data' Attributes1 Id TypedUntypedBindings ':' Expr
+    {% onlyErased (List1.toList $2) >>= \e ->
+       return $ DataSig (getRange ($1,$2,$3,$4,$5,$6)) e $3 $4 $6 }
+
+-- Andreas, 2012-03-16:  The Expr3NoCurly instead of Id in everything
+-- following 'record' is to remove the (harmless) shift/reduce conflict
+-- introduced by record update expressions.
+
+-- Record declarations.
+Record :: { Declaration }
+Record : 'record' Expr3NoCurly TypedUntypedBindings ':' Expr 'where'
+            RecordDeclarations
+         {% exprToName $2 >>= \ n -> let (dir, ds) = $7 in
+            return $ Record (getRange ($1,$2,$3,$4,$5,$6,$7))
+                       defaultErased n dir $3 $5 ds }
+       | 'record' Attributes1 Expr3NoCurly TypedUntypedBindings ':' Expr
+            'where'
+            RecordDeclarations
+         {% onlyErased (List1.toList $2) >>= \e ->
+            exprToName $3                >>= \n ->
+            let (dir, ds) = $8 in
+            return $ Record (getRange (($1,$2,$3,$4),($5,$6,$7,$8)))
+                       e n dir $4 $6 ds }
+       | 'record' Expr3NoCurly TypedUntypedBindings 'where'
+            RecordDeclarations
+         {% exprToName $2 >>= \ n -> let (dir, ds) = $5 in return $ RecordDef (getRange ($1,$2,$3,$4,$5)) n dir $3 ds }
+
+-- Record type signature. In mutual blocks.
+RecordSig :: { Declaration }
+RecordSig
+  : 'record' Expr3NoCurly TypedUntypedBindings ':' Expr
+    {% exprToName $2 >>= \n ->
+       return $ RecordSig (getRange ($1,$2,$3,$4,$5))
+                  defaultErased n $3 $5 }
+  | 'record' Attributes1 Expr3NoCurly TypedUntypedBindings ':' Expr
+    {% onlyErased (List1.toList $2) >>= \e ->
+       exprToName $3                >>= \n ->
+       return $ RecordSig (getRange ($1,$2,$3,$4,$5,$6)) e n $4 $6 }
+
+Constructor :: { Declaration }
+Constructor : 'data' '_' 'where' Declarations0
+  { LoneConstructor (getRange ($1,$4)) $4 }
+
+-- Declaration of record constructor name.
+RecordConstructorName :: { (Name, IsInstance) }
+RecordConstructorName :                  'constructor' Id       { ($2, NotInstanceDef) }
+                      | 'instance' vopen 'constructor' Id close { ($4, InstanceDef (getRange $1)) }
+
+
+-- Fixity declarations.
+Infix :: { Declaration }
+Infix : 'infix'  Float SpaceBIds  { Infix (Fixity (getRange ($1,$2,$3)) (Related $ rangedThing $2) NonAssoc)   $3 }
+      | 'infixl' Float SpaceBIds  { Infix (Fixity (getRange ($1,$2,$3)) (Related $ rangedThing $2) LeftAssoc)  $3 }
+      | 'infixr' Float SpaceBIds  { Infix (Fixity (getRange ($1,$2,$3)) (Related $ rangedThing $2) RightAssoc) $3 }
+
+-- Field declarations.
+Fields :: { Declaration }
+Fields : 'field' ArgTypeSignaturesOrEmpty
+            { let
+                inst i = case getHiding i of
+                           Instance _ -> InstanceDef noRange  -- no @instance@ keyword here
+                           _          -> NotInstanceDef
+                toField (Arg info (TypeSig info' tac x t)) = FieldSig (inst info') tac x (Arg info t)
+              in Field (fuseRange $1 $2) $ map toField $2 }
+  -- | 'field' ModalArgTypeSignatures
+  --           { let
+  --               inst i = case getHiding i of
+  --                          Instance _ -> InstanceDef
+  --                          _          -> NotInstanceDef
+  --               toField (Arg info (TypeSig info' x t)) = FieldSig (inst info') x (Arg info t)
+  --             in Field (fuseRange $1 $2) $ map toField $2 }
+
+-- Variable declarations for automatic generalization
+Generalize :: { Declaration }
+Generalize : 'variable' ArgTypeSignaturesOrEmpty
+            { let
+                toGeneralize (Arg info (TypeSig _ tac x t)) = TypeSig info tac x t
+              in Generalize (fuseRange $1 $2) (map toGeneralize $2) }
+
+-- Mutually recursive declarations.
+Mutual :: { Declaration }
+Mutual : 'mutual' Declarations0  { Mutual (fuseRange $1 $2) $2 }
+       | 'interleaved' 'mutual' Declarations0 { InterleavedMutual (getRange ($1,$2,$3)) $3 }
+
+-- Abstract declarations.
+Abstract :: { Declaration }
+Abstract : 'abstract' Declarations0  { Abstract (fuseRange $1 $2) $2 }
+
+
+-- Private can only appear on the top-level (or rather the module level).
+Private :: { Declaration }
+Private : 'private' Declarations0        { Private (fuseRange $1 $2) UserWritten $2 }
+
+
+-- Instance declarations.
+Instance :: { Declaration }
+Instance : 'instance' Declarations0  { InstanceB (getRange $1) $2 }
+
+
+-- Macro declarations.
+Macro :: { Declaration }
+Macro : 'macro' Declarations0 { Macro (fuseRange $1 $2) $2 }
+
+
+-- Postulates.
+Postulate :: { Declaration }
+Postulate : 'postulate' Declarations0 { Postulate (fuseRange $1 $2) $2 }
+
+-- Primitives. Can only contain type signatures.
+Primitive :: { Declaration }
+Primitive : 'primitive' ArgTypeSignaturesOrEmpty  {
+  let { setArg (Arg info (TypeSig _ tac x t)) = TypeSig info tac x t
+      ; setArg _ = __IMPOSSIBLE__ } in
+  Primitive (fuseRange $1 $2) (map setArg $2) }
+
+-- Unquoting declarations.
+UnquoteDecl :: { Declaration }
+UnquoteDecl
+  : 'unquoteDecl' '=' Expr { UnquoteDecl (fuseRange $1 $3) [] $3 }
+  | 'unquoteDecl' 'data' Id '=' Expr { UnquoteData (getRange($1, $2, $5)) $3 [] $5 }
+  | 'unquoteDecl' 'data' Id 'constructor' SpaceIds '=' Expr { UnquoteData (getRange($1, $2, $4, $7)) $3 (List1.toList $5) $7 }
+  | 'unquoteDecl' SpaceIds '=' Expr { UnquoteDecl (fuseRange $1 $4) (List1.toList $2) $4 }
+  | 'unquoteDef'  SpaceIds '=' Expr { UnquoteDef (fuseRange $1 $4) (List1.toList $2) $4 }
+
+-- Syntax declaration (To declare eg. mixfix binders)
+Syntax :: { Declaration }
+Syntax : 'syntax' Id HoleNames '=' SimpleIds  {%
+  case $2 of
+    Name _ _ (_ :| []) -> case mkNotation (DL.toList $3) (reverse $5) of
+      Left err -> parseError $ "Malformed syntax declaration: " ++ err
+      Right n -> return $ Syntax $2 n
+    _ -> parseError "Syntax declarations are allowed only for simple names (without holes)"
+}
+
+-- Pattern synonyms.
+PatternSyn :: { Declaration }
+PatternSyn : 'pattern' Id PatternSynArgs '=' Expr {% do
+  p <- exprToPattern $5
+  return (PatternSyn (getRange ($1,$2,$3,$4,$5)) $2 $3 p)
+  }
+
+PatternSynArgs :: { [Arg Name] }
+PatternSynArgs : DomainFreeBindings    {% patternSynArgs $1 }
+
+-- The list should be reversed.
+
+SimpleIds :: { [RString] }
+SimpleIds : SimpleId           { [$1] }
+          | SimpleIds SimpleId { $2 : $1 }
+
+-- The list should be reversed.
+
+SimpleIdsOrWildcards :: { List1 RString }
+SimpleIdsOrWildcards
+  : SimpleIdOrWildcard                      { List1.singleton $1 }
+  | SimpleIdsOrWildcards SimpleIdOrWildcard { $2 <| $1 }
+
+HoleNames :: { DList (NamedArg HoleName) }
+HoleNames :                    { mempty }
+          | HoleNames HoleName { $1 `DL.snoc` $2 }
+
+HoleName :: { NamedArg HoleName }
+HoleName
+  : SimpleTopHole { defaultNamedArg $1 }
+  | '{'  SimpleHole '}'  { hide         $ defaultNamedArg $2 }
+  | '{{' SimpleHole '}}' { makeInstance $ defaultNamedArg $2 }
+  | '{'  SimpleId '=' SimpleHole '}'  { hide         $ defaultArg $ userNamed $2 $4 }
+  | '{{' SimpleId '=' SimpleHole '}}' { makeInstance $ defaultArg $ userNamed $2 $4 }
+
+SimpleTopHole :: { HoleName }
+SimpleTopHole
+  : SimpleId { ExprHole $1 }
+  | '(' '\\' SimpleIdsOrWildcards '->' SimpleId ')'
+    { LambdaHole (List1.reverse $3) $5 }
+
+SimpleHole :: { HoleName }
+SimpleHole
+  : SimpleId { ExprHole $1 }
+  | '\\' SimpleIdsOrWildcards '->' SimpleId
+    { LambdaHole (List1.reverse $2) $4 }
+
+-- Discard the interval.
+SimpleId :: { RString }
+SimpleId : id  { Ranged (getRange $ fst $1) (stringToRawName $ snd $1) }
+
+SimpleIdOrWildcard :: { RString }
+SimpleIdOrWildcard
+  : SimpleId { $1 }
+  | '_'      { Ranged (getRange $1) "_" }
+
+MaybeOpen :: { Maybe Range }
+MaybeOpen : 'open'      { Just (getRange $1) }
+          | {- empty -} { Nothing }
+
+-- Open
+Open :: { List1 Declaration }
+Open : MaybeOpen 'import' ModuleName OpenArgs ImportDirective {%
+    let
+    { doOpen = maybe DontOpen (const DoOpen) $1
+    ; m   = $3
+    ; es  = $4
+    ; dir = $5
+    ; r   = getRange ($1, $2, m, es, dir)
+    ; mr  = getRange m
+    ; unique = hashString $ prettyShow $ (Strict.Nothing :: Strict.Maybe ()) <$ r
+         -- turn range into unique id, but delete file path
+         -- which is absolute and messes up suite of failing tests
+         -- (different hashs on different installations)
+         -- TODO: Don't use (insecure) hashes in this way.
+    ; fresh  = Name mr NotInScope $ singleton $ Id $ stringToRawName $ ".#" ++ prettyShow m ++ "-" ++ show unique
+    ; fresh' = Name mr NotInScope $ singleton $ Id $ stringToRawName $ ".#" ++ prettyShow m ++ "-" ++ show (unique + 1)
+    ; impStm asR = Import noRange m (Just (AsName (Right fresh) asR)) DontOpen defaultImportDir
+    ; appStm m' es =
+        Private r Inserted
+          [ ModuleMacro r defaultErased m'
+             (SectionApp (getRange es) []
+               (rawApp (Ident (QName fresh) :| es)))
+             doOpen dir
+          ]
+    ; (initArgs, last2Args) = splitAt (length es - 2) es
+    ; parseAsClause = case last2Args of
+      { [ Ident (QName (Name asR InScope (Id x :| [])))
+        , e
+          -- Andreas, 2018-11-03, issue #3364, accept anything after 'as'
+          -- but require it to be a 'Name' in the scope checker.
+        ] | rawNameToString x == "as" -> Just . (asR,) $
+          if | Ident (QName m') <- e -> Right m'
+             | otherwise             -> Left e
+      ; _ -> Nothing
+      }
+    } in
+    case es of
+      { [] -> return $ singleton $ Import r m Nothing doOpen dir
+      ; _ | Just (asR, m') <- parseAsClause -> return $
+              if null initArgs then singleton
+                 ( Import (getRange (m, asR, m', dir)) m
+                     (Just (AsName m' asR)) doOpen dir
+                 )
+              else impStm asR :| [ appStm (fromRight (const fresh') m') initArgs ]
+          -- Andreas, 2017-05-13, issue #2579
+          -- Nisse reports that importing with instantation but without open
+          -- could be usefule for bringing instances into scope.
+          -- Ulf, 2018-12-6: Not since fixes of #1913 and #2489 which require
+          -- instances to be in scope.
+          | DontOpen <- doOpen -> parseErrorRange $2 "An import statement with module instantiation is useless without either an `open' keyword or an `as` binding giving a name to the instantiated module."
+          | otherwise -> return $
+              impStm noRange :|
+              appStm (noName $ beginningOf $ getRange m) es :
+              []
+      }
+  }
+  |'open' ModuleName OpenArgs ImportDirective {
+    let
+    { m   = $2
+    ; es  = $3
+    ; dir = $4
+    ; r   = getRange ($1, m, es, dir)
+    } in singleton $
+      case es of
+      { []  -> Open r m dir
+      ; _   -> Private r Inserted
+                 [ ModuleMacro r defaultErased
+                     (noName $ beginningOf $ getRange m)
+                     (SectionApp (getRange (m , es)) []
+                        (rawApp (Ident m :| es)))
+                     DoOpen dir
+                 ]
+      }
+  }
+  | 'open' ModuleName '{{' '...' DoubleCloseBrace ImportDirective {
+    let r = getRange $2 in singleton $
+      Private r Inserted
+      [ ModuleMacro r defaultErased (noName $ beginningOf $ getRange $2)
+          (RecordModuleInstance r $2) DoOpen $6
+      ]
+  }
+
+OpenArgs :: { [Expr] }
+OpenArgs : {- empty -}    { [] }
+         | Expr3 OpenArgs { $1 : $2 }
+
+ModuleApplication :: { Telescope -> Parser ModuleApplication }
+ModuleApplication : ModuleName '{{' '...' DoubleCloseBrace { (\ts ->
+                    if null ts then return $ RecordModuleInstance (getRange ($1,$2,$3,$4)) $1
+                    else parseError "No bindings allowed for record module with non-canonical implicits" )
+                    }
+                  | ModuleName OpenArgs {
+                    (\ts -> return $ SectionApp (getRange ($1, $2)) ts (rawApp (Ident $1 :| $2)) ) }
+
+
+-- Module instantiation
+ModuleMacro :: { Declaration }
+ModuleMacro
+  : 'module' Attributes ModuleName TypedUntypedBindings '='
+      ModuleApplication ImportDirective
+    {% do { ma     <- $6 (map addType $4)
+          ; erased <- onlyErased $2
+          ; name   <- ensureUnqual $3
+          ; return $ ModuleMacro (getRange ($1, $2, $3, ma, $7))
+                       erased name ma DontOpen $7
+          }
+    }
+  | 'open' 'module' Attributes Id TypedUntypedBindings '='
+      ModuleApplication ImportDirective
+    {% do { ma     <- $7 (map addType $5)
+          ; erased <- onlyErased $3
+          ; return $ ModuleMacro (getRange ($1, $2, $3, $4, ma, $8))
+                       erased $4 ma DoOpen $8
+          } }
+
+-- Module
+Module :: { Declaration }
+Module
+  : 'module' Attributes ModuleName TypedUntypedBindings 'where'
+      Declarations0
+    {% onlyErased $2 >>= \erased ->
+       return $ Module (getRange ($1,$2,$3,$4,$5,$6)) erased
+                  $3 (map addType $4) $6 }
+  | 'module' Attributes Underscore TypedUntypedBindings 'where'
+      Declarations0
+    {% onlyErased $2 >>= \erased ->
+       return $ Module (getRange ($1,$2,$3,$4,$5,$6)) erased
+                  (QName $3) (map addType $4) $6 }
+
+Underscore :: { Name }
+Underscore : '_' { noName (getRange $1) }
+
+TopLevel :: { [Declaration] }
+TopLevel : TopDeclarations { figureOutTopLevelModule $1 }
+
+Pragma :: { Declaration }
+Pragma : DeclarationPragma  { Pragma $1 }
+
+DeclarationPragma :: { Pragma }
+DeclarationPragma
+  : BuiltinPragma            { $1 }
+  | RewritePragma            { $1 }
+  | CompilePragma            { $1 }
+  | ForeignPragma            { $1 }
+  | StaticPragma             { $1 }
+  | InjectivePragma          { $1 }
+  | InlinePragma             { $1 }
+  | NoInlinePragma           { $1 }
+  | ImpossiblePragma         { $1 }
+  | TerminatingPragma        { $1 }
+  | NonTerminatingPragma     { $1 }
+  | NoTerminationCheckPragma { $1 }
+  | NonCoveringPragma        { $1 }
+  | NotProjectionLikePragma  { $1 }
+  | WarningOnUsagePragma     { $1 }
+  | WarningOnImportPragma    { $1 }
+  | MeasurePragma            { $1 }
+  | CatchallPragma           { $1 }
+  | DisplayPragma            { $1 }
+  | EtaPragma                { $1 }
+  | NoPositivityCheckPragma  { $1 }
+  | NoUniverseCheckPragma    { $1 }
+  | PolarityPragma           { $1 }
+  | OptionsPragma            { $1 }
+    -- Andreas, 2014-03-06
+    -- OPTIONS pragma not allowed everywhere, but don't give parse error.
+    -- Give better error during type checking instead.
+
+OptionsPragma :: { Pragma }
+OptionsPragma :
+  '{-#' 'OPTIONS' PragmaStrings '#-}'
+  { OptionsPragma (getRange ($1, $2, map fst $3, $4)) (map snd $3) }
+
+BuiltinPragma :: { Pragma }
+BuiltinPragma
+    : '{-#' 'BUILTIN' string PragmaQName '#-}'
+      { BuiltinPragma (getRange ($1,$2,fst $3,$4,$5)) (mkRString $3) $4 }
+    -- Extra rule to accept keyword REWRITE also as built-in:
+    | '{-#' 'BUILTIN' 'REWRITE' PragmaQName '#-}'
+      { BuiltinPragma (getRange ($1,$2,$3,$4,$5)) (Ranged (getRange $3) "REWRITE") $4 }
+
+RewritePragma :: { Pragma }
+RewritePragma
+    : '{-#' 'REWRITE' PragmaQNames '#-}'
+      { RewritePragma (getRange ($1,$2,$3,$4)) (getRange $2) $3 }
+
+ForeignPragma :: { Pragma }
+ForeignPragma
+  : '{-#' 'FOREIGN' string ForeignCode '#-}'
+    { ForeignPragma (getRange ($1, $2, fst $3, $5))
+        (mkRString $3) (recoverLayout (DL.toList $4)) }
+
+CompilePragma :: { Pragma }
+CompilePragma
+  : '{-#' 'COMPILE' string PragmaQName PragmaStrings '#-}'
+    { CompilePragma (getRange ($1, $2, fst $3, $4, map fst $5, $6))
+        (mkRString $3) $4 (unwords (map snd $5)) }
+
+StaticPragma :: { Pragma }
+StaticPragma
+  : '{-#' 'STATIC' PragmaQName '#-}'
+    { StaticPragma (getRange ($1,$2,$3,$4)) $3 }
+
+InlinePragma :: { Pragma }
+InlinePragma
+  : '{-#' 'INLINE' PragmaQName '#-}'
+    { InlinePragma (getRange ($1,$2,$3,$4)) True $3 }
+
+NoInlinePragma :: { Pragma }
+NoInlinePragma
+  : '{-#' 'NOINLINE' PragmaQName '#-}'
+    { InlinePragma (getRange ($1,$2,$3,$4)) False $3 }
+
+NotProjectionLikePragma :: { Pragma }
+NotProjectionLikePragma
+  : '{-#' 'NOT_PROJECTION_LIKE' PragmaQName '#-}'
+    { NotProjectionLikePragma (getRange ($1,$2,$3,$4)) $3 }
+
+InjectivePragma :: { Pragma }
+InjectivePragma
+  : '{-#' 'INJECTIVE' PragmaQName '#-}'
+    { InjectivePragma (getRange ($1,$2,$3,$4)) $3 }
+
+DisplayPragma :: { Pragma }
+DisplayPragma
+  : '{-#' 'DISPLAY' string PragmaStrings '#-}'
+    {% let (r, s) = $3 in
+       parseDisplayPragma (getRange ($1, $2, r, map fst $4, $5))
+         (iStart r) (unwords (s : map snd $4)) }
+
+EtaPragma :: { Pragma }
+EtaPragma
+  : '{-#' 'ETA' PragmaQName '#-}'
+    { EtaPragma (getRange ($1,$2,$3,$4)) $3 }
+
+NoTerminationCheckPragma :: { Pragma }
+NoTerminationCheckPragma
+  : '{-#' 'NO_TERMINATION_CHECK' '#-}'
+    { TerminationCheckPragma (getRange ($1,$2,$3)) NoTerminationCheck }
+
+NonTerminatingPragma :: { Pragma }
+NonTerminatingPragma
+  : '{-#' 'NON_TERMINATING' '#-}'
+    { TerminationCheckPragma (getRange ($1,$2,$3)) NonTerminating }
+
+TerminatingPragma :: { Pragma }
+TerminatingPragma
+  : '{-#' 'TERMINATING' '#-}'
+    { TerminationCheckPragma (getRange ($1,$2,$3)) Terminating }
+
+NonCoveringPragma :: { Pragma }
+NonCoveringPragma
+  : '{-#' 'NON_COVERING' '#-}'
+    { NoCoverageCheckPragma (getRange ($1,$2,$3)) }
+
+MeasurePragma :: { Pragma }
+MeasurePragma
+  : '{-#' 'MEASURE' PragmaName '#-}'
+    { let r = getRange ($1, $2, $3, $4) in
+      TerminationCheckPragma r (TerminationMeasure r $3) }
+
+CatchallPragma :: { Pragma }
+CatchallPragma
+  : '{-#' 'CATCHALL' '#-}'
+    { CatchallPragma (getRange ($1,$2,$3)) }
+
+ImpossiblePragma :: { Pragma }
+ImpossiblePragma
+  : '{-#' 'IMPOSSIBLE' PragmaStrings '#-}'
+    { ImpossiblePragma (getRange ($1, $2, map fst $3, $4))
+        (map snd $3) }
+
+NoPositivityCheckPragma :: { Pragma }
+NoPositivityCheckPragma
+  : '{-#' 'NO_POSITIVITY_CHECK' '#-}'
+    { NoPositivityCheckPragma (getRange ($1,$2,$3)) }
+
+NoUniverseCheckPragma :: { Pragma }
+NoUniverseCheckPragma
+  : '{-#' 'NO_UNIVERSE_CHECK' '#-}'
+    { NoUniverseCheckPragma (getRange ($1,$2,$3)) }
+
+PolarityPragma :: { Pragma }
+PolarityPragma
+  : '{-#' 'POLARITY' PragmaName Polarities '#-}'
+    { let (rs, occs) = unzip (reverse $4) in
+      PolarityPragma (getRange ($1,$2,$3,rs,$5)) $3 occs }
+
+WarningOnUsagePragma :: { Pragma }
+WarningOnUsagePragma
+  : '{-#' 'WARNING_ON_USAGE' PragmaQName literal '#-}'
+  {%  case $4 of
+        { Ranged r (LitString str) -> return $ WarningOnUsage (getRange ($1,$2,$3,r,$5)) $3 str
+        ; _ -> parseError "Expected string literal"
+        }
+  }
+
+WarningOnImportPragma :: { Pragma }
+WarningOnImportPragma
+  : '{-#' 'WARNING_ON_IMPORT' literal '#-}'
+  {%  case $3 of
+        { Ranged r (LitString str) -> return $ WarningOnImport (getRange ($1,$2,r,$4)) str
+        ; _ -> parseError "Expected string literal"
+        }
+  }
+
+-- Possibly empty list of polarities. Reversed.
+Polarities :: { [(Range, Occurrence)] }
+Polarities : {- empty -}          { [] }
+           | Polarities Polarity  { $2 : $1 }
+
+Polarity :: { (Range, Occurrence) }
+Polarity : string {% polarity $1 }
+
+{--------------------------------------------------------------------------
+    Sequences of declarations
+ --------------------------------------------------------------------------}
+
+-- A variant of TypeSignatures which uses ArgTypeSigs instead of
+-- TypeSigs.
+ArgTypeSignatures :: { List1 (Arg TypeSignature) }
+ArgTypeSignatures
+    : vopen ArgTypeSignatures1 close   { List1.reverse $2 }
+
+-- Inside the layout block.
+ArgTypeSignatures1 :: { List1 (Arg TypeSignature) }
+ArgTypeSignatures1
+    : ArgTypeSignatures1 semi ArgTypeSigs { List1.reverse $3 <> $1 }
+    | ArgTypeSigs                         { List1.reverse $1 }
+
+-- A variant of TypeSignatures which uses ArgTypeSigs instead of
+-- TypeSigs.
+ArgTypeSignaturesOrEmpty :: { [Arg TypeSignature] }
+ArgTypeSignaturesOrEmpty
+    : vopen ArgTypeSignatures0 close   { reverse $2 }
+
+-- Inside the layout block.
+ArgTypeSignatures0 :: { [Arg TypeSignature] }
+ArgTypeSignatures0
+    : ArgTypeSignatures0 semi ArgTypeSigs { reverse (List1.toList $3) ++ $1 }
+    | ArgTypeSigs                         { reverse (List1.toList $1) }
+    | {- empty -}                         { [] }
+
+-- Record declarations, including an optional record constructor name.
+RecordDeclarations :: { (RecordDirectives, [Declaration]) }
+RecordDeclarations
+    : vopen RecordDirectives close                    {% verifyRecordDirectives $2 <&> (,[]) }
+    | vopen RecordDirectives semi Declarations1 close {% verifyRecordDirectives $2 <&> (, List1.toList $4) }
+    | vopen Declarations1 close                       { (emptyRecordDirectives, List1.toList $2) }
+
+
+RecordDirectives :: { [RecordDirective] }
+RecordDirectives
+    : {- empty -}                           { [] }
+    | RecordDirectives semi RecordDirective { $3 : $1 }
+    | RecordDirective                       { [$1] }
+
+RecordDirective :: { RecordDirective }
+RecordDirective
+    : RecordConstructorName { uncurry Constructor $1 }
+    | RecordInduction       { Induction $1 }
+    | RecordEta             { Eta $1 }
+    | RecordPatternMatching { PatternOrCopattern $1 }
+
+RecordEta :: { Ranged HasEta0 }
+RecordEta
+    : 'eta-equality'    { Ranged (getRange $1) YesEta }
+    | 'no-eta-equality' { Ranged (getRange $1) (NoEta ()) }
+
+-- Directive 'pattern' if a decision between matching on constructor/record pattern
+-- or copattern matching is needed.
+-- Such decision is only needed for 'no-eta-equality' records.
+-- But eta could be turned off automatically, thus, we do not bundle this
+-- with the 'no-eta-equality' declaration.
+-- Nor with the 'constructor' declaration, since it applies also to
+-- the record pattern.
+RecordPatternMatching :: { Range }
+RecordPatternMatching
+    : 'pattern'     { getRange $1 }
+
+-- Declaration of record as 'inductive' or 'coinductive'.
+RecordInduction :: { Ranged Induction }
+RecordInduction
+    : 'inductive'   { Ranged (getRange $1) Inductive   }
+    | 'coinductive' { Ranged (getRange $1) CoInductive }
+
+Opaque :: { Declaration }
+  : 'opaque' Declarations0     { Opaque (getRange ($1, $2)) $2 }
+
+Unfolding :: { Declaration }
+  : 'unfolding' UnfoldingNames { Unfolding (getRange ($1, $2)) $2 }
+
+UnfoldingNames :: { [QName] }
+UnfoldingNames
+    : QId UnfoldingNames { $1:$2 }
+    | {- empty -}        { [] }
+
+-- Arbitrary declarations
+Declarations :: { List1 Declaration }
+Declarations
+    : vopen Declarations1 close { $2 }
+
+-- Arbitrary declarations (possibly empty)
+Declarations0 :: { [Declaration] }
+Declarations0
+    : vopen close  { [] }
+    | Declarations { List1.toList $1 }
+
+Declarations1 :: { List1 Declaration }
+Declarations1
+    : Declaration semi Declarations1 { $1 <> $3 }
+    | Declaration vsemi              { $1 } -- #3046
+    | Declaration                    { $1 }
+
+TopDeclarations :: { [Declaration] }
+TopDeclarations
+  : {- empty -}   { [] }
+  | Declarations1 { List1.toList $1 }
+
+{
+
+{--------------------------------------------------------------------------
+    Parsers
+ --------------------------------------------------------------------------}
+
+-- | Parse the token stream. Used by the TeX compiler.
+tokensParser :: Parser [Token]
+
+-- | Parse an expression. Could be used in interactions.
+exprParser :: Parser Expr
+
+-- | Parse an expression followed by a where clause. Could be used in interactions.
+exprWhereParser :: Parser ExprWhere
+
+-- | Parse a module.
+moduleParser :: Parser Module
+
+
+{--------------------------------------------------------------------------
+    Happy stuff
+ --------------------------------------------------------------------------}
+
+-- | Required by Happy.
+happyError :: Parser a
+happyError = parseError "Parse error"
+
+
+{--------------------------------------------------------------------------
+    Utility functions
+ --------------------------------------------------------------------------}
+
+-- | Grab leading OPTIONS pragmas.
+takeOptionsPragmas :: [Declaration] -> Module
+takeOptionsPragmas = uncurry Mod . spanJust (\ d -> case d of
+  Pragma p@OptionsPragma{} -> Just p
+  _                        -> Nothing)
+
+-- | Insert a top-level module if there is none.
+--   Also fix-up for the case the declarations in the top-level module
+--   are not indented (this is allowed as a special case).
+figureOutTopLevelModule :: [Declaration] -> [Declaration]
+figureOutTopLevelModule ds =
+  case spanAllowedBeforeModule ds of
+    -- Andreas 2016-02-01, issue #1388.
+    -- We need to distinguish two additional cases.
+
+    -- Case 1: Regular file layout: imports followed by one module. Nothing to do.
+    (ds0, [ Module{} ]) -> ds
+
+    -- Case 2: The declarations in the module are not indented.
+    -- This is allowed for the top level module, and thus rectified here.
+    (ds0, Module r erased m tel [] : ds2) ->
+      ds0 ++ [Module r erased m tel ds2]
+
+    -- Case 3: There is a module with indented declarations,
+    -- followed by non-indented declarations.  This should be a
+    -- parse error and be reported later (see @toAbstract TopLevel{}@),
+    -- thus, we do not do anything here.
+    (ds0, Module r _ m tel ds1 : ds2) -> ds  -- Gives parse error in scope checker.
+    -- OLD code causing issue 1388:
+    -- (ds0, Module r m tel ds1 : ds2) -> ds0 ++ [Module r m tel $ ds1 ++ ds2]
+
+    -- Case 4: a top-level module declaration is missing.
+    -- Andreas, 2017-01-01, issue #2229:
+    -- Put everything (except OPTIONS pragmas) into an anonymous module.
+    _ -> ds0 ++ [Module r defaultErased (QName $ noName r) [] ds1]
+      where
+      (ds0, ds1) = (`span` ds) $ \case
+        Pragma OptionsPragma{} -> True
+        _ -> False
+      -- Andreas, 2017-05-17, issue #2574.
+      -- Since the module noName will act as jump target, it needs a range.
+      -- We use the beginning of the file as beginning of the top level module.
+      r = beginningOfFile $ getRange ds1
+
+-- | Create a name from a string.
+
+mkName :: (Interval, String) -> Parser Name
+mkName (i, s) = do
+    let xs = C.stringNameParts s
+    mapM_ isValidId xs
+    unless (alternating xs) $ parseError $ "a name cannot contain two consecutive underscores"
+    return $ Name (getRange i) InScope xs
+    where
+        isValidId Hole   = return ()
+        isValidId (Id y) = do
+          let x = rawNameToString y
+              err = "in the name " ++ s ++ ", the part " ++ x ++ " is not valid"
+          case parse defaultParseFlags [0] (lexer return) x of
+            ParseOk _ TokId{}  -> return ()
+            ParseFailed{}      -> parseError err
+            ParseOk _ TokEOF{} -> parseError err
+            ParseOk _ t   -> parseError . ((err ++ " because it is ") ++) $ case t of
+              TokId{}       -> __IMPOSSIBLE__
+              TokQId{}      -> __IMPOSSIBLE__ -- "qualified"
+              TokKeyword{}  -> "a keyword"
+              TokLiteral{}  -> "a literal"
+              TokSymbol s _ -> case s of
+                SymDot               -> __IMPOSSIBLE__ -- "reserved"
+                SymSemi              -> "used to separate declarations"
+                SymVirtualSemi       -> __IMPOSSIBLE__
+                SymBar               -> "used for with-arguments"
+                SymColon             -> "part of declaration syntax"
+                SymArrow             -> "the function arrow"
+                SymEqual             -> "part of declaration syntax"
+                SymLambda            -> "used for lambda-abstraction"
+                SymUnderscore        -> "used for anonymous identifiers"
+                SymQuestionMark      -> "a meta variable"
+                SymAs                -> "used for as-patterns"
+                SymOpenParen         -> "used to parenthesize expressions"
+                SymCloseParen        -> "used to parenthesize expressions"
+                SymOpenIdiomBracket  -> "an idiom bracket"
+                SymCloseIdiomBracket -> "an idiom bracket"
+                SymDoubleOpenBrace   -> "used for instance arguments"
+                SymDoubleCloseBrace  -> "used for instance arguments"
+                SymOpenBrace         -> "used for hidden arguments"
+                SymCloseBrace        -> "used for hidden arguments"
+                SymOpenVirtualBrace  -> __IMPOSSIBLE__
+                SymCloseVirtualBrace -> __IMPOSSIBLE__
+                SymOpenPragma        -> __IMPOSSIBLE__ -- "used for pragmas"
+                SymClosePragma       -> __IMPOSSIBLE__ -- "used for pragmas"
+                SymEllipsis          -> "used for function clauses"
+                SymDotDot            -> __IMPOSSIBLE__ -- "a modality"
+                SymEndComment        -> "the end-of-comment brace"
+              TokString{}   -> __IMPOSSIBLE__
+              TokTeX{}      -> __IMPOSSIBLE__  -- used by the LaTeX backend only
+              TokMarkup{}   -> __IMPOSSIBLE__  -- ditto
+              TokComment{}  -> __IMPOSSIBLE__
+              TokDummy{}    -> __IMPOSSIBLE__
+              TokEOF{}      -> __IMPOSSIBLE__
+
+        -- we know that there are no two Ids in a row
+        alternating (Hole :| Hole : _) = False
+        alternating (_    :| x   : xs) = alternating $ x :| xs
+        alternating (_    :|       []) = True
+
+-- | Create a qualified name from a list of strings
+mkQName :: [(Interval, String)] -> Parser QName
+mkQName ss = do
+    xs <- mapM mkName ss
+    return $ foldr Qual (QName $ last xs) (init xs)
+
+mkDomainFree_ :: (NamedArg Binder -> NamedArg Binder) -> Maybe Pattern -> Name -> NamedArg Binder
+mkDomainFree_ f p n = f $ defaultNamedArg $ Binder p $ mkBoundName_ n
+
+mkRString :: (Interval, String) -> RString
+mkRString (i, s) = Ranged (getRange i) s
+
+-- | Create a qualified name from a string (used in pragmas).
+--   Range of each name component is range of whole string.
+--   TODO: precise ranges!
+
+pragmaQName :: (Interval, String) -> Parser QName
+pragmaQName (r, s) = do
+  let ss = chopWhen (== '.') s
+  mkQName $ map (r,) ss
+
+mkNamedArg :: Maybe QName -> Either QName Range -> Parser (NamedArg BoundName)
+mkNamedArg x y = do
+  lbl <- case x of
+           Nothing        -> return $ Just $ WithOrigin UserWritten $ unranged "_"
+           Just (QName x) -> return $ Just $ WithOrigin UserWritten $ Ranged (getRange x) $ prettyShow x
+           _              -> parseError "expected unqualified variable name"
+  var <- case y of
+           Left (QName y) -> return $ mkBoundName y noFixity'
+           Right r        -> return $ mkBoundName (noName r) noFixity'
+           _              -> parseError "expected unqualified variable name"
+  return $ defaultArg $ Named lbl var
+
+-- | Polarity parser.
+
+polarity :: (Interval, String) -> Parser (Range, Occurrence)
+polarity (i, s) =
+  case s of
+    "_"  -> ret Unused
+    "++" -> ret StrictPos
+    "+"  -> ret JustPos
+    "-"  -> ret JustNeg
+    "*"  -> ret Mixed
+    _    -> parseError $ "Not a valid polarity: " ++ s
+  where
+  ret x = return (getRange i, x)
+
+recoverLayout :: [(Interval, String)] -> String
+recoverLayout [] = ""
+recoverLayout xs@((i, _) : _) = go (iStart i) xs
+  where
+    c0 = posCol (iStart i)
+
+    go cur [] = ""
+    go cur ((i, s) : xs) = padding cur (iStart i) ++ s ++ go (iEnd i) xs
+
+    padding Pn{ posLine = l1, posCol = c1 } Pn{ posLine = l2, posCol = c2 }
+      | l1 < l2  = List.genericReplicate (l2 - l1) '\n' ++ List.genericReplicate (max 0 (c2 - c0)) ' '
+      | l1 == l2 = List.genericReplicate (c2 - c1) ' '
+
+ensureUnqual :: QName -> Parser Name
+ensureUnqual (QName x) = return x
+ensureUnqual q@Qual{}  = parseError' (rStart' $ getRange q) "Qualified name not allowed here"
+
+-- | Match a particular name.
+isName :: String -> (Interval, String) -> Parser ()
+isName s (_,s')
+    | s == s'   = return ()
+    | otherwise = parseError $ "expected " ++ s ++ ", found " ++ s'
+
+-- Lambinds
+
+-- | Result of parsing @LamBinds@.
+data LamBinds' a = LamBinds
+  { lamBindings   :: a             -- ^ A number of domain-free or typed bindings or record patterns.
+  , absurdBinding :: Maybe Hiding  -- ^ Followed by possibly a final absurd pattern.
+  } deriving (Functor)
+type LamBinds = LamBinds' [LamBinding]
+
+mkAbsurdBinding :: Hiding -> LamBinds
+mkAbsurdBinding = LamBinds [] . Just
+
+mkLamBinds :: a -> LamBinds' a
+mkLamBinds bs = LamBinds bs Nothing
+
+-- | Build a forall pi (forall x y z -> ...)
+forallPi :: List1 LamBinding -> Expr -> Expr
+forallPi bs e = Pi (fmap addType bs) e
+
+-- | Converts lambda bindings to typed bindings.
+addType :: LamBinding -> TypedBinding
+addType (DomainFull b) = b
+addType (DomainFree x) = TBind r (singleton x) $ Underscore r Nothing
+  where r = getRange x
+
+-- | Returns the value of the first erasure attribute, if any, or else
+-- the default value of type 'Erased'.
+--
+-- Raises warnings for all attributes except for erasure attributes,
+-- and for multiple erasure attributes.
+
+onlyErased
+  :: [Attr]  -- ^ The attributes, in reverse order.
+  -> Parser Erased
+onlyErased as = do
+  es <- catMaybes <$> mapM onlyErased' (reverse as)
+  case es of
+    []     -> return defaultErased
+    [e]    -> return e
+    e : es -> do
+      parseWarning $ MultipleAttributes (getRange es) (Just "erasure")
+      return e
+  where
+  onlyErased' a = case theAttr a of
+    RelevanceAttribute{} -> unsup "Relevance"
+    CohesionAttribute{}  -> unsup "Cohesion"
+    LockAttribute{}      -> unsup "Lock"
+    TacticAttribute{}    -> unsup "Tactic"
+    QuantityAttribute q  -> maybe (unsup "Linearity") (return . Just) $ erasedFromQuantity q
+    where
+    unsup s = do
+      parseWarning $ UnsupportedAttribute (attrRange a) (Just s)
+      return Nothing
+
+-- | Constructs extended lambdas.
+
+extLam
+  :: Range            -- ^ The range of the lambda symbol and @where@ or
+                      --   the braces.
+  -> [Attr]           -- ^ The attributes in reverse order.
+  -> List1 LamClause  -- ^ The clauses in reverse order.
+  -> Parser Expr
+extLam symbolRange attrs cs = do
+  e <- onlyErased attrs
+  let cs' = List1.reverse cs
+  return $ ExtendedLam (getRange (symbolRange, e, cs')) e cs'
+
+-- | Constructs extended or absurd lambdas.
+
+extOrAbsLam
+  :: Range   -- ^ The range of the lambda symbol.
+  -> [Attr]  -- ^ The attributes, in reverse order.
+  -> Either ([LamBinding], Hiding) (List1 Expr)
+  -> Parser Expr
+extOrAbsLam lambdaRange attrs cs = case cs of
+  Right es -> do
+    -- It is of the form @\ { p1 ... () }@.
+    e  <- onlyErased attrs
+    cl <- mkAbsurdLamClause False es
+    return $ ExtendedLam (getRange (lambdaRange, e, es)) e $ singleton cl
+  Left (bs, h) -> do
+    mapM_ (\a -> parseWarning $
+                   UnsupportedAttribute (attrRange a) Nothing)
+          (reverse attrs)
+    List1.ifNull bs
+      {-then-} (return $ AbsurdLam r h)
+      {-else-} $ \ bs -> return $ Lam r bs (AbsurdLam r h)
+    where
+    r = fuseRange lambdaRange bs
+
+-- | Interpret an expression as a list of names and (not parsed yet) as-patterns
+
+exprAsTele :: Expr -> List1 Expr
+exprAsTele (RawApp _ es) = List2.toList1 es
+exprAsTele e             = singleton e
+
+exprAsNamesAndPatterns :: Expr -> Maybe (List1 (Name, Maybe Expr))
+exprAsNamesAndPatterns = mapM exprAsNameAndPattern . exprAsTele
+
+exprAsNameAndPattern :: Expr -> Maybe (Name, Maybe Expr)
+exprAsNameAndPattern (Ident (QName x)) = Just (x, Nothing)
+exprAsNameAndPattern (Underscore r _)  = Just (setRange r simpleHole, Nothing)
+exprAsNameAndPattern (As _ n e)        = Just (n, Just e)
+exprAsNameAndPattern (Paren r e)       = Just (setRange r simpleHole, Just e)
+exprAsNameAndPattern _                 = Nothing
+
+-- interpret an expression as name or list of hidden / instance names
+exprAsNameOrHiddenNames :: Expr -> Maybe (List1 (NamedArg (Name, Maybe Expr)))
+exprAsNameOrHiddenNames = \case
+  HiddenArg _ (Named Nothing e) ->
+    fmap (hide . defaultNamedArg) <$> exprAsNamesAndPatterns e
+  InstanceArg _ (Named Nothing e) ->
+    fmap (makeInstance . defaultNamedArg) <$> exprAsNamesAndPatterns e
+  e ->
+    singleton . defaultNamedArg <$> exprAsNameAndPattern e
+
+boundNamesOrAbsurd :: List1 Expr -> Parser (Either (List1 (NamedArg Binder)) (List1 Expr))
+boundNamesOrAbsurd es
+  | any isAbsurd es = return $ Right es
+  | otherwise       =
+    case mapM exprAsNameAndPattern es of
+        Nothing   -> parseError $ "expected sequence of bound identifiers"
+        Just good -> fmap Left $ forM good $ \ (n, me) -> do
+                       p <- traverse exprToPattern me
+                       return (defaultNamedArg (Binder p (mkBoundName_ n)))
+
+  where
+
+    isAbsurd :: Expr -> Bool
+    isAbsurd (Absurd _)                  = True
+    isAbsurd (HiddenArg _ (Named _ e))   = isAbsurd e
+    isAbsurd (InstanceArg _ (Named _ e)) = isAbsurd e
+    isAbsurd (Paren _ e)                 = isAbsurd e
+    isAbsurd (As _ _ e)                  = isAbsurd e
+    isAbsurd (RawApp _ es)               = any isAbsurd es
+    isAbsurd _                           = False
+
+-- | Match a pattern-matching "assignment" statement @p <- e@
+exprToAssignment :: Expr -> Parser (Maybe (Pattern, Range, Expr))
+exprToAssignment e@(RawApp r es)
+  | (es1, arr : es2) <- List2.break isLeftArrow es =
+    case filter isLeftArrow es2 of
+      arr : _ -> parseError' (rStart' $ getRange arr) $ "Unexpected " ++ prettyShow arr
+      [] ->
+        -- Andreas, 2021-05-06, issue #5365
+        -- Handle pathological cases like @do <-@ and @do x <-@.
+        case (es1, es2) of
+          (e1:rest1, e2:rest2) -> do
+            p <- exprToPattern $ rawApp $ e1 :| rest1
+            pure $ Just (p, getRange arr, rawApp (e2 :| rest2))
+          _ -> parseError' (rStart' $ getRange e) $ "Incomplete binding " ++ prettyShow e
+  where
+    isLeftArrow (Ident (QName (Name _ _ (Id arr :| [])))) =
+      arr `elem` ["<-", "\x2190"]  -- \leftarrow [issue #5465, unicode might crash happy]
+    isLeftArrow _ = False
+exprToAssignment _ = pure Nothing
+
+-- | Build a with-block
+buildWithBlock ::
+  [Either RewriteEqn (List1 (Named Name Expr))] ->
+  Parser ([RewriteEqn], [Named Name Expr])
+buildWithBlock rees = case groupByEither rees of
+  (Left rs : rest) -> (List1.toList rs,) <$> finalWith rest
+  rest             -> ([],) <$> finalWith rest
+
+  where
+
+    finalWith :: (HasRange a, HasRange b) =>
+                 [Either (List1 a) (List1 (List1 b))] -> Parser [b]
+    finalWith []             = pure $ []
+    finalWith [Right ees]    = pure $ List1.toList $ sconcat ees
+    finalWith (Right{} : tl) = parseError' (rStart' $ getRange tl)
+      "Cannot use rewrite / pattern-matching with after a with-abstraction."
+
+-- | Build a with-statement
+buildWithStmt :: List1 (Named Name Expr) ->
+                 Parser [Either RewriteEqn (List1 (Named Name Expr))]
+buildWithStmt nes = do
+  ws <- mapM buildSingleWithStmt (List1.toList nes)
+  let rws = groupByEither ws
+  pure $ map (first (Invert ())) rws
+
+buildSingleWithStmt ::
+  Named Name Expr ->
+  Parser (Either (Named Name (Pattern, Expr)) (Named Name Expr))
+buildSingleWithStmt e = do
+  mpatexpr <- exprToAssignment (namedThing e)
+  pure $ case mpatexpr of
+    Just (pat, _, expr) -> Left ((pat, expr) <$ e)
+    Nothing             -> Right e
+
+fromWithApp :: Expr -> List1 Expr
+fromWithApp = \case
+  WithApp _ e es -> e :| es
+  e              -> singleton e
+
+-- | Build a do-statement
+defaultBuildDoStmt :: Expr -> [LamClause] -> Parser DoStmt
+defaultBuildDoStmt e (_ : _) = parseError' (rStart' $ getRange e) "Only pattern matching do-statements can have where clauses."
+defaultBuildDoStmt e []      = pure $ DoThen e
+
+buildDoStmt :: Expr -> [LamClause] -> Parser DoStmt
+buildDoStmt (Let r ds Nothing) [] = return $ DoLet r ds
+buildDoStmt e@(RawApp r _)    cs = do
+  mpatexpr <- exprToAssignment e
+  case mpatexpr of
+    Just (pat, r, expr) -> pure $ DoBind r pat expr cs
+    Nothing -> defaultBuildDoStmt e cs
+buildDoStmt e cs = defaultBuildDoStmt e cs
+
+
+-- | Extract record directives
+extractRecordDirectives :: [Declaration] -> Parser (RecordDirectives, [Declaration])
+extractRecordDirectives ds = do
+  let (dirs, rest) = spanJust isRecordDirective ds
+  dir <- verifyRecordDirectives dirs
+  pure (dir, rest)
+
+-- | Check for duplicate record directives.
+verifyRecordDirectives :: [RecordDirective] -> Parser RecordDirectives
+verifyRecordDirectives ds
+  | null rs   = return (RecordDirectives (listToMaybe is) (listToMaybe es) (listToMaybe ps) (listToMaybe cs))
+      -- Here, all the lists is, es, cs, ps are at most singletons.
+  | otherwise = parseErrorRange (head rs) $ unlines $ "Repeated record directives at:" : map prettyShow rs
+  where
+  errorFromList []  = []
+  errorFromList [x] = []
+  errorFromList xs  = map getRange xs
+  rs  = List.sort $ concat [ errorFromList is, errorFromList es', errorFromList cs, errorFromList ps ]
+  es  = map rangedThing es'
+  is  = [ i      | Induction i          <- ds ]
+  es' = [ e      | Eta e                <- ds ]
+  cs  = [ (c, i) | Constructor c i      <- ds ]
+  ps  = [ r      | PatternOrCopattern r <- ds ]
+
+
+-- | Breaks up a string into substrings. Returns every maximal
+-- subsequence of zero or more characters distinct from @'.'@.
+--
+-- > splitOnDots ""         == [""]
+-- > splitOnDots "foo.bar"  == ["foo", "bar"]
+-- > splitOnDots ".foo.bar" == ["", "foo", "bar"]
+-- > splitOnDots "foo.bar." == ["foo", "bar", ""]
+-- > splitOnDots "foo..bar" == ["foo", "", "bar"]
+splitOnDots :: String -> [String]
+splitOnDots ""        = [""]
+splitOnDots ('.' : s) = [] : splitOnDots s
+splitOnDots (c   : s) = case splitOnDots s of
+  p : ps -> (c : p) : ps
+
+
+-- | Returns 'True' iff the name is a valid Haskell (hierarchical)
+-- module name.
+validHaskellModuleName :: String -> Bool
+validHaskellModuleName = all ok . splitOnDots
+  where
+  -- Checks if a dot-less module name is well-formed.
+  ok :: String -> Bool
+  ok []      = False
+  ok (c : s) =
+    isUpper c &&
+    all (\c -> isLower c || c == '_' ||
+               isUpper c ||
+               generalCategory c == DecimalNumber ||
+               c == '\'')
+        s
+
+{--------------------------------------------------------------------------
+    Patterns
+ --------------------------------------------------------------------------}
+
+-- | Turn an expression into a left hand side.
+exprToLHS :: Expr -> Parser ([RewriteEqn] -> [WithExpr] -> LHS)
+exprToLHS e = LHS <$> exprToPattern e
+
+-- | Turn an expression into a pattern. Fails if the expression is not a
+--   valid pattern.
+exprToPattern :: Expr -> Parser Pattern
+exprToPattern e = case C.isPattern e of
+  Nothing -> parseErrorRange e $ "Not a valid pattern: " ++ prettyShow e
+  Just p  -> pure p
+
+opAppExprToPattern :: OpApp Expr -> Parser Pattern
+opAppExprToPattern (SyntaxBindingLambda _ _ _) = parseError "Syntax binding lambda cannot appear in a pattern"
+opAppExprToPattern (Ordinary e) = exprToPattern e
+
+-- | Turn an expression into a name. Fails if the expression is not a
+--   valid identifier.
+exprToName :: Expr -> Parser Name
+exprToName (Ident (QName x)) = return x
+exprToName e = parseErrorRange e $ "Not a valid identifier: " ++ prettyShow e
+
+isEqual :: Expr -> Maybe (Expr, Expr)
+isEqual = \case
+    Equal _ a b -> Just (a, b)
+    _           -> Nothing
+
+-- | When given expression is @e1 = e2@, turn it into a named expression.
+--   Call this inside an implicit argument @{e}@ or @{{e}}@, where
+--   an equality must be a named argument (rather than a cubical partial match).
+maybeNamed :: Expr -> Parser (Named_ Expr)
+maybeNamed e =
+  case isEqual e of
+    Nothing       -> return $ unnamed e
+    Just (e1, e2) -> do
+      let succeed x = return $ named (WithOrigin UserWritten $ Ranged (getRange e1) x) e2
+      case e1 of
+        Ident (QName x) -> succeed $ nameToRawName x
+        -- We could have the following, but names of arguments cannot be _.
+        -- Underscore{}    -> succeed $ "_"
+        _ -> parseErrorRange e $ "Not a valid named argument: " ++ prettyShow e
+
+patternSynArgs :: [NamedArg Binder] -> Parser [Arg Name]
+patternSynArgs = mapM pSynArg
+  where
+    pSynArg x
+      | let h = getHiding x, h `notElem` [Hidden, NotHidden] =
+          abort $ prettyShow h ++ " arguments not allowed to pattern synonyms"
+      | not (isRelevant x) =
+          abort "Arguments to pattern synonyms must be relevant"
+      | Just p <- binderPattern (namedArg x) =
+          abort "Arguments to pattern synonyms cannot be patterns themselves"
+      | otherwise = return $ fmap (boundName . binderName . namedThing) x
+      where
+      abort s = parseError $
+        "Illegal pattern synonym argument  " ++ prettyShow x ++ "\n" ++
+        "(" ++ s ++ ".)"
+
+mkLamClause
+  :: Bool   -- ^ Catch-all?
+  -> [Expr] -- ^ Possibly empty list of patterns.
+  -> RHS
+  -> Parser LamClause
+mkLamClause catchAll es rhs = mapM exprToPattern es <&> \ ps ->
+  LamClause{ lamLHS = ps, lamRHS = rhs, lamCatchAll = catchAll }
+
+mkAbsurdLamClause :: Bool -> List1 Expr -> Parser LamClause
+mkAbsurdLamClause catchAll es = mkLamClause catchAll (List1.toList es) AbsurdRHS
+
+parsePanic s = parseError $ "Internal parser error: " ++ s ++ ". Please report this as a bug."
+
+{- RHS or type signature -}
+
+data RHSOrTypeSigs
+ = JustRHS RHS
+ | TypeSigsRHS Expr
+ deriving Show
+
+patternToNames :: Pattern -> Parser (List1 (ArgInfo, Name))
+patternToNames = \case
+    IdentP _ (QName i)       -> return $ singleton $ (defaultArgInfo, i)
+    WildP r                  -> return $ singleton $ (defaultArgInfo, C.noName r)
+    DotP _ (Ident (QName i)) -> return $ singleton $ (setRelevance Irrelevant defaultArgInfo, i)
+    RawAppP _ ps             -> sconcat . List2.toList1 <$> mapM patternToNames ps
+    p                        -> parseError $
+      "Illegal name in type signature: " ++ prettyShow p
+
+funClauseOrTypeSigs :: [Attr] -> ([RewriteEqn] -> [WithExpr] -> LHS)
+                    -> [Either RewriteEqn (List1 (Named Name Expr))]
+                    -> RHSOrTypeSigs
+                    -> WhereClause -> Parser (List1 Declaration)
+funClauseOrTypeSigs attrs lhs' with mrhs wh = do
+  (rs , es) <- buildWithBlock with
+  let lhs = lhs' rs (map (fmap observeModifiers) es)
+  -- traceShowM lhs
+  case mrhs of
+    JustRHS rhs   -> do
+      unless (null attrs) $ parseErrorRange attrs $ "A function clause cannot have attributes"
+      return $ singleton $ FunClause lhs rhs wh False
+    TypeSigsRHS e -> case wh of
+      NoWhere -> case lhs of
+        LHS p _ _ | hasEllipsis p -> parseError "The ellipsis ... cannot have a type signature"
+        LHS _ _ (_:_) -> parseError "Illegal: with in type signature"
+        LHS _ (_:_) _ -> parseError "Illegal: rewrite in type signature"
+        LHS p _ _ | hasWithPatterns p -> parseError "Illegal: with patterns in type signature"
+        LHS p [] [] -> forMM (patternToNames p) $ \ (info, x) -> do
+          info <- applyAttrs attrs info
+          return $ typeSig info (getTacticAttr attrs) x e
+      _ -> parseError "A type signature cannot have a where clause"
+
+parseDisplayPragma :: Range -> Position -> String -> Parser Pragma
+parseDisplayPragma r pos s =
+  case parsePosString pos defaultParseFlags [normal] funclauseParser s of
+    ParseOk s (FunClause (LHS lhs [] []) (RHS rhs) NoWhere ca :| []) | null (parseInp s) ->
+      return $ DisplayPragma r lhs rhs
+    _ -> parseError "Invalid DISPLAY pragma. Should have form {-# DISPLAY LHS = RHS #-}."
+
+typeSig :: ArgInfo -> TacticAttribute -> Name -> Expr -> Declaration
+typeSig i tac n e = TypeSig i tac n (Generalized e)
+
+-- * Attributes
+
+-- | Parsed attribute.
+
+data Attr = Attr
+  { attrRange :: Range       -- ^ Range includes the @.
+  , attrName  :: String      -- ^ Concrete, user written attribute for error reporting.
+  , theAttr   :: Attribute   -- ^ Parsed attribute.
+  }
+
+instance HasRange Attr where
+  getRange = attrRange
+
+instance SetRange Attr where
+  setRange r (Attr _ x a) = Attr r x a
+
+-- | Parse an attribute.
+toAttribute :: Range -> Expr -> Parser Attr
+toAttribute r e = do
+  attr <- maybe failure (return . Attr r s) $ exprToAttribute e
+  modify' (\ st -> st{ parseAttributes = (theAttr attr, r, s) : parseAttributes st })
+  return attr
+  where
+  s = prettyShow e
+  failure = parseErrorRange e $ "Unknown attribute: " ++ s
+
+-- | Apply an attribute to thing (usually `Arg`).
+--   This will fail if one of the attributes is already set
+--   in the thing to something else than the default value.
+applyAttr :: (LensAttribute a) => Attr -> a -> Parser a
+applyAttr attr@(Attr _ _ a) = maybe failure return . setPristineAttribute a
+  where
+  failure = errorConflictingAttribute attr
+
+-- | Apply attributes to thing (usually `Arg`).
+--   Expects a reversed list of attributes.
+--   This will fail if one of the attributes is already set
+--   in the thing to something else than the default value.
+applyAttrs :: LensAttribute a => [Attr] -> a -> Parser a
+applyAttrs rattrs arg = do
+  let attrs = reverse rattrs
+  checkForUniqueAttribute (isJust . isQuantityAttribute ) attrs
+  checkForUniqueAttribute (isJust . isRelevanceAttribute) attrs
+  checkForUniqueAttribute (isJust . isTacticAttribute)    attrs
+  foldM (flip applyAttr) arg attrs
+
+applyAttrs1 :: LensAttribute a => List1 Attr -> a -> Parser a
+applyAttrs1 = applyAttrs . List1.toList
+
+-- | Set the tactic attribute of a binder
+setTacticAttr :: List1 Attr -> NamedArg Binder -> NamedArg Binder
+setTacticAttr as = updateNamedArg $ fmap $ \ b ->
+  case getTacticAttr $ List1.toList as of
+    Just t  -> b { bnameTactic = Just t }
+    Nothing -> b
+
+-- | Get the tactic attribute if present.
+getTacticAttr :: [Attr] -> TacticAttribute
+getTacticAttr as =
+  case tacticAttributes [ a | Attr _ _ a <- as ] of
+    [TacticAttribute e] -> Just e
+    []                  -> Nothing
+    _                   -> __IMPOSSIBLE__
+
+-- | Report a parse error if two attributes in the list are of the same kind,
+--   thus, present conflicting information.
+checkForUniqueAttribute :: (Attribute -> Bool) -> [Attr] -> Parser ()
+checkForUniqueAttribute p attrs = do
+  let pAttrs = filter (p . theAttr) attrs
+  when (length pAttrs >= 2) $
+    errorConflictingAttributes pAttrs
+
+-- | Report an attribute as conflicting (e.g., with an already set value).
+errorConflictingAttribute :: Attr -> Parser a
+errorConflictingAttribute a = parseErrorRange a $ "Conflicting attribute: " ++ attrName a
+
+-- | Report attributes as conflicting (e.g., with each other).
+--   Precondition: List not emtpy.
+errorConflictingAttributes :: [Attr] -> Parser a
+errorConflictingAttributes [a] = errorConflictingAttribute a
+errorConflictingAttributes as  = parseErrorRange as $
+  "Conflicting attributes: " ++ unwords (map attrName as)
+}
diff --git a/src/full/Agda/Syntax/Parser/StringLiterals.hs b/src/full/Agda/Syntax/Parser/StringLiterals.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/StringLiterals.hs
@@ -0,0 +1,210 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| The code to lex string and character literals. Basically the same code
+    as in GHC.
+-}
+module Agda.Syntax.Parser.StringLiterals
+    ( litString, litChar
+    ) where
+
+import Data.Bifunctor
+import Data.Char
+import qualified Data.Text as T
+
+import Agda.Syntax.Common (pattern Ranged)
+import Agda.Syntax.Parser.Alex
+import Agda.Syntax.Parser.Monad
+import Agda.Syntax.Parser.Tokens
+import Agda.Syntax.Parser.LookAhead
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+
+{--------------------------------------------------------------------------
+    Exported actions
+ --------------------------------------------------------------------------}
+
+-- | Lex a string literal. Assumes that a double quote has been lexed.
+litString :: LexAction Token
+litString = stringToken '"' $ \ i s ->
+  return $ TokLiteral $ Ranged (getRange i) $ LitString $ T.pack s
+
+{-| Lex a character literal. Assumes that a single quote has been lexed.  A
+    character literal is lexed in exactly the same way as a string literal.
+    Only before returning the token do we check that the lexed string is of
+    length 1. This is maybe not the most efficient way of doing things, but on
+    the other hand it will only be inefficient if there is a lexical error.
+-}
+litChar :: LexAction Token
+litChar = stringToken '\'' $ \ i -> \case
+  [c] -> return $ TokLiteral $ Ranged (getRange i) $ LitChar c
+  _   -> lexError "character literal must contain a single character"
+
+
+{--------------------------------------------------------------------------
+    Errors
+ --------------------------------------------------------------------------}
+
+-- | Custom error function.
+litError :: String -> LookAhead a
+litError msg =
+    do  sync
+        liftP $ lexError $
+            "Lexical error in string or character literal: " ++ msg
+
+
+{--------------------------------------------------------------------------
+    The meat
+ --------------------------------------------------------------------------}
+
+-- | The general function to lex a string or character literal token. The
+--   character argument is the delimiter (@\"@ for strings and @\'@ for
+--   characters).
+stringToken :: Char -> (Interval -> String -> Parser tok) -> LexAction tok
+stringToken del mkTok = LexAction $ \ inp inp' n ->
+    do  setLastPos (backupPos $ lexPos inp')
+        setLexInput inp'
+        -- TODO: Should setPrevToken be run here? Compare with
+        -- Agda.Syntax.Parser.LexActions.token.
+        tok <- runLookAhead litError $ lexString del ""
+        i   <- getParseInterval
+        mkTok i tok
+
+
+-- | This is where the work happens. The string argument is an accumulating
+--   parameter for the string being lexed.
+lexString :: Char -> String -> LookAhead String
+lexString del s =
+
+    do  c <- nextChar
+        case c of
+
+            c | c == del  -> sync >> return (reverse s)
+
+            '\\' ->
+                do  c' <- nextChar
+                    case c' of
+                        '&'             -> sync >> lexString del s
+                        c | isSpace c   -> sync >> lexStringGap del s
+                        _               -> normalChar
+
+            _ -> normalChar
+    where
+        normalChar =
+            do  rollback
+                c <- lexChar
+                lexString del (c:s)
+
+
+-- | A string gap consists of whitespace (possibly including line breaks)
+--   enclosed in backslashes. The gap is not part of the resulting string.
+lexStringGap :: Char -> String -> LookAhead String
+lexStringGap del s =
+    do  c <- eatNextChar
+        case c of
+            '\\'            -> lexString del s
+            c | isSpace c   -> lexStringGap del s
+            _               -> lookAheadError "non-space in string gap"
+
+-- | Lex a single character.
+lexChar :: LookAhead Char
+lexChar =
+    do  c <- eatNextChar
+        case c of
+            '\\'    -> lexEscape
+            _       -> return c
+
+-- | Lex an escaped character. Assumes the backslash has been lexed.
+lexEscape :: LookAhead Char
+lexEscape =
+    do  c <- eatNextChar
+        case c of
+            '^'     -> do c <- eatNextChar
+                          if c >= '@' && c <= '_'
+                            then return (chr (ord c - ord '@'))
+                            else lookAheadError "invalid control character"
+
+            'x'     -> readNum isHexDigit 16 digitToInt
+            'o'     -> readNum isOctDigit  8 digitToInt
+            x | isDigit x
+                    -> readNumAcc isDigit 10 digitToInt (digitToInt x)
+
+            c ->
+                -- Try to match the input (starting with c) against the
+                -- silly escape codes.
+                do  esc <- match' c (map (second return) sillyEscapeChars)
+                                    (lookAheadError "bad escape code")
+                    sync
+                    return esc
+
+-- | Read a number in the specified base.
+readNum :: (Char -> Bool) -> Int -> (Char -> Int) -> LookAhead Char
+readNum isDigit base conv =
+    do  c <- eatNextChar
+        if isDigit c
+            then readNumAcc isDigit base conv (conv c)
+            else lookAheadError "non-digit in numeral"
+
+-- | Same as 'readNum' but with an accumulating parameter.
+readNumAcc :: (Char -> Bool) -> Int -> (Char -> Int) -> Int -> LookAhead Char
+readNumAcc isDigit base conv i = scan i
+    where
+        scan i =
+            do  inp <- getInput
+                c   <- nextChar
+                case c of
+                    c | isDigit c -> scan (i*base + conv c)
+                    _             ->
+                        do  setInput inp
+                            sync
+                            if i >= ord minBound && i <= ord maxBound
+                                then return (chr i)
+                                else lookAheadError "character literal out of bounds"
+
+-- | The escape codes.
+sillyEscapeChars :: [(String, Char)]
+sillyEscapeChars =
+    [ ("a", '\a')
+    , ("b", '\b')
+    , ("f", '\f')
+    , ("n", '\n')
+    , ("r", '\r')
+    , ("t", '\t')
+    , ("v", '\v')
+    , ("\\", '\\')
+    , ("\"", '\"')
+    , ("'", '\'')
+    , ("NUL", '\NUL')
+    , ("SOH", '\SOH')
+    , ("STX", '\STX')
+    , ("ETX", '\ETX')
+    , ("EOT", '\EOT')
+    , ("ENQ", '\ENQ')
+    , ("ACK", '\ACK')
+    , ("BEL", '\BEL')
+    , ("BS", '\BS')
+    , ("HT", '\HT')
+    , ("LF", '\LF')
+    , ("VT", '\VT')
+    , ("FF", '\FF')
+    , ("CR", '\CR')
+    , ("SO", '\SO')
+    , ("SI", '\SI')
+    , ("DLE", '\DLE')
+    , ("DC1", '\DC1')
+    , ("DC2", '\DC2')
+    , ("DC3", '\DC3')
+    , ("DC4", '\DC4')
+    , ("NAK", '\NAK')
+    , ("SYN", '\SYN')
+    , ("ETB", '\ETB')
+    , ("CAN", '\CAN')
+    , ("EM", '\EM')
+    , ("SUB", '\SUB')
+    , ("ESC", '\ESC')
+    , ("FS", '\FS')
+    , ("GS", '\GS')
+    , ("RS", '\RS')
+    , ("US", '\US')
+    , ("SP", '\SP')
+    , ("DEL", '\DEL')
+    ]
diff --git a/src/full/Agda/Syntax/Parser/Tokens.hs b/src/full/Agda/Syntax/Parser/Tokens.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Parser/Tokens.hs
@@ -0,0 +1,113 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.Parser.Tokens
+    ( Token(..)
+    , Keyword(..)
+    , layoutKeywords
+    , Symbol(..)
+    ) where
+
+import Agda.Syntax.Literal (RLiteral)
+import Agda.Syntax.Position
+
+data Keyword
+        = KwLet | KwIn | KwWhere | KwData | KwCoData | KwDo
+        | KwPostulate | KwAbstract | KwPrivate | KwInstance
+        | KwInterleaved | KwMutual
+        | KwOverlap
+        | KwOpen | KwImport | KwModule | KwPrimitive | KwMacro
+        | KwInfix | KwInfixL | KwInfixR | KwWith | KwRewrite
+        | KwForall | KwRecord | KwConstructor | KwField
+        | KwInductive | KwCoInductive
+        | KwEta | KwNoEta
+        | KwHiding | KwUsing | KwRenaming | KwTo | KwPublic
+        | KwOpaque | KwUnfolding
+        | KwOPTIONS | KwBUILTIN | KwLINE
+        | KwFOREIGN | KwCOMPILE
+        | KwIMPOSSIBLE | KwSTATIC | KwINJECTIVE | KwINLINE | KwNOINLINE
+        | KwETA
+        | KwNO_TERMINATION_CHECK | KwTERMINATING | KwNON_TERMINATING
+        | KwNOT_PROJECTION_LIKE
+        | KwNON_COVERING
+        | KwWARNING_ON_USAGE | KwWARNING_ON_IMPORT
+        | KwMEASURE | KwDISPLAY
+        | KwREWRITE
+        | KwQuote | KwQuoteTerm
+        | KwUnquote | KwUnquoteDecl | KwUnquoteDef
+        | KwSyntax
+        | KwPatternSyn | KwTactic | KwCATCHALL
+        | KwVariable
+        | KwNO_POSITIVITY_CHECK | KwPOLARITY
+        | KwNO_UNIVERSE_CHECK
+    deriving (Eq, Show)
+
+-- | Unconditional layout keywords.
+--
+-- Some keywords introduce layout only in certain circumstances,
+-- these are not included here.
+--
+layoutKeywords :: [Keyword]
+layoutKeywords =
+    [ KwAbstract
+    , KwDo
+    , KwField
+    , KwInstance
+    , KwLet
+    , KwMacro
+    , KwMutual
+    , KwPostulate
+    , KwPrimitive
+    , KwPrivate
+    , KwVariable
+    , KwWhere
+    , KwOpaque
+    ]
+
+data Symbol
+        = SymDot | SymSemi | SymVirtualSemi | SymBar
+        | SymColon | SymArrow | SymEqual | SymLambda
+        | SymUnderscore | SymQuestionMark   | SymAs
+        | SymOpenParen        | SymCloseParen
+        | SymOpenIdiomBracket | SymCloseIdiomBracket | SymEmptyIdiomBracket
+        | SymDoubleOpenBrace  | SymDoubleCloseBrace
+        | SymOpenBrace        | SymCloseBrace
+        | SymOpenVirtualBrace | SymCloseVirtualBrace
+        | SymOpenPragma       | SymClosePragma | SymEllipsis | SymDotDot
+        | SymEndComment -- ^ A misplaced end-comment "-}".
+    deriving (Eq, Show)
+
+data Token
+          -- Keywords
+        = TokKeyword Keyword Interval
+          -- Identifiers and operators
+        | TokId         (Interval, String)
+        | TokQId        [(Interval, String)]
+                        -- Non-empty namespace. The intervals for
+                        -- "A.B.x" correspond to "A.", "B." and "x".
+          -- Literals
+        | TokLiteral    RLiteral
+          -- Special symbols
+        | TokSymbol Symbol Interval
+          -- Other tokens
+        | TokString (Interval, String)
+            -- ^ Arbitrary string (not enclosed in double quotes), used in pragmas.
+        | TokTeX (Interval, String)
+        | TokMarkup (Interval, String)
+        | TokComment (Interval, String)
+        | TokDummy      -- Dummy token to make Happy not complain
+                        -- about overlapping cases.
+        | TokEOF Interval
+    deriving (Eq, Show)
+
+instance HasRange Token where
+  getRange (TokKeyword _ i)    = getRange i
+  getRange (TokId (i, _))      = getRange i
+  getRange (TokQId iss)        = getRange (map fst iss)
+  getRange (TokLiteral lit)    = getRange lit
+  getRange (TokSymbol _ i)     = getRange i
+  getRange (TokString (i, _))  = getRange i
+  getRange (TokTeX (i, _))     = getRange i
+  getRange (TokMarkup (i, _))  = getRange i
+  getRange (TokComment (i, _)) = getRange i
+  getRange TokDummy            = noRange
+  getRange (TokEOF i)          = getRange i
diff --git a/src/full/Agda/Syntax/Position.hs b/src/full/Agda/Syntax/Position.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Position.hs
@@ -0,0 +1,726 @@
+{-# LANGUAGE DataKinds            #-}
+{-# LANGUAGE UndecidableInstances #-} -- Due to KILLRANGE vararg typeclass
+
+{-| Position information for syntax. Crucial for giving good error messages.
+-}
+
+module Agda.Syntax.Position
+  ( -- * Positions
+    Position
+  , PositionWithoutFile
+  , Position'(..)
+  , SrcFile
+  , RangeFile(..)
+  , mkRangeFile
+  , positionInvariant
+  , startPos
+  , movePos
+  , movePosByString
+  , backupPos
+  , startPos'
+
+    -- * Intervals
+  , Interval
+  , IntervalWithoutFile
+  , Interval'(..)
+  , intervalInvariant
+  , posToInterval
+  , getIntervalFile
+  , iLength
+  , fuseIntervals
+  , setIntervalFile
+
+    -- * Ranges
+  , Range
+  , Range'(..)
+  , rangeInvariant
+  , consecutiveAndSeparated
+  , intervalsToRange
+  , intervalToRange
+  , rangeIntervals
+  , rangeFile
+  , rangeModule'
+  , rangeModule
+  , rightMargin
+  , noRange
+  , posToRange, posToRange'
+  , rStart, rStart'
+  , rEnd, rEnd'
+  , rangeToInterval
+  , rangeToIntervalWithFile
+  , continuous
+  , continuousPerLine
+  , PrintRange(..)
+  , HasRange(..)
+  , SetRange(..)
+  , KillRange(..)
+  , KillRangeT
+  , killRangeMap
+  , KILLRANGE(..)
+  , withRangeOf
+  , fuseRange
+  , fuseRanges
+  , beginningOf
+  , beginningOfFile
+  , interleaveRanges
+  ) where
+
+import Prelude hiding ( null )
+
+import Control.DeepSeq
+import Control.Monad
+import Control.Monad.Writer (runWriter, tell)
+
+import qualified Data.Foldable as Fold
+import Data.Function (on)
+import Data.Int
+import Data.List (sort)
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Sequence (Seq)
+import qualified Data.Sequence as Seq
+import Data.Semigroup (Semigroup(..))
+import Data.Void
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.TopLevelModuleName.Boot (TopLevelModuleName'(..))
+
+import Agda.Utils.FileName
+import Agda.Utils.List
+import Agda.Utils.List1 (List1)
+import Agda.Utils.List2 (List2)
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+
+import Agda.Utils.TypeLevel (IsBase, All, Domains)
+
+import Agda.Utils.Impossible
+
+{--------------------------------------------------------------------------
+    Types and classes
+ --------------------------------------------------------------------------}
+
+-- | Represents a point in the input.
+--
+-- If two positions have the same 'srcFile' and 'posPos' components,
+-- then the final two components should be the same as well, but since
+-- this can be hard to enforce the program should not rely too much on
+-- the last two components; they are mainly there to improve error
+-- messages for the user.
+--
+-- Note the invariant which positions have to satisfy: 'positionInvariant'.
+data Position' a = Pn
+  { srcFile :: !a
+    -- ^ File.
+  , posPos  :: !Int32
+    -- ^ Position, counting from 1.
+  , posLine :: !Int32
+    -- ^ Line number, counting from 1.
+  , posCol  :: !Int32
+    -- ^ Column number, counting from 1.
+  }
+  deriving (Show, Functor, Foldable, Traversable, Generic)
+
+positionInvariant :: Position' a -> Bool
+positionInvariant p =
+  posPos p > 0 && posLine p > 0 && posCol p > 0
+
+importantPart :: Position' a -> (a, Int32)
+importantPart p = (srcFile p, posPos p)
+
+instance Eq a => Eq (Position' a) where
+  (==) = (==) `on` importantPart
+
+instance Ord a => Ord (Position' a) where
+  compare = compare `on` importantPart
+
+type SrcFile = Strict.Maybe RangeFile
+
+-- | File information used in the 'Position', 'Interval' and 'Range'
+-- types.
+data RangeFile = RangeFile
+  { rangeFilePath :: !AbsolutePath
+    -- ^ The file's path.
+  , rangeFileName :: !(Maybe (TopLevelModuleName' Range))
+    -- ^ The file's top-level module name (if applicable).
+    --
+    -- This field is optional, but some things may break if the field
+    -- is not instantiated with an actual top-level module name. For
+    -- instance, the 'Eq' and 'Ord' instances only make use of this
+    -- field.
+    --
+    -- The field uses 'Maybe' rather than 'Strict.Maybe' because it
+    -- should be possible to instantiate it with something that is not
+    -- yet defined (see 'Agda.Interaction.Imports.parseSource').
+    --
+    -- This '(TopLevelModuleName' Range)' should not contain a range.
+  }
+  deriving (Show, Generic)
+
+-- | A smart constructor for 'RangeFile'.
+
+mkRangeFile :: AbsolutePath -> Maybe (TopLevelModuleName' Range) -> RangeFile
+mkRangeFile f top = RangeFile
+  { rangeFilePath = f
+  , rangeFileName = killRange top
+  }
+
+-- | Only the 'rangeFileName' component is compared.
+
+instance Eq RangeFile where
+  (==) = (==) `on` rangeFileName
+
+-- | Only the 'rangeFileName' component is compared.
+
+instance Ord RangeFile where
+  compare = compare `on` rangeFileName
+
+instance NFData RangeFile where
+  rnf (RangeFile _ n) = rnf n
+
+type Position            = Position' SrcFile
+type PositionWithoutFile = Position' ()
+
+instance NFData Position where
+  rnf = (`seq` ())
+
+instance NFData PositionWithoutFile where
+  rnf = (`seq` ())
+
+-- | An interval. The @iEnd@ position is not included in the interval.
+--
+-- Note the invariant which intervals have to satisfy: 'intervalInvariant'.
+data Interval' a = Interval { iStart, iEnd :: !(Position' a) }
+  deriving (Show, Eq, Ord, Functor, Foldable, Traversable, Generic)
+
+type Interval            = Interval' SrcFile
+type IntervalWithoutFile = Interval' ()
+
+instance NFData Interval where
+  rnf = (`seq` ())
+
+instance NFData IntervalWithoutFile where
+  rnf = (`seq` ())
+
+intervalInvariant :: Ord a => Interval' a -> Bool
+intervalInvariant i =
+  all positionInvariant [iStart i, iEnd i]
+    &&
+  iStart i <= iEnd i
+    &&
+  srcFile (iStart i) == srcFile (iEnd i)
+
+-- | Sets the 'srcFile' components of the interval.
+
+setIntervalFile :: a -> Interval' b -> Interval' a
+setIntervalFile f (Interval p1 p2) =
+  Interval (p1 { srcFile = f }) (p2 { srcFile = f })
+
+-- | Gets the 'srcFile' component of the interval. Because of the invariant,
+--   they are both the same.
+getIntervalFile :: Interval' a -> a
+getIntervalFile = srcFile . iStart
+
+-- | Converts a file name and two positions to an interval.
+posToInterval ::
+  a -> PositionWithoutFile -> PositionWithoutFile -> Interval' a
+posToInterval f p1 p2 = setIntervalFile f $
+  if p1 < p2
+  then Interval p1 p2
+  else Interval p2 p1
+
+-- | The length of an interval.
+iLength :: Interval' a -> Int32
+iLength i = posPos (iEnd i) - posPos (iStart i)
+
+-- | A range is a file name, plus a sequence of intervals, assumed to
+-- point to the given file. The intervals should be consecutive and
+-- separated.
+--
+-- Note the invariant which ranges have to satisfy: 'rangeInvariant'.
+data Range' a
+  = NoRange
+  | Range !a (Seq IntervalWithoutFile)
+  deriving
+    (Show, Eq, Ord, Functor, Foldable, Traversable, Generic)
+
+type Range = Range' SrcFile
+
+instance NFData a => NFData (Range' a)
+
+instance Null (Range' a) where
+  null NoRange = True
+  null Range{} = False
+
+  empty = NoRange
+
+instance Eq a => Semigroup (Range' a) where
+  NoRange <> r = r
+  r <> NoRange = r
+  Range f is <> Range f' is'
+    | f /= f'   = __IMPOSSIBLE__
+    | otherwise = Range f (is <> is')
+
+instance Eq a => Monoid (Range' a) where
+  mempty  = empty
+  mappend = (<>)
+
+-- | The intervals that make up the range. The intervals are
+-- consecutive and separated ('consecutiveAndSeparated').
+rangeIntervals :: Range' a -> [IntervalWithoutFile]
+rangeIntervals NoRange      = []
+rangeIntervals (Range _ is) = Fold.toList is
+
+-- | Turns a file name plus a list of intervals into a range.
+--
+-- Precondition: 'consecutiveAndSeparated'.
+intervalsToRange :: a -> [IntervalWithoutFile] -> Range' a
+intervalsToRange _ [] = NoRange
+intervalsToRange f is = Range f (Seq.fromList is)
+
+-- | Are the intervals consecutive and separated, do they all point to
+-- the same file, and do they satisfy the interval invariant?
+consecutiveAndSeparated :: Ord a => [Interval' a] -> Bool
+consecutiveAndSeparated is =
+  all intervalInvariant is
+    &&
+  allEqual (map (srcFile . iStart) is)
+    &&
+  allConsecutive (\ i j -> iEnd i < iStart j) is
+
+-- | Range invariant.
+rangeInvariant :: Ord a => Range' a -> Bool
+rangeInvariant r =
+  consecutiveAndSeparated (rangeIntervals r)
+    &&
+  case r of
+    Range _ is -> not (null is)
+    NoRange    -> True
+
+-- | The file the range is pointing to.
+rangeFile :: Range -> SrcFile
+rangeFile NoRange     = Strict.Nothing
+rangeFile (Range f _) = f
+
+-- | The range's top-level module name, if any.
+--
+-- If there is no range, then 'Nothing' is returned. If there is a
+-- range without a module name, then @'Just' 'Nothing'@ is returned.
+rangeModule' :: Range -> Maybe (Maybe (TopLevelModuleName' Range))
+rangeModule' NoRange     = Nothing
+rangeModule' (Range f _) = Just $ case f of
+  Strict.Nothing -> Nothing
+  Strict.Just f  -> rangeFileName f
+
+-- | The range's top-level module name, if any.
+rangeModule :: Range -> Maybe (TopLevelModuleName' Range)
+rangeModule = join . rangeModule'
+
+-- | Conflate a range to its right margin.
+rightMargin :: Range -> Range
+rightMargin r@NoRange      = r
+rightMargin r@(Range f is) = case Seq.viewr is of
+  Seq.EmptyR -> __IMPOSSIBLE__
+  _ Seq.:> i -> intervalToRange f (i { iStart = iEnd i })
+
+-- | Wrapper to indicate that range should be printed.
+newtype PrintRange a = PrintRange a
+  deriving (Eq, Ord, HasRange, SetRange, KillRange)
+
+-- | Things that have a range are instances of this class.
+class HasRange a where
+  getRange :: a -> Range
+
+  default getRange :: (Foldable t, HasRange b, t b ~ a) => a -> Range
+  getRange = Fold.foldr fuseRange noRange
+  {-# INLINABLE getRange #-}
+
+instance HasRange Interval where
+    getRange i =
+      intervalToRange (srcFile (iStart i))
+                      (setIntervalFile () i)
+
+instance HasRange Range where
+    getRange = id
+
+instance HasRange () where
+  getRange _ = noRange
+
+instance HasRange Bool where
+    getRange _ = noRange
+
+instance HasRange (TopLevelModuleName' Range) where
+  getRange = moduleNameRange
+
+instance SetRange (TopLevelModuleName' Range) where
+  setRange r (TopLevelModuleName _ h x) = TopLevelModuleName r h x
+
+instance KillRange (TopLevelModuleName' Range) where
+  killRange (TopLevelModuleName _ h x) = TopLevelModuleName noRange h x
+
+-- | Precondition: The ranges of the list elements must point to the
+-- same file (or be empty).
+instance HasRange a => HasRange [a]
+
+-- | Precondition: The ranges of the list elements must point to the
+-- same file (or be empty).
+instance HasRange a => HasRange (List1 a)
+instance HasRange a => HasRange (List2 a)
+instance HasRange a => HasRange (Maybe a)
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b) => HasRange (a,b) where
+    getRange = uncurry fuseRange
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b, HasRange c) => HasRange (a,b,c) where
+    getRange (x,y,z) = getRange (x,(y,z))
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b, HasRange c, HasRange d) => HasRange (a,b,c,d) where
+    getRange (x,y,z,w) = getRange (x,(y,(z,w)))
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b, HasRange c, HasRange d, HasRange e) => HasRange (a,b,c,d,e) where
+    getRange (x,y,z,w,v) = getRange (x,(y,(z,(w,v))))
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b, HasRange c, HasRange d, HasRange e, HasRange f) => HasRange (a,b,c,d,e,f) where
+    getRange (x,y,z,w,v,u) = getRange (x,(y,(z,(w,(v,u)))))
+
+-- | Precondition: The ranges of the tuple elements must point to the
+-- same file (or be empty).
+instance (HasRange a, HasRange b, HasRange c, HasRange d, HasRange e, HasRange f, HasRange g) => HasRange (a,b,c,d,e,f,g) where
+    getRange (x,y,z,w,v,u,t) = getRange (x,(y,(z,(w,(v,(u,t))))))
+
+instance (HasRange a, HasRange b) => HasRange (Either a b) where
+    getRange = either getRange getRange
+
+-- | If it is also possible to set the range, this is the class.
+--
+--   Instances should satisfy @'getRange' ('setRange' r x) == r@.
+class HasRange a => SetRange a where
+  setRange :: Range -> a -> a
+
+  default setRange :: (Functor f, SetRange b, f b ~ a) => Range -> a -> a
+  setRange = fmap . setRange
+
+instance SetRange Range where
+  setRange = const
+
+instance SetRange a => SetRange [a]
+instance SetRange a => SetRange (Maybe a)
+
+-- | Killing the range of an object sets all range information to 'noRange'.
+class KillRange a where
+  killRange :: KillRangeT a
+
+  default killRange :: (Functor f, KillRange b, f b ~ a) => KillRangeT a
+  killRange = fmap killRange
+
+type KillRangeT a = a -> a
+
+class KILLRANGE t b where
+  killRangeN :: IsBase t ~ b => All KillRange (Domains t) =>
+                t -> t
+
+instance IsBase t ~ 'True => KILLRANGE t 'True where
+  {-# INLINE killRangeN #-}
+  killRangeN v = v
+
+instance KILLRANGE t (IsBase t) => KILLRANGE (a -> t) 'False where
+  {-# INLINE killRangeN #-}
+  killRangeN f a = killRangeN (f (killRange a))
+
+-- | Remove ranges in keys and values of a map.
+killRangeMap :: (KillRange k, KillRange v) => KillRangeT (Map k v)
+killRangeMap = Map.mapKeysMonotonic killRange . Map.map killRange
+
+instance KillRange Range where
+  killRange _ = noRange
+
+instance KillRange Void where
+  killRange = id
+
+instance KillRange () where
+  killRange = id
+
+instance KillRange Bool where
+  killRange = id
+
+instance KillRange Int where
+  killRange = id
+
+instance KillRange Integer where
+  killRange = id
+
+instance KillRange Permutation where
+  killRange = id
+
+-- | Overlaps with @KillRange [a]@.
+instance {-# OVERLAPPING #-} KillRange String where
+  killRange = id
+
+instance {-# OVERLAPPABLE #-} KillRange a => KillRange [a]
+instance {-# OVERLAPPABLE #-} KillRange a => KillRange (Map k a)
+
+instance KillRange a => KillRange (Drop a)
+instance KillRange a => KillRange (List1 a)
+instance KillRange a => KillRange (List2 a)
+instance KillRange a => KillRange (Maybe a)
+instance KillRange a => KillRange (Strict.Maybe a)
+
+instance {-# OVERLAPPABLE #-} (Ord a, KillRange a) => KillRange (Set a) where
+  killRange = Set.map killRange
+
+instance (KillRange a, KillRange b) => KillRange (a, b) where
+  killRange (x, y) = (killRange x, killRange y)
+
+instance (KillRange a, KillRange b, KillRange c) =>
+         KillRange (a, b, c) where
+  killRange (x, y, z) = killRangeN (,,) x y z
+
+instance (KillRange a, KillRange b, KillRange c, KillRange d) =>
+         KillRange (a, b, c, d) where
+  killRange (x, y, z, u) = killRangeN (,,,) x y z u
+
+instance (KillRange a, KillRange b) => KillRange (Either a b) where
+  killRange (Left  x) = Left  $ killRange x
+  killRange (Right x) = Right $ killRange x
+
+{--------------------------------------------------------------------------
+    Functions on positions and ranges
+ --------------------------------------------------------------------------}
+
+-- | The first position in a file: position 1, line 1, column 1.
+startPos' :: a -> Position' a
+startPos' f = Pn
+  { srcFile = f
+  , posPos  = 1
+  , posLine = 1
+  , posCol  = 1
+  }
+
+-- | The first position in a file: position 1, line 1, column 1.
+startPos :: Maybe RangeFile -> Position
+startPos = startPos' . Strict.toStrict
+
+-- | Ranges between two unknown positions
+noRange :: Range' a
+noRange = NoRange
+
+-- | Advance the position by one character.
+--   A newline character (@'\n'@) moves the position to the first
+--   character in the next line. Any other character moves the
+--   position to the next column.
+movePos :: Position' a -> Char -> Position' a
+movePos (Pn f p l c) '\n' = Pn f (p + 1) (l + 1) 1
+movePos (Pn f p l c) _    = Pn f (p + 1) l (c + 1)
+
+-- | Advance the position by a string.
+--
+--   > movePosByString = foldl' movePos
+movePosByString :: Foldable t => Position' a -> t Char -> Position' a
+movePosByString = Fold.foldl' movePos
+
+-- | Backup the position by one character.
+--
+-- Precondition: The character must not be @'\n'@.
+backupPos :: Position' a -> Position' a
+backupPos (Pn f p l c) = Pn f (p - 1) l (c - 1)
+
+-- | Converts a file name and two positions to a range.
+posToRange' ::
+  a -> PositionWithoutFile -> PositionWithoutFile -> Range' a
+posToRange' f p1 p2 = intervalToRange f (posToInterval () p1 p2)
+
+-- | Converts two positions to a range.
+--
+-- Precondition: The positions have to point to the same file.
+posToRange :: Position' a -> Position' a -> Range' a
+posToRange p1 p2 =
+  posToRange' (srcFile p1) (p1 { srcFile = () }) (p2 { srcFile = () })
+
+-- | Converts a file name and an interval to a range.
+intervalToRange :: a -> IntervalWithoutFile -> Range' a
+intervalToRange f i = Range f (Seq.singleton i)
+
+-- | Converts a range to an interval, if possible.
+rangeToIntervalWithFile :: Range' a -> Maybe (Interval' a)
+rangeToIntervalWithFile NoRange      = Nothing
+rangeToIntervalWithFile (Range f is) = case (Seq.viewl is, Seq.viewr is) of
+  (head Seq.:< _, _ Seq.:> last) -> Just $ setIntervalFile f $
+                                      Interval { iStart = iStart head
+                                               , iEnd   = iEnd   last
+                                               }
+  _                              -> __IMPOSSIBLE__
+
+-- | Converts a range to an interval, if possible. Note that the
+-- information about the source file is lost.
+rangeToInterval :: Range' a -> Maybe IntervalWithoutFile
+rangeToInterval NoRange      = Nothing
+rangeToInterval (Range _ is) = case (Seq.viewl is, Seq.viewr is) of
+  (head Seq.:< _, _ Seq.:> last) -> Just $
+                                      Interval { iStart = iStart head
+                                               , iEnd   = iEnd   last
+                                               }
+  _                              -> __IMPOSSIBLE__
+
+-- | Returns the shortest continuous range containing the given one.
+continuous :: Range' a -> Range' a
+continuous NoRange = NoRange
+continuous r@(Range f _) = case rangeToInterval r of
+  Nothing -> __IMPOSSIBLE__
+  Just i  -> intervalToRange f i
+
+-- | Removes gaps between intervals on the same line.
+continuousPerLine :: Ord a => Range' a -> Range' a
+continuousPerLine r@NoRange     = r
+continuousPerLine r@(Range f _) =
+  Range f (Seq.unfoldr step (rangeIntervals r))
+  where
+  step []  = Nothing
+  step [i] = Just (i, [])
+  step (i : is@(j : js))
+    | sameLine  = step (fuseIntervals i j : js)
+    | otherwise = Just (i, is)
+    where
+    sameLine = posLine (iEnd i) == posLine (iStart j)
+
+-- | The initial position in the range, if any.
+rStart' :: Range' a -> Maybe PositionWithoutFile
+rStart' r = iStart <$> rangeToInterval r
+
+-- | The initial position in the range, if any.
+rStart :: Range' a -> Maybe (Position' a)
+rStart NoRange       = Nothing
+rStart r@(Range f _) = (\p -> p { srcFile = f }) <$> rStart' r
+
+-- | The position after the final position in the range, if any.
+rEnd' :: Range' a -> Maybe PositionWithoutFile
+rEnd' r = iEnd <$> rangeToInterval r
+
+-- | The position after the final position in the range, if any.
+rEnd :: Range' a -> Maybe (Position' a)
+rEnd NoRange       = Nothing
+rEnd r@(Range f _) = (\p -> p { srcFile = f }) <$> rEnd' r
+
+-- | Finds the least interval which covers the arguments.
+--
+-- Precondition: The intervals must point to the same file.
+fuseIntervals :: Ord a => Interval' a -> Interval' a -> Interval' a
+fuseIntervals x y = Interval { iStart = s, iEnd = e }
+    where
+    s = headWithDefault __IMPOSSIBLE__ $ sort [iStart x, iStart y]
+    e = lastWithDefault __IMPOSSIBLE__ $ sort [iEnd   x, iEnd   y]
+
+-- | @fuseRanges r r'@ unions the ranges @r@ and @r'@.
+--
+--   Meaning it finds the least range @r0@ that covers @r@ and @r'@.
+--
+-- Precondition: The ranges must point to the same file (or be empty).
+fuseRanges :: (Ord a) => Range' a -> Range' a -> Range' a
+fuseRanges NoRange       is2           = is2
+fuseRanges is1           NoRange       = is1
+fuseRanges (Range f is1) (Range _ is2) = Range f (fuse is1 is2)
+  where
+  fuse is1 is2 = case (Seq.viewl is1, Seq.viewr is1,
+                       Seq.viewl is2, Seq.viewr is2) of
+    (Seq.EmptyL, _, _, _) -> is2
+    (_, _, Seq.EmptyL, _) -> is1
+    (s1 Seq.:< r1, l1 Seq.:> e1, s2 Seq.:< r2, l2 Seq.:> e2)
+        -- Special cases.
+      | iEnd e1 <  iStart s2 -> is1 Seq.>< is2
+      | iEnd e2 <  iStart s1 -> is2 Seq.>< is1
+      | iEnd e1 == iStart s2 -> mergeTouching l1 e1 s2 r2
+      | iEnd e2 == iStart s1 -> mergeTouching l2 e2 s1 r1
+        -- General cases.
+      | iEnd s1 <  iStart s2 -> outputLeftPrefix s1 r1 s2 is2
+      | iEnd s2 <  iStart s1 -> outputLeftPrefix s2 r2 s1 is1
+      | iEnd s1 <  iEnd   s2 -> fuseSome s1 r1 s2 r2
+      | otherwise            -> fuseSome s2 r2 s1 r1
+    _ -> __IMPOSSIBLE__
+
+  mergeTouching l e s r = l Seq.>< i Seq.<| r
+    where
+    i = Interval { iStart = iStart e, iEnd = iEnd s }
+
+  -- The following two functions could use binary search instead of
+  -- linear.
+
+  outputLeftPrefix s1 r1 s2 is2 = s1 Seq.<| r1' Seq.>< fuse r1'' is2
+    where
+    (r1', r1'') = Seq.spanl (\s -> iEnd s < iStart s2) r1
+
+  fuseSome s1 r1 s2 r2 = fuse r1' (fuseIntervals s1 s2 Seq.<| r2)
+    where
+    r1' = Seq.dropWhileL (\s -> iEnd s <= iEnd s2) r1
+
+{-# INLINE fuseRange #-}
+-- | Precondition: The ranges must point to the same file (or be
+-- empty).
+fuseRange :: (HasRange u, HasRange t) => u -> t -> Range
+fuseRange x y = fuseRanges (getRange x) (getRange y)
+
+-- | @beginningOf r@ is an empty range (a single, empty interval)
+-- positioned at the beginning of @r@. If @r@ does not have a
+-- beginning, then 'noRange' is returned.
+beginningOf :: Range -> Range
+beginningOf NoRange       = NoRange
+beginningOf r@(Range f _) = case rStart' r of
+  Nothing  -> __IMPOSSIBLE__
+  Just pos -> posToRange' f pos pos
+
+-- | @beginningOfFile r@ is an empty range (a single, empty interval)
+-- at the beginning of @r@'s starting position's file. If there is no
+-- such position, then an empty range is returned.
+beginningOfFile :: Range -> Range
+beginningOfFile NoRange     = NoRange
+beginningOfFile (Range f _) = posToRange' f p p
+  where p = startPos' ()
+
+-- | @x \`withRangeOf\` y@ sets the range of @x@ to the range of @y@.
+withRangeOf :: (SetRange t, HasRange u) => t -> u -> t
+x `withRangeOf` y = setRange (getRange y) x
+
+-- | Interleaves two streams of ranged elements
+--
+--   It will report the conflicts as a list of conflicting pairs.
+--   In case of conflict, the element with the earliest start position
+--   is placed first. In case of a tie, the element with the earliest
+--   ending position is placed first. If both tie, the element from the
+--   first list is placed first.
+interleaveRanges :: (HasRange a) => [a] -> [a] -> ([a], [(a,a)])
+interleaveRanges as bs = runWriter $ go as bs
+  where
+    go []         as = return as
+    go as         [] = return as
+    go as@(a:as') bs@(b:bs') =
+      let ra = getRange a
+          rb = getRange b
+
+          ra0 = rStart ra
+          rb0 = rStart rb
+
+          ra1 = rEnd ra
+          rb1 = rEnd rb
+      in
+      if ra1 <= rb0 then
+        (a:) <$> go as' bs
+      else if rb1 <= ra0 then
+        (b:) <$> go as bs'
+      else do
+        tell [(a,b)]
+        if ra0 < rb0 || (ra0 == rb0 && ra1 <= rb1) then
+          (a:) <$> go as' bs
+        else
+          (b:) <$> go as bs'
diff --git a/src/full/Agda/Syntax/Position.hs-boot b/src/full/Agda/Syntax/Position.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Position.hs-boot
@@ -0,0 +1,3 @@
+module Agda.Syntax.Position where
+
+class KillRange a
diff --git a/src/full/Agda/Syntax/Reflected.hs b/src/full/Agda/Syntax/Reflected.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Reflected.hs
@@ -0,0 +1,76 @@
+{-# OPTIONS_GHC -fwarn-missing-signatures #-}
+
+module Agda.Syntax.Reflected where
+
+import Data.Text (Text)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Literal
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Internal (Dom)
+
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+
+type Args       = [Arg Term]
+
+data Elim' a = Apply (Arg a) -- no record projections for now
+  deriving (Show)
+type Elim = Elim' Term
+type Elims = [Elim]
+
+argsToElims :: Args -> Elims
+argsToElims = map Apply
+
+data Abs a = Abs String a
+  deriving (Show)
+
+data Term = Var Int Elims
+          | Con QName Elims
+          | Def QName Elims
+          | Meta MetaId Elims
+          | Lam Hiding (Abs Term)
+          | ExtLam (List1 Clause) Elims
+          | Pi (Dom Type) (Abs Type)
+          | Sort Sort
+          | Lit Literal
+          | Unknown
+  deriving (Show)
+
+type Type = Term
+
+data Sort = SetS Term
+          | LitS Integer
+          | PropS Term
+          | PropLitS Integer
+          | InfS Integer
+          | UnknownS
+  deriving (Show)
+
+data Pattern = ConP QName [Arg Pattern]
+             | DotP Term
+             | VarP Int
+             | LitP Literal
+             | AbsurdP Int
+             | ProjP QName
+  deriving (Show)
+
+data Clause
+  = Clause
+    { clauseTel  :: [(Text, Arg Type)]
+    , clausePats :: [Arg Pattern]
+    , clauseRHS  :: Term
+    }
+  | AbsurdClause
+    { clauseTel  :: [(Text, Arg Type)]
+    , clausePats :: [Arg Pattern]
+    }
+  deriving (Show)
+
+data Definition = FunDef Type [Clause]
+                | DataDef   -- nothing for now
+                | RecordDef -- nothing for now
+                | DataConstructor
+                | Axiom
+                | Primitive
+  deriving (Show)
diff --git a/src/full/Agda/Syntax/Scope/Base.hs b/src/full/Agda/Syntax/Scope/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Scope/Base.hs
@@ -0,0 +1,1451 @@
+{-# LANGUAGE GADTs              #-}
+
+{-| This module defines the notion of a scope and operations on scopes.
+-}
+module Agda.Syntax.Scope.Base where
+
+import Prelude hiding ( null, length )
+
+import Control.Arrow (first, second, (&&&))
+import Control.DeepSeq
+import Control.Monad
+
+import Data.Either (partitionEithers)
+import Data.Foldable ( length, toList )
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Maybe
+import Data.Semigroup ( Semigroup(..) )
+
+import GHC.Generics (Generic)
+
+import Agda.Benchmarking
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Fixity
+import Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Concrete.Name as C
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Fixity as C
+
+import Agda.Utils.AssocList (AssocList)
+import qualified Agda.Utils.AssocList as AssocList
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import Agda.Utils.List2 ( List2 )
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.List2 as List2
+import Agda.Utils.Maybe (filterMaybe)
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty hiding ((<>))
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Singleton
+import qualified Agda.Utils.Map as Map
+
+import Agda.Utils.Impossible
+
+-- * Scope representation
+
+-- | A scope is a named collection of names partitioned into public and private
+--   names.
+data Scope = Scope
+      { scopeName           :: A.ModuleName
+      , scopeParents        :: [A.ModuleName]
+      , scopeNameSpaces     :: ScopeNameSpaces
+      , scopeImports        :: Map C.QName A.ModuleName
+      , scopeDatatypeModule :: Maybe DataOrRecordModule
+      }
+  deriving (Eq, Show, Generic)
+
+data DataOrRecordModule
+  = IsDataModule
+  | IsRecordModule
+  deriving (Show, Eq, Enum, Bounded, Generic)
+
+-- | See 'Agda.Syntax.Common.Access'.
+data NameSpaceId
+  = PrivateNS        -- ^ Things not exported by this module.
+  | PublicNS         -- ^ Things defined and exported by this module.
+  | ImportedNS       -- ^ Things from open public, exported by this module.
+  deriving (Eq, Bounded, Enum, Show, Generic)
+
+allNameSpaces :: [NameSpaceId]
+allNameSpaces = [minBound..maxBound]
+
+type ScopeNameSpaces = [(NameSpaceId, NameSpace)]
+
+localNameSpace :: Access -> NameSpaceId
+localNameSpace PublicAccess    = PublicNS
+localNameSpace PrivateAccess{} = PrivateNS
+
+nameSpaceAccess :: NameSpaceId -> Access
+nameSpaceAccess PrivateNS = PrivateAccess Inserted
+nameSpaceAccess _         = PublicAccess
+
+-- | Get a 'NameSpace' from 'Scope'.
+scopeNameSpace :: NameSpaceId -> Scope -> NameSpace
+scopeNameSpace ns = fromMaybe __IMPOSSIBLE__ . lookup ns . scopeNameSpaces
+
+-- | A lens for 'scopeNameSpaces'
+updateScopeNameSpaces :: (ScopeNameSpaces -> ScopeNameSpaces) -> Scope -> Scope
+updateScopeNameSpaces f s = s { scopeNameSpaces = f (scopeNameSpaces s) }
+
+-- | ``Monadic'' lens (Functor sufficient).
+updateScopeNameSpacesM ::
+  (Functor m) => (ScopeNameSpaces -> m ScopeNameSpaces) -> Scope -> m Scope
+updateScopeNameSpacesM f s = for (f $ scopeNameSpaces s) $ \ x ->
+  s { scopeNameSpaces = x }
+
+-- | The complete information about the scope at a particular program point
+--   includes the scope stack, the local variables, and the context precedence.
+data ScopeInfo = ScopeInfo
+      { _scopeCurrent       :: A.ModuleName
+      , _scopeModules       :: Map A.ModuleName Scope
+      , _scopeVarsToBind    :: LocalVars     -- ^ The variables that will be bound at the end
+                                             --   of the current block of variables (i.e. clause).
+                                             --   We collect them here instead of binding them
+                                             --   immediately so we can avoid shadowing between
+                                             --   variables in the same variable block.
+      , _scopeLocals        :: LocalVars
+      , _scopePrecedence    :: !PrecedenceStack
+      , _scopeInverseName   :: NameMap
+      , _scopeInverseModule :: ModuleMap
+      , _scopeInScope       :: InScopeSet
+      , _scopeFixities      :: C.Fixities    -- ^ Maps concrete names C.Name to fixities
+      , _scopePolarities    :: C.Polarities  -- ^ Maps concrete names C.Name to polarities
+      }
+  deriving (Show, Generic)
+
+-- | For the sake of highlighting, the '_scopeInverseName' map also stores
+--   the 'KindOfName' of an @A.QName@.
+data NameMapEntry = NameMapEntry
+  { qnameKind     :: KindOfName     -- ^ The 'anameKind'.
+  , qnameConcrete :: List1 C.QName  -- ^ Possible renderings of the abstract name.
+  }
+  deriving (Show, Generic)
+
+-- | Invariant: the 'KindOfName' components should be equal
+--   whenever we have to concrete renderings of an abstract name.
+instance Semigroup NameMapEntry where
+  NameMapEntry k xs <> NameMapEntry _ ys = NameMapEntry k (xs <> ys)
+
+type NameMap   = Map A.QName      NameMapEntry
+type ModuleMap = Map A.ModuleName [C.QName]
+-- type ModuleMap = Map A.ModuleName (List1 C.QName)
+
+instance Eq ScopeInfo where
+  ScopeInfo c1 m1 v1 l1 p1 _ _ _ _ _ == ScopeInfo c2 m2 v2 l2 p2 _ _ _ _ _ =
+    c1 == c2 && m1 == m2 && v1 == v2 && l1 == l2 && p1 == p2
+
+-- | Local variables.
+type LocalVars = AssocList C.Name LocalVar
+
+-- | For each bound variable, we want to know whether it was bound by a
+--   λ, Π, module telescope, pattern, or @let@.
+data BindingSource
+  = LambdaBound  -- ^ @λ@ (currently also used for @Π@ and module parameters)
+  | PatternBound -- ^ @f ... =@
+  | LetBound     -- ^ @let ... in@
+  | WithBound    -- ^ @| ... in q@
+  deriving (Show, Eq, Generic)
+
+instance Pretty BindingSource where
+  pretty = \case
+    LambdaBound  -> "local"
+    PatternBound -> "pattern"
+    LetBound     -> "let-bound"
+    WithBound    -> "with-bound"
+
+-- | A local variable can be shadowed by an import.
+--   In case of reference to a shadowed variable, we want to report
+--   a scope error.
+data LocalVar = LocalVar
+  { localVar           :: A.Name
+    -- ^ Unique ID of local variable.
+  , localBindingSource :: BindingSource
+    -- ^ Kind of binder used to introduce the variable (@λ@, @let@, ...).
+  , localShadowedBy    :: [AbstractName]
+     -- ^ If this list is not empty, the local variable is
+     --   shadowed by one or more imports.
+  }
+  deriving (Show, Generic)
+
+instance Eq LocalVar where
+  (==) = (==) `on` localVar
+
+instance Ord LocalVar where
+  compare = compare `on` localVar
+
+-- | We show shadowed variables as prefixed by a ".", as not in scope.
+instance Pretty LocalVar where
+  pretty (LocalVar x _ []) = pretty x
+  pretty (LocalVar x _ xs) = "." P.<> pretty x
+
+-- | Shadow a local name by a non-empty list of imports.
+shadowLocal :: List1 AbstractName -> LocalVar -> LocalVar
+shadowLocal ys (LocalVar x b zs) = LocalVar x b (List1.toList ys ++ zs)
+
+-- | Treat patternBound variable as a module parameter
+patternToModuleBound :: LocalVar -> LocalVar
+patternToModuleBound x
+ | localBindingSource x == PatternBound =
+   x { localBindingSource = LambdaBound }
+ | otherwise                     = x
+
+-- | Project name of unshadowed local variable.
+notShadowedLocal :: LocalVar -> Maybe A.Name
+notShadowedLocal (LocalVar x _ []) = Just x
+notShadowedLocal _ = Nothing
+
+-- | Get all locals that are not shadowed __by imports__.
+notShadowedLocals :: LocalVars -> AssocList C.Name A.Name
+notShadowedLocals = mapMaybe $ \ (c,x) -> (c,) <$> notShadowedLocal x
+
+-- | Lenses for ScopeInfo components
+scopeCurrent :: Lens' ScopeInfo A.ModuleName
+scopeCurrent f s =
+  f (_scopeCurrent s) <&>
+  \x -> s { _scopeCurrent = x }
+
+scopeModules :: Lens' ScopeInfo (Map A.ModuleName Scope)
+scopeModules f s =
+  f (_scopeModules s) <&>
+  \x -> s { _scopeModules = x }
+
+scopeVarsToBind :: Lens' ScopeInfo LocalVars
+scopeVarsToBind f s =
+  f (_scopeVarsToBind s) <&>
+  \x -> s { _scopeVarsToBind = x }
+
+scopeLocals :: Lens' ScopeInfo LocalVars
+scopeLocals f s =
+  f (_scopeLocals s) <&>
+  \x -> s { _scopeLocals = x }
+
+scopePrecedence :: Lens' ScopeInfo PrecedenceStack
+scopePrecedence f s =
+  f (_scopePrecedence s) <&>
+  \x -> s { _scopePrecedence = x }
+
+scopeInverseName :: Lens' ScopeInfo NameMap
+scopeInverseName f s =
+  f (_scopeInverseName s) <&>
+  \x -> s { _scopeInverseName = x }
+
+scopeInverseModule :: Lens' ScopeInfo ModuleMap
+scopeInverseModule f s =
+  f (_scopeInverseModule s) <&>
+  \x -> s { _scopeInverseModule = x }
+
+scopeInScope :: Lens' ScopeInfo InScopeSet
+scopeInScope f s =
+  f (_scopeInScope s) <&>
+  \x -> s { _scopeInScope = x }
+
+scopeFixities :: Lens' ScopeInfo C.Fixities
+scopeFixities f s =
+  f (_scopeFixities s) <&>
+  \x -> s { _scopeFixities = x }
+
+scopePolarities :: Lens' ScopeInfo C.Polarities
+scopePolarities f s =
+  f (_scopePolarities s) <&>
+  \x -> s { _scopePolarities = x }
+
+scopeFixitiesAndPolarities :: Lens' ScopeInfo (C.Fixities, C.Polarities)
+scopeFixitiesAndPolarities f s =
+  f' (_scopeFixities s) (_scopePolarities s) <&>
+  \ (fixs, pols) -> s { _scopeFixities = fixs, _scopePolarities = pols }
+  where
+  -- Andreas, 2019-08-18: strict matching avoids space leak, see #1829.
+  f' !fixs !pols = f (fixs, pols)
+  -- Andrea comments on https://github.com/agda/agda/issues/1829#issuecomment-522312084
+  -- on a naive version without the bang patterns:
+  --
+  -- useScope (because of useR) forces the result of projecting the
+  -- lens, this usually prevents retaining the whole structure when we
+  -- only need a field.  However your combined lens adds an extra layer
+  -- of laziness with the pairs, so the actual projections remain
+  -- unforced.
+  --
+  -- I guess scopeFixitiesAndPolarities could add some strictness when building the pair?
+
+-- | Lens for 'scopeVarsToBind'.
+updateVarsToBind :: (LocalVars -> LocalVars) -> ScopeInfo -> ScopeInfo
+updateVarsToBind = over scopeVarsToBind
+
+setVarsToBind :: LocalVars -> ScopeInfo -> ScopeInfo
+setVarsToBind = set scopeVarsToBind
+
+-- | Lens for 'scopeLocals'.
+updateScopeLocals :: (LocalVars -> LocalVars) -> ScopeInfo -> ScopeInfo
+updateScopeLocals = over scopeLocals
+
+setScopeLocals :: LocalVars -> ScopeInfo -> ScopeInfo
+setScopeLocals = set scopeLocals
+
+------------------------------------------------------------------------
+-- * Name spaces
+--
+-- Map concrete names to lists of abstract names.
+------------------------------------------------------------------------
+
+-- | A @NameSpace@ contains the mappings from concrete names that the user can
+--   write to the abstract fully qualified names that the type checker wants to
+--   read.
+data NameSpace = NameSpace
+      { nsNames   :: NamesInScope
+        -- ^ Maps concrete names to a list of abstract names.
+      , nsModules :: ModulesInScope
+        -- ^ Maps concrete module names to a list of abstract module names.
+      , nsInScope :: InScopeSet
+        -- ^ All abstract names targeted by a concrete name in scope.
+        --   Computed by 'recomputeInScopeSets'.
+      }
+  deriving (Eq, Show, Generic)
+
+type ThingsInScope a = Map C.Name (List1 a)
+type NamesInScope    = ThingsInScope AbstractName
+type ModulesInScope  = ThingsInScope AbstractModule
+type InScopeSet      = Set A.QName
+
+-- | Set of types consisting of exactly 'AbstractName' and 'AbstractModule'.
+--
+--   A GADT just for some dependent-types trickery.
+data InScopeTag a where
+  NameTag   :: InScopeTag AbstractName
+  ModuleTag :: InScopeTag AbstractModule
+
+-- | Type class for some dependent-types trickery.
+class Ord a => InScope a where
+  inScopeTag :: InScopeTag a
+
+instance InScope AbstractName where
+  inScopeTag = NameTag
+
+instance InScope AbstractModule where
+  inScopeTag = ModuleTag
+
+-- | @inNameSpace@ selects either the name map or the module name map from
+--   a 'NameSpace'.  What is selected is determined by result type
+--   (using the dependent-type trickery).
+inNameSpace :: forall a. InScope a => NameSpace -> ThingsInScope a
+inNameSpace = case inScopeTag :: InScopeTag a of
+  NameTag   -> nsNames
+  ModuleTag -> nsModules
+
+-- | Non-dependent tag for name or module.
+data NameOrModule = NameNotModule | ModuleNotName
+  deriving (Eq, Ord, Show, Enum, Bounded, Generic)
+
+------------------------------------------------------------------------
+-- * Decorated names
+--
+-- - What kind of name? (defined, constructor...)
+-- - Where does the name come from? (to explain to user)
+------------------------------------------------------------------------
+
+-- | For the sake of parsing left-hand sides, we distinguish
+--   constructor and record field names from defined names.
+
+-- Note: order does matter in this enumeration, see 'isDefName'.
+data KindOfName
+  = ConName                  -- ^ Constructor name ('Inductive' or don't know).
+  | CoConName                -- ^ Constructor name (definitely 'CoInductive').
+  | FldName                  -- ^ Record field name.
+  | PatternSynName           -- ^ Name of a pattern synonym.
+  | GeneralizeName           -- ^ Name to be generalized
+  | DisallowedGeneralizeName -- ^ Generalizable variable from a let open
+  | MacroName                -- ^ Name of a macro
+  | QuotableName             -- ^ A name that can only be quoted.
+  -- Previous category @DefName@:
+  -- (Refined in a flat manner as Enum and Bounded are not hereditary.)
+  | DataName                 -- ^ Name of a @data@.
+  | RecName                  -- ^ Name of a @record@.
+  | FunName                  -- ^ Name of a defined function.
+  | AxiomName                -- ^ Name of a @postulate@.
+  | PrimName                 -- ^ Name of a @primitive@.
+  | OtherDefName             -- ^ A @DefName@, but either other kind or don't know which kind.
+  -- End @DefName@.  Keep these together in sequence, for sake of @isDefName@!
+  deriving (Eq, Ord, Show, Enum, Bounded, Generic)
+
+isDefName :: KindOfName -> Bool
+isDefName = (>= DataName)
+
+isConName :: KindOfName -> Maybe Induction
+isConName = \case
+  ConName   -> Just Inductive
+  CoConName -> Just CoInductive
+  _ -> Nothing
+
+conKindOfName :: Induction -> KindOfName
+conKindOfName = \case
+  Inductive   -> ConName
+  CoInductive -> CoConName
+
+-- | For ambiguous constructors, we might have both alternatives of 'Induction'.
+--   In this case, we default to 'ConName'.
+conKindOfName' :: Foldable t => t Induction -> KindOfName
+conKindOfName' = conKindOfName . approxConInduction
+
+-- | For ambiguous constructors, we might have both alternatives of 'Induction'.
+--   In this case, we default to 'Inductive'.
+approxConInduction :: Foldable t => t Induction -> Induction
+approxConInduction = fromMaybe Inductive . exactConInduction
+
+exactConInduction :: Foldable t => t Induction -> Maybe Induction
+exactConInduction is = case toList is of
+  [CoInductive] -> Just CoInductive
+  [Inductive]   -> Just Inductive
+  _ -> Nothing
+
+-- | Only return @[Co]ConName@ if no ambiguity.
+exactConName :: Foldable t => t Induction -> Maybe KindOfName
+exactConName = fmap conKindOfName . exactConInduction
+
+-- | A set of 'KindOfName', for the sake of 'elemKindsOfNames'.
+data KindsOfNames
+  = AllKindsOfNames
+  | SomeKindsOfNames   (Set KindOfName)  -- ^ Only these kinds.
+  | ExceptKindsOfNames (Set KindOfName)  -- ^ All but these Kinds.
+
+elemKindsOfNames :: KindOfName -> KindsOfNames -> Bool
+elemKindsOfNames k = \case
+  AllKindsOfNames       -> True
+  SomeKindsOfNames   ks -> k `Set.member` ks
+  ExceptKindsOfNames ks -> k `Set.notMember` ks
+
+allKindsOfNames :: KindsOfNames
+allKindsOfNames = AllKindsOfNames
+
+someKindsOfNames :: [KindOfName] -> KindsOfNames
+someKindsOfNames = SomeKindsOfNames . Set.fromList
+
+exceptKindsOfNames :: [KindOfName] -> KindsOfNames
+exceptKindsOfNames = ExceptKindsOfNames . Set.fromList
+
+-- | Decorate something with 'KindOfName'
+
+data WithKind a = WithKind
+  { theKind     :: KindOfName
+  , kindedThing :: a
+  } deriving (Show, Eq, Ord, Functor, Foldable, Traversable)
+
+-- | Where does a name come from?
+--
+--   This information is solely for reporting to the user,
+--   see 'Agda.Interaction.InteractionTop.whyInScope'.
+data WhyInScope
+  = Defined
+    -- ^ Defined in this module.
+  | Opened C.QName WhyInScope
+    -- ^ Imported from another module.
+  | Applied C.QName WhyInScope
+    -- ^ Imported by a module application.
+  deriving (Show, Generic)
+
+-- | A decoration of 'Agda.Syntax.Abstract.Name.QName'.
+data AbstractName = AbsName
+  { anameName    :: A.QName
+    -- ^ The resolved qualified name.
+  , anameKind    :: KindOfName
+    -- ^ The kind (definition, constructor, record field etc.).
+  , anameLineage :: WhyInScope
+    -- ^ Explanation where this name came from.
+  , anameMetadata :: NameMetadata
+    -- ^ Additional information needed during scope checking. Currently used
+    --   for generalized data/record params.
+  }
+  deriving (Show, Generic)
+
+data NameMetadata = NoMetadata
+                  | GeneralizedVarsMetadata (Map A.QName A.Name)
+  deriving (Show, Generic)
+
+-- | A decoration of abstract syntax module names.
+data AbstractModule = AbsModule
+  { amodName    :: A.ModuleName
+    -- ^ The resolved module name.
+  , amodLineage :: WhyInScope
+    -- ^ Explanation where this name came from.
+  }
+  deriving (Show, Generic)
+
+instance Eq AbstractName where
+  (==) = (==) `on` anameName
+
+instance Ord AbstractName where
+  compare = compare `on` anameName
+
+instance LensFixity AbstractName where
+  lensFixity = lensAnameName . lensFixity
+
+-- | Van Laarhoven lens on 'anameName'.
+lensAnameName :: Lens' AbstractName A.QName
+lensAnameName f am = f (anameName am) <&> \ m -> am { anameName = m }
+
+instance Eq AbstractModule where
+  (==) = (==) `on` amodName
+
+instance Ord AbstractModule where
+  compare = compare `on` amodName
+
+-- | Van Laarhoven lens on 'amodName'.
+lensAmodName :: Lens' AbstractModule A.ModuleName
+lensAmodName f am = f (amodName am) <&> \ m -> am { amodName = m }
+
+
+data ResolvedName
+  = -- | Local variable bound by λ, Π, module telescope, pattern, @let@.
+    VarName
+    { resolvedVar           :: A.Name
+    , resolvedBindingSource :: BindingSource    -- ^ What kind of binder?
+    }
+
+  | -- | Function, data/record type, postulate.
+    DefinedName Access AbstractName A.Suffix -- ^ 'anameKind' can be 'DefName', 'MacroName', 'QuotableName'.
+
+  | -- | Record field name.  Needs to be distinguished to parse copatterns.
+    FieldName (List1 AbstractName)       -- ^ @('FldName' ==) . 'anameKind'@ for all names.
+
+  | -- | Data or record constructor name.
+    ConstructorName (Set Induction) (List1 AbstractName) -- ^ @isJust . 'isConName' . 'anameKind'@ for all names.
+
+  | -- | Name of pattern synonym.
+    PatternSynResName (List1 AbstractName) -- ^ @('PatternSynName' ==) . 'anameKind'@ for all names.
+
+  | -- | Unbound name.
+    UnknownName
+  deriving (Show, Eq, Generic)
+
+instance Pretty ResolvedName where
+  pretty = \case
+    VarName x b          -> pretty b <+> "variable" <+> pretty x
+    DefinedName a x s    -> pretty a      <+> (pretty x <> pretty s)
+    FieldName xs         -> "field"       <+> pretty xs
+    ConstructorName _ xs -> "constructor" <+> pretty xs
+    PatternSynResName x  -> "pattern"     <+> pretty x
+    UnknownName          -> "<unknown name>"
+
+instance Pretty A.Suffix where
+  pretty NoSuffix   = mempty
+  pretty (Suffix i) = text (show i)
+
+-- | Why is a resolved name ambiguous?  What did it resolve to?
+--
+--   Invariant (statically enforced): At least two resolvents in total.
+data AmbiguousNameReason
+  = AmbiguousLocalVar LocalVar (List1 AbstractName)
+      -- ^ The name resolves both to a local variable and some declared names.
+  | AmbiguousDeclName (List2 AbstractName)
+      -- ^ The name resolves to at least 2 declared names.
+  deriving (Show, Generic)
+
+-- | The flat list of ambiguous names in 'AmbiguousNameReason'.
+ambiguousNamesInReason :: AmbiguousNameReason -> List2 (A.QName)
+ambiguousNamesInReason = \case
+  AmbiguousLocalVar (LocalVar y _ _) xs -> List2.cons (A.qualify_ y) $ fmap anameName xs
+  AmbiguousDeclName xs -> fmap anameName xs
+
+data WhyInScopeData
+  = WhyInScopeData
+      C.QName
+        -- ^ The name @x@ this explanation is about.
+      FilePath
+        -- ^ The directory in which the current module resides.
+      (Maybe LocalVar)
+        -- ^ The local variable that @x@ could denote, if any.
+      [AbstractName]
+        -- ^ The defined names that @x@ could denote.
+      [AbstractModule]
+        -- ^ The modules that @x@ could denote.
+
+whyInScopeDataFromAmbiguousNameReason :: C.QName -> AmbiguousNameReason -> WhyInScopeData
+whyInScopeDataFromAmbiguousNameReason q = \case
+  AmbiguousLocalVar x ys -> WhyInScopeData q empty (Just x) (toList ys) empty
+  AmbiguousDeclName ys   -> WhyInScopeData q empty Nothing  (toList ys) empty
+
+-- * Operations on name and module maps.
+
+mergeNames :: Eq a => ThingsInScope a -> ThingsInScope a -> ThingsInScope a
+mergeNames = Map.unionWith List1.union
+
+mergeNamesMany :: Eq a => [ThingsInScope a] -> ThingsInScope a
+mergeNamesMany = Map.unionsWith List1.union
+
+------------------------------------------------------------------------
+-- * Operations on name spaces
+------------------------------------------------------------------------
+
+-- | The empty name space.
+emptyNameSpace :: NameSpace
+emptyNameSpace = NameSpace Map.empty Map.empty Set.empty
+
+
+-- | Map functions over the names and modules in a name space.
+mapNameSpace :: (NamesInScope   -> NamesInScope  ) ->
+                (ModulesInScope -> ModulesInScope) ->
+                (InScopeSet     -> InScopeSet    ) ->
+                NameSpace -> NameSpace
+mapNameSpace fd fm fs ns =
+  ns { nsNames   = fd $ nsNames   ns
+     , nsModules = fm $ nsModules ns
+     , nsInScope = fs $ nsInScope ns
+     }
+
+-- | Zip together two name spaces.
+zipNameSpace :: (NamesInScope   -> NamesInScope   -> NamesInScope  ) ->
+                (ModulesInScope -> ModulesInScope -> ModulesInScope) ->
+                (InScopeSet     -> InScopeSet     -> InScopeSet    ) ->
+                NameSpace -> NameSpace -> NameSpace
+zipNameSpace fd fm fs ns1 ns2 =
+  ns1 { nsNames   = nsNames   ns1 `fd` nsNames   ns2
+      , nsModules = nsModules ns1 `fm` nsModules ns2
+      , nsInScope = nsInScope ns1 `fs` nsInScope ns2
+      }
+
+-- | Map monadic function over a namespace.
+mapNameSpaceM :: Applicative m =>
+  (NamesInScope   -> m NamesInScope  ) ->
+  (ModulesInScope -> m ModulesInScope) ->
+  (InScopeSet     -> m InScopeSet    ) ->
+  NameSpace -> m NameSpace
+mapNameSpaceM fd fm fs ns = update ns <$> fd (nsNames ns) <*> fm (nsModules ns) <*> fs (nsInScope ns)
+  where
+    update ns ds ms is = ns { nsNames = ds, nsModules = ms, nsInScope = is }
+
+------------------------------------------------------------------------
+-- * General operations on scopes
+------------------------------------------------------------------------
+
+instance Null Scope where
+  empty = emptyScope
+  null  = __IMPOSSIBLE__
+    -- TODO: define when needed, careful about scopeNameSpaces!
+
+instance Null ScopeInfo where
+  empty = emptyScopeInfo
+  null  = __IMPOSSIBLE__
+    -- TODO: define when needed, careful about _scopeModules!
+
+-- | The empty scope.
+emptyScope :: Scope
+emptyScope = Scope
+  { scopeName           = noModuleName
+  , scopeParents        = []
+  , scopeNameSpaces     = [ (nsid, emptyNameSpace) | nsid <- allNameSpaces ]
+      -- Note (Andreas, 2019-08-19):  Cannot have [] here because
+      -- zipScope assumes all NameSpaces to be present and in the same order.
+  , scopeImports        = Map.empty
+  , scopeDatatypeModule = Nothing
+  }
+
+-- | The empty scope info.
+emptyScopeInfo :: ScopeInfo
+emptyScopeInfo = ScopeInfo
+  { _scopeCurrent       = noModuleName
+  , _scopeModules       = Map.singleton noModuleName emptyScope
+  , _scopeVarsToBind    = []
+  , _scopeLocals        = []
+  , _scopePrecedence    = []
+  , _scopeInverseName   = Map.empty
+  , _scopeInverseModule = Map.empty
+  , _scopeInScope       = Set.empty
+  , _scopeFixities      = Map.empty
+  , _scopePolarities    = Map.empty
+  }
+
+-- | Map functions over the names and modules in a scope.
+mapScope :: (NameSpaceId -> NamesInScope   -> NamesInScope  ) ->
+            (NameSpaceId -> ModulesInScope -> ModulesInScope) ->
+            (NameSpaceId -> InScopeSet    -> InScopeSet     ) ->
+            Scope -> Scope
+mapScope fd fm fs = updateScopeNameSpaces $ AssocList.mapWithKey mapNS
+  where
+    mapNS acc = mapNameSpace (fd acc) (fm acc) (fs acc)
+
+-- | Same as 'mapScope' but applies the same function to all name spaces.
+mapScope_ :: (NamesInScope   -> NamesInScope  ) ->
+             (ModulesInScope -> ModulesInScope) ->
+             (InScopeSet     -> InScopeSet    ) ->
+             Scope -> Scope
+mapScope_ fd fm fs = mapScope (const fd) (const fm) (const fs)
+
+-- | Same as 'mapScope' but applies the function only on the given name space.
+mapScopeNS :: NameSpaceId
+           -> (NamesInScope   -> NamesInScope  )
+           -> (ModulesInScope -> ModulesInScope)
+           -> (InScopeSet    -> InScopeSet     )
+           -> Scope -> Scope
+mapScopeNS nsid fd fm fs = modifyNameSpace nsid $ mapNameSpace fd fm fs
+
+-- | Map monadic functions over the names and modules in a scope.
+mapScopeM :: Applicative m =>
+  (NameSpaceId -> NamesInScope   -> m NamesInScope  ) ->
+  (NameSpaceId -> ModulesInScope -> m ModulesInScope) ->
+  (NameSpaceId -> InScopeSet     -> m InScopeSet    ) ->
+  Scope -> m Scope
+mapScopeM fd fm fs = updateScopeNameSpacesM $ AssocList.mapWithKeyM mapNS
+  where
+    mapNS acc = mapNameSpaceM (fd acc) (fm acc) (fs acc)
+
+-- | Same as 'mapScopeM' but applies the same function to both the public and
+--   private name spaces.
+mapScopeM_ :: Applicative m =>
+  (NamesInScope   -> m NamesInScope  ) ->
+  (ModulesInScope -> m ModulesInScope) ->
+  (InScopeSet     -> m InScopeSet    ) ->
+  Scope -> m Scope
+mapScopeM_ fd fm fs = mapScopeM (const fd) (const fm) (const fs)
+
+-- | Zip together two scopes. The resulting scope has the same name as the
+--   first scope.
+zipScope :: (NameSpaceId -> NamesInScope   -> NamesInScope   -> NamesInScope  ) ->
+            (NameSpaceId -> ModulesInScope -> ModulesInScope -> ModulesInScope) ->
+            (NameSpaceId -> InScopeSet     -> InScopeSet     -> InScopeSet    ) ->
+            Scope -> Scope -> Scope
+zipScope fd fm fs s1 s2 =
+  s1 { scopeNameSpaces =
+         [ (nsid, zipNS nsid ns1 ns2)
+         | ((nsid, ns1), (nsid', ns2)) <-
+             fromMaybe __IMPOSSIBLE__ $
+               zipWith' (,) (scopeNameSpaces s1) (scopeNameSpaces s2)
+         , assert (nsid == nsid')
+         ]
+     , scopeImports  = (Map.union `on` scopeImports)  s1 s2
+     }
+  where
+    assert True  = True
+    assert False = __IMPOSSIBLE__
+    zipNS acc = zipNameSpace (fd acc) (fm acc) (fs acc)
+
+-- | Same as 'zipScope' but applies the same function to both the public and
+--   private name spaces.
+zipScope_ :: (NamesInScope   -> NamesInScope   -> NamesInScope  ) ->
+             (ModulesInScope -> ModulesInScope -> ModulesInScope) ->
+             (InScopeSet     -> InScopeSet     -> InScopeSet    ) ->
+             Scope -> Scope -> Scope
+zipScope_ fd fm fs = zipScope (const fd) (const fm) (const fs)
+
+-- | Recompute the inScope sets of a scope.
+recomputeInScopeSets :: Scope -> Scope
+recomputeInScopeSets = updateScopeNameSpaces (map $ second recomputeInScope)
+  where
+    recomputeInScope ns = ns { nsInScope = allANames $ nsNames ns }
+    allANames :: NamesInScope -> InScopeSet
+    allANames = Set.fromList . map anameName . List1.concat . Map.elems
+
+-- | Filter a scope keeping only concrete names matching the predicates.
+--   The first predicate is applied to the names and the second to the modules.
+filterScope :: (C.Name -> Bool) -> (C.Name -> Bool) -> Scope -> Scope
+filterScope pd pm = recomputeInScopeSets .  mapScope_ (Map.filterKeys pd) (Map.filterKeys pm) id
+  -- We don't have enough information in the in scope set to do an
+  -- incremental update here, so just recompute it from the name map.
+
+-- | Return all names in a scope.
+allNamesInScope :: InScope a => Scope -> ThingsInScope a
+allNamesInScope = mergeNamesMany . map (inNameSpace . snd) . scopeNameSpaces
+
+allNamesInScope' :: InScope a => Scope -> ThingsInScope (a, Access)
+allNamesInScope' s =
+  mergeNamesMany [ fmap (, nameSpaceAccess nsId) <$> inNameSpace ns
+                 | (nsId, ns) <- scopeNameSpaces s ]
+
+-- | Look up a single name in the current scope.
+--
+-- This is equivalent to @Map.lookup n . allNamesInScope'@, but more efficient
+-- when only a single name needs to be looked up.
+findNameInScope :: InScope a => C.Name -> Scope -> [(a, Access)]
+findNameInScope n s =
+  [ (name, nameSpaceAccess nsId)
+  | (nsId, ns) <- scopeNameSpaces s
+  , name <- List1.toList' $ Map.lookup n $ inNameSpace ns
+  ]
+
+-- | Returns the scope's non-private names.
+exportedNamesInScope :: InScope a => Scope -> ThingsInScope a
+exportedNamesInScope = namesInScope [PublicNS, ImportedNS]
+
+namesInScope :: InScope a => [NameSpaceId] -> Scope -> ThingsInScope a
+namesInScope ids s =
+  mergeNamesMany [ inNameSpace (scopeNameSpace nsid s) | nsid <- ids ]
+
+allThingsInScope :: Scope -> NameSpace
+allThingsInScope s =
+  NameSpace { nsNames   = allNamesInScope s
+            , nsModules = allNamesInScope s
+            , nsInScope = Set.unions $ map (nsInScope . snd) $ scopeNameSpaces s
+            }
+
+thingsInScope :: [NameSpaceId] -> Scope -> NameSpace
+thingsInScope fs s =
+  NameSpace { nsNames   = namesInScope fs s
+            , nsModules = namesInScope fs s
+            , nsInScope = Set.unions [ nsInScope $ scopeNameSpace nsid s | nsid <- fs ]
+            }
+
+-- | Merge two scopes. The result has the name of the first scope.
+mergeScope :: Scope -> Scope -> Scope
+mergeScope = zipScope_ mergeNames mergeNames Set.union
+
+-- | Merge a non-empty list of scopes. The result has the name of the first
+--   scope in the list.
+mergeScopes :: [Scope] -> Scope
+mergeScopes [] = __IMPOSSIBLE__
+mergeScopes ss = foldr1 mergeScope ss
+
+-- * Specific operations on scopes
+
+-- | Move all names in a scope to the given name space (except never move from
+--   Imported to Public).
+setScopeAccess :: NameSpaceId -> Scope -> Scope
+setScopeAccess a s = (`updateScopeNameSpaces` s) $ AssocList.mapWithKey $ const . ns
+  where
+    zero  = emptyNameSpace
+    one   = allThingsInScope s
+    imp   = thingsInScope [ImportedNS] s
+    noimp = thingsInScope [PublicNS, PrivateNS] s
+
+    ns b = case (a, b) of
+      (PublicNS, PublicNS)   -> noimp
+      (PublicNS, ImportedNS) -> imp
+      _ | a == b             -> one
+        | otherwise          -> zero
+
+-- | Update a particular name space.
+setNameSpace :: NameSpaceId -> NameSpace -> Scope -> Scope
+setNameSpace nsid ns = modifyNameSpace nsid $ const ns
+
+-- | Modify a particular name space.
+modifyNameSpace :: NameSpaceId -> (NameSpace -> NameSpace) -> Scope -> Scope
+modifyNameSpace nsid f = updateScopeNameSpaces $ AssocList.updateAt nsid f
+
+-- | Add a name to a scope.
+addNameToScope :: NameSpaceId -> C.Name -> AbstractName -> Scope -> Scope
+addNameToScope nsid x y =
+  mapScopeNS nsid
+    (Map.insertWith (flip List1.union) x $ singleton y)  -- bind name x ↦ y
+    id                                        -- no change to modules
+    (Set.insert $ anameName y)                -- y is in scope now
+
+-- | Remove a name from a scope. Caution: does not update the nsInScope set.
+--   This is only used by rebindName and in that case we add the name right
+--   back (but with a different kind).
+removeNameFromScope :: NameSpaceId -> C.Name -> Scope -> Scope
+removeNameFromScope nsid x = mapScopeNS nsid (Map.delete x) id id
+
+-- | Add a module to a scope.
+addModuleToScope :: NameSpaceId -> C.Name -> AbstractModule -> Scope -> Scope
+addModuleToScope nsid x m = mapScopeNS nsid id addM id
+  where addM = Map.insertWith (flip List1.union) x (singleton m)
+
+-- | When we get here we cannot have both @using@ and @hiding@.
+data UsingOrHiding
+  = UsingOnly  [C.ImportedName]
+  | HidingOnly [C.ImportedName]
+
+usingOrHiding :: C.ImportDirective -> UsingOrHiding
+usingOrHiding i =
+  case (using i, hiding i) of
+    (UseEverything, ys) -> HidingOnly ys
+    (Using xs     , []) -> UsingOnly  xs
+    _                   -> __IMPOSSIBLE__
+
+-- | Apply an 'ImportDirective' to a scope:
+--
+--   1. rename keys (C.Name) according to @renaming@;
+--
+--   2. for untouched keys, either of
+--
+--      a) remove keys according to @hiding@, or
+--      b) filter keys according to @using@.
+--
+--   Both steps could be done in one pass, by first preparing key-filtering
+--   functions @C.Name -> Maybe C.Name@ for defined names and module names.
+--   However, the penalty of doing it in two passes should not be too high.
+--   (Doubling the run time.)
+applyImportDirective :: C.ImportDirective -> Scope -> Scope
+applyImportDirective dir = fst . applyImportDirective_ dir
+
+-- | Version of 'applyImportDirective' that also returns sets of name
+--   and module name clashes introduced by @renaming@ to identifiers
+--   that are already imported by @using@ or lack of @hiding@.
+applyImportDirective_
+  :: C.ImportDirective
+  -> Scope
+  -> (Scope, (Set C.Name, Set C.Name)) -- ^ Merged scope, clashing names, clashing module names.
+applyImportDirective_ dir@(ImportDirective{ impRenaming }) s
+  | null dir  = (s, (empty, empty))
+      -- Since each run of applyImportDirective rebuilds the scope
+      -- with cost O(n log n) time, it makes sense to test for the identity.
+  | otherwise = (recomputeInScopeSets $ mergeScope sUse sRen, (nameClashes, moduleClashes))
+  where
+    -- Names kept via using/hiding.
+    sUse :: Scope
+    sUse = useOrHide (usingOrHiding dir) s
+
+    -- Things kept (under a different name) via renaming.
+    sRen :: Scope
+    sRen = rename impRenaming s
+
+    -- Which names are considered to be defined by a module?
+    -- The ones actually defined there publicly ('publicNS')
+    -- and the ones imported publicly ('ImportedNS')?
+    exportedNSs = [PublicNS, ImportedNS]
+
+    -- Name clashes introduced by the @renaming@ clause.
+    nameClashes :: Set C.Name
+    nameClashes = Map.keysSet rNames `Set.intersection` Map.keysSet uNames
+      -- NB: `intersection` returns a subset of the first argument.
+      -- To get the correct error location, i.e., in the @renaming@ clause
+      -- rather than at the definition location, we neet to return
+      -- names from the @renaming@ clause.  (Issue #4154.)
+      where
+      uNames, rNames :: NamesInScope
+      uNames = namesInScope exportedNSs sUse
+      rNames = namesInScope exportedNSs sRen
+
+    -- Module name clashes introduced by the @renaming@ clause.
+
+    -- Note: need to cut and paste because of 'InScope' dependent types trickery.
+    moduleClashes :: Set C.Name
+    moduleClashes = Map.keysSet uModules `Set.intersection` Map.keysSet rModules
+      where
+      uModules, rModules :: ModulesInScope
+      uModules = namesInScope exportedNSs sUse
+      rModules = namesInScope exportedNSs sRen
+
+
+    -- Restrict scope by directive.
+    useOrHide :: UsingOrHiding -> Scope -> Scope
+    useOrHide (UsingOnly  xs) = filterNames Set.member xs
+       -- Filter scope, keeping only xs.
+    useOrHide (HidingOnly xs) = filterNames Set.notMember $ map renFrom impRenaming ++ xs
+       -- Filter out xs and the to be renamed names from scope.
+
+    -- Filter scope by (`rel` xs).
+    -- O(n * log (length xs)).
+    filterNames :: (C.Name -> Set C.Name -> Bool) -> [C.ImportedName] ->
+                   Scope -> Scope
+    filterNames rel xs = filterScope (`rel` Set.fromList ds) (`rel` Set.fromList ms)
+      where
+        (ds, ms) = partitionEithers $ for xs $ \case
+          ImportedName   x -> Left x
+          ImportedModule m -> Right m
+
+    -- Apply a renaming to a scope.
+    -- O(n * (log n + log (length rho))).
+    rename :: [C.Renaming] -> Scope -> Scope
+    rename rho = mapScope_ (updateFxs .
+                            updateThingsInScope (AssocList.apply drho))
+                           (updateThingsInScope (AssocList.apply mrho))
+                           id
+      where
+        (drho, mrho) = partitionEithers $ for rho $ \case
+          Renaming (ImportedName   x) (ImportedName   y) _fx _ -> Left  (x, y)
+          Renaming (ImportedModule x) (ImportedModule y) _fx _ -> Right (x, y)
+          _ -> __IMPOSSIBLE__
+
+        fixities :: AssocList C.Name Fixity
+        fixities = (`mapMaybe` rho) $ \case
+          Renaming _ (ImportedName y) (Just fx)  _ -> Just (y, fx)
+          _ -> Nothing
+
+        -- Update fixities of abstract names targeted by renamed imported identifies.
+        updateFxs :: NamesInScope -> NamesInScope
+        updateFxs m = foldl upd m fixities
+          where
+          -- Update fixity of all abstract names targeted by concrete name y.
+          upd m (y, fx) = Map.adjust (fmap $ set lensFixity fx) y m
+
+        updateThingsInScope
+          :: forall a. SetBindingSite a
+          => (C.Name -> Maybe C.Name)
+          -> ThingsInScope a -> ThingsInScope a
+        updateThingsInScope f = Map.fromListWith __IMPOSSIBLE__ . mapMaybe upd . Map.toAscList
+          where
+          upd :: (C.Name, List1 a) -> Maybe (C.Name, List1 a)
+          upd (x, ys) = f x <&> \ x' -> (x', setBindingSite (getRange x') ys)
+
+-- | Rename the abstract names in a scope.
+renameCanonicalNames :: Map A.QName A.QName -> Map A.ModuleName A.ModuleName ->
+                        Scope -> Scope
+renameCanonicalNames renD renM = mapScope_ renameD renameM (Set.map newName)
+  where
+    newName x = Map.findWithDefault x x renD
+    newMod  x = Map.findWithDefault x x renM
+
+    renameD = Map.map $ fmap $ over lensAnameName newName
+    renameM = Map.map $ fmap $ over lensAmodName  newMod
+
+-- | Remove private name space of a scope.
+--
+--   Should be a right identity for 'exportedNamesInScope'.
+--   @exportedNamesInScope . restrictPrivate == exportedNamesInScope@.
+restrictPrivate :: Scope -> Scope
+restrictPrivate s = setNameSpace PrivateNS emptyNameSpace
+                  $ s { scopeImports = Map.empty }
+
+-- | Remove private things from the given module from a scope.
+restrictLocalPrivate :: ModuleName -> Scope -> Scope
+restrictLocalPrivate m =
+  mapScopeNS PrivateNS
+    (Map.mapMaybe rName)
+    (Map.mapMaybe rMod)
+    (Set.filter (not . (`isInModule` m)))
+  where
+    rName as = List1.nonEmpty $ List1.filter (not . (`isInModule`        m) . anameName) as
+    rMod  as = List1.nonEmpty $ List1.filter (not . (`isLtChildModuleOf` m) . amodName)  as
+
+-- | Filter privates out of a `ScopeInfo`
+withoutPrivates :: ScopeInfo -> ScopeInfo
+withoutPrivates scope = over scopeModules (fmap $ restrictLocalPrivate m) scope
+  where
+  m = scope ^. scopeCurrent
+
+-- | Disallow using generalized variables from the scope
+disallowGeneralizedVars :: Scope -> Scope
+disallowGeneralizedVars = mapScope_ ((fmap . fmap) disallow) id id
+  where
+    disallow a = a { anameKind = disallowGen (anameKind a) }
+    disallowGen GeneralizeName = DisallowedGeneralizeName
+    disallowGen k              = k
+
+-- | Add an explanation to why things are in scope.
+inScopeBecause :: (WhyInScope -> WhyInScope) -> Scope -> Scope
+inScopeBecause f = mapScope_ mapName mapMod id
+  where
+    mapName = fmap . fmap $ \a -> a { anameLineage = f $ anameLineage a }
+    mapMod  = fmap . fmap $ \a -> a { amodLineage  = f $ amodLineage a  }
+
+-- | Get the public parts of the public modules of a scope
+publicModules :: ScopeInfo -> Map A.ModuleName Scope
+publicModules scope = Map.filterWithKey (\ m _ -> reachable m) allMods
+  where
+    -- Get all modules in the ScopeInfo.
+    allMods   = Map.map restrictPrivate $ scope ^. scopeModules
+    root      = scope ^. scopeCurrent
+
+    modules s = map amodName $ List1.concat $ Map.elems $ allNamesInScope s
+
+    chase m = m : concatMap chase ms
+      where ms = maybe __IMPOSSIBLE__ modules $ Map.lookup m allMods
+
+    reachable = (`elem` chase root)
+
+publicNames :: ScopeInfo -> Set AbstractName
+publicNames scope =
+  Set.fromList $ List1.concat $ Map.elems $
+  exportedNamesInScope $ mergeScopes $ Map.elems $ publicModules scope
+
+everythingInScope :: ScopeInfo -> NameSpace
+everythingInScope scope = allThingsInScope $ mergeScopes $
+    (s0 :) $ map look $ scopeParents s0
+  where
+    look m = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+    s0     = look $ scope ^. scopeCurrent
+
+everythingInScopeQualified :: ScopeInfo -> NameSpace
+everythingInScopeQualified scope =
+  allThingsInScope $ mergeScopes $
+    chase Set.empty scopes
+  where
+    s0      = look $ scope ^. scopeCurrent
+    scopes  = s0 : map look (scopeParents s0)
+    look m  = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+    lookP   = restrictPrivate . look
+
+    -- We start with the current module and all its parents and look through
+    -- all their imports and submodules.
+    chase seen [] = []
+    chase seen (s : ss)
+      | Set.member name seen = chase seen ss
+      | otherwise = s : chase (Set.insert name seen) (imports ++ submods ++ ss)
+      where
+        -- #4166: only include things that are actually in scope here
+        inscope x _ = isInScope x == InScope
+        name    = scopeName s
+        imports = map lookP $ Map.elems $ scopeImports s
+        submods = map (lookP . amodName) $ List1.concat $ Map.elems $ Map.filterWithKey inscope $ allNamesInScope s
+
+-- | Get all concrete names in scope. Includes bound variables.
+concreteNamesInScope :: ScopeInfo -> Set C.QName
+concreteNamesInScope scope =
+  Set.unions [ build allNamesInScope root, imported, locals ]
+  where
+    current = moduleScope $ scope ^. scopeCurrent
+    root    = mergeScopes $ current : map moduleScope (scopeParents current)
+
+    locals  = Set.fromList [ C.QName x | (x, _) <- scope ^. scopeLocals ]
+
+    imported = Set.unions
+               [ qual c (build exportedNamesInScope $ moduleScope a)
+               | (c, a) <- Map.toList $ scopeImports root ]
+    qual c = Set.map (q c)
+      where
+        q (C.QName x)  = C.Qual x
+        q (C.Qual m x) = C.Qual m . q x
+
+    build :: (forall a. InScope a => Scope -> ThingsInScope a) -> Scope -> Set C.QName
+    build getNames s = Set.unions $
+        Set.fromAscList
+          (map C.QName $
+           Map.keys (getNames s :: ThingsInScope AbstractName)) :
+          [ Set.mapMonotonic (\ y -> C.Qual x y) $
+              build exportedNamesInScope $ moduleScope m
+          | (x, mods) <- Map.toList (getNames s)
+          , prettyShow x /= "_"
+          , AbsModule m _ <- List1.toList mods
+          ]
+
+    moduleScope :: A.ModuleName -> Scope
+    moduleScope m = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+
+-- | Look up a name in the scope
+scopeLookup :: InScope a => C.QName -> ScopeInfo -> [a]
+scopeLookup q scope = map fst $ scopeLookup' q scope
+
+scopeLookup' :: forall a. InScope a => C.QName -> ScopeInfo -> [(a, Access)]
+scopeLookup' q scope =
+  nubOn fst $
+    findName q root ++ maybeToList topImports ++ imports
+  where
+
+    -- 1. Finding a name in the current scope and its parents.
+
+    moduleScope :: A.ModuleName -> Scope
+    moduleScope m = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+
+    current :: Scope
+    current = moduleScope $ scope ^. scopeCurrent
+
+    root    :: Scope
+    root    = mergeScopes $ current : map moduleScope (scopeParents current)
+
+    -- Find a concrete, possibly qualified name in scope @s@.
+    findName :: forall a. InScope a => C.QName -> Scope -> [(a, Access)]
+    findName q0 s = case q0 of
+      C.QName x  -> findNameInScope x s
+      C.Qual x q -> do
+        let -- Get the modules named @x@ in scope @s@.
+            mods :: [A.ModuleName]
+            mods = amodName . fst <$> findNameInScope x s
+            -- Get the definitions named @x@ in scope @s@ and interpret them as modules.
+            -- Andreas, 2013-05-01: Issue 836 debates this feature:
+            -- Qualified constructors are qualified by their datatype rather than a module
+            defs :: [A.ModuleName] -- NB:: Defined but not used
+            defs = qnameToMName . anameName . fst <$> findNameInScope x s
+        -- Andreas, 2013-05-01:  Issue 836 complains about the feature
+        -- that constructors can also be qualified by their datatype
+        -- and projections by their record type.  This feature is off
+        -- if we just consider the modules:
+        m <- mods
+        -- The feature is on if we consider also the data and record types:
+        -- trace ("mods ++ defs = " ++ show (mods ++ defs)) $ do
+        -- m <- nub $ mods ++ defs -- record types will appear both as a mod and a def
+        -- Get the scope of module m, if any, and remove its private definitions.
+        let ss  = Map.lookup m $ scope ^. scopeModules
+            ss' = restrictPrivate <$> ss
+        -- trace ("ss  = " ++ show ss ) $ do
+        -- trace ("ss' = " ++ show ss') $ do
+        s' <- maybeToList ss'
+        findName q s'
+
+    -- 2. Finding a name in the top imports.
+
+    topImports :: Maybe (a, Access)
+    topImports = case (inScopeTag :: InScopeTag a) of
+      NameTag   -> Nothing
+      ModuleTag -> first (`AbsModule` Defined) <$> imported q
+
+    imported :: C.QName -> Maybe (A.ModuleName, Access)
+    imported q = fmap (,PublicAccess) $ Map.lookup q $ scopeImports root
+
+    -- 3. Finding a name in the imports belonging to an initial part of the qualifier.
+
+    imports :: [(a, Access)]
+    imports = do
+      (m, x) <- splitName q
+      m <- maybeToList $ fst <$> imported m
+      findName x $ restrictPrivate $ moduleScope m
+
+    -- return all possible splittings, e.g.
+    -- splitName X.Y.Z = [(X, Y.Z), (X.Y, Z)]
+    splitName :: C.QName -> [(C.QName, C.QName)]
+    splitName (C.QName x)  = []
+    splitName (C.Qual x q) =
+      (C.QName x, q) : [ (C.Qual x m, r) | (m, r) <- splitName q ]
+
+
+-- * Inverse look-up
+
+data AllowAmbiguousNames
+  = AmbiguousAnything
+      -- ^ Used for instance arguments to check whether a name is in scope,
+      --   but we do not care whether is is ambiguous
+  | AmbiguousConProjs
+      -- ^ Ambiguous constructors, projections, or pattern synonyms.
+  | AmbiguousNothing
+  deriving (Eq)
+
+isNameInScope :: A.QName -> ScopeInfo -> Bool
+isNameInScope q scope =
+  billToPure [ Scoping, InverseScopeLookup ] $
+  Set.member q (scope ^. scopeInScope)
+
+isNameInScopeUnqualified :: A.QName -> ScopeInfo -> Bool
+isNameInScopeUnqualified q scope =
+  case inverseScopeLookupName' AmbiguousNothing q scope of
+    C.QName{} : _ -> True -- NOTE: inverseScopeLookupName' puts unqualified names first
+    _             -> False
+
+-- | Find the concrete names that map (uniquely) to a given abstract qualified name.
+--   Sort by number of modules in the qualified name, unqualified names first.
+inverseScopeLookupName :: A.QName -> ScopeInfo -> [C.QName]
+inverseScopeLookupName = inverseScopeLookupName' AmbiguousConProjs
+
+inverseScopeLookupName' :: AllowAmbiguousNames -> A.QName -> ScopeInfo -> [C.QName]
+inverseScopeLookupName' amb q scope =
+  maybe [] (List1.toList . qnameConcrete) $ inverseScopeLookupName'' amb q scope
+
+-- | A version of 'inverseScopeLookupName' that also delivers the 'KindOfName'.
+--   Used in highlighting.
+inverseScopeLookupName'' :: AllowAmbiguousNames -> A.QName -> ScopeInfo -> Maybe NameMapEntry
+inverseScopeLookupName'' amb q scope = billToPure [ Scoping , InverseScopeLookup ] $ do
+  NameMapEntry k xs <- Map.lookup q (scope ^. scopeInverseName)
+  NameMapEntry k <$> do List1.nonEmpty $ best $ List1.filter unambiguousName xs
+  where
+    best :: [C.QName] -> [C.QName]
+    best = List.sortOn $ length . C.qnameParts
+
+    unique :: forall a . [a] -> Bool
+    unique []      = __IMPOSSIBLE__
+    unique [_]     = True
+    unique (_:_:_) = False
+
+    unambiguousName :: C.QName -> Bool
+    unambiguousName q = or
+      [ amb == AmbiguousAnything
+      , unique xs
+      , amb == AmbiguousConProjs && or
+          [ all (isJust . isConName) (k:ks)
+          , k `elem` [ FldName, PatternSynName ] && all (k ==) ks
+          ]
+      ]
+      where
+      xs   = scopeLookup q scope
+      k:ks = map anameKind xs
+
+-- | Find the concrete names that map (uniquely) to a given abstract module name.
+--   Sort by length, shortest first.
+inverseScopeLookupModule :: A.ModuleName -> ScopeInfo -> [C.QName]
+inverseScopeLookupModule = inverseScopeLookupModule' AmbiguousNothing
+
+inverseScopeLookupModule' :: AllowAmbiguousNames -> A.ModuleName -> ScopeInfo -> [C.QName]
+inverseScopeLookupModule' amb m scope = billToPure [ Scoping , InverseScopeLookup ] $
+  best $ filter unambiguousModule $ findModule m
+  where
+    findModule m = fromMaybe [] $ Map.lookup m (scope ^. scopeInverseModule)
+
+    best :: [C.QName] -> [C.QName]
+    best = List.sortOn $ length . C.qnameParts
+
+    unique :: forall a . [a] -> Bool
+    unique []      = __IMPOSSIBLE__
+    unique [_]     = True
+    unique (_:_:_) = False
+
+    unambiguousModule q = amb == AmbiguousAnything || unique (scopeLookup q scope :: [AbstractModule])
+
+recomputeInverseScopeMaps :: ScopeInfo -> ScopeInfo
+recomputeInverseScopeMaps scope = billToPure [ Scoping , InverseScopeLookup ] $
+  scope { _scopeInverseName   = nameMap
+        , _scopeInverseModule = Map.fromList [ (x, findModule x) | x <- Map.keys moduleMap ++ Map.keys importMap ]
+        , _scopeInScope       = nsInScope $ everythingInScopeQualified scope
+        }
+  where
+    this = scope ^. scopeCurrent
+    current = this : scopeParents (moduleScope this)
+    scopes  = [ (m, restrict m s) | (m, s) <- Map.toList (scope ^. scopeModules) ]
+
+    moduleScope :: A.ModuleName -> Scope
+    moduleScope m = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+
+    restrict m s | m `elem` current = s
+                 | otherwise = restrictPrivate s
+
+    internalName :: C.QName -> Bool
+    internalName C.QName{} = False
+    internalName (C.Qual m n) = intern m || internalName n
+      where
+      -- Recognize fresh names created Parser.y
+      intern (C.Name _ _ (C.Id ('.' : '#' : _) :| [])) = True
+      intern _ = False
+
+    findName :: Ord a => Map a [(A.ModuleName, C.Name)] -> a -> [C.QName]
+    findName table q = do
+      (m, x) <- fromMaybe [] $ Map.lookup q table
+      if m `elem` current
+        then return (C.QName x)
+        else do
+          y <- findModule m
+          let z = C.qualify y x
+          guard $ not $ internalName z
+          return z
+
+    findModule :: A.ModuleName -> [C.QName]
+    findModule q = findName moduleMap q ++
+                   fromMaybe [] (Map.lookup q importMap)
+
+    importMap = Map.fromListWith (++) $ do
+      (m, s) <- scopes
+      (x, y) <- Map.toList $ scopeImports s
+      return (y, singleton x)
+
+    moduleMap = Map.fromListWith (++) $ do
+      (m, s)  <- scopes
+      (x, ms) <- Map.toList (allNamesInScope s)
+      q       <- amodName <$> List1.toList ms
+      return (q, singleton (m, x))
+
+    nameMap :: NameMap
+    nameMap = Map.fromListWith (<>) $ do
+      (m, s)  <- scopes
+      (x, ms) <- Map.toList (allNamesInScope s)
+      (q, k)  <- (anameName &&& anameKind) <$> List1.toList ms
+      let ret z = return (q, NameMapEntry k $ singleton z)
+      if m `elem` current
+        then ret $ C.QName x
+        else do
+          y <- findModule m
+          let z = C.qualify y x
+          guard $ not $ internalName z
+          ret z
+
+------------------------------------------------------------------------
+-- * Update binding site
+------------------------------------------------------------------------
+
+-- | Set the 'nameBindingSite' in an abstract name.
+class SetBindingSite a where
+  setBindingSite :: Range -> a -> a
+
+  default setBindingSite
+    :: (SetBindingSite b, Functor t, t b ~ a)
+    => Range -> a -> a
+  setBindingSite = fmap . setBindingSite
+
+instance SetBindingSite a => SetBindingSite [a]
+instance SetBindingSite a => SetBindingSite (List1 a)
+
+instance SetBindingSite A.Name where
+  setBindingSite r x = x { nameBindingSite = r }
+
+instance SetBindingSite A.QName where
+  setBindingSite r x = x { qnameName = setBindingSite r $ qnameName x }
+
+-- | Sets the binding site of all names in the path.
+instance SetBindingSite A.ModuleName where
+  setBindingSite r (MName x) = MName $ setBindingSite r x
+
+instance SetBindingSite AbstractName where
+  setBindingSite r x = x { anameName = setBindingSite r $ anameName x }
+
+instance SetBindingSite AbstractModule where
+  setBindingSite r x = x { amodName = setBindingSite r $ amodName x }
+
+
+------------------------------------------------------------------------
+-- * (Debug) printing
+------------------------------------------------------------------------
+
+instance Pretty AbstractName where
+  pretty = pretty . anameName
+
+instance Pretty AbstractModule where
+  pretty = pretty . amodName
+
+instance Pretty NameSpaceId where
+  pretty = text . \case
+    PublicNS        -> "public"
+    PrivateNS       -> "private"
+    ImportedNS      -> "imported"
+
+instance Pretty NameSpace where
+  pretty = vcat . prettyNameSpace
+
+prettyNameSpace :: NameSpace -> [Doc]
+prettyNameSpace (NameSpace names mods _) =
+    blockOfLines "names"   (map pr $ Map.toList names) ++
+    blockOfLines "modules" (map pr $ Map.toList mods)
+  where
+    pr :: (Pretty a, Pretty b) => (a,b) -> Doc
+    pr (x, y) = pretty x <+> "-->" <+> pretty y
+
+instance Pretty Scope where
+  pretty scope@Scope{ scopeName = name, scopeParents = parents, scopeImports = imps } =
+    vcat $ concat
+      [ [ "scope" <+> pretty name ]
+      , scopeNameSpaces scope >>= \ (nsid, ns) -> do
+          block (pretty nsid) $ prettyNameSpace ns
+      , ifNull (Map.keys imps) [] {-else-} $ \ ks ->
+          block "imports" [ prettyList ks ]
+      ]
+    where
+    block :: Doc -> [Doc] -> [Doc]
+    block hd = map (nest 2) . blockOfLines hd
+
+-- | Add first string only if list is non-empty.
+blockOfLines :: Doc -> [Doc] -> [Doc]
+blockOfLines _  [] = []
+blockOfLines hd ss = hd : map (nest 2) ss
+
+instance Pretty ScopeInfo where
+  pretty (ScopeInfo this mods toBind locals ctx _ _ _ _ _) = vcat $ concat
+    [ [ "ScopeInfo"
+      , nest 2 $ "current =" <+> pretty this
+      ]
+    , [ nest 2 $ "toBind  =" <+> pretty locals | not (null toBind) ]
+    , [ nest 2 $ "locals  =" <+> pretty locals | not (null locals) ]
+    , [ nest 2 $ "context =" <+> pretty ctx
+      , nest 2 $ "modules"
+      ]
+    , map (nest 4 . pretty) $ Map.elems mods
+    ]
+
+------------------------------------------------------------------------
+-- * Boring instances
+------------------------------------------------------------------------
+
+instance KillRange ScopeInfo where
+  killRange m = m
+
+instance HasRange AbstractName where
+  getRange = getRange . anameName
+
+instance SetRange AbstractName where
+  setRange r x = x { anameName = setRange r $ anameName x }
+
+instance NFData Scope
+instance NFData DataOrRecordModule
+instance NFData NameSpaceId
+instance NFData ScopeInfo
+instance NFData KindOfName
+instance NFData NameMapEntry
+instance NFData BindingSource
+instance NFData LocalVar
+instance NFData NameSpace
+instance NFData NameOrModule
+instance NFData WhyInScope
+instance NFData AbstractName
+instance NFData NameMetadata
+instance NFData AbstractModule
+instance NFData ResolvedName
+instance NFData AmbiguousNameReason
diff --git a/src/full/Agda/Syntax/Scope/Flat.hs b/src/full/Agda/Syntax/Scope/Flat.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Scope/Flat.hs
@@ -0,0 +1,109 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Flattened scopes.
+module Agda.Syntax.Scope.Flat
+  ( FlatScope
+  , flattenScope
+  , getDefinedNames
+  , localNames
+  ) where
+
+import Data.Bifunctor
+import Data.Either (partitionEithers)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import qualified Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Concrete
+import Agda.Syntax.Notation
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad
+
+import Agda.TypeChecking.Monad.Debug
+
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Syntax.Common.Pretty
+
+-- | Flattened scopes.
+newtype FlatScope = Flat (Map QName (List1 AbstractName))
+  deriving Pretty
+
+-- | Compute a flattened scope. Only include unqualified names or names
+-- qualified by modules in the first argument.
+flattenScope :: [[Name]] -> ScopeInfo -> FlatScope
+flattenScope ms scope =
+  Flat $
+  Map.unionWith (<>)
+    (build ms allNamesInScope root)
+    imported
+  where
+    current = moduleScope $ scope ^. scopeCurrent
+    root    = mergeScopes $ current : map moduleScope (scopeParents current)
+
+    imported = Map.unionsWith (<>)
+               [ qual c (build ms' exportedNamesInScope $ moduleScope a)
+               | (c, a) <- Map.toList $ scopeImports root
+               , let -- get the suffixes of c in ms
+                     ms' = mapMaybe (List.stripPrefix $ List1.toList $ qnameParts c) ms
+               , not $ null ms' ]
+    qual c = Map.mapKeysMonotonic (q c)
+      where
+        q (QName x)  = Qual x
+        q (Qual m x) = Qual m . q x
+
+    build :: [[Name]] -> (forall a. InScope a => Scope -> ThingsInScope a) -> Scope -> Map QName (List1 AbstractName)
+    build ms getNames s = Map.unionsWith (<>) $
+        Map.mapKeysMonotonic QName (getNames s) :
+          [ Map.mapKeysMonotonic (\ y -> Qual x y) $
+              build ms' exportedNamesInScope $ moduleScope m
+          | (x, mods) <- Map.toList (getNames s)
+          , let ms' = [ tl | hd:tl <- ms, hd == x ]
+          , not $ null ms'
+          , AbsModule m _ <- List1.toList mods
+          ]
+
+    moduleScope :: A.ModuleName -> Scope
+    moduleScope m = fromMaybe __IMPOSSIBLE__ $ Map.lookup m $ scope ^. scopeModules
+
+-- | Compute all defined names in scope and their fixities/notations.
+-- Note that overloaded names (constructors) can have several
+-- fixities/notations. Then we 'mergeNotations'. (See issue 1194.)
+getDefinedNames :: KindsOfNames -> FlatScope -> [List1 NewNotation]
+getDefinedNames kinds (Flat names) =
+  [ mergeNotations $ fmap (namesToNotation x . A.qnameName . anameName) ds
+  | (x, ds) <- Map.toList names
+  , any ((`elemKindsOfNames` kinds) . anameKind) ds
+  ]
+  -- Andreas, 2013-03-21 see Issue 822
+  -- Names can have different kinds, i.e., 'defined' and 'constructor'.
+  -- We need to consider all names that have *any* matching kind,
+  -- not only those whose first appearing kind is matching.
+
+-- | Compute all names (first component) and operators/notations
+-- (second component) in scope.
+localNames :: FlatScope -> ScopeM ([QName], [NewNotation])
+localNames flat = do
+  let defs = getDefinedNames allKindsOfNames flat
+  locals <- nubOn fst . notShadowedLocals <$> getLocalVars
+  -- Note: Debug printout aligned with the one in
+  -- Agda.Syntax.Concrete.Operators.buildParsers.
+  reportS "scope.operators" 50
+    [ "flat  = " ++ prettyShow flat
+    , "defs  = " ++ prettyShow defs
+    , "locals= " ++ prettyShow locals
+    ]
+  let localNots  = map localOp locals
+      notLocal   = not . hasElem (map notaName localNots) . notaName
+      otherNots  = concatMap (List1.filter notLocal) defs
+  return $ second (map useDefaultFixity) $ split $ localNots ++ otherNots
+  where
+    localOp (x, y) = namesToNotation (QName x) y
+    split          = partitionEithers . concatMap opOrNot
+    opOrNot n      = Left (notaName n) :
+                     [Right n | not (null (notation n))]
diff --git a/src/full/Agda/Syntax/Scope/Monad.hs b/src/full/Agda/Syntax/Scope/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Scope/Monad.hs
@@ -0,0 +1,1049 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+{-| The scope monad with operations.
+-}
+
+module Agda.Syntax.Scope.Monad where
+
+import Prelude hiding (null)
+
+import Control.Arrow ((***))
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.State
+
+import Data.Either ( partitionEithers )
+import Data.Foldable (all, traverse_)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.HashMap.Strict as HMap
+import qualified Data.HashSet as HSet
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Traversable hiding (for)
+
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Warnings
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Fixity
+import Agda.Syntax.Notation
+import Agda.Syntax.Abstract.Name as A
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract (ScopeCopyInfo(..))
+import Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Fixity
+import Agda.Syntax.Concrete.Definitions ( DeclarationWarning(..) ,DeclarationWarning'(..) )
+  -- TODO: move the relevant warnings out of there
+import Agda.Syntax.Scope.Base as A
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+  ( HasBuiltins, getBuiltinName'
+  , builtinProp, builtinSet, builtinStrictSet, builtinPropOmega, builtinSetOmega, builtinSSetOmega )
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Monad.Trace
+import Agda.TypeChecking.Positivity.Occurrence (Occurrence)
+import Agda.TypeChecking.Warnings ( warning, warning' )
+
+import qualified Agda.Utils.AssocList as AssocList
+import Agda.Utils.CallStack ( CallStack, HasCallStack, withCallerCallStack )
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|), nonEmpty, toList)
+import Agda.Utils.List2 (List2(List2), toList)
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.List2 as List2
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Suffix as C
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * The scope checking monad
+---------------------------------------------------------------------------
+
+-- | To simplify interaction between scope checking and type checking (in
+--   particular when chasing imports), we use the same monad.
+type ScopeM = TCM
+
+-- Debugging
+
+printLocals :: Int -> String -> ScopeM ()
+printLocals v s = verboseS "scope.top" v $ do
+  locals <- getLocalVars
+  reportSLn "scope.top" v $ s ++ " " ++ prettyShow locals
+
+scopeWarning' :: CallStack -> DeclarationWarning' -> ScopeM ()
+scopeWarning' loc = warning' loc . NicifierIssue . DeclarationWarning loc
+
+scopeWarning :: HasCallStack => DeclarationWarning' -> ScopeM ()
+scopeWarning = withCallerCallStack scopeWarning'
+
+---------------------------------------------------------------------------
+-- * General operations
+---------------------------------------------------------------------------
+
+isDatatypeModule :: ReadTCState m => A.ModuleName -> m (Maybe DataOrRecordModule)
+isDatatypeModule m = do
+   scopeDatatypeModule . Map.findWithDefault __IMPOSSIBLE__ m <$> useScope scopeModules
+
+getCurrentModule :: ReadTCState m => m A.ModuleName
+getCurrentModule = setRange noRange <$> useScope scopeCurrent
+
+setCurrentModule :: MonadTCState m => A.ModuleName -> m ()
+setCurrentModule m = modifyScope $ set scopeCurrent m
+
+withCurrentModule :: (ReadTCState m, MonadTCState m) => A.ModuleName -> m a -> m a
+withCurrentModule new action = do
+  old <- getCurrentModule
+  setCurrentModule new
+  x   <- action
+  setCurrentModule old
+  return x
+
+withCurrentModule' :: (MonadTrans t, Monad (t ScopeM)) => A.ModuleName -> t ScopeM a -> t ScopeM a
+withCurrentModule' new action = do
+  old <- lift getCurrentModule
+  lift $ setCurrentModule new
+  x   <- action
+  lift $ setCurrentModule old
+  return x
+
+getNamedScope :: A.ModuleName -> ScopeM Scope
+getNamedScope m = do
+  scope <- getScope
+  case Map.lookup m (scope ^. scopeModules) of
+    Just s  -> return s
+    Nothing -> do
+      reportSLn "" 0 $ "ERROR: In scope\n" ++ prettyShow scope ++ "\nNO SUCH SCOPE " ++ prettyShow m
+      __IMPOSSIBLE__
+
+getCurrentScope :: ScopeM Scope
+getCurrentScope = getNamedScope =<< getCurrentModule
+
+-- | Create a new module with an empty scope.
+--   If the module is not new (e.g. duplicate @import@),
+--   don't erase its contents.
+--   (@Just@ if it is a datatype or record module.)
+createModule :: Maybe DataOrRecordModule -> A.ModuleName -> ScopeM ()
+createModule b m = do
+  reportSLn "scope.createModule" 10 $ "createModule " ++ prettyShow m
+  s <- getCurrentScope
+  let parents = scopeName s : scopeParents s
+      sm = emptyScope { scopeName           = m
+                      , scopeParents        = parents
+                      , scopeDatatypeModule = b }
+  -- Andreas, 2015-07-02: internal error if module is not new.
+  -- Ulf, 2016-02-15: It's not new if multiple imports (#1770).
+  -- Andreas, 2020-05-18, issue #3933:
+  -- If it is not new (but apparently did not clash),
+  -- we do not erase its contents for reasons of monotonicity.
+  modifyScopes $ Map.insertWith mergeScope m sm
+
+-- | Apply a function to the scope map.
+modifyScopes :: (Map A.ModuleName Scope -> Map A.ModuleName Scope) -> ScopeM ()
+modifyScopes = modifyScope . over scopeModules
+
+-- | Apply a function to the given scope.
+modifyNamedScope :: A.ModuleName -> (Scope -> Scope) -> ScopeM ()
+modifyNamedScope m f = modifyScopes $ Map.adjust f m
+
+setNamedScope :: A.ModuleName -> Scope -> ScopeM ()
+setNamedScope m s = modifyNamedScope m $ const s
+
+-- | Apply a monadic function to the top scope.
+modifyNamedScopeM :: A.ModuleName -> (Scope -> ScopeM (a, Scope)) -> ScopeM a
+modifyNamedScopeM m f = do
+  (a, s) <- f =<< getNamedScope m
+  setNamedScope m s
+  return a
+
+-- | Apply a function to the current scope.
+modifyCurrentScope :: (Scope -> Scope) -> ScopeM ()
+modifyCurrentScope f = getCurrentModule >>= (`modifyNamedScope` f)
+
+modifyCurrentScopeM :: (Scope -> ScopeM (a, Scope)) -> ScopeM a
+modifyCurrentScopeM f = getCurrentModule >>= (`modifyNamedScopeM` f)
+
+-- | Apply a function to the public or private name space.
+modifyCurrentNameSpace :: NameSpaceId -> (NameSpace -> NameSpace) -> ScopeM ()
+modifyCurrentNameSpace acc f = modifyCurrentScope $ updateScopeNameSpaces $
+  AssocList.updateAt acc f
+
+setContextPrecedence :: PrecedenceStack -> ScopeM ()
+setContextPrecedence = modifyScope_ . set scopePrecedence
+
+withContextPrecedence :: ReadTCState m => Precedence -> m a -> m a
+withContextPrecedence p =
+  locallyTCState (stScope . scopePrecedence) $ pushPrecedence p
+
+getLocalVars :: ReadTCState m => m LocalVars
+getLocalVars = useScope scopeLocals
+
+modifyLocalVars :: (LocalVars -> LocalVars) -> ScopeM ()
+modifyLocalVars = modifyScope_ . updateScopeLocals
+
+setLocalVars :: LocalVars -> ScopeM ()
+setLocalVars vars = modifyLocalVars $ const vars
+
+-- | Run a computation without changing the local variables.
+withLocalVars :: ScopeM a -> ScopeM a
+withLocalVars = bracket_ getLocalVars setLocalVars
+
+-- | Run a computation outside some number of local variables and add them back afterwards. This
+--   lets you bind variables in the middle of the context and is used when binding generalizable
+--   variables (#3735).
+outsideLocalVars :: Int -> ScopeM a -> ScopeM a
+outsideLocalVars n m = do
+  inner <- take n <$> getLocalVars
+  modifyLocalVars (drop n)
+  x <- m
+  modifyLocalVars (inner ++)
+  return x
+
+-- | Check that the newly added variable have unique names.
+
+withCheckNoShadowing :: ScopeM a -> ScopeM a
+withCheckNoShadowing = bracket_ getLocalVars $ \ lvarsOld ->
+  checkNoShadowing lvarsOld =<< getLocalVars
+
+checkNoShadowing :: LocalVars  -- ^ Old local scope
+                 -> LocalVars  -- ^ New local scope
+                 -> ScopeM ()
+checkNoShadowing old new = do
+  opts <- pragmaOptions
+  when (ShadowingInTelescope_ `Set.member`
+          (optWarningMode opts ^. warningSet)) $ do
+    -- LocalVars is currnently an AssocList so the difference between
+    -- two local scope is the left part of the new one.
+    let diff = dropEnd (length old) new
+    -- Filter out the underscores.
+    let newNames = filter (not . isNoName) $ AssocList.keys diff
+    -- Associate each name to its occurrences.
+    let nameOccs1 :: [(C.Name, List1 Range)]
+        nameOccs1 = Map.toList $ Map.fromListWith (<>) $ map pairWithRange newNames
+    -- Warn if we have two or more occurrences of the same name.
+    let nameOccs2 :: [(C.Name, List2 Range)]
+        nameOccs2 = mapMaybe (traverseF List2.fromList1Maybe) nameOccs1
+    caseList nameOccs2 (return ()) $ \ c conflicts -> do
+      scopeWarning $ ShadowingInTelescope $ c :| conflicts
+  where
+    pairWithRange :: C.Name -> (C.Name, List1 Range)
+    pairWithRange n = (n, singleton $ getRange n)
+
+getVarsToBind :: ScopeM LocalVars
+getVarsToBind = useScope scopeVarsToBind
+
+addVarToBind :: C.Name -> LocalVar -> ScopeM ()
+addVarToBind x y = modifyScope_ $ updateVarsToBind $ AssocList.insert x y
+
+-- | After collecting some variable names in the scopeVarsToBind,
+--   bind them all simultaneously.
+bindVarsToBind :: ScopeM ()
+bindVarsToBind = do
+  vars <- getVarsToBind
+  modifyLocalVars (vars ++)
+  printLocals 10 "bound variables:"
+  modifyScope_ $ setVarsToBind []
+
+annotateDecls :: ReadTCState m => m [A.Declaration] -> m A.Declaration
+annotateDecls m = do
+  ds <- m
+  s  <- getScope
+  return $ A.ScopedDecl s ds
+
+annotateExpr :: ReadTCState m => m A.Expr -> m A.Expr
+annotateExpr m = do
+  e <- m
+  s <- getScope
+  return $ A.ScopedExpr s e
+
+---------------------------------------------------------------------------
+-- * Names
+---------------------------------------------------------------------------
+
+-- | Create a fresh abstract name from a concrete name.
+--
+--   This function is used when we translate a concrete name
+--   in a binder.  The 'Range' of the concrete name is
+--   saved as the 'nameBindingSite' of the abstract name.
+freshAbstractName :: Fixity' -> C.Name -> ScopeM A.Name
+freshAbstractName fx x = do
+  i <- fresh
+  return $ A.Name
+    { nameId          = i
+    , nameConcrete    = x
+    , nameCanonical   = x
+    , nameBindingSite = getRange x
+    , nameFixity      = fx
+    , nameIsRecordName = False
+    }
+
+-- | @freshAbstractName_ = freshAbstractName noFixity'@
+freshAbstractName_ :: C.Name -> ScopeM A.Name
+freshAbstractName_ = freshAbstractName noFixity'
+
+-- | Create a fresh abstract qualified name.
+freshAbstractQName :: Fixity' -> C.Name -> ScopeM A.QName
+freshAbstractQName fx x = do
+  y <- freshAbstractName fx x
+  m <- getCurrentModule
+  return $ A.qualify m y
+
+freshAbstractQName' :: C.Name -> ScopeM A.QName
+freshAbstractQName' x = do
+  fx <- getConcreteFixity x
+  freshAbstractQName fx x
+
+-- | Create a concrete name that is not yet in scope.
+-- | NOTE: See @chooseName@ in @Agda.Syntax.Translation.AbstractToConcrete@ for similar logic.
+-- | NOTE: See @withName@ in @Agda.Syntax.Translation.ReflectedToAbstract@ for similar logic.
+freshConcreteName :: Range -> Int -> String -> ScopeM C.Name
+freshConcreteName r i s = do
+  let cname = C.Name r C.NotInScope $ singleton $ Id $ stringToRawName $ s ++ show i
+  resolveName (C.QName cname) >>= \case
+    UnknownName -> return cname
+    _           -> freshConcreteName r (i + 1) s
+
+---------------------------------------------------------------------------
+-- * Resolving names
+---------------------------------------------------------------------------
+
+-- | Look up the abstract name referred to by a given concrete name.
+resolveName :: C.QName -> ScopeM ResolvedName
+resolveName = resolveName' allKindsOfNames Nothing
+
+-- | Look up the abstract name corresponding to a concrete name of
+--   a certain kind and/or from a given set of names.
+--   Sometimes we know already that we are dealing with a constructor
+--   or pattern synonym (e.g. when we have parsed a pattern).
+--   Then, we can ignore conflicting definitions of that name
+--   of a different kind. (See issue 822.)
+resolveName' ::
+  KindsOfNames -> Maybe (Set A.Name) -> C.QName -> ScopeM ResolvedName
+resolveName' kinds names x = runExceptT (tryResolveName kinds names x) >>= \case
+  Left reason  -> do
+    reportS "scope.resolve" 60 $ unlines $
+      "resolveName': ambiguous name" :
+      map (show . qnameName) (toList $ ambiguousNamesInReason reason)
+    setCurrentRange x $ typeError $ AmbiguousName x reason
+  Right x' -> return x'
+
+tryResolveName
+  :: forall m. (ReadTCState m, HasBuiltins m, MonadError AmbiguousNameReason m)
+  => KindsOfNames       -- ^ Restrict search to these kinds of names.
+  -> Maybe (Set A.Name) -- ^ Unless 'Nothing', restrict search to match any of these names.
+  -> C.QName            -- ^ Name to be resolved
+  -> m ResolvedName     -- ^ If illegally ambiguous, throw error with the ambiguous name.
+tryResolveName kinds names x = do
+  scope <- getScope
+  let vars     = AssocList.mapKeysMonotonic C.QName $ scope ^. scopeLocals
+  case lookup x vars of
+
+    -- Case: we have a local variable x, but is (perhaps) shadowed by some imports ys.
+    Just var@(LocalVar y b ys) ->
+      -- We may ignore the imports filtered out by the @names@ filter.
+      case nonEmpty $ filterNames id ys of
+        Nothing  -> return $ VarName y{ nameConcrete = unqualify x } b
+        Just ys' -> throwError $ AmbiguousLocalVar var ys'
+
+    -- Case: we do not have a local variable x.
+    Nothing -> do
+      -- Consider only names that are in the given set of names and
+      -- are of one of the given kinds
+      let filtKind = filter $ (`elemKindsOfNames` kinds) . anameKind . fst
+          possibleNames z = filtKind $ filterNames fst $ scopeLookup' z scope
+      -- If the name has a suffix, also consider the possibility that
+      -- the base name is in scope (e.g. the builtin sorts `Set` and `Prop`).
+      canHaveSuffix <- canHaveSuffixTest
+      let (xsuffix, xbase) = (C.lensQNameName . nameSuffix) (,Nothing) x
+          possibleBaseNames = filter (canHaveSuffix . anameName . fst) $ possibleNames xbase
+          suffixedNames = (,) <$> fromConcreteSuffix xsuffix <*> nonEmpty possibleBaseNames
+      case (nonEmpty $ possibleNames x) of
+        Just ds  | let ks = fmap (isConName . anameKind . fst) ds
+                 , all isJust ks
+                 , isNothing suffixedNames ->
+          return $ ConstructorName (Set.fromList $ List1.catMaybes ks) $ fmap (upd . fst) ds
+
+        Just ds  | all ((FldName ==) . anameKind . fst) ds , isNothing suffixedNames ->
+          return $ FieldName $ fmap (upd . fst) ds
+
+        Just ds  | all ((PatternSynName ==) . anameKind . fst) ds , isNothing suffixedNames ->
+          return $ PatternSynResName $ fmap (upd . fst) ds
+
+        Just ((d, a) :| ds) -> case (suffixedNames, ds) of
+          (Nothing, []) ->
+            return $ DefinedName a (upd d) A.NoSuffix
+          (Nothing, (d',_) : ds') ->
+            throwError $ AmbiguousDeclName $ List2 d d' $ map fst ds'
+          (Just (_, ss), _) ->
+            throwError $ AmbiguousDeclName $ List2.append (d :| map fst ds) (fmap fst ss)
+
+        Nothing -> case suffixedNames of
+          Nothing -> return UnknownName
+          Just (suffix , (d, a) :| []) -> return $ DefinedName a (upd d) suffix
+          Just (suffix , (d1,_) :| (d2,_) : sds) ->
+            throwError $ AmbiguousDeclName $ List2 d1 d2 $ map fst sds
+
+  where
+  -- @names@ intended semantics: a filter on names.
+  -- @Nothing@: don't filter out anything.
+  -- @Just ns@: filter by membership in @ns@.
+  filterNames :: forall a. (a -> AbstractName) -> [a] -> [a]
+  filterNames = case names of
+    Nothing -> \ f -> id
+    Just ns -> \ f -> filter $ (`Set.member` ns) . A.qnameName . anameName . f
+    -- lambda-dropped style by intention
+  upd d = updateConcreteName d $ unqualify x
+  updateConcreteName :: AbstractName -> C.Name -> AbstractName
+  updateConcreteName d@(AbsName { anameName = A.QName qm qn }) x =
+    d { anameName = A.QName (setRange (getRange x) qm) (qn { nameConcrete = x }) }
+  fromConcreteSuffix = \case
+    Nothing              -> Nothing
+    Just C.Prime{}       -> Nothing
+    Just (C.Index i)     -> Just $ A.Suffix i
+    Just (C.Subscript i) -> Just $ A.Suffix i
+
+-- | Test if a given abstract name can appear with a suffix. Currently
+--   only true for the names of builtin sorts.
+canHaveSuffixTest :: HasBuiltins m => m (A.QName -> Bool)
+canHaveSuffixTest = do
+  builtinProp <- getBuiltinName' builtinProp
+  builtinSet  <- getBuiltinName' builtinSet
+  builtinSSet <- getBuiltinName' builtinStrictSet
+  builtinPropOmega <- getBuiltinName' builtinPropOmega
+  builtinSetOmega <- getBuiltinName' builtinSetOmega
+  builtinSSetOmega <- getBuiltinName' builtinSSetOmega
+  return $ \x -> Just x `elem` [builtinProp, builtinSet, builtinSSet, builtinPropOmega, builtinSetOmega, builtinSSetOmega]
+
+-- | Look up a module in the scope.
+resolveModule :: C.QName -> ScopeM AbstractModule
+resolveModule x = do
+  ms <- scopeLookup x <$> getScope
+  caseMaybe (nonEmpty ms) (typeError $ NoSuchModule x) $ \ case
+    AbsModule m why :| [] -> return $ AbsModule (m `withRangeOf` x) why
+    ms                    -> typeError $ AmbiguousModule x (fmap amodName ms)
+
+-- | Get the fixity of a not yet bound name.
+getConcreteFixity :: C.Name -> ScopeM Fixity'
+getConcreteFixity x = Map.findWithDefault noFixity' x <$> useScope scopeFixities
+
+-- | Get the polarities of a not yet bound name.
+getConcretePolarity :: C.Name -> ScopeM (Maybe [Occurrence])
+getConcretePolarity x = Map.lookup x <$> useScope scopePolarities
+
+instance MonadFixityError ScopeM where
+  throwMultipleFixityDecls xs         = case xs of
+    (x, _) : _ -> setCurrentRange (getRange x) $ typeError $ MultipleFixityDecls xs
+    []         -> __IMPOSSIBLE__
+  throwMultiplePolarityPragmas xs     = case xs of
+    x : _ -> setCurrentRange (getRange x) $ typeError $ MultiplePolarityPragmas xs
+    []    -> __IMPOSSIBLE__
+  warnUnknownNamesInFixityDecl        = scopeWarning . UnknownNamesInFixityDecl
+  warnUnknownNamesInPolarityPragmas   = scopeWarning . UnknownNamesInPolarityPragmas
+  warnUnknownFixityInMixfixDecl       = scopeWarning . UnknownFixityInMixfixDecl
+  warnPolarityPragmasButNotPostulates = scopeWarning . PolarityPragmasButNotPostulates
+
+-- | Collect the fixity/syntax declarations and polarity pragmas from the list
+--   of declarations and store them in the scope.
+computeFixitiesAndPolarities :: DoWarn -> [C.Declaration] -> ScopeM a -> ScopeM a
+computeFixitiesAndPolarities warn ds cont = do
+  fp <- fixitiesAndPolarities warn ds
+  -- Andreas, 2019-08-16:
+  -- Since changing fixities and polarities does not affect the name sets,
+  -- we do not need to invoke @modifyScope@ here
+  -- (which does @recomputeInverseScopeMaps@).
+  -- A simple @locallyScope@ is sufficient.
+  locallyScope scopeFixitiesAndPolarities (const fp) cont
+
+-- | Get the notation of a name. The name is assumed to be in scope.
+getNotation
+  :: C.QName
+  -> Set A.Name
+     -- ^ The name must correspond to one of the names in this set.
+  -> ScopeM NewNotation
+getNotation x ns = do
+  r <- resolveName' allKindsOfNames (Just ns) x
+  case r of
+    VarName y _         -> return $ namesToNotation x y
+    DefinedName _ d _   -> return $ notation d
+    FieldName ds        -> return $ oneNotation ds
+    ConstructorName _ ds-> return $ oneNotation ds
+    PatternSynResName n -> return $ oneNotation n
+    UnknownName         -> __IMPOSSIBLE__
+  where
+    notation = namesToNotation x . qnameName . anameName
+    oneNotation = List1.head . mergeNotations . fmap notation
+
+---------------------------------------------------------------------------
+-- * Binding names
+---------------------------------------------------------------------------
+
+-- | Bind a variable.
+bindVariable
+  :: A.BindingSource -- ^ @λ@, @Π@, @let@, ...?
+  -> C.Name          -- ^ Concrete name.
+  -> A.Name          -- ^ Abstract name.
+  -> ScopeM ()
+bindVariable b x y = modifyLocalVars $ AssocList.insert x $ LocalVar y b []
+
+-- | Temporarily unbind a variable. Used for non-recursive lets.
+unbindVariable :: C.Name -> ScopeM a -> ScopeM a
+unbindVariable x = bracket_ (getLocalVars <* modifyLocalVars (AssocList.delete x)) (modifyLocalVars . const)
+
+-- | Bind a defined name. Must not shadow anything.
+bindName :: Access -> KindOfName -> C.Name -> A.QName -> ScopeM ()
+bindName acc kind x y = bindName' acc kind NoMetadata x y
+
+bindName' :: Access -> KindOfName -> NameMetadata -> C.Name -> A.QName -> ScopeM ()
+bindName' acc kind meta x y = whenJustM (bindName'' acc kind meta x y) typeError
+
+-- | Bind a name. Returns the 'TypeError' if exists, but does not throw it.
+bindName'' :: Access -> KindOfName -> NameMetadata -> C.Name -> A.QName -> ScopeM (Maybe TypeError)
+bindName'' acc kind meta x y = do
+  when (isNoName x) $ modifyScopes $ Map.map $ removeNameFromScope PrivateNS x
+  r  <- resolveName (C.QName x)
+  let y' :: Either TypeError AbstractName
+      y' = case r of
+        -- Binding an anonymous declaration always succeeds.
+        -- In case it's not the first one, we simply remove the one that came before
+        _ | isNoName x      -> success
+        DefinedName _ d _   -> clash $ anameName d
+        VarName z _         -> clash $ A.qualify_ z
+        FieldName       ds  -> ambiguous (== FldName) ds
+        ConstructorName i ds-> ambiguous (isJust . isConName) ds
+        PatternSynResName n -> ambiguous (== PatternSynName) n
+        UnknownName         -> success
+  let ns = if isNoName x then PrivateNS else localNameSpace acc
+  traverse_ (modifyCurrentScope . addNameToScope ns x) y'
+  pure $ either Just (const Nothing) y'
+  where
+    success = Right $ AbsName y kind Defined meta
+    clash n = Left $ ClashingDefinition (C.QName x) n Nothing
+
+    ambiguous f ds =
+      if f kind && all (f . anameKind) ds
+      then success else clash $ anameName (List1.head ds)
+
+-- | Rebind a name. Use with care!
+--   Ulf, 2014-06-29: Currently used to rebind the name defined by an
+--   unquoteDecl, which is a 'QuotableName' in the body, but a 'DefinedName'
+--   later on.
+rebindName :: Access -> KindOfName -> C.Name -> A.QName -> ScopeM ()
+rebindName acc kind x y = do
+  if kind == ConName
+    then modifyCurrentScope $
+           mapScopeNS (localNameSpace acc)
+                      (Map.update (nonEmpty . List1.filter ((ConName ==) . anameKind)) x)
+                      id
+                      id
+    else modifyCurrentScope $ removeNameFromScope (localNameSpace acc) x
+  bindName acc kind x y
+
+-- | Bind a module name.
+bindModule :: Access -> C.Name -> A.ModuleName -> ScopeM ()
+bindModule acc x m = modifyCurrentScope $
+  addModuleToScope (localNameSpace acc) x (AbsModule m Defined)
+
+-- | Bind a qualified module name. Adds it to the imports field of the scope.
+bindQModule :: Access -> C.QName -> A.ModuleName -> ScopeM ()
+bindQModule acc q m = modifyCurrentScope $ \s ->
+  s { scopeImports = Map.insert q m (scopeImports s) }
+
+---------------------------------------------------------------------------
+-- * Module manipulation operations
+---------------------------------------------------------------------------
+
+-- | Clear the scope of any no names.
+stripNoNames :: ScopeM ()
+stripNoNames = modifyScopes $ Map.map $ mapScope_ stripN stripN id
+  where
+    stripN = Map.filterWithKey $ const . not . isNoName
+
+type WSM = StateT ScopeMemo ScopeM
+
+data ScopeMemo = ScopeMemo
+  { memoNames   :: A.Ren A.QName
+  , memoModules :: Map ModuleName (ModuleName, Bool)
+    -- ^ Bool: did we copy recursively? We need to track this because we don't
+    --   copy recursively when creating new modules for reexported functions
+    --   (issue1985), but we might need to copy recursively later.
+  }
+
+memoToScopeInfo :: ScopeMemo -> ScopeCopyInfo
+memoToScopeInfo (ScopeMemo names mods) =
+  ScopeCopyInfo { renNames   = names
+                , renModules = Map.map (pure . fst) mods }
+
+-- | Mark a name as being a copy in the TC state.
+copyName :: A.QName -> A.QName -> ScopeM ()
+copyName from to = do
+  from <- fromMaybe from . HMap.lookup from <$> useTC stCopiedNames
+  modifyTCLens stCopiedNames $ HMap.insert to from
+  let
+    k Nothing  = Just (HSet.singleton to)
+    k (Just s) = Just (HSet.insert to s)
+  modifyTCLens stNameCopies $ HMap.alter k from
+
+-- | Create a new scope with the given name from an old scope. Renames
+--   public names in the old scope to match the new name and returns the
+--   renamings.
+copyScope :: C.QName -> A.ModuleName -> Scope -> ScopeM (Scope, ScopeCopyInfo)
+copyScope oldc new0 s = (inScopeBecause (Applied oldc) *** memoToScopeInfo) <$> runStateT (copy new0 s) (ScopeMemo mempty mempty)
+  where
+    copy :: A.ModuleName -> Scope -> WSM Scope
+    copy new s = do
+      lift $ reportSLn "scope.copy" 20 $ "Copying scope " ++ prettyShow old ++ " to " ++ prettyShow new
+      lift $ reportSLn "scope.copy" 50 $ prettyShow s
+      s0 <- lift $ getNamedScope new
+      -- Delete private names, then copy names and modules. Recompute inScope
+      -- set rather than trying to copy it.
+      s' <- recomputeInScopeSets <$> mapScopeM_ copyD copyM return (setNameSpace PrivateNS emptyNameSpace s)
+      -- Fix name and parent.
+      return $ s' { scopeName    = scopeName s0
+                  , scopeParents = scopeParents s0
+                  }
+      where
+        rnew = getRange new
+        new' = killRange new
+        newL = A.mnameToList new'
+        old  = scopeName s
+
+        copyD :: NamesInScope -> WSM NamesInScope
+        copyD = traverse $ mapM $ onName renName
+
+        copyM :: ModulesInScope -> WSM ModulesInScope
+        copyM = traverse $ mapM $ lensAmodName renMod
+
+        onName :: (A.QName -> WSM A.QName) -> AbstractName -> WSM AbstractName
+        onName f d =
+          case anameKind d of
+            PatternSynName -> return d  -- Pattern synonyms are simply aliased, not renamed
+            _ -> lensAnameName f d
+
+        -- Adding to memo structure.
+        addName x y     = modify $ \ i -> i { memoNames   = Map.insertWith (<>) x (pure y) (memoNames i) }
+        addMod  x y rec = modify $ \ i -> i { memoModules = Map.insert x (y, rec) (memoModules i) }
+
+        -- Querying the memo structure.
+        findName x = gets (Map.lookup x . memoNames) -- NB:: Defined but not used
+        findMod  x = gets (Map.lookup x . memoModules)
+
+        refresh :: A.Name -> WSM A.Name
+        refresh x = do
+          i <- lift fresh
+          return $ x { A.nameId = i }
+
+        -- Change a binding M.x -> old.M'.y to M.x -> new.M'.y
+        renName :: A.QName -> WSM A.QName
+        renName x = do
+          -- Issue 1985: For re-exported names we can't use new' as the
+          -- module, since it has the wrong telescope. Example:
+          --
+          --    module M1 (A : Set) where
+          --      module M2 (B : Set) where
+          --        postulate X : Set
+          --      module M3 (C : Set) where
+          --        module M4 (D E : Set) where
+          --          open M2 public
+          --
+          --    module M = M1.M3 A C
+          --
+          -- Here we can't copy M1.M2.X to M.M4.X since we need
+          -- X : (B : Set) → Set, but M.M4 has telescope (D E : Set). Thus, we
+          -- would break the invariant that all functions in a module share the
+          -- module telescope. Instead we copy M1.M2.X to M.M2.X for a fresh
+          -- module M2 that gets the right telescope.
+          m <- if x `isInModule` old
+                 then return new'
+                 else renMod' False (qnameModule x)
+                          -- Don't copy recursively here, we only know that the
+                          -- current name x should be copied.
+          -- Generate a fresh name for the target.
+          -- Andreas, 2015-08-11 Issue 1619:
+          -- Names copied by a module macro should get the module macro's
+          -- range as declaration range
+          -- (maybe rather the one of the open statement).
+          -- For now, we just set their range
+          -- to the new module name's one, which fixes issue 1619.
+          y <- setRange rnew . A.qualify m <$> refresh (qnameName x)
+          lift $ reportSLn "scope.copy" 50 $ "  Copying " ++ prettyShow x ++ " to " ++ prettyShow y
+          addName x y
+          lift (copyName x y)
+          return y
+
+        -- Change a binding M.x -> old.M'.y to M.x -> new.M'.y
+        renMod :: A.ModuleName -> WSM A.ModuleName
+        renMod = renMod' True
+
+        renMod' rec x = do
+          -- Andreas, issue 1607:
+          -- If we have already copied this module, return the copy.
+          z <- findMod x
+          case z of
+            Just (y, False) | rec -> y <$ copyRec x y
+            Just (y, _)           -> return y
+            Nothing -> do
+            -- Ulf (issue 1985): If copying a reexported module we put it at the
+            -- top-level, to make sure we don't mess up the invariant that all
+            -- (abstract) names M.f share the argument telescope of M.
+            let newM = if x `isLtChildModuleOf` old then newL else mnameToList new0
+
+            y <- do
+               -- Andreas, Jesper, 2015-07-02: Issue 1597
+               -- Don't blindly drop a prefix of length of the old qualifier.
+               -- If things are imported by open public they do not have the old qualifier
+               -- as prefix.  Those need just to be linked, not copied.
+               -- return $ A.mnameFromList $ (newL ++) $ drop (size old) $ A.mnameToList x
+               -- caseMaybe (stripPrefix (A.mnameToList old) (A.mnameToList x)) (return x) $ \ suffix -> do
+               --   return $ A.mnameFromList $ newL ++ suffix
+               -- Ulf, 2016-02-22: #1726
+               -- We still need to copy modules from 'open public'. Same as in renName.
+               y <- refresh $ lastWithDefault __IMPOSSIBLE__ $ A.mnameToList x
+               return $ A.mnameFromList $ newM ++ [y]
+            -- Andreas, Jesper, 2015-07-02: Issue 1597
+            -- Don't copy a module over itself, it will just be emptied of its contents.
+            if (x == y) then return x else do
+            lift $ reportSLn "scope.copy" 50 $ "  Copying module " ++ prettyShow x ++ " to " ++ prettyShow y
+            addMod x y rec
+            lift $ createModule Nothing y
+            -- We need to copy the contents of included modules recursively (only when 'rec')
+            when rec $ copyRec x y
+            return y
+          where
+            copyRec x y = do
+              s0 <- lift $ getNamedScope x
+              s  <- withCurrentModule' y $ copy y s0
+              lift $ modifyNamedScope y (const s)
+
+---------------------------------------------------------------------------
+-- * Import directives
+---------------------------------------------------------------------------
+
+-- | Warn about useless fixity declarations in @renaming@ directives.
+--   Monadic for the sake of error reporting.
+checkNoFixityInRenamingModule :: [C.Renaming] -> ScopeM ()
+checkNoFixityInRenamingModule ren = do
+  whenJust (nonEmpty $ mapMaybe rangeOfUselessInfix ren) $ \ rs -> do
+    setCurrentRange rs $ do
+      warning $ FixityInRenamingModule rs
+  where
+  rangeOfUselessInfix :: C.Renaming -> Maybe Range
+  rangeOfUselessInfix = \case
+    Renaming ImportedModule{} _ mfx _ -> getRange <$> mfx
+    _ -> Nothing
+
+-- Moved here carefully from Parser.y to preserve the archaeological artefact
+-- dating from Oct 2005 (5ba14b647b9bd175733f9563e744176425c39126).
+-- | Check that an import directive doesn't contain repeated names.
+verifyImportDirective :: [C.ImportedName] -> C.HidingDirective -> C.RenamingDirective -> ScopeM ()
+verifyImportDirective usn hdn ren =
+    case filter (not . null . List1.tail)
+         $ List1.group
+         $ List.sort xs
+    of
+        []  -> return ()
+        yss -> setCurrentRange yss $ genericError $
+                "Repeated name" ++ s ++ " in import directive: " ++
+                concat (List.intersperse ", " $ map (prettyShow . List1.head) yss)
+            where
+                s = case yss of
+                        [_] -> ""
+                        _   -> "s"
+    where
+        xs = usn ++ hdn ++ map renFrom ren
+
+-- | Apply an import directive and check that all the names mentioned actually
+--   exist.
+--
+--   Monadic for the sake of error reporting.
+applyImportDirectiveM
+  :: C.QName                           -- ^ Name of the scope, only for error reporting.
+  -> C.ImportDirective                 -- ^ Description of how scope is to be modified.
+  -> Scope                             -- ^ Input scope.
+  -> ScopeM (A.ImportDirective, Scope) -- ^ Scope-checked description, output scope.
+applyImportDirectiveM m (ImportDirective rng usn' hdn' ren' public) scope0 = do
+
+    -- Module names do not come with fixities, thus, we should complain if the
+    -- user has supplied fixity annotations to @renaming module@ clauses.
+    checkNoFixityInRenamingModule ren'
+
+    -- Andreas, 2020-06-06, issue #4707
+    -- Duplicates in @using@ directive are dropped with a warning.
+    usingList <- discardDuplicatesInUsing usn'
+
+    -- The following check was originally performed by the parser.
+    -- The Great Ulf Himself added the check back in the dawn of time
+    -- (5ba14b647b9bd175733f9563e744176425c39126)
+    -- when Agda 2 wasn't even believed to exist yet.
+    verifyImportDirective usingList hdn' ren'
+
+    -- We start by checking that all of the names talked about in the import
+    -- directive do exist.  If some do not then we remove them and raise a warning.
+    let (missingExports, namesA) = checkExist $ usingList ++ hdn' ++ map renFrom ren'
+    unless (null missingExports) $ setCurrentRange rng $ do
+      reportSLn "scope.import.apply" 20 $ "non existing names: " ++ prettyShow missingExports
+      warning $ ModuleDoesntExport m (Map.keys namesInScope) (Map.keys modulesInScope) missingExports
+
+    -- We can now define a cleaned-up version of the import directive.
+    let notMissing = not . (missingExports `hasElem`)  -- #3997, efficient lookup in missingExports
+    let usn = filter notMissing usingList        -- remove missingExports from usn'
+    let hdn = filter notMissing hdn'             -- remove missingExports from hdn'
+    let ren = filter (notMissing . renFrom) ren'                   -- and from ren'
+    let dir = ImportDirective rng (mapUsing (const usn) usn') hdn ren public
+
+    -- Convenient shorthands for defined names and names brought into scope:
+    let names        = map renFrom ren ++ hdn ++ usn
+    let definedNames = map renTo ren
+    let targetNames  = usn ++ definedNames
+
+    -- Efficient test of (`elem` names):
+    let inNames      = (names `hasElem`)
+
+    -- Efficient test of whether a module import should be added to the import
+    -- of a definition (like a data or record definition).
+    let extra x = inNames (ImportedName   x)
+               && notMissing (ImportedModule x)
+               && (not . inNames $ ImportedModule x)
+                  -- The last test implies that @hiding (module M)@ prevents @module M@
+                  -- from entering the @using@ list in @addExtraModule@.
+
+    dir' <- sanityCheck (not . inNames) $ addExtraModules extra dir
+
+    -- Check for duplicate imports in a single import directive.
+    -- @dup@ : To be imported names that are mentioned more than once.
+    unlessNull (allDuplicates targetNames) $ \ dup ->
+      typeError $ DuplicateImports m dup
+
+    -- Apply the import directive.
+    let (scope', (nameClashes, moduleClashes)) = applyImportDirective_ dir' scope
+
+    -- Andreas, 2019-11-08, issue #4154, report clashes
+    -- introduced by the @renaming@.
+    unless (null nameClashes) $
+      warning $ ClashesViaRenaming NameNotModule $ Set.toList nameClashes
+    unless (null moduleClashes) $
+      warning $ ClashesViaRenaming ModuleNotName $ Set.toList moduleClashes
+
+    -- Look up the defined names in the new scope.
+    let namesInScope'   = (allNamesInScope scope' :: ThingsInScope AbstractName)
+    let modulesInScope' = (allNamesInScope scope' :: ThingsInScope AbstractModule)
+    let look x = List1.head . Map.findWithDefault __IMPOSSIBLE__ x
+    -- We set the ranges to the ranges of the concrete names in order to get
+    -- highlighting for the names in the import directive.
+    let definedA = for definedNames $ \case
+          ImportedName   x -> ImportedName   . (x,) . setRange (getRange x) . anameName $ look x namesInScope'
+          ImportedModule x -> ImportedModule . (x,) . setRange (getRange x) . amodName  $ look x modulesInScope'
+
+    let adir = mapImportDir namesA definedA dir
+    return (adir, scope') -- TODO Issue 1714: adir
+
+  where
+    -- Andreas, 2020-06-23, issue #4773, fixing regression in 2.5.1.
+    -- Import directive may not mention private things.
+    -- ```agda
+    --   module M where private X = Set
+    --   module N = M using (X)
+    -- ```
+    -- Further, modules (N) need not copy private things (X) from other
+    -- modules (M) ever, since they cannot legally referred to
+    -- (neither through qualification (N.X) nor open N).
+    -- Thus, we can unconditionally remove private definitions
+    -- before we apply the import directive.
+    scope = restrictPrivate scope0
+
+    -- Return names in the @using@ directive, discarding duplicates.
+    -- Monadic for the sake of throwing warnings.
+    discardDuplicatesInUsing :: C.Using -> ScopeM [C.ImportedName]
+    discardDuplicatesInUsing = \case
+      UseEverything -> return []
+      Using  xs     -> do
+        let (ys, dups) = nubAndDuplicatesOn id xs
+        List1.unlessNull dups $ warning . DuplicateUsing
+        return ys
+
+    -- If both @using@ and @hiding@ directive are present,
+    -- the hiding directive may only contain modules whose twins are mentioned.
+    -- Monadic for the sake of error reporting.
+    sanityCheck notMentioned = \case
+      dir@(ImportDirective{ using = Using{}, hiding = ys }) -> do
+          let useless = \case
+                ImportedName{}   -> True
+                ImportedModule y -> notMentioned (ImportedName y)
+          unlessNull (filter useless ys) $ warning . UselessHiding
+          -- We can empty @hiding@ now, since there is an explicit @using@ directive
+          -- and @hiding@ served its purpose to prevent modules to enter the @Using@ list.
+          return dir{ hiding = [] }
+      dir -> return dir
+
+    addExtraModules :: (C.Name -> Bool) -> C.ImportDirective -> C.ImportDirective
+    addExtraModules extra dir =
+      dir{ using       = mapUsing (concatMap addExtra) $ using dir
+         , hiding      = concatMap addExtra            $ hiding dir
+         , impRenaming = concatMap extraRenaming       $ impRenaming dir
+         }
+      where
+        addExtra f@(ImportedName y) | extra y = [f, ImportedModule y]
+        addExtra m = [m]
+
+        extraRenaming = \case
+          r@(Renaming (ImportedName y) (ImportedName z) _fixity rng) | extra y ->
+             [ r , Renaming (ImportedModule y) (ImportedModule z) Nothing rng ]
+          r -> [r]
+
+    -- Names and modules (abstract) in scope before the import.
+    namesInScope   = (allNamesInScope scope :: ThingsInScope AbstractName)
+    modulesInScope = (allNamesInScope scope :: ThingsInScope AbstractModule)
+    concreteNamesInScope = (Map.keys namesInScope ++ Map.keys modulesInScope :: [C.Name])
+
+    -- AST versions of the concrete names passed as an argument.
+    -- We get back a pair consisting of a list of missing exports first,
+    -- and a list of successful imports second.
+    checkExist :: [ImportedName] -> ([ImportedName], [ImportedName' (C.Name, A.QName) (C.Name, A.ModuleName)])
+    checkExist xs = partitionEithers $ for xs $ \ name -> case name of
+      ImportedName x   -> ImportedName   . (x,) . setRange (getRange x) . anameName <$> resolve name x namesInScope
+      ImportedModule x -> ImportedModule . (x,) . setRange (getRange x) . amodName  <$> resolve name x modulesInScope
+      where
+        resolve :: Ord a => err -> a -> Map a (List1 b) -> Either err b
+        resolve err x m = maybe (Left err) (Right . List1.head) $ Map.lookup x m
+
+-- | Translation of @ImportDirective@.
+mapImportDir
+  :: (Ord n1, Ord m1)
+  => [ImportedName' (n1,n2) (m1,m2)]  -- ^ Translation of imported names.
+  -> [ImportedName' (n1,n2) (m1,m2)]  -- ^ Translation of names defined by this import.
+  -> ImportDirective' n1 m1
+  -> ImportDirective' n2 m2
+mapImportDir src0 tgt0 (ImportDirective r u h ren open) =
+  ImportDirective r
+    (mapUsing (map (lookupImportedName src)) u)
+    (map (lookupImportedName src) h)
+    (map (mapRenaming src tgt) ren)
+    open
+  where
+  src = importedNameMapFromList src0
+  tgt = importedNameMapFromList tgt0
+
+-- | A finite map for @ImportedName@s.
+
+data ImportedNameMap n1 n2 m1 m2 = ImportedNameMap
+  { inameMap   :: Map n1 n2
+  , imoduleMap :: Map m1 m2
+  }
+
+-- | Create a 'ImportedNameMap'.
+importedNameMapFromList
+  :: (Ord n1, Ord m1)
+  => [ImportedName' (n1,n2) (m1,m2)]
+  -> ImportedNameMap n1 n2 m1 m2
+importedNameMapFromList = foldr (flip add) $ ImportedNameMap Map.empty Map.empty
+  where
+  add (ImportedNameMap nm mm) = \case
+    ImportedName   (x,y) -> ImportedNameMap (Map.insert x y nm) mm
+    ImportedModule (x,y) -> ImportedNameMap nm (Map.insert x y mm)
+
+-- | Apply a 'ImportedNameMap'.
+lookupImportedName
+  :: (Ord n1, Ord m1)
+  => ImportedNameMap n1 n2 m1 m2
+  -> ImportedName' n1 m1
+  -> ImportedName' n2 m2
+lookupImportedName (ImportedNameMap nm mm) = \case
+    ImportedName   x -> ImportedName   $ Map.findWithDefault __IMPOSSIBLE__ x nm
+    ImportedModule x -> ImportedModule $ Map.findWithDefault __IMPOSSIBLE__ x mm
+
+-- | Translation of @Renaming@.
+mapRenaming
+  ::  (Ord n1, Ord m1)
+  => ImportedNameMap n1 n2 m1 m2  -- ^ Translation of 'renFrom' names and module names.
+  -> ImportedNameMap n1 n2 m1 m2  -- ^ Translation of 'rento'   names and module names.
+  -> Renaming' n1 m1  -- ^ Renaming before translation (1).
+  -> Renaming' n2 m2  -- ^ Renaming after  translation (2).
+mapRenaming src tgt (Renaming from to fixity r) =
+  Renaming (lookupImportedName src from) (lookupImportedName tgt to) fixity r
+
+---------------------------------------------------------------------------
+-- * Opening a module
+---------------------------------------------------------------------------
+
+data OpenKind = LetOpenModule | TopOpenModule
+
+noGeneralizedVarsIfLetOpen :: OpenKind -> Scope -> Scope
+noGeneralizedVarsIfLetOpen TopOpenModule = id
+noGeneralizedVarsIfLetOpen LetOpenModule = disallowGeneralizedVars
+
+-- | Open a module.
+openModule_ :: OpenKind -> C.QName -> C.ImportDirective -> ScopeM A.ImportDirective
+openModule_ kind cm dir = openModule kind Nothing cm dir
+
+-- | Open a module, possibly given an already resolved module name.
+openModule :: OpenKind -> Maybe A.ModuleName  -> C.QName -> C.ImportDirective -> ScopeM A.ImportDirective
+openModule kind mam cm dir = do
+  current <- getCurrentModule
+  m <- caseMaybe mam (amodName <$> resolveModule cm) return
+  let acc | Nothing <- publicOpen dir     = PrivateNS
+          | m `isLtChildModuleOf` current = PublicNS
+          | otherwise                     = ImportedNS
+
+  -- Get the scope exported by module to be opened.
+  (adir, s') <- applyImportDirectiveM cm dir . inScopeBecause (Opened cm) .
+                noGeneralizedVarsIfLetOpen kind =<< getNamedScope m
+  let s  = setScopeAccess acc s'
+  let ns = scopeNameSpace acc s
+  modifyCurrentScope (`mergeScope` s)
+  -- Andreas, 2018-06-03, issue #3057:
+  -- If we simply check for ambiguous exported identifiers _after_
+  -- importing the new identifiers into the current scope, we also
+  -- catch the case of importing an ambiguous identifier.
+  checkForClashes
+
+  -- Importing names might shadow existing locals.
+  verboseS "scope.locals" 10 $ do
+    locals <- mapMaybe (\ (c,x) -> c <$ notShadowedLocal x) <$> getLocalVars
+    let newdefs = Map.keys $ nsNames ns
+        shadowed = locals `List.intersect` newdefs
+    reportSLn "scope.locals" 10 $ "opening module shadows the following locals vars: " ++ prettyShow shadowed
+  -- Andreas, 2014-09-03, issue 1266: shadow local variables by imported defs.
+  modifyLocalVars $ AssocList.mapWithKey $ \ c x ->
+    case Map.lookup c $ nsNames ns of
+      Nothing -> x
+      Just ys -> shadowLocal ys x
+
+  return adir
+
+  where
+    -- Only checks for clashes that would lead to the same
+    -- name being exported twice from the module.
+    checkForClashes = when (isJust $ publicOpen dir) $ do
+
+        exported <- allThingsInScope . restrictPrivate <$> (getNamedScope =<< getCurrentModule)
+
+        -- Get all exported concrete names that are mapped to at least 2 abstract names
+        let defClashes = filter (\ (_c, as) -> length as >= 2) $ Map.toList $ nsNames exported
+            modClashes = filter (\ (_c, as) -> length as >= 2) $ Map.toList $ nsModules exported
+
+            -- No ambiguity if concrete identifier is only mapped to
+            -- constructor names or only to projection names or only to pattern synonyms.
+            defClash (_, qs) = not $ or
+              [ all (isJust . isConName) ks
+              , all (== FldName)         ks
+              , all (== PatternSynName)  ks
+              ]
+              where ks = fmap anameKind qs
+        -- We report the first clashing exported identifier.
+        unlessNull (filter defClash defClashes) $
+          \ ((x, q :| _) : _) -> typeError $ ClashingDefinition (C.QName x) (anameName q) Nothing
+
+        unlessNull modClashes $ \ ((_, ms) : _) -> do
+          caseMaybe (List1.last2 ms) __IMPOSSIBLE__ $ \ (m0, m1) -> do
+            typeError $ ClashingModule (amodName m0) (amodName m1)
diff --git a/src/full/Agda/Syntax/TopLevelModuleName.hs b/src/full/Agda/Syntax/TopLevelModuleName.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/TopLevelModuleName.hs
@@ -0,0 +1,205 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- Top-level module names
+------------------------------------------------------------------------
+
+module Agda.Syntax.TopLevelModuleName
+  ( module Agda.Syntax.TopLevelModuleName
+  , module Agda.Syntax.TopLevelModuleName.Boot
+  ) where
+
+import Agda.Syntax.TopLevelModuleName.Boot
+
+import Control.DeepSeq
+
+import Data.Function (on)
+import qualified Data.List as List
+import qualified Data.Text as T
+
+import GHC.Generics (Generic)
+
+import System.FilePath
+
+import qualified Agda.Syntax.Abstract.Name as A
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Position
+
+import Agda.Utils.FileName
+import Agda.Utils.Hash
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+import qualified Agda.Utils.List1 as List1
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+------------------------------------------------------------------------
+-- Raw top-level module names
+
+-- | Raw top-level module names (with linear-time comparisons).
+
+data RawTopLevelModuleName = RawTopLevelModuleName
+  { rawModuleNameRange :: Range
+  , rawModuleNameParts :: TopLevelModuleNameParts
+  }
+  deriving (Show, Generic)
+
+instance Eq RawTopLevelModuleName where
+  (==) = (==) `on` rawModuleNameParts
+
+instance Ord RawTopLevelModuleName where
+  compare = compare `on` rawModuleNameParts
+
+instance Sized RawTopLevelModuleName where
+  size = size . rawModuleNameParts
+  natSize = natSize . rawModuleNameParts
+
+instance Pretty RawTopLevelModuleName where
+  pretty = text . rawTopLevelModuleNameToString
+
+instance HasRange RawTopLevelModuleName where
+  getRange = rawModuleNameRange
+
+instance SetRange RawTopLevelModuleName where
+  setRange r (RawTopLevelModuleName _ x) = RawTopLevelModuleName r x
+
+instance KillRange RawTopLevelModuleName where
+  killRange (RawTopLevelModuleName _ x) =
+    RawTopLevelModuleName noRange x
+
+instance C.IsNoName RawTopLevelModuleName where
+  isNoName m = rawModuleNameParts m == singleton "_"
+
+-- | The 'Range' is not forced.
+
+instance NFData RawTopLevelModuleName where
+  rnf (RawTopLevelModuleName _ x) = rnf x
+
+-- | Turns a raw top-level module name into a string.
+
+rawTopLevelModuleNameToString :: RawTopLevelModuleName -> String
+rawTopLevelModuleNameToString =
+  List.intercalate "." .
+  map T.unpack . List1.toList . rawModuleNameParts
+
+-- | Hashes a raw top-level module name.
+
+hashRawTopLevelModuleName :: RawTopLevelModuleName -> ModuleNameHash
+hashRawTopLevelModuleName =
+  ModuleNameHash . hashString . rawTopLevelModuleNameToString
+
+-- | Turns a qualified name into a 'RawTopLevelModuleName'. The
+-- qualified name is assumed to represent a top-level module name.
+
+rawTopLevelModuleNameForQName :: C.QName -> RawTopLevelModuleName
+rawTopLevelModuleNameForQName q = RawTopLevelModuleName
+  { rawModuleNameRange = getRange q
+  , rawModuleNameParts =
+      fmap (T.pack . C.nameToRawName) $ C.qnameParts q
+  }
+
+-- | Computes the 'RawTopLevelModuleName' corresponding to the given
+-- module name, which is assumed to represent a top-level module name.
+--
+-- Precondition: The module name must be well-formed.
+
+rawTopLevelModuleNameForModuleName ::
+  A.ModuleName -> RawTopLevelModuleName
+rawTopLevelModuleNameForModuleName (A.MName []) = __IMPOSSIBLE__
+rawTopLevelModuleNameForModuleName (A.MName ms) =
+  List1.ifNull ms __IMPOSSIBLE__ $ \ms ->
+  RawTopLevelModuleName
+    { rawModuleNameRange = getRange ms
+    , rawModuleNameParts =
+        fmap (T.pack . C.nameToRawName . A.nameConcrete) ms
+    }
+
+-- | Computes the top-level module name.
+--
+-- Precondition: The 'C.Module' has to be well-formed.
+-- This means that there are only allowed declarations before the
+-- first module declaration, typically import declarations.
+-- See 'spanAllowedBeforeModule'.
+
+rawTopLevelModuleNameForModule :: C.Module -> RawTopLevelModuleName
+rawTopLevelModuleNameForModule (C.Mod _ []) = __IMPOSSIBLE__
+rawTopLevelModuleNameForModule (C.Mod _ ds) =
+  case C.spanAllowedBeforeModule ds of
+    (_, C.Module _ _ n _ _ : _) -> rawTopLevelModuleNameForQName n
+    _                           -> __IMPOSSIBLE__
+
+------------------------------------------------------------------------
+-- Top-level module names
+
+-- | Top-level module names (with constant-time comparisons).
+
+type TopLevelModuleName = TopLevelModuleName' Range
+
+instance Sized TopLevelModuleName where
+  size = size . rawTopLevelModuleName
+  natSize = natSize . rawTopLevelModuleName
+
+instance Pretty TopLevelModuleName where
+  pretty = pretty . rawTopLevelModuleName
+
+-- | A lens focusing on the 'moduleNameParts'.
+
+lensTopLevelModuleNameParts ::
+  Lens' TopLevelModuleName TopLevelModuleNameParts
+lensTopLevelModuleNameParts f m =
+  f (moduleNameParts m) <&> \ xs -> m{ moduleNameParts = xs }
+
+-- | Converts a top-level module name to a raw top-level module name.
+
+rawTopLevelModuleName :: TopLevelModuleName -> RawTopLevelModuleName
+rawTopLevelModuleName m = RawTopLevelModuleName
+  { rawModuleNameRange = moduleNameRange m
+  , rawModuleNameParts = moduleNameParts m
+  }
+
+-- | Converts a raw top-level module name and a hash to a top-level
+-- module name.
+--
+-- This function does not ensure that there are no hash collisions,
+-- that is taken care of by
+-- 'Agda.TypeChecking.Monad.State.topLevelModuleName'.
+
+unsafeTopLevelModuleName ::
+  RawTopLevelModuleName -> ModuleNameHash -> TopLevelModuleName
+unsafeTopLevelModuleName m h = TopLevelModuleName
+  { moduleNameRange = rawModuleNameRange m
+  , moduleNameParts = rawModuleNameParts m
+  , moduleNameId    = h
+  }
+
+-- | A corresponding 'C.QName'. The range of each 'Name' part is the
+-- whole range of the 'TopLevelModuleName'.
+
+topLevelModuleNameToQName :: TopLevelModuleName -> C.QName
+topLevelModuleNameToQName m =
+  List1.foldr C.Qual C.QName $
+  fmap (C.Name (getRange m) C.NotInScope .
+        C.stringNameParts . T.unpack) $
+  moduleNameParts m
+
+-- | Turns a top-level module name into a file name with the given
+-- suffix.
+
+moduleNameToFileName :: TopLevelModuleName -> String -> FilePath
+moduleNameToFileName TopLevelModuleName{ moduleNameParts = ms } ext =
+  joinPath (map T.unpack $ List1.init ms) </>
+  T.unpack (List1.last ms) <.> ext
+
+-- | Finds the current project's \"root\" directory, given a project
+-- file and the corresponding top-level module name.
+--
+-- Example: If the module \"A.B.C\" is located in the file
+-- \"/foo/A/B/C.agda\", then the root is \"/foo/\".
+--
+-- Precondition: The module name must be well-formed.
+
+projectRoot :: AbsolutePath -> TopLevelModuleName -> AbsolutePath
+projectRoot file TopLevelModuleName{ moduleNameParts = m } =
+  mkAbsolute $
+    iterate takeDirectory (filePath file) !! length m
diff --git a/src/full/Agda/Syntax/TopLevelModuleName/Boot.hs b/src/full/Agda/Syntax/TopLevelModuleName/Boot.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/TopLevelModuleName/Boot.hs
@@ -0,0 +1,60 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Syntax.TopLevelModuleName.Boot where
+
+import Agda.Utils.List1 (List1)
+import Agda.Utils.BiMap (HasTag, Tag, tag)
+
+import Control.DeepSeq (NFData, rnf)
+import Data.Function (on)
+import Data.Hashable (Hashable, hashWithSalt)
+import Data.Text (Text)
+import Data.Word (Word64)
+import GHC.Generics (Generic)
+
+newtype ModuleNameHash = ModuleNameHash { moduleNameHash :: Word64 }
+  deriving (Eq, Ord, Hashable)
+
+instance NFData ModuleNameHash where
+  rnf _ = ()
+
+instance HasTag ModuleNameHash where
+  type Tag ModuleNameHash = ModuleNameHash
+  tag = Just . id
+
+noModuleNameHash :: ModuleNameHash
+noModuleNameHash = ModuleNameHash 0
+
+-- | The record selector is not included in the resulting strings.
+
+instance Show ModuleNameHash where
+  showsPrec p (ModuleNameHash h) = showParen (p > 0) $
+    showString "ModuleNameHash " . shows h
+
+type TopLevelModuleNameParts = List1 Text
+
+data TopLevelModuleName' range = TopLevelModuleName
+  { moduleNameRange :: range
+  , moduleNameId    :: {-# UNPACK #-} !ModuleNameHash
+  , moduleNameParts :: TopLevelModuleNameParts
+  }
+  deriving (Show, Generic)
+
+instance HasTag (TopLevelModuleName' range) where
+  type Tag (TopLevelModuleName' range) = ModuleNameHash
+  tag = Just . moduleNameId
+
+instance Eq (TopLevelModuleName' range) where
+  (==) = (==) `on` moduleNameId
+
+instance Ord (TopLevelModuleName' range) where
+  compare = compare `on` moduleNameId
+
+instance Hashable (TopLevelModuleName' range) where
+  hashWithSalt salt = hashWithSalt salt . moduleNameId
+
+-- | The 'range' is not forced.
+
+instance NFData (TopLevelModuleName' range) where
+  rnf (TopLevelModuleName _ x y) = rnf (x, y)
+
diff --git a/src/full/Agda/Syntax/Translation/AbstractToConcrete.hs b/src/full/Agda/Syntax/Translation/AbstractToConcrete.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Translation/AbstractToConcrete.hs
@@ -0,0 +1,1876 @@
+{-# LANGUAGE CPP #-}
+
+-- {-# OPTIONS -fwarn-unused-binds #-}
+
+{-| The translation of abstract syntax to concrete syntax has two purposes.
+    First it allows us to pretty print abstract syntax values without having to
+    write a dedicated pretty printer, and second it serves as a sanity check
+    for the concrete to abstract translation: translating from concrete to
+    abstract and then back again should be (more or less) the identity.
+-}
+module Agda.Syntax.Translation.AbstractToConcrete
+    ( ToConcrete(..)
+    , toConcreteCtx
+    , abstractToConcrete_
+    , abstractToConcreteScope
+    , abstractToConcreteHiding
+    , runAbsToCon
+    , RangeAndPragma(..)
+    , abstractToConcreteCtx
+    , withScope
+    , preserveInteractionIds
+    , MonadAbsToCon, AbsToCon, Env
+    , noTakenNames
+    , lookupQName
+    ) where
+
+import Prelude hiding (null)
+
+import Control.Monad        ( (<=<), forM, forM_, guard, liftM2 )
+import Control.Monad.Except ( runExceptT )
+import Control.Monad.Reader ( MonadReader(..), asks, runReaderT )
+import Control.Monad.State  ( StateT(..), runStateT )
+
+import qualified Control.Monad.Fail as Fail
+
+import Data.Bifunctor       ( first )
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.Monoid hiding ((<>))
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Map (Map)
+import qualified Data.Foldable as Fold
+import Data.Void
+import Data.List (sortBy)
+import Data.Semigroup ( Semigroup, (<>), sconcat )
+import Data.String
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+import Agda.Syntax.Info as A
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Fixity
+import Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Pattern as C
+import Agda.Syntax.Concrete.Glyph
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views as A
+import Agda.Syntax.Abstract.Pattern as A
+import Agda.Syntax.Abstract.PatternSynonyms
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Scope.Monad ( tryResolveName )
+
+import Agda.TypeChecking.Monad.State (getScope, getAllPatternSyns)
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.MetaVars
+import Agda.TypeChecking.Monad.Pure
+import Agda.TypeChecking.Monad.Signature
+import {-# SOURCE #-} Agda.TypeChecking.Pretty (prettyTCM)
+import Agda.Interaction.Options
+
+import qualified Agda.Utils.AssocList as AssocList
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|), (<|) )
+import Agda.Utils.List2 (List2, pattern List2)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Aspect as Asp
+import Agda.Syntax.Common.Pretty hiding ((<>))
+import Agda.Utils.Singleton
+import Agda.Utils.Suffix
+
+import Agda.Utils.Impossible
+
+-- Environment ------------------------------------------------------------
+
+data Env = Env { takenVarNames :: Set A.Name
+                  -- ^ Abstract names currently in scope. Unlike the
+                  --   ScopeInfo, this includes names for hidden
+                  --   arguments inserted by the system.
+               , takenDefNames :: Set C.NameParts
+                  -- ^ Concrete names of all definitions in scope
+               , currentScope :: ScopeInfo
+               , builtins     :: Map BuiltinId A.QName
+                  -- ^ Certain builtins (like `fromNat`) have special printing
+               , preserveIIds :: Bool
+                  -- ^ Preserve interaction point ids
+               , foldPatternSynonyms :: Bool
+               }
+
+makeEnv :: MonadAbsToCon m => ScopeInfo -> m Env
+makeEnv scope = do
+      -- zero and suc doesn't have to be in scope for natural number literals to work
+  let noScopeCheck b = b `elem` [builtinZero, builtinSuc]
+      name (I.Def q _)   = Just q
+      name (I.Con q _ _) = Just (I.conName q)
+      name _             = Nothing
+      builtin b = getBuiltin' b >>= \ case
+        Just v | Just q <- name v,
+                 noScopeCheck b || isNameInScope q scope -> return [(b, q)]
+        _                                                -> return []
+  ctxVars <- map (fst . I.unDom) <$> asksTC envContext
+  letVars <- Map.keys <$> asksTC envLetBindings
+  let vars = ctxVars ++ letVars
+
+  -- pick concrete names for in-scope names now so we don't
+  -- accidentally shadow them
+  forM_ (scope ^. scopeLocals) $ \(y , x) -> do
+    pickConcreteName (localVar x) y
+
+  builtinList <- concat <$> mapM builtin [ builtinFromNat, builtinFromString, builtinFromNeg, builtinZero, builtinSuc ]
+  foldPatSyns <- optPrintPatternSynonyms <$> pragmaOptions
+  return $
+    Env { takenVarNames = Set.fromList vars
+        , takenDefNames = defs
+        , currentScope = scope
+        , builtins     = Map.fromListWith __IMPOSSIBLE__ builtinList
+        , preserveIIds = False
+        , foldPatternSynonyms = foldPatSyns
+        }
+  where
+    defs = Set.map nameParts . Map.keysSet $
+        Map.filterWithKey usefulDef $
+        nsNames $ everythingInScope scope
+
+    -- Jesper, 2018-12-10: It's fine to shadow generalizable names as
+    -- they will never show up directly in printed terms.
+    notGeneralizeName AbsName{ anameKind = k }  =
+      not (k == GeneralizeName || k == DisallowedGeneralizeName)
+
+    usefulDef C.NoName{} _ = False
+    usefulDef C.Name{} names = all notGeneralizeName names
+
+    nameParts (C.NoName {}) = __IMPOSSIBLE__
+    nameParts (C.Name { nameNameParts }) = nameNameParts
+
+currentPrecedence :: AbsToCon PrecedenceStack
+currentPrecedence = asks $ (^. scopePrecedence) . currentScope
+
+preserveInteractionIds :: AbsToCon a -> AbsToCon a
+preserveInteractionIds = local $ \ e -> e { preserveIIds = True }
+
+withPrecedence' :: PrecedenceStack -> AbsToCon a -> AbsToCon a
+withPrecedence' ps = local $ \e ->
+  e { currentScope = set scopePrecedence ps (currentScope e) }
+
+withPrecedence :: Precedence -> AbsToCon a -> AbsToCon a
+withPrecedence p ret = do
+  ps <- currentPrecedence
+  withPrecedence' (pushPrecedence p ps) ret
+
+withScope :: ScopeInfo -> AbsToCon a -> AbsToCon a
+withScope scope = local $ \e -> e { currentScope = scope }
+
+noTakenNames :: AbsToCon a -> AbsToCon a
+noTakenNames = local $ \e -> e { takenVarNames = Set.empty }
+
+dontFoldPatternSynonyms :: AbsToCon a -> AbsToCon a
+dontFoldPatternSynonyms = local $ \ e -> e { foldPatternSynonyms = False }
+
+-- | Bind a concrete name to an abstract in the translation environment.
+addBinding :: C.Name -> A.Name -> Env -> Env
+addBinding y x e =
+  e { takenVarNames = Set.insert x $ takenVarNames e
+    , currentScope = (`updateScopeLocals` currentScope e) $
+        AssocList.insert y (LocalVar x __IMPOSSIBLE__ [])
+    }
+
+-- | Get a function to check if a name refers to a particular builtin function.
+isBuiltinFun :: AbsToCon (A.QName -> BuiltinId -> Bool)
+isBuiltinFun = asks $ is . builtins
+  where is m q b = Just q == Map.lookup b m
+
+-- | Resolve a concrete name. If illegally ambiguous fail with the ambiguous names.
+resolveName :: KindsOfNames -> Maybe (Set A.Name) -> C.QName -> AbsToCon (Either AmbiguousNameReason ResolvedName)
+resolveName kinds candidates q = runExceptT $ tryResolveName kinds candidates q
+
+-- | Treat illegally ambiguous names as UnknownNames.
+resolveName_ :: C.QName -> [A.Name] -> AbsToCon ResolvedName
+resolveName_ q cands = fromRight (const UnknownName) <$> resolveName allKindsOfNames (Just $ Set.fromList cands) q
+
+-- The Monad --------------------------------------------------------------
+
+-- | The function 'runAbsToCon' can target any monad that satisfies
+-- the constraints of 'MonadAbsToCon'.
+type MonadAbsToCon m =
+  ( MonadFresh NameId m
+  , MonadInteractionPoints m
+  , MonadStConcreteNames m
+  , HasOptions m
+  , PureTCM m
+  , IsString (m Doc)
+  , Null (m Doc)
+  , Semigroup (m Doc)
+  )
+
+newtype AbsToCon a = AbsToCon
+  { unAbsToCon :: forall m.
+      ( MonadReader Env m
+      , MonadAbsToCon m
+      ) => m a
+  }
+
+-- TODO: Is there some way to automatically derive these boilerplate
+-- instances?  GeneralizedNewtypeDeriving fails us here.
+instance Functor AbsToCon where
+  fmap f x = AbsToCon $ f <$> unAbsToCon x
+
+instance Applicative AbsToCon where
+  pure x = AbsToCon $ pure x
+  f <*> m = AbsToCon $ unAbsToCon f <*> unAbsToCon m
+
+instance Monad AbsToCon where
+  -- ASR (2021-02-07). The eta-expansion @\m' -> unAbsToCon m'@ is
+  -- required by GHC >= 9.0.1 (see Issue #4955).
+  m >>= f = AbsToCon $ unAbsToCon m >>= (\m' -> unAbsToCon m'). f
+#if __GLASGOW_HASKELL__ < 808
+  fail = Fail.fail
+#endif
+
+instance Fail.MonadFail AbsToCon where
+  fail = error
+
+instance MonadReader Env AbsToCon where
+  ask = AbsToCon ask
+  local f m = AbsToCon $ local f $ unAbsToCon m
+
+instance MonadTCEnv AbsToCon where
+  askTC = AbsToCon askTC
+  localTC f m = AbsToCon $ localTC f $ unAbsToCon m
+
+instance ReadTCState AbsToCon where
+  getTCState = AbsToCon getTCState
+  locallyTCState l f m = AbsToCon $ locallyTCState l f $ unAbsToCon m
+
+instance MonadStConcreteNames AbsToCon where
+  -- ASR (2021-02-07). The eta-expansion @\m' -> unAbsToCon m'@ is
+  -- required by GHC >= 9.0.1 (see Issue #4955).
+  runStConcreteNames m =
+    AbsToCon $ runStConcreteNames $ StateT $ (\m' -> unAbsToCon m') . runStateT m
+
+instance HasBuiltins AbsToCon where
+  getBuiltinThing x = AbsToCon $ getBuiltinThing x
+
+instance HasOptions AbsToCon where
+  pragmaOptions = AbsToCon pragmaOptions
+  commandLineOptions = AbsToCon commandLineOptions
+
+instance MonadDebug AbsToCon where
+  formatDebugMessage k n s      = AbsToCon $ formatDebugMessage k n s
+  traceDebugMessage  k n s cont = AbsToCon $ traceDebugMessage  k n s $ unAbsToCon cont  -- can't eta-reduce!
+  verboseBracket     k n s cont = AbsToCon $ verboseBracket     k n s $ unAbsToCon cont  -- because of GHC-9.0
+
+  getVerbosity      = defaultGetVerbosity
+  getProfileOptions = defaultGetProfileOptions
+  isDebugPrinting   = defaultIsDebugPrinting
+  nowDebugPrinting  = defaultNowDebugPrinting
+
+instance HasConstInfo AbsToCon where
+  getConstInfo' a      = AbsToCon (getConstInfo' a)
+  getRewriteRulesFor a = AbsToCon (getRewriteRulesFor a)
+
+instance MonadAddContext AbsToCon where
+  addCtx a b c = AbsToCon (addCtx a b (unAbsToCon c))
+
+  addLetBinding' o a b c d =
+    AbsToCon (addLetBinding' o a b c (unAbsToCon d))
+
+  updateContext a b c = AbsToCon (updateContext a b (unAbsToCon c))
+
+  withFreshName a b c =
+    AbsToCon (withFreshName a b (\x -> unAbsToCon (c x)))
+
+instance MonadReduce AbsToCon where
+  liftReduce a = AbsToCon (liftReduce a)
+
+instance PureTCM AbsToCon where
+
+instance MonadFresh NameId AbsToCon where
+  fresh = AbsToCon fresh
+
+instance MonadInteractionPoints AbsToCon where
+  freshInteractionId        = AbsToCon freshInteractionId
+  modifyInteractionPoints a = AbsToCon (modifyInteractionPoints a)
+
+instance IsString (AbsToCon Doc) where
+  fromString a = AbsToCon (fromString a)
+
+instance Null (AbsToCon Doc) where
+  empty = AbsToCon empty
+  null  = __IMPOSSIBLE__
+
+instance Semigroup (AbsToCon Doc) where
+  a <> b = AbsToCon (unAbsToCon a <> unAbsToCon b)
+
+runAbsToCon :: MonadAbsToCon m => AbsToCon c -> m c
+runAbsToCon m = do
+  scope <- getScope
+  verboseBracket "toConcrete" 50 "runAbsToCon" $ do
+    reportSLn "toConcrete" 50 $ render $ hsep $
+      [ "entering AbsToCon with scope:"
+      , prettyList_ (map (text . C.nameToRawName . fst) $ scope ^. scopeLocals)
+      ]
+    x <- runReaderT (unAbsToCon m) =<< makeEnv scope
+    reportSLn "toConcrete" 50 $ "leaving AbsToCon"
+    return x
+
+abstractToConcreteScope :: (ToConcrete a, MonadAbsToCon m)
+                        => ScopeInfo -> a -> m (ConOfAbs a)
+abstractToConcreteScope scope a = runReaderT (unAbsToCon $ toConcrete a) =<< makeEnv scope
+
+abstractToConcreteCtx :: (ToConcrete a, MonadAbsToCon m)
+                      => Precedence -> a -> m (ConOfAbs a)
+abstractToConcreteCtx ctx x = runAbsToCon $ withPrecedence ctx (toConcrete x)
+
+abstractToConcrete_ :: (ToConcrete a, MonadAbsToCon m)
+                    => a -> m (ConOfAbs a)
+abstractToConcrete_ = runAbsToCon . toConcrete
+
+abstractToConcreteHiding :: (LensHiding i, ToConcrete a, MonadAbsToCon m)
+                         => i -> a -> m (ConOfAbs a)
+abstractToConcreteHiding i = runAbsToCon . toConcreteHiding i
+
+-- Dealing with names -----------------------------------------------------
+
+-- | Names in abstract syntax are fully qualified, but the concrete syntax
+--   requires non-qualified names in places. In theory (if all scopes are
+--   correct), we should get a non-qualified name when translating back to a
+--   concrete name, but I suspect the scope isn't always perfect. In these
+--   cases we just throw away the qualified part. It's just for pretty printing
+--   anyway...
+unsafeQNameToName :: C.QName -> C.Name
+unsafeQNameToName = C.unqualify
+
+lookupQName :: AllowAmbiguousNames -> A.QName -> AbsToCon C.QName
+lookupQName ambCon x | Just s <- getGeneralizedFieldName x =
+  return (C.QName $ C.Name noRange C.InScope $ C.stringNameParts s)
+lookupQName ambCon x = do
+  ys <- asks (inverseScopeLookupName' ambCon x . currentScope)
+  reportSLn "scope.inverse" 100 $
+    "inverse looking up abstract name " ++ prettyShow x ++ " yields " ++ prettyShow ys
+  loop ys
+
+  where
+    -- Found concrete name: check that it is not shadowed by a local
+    loop (qy@Qual{}      : _ ) = return qy -- local names cannot be qualified
+    loop (qy@(C.QName y) : ys) = lookupNameInScope y >>= \case
+      Just x' | x' /= qnameName x -> loop ys
+      _ -> return qy
+    -- Found no concrete name: make up a new one
+    loop [] = case qnameToConcrete x of
+      qy@Qual{}    -> return $ setNotInScope qy
+      qy@C.QName{} -> C.QName <$> chooseName (qnameName x)
+
+lookupModule :: A.ModuleName -> AbsToCon C.QName
+lookupModule (A.MName []) = return $ C.QName $ C.simpleName "-1"
+  -- Andreas, 2016-10-10 it can happen that we have an empty module name
+  -- for instance when we query the current module inside the
+  -- frontmatter or module telescope of the top level module.
+  -- In this case, we print it as an invalid module name.
+  -- (Should only affect debug printing.)
+lookupModule x =
+    do  scope <- asks currentScope
+        case inverseScopeLookupModule x scope of
+            (y : _) -> return y
+            []      -> return $ mnameToConcrete x
+                -- this is what happens for names that are not in scope (private names)
+
+-- | Is this concrete name currently in use by a particular abstract
+--   name in the current scope?
+lookupNameInScope :: C.Name -> AbsToCon (Maybe A.Name)
+lookupNameInScope y =
+  asks ((fmap localVar . lookup y) . ((^. scopeLocals) . currentScope))
+
+-- | Have we already committed to a specific concrete name for this
+--   abstract name? If yes, return the concrete name(s).
+hasConcreteNames :: (MonadStConcreteNames m) => A.Name -> m [C.Name]
+hasConcreteNames x = Map.findWithDefault [] x <$> useConcreteNames
+
+-- | Commit to a specific concrete name for printing the given
+--   abstract name. If the abstract name already has associated
+---  concrete name(s), the new name is only used when all previous
+---  names are shadowed. Precondition: the abstract name should be in
+--   scope.
+pickConcreteName :: (MonadStConcreteNames m) => A.Name -> C.Name -> m ()
+pickConcreteName x y = modifyConcreteNames $ flip Map.alter x $ \case
+    Nothing   -> Just $ [y]
+    (Just ys) -> Just $ ys ++ [y]
+
+-- | For the given abstract name, return the names that could shadow it.
+shadowingNames :: (ReadTCState m, MonadStConcreteNames m)
+               => A.Name -> m (Set RawName)
+shadowingNames x =
+  Set.fromList . Fold.toList . Map.findWithDefault mempty x <$>
+    useR stShadowingNames
+
+toConcreteName :: A.Name -> AbsToCon C.Name
+toConcreteName x | y <- nameConcrete x , isNoName y = return y
+toConcreteName x = (Map.findWithDefault [] x <$> useConcreteNames) >>= loop
+  where
+    -- case: we already have picked some name(s) for x
+    loop (y:ys) = ifM (isGoodName x y) (return y) (loop ys)
+
+    -- case: we haven't picked a concrete name yet, or all previously
+    -- picked names are shadowed, so we pick a new name now
+    loop [] = do
+      y <- chooseName x
+      pickConcreteName x y
+      return y
+
+    -- Is 'y' a good concrete name for abstract name 'x'?
+    isGoodName :: A.Name -> C.Name -> AbsToCon Bool
+    isGoodName x y = do
+      zs <- asks (Set.toList . takenVarNames)
+      allM zs $ \z -> if x == z then return True else do
+        czs <- hasConcreteNames z
+        return $ notElem y czs
+
+
+-- | Choose a new unshadowed name for the given abstract name
+-- | NOTE: See @withName@ in @Agda.Syntax.Translation.ReflectedToAbstract@ for similar logic.
+-- | NOTE: See @freshConcreteName@ in @Agda.Syntax.Scope.Monad@ also for similar logic.
+chooseName :: A.Name -> AbsToCon C.Name
+chooseName x = lookupNameInScope (nameConcrete x) >>= \case
+  -- If the name is currently in scope, we do not rename it
+  Just x' | x == x' -> do
+    reportSLn "toConcrete.bindName" 80 $
+      "name " ++ C.nameToRawName (nameConcrete x) ++ " already in scope, so not renaming"
+    return $ nameConcrete x
+  -- Otherwise we pick a name that does not shadow other names
+  _ -> do
+    takenDefs <- asks takenDefNames
+    taken   <- takenNames
+    toAvoid <- shadowingNames x
+    glyphMode <- optUseUnicode <$> pragmaOptions
+    let freshNameMode = case glyphMode of
+          UnicodeOk -> A.UnicodeSubscript
+          AsciiOnly -> A.AsciiCounter
+
+        shouldAvoid C.NoName {} = False
+        shouldAvoid name@C.Name { nameNameParts } =
+          let raw = C.nameToRawName name in
+          nameNameParts `Set.member` takenDefs ||
+          raw `Set.member` taken ||
+          raw `Set.member` toAvoid
+
+        y = firstNonTakenName freshNameMode shouldAvoid $ nameConcrete x
+    reportSLn "toConcrete.bindName" 80 $ render $ vcat
+      [ "picking concrete name for:" <+> text (C.nameToRawName $ nameConcrete x)
+      , "names already taken:      " <+> prettyList_ (Set.toList taken)
+      , "names to avoid:           " <+> prettyList_ (Set.toList toAvoid)
+      , "concrete name chosen:     " <+> text (C.nameToRawName y)
+      ]
+    return y
+
+  where
+    takenNames :: AbsToCon (Set RawName)
+    takenNames = do
+      ys0 <- asks takenVarNames
+      reportSLn "toConcrete.bindName" 90 $ render $ "abstract names of local vars: " <+> prettyList_ (map (C.nameToRawName . nameConcrete) $ Set.toList ys0)
+      ys <- Set.fromList . concat <$> mapM hasConcreteNames (Set.toList ys0)
+      return $ Set.map C.nameToRawName ys
+
+
+-- | Add a abstract name to the scope and produce an available concrete version of it.
+bindName :: A.Name -> (C.Name -> AbsToCon a) -> AbsToCon a
+bindName x ret = do
+  y <- toConcreteName x
+  reportSLn "toConcrete.bindName" 30 $ "adding " ++ C.nameToRawName (nameConcrete x) ++ " to the scope under concrete name " ++ C.nameToRawName y
+  local (addBinding y x) $ ret y
+
+-- | Like 'bindName', but do not care whether name is already taken.
+bindName' :: A.Name -> AbsToCon a -> AbsToCon a
+bindName' x ret = do
+  reportSLn "toConcrete.bindName" 30 $ "adding " ++ C.nameToRawName (nameConcrete x) ++ " to the scope with forced name"
+  pickConcreteName x y
+  applyUnless (isNoName y) (local $ addBinding y x) ret
+  where y = nameConcrete x
+
+-- Dealing with precedences -----------------------------------------------
+
+-- | General bracketing function.
+bracket' ::    (e -> e)             -- ^ the bracketing function
+            -> (PrecedenceStack -> Bool) -- ^ Should we bracket things
+                                    --   which have the given
+                                    --   precedence?
+            -> e -> AbsToCon e
+bracket' paren needParen e =
+    do  p <- currentPrecedence
+        return $ if needParen p then paren e else e
+
+-- | Expression bracketing
+bracket :: (PrecedenceStack -> Bool) -> AbsToCon C.Expr -> AbsToCon C.Expr
+bracket par m =
+    do  e <- m
+        bracket' (Paren (getRange e)) par e
+
+-- | Pattern bracketing
+bracketP_ :: (PrecedenceStack -> Bool) -> AbsToCon C.Pattern -> AbsToCon C.Pattern
+bracketP_ par m =
+    do  e <- m
+        bracket' (ParenP (getRange e)) par e
+
+{- UNUSED
+-- | Pattern bracketing
+bracketP :: (PrecedenceStack -> Bool) -> (C.Pattern -> AbsToCon a)
+                                 -> ((C.Pattern -> AbsToCon a) -> AbsToCon a)
+                                 -> AbsToCon a
+bracketP par ret m = m $ \p -> do
+    p <- bracket' (ParenP $ getRange p) par p
+    ret p
+-}
+
+-- | Applications where the argument is a lambda without parentheses need
+--   parens more often than other applications.
+isLambda :: NamedArg A.Expr -> Bool
+isLambda e | notVisible e = False
+isLambda e =
+  case unScope $ namedArg e of
+    A.Lam{}         -> True
+    A.AbsurdLam{}   -> True
+    A.ExtendedLam{} -> True
+    _               -> False
+
+-- Dealing with infix declarations ----------------------------------------
+
+-- | If a name is defined with a fixity that differs from the default, we have
+--   to generate a fixity declaration for that name.
+withInfixDecl :: DefInfo -> C.Name -> AbsToCon [C.Declaration] -> AbsToCon [C.Declaration]
+withInfixDecl i x m = ((fixDecl ++ synDecl) ++) <$> m
+  where
+  fixDecl = [ C.Infix (theFixity $ defFixity i) $ singleton x
+            | theFixity (defFixity i) /= noFixity
+            ]
+  synDecl = [ C.Syntax x $ theNotation $ defFixity i ]
+
+-- Dealing with private definitions ---------------------------------------
+
+-- | Add @abstract@, @private@, @instance@ modifiers.
+withAbstractPrivate :: DefInfo -> AbsToCon [C.Declaration] -> AbsToCon [C.Declaration]
+withAbstractPrivate i m =
+    priv (defAccess i)
+      . abst (A.defAbstract i)
+      . addInstanceB (case A.defInstance i of InstanceDef r -> Just r; NotInstanceDef -> Nothing)
+      <$> m
+    where
+        priv (PrivateAccess UserWritten)
+                         ds = [ C.Private  (getRange ds) UserWritten ds ]
+        priv _           ds = ds
+        abst AbstractDef ds = [ C.Abstract (getRange ds) ds ]
+        abst ConcreteDef ds = ds
+
+addInstanceB :: Maybe Range -> [C.Declaration] -> [C.Declaration]
+addInstanceB (Just r) ds = [ C.InstanceB r ds ]
+addInstanceB Nothing  ds = ds
+
+-- The To Concrete Class --------------------------------------------------
+
+class ToConcrete a where
+    type ConOfAbs a
+    toConcrete :: a -> AbsToCon (ConOfAbs a)
+    bindToConcrete :: a -> (ConOfAbs a -> AbsToCon b) -> AbsToCon b
+
+    -- Christian Sattler, 2017-08-05:
+    -- These default implementations are not valid semantically (at least
+    -- the second one). Perhaps they (it) should be removed.
+    toConcrete     x     = bindToConcrete x return
+    bindToConcrete x ret = ret =<< toConcrete x
+
+-- | Translate something in a context of the given precedence.
+toConcreteCtx :: ToConcrete a => Precedence -> a -> AbsToCon (ConOfAbs a)
+toConcreteCtx p x = withPrecedence p $ toConcrete x
+
+-- | Translate something in a context of the given precedence.
+bindToConcreteCtx :: ToConcrete a => Precedence -> a -> (ConOfAbs a -> AbsToCon b) -> AbsToCon b
+bindToConcreteCtx p x ret = withPrecedence p $ bindToConcrete x ret
+
+-- | Translate something in the top context.
+toConcreteTop :: ToConcrete a => a -> AbsToCon (ConOfAbs a)
+toConcreteTop = toConcreteCtx TopCtx
+
+-- | Translate something in the top context.
+bindToConcreteTop :: ToConcrete a => a -> (ConOfAbs a -> AbsToCon b) -> AbsToCon b
+bindToConcreteTop = bindToConcreteCtx TopCtx
+
+-- | Translate something in a context indicated by 'Hiding' info.
+toConcreteHiding :: (LensHiding h, ToConcrete a) => h -> a -> AbsToCon (ConOfAbs a)
+toConcreteHiding h =
+  case getHiding h of
+    NotHidden  -> toConcrete
+    Hidden     -> toConcreteTop
+    Instance{} -> toConcreteTop
+
+-- | Translate something in a context indicated by 'Hiding' info.
+bindToConcreteHiding :: (LensHiding h, ToConcrete a) => h -> a -> (ConOfAbs a -> AbsToCon b) -> AbsToCon b
+bindToConcreteHiding h =
+  case getHiding h of
+    NotHidden  -> bindToConcrete
+    Hidden     -> bindToConcreteTop
+    Instance{} -> bindToConcreteTop
+
+-- General instances ------------------------------------------------------
+
+instance ToConcrete () where
+  type ConOfAbs () = ()
+  toConcrete = pure
+
+instance ToConcrete Bool where
+  type ConOfAbs Bool = Bool
+  toConcrete = pure
+
+instance ToConcrete Char where
+  type ConOfAbs Char = Char
+  toConcrete = pure
+
+instance ToConcrete a => ToConcrete [a] where
+    type ConOfAbs [a] = [ConOfAbs a]
+
+    toConcrete     = mapM toConcrete
+    bindToConcrete []     ret = ret []
+    bindToConcrete (a:as) ret = bindToConcrete (a :| as) $ \ (c :| cs) -> ret (c:cs)
+
+instance ToConcrete a => ToConcrete (List1 a) where
+    type ConOfAbs (List1 a) = List1 (ConOfAbs a)
+
+    toConcrete     = mapM toConcrete
+    -- Andreas, 2017-04-11, Issue #2543
+    -- The naive `thread'ing does not work as we have to undo
+    -- changes to the Precedence.
+    -- bindToConcrete = thread bindToConcrete
+    bindToConcrete (a :| as) ret = do
+      p <- currentPrecedence  -- save precedence
+      bindToConcrete a $ \ c ->
+        withPrecedence' p $ -- reset precedence
+          bindToConcrete as $ \ cs ->
+            ret (c :| cs)
+
+instance (ToConcrete a1, ToConcrete a2) => ToConcrete (Either a1 a2) where
+    type ConOfAbs (Either a1 a2) = Either (ConOfAbs a1) (ConOfAbs a2)
+
+    toConcrete = traverseEither toConcrete toConcrete
+    bindToConcrete (Left x) ret =
+        bindToConcrete x $ \x ->
+        ret (Left x)
+    bindToConcrete (Right y) ret =
+        bindToConcrete y $ \y ->
+        ret (Right y)
+
+instance (ToConcrete a1, ToConcrete a2) => ToConcrete (a1, a2) where
+    type ConOfAbs (a1, a2) = (ConOfAbs a1, ConOfAbs a2)
+
+    toConcrete (x,y) = liftM2 (,) (toConcrete x) (toConcrete y)
+    bindToConcrete (x,y) ret =
+        bindToConcrete x $ \x ->
+        bindToConcrete y $ \y ->
+        ret (x,y)
+
+instance (ToConcrete a1, ToConcrete a2, ToConcrete a3) => ToConcrete (a1,a2,a3) where
+    type ConOfAbs (a1, a2, a3) = (ConOfAbs a1, ConOfAbs a2, ConOfAbs a3)
+
+    toConcrete (x,y,z) = reorder <$> toConcrete (x,(y,z))
+        where
+            reorder (x,(y,z)) = (x,y,z)
+
+    bindToConcrete (x,y,z) ret = bindToConcrete (x,(y,z)) $ ret . reorder
+        where
+            reorder (x,(y,z)) = (x,y,z)
+
+instance ToConcrete a => ToConcrete (Arg a) where
+    type ConOfAbs (Arg a) = Arg (ConOfAbs a)
+
+    toConcrete (Arg i a) = Arg i <$> toConcreteHiding i a
+
+    bindToConcrete (Arg info x) ret =
+      bindToConcreteHiding info x $ ret . Arg info
+
+instance ToConcrete a => ToConcrete (WithHiding a) where
+  type ConOfAbs (WithHiding a) = WithHiding (ConOfAbs a)
+
+  toConcrete     (WithHiding h a) = WithHiding h <$> toConcreteHiding h a
+  bindToConcrete (WithHiding h a) ret = bindToConcreteHiding h a $ \ a ->
+    ret $ WithHiding h a
+
+instance ToConcrete a => ToConcrete (Named name a)  where
+    type ConOfAbs (Named name a) = Named name (ConOfAbs a)
+    toConcrete = traverse toConcrete
+    bindToConcrete (Named n x) ret = bindToConcrete x $ ret . Named n
+
+instance ToConcrete a => ToConcrete (Ranged a)  where
+    type ConOfAbs (Ranged a) = Ranged (ConOfAbs a)
+    toConcrete = traverse toConcrete
+    bindToConcrete (Ranged r x) ret = bindToConcrete x $ ret . Ranged r
+
+-- Names ------------------------------------------------------------------
+
+instance ToConcrete A.Name where
+  type ConOfAbs A.Name = C.Name
+
+  toConcrete       = toConcreteName
+  bindToConcrete x = bindName x
+
+instance ToConcrete BindName where
+  type ConOfAbs BindName = C.BoundName
+
+  toConcrete       = fmap C.mkBoundName_ . toConcreteName . unBind
+  bindToConcrete x = bindName (unBind x) . (. C.mkBoundName_)
+
+instance ToConcrete A.QName where
+  type ConOfAbs A.QName = C.QName
+
+  toConcrete = lookupQName AmbiguousConProjs
+
+instance ToConcrete A.ModuleName where
+  type ConOfAbs A.ModuleName = C.QName
+  toConcrete = lookupModule
+
+instance ToConcrete AbstractName where
+  type ConOfAbs AbstractName = C.QName
+  toConcrete = toConcrete . anameName
+
+-- | Assumes name is not 'UnknownName'.
+instance ToConcrete ResolvedName where
+  type ConOfAbs ResolvedName = C.QName
+
+  toConcrete = \case
+    VarName x _          -> C.QName <$> toConcrete x
+    DefinedName _ x s    -> addSuffixConcrete s $ toConcrete x
+    FieldName xs         -> toConcrete (List1.head xs)
+    ConstructorName _ xs -> toConcrete (List1.head xs)
+    PatternSynResName xs -> toConcrete (List1.head xs)
+    UnknownName          -> __IMPOSSIBLE__
+
+addSuffixConcrete :: HasOptions m => A.Suffix -> m C.QName -> m C.QName
+addSuffixConcrete A.NoSuffix x = x
+addSuffixConcrete (A.Suffix i) x = do
+  glyphMode <- optUseUnicode <$> pragmaOptions
+  addSuffixConcrete' glyphMode i <$> x
+
+addSuffixConcrete' :: UnicodeOrAscii -> Integer -> C.QName -> C.QName
+addSuffixConcrete' glyphMode i = set (C.lensQNameName . nameSuffix) suffix
+  where
+    suffix = Just $ case glyphMode of
+      UnicodeOk -> Subscript $ fromInteger i
+      AsciiOnly -> Index $ fromInteger i
+
+-- Expression instance ----------------------------------------------------
+
+instance ToConcrete A.Expr where
+    type ConOfAbs A.Expr = C.Expr
+
+    toConcrete (Var x)             = KnownIdent Asp.Bound . C.QName <$> toConcrete x
+    toConcrete (Def' x suffix)     = KnownIdent Asp.Function <$> addSuffixConcrete suffix (toConcrete x)
+    toConcrete (Proj ProjPrefix p) = KnownIdent Asp.Field <$> toConcrete (headAmbQ p)
+    toConcrete (Proj _          p) = C.Dot noRange . KnownIdent Asp.Field <$> toConcrete (headAmbQ p)
+    toConcrete (A.Macro x)         = KnownIdent Asp.Macro <$> toConcrete x
+    toConcrete e@(Con c)           = tryToRecoverPatternSyn e $ KnownIdent (Asp.Constructor Inductive) <$> toConcrete (headAmbQ c)
+        -- for names we have to use the name from the info, since the abstract
+        -- name has been resolved to a fully qualified name (except for
+        -- variables)
+    toConcrete e@(A.Lit i (LitQName x)) = tryToRecoverPatternSyn e $ do
+      x <- lookupQName AmbiguousNothing x
+      let r = getRange i
+      bracket appBrackets $ return $
+        C.App r (C.Quote r) (defaultNamedArg $ C.Ident x)
+    toConcrete e@(A.Lit i l) = tryToRecoverPatternSyn e $ return $ C.Lit (getRange i) l
+
+    -- Andreas, 2014-05-17  We print question marks with their
+    -- interaction id, in case @metaNumber /= Nothing@
+    -- Ulf, 2017-09-20  ... or @preserveIIds == True@.
+    toConcrete (A.QuestionMark i ii) = do
+      preserve <- asks preserveIIds
+      return $ C.QuestionMark (getRange i) $
+                 interactionId ii <$ guard (preserve || isJust (metaNumber i))
+
+    toConcrete (A.Underscore i) =
+      C.Underscore (getRange i) <$>
+      traverse (render <.> prettyTCM)
+        (NamedMeta (metaNameSuggestion i) <$> metaNumber i)
+
+    toConcrete (A.Dot i e) =
+      C.Dot (getRange i) <$> toConcrete e
+
+    toConcrete e@(A.App i e1 e2) = do
+      is <- isBuiltinFun
+      -- Special printing of desugared overloaded literals:
+      --  fromNat 4        --> 4
+      --  fromNeg 4        --> -4
+      --  fromString "foo" --> "foo"
+      -- Only when the corresponding conversion function is in scope and was
+      -- inserted by the system.
+      case (getHead e1, namedArg e2) of
+        (Just (HdDef q), l@A.Lit{})
+          | any (is q) [builtinFromNat, builtinFromString], visible e2,
+            getOrigin i == Inserted -> toConcrete l
+        (Just (HdDef q), A.Lit r (LitNat n))
+          | q `is` builtinFromNeg, visible e2,
+            getOrigin i == Inserted -> toConcrete (A.Lit r (LitNat (-n)))
+        _ ->
+          tryToRecoverPatternSyn e
+          $ tryToRecoverOpApp e
+          $ tryToRecoverNatural e
+          -- or fallback to App
+          $ bracket (appBrackets' $ preferParenless (appParens i) && isLambda e2)
+          $ do e1' <- toConcreteCtx FunctionCtx e1
+               e2' <- toConcreteCtx (ArgumentCtx $ appParens i) e2
+               return $ C.App (getRange i) e1' e2'
+
+    toConcrete (A.WithApp i e es) =
+      bracket withAppBrackets $ do
+        e <- toConcreteCtx WithFunCtx e
+        es <- mapM (toConcreteCtx WithArgCtx) es
+        return $ C.WithApp (getRange i) e es
+
+    toConcrete (A.AbsurdLam i h) =
+      bracket lamBrackets $ return $ C.AbsurdLam (getRange i) h
+    toConcrete e@(A.Lam i _ _) =
+      tryToRecoverOpApp e $   -- recover sections
+        bindToConcrete (fmap makeDomainFree bs) $ \ bs' -> do
+          List1.ifNull (catMaybes bs')
+            {-then-} (toConcrete e')
+            {-else-} $ \ bs -> bracket lamBrackets $
+              C.Lam (getRange i) bs <$> toConcreteTop e'
+      where
+          (bs, e') = lamView e
+          -- #3238 GA: We drop the hidden lambda abstractions which have
+          -- been inserted by the machine rather than the user. This means
+          -- that the result of lamView may actually be an empty list of
+          -- binders.
+          lamView :: A.Expr -> ([A.LamBinding], A.Expr)
+          lamView (A.Lam _ b@(A.DomainFree _ x) e)
+            | isInsertedHidden x = lamView e
+            | otherwise = case lamView e of
+              (bs@(A.DomainFree{} : _), e) -> (b:bs, e)
+              _                            -> ([b] , e)
+          lamView (A.Lam _ b@(A.DomainFull A.TLet{}) e) = case lamView e of
+            (bs@(A.DomainFull _ : _), e) -> (b:bs, e)
+            _                            -> ([b], e)
+          lamView (A.Lam _ (A.DomainFull (A.TBind r t xs ty)) e) =
+            case List1.filter (not . isInsertedHidden) xs of
+              []    -> lamView e
+              x:xs' -> let b = A.DomainFull (A.TBind r t (x :| xs') ty) in
+                case lamView e of
+                  (bs@(A.DomainFull _ : _), e) -> (b:bs, e)
+                  _                            -> ([b], e)
+          lamView e = ([], e)
+    toConcrete (A.ExtendedLam i di erased qname cs) =
+        bracket lamBrackets $ do
+          decls <- sconcat <$> toConcrete cs
+          puns  <- optHiddenArgumentPuns <$> pragmaOptions
+          let -- If --hidden-argument-puns is active, then {x} is
+              -- replaced by {(x)} and ⦃ x ⦄ by ⦃ (x) ⦄.
+              noPun (Named Nothing p@C.IdentP{}) | puns =
+                Named Nothing (C.ParenP noRange p)
+              noPun p = p
+
+              namedPat np = case getHiding np of
+                 NotHidden  -> namedArg np
+                 Hidden     -> C.HiddenP noRange (noPun (unArg np))
+                 Instance{} -> C.InstanceP noRange (noPun (unArg np))
+              -- we know all lhs are of the form `.extlam p1 p2 ... pn`,
+              -- with the name .extlam leftmost. It is our mission to remove it.
+          let removeApp :: C.Pattern -> AbsToCon [C.Pattern]
+              removeApp (C.RawAppP _ (List2 _ p ps)) = return $ p:ps
+              removeApp (C.AppP (C.IdentP _ _) np) = return [namedPat np]
+              removeApp (C.AppP p np)            = removeApp p <&> (++ [namedPat np])
+              -- Andreas, 2018-06-18, issue #3136
+              -- Empty pattern list also allowed in extended lambda,
+              -- thus, we might face the unapplied .extendedlambda identifier.
+              removeApp x@C.IdentP{} = return []
+
+              removeApp p = do
+                reportSLn "extendedlambda" 50 $ "abstractToConcrete removeApp p = " ++ show p
+                return [p] -- __IMPOSSIBLE__
+                  -- Andreas, this is actually not impossible,
+                  -- my strictification exposed this sleeping bug
+          let decl2clause (C.FunClause (C.LHS p [] []) rhs C.NoWhere ca) = do
+                reportSLn "extendedlambda" 50 $ "abstractToConcrete extended lambda pattern p = " ++ show p
+                ps <- removeApp p
+                reportSLn "extendedlambda" 50 $ "abstractToConcrete extended lambda patterns ps = " ++ prettyShow ps
+                return $ LamClause ps rhs ca
+              decl2clause _ = __IMPOSSIBLE__
+          C.ExtendedLam (getRange i) erased <$>
+            mapM decl2clause decls
+
+    toConcrete (A.Pi _ tel1 e0) = do
+      let (tel, e) = piTel1 tel1 e0
+      bracket piBrackets $
+         bindToConcrete tel $ \ tel' ->
+           C.makePi (List1.catMaybes tel') <$> toConcreteTop e
+      where
+        piTel1 tel e         = first (List1.appendList tel) $ piTel e
+        piTel (A.Pi _ tel e) = first List1.toList $ piTel1 tel e
+        piTel e              = ([], e)
+
+    toConcrete (A.Generalized _ e) = C.Generalized <$> toConcrete e
+
+    toConcrete (A.Fun i a b) =
+        bracket piBrackets
+        $ do a' <- toConcreteCtx ctx a
+             b' <- toConcreteTop b
+             -- NOTE We set relevance to Relevant in arginfo because we wrap
+             -- with C.Dot or C.DoubleDot using addRel instead.
+             let dom = setRelevance Relevant $ setModality (getModality a') $ defaultArg $ addRel a' $ mkArg a'
+             return $ C.Fun (getRange i) dom b'
+             -- Andreas, 2018-06-14, issue #2513
+             -- TODO: print attributes
+        where
+            ctx = if isRelevant a then FunctionSpaceDomainCtx else DotPatternCtx
+            addRel a e = case getRelevance a of
+                           Irrelevant -> C.Dot (getRange a) e
+                           NonStrict  -> C.DoubleDot (getRange a) e
+                           _          -> e
+            mkArg (Arg info e) = case getHiding info of
+                                          Hidden     -> HiddenArg   (getRange e) (unnamed e)
+                                          Instance{} -> InstanceArg (getRange e) (unnamed e)
+                                          NotHidden  -> e
+
+    toConcrete (A.Let i ds e) =
+        bracket lamBrackets
+        $ bindToConcrete ds $ \ds' -> do
+             e'  <- toConcreteTop e
+             return $ C.mkLet (getRange i) (concat ds') e'
+
+    toConcrete (A.Rec i fs) =
+      bracket appBrackets $ do
+        C.Rec (getRange i) . map (fmap (\x -> ModuleAssignment x [] defaultImportDir)) <$> toConcreteTop fs
+
+    toConcrete (A.RecUpdate i e fs) =
+      bracket appBrackets $ do
+        C.RecUpdate (getRange i) <$> toConcrete e <*> toConcreteTop fs
+
+    toConcrete (A.ScopedExpr _ e) = toConcrete e
+    toConcrete (A.Quote i) = return $ C.Quote (getRange i)
+    toConcrete (A.QuoteTerm i) = return $ C.QuoteTerm (getRange i)
+    toConcrete (A.Unquote i) = return $ C.Unquote (getRange i)
+
+    -- Andreas, 2012-04-02: TODO!  print DontCare as irrAxiom
+    -- Andreas, 2010-10-05 print irrelevant things as ordinary things
+    toConcrete (A.DontCare e) = C.Dot r . C.Paren r  <$> toConcrete e
+       where r = getRange e
+    toConcrete (A.PatternSyn n) = C.Ident <$> toConcrete (headAmbQ n)
+
+makeDomainFree :: A.LamBinding -> A.LamBinding
+makeDomainFree b@(A.DomainFull (A.TBind _ tac (x :| []) t)) =
+  case unScope t of
+    A.Underscore A.MetaInfo{metaNumber = Nothing} ->
+      A.DomainFree (tbTacticAttr tac) x
+    _ -> b
+makeDomainFree b = b
+
+-- Christian Sattler, 2017-08-05, fixing #2669
+-- Both methods of ToConcrete (FieldAssignment' a) (FieldAssignment' c) need
+-- to be implemented, each in terms of the corresponding one of ToConcrete a c.
+-- This mirrors the instance ToConcrete (Arg a) (Arg c).
+-- The default implementations of ToConcrete are not valid semantically.
+instance ToConcrete a => ToConcrete (FieldAssignment' a) where
+    type ConOfAbs (FieldAssignment' a) = FieldAssignment' (ConOfAbs a)
+    toConcrete = traverse toConcrete
+
+    bindToConcrete (FieldAssignment name a) ret =
+      bindToConcrete a $ ret . FieldAssignment name
+
+
+-- Binder instances -------------------------------------------------------
+
+-- If there is no label we set it to the bound name, to make renaming the bound
+-- name safe.
+forceNameIfHidden :: NamedArg A.Binder -> NamedArg A.Binder
+forceNameIfHidden x
+  | isJust $ getNameOf  x = x
+  | visible x             = x
+  | otherwise             = setNameOf (Just name) x
+  where
+    name = WithOrigin Inserted
+         $ Ranged (getRange x)
+         $ C.nameToRawName $ nameConcrete
+         $ unBind $ A.binderName $ namedArg x
+
+instance ToConcrete a => ToConcrete (A.Binder' a) where
+  type ConOfAbs (A.Binder' a) = C.Binder' (ConOfAbs a)
+
+  bindToConcrete (A.Binder p a) ret =
+    bindToConcrete a $ \ a ->
+    bindToConcrete p $ \ p ->
+    ret $ C.Binder p a
+
+instance ToConcrete A.LamBinding where
+    type ConOfAbs A.LamBinding = Maybe C.LamBinding
+
+    bindToConcrete (A.DomainFree t x) ret = do
+      t <- traverse toConcrete t
+      let setTac x = x { bnameTactic = t }
+      bindToConcrete (forceNameIfHidden x) $
+        ret . Just . C.DomainFree . updateNamedArg (fmap setTac)
+    bindToConcrete (A.DomainFull b) ret = bindToConcrete b $ ret . fmap C.DomainFull
+
+instance ToConcrete A.TypedBinding where
+    type ConOfAbs A.TypedBinding = Maybe C.TypedBinding
+
+    bindToConcrete (A.TBind r t xs e) ret = do
+        tac <- traverse toConcrete (tbTacticAttr t)
+        bindToConcrete (fmap forceNameIfHidden xs) $ \ xs -> do
+          e <- toConcreteTop e
+          let setTac x = x { bnameTactic = tac , C.bnameIsFinite = tbFinite t }
+          ret $ Just $ C.TBind r (fmap (updateNamedArg (fmap setTac)) xs) e
+    bindToConcrete (A.TLet r lbs) ret =
+        bindToConcrete lbs $ \ ds -> do
+        ret $ C.mkTLet r $ concat ds
+
+instance ToConcrete A.LetBinding where
+    type ConOfAbs A.LetBinding = [C.Declaration]
+
+    bindToConcrete (A.LetBind i info x t e) ret =
+        bindToConcrete x $ \ x ->
+        do (t, (e, [], [], [])) <- toConcrete (t, A.RHS e Nothing)
+           ret $ addInstanceB (if isInstance info then Just noRange else Nothing) $
+               [ C.TypeSig info Nothing (C.boundName x) t
+               , C.FunClause
+                   (C.LHS (C.IdentP True $ C.QName $ C.boundName x) [] [])
+                   e C.NoWhere False
+               ]
+    -- TODO: bind variables
+    bindToConcrete (LetPatBind i p e) ret = do
+        p <- toConcrete p
+        e <- toConcrete e
+        ret [ C.FunClause (C.LHS p [] []) (C.RHS e) NoWhere False ]
+    bindToConcrete (LetApply i erased x modapp _ _) ret = do
+      x' <- unqualify <$> toConcrete x
+      modapp <- toConcrete modapp
+      let r = getRange modapp
+          open = fromMaybe DontOpen $ minfoOpenShort i
+          dir  = fromMaybe defaultImportDir{ importDirRange = r } $ minfoDirective i
+      -- This is no use since toAbstract LetDefs is in localToAbstract.
+      local (openModule' x dir id) $
+        ret [ C.ModuleMacro (getRange i) erased x' modapp open dir ]
+    bindToConcrete (LetOpen i x _) ret = do
+      x' <- toConcrete x
+      let dir = fromMaybe defaultImportDir $ minfoDirective i
+      local (openModule' x dir restrictPrivate) $
+            ret [ C.Open (getRange i) x' dir ]
+    bindToConcrete (LetDeclaredVariable _) ret =
+      -- Note that the range of the declaration site is dropped.
+      ret []
+
+instance ToConcrete A.WhereDeclarations where
+  type ConOfAbs A.WhereDeclarations = WhereClause
+
+  bindToConcrete (A.WhereDecls _ _ Nothing) ret = ret C.NoWhere
+  bindToConcrete (A.WhereDecls (Just am) False
+                    (Just (A.Section _ erased _ _ ds)))
+                 ret = do
+    ds' <- declsToConcrete ds
+    cm  <- unqualify <$> lookupModule am
+    -- Andreas, 2016-07-08 I put PublicAccess in the following SomeWhere
+    -- Should not really matter for printing...
+    let wh' = if isNoName cm && not (isErased erased)
+              then AnyWhere noRange ds'
+              else SomeWhere noRange erased cm PublicAccess ds'
+    local (openModule' am defaultImportDir id) $ ret wh'
+  bindToConcrete (A.WhereDecls _ _ (Just d)) ret =
+    ret . AnyWhere noRange =<< toConcrete d
+
+mergeSigAndDef :: [C.Declaration] -> [C.Declaration]
+mergeSigAndDef (C.RecordSig _ er x bs e : C.RecordDef r y dir _ fs : ds)
+  | x == y = C.Record r er y dir bs e fs : mergeSigAndDef ds
+mergeSigAndDef (C.DataSig _ er x bs e : C.DataDef r y _ cs : ds)
+  | x == y = C.Data r er y bs e cs : mergeSigAndDef ds
+mergeSigAndDef (d : ds) = d : mergeSigAndDef ds
+mergeSigAndDef [] = []
+
+openModule' :: A.ModuleName -> C.ImportDirective -> (Scope -> Scope) -> Env -> Env
+openModule' x dir restrict env = env{currentScope = set scopeModules mods' sInfo}
+  where sInfo = currentScope env
+        amod  = sInfo ^. scopeCurrent
+        mods  = sInfo ^. scopeModules
+        news  = setScopeAccess PrivateNS
+                $ applyImportDirective dir
+                $ maybe emptyScope restrict
+                $ Map.lookup x mods
+        mods' = Map.update (Just . (`mergeScope` news)) amod mods
+
+
+-- Declaration instances --------------------------------------------------
+
+declsToConcrete :: [A.Declaration] -> AbsToCon [C.Declaration]
+declsToConcrete ds = mergeSigAndDef . concat <$> toConcrete ds
+
+instance ToConcrete A.RHS where
+    type ConOfAbs A.RHS = (C.RHS, [C.RewriteEqn], [C.WithExpr], [C.Declaration])
+
+    toConcrete (A.RHS e (Just c)) = return (C.RHS c, [], [], [])
+    toConcrete (A.RHS e Nothing) = do
+      e <- toConcrete e
+      return (C.RHS e, [], [], [])
+    toConcrete A.AbsurdRHS = return (C.AbsurdRHS, [], [], [])
+    toConcrete (A.WithRHS _ es cs) = do
+      es <- do es <- toConcrete es
+               forM es $ \ (Named n e) -> do
+                 n <- traverse toConcrete n
+                 pure $ Named (C.boundName <$> n) e
+      cs <- noTakenNames $ sconcat <$> toConcrete cs
+      return (C.AbsurdRHS, [], es, List1.toList cs)
+    toConcrete (A.RewriteRHS xeqs _spats rhs wh) = do
+      wh <- maybe (return []) toConcrete $ A.whereDecls wh
+      (rhs, eqs', es, whs) <- toConcrete rhs
+      unless (null eqs') __IMPOSSIBLE__
+      eqs <- toConcrete xeqs
+      return (rhs, eqs, es, wh ++ whs)
+
+instance (ToConcrete p, ToConcrete a) => ToConcrete (RewriteEqn' qn A.BindName p a) where
+  type ConOfAbs (RewriteEqn' qn A.BindName p a) = (RewriteEqn' () C.Name (ConOfAbs p) (ConOfAbs a))
+
+  toConcrete = \case
+    Rewrite es    -> Rewrite <$> mapM (toConcrete . (\ (_, e) -> ((),e))) es
+    Invert qn pes -> fmap (Invert ()) $ forM pes $ \ (Named n pe) -> do
+      pe <- toConcrete pe
+      n  <- toConcrete n
+      pure $ Named n pe
+
+instance ToConcrete (Maybe A.BindName) where
+  type ConOfAbs (Maybe A.BindName) = Maybe C.Name
+  toConcrete = traverse (C.boundName <.> toConcrete)
+
+instance ToConcrete (Maybe A.QName) where
+  type ConOfAbs (Maybe A.QName) = Maybe C.Name
+
+  toConcrete = mapM (toConcrete . qnameName)
+
+instance ToConcrete (Constr A.Constructor) where
+  type ConOfAbs (Constr A.Constructor) = C.Declaration
+
+  toConcrete (Constr (A.ScopedDecl scope [d])) =
+    withScope scope $ toConcrete (Constr d)
+  toConcrete (Constr (A.Axiom _ i info Nothing x t)) = do
+    x' <- unsafeQNameToName <$> toConcrete x
+    t' <- toConcreteTop t
+    return $ C.TypeSig info Nothing x' t'
+  toConcrete (Constr (A.Axiom _ _ _ (Just _) _ _)) = __IMPOSSIBLE__
+  toConcrete (Constr d) = headWithDefault __IMPOSSIBLE__ <$> toConcrete d
+
+instance (ToConcrete a, ConOfAbs a ~ C.LHS) => ToConcrete (A.Clause' a) where
+  type ConOfAbs (A.Clause' a) = List1 C.Declaration
+
+  toConcrete (A.Clause lhs _ rhs wh catchall) =
+      bindToConcrete lhs $ \case
+          C.LHS p _ _ -> do
+            bindToConcrete wh $ \ wh' -> do
+                (rhs', eqs, with, wcs) <- toConcreteTop rhs
+                return $ FunClause (C.LHS p eqs with) rhs' wh' catchall :| wcs
+
+instance ToConcrete A.ModuleApplication where
+  type ConOfAbs A.ModuleApplication = C.ModuleApplication
+
+  toConcrete (A.SectionApp tel y es) = do
+    y  <- toConcreteCtx FunctionCtx y
+    bindToConcrete tel $ \ tel -> do
+      es <- toConcreteCtx argumentCtx_ es
+      let r = fuseRange y es
+      return $ C.SectionApp r (catMaybes tel) (foldl (C.App r) (C.Ident y) es)
+
+  toConcrete (A.RecordModuleInstance recm) = do
+    recm <- toConcrete recm
+    return $ C.RecordModuleInstance (getRange recm) recm
+
+instance ToConcrete A.Declaration where
+  type ConOfAbs A.Declaration = [C.Declaration]
+
+  toConcrete (ScopedDecl scope ds) =
+    withScope scope (declsToConcrete ds)
+
+  toConcrete (A.Axiom _ i info mp x t) = do
+    x' <- unsafeQNameToName <$> toConcrete x
+    withAbstractPrivate i $
+      withInfixDecl i x'  $ do
+      t' <- toConcreteTop t
+      return $
+        (case mp of
+           Nothing   -> []
+           Just occs -> [C.Pragma (PolarityPragma noRange x' occs)]) ++
+        [C.Postulate (getRange i) [C.TypeSig info Nothing x' t']]
+
+  toConcrete (A.Generalize s i j x t) = do
+    x' <- unsafeQNameToName <$> toConcrete x
+    tac <- traverse toConcrete (defTactic i)
+    withAbstractPrivate i $
+      withInfixDecl i x'  $ do
+      t' <- toConcreteTop t
+      return [C.Generalize (getRange i) [C.TypeSig j tac x' $ C.Generalized t']]
+
+  toConcrete (A.Field i x t) = do
+    x' <- unsafeQNameToName <$> toConcrete x
+    tac <- traverse toConcrete (defTactic i)
+    withAbstractPrivate i $
+      withInfixDecl i x'  $ do
+      t' <- toConcreteTop t
+      return [C.FieldSig (A.defInstance i) tac x' t']
+
+  toConcrete (A.Primitive i x t) = do
+    x' <- unsafeQNameToName <$> toConcrete x
+    withAbstractPrivate i $
+      withInfixDecl i x'  $ do
+      t' <- traverse toConcreteTop t
+      return [C.Primitive (getRange i) [C.TypeSig (argInfo t') Nothing x' (unArg t')]]
+        -- Primitives are always relevant.
+
+  toConcrete (A.FunDef i _ cs) =
+    withAbstractPrivate i $ List1.concat <$> toConcrete cs
+
+  toConcrete (A.DataSig i erased x bs t) =
+    withAbstractPrivate i $
+    bindToConcrete (A.generalizeTel bs) $ \ tel' -> do
+      x' <- unsafeQNameToName <$> toConcrete x
+      t' <- toConcreteTop t
+      return [ C.DataSig (getRange i) erased x'
+                 (map C.DomainFull $ catMaybes tel') t' ]
+
+  toConcrete (A.DataDef i x uc bs cs) =
+    withAbstractPrivate i $
+    bindToConcrete (map makeDomainFree $ dataDefParams bs) $ \ tel' -> do
+      (x',cs') <- first unsafeQNameToName <$> toConcrete (x, map Constr cs)
+      return [ C.DataDef (getRange i) x' (catMaybes tel') cs' ]
+
+  toConcrete (A.RecSig i erased x bs t) =
+    withAbstractPrivate i $
+    bindToConcrete (A.generalizeTel bs) $ \ tel' -> do
+      x' <- unsafeQNameToName <$> toConcrete x
+      t' <- toConcreteTop t
+      return [ C.RecordSig (getRange i) erased x'
+                 (map C.DomainFull $ catMaybes tel') t' ]
+
+  toConcrete (A.RecDef  i x uc dir bs t cs) =
+    withAbstractPrivate i $
+    bindToConcrete (map makeDomainFree $ dataDefParams bs) $ \ tel' -> do
+      (x',cs') <- first unsafeQNameToName <$> toConcrete (x, map Constr cs)
+      return [ C.RecordDef (getRange i) x' (dir { recConstructor = Nothing }) (catMaybes tel') cs' ]
+
+  toConcrete (A.Mutual i ds) = pure . C.Mutual noRange <$> declsToConcrete ds
+
+  toConcrete (A.Section i erased x (A.GeneralizeTel _ tel) ds) = do
+    x <- toConcrete x
+    bindToConcrete tel $ \ tel -> do
+      ds <- declsToConcrete ds
+      return [ C.Module (getRange i) erased x (catMaybes tel) ds ]
+
+  toConcrete (A.Apply i erased x modapp _ _) = do
+    x  <- unsafeQNameToName <$> toConcrete x
+    modapp <- toConcrete modapp
+    let r = getRange modapp
+        open = fromMaybe DontOpen $ minfoOpenShort i
+        dir  = fromMaybe defaultImportDir{ importDirRange = r } $ minfoDirective i
+    return [ C.ModuleMacro (getRange i) erased x modapp open dir ]
+
+  toConcrete (A.Import i x _) = do
+    x <- toConcrete x
+    let open = fromMaybe DontOpen $ minfoOpenShort i
+        dir  = fromMaybe defaultImportDir $ minfoDirective i
+    return [ C.Import (getRange i) x Nothing open dir]
+
+  toConcrete (A.Pragma i p)     = do
+    p <- toConcrete $ RangeAndPragma (getRange i) p
+    return [C.Pragma p]
+
+  toConcrete (A.Open i x _) = do
+    x <- toConcrete x
+    return [C.Open (getRange i) x defaultImportDir]
+
+  toConcrete (A.PatternSynDef x xs p) = do
+    C.QName x <- toConcrete x
+    bindToConcrete (map (fmap A.unBind) xs) $ \ xs ->
+      singleton . C.PatternSyn (getRange x) x xs <$> do
+        dontFoldPatternSynonyms $ toConcrete (vacuous p :: A.Pattern)
+
+  toConcrete (A.UnquoteDecl _ i xs e) = do
+    let unqual (C.QName x) = return x
+        unqual _           = __IMPOSSIBLE__
+    xs <- mapM (unqual <=< toConcrete) xs
+    (:[]) . C.UnquoteDecl (getRange i) xs <$> toConcrete e
+
+  toConcrete (A.UnquoteDef i xs e) = do
+    let unqual (C.QName x) = return x
+        unqual _           = __IMPOSSIBLE__
+    xs <- mapM (unqual <=< toConcrete) xs
+    (:[]) . C.UnquoteDef (getRange i) xs <$> toConcrete e
+
+  toConcrete (A.UnquoteData i xs uc j cs e) = __IMPOSSIBLE__
+  toConcrete (A.UnfoldingDecl r ns) = pure []
+
+data RangeAndPragma = RangeAndPragma Range A.Pragma
+
+instance ToConcrete RangeAndPragma where
+  type ConOfAbs RangeAndPragma = C.Pragma
+
+  toConcrete (RangeAndPragma r p) = case p of
+    A.OptionsPragma xs  -> return $ C.OptionsPragma r xs
+    A.BuiltinPragma b x       -> C.BuiltinPragma r b <$> toConcrete x
+    A.BuiltinNoDefPragma b _kind x -> C.BuiltinPragma r b <$> toConcrete x
+    A.RewritePragma r' x      -> C.RewritePragma r r' <$> toConcrete x
+    A.CompilePragma b x s -> do
+      x <- toConcrete x
+      return $ C.CompilePragma r b x s
+    A.StaticPragma x -> C.StaticPragma r <$> toConcrete x
+    A.InjectivePragma x -> C.InjectivePragma r <$> toConcrete x
+    A.InlinePragma b x -> C.InlinePragma r b <$> toConcrete x
+    A.NotProjectionLikePragma q -> C.NotProjectionLikePragma r <$> toConcrete q
+    A.EtaPragma x    -> C.EtaPragma    r <$> toConcrete x
+    A.DisplayPragma f ps rhs ->
+      C.DisplayPragma r <$> toConcrete (A.DefP (PatRange noRange) (unambiguous f) ps) <*> toConcrete rhs
+
+-- Left hand sides --------------------------------------------------------
+
+instance ToConcrete A.SpineLHS where
+  type ConOfAbs A.SpineLHS = C.LHS
+
+  bindToConcrete lhs = bindToConcrete (A.spineToLhs lhs :: A.LHS)
+
+instance ToConcrete A.LHS where
+    type ConOfAbs A.LHS = C.LHS
+
+    bindToConcrete (A.LHS i lhscore) ret = do
+      bindToConcreteCtx TopCtx lhscore $ \ lhs ->
+          ret $ C.LHS (reintroduceEllipsis (lhsEllipsis i) lhs) [] []
+
+instance ToConcrete A.LHSCore where
+  type ConOfAbs A.LHSCore = C.Pattern
+  bindToConcrete = bindToConcrete . lhsCoreToPattern
+
+appBracketsArgs :: [arg] -> PrecedenceStack -> Bool
+appBracketsArgs []    _   = False
+appBracketsArgs (_:_) ctx = appBrackets ctx
+
+-- Auxiliary wrappers for processing the bindings in patterns in the right order.
+newtype UserPattern a  = UserPattern a
+newtype SplitPattern a = SplitPattern a
+newtype BindingPattern = BindingPat A.Pattern
+newtype FreshenName = FreshenName BindName
+
+instance ToConcrete FreshenName where
+  type ConOfAbs FreshenName = A.Name
+  bindToConcrete (FreshenName BindName{ unBind = x }) ret = bindToConcrete x $ \ y -> ret x { nameConcrete = y }
+
+-- Pass 1: (Issue #2729)
+-- Takes care of binding the originally user-written pattern variables, but doesn't actually
+-- translate anything to Concrete.
+instance ToConcrete (UserPattern A.Pattern) where
+  type ConOfAbs (UserPattern A.Pattern) = A.Pattern
+
+  bindToConcrete (UserPattern p) ret = do
+    reportSLn "toConcrete.pat" 100 $ "binding pattern (pass 1)" ++ show p
+    case p of
+      A.VarP bx -> do
+        let x = unBind bx
+        case isInScope x of
+          InScope            -> bindName' x $ ret $ A.VarP bx
+          C.NotInScope       -> bindName x $ \y ->
+                                ret $ A.VarP $ mkBindName $ x { nameConcrete = y }
+      A.WildP{}              -> ret p
+      A.ProjP{}              -> ret p
+      A.AbsurdP{}            -> ret p
+      A.LitP{}               -> ret p
+      A.DotP{}               -> ret p
+      A.EqualP{}             -> ret p
+      -- Andreas, 2017-09-03, issue #2729:
+      -- Do not go into patterns generated by case-split here!
+      -- They are treated in a second pass.
+      A.ConP i c args
+        | conPatOrigin i == ConOSplit -> ret p
+        | otherwise          -> bindToConcrete (map UserPattern args) $ ret . A.ConP i c
+      A.DefP i f args        -> bindToConcrete (map UserPattern args) $ ret . A.DefP i f
+      A.PatternSynP i f args -> bindToConcrete (map UserPattern args) $ ret . A.PatternSynP i f
+      A.RecP i args          -> bindToConcrete ((map . fmap) UserPattern args) $ ret . A.RecP i
+      A.AsP i x p            -> bindName' (unBind x) $
+                                bindToConcrete (UserPattern p) $ \ p ->
+                                ret (A.AsP i x p)
+      A.WithP i p            -> bindToConcrete (UserPattern p) $ ret . A.WithP i
+      A.AnnP i a p           -> bindToConcrete (UserPattern p) $ ret . A.AnnP i a
+
+instance ToConcrete (UserPattern (NamedArg A.Pattern)) where
+  type ConOfAbs (UserPattern (NamedArg A.Pattern)) = NamedArg A.Pattern
+
+  bindToConcrete (UserPattern np) ret =
+    case getOrigin np of
+      CaseSplit -> ret np
+      _         -> bindToConcrete (fmap (fmap UserPattern) np) ret
+
+-- Pass 2a: locate case-split pattern.  Don't bind anything!
+instance ToConcrete (SplitPattern A.Pattern) where
+  type ConOfAbs (SplitPattern A.Pattern) = A.Pattern
+
+  bindToConcrete (SplitPattern p) ret = do
+    reportSLn "toConcrete.pat" 100 $ "binding pattern (pass 2a)" ++ show p
+    case p of
+      A.VarP x               -> ret p
+      A.WildP{}              -> ret p
+      A.ProjP{}              -> ret p
+      A.AbsurdP{}            -> ret p
+      A.LitP{}               -> ret p
+      A.DotP{}               -> ret p
+      A.EqualP{}             -> ret p
+      -- Andreas, 2017-09-03, issue #2729:
+      -- For patterns generated by case-split here, switch to freshening & binding.
+      A.ConP i c args
+        | conPatOrigin i == ConOSplit
+                             -> bindToConcrete ((map . fmap . fmap) BindingPat args) $ ret . A.ConP i c
+        | otherwise          -> bindToConcrete (map SplitPattern args) $ ret . A.ConP i c
+      A.DefP i f args        -> bindToConcrete (map SplitPattern args) $ ret . A.DefP i f
+      A.PatternSynP i f args -> bindToConcrete (map SplitPattern args) $ ret . A.PatternSynP i f
+      A.RecP i args          -> bindToConcrete ((map . fmap) SplitPattern args) $ ret . A.RecP i
+      A.AsP i x p            -> bindToConcrete (SplitPattern p)  $ \ p ->
+                                ret (A.AsP i x p)
+      A.WithP i p            -> bindToConcrete (SplitPattern p) $ ret . A.WithP i
+      A.AnnP i a p           -> bindToConcrete (SplitPattern p) $ ret . A.AnnP i a
+
+instance ToConcrete (SplitPattern (NamedArg A.Pattern)) where
+  type ConOfAbs (SplitPattern (NamedArg A.Pattern)) = NamedArg A.Pattern
+  bindToConcrete (SplitPattern np) ret =
+    case getOrigin np of
+      CaseSplit -> bindToConcrete (fmap (fmap BindingPat  ) np) ret
+      _         -> bindToConcrete (fmap (fmap SplitPattern) np) ret
+
+
+-- Pass 2b:
+-- Takes care of freshening and binding pattern variables introduced by case split.
+-- Still does not translate anything to Concrete.
+instance ToConcrete BindingPattern where
+  type ConOfAbs BindingPattern = A.Pattern
+  bindToConcrete (BindingPat p) ret = do
+    reportSLn "toConcrete.pat" 100 $ "binding pattern (pass 2b)" ++ show p
+    case p of
+      A.VarP x               -> bindToConcrete (FreshenName x) $ ret . A.VarP . mkBindName
+      A.WildP{}              -> ret p
+      A.ProjP{}              -> ret p
+      A.AbsurdP{}            -> ret p
+      A.LitP{}               -> ret p
+      A.DotP{}               -> ret p
+      A.EqualP{}             -> ret p
+      A.ConP i c args        -> bindToConcrete (map (updateNamedArg BindingPat) args) $ ret . A.ConP i c
+      A.DefP i f args        -> bindToConcrete (map (updateNamedArg BindingPat) args) $ ret . A.DefP i f
+      A.PatternSynP i f args -> bindToConcrete (map (updateNamedArg BindingPat) args) $ ret . A.PatternSynP i f
+      A.RecP i args          -> bindToConcrete ((map . fmap)        BindingPat args) $ ret . A.RecP i
+      A.AsP i x p            -> bindToConcrete (FreshenName x) $ \ x ->
+                                bindToConcrete (BindingPat p)  $ \ p ->
+                                ret (A.AsP i (mkBindName x) p)
+      A.WithP i p            -> bindToConcrete (BindingPat p) $ ret . A.WithP i
+      A.AnnP i a p           -> bindToConcrete (BindingPat p) $ ret . A.AnnP i a
+
+instance ToConcrete A.Pattern where
+  type ConOfAbs A.Pattern = C.Pattern
+
+  bindToConcrete p ret = do
+    prec <- currentPrecedence
+    bindToConcrete (UserPattern p) $ \ p -> do
+      bindToConcrete (SplitPattern p) $ \ p -> do
+        ret =<< do withPrecedence' prec $ toConcrete p
+  toConcrete p =
+    case p of
+      A.VarP x ->
+        C.IdentP True . C.QName . C.boundName <$> toConcrete x
+
+      A.WildP i ->
+        return $ C.WildP (getRange i)
+
+      A.ConP i c args  -> tryOp (headAmbQ c) (A.ConP i c) args
+
+      A.ProjP i ProjPrefix p -> C.IdentP True <$> toConcrete (headAmbQ p)
+      A.ProjP i _          p -> C.DotP noRange . C.Ident <$> toConcrete (headAmbQ p)
+
+      A.DefP i x args -> tryOp (headAmbQ x) (A.DefP i x)  args
+
+      A.AsP i x p -> do
+        (x, p) <- toConcreteCtx argumentCtx_ (x, p)
+        return $ C.AsP (getRange i) (C.boundName x) p
+
+      A.AbsurdP i ->
+        return $ C.AbsurdP (getRange i)
+
+      A.LitP i (LitQName x) -> do
+        x <- lookupQName AmbiguousNothing x
+        bracketP_ appBrackets $ return $
+          C.AppP (C.QuoteP (getRange i))
+            (defaultNamedArg (C.IdentP True x))
+      A.LitP i l ->
+        return $ C.LitP (getRange i) l
+
+      -- Andreas, 2018-06-19, issue #3130
+      -- Print .p as .(p) if p is a projection
+      -- to avoid confusion with projection pattern.
+      A.DotP i e@A.Proj{} -> C.DotP r . C.Paren r <$> toConcreteCtx TopCtx e
+        where r = getRange i
+
+      -- gallais, 2019-02-12, issue #3491
+      -- Print p as .(p) if p is a variable but there is a projection of the
+      -- same name in scope.
+      A.DotP i e@(A.Var v) -> do
+        let r = getRange i
+        -- Erase @v@ to a concrete name and resolve it back to check whether
+        -- we have a conflicting field name.
+        cn <- toConcreteName v
+        resolveName (someKindsOfNames [FldName]) Nothing (C.QName cn) >>= \ case
+          -- If we do then we print .(v) rather than .v
+          Right FieldName{} -> do
+            reportSLn "print.dotted" 50 $ "Wrapping ambiguous name " ++ prettyShow (nameConcrete v)
+            C.DotP r . C.Paren r <$> toConcrete (A.Var v)
+          Right _ -> printDotDefault i e
+          Left _ -> __IMPOSSIBLE__
+
+      A.DotP i e -> printDotDefault i e
+
+      A.EqualP i es -> do
+        C.EqualP (getRange i) <$> toConcrete es
+
+      A.PatternSynP i n args -> tryOp (headAmbQ n) (A.PatternSynP i n) args
+
+      A.RecP i as ->
+        C.RecP (getRange i) <$> mapM (traverse toConcrete) as
+
+      A.WithP i p -> C.WithP (getRange i) <$> toConcreteCtx WithArgCtx p
+
+      A.AnnP i a p -> toConcrete p -- TODO: print type annotation
+
+    where
+
+    printDotDefault :: PatInfo -> A.Expr -> AbsToCon C.Pattern
+    printDotDefault i e = do
+      c <- toConcreteCtx DotPatternCtx e
+      let r = getRange i
+      case c of
+        -- Andreas, 2016-02-04 print ._ pattern as _ pattern,
+        -- following the fusing of WildP and ImplicitP.
+        C.Underscore{} -> return $ C.WildP r
+        _ -> return $ C.DotP r c
+
+    tryOp :: A.QName -> (A.Patterns -> A.Pattern) -> A.Patterns -> AbsToCon C.Pattern
+    tryOp x f args = do
+      -- Andreas, 2016-02-04, Issue #1792
+      -- To prevent failing of tryToRecoverOpAppP for overapplied operators,
+      -- we take off the exceeding arguments first
+      -- and apply them pointwise with C.AppP later.
+      let (args1, args2) = splitAt (numHoles x) args
+      let funCtx = applyUnless (null args2) (withPrecedence FunctionCtx)
+      tryToRecoverPatternSynP (f args) $ funCtx (tryToRecoverOpAppP $ f args1) >>= \case
+        Just c  -> applyTo args2 c
+        Nothing -> applyTo args . C.IdentP True =<< toConcrete x
+    -- Note: applyTo [] c = return c
+    applyTo args c = bracketP_ (appBracketsArgs args) $ do
+      foldl C.AppP c <$>
+        (mapM avoidPun =<< toConcreteCtx argumentCtx_ args)
+
+    -- If --hidden-argument-puns is active, then {x} is replaced by
+    -- {(x)} and ⦃ x ⦄ by ⦃ (x) ⦄.
+    avoidPun :: NamedArg C.Pattern -> AbsToCon (NamedArg C.Pattern)
+    avoidPun arg =
+      ifM (optHiddenArgumentPuns <$> pragmaOptions)
+          (return $ case arg of
+             Arg i (Named Nothing x@C.IdentP{}) | notVisible i ->
+               Arg i (Named Nothing (C.ParenP noRange x))
+             arg -> arg)
+          (return arg)
+
+instance ToConcrete (Maybe A.Pattern) where
+  type ConOfAbs (Maybe A.Pattern) = Maybe C.Pattern
+
+  toConcrete = traverse toConcrete
+
+-- Helpers for recovering natural number literals
+
+tryToRecoverNatural :: A.Expr -> AbsToCon C.Expr -> AbsToCon C.Expr
+tryToRecoverNatural e def = do
+  is <- isBuiltinFun
+  caseMaybe (recoverNatural is e) def $ return . C.Lit noRange . LitNat
+
+recoverNatural :: (A.QName -> BuiltinId -> Bool) -> A.Expr -> Maybe Integer
+recoverNatural is e = explore (`is` builtinZero) (`is` builtinSuc) 0 e
+  where
+    explore :: (A.QName -> Bool) -> (A.QName -> Bool) -> Integer -> A.Expr -> Maybe Integer
+    explore isZero isSuc k (A.App _ (A.Con c) t) | Just f <- getUnambiguous c, isSuc f
+                                                = (explore isZero isSuc $! k + 1) (namedArg t)
+    explore isZero isSuc k (A.Con c) | Just x <- getUnambiguous c, isZero x = Just k
+    explore isZero isSuc k (A.Lit _ (LitNat l)) = Just (k + l)
+    explore _ _ _ _                             = Nothing
+
+-- Helpers for recovering C.OpApp ------------------------------------------
+
+data Hd = HdVar A.Name | HdCon A.QName | HdDef A.QName | HdSyn A.QName
+
+data MaybeSection a
+  = YesSection
+  | NoSection a
+  deriving (Eq, Show, Functor, Foldable, Traversable)
+
+fromNoSection :: a -> MaybeSection a -> a
+fromNoSection fallback = \case
+  YesSection  -> fallback
+  NoSection x -> x
+
+instance HasRange a => HasRange (MaybeSection a) where
+  getRange = \case
+    YesSection  -> noRange
+    NoSection a -> getRange a
+
+getHead :: A.Expr -> Maybe Hd
+getHead (Var x)          = Just (HdVar x)
+getHead (Def f)          = Just (HdDef f)
+getHead (Proj o f)       = Just (HdDef $ headAmbQ f)
+getHead (Con c)          = Just (HdCon $ headAmbQ c)
+getHead (A.PatternSyn n) = Just (HdSyn $ headAmbQ n)
+getHead _                = Nothing
+
+cOpApp :: Asp.NameKind -> Range -> C.QName -> A.Name -> List1 (MaybeSection C.Expr) -> C.Expr
+cOpApp nk r x n es =
+  C.KnownOpApp nk r x (Set.singleton n) $
+  fmap (defaultNamedArg . placeholder) $
+  List1.toList eps
+  where
+    x0 = C.unqualify x
+    positions | isPrefix  x0 =              (const Middle <$> List1.drop 1 es) `List1.snoc` End
+              | isPostfix x0 = Beginning :| (const Middle <$> List1.drop 1 es)
+              | isInfix x0   = Beginning :| (const Middle <$> List1.drop 2 es) ++ [ End ]
+              | otherwise    =               const Middle <$> es
+    eps = List1.zip es positions
+    placeholder (YesSection , pos ) = Placeholder pos
+    placeholder (NoSection e, _pos) = noPlaceholder (Ordinary e)
+
+tryToRecoverOpApp :: A.Expr -> AbsToCon C.Expr -> AbsToCon C.Expr
+tryToRecoverOpApp e def = fromMaybeM def $
+  recoverOpApp bracket (isLambda . defaultNamedArg) cOpApp view e
+  where
+    view :: A.Expr -> Maybe (Hd, [NamedArg (MaybeSection (AppInfo, A.Expr))])
+    view e
+        -- Do we have a series of inserted lambdas?
+      | Just xs@(_:_) <- traverse insertedName bs =
+        (,) <$> getHead hd <*> sectionArgs (map (unBind . A.binderName) xs) args
+      where
+        LamView     bs body = A.lamView e
+        Application hd args = A.appView' body
+
+        -- Only inserted domain-free visible lambdas come from sections.
+        insertedName (A.DomainFree _ x)
+          | getOrigin x == Inserted && visible x = Just $ namedArg x
+        insertedName _ = Nothing
+
+        -- Build section arguments. Need to check that:
+        -- lambda bound variables appear in the right order and only as
+        -- top-level arguments.
+        sectionArgs :: [A.Name] -> [NamedArg (AppInfo, A.Expr)] -> Maybe [NamedArg (MaybeSection (AppInfo, A.Expr))]
+        sectionArgs xs = go xs
+          where
+            noXs = getAll . foldExpr (\ case A.Var x -> All (x `notElem` xs)
+                                             _       -> All True) . snd . namedArg
+            go [] [] = return []
+            go (y : ys) (arg : args)
+              | visible arg
+              , A.Var y' <- snd $ namedArg arg
+              , y == y' = (fmap (YesSection <$) arg :) <$> go ys args
+            go ys (arg : args)
+              | visible arg, noXs arg = ((fmap . fmap) NoSection arg :) <$> go ys args
+            go _ _ = Nothing
+
+    view e = (, (map . fmap . fmap) NoSection args) <$> getHead hd
+      where Application hd args = A.appView' e
+
+tryToRecoverOpAppP :: A.Pattern -> AbsToCon (Maybe C.Pattern)
+tryToRecoverOpAppP p = do
+  res <- recoverOpApp bracketP_ (const False) (const opApp) view p
+  reportS "print.op" 90
+    [ "tryToRecoverOpApp"
+    , "in:  " ++ show p
+    , "out: " ++ show res
+    ]
+  return res
+  where
+    opApp r x n ps = C.OpAppP r x (Set.singleton n) $
+      fmap (defaultNamedArg . fromNoSection __IMPOSSIBLE__) $
+      -- `view` does not generate any `Nothing`s
+      List1.toList ps
+
+    appInfo = defaultAppInfo_
+
+    view :: A.Pattern -> Maybe (Hd, [NamedArg (MaybeSection (AppInfo, A.Pattern))])
+    view = \case
+      ConP _        cs ps -> Just (HdCon (headAmbQ cs), (map . fmap . fmap) (NoSection . (appInfo,)) ps)
+      DefP _        fs ps -> Just (HdDef (headAmbQ fs), (map . fmap . fmap) (NoSection . (appInfo,)) ps)
+      PatternSynP _ ns ps -> Just (HdSyn (headAmbQ ns), (map . fmap . fmap) (NoSection . (appInfo,)) ps)
+      _                   -> Nothing
+      -- ProjP _ _ d   -> Just (HdDef (headAmbQ d), [])   -- ? Andreas, 2016-04-21
+
+recoverOpApp :: forall a c . (ToConcrete a, c ~ ConOfAbs a, HasRange c)
+  => ((PrecedenceStack -> Bool) -> AbsToCon c -> AbsToCon c)
+  -> (a -> Bool)  -- ^ Check for lambdas
+  -> (Asp.NameKind -> Range -> C.QName -> A.Name -> List1 (MaybeSection c) -> c)  -- ^ @opApp@
+  -> (a -> Maybe (Hd, [NamedArg (MaybeSection (AppInfo, a))]))
+  -> a
+  -> AbsToCon (Maybe c)
+recoverOpApp bracket isLam opApp view e = case view e of
+  Nothing -> mDefault
+  Just (hd, args)
+    | all visible args    -> do
+      let  args' = map namedArg args
+      case hd of
+        HdVar  n
+          | isNoName n    -> mDefault
+          | otherwise     -> doQNameHelper (Left n) args'
+        HdDef qn
+          | isExtendedLambdaName qn
+                          -> mDefault
+          | otherwise     -> doQNameHelper (Right qn) args'
+        -- HdDef qn          -> doQNameHelper (Right qn) args'
+        HdCon qn          -> doQNameHelper (Right qn) args'
+        HdSyn qn          -> doQNameHelper (Right qn) args'
+    | otherwise           -> mDefault
+  where
+  mDefault = return Nothing
+
+  skipParens :: MaybeSection (AppInfo, a) -> Bool
+  skipParens = \case
+     YesSection       -> False
+     NoSection (i, e) -> isLam e && preferParenless (appParens i)
+
+  doQNameHelper :: Either A.Name A.QName -> [MaybeSection (AppInfo, a)] -> AbsToCon (Maybe c)
+  doQNameHelper n args = do
+    x <- either (C.QName <.> toConcrete) toConcrete n
+    let n' = either id A.qnameName n
+    -- #1346: The fixity of the abstract name is not necessarily correct, it depends on which
+    -- concrete name we choose! Make sure to resolve ambiguities with n'.
+    (fx, nk) <- resolveName_ x [n'] <&> \ case
+      VarName y _                -> (y ^. lensFixity, Asp.Bound)
+      DefinedName _ q _          -> (q ^. lensFixity, Asp.Function)
+      FieldName (q :| _)         -> (q ^. lensFixity, Asp.Field)
+      ConstructorName _ (q :| _) -> (q ^. lensFixity, Asp.Constructor Asp.Inductive)
+      PatternSynResName (q :| _) -> (q ^. lensFixity, Asp.Constructor Asp.Inductive)
+      UnknownName                -> (noFixity, Asp.Bound)
+    List1.ifNull args {-then-} mDefault {-else-} $ \ as ->
+      doQName nk fx x n' as (C.nameParts $ C.unqualify x)
+
+  doQName :: Asp.NameKind -> Fixity -> C.QName -> A.Name -> List1 (MaybeSection (AppInfo, a)) -> NameParts -> AbsToCon (Maybe c)
+
+  -- fall-back (wrong number of arguments or no holes)
+  doQName nk _ x _ as xs
+    | length as /= numHoles x = mDefault
+
+  -- binary case
+  doQName nk fixity x n (a1 :| as) xs
+    | Hole <- List1.head xs
+    , Hole <- List1.last xs = do
+        let (as', an) = List1.ifNull as {-then-} __IMPOSSIBLE__ {-else-} List1.initLast
+        Just <$> do
+          bracket (opBrackets' (skipParens an) fixity) $ do
+            e1 <- traverse (toConcreteCtx (LeftOperandCtx fixity) . snd) a1
+            es <- (mapM . traverse) (toConcreteCtx InsideOperandCtx . snd) as'
+            en <- traverse (uncurry $ toConcreteCtx . RightOperandCtx fixity . appParens) an
+            return $ opApp nk (getRange (e1, en)) x n (e1 :| es ++ [en])
+
+  -- prefix
+  doQName nk fixity x n as xs
+    | Hole <- List1.last xs = do
+        let (as', an) = List1.initLast as
+        Just <$> do
+          bracket (opBrackets' (skipParens an) fixity) $ do
+            es <- (mapM . traverse) (toConcreteCtx InsideOperandCtx . snd) as'
+            en <- traverse (\ (i, e) -> toConcreteCtx (RightOperandCtx fixity $ appParens i) e) an
+            return $ opApp nk (getRange (n, en)) x n (List1.snoc es en)
+
+  -- postfix
+  doQName nk fixity x n as xs
+    | Hole <- List1.head xs = do
+        let a1  = List1.head as
+            as' = List1.tail as
+        e1 <- traverse (toConcreteCtx (LeftOperandCtx fixity) . snd) a1
+        es <- (mapM . traverse) (toConcreteCtx InsideOperandCtx . snd) as'
+        Just <$> do
+          bracket (opBrackets fixity) $
+            return $ opApp nk (getRange (e1, n)) x n (e1 :| es)
+
+  -- roundfix
+  doQName nk _ x n as _ = do
+    es <- (mapM . traverse) (toConcreteCtx InsideOperandCtx . snd) as
+    Just <$> do
+      bracket roundFixBrackets $
+        return $ opApp nk (getRange x) x n es
+
+-- Recovering pattern synonyms --------------------------------------------
+
+-- | Recover pattern synonyms for expressions.
+tryToRecoverPatternSyn :: A.Expr -> AbsToCon C.Expr -> AbsToCon C.Expr
+tryToRecoverPatternSyn e fallback
+  | userWritten e = fallback
+  | litOrCon e    = recoverPatternSyn apply matchPatternSyn e fallback
+  | otherwise     = fallback
+  where
+    userWritten (A.App info _ _) = getOrigin info == UserWritten
+    userWritten _                = False  -- this means we always use pattern synonyms for nullary constructors
+
+    -- Only literals or constructors can head pattern synonym definitions
+    litOrCon e =
+      case A.appView e of
+        Application Con{}   _ -> True
+        Application A.Lit{} _ -> True
+        _                     -> False
+
+    apply c args = A.unAppView $ Application (A.PatternSyn $ unambiguous c) args
+
+-- | Recover pattern synonyms in patterns.
+tryToRecoverPatternSynP :: A.Pattern -> AbsToCon C.Pattern -> AbsToCon C.Pattern
+tryToRecoverPatternSynP = recoverPatternSyn apply matchPatternSynP
+  where apply c args = PatternSynP patNoRange (unambiguous c) args
+
+-- | General pattern synonym recovery parameterised over expression type
+recoverPatternSyn :: ToConcrete a =>
+  (A.QName -> [NamedArg a] -> a)         -> -- applySyn
+  (PatternSynDefn -> a -> Maybe [Arg a]) -> -- match
+  a -> AbsToCon (ConOfAbs a) -> AbsToCon (ConOfAbs a)
+recoverPatternSyn applySyn match e fallback = do
+  doFold <- asks foldPatternSynonyms
+  if not doFold then fallback else do
+    psyns  <- getAllPatternSyns
+    scope  <- getScope
+    reportSLn "toConcrete.patsyn" 100 $ render $ hsep $
+      [ "Scope when attempting to recover pattern synonyms:"
+      , pretty scope
+      ]
+    let isConP ConP{} = True    -- #2828: only fold pattern synonyms with
+        isConP _      = False   --        constructor rhs
+        cands = [ (q, args, score rhs)
+                | (q, psyndef@(_, rhs)) <- reverse $ Map.toList psyns
+                , isConP rhs
+                , Just args <- [match psyndef e]
+                -- #3879: only fold pattern synonyms with an unqualified concrete name in scope
+                -- Note that we only need to consider the head of the inverse lookup result: they
+                -- are already sorted from shortest to longest!
+                , C.QName{} <- Fold.toList $ listToMaybe $ inverseScopeLookupName q scope
+                ]
+        cmp (_, _, x) (_, _, y) = compare y x
+    reportSLn "toConcrete.patsyn" 50 $ render $ hsep $
+      [ "Found pattern synonym candidates:"
+      , prettyList_ $ map (\ (q,_,_) -> q) cands
+      ]
+    case sortBy cmp cands of
+      (q, args, _) : _ -> toConcrete $ applySyn q $ (map . fmap) unnamed args
+      []               -> fallback
+  where
+    -- Heuristic to pick the best pattern synonym: the one that folds the most
+    -- constructors.
+    score :: Pattern' Void -> Int
+    score = getSum . foldAPattern con
+      where con ConP{} = 1
+            con _      = 0
+
+-- Some instances that are related to interaction with users -----------
+
+instance ToConcrete InteractionId where
+    type ConOfAbs InteractionId = C.Expr
+    toConcrete (InteractionId i) = return $ C.QuestionMark noRange (Just i)
+
+instance ToConcrete NamedMeta where
+    type ConOfAbs NamedMeta = C.Expr
+    toConcrete i =
+      C.Underscore noRange . Just . render <$> prettyTCM i
diff --git a/src/full/Agda/Syntax/Translation/ConcreteToAbstract.hs b/src/full/Agda/Syntax/Translation/ConcreteToAbstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Translation/ConcreteToAbstract.hs
@@ -0,0 +1,3303 @@
+
+{-| Translation from "Agda.Syntax.Concrete" to "Agda.Syntax.Abstract".
+    Involves scope analysis,
+    figuring out infix operator precedences and tidying up definitions.
+-}
+
+module Agda.Syntax.Translation.ConcreteToAbstract
+    ( ToAbstract(..), localToAbstract
+    , concreteToAbstract_
+    , concreteToAbstract
+    , NewModuleQName(..)
+    , TopLevel(..)
+    , TopLevelInfo(..)
+    , topLevelModuleName
+    , AbstractRHS
+    , NewModuleName, OldModuleName
+    , NewName, OldQName
+    , PatName, APatName
+    , importPrimitives
+    , checkAttributes
+    ) where
+
+import Prelude hiding ( null )
+
+import Control.Monad        ( (>=>), (<=<), foldM, forM, forM_, zipWithM, zipWithM_ )
+import Control.Applicative  ( liftA2, liftA3 )
+import Control.Monad.Except ( MonadError(..) )
+
+import Data.Bifunctor
+import Data.Foldable (traverse_)
+import Data.Set (Set)
+import Data.Map (Map)
+import Data.Functor (void)
+import qualified Data.List as List
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+import qualified Data.HashSet as HashSet
+import Data.Maybe
+import Data.Void
+
+import Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Attribute
+import Agda.Syntax.Concrete.Generic
+import Agda.Syntax.Concrete.Operators
+import Agda.Syntax.Concrete.Pattern
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pattern as A ( patternVars, checkPatternLinearity, containsAsPattern, lhsCoreApp, lhsCoreWith )
+import Agda.Syntax.Abstract.Pretty
+import qualified Agda.Syntax.Internal as I
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+import Agda.Syntax.Common
+import Agda.Syntax.Info as Info
+import Agda.Syntax.Concrete.Definitions as C
+import Agda.Syntax.Fixity
+import Agda.Syntax.Concrete.Fixity (DoWarn(..))
+import Agda.Syntax.Notation
+import Agda.Syntax.Scope.Base as A
+import Agda.Syntax.Scope.Monad
+import Agda.Syntax.Translation.AbstractToConcrete (ToConcrete, ConOfAbs)
+import Agda.Syntax.DoNotation
+import Agda.Syntax.IdiomBrackets
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Monad.Base hiding (ModuleInfo, MetaInfo)
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Trace (traceCall, setCurrentRange)
+import Agda.TypeChecking.Monad.State hiding (topLevelModuleName)
+import qualified Agda.TypeChecking.Monad.State as S
+import Agda.TypeChecking.Monad.Signature (notUnderOpaque)
+import Agda.TypeChecking.Monad.MetaVars (registerInteractionPoint)
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Env (insideDotPattern, isInsideDotPattern, getCurrentPath)
+import Agda.TypeChecking.Rules.Builtin (isUntypedBuiltin, bindUntypedBuiltin, builtinKindOfName)
+
+import Agda.TypeChecking.Patterns.Abstract (expandPatternSynonyms)
+import Agda.TypeChecking.Pretty hiding (pretty, prettyA)
+import Agda.TypeChecking.Quote (quotedName)
+import Agda.TypeChecking.Opacity
+import Agda.TypeChecking.Warnings
+
+import Agda.Interaction.FindFile (checkModuleName, rootNameModule, SourceFile(SourceFile))
+-- import Agda.Interaction.Imports  -- for type-checking in ghci
+import {-# SOURCE #-} Agda.Interaction.Imports (scopeCheckImport)
+import Agda.Interaction.Options
+import qualified Agda.Interaction.Options.Lenses as Lens
+import Agda.Interaction.Options.Warnings
+
+import qualified Agda.Utils.AssocList as AssocList
+import Agda.Utils.CallStack ( HasCallStack, withCurrentCallStack )
+import Agda.Utils.Char
+import Agda.Utils.Either
+import Agda.Utils.FileName
+import Agda.Utils.Function ( applyWhen )
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import Agda.Utils.List2 ( List2, pattern List2 )
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.Map as Map
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Syntax.Common.Pretty (render, Pretty, pretty, prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+import Agda.ImpossibleTest (impossibleTest, impossibleTestReduceM)
+
+{--------------------------------------------------------------------------
+    Exceptions
+ --------------------------------------------------------------------------}
+
+notAnExpression :: (HasCallStack, MonadTCError m) => C.Expr -> m a
+notAnExpression = locatedTypeError NotAnExpression
+
+nothingAppliedToHiddenArg :: (HasCallStack, MonadTCError m) => C.Expr -> m a
+nothingAppliedToHiddenArg = locatedTypeError NothingAppliedToHiddenArg
+
+nothingAppliedToInstanceArg :: (HasCallStack, MonadTCError m) => C.Expr -> m a
+nothingAppliedToInstanceArg = locatedTypeError NothingAppliedToInstanceArg
+
+notAValidLetBinding :: (HasCallStack, MonadTCError m) => C.NiceDeclaration -> m a
+notAValidLetBinding = locatedTypeError NotAValidLetBinding
+
+{--------------------------------------------------------------------------
+    Helpers
+ --------------------------------------------------------------------------}
+--UNUSED Liang-Ting Chen 2019-07-16
+--annotateDecl :: ScopeM A.Declaration -> ScopeM A.Declaration
+--annotateDecl m = annotateDecls $ (:[]) <$> m
+
+-- | Make sure that there are no dot patterns (called on pattern synonyms).
+noDotorEqPattern :: String -> A.Pattern' e -> ScopeM (A.Pattern' Void)
+noDotorEqPattern err = dot
+  where
+    dot :: A.Pattern' e -> ScopeM (A.Pattern' Void)
+    dot = \case
+      A.VarP x               -> pure $ A.VarP x
+      A.ConP i c args        -> A.ConP i c <$> (traverse $ traverse $ traverse dot) args
+      A.ProjP i o d          -> pure $ A.ProjP i o d
+      A.WildP i              -> pure $ A.WildP i
+      A.AsP i x p            -> A.AsP i x <$> dot p
+      A.DotP{}               -> genericError err
+      A.EqualP{}             -> genericError err   -- Andrea: so we also disallow = patterns, reasonable?
+      A.AbsurdP i            -> pure $ A.AbsurdP i
+      A.LitP i l             -> pure $ A.LitP i l
+      A.DefP i f args        -> A.DefP i f <$> (traverse $ traverse $ traverse dot) args
+      A.PatternSynP i c args -> A.PatternSynP i c <$> (traverse $ traverse $ traverse dot) args
+      A.RecP i fs            -> A.RecP i <$> (traverse $ traverse dot) fs
+      A.WithP i p            -> A.WithP i <$> dot p
+      A.AnnP i a p           -> genericError err   -- TODO: should this be allowed?
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Make sure that there are no dot patterns (WAS: called on pattern synonyms).
+--noDotPattern :: String -> A.Pattern' e -> ScopeM (A.Pattern' Void)
+--noDotPattern err = traverse $ const $ genericError err
+
+newtype RecordConstructorType = RecordConstructorType [C.Declaration]
+
+instance ToAbstract RecordConstructorType where
+  type AbsOfCon RecordConstructorType = A.Expr
+  toAbstract (RecordConstructorType ds) = recordConstructorType ds
+
+-- | Compute the type of the record constructor (with bogus target type)
+recordConstructorType :: [C.Declaration] -> ScopeM A.Expr
+recordConstructorType decls =
+    -- Nicify all declarations since there might be fixity declarations after
+    -- the the last field. Use NoWarn to silence fixity warnings. We'll get
+    -- them again when scope checking the declarations to build the record
+    -- module.
+    niceDecls NoWarn decls $ buildType . takeFields
+  where
+    takeFields = List.dropWhileEnd notField
+
+    notField NiceField{} = False
+    notField _           = True
+
+    buildType :: [C.NiceDeclaration] -> ScopeM A.Expr
+      -- TODO: Telescope instead of Expr in abstract RecDef
+    buildType ds = do
+      -- The constructor target type is computed in the type checker.
+      -- For now, we put a dummy expression there.
+      -- Andreas, 2022-10-06, issue #6165:
+      -- The dummy was builtinSet, but this might not be defined yet.
+      let dummy = A.Lit empty $ LitString "TYPE"
+      tel   <- catMaybes <$> mapM makeBinding ds
+      return $ A.mkPi (ExprRange (getRange ds)) tel dummy
+
+    makeBinding :: C.NiceDeclaration -> ScopeM (Maybe A.TypedBinding)
+    makeBinding d = do
+      let failure = typeError $ NotValidBeforeField d
+          r       = getRange d
+          mkLet d = Just . A.TLet r <$> toAbstract (LetDef d)
+      setCurrentRange r $ case d of
+
+        C.NiceField r pr ab inst tac x a -> do
+          fx  <- getConcreteFixity x
+          let bv = unnamed (C.mkBinder $ (C.mkBoundName x fx) { bnameTactic = tac }) <$ a
+          toAbstract $ C.TBind r (singleton bv) (unArg a)
+
+        -- Public open is allowed and will take effect when scope checking as
+        -- proper declarations.
+        C.NiceOpen r m dir -> do
+          mkLet $ C.NiceOpen r m dir{ publicOpen = Nothing }
+        C.NiceModuleMacro r p e x modapp open dir -> do
+          mkLet $ C.NiceModuleMacro r p e x modapp open
+                    dir{ publicOpen = Nothing }
+
+        -- Do some rudimentary matching here to get NotValidBeforeField instead
+        -- of NotAValidLetDecl.
+        C.NiceMutual _ _ _ _
+          [ C.FunSig _ _ _ _ macro _ _ _ _ _
+          , C.FunDef _ _ abstract _ _ _ _
+             [ C.Clause _ _ (C.LHS _p [] []) (C.RHS _) NoWhere [] ]
+          ] | abstract /= AbstractDef && macro /= MacroDef -> do
+          mkLet d
+
+        C.NiceLoneConstructor{} -> failure
+        C.NiceMutual{}        -> failure
+        -- TODO: some of these cases might be __IMPOSSIBLE__
+        C.Axiom{}             -> failure
+        C.PrimitiveFunction{} -> failure
+        C.NiceModule{}        -> failure
+        C.NiceImport{}        -> failure
+        C.NicePragma{}        -> failure
+        C.NiceRecSig{}        -> failure
+        C.NiceDataSig{}       -> failure
+        C.NiceFunClause{}     -> failure
+        C.FunSig{}            -> failure  -- Note: these are bundled with FunDef in NiceMutual
+        C.FunDef{}            -> failure
+        C.NiceDataDef{}       -> failure
+        C.NiceRecDef{}        -> failure
+        C.NicePatternSyn{}    -> failure
+        C.NiceGeneralize{}    -> failure
+        C.NiceUnquoteDecl{}   -> failure
+        C.NiceUnquoteDef{}    -> failure
+        C.NiceUnquoteData{}   -> failure
+        C.NiceOpaque{}        -> failure
+
+checkModuleApplication
+  :: C.ModuleApplication
+  -> ModuleName
+  -> C.Name
+  -> C.ImportDirective
+  -> ScopeM (A.ModuleApplication, ScopeCopyInfo, A.ImportDirective)
+
+checkModuleApplication (C.SectionApp _ tel e) m0 x dir' = do
+  reportSDoc "scope.decl" 70 $ vcat $
+    [ text $ "scope checking ModuleApplication " ++ prettyShow x
+    ]
+
+  -- For the following, set the current module to be m0.
+  withCurrentModule m0 $ do
+    -- Check that expression @e@ is of the form @m args@.
+    (m, args) <- parseModuleApplication e
+    -- Scope check the telescope (introduces bindings!).
+    tel' <- catMaybes <$> toAbstract tel
+    -- Scope check the old module name and the module args.
+    m1    <- toAbstract $ OldModuleName m
+    args' <- toAbstractCtx (ArgumentCtx PreferParen) args
+    -- Copy the scope associated with m and take the parts actually imported.
+    (adir, s) <- applyImportDirectiveM (C.QName x) dir' =<< getNamedScope m1
+    (s', copyInfo) <- copyScope m m0 s
+    -- Set the current scope to @s'@
+    modifyCurrentScope $ const s'
+    printScope "mod.inst" 20 "copied source module"
+    reportSDoc "scope.mod.inst" 30 $ return $ pretty copyInfo
+    let amodapp = A.SectionApp tel' m1 args'
+    reportSDoc "scope.decl" 70 $ vcat $
+      [ text $ "scope checked ModuleApplication " ++ prettyShow x
+      ]
+    reportSDoc "scope.decl" 70 $ vcat $
+      [ nest 2 $ prettyA amodapp
+      ]
+    return (amodapp, copyInfo, adir)
+
+checkModuleApplication (C.RecordModuleInstance _ recN) m0 x dir' =
+  withCurrentModule m0 $ do
+    m1 <- toAbstract $ OldModuleName recN
+    s <- getNamedScope m1
+    (adir, s) <- applyImportDirectiveM recN dir' s
+    (s', copyInfo) <- copyScope recN m0 s
+    modifyCurrentScope $ const s'
+
+    printScope "mod.inst" 20 "copied record module"
+    return (A.RecordModuleInstance m1, copyInfo, adir)
+
+-- | @checkModuleMacro mkApply range access concreteName modapp open dir@
+--
+--   Preserves local variables.
+
+checkModuleMacro
+  :: (ToConcrete a, Pretty (ConOfAbs a))
+  => (ModuleInfo
+      -> Erased
+      -> ModuleName
+      -> A.ModuleApplication
+      -> ScopeCopyInfo
+      -> A.ImportDirective
+      -> a)
+  -> OpenKind
+  -> Range
+  -> Access
+  -> Erased
+  -> C.Name
+  -> C.ModuleApplication
+  -> OpenShortHand
+  -> C.ImportDirective
+  -> ScopeM a
+checkModuleMacro apply kind r p e x modapp open dir = do
+    reportSDoc "scope.decl" 70 $ vcat $
+      [ text $ "scope checking ModuleMacro " ++ prettyShow x
+      ]
+    dir <- notPublicWithoutOpen open dir
+
+    m0 <- toAbstract (NewModuleName x)
+    reportSDoc "scope.decl" 90 $ "NewModuleName: m0 =" <+> prettyA m0
+
+    printScope "mod.inst" 20 "module macro"
+
+    -- If we're opening a /named/ module, the import directive is
+    -- applied to the "open", otherwise to the module itself. However,
+    -- "public" is always applied to the "open".
+    let (moduleDir, openDir) = case (open, isNoName x) of
+          (DoOpen,   False) -> (defaultImportDir, dir)
+          (DoOpen,   True)  -> ( dir { publicOpen = Nothing }
+                               , defaultImportDir { publicOpen = publicOpen dir }
+                               )
+          (DontOpen, _)     -> (dir, defaultImportDir)
+
+    -- Restore the locals after module application has been checked.
+    (modapp', copyInfo, adir') <- withLocalVars $ checkModuleApplication modapp m0 x moduleDir
+    printScope "mod.inst.app" 20 "checkModuleMacro, after checkModuleApplication"
+
+    reportSDoc "scope.decl" 90 $ "after mod app: trying to print m0 ..."
+    reportSDoc "scope.decl" 90 $ "after mod app: m0 =" <+> prettyA m0
+
+    bindModule p x m0
+    reportSDoc "scope.decl" 90 $ "after bindMod: m0 =" <+> prettyA m0
+
+    printScope "mod.inst.copy.after" 20 "after copying"
+
+    -- Open the module if DoOpen.
+    -- Andreas, 2014-09-02: @openModule@ might shadow some locals!
+    adir <- case open of
+      DontOpen -> return adir'
+      DoOpen   -> do
+        adir'' <- openModule kind (Just m0) (C.QName x) openDir
+        -- Andreas, 2020-05-14, issue #4656
+        -- Keep the more meaningful import directive for highlighting
+        -- (the other one is a defaultImportDir).
+        return $ if isNoName x then adir' else adir''
+
+    printScope "mod.inst" 20 $ show open
+    reportSDoc "scope.decl" 90 $ "after open   : m0 =" <+> prettyA m0
+
+    stripNoNames
+    printScope "mod.inst" 10 $ "after stripping"
+    reportSDoc "scope.decl" 90 $ "after stripNo: m0 =" <+> prettyA m0
+
+    let m      = m0 `withRangesOf` singleton x
+        adecl  = apply info e m modapp' copyInfo adir
+
+    reportSDoc "scope.decl" 70 $ vcat $
+      [ text $ "scope checked ModuleMacro " ++ prettyShow x
+      ]
+    reportSLn  "scope.decl" 90 $ "info    = " ++ show info
+    reportSLn  "scope.decl" 90 $ "m       = " ++ prettyShow m
+    reportSLn  "scope.decl" 90 $ "modapp' = " ++ show modapp'
+    reportSDoc "scope.decl" 90 $ return $ pretty copyInfo
+    reportSDoc "scope.decl" 70 $ nest 2 $ prettyA adecl
+    return adecl
+  where
+    info = ModuleInfo
+             { minfoRange  = r
+             , minfoAsName = Nothing
+             , minfoAsTo   = renamingRange dir
+             , minfoOpenShort = Just open
+             , minfoDirective = Just dir
+             }
+
+-- | The @public@ keyword must only be used together with @open@.
+
+notPublicWithoutOpen :: OpenShortHand -> C.ImportDirective -> ScopeM C.ImportDirective
+notPublicWithoutOpen DoOpen   dir = return dir
+notPublicWithoutOpen DontOpen dir = do
+  whenJust (publicOpen dir) $ \ r ->
+    setCurrentRange r $ warning UselessPublic
+  return $ dir { publicOpen = Nothing }
+
+-- | Computes the range of all the \"to\" keywords used in a renaming
+-- directive.
+
+renamingRange :: C.ImportDirective -> Range
+renamingRange = getRange . map renToRange . impRenaming
+
+-- | Scope check a 'NiceOpen'.
+checkOpen
+  :: Range                -- ^ Range of @open@ statement.
+  -> Maybe A.ModuleName   -- ^ Resolution of concrete module name (if already resolved).
+  -> C.QName              -- ^ Module to open.
+  -> C.ImportDirective    -- ^ Scope modifier.
+  -> ScopeM (ModuleInfo, A.ModuleName, A.ImportDirective) -- ^ Arguments of 'A.Open'
+checkOpen r mam x dir = do
+  reportSDoc "scope.decl" 70 $ do
+    cm <- getCurrentModule
+    vcat $
+      [ text   "scope checking NiceOpen " <> return (pretty x)
+      , text   "  getCurrentModule       = " <> prettyA cm
+      , text $ "  getCurrentModule (raw) = " ++ show cm
+      , text $ "  C.ImportDirective      = " ++ prettyShow dir
+      ]
+  -- Andreas, 2017-01-01, issue #2377: warn about useless `public`
+  whenJust (publicOpen dir) $ \ r -> do
+    whenM ((A.noModuleName ==) <$> getCurrentModule) $ do
+      setCurrentRange r $ warning UselessPublic
+
+  m <- caseMaybe mam (toAbstract (OldModuleName x)) return
+  printScope "open" 20 $ "opening " ++ prettyShow x
+  adir <- openModule TopOpenModule (Just m) x dir
+  printScope "open" 20 $ "result:"
+  let minfo = ModuleInfo
+        { minfoRange     = r
+        , minfoAsName    = Nothing
+        , minfoAsTo      = renamingRange dir
+        , minfoOpenShort = Nothing
+        , minfoDirective = Just dir
+        }
+  let adecls = [A.Open minfo m adir]
+  reportSDoc "scope.decl" 70 $ vcat $
+    text ( "scope checked NiceOpen " ++ prettyShow x
+         ) : map (nest 2 . prettyA) adecls
+  return (minfo, m, adir)
+
+-- | Check a literal, issuing an error warning for bad literals.
+checkLiteral :: Literal -> ScopeM ()
+checkLiteral = \case
+  LitChar   c   -> when (isSurrogateCodePoint c) $ warning $ InvalidCharacterLiteral c
+  LitNat    _   -> return ()
+  LitWord64 _   -> return ()
+  LitFloat  _   -> return ()
+  LitString _   -> return ()
+  LitQName  _   -> return ()
+  LitMeta   _ _ -> return ()
+
+{--------------------------------------------------------------------------
+    Translation
+ --------------------------------------------------------------------------}
+
+concreteToAbstract_ :: ToAbstract c => c -> ScopeM (AbsOfCon c)
+concreteToAbstract_ = toAbstract
+
+concreteToAbstract :: ToAbstract c => ScopeInfo -> c -> ScopeM (AbsOfCon c)
+concreteToAbstract scope x = withScope_ scope (toAbstract x)
+
+-- | Things that can be translated to abstract syntax are instances of this
+--   class.
+class ToAbstract c where
+    type AbsOfCon c
+    toAbstract :: c -> ScopeM (AbsOfCon c)
+
+-- | This function should be used instead of 'toAbstract' for things that need
+--   to keep track of precedences to make sure that we don't forget about it.
+toAbstractCtx :: ToAbstract c => Precedence -> c-> ScopeM (AbsOfCon c)
+toAbstractCtx ctx c = withContextPrecedence ctx $ toAbstract c
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--toAbstractTopCtx :: ToAbstract c a => c -> ScopeM a
+--toAbstractTopCtx = toAbstractCtx TopCtx
+
+toAbstractHiding :: (LensHiding h, ToAbstract c) => h -> c -> ScopeM (AbsOfCon c)
+toAbstractHiding h | visible h = toAbstract -- don't change precedence if visible
+toAbstractHiding _             = toAbstractCtx TopCtx
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--setContextCPS :: Precedence -> (a -> ScopeM b) ->
+--                 ((a -> ScopeM b) -> ScopeM b) -> ScopeM b
+--setContextCPS p ret f = do
+--  old <- useScope scopePrecedence
+--  withContextPrecedence p $ f $ \ x -> setContextPrecedence old >> ret x
+--
+--localToAbstractCtx :: ToAbstract c =>
+--                     Precedence -> c -> (AbsOfCon -> ScopeM (AbsOfCon c)) -> ScopeM (AbsOfCon c)
+--localToAbstractCtx ctx c ret = setContextCPS ctx ret (localToAbstract c)
+
+-- | This operation does not affect the scope, i.e. the original scope
+--   is restored upon completion.
+localToAbstract :: ToAbstract c => c -> (AbsOfCon c -> ScopeM b) -> ScopeM b
+localToAbstract x ret = fst <$> localToAbstract' x ret
+
+-- | Like 'localToAbstract' but returns the scope after the completion of the
+--   second argument.
+localToAbstract' :: ToAbstract c => c -> (AbsOfCon c -> ScopeM b) -> ScopeM (b, ScopeInfo)
+localToAbstract' x ret = do
+  scope <- getScope
+  withScope scope $ ret =<< toAbstract x
+
+instance ToAbstract () where
+  type AbsOfCon () = ()
+  toAbstract = pure
+
+instance (ToAbstract c1, ToAbstract c2) => ToAbstract (c1, c2) where
+  type AbsOfCon (c1, c2) = (AbsOfCon c1, AbsOfCon c2)
+  toAbstract (x,y) = (,) <$> toAbstract x <*> toAbstract y
+
+instance (ToAbstract c1, ToAbstract c2, ToAbstract c3) => ToAbstract (c1, c2, c3) where
+  type AbsOfCon (c1, c2, c3) = (AbsOfCon c1, AbsOfCon c2, AbsOfCon c3)
+  toAbstract (x,y,z) = flatten <$> toAbstract (x,(y,z))
+    where
+      flatten (x,(y,z)) = (x,y,z)
+
+instance ToAbstract c => ToAbstract [c] where
+  type AbsOfCon [c] = [AbsOfCon c]
+  toAbstract = mapM toAbstract
+
+instance ToAbstract c => ToAbstract (List1 c) where
+  type AbsOfCon (List1 c) = List1 (AbsOfCon c)
+  toAbstract = mapM toAbstract
+
+instance (ToAbstract c1, ToAbstract c2) => ToAbstract (Either c1 c2) where
+  type AbsOfCon (Either c1 c2) = Either (AbsOfCon c1) (AbsOfCon c2)
+  toAbstract = traverseEither toAbstract toAbstract
+
+instance ToAbstract c => ToAbstract (Maybe c) where
+  type AbsOfCon (Maybe c) = Maybe (AbsOfCon c)
+  toAbstract = traverse toAbstract
+
+-- Names ------------------------------------------------------------------
+
+data NewName a = NewName
+  { newBinder   :: A.BindingSource -- what kind of binder?
+  , newName     :: a
+  } deriving (Functor)
+
+data OldQName = OldQName
+  C.QName              -- ^ Concrete name to be resolved
+  (Maybe (Set A.Name)) -- ^ If a set is given, then the first name must
+                       --   correspond to one of the names in the set.
+
+-- | We sometimes do not want to fail hard if the name is not actually
+--   in scope because we have a strategy to recover from this problem
+--   (e.g. drop the offending COMPILE pragma)
+data MaybeOldQName = MaybeOldQName OldQName
+
+newtype OldName a = OldName a
+
+-- | Wrapper to resolve a name to a 'ResolvedName' (rather than an 'A.Expr').
+data ResolveQName = ResolveQName C.QName
+
+data PatName      = PatName C.QName (Maybe (Set A.Name))
+  -- ^ If a set is given, then the first name must correspond to one
+  -- of the names in the set.
+
+instance ToAbstract (NewName C.Name) where
+  type AbsOfCon (NewName C.Name) = A.Name
+  toAbstract (NewName b x) = do
+    y <- freshAbstractName_ x
+    bindVariable b x y
+    return y
+
+instance ToAbstract (NewName C.BoundName) where
+  type AbsOfCon (NewName C.BoundName) = A.BindName
+  toAbstract NewName{ newBinder = b, newName = BName{ boundName = x, bnameFixity = fx }} = do
+    y <- freshAbstractName fx x
+    bindVariable b x y
+    return $ A.BindName y
+
+instance ToAbstract OldQName where
+  type AbsOfCon OldQName = A.Expr
+  toAbstract q@(OldQName x _) =
+    fromMaybeM (notInScopeError x) $ toAbstract (MaybeOldQName q)
+
+instance ToAbstract MaybeOldQName where
+  type AbsOfCon MaybeOldQName = Maybe A.Expr
+  toAbstract (MaybeOldQName (OldQName x ns)) = do
+    qx <- resolveName' allKindsOfNames ns x
+    reportSLn "scope.name" 10 $ "resolved " ++ prettyShow x ++ ": " ++ prettyShow qx
+    case qx of
+      VarName x' _         -> return $ Just $ A.Var x'
+      DefinedName _ d suffix -> do
+        raiseWarningsOnUsage $ anameName d
+        -- then we take note of generalized names used
+        case anameKind d of
+          GeneralizeName -> do
+            gvs <- useTC stGeneralizedVars
+            case gvs of   -- Subtle: Use (left-biased) union instead of insert to keep the old name if
+                          -- already present. This way we can sort by source location when generalizing
+                          -- (Issue 3354).
+                Just s -> stGeneralizedVars `setTCLens` Just (s `Set.union` Set.singleton (anameName d))
+                Nothing -> typeError $ GeneralizeNotSupportedHere $ anameName d
+          DisallowedGeneralizeName -> typeError $ GeneralizedVarInLetOpenedModule $ anameName d
+          _ -> return ()
+        -- and then we return the name
+        return $ withSuffix suffix $ nameToExpr d
+        where
+          withSuffix NoSuffix   e         = Just e
+          withSuffix s@Suffix{} (A.Def x) = Just $ A.Def' x s
+          withSuffix _          _         = Nothing
+
+      FieldName     ds     -> ambiguous (A.Proj ProjPrefix) ds
+      ConstructorName _ ds -> ambiguous A.Con ds
+      PatternSynResName ds -> ambiguous A.PatternSyn ds
+      UnknownName          -> pure Nothing
+    where
+      ambiguous :: (AmbiguousQName -> A.Expr) -> List1 AbstractName -> ScopeM (Maybe A.Expr)
+      ambiguous f ds = do
+        let xs = fmap anameName ds
+        raiseWarningsOnUsageIfUnambiguous xs
+        return $ Just $ f $ AmbQ xs
+
+      -- Note: user warnings on ambiguous names will be raised by the type checker,
+      -- see storeDiamsbiguatedName.
+      raiseWarningsOnUsageIfUnambiguous :: List1 A.QName -> ScopeM ()
+      raiseWarningsOnUsageIfUnambiguous = \case
+        x :| [] -> raiseWarningsOnUsage x
+        _       -> return ()
+
+
+instance ToAbstract ResolveQName where
+  type AbsOfCon ResolveQName = ResolvedName
+  toAbstract (ResolveQName x) = resolveName x >>= \case
+    UnknownName -> notInScopeError x
+    q -> return q
+
+data APatName = VarPatName A.Name
+              | ConPatName (List1 AbstractName)
+              | PatternSynPatName (List1 AbstractName)
+
+instance ToAbstract PatName where
+  type AbsOfCon PatName = APatName
+  toAbstract (PatName x ns) = do
+    reportSLn "scope.pat" 10 $ "checking pattern name: " ++ prettyShow x
+    rx <- resolveName' (someKindsOfNames [ConName, CoConName, PatternSynName]) ns x
+          -- Andreas, 2013-03-21 ignore conflicting names which cannot
+          -- be meant since we are in a pattern
+          -- Andreas, 2020-04-11 CoConName:
+          -- coinductive constructors will be rejected later, in the type checker
+    reportSLn "scope.pat" 20 $ "resolved as " ++ prettyShow rx
+    case (rx, x) of
+      (VarName y _,       C.QName x)                           -> bindPatVar x
+      (FieldName d,       C.QName x)                           -> bindPatVar x
+      (DefinedName _ d _, C.QName x) | isDefName (anameKind d) -> bindPatVar x
+      (UnknownName,       C.QName x)                           -> bindPatVar x
+      (ConstructorName _ ds, _)                                -> patCon ds
+      (PatternSynResName d, _)                                 -> patSyn d
+      _ -> genericError $ "Cannot pattern match on non-constructor " ++ prettyShow x
+    where
+      bindPatVar = VarPatName <.> bindPatternVariable
+      patCon ds = do
+        reportSLn "scope.pat" 10 $ "it was a con: " ++ prettyShow (fmap anameName ds)
+        return $ ConPatName ds
+      patSyn ds = do
+        reportSLn "scope.pat" 10 $ "it was a pat syn: " ++ prettyShow (fmap anameName ds)
+        return $ PatternSynPatName ds
+
+-- | Translate and possibly bind a pattern variable
+--   (which could have been bound before due to non-linearity).
+bindPatternVariable :: C.Name -> ScopeM A.Name
+bindPatternVariable x = do
+  y <- (AssocList.lookup x <$> getVarsToBind) >>= \case
+    Just (LocalVar y _ _) -> do
+      reportSLn "scope.pat" 10 $ "it was a old var: " ++ prettyShow x
+      return $ setRange (getRange x) y
+    Nothing -> do
+      reportSLn "scope.pat" 10 $ "it was a new var: " ++ prettyShow x
+      freshAbstractName_ x
+  addVarToBind x $ LocalVar y PatternBound []
+  return y
+
+class ToQName a where
+  toQName :: a -> C.QName
+
+instance ToQName C.Name  where toQName = C.QName
+instance ToQName C.QName where toQName = id
+
+-- Should be a defined name.
+instance ToQName a => ToAbstract (OldName a) where
+  type AbsOfCon (OldName a) = A.QName
+  toAbstract (OldName x) = do
+    rx <- resolveName (toQName x)
+    case rx of
+      DefinedName _ d NoSuffix -> return $ anameName d
+      DefinedName _ d Suffix{} -> notInScopeError (toQName x)
+      -- We can get the cases below for DISPLAY pragmas
+      ConstructorName _ ds -> return $ anameName (List1.head ds)   -- We'll throw out this one, so it doesn't matter which one we pick
+      FieldName ds         -> return $ anameName (List1.head ds)
+      PatternSynResName ds -> return $ anameName (List1.head ds)
+      VarName x _          -> genericError $ "Not a defined name: " ++ prettyShow x
+      UnknownName          -> notInScopeError (toQName x)
+
+-- | Resolve a non-local name and return its possibly ambiguous abstract name.
+toAbstractExistingName :: ToQName a => a -> ScopeM (List1 AbstractName)
+toAbstractExistingName x = resolveName (toQName x) >>= \case
+    DefinedName _ d NoSuffix -> return $ singleton d
+    DefinedName _ d Suffix{} -> notInScopeError (toQName x)
+    ConstructorName _ ds     -> return ds
+    FieldName ds             -> return ds
+    PatternSynResName ds     -> return ds
+    VarName x _              -> genericError $ "Not a defined name: " ++ prettyShow x
+    UnknownName              -> notInScopeError (toQName x)
+
+newtype NewModuleName      = NewModuleName      C.Name
+newtype NewModuleQName     = NewModuleQName     C.QName
+newtype OldModuleName      = OldModuleName      C.QName
+
+freshQModule :: A.ModuleName -> C.Name -> ScopeM A.ModuleName
+freshQModule m x = A.qualifyM m . mnameFromList1 . singleton <$> freshAbstractName_ x
+
+checkForModuleClash :: C.Name -> ScopeM ()
+checkForModuleClash x = do
+  ms :: [AbstractModule] <- scopeLookup (C.QName x) <$> getScope
+  unless (null ms) $ do
+    reportSLn "scope.clash" 20 $ "clashing modules ms = " ++ prettyShow ms
+    reportSLn "scope.clash" 60 $ "clashing modules ms = " ++ show ms
+    setCurrentRange x $
+      typeError $ ShadowedModule x $
+                map ((`withRangeOf` x) . amodName) ms
+
+instance ToAbstract NewModuleName where
+  type AbsOfCon NewModuleName = A.ModuleName
+  toAbstract (NewModuleName x) = do
+    checkForModuleClash x
+    m <- getCurrentModule
+    y <- freshQModule m x
+    createModule Nothing y
+    return y
+
+instance ToAbstract NewModuleQName where
+  type AbsOfCon NewModuleQName = A.ModuleName
+  toAbstract (NewModuleQName m) = toAbs noModuleName m
+    where
+      toAbs m (C.QName x)  = do
+        y <- freshQModule m x
+        createModule Nothing y
+        return y
+      toAbs m (C.Qual x q) = do
+        m' <- freshQModule m x
+        toAbs m' q
+
+instance ToAbstract OldModuleName where
+  type AbsOfCon OldModuleName = A.ModuleName
+
+  toAbstract (OldModuleName q) = setCurrentRange q $ do
+    amodName <$> resolveModule q
+
+-- Expressions ------------------------------------------------------------
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Peel off 'C.HiddenArg' and represent it as an 'NamedArg'.
+--mkNamedArg :: C.Expr -> NamedArg C.Expr
+--mkNamedArg (C.HiddenArg   _ e) = Arg (hide         defaultArgInfo) e
+--mkNamedArg (C.InstanceArg _ e) = Arg (makeInstance defaultArgInfo) e
+--mkNamedArg e                   = Arg defaultArgInfo $ unnamed e
+
+-- | Peel off 'C.HiddenArg' and represent it as an 'Arg', throwing away any name.
+mkArg' :: ArgInfo -> C.Expr -> Arg C.Expr
+mkArg' info (C.HiddenArg   _ e) = Arg (hide         info) $ namedThing e
+mkArg' info (C.InstanceArg _ e) = Arg (makeInstance info) $ namedThing e
+mkArg' info e                   = Arg (setHiding NotHidden info) e
+--UNUSED Liang-Ting 2019-07-16
+---- | By default, arguments are @Relevant@.
+--mkArg :: C.Expr -> Arg C.Expr
+--mkArg e = mkArg' defaultArgInfo e
+
+inferParenPreference :: C.Expr -> ParenPreference
+inferParenPreference C.Paren{} = PreferParen
+inferParenPreference _         = PreferParenless
+
+-- | Parse a possibly dotted and braced @C.Expr@ as @A.Expr@,
+--   interpreting dots as relevance and braces as hiding.
+--   Only accept a layer of dotting/bracing if the respective accumulator is @Nothing@.
+toAbstractDotHiding :: Maybe Relevance -> Maybe Hiding -> Precedence -> C.Expr -> ScopeM (A.Expr, Relevance, Hiding)
+toAbstractDotHiding mr mh prec e = do
+    reportSLn "scope.irrelevance" 100 $ "toAbstractDotHiding: " ++ render (pretty e)
+    traceCall (ScopeCheckExpr e) $ case e of
+
+      C.RawApp _ es     -> toAbstractDotHiding mr mh prec =<< parseApplication es
+      C.Paren _ e       -> toAbstractDotHiding mr mh TopCtx e
+
+      C.Dot _ e
+        | Nothing <- mr -> toAbstractDotHiding (Just Irrelevant) mh prec e
+
+      C.DoubleDot _ e
+        | Nothing <- mr -> toAbstractDotHiding (Just NonStrict) mh prec e
+
+      C.HiddenArg _ (Named Nothing e)
+        | Nothing <- mh -> toAbstractDotHiding mr (Just Hidden) TopCtx e
+
+      C.InstanceArg _ (Named Nothing e)
+        | Nothing <- mh -> toAbstractDotHiding mr (Just $ Instance NoOverlap) TopCtx e
+
+      e                 -> (, fromMaybe Relevant mr, fromMaybe NotHidden mh) <$>
+                             toAbstractCtx prec e
+
+-- | Translate concrete expression under at least one binder into nested
+--   lambda abstraction in abstract syntax.
+toAbstractLam :: Range -> List1 C.LamBinding -> C.Expr -> Precedence -> ScopeM A.Expr
+toAbstractLam r bs e ctx = do
+  -- Translate the binders
+  lvars0 <- getLocalVars
+  localToAbstract (fmap (C.DomainFull . makeDomainFull) bs) $ \ bs -> do
+    lvars1 <- getLocalVars
+    checkNoShadowing lvars0 lvars1
+    -- Translate the body
+    e <- toAbstractCtx ctx e
+    -- We have at least one binder.  Get first @b@ and rest @bs@.
+    return $ case List1.catMaybes bs of
+      -- Andreas, 2020-06-18
+      -- There is a pathological case in which we end up without binder:
+      --   λ (let
+      --        mutual -- warning: empty mutual block
+      --     ) -> Set
+      []   -> e
+      b:bs -> A.Lam (ExprRange r) b $ foldr mkLam e bs
+  where
+    mkLam b e = A.Lam (ExprRange $ fuseRange b e) b e
+
+-- | Scope check extended lambda expression.
+scopeCheckExtendedLam ::
+  Range -> Erased -> List1 C.LamClause -> ScopeM A.Expr
+scopeCheckExtendedLam r e cs = do
+  whenM isInsideDotPattern $
+    genericError "Extended lambdas are not allowed in dot patterns"
+
+  -- Find an unused name for the extended lambda definition.
+  cname <- freshConcreteName r 0 extendedLambdaName
+  name  <- freshAbstractName_ cname
+  a <- asksTC (^. lensIsAbstract)
+  reportSDoc "scope.extendedLambda" 10 $ vcat
+    [ text $ "new extended lambda name (" ++ show a ++ "): " ++ prettyShow name
+    ]
+  verboseS "scope.extendedLambda" 60 $ do
+    forM_ cs $ \ c -> do
+      reportSLn "scope.extendedLambda" 60 $ "extended lambda lhs: " ++ show (C.lamLHS c)
+  qname <- qualifyName_ name
+  bindName (PrivateAccess Inserted) FunName cname qname
+
+  -- Andreas, 2019-08-20
+  -- Keep the following __IMPOSSIBLE__, which is triggered by -v scope.decl.trace:80,
+  -- for testing issue #4016.
+  d <- C.FunDef r [] a NotInstanceDef __IMPOSSIBLE__ __IMPOSSIBLE__ cname . List1.toList <$> do
+          forM cs $ \ (LamClause ps rhs ca) -> do
+            let p   = C.rawAppP $
+                        (killRange $ IdentP True $ C.QName cname) :| ps
+            let lhs = C.LHS p [] []
+            return $ C.Clause cname ca lhs rhs NoWhere []
+  scdef <- toAbstract d
+
+  -- Create the abstract syntax for the extended lambda.
+  case scdef of
+    A.ScopedDecl si [A.FunDef di qname' cs] -> do
+      setScope si  -- This turns into an A.ScopedExpr si $ A.ExtendedLam...
+      return $
+        A.ExtendedLam (ExprRange r) di e qname' $
+        List1.fromListSafe __IMPOSSIBLE__ cs
+    _ -> __IMPOSSIBLE__
+
+-- | Scope check an expression.
+
+instance ToAbstract C.Expr where
+  type AbsOfCon C.Expr = A.Expr
+
+  toAbstract e =
+    traceCall (ScopeCheckExpr e) $ annotateExpr $ case e of
+
+  -- Names
+      Ident x -> toAbstract (OldQName x Nothing)
+      KnownIdent _ x -> toAbstract (OldQName x Nothing)
+      -- Just discard the syntax highlighting information.
+
+  -- Literals
+      C.Lit r l -> do
+        checkLiteral l
+        case l of
+          LitNat n -> do
+            let builtin | n < 0     = Just <$> primFromNeg    -- negative literals are only allowed if FROMNEG is defined
+                        | otherwise = ensureInScope =<< getBuiltin' builtinFromNat
+            builtin >>= \case
+              Just (I.Def q _) -> return $ mkApp q $ A.Lit i $ LitNat $ abs n
+              _                -> return alit
+
+          LitString s -> do
+            getBuiltin' builtinFromString >>= ensureInScope >>= \case
+              Just (I.Def q _) -> return $ mkApp q alit
+              _                -> return alit
+
+          _ -> return alit
+        where
+        i       = ExprRange r
+        alit    = A.Lit i l
+        mkApp q = A.App (defaultAppInfo r) (A.Def q) . defaultNamedArg
+
+        -- #4925: Require fromNat/fromNeg to be in scope *unqualified* for literal overloading to
+        -- apply.
+        ensureInScope :: Maybe I.Term -> ScopeM (Maybe I.Term)
+        ensureInScope v@(Just (I.Def q _)) =
+          ifM (isNameInScopeUnqualified q <$> getScope) (return v) (return Nothing)
+        ensureInScope _ = return Nothing
+
+  -- Meta variables
+      C.QuestionMark r n -> do
+        scope <- getScope
+        -- Andreas, 2014-04-06 create interaction point.
+        ii <- registerInteractionPoint True r n
+        let info = MetaInfo
+             { metaRange  = r
+             , metaScope  = scope
+             , metaNumber = Nothing
+             , metaNameSuggestion = ""
+             }
+        return $ A.QuestionMark info ii
+      C.Underscore r n -> do
+        scope <- getScope
+        return $ A.Underscore $ MetaInfo
+                    { metaRange  = r
+                    , metaScope  = scope
+                    , metaNumber = __IMPOSSIBLE__ =<< n
+                    , metaNameSuggestion = fromMaybe "" n
+                    }
+
+  -- Raw application
+      C.RawApp r es -> do
+        e <- parseApplication es
+        toAbstract e
+
+  -- Application
+      C.App r e1 e2 -> do
+        -- Andreas, 2021-02-10, issue #3289: reject @e {.p}@ and @e ⦃ .p ⦄@.
+
+        -- Raise an error if argument is a C.Dot with Hiding info.
+        case namedArg e2 of
+          C.Dot{} | notVisible e2 -> setCurrentRange e2 $ typeError $ IllegalHidingInPostfixProjection e2
+          _ -> return ()
+
+        let parenPref = inferParenPreference (namedArg e2)
+            info = (defaultAppInfo r) { appOrigin = UserWritten, appParens = parenPref }
+        e1 <- toAbstractCtx FunctionCtx e1
+        e2 <- toAbstractCtx (ArgumentCtx parenPref) e2
+        return $ A.App info e1 e2
+
+  -- Operator application
+      C.OpApp r op ns es -> toAbstractOpApp op ns es
+      C.KnownOpApp _ r op ns es -> toAbstractOpApp op ns es
+
+  -- With application
+      C.WithApp r e es -> do
+        e  <- toAbstractCtx WithFunCtx e
+        es <- mapM (toAbstractCtx WithArgCtx) es
+        return $ A.WithApp (ExprRange r) e es
+
+  -- Misplaced hidden argument
+      C.HiddenArg _ _ -> nothingAppliedToHiddenArg e
+      C.InstanceArg _ _ -> nothingAppliedToInstanceArg e
+
+  -- Lambda
+      C.AbsurdLam r h -> return $ A.AbsurdLam (ExprRange r) h
+
+      C.Lam r bs e -> toAbstractLam r bs e TopCtx
+
+  -- Extended Lambda
+      C.ExtendedLam r e cs -> scopeCheckExtendedLam r e cs
+
+  -- Relevant and irrelevant non-dependent function type
+      C.Fun r (Arg info1 e1) e2 -> do
+        let arg = mkArg' info1 e1
+        let mr = case getRelevance arg of
+              Relevant  -> Nothing
+              r         -> Just r
+        let mh = case getHiding arg of
+              NotHidden -> Nothing
+              h         -> Just h
+        Arg info (e1', rel, hid) <- traverse (toAbstractDotHiding mr mh FunctionSpaceDomainCtx) arg
+        let updRel = case rel of
+              Relevant -> id
+              rel      -> setRelevance rel
+        let updHid = case hid of
+              NotHidden -> id
+              hid       -> setHiding hid
+        A.Fun (ExprRange r) (Arg (updRel $ updHid info) e1') <$> toAbstractCtx TopCtx e2
+
+  -- Dependent function type
+      e0@(C.Pi tel e) -> do
+        lvars0 <- getLocalVars
+        localToAbstract tel $ \tel -> do
+          lvars1 <- getLocalVars
+          checkNoShadowing lvars0 lvars1
+          e <- toAbstractCtx TopCtx e
+          let info = ExprRange (getRange e0)
+          return $ A.mkPi info (List1.catMaybes tel) e
+
+  -- Let
+      e0@(C.Let _ ds (Just e)) ->
+        ifM isInsideDotPattern (genericError $ "Let-expressions are not allowed in dot patterns") $
+        localToAbstract (LetDefs ds) $ \ds' -> do
+          e <- toAbstractCtx TopCtx e
+          let info = ExprRange (getRange e0)
+          return $ A.mkLet info ds' e
+      C.Let _ _ Nothing -> genericError "Missing body in let-expression"
+
+  -- Record construction
+      C.Rec r fs  -> do
+        fs' <- toAbstractCtx TopCtx fs
+        let ds'  = [ d | Right (_, Just d) <- fs' ]
+            fs'' = map (mapRight fst) fs'
+            i    = ExprRange r
+        return $ A.mkLet i ds' (A.Rec i fs'')
+
+  -- Record update
+      C.RecUpdate r e fs -> do
+        A.RecUpdate (ExprRange r) <$> toAbstract e <*> toAbstractCtx TopCtx fs
+
+  -- Parenthesis
+      C.Paren _ e -> toAbstractCtx TopCtx e
+
+  -- Idiom brackets
+      C.IdiomBrackets r es ->
+        toAbstractCtx TopCtx =<< parseIdiomBracketsSeq r es
+
+  -- Do notation
+      C.DoBlock r ss ->
+        toAbstractCtx TopCtx =<< desugarDoNotation r ss
+
+  -- Post-fix projections
+      C.Dot r e  -> A.Dot (ExprRange r) <$> toAbstract e
+
+  -- Pattern things
+      C.As _ _ _ -> notAnExpression e
+      C.Absurd _ -> notAnExpression e
+
+  -- Impossible things
+      C.Equal{} -> genericError "Parse error: unexpected '='"
+      C.Ellipsis _ -> genericError "Parse error: unexpected '...'"
+      C.DoubleDot _ _ -> genericError "Parse error: unexpected '..'"
+
+  -- Quoting
+      C.Quote r -> return $ A.Quote (ExprRange r)
+      C.QuoteTerm r -> return $ A.QuoteTerm (ExprRange r)
+      C.Unquote r -> return $ A.Unquote (ExprRange r)
+
+      C.Tactic r e -> genericError "Syntax error: 'tactic' can only appear in attributes"
+
+  -- DontCare
+      C.DontCare e -> A.DontCare <$> toAbstract e
+
+  -- forall-generalize
+      C.Generalized e -> do
+        (s, e) <- collectGeneralizables $ toAbstract e
+        pure $ A.generalized s e
+
+instance ToAbstract C.ModuleAssignment where
+  type AbsOfCon C.ModuleAssignment = (A.ModuleName, Maybe A.LetBinding)
+  toAbstract (C.ModuleAssignment m es i)
+    | null es && isDefaultImportDir i = (, Nothing) <$> toAbstract (OldModuleName m)
+    | otherwise = do
+        x <- C.NoName (getRange m) <$> fresh
+        r <- checkModuleMacro LetApply LetOpenModule
+               (getRange (m, es, i)) PublicAccess defaultErased x
+               (C.SectionApp (getRange (m , es)) [] (rawApp (Ident m :| es)))
+               DontOpen i
+        case r of
+          LetApply _ _ m' _ _ _ -> return (m', Just r)
+          _ -> __IMPOSSIBLE__
+
+instance ToAbstract c => ToAbstract (FieldAssignment' c) where
+  type AbsOfCon (FieldAssignment' c) = FieldAssignment' (AbsOfCon c)
+
+  toAbstract = traverse toAbstract
+
+instance ToAbstract (C.Binder' (NewName C.BoundName)) where
+  type AbsOfCon (C.Binder' (NewName C.BoundName)) = A.Binder
+
+  toAbstract (C.Binder p n) = do
+    let name = C.boundName $ newName n
+    -- If we do have a pattern then the variable needs to be inserted
+    -- so we do need a proper internal name for it.
+    n <- if not (isNoName name && isJust p) then pure n else do
+           n' <- freshConcreteName (getRange $ newName n) 0 patternInTeleName
+           pure $ fmap (\ n -> n { C.boundName = n' }) n
+    n <- toAbstract n
+    -- Expand puns if optHiddenArgumentPuns is True.
+    puns <- optHiddenArgumentPuns <$> pragmaOptions
+    p <- return $ if puns then fmap expandPuns p else p
+    -- Actually parsing the pattern, checking it is linear,
+    -- and bind its variables
+    p <- traverse parsePattern p
+    p <- toAbstract p
+    checkPatternLinearity p $ \ys ->
+      typeError $ RepeatedVariablesInPattern ys
+    bindVarsToBind
+    p <- toAbstract p
+    pure $ A.Binder p n
+
+instance ToAbstract C.LamBinding where
+  type AbsOfCon C.LamBinding = Maybe A.LamBinding
+
+  toAbstract (C.DomainFree x)  = do
+    tac <- traverse toAbstract $ bnameTactic $ C.binderName $ namedArg x
+    Just . A.DomainFree tac <$> toAbstract (updateNamedArg (fmap $ NewName LambdaBound) x)
+  toAbstract (C.DomainFull tb) = fmap A.DomainFull <$> toAbstract tb
+
+makeDomainFull :: C.LamBinding -> C.TypedBinding
+makeDomainFull (C.DomainFull b) = b
+makeDomainFull (C.DomainFree x) = C.TBind r (singleton x) $ C.Underscore r Nothing
+  where r = getRange x
+
+instance ToAbstract C.TypedBinding where
+  type AbsOfCon C.TypedBinding = Maybe A.TypedBinding
+
+  toAbstract (C.TBind r xs t) = do
+    t' <- toAbstractCtx TopCtx t
+    tac <- traverse toAbstract $
+      -- Invariant: all tactics are the same
+      -- (distributed in the parser, TODO: don't)
+      case List1.mapMaybe (bnameTactic . C.binderName . namedArg) xs of
+        []      -> Nothing
+        tac : _ -> Just tac
+
+    let fin = all (bnameIsFinite . C.binderName . namedArg) xs
+    xs' <- toAbstract $ fmap (updateNamedArg (fmap $ NewName LambdaBound)) xs
+
+    return $ Just $ A.TBind r (TypedBindingInfo tac fin) xs' t'
+  toAbstract (C.TLet r ds) = A.mkTLet r <$> toAbstract (LetDefs ds)
+
+-- | Scope check a module (top level function).
+--
+scopeCheckNiceModule
+  :: Range
+  -> Access
+  -> Erased
+  -> C.Name
+  -> C.Telescope
+  -> ScopeM [A.Declaration]
+  -> ScopeM A.Declaration
+       -- ^ The returned declaration is an 'A.Section'.
+scopeCheckNiceModule r p e name tel checkDs
+  | telHasOpenStmsOrModuleMacros tel = do
+      -- Andreas, 2013-12-10:
+      -- If the module telescope contains open statements
+      -- or module macros (Issue 1299),
+      -- add an extra anonymous module around the current one.
+      -- Otherwise, the open statements would create
+      -- identifiers in the parent scope of the current module.
+      -- But open statements in the module telescope should
+      -- only affect the current module!
+      scopeCheckNiceModule noRange p e noName_ [] $ singleton <$>
+        scopeCheckNiceModule_ PublicAccess  -- See #4350
+
+  | otherwise = do
+        scopeCheckNiceModule_ p
+  where
+    -- The actual workhorse:
+    scopeCheckNiceModule_ :: Access -> ScopeM A.Declaration
+    scopeCheckNiceModule_ p = do
+
+      -- Check whether we are dealing with an anonymous module.
+      -- This corresponds to a Coq/LEGO section.
+      (name, p', open) <- do
+        if isNoName name then do
+          (i :: NameId) <- fresh
+          return (C.NoName (getRange name) i, PrivateAccess Inserted, True)
+         else return (name, p, False)
+
+      -- Check and bind the module, using the supplied check for its contents.
+      aname <- toAbstract (NewModuleName name)
+      d <- snd <$> do
+        scopeCheckModule r e (C.QName name) aname tel checkDs
+      bindModule p' name aname
+
+      -- If the module was anonymous open it public
+      -- unless it's private, in which case we just open it (#2099)
+      when open $
+       void $ -- We can discard the returned default A.ImportDirective.
+        openModule TopOpenModule (Just aname) (C.QName name) $
+          defaultImportDir { publicOpen = boolToMaybe (p == PublicAccess) noRange }
+      return d
+
+-- | Check whether a telescope has open declarations or module macros.
+telHasOpenStmsOrModuleMacros :: C.Telescope -> Bool
+telHasOpenStmsOrModuleMacros = any yesBind
+  where
+    yesBind C.TBind{}     = False
+    yesBind (C.TLet _ ds) = any yes ds
+    yes C.ModuleMacro{}   = True
+    yes C.Open{}          = True
+    yes C.Import{}        = True -- not __IMPOSSIBLE__, see Issue #1718
+      -- However, it does not matter what we return here, as this will
+      -- become an error later: "Not a valid let-declaration".
+      -- (Andreas, 2015-11-17)
+    yes (C.Mutual   _ ds) = any yes ds
+    yes (C.Abstract _ ds) = any yes ds
+    yes (C.Private _ _ ds) = any yes ds
+    yes _                 = False
+
+{- UNUSED
+telHasLetStms :: C.Telescope -> Bool
+telHasLetStms = any isLetBind
+  where
+    isLetBind C.TBind{} = False
+    isLetBind C.TLet{}  = True
+-}
+
+-- | We for now disallow let-bindings in @data@ and @record@ telescopes.
+--   This due "nested datatypes"; there is no easy interpretation of
+--   @
+--      data D (A : Set) (open M A) (b : B) : Set where
+--        c : D (A × A) b → D A b
+--   @
+--   where @B@ is brought in scope by @open M A@.
+
+class EnsureNoLetStms a where
+  ensureNoLetStms :: a -> ScopeM ()
+
+  default ensureNoLetStms :: (Foldable t, EnsureNoLetStms b, t b ~ a) => a -> ScopeM ()
+  ensureNoLetStms = traverse_ ensureNoLetStms
+
+instance EnsureNoLetStms C.Binder where
+  ensureNoLetStms arg@(C.Binder p n) =
+    when (isJust p) $ typeError $ IllegalPatternInTelescope arg
+
+instance EnsureNoLetStms C.TypedBinding where
+  ensureNoLetStms = \case
+    tb@C.TLet{}    -> typeError $ IllegalLetInTelescope tb
+    C.TBind _ xs _ -> traverse_ (ensureNoLetStms . namedArg) xs
+
+instance EnsureNoLetStms a => EnsureNoLetStms (LamBinding' a) where
+  ensureNoLetStms = \case
+    -- GA: DO NOT use traverse here: `LamBinding'` only uses its parameter in
+    --     the DomainFull constructor so we would miss out on some potentially
+    --     illegal lets! Cf. #4402
+    C.DomainFree a -> ensureNoLetStms a
+    C.DomainFull a -> ensureNoLetStms a
+
+instance EnsureNoLetStms a => EnsureNoLetStms (Named_ a) where
+instance EnsureNoLetStms a => EnsureNoLetStms (NamedArg a) where
+instance EnsureNoLetStms a => EnsureNoLetStms [a] where
+
+
+-- | Returns the scope inside the checked module.
+scopeCheckModule
+  :: Range                   -- ^ The range of the module.
+  -> Erased                  -- ^ Is the module erased?
+  -> C.QName                 -- ^ The concrete name of the module.
+  -> A.ModuleName            -- ^ The abstract name of the module.
+  -> C.Telescope             -- ^ The module telescope.
+  -> ScopeM [A.Declaration]  -- ^ The code for checking the module contents.
+  -> ScopeM (ScopeInfo, A.Declaration)
+       -- ^ The returned declaration is an 'A.Section'.
+scopeCheckModule r e x qm tel checkDs = do
+  printScope "module" 20 $ "checking module " ++ prettyShow x
+  -- Andreas, 2013-12-10: Telescope does not live in the new module
+  -- but its parent, so check it before entering the new module.
+  -- This is important for Nicolas Pouillard's open parametrized modules
+  -- statements inside telescopes.
+  res <- withLocalVars $ do
+    tel <- toAbstract (GenTel tel)
+    withCurrentModule qm $ do
+      -- pushScope m
+      -- qm <- getCurrentModule
+      printScope "module" 20 $ "inside module " ++ prettyShow x
+      ds    <- checkDs
+      scope <- getScope
+      return (scope, A.Section r e (qm `withRangesOfQ` x) tel ds)
+
+  -- Binding is done by the caller
+  printScope "module" 20 $ "after module " ++ prettyShow x
+  return res
+
+-- | Temporary data type to scope check a file.
+data TopLevel a = TopLevel
+  { topLevelPath           :: AbsolutePath
+    -- ^ The file path from which we loaded this module.
+  , topLevelExpectedName   :: TopLevelModuleName
+    -- ^ The expected module name
+    --   (coming from the import statement that triggered scope checking this file).
+  , topLevelTheThing       :: a
+    -- ^ The file content.
+  }
+
+data TopLevelInfo = TopLevelInfo
+        { topLevelDecls :: [A.Declaration]
+        , topLevelScope :: ScopeInfo  -- ^ as seen from inside the module
+        }
+
+-- | The top-level module name.
+
+topLevelModuleName :: TopLevelInfo -> A.ModuleName
+topLevelModuleName = (^. scopeCurrent) . topLevelScope
+
+-- | Top-level declarations are always
+--   @
+--     (import|open)*         -- a bunch of possibly opened imports
+--     module ThisModule ...  -- the top-level module of this file
+--   @
+instance ToAbstract (TopLevel [C.Declaration]) where
+    type AbsOfCon (TopLevel [C.Declaration]) = TopLevelInfo
+
+    toAbstract (TopLevel file expectedMName ds) =
+      -- A file is a bunch of preliminary decls (imports etc.)
+      -- plus a single module decl.
+      case C.spanAllowedBeforeModule ds of
+
+        -- If there are declarations after the top-level module
+        -- we have to report a parse error here.
+        (_, C.Module{} : d : _) -> setCurrentRange d $
+          genericError $ "No declarations allowed after top-level module."
+
+        -- Otherwise, proceed.
+        (outsideDecls, [ C.Module r e m0 tel insideDecls ]) -> do
+          -- If the module name is _ compute the name from the file path
+          (m, top) <- if isNoName m0
+                then do
+                  -- Andreas, 2017-07-28, issue #1077
+                  -- Check if the insideDecls end in a single module which has the same
+                  -- name as the file.  In this case, it is highly likely that the user
+                  -- put some non-allowed declarations before the top-level module in error.
+                  -- Andreas, 2017-10-19, issue #2808
+                  -- Widen this check to:
+                  -- If the first module of the insideDecls has the same name as the file,
+                  -- report an error.
+                  case flip span insideDecls $ \case { C.Module{} -> False; _ -> True } of
+                    (ds0, (C.Module _ _ m1 _ _ : _))
+                       | rawTopLevelModuleNameForQName m1 ==
+                         rawTopLevelModuleName expectedMName
+                         -- If the anonymous module comes from the user,
+                         -- the range cannot be the beginningOfFile.
+                         -- That is the range if the parser inserted the anon. module.
+                       , r == beginningOfFile (getRange insideDecls) -> do
+
+                         -- GA #4888: We know we are in a bad place. But we still scopecheck
+                         -- the initial segment on the off chance we generate a better error
+                         -- message.
+                         void importPrimitives
+                         void $ toAbstract (Declarations outsideDecls)
+                         void $ toAbstract (Declarations ds0)
+                         -- Fail with a crude error otherwise
+                         setCurrentRange ds0 $ genericError
+                           "Illegal declaration(s) before top-level module"
+
+                    -- Otherwise, reconstruct the top-level module name
+                    _ -> do
+                      let m = C.QName $ setRange (getRange m0) $
+                              C.simpleName $ stringToRawName $
+                              rootNameModule file
+                      top <- S.topLevelModuleName
+                               (rawTopLevelModuleNameForQName m)
+                      return (m, top)
+                -- Andreas, 2017-05-17, issue #2574, keep name as jump target!
+                -- Andreas, 2016-07-12, ALTERNATIVE:
+                -- -- We assign an anonymous file module the name expected from
+                -- -- its import.  For flat file structures, this is the same.
+                -- -- For hierarchical file structures, this reverses the behavior:
+                -- -- Loading the file by itself will fail, but it can be imported.
+                -- -- The previous behavior is: it can be loaded by itself, but not
+                -- -- be imported
+                -- then return $ C.fromTopLevelModuleName expectedMName
+                else do
+                -- Andreas, 2014-03-28  Issue 1078
+                -- We need to check the module name against the file name here.
+                -- Otherwise one could sneak in a lie and confuse the scope
+                -- checker.
+                  top <- S.topLevelModuleName
+                           (rawTopLevelModuleNameForQName m0)
+                  checkModuleName top (SourceFile file) (Just expectedMName)
+                  return (m0, top)
+          setTopLevelModule top
+          am <- toAbstract (NewModuleQName m)
+          primitiveImport <- importPrimitives
+          -- Scope check the declarations outside
+          outsideDecls <- toAbstract (Declarations outsideDecls)
+          (insideScope, insideDecl) <- scopeCheckModule r e m am tel $
+             toAbstract (Declarations insideDecls)
+          -- Andreas, 2020-05-13, issue #1804, #4647
+          -- Do not eagerly remove private definitions, only when serializing
+          -- let scope = over scopeModules (fmap $ restrictLocalPrivate am) insideScope
+          let scope = insideScope
+          setScope scope
+
+          -- While scope-checking the top-level module we might have
+          -- encountered several (possibly nested) opaque blocks. We
+          -- must now ensure that these have transitively-closed
+          -- unfolding sets.
+          saturateOpaqueBlocks (outsideDecls ++ [ insideDecl ])
+
+          return $ TopLevelInfo (primitiveImport ++ outsideDecls ++ [ insideDecl ]) scope
+
+        -- We already inserted the missing top-level module, see
+        -- 'Agda.Syntax.Parser.Parser.figureOutTopLevelModule',
+        -- thus, this case is impossible:
+        _ -> __IMPOSSIBLE__
+
+-- | Declaration @open import Agda.Primitive using (Set)@ when 'optImportSorts'.
+--   @Prop@ is added when 'optProp', and @SSet@ when 'optTwoLevel'.
+importPrimitives :: ScopeM [A.Declaration]
+importPrimitives = do
+  ifNotM (optImportSorts <$> pragmaOptions) (return []) {- else -} do
+    prop     <- optProp     <$> pragmaOptions
+    twoLevel <- optTwoLevel <$> pragmaOptions
+    -- Add implicit `open import Agda.Primitive using (Prop; Set; SSet)`
+    let agdaPrimitiveName   = Qual (C.simpleName "Agda") $ C.QName $ C.simpleName "Primitive"
+        usingDirective      = map (ImportedName . C.simpleName) $ concat
+          [ [ "Prop" | prop     ]
+          , [ "Set"  | True     ]
+          , [ "SSet" | twoLevel ]
+          ]
+        directives          = ImportDirective noRange (Using usingDirective) [] [] Nothing
+        importAgdaPrimitive = [C.Import noRange agdaPrimitiveName Nothing C.DoOpen directives]
+    toAbstract (Declarations importAgdaPrimitive)
+
+-- | runs Syntax.Concrete.Definitions.niceDeclarations on main module
+niceDecls :: DoWarn -> [C.Declaration] -> ([NiceDeclaration] -> ScopeM a) -> ScopeM a
+niceDecls warn ds ret = setCurrentRange ds $ computeFixitiesAndPolarities warn ds $ do
+
+  -- Some pragmas are not allowed in safe mode unless we are in a builtin module.
+  -- So we need to tell the nicifier whether it should yell about unsafe pragmas.
+  isSafe <- Lens.getSafeMode <$> pragmaOptions
+  safeButNotBuiltin <- and2M
+    -- NB: BlockArguments allow bullet-point style argument lists using @do@, hehe!
+    do pure isSafe
+    do not <$> do Lens.isBuiltinModuleWithSafePostulates . filePath =<< getCurrentPath
+
+  -- We need to pass the fixities to the nicifier for clause grouping.
+  fixs <- useScope scopeFixities
+
+  -- Run nicifier.
+  let (result, warns) = runNice (NiceEnv safeButNotBuiltin) $ niceDeclarations fixs ds
+
+  -- Respect the @DoWarn@ directive. For this to be sound, we need to know for
+  -- sure that each @Declaration@ is checked at least once with @DoWarn@.
+  unless (warn == NoWarn || null warns) $ do
+    -- If there are some warnings and the --safe flag is set,
+    -- we check that none of the NiceWarnings are fatal
+    when isSafe $ do
+      let (errs, ws) = List.partition unsafeDeclarationWarning warns
+      -- If some of them are, we fail
+      unless (null errs) $ do
+        warnings $ NicifierIssue <$> ws
+        tcerrs <- mapM warning_ $ NicifierIssue <$> errs
+        setCurrentRange errs $ typeError $ NonFatalErrors tcerrs
+    -- Otherwise we simply record the warnings
+    mapM_ (\ w -> warning' (dwLocation w) $ NicifierIssue w) warns
+  case result of
+    Left (DeclarationException loc e) -> do
+      reportSLn "error" 2 $ "Error raised at " ++ prettyShow loc
+      throwError $ Exception (getRange e) $ pretty e
+    Right ds -> ret ds
+
+-- | Wrapper to avoid instance conflict with generic list instance.
+newtype Declarations = Declarations [C.Declaration]
+
+instance ToAbstract Declarations where
+  type AbsOfCon Declarations = [A.Declaration]
+
+  toAbstract (Declarations ds) = niceDecls DoWarn ds toAbstract
+
+newtype LetDefs = LetDefs (List1 C.Declaration)
+newtype LetDef = LetDef NiceDeclaration
+
+instance ToAbstract LetDefs where
+  type AbsOfCon LetDefs = [A.LetBinding]
+
+  toAbstract (LetDefs ds) =
+    List1.concat <$> niceDecls DoWarn (List1.toList ds) (toAbstract . map LetDef)
+
+instance ToAbstract LetDef where
+  type AbsOfCon LetDef = List1 A.LetBinding
+  toAbstract (LetDef d) =
+    case d of
+      NiceMutual _ _ _ _ d@[C.FunSig _ _ _ instanc macro info _ _ x t, C.FunDef _ _ abstract _ _ _ _ [cl]] ->
+          do  when (abstract == AbstractDef) $ do
+                genericError $ "`abstract` not allowed in let expressions"
+              when (macro == MacroDef) $ do
+                genericError $ "Macros cannot be defined in a let expression"
+              t <- toAbstract t
+              -- We bind the name here to make sure it's in scope for the LHS (#917).
+              -- It's unbound for the RHS in letToAbstract.
+              fx <- getConcreteFixity x
+              x  <- A.unBind <$> toAbstract (NewName LetBound $ mkBoundName x fx)
+              (x', e) <- letToAbstract cl
+              -- If InstanceDef set info to Instance
+              let info' = case instanc of
+                    InstanceDef _  -> makeInstance info
+                    NotInstanceDef -> info
+              -- There are sometimes two instances of the
+              -- let-bound variable, one declaration and one
+              -- definition. The first list element below is
+              -- used to highlight the declared instance in the
+              -- right way (see Issue 1618).
+              return $ A.LetDeclaredVariable (A.mkBindName (setRange (getRange x') x)) :|
+                     [ A.LetBind (LetRange $ getRange d) info' (A.mkBindName x) t e
+                     ]
+
+      -- irrefutable let binding, like  (x , y) = rhs
+      NiceFunClause r PublicAccess ConcreteDef tc cc catchall d@(C.FunClause lhs@(C.LHS p0 [] []) rhs0 wh ca) -> do
+        noWhereInLetBinding wh
+        rhs <- letBindingMustHaveRHS rhs0
+        -- Expand puns if optHiddenArgumentPuns is True.
+        puns <- optHiddenArgumentPuns <$> pragmaOptions
+        p0   <- return $ if puns then expandPuns p0 else p0
+        mp   <- setCurrentRange p0 $
+                  (Right <$> parsePattern p0)
+                    `catchError`
+                  (return . Left)
+        case mp of
+          Right p -> do
+            rhs <- toAbstract rhs
+            setCurrentRange p0 $ do
+              p   <- toAbstract p
+              checkValidLetPattern p
+              checkPatternLinearity p $ \ys ->
+                typeError $ RepeatedVariablesInPattern ys
+              bindVarsToBind
+              p   <- toAbstract p
+              return $ singleton $ A.LetPatBind (LetRange r) p rhs
+          -- It's not a record pattern, so it should be a prefix left-hand side
+          Left err ->
+            case definedName p0 of
+              Nothing -> throwError err
+              Just x  -> toAbstract $ LetDef $ NiceMutual r tc cc YesPositivityCheck
+                [ C.FunSig r PublicAccess ConcreteDef NotInstanceDef NotMacroDef
+                    (setOrigin Inserted defaultArgInfo) tc cc x (C.Underscore (getRange x) Nothing)
+                , C.FunDef r __IMPOSSIBLE__ ConcreteDef NotInstanceDef __IMPOSSIBLE__ __IMPOSSIBLE__ __IMPOSSIBLE__
+                  [C.Clause x (ca || catchall) lhs (C.RHS rhs) NoWhere []]
+                ]
+            where
+              definedName (C.IdentP _ (C.QName x)) = Just x
+              definedName C.IdentP{}             = Nothing
+              definedName (C.RawAppP _ (List2 p _ _)) = definedName p
+              definedName (C.ParenP _ p)         = definedName p
+              definedName C.WildP{}              = Nothing   -- for instance let _ + x = x in ... (not allowed)
+              definedName C.AbsurdP{}            = Nothing
+              definedName C.AsP{}                = Nothing
+              definedName C.DotP{}               = Nothing
+              definedName C.EqualP{}             = Nothing
+              definedName C.LitP{}               = Nothing
+              definedName C.RecP{}               = Nothing
+              definedName C.QuoteP{}             = Nothing
+              definedName C.HiddenP{}            = Nothing -- Not impossible, see issue #2291
+              definedName C.InstanceP{}          = Nothing
+              definedName C.WithP{}              = Nothing
+              definedName C.AppP{}               = Nothing -- Not impossible, see issue #4586
+              definedName C.OpAppP{}             = __IMPOSSIBLE__
+              definedName C.EllipsisP{}          = Nothing -- Not impossible, see issue #3937
+
+      -- You can't open public in a let
+      NiceOpen r x dirs -> do
+        whenJust (publicOpen dirs) $ \r -> setCurrentRange r $ warning UselessPublic
+        m    <- toAbstract (OldModuleName x)
+        adir <- openModule_ LetOpenModule x dirs
+        let minfo = ModuleInfo
+              { minfoRange  = r
+              , minfoAsName = Nothing
+              , minfoAsTo   = renamingRange dirs
+              , minfoOpenShort = Nothing
+              , minfoDirective = Just dirs
+              }
+        return $ singleton $ A.LetOpen minfo m adir
+
+      NiceModuleMacro r p erased x modapp open dir -> do
+        whenJust (publicOpen dir) $ \ r -> setCurrentRange r $ warning UselessPublic
+        -- Andreas, 2014-10-09, Issue 1299: module macros in lets need
+        -- to be private
+        singleton <$> checkModuleMacro LetApply LetOpenModule r
+                        (PrivateAccess Inserted) erased x modapp open dir
+
+      _   -> notAValidLetBinding d
+    where
+        letToAbstract (C.Clause top _catchall (C.LHS p [] []) rhs0 wh []) = do
+            noWhereInLetBinding wh
+            rhs <- letBindingMustHaveRHS rhs0
+            (x, args) <- do
+              res <- setCurrentRange p $ parseLHS (C.QName top) p
+              case res of
+                C.LHSHead x args -> return (x, args)
+                C.LHSProj{} -> genericError $ "Copatterns not allowed in let bindings"
+                C.LHSWith{} -> genericError $ "`with` patterns not allowed in let bindings"
+                C.LHSEllipsis{} -> genericError "`...` not allowed in let bindings"
+
+            e <- localToAbstract args $ \args -> do
+                bindVarsToBind
+                -- Make sure to unbind the function name in the RHS, since lets are non-recursive.
+                rhs <- unbindVariable top $ toAbstract rhs
+                foldM lambda rhs (reverse args)  -- just reverse because these are DomainFree
+            return (x, e)
+        letToAbstract _ = notAValidLetBinding d
+
+        -- Named patterns not allowed in let definitions
+        lambda e (Arg info (Named Nothing (A.VarP x))) =
+                return $ A.Lam i (A.mkDomainFree $ unnamedArg info $ A.mkBinder x) e
+            where i = ExprRange (fuseRange x e)
+        lambda e (Arg info (Named Nothing (A.WildP i))) =
+            do  x <- freshNoName (getRange i)
+                return $ A.Lam i' (A.mkDomainFree $ unnamedArg info $ A.mkBinder_ x) e
+            where i' = ExprRange (fuseRange i e)
+        lambda _ _ = notAValidLetBinding d
+
+        noWhereInLetBinding :: C.WhereClause -> ScopeM ()
+        noWhereInLetBinding = \case
+          NoWhere -> return ()
+          wh -> setCurrentRange wh $ genericError $ "`where` clauses not allowed in let bindings"
+        letBindingMustHaveRHS :: C.RHS -> ScopeM C.Expr
+        letBindingMustHaveRHS = \case
+          C.RHS e -> return e
+          C.AbsurdRHS -> genericError $ "Missing right hand side in let binding"
+
+        -- Only record patterns allowed, but we do not exclude data constructors here.
+        -- They will fail in the type checker.
+        checkValidLetPattern :: A.Pattern' e -> ScopeM ()
+        checkValidLetPattern = \case
+            A.VarP{}             -> yes
+            A.ConP _ _ ps        -> mapM_ (checkValidLetPattern . namedArg) ps
+            A.ProjP{}            -> no
+            A.DefP{}             -> no
+            A.WildP{}            -> yes
+            A.AsP _ _ p          -> checkValidLetPattern p
+            A.DotP{}             -> no
+            A.AbsurdP{}          -> no
+            A.LitP{}             -> no
+            A.PatternSynP _ _ ps -> mapM_ (checkValidLetPattern . namedArg) ps
+            A.RecP _ fs          -> mapM_ (checkValidLetPattern . _exprFieldA) fs
+            A.EqualP{}           -> no
+            A.WithP{}            -> no
+            A.AnnP _ _ p         -> checkValidLetPattern p
+          where
+          yes = return ()
+          no  = genericError "Not a valid let pattern"
+
+
+instance ToAbstract NiceDeclaration where
+  type AbsOfCon NiceDeclaration = A.Declaration
+
+  toAbstract d = annotateDecls $
+    traceS "scope.decl.trace" 50
+      [ "scope checking declaration"
+      , "  " ++  prettyShow d
+      ] $
+    traceS "scope.decl.trace" 80  -- keep this debug message for testing issue #4016
+      [ "scope checking declaration (raw)"
+      , "  " ++  show d
+      ] $
+    traceCall (ScopeCheckDeclaration d) $
+    -- Andreas, 2015-10-05, Issue 1677:
+    -- We record in the environment whether we are scope checking an
+    -- abstract definition.  This way, we can propagate this attribute
+    -- the extended lambdas.
+    caseMaybe (niceHasAbstract d) id (\ a -> localTC $ \ e -> e { envAbstractMode = aDefToMode a }) $
+    case d of
+
+  -- Axiom (actual postulate)
+    C.Axiom r p a i rel x t -> do
+      -- check that we do not postulate in --safe mode, unless it is a
+      -- builtin module with safe postulates
+      whenM ((Lens.getSafeMode <$> commandLineOptions) `and2M`
+             (not <$> (Lens.isBuiltinModuleWithSafePostulates . filePath =<< getCurrentPath)))
+            (warning $ SafeFlagPostulate x)
+      -- check the postulate
+      singleton <$> toAbstractNiceAxiom AxiomName d
+
+    C.NiceGeneralize r p i tac x t -> do
+      reportSLn "scope.decl" 10 $ "found nice generalize: " ++ prettyShow x
+      tac <- traverse (toAbstractCtx TopCtx) tac
+      t_ <- toAbstractCtx TopCtx t
+      let (s, t) = unGeneralized t_
+      reportSLn "scope.decl" 50 $ "generalizations: " ++ show (Set.toList s, t)
+      f <- getConcreteFixity x
+      y <- freshAbstractQName f x
+      bindName p GeneralizeName x y
+      let info = (mkDefInfo x f p ConcreteDef r) { defTactic = tac }
+      return [A.Generalize s info i y t]
+
+  -- Fields
+    C.NiceField r p a i tac x t -> do
+      unless (p == PublicAccess) $ genericError "Record fields can not be private"
+      -- Interaction points for record fields have already been introduced
+      -- when checking the type of the record constructor.
+      -- To avoid introducing interaction points (IP) twice, we turn
+      -- all question marks to underscores.  (See issue 1138.)
+      let maskIP (C.QuestionMark r _) = C.Underscore r Nothing
+          maskIP e                     = e
+      tac <- traverse (toAbstractCtx TopCtx) tac
+      t' <- toAbstractCtx TopCtx $ mapExpr maskIP t
+      f  <- getConcreteFixity x
+      y  <- freshAbstractQName f x
+      -- Andreas, 2018-06-09 issue #2170
+      -- We want dependent irrelevance without irrelevant projections,
+      -- thus, do not disable irrelevant projections via the scope checker.
+      -- irrProj <- optIrrelevantProjections <$> pragmaOptions
+      -- unless (isIrrelevant t && not irrProj) $
+      --   -- Andreas, 2010-09-24: irrelevant fields are not in scope
+      --   -- this ensures that projections out of irrelevant fields cannot occur
+      --   -- Ulf: unless you turn on --irrelevant-projections
+      bindName p FldName x y
+      let info = (mkDefInfoInstance x f p a i NotMacroDef r) { defTactic = tac }
+      return [ A.Field info y t' ]
+
+  -- Primitive function
+    PrimitiveFunction r p a x t -> notAffectedByOpaque $ do
+      t' <- traverse (toAbstractCtx TopCtx) t
+      f  <- getConcreteFixity x
+      y  <- freshAbstractQName f x
+      bindName p PrimName x y
+      unfoldFunction y
+      let di = mkDefInfo x f p a r
+      return [ A.Primitive di y t' ]
+
+  -- Definitions (possibly mutual)
+    NiceMutual r tc cc pc ds -> do
+      reportSLn "scope.mutual" 20 ("starting checking mutual definitions: " ++ prettyShow ds)
+      ds' <- toAbstract ds
+      reportSLn "scope.mutual" 20 ("finishing checking mutual definitions")
+      -- We only termination check blocks that do not have a measure.
+      return [ A.Mutual (MutualInfo tc cc pc r) ds' ]
+
+    C.NiceRecSig r er p a _pc _uc x ls t -> do
+      ensureNoLetStms ls
+      withLocalVars $ do
+        (ls', _) <- withCheckNoShadowing $
+          -- Minor hack: record types don't have indices so we include t when
+          -- computing generalised parameters, but in the type checker any named
+          -- generalizable arguments in the sort should be bound variables.
+          toAbstract (GenTelAndType (map makeDomainFull ls) t)
+        t' <- toAbstract t
+        f  <- getConcreteFixity x
+        x' <- freshAbstractQName f x
+        bindName' p RecName (GeneralizedVarsMetadata $ generalizeTelVars ls') x x'
+        return [ A.RecSig (mkDefInfo x f p a r) er x' ls' t' ]
+
+    C.NiceDataSig r er p a pc uc x ls t -> do
+        reportSLn "scope.data.sig" 20 ("checking DataSig for " ++ prettyShow x)
+        ensureNoLetStms ls
+        withLocalVars $ do
+          ls' <- withCheckNoShadowing $
+            toAbstract $ GenTel $ map makeDomainFull ls
+          t'  <- toAbstract $ C.Generalized t
+          f  <- getConcreteFixity x
+          x' <- freshAbstractQName f x
+          mErr <- bindName'' p DataName (GeneralizedVarsMetadata $ generalizeTelVars ls') x x'
+          whenJust mErr $ \case
+            err@(ClashingDefinition cn an _) -> do
+              resolveName (C.QName x) >>= \case
+                -- #4435: if a data type signature causes a ClashingDefinition error, and if
+                -- the data type name is bound to an Axiom, then the error may be caused by
+                -- the illegal type signature. Convert the NiceDataSig into a NiceDataDef
+                -- (which removes the type signature) and suggest it as a possible fix.
+                DefinedName p ax NoSuffix | anameKind ax == AxiomName -> do
+                  let suggestion = NiceDataDef r Inserted a pc uc x ls []
+                  typeError $ ClashingDefinition cn an (Just suggestion)
+                _ -> typeError err
+            otherErr -> typeError otherErr
+          return [ A.DataSig (mkDefInfo x f p a r) er x' ls' t' ]
+
+  -- Type signatures
+    C.FunSig r p a i m rel _ _ x t -> do
+        let kind = if m == MacroDef then MacroName else FunName
+        singleton <$> toAbstractNiceAxiom kind (C.Axiom r p a i rel x t)
+
+  -- Function definitions
+    C.FunDef r ds a i _ _ x cs -> do
+        printLocals 10 $ "checking def " ++ prettyShow x
+        (x',cs) <- toAbstract (OldName x,cs)
+        -- Andreas, 2017-12-04 the name must reside in the current module
+        unlessM ((A.qnameModule x' ==) <$> getCurrentModule) $
+          __IMPOSSIBLE__
+        f <- getConcreteFixity x
+
+        unfoldFunction x'
+        di <- updateDefInfoOpacity (mkDefInfoInstance x f PublicAccess a i NotMacroDef r)
+        return [ A.FunDef di x' cs ]
+
+  -- Uncategorized function clauses
+    C.NiceFunClause _ _ _ _ _ _ (C.FunClause lhs _ _ _) ->
+      genericError $
+        "Missing type signature for left hand side " ++ prettyShow lhs
+    C.NiceFunClause{} -> __IMPOSSIBLE__
+
+  -- Data definitions
+    C.NiceDataDef r o a _ uc x pars cons -> notAffectedByOpaque $ do
+        reportSLn "scope.data.def" 20 ("checking " ++ show o ++ " DataDef for " ++ prettyShow x)
+        (p, ax) <- resolveName (C.QName x) >>= \case
+          DefinedName p ax NoSuffix -> do
+            clashUnless x DataName ax  -- Andreas 2019-07-07, issue #3892
+            livesInCurrentModule ax  -- Andreas, 2017-12-04, issue #2862
+            clashIfModuleAlreadyDefinedInCurrentModule x ax
+            return (p, ax)
+          _ -> genericError $ "Missing type signature for data definition " ++ prettyShow x
+        ensureNoLetStms pars
+        withLocalVars $ do
+          gvars <- bindGeneralizablesIfInserted o ax
+          -- Check for duplicate constructors
+          do cs <- mapM conName cons
+             unlessNull (duplicates cs) $ \ dups -> do
+               let bad = filter (`elem` dups) cs
+               setCurrentRange bad $
+                 typeError $ DuplicateConstructors dups
+
+          pars <- catMaybes <$> toAbstract pars
+          let x' = anameName ax
+          -- Create the module for the qualified constructors
+          checkForModuleClash x -- disallow shadowing previously defined modules
+          let m = qnameToMName x'
+          createModule (Just IsDataModule) m
+          bindModule p x m  -- make it a proper module
+          cons <- toAbstract (map (DataConstrDecl m a p) cons)
+          printScope "data" 20 $ "Checked data " ++ prettyShow x
+          f <- getConcreteFixity x
+          return [ A.DataDef (mkDefInfo x f PublicAccess a r) x' uc (DataDefParams gvars pars) cons ]
+      where
+        conName (C.Axiom _ _ _ _ _ c _) = return c
+        conName d = errorNotConstrDecl d
+
+  -- Record definitions (mucho interesting)
+    C.NiceRecDef r o a _ uc x (RecordDirectives ind eta pat cm) pars fields -> notAffectedByOpaque $ do
+      reportSLn "scope.rec.def" 20 ("checking " ++ show o ++ " RecDef for " ++ prettyShow x)
+      -- #3008: Termination pragmas are ignored in records
+      checkNoTerminationPragma InRecordDef fields
+      -- Andreas, 2020-04-19, issue #4560
+      -- 'pattern' declaration is incompatible with 'coinductive' or 'eta-equality'.
+      pat <- case pat of
+        Just r
+          | Just (Ranged _ CoInductive) <- ind -> Nothing <$ warn "coinductive"
+          | Just YesEta                 <- eta -> Nothing <$ warn "eta"
+          | otherwise -> return pat
+          where warn = setCurrentRange r . warning . UselessPatternDeclarationForRecord
+        Nothing -> return pat
+
+      (p, ax) <- resolveName (C.QName x) >>= \case
+        DefinedName p ax NoSuffix -> do
+          clashUnless x RecName ax  -- Andreas 2019-07-07, issue #3892
+          livesInCurrentModule ax  -- Andreas, 2017-12-04, issue #2862
+          clashIfModuleAlreadyDefinedInCurrentModule x ax
+          return (p, ax)
+        _ -> genericError $ "Missing type signature for record definition " ++ prettyShow x
+      ensureNoLetStms pars
+      withLocalVars $ do
+        gvars <- bindGeneralizablesIfInserted o ax
+        -- Check that the generated module doesn't clash with a previously
+        -- defined module
+        checkForModuleClash x
+        pars   <- catMaybes <$> toAbstract pars
+        let x' = anameName ax
+        -- We scope check the fields a first time when putting together
+        -- the type of the constructor.
+        contel <- localToAbstract (RecordConstructorType fields) return
+        m0     <- getCurrentModule
+        let m = A.qualifyM m0 $ mnameFromList1 $ singleton $ List1.last $ qnameToList x'
+        printScope "rec" 15 "before record"
+        createModule (Just IsRecordModule) m
+        -- We scope check the fields a second time, as actual fields.
+        afields <- withCurrentModule m $ do
+          afields <- toAbstract (Declarations fields)
+          printScope "rec" 15 "checked fields"
+          return afields
+        -- Andreas, 2017-07-13 issue #2642 disallow duplicate fields
+        -- Check for duplicate fields. (See "Check for duplicate constructors")
+        do let fs :: [C.Name]
+               fs = concat $ forMaybe fields $ \case
+                 C.Field _ fs -> Just $ fs <&> \case
+                   -- a Field block only contains field signatures
+                   C.FieldSig _ _ f _ -> f
+                   _ -> __IMPOSSIBLE__
+                 _ -> Nothing
+           unlessNull (duplicates fs) $ \ dups -> do
+             let bad = filter (`elem` dups) fs
+             setCurrentRange bad $
+               typeError $ DuplicateFields dups
+        bindModule p x m
+        let kind = maybe ConName (conKindOfName . rangedThing) ind
+        -- Andreas, 2019-11-11, issue #4189, no longer add record constructor to record module.
+        cm' <- forM cm $ \ (c, _) -> bindRecordConstructorName c kind a p
+        let inst = caseMaybe cm NotInstanceDef snd
+        printScope "rec" 15 "record complete"
+        f <- getConcreteFixity x
+        let params = DataDefParams gvars pars
+        let dir' = RecordDirectives ind eta pat cm'
+        return [ A.RecDef (mkDefInfoInstance x f PublicAccess a inst NotMacroDef r) x' uc dir' params contel afields ]
+
+    NiceModule r p a e x@(C.QName name) tel ds -> notAffectedByOpaque $ do
+      reportSDoc "scope.decl" 70 $ vcat $
+        [ text $ "scope checking NiceModule " ++ prettyShow x
+        ]
+
+      adecl <- traceCall (ScopeCheckDeclaration $
+                          NiceModule r p a e x tel []) $ do
+        scopeCheckNiceModule r p e name tel $
+          toAbstract (Declarations ds)
+
+      reportSDoc "scope.decl" 70 $ vcat $
+        [ text $ "scope checked NiceModule " ++ prettyShow x
+        , nest 2 $ prettyA adecl
+        ]
+      return [ adecl ]
+
+    NiceModule _ _ _ _ m@C.Qual{} _ _ ->
+      genericError $ "Local modules cannot have qualified names"
+
+    NiceModuleMacro r p e x modapp open dir -> do
+      reportSDoc "scope.decl" 70 $ vcat $
+        [ text $ "scope checking NiceModuleMacro " ++ prettyShow x
+        ]
+
+      adecl <- checkModuleMacro Apply TopOpenModule
+                 r p e x modapp open dir
+
+      reportSDoc "scope.decl" 70 $ vcat $
+        [ text $ "scope checked NiceModuleMacro " ++ prettyShow x
+        , nest 2 $ prettyA adecl
+        ]
+      return [ adecl ]
+
+    NiceOpen r x dir -> do
+      (minfo, m, adir) <- checkOpen r Nothing x dir
+      return [A.Open minfo m adir]
+
+    NicePragma r p -> do
+      ps <- toAbstract p  -- could result in empty list of pragmas
+      return $ map (A.Pragma r) ps
+
+    NiceImport r x as open dir -> setCurrentRange r $ do
+      dir <- notPublicWithoutOpen open dir
+
+      -- Andreas, 2018-11-03, issue #3364, parse expression in as-clause as Name.
+      let illformedAs s = setCurrentRange as $ do
+            -- If @as@ is followed by something that is not a simple name,
+            -- throw a warning and discard the as-clause.
+            Nothing <$ warning (IllformedAsClause s)
+      as <- case as of
+        -- Ok if no as-clause or it (already) contains a Name.
+        Nothing -> return Nothing
+        Just (AsName (Right asName) r)                    -> return $ Just $ AsName asName r
+        Just (AsName (Left (C.Ident (C.QName asName))) r) -> return $ Just $ AsName asName r
+        Just (AsName (Left C.Underscore{})     r)         -> return $ Just $ AsName underscore r
+        Just (AsName (Left (C.Ident C.Qual{})) r) -> illformedAs "; a qualified name is not allowed here"
+        Just (AsName (Left e)                  r) -> illformedAs ""
+
+      top <- S.topLevelModuleName (rawTopLevelModuleNameForQName x)
+      -- First scope check the imported module and return its name and
+      -- interface. This is done with that module as the top-level module.
+      -- This is quite subtle. We rely on the fact that when setting the
+      -- top-level module and generating a fresh module name, the generated
+      -- name will be exactly the same as the name generated when checking
+      -- the imported module.
+      (m, i) <- withCurrentModule noModuleName $
+                withTopLevelModule top $ do
+        m <- toAbstract $ NewModuleQName x  -- (No longer erases the contents of @m@.)
+        printScope "import" 10 "before import:"
+        (m, i) <- scopeCheckImport top m
+        printScope "import" 10 $ "scope checked import: " ++ prettyShow i
+        -- We don't want the top scope of the imported module (things happening
+        -- before the module declaration)
+        return (m, Map.delete noModuleName i)
+
+      -- Bind the desired module name to the right abstract name.
+      (name, theAsSymbol, theAsName) <- case as of
+
+         Just a | let y = asName a, not (isNoName y) -> do
+           bindModule (PrivateAccess Inserted) y m
+           return (C.QName y, asRange a, Just y)
+
+         _ -> do
+           -- Don't bind if @import ... as _@ with "no name"
+           whenNothing as $ bindQModule (PrivateAccess Inserted) x m
+           return (x, noRange, Nothing)
+
+      -- Open if specified, otherwise apply import directives
+      adir <- case open of
+
+        -- With @open@ import directives apply to the opening.
+        -- The module is thus present in its qualified form without restrictions.
+        DoOpen   -> do
+
+          -- Merge the imported scopes with the current scopes.
+          -- This might override a previous import of @m@, but monotonously (add stuff).
+          modifyScopes $ \ ms -> Map.unionWith mergeScope (Map.delete m ms) i
+
+          -- Andreas, 2019-05-29, issue #3818.
+          -- Pass the resolved name to open instead triggering another resolution.
+          -- This helps in situations like
+          -- @
+          --    module Top where
+          --    module M where
+          --    open import M
+          -- @
+          -- It is clear than in @open import M@, name @M@ must refer to a file
+          -- rather than the above defined local module @M@.
+          -- This already worked in the situation
+          -- @
+          --    module Top where
+          --    module M where
+          --    import M
+          -- @
+          -- Note that the manual desugaring of @open import@ as
+          -- @
+          --    module Top where
+          --    module M where
+          --    import M
+          --    open M
+          -- @
+          -- will not work, as @M@ is now ambiguous in @open M@;
+          -- the information that @M@ is external is lost here.
+          (_minfo, _m, adir) <- checkOpen r (Just m) name dir
+          return adir
+
+        -- If not opening, import directives are applied to the original scope.
+        DontOpen -> do
+          (adir, i') <- Map.adjustM' (applyImportDirectiveM x dir) m i
+          -- Andreas, 2020-05-18, issue #3933
+          -- We merge the new imports without deleting old imports, to be monotone.
+          modifyScopes $ \ ms -> Map.unionWith mergeScope ms i'
+          return adir
+
+      printScope "import" 10 "merged imported sig:"
+      let minfo = ModuleInfo
+            { minfoRange     = r
+            , minfoAsName    = theAsName
+            , minfoAsTo      = getRange (theAsSymbol, renamingRange dir)
+            , minfoOpenShort = Just open
+            , minfoDirective = Just dir
+            }
+      return [ A.Import minfo m adir ]
+
+    NiceUnquoteDecl r p a i tc cc xs e -> do
+      fxs <- mapM getConcreteFixity xs
+      ys <- zipWithM freshAbstractQName fxs xs
+      zipWithM_ (bindName p QuotableName) xs ys
+      e <- toAbstract e
+      zipWithM_ (rebindName p OtherDefName) xs ys
+      let mi = MutualInfo tc cc YesPositivityCheck r
+      mapM_ unfoldFunction ys
+      opaque <- contextIsOpaque
+      return [ A.Mutual mi
+        [ A.UnquoteDecl mi
+            [ (mkDefInfoInstance x fx p a i NotMacroDef r) { Info.defOpaque = opaque } | (fx, x) <- zip fxs xs ]
+          ys e
+        ] ]
+
+    NiceUnquoteDef r p a _ _ xs e -> do
+      fxs <- mapM getConcreteFixity xs
+      ys <- mapM (toAbstract . OldName) xs
+      zipWithM_ (rebindName p QuotableName) xs ys
+      e <- toAbstract e
+      zipWithM_ (rebindName p OtherDefName) xs ys
+      mapM_ unfoldFunction ys
+      opaque <- contextIsOpaque
+      return [ A.UnquoteDef [ (mkDefInfo x fx PublicAccess a r) { Info.defOpaque = opaque } | (fx, x) <- zip fxs xs ] ys e ]
+
+    NiceUnquoteData r p a pc uc x cs e -> notAffectedByOpaque $ do
+      fx <- getConcreteFixity x
+      x' <- freshAbstractQName fx x
+      bindName p QuotableName x x'
+
+      -- Create the module for the qualified constructors
+      checkForModuleClash x
+      let m = qnameToMName x'
+      createModule (Just IsDataModule) m
+      bindModule p x m  -- make it a proper module
+
+      cs' <- mapM (bindUnquoteConstructorName m p) cs
+
+      e <- withCurrentModule m $ toAbstract e
+
+      rebindName p DataName x x'
+      zipWithM_ (rebindName p ConName) cs cs'
+      withCurrentModule m $ zipWithM_ (rebindName p ConName) cs cs'
+
+      fcs <- mapM getConcreteFixity cs
+      let mi = MutualInfo TerminationCheck YesCoverageCheck pc r
+      return
+        [ A.Mutual
+          mi [A.UnquoteData
+            [ mkDefInfo x fx p a r ] x' uc
+            [ mkDefInfo c fc p a r | (fc, c) <- zip fcs cs] cs' e ]
+        ]
+
+    NicePatternSyn r a n as p -> do
+      reportSLn "scope.pat" 10 $ "found nice pattern syn: " ++ prettyShow n
+      (as, p) <- withLocalVars $ do
+         -- Expand puns if optHiddenArgumentPuns is True.
+         puns <- optHiddenArgumentPuns <$> pragmaOptions
+         p <- return $ if puns then expandPuns p else p
+         p <- toAbstract =<< parsePatternSyn p
+         when (containsAsPattern p) $
+           typeError $ GenericError $
+             "@-patterns are not allowed in pattern synonyms"
+         checkPatternLinearity p $ \ys ->
+           typeError $ RepeatedVariablesInPattern ys
+         bindVarsToBind
+         let err = "Dot or equality patterns are not allowed in pattern synonyms. Maybe use '_' instead."
+         p <- noDotorEqPattern err p
+         as <- (traverse . mapM) (unVarName <=< resolveName . C.QName) as
+         unlessNull (patternVars p List.\\ map unArg as) $ \ xs -> do
+           typeError $ UnboundVariablesInPatternSynonym xs
+         return (as, p)
+      y <- freshAbstractQName' n
+      bindName a PatternSynName n y
+      -- Expanding pattern synonyms already at definition makes it easier to
+      -- fold them back when printing (issue #2762).
+      ep <- expandPatternSynonyms p
+      modifyPatternSyns (Map.insert y (as, ep))
+      return [A.PatternSynDef y (map (fmap BindName) as) p]   -- only for highlighting, so use unexpanded version
+      where unVarName (VarName a _) = return a
+            unVarName _ = typeError $ UnusedVariableInPatternSynonym
+
+    d@NiceLoneConstructor{} -> withCurrentCallStack $ \ stk -> do
+      warning $ NicifierIssue (DeclarationWarning stk (InvalidConstructorBlock (getRange d)))
+      pure []
+
+    NiceOpaque r names decls -> do
+      -- The names in an 'unfolding' clause must be unambiguous names of
+      -- definitions:
+      let
+        findName c = resolveName c >>= \case
+          A.DefinedName _ an _           -> pure (anameName an)
+          A.FieldName (an :| [])         -> pure (anameName an)
+          A.ConstructorName _ (an :| []) -> pure (anameName an)
+
+          A.UnknownName -> notInScopeError c
+          _ -> typeError . GenericDocError =<<
+            "Name in unfolding clause should be unambiguous defined name:" <+> prettyTCM c
+
+      -- Resolve all the names, and use them as an initial unfolding
+      -- set:
+      names  <- traverse findName names
+      -- Generate the identifier for this block:
+      oid    <- fresh
+      -- Record the parent unfolding block, if any:
+      parent <- asksTC envCurrentOpaqueId
+
+      stOpaqueBlocks `modifyTCLens` Map.insert oid OpaqueBlock
+        { opaqueId        = oid
+        , opaqueUnfolding = HashSet.fromList names
+        , opaqueDecls     = mempty
+        , opaqueParent    = parent
+        , opaqueRange     = r
+        }
+
+      -- Keep going!
+      localTC (\e -> e { envCurrentOpaqueId = Just oid }) $ do
+        out <- traverse toAbstract decls
+        unless (any interestingOpaqueDecl out) $ warning UselessOpaque
+        pure $ UnfoldingDecl r names:out
+    where
+      -- checking postulate or type sig. without checking safe flag
+      toAbstractNiceAxiom :: KindOfName -> C.NiceDeclaration -> ScopeM A.Declaration
+      toAbstractNiceAxiom kind (C.Axiom r p a i info x t) = do
+        t' <- toAbstractCtx TopCtx t
+        f  <- getConcreteFixity x
+        mp <- getConcretePolarity x
+        y  <- freshAbstractQName f x
+        let isMacro | kind == MacroName = MacroDef
+                    | otherwise         = NotMacroDef
+        bindName p kind x y
+        definfo <- updateDefInfoOpacity $ mkDefInfoInstance x f p a i isMacro r
+        return $ A.Axiom kind definfo info mp y t'
+      toAbstractNiceAxiom _ _ = __IMPOSSIBLE__
+
+      interestingOpaqueDecl :: A.Declaration -> Bool
+      interestingOpaqueDecl (A.Mutual _ ds)     = any interestingOpaqueDecl ds
+      interestingOpaqueDecl (A.ScopedDecl _ ds) = any interestingOpaqueDecl ds
+
+      interestingOpaqueDecl A.FunDef{}      = True
+      interestingOpaqueDecl A.UnquoteDecl{} = True
+      interestingOpaqueDecl A.UnquoteDef{}  = True
+
+      interestingOpaqueDecl _ = False
+
+-- | Add a 'QName' to the set of declarations /contained in/ the current
+-- opaque block.
+unfoldFunction :: A.QName -> ScopeM ()
+unfoldFunction qn = asksTC envCurrentOpaqueId >>= \case
+  Just id -> do
+    let go Nothing   = __IMPOSSIBLE__
+        go (Just ob) = Just ob{ opaqueDecls = qn `HashSet.insert` opaqueDecls ob }
+    stOpaqueBlocks `modifyTCLens` Map.alter go id
+  Nothing -> pure ()
+
+-- | Look up the current opaque identifier as a value in 'IsOpaque'.
+contextIsOpaque :: ScopeM IsOpaque
+contextIsOpaque =  maybe TransparentDef OpaqueDef <$> asksTC envCurrentOpaqueId
+
+updateDefInfoOpacity :: DefInfo -> ScopeM DefInfo
+updateDefInfoOpacity di = (\a -> di { Info.defOpaque = a }) <$> contextIsOpaque
+
+-- | Raise a warning indicating that the current Declaration is not
+-- affected by opacity, but only if we are actually in an Opaque block.
+notAffectedByOpaque :: ScopeM a -> ScopeM a
+notAffectedByOpaque k = do
+  t <- asksTC envCheckingWhere
+  unless t $
+    maybe (pure ()) (const (warning NotAffectedByOpaque)) =<< asksTC envCurrentOpaqueId
+  notUnderOpaque k
+
+unGeneralized :: A.Expr -> (Set.Set I.QName, A.Expr)
+unGeneralized (A.Generalized s t) = (s, t)
+unGeneralized (A.ScopedExpr si e) = A.ScopedExpr si <$> unGeneralized e
+unGeneralized t = (mempty, t)
+
+alreadyGeneralizing :: ScopeM Bool
+alreadyGeneralizing = isJust <$> useTC stGeneralizedVars
+
+collectGeneralizables :: ScopeM a -> ScopeM (Set I.QName, a)
+collectGeneralizables m =
+  -- #5683: No nested generalization
+  ifM alreadyGeneralizing ((Set.empty,) <$> m) $
+  {-else-} bracket_ open close $ do
+      a <- m
+      s <- useTC stGeneralizedVars
+      case s of
+          Nothing -> __IMPOSSIBLE__
+          Just s -> return (s, a)
+  where
+    open = do
+        gvs <- useTC stGeneralizedVars
+        stGeneralizedVars `setTCLens` Just mempty
+        pure gvs
+    close = (stGeneralizedVars `setTCLens`)
+
+createBoundNamesForGeneralizables :: Set I.QName -> ScopeM (Map I.QName I.Name)
+createBoundNamesForGeneralizables vs =
+  flip Map.traverseWithKey (Map.fromSet (const ()) vs) $ \ q _ -> do
+    let x  = nameConcrete $ qnameName q
+        fx = nameFixity   $ qnameName q
+    freshAbstractName fx x
+
+collectAndBindGeneralizables :: ScopeM a -> ScopeM (Map I.QName I.Name, a)
+collectAndBindGeneralizables m = do
+  fvBefore <- length <$> getLocalVars
+  (s, res) <- collectGeneralizables m
+  fvAfter  <- length <$> getLocalVars
+  -- We should bind the named generalizable variables as fresh variables
+  binds <- createBoundNamesForGeneralizables s
+  -- Issue #3735: We need to bind the generalizable variables outside any variables bound by `m`.
+  outsideLocalVars (fvAfter - fvBefore) $ bindGeneralizables binds
+  return (binds, res)
+
+bindGeneralizables :: Map A.QName A.Name -> ScopeM ()
+bindGeneralizables vars =
+  forM_ (Map.toList vars) $ \ (q, y) ->
+    bindVariable LambdaBound (nameConcrete $ qnameName q) y
+
+-- | Bind generalizable variables if data or record decl was split by the system
+--   (origin == Inserted)
+bindGeneralizablesIfInserted :: Origin -> AbstractName -> ScopeM (Set A.Name)
+bindGeneralizablesIfInserted Inserted y = bound <$ bindGeneralizables gvars
+  where gvars = case anameMetadata y of
+          GeneralizedVarsMetadata gvars -> gvars
+          NoMetadata                    -> Map.empty
+        bound = Set.fromList (Map.elems gvars)
+bindGeneralizablesIfInserted UserWritten _ = return Set.empty
+bindGeneralizablesIfInserted _ _           = __IMPOSSIBLE__
+
+newtype GenTel = GenTel C.Telescope
+data GenTelAndType = GenTelAndType C.Telescope C.Expr
+
+instance ToAbstract GenTel where
+  type AbsOfCon GenTel = A.GeneralizeTelescope
+  toAbstract (GenTel tel) =
+    uncurry A.GeneralizeTel <$> collectAndBindGeneralizables (catMaybes <$> toAbstract tel)
+
+instance ToAbstract GenTelAndType where
+  type AbsOfCon GenTelAndType = (A.GeneralizeTelescope, A.Expr)
+
+  toAbstract (GenTelAndType tel t) = do
+    (binds, (tel, t)) <- collectAndBindGeneralizables $
+                          (,) <$> toAbstract tel <*> toAbstract t
+    return (A.GeneralizeTel binds (catMaybes tel), t)
+
+-- | Make sure definition is in same module as signature.
+class LivesInCurrentModule a where
+  livesInCurrentModule :: a -> ScopeM ()
+
+instance LivesInCurrentModule AbstractName where
+  livesInCurrentModule = livesInCurrentModule . anameName
+
+instance LivesInCurrentModule A.QName where
+  livesInCurrentModule x = do
+    m <- getCurrentModule
+    reportS "scope.data.def" 30
+      [ "  A.QName of data type: " ++ prettyShow x
+      , "  current module: " ++ prettyShow m
+      ]
+    unless (A.qnameModule x == m) $
+      genericError $ "Definition in different module than its type signature"
+
+-- | Unless the resolved 'AbstractName' has the given 'KindOfName',
+--   report a 'ClashingDefinition' for the 'C.Name'.
+clashUnless :: C.Name -> KindOfName -> AbstractName -> ScopeM ()
+clashUnless x k ax = unless (anameKind ax == k) $
+  typeError $ ClashingDefinition (C.QName x) (anameName ax) Nothing
+
+-- | If a (data/record) module with the given name is already present in the current module,
+--   we take this as evidence that a data/record with that name is already defined.
+clashIfModuleAlreadyDefinedInCurrentModule :: C.Name -> AbstractName -> ScopeM ()
+clashIfModuleAlreadyDefinedInCurrentModule x ax = do
+  datRecMods <- catMaybes <$> do
+    mapM (isDatatypeModule . amodName) =<< lookupModuleInCurrentModule x
+  unlessNull datRecMods $ const $
+    typeError $ ClashingDefinition (C.QName x) (anameName ax) Nothing
+
+lookupModuleInCurrentModule :: C.Name -> ScopeM [AbstractModule]
+lookupModuleInCurrentModule x =
+  List1.toList' . Map.lookup x . nsModules . thingsInScope [PublicNS, PrivateNS] <$> getCurrentScope
+
+data DataConstrDecl = DataConstrDecl A.ModuleName IsAbstract Access C.NiceDeclaration
+
+-- | Bind a @data@ constructor.
+bindConstructorName
+  :: ModuleName      -- ^ Name of @data@/@record@ module.
+  -> C.Name          -- ^ Constructor name.
+  -> IsAbstract
+  -> Access
+  -> ScopeM A.QName
+bindConstructorName m x a p = do
+  f <- getConcreteFixity x
+  -- The abstract name is the qualified one
+  y <- withCurrentModule m $ freshAbstractQName f x
+  -- Bind it twice, once unqualified and once qualified
+  bindName p' ConName x y
+  withCurrentModule m $ bindName p'' ConName x y
+  return y
+  where
+    -- An abstract constructor is private (abstract constructor means
+    -- abstract datatype, so the constructor should not be exported).
+    p' = case a of
+           AbstractDef -> PrivateAccess Inserted
+           _           -> p
+    p'' = case a of
+            AbstractDef -> PrivateAccess Inserted
+            _           -> PublicAccess
+
+-- | Record constructors do not live in the record module (as it is parameterized).
+--   Abstract constructors are bound privately, so that they are not exported.
+bindRecordConstructorName :: C.Name -> KindOfName -> IsAbstract -> Access -> ScopeM A.QName
+bindRecordConstructorName x kind a p = do
+  y <- freshAbstractQName' x
+  bindName p' kind x y
+  return y
+  where
+    -- An abstract constructor is private (abstract constructor means
+    -- abstract datatype, so the constructor should not be exported).
+    p' = case a of
+           AbstractDef -> PrivateAccess Inserted
+           _           -> p
+
+bindUnquoteConstructorName :: ModuleName -> Access -> C.Name -> TCM A.QName
+bindUnquoteConstructorName m p c = do
+
+  r <- resolveName (C.QName c)
+  fc <- getConcreteFixity c
+  c' <- withCurrentModule m $ freshAbstractQName fc c
+  let aname qn = AbsName qn QuotableName Defined NoMetadata
+      addName = modifyCurrentScope $ addNameToScope (localNameSpace p) c $ aname c'
+      success = addName >> (withCurrentModule m $ addName)
+  case r of
+    _ | isNoName c       -> success
+    UnknownName          -> success
+    ConstructorName i ds -> if all (isJust . isConName . anameKind) ds
+      then success
+      else typeError $ ClashingDefinition (C.QName c) (anameName $ List1.head ds) Nothing
+    _ -> typeError $ GenericError $
+       "The name " ++ prettyShow c ++ " already has non-constructor definitions"
+  return c'
+
+instance ToAbstract DataConstrDecl where
+  type AbsOfCon DataConstrDecl = A.Declaration
+
+  toAbstract (DataConstrDecl m a p d) = do
+    case d of
+      C.Axiom r p1 a1 i info x t -> do -- rel==Relevant
+        -- unless (p1 == p) __IMPOSSIBLE__  -- This invariant is currently violated by test/Succeed/Issue282.agda
+        unless (a1 == a) __IMPOSSIBLE__
+        t' <- toAbstractCtx TopCtx t
+        -- The abstract name is the qualified one
+        -- Bind it twice, once unqualified and once qualified
+        f <- getConcreteFixity x
+        y <- bindConstructorName m x a p
+        printScope "con" 15 "bound constructor"
+        return $ A.Axiom ConName (mkDefInfoInstance x f p a i NotMacroDef r)
+                         info Nothing y t'
+      _ -> errorNotConstrDecl d
+
+errorNotConstrDecl :: C.NiceDeclaration -> ScopeM a
+errorNotConstrDecl d = setCurrentRange d $
+  typeError $ IllegalDeclarationInDataDefinition $ notSoNiceDeclarations d
+
+instance ToAbstract C.Pragma where
+  type AbsOfCon C.Pragma = [A.Pragma]
+
+  toAbstract (C.ImpossiblePragma _ strs) =
+    case strs of
+      "ReduceM" : _ -> impossibleTestReduceM strs
+      _ -> impossibleTest strs
+  toAbstract (C.OptionsPragma _ opts) = return [ A.OptionsPragma opts ]
+  toAbstract (C.RewritePragma _ _ []) = [] <$ warning EmptyRewritePragma
+  toAbstract (C.RewritePragma _ r xs) = singleton . A.RewritePragma r . concat <$> do
+   forM xs $ \ x -> do
+    e <- toAbstract $ OldQName x Nothing
+    case e of
+      A.Def x          -> return [ x ]
+      A.Proj _ p | Just x <- getUnambiguous p -> return [ x ]
+      A.Proj _ x       -> genericError $ "REWRITE used on ambiguous name " ++ prettyShow x
+      A.Con c | Just x <- getUnambiguous c -> return [ x ]
+      A.Con x          -> genericError $ "REWRITE used on ambiguous name " ++ prettyShow x
+      A.Var x          -> genericError $ "REWRITE used on parameter " ++ prettyShow x ++ " instead of on a defined symbol"
+      _       -> __IMPOSSIBLE__
+  toAbstract (C.ForeignPragma _ rb s) = [] <$ addForeignCode (rangedThing rb) s
+  toAbstract (C.CompilePragma _ rb x s) = do
+    me <- toAbstract $ MaybeOldQName $ OldQName x Nothing
+    case me of
+      Nothing -> [] <$ notInScopeWarning x
+      Just e  -> do
+        let err what = genericError $ "Cannot COMPILE " ++ what ++ " " ++ prettyShow x
+        y <- case e of
+          A.Def x             -> return x
+          A.Proj _ p | Just x <- getUnambiguous p -> return x
+          A.Proj _ x          -> err "ambiguous projection"
+          A.Con c | Just x <- getUnambiguous c -> return x
+          A.Con x             -> err "ambiguous constructor"
+          A.PatternSyn{}      -> err "pattern synonym"
+          A.Var{}             -> err "local variable"
+          _                   -> __IMPOSSIBLE__
+        return [ A.CompilePragma rb y s ]
+
+  toAbstract (C.StaticPragma _ x) = do
+      e <- toAbstract $ OldQName x Nothing
+      y <- case e of
+          A.Def  x -> return x
+          A.Proj _ p | Just x <- getUnambiguous p -> return x
+          A.Proj _ x -> genericError $
+            "STATIC used on ambiguous name " ++ prettyShow x
+          _        -> genericError "Target of STATIC pragma should be a function"
+      return [ A.StaticPragma y ]
+  toAbstract (C.InjectivePragma _ x) = do
+      e <- toAbstract $ OldQName x Nothing
+      y <- case e of
+          A.Def  x -> return x
+          A.Proj _ p | Just x <- getUnambiguous p -> return x
+          A.Proj _ x -> genericError $
+            "INJECTIVE used on ambiguous name " ++ prettyShow x
+          _        -> genericError "Target of INJECTIVE pragma should be a defined symbol"
+      return [ A.InjectivePragma y ]
+  toAbstract (C.InlinePragma _ b x) = do
+      e <- toAbstract $ OldQName x Nothing
+      let sINLINE = if b then "INLINE" else "NOINLINE"
+      let ret y = return [ A.InlinePragma b y ]
+      case e of
+          A.Con (AmbQ xs) -> concatMapM ret $ List1.toList xs
+          A.Def  x -> ret x
+          A.Proj _ p | Just x <- getUnambiguous p -> ret x
+          A.Proj _ x -> genericError $
+            sINLINE ++ " used on ambiguous name " ++ prettyShow x
+          _ -> genericError $ ("Target of " ++) $ applyWhen b ("NO" ++) "INLINE pragma should be a function or constructor"
+  toAbstract (C.NotProjectionLikePragma _ x) = do
+      e <- toAbstract $ OldQName x Nothing
+      y <- case e of
+          A.Def  x -> return x
+          A.Proj _ p | Just x <- getUnambiguous p -> return x
+          A.Proj _ x -> genericError $
+            "NOT_PROJECTION_LIKE used on ambiguous name " ++ prettyShow x
+          _        -> genericError $ "Target of NOT_PROJECTION_LIKE pragma should be a function"
+      return [ A.NotProjectionLikePragma y ]
+  toAbstract (C.BuiltinPragma _ rb qx)
+    | Just b' <- b, isUntypedBuiltin b' = do
+        q <- toAbstract $ ResolveQName qx
+        bindUntypedBuiltin b' q
+        return [ A.BuiltinPragma rb q ]
+        -- Andreas, 2015-02-14
+        -- Some builtins cannot be given a valid Agda type,
+        -- thus, they do not come with accompanying postulate or definition.
+    | Just b' <- b, isBuiltinNoDef b' = do
+          case qx of
+            C.QName x -> do
+              -- The name shouldn't exist yet. If it does, we raise a warning
+              -- and drop the existing definition.
+              unlessM ((UnknownName ==) <$> resolveName qx) $ do
+                genericWarning $ P.text $
+                   "BUILTIN " ++ getBuiltinId b' ++ " declares an identifier " ++
+                   "(no longer expects an already defined identifier)"
+                modifyCurrentScope $ removeNameFromScope PublicNS x
+              -- We then happily bind the name
+              y <- freshAbstractQName' x
+              let kind = fromMaybe __IMPOSSIBLE__ $ builtinKindOfName b'
+              bindName PublicAccess kind x y
+              return [ A.BuiltinNoDefPragma rb kind y ]
+            _ -> genericError $
+              "Pragma BUILTIN " ++ getBuiltinId b' ++ ": expected unqualified identifier, " ++
+              "but found " ++ prettyShow qx
+    | otherwise = do
+          q0 <- toAbstract $ ResolveQName qx
+
+          -- Andreas, 2020-04-12, pr #4574.  For highlighting purposes:
+          -- Rebind 'BuiltinPrim' as 'PrimName' and similar.
+          q <- case (q0, b >>= builtinKindOfName, qx) of
+            (DefinedName acc y suffix, Just kind, C.QName x)
+              | anameKind y /= kind
+              , kind `elem` [ PrimName, AxiomName ] -> do
+                  rebindName acc kind x $ anameName y
+                  return $ DefinedName acc y{ anameKind = kind } suffix
+            _ -> return q0
+
+          return [ A.BuiltinPragma rb q ]
+    where b = builtinById (rangedThing rb)
+
+  toAbstract (C.EtaPragma _ x) = do
+    e <- toAbstract $ OldQName x Nothing
+    case e of
+      A.Def x -> return [ A.EtaPragma x ]
+      _       -> do
+       e <- showA e
+       genericError $ "Pragma ETA: expected identifier, " ++
+         "but found expression " ++ e
+
+  toAbstract (C.DisplayPragma _ lhs rhs) = withLocalVars $ do
+    let err = genericError "DISPLAY pragma left-hand side must have form 'f e1 .. en'"
+        getHead (C.IdentP _ x)        = return x
+        getHead (C.RawAppP _ (List2 p _ _)) = getHead p
+        getHead _                     = err
+
+    top <- getHead lhs
+
+    (isPatSyn, hd) <- do
+      qx <- resolveName' allKindsOfNames Nothing top
+      case qx of
+        VarName x' _                -> return . (False,) $ A.qnameFromList $ singleton x'
+        DefinedName _ d NoSuffix    -> return . (False,) $ anameName d
+        DefinedName _ d Suffix{}    -> genericError $ "Invalid pattern " ++ prettyShow top
+        FieldName     (d :| [])     -> return . (False,) $ anameName d
+        FieldName ds                -> genericError $ "Ambiguous projection " ++ prettyShow top ++ ": " ++ prettyShow (fmap anameName ds)
+        ConstructorName _ (d :| []) -> return . (False,) $ anameName d
+        ConstructorName _ ds        -> genericError $ "Ambiguous constructor " ++ prettyShow top ++ ": " ++ prettyShow (fmap anameName ds)
+        UnknownName                 -> notInScopeError top
+        PatternSynResName (d :| []) -> return . (True,) $ anameName d
+        PatternSynResName ds        -> genericError $ "Ambiguous pattern synonym" ++ prettyShow top ++ ": " ++ prettyShow (fmap anameName ds)
+
+    lhs <- toAbstract $ LeftHandSide top lhs
+    ps  <- case lhs of
+             A.LHS _ (A.LHSHead _ ps) -> return ps
+             _ -> err
+
+    -- Andreas, 2016-08-08, issue #2132
+    -- Remove pattern synonyms on lhs
+    (hd, ps) <- do
+      let mkP | isPatSyn  = A.PatternSynP (PatRange $ getRange lhs) (unambiguous hd)
+              | otherwise = A.DefP (PatRange $ getRange lhs) (unambiguous hd)
+      p <- expandPatternSynonyms $ mkP ps
+      case p of
+        A.DefP _ f ps | Just hd <- getUnambiguous f -> return (hd, ps)
+        A.ConP _ c ps | Just hd <- getUnambiguous c -> return (hd, ps)
+        A.PatternSynP{} -> __IMPOSSIBLE__
+        _ -> err
+
+    rhs <- toAbstract rhs
+    return [A.DisplayPragma hd ps rhs]
+
+  -- A warning attached to an ambiguous name shall apply to all disambiguations.
+  toAbstract (C.WarningOnUsage _ x str) = do
+    ys <- fmap anameName <$> toAbstractExistingName x
+    forM_ ys $ \ qn -> stLocalUserWarnings `modifyTCLens` Map.insert qn str
+    return []
+
+  toAbstract (C.WarningOnImport _ str) = do
+    stWarningOnImport `setTCLens` Just str
+    pure []
+
+  -- Termination, Coverage, Positivity, Universe, and Catchall
+  -- pragmes are handled by the nicifier
+  toAbstract C.TerminationCheckPragma{}  = __IMPOSSIBLE__
+  toAbstract C.NoCoverageCheckPragma{}   = __IMPOSSIBLE__
+  toAbstract C.NoPositivityCheckPragma{} = __IMPOSSIBLE__
+  toAbstract C.NoUniverseCheckPragma{}   = __IMPOSSIBLE__
+  toAbstract C.CatchallPragma{}          = __IMPOSSIBLE__
+
+  -- Polarity pragmas are handled by the niceifier.
+  toAbstract C.PolarityPragma{} = __IMPOSSIBLE__
+
+instance ToAbstract C.Clause where
+  type AbsOfCon C.Clause = A.Clause
+
+  toAbstract (C.Clause top catchall lhs@(C.LHS p eqs with) rhs wh wcs) = withLocalVars $ do
+    -- Jesper, 2018-12-10, #3095: pattern variables bound outside the
+    -- module are locally treated as module parameters
+    modifyScope_ $ updateScopeLocals $ map $ second patternToModuleBound
+    -- Andreas, 2012-02-14: need to reset local vars before checking subclauses
+    vars0 <- getLocalVars
+    lhs' <- toAbstract $ LeftHandSide (C.QName top) p
+    printLocals 10 "after lhs:"
+    vars1 <- getLocalVars
+    eqs <- mapM (toAbstractCtx TopCtx) eqs
+    vars2 <- getLocalVars
+    let vars = dropEnd (length vars1) vars2 ++ vars0
+    let wcs' = (vars, wcs)
+
+    -- Handle rewrite equations first.
+    if not (null eqs)
+      then do
+        rhs <- toAbstractCtx TopCtx $ RightHandSide eqs with wcs' rhs wh
+        rhs <- toAbstract rhs
+        return $ A.Clause lhs' [] rhs A.noWhereDecls catchall
+      else do
+        -- the right hand side is checked with the module of the local definitions opened
+        (rhs, ds) <- whereToAbstract (getRange wh) wh $
+                       toAbstractCtx TopCtx $ RightHandSide [] with wcs' rhs NoWhere
+        rhs <- toAbstract rhs
+        return $ A.Clause lhs' [] rhs ds catchall
+
+
+whereToAbstract
+  :: Range                            -- ^ The range of the @where@ block.
+  -> C.WhereClause                    -- ^ The @where@ block.
+  -> ScopeM a                         -- ^ The scope-checking task to be run in the context of the @where@ module.
+  -> ScopeM (a, A.WhereDeclarations)  -- ^ Additionally return the scope-checked contents of the @where@ module.
+whereToAbstract r wh inner = do
+  case wh of
+    NoWhere       -> ret
+    AnyWhere _ [] -> warnEmptyWhere
+    AnyWhere _ ds -> enter $ do
+      -- Andreas, 2016-07-17 issues #2081 and #2101
+      -- where-declarations are automatically private.
+      -- This allows their type signature to be checked InAbstractMode.
+      whereToAbstract1 r defaultErased Nothing
+        (singleton $ C.Private noRange Inserted ds) inner
+    SomeWhere _ e m a ds0 -> enter $
+      List1.ifNull ds0 warnEmptyWhere {-else-} $ \ds -> do
+      -- Named where-modules do not default to private.
+      whereToAbstract1 r e (Just (m, a)) ds inner
+  where
+  enter = localTC $ \env -> env { envCheckingWhere = True }
+  ret = (,A.noWhereDecls) <$> inner
+  warnEmptyWhere = do
+    setCurrentRange r $ warning EmptyWhere
+    ret
+
+whereToAbstract1
+  :: Range                            -- ^ The range of the @where@-block.
+  -> Erased                           -- ^ Is the where module erased?
+  -> Maybe (C.Name, Access)           -- ^ The name of the @where@ module (if any).
+  -> List1 C.Declaration              -- ^ The contents of the @where@ module.
+  -> ScopeM a                         -- ^ The scope-checking task to be run in the context of the @where@ module.
+  -> ScopeM (a, A.WhereDeclarations)  -- ^ Additionally return the scope-checked contents of the @where@ module.
+whereToAbstract1 r e whname whds inner = do
+  -- ASR (16 November 2015) Issue 1137: We ban termination
+  -- pragmas inside `where` clause.
+  checkNoTerminationPragma InWhereBlock whds
+
+  -- Create a fresh concrete name if there isn't (a proper) one.
+  (m, acc) <- do
+    case whname of
+      Just (m, acc) | not (isNoName m) -> return (m, acc)
+      _ -> fresh <&> \ x -> (C.NoName (getRange whname) x, PrivateAccess Inserted)
+           -- unnamed where's are private
+  old <- getCurrentModule
+  am  <- toAbstract (NewModuleName m)
+  (scope, d) <- scopeCheckModule r e (C.QName m) am [] $
+                toAbstract $ Declarations $ List1.toList whds
+  setScope scope
+  x <- inner
+  setCurrentModule old
+  bindModule acc m am
+  -- Issue 848: if the module was anonymous (module _ where) open it public
+  let anonymousSomeWhere = maybe False (isNoName . fst) whname
+  when anonymousSomeWhere $
+   void $ -- We can ignore the returned default A.ImportDirective.
+    openModule TopOpenModule (Just am) (C.QName m) $
+      defaultImportDir { publicOpen = Just noRange }
+  return (x, A.WhereDecls (Just am) (isNothing whname) $ singleton d)
+
+data TerminationOrPositivity = Termination | Positivity
+  deriving (Show)
+
+data WhereOrRecord = InWhereBlock | InRecordDef
+
+checkNoTerminationPragma :: FoldDecl a => WhereOrRecord -> a -> ScopeM ()
+checkNoTerminationPragma b ds =
+  -- foldDecl traverses into all sub-declarations.
+  forM_ (foldDecl (isPragma >=> isTerminationPragma) ds) \ (p, r) ->
+    setCurrentRange r $ warning $ UselessPragma r $ P.vcat
+      [ P.text $ show p ++ " pragmas are ignored in " ++ what b
+      , P.text $ "(see " ++ issue b ++ ")"
+      ]
+  where
+    what InWhereBlock = "where clauses"
+    what InRecordDef  = "record definitions"
+    github n = "https://github.com/agda/agda/issues/" ++ show n
+    issue InWhereBlock = github 3355
+    issue InRecordDef  = github 3008
+
+    isTerminationPragma :: C.Pragma -> [(TerminationOrPositivity, Range)]
+    isTerminationPragma = \case
+      C.TerminationCheckPragma r _  -> [(Termination, r)]
+      C.NoPositivityCheckPragma r   -> [(Positivity, r)]
+      C.OptionsPragma _ _           -> []
+      C.BuiltinPragma _ _ _         -> []
+      C.RewritePragma _ _ _         -> []
+      C.ForeignPragma _ _ _         -> []
+      C.CompilePragma _ _ _ _       -> []
+      C.StaticPragma _ _            -> []
+      C.InlinePragma _ _ _          -> []
+      C.ImpossiblePragma _ _        -> []
+      C.EtaPragma _ _               -> []
+      C.WarningOnUsage _ _ _        -> []
+      C.WarningOnImport _ _         -> []
+      C.InjectivePragma _ _         -> []
+      C.DisplayPragma _ _ _         -> []
+      C.CatchallPragma _            -> []
+      C.NoCoverageCheckPragma _     -> []
+      C.PolarityPragma _ _ _        -> []
+      C.NoUniverseCheckPragma _     -> []
+      C.NotProjectionLikePragma _ _ -> []
+
+data RightHandSide = RightHandSide
+  { _rhsRewriteEqn :: [RewriteEqn' () A.BindName A.Pattern A.Expr]
+    -- ^ @rewrite e | with p <- e in eq@ (many)
+  , _rhsWithExpr   :: [C.WithExpr]
+    -- ^ @with e@ (many)
+  , _rhsSubclauses :: (LocalVars, [C.Clause])
+    -- ^ the subclauses spawned by a with (monadic because we need to reset the local vars before checking these clauses)
+  , _rhs           :: C.RHS
+  , _rhsWhere      :: WhereClause
+      -- ^ @where@ module.
+  }
+
+data AbstractRHS
+  = AbsurdRHS'
+  | WithRHS' [A.WithExpr] (List1 (ScopeM C.Clause))
+    -- ^ The with clauses haven't been translated yet
+  | RHS' A.Expr C.Expr
+  | RewriteRHS' [RewriteEqn' () A.BindName A.Pattern A.Expr] AbstractRHS A.WhereDeclarations
+
+qualifyName_ :: A.Name -> ScopeM A.QName
+qualifyName_ x = do
+  m <- getCurrentModule
+  return $ A.qualify m x
+
+withFunctionName :: String -> ScopeM A.QName
+withFunctionName s = do
+  NameId i _ <- fresh
+  qualifyName_ =<< freshName_ (s ++ show i)
+
+instance ToAbstract (RewriteEqn' () A.BindName A.Pattern A.Expr) where
+  type AbsOfCon (RewriteEqn' () A.BindName A.Pattern A.Expr) = A.RewriteEqn
+  toAbstract = \case
+    Rewrite es -> fmap Rewrite $ forM es $ \ (_, e) -> do
+      qn <- withFunctionName "-rewrite"
+      pure (qn, e)
+    Invert _ pes -> do
+      qn <- withFunctionName "-invert"
+      pure $ Invert qn pes
+
+instance ToAbstract C.RewriteEqn where
+  type AbsOfCon C.RewriteEqn = RewriteEqn' () A.BindName A.Pattern A.Expr
+  toAbstract = \case
+    Rewrite es   -> Rewrite <$> mapM toAbstract es
+    Invert _ npes -> Invert () <$> do
+      -- Given a list of irrefutable with expressions of the form @p <- e in q@
+      let (nps, es) = List1.unzip
+                    $ fmap (\ (Named nm (p, e)) -> ((nm, p), e)) npes
+      -- we first check the expressions @e@: the patterns may shadow some of the
+      -- variables mentioned in them!
+      es <- toAbstract es
+      -- we then parse the pairs of patterns @p@ and names @q@ for the equality
+      -- constraints of the form @p ≡ e@.
+      nps <- forM nps $ \ (n, p) -> do
+        -- first the pattern
+        -- Expand puns if optHiddenArgumentPuns is True.
+        puns <- optHiddenArgumentPuns <$> pragmaOptions
+        p <- return $ if puns then expandPuns p else p
+        p <- parsePattern p
+        p <- toAbstract p
+        checkPatternLinearity p (typeError . RepeatedVariablesInPattern)
+        bindVarsToBind
+        p <- toAbstract p
+        -- and then the name
+        n <- toAbstract $ fmap (NewName WithBound . C.mkBoundName_) n
+        pure (n, p)
+      -- we finally reassemble the telescope
+      pure $ List1.zipWith (\ (n,p) e -> Named n (p, e)) nps es
+
+instance ToAbstract AbstractRHS where
+  type AbsOfCon AbstractRHS = A.RHS
+
+  toAbstract AbsurdRHS'            = return A.AbsurdRHS
+  toAbstract (RHS' e c)            = return $ A.RHS e $ Just c
+  toAbstract (RewriteRHS' eqs rhs wh) = do
+    eqs <- toAbstract eqs
+    rhs <- toAbstract rhs
+    return $ RewriteRHS eqs [] rhs wh
+  toAbstract (WithRHS' es cs) = do
+    aux <- withFunctionName "with-"
+    A.WithRHS aux es <$> do toAbstract =<< sequence cs
+
+instance ToAbstract RightHandSide where
+  type AbsOfCon RightHandSide = AbstractRHS
+  toAbstract (RightHandSide eqs@(_:_) es cs rhs wh)               = do
+    (rhs, ds) <- whereToAbstract (getRange wh) wh $
+                   toAbstract (RightHandSide [] es cs rhs NoWhere)
+    return $ RewriteRHS' eqs rhs ds
+  toAbstract (RightHandSide [] []    (_  , _:_) _          _)  = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] (_:_) _         (C.RHS _)   _)  = typeError $ BothWithAndRHS
+  toAbstract (RightHandSide [] []    (_  , []) rhs         NoWhere) = toAbstract rhs
+  toAbstract (RightHandSide [] nes   (lv , c:cs) C.AbsurdRHS NoWhere) = do
+    let (ns , es) = unzipWith (\ (Named nm e) -> (NewName WithBound . C.mkBoundName_ <$> nm, e)) nes
+    es <- toAbstractCtx TopCtx es
+    lvars0 <- getLocalVars
+    ns <- toAbstract ns
+    lvars1 <- getLocalVars
+    let lv' = dropEnd (length lvars0) lvars1 ++ lv
+    let cs' = for (c :| cs) $ \ c -> setLocalVars lv' $> c
+    let nes = zipWith Named ns es
+    return $ WithRHS' nes cs'
+  -- TODO: some of these might be possible
+  toAbstract (RightHandSide [] (_ : _) _ C.AbsurdRHS  AnyWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] (_ : _) _ C.AbsurdRHS SomeWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] (_ : _) _ C.AbsurdRHS   NoWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] []     (_, []) C.AbsurdRHS  AnyWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] []     (_, []) C.AbsurdRHS SomeWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] []     (_, []) C.RHS{}      AnyWhere{}) = __IMPOSSIBLE__
+  toAbstract (RightHandSide [] []     (_, []) C.RHS{}     SomeWhere{}) = __IMPOSSIBLE__
+
+instance ToAbstract C.RHS where
+    type AbsOfCon C.RHS = AbstractRHS
+
+    toAbstract C.AbsurdRHS = return $ AbsurdRHS'
+    toAbstract (C.RHS e)   = RHS' <$> toAbstract e <*> pure e
+
+data LeftHandSide = LeftHandSide C.QName C.Pattern
+
+instance ToAbstract LeftHandSide where
+    type AbsOfCon LeftHandSide = A.LHS
+
+    toAbstract (LeftHandSide top lhs) =
+      traceCall (ScopeCheckLHS top lhs) $ do
+        reportSLn "scope.lhs" 5 $ "original lhs: " ++ prettyShow lhs
+        reportSLn "scope.lhs" 60 $ "patternQNames: " ++ prettyShow (patternQNames lhs)
+        reportSLn "scope.lhs" 60 $ "original lhs (raw): " ++ show lhs
+
+        -- Expand puns if optHiddenArgumentPuns is True. Note that pun
+        -- expansion should happen before the left-hand side is
+        -- parsed, because {(x)} is not treated as a pun, whereas {x}
+        -- is.
+        puns <- optHiddenArgumentPuns <$> pragmaOptions
+        lhs  <- return $ if puns then expandPuns lhs else lhs
+        reportSLn "scope.lhs" 5 $
+          "lhs with expanded puns: " ++ prettyShow lhs
+        reportSLn "scope.lhs" 60 $
+          "lhs with expanded puns (raw): " ++ show lhs
+
+        lhscore <- parseLHS top lhs
+        let ell = hasExpandedEllipsis lhscore
+        reportSLn "scope.lhs" 5 $ "parsed lhs: " ++ prettyShow lhscore
+        reportSLn "scope.lhs" 60 $ "parsed lhs (raw): " ++ show lhscore
+        printLocals 10 "before lhs:"
+        -- error if copattern parsed but --no-copatterns option
+        unlessM (optCopatterns <$> pragmaOptions) $
+          when (hasCopatterns lhscore) $
+            typeError $ NeedOptionCopatterns
+        -- scope check patterns except for dot patterns
+        lhscore <- toAbstract lhscore
+        bindVarsToBind
+        -- reportSLn "scope.lhs" 5 $ "parsed lhs patterns: " ++ prettyShow lhscore  -- TODO: Pretty A.LHSCore'
+        reportSLn "scope.lhs" 60 $ "parsed lhs patterns: " ++ show lhscore
+        printLocals 10 "checked pattern:"
+        -- scope check dot patterns
+        lhscore <- toAbstract lhscore
+        -- reportSLn "scope.lhs" 5 $ "parsed lhs dot patterns: " ++ prettyShow lhscore  -- TODO: Pretty A.LHSCore'
+        reportSLn "scope.lhs" 60 $ "parsed lhs dot patterns: " ++ show lhscore
+        printLocals 10 "checked dots:"
+        return $ A.LHS (LHSInfo (getRange lhs) ell) lhscore
+
+-- | Expands hidden argument puns.
+
+expandPuns :: C.Pattern -> C.Pattern
+expandPuns p = case p of
+  C.AppP p1 p2       -> C.AppP (expandPuns p1)
+                          ((fmap . fmap) expandPuns p2)
+  C.RawAppP r ps     -> C.RawAppP r (fmap expandPuns ps)
+  C.OpAppP r q xs ps -> C.OpAppP r q xs
+                          ((fmap . fmap . fmap) expandPuns ps)
+  C.ParenP r p       -> C.ParenP r (expandPuns p)
+  C.AsP r x p        -> C.AsP r x (expandPuns p)
+  C.RecP r ps        -> C.RecP r (fmap (fmap expandPuns) ps)
+  C.WithP r p        -> C.WithP r (expandPuns p)
+  C.EllipsisP r mp   -> C.EllipsisP r (fmap expandPuns mp)
+  C.IdentP{}         -> p
+  C.QuoteP{}         -> p
+  C.WildP{}          -> p
+  C.AbsurdP{}        -> p
+  C.DotP{}           -> p
+  C.LitP{}           -> p
+  C.EqualP{}         -> p
+
+  C.HiddenP r p   -> C.HiddenP r (expand (fmap expandPuns p))
+  C.InstanceP r p -> C.InstanceP r (expand (fmap expandPuns p))
+  where
+  -- Only patterns of the form {x} or ⦃ x ⦄, where x is an unqualified
+  -- name (not @_@), are interpreted as puns.
+  expand :: Named_ C.Pattern -> Named_ C.Pattern
+  expand (Named { nameOf     = Nothing
+                , namedThing = C.IdentP _ q@(C.QName x@C.Name{})
+                }) =
+    Named { namedThing = C.IdentP False q
+          , nameOf     = Just $
+                         WithOrigin
+                           { woOrigin = ExpandedPun
+                           , woThing  = unranged (prettyShow x)
+                           }
+          }
+  expand p = p
+
+hasExpandedEllipsis :: C.LHSCore -> ExpandedEllipsis
+hasExpandedEllipsis core = case core of
+  C.LHSHead{}       -> NoEllipsis
+  C.LHSProj{}       -> hasExpandedEllipsis $ namedArg $ C.lhsFocus core -- can this ever be ExpandedEllipsis?
+  C.LHSWith{}       -> hasExpandedEllipsis $ C.lhsHead core
+  C.LHSEllipsis r p -> case p of
+    C.LHSWith p wps _ -> hasExpandedEllipsis p <> ExpandedEllipsis r (length wps)
+    C.LHSHead{}       -> ExpandedEllipsis r 0
+    C.LHSProj{}       -> ExpandedEllipsis r 0
+    C.LHSEllipsis{}   -> __IMPOSSIBLE__
+
+-- | Merges adjacent EqualP patterns into one:
+-- type checking expects only one pattern for each domain in the telescope.
+mergeEqualPs :: [NamedArg (Pattern' e)] -> ScopeM [NamedArg (Pattern' e)]
+mergeEqualPs = go (empty, [])
+  where
+    go acc (p@(Arg ai (Named mn (A.EqualP r es))) : ps) = setCurrentRange p $ do
+      -- Face constraint patterns must be defaultNamedArg; check this:
+      unless (getModality ai == defaultModality) __IMPOSSIBLE__
+      when (notVisible ai) $
+        warning $ FaceConstraintCannotBeHidden ai
+      whenJust mn $ \ x -> setCurrentRange x $
+        warning $ FaceConstraintCannotBeNamed x
+      go (acc `mappend` (r, es)) ps
+    go (r, es@(_:_)) ps = (defaultNamedArg (A.EqualP r es) :) <$> mergeEqualPs ps
+    go (_, []) []       = return []
+    go (_, []) (p : ps) = (p :) <$> mergeEqualPs ps
+
+-- does not check pattern linearity
+instance ToAbstract C.LHSCore where
+    type AbsOfCon C.LHSCore = (A.LHSCore' C.Expr)
+
+    toAbstract (C.LHSHead x ps) = do
+        x <- withLocalVars $ do
+          setLocalVars []
+          toAbstract (OldName x)
+        A.LHSHead x <$> do mergeEqualPs =<< toAbstract ps
+    toAbstract (C.LHSProj d ps1 l ps2) = do
+        unless (null ps1) $ typeError $ IllformedProjectionPatternConcrete (foldl C.AppP (C.IdentP True d) ps1)
+        qx <- resolveName d
+        ds <- case qx of
+                FieldName ds -> return $ fmap anameName ds
+                UnknownName -> notInScopeError d
+                _           -> genericError $
+                  "head of copattern needs to be a field identifier, but "
+                  ++ prettyShow d ++ " isn't one"
+        A.LHSProj (AmbQ ds) <$> toAbstract l <*> (mergeEqualPs =<< toAbstract ps2)
+    toAbstract (C.LHSWith core wps ps) = do
+      liftA2 A.lhsCoreApp
+        (liftA2 A.lhsCoreWith
+          (toAbstract core)
+          (map defaultArg <$> toAbstract wps))
+        (toAbstract ps)
+    -- In case of a part of the LHS which was expanded from an ellipsis,
+    -- we flush the @scopeVarsToBind@ in order to allow variables bound
+    -- in the ellipsis to be shadowed.
+    toAbstract (C.LHSEllipsis _ p) = do
+      ap <- toAbstract p
+      bindVarsToBind
+      return ap
+
+instance ToAbstract c => ToAbstract (WithHiding c) where
+  type AbsOfCon (WithHiding c) = WithHiding (AbsOfCon c)
+  toAbstract (WithHiding h a) = WithHiding h <$> toAbstractHiding h a
+
+instance ToAbstract c => ToAbstract (Arg c) where
+    type AbsOfCon (Arg c) = Arg (AbsOfCon c)
+    toAbstract (Arg info e) =
+        Arg info <$> toAbstractHiding info e
+
+instance ToAbstract c => ToAbstract (Named name c) where
+    type AbsOfCon (Named name c) = Named name (AbsOfCon c)
+    toAbstract = traverse toAbstract
+
+instance ToAbstract c => ToAbstract (Ranged c) where
+    type AbsOfCon (Ranged c) = Ranged (AbsOfCon c)
+    toAbstract = traverse toAbstract
+
+{- DOES NOT WORK ANYMORE with pattern synonyms
+instance ToAbstract c a => ToAbstract (A.LHSCore' c) (A.LHSCore' a) where
+    toAbstract = mapM toAbstract
+-}
+
+instance ToAbstract (A.LHSCore' C.Expr) where
+    type AbsOfCon (A.LHSCore' C.Expr) = A.LHSCore' A.Expr
+    toAbstract (A.LHSHead f ps)         = A.LHSHead f <$> mapM toAbstract ps
+    toAbstract (A.LHSProj d lhscore ps) = A.LHSProj d <$> mapM toAbstract lhscore <*> mapM toAbstract ps
+    toAbstract (A.LHSWith core wps ps)  = liftA3 A.LHSWith (toAbstract core) (toAbstract wps) (toAbstract ps)
+
+-- Patterns are done in two phases. First everything but the dot patterns, and
+-- then the dot patterns. This is because dot patterns can refer to variables
+-- bound anywhere in the pattern.
+
+instance ToAbstract (A.Pattern' C.Expr) where
+  type AbsOfCon (A.Pattern' C.Expr) = A.Pattern' A.Expr
+  toAbstract = traverse $ insideDotPattern . toAbstractCtx DotPatternCtx  -- Issue #3033
+
+resolvePatternIdentifier
+  :: Bool -- ^ Is the identifier allowed to refer to a constructor (or
+          --   a pattern synonym)?
+  -> Range -> C.QName -> Maybe (Set A.Name) -> ScopeM (A.Pattern' C.Expr)
+resolvePatternIdentifier canBeConstructor r x ns = do
+  reportSLn "scope.pat" 60 $ "resolvePatternIdentifier " ++ prettyShow x ++ " at source position " ++ prettyShow r
+  px <- toAbstract (PatName x ns)
+  case px of
+    VarPatName y         -> do
+      reportSLn "scope.pat" 60 $ "  resolved to VarPatName " ++ prettyShow y ++ " with range " ++ prettyShow (getRange y)
+      return $ VarP $ A.mkBindName y
+    ConPatName ds ->
+      if canBeConstructor
+      then return $ ConP (ConPatInfo ConOCon (PatRange r) ConPatEager)
+                         (AmbQ $ fmap anameName ds) []
+      else err "constructor"
+    PatternSynPatName ds ->
+      if canBeConstructor
+      then return $ PatternSynP (PatRange r)
+                                (AmbQ $ fmap anameName ds) []
+      else err "pattern synonym"
+  where
+  err s =
+    setCurrentRange r $
+    typeError $ GenericError $
+      "A pun must not use the " ++ s ++ " " ++ prettyShow x
+
+-- | Apply an abstract syntax pattern head to pattern arguments.
+--
+--   Fails with 'InvalidPattern' if head is not a constructor pattern
+--   (or similar) that can accept arguments.
+--
+applyAPattern
+  :: C.Pattern            -- ^ The application pattern in concrete syntax.
+  -> A.Pattern' C.Expr    -- ^ Head of application.
+  -> NAPs C.Expr          -- ^ Arguments of application.
+  -> ScopeM (A.Pattern' C.Expr)
+applyAPattern p0 p ps = do
+  setRange (getRange p0) <$> do
+    case p of
+      A.ConP i x as        -> return $ A.ConP        i x (as ++ ps)
+      A.DefP i x as        -> return $ A.DefP        i x (as ++ ps)
+      A.PatternSynP i x as -> return $ A.PatternSynP i x (as ++ ps)
+      -- Dotted constructors are turned into "lazy" constructor patterns.
+      A.DotP i (Ident x)   -> resolveName x >>= \case
+        ConstructorName _ ds -> do
+          let cpi = ConPatInfo ConOCon i ConPatLazy
+              c   = AmbQ (fmap anameName ds)
+          return $ A.ConP cpi c ps
+        _ -> failure
+      A.DotP{}    -> failure
+      A.VarP{}    -> failure
+      A.ProjP{}   -> failure
+      A.WildP{}   -> failure
+      A.AsP{}     -> failure
+      A.AbsurdP{} -> failure
+      A.LitP{}    -> failure
+      A.RecP{}    -> failure
+      A.EqualP{}  -> failure
+      A.WithP{}   -> failure
+      A.AnnP{}    -> failure
+  where
+    failure = typeError $ InvalidPattern p0
+
+instance ToAbstract C.Pattern where
+    type AbsOfCon C.Pattern = A.Pattern' C.Expr
+
+    toAbstract (C.IdentP canBeConstructor x) =
+      resolvePatternIdentifier canBeConstructor (getRange x) x Nothing
+
+    toAbstract (AppP (QuoteP _) p)
+      | IdentP _ x <- namedArg p,
+        visible p = do
+      e <- toAbstract (OldQName x Nothing)
+      A.LitP (PatRange $ getRange x) . LitQName <$> quotedName e
+
+    toAbstract (QuoteP r) =
+      genericError "quote must be applied to an identifier"
+
+    toAbstract p0@(AppP p q) = do
+        reportSLn "scope.pat" 50 $ "distributeDots before = " ++ show p
+        p <- distributeDots p
+        reportSLn "scope.pat" 50 $ "distributeDots after  = " ++ show p
+        (p', q') <- toAbstract (p, q)
+        applyAPattern p0 p' $ singleton q'
+
+        where
+            distributeDots :: C.Pattern -> ScopeM C.Pattern
+            distributeDots p@(C.DotP r e) = distributeDotsExpr r e
+            distributeDots p = return p
+
+            distributeDotsExpr :: Range -> C.Expr -> ScopeM C.Pattern
+            distributeDotsExpr r e = parseRawApp e >>= \case
+              C.App r e a     ->
+                AppP <$> distributeDotsExpr r e
+                     <*> (traverse . traverse) (distributeDotsExpr r) a
+              OpApp r q ns as ->
+                case (traverse . traverse . traverse) fromNoPlaceholder as of
+                  Just as -> OpAppP r q ns <$>
+                    (traverse . traverse . traverse) (distributeDotsExpr r) as
+                  Nothing -> return $ C.DotP r e
+              Paren r e -> ParenP r <$> distributeDotsExpr r e
+              _ -> return $ C.DotP r e
+
+            fromNoPlaceholder :: MaybePlaceholder (OpApp a) -> Maybe a
+            fromNoPlaceholder (NoPlaceholder _ (Ordinary e)) = Just e
+            fromNoPlaceholder _ = Nothing
+
+            parseRawApp :: C.Expr -> ScopeM C.Expr
+            parseRawApp (RawApp r es) = parseApplication es
+            parseRawApp e             = return e
+
+    toAbstract p0@(OpAppP r op ns ps) = do
+        reportSLn "scope.pat" 60 $ "ConcreteToAbstract.toAbstract OpAppP{}: " ++ show p0
+        p  <- resolvePatternIdentifier True (getRange op) op (Just ns)
+        ps <- toAbstract ps
+        applyAPattern p0 p ps
+
+    toAbstract (EllipsisP _ mp) = maybe __IMPOSSIBLE__ toAbstract mp
+
+    -- Removed when parsing
+    toAbstract (HiddenP _ _)   = __IMPOSSIBLE__
+    toAbstract (InstanceP _ _) = __IMPOSSIBLE__
+    toAbstract (RawAppP _ _)   = __IMPOSSIBLE__
+
+    toAbstract p@(C.WildP r)    = return $ A.WildP (PatRange r)
+    -- Andreas, 2015-05-28 futile attempt to fix issue 819: repeated variable on lhs "_"
+    -- toAbstract p@(C.WildP r)    = A.VarP <$> freshName r "_"
+    toAbstract (C.ParenP _ p)   = toAbstract p
+    toAbstract (C.LitP r l)     = setCurrentRange r $ A.LitP (PatRange r) l <$ checkLiteral l
+
+    toAbstract p0@(C.AsP r x p) = do
+        -- Andreas, 2018-06-30, issue #3147: as-variables can be non-linear a priori!
+        -- x <- toAbstract (NewName PatternBound x)
+        -- Andreas, 2020-05-01, issue #4631: as-variables should not shadow constructors.
+        -- x <- bindPatternVariable x
+      toAbstract (PatName (C.QName x) Nothing) >>= \case
+        VarPatName x        -> A.AsP (PatRange r) (A.mkBindName x) <$> toAbstract p
+        ConPatName{}        -> ignoreAsPat False
+        PatternSynPatName{} -> ignoreAsPat True
+      where
+      -- An @-bound name which shadows a constructor is illegal and becomes dead code.
+      ignoreAsPat b = do
+        setCurrentRange x $ warning $ AsPatternShadowsConstructorOrPatternSynonym b
+        toAbstract p
+
+    toAbstract p0@(C.EqualP r es)  = return $ A.EqualP (PatRange r) es
+
+    -- We have to do dot patterns at the end since they can
+    -- refer to the variables bound by the other patterns.
+    toAbstract p0@(C.DotP r e) = do
+      let fallback = return $ A.DotP (PatRange r) e
+      case e of
+        C.Ident x -> resolveName x >>= \case
+          -- Andreas, 2018-06-19, #3130
+          -- We interpret .x as postfix projection if x is a field name in scope
+          FieldName xs -> return $ A.ProjP (PatRange r) ProjPostfix $ AmbQ $
+            fmap anameName xs
+          _ -> fallback
+        _ -> fallback
+
+    toAbstract p0@(C.AbsurdP r)    = return $ A.AbsurdP (PatRange r)
+    toAbstract (C.RecP r fs)       = A.RecP (PatRange r) <$> mapM (traverse toAbstract) fs
+    toAbstract (C.WithP r p)       = A.WithP (PatRange r) <$> toAbstract p
+
+-- | An argument @OpApp C.Expr@ to an operator can have binders,
+--   in case the operator is some @syntax@-notation.
+--   For these binders, we have to create lambda-abstractions.
+toAbstractOpArg :: Precedence -> OpApp C.Expr -> ScopeM A.Expr
+toAbstractOpArg ctx (Ordinary e)                 = toAbstractCtx ctx e
+toAbstractOpArg ctx (SyntaxBindingLambda r bs e) = toAbstractLam r bs e ctx
+
+-- | Turn an operator application into abstract syntax. Make sure to
+-- record the right precedences for the various arguments.
+toAbstractOpApp :: C.QName -> Set A.Name -> OpAppArgs -> ScopeM A.Expr
+toAbstractOpApp op ns es = do
+    -- Replace placeholders with bound variables.
+    (binders, es) <- replacePlaceholders es
+    -- Get the notation for the operator.
+    nota <- getNotation op ns
+    let parts = notation nota
+    -- We can throw away the @VarPart@s, since binders
+    -- have been preprocessed into @OpApp C.Expr@.
+    let nonBindingParts = filter (not . isBinder) parts
+    -- We should be left with as many holes as we have been given args @es@.
+    -- If not, crash.
+    unless (length (filter isAHole nonBindingParts) == length es) __IMPOSSIBLE__
+    -- Translate operator and its arguments (each in the right context).
+    op <- toAbstract (OldQName op (Just ns))
+    es <- left (notaFixity nota) nonBindingParts es
+    -- Prepend the generated section binders (if any).
+    let body = List.foldl' app op es
+    return $ foldr (A.Lam (ExprRange (getRange body))) body binders
+  where
+    -- Build an application in the abstract syntax, with correct Range.
+    app e (pref, arg) = A.App info e arg
+      where info = (defaultAppInfo r) { appOrigin = getOrigin arg
+                                      , appParens = pref }
+            r = fuseRange e arg
+
+    inferParenPref :: NamedArg (Either A.Expr (OpApp C.Expr)) -> ParenPreference
+    inferParenPref e =
+      case namedArg e of
+        Right (Ordinary e) -> inferParenPreference e
+        Left{}             -> PreferParenless  -- variable inserted by section expansion
+        Right{}            -> PreferParenless  -- syntax lambda
+
+    -- Translate an argument. Returns the paren preference for the argument, so
+    -- we can build the correct info for the A.App node.
+    toAbsOpArg :: Precedence ->
+                  NamedArg (Either A.Expr (OpApp C.Expr)) ->
+                  ScopeM (ParenPreference, NamedArg A.Expr)
+    toAbsOpArg cxt e = (pref,) <$> (traverse . traverse) (either return (toAbstractOpArg cxt)) e
+      where pref = inferParenPref e
+
+    -- The hole left to the first @IdPart@ is filled with an expression in @LeftOperandCtx@.
+    left f (IdPart _ : xs) es = inside f xs es
+    left f (_ : xs) (e : es) = do
+        e  <- toAbsOpArg (LeftOperandCtx f) e
+        es <- inside f xs es
+        return (e : es)
+    left f (_  : _)  [] = __IMPOSSIBLE__
+    left f []        _  = __IMPOSSIBLE__
+
+    -- The holes in between the @IdPart@s is filled with an expression in @InsideOperandCtx@.
+    inside f [x]          es    = right f x es
+    inside f (IdPart _ : xs) es = inside f xs es
+    inside f (_  : xs) (e : es) = do
+        e  <- toAbsOpArg InsideOperandCtx e
+        es <- inside f xs es
+        return (e : es)
+    inside _ (_ : _) [] = __IMPOSSIBLE__
+    inside _ []         _  = __IMPOSSIBLE__
+
+    -- The hole right of the last @IdPart@ is filled with an expression in @RightOperandCtx@.
+    right _ (IdPart _)  [] = return []
+    right f _          [e] = do
+        let pref = inferParenPref e
+        e <- toAbsOpArg (RightOperandCtx f pref) e
+        return [e]
+    right _ _     _  = __IMPOSSIBLE__
+
+    replacePlaceholders ::
+      OpAppArgs' e ->
+      ScopeM ([A.LamBinding], [NamedArg (Either A.Expr (OpApp e))])
+    replacePlaceholders []       = return ([], [])
+    replacePlaceholders (a : as) = case namedArg a of
+      NoPlaceholder _ x -> mapSnd (set (Right x) a :) <$>
+                             replacePlaceholders as
+      Placeholder _     -> do
+        x <- freshName noRange "section"
+        let i = setOrigin Inserted $ argInfo a
+        (ls, ns) <- replacePlaceholders as
+        return ( A.mkDomainFree (unnamedArg i $ A.mkBinder_ x) : ls
+               , set (Left (Var x)) a : ns
+               )
+      where
+      set :: a -> NamedArg b -> NamedArg a
+      set x arg = fmap (fmap (const x)) arg
+
+-- | Raises an error if the list of attributes contains an unsupported
+-- attribute.
+
+checkAttributes :: Attributes -> ScopeM ()
+checkAttributes []                     = return ()
+checkAttributes ((attr, r, s) : attrs) =
+  case attr of
+    RelevanceAttribute{}    -> cont
+    TacticAttribute{}       -> cont
+    LockAttribute IsNotLock -> cont
+    LockAttribute IsLock{}  -> do
+      unlessM (optGuarded <$> pragmaOptions) $
+        setCurrentRange r $ typeError $ AttributeKindNotEnabled "Lock" "--guarded" s
+      cont
+    QuantityAttribute Quantityω{} -> cont
+    QuantityAttribute Quantity1{} -> __IMPOSSIBLE__
+    QuantityAttribute Quantity0{} -> do
+      unlessM (optErasure <$> pragmaOptions) $
+        setCurrentRange r $ typeError $ AttributeKindNotEnabled "Erasure" "--erasure" s
+      cont
+    CohesionAttribute{} -> do
+      unlessM (optCohesion <$> pragmaOptions) $
+        setCurrentRange r $ typeError $ AttributeKindNotEnabled "Cohesion" "--cohesion" s
+      cont
+  where
+  cont = checkAttributes attrs
+
+{--------------------------------------------------------------------------
+    Things we parse but are not part of the Agda file syntax
+ --------------------------------------------------------------------------}
+
+-- | Content of interaction hole.
+
+instance ToAbstract C.HoleContent where
+  type AbsOfCon C.HoleContent = A.HoleContent
+  toAbstract = \case
+    HoleContentExpr e     -> HoleContentExpr <$> toAbstract e
+    HoleContentRewrite es -> HoleContentRewrite <$> toAbstract es
diff --git a/src/full/Agda/Syntax/Translation/InternalToAbstract.hs b/src/full/Agda/Syntax/Translation/InternalToAbstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Translation/InternalToAbstract.hs
@@ -0,0 +1,1559 @@
+{-# LANGUAGE NondecreasingIndentation   #-}
+
+{-|
+    Translating from internal syntax to abstract syntax. Enables nice
+    pretty printing of internal syntax.
+
+    TODO
+
+        - numbers on metas
+        - fake dependent functions to independent functions
+        - meta parameters
+        - shadowing
+-}
+module Agda.Syntax.Translation.InternalToAbstract
+  ( Reify(..)
+  , MonadReify
+  , NamedClause(..)
+  , reifyPatterns
+  , reifyUnblocked
+  , blankNotInScope
+  , reifyDisplayFormP
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Applicative ( liftA2 )
+import Control.Arrow       ( (&&&) )
+import Control.Monad       ( filterM, forM )
+
+import qualified Data.List as List
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.Semigroup ( Semigroup, (<>) )
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Text as T
+import Data.Traversable (mapM)
+
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Concrete (FieldAssignment'(..))
+import Agda.Syntax.Info as Info
+import Agda.Syntax.Abstract as A hiding (Binder)
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pattern
+import Agda.Syntax.Abstract.Pretty
+import Agda.Syntax.Abstract.UsedNames
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern as I
+import Agda.Syntax.Scope.Base (inverseScopeLookupName)
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import {-# SOURCE #-} Agda.TypeChecking.Records
+import Agda.TypeChecking.CompiledClause (CompiledClauses'(Fail))
+import Agda.TypeChecking.DisplayForm
+import Agda.TypeChecking.Level
+import {-# SOURCE #-} Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.SyntacticEquality
+import Agda.TypeChecking.Telescope
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+
+-- | Like @reify@ but instantiates blocking metas, useful for reporting.
+reifyUnblocked :: Reify i => i -> TCM (ReifiesTo i)
+reifyUnblocked t = locallyTCState stInstantiateBlocking (const True) $ reify t
+
+
+-- Composition of reified applications ------------------------------------
+--UNUSED Liang-Ting 2019-07-16
+---- | Drops hidden arguments unless --show-implicit.
+--napps :: Expr -> [NamedArg Expr] -> TCM Expr
+--napps e = nelims e . map I.Apply
+
+{-# SPECIALIZE apps :: Expr -> [Arg Expr] -> TCM Expr #-}
+-- | Drops hidden arguments unless --show-implicit.
+apps :: MonadReify m => Expr -> [Arg Expr] -> m Expr
+apps e = elims e . map I.Apply
+
+-- Composition of reified eliminations ------------------------------------
+
+{-# SPECIALIZE nelims :: Expr -> [I.Elim' (Named_ Expr)] -> TCM Expr #-}
+-- | Drops hidden arguments unless --show-implicit.
+nelims :: MonadReify m => Expr -> [I.Elim' (Named_ Expr)] -> m Expr
+nelims e [] = return e
+nelims e (I.IApply x y r : es) =
+  nelims (A.App defaultAppInfo_ e $ defaultArg r) es
+nelims e (I.Apply arg : es) = do
+  arg <- reify arg  -- This replaces the arg by _ if irrelevant
+  dontShowImp <- not <$> showImplicitArguments
+  let hd | notVisible arg && dontShowImp = e
+         | otherwise                     = A.App defaultAppInfo_ e arg
+  nelims hd es
+nelims e (I.Proj ProjPrefix d : es)             = nelimsProjPrefix e d es
+nelims e (I.Proj o          d : es) | isSelf e  = nelims (A.Proj ProjPrefix $ unambiguous d) es
+                                    | otherwise =
+  nelims (A.App defaultAppInfo_ e (defaultNamedArg $ A.Proj o $ unambiguous d)) es
+
+{-# SPECIALIZE nelimsProjPrefix :: Expr -> QName -> [I.Elim' (Named_ Expr)] -> TCM Expr #-}
+nelimsProjPrefix :: MonadReify m => Expr -> QName -> [I.Elim' (Named_ Expr)] -> m Expr
+nelimsProjPrefix e d es =
+  nelims (A.App defaultAppInfo_ (A.Proj ProjPrefix $ unambiguous d) $ defaultNamedArg e) es
+
+-- | If we are referencing the record from inside the record definition, we don't insert an
+-- | A.App
+isSelf :: Expr -> Bool
+isSelf = \case
+  A.Var n -> nameIsRecordName n
+  _ -> False
+
+{-# SPECIALIZE elims :: Expr -> [I.Elim' Expr] -> TCM Expr #-}
+-- | Drops hidden arguments unless --show-implicit.
+elims :: MonadReify m => Expr -> [I.Elim' Expr] -> m Expr
+elims e = nelims e . map (fmap unnamed)
+
+-- Omitting information ---------------------------------------------------
+
+noExprInfo :: ExprInfo
+noExprInfo = ExprRange noRange
+
+-- Conditional reification to omit terms that are not shown --------------
+
+{-# INLINE reifyWhenE #-}
+reifyWhenE :: (Reify i, MonadReify m, Underscore (ReifiesTo i)) => Bool -> i -> m (ReifiesTo i)
+reifyWhenE True  i = reify i
+reifyWhenE False t = return underscore
+
+-- Reification ------------------------------------------------------------
+
+type MonadReify m =
+  ( PureTCM m
+  , MonadInteractionPoints m
+  , MonadFresh NameId m
+  )
+
+class Reify i where
+    type ReifiesTo i
+
+    reify :: MonadReify m => i -> m (ReifiesTo i)
+
+    --   @reifyWhen False@ should produce an 'underscore'.
+    --   This function serves to reify hidden/irrelevant things.
+    reifyWhen :: MonadReify m => Bool -> i -> m (ReifiesTo i)
+    reifyWhen _ = reify
+
+instance Reify Bool where
+    type ReifiesTo Bool = Bool
+    reify = return
+
+instance Reify Char where
+    type ReifiesTo Char = Char
+    reify = return
+
+instance Reify Name where
+    type ReifiesTo Name = Name
+    reify = return
+
+instance Reify Expr where
+    type ReifiesTo Expr = Expr
+
+    reifyWhen = reifyWhenE
+    reify = return
+
+instance Reify MetaId where
+    type ReifiesTo MetaId = Expr
+
+    reifyWhen = reifyWhenE
+    reify x = do
+      b <- asksTC envPrintMetasBare
+      mi  <- mvInfo <$> lookupLocalMeta x
+      let mi' = Info.MetaInfo
+                 { metaRange          = getRange $ miClosRange mi
+                 , metaScope          = clScope $ miClosRange mi
+                 , metaNumber         = if b then Nothing else Just x
+                 , metaNameSuggestion = if b then "" else miNameSuggestion mi
+                 }
+          underscore = return $ A.Underscore mi'
+      -- If we are printing a term that will be pasted into the user
+      -- source, we turn all unsolved (non-interaction) metas into
+      -- interaction points
+      isInteractionMeta x >>= \case
+        Nothing | b -> do
+          ii <- registerInteractionPoint False noRange Nothing
+          connectInteractionPoint ii x
+          return $ A.QuestionMark mi' ii
+        Just ii | b -> underscore
+        Nothing     -> underscore
+        Just ii     -> return $ A.QuestionMark mi' ii
+{-# SPECIALIZE reify :: MetaId -> TCM (ReifiesTo MetaId) #-}
+
+instance Reify DisplayTerm where
+  type ReifiesTo DisplayTerm = Expr
+
+  reifyWhen = reifyWhenE
+  reify = \case
+    DTerm' v es       -> elims ==<< (reifyTerm False v, reify es)
+    DDot'  v es       -> elims ==<< (reify v, reify es)
+    DCon c ci vs      -> recOrCon (conName c) ci =<< reify vs
+    DDef f es         -> elims (A.Def f) =<< reify es
+    DWithApp u us es0 -> do
+      (e, es) <- reify (u, us)
+      elims (if null es then e else A.WithApp noExprInfo e es) =<< reify es0
+{-# SPECIALIZE reify :: DisplayTerm -> TCM (ReifiesTo DisplayTerm) #-}
+
+{-# SPECIALIZE reifyDisplayForm :: QName -> I.Elims -> TCM A.Expr -> TCM A.Expr #-}
+-- | @reifyDisplayForm f vs fallback@
+--   tries to rewrite @f vs@ with a display form for @f@.
+--   If successful, reifies the resulting display term,
+--   otherwise, does @fallback@.
+reifyDisplayForm :: MonadReify m => QName -> I.Elims -> m A.Expr -> m A.Expr
+reifyDisplayForm f es fallback =
+  ifNotM displayFormsEnabled fallback $ {- else -}
+    caseMaybeM (displayForm f es) fallback reify
+
+{-# SPECIALIZE reifyDisplayFormP :: QName -> A.Patterns -> A.Patterns -> TCM (QName, A.Patterns) #-}
+-- | @reifyDisplayFormP@ tries to recursively
+--   rewrite a lhs with a display form.
+--
+--   Note: we are not necessarily in the empty context upon entry!
+reifyDisplayFormP ::
+     forall m.
+     MonadReify m
+  => QName         -- ^ LHS head symbol
+  -> A.Patterns    -- ^ Patterns to be taken into account to find display form.
+  -> A.Patterns    -- ^ Remaining trailing patterns ("with patterns").
+  -> m (QName, A.Patterns) -- ^ New head symbol and new patterns.
+reifyDisplayFormP f ps wps = do
+  let fallback = return (f, ps ++ wps)
+  ifNotM displayFormsEnabled fallback $ {- else -} do
+    -- Try to rewrite @f 0 1 2 ... |ps|-1@ to a dt.
+    -- Andreas, 2014-06-11  Issue 1177:
+    -- I thought we need to add the placeholders for ps to the context,
+    -- because otherwise displayForm will not raise the display term
+    -- and we will have variable clashes.
+    -- But apparently, it has no influence...
+    -- Ulf, can you add an explanation?
+    md <- -- addContext (replicate (length ps) "x") $
+      displayForm f $ zipWith (\ p i -> I.Apply $ p $> I.var i) ps [0..]
+    reportSLn "reify.display" 60 $
+      "display form of " ++ prettyShow f ++ " " ++ show ps ++ " " ++ show wps ++ ":\n  " ++ show md
+    case md of
+      Just d  | okDisplayForm d -> do
+        -- In the display term @d@, @var i@ should be a placeholder
+        -- for the @i@th pattern of @ps@.
+        -- Andreas, 2014-06-11:
+        -- Are we sure that @d@ did not use @var i@ otherwise?
+        (f', ps', wps') <- displayLHS ps d
+        reportSDoc "reify.display" 70 $ do
+          doc <- prettyA $ SpineLHS empty f' (ps' ++ wps' ++ wps)
+          return $ vcat
+            [ "rewritten lhs to"
+            , "  lhs' = " <+> doc
+            ]
+        reifyDisplayFormP f' ps' (wps' ++ wps)
+      _ -> do
+        reportSLn "reify.display" 70 $ "display form absent or not valid as lhs"
+        fallback
+  where
+    -- Andreas, 2015-05-03: Ulf, please comment on what
+    -- is the idea behind okDisplayForm.
+    -- Ulf, 2016-04-15: okDisplayForm should return True if the display form
+    -- can serve as a valid left-hand side. That means checking that it is a
+    -- defined name applied to valid lhs eliminators (projections or
+    -- applications to constructor patterns).
+    okDisplayForm :: DisplayTerm -> Bool
+    okDisplayForm = \case
+      DWithApp d ds es ->
+        okDisplayForm d && all okDisplayTerm ds  && all okToDropE es
+        -- Andreas, 2016-05-03, issue #1950.
+        -- We might drop trailing hidden trivial (=variable) patterns.
+      DTerm' (I.Def f es') es -> all okElim es' && all okElim es
+      DDef f es               -> all okDElim es
+      DDot'{}                 -> False
+      DCon{}                  -> False
+      DTerm'{}                -> False
+
+    okDisplayTerm :: DisplayTerm -> Bool
+    okDisplayTerm = \case
+      DTerm' v es -> null es && okTerm v
+      DDot'{}     -> True
+      DCon{}      -> True
+      DDef{}      -> False
+      DWithApp{}  -> False
+
+    okDElim :: Elim' DisplayTerm -> Bool
+    okDElim (I.IApply x y r) = okDisplayTerm r
+    okDElim (I.Apply v) = okDisplayTerm $ unArg v
+    okDElim I.Proj{}    = True
+
+    okToDropE :: Elim' Term -> Bool
+    okToDropE (I.Apply v) = okToDrop v
+    okToDropE I.Proj{}    = False
+    okToDropE (I.IApply x y r) = False
+
+    okToDrop :: Arg I.Term -> Bool
+    okToDrop arg = notVisible arg && case unArg arg of
+      I.Var _ []   -> True
+      I.DontCare{} -> True  -- no matching on irrelevant things.  __IMPOSSIBLE__ anyway?
+      I.Level{}    -> True  -- no matching on levels. __IMPOSSIBLE__ anyway?
+      _ -> False
+
+    okArg :: Arg I.Term -> Bool
+    okArg = okTerm . unArg
+
+    okElim :: Elim' I.Term -> Bool
+    okElim (I.IApply x y r) = okTerm r
+    okElim (I.Apply a) = okArg a
+    okElim I.Proj{}  = True
+
+    okTerm :: I.Term -> Bool
+    okTerm (I.Var _ []) = True
+    okTerm (I.Con c ci vs) = all okElim vs
+    okTerm (I.Def x []) = isNoName $ qnameToConcrete x -- Handling wildcards in display forms
+    okTerm _            = False
+
+    -- Flatten a dt into (parentName, parentElims, withArgs).
+    flattenWith :: DisplayTerm -> (QName, [I.Elim' DisplayTerm], [I.Elim' DisplayTerm])
+    flattenWith (DWithApp d ds1 es2) =
+      let (f, es, ds0) = flattenWith d
+      in  (f, es, ds0 ++ map (I.Apply . defaultArg) ds1 ++ map (fmap DTerm) es2)
+    flattenWith (DDef f es) = (f, es, [])     -- .^ hacky, but we should only hit this when printing debug info
+    flattenWith (DTerm' (I.Def f es') es) = (f, map (fmap DTerm) $ es' ++ es, [])
+    flattenWith _ = __IMPOSSIBLE__
+
+    displayLHS
+      :: MonadReify m
+      => A.Patterns   -- Patterns to substituted into display term.
+      -> DisplayTerm  -- Display term.
+      -> m (QName, A.Patterns, A.Patterns)  -- New head, patterns, with-patterns.
+    displayLHS ps d = do
+        let (f, vs, es) = flattenWith d
+        ps  <- mapM elimToPat vs
+        wps <- mapM (updateNamedArg (A.WithP empty) <.> elimToPat) es
+        return (f, ps, wps)
+      where
+        argToPat :: MonadReify m => Arg DisplayTerm -> m (NamedArg A.Pattern)
+        argToPat arg = traverse termToPat arg
+
+        elimToPat :: MonadReify m => I.Elim' DisplayTerm -> m (NamedArg A.Pattern)
+        elimToPat (I.IApply _ _ r) = argToPat (Arg defaultArgInfo r)
+        elimToPat (I.Apply arg) = argToPat arg
+        elimToPat (I.Proj o d)  = return $ defaultNamedArg $ A.ProjP patNoRange o $ unambiguous d
+
+        -- Substitute variables in display term by patterns.
+        termToPat :: MonadReify m => DisplayTerm -> m (Named_ A.Pattern)
+
+        -- Main action HERE:
+        termToPat (DTerm (I.Var n [])) =
+          return $ unArg $ fromMaybe __IMPOSSIBLE__ $ ps !!! n
+
+        termToPat (DCon c ci vs)          = fmap unnamed <$> tryRecPFromConP =<< do
+           A.ConP (ConPatInfo ci patNoRange ConPatEager) (unambiguous (conName c)) <$> mapM argToPat vs
+
+        termToPat (DTerm' (I.Con c ci vs) es) = fmap unnamed <$> tryRecPFromConP =<< do
+           A.ConP (ConPatInfo ci patNoRange ConPatEager) (unambiguous (conName c)) <$>
+             mapM (elimToPat . fmap DTerm) (vs ++ es)
+
+        termToPat (DTerm (I.Def _ [])) = return $ unnamed $ A.WildP patNoRange
+        termToPat (DDef _ [])          = return $ unnamed $ A.WildP patNoRange
+
+        termToPat (DTerm (I.Lit l))    = return $ unnamed $ A.LitP patNoRange l
+
+        termToPat (DDot' v es) =
+          unnamed . A.DotP patNoRange <$> do elims ==<< (termToExpr v, reify es)
+
+        termToPat v =
+          unnamed . A.DotP patNoRange <$> reify v
+
+        len = length ps
+
+        argsToExpr :: MonadReify m => I.Args -> m [Arg A.Expr]
+        argsToExpr = mapM (traverse termToExpr)
+
+        -- TODO: restructure this to avoid having to repeat the code for reify
+        termToExpr :: MonadReify m => Term -> m A.Expr
+        termToExpr v = do
+          reportSLn "reify.display" 60 $ "termToExpr " ++ show v
+          -- After unSpine, a Proj elimination is __IMPOSSIBLE__!
+          case unSpine v of
+            I.Con c ci es -> do
+              let vs = fromMaybe __IMPOSSIBLE__ $ mapM isApplyElim es
+              apps (A.Con (unambiguous (conName c))) =<< argsToExpr vs
+            I.Def f es -> do
+              let vs = fromMaybe __IMPOSSIBLE__ $ mapM isApplyElim es
+              apps (A.Def f) =<< argsToExpr vs
+            I.Var n es -> do
+              let vs = fromMaybe __IMPOSSIBLE__ $ mapM isApplyElim es
+              -- Andreas, 2014-06-11  Issue 1177
+              -- due to β-normalization in substitution,
+              -- even the pattern variables @n < len@ can be
+              -- applied to some args @vs@.
+              e <- if n < len
+                   then return $ A.patternToExpr $ namedArg $ indexWithDefault __IMPOSSIBLE__ ps n
+                   else reify (I.var (n - len))
+              apps e =<< argsToExpr vs
+            _ -> return underscore
+
+instance Reify Literal where
+  type ReifiesTo Literal = Expr
+
+  reifyWhen = reifyWhenE
+  reify l = return $ A.Lit empty l; {-# INLINE reify #-}
+
+instance Reify Term where
+  type ReifiesTo Term = Expr
+
+  reifyWhen = reifyWhenE
+  reify v = reifyTerm True v; {-# INLINE reify #-}
+
+{-# SPECIALIZE reifyPathPConstAsPath :: QName -> Elims -> TCM (QName, Elims) #-}
+reifyPathPConstAsPath :: MonadReify m => QName -> Elims -> m (QName, Elims)
+reifyPathPConstAsPath x es@[I.Apply l, I.Apply t, I.Apply lhs, I.Apply rhs] = do
+   reportSLn "reify.def" 100 $ "reifying def path " ++ show (x,es)
+   mpath  <- getBuiltinName' builtinPath
+   mpathp <- getBuiltinName' builtinPathP
+   let fallback = return (x,es)
+   case (,) <$> mpath <*> mpathp of
+     Just (path,pathp) | x == pathp -> do
+       let a = case unArg t of
+                I.Lam _ (NoAbs _ b)    -> Just b
+                I.Lam _ (Abs   _ b)
+                  | not $ 0 `freeIn` b -> Just (strengthen impossible b)
+                _                      -> Nothing
+       case a of
+         Just a -> return (path, [I.Apply l, I.Apply (setHiding Hidden $ defaultArg a), I.Apply lhs, I.Apply rhs])
+         Nothing -> fallback
+     _ -> fallback
+reifyPathPConstAsPath x es = return (x,es)
+
+{-# SPECIALIZE tryReifyAsLetBinding :: Term -> TCM Expr -> TCM Expr #-}
+-- | Check if the term matches an existing let-binding, in that case use the corresponding variable,
+--   otherwise reify using the continuation.
+tryReifyAsLetBinding :: MonadReify m => Term -> m Expr -> m Expr
+tryReifyAsLetBinding v fallback = ifM (asksTC $ not . envFoldLetBindings) fallback $ do
+  letBindings <- do
+    binds  <- asksTC (Map.toAscList . envLetBindings)
+    opened <- forM binds $ \ (name, open) -> (,name) <$> getOpen open
+    return [ (body, name) | (LetBinding UserWritten body _, name) <- opened, not $ isNoName name ]  -- Only fold user-written lets
+  matchingBindings <- filterM (\t -> checkSyntacticEquality v (fst t) (\_ _ -> return True) (\_ _ -> return False)) letBindings
+  case matchingBindings of
+    (_, name) : _ -> return $ A.Var name
+    []            -> fallback
+
+{-# SPECIALIZE reifyTerm :: Bool -> Term -> TCM Expr #-}
+reifyTerm ::
+      MonadReify m
+   => Bool           -- ^ Try to expand away anonymous definitions?
+   -> Term
+   -> m Expr
+reifyTerm expandAnonDefs0 v0 = tryReifyAsLetBinding v0 $ do
+  -- Jesper 2018-11-02: If 'PrintMetasBare', drop all meta eliminations.
+  metasBare <- asksTC envPrintMetasBare
+  reportSDoc "reify.term" 80 $ pure $ "reifyTerm v0 = " <+> pretty v0
+  v <- instantiate v0 >>= \case
+    I.MetaV x _ | metasBare -> return $ I.MetaV x []
+    v -> return v
+  reportSDoc "reify.term" 80 $ pure $ "reifyTerm v = " <+> pretty v
+  -- Ulf 2014-07-10: Don't expand anonymous when display forms are disabled
+  -- (i.e. when we don't care about nice printing)
+  expandAnonDefs <- return expandAnonDefs0 `and2M` displayFormsEnabled
+  -- Andreas, 2016-07-21 if --postfix-projections
+  -- then we print system-generated projections as postfix, else prefix.
+  havePfp <- optPostfixProjections <$> pragmaOptions
+  let pred = if havePfp then (== ProjPrefix) else (/= ProjPostfix)
+  reportSDoc "reify.term" 80 $ pure $ "reifyTerm (unSpine v) = " <+> pretty (unSpine' pred v)
+  case unSpine' pred v of
+    -- Hack to print generalized field projections with nicer names. Should
+    -- only show up in errors. Check the spined form!
+    _ | I.Var n (I.Proj _ p : es) <- v,
+        Just name <- getGeneralizedFieldName p -> do
+      let fakeName = (qnameName p) {nameConcrete = C.simpleName name} -- TODO: infix names!?
+      elims (A.Var fakeName) =<< reify es
+    I.Var n es -> do
+      x <- fromMaybeM (freshName_ $ "@" ++ show n) $ nameOfBV' n
+      elims (A.Var x) =<< reify es
+    I.Def x es -> do
+      reportSDoc "reify.def" 80 $ return $ "reifying def" <+> pretty x
+      (x, es) <- reifyPathPConstAsPath x es
+      reifyDisplayForm x es $ reifyDef expandAnonDefs x es
+    I.Con c ci vs -> do
+      let x = conName c
+      isR <- isGeneratedRecordConstructor x
+      if isR || ci == ConORec
+        then do
+          showImp <- showImplicitArguments
+          let keep (a, v) = showImp || visible a
+          r <- getConstructorData x
+          xs <- fromMaybe __IMPOSSIBLE__ <$> getRecordFieldNames_ r
+          vs <- map unArg <$> reify (fromMaybe __IMPOSSIBLE__ $ allApplyElims vs)
+          return $ A.Rec noExprInfo $ map (Left . uncurry FieldAssignment . mapFst unDom) $ filter keep $ zip xs vs
+        else reifyDisplayForm x vs $ do
+          def <- getConstInfo x
+          let Constructor {conPars = np} = theDef def
+          -- if we are the the module that defines constructor x
+          -- then we have to drop at least the n module parameters
+          n <- getDefFreeVars x
+          -- the number of parameters is greater (if the data decl has
+          -- extra parameters) or equal (if not) to n
+          when (n > np) __IMPOSSIBLE__
+          let h = A.Con (unambiguous x)
+          if null vs
+            then return h
+            else do
+              es <- reify (map (fromMaybe __IMPOSSIBLE__ . isApplyElim) vs)
+              -- Andreas, 2012-04-20: do not reify parameter arguments of constructor
+              -- if the first regular constructor argument is hidden
+              -- we turn it into a named argument, in order to avoid confusion
+              -- with the parameter arguments which can be supplied in abstract syntax
+              --
+              -- Andreas, 2012-09-17: this does not remove all sources of confusion,
+              -- since parameters could have the same name as regular arguments
+              -- (see for example the parameter {i} to Data.Star.Star, which is also
+              -- the first argument to the cons).
+              -- @data Star {i}{I : Set i} ... where cons : {i :  I} ...@
+              if np == 0
+                then apps h es
+                else do
+                  -- Get name of first argument from type of constructor.
+                  -- Here, we need the reducing version of @telView@
+                  -- because target of constructor could be a definition
+                  -- expanding into a function type.  See test/succeed/NameFirstIfHidden.agda.
+                  TelV tel _ <- telView (defType def)
+                  let (pars, rest) = splitAt np $ telToList tel
+                  case rest of
+                    -- Andreas, 2012-09-18
+                    -- If the first regular constructor argument is hidden,
+                    -- we keep the parameters to avoid confusion.
+                    (Dom {domInfo = info} : _) | notVisible info -> do
+                      let us = for (drop n pars) $ \(Dom {domInfo = ai}) ->
+                            -- setRelevance Relevant $
+                            hideOrKeepInstance $ Arg ai underscore
+                      apps h $ us ++ es -- Note: unless --show-implicit, @apps@ will drop @us@.
+                    -- otherwise, we drop all parameters
+                    _ -> apps h es
+
+--    I.Lam info b | isAbsurdBody b -> return $ A. AbsurdLam noExprInfo $ getHiding info
+    I.Lam info b    -> do
+      (x,e) <- reify b
+      -- #4160: Hacky solution: if --show-implicit, treat all lambdas as user-written. This will
+      -- prevent them from being dropped by AbstractToConcrete (where we don't have easy access to
+      -- the --show-implicit flag.
+      info <- ifM showImplicitArguments (return $ setOrigin UserWritten info) (return info)
+      return $ A.Lam exprNoRange (mkDomainFree $ unnamedArg info $ mkBinder_ x) e
+      -- Andreas, 2011-04-07 we do not need relevance information at internal Lambda
+    I.Lit l        -> reify l
+    I.Level l      -> reify l
+    I.Pi a b       -> case b of
+        NoAbs _ b'
+          | visible a, not (domIsFinite a) -> uncurry (A.Fun $ noExprInfo) <$> reify (a, b')
+            -- Andreas, 2013-11-11 Hidden/Instance I.Pi must be A.Pi
+            -- since (a) the syntax {A} -> B or {{A}} -> B is not legal
+            -- and (b) the name of the binder might matter.
+            -- See issue 951 (a) and 952 (b).
+            --
+            -- Amy, 2022-09-05: Can't be finite either, since otherwise
+            -- we say ".(IsOne φ) → A ≠ .(IsOne φ) → A" with no
+            -- indication of which is finite and which isn't
+          | otherwise   -> mkPi b =<< reify a
+        b               -> mkPi b =<< do
+          ifM (domainFree a (absBody b))
+            {- then -} (pure $ Arg (domInfo a) underscore)
+            {- else -} (reify a)
+      where
+        mkPi b (Arg info a') = ifM (skipGeneralizedParameter info) (snd <$> reify b) $ do
+          tac <- traverse (Ranged noRange <.> reify) $ domTactic a
+          (x, b) <- reify b
+          let xs = singleton $ Arg info $ Named (domName a) $ mkBinder_ x
+          return $ A.Pi noExprInfo
+            (singleton $ TBind noRange (TypedBindingInfo tac (domIsFinite a)) xs a')
+            b
+        -- We can omit the domain type if it doesn't have any free variables
+        -- and it's mentioned in the target type.
+        domainFree a b = do
+          df <- asksTC envPrintDomainFreePi
+          return $ df && freeIn 0 b && closed a
+
+        skipGeneralizedParameter :: MonadReify m => ArgInfo -> m Bool
+        skipGeneralizedParameter info = (not <$> showGeneralizedArguments) <&> (&& (argInfoOrigin info == Generalization))
+
+    I.Sort s     -> reify s
+    I.MetaV x es -> do
+          x' <- reify x
+
+          es' <- reify es
+
+          mv <- lookupLocalMeta x
+          (msub1,meta_tel,msub2) <- do
+            local_chkpt <- viewTC eCurrentCheckpoint
+            (chkpt, tel, msub2) <- enterClosure mv $ \ _ ->
+                               (,,) <$> viewTC eCurrentCheckpoint
+                                    <*> getContextTelescope
+                                    <*> viewTC (eCheckpoints . key local_chkpt)
+            (,,) <$> viewTC (eCheckpoints . key chkpt) <*> pure tel <*> pure msub2
+
+          opt_show_ids <- showIdentitySubstitutions
+          let
+              addNames []    es = map (fmap unnamed) es
+              addNames _     [] = []
+              addNames xs     (I.Proj{} : _) = __IMPOSSIBLE__
+              addNames xs     (I.IApply x y r : es) =
+                -- Needs to be I.Apply so it can have an Origin field.
+                addNames xs (I.Apply (defaultArg r) : es)
+              addNames (x:xs) (I.Apply arg : es) =
+                I.Apply (Named (Just x) <$> (setOrigin Substitution arg)) : addNames xs es
+
+              p = mvPermutation mv
+              applyPerm p vs = permute (takeP (size vs) p) vs
+
+              names = map (WithOrigin Inserted . unranged) $ p `applyPerm` teleNames meta_tel
+              named_es' = addNames names es'
+
+              dropIdentitySubs sub_local2G sub_tel2G =
+                 let
+                     args_G = applySubst sub_tel2G $ p `applyPerm` (teleArgs meta_tel :: [Arg Term])
+                     es_G = sub_local2G `applySubst` es
+                     sameVar x (I.Apply y) = isJust xv && xv == deBruijnView (unArg y)
+                      where
+                       xv = deBruijnView $ unArg x
+                     sameVar _ _ = False
+                     dropArg = take (size names) $ zipWith sameVar args_G es_G
+                     doDrop (b : xs)  (e : es) = (if b then id else (e :)) $ doDrop xs es
+                     doDrop []        es = es
+                     doDrop _         [] = []
+                 in doDrop dropArg $ named_es'
+
+              simpl_named_es' | opt_show_ids                 = named_es'
+                              | Just sub_mtel2local <- msub1 = dropIdentitySubs IdS           sub_mtel2local
+                              | Just sub_local2mtel <- msub2 = dropIdentitySubs sub_local2mtel IdS
+                              | otherwise                    = named_es'
+
+          nelims x' simpl_named_es'
+
+    I.DontCare v -> do
+      showIrr <- optShowIrrelevant <$> pragmaOptions
+      if | showIrr   -> reifyTerm expandAnonDefs v
+         | otherwise -> return underscore
+    I.Dummy s [] -> return $ A.Lit empty $ LitString (T.pack s)
+    I.Dummy "applyE" es | I.Apply (Arg _ h) : es' <- es -> do
+                            h <- reify h
+                            es' <- reify es'
+                            elims h es'
+                        | otherwise -> __IMPOSSIBLE__
+    I.Dummy s es -> do
+      s <- reify (I.Dummy s [])
+      es <- reify es
+      elims s es
+  where
+    -- Andreas, 2012-10-20  expand a copy if not in scope
+    -- to improve error messages.
+    -- Don't do this if we have just expanded into a display form,
+    -- otherwise we loop!
+    reifyDef :: MonadReify m => Bool -> QName -> I.Elims -> m Expr
+    reifyDef True x es =
+      ifM (not . null . inverseScopeLookupName x <$> getScope) (reifyDef' x es) $ do
+      r <- reduceDefCopy x es
+      case r of
+        YesReduction _ v -> do
+          reportS "reify.anon" 60
+            [ "reduction on defined ident. in anonymous module"
+            , "x = " ++ prettyShow x
+            , "v = " ++ show v
+            ]
+          reify v
+        NoReduction () -> do
+          reportS "reify.anon" 60
+            [ "no reduction on defined ident. in anonymous module"
+            , "x  = " ++ prettyShow x
+            , "es = " ++ show es
+            ]
+          reifyDef' x es
+    reifyDef _ x es = reifyDef' x es
+
+    reifyDef' :: MonadReify m => QName -> I.Elims -> m Expr
+    reifyDef' x es = do
+      reportSLn "reify.def" 60 $ "reifying call to " ++ prettyShow x
+      -- We should drop this many arguments from the local context.
+      n <- getDefFreeVars x
+      reportSLn "reify.def" 70 $ "freeVars for " ++ prettyShow x ++ " = " ++ show n
+      -- If the definition is not (yet) in the signature,
+      -- we just do the obvious.
+      let fallback _ = elims (A.Def x) =<< reify (drop n es)
+      caseEitherM (getConstInfo' x) fallback $ \ defn -> do
+      let def = theDef defn
+
+      -- Check if we have an absurd lambda.
+      case def of
+       Function{ funCompiled = Just Fail{}, funClauses = [cl] }
+          | isAbsurdLambdaName x -> do
+                  -- get hiding info from last pattern, which should be ()
+                  let (ps, p) = fromMaybe __IMPOSSIBLE__ $ initLast $ namedClausePats cl
+                  let h = getHiding p
+                      n = length ps  -- drop all args before the absurd one
+                      absLam = A.AbsurdLam exprNoRange h
+                  if | n > length es -> do -- We don't have all arguments before the absurd one!
+                        let name (I.VarP _ x) = patVarNameToString $ dbPatVarName x
+                            name _            = __IMPOSSIBLE__  -- only variables before absurd pattern
+                            vars = map (getArgInfo &&& name . namedArg) $ drop (length es) ps
+                            lam (i, s) = do
+                              x <- freshName_ s
+                              return $ A.Lam exprNoRange (A.mkDomainFree $ unnamedArg i $ A.mkBinder_ x)
+                        foldr ($) absLam <$> mapM lam vars
+                      | otherwise -> elims absLam =<< reify (drop n es)
+
+      -- Otherwise (no absurd lambda):
+       _ -> do
+
+        -- Andrea(s), 2016-07-06
+        -- Extended lambdas are not considered to be projection like,
+        -- as they are mutually recursive with their parent.
+        -- Thus we do not have to consider padding them.
+
+        -- Check whether we have an extended lambda and display forms are on.
+        df <- displayFormsEnabled
+
+        -- #3004: give up if we have to print a pattern lambda inside its own body!
+        alreadyPrinting <- viewTC ePrintingPatternLambdas
+
+        extLam <- case def of
+          Function{ funExtLam = Just{}, funProjection = Right{} } -> __IMPOSSIBLE__
+          Function{ funExtLam = Just (ExtLamInfo m b sys) } ->
+            Just . (,Strict.toLazy sys) . size <$> lookupSection m
+          _ -> return Nothing
+
+        -- Amy, 2023-04-12: Don't reify clauses generated by the cubical
+        -- coverage checker when printing an extended lambda. We can
+        -- identify these clauses by looking for patterns headed by DefP
+        -- (either transpX or hcomp associated with a data type).
+        --
+        -- Since these are always automatically derived, printing them
+        -- is noise, and shows up even in non-cubical modules, as long
+        -- as an imported extended lambda is defined cubical-compatibly.
+        let insClause = hasDefP . namedClausePats
+        case extLam of
+          Just (pars, sys) | df, x `notElem` alreadyPrinting ->
+            locallyTC ePrintingPatternLambdas (x :) $
+            reifyExtLam x (defArgInfo defn) pars sys
+              (filter (not . insClause) (defClauses defn)) es
+
+        -- Otherwise (ordinary function call):
+          _ -> do
+           (pad, nes :: [Elim' (Named_ Term)]) <- case def of
+
+            Function{ funProjection = Right Projection{ projIndex = np } } | np > 0 -> do
+              reportSLn "reify.def" 70 $ "  def. is a projection with projIndex = " ++ show np
+
+              -- This is tricky:
+              --  * getDefFreeVars x tells us how many arguments
+              --    are part of the local context
+              --  * some of those arguments might have been dropped
+              --    due to projection likeness
+              --  * when showImplicits is on we'd like to see the dropped
+              --    projection arguments
+
+              TelV tel _ <- telViewUpTo np (defType defn)
+              let (as, rest) = splitAt (np - 1) $ telToList tel
+                  dom = headWithDefault __IMPOSSIBLE__ rest
+
+              -- These are the dropped projection arguments
+              scope <- getScope
+              let underscore = A.Underscore $ Info.emptyMetaInfo { metaScope = scope }
+              let pad :: [NamedArg Expr]
+                  pad = for as $ \ (Dom{domInfo = ai, unDom = (x, _)}) ->
+                    Arg ai $ Named (Just $ WithOrigin Inserted $ unranged x) underscore
+                      -- TODO #3353 Origin from Dom?
+
+              -- Now pad' ++ es' = drop n (pad ++ es)
+              let pad' = drop n pad
+                  es'  = drop (max 0 (n - size pad)) es
+              -- Andreas, 2012-04-21: get rid of hidden underscores {_} and {{_}}
+              -- Keep non-hidden arguments of the padding.
+              --
+              -- Andreas, 2016-12-20, issue #2348:
+              -- Let @padTail@ be the list of arguments of the padding
+              -- (*) after the last visible argument of the padding, and
+              -- (*) with the same visibility as the first regular argument.
+              -- If @padTail@ is not empty, we need to
+              -- print the first regular argument with name.
+              -- We further have to print all elements of @padTail@
+              -- which have the same name and visibility of the
+              -- first regular argument.
+              showImp <- showImplicitArguments
+
+              -- Get the visible arguments of the padding and the rest
+              -- after the last visible argument.
+              let (padVisNamed, padRest) = filterAndRest visible pad'
+
+              -- Remove the names from the visible arguments.
+              let padVis  = map (fmap $ unnamed . namedThing) padVisNamed
+
+              -- Keep only the rest with the same visibility of @dom@...
+              let padTail = filter (sameHiding dom) padRest
+
+              -- ... and even the same name.
+              let padSame = filter ((Just (fst $ unDom dom) ==) . bareNameOf) padTail
+
+              return $ if null padTail || not showImp
+                then (padVis           , map (fmap unnamed) es')
+                else (padVis ++ padSame, nameFirstIfHidden dom es')
+
+            -- If it is not a projection(-like) function, we need no padding.
+            _ -> return ([], map (fmap unnamed) $ drop n es)
+
+           reportSDoc "reify.def" 100 $ return $ vcat
+             [ "  pad =" <+> pshow pad
+             , "  nes =" <+> pshow nes
+             ]
+           let hd0 | isProperProjection def = A.Proj ProjPrefix $ AmbQ $ singleton x
+                   | otherwise = A.Def x
+           let hd = List.foldl' (A.App defaultAppInfo_) hd0 pad
+           nelims hd =<< reify nes
+
+    -- Andreas, 2016-07-06 Issue #2047
+
+    -- With parameter refinement, the "parameter" patterns of an extended
+    -- lambda can now be different from variable patterns.  If we just drop
+    -- them (plus the associated arguments to the extended lambda), we produce
+    -- something
+
+    -- i) that violates internal invariants.  In particular, the permutation
+    -- dbPatPerm from the patterns to the telescope can no longer be
+    -- computed.  (And in fact, dropping from the start of the telescope is
+    -- just plainly unsound then.)
+
+    -- ii) prints the wrong thing (old fix for #2047)
+
+    -- What we do now, is more sound, although not entirely satisfying:
+    -- When the "parameter" patterns of an external lambdas are not variable
+    -- patterns, we fall back to printing the internal function created for the
+    -- extended lambda, instead trying to construct the nice syntax.
+
+    reifyExtLam
+      :: MonadReify m
+      => QName -> ArgInfo -> Int -> Maybe System -> [I.Clause]
+      -> I.Elims -> m Expr
+    reifyExtLam x ai npars msys cls es = do
+      reportSLn "reify.def" 10 $ "reifying extended lambda " ++ prettyShow x
+      reportSLn "reify.def" 50 $ render $ nest 2 $ vcat
+        [ "npars =" <+> pretty npars
+        , "es    =" <+> fsep (map (prettyPrec 10) es)
+        , "def   =" <+> vcat (map pretty cls) ]
+      -- As extended lambda clauses live in the top level, we add the whole
+      -- section telescope to the number of parameters.
+      let (pares, rest) = splitAt npars es
+      let pars = fromMaybe __IMPOSSIBLE__ $ allApplyElims pares
+
+      -- Since we applying the clauses to the parameters,
+      -- we do not need to drop their initial "parameter" patterns
+      -- (this is taken care of by @apply@).
+      cls <- caseMaybe msys
+               (mapM (reify . NamedClause x False . (`apply` pars)) cls)
+               (reify . QNamed x . (`apply` pars))
+      let cx     = nameConcrete $ qnameName x
+          dInfo  = mkDefInfo cx noFixity' PublicAccess ConcreteDef
+                     (getRange x)
+          erased = case getQuantity ai of
+            Quantity0 o -> Erased o
+            Quantityω o -> NotErased o
+            Quantity1 o -> __IMPOSSIBLE__
+          lam = case cls of
+            []       -> A.AbsurdLam exprNoRange NotHidden
+            (cl:cls) -> A.ExtendedLam exprNoRange dInfo erased x (cl :| cls)
+      elims lam =<< reify rest
+
+-- | @nameFirstIfHidden (x:a) ({e} es) = {x = e} es@
+nameFirstIfHidden :: Dom (ArgName, t) -> [Elim' a] -> [Elim' (Named_ a)]
+nameFirstIfHidden dom (I.Apply (Arg info e) : es) | notVisible info =
+  I.Apply (Arg info (Named (Just $ WithOrigin Inserted $ unranged $ fst $ unDom dom) e)) :
+  map (fmap unnamed) es
+nameFirstIfHidden _ es =
+  map (fmap unnamed) es
+
+instance Reify i => Reify (Named n i) where
+  type ReifiesTo (Named n i) = Named n (ReifiesTo i)
+
+  reify = traverse reify
+  reifyWhen b = traverse (reifyWhen b)
+
+-- | Skip reification of implicit and irrelevant args if option is off.
+instance Reify i => Reify (Arg i) where
+  type ReifiesTo (Arg i) = Arg (ReifiesTo i)
+
+  reify (Arg info i) = Arg info <$> (flip reifyWhen i =<< condition)
+    where condition = (return (argInfoHiding info /= Hidden) `or2M` showImplicitArguments)
+              `and2M` (return (getRelevance info /= Irrelevant) `or2M` showIrrelevantArguments)
+  reifyWhen b i = traverse (reifyWhen b) i
+{-# SPECIALIZE reify :: Reify i => Arg i -> TCM (ReifiesTo (Arg i)) #-}
+
+-- instance Reify Elim Expr where
+--   reifyWhen = reifyWhenE
+--   reify = \case
+--     I.IApply x y r -> appl "iapply" <$> reify (defaultArg r :: Arg Term)
+--     I.Apply v -> appl "apply" <$> reify v
+--     I.Proj f  -> appl "proj"  <$> reify ((defaultArg $ I.Def f []) :: Arg Term)
+--     where
+--       appl :: String -> Arg Expr -> Expr
+--       appl s v = A.App exprInfo (A.Lit empty (LitString s)) $ fmap unnamed v
+
+data NamedClause = NamedClause QName Bool I.Clause
+  -- ^ Also tracks whether module parameters should be dropped from the patterns.
+
+-- The Monoid instance for Data.Map doesn't require that the values are a
+-- monoid.
+newtype MonoidMap k v = MonoidMap { _unMonoidMap :: Map.Map k v }
+
+instance (Ord k, Monoid v) => Semigroup (MonoidMap k v) where
+  MonoidMap m1 <> MonoidMap m2 = MonoidMap (Map.unionWith mappend m1 m2)
+
+instance (Ord k, Monoid v) => Monoid (MonoidMap k v) where
+  mempty = MonoidMap Map.empty
+  mappend = (<>)
+
+-- | Removes argument names.  Preserves names present in the source.
+removeNameUnlessUserWritten :: (LensNamed a, LensOrigin (NameOf a)) => a -> a
+removeNameUnlessUserWritten a
+  | (getOrigin <$> getNameOf a) == Just UserWritten = a
+  | otherwise = setNameOf Nothing a
+
+{-# SPECIALIZE stripImplicits :: Set Name  -> A.Patterns -> A.Patterns -> TCM A.Patterns #-}
+-- | Removes implicit arguments that are not needed, that is, that don't bind
+--   any variables that are actually used and doesn't do pattern matching.
+--   Doesn't strip any arguments that were written explicitly by the user.
+stripImplicits :: MonadReify m
+  => Set Name -- ^ Variables to always include (occurs on RHS of clause)
+  -> A.Patterns -> A.Patterns -> m A.Patterns
+stripImplicits toKeep params ps = do
+  -- if --show-implicit we don't need the names
+  ifM showImplicitArguments (return $ map (fmap removeNameUnlessUserWritten) ps) $ do
+    reportSDoc "reify.implicit" 100 $ return $ vcat
+      [ "stripping implicits"
+      , nest 2 $ "ps   =" <+> pshow ps
+      ]
+    let ps' = blankDots $ strip ps
+    reportSDoc "reify.implicit" 100 $ return $ vcat
+      [ nest 2 $ "ps'  =" <+> pshow ps'
+      ]
+    return ps'
+    where
+      -- Replace variables in dot patterns by an underscore _ if they are hidden
+      -- in the pattern. This is slightly nicer than making the implicts explicit.
+      blankDots ps = blank (varsBoundIn $ params ++ ps) ps
+
+      strip ps = stripArgs True ps
+        where
+          stripArgs _ [] = []
+          stripArgs fixedPos (a : as)
+            -- A hidden non-UserWritten variable is removed if not needed for
+            -- correct position of the following hidden arguments.
+            | canStrip a =
+                 if   all canStrip $ takeWhile isUnnamedHidden as
+                 then stripArgs False as
+                 else goWild
+            -- Other arguments are kept.
+            | otherwise = stripName fixedPos (stripArg a) : stripArgs True as
+            where
+              a'     = setNamedArg a $ A.WildP $ Info.PatRange $ getRange a
+              goWild = stripName fixedPos a' : stripArgs True as
+
+          stripName True  = fmap removeNameUnlessUserWritten
+          stripName False = id
+
+          -- TODO: vars appearing in EqualPs shouldn't be stripped.
+          canStrip a = and
+            [ notVisible a
+            , getOrigin a `notElem` [ UserWritten , CaseSplit ]
+            , (getOrigin <$> getNameOf a) /= Just UserWritten
+            , varOrDot (namedArg a)
+            , not $ mustKeepVar (namedArg a)
+            ]
+
+          mustKeepVar (A.VarP (A.BindName x)) = Set.member x toKeep
+          mustKeepVar _                       = False
+
+          isUnnamedHidden x = notVisible x && isNothing (getNameOf x) && isNothing (isProjP x)
+
+          stripArg a = fmap (fmap stripPat) a
+
+          stripPat = \case
+            p@(A.VarP _)        -> p
+            A.ConP i c ps       -> A.ConP i c $ stripArgs True ps
+            p@A.ProjP{}         -> p
+            p@(A.DefP _ _ _)    -> p
+            p@(A.DotP _ _e)     -> p
+            p@(A.WildP _)       -> p
+            p@(A.AbsurdP _)     -> p
+            p@(A.LitP _ _)      -> p
+            A.AsP i x p         -> A.AsP i x $ stripPat p
+            A.PatternSynP _ _ _ -> __IMPOSSIBLE__
+            A.RecP i fs         -> A.RecP i $ map (fmap stripPat) fs  -- TODO Andreas: is this right?
+            p@A.EqualP{}        -> p -- EqualP cannot be blanked.
+            A.WithP i p         -> A.WithP i $ stripPat p -- TODO #2822: right?
+            A.AnnP i a p        -> A.AnnP i a $ stripPat p
+
+          varOrDot A.VarP{}      = True
+          varOrDot A.WildP{}     = True
+          varOrDot A.DotP{}      = True
+          varOrDot (A.ConP cpi _ ps) | conPatOrigin cpi == ConOSystem
+                                 = conPatLazy cpi == ConPatLazy || all (varOrDot . namedArg) ps
+          varOrDot _             = False
+
+{-# SPECIALIZE blankNotInScope :: BlankVars a => a -> TCM a #-}
+{-# SPECIALIZE blankNotInScope :: Expr -> TCM Expr #-}
+-- | @blankNotInScope e@ replaces variables in expression @e@ with @_@
+-- if they are currently not in scope.
+blankNotInScope :: (MonadTCEnv m, MonadDebug m, BlankVars a) => a -> m a
+blankNotInScope e = do
+  ctxNames <- getContextNames
+  letNames <- map fst <$> getLetBindings
+  let names = Set.fromList . filter ((== C.InScope) . C.isInScope) $ ctxNames ++ letNames
+  reportSDoc "reify.blank" 80 . pure $ "names in scope for blanking:" <+> pretty names
+  return $ blank names e
+
+
+-- | @blank bound e@ replaces all variables in expression @e@ that are not in @bound@ by
+--   an underscore @_@. It is used for printing dot patterns: we don't want to
+--   make implicit variables explicit, so we blank them out in the dot patterns
+--   instead (this is fine since dot patterns can be inferred anyway).
+
+class BlankVars a where
+  blank :: Set Name -> a -> a
+
+  default blank :: (Functor f, BlankVars b, f b ~ a) => Set Name -> a -> a
+  blank = fmap . blank
+
+instance BlankVars a => BlankVars (Arg a)
+instance BlankVars a => BlankVars (Named s a)
+instance BlankVars a => BlankVars [a]
+instance BlankVars a => BlankVars (List1 a)
+instance BlankVars a => BlankVars (FieldAssignment' a)
+-- instance BlankVars a => BlankVars (A.Pattern' a)         -- see case EqualP !
+
+instance (BlankVars a, BlankVars b) => BlankVars (a, b) where
+  blank bound (x, y) = (blank bound x, blank bound y)
+
+instance (BlankVars a, BlankVars b) => BlankVars (Either a b) where
+  blank bound (Left x)  = Left $ blank bound x
+  blank bound (Right y) = Right $ blank bound y
+
+instance BlankVars A.ProblemEq where
+  blank bound = id
+
+instance BlankVars A.Clause where
+  blank bound (A.Clause lhs strippedPats rhs wh ca)
+    | null wh =
+        A.Clause (blank bound' lhs)
+                 (blank bound' strippedPats)
+                 (blank bound' rhs) noWhereDecls ca
+    | otherwise = __IMPOSSIBLE__
+    where bound' = varsBoundIn lhs `Set.union` bound
+
+instance BlankVars A.LHS where
+  blank bound (A.LHS i core) = A.LHS i $ blank bound core
+
+instance BlankVars A.LHSCore where
+  blank bound (A.LHSHead f ps) = A.LHSHead f $ blank bound ps
+  blank bound (A.LHSProj p b ps) = uncurry (A.LHSProj p) $ blank bound (b, ps)
+  blank bound (A.LHSWith h wps ps) = uncurry (uncurry A.LHSWith) $ blank bound ((h, wps), ps)
+
+instance BlankVars A.Pattern where
+  blank bound p = case p of
+    A.VarP _      -> p   -- do not blank pattern vars
+    A.ConP c i ps -> A.ConP c i $ blank bound ps
+    A.ProjP{}     -> p
+    A.DefP i f ps -> A.DefP i f $ blank bound ps
+    A.DotP i e    -> A.DotP i $ blank bound e
+    A.WildP _     -> p
+    A.AbsurdP _   -> p
+    A.LitP _ _    -> p
+    A.AsP i n p   -> A.AsP i n $ blank bound p
+    A.PatternSynP _ _ _ -> __IMPOSSIBLE__
+    A.RecP i fs   -> A.RecP i $ blank bound fs
+    A.EqualP{}    -> p
+    A.WithP i p   -> A.WithP i (blank bound p)
+    A.AnnP i a p  -> A.AnnP i (blank bound a) (blank bound p)
+
+instance BlankVars A.Expr where
+  blank bound e = case e of
+    A.ScopedExpr i e         -> A.ScopedExpr i $ blank bound e
+    A.Var x                  -> if x `Set.member` bound then e
+                                else A.Underscore emptyMetaInfo  -- Here is the action!
+    A.Def' _ _               -> e
+    A.Proj{}                 -> e
+    A.Con _                  -> e
+    A.Lit _ _                -> e
+    A.QuestionMark{}         -> e
+    A.Underscore _           -> e
+    A.Dot i e                -> A.Dot i $ blank bound e
+    A.App i e1 e2            -> uncurry (A.App i) $ blank bound (e1, e2)
+    A.WithApp i e es         -> uncurry (A.WithApp i) $ blank bound (e, es)
+    A.Lam i b e              -> let bound' = varsBoundIn b `Set.union` bound
+                                in  A.Lam i (blank bound b) (blank bound' e)
+    A.AbsurdLam _ _          -> e
+    A.ExtendedLam i d e f cs -> A.ExtendedLam i d e f $ blank bound cs
+    A.Pi i tel e             -> let bound' = varsBoundIn tel `Set.union` bound
+                                in  uncurry (A.Pi i) $ blank bound' (tel, e)
+    A.Generalized {}         -> __IMPOSSIBLE__
+    A.Fun i a b              -> uncurry (A.Fun i) $ blank bound (a, b)
+    A.Let _ _ _              -> __IMPOSSIBLE__
+    A.Rec i es               -> A.Rec i $ blank bound es
+    A.RecUpdate i e es       -> uncurry (A.RecUpdate i) $ blank bound (e, es)
+    A.Quote {}               -> __IMPOSSIBLE__
+    A.QuoteTerm {}           -> __IMPOSSIBLE__
+    A.Unquote {}             -> __IMPOSSIBLE__
+    A.DontCare v             -> A.DontCare $ blank bound v
+    A.PatternSyn {}          -> e
+    A.Macro {}               -> e
+
+instance BlankVars A.ModuleName where
+  blank bound = id
+
+instance BlankVars RHS where
+  blank bound (RHS e mc)             = RHS (blank bound e) mc
+  blank bound AbsurdRHS              = AbsurdRHS
+  blank bound (WithRHS _ es clauses) = __IMPOSSIBLE__ -- NZ
+  blank bound (RewriteRHS xes spats rhs _) = __IMPOSSIBLE__ -- NZ
+
+instance BlankVars A.LamBinding where
+  blank bound b@A.DomainFree{} = b
+  blank bound (A.DomainFull bs) = A.DomainFull $ blank bound bs
+
+instance BlankVars TypedBinding where
+  blank bound (TBind r t n e) = TBind r t n $ blank bound e
+  blank bound (TLet _ _)    = __IMPOSSIBLE__ -- Since the internal syntax has no let bindings left
+
+
+-- | Collect the binders in some abstract syntax lhs.
+
+class Binder a where
+  varsBoundIn :: a -> Set Name
+
+  default varsBoundIn :: (Foldable f, Binder b, f b ~ a) => a -> Set Name
+  varsBoundIn = foldMap varsBoundIn
+
+instance Binder A.LHS where
+  varsBoundIn (A.LHS _ core) = varsBoundIn core
+
+instance Binder A.LHSCore where
+  varsBoundIn (A.LHSHead _ ps)     = varsBoundIn ps
+  varsBoundIn (A.LHSProj _ b ps)   = varsBoundIn (b, ps)
+  varsBoundIn (A.LHSWith h wps ps) = varsBoundIn ((h, wps), ps)
+
+instance Binder A.Pattern where
+  varsBoundIn = foldAPattern $ \case
+    A.VarP x            -> varsBoundIn x
+    A.AsP _ x _         -> empty    -- Not x because of #2414 (?)
+    A.ConP _ _ _        -> empty
+    A.ProjP{}           -> empty
+    A.DefP _ _ _        -> empty
+    A.WildP{}           -> empty
+    A.DotP{}            -> empty
+    A.AbsurdP{}         -> empty
+    A.LitP{}            -> empty
+    A.PatternSynP _ _ _ -> empty
+    A.RecP _ _          -> empty
+    A.EqualP{}          -> empty
+    A.WithP _ _         -> empty
+    A.AnnP{}            -> empty
+
+instance Binder a => Binder (A.Binder' a) where
+  varsBoundIn (A.Binder p n) = varsBoundIn (p, n)
+
+instance Binder A.LamBinding where
+  varsBoundIn (A.DomainFree _ x) = varsBoundIn x
+  varsBoundIn (A.DomainFull b)   = varsBoundIn b
+
+instance Binder TypedBinding where
+  varsBoundIn (TBind _ _ xs _) = varsBoundIn xs
+  varsBoundIn (TLet _ bs)      = varsBoundIn bs
+
+instance Binder BindName where
+  varsBoundIn x = singleton (unBind x)
+
+instance Binder A.LetBinding where
+  varsBoundIn (LetBind _ _ x _ _) = varsBoundIn x
+  varsBoundIn (LetPatBind _ p _)  = varsBoundIn p
+  varsBoundIn LetApply{}          = empty
+  varsBoundIn LetOpen{}           = empty
+  varsBoundIn LetDeclaredVariable{} = empty
+
+instance Binder a => Binder (FieldAssignment' a)
+instance Binder a => Binder (Arg a)
+instance Binder a => Binder (Named x a)
+instance Binder a => Binder [a]
+instance Binder a => Binder (List1 a)
+instance Binder a => Binder (Maybe a)
+
+instance (Binder a, Binder b) => Binder (a, b) where
+  varsBoundIn (x, y) = varsBoundIn x `Set.union` varsBoundIn y
+
+{-# SPECIALIZE reifyPatterns :: [NamedArg I.DeBruijnPattern] -> TCM [NamedArg A.Pattern] #-}
+-- | Assumes that pattern variables have been added to the context already.
+--   Picks pattern variable names from context.
+reifyPatterns :: MonadReify m => [NamedArg I.DeBruijnPattern] -> m [NamedArg A.Pattern]
+reifyPatterns = mapM $ (stripNameFromExplicit . stripHidingFromPostfixProj) <.>
+                       traverse (traverse reifyPat)
+  where
+    -- #4399 strip also empty names
+    stripNameFromExplicit :: NamedArg p -> NamedArg p
+    stripNameFromExplicit a
+      | visible a || maybe True (liftA2 (||) null isNoName) (bareNameOf a) =
+          fmap (unnamed . namedThing) a
+      | otherwise = a
+
+    stripHidingFromPostfixProj :: IsProjP p => NamedArg p -> NamedArg p
+    stripHidingFromPostfixProj a = case isProjP a of
+      Just (o, _) | o /= ProjPrefix -> setHiding NotHidden a
+      _                             -> a
+
+    reifyPat :: MonadReify m => I.DeBruijnPattern -> m A.Pattern
+    reifyPat p = do
+     reportSDoc "reify.pat" 80 $ return $ "reifying pattern" <+> pretty p
+     keepVars <- optKeepPatternVariables <$> pragmaOptions
+     case p of
+      -- Possibly expanded literal pattern (see #4215)
+      p | Just (PatternInfo PatOLit asB) <- patternInfo p -> do
+        reduce (I.patternToTerm p) >>= \case
+          I.Lit l -> addAsBindings asB $ return $ A.LitP empty l
+          _       -> __IMPOSSIBLE__
+      I.VarP i x -> addAsBindings (patAsNames i) $ case patOrigin i of
+        o@PatODot  -> reifyDotP o $ var $ dbPatVarIndex x
+        PatOWild   -> return $ A.WildP patNoRange
+        PatOAbsurd -> return $ A.AbsurdP patNoRange
+        _          -> reifyVarP x
+      I.DotP i v -> addAsBindings (patAsNames i) $ case patOrigin i of
+        PatOWild   -> return $ A.WildP patNoRange
+        PatOAbsurd -> return $ A.AbsurdP patNoRange
+        -- If Agda turned a user variable @x@ into @.x@, print it back as @x@.
+        o@(PatOVar x) | I.Var i [] <- v -> do
+          x' <- nameOfBV i
+          if nameConcrete x == nameConcrete x' then
+            return $ A.VarP $ mkBindName x'
+          else
+            reifyDotP o v
+        o -> reifyDotP o v
+      I.LitP i l  -> addAsBindings (patAsNames i) $ return $ A.LitP empty l
+      I.ProjP o d -> return $ A.ProjP patNoRange o $ unambiguous d
+      I.ConP c cpi ps | conPRecord cpi -> addAsBindings (patAsNames $ conPInfo cpi) $
+        case patOrigin (conPInfo cpi) of
+          PatOWild   -> return $ A.WildP patNoRange
+          PatOAbsurd -> return $ A.AbsurdP patNoRange
+          PatOVar x | keepVars -> return $ A.VarP $ mkBindName x
+          _               -> reifyConP c cpi ps
+      I.ConP c cpi ps -> addAsBindings (patAsNames $ conPInfo cpi) $ reifyConP c cpi ps
+      I.DefP i f ps  -> addAsBindings (patAsNames i) $ case patOrigin i of
+        PatOWild   -> return $ A.WildP patNoRange
+        PatOAbsurd -> return $ A.AbsurdP patNoRange
+        PatOVar x | keepVars -> return $ A.VarP $ mkBindName x
+        _ -> A.DefP patNoRange (unambiguous f) <$> reifyPatterns ps
+      I.IApplyP i _ _ x -> addAsBindings (patAsNames i) $ case patOrigin i of
+        o@PatODot  -> reifyDotP o $ var $ dbPatVarIndex x
+        PatOWild   -> return $ A.WildP patNoRange
+        PatOAbsurd -> return $ A.AbsurdP patNoRange
+        _          -> reifyVarP x
+
+    reifyVarP :: MonadReify m => DBPatVar -> m A.Pattern
+    reifyVarP x = do
+      n <- nameOfBV $ dbPatVarIndex x
+      let y = dbPatVarName x
+      if | y == "_" -> return $ A.VarP $ mkBindName n
+           -- Andreas, 2017-09-03: TODO for #2580
+           -- Patterns @VarP "()"@ should have been replaced by @AbsurdP@, but the
+           -- case splitter still produces them.
+         | prettyShow (nameConcrete n) == "()" -> return $ A.VarP (mkBindName n)
+           -- Andreas, 2017-09-03, issue #2729
+           -- Restore original pattern name.  AbstractToConcrete picks unique names.
+         | otherwise -> return $ A.VarP $
+             mkBindName n { nameConcrete = C.simpleName y }
+
+    reifyDotP :: MonadReify m => PatOrigin -> Term -> m A.Pattern
+    reifyDotP o v = do
+      keepVars <- optKeepPatternVariables <$> pragmaOptions
+      if | PatOVar x <- o , keepVars       -> return $ A.VarP $ mkBindName x
+         | otherwise                       -> A.DotP patNoRange <$> reify v
+
+    reifyConP :: MonadReify m
+              => ConHead -> ConPatternInfo -> [NamedArg DeBruijnPattern]
+              -> m A.Pattern
+    reifyConP c cpi ps = do
+      tryRecPFromConP =<< do A.ConP ci (unambiguous (conName c)) <$> reifyPatterns ps
+      where
+        ci = ConPatInfo origin patNoRange lazy
+        lazy | conPLazy cpi = ConPatLazy
+             | otherwise    = ConPatEager
+        origin = fromConPatternInfo cpi
+
+    addAsBindings :: Functor m => [A.Name] -> m A.Pattern -> m A.Pattern
+    addAsBindings xs p = foldr (fmap . AsP patNoRange . mkBindName) p xs
+
+{-# SPECIALIZE tryRecPFromConP :: A.Pattern -> TCM A.Pattern #-}
+-- | If the record constructor is generated or the user wrote a record pattern,
+--   turn constructor pattern into record pattern.
+--   Otherwise, keep constructor pattern.
+tryRecPFromConP :: MonadReify m => A.Pattern -> m A.Pattern
+tryRecPFromConP p = do
+  let fallback = return p
+  case p of
+    A.ConP ci c ps -> do
+        reportSLn "reify.pat" 60 $ "tryRecPFromConP " ++ prettyShow c
+        caseMaybeM (isRecordConstructor $ headAmbQ c) fallback $ \ (r, def) -> do
+          -- If the record constructor is generated or the user wrote a record pattern,
+          -- print record pattern.
+          -- Otherwise, print constructor pattern.
+          if recNamedCon def && conPatOrigin ci /= ConORec then fallback else do
+            fs <- fromMaybe __IMPOSSIBLE__ <$> getRecordFieldNames_ r
+            unless (length fs == length ps) __IMPOSSIBLE__
+            return $ A.RecP patNoRange $ zipWith mkFA fs ps
+        where
+          mkFA ax nap = FieldAssignment (unDom ax) (namedArg nap)
+    _ -> __IMPOSSIBLE__
+
+{-# SPECIALIZE recOrCon :: QName -> ConOrigin -> [Arg Expr] -> TCM A.Expr #-}
+-- | If the record constructor is generated or the user wrote a record expression,
+--   turn constructor expression into record expression.
+--   Otherwise, keep constructor expression.
+recOrCon :: MonadReify m => QName -> ConOrigin -> [Arg Expr] -> m A.Expr
+recOrCon c co es = do
+  reportSLn "reify.expr" 60 $ "recOrCon " ++ prettyShow c
+  caseMaybeM (isRecordConstructor c) fallback $ \ (r, def) -> do
+    -- If the record constructor is generated or the user wrote a record expression,
+    -- print record expression.
+    -- Otherwise, print constructor expression.
+    if recNamedCon def && co /= ConORec then fallback else do
+      fs <- fromMaybe __IMPOSSIBLE__ <$> getRecordFieldNames_ r
+      unless (length fs == length es) __IMPOSSIBLE__
+      return $ A.Rec empty $ zipWith mkFA fs es
+  where
+  fallback = apps (A.Con (unambiguous c)) es
+  mkFA ax  = Left . FieldAssignment (unDom ax) . unArg
+
+instance Reify (QNamed I.Clause) where
+  type ReifiesTo (QNamed I.Clause) = A.Clause
+
+  reify (QNamed f cl) = reify (NamedClause f True cl); {-# INLINE reify #-}
+
+instance Reify NamedClause where
+  type ReifiesTo NamedClause = A.Clause
+
+  reify (NamedClause f toDrop cl) = addContext (clauseTel cl) $ do
+    reportSDoc "reify.clause" 60 $ return $ vcat
+      [ "reifying NamedClause"
+      , "  f      =" <+> pretty f
+      , "  toDrop =" <+> pshow toDrop
+      , "  cl     =" <+> pretty cl
+      ]
+
+    let clBody = clauseBody cl
+        rhsVars = maybe [] freeVars clBody
+
+    rhsBody     <- traverse reify clBody
+    rhsVarNames <- mapM nameOfBV' rhsVars
+    let rhsUsedNames = maybe mempty allUsedNames rhsBody
+        rhsUsedVars  = [i | (i, Just n) <- zip rhsVars rhsVarNames, n `Set.member` rhsUsedNames]
+
+    reportSDoc "reify.clause" 60 $ return $ "RHS:" <+> pretty clBody
+    reportSDoc "reify.clause" 60 $ return $ "variables occurring on RHS:" <+> pretty rhsVars
+      <+> "variable names:" <+> pretty rhsVarNames
+      <+> parens (maybe "no clause body" (const "there was a clause body") clBody)
+    reportSDoc "reify.clause" 60 $ return $ "names occurring on RHS" <+> pretty (Set.toList rhsUsedNames)
+
+    let ell = clauseEllipsis cl
+    ps  <- reifyPatterns $ namedClausePats cl
+    lhs <- uncurry (SpineLHS $ empty { lhsEllipsis = ell }) <$> reifyDisplayFormP f ps []
+    -- Unless @toDrop@ we have already dropped the module patterns from the clauses
+    -- (e.g. for extended lambdas). We still get here with toDrop = True and
+    -- pattern lambdas when doing make-case, so take care to drop the right
+    -- number of parameters.
+    (params , lhs) <- if not toDrop then return ([] , lhs) else do
+      nfv <- getDefModule f >>= \case
+        Left _  -> return 0
+        Right m -> size <$> lookupSection m
+      return $ splitParams nfv lhs
+    lhs <- stripImps rhsUsedNames params lhs
+    let rhs    = caseMaybe rhsBody AbsurdRHS $ \ e -> RHS e Nothing
+        result = A.Clause (spineToLhs lhs) [] rhs A.noWhereDecls (I.clauseCatchall cl)
+    return result
+    where
+      splitParams n (SpineLHS i f ps) =
+        let (params , pats) = splitAt n ps
+        in  (params , SpineLHS i f pats)
+      stripImps :: MonadReify m => Set Name -> [NamedArg A.Pattern] -> SpineLHS -> m SpineLHS
+      stripImps rhsUsedNames params (SpineLHS i f ps) =  SpineLHS i f <$> stripImplicits rhsUsedNames params ps
+{-# SPECIALIZE reify :: NamedClause -> TCM (ReifiesTo NamedClause) #-}
+
+instance Reify (QNamed System) where
+  type ReifiesTo (QNamed System) = [A.Clause]
+
+  reify (QNamed f (System tel sys)) = addContext tel $ do
+    reportS "reify.system" 40 $ show tel : map show sys
+    view <- intervalView'
+    unview <- intervalUnview'
+    sys <- flip filterM sys $ \ (phi,t) -> do
+      allM phi $ \ (u,b) -> do
+        u <- reduce u
+        return $ case (view u, b) of
+          (IZero, True) -> False
+          (IOne, False) -> False
+          _ -> True
+    forM sys $ \ (alpha,u) -> do
+      rhs <- RHS <$> reify u <*> pure Nothing
+      ep <- fmap (A.EqualP patNoRange) . forM alpha $ \ (phi,b) -> do
+        let
+            d True = unview IOne
+            d False = unview IZero
+        reify (phi, d b)
+
+      ps <- reifyPatterns $ teleNamedArgs tel
+      ps <- stripImplicits mempty [] $ ps ++ [defaultNamedArg ep]
+      let
+        lhs = SpineLHS empty f ps
+        result = A.Clause (spineToLhs lhs) [] rhs A.noWhereDecls False
+      return result
+{-# SPECIALIZE reify :: QNamed System -> TCM (ReifiesTo (QNamed System)) #-}
+
+instance Reify I.Type where
+    type ReifiesTo I.Type = A.Type
+
+    reifyWhen = reifyWhenE; {-# INLINE reifyWhen #-}
+    reify (I.El _ t) = reify t; {-# INLINE reify #-}
+
+instance Reify Sort where
+    type ReifiesTo Sort = Expr
+
+    reifyWhen = reifyWhenE
+
+    reify s = do
+      s <- instantiateFull s
+      SortKit{..} <- infallibleSortKit
+      case s of
+        I.Univ u (I.ClosedLevel 0) -> return $ A.Def' (nameOfUniv USmall u) A.NoSuffix
+        I.Univ u (I.ClosedLevel n) -> return $ A.Def' (nameOfUniv USmall u) (A.Suffix n)
+        I.Univ u a -> do
+          a <- reify a
+          return $ A.App defaultAppInfo_ (A.Def $ nameOfUniv USmall u) (defaultNamedArg a)
+        I.Inf u 0 -> return $ A.Def' (nameOfUniv ULarge u) A.NoSuffix
+        I.Inf u n -> return $ A.Def' (nameOfUniv ULarge u) (A.Suffix n)
+        I.SizeUniv  -> do
+          I.Def sizeU [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSizeUniv
+          return $ A.Def sizeU
+        I.LockUniv  -> do
+          lockU <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinLockUniv
+          return $ A.Def lockU
+        I.LevelUniv -> do
+          levelU <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinLevelUniv
+          return $ A.Def levelU
+        I.IntervalUniv -> do
+          intervalU <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinIntervalUniv
+          return $ A.Def intervalU
+        I.PiSort a s1 s2 -> do
+          pis <- freshName_ ("piSort" :: String) -- TODO: hack
+          (e1,e2) <- reify (s1, I.Lam defaultArgInfo $ fmap Sort s2)
+          let app x y = A.App defaultAppInfo_ x (defaultNamedArg y)
+          return $ A.Var pis `app` e1 `app` e2
+        I.FunSort s1 s2 -> do
+          funs <- freshName_ ("funSort" :: String) -- TODO: hack
+          (e1,e2) <- reify (s1 , s2)
+          let app x y = A.App defaultAppInfo_ x (defaultNamedArg y)
+          return $ A.Var funs `app` e1 `app` e2
+        I.UnivSort s -> do
+          univs <- freshName_ ("univSort" :: String) -- TODO: hack
+          e <- reify s
+          return $ A.App defaultAppInfo_ (A.Var univs) $ defaultNamedArg e
+        I.MetaS x es -> reify $ I.MetaV x es
+        I.DefS d es -> reify $ I.Def d es
+        I.DummyS s -> return $ A.Lit empty $ LitString $ T.pack s
+{-# SPECIALIZE reify :: Sort -> TCM (ReifiesTo Sort) #-}
+
+instance Reify Level where
+  type ReifiesTo Level = Expr
+
+  reifyWhen = reifyWhenE
+  reify l   = ifM haveLevels (reify =<< reallyUnLevelView l) $ {-else-} do
+    -- Andreas, 2017-09-18, issue #2754
+    -- While type checking the level builtins, they are not
+    -- available for debug printing.  Thus, print some garbage instead.
+    name <- freshName_ (".#Lacking_Level_Builtins#" :: String)
+    return $ A.Var name
+{-# SPECIALIZE reify :: Level -> TCM (ReifiesTo Level) #-}
+
+instance (Free i, Reify i) => Reify (Abs i) where
+  type ReifiesTo (Abs i) = (Name, ReifiesTo i)
+
+  reify (NoAbs x v) = freshName_ x >>= \name -> (name,) <$> reify v
+  reify (Abs s v) = do
+
+    -- If the bound variable is free in the body, then the name "_" is
+    -- replaced by "z".
+    s <- return $ if isUnderscore s && 0 `freeIn` v then "z" else s
+
+    x <- C.setNotInScope <$> freshName_ s
+    e <- addContext x -- type doesn't matter
+         $ reify v
+    return (x,e)
+{-# SPECIALIZE reify :: (Free i, Reify i) -> Abs i -> TCM (ReifiesTo (Abs i)) #-}
+
+instance Reify I.Telescope where
+  type ReifiesTo I.Telescope = A.Telescope
+
+  reify EmptyTel = return []
+  reify (ExtendTel arg tel) = do
+    Arg info e <- reify arg
+    (x, bs)  <- reify tel
+    let r    = getRange e
+        name = domName arg
+    tac <- traverse (Ranged noRange <.> reify) $ domTactic arg
+    let xs = singleton $ Arg info $ Named name $ A.mkBinder_ x
+    return $ TBind r (TypedBindingInfo tac (domIsFinite arg)) xs e : bs
+{-# SPECIALIZE reify :: I.Telescope -> TCM (ReifiesTo I.Telescope) #-}
+
+instance Reify i => Reify (Dom i) where
+    type ReifiesTo (Dom i) = Arg (ReifiesTo i)
+
+    reify (Dom{domInfo = info, unDom = i}) = Arg info <$> reify i
+    {-# INLINE reify #-}
+
+instance Reify i => Reify (I.Elim' i)  where
+  type ReifiesTo (I.Elim' i) = I.Elim' (ReifiesTo i)
+
+  reify = traverse reify
+  reifyWhen b = traverse (reifyWhen b)
+
+instance Reify i => Reify [i] where
+  type ReifiesTo [i] = [ReifiesTo i]
+
+  reify = traverse reify
+  reifyWhen b = traverse (reifyWhen b)
+
+instance (Reify i1, Reify i2) => Reify (i1, i2) where
+    type ReifiesTo (i1, i2) = (ReifiesTo i1, ReifiesTo i2)
+    reify (x,y) = (,) <$> reify x <*> reify y
+
+instance (Reify i1, Reify i2, Reify i3) => Reify (i1,i2,i3) where
+    type ReifiesTo (i1, i2, i3) = (ReifiesTo i1, ReifiesTo i2, ReifiesTo i3)
+    reify (x,y,z) = (,,) <$> reify x <*> reify y <*> reify z
+
+instance (Reify i1, Reify i2, Reify i3, Reify i4) => Reify (i1,i2,i3,i4) where
+    type ReifiesTo (i1, i2, i3, i4) = (ReifiesTo i1, ReifiesTo i2, ReifiesTo i3, ReifiesTo i4)
+    reify (x,y,z,w) = (,,,) <$> reify x <*> reify y <*> reify z <*> reify w
diff --git a/src/full/Agda/Syntax/Translation/ReflectedToAbstract.hs b/src/full/Agda/Syntax/Translation/ReflectedToAbstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Translation/ReflectedToAbstract.hs
@@ -0,0 +1,321 @@
+{-# OPTIONS_GHC -fwarn-missing-signatures #-}
+
+module Agda.Syntax.Translation.ReflectedToAbstract where
+
+import Control.Arrow        ( (***) )
+import Control.Monad        ( foldM )
+import Control.Monad.Except ( MonadError )
+import Control.Monad.Reader ( MonadReader(..), asks, reader, runReaderT )
+
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Text (Text)
+import qualified Data.Text as Text
+
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+import Agda.Syntax.Info
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract
+  ( Name, QName, QNamed(QNamed)
+  , isNoName, nameConcrete, nextName, qualify, unambiguous
+  )
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pattern
+import Agda.Syntax.Reflected as R
+import Agda.Syntax.Internal (Dom,Dom'(..))
+
+import Agda.Interaction.Options (optUseUnicode, UnicodeOrAscii(..))
+import Agda.TypeChecking.Monad as M hiding (MetaInfo)
+import Agda.Syntax.Scope.Monad (getCurrentModule)
+
+import Agda.Utils.Impossible
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Functor
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+type Vars = [(Name,R.Type)]
+
+type MonadReflectedToAbstract m =
+  ( MonadReader Vars m
+  , MonadFresh NameId m
+  , MonadError TCErr m
+  , MonadTCEnv m
+  , ReadTCState m
+  , HasOptions m
+  , HasBuiltins m
+  , HasConstInfo m
+  )
+
+-- | Adds a new unique name to the current context.
+--   NOTE: See @chooseName@ in @Agda.Syntax.Translation.AbstractToConcrete@ for similar logic.
+--   NOTE: See @freshConcreteName@ in @Agda.Syntax.Scope.Monad@ also for similar logic.
+withName :: MonadReflectedToAbstract m => String -> (Name -> m a) -> m a
+withName s = withVar s R.Unknown
+
+withVar :: MonadReflectedToAbstract m => String -> R.Type -> (Name -> m a) -> m a
+withVar s t f = do
+  name <- freshName_ s
+  ctx  <- asks $ map $ nameConcrete . fst
+  glyphMode <- optUseUnicode <$> M.pragmaOptions
+  let freshNameMode = case glyphMode of
+        UnicodeOk -> A.UnicodeSubscript
+        AsciiOnly -> A.AsciiCounter
+  let name' = headWithDefault __IMPOSSIBLE__ $ filter (notTaken ctx) $ iterate (nextName freshNameMode) name
+  local ((name,t):) $ f name'
+  where
+    notTaken xs x = isNoName x || nameConcrete x `notElem` xs
+
+withNames :: MonadReflectedToAbstract m => [String] -> ([Name] -> m a) -> m a
+withNames ss = withVars $ zip ss $ repeat R.Unknown
+
+withVars :: MonadReflectedToAbstract m => [(String, R.Type)] -> ([Name] -> m a) -> m a
+withVars ss f = case ss of
+  []     -> f []
+  ((s,t):ss) -> withVar s t $ \n -> withVars ss $ \ns -> f (n:ns)
+
+-- | Returns the name and type of the variable with the given de Bruijn index.
+askVar :: MonadReflectedToAbstract m => Int -> m (Maybe (Name,R.Type))
+askVar i = reader (!!! i)
+
+askName :: MonadReflectedToAbstract m => Int -> m (Maybe Name)
+askName i = fmap fst <$> askVar i
+
+class ToAbstract r where
+  type AbsOfRef r
+  toAbstract :: MonadReflectedToAbstract m => r -> m (AbsOfRef r)
+
+  default toAbstract
+    :: (Traversable t, ToAbstract s, t s ~ r, t (AbsOfRef s) ~ (AbsOfRef r))
+    => MonadReflectedToAbstract m => r -> m (AbsOfRef r)
+  toAbstract = traverse toAbstract
+
+-- | Translate reflected syntax to abstract, using the names from the current typechecking context.
+toAbstract_ ::
+  (ToAbstract r
+  , MonadFresh NameId m
+  , MonadError TCErr m
+  , MonadTCEnv m
+  , ReadTCState m
+  , HasOptions m
+  , HasBuiltins m
+  , HasConstInfo m
+  ) => r -> m (AbsOfRef r)
+toAbstract_ = withShowAllArguments . toAbstractWithoutImplicit
+
+-- | Drop implicit arguments unless --show-implicit is on.
+toAbstractWithoutImplicit ::
+  (ToAbstract r
+  , MonadFresh NameId m
+  , MonadError TCErr m
+  , MonadTCEnv m
+  , ReadTCState m
+  , HasOptions m
+  , HasBuiltins m
+  , HasConstInfo m
+  ) => r -> m (AbsOfRef r)
+toAbstractWithoutImplicit x = do
+  xs <- killRange <$> getContextNames
+  let ctx = zip xs $ repeat R.Unknown
+  runReaderT (toAbstract x) ctx
+
+instance ToAbstract r => ToAbstract (Named name r) where
+  type AbsOfRef (Named name r) = Named name (AbsOfRef r)
+
+instance ToAbstract r => ToAbstract (Arg r) where
+  type AbsOfRef (Arg r) = NamedArg (AbsOfRef r)
+  toAbstract (Arg i x) = Arg i <$> toAbstract (unnamed x)
+
+instance ToAbstract r => ToAbstract [Arg r] where
+  type AbsOfRef [Arg r] = [NamedArg (AbsOfRef r)]
+
+-- instance ToAbstract r A.Expr => ToAbstract (Dom r, Name) (A.TypedBinding) where
+instance (ToAbstract r, AbsOfRef r ~ A.Expr) => ToAbstract (Dom r, Name) where
+  type AbsOfRef (Dom r, Name) = A.TypedBinding
+  toAbstract (Dom{domInfo = i, domIsFinite = isfin, unDom = x, domTactic = tac}, name) = do
+    dom <- toAbstract x
+    -- TODO(Amy): Anyone know why this discards the tactic? It was like
+    -- that when I got here!
+    return $ A.TBind noRange
+      (A.TypedBindingInfo Nothing isfin)
+      (singleton $ unnamedArg i $ A.mkBinder_ name)
+      dom
+
+instance ToAbstract (A.Expr, Elim) where
+  type AbsOfRef (A.Expr, Elim) = A.Expr
+  toAbstract (f, Apply arg) = do
+    arg     <- toAbstract arg
+    showImp <- showImplicitArguments
+    return $ if showImp || visible arg
+             then A.App (setOrigin Reflected defaultAppInfo_) f arg
+             else f
+
+instance ToAbstract (A.Expr, Elims) where
+  type AbsOfRef (A.Expr, Elims) = A.Expr
+  toAbstract (f, elims) = foldM (curry toAbstract) f elims
+
+instance ToAbstract r => ToAbstract (R.Abs r) where
+  type AbsOfRef (R.Abs r) = (AbsOfRef r, Name)
+  toAbstract (Abs s x) = withName s' $ \name -> (,name) <$> toAbstract x
+    where s' = if (isNoName s) then "z" else s -- TODO: only do this when var is free
+
+instance ToAbstract Literal where
+  type AbsOfRef Literal = A.Expr
+  toAbstract l = return $ A.Lit empty l
+
+instance ToAbstract Term where
+  type AbsOfRef Term = A.Expr
+  toAbstract = \case
+    R.Var i es -> do
+      name <- mkVarName i
+      toAbstract (A.Var name, es)
+    R.Con c es -> toAbstract (A.Con (unambiguous $ killRange c), es)
+    R.Def f es -> do
+      af <- mkDef (killRange f)
+      toAbstract (af, es)
+    R.Lam h t  -> do
+      (e, name) <- toAbstract t
+      let info  = setHiding h $ setOrigin Reflected defaultArgInfo
+      return $ A.Lam exprNoRange (A.mkDomainFree $ unnamedArg info $ A.mkBinder_ name) e
+    R.ExtLam cs es -> do
+      name <- freshName_ extendedLambdaName
+      m    <- getCurrentModule
+      let qname   = qualify m name
+          cname   = nameConcrete name
+          defInfo = mkDefInfo cname noFixity' PublicAccess ConcreteDef noRange
+      cs <- toAbstract $ fmap (QNamed qname) cs
+      toAbstract
+        (A.ExtendedLam exprNoRange defInfo defaultErased qname cs, es)
+    R.Pi a b   -> do
+      (b, name) <- toAbstract b
+      a         <- toAbstract (a, name)
+      return $ A.Pi exprNoRange (singleton a) b
+    R.Sort s   -> toAbstract s
+    R.Lit l    -> toAbstract l
+    R.Meta x es    -> do
+      info <- mkMetaInfo
+      let info' = info{ metaNumber = Just x }
+      toAbstract (A.Underscore info', es)
+    R.Unknown      -> A.Underscore <$> mkMetaInfo
+
+mkMetaInfo :: ReadTCState m => m MetaInfo
+mkMetaInfo = do
+  scope <- getScope
+  return $ emptyMetaInfo { metaScope = scope }
+
+mkDef :: HasConstInfo m => QName -> m A.Expr
+mkDef f = getConstInfo f <&> theDef <&> \case
+
+  Constructor{}
+    -> A.Con $ unambiguous f
+
+  Function{ funProjection = Right Projection{ projProper = Just{} } }
+    -> A.Proj ProjSystem $ unambiguous f
+
+  d@Function{} | isMacro d
+    -> A.Macro f
+
+  _ -> A.Def f
+
+mkApp :: A.Expr -> A.Expr -> A.Expr
+mkApp e1 e2 = A.App (setOrigin Reflected defaultAppInfo_) e1 $ defaultNamedArg e2
+
+
+mkVar :: MonadReflectedToAbstract m => Int -> m (Name, R.Type)
+mkVar i = ifJustM (askVar i) return $ do
+  cxt   <- getContextTelescope
+  names <- asks $ drop (size cxt) . reverse . map fst
+  withShowAllArguments' False $ typeError $ DeBruijnIndexOutOfScope i cxt names
+
+mkVarName :: MonadReflectedToAbstract m => Int -> m Name
+mkVarName i = fst <$> mkVar i
+
+annotatePattern :: MonadReflectedToAbstract m => Int -> R.Type -> A.Pattern -> m A.Pattern
+annotatePattern _ R.Unknown p = return p
+annotatePattern i t p = local (drop $ i + 1) $ do
+  t <- toAbstract t  -- go into the right context for translating the type
+  return $ A.AnnP patNoRange t p
+
+instance ToAbstract Sort where
+  type AbsOfRef Sort = A.Expr
+  toAbstract s = do
+    setName <- fromMaybe __IMPOSSIBLE__ <$> getBuiltinName' builtinSet
+    propName <- fromMaybe __IMPOSSIBLE__ <$> getBuiltinName' builtinProp
+    infName <- fromMaybe __IMPOSSIBLE__ <$> getBuiltinName' builtinSetOmega
+    case s of
+      SetS x -> mkApp (A.Def setName) <$> toAbstract x
+      LitS x -> return $ A.Def' setName $ A.Suffix x
+      PropS x -> mkApp (A.Def propName) <$> toAbstract x
+      PropLitS x -> return $ A.Def' propName $ A.Suffix x
+      InfS x -> return $ A.Def' infName $ A.Suffix x
+      UnknownS -> mkApp (A.Def setName) . A.Underscore <$> mkMetaInfo
+
+instance ToAbstract R.Pattern where
+  type AbsOfRef R.Pattern = A.Pattern
+  toAbstract pat = case pat of
+    R.ConP c args -> do
+      args <- toAbstract args
+      return $ A.ConP (ConPatInfo ConOCon patNoRange ConPatEager) (unambiguous $ killRange c) args
+    R.DotP t -> A.DotP patNoRange <$> toAbstract t
+    R.VarP i -> do
+      (x, t) <- mkVar i
+      annotatePattern i t $ A.VarP $ A.mkBindName x
+    R.LitP l  -> return $ A.LitP patNoRange l
+    R.AbsurdP i -> do
+      (_, t) <- mkVar i
+      annotatePattern i t $ A.AbsurdP patNoRange
+    R.ProjP d -> return $ A.ProjP patNoRange ProjSystem $ unambiguous $ killRange d
+
+instance ToAbstract (QNamed R.Clause) where
+  type AbsOfRef (QNamed R.Clause) = A.Clause
+
+  toAbstract (QNamed name (R.Clause tel pats rhs)) = withVars (map (Text.unpack *** unArg) tel) $ \_ -> do
+    checkClauseTelescopeBindings tel pats
+    pats <- toAbstract pats
+    rhs  <- toAbstract rhs
+    let lhs = spineToLhs $ A.SpineLHS empty name pats
+    return $ A.Clause lhs [] (A.RHS rhs Nothing) A.noWhereDecls False
+  toAbstract (QNamed name (R.AbsurdClause tel pats)) = withVars (map (Text.unpack *** unArg) tel) $ \_ -> do
+    checkClauseTelescopeBindings tel pats
+    pats <- toAbstract pats
+    let lhs = spineToLhs $ A.SpineLHS empty name pats
+    return $ A.Clause lhs [] A.AbsurdRHS A.noWhereDecls False
+
+instance ToAbstract [QNamed R.Clause] where
+  type AbsOfRef [QNamed R.Clause] = [A.Clause]
+  toAbstract = traverse toAbstract
+
+instance ToAbstract (List1 (QNamed R.Clause)) where
+  type AbsOfRef (List1 (QNamed R.Clause)) = List1 A.Clause
+  toAbstract = traverse toAbstract
+
+-- | Check that all variables in the telescope are bound in the left-hand side. Since we check the
+--   telescope by attaching type annotations to the pattern variables there needs to be somewhere to
+--   put the annotation. Also, since the lhs is where the variables are actually bound, missing a
+--   binding for a variable that's used later in the telescope causes unbound variable panic
+--   (see #5044).
+checkClauseTelescopeBindings :: MonadReflectedToAbstract m => [(Text, Arg R.Type)] -> [Arg R.Pattern] -> m ()
+checkClauseTelescopeBindings tel pats =
+  case reverse [ x | ((x, _), i) <- zip (reverse tel) [0..], not $ Set.member i bs ] of
+    [] -> return ()
+    xs -> genericDocError $ (singPlural xs id (<> "s") "Missing bindings for telescope variable") <?>
+                              (fsep (punctuate ", " $ map (text . Text.unpack) xs) <> ".") $$
+                             "All variables in the clause telescope must be bound in the left-hand side."
+  where
+    bs = boundVars pats
+
+    boundVars = Set.unions . map (bound . unArg)
+    bound (R.VarP i)    = Set.singleton i
+    bound (R.ConP _ ps) = boundVars ps
+    bound R.DotP{}      = Set.empty
+    bound R.LitP{}      = Set.empty
+    bound (R.AbsurdP i) = Set.singleton i
+    bound R.ProjP{}     = Set.empty
diff --git a/src/full/Agda/Syntax/Treeless.hs b/src/full/Agda/Syntax/Treeless.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Syntax/Treeless.hs
@@ -0,0 +1,294 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE PatternSynonyms #-}
+
+-- | The treeless syntax is intended to be used as input for the compiler backends.
+-- It is more low-level than Internal syntax and is not used for type checking.
+--
+-- Some of the features of treeless syntax are:
+-- - case expressions instead of case trees
+-- - no instantiated datatypes / constructors
+module Agda.Syntax.Treeless
+    ( module Agda.Syntax.Abstract.Name
+    , module Agda.Syntax.Treeless
+    ) where
+
+import Control.Arrow (first, second)
+import Control.DeepSeq
+
+import Data.Word
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract.Name
+
+data Compiled = Compiled
+  { cTreeless :: TTerm
+  , cArgUsage :: Maybe [ArgUsage]
+      -- ^ 'Nothing' if treeless usage analysis has not run yet.
+  }
+  deriving (Show, Eq, Ord, Generic)
+
+-- | Usage status of function arguments in treeless code.
+data ArgUsage
+  = ArgUsed
+  | ArgUnused
+  deriving (Show, Eq, Ord, Generic)
+
+-- | The treeless compiler can behave differently depending on the target
+--   language evaluation strategy. For instance, more aggressive erasure for
+--   lazy targets.
+data EvaluationStrategy = LazyEvaluation | EagerEvaluation
+  deriving (Eq, Show)
+
+type Args = [TTerm]
+
+-- this currently assumes that TApp is translated in a lazy/cbn fashion.
+-- The AST should also support strict translation.
+--
+-- | Treeless Term. All local variables are using de Bruijn indices.
+data TTerm = TVar Int
+           | TPrim TPrim
+           | TDef QName
+           | TApp TTerm Args
+           | TLam TTerm
+           | TLit Literal
+           | TCon QName
+           | TLet TTerm TTerm
+           -- ^ introduces a new (non-recursive) local binding. The bound term
+           -- MUST only be evaluated if it is used inside the body.
+           -- Sharing may happen, but is optional.
+           -- It is also perfectly valid to just inline the bound term in the body.
+           | TCase Int CaseInfo TTerm [TAlt]
+           -- ^ Case scrutinee (always variable), case type, default value, alternatives
+           -- First, all TACon alternatives are tried; then all TAGuard alternatives
+           -- in top to bottom order.
+           -- TACon alternatives must not overlap.
+           | TUnit -- used for levels right now
+           | TSort
+           | TErased
+           | TCoerce TTerm  -- ^ Used by the GHC backend
+           | TError TError
+           -- ^ A runtime error, something bad has happened.
+  deriving (Show, Eq, Ord, Generic)
+
+-- | Compiler-related primitives. This are NOT the same thing as primitives
+-- in Agda's surface or internal syntax!
+-- Some of the primitives have a suffix indicating which type of arguments they take,
+-- using the following naming convention:
+-- Char | Type
+-- C    | Character
+-- F    | Float
+-- I    | Integer
+-- Q    | QName
+-- S    | String
+data TPrim
+  = PAdd | PAdd64
+  | PSub | PSub64
+  | PMul | PMul64
+  | PQuot | PQuot64
+  | PRem  | PRem64
+  | PGeq
+  | PLt   | PLt64
+  | PEqI  | PEq64
+  | PEqF
+  | PEqS
+  | PEqC
+  | PEqQ
+  | PIf
+  | PSeq
+  | PITo64 | P64ToI
+  deriving (Show, Eq, Ord, Generic)
+
+isPrimEq :: TPrim -> Bool
+isPrimEq p = p `elem` [PEqI, PEqF, PEqS, PEqC, PEqQ, PEq64]
+
+-- | Strip leading coercions and indicate whether there were some.
+coerceView :: TTerm -> (Bool, TTerm)
+coerceView = \case
+  TCoerce t -> (True,) $ snd $ coerceView t
+  t         -> (False, t)
+
+mkTApp :: TTerm -> Args -> TTerm
+mkTApp x           [] = x
+mkTApp (TApp x as) bs = TApp x (as ++ bs)
+mkTApp x           as = TApp x as
+
+tAppView :: TTerm -> (TTerm, [TTerm])
+tAppView = \case
+  TApp a bs -> second (++ bs) $ tAppView a
+  t         -> (t, [])
+
+-- | Expose the format @coerce f args@.
+--
+--   We fuse coercions, even if interleaving with applications.
+--   We assume that coercion is powerful enough to satisfy
+--   @
+--      coerce (coerce f a) b = coerce f a b
+--   @
+coerceAppView :: TTerm -> ((Bool, TTerm), [TTerm])
+coerceAppView = \case
+  TCoerce t -> first ((True,) . snd) $ coerceAppView t
+  TApp a bs -> second (++ bs) $ coerceAppView a
+  t         -> ((False, t), [])
+
+tLetView :: TTerm -> ([TTerm], TTerm)
+tLetView (TLet e b) = first (e :) $ tLetView b
+tLetView e          = ([], e)
+
+tLamView :: TTerm -> (Int, TTerm)
+tLamView = go 0
+  where go n (TLam b) = go (n + 1) b
+        go n t        = (n, t)
+
+mkTLam :: Int -> TTerm -> TTerm
+mkTLam n b = foldr ($) b $ replicate n TLam
+
+-- | Introduces a new binding
+mkLet :: TTerm -> TTerm -> TTerm
+mkLet x body = TLet x body
+
+tInt :: Integer -> TTerm
+tInt = TLit . LitNat
+
+intView :: TTerm -> Maybe Integer
+intView (TLit (LitNat x)) = Just x
+intView _ = Nothing
+
+word64View :: TTerm -> Maybe Word64
+word64View (TLit (LitWord64 x)) = Just x
+word64View _ = Nothing
+
+tPlusK :: Integer -> TTerm -> TTerm
+tPlusK 0 n = n
+tPlusK k n | k < 0 = tOp PSub n (tInt (-k))
+tPlusK k n = tOp PAdd (tInt k) n
+
+-- -(k + n)
+tNegPlusK :: Integer -> TTerm -> TTerm
+tNegPlusK k n = tOp PSub (tInt (-k)) n
+
+plusKView :: TTerm -> Maybe (Integer, TTerm)
+plusKView (TApp (TPrim PAdd) [k, n]) | Just k <- intView k = Just (k, n)
+plusKView (TApp (TPrim PSub) [n, k]) | Just k <- intView k = Just (-k, n)
+plusKView _ = Nothing
+
+negPlusKView :: TTerm -> Maybe (Integer, TTerm)
+negPlusKView (TApp (TPrim PSub) [k, n]) | Just k <- intView k = Just (-k, n)
+negPlusKView _ = Nothing
+
+tOp :: TPrim -> TTerm -> TTerm -> TTerm
+tOp op a b = TPOp op a b
+
+pattern TPOp :: TPrim -> TTerm -> TTerm -> TTerm
+pattern TPOp op a b = TApp (TPrim op) [a, b]
+
+pattern TPFn :: TPrim -> TTerm -> TTerm
+pattern TPFn op a = TApp (TPrim op) [a]
+
+tUnreachable :: TTerm
+tUnreachable = TError TUnreachable
+
+tIfThenElse :: TTerm -> TTerm -> TTerm -> TTerm
+tIfThenElse c i e = TApp (TPrim PIf) [c, i, e]
+
+data CaseType
+  = CTData QName
+    -- Case on datatype.
+  | CTNat
+  | CTInt
+  | CTChar
+  | CTString
+  | CTFloat
+  | CTQName
+  deriving (Show, Eq, Ord, Generic)
+
+data CaseInfo = CaseInfo
+  { caseLazy :: Bool
+  , caseErased :: Erased
+    -- ^ Is this a match on an erased argument?
+  , caseType :: CaseType }
+  deriving (Show, Eq, Ord, Generic)
+
+data TAlt
+  = TACon    { aCon  :: QName, aArity :: Int, aBody :: TTerm }
+  -- ^ Matches on the given constructor. If the match succeeds,
+  -- the pattern variables are prepended to the current environment
+  -- (pushes all existing variables aArity steps further away)
+  | TAGuard  { aGuard :: TTerm, aBody :: TTerm }
+  -- ^ Binds no variables
+  --
+  -- The guard must only use the variable that the case expression
+  -- matches on.
+  | TALit    { aLit :: Literal,   aBody:: TTerm }
+  deriving (Show, Eq, Ord, Generic)
+
+data TError
+  = TUnreachable
+  -- ^ Code which is unreachable. E.g. absurd branches or missing case defaults.
+  -- Runtime behaviour of unreachable code is undefined, but preferably
+  -- the program will exit with an error message. The compiler is free
+  -- to assume that this code is unreachable and to remove it.
+  | TMeta String
+  -- ^ Code which could not be obtained because of a hole in the program.
+  -- This should throw a runtime error.
+  -- The string gives some information about the meta variable that got compiled.
+  deriving (Show, Eq, Ord, Generic)
+
+
+class Unreachable a where
+  -- | Checks if the given expression is unreachable or not.
+  isUnreachable :: a -> Bool
+
+instance Unreachable TAlt where
+  isUnreachable = isUnreachable . aBody
+
+instance Unreachable TTerm where
+  isUnreachable (TError TUnreachable{}) = True
+  isUnreachable (TLet _ b) = isUnreachable b
+  isUnreachable _ = False
+
+instance KillRange Compiled where
+  killRange c = c -- bogus, but not used anyway
+
+
+-- * Utilities for ArgUsage
+---------------------------------------------------------------------------
+
+-- | @filterUsed used args@ drops those @args@ which are labelled
+-- @ArgUnused@ in list @used@.
+--
+-- Specification:
+--
+-- @
+--   filterUsed used args = [ a | (a, ArgUsed) <- zip args $ used ++ repeat ArgUsed ]
+-- @
+--
+-- Examples:
+--
+-- @
+--   filterUsed []                 == id
+--   filterUsed (repeat ArgUsed)   == id
+--   filterUsed (repeat ArgUnused) == const []
+-- @
+filterUsed :: [ArgUsage] -> [a] -> [a]
+filterUsed = curry $ \case
+  ([], args) -> args
+  (_ , [])   -> []
+  (ArgUsed   : used, a : args) -> a : filterUsed used args
+  (ArgUnused : used, a : args) ->     filterUsed used args
+
+-- NFData instances
+---------------------------------------------------------------------------
+
+instance NFData Compiled
+instance NFData ArgUsage
+instance NFData TTerm
+instance NFData TPrim
+instance NFData CaseType
+instance NFData CaseInfo
+instance NFData TAlt
+instance NFData TError
diff --git a/src/full/Agda/Termination/CallGraph.hs b/src/full/Agda/Termination/CallGraph.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/CallGraph.hs
@@ -0,0 +1,232 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ImplicitParams             #-}
+
+-- | Call graphs and related concepts, more or less as defined in
+--     \"A Predicative Analysis of Structural Recursion\" by
+--     Andreas Abel and Thorsten Altenkirch.
+
+-- Originally copied from Agda1 sources.
+
+module Agda.Termination.CallGraph
+  ( -- * Calls
+    Node
+  , Call, mkCall, mkCall', source, target, callMatrixSet
+  , (>*<)
+    -- * Call graphs
+  , CallGraph(..)
+  , targetNodes
+  , fromList
+  , toList
+  , union
+  , insert
+  , complete, completionStep
+  -- , prettyBehaviour
+  ) where
+
+import Prelude hiding (null)
+
+import qualified Data.List as List
+import Data.Set (Set)
+
+import Agda.Termination.CallMatrix (CallMatrix, CallMatrixAug(..), CMSet(..), CallComb(..))
+import qualified Agda.Termination.CallMatrix as CMSet
+import Agda.Termination.CutOff
+
+import Agda.Utils.Favorites (Favorites)
+import qualified Agda.Utils.Favorites as Fav
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional (Edge(..),Graph(..))
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+
+import Agda.Utils.Function
+
+import Agda.Utils.Null
+import Agda.Utils.PartialOrd
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Tuple
+
+------------------------------------------------------------------------
+-- Calls
+
+-- | Call graph nodes.
+--
+--   Machine integer 'Int' is sufficient, since we cannot index more than
+--   we have addresses on our machine.
+
+type Node = Int
+
+-- | Calls are edges in the call graph.
+--   It can be labelled with several call matrices if there
+--   are several pathes from one function to another.
+
+type Call cinfo = Edge Node (CMSet cinfo)
+
+callMatrixSet :: Call cinfo -> CMSet cinfo
+callMatrixSet = label
+
+-- | Make a call with a single matrix.
+mkCall :: Node -> Node -> CallMatrix -> cinfo -> Call cinfo
+mkCall s t m cinfo = Edge s t $ singleton $ CallMatrixAug m cinfo
+
+-- | Make a call with empty @cinfo@.
+mkCall' :: Monoid cinfo => Node -> Node -> CallMatrix -> Call cinfo
+mkCall' s t m = mkCall s t m mempty
+
+------------------------------------------------------------------------
+-- Call graphs
+
+-- | A call graph is a set of calls. Every call also has some
+-- associated meta information, which should be 'Monoid'al so that the
+-- meta information for different calls can be combined when the calls
+-- are combined.
+
+newtype CallGraph cinfo = CallGraph { theCallGraph :: Graph Node (CMSet cinfo) }
+  deriving (Show)
+
+
+-- | Returns all the nodes with incoming edges.  Somewhat expensive. @O(e)@.
+
+targetNodes :: CallGraph cinfo -> Set Node
+targetNodes = Graph.targetNodes . theCallGraph
+
+-- | Converts a call graph to a list of calls with associated meta
+--   information.
+
+toList :: CallGraph cinfo -> [Call cinfo]
+toList = Graph.edges . theCallGraph
+
+-- | Converts a list of calls with associated meta information to a
+--   call graph.
+
+fromListCG :: [Call cinfo] -> CallGraph cinfo
+fromListCG = CallGraph . Graph.fromEdgesWith CMSet.union
+
+-- | 'null' checks whether the call graph is completely disconnected.
+instance Null (CallGraph cinfo) where
+  empty = CallGraph Graph.empty
+  null  = List.all (null . label) . toList
+
+-- | Takes the union of two call graphs.
+
+union :: CallGraph cinfo -> CallGraph cinfo -> CallGraph cinfo
+union (CallGraph cs1) (CallGraph cs2) = CallGraph $
+  Graph.unionWith CMSet.union cs1 cs2
+
+-- | 'CallGraph' is a monoid under 'union'.
+
+instance Semigroup (CallGraph cinfo) where
+  (<>) = union
+
+instance Monoid (CallGraph cinfo) where
+  mempty  = empty
+  mappend = (<>)
+
+instance Singleton (Call cinfo) (CallGraph cinfo) where
+  singleton = fromList . singleton
+
+instance Collection (Call cinfo) (CallGraph cinfo) where
+  fromList = fromListCG
+
+-- | Inserts a call into a call graph.
+
+insert :: Node -> Node -> CallMatrix -> cinfo
+       -> CallGraph cinfo -> CallGraph cinfo
+insert s t cm cinfo = CallGraph . Graph.insertEdgeWith CMSet.union e . theCallGraph
+  where e = mkCall s t cm cinfo
+
+
+-- * Combination of a new thing with an old thing
+--   returning a really new things and updated old things.
+
+type CombineNewOldT a = a -> a -> (a, a)
+
+class CombineNewOld a where
+  combineNewOld :: CombineNewOldT a
+
+instance PartialOrd a => CombineNewOld (Favorites a) where
+  combineNewOld new old = (new', Fav.unionCompared (new', old'))
+    where (new', old') = Fav.compareFavorites new old
+
+deriving instance CombineNewOld (CMSet cinfo)
+
+instance (Monoid a, CombineNewOld a, Ord n) => CombineNewOld (Graph n a) where
+  combineNewOld new old = Graph.unzip $ Graph.unionWith comb new' old'
+    where
+      new' = (,mempty) <$> new
+      old' = (mempty,) <$> old
+      comb (new1,old1) (new2,old2)  -- TODO: ensure old1 is null
+        = mapFst (new2 `mappend`) $ combineNewOld new1 old2
+        -- -- | old1 == mempty = mapFst (new2 `mappend`) $ combineNewOld new1 old2
+        -- -- | otherwise      = __IMPOSSIBLE__
+
+      -- Filter unlabelled edges from the resulting new graph.
+      -- filt = Graph.filterEdges (not . null)
+
+-- | Call graph combination.
+--
+--   Application of '>*<' to all pairs @(c1,c2)@
+--   for which @'source' c1 = 'target' c2@.)
+
+-- GHC supports implicit-parameter constraints in instance declarations
+-- only from 7.4.  To maintain compatibility with 7.2, we skip this instance:
+-- KEEP:
+-- instance (Monoid cinfo, ?cutoff :: CutOff) => CombineNewOld (CallGraph cinfo) where
+--   combineNewOld (CallGraph new) (CallGraph old) = CallGraph -*- CallGraph $ combineNewOld comb old
+--     -- combined calls:
+--     where comb = Graph.composeWith (>*<) CMSet.union new old
+
+-- Non-overloaded version:
+combineNewOldCallGraph :: (Monoid cinfo, ?cutoff :: CutOff) => CombineNewOldT (CallGraph cinfo)
+combineNewOldCallGraph (CallGraph new) (CallGraph old) = CallGraph -*- CallGraph $ combineNewOld comb old
+    -- combined calls:
+    where comb = Graph.composeWith (>*<) CMSet.union new old
+
+-- | Call graph comparison.
+--   A graph @cs'@ is ``worse'' than @cs@ if it has a new edge (call)
+--   or a call got worse, which means that one of its elements
+--   that was better or equal to 'Le' moved a step towards 'Un'.
+--
+--   A call graph is complete if combining it with itself does not make it
+--   any worse.  This is sound because of monotonicity:  By combining a graph
+--   with itself, it can only get worse, but if it does not get worse after
+--   one such step, it gets never any worse.
+
+-- | @'complete' cs@ completes the call graph @cs@. A call graph is
+-- complete if it contains all indirect calls; if @f -> g@ and @g ->
+-- h@ are present in the graph, then @f -> h@ should also be present.
+
+complete :: (?cutoff :: CutOff) => Monoid cinfo => CallGraph cinfo -> CallGraph cinfo
+complete cs = repeatWhile (mapFst (not . null) . completionStep cs) cs
+
+completionStep :: (?cutoff :: CutOff) => Monoid cinfo =>
+  CallGraph cinfo -> CallGraph cinfo -> (CallGraph cinfo, CallGraph cinfo)
+completionStep gOrig gThis = combineNewOldCallGraph gOrig gThis
+
+------------------------------------------------------------------------
+-- * Printing
+------------------------------------------------------------------------
+
+-- | Displays the recursion behaviour corresponding to a call graph.
+
+instance Pretty cinfo => Pretty (CallGraph cinfo) where
+  pretty = vcat . map prettyCall . toList
+    where
+    prettyCall e = if null (callMatrixSet e) then empty else align 20 $
+      [ ("Source:",    text $ show $ source e)
+      , ("Target:",    text $ show $ target e)
+      , ("Matrix:",    pretty $ callMatrixSet e)
+      ]
+
+-- -- | Displays the recursion behaviour corresponding to a call graph.
+
+-- prettyBehaviour :: Show cinfo => CallGraph cinfo -> Doc
+-- prettyBehaviour = vcat . map prettyCall . filter toSelf . toList
+--   where
+--   toSelf c = source c == target c
+
+--   prettyCall e = vcat $ map text
+--     [ "Function:  " ++ show (source e)
+-- --    , "Behaviour: " ++ show (diagonal $ mat $ cm c)  -- TODO
+-- --    , "Meta info: " ++ show cinfo
+--     ]
diff --git a/src/full/Agda/Termination/CallMatrix.hs b/src/full/Agda/Termination/CallMatrix.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/CallMatrix.hs
@@ -0,0 +1,209 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ImplicitParams             #-}
+
+module Agda.Termination.CallMatrix where
+
+-- module Agda.Termination.CallMatrix
+--   ( CallMatrix'(..), CallMatrix
+--   , callMatrix
+--   , CallComb(..)
+--   , tests
+--   ) where
+
+
+import Agda.Termination.CutOff
+import Agda.Termination.Order as Order
+import Agda.Termination.SparseMatrix as Matrix
+import Agda.Termination.Semiring (HasZero(..))
+
+import Agda.Utils.Favorites (Favorites)
+import qualified Agda.Utils.Favorites as Fav
+
+import Agda.Utils.Null
+import Agda.Utils.PartialOrd
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+
+------------------------------------------------------------------------
+--  * Call matrices
+------------------------------------------------------------------------
+
+-- | Call matrix indices = function argument indices.
+--
+--   Machine integer 'Int' is sufficient, since we cannot index more arguments
+--   than we have addresses on our machine.
+
+type ArgumentIndex = Int
+
+-- | Call matrices.
+--
+--   A call matrix for a call @f --> g@ has dimensions @ar(g) × ar(f)@.
+--
+--   Each column corresponds to one formal argument of caller @f@.
+--   Each row corresponds to one argument in the call to @g@.
+--
+--   In the presence of dot patterns, a call argument can be related
+--   to /several/ different formal arguments of @f@.
+--
+--   See e.g. @test/succeed/DotPatternTermination.agda@:
+--
+--   @
+--     data D : Nat -> Set where
+--       cz : D zero
+--       c1 : forall n -> D n -> D (suc n)
+--       c2 : forall n -> D n -> D n
+--
+--     f : forall n -> D n -> Nat
+--     f .zero    cz        = zero
+--     f .(suc n) (c1  n d) = f n (c2 n d)
+--     f n        (c2 .n d) = f n d
+--   @
+--
+--   Call matrices (without guardedness) are
+--
+--   @
+--           -1 -1   n < suc n  and       n <  c1 n d
+--            ?  =                   c2 n d <= c1 n d
+--
+--            = -1   n <= n     and  n < c2 n d
+--            ? -1                   d < c2 n d
+--   @
+--
+--   Here is a part of the original documentation for call matrices
+--   (kept for historical reasons):
+--
+--   This datatype encodes information about a single recursive
+--   function application. The columns of the call matrix stand for
+--   'source' function arguments (patterns). The rows of the matrix stand for
+--   'target' function arguments. Element @(i, j)@ in the matrix should
+--   be computed as follows:
+--
+--     * 'Order.lt' (less than) if the @j@-th argument to the 'target'
+--       function is structurally strictly smaller than the @i@-th
+--       pattern.
+--
+--     * 'Order.le' (less than or equal) if the @j@-th argument to the
+--       'target' function is structurally smaller than the @i@-th
+--       pattern.
+--
+--     * 'Order.unknown' otherwise.
+
+
+newtype CallMatrix' a = CallMatrix { mat :: Matrix ArgumentIndex a }
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable, PartialOrd)
+
+type CallMatrix = CallMatrix' Order
+
+deriving instance NotWorse CallMatrix
+
+instance HasZero a => Diagonal (CallMatrix' a) a where
+  diagonal = diagonal . mat
+
+
+-- | Call matrix multiplication and call combination.
+
+class CallComb a where
+  (>*<) :: (?cutoff :: CutOff) => a -> a -> a
+
+-- | Call matrix multiplication.
+--
+--   @f --(m1)--> g --(m2)--> h@  is combined to @f --(m2 `mul` m1)--> h@
+--
+--   Note the reversed order of multiplication:
+--   The matrix @c1@ of the second call @g-->h@ in the sequence
+--   @f-->g-->h@ is multiplied with the matrix @c2@ of the first call.
+--
+--   Preconditions:
+--   @m1@ has dimensions @ar(g) × ar(f)@.
+--   @m2@ has dimensions @ar(h) × ar(g)@.
+--
+--   Postcondition:
+--   @m1 >*< m2@ has dimensions @ar(h) × ar(f)@.
+
+instance CallComb CallMatrix where
+  CallMatrix m1 >*< CallMatrix m2 = CallMatrix $ mul orderSemiring m2 m1
+
+{- UNUSED, BUT DON'T REMOVE!
+-- | Call matrix addition = minimum = pick worst information.
+addCallMatrices :: (?cutoff :: CutOff) => CallMatrix -> CallMatrix -> CallMatrix
+addCallMatrices cm1 cm2 = CallMatrix $
+  add (Semiring.add orderSemiring) (mat cm1) (mat cm2)
+-}
+
+------------------------------------------------------------------------
+-- * Call matrix augmented with path information.
+------------------------------------------------------------------------
+
+-- | Call matrix augmented with path information.
+
+data CallMatrixAug cinfo = CallMatrixAug
+  { augCallMatrix :: CallMatrix -- ^ The matrix of the (composed call).
+  , augCallInfo   :: cinfo      -- ^ Meta info, like call path.
+  }
+  deriving (Eq, Show)
+
+instance Diagonal (CallMatrixAug cinfo) Order where
+  diagonal = diagonal . augCallMatrix
+
+instance PartialOrd (CallMatrixAug cinfo) where
+  comparable m m' = comparable (augCallMatrix m) (augCallMatrix m')
+
+instance NotWorse (CallMatrixAug cinfo) where
+  c1 `notWorse` c2 = augCallMatrix c1 `notWorse` augCallMatrix c2
+
+-- | Augmented call matrix multiplication.
+
+instance Monoid cinfo => CallComb (CallMatrixAug cinfo) where
+  CallMatrixAug m1 p1 >*< CallMatrixAug m2 p2 =
+    CallMatrixAug (m1 >*< m2) (mappend p1 p2)
+
+-- | Non-augmented call matrix.
+
+noAug :: Monoid cinfo => CallMatrix -> CallMatrixAug cinfo
+noAug m = CallMatrixAug m mempty
+
+------------------------------------------------------------------------
+-- * Sets of incomparable call matrices augmented with path information.
+------------------------------------------------------------------------
+
+-- | Sets of incomparable call matrices augmented with path information.
+--   Use overloaded 'null', 'empty', 'singleton', 'mappend'.
+newtype CMSet cinfo = CMSet { cmSet :: Favorites (CallMatrixAug cinfo) }
+  deriving ( Show, Semigroup, Monoid, Null, Singleton (CallMatrixAug cinfo) )
+
+-- | Call matrix set product is the Cartesian product.
+
+instance Monoid cinfo => CallComb (CMSet cinfo) where
+  CMSet as >*< CMSet bs = CMSet $ Fav.fromList $
+    [ a >*< b | a <- Fav.toList as, b <- Fav.toList bs ]
+
+-- | Insert into a call matrix set.
+
+insert :: CallMatrixAug cinfo -> CMSet cinfo -> CMSet cinfo
+insert a (CMSet as) = CMSet $ Fav.insert a as
+
+-- | Union two call matrix sets.
+
+union :: CMSet cinfo -> CMSet cinfo -> CMSet cinfo
+union = mappend
+-- union (CMSet as) (CMSet bs) = CMSet $ Fav.union as bs
+
+-- | Convert into a list of augmented call matrices.
+
+toList :: CMSet cinfo -> [CallMatrixAug cinfo]
+toList (CMSet as) = Fav.toList as
+
+------------------------------------------------------------------------
+-- * Printing
+------------------------------------------------------------------------
+
+instance Pretty CallMatrix where
+  pretty (CallMatrix m) = pretty m
+
+instance Pretty cinfo => Pretty (CallMatrixAug cinfo) where
+  pretty (CallMatrixAug m cinfo) = pretty cinfo $$ pretty m
+
+instance Pretty cinfo => Pretty (CMSet cinfo) where
+  pretty = vcat . punctuate newLine . map pretty . toList
+    where newLine = "\n"
diff --git a/src/full/Agda/Termination/CutOff.hs b/src/full/Agda/Termination/CutOff.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/CutOff.hs
@@ -0,0 +1,33 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Defines 'CutOff' type which is used in "Agda.Interaction.Options".
+--   This module's purpose is to eliminate the dependency of
+--   "Agda.TypeChecking.Monad.Base" on the termination checker and
+--   everything it imports.
+
+module Agda.Termination.CutOff
+  ( CutOff(CutOff, DontCutOff)
+  , defaultCutOff
+  ) where
+
+import Control.DeepSeq
+
+-- | Cut off structural order comparison at some depth in termination checker?
+
+data CutOff
+  = CutOff !Int -- ^ @c >= 0@ means: record decrease up to including @c+1@.
+  | DontCutOff
+  deriving (Eq , Ord)
+
+instance Show CutOff where
+  show (CutOff k) = show k
+  show DontCutOff = "∞"
+
+instance NFData CutOff where
+  rnf (CutOff _) = ()
+  rnf DontCutOff = ()
+
+-- | The default termination depth.
+
+defaultCutOff :: CutOff
+defaultCutOff = CutOff 0 -- minimum value
diff --git a/src/full/Agda/Termination/Monad.hs b/src/full/Agda/Termination/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/Monad.hs
@@ -0,0 +1,628 @@
+
+-- | The monad for the termination checker.
+--
+--   The termination monad @TerM@ is an extension of
+--   the type checking monad 'TCM' by an environment
+--   with information needed by the termination checker.
+
+module Agda.Termination.Monad where
+
+import Prelude hiding (null)
+
+import Control.Applicative hiding (empty)
+
+import qualified Control.Monad.Fail as Fail
+
+import Control.Monad          ( forM )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Except
+import Control.Monad.Reader
+
+import Data.DList (DList)
+import qualified Data.DList as DL
+import Data.Semigroup ( Semigroup(..) )
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options (optTerminationDepth)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Literal
+
+import Agda.Termination.CutOff
+import Agda.Termination.Order (Order,le,unknown)
+import Agda.Termination.RecCheck (MutualNames, anyDefs)
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Monad.Benchmark
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Benchmark as B
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List   ( hasElem )
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Monoid
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (Pretty, prettyShow)
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.VarSet (VarSet)
+import qualified Agda.Utils.VarSet as VarSet
+
+import Agda.Utils.Impossible
+
+-- | The target of the function we are checking.
+
+data Target
+  = TargetDef QName
+      -- ^ The target of recursion is a @record@, @data@, or unreducible @Def@.
+  | TargetRecord
+      -- ^ We are termination-checking a record.
+  | TargetOther
+      -- ^ None of the above two or unknown.
+  deriving (Eq, Show)
+
+-- | The current guardedness level.
+
+type Guarded = Order
+
+-- | The termination environment.
+
+data TerEnv = TerEnv
+
+  -- First part: options, configuration.
+
+  { terUseDotPatterns :: Bool
+    -- ^ Are we mining dot patterns to find evindence of structal descent?
+  , terSizeSuc :: Maybe QName
+    -- ^ The name of size successor, if any.
+  , terSharp   :: Maybe QName
+    -- ^ The name of the delay constructor (sharp), if any.
+  , terCutOff  :: CutOff
+    -- ^ Depth at which to cut off the structural order.
+
+  -- Second part: accumulated info during descent into decls./term.
+
+  , terCurrent :: QName
+    -- ^ The name of the function we are currently checking.
+  , terMutual  :: MutualNames
+    -- ^ The names of the functions in the mutual block we are checking.
+    --   This includes the internally generated functions
+    --   (with, extendedlambda, coinduction).
+  , terUserNames :: Set QName
+    -- ^ The list of name actually appearing in the file (abstract syntax).
+    --   Excludes the internally generated functions.
+  , terHaveInlinedWith :: Bool
+    -- ^ Does the actual clause result from with-inlining?
+    --   (If yes, it may be ill-typed.)
+  , terTarget  :: Target
+    -- ^ Target type of the function we are currently termination checking.
+    --   Only the constructors of 'Target' are considered guarding.
+  , terMaskArgs :: [Bool]
+    -- ^ Only consider the 'notMasked' 'False' arguments for establishing termination.
+    --   See issue #1023.
+  , terMaskResult :: Bool
+    -- ^ Only consider guardedness if 'False' (not masked).
+  , _terSizeDepth :: Int  -- lazy by intention!
+    -- ^ How many @SIZELT@ relations do we have in the context
+    --   (= clause telescope).  Used to approximate termination
+    --   for metas in call args.
+  , terPatterns :: MaskedDeBruijnPatterns
+    -- ^ The patterns of the clause we are checking.
+  , terPatternsRaise :: !Int
+    -- ^ Number of additional binders we have gone under
+    --   (and consequently need to raise the patterns to compare to terms).
+    --   Updated during call graph extraction, hence strict.
+  , terGuarded :: !Guarded
+    -- ^ The current guardedness status.  Changes as we go deeper into the term.
+    --   Updated during call graph extraction, hence strict.
+  , terUseSizeLt :: Bool
+    -- ^ When extracting usable size variables during construction of the call
+    --   matrix, can we take the variable for use with SIZELT constraints from the context?
+    --   Yes, if we are under an inductive constructor.
+    --   No, if we are under a record constructor.
+    --   (See issue #1015).
+  , terUsableVars :: VarSet
+    -- ^ Pattern variables that can be compared to argument variables using SIZELT.
+  }
+
+-- | An empty termination environment.
+--
+--   Values are set to a safe default meaning that with these
+--   initial values the termination checker will not miss
+--   termination errors it would have seen with better settings
+--   of these values.
+--
+--   Values that do not have a safe default are set to
+--   @__IMPOSSIBLE__@.
+
+defaultTerEnv :: TerEnv
+defaultTerEnv = TerEnv
+  { terUseDotPatterns           = False -- must be False initially!
+  , terSizeSuc                  = Nothing
+  , terSharp                    = Nothing
+  , terCutOff                   = defaultCutOff
+  , terUserNames                = __IMPOSSIBLE__ -- needs to be set!
+  , terMutual                   = __IMPOSSIBLE__ -- needs to be set!
+  , terCurrent                  = __IMPOSSIBLE__ -- needs to be set!
+  , terHaveInlinedWith          = False
+  , terTarget                   = TargetOther
+  , terMaskArgs                 = repeat False   -- use all arguments (mask none)
+  , terMaskResult               = False          -- use result (do not mask)
+  , _terSizeDepth               = __IMPOSSIBLE__ -- needs to be set!
+  , terPatterns                 = __IMPOSSIBLE__ -- needs to be set!
+  , terPatternsRaise            = 0
+  , terGuarded                  = le -- not initially guarded
+  , terUseSizeLt                = False -- initially, not under data constructor
+  , terUsableVars               = VarSet.empty
+  }
+
+-- | Termination monad service class.
+
+class (Functor m, Monad m) => MonadTer m where
+  terAsk   :: m TerEnv
+  terLocal :: (TerEnv -> TerEnv) -> m a -> m a
+
+  terAsks :: (TerEnv -> a) -> m a
+  terAsks f = f <$> terAsk
+
+-- | Termination monad.
+
+newtype TerM a = TerM { terM :: ReaderT TerEnv TCM a }
+  deriving ( Functor
+           , Applicative
+           , Monad
+           , Fail.MonadFail
+           , MonadError TCErr
+           , MonadStatistics
+           , HasOptions
+           , HasBuiltins
+           , MonadDebug
+           , HasConstInfo
+           , MonadIO
+           , MonadTCEnv
+           , MonadTCState
+           , MonadTCM
+           , ReadTCState
+           , MonadReduce
+           , MonadAddContext
+           , PureTCM
+           )
+
+-- This could be derived automatically, but the derived type family becomes `BenchPhase (ReaderT TerEnv TCM)` which
+-- is *fine* but triggers complaints that the "type family application is no smaller than the instance head, why not
+-- nuke everything with UndecidableInstances".
+instance MonadBench TerM where
+  type BenchPhase TerM = Phase
+  getBenchmark              = TerM $ B.getBenchmark
+  putBenchmark              = TerM . B.putBenchmark
+  modifyBenchmark           = TerM . B.modifyBenchmark
+  finally (TerM m) (TerM f) = TerM $ (B.finally m f)
+
+instance MonadTer TerM where
+  terAsk     = TerM $ ask
+  terLocal f = TerM . local f . terM
+
+-- | Generic run method for termination monad.
+runTer :: TerEnv -> TerM a -> TCM a
+runTer tenv (TerM m) = runReaderT m tenv
+
+-- | Run TerM computation in default environment (created from options).
+
+runTerDefault :: TerM a -> TCM a
+runTerDefault cont = do
+
+  -- Assemble then initial configuration of the termination environment.
+
+  cutoff <- optTerminationDepth <$> pragmaOptions
+
+  -- Get the name of size suc (if sized types are enabled)
+  suc <- sizeSucName
+
+  -- The name of sharp (if available).
+  sharp <- fmap nameOfSharp <$> coinductionKit
+
+  let tenv = defaultTerEnv
+        { terSizeSuc                  = suc
+        , terSharp                    = sharp
+        , terCutOff                   = cutoff
+        }
+
+  runTer tenv cont
+
+-- -- * Termination monad is a 'MonadTCM'.
+
+-- instance MonadError TCErr TerM where
+--   throwError = liftTCM . throwError
+--   catchError m handler = TerM $ ReaderT $ \ tenv -> do
+--     runTer tenv m `catchError` (\ err -> runTer tenv $ handler err)
+
+instance Semigroup m => Semigroup (TerM m) where
+  (<>) = liftA2 (<>)
+
+instance (Semigroup m, Monoid m) => Monoid (TerM m) where
+  mempty  = pure mempty
+  mappend = (<>)
+  mconcat = mconcat <.> sequence
+
+-- * Modifiers and accessors for the termination environment in the monad.
+
+terGetUseDotPatterns :: TerM Bool
+terGetUseDotPatterns = terAsks terUseDotPatterns
+
+terSetUseDotPatterns :: Bool -> TerM a -> TerM a
+terSetUseDotPatterns b = terLocal $ \ e -> e { terUseDotPatterns = b }
+
+terGetSizeSuc :: TerM (Maybe QName)
+terGetSizeSuc = terAsks terSizeSuc
+
+terGetCurrent :: TerM QName
+terGetCurrent = terAsks terCurrent
+
+terSetCurrent :: QName -> TerM a -> TerM a
+terSetCurrent q = terLocal $ \ e -> e { terCurrent = q }
+
+terGetSharp :: TerM (Maybe QName)
+terGetSharp = terAsks terSharp
+
+terGetCutOff :: TerM CutOff
+terGetCutOff = terAsks terCutOff
+
+terGetMutual :: TerM MutualNames
+terGetMutual = terAsks terMutual
+
+terGetUserNames :: TerM (Set QName)
+terGetUserNames = terAsks terUserNames
+
+terGetTarget :: TerM Target
+terGetTarget = terAsks terTarget
+
+terSetTarget :: Target -> TerM a -> TerM a
+terSetTarget t = terLocal $ \ e -> e { terTarget = t }
+
+terGetHaveInlinedWith :: TerM Bool
+terGetHaveInlinedWith = terAsks terHaveInlinedWith
+
+terSetHaveInlinedWith :: TerM a -> TerM a
+terSetHaveInlinedWith = terLocal $ \ e -> e { terHaveInlinedWith = True }
+
+terGetMaskArgs :: TerM [Bool]
+terGetMaskArgs = terAsks terMaskArgs
+
+terSetMaskArgs :: [Bool] -> TerM a -> TerM a
+terSetMaskArgs b = terLocal $ \ e -> e { terMaskArgs = b }
+
+terGetMaskResult :: TerM Bool
+terGetMaskResult = terAsks terMaskResult
+
+terSetMaskResult :: Bool -> TerM a -> TerM a
+terSetMaskResult b = terLocal $ \ e -> e { terMaskResult = b }
+
+terGetPatterns :: TerM (MaskedDeBruijnPatterns)
+terGetPatterns = do
+  n   <- terAsks terPatternsRaise
+  mps <- terAsks terPatterns
+  return $ if n == 0 then mps else map (fmap (raise n)) mps
+
+terSetPatterns :: MaskedDeBruijnPatterns -> TerM a -> TerM a
+terSetPatterns ps = terLocal $ \ e -> e { terPatterns = ps }
+
+terRaise :: TerM a -> TerM a
+terRaise = terLocal $ \ e -> e { terPatternsRaise = terPatternsRaise e + 1 }
+
+terGetGuarded :: TerM Guarded
+terGetGuarded = terAsks terGuarded
+
+terModifyGuarded :: (Order -> Order) -> TerM a -> TerM a
+terModifyGuarded f = terLocal $ \ e -> e { terGuarded = f $ terGuarded e }
+
+terSetGuarded :: Order -> TerM a -> TerM a
+terSetGuarded = terModifyGuarded . const
+
+terUnguarded :: TerM a -> TerM a
+terUnguarded = terSetGuarded unknown
+
+-- | Lens for '_terSizeDepth'.
+
+terSizeDepth :: Lens' TerEnv Int
+terSizeDepth f e = f (_terSizeDepth e) <&> \ i -> e { _terSizeDepth = i }
+
+-- | Lens for 'terUsableVars'.
+
+terGetUsableVars :: TerM VarSet
+terGetUsableVars = terAsks terUsableVars
+
+terModifyUsableVars :: (VarSet -> VarSet) -> TerM a -> TerM a
+terModifyUsableVars f = terLocal $ \ e -> e { terUsableVars = f $ terUsableVars e }
+
+terSetUsableVars :: VarSet -> TerM a -> TerM a
+terSetUsableVars = terModifyUsableVars . const
+
+-- | Lens for 'terUseSizeLt'.
+
+terGetUseSizeLt :: TerM Bool
+terGetUseSizeLt = terAsks terUseSizeLt
+
+terModifyUseSizeLt :: (Bool -> Bool) -> TerM a -> TerM a
+terModifyUseSizeLt f = terLocal $ \ e -> e { terUseSizeLt = f $ terUseSizeLt e }
+
+terSetUseSizeLt :: Bool -> TerM a -> TerM a
+terSetUseSizeLt = terModifyUseSizeLt . const
+
+-- | Compute usable vars from patterns and run subcomputation.
+withUsableVars :: UsableSizeVars a => a -> TerM b -> TerM b
+withUsableVars pats m = do
+  vars <- usableSizeVars pats
+  reportSLn "term.size" 70 $ "usableSizeVars = " ++ show vars
+  reportSDoc "term.size" 20 $ if null vars then "no usuable size vars" else
+    "the size variables amoung these variables are usable: " <+>
+      sep (map (prettyTCM . var) $ VarSet.toList vars)
+  terSetUsableVars vars $ m
+
+-- | Set 'terUseSizeLt' when going under constructor @c@.
+conUseSizeLt :: QName -> TerM a -> TerM a
+conUseSizeLt c m = do
+  ifM (liftTCM $ isEtaOrCoinductiveRecordConstructor c)  -- Non-eta inductive records are the same as datatypes
+    (terSetUseSizeLt False m)
+    (terSetUseSizeLt True m)
+
+-- | Set 'terUseSizeLt' for arguments following projection @q@.
+--   We disregard j<i after a non-coinductive projection.
+--   However, the projection need not be recursive (Issue 1470).
+projUseSizeLt :: QName -> TerM a -> TerM a
+projUseSizeLt q m = do
+  co <- isCoinductiveProjection False q
+  reportSLn "term.size" 20 $ applyUnless co ("not " ++) $
+    "using SIZELT vars after projection " ++ prettyShow q
+  terSetUseSizeLt co m
+
+-- | For termination checking purposes flat should not be considered a
+--   projection. That is, it flat doesn't preserve either structural order
+--   or guardedness like other projections do.
+--   Andreas, 2012-06-09: the same applies to projections of recursive records.
+isProjectionButNotCoinductive :: MonadTCM tcm => QName -> tcm Bool
+isProjectionButNotCoinductive qn = liftTCM $ do
+  b <- isProjectionButNotCoinductive' qn
+  reportSDoc "term.proj" 60 $ do
+    "identifier" <+> prettyTCM qn <+> do
+      text $
+        if b then "is an inductive projection"
+          else "is either not a projection or coinductive"
+  return b
+  where
+    isProjectionButNotCoinductive' qn = do
+      flat <- fmap nameOfFlat <$> coinductionKit
+      if Just qn == flat
+        then return False
+        else do
+          mp <- isProjection qn
+          case mp of
+            Just Projection{ projProper = Just{}, projFromType = t }
+              -> isInductiveRecord (unArg t)
+            _ -> return False
+
+-- | Check whether a projection belongs to a coinductive record
+--   and is actually recursive.
+--   E.g.
+--   @
+--      isCoinductiveProjection (Stream.head) = return False
+--
+--      isCoinductiveProjection (Stream.tail) = return True
+--   @
+isCoinductiveProjection :: MonadTCM tcm => Bool -> QName -> tcm Bool
+isCoinductiveProjection mustBeRecursive q = liftTCM $ do
+  reportSLn "term.guardedness" 40 $ "checking isCoinductiveProjection " ++ prettyShow q
+  flat <- fmap nameOfFlat <$> coinductionKit
+  -- yes for ♭
+  if Just q == flat then return True else do
+    pdef <- getConstInfo q
+    case isProjection_ (theDef pdef) of
+      Just Projection{ projProper = Just{}, projFromType = Arg _ r, projIndex = n } ->
+        caseMaybeM (isRecord r) __IMPOSSIBLE__ $ \ rdef -> do
+          -- no for inductive or non-recursive record
+          if recInduction rdef /= Just CoInductive then return False else do
+            reportSLn "term.guardedness" 40 $ prettyShow q ++ " is coinductive; record type is " ++ prettyShow r
+            if not mustBeRecursive then return True else do
+              reportSLn "term.guardedness" 40 $ prettyShow q ++ " must be recursive"
+              if not (safeRecRecursive rdef) then return False else do
+                reportSLn "term.guardedness" 40 $ prettyShow q ++ " has been declared recursive, doing actual check now..."
+                -- TODO: the following test for recursiveness of a projection should be cached.
+                -- E.g., it could be stored in the @Projection@ component.
+                -- Now check if type of field mentions mutually recursive symbol.
+                -- Get the type of the field by dropping record parameters and record argument.
+                let TelV tel core = telView' (defType pdef)
+                    (pars, tel') = splitAt n $ telToList tel
+                    mut = fromMaybe __IMPOSSIBLE__ $ recMutual rdef
+                -- Check if any recursive symbols appear in the record type.
+                -- Q (2014-07-01): Should we normalize the type?
+                -- A (2017-01-13): Yes, since we also normalize during positivity check?
+                -- See issue #1899.
+                reportSDoc "term.guardedness" 40 $ inTopContext $ sep
+                  [ "looking for recursive occurrences of"
+                  , sep (map prettyTCM mut)
+                  , "in"
+                  , addContext pars $ prettyTCM (telFromList tel')
+                  , "and"
+                  , addContext tel $ prettyTCM core
+                  ]
+                when (null mut) __IMPOSSIBLE__
+                names <- anyDefs (mut `hasElem`) (map (snd . unDom) tel', core)
+                reportSDoc "term.guardedness" 40 $
+                  "found" <+> if null names then "none" else sep (map prettyTCM $ Set.toList names)
+                return $ not $ null names
+      _ -> do
+        reportSLn "term.guardedness" 40 $ prettyShow q ++ " is not a proper projection"
+        return False
+  where
+  -- Andreas, 2018-02-24, issue #2975, example:
+  -- @
+  -- record R : Set where
+  --   coinductive
+  --   field force : R
+
+  --   r : R
+  --   force r = r
+  -- @
+  -- The termination checker expects the positivity checker to have run on the
+  -- record declaration R to know whether R is recursive.
+  -- However, here, because the awkward processing of record declarations (see #434),
+  -- that has not happened.  To avoid crashing (as in Agda 2.5.3),
+  -- we rather give the possibly wrong answer here,
+  -- restoring the behavior of Agda 2.5.2.  TODO: fix record declaration checking.
+  safeRecRecursive :: Defn -> Bool
+  safeRecRecursive (Record { recMutual = Just qs }) = not $ null qs
+  safeRecRecursive _ = False
+
+-- * De Bruijn pattern stuff
+
+-- | How long is the path to the deepest atomic pattern?
+patternDepth :: forall a. Pattern' a -> Int
+patternDepth = getMaxNat . foldrPattern depth where
+  depth :: Pattern' a -> MaxNat -> MaxNat
+  depth ConP{} = succ      -- add 1 to the maximum of the depth of the subpatterns
+  depth _      = id        -- atomic pattern (leaf) has depth 0
+
+-- | A dummy pattern used to mask a pattern that cannot be used
+--   for structural descent.
+
+unusedVar :: DeBruijnPattern
+unusedVar = litP (LitString "term.unused.pat.var")
+
+-- | Extract variables from 'DeBruijnPattern's that could witness a decrease
+--   via a SIZELT constraint.
+--
+--   These variables must be under an inductive constructor (with no record
+--   constructor in the way), or after a coinductive projection (with no
+--   inductive one in the way).
+
+class UsableSizeVars a where
+  usableSizeVars :: a -> TerM VarSet
+
+instance UsableSizeVars DeBruijnPattern where
+  usableSizeVars = foldrPattern $ \case
+    VarP _ x   -> const $ ifM terGetUseSizeLt (return $ VarSet.singleton $ dbPatVarIndex x) $
+                   {-else-} return mempty
+    ConP c _ _ -> conUseSizeLt $ conName c
+    LitP{}     -> none
+    DotP{}     -> none
+    ProjP{}    -> none
+    IApplyP{}  -> none
+    DefP{} -> none
+    where none _ = return mempty
+
+instance UsableSizeVars [DeBruijnPattern] where
+  usableSizeVars ps =
+    case ps of
+      []               -> return mempty
+      (ProjP _ q : ps) -> projUseSizeLt q $ usableSizeVars ps
+      (p         : ps) -> mappend <$> usableSizeVars p <*> usableSizeVars ps
+
+instance UsableSizeVars (Masked DeBruijnPattern) where
+  usableSizeVars (Masked m p) = (`foldrPattern` p) $ \case
+    VarP _ x   -> const $ ifM terGetUseSizeLt (return $ VarSet.singleton $ dbPatVarIndex x) $
+                   {-else-} return mempty
+    ConP c _ _ -> if m then none else conUseSizeLt $ conName c
+    LitP{}     -> none
+    DotP{}     -> none
+    ProjP{}    -> none
+    IApplyP{}  -> none
+    DefP{}     -> none
+    where none _ = return mempty
+
+instance UsableSizeVars MaskedDeBruijnPatterns where
+  usableSizeVars ps =
+    case ps of
+      []                          -> return mempty
+      (Masked _ (ProjP _ q) : ps) -> projUseSizeLt q $ usableSizeVars ps
+      (p                    : ps) -> mappend <$> usableSizeVars p <*> usableSizeVars ps
+
+-- * Masked patterns (which are not eligible for structural descent, only for size descent)
+--   See issue #1023.
+
+type MaskedDeBruijnPatterns = [Masked DeBruijnPattern]
+
+data Masked a = Masked
+  { getMask   :: Bool  -- ^ True if thing not eligible for structural descent.
+  , getMasked :: a     -- ^ Thing.
+  } deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+masked :: a -> Masked a
+masked = Masked True
+
+notMasked :: a -> Masked a
+notMasked = Masked False
+
+instance Decoration Masked where
+  traverseF f (Masked m a) = Masked m <$> f a
+
+-- | Print masked things in double parentheses.
+instance PrettyTCM a => PrettyTCM (Masked a) where
+  prettyTCM (Masked m a) = applyWhen m (parens . parens) $ prettyTCM a
+
+-- * Call pathes
+
+-- | Call paths.
+
+-- An old comment:
+--
+--   The call information is stored as free monoid
+--   over 'CallInfo'.  As long as we never look at it,
+--   only accumulate it, it does not matter whether we use
+--   'Set', (nub) list, or 'Tree'.
+--   Internally, due to lazyness, it is anyway a binary tree of
+--   'mappend' nodes and singleton leafs.
+--   Since we define no order on 'CallInfo' (expensive),
+--   we cannot use a 'Set' or nub list.
+--   Performance-wise, I could not see a difference between Set and list.
+--
+-- If the binary tree is balanced "incorrectly", then forcing it could
+-- be expensive, so a switch was made to difference lists.
+
+newtype CallPath = CallPath (DList CallInfo)
+  deriving (Show, Semigroup, Monoid)
+
+-- | The calls making up the call path.
+
+callInfos :: CallPath -> [CallInfo]
+callInfos (CallPath cs) = DL.toList cs
+
+-- | Only show intermediate nodes.  (Drop last 'CallInfo').
+instance Pretty CallPath where
+  pretty cis0 = if null cis then empty else
+    P.hsep (map (\ ci -> arrow P.<+> P.pretty ci) cis) P.<+> arrow
+    where
+      cis   = init (callInfos cis0)
+      arrow = "-->"
+
+-- * Size depth estimation
+
+-- | A very crude way of estimating the @SIZELT@ chains
+--   @i > j > k@ in context.  Returns 3 in this case.
+--   Overapproximates.
+class TerSetSizeDepth b where
+  terSetSizeDepth :: b -> TerM a -> TerM a
+
+instance TerSetSizeDepth Telescope where
+  terSetSizeDepth = terSetSizeDepth . telToList
+
+-- TODO: more precise analysis, constructing a tree
+-- of relations between size variables.
+instance TerSetSizeDepth ListTel where
+  terSetSizeDepth doms cont = do
+    n <- liftTCM $ sum <$> do
+      forM doms $ \ dom -> do
+        -- Andreas, 2022-03-12, TODO:
+        -- use ifBlocked?  Shouldn't blocked types be treated like metas?
+        a <- reduce $ snd $ unDom dom
+        ifM (isJust <$> isSizeType a) (return 1) {- else -} $
+          case unEl a of
+            MetaV{} -> return 1
+            _       -> return 0
+    terLocal (set terSizeDepth n) cont
diff --git a/src/full/Agda/Termination/Order.hs b/src/full/Agda/Termination/Order.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/Order.hs
@@ -0,0 +1,319 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ImplicitParams    #-}
+
+-- | An Abstract domain of relative sizes, i.e., differences
+--   between size of formal function parameter and function argument
+--   in recursive call; used in the termination checker.
+
+module Agda.Termination.Order
+  ( -- * Structural orderings
+    Order(..), decr
+  , increase, decrease, setUsability
+  , (.*.)
+  , supremum, infimum
+  , orderSemiring
+  , le, lt, unknown, orderMat, collapseO
+  , nonIncreasing, decreasing, isDecr
+  , NotWorse(..)
+  , isOrder
+  ) where
+
+import qualified Data.Foldable as Fold
+import qualified Data.List as List
+
+import Agda.Termination.CutOff
+import Agda.Termination.SparseMatrix as Matrix
+import Agda.Termination.Semiring (HasZero(..), Semiring)
+import qualified Agda.Termination.Semiring as Semiring
+
+import Agda.Utils.PartialOrd
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- Structural orderings
+
+-- | In the paper referred to above, there is an order R with
+-- @'Unknown' '<=' 'Le' '<=' 'Lt'@.
+--
+-- This is generalized to @'Unknown' '<=' 'Decr k'@ where
+-- @Decr 1@ replaces @Lt@ and @Decr 0@ replaces @Le@.
+-- A negative decrease means an increase.  The generalization
+-- allows the termination checker to record an increase by 1 which
+-- can be compensated by a following decrease by 2 which results in
+-- an overall decrease.
+--
+-- However, the termination checker of the paper itself terminates because
+-- there are only finitely many different call-matrices.  To maintain
+-- termination of the terminator we set a @cutoff@ point which determines
+-- how high the termination checker can count.  This value should be
+-- set by a global or file-wise option.
+--
+-- See 'Call' for more information.
+--
+-- TODO: document orders which are call-matrices themselves.
+data Order
+  = Decr !Bool {-# UNPACK #-} !Int
+    -- ^ Decrease of callee argument wrt. caller parameter.
+    --
+    --   The @Bool@ indicates whether the decrease (if any) is usable.
+    --   In any chain, there needs to be one usable decrease.
+    --   Unusable decreases come from SIZELT constraints which are
+    --   not in inductive pattern match or a coinductive copattern match.
+    --   See issue #2331.
+    --
+    --   UPDATE: Andreas, 2017-07-26:
+    --   Feature #2331 is unsound due to size quantification in terms.
+    --   While the infrastructure for usable/unusable decrease remains in
+    --   place, no unusable decreases are generated by TermCheck.
+  | Unknown
+    -- ^ No relation, infinite increase, or increase beyond termination depth.
+  | Mat {-# UNPACK #-} !(Matrix Int Order)
+    -- ^ Matrix-shaped order, currently UNUSED.
+  deriving (Eq, Ord, Show)
+
+-- instance Show Order where
+--   show (Decr u k) = if u then show (- k) else "(" ++ show (-k) ++ ")"
+--   show Unknown    = "."
+--   show (Mat m)    = "Mat " ++ show m
+
+instance HasZero Order where
+  zeroElement = Unknown
+
+-- | Information order: 'Unknown' is least information.
+--   The more we decrease, the more information we have.
+--
+--   When having comparable call-matrices, we keep the lesser one.
+--   Call graph completion works toward losing the good calls,
+--   tending towards Unknown (the least information).
+instance PartialOrd Order where
+  comparable o o' = case (o, o') of
+    (Unknown, Unknown) -> POEQ
+    (Unknown, _      ) -> POLT
+    (_      , Unknown) -> POGT
+    (Decr u k, Decr u' l) -> comparableBool u u' `orPO` comparableOrd k l
+    -- Matrix-shaped orders are no longer supported
+    (Mat{}  , _      ) -> __IMPOSSIBLE__
+    (_      , Mat{}  ) -> __IMPOSSIBLE__
+    where
+    comparableBool = curry $ \case
+      (False, True) -> POLT
+      (True, False) -> POGT
+      _ -> POEQ
+
+-- | A partial order, aimed at deciding whether a call graph gets
+--   worse during the completion.
+--
+class NotWorse a where
+  notWorse :: a -> a -> Bool
+
+-- | It does not get worse then ``increase''.
+--   If we are still decreasing, it can get worse: less decreasing.
+instance NotWorse Order where
+  o        `notWorse` Unknown  = True            -- we are unboundedly increasing
+  Unknown  `notWorse` Decr _ k = k < 0           -- we are increasing
+  Decr u l `notWorse` Decr u' k = k < 0   -- we are increasing or
+    || l >= k && (u || not u')            -- we are decreasing, but not less, and not less usable
+  -- Matrix-shaped orders are no longer supported
+  Mat m   `notWorse` o       = __IMPOSSIBLE__
+  o       `notWorse` Mat m   = __IMPOSSIBLE__
+{-
+  Mat m   `notWorse` Mat n   = m `notWorse` n  -- matrices are compared pointwise
+  o       `notWorse` Mat n   = o `notWorse` collapse n  -- or collapsed (sound?)
+  Mat m   `notWorse` o       = collapse m `notWorse` o
+-}
+
+-- | We assume the matrices have the same dimension.
+instance (Ord i, HasZero o, NotWorse o) => NotWorse (Matrix i o) where
+  m `notWorse` n
+    | size m /= size n = __IMPOSSIBLE__
+    | otherwise        = Fold.and $ zipMatrices onlym onlyn both trivial m n
+    where
+    -- If an element is only in @m@, then its 'Unknown' in @n@
+    -- so it gotten better at best, in any case, not worse.
+    onlym o = True     -- @== o `notWorse` Unknown@
+    onlyn o = zeroElement `notWorse` o
+    both    = notWorse
+    trivial = id  -- @True@ counts as zero as it is neutral for @and@
+
+-- | Raw increase which does not cut off.
+increase :: Int -> Order -> Order
+increase i = \case
+  Unknown  -> Unknown
+  Decr u k -> Decr u $ k - i   -- TODO: should we set u to False if k - i < 0 ?
+  Mat m    -> Mat $ fmap (increase i) m
+
+-- | Raw decrease which does not cut off.
+decrease :: Int -> Order -> Order
+decrease i o = increase (-i) o
+
+setUsability :: Bool -> Order -> Order
+setUsability u o = case o of
+  Decr _ k -> Decr u k
+  Unknown  -> o
+  Mat{}    -> o
+
+-- | Smart constructor for @Decr k :: Order@ which cuts off too big values.
+--
+-- Possible values for @k@: @- ?cutoff '<=' k '<=' ?cutoff + 1@.
+
+decr :: (?cutoff :: CutOff) => Bool -> Int -> Order
+decr u k = case ?cutoff of
+  CutOff c | k < -c -> Unknown
+           | k > c  -> Decr u $ c + 1
+  _                 -> Decr u k
+
+-- | Smart constructor for matrix shaped orders, avoiding empty and singleton matrices.
+orderMat :: Matrix Int Order -> Order
+orderMat m
+ | Matrix.isEmpty m        = le     -- 0x0 Matrix = neutral element
+ | Just o <- isSingleton m = o      -- 1x1 Matrix
+ | otherwise               = Mat m  -- nxn Matrix
+
+withinCutOff :: (?cutoff :: CutOff) => Int -> Bool
+withinCutOff k = case ?cutoff of
+  DontCutOff -> True
+  CutOff c   -> k >= -c && k <= c + 1
+
+isOrder :: (?cutoff :: CutOff) => Order -> Bool
+isOrder (Decr _ k) = withinCutOff k
+isOrder Unknown    = True
+isOrder (Mat m)    = False  -- TODO: extend to matrices
+
+-- | @le@, @lt@, @decreasing@, @unknown@: for backwards compatibility, and for external use.
+le :: Order
+le = Decr False 0
+
+-- | Usable decrease.
+lt :: Order
+lt = Decr True 1
+
+unknown :: Order
+unknown = Unknown
+
+nonIncreasing :: Order -> Bool
+nonIncreasing (Decr _ k) = k >= 0
+nonIncreasing _          = False
+
+-- | Decreasing and usable?
+decreasing :: Order -> Bool
+decreasing (Decr u k) = u && k > 0
+decreasing _ = False
+
+-- | Matrix-shaped order is decreasing if any diagonal element is decreasing.
+isDecr :: Order -> Bool
+isDecr (Mat m) = any isDecr $ diagonal m
+isDecr o = decreasing o
+
+instance Pretty Order where
+  pretty (Decr u 0) = "="
+  pretty (Decr u k) = mparens (not u) $ text $ show (negate k)
+  pretty Unknown    = "?"
+  pretty (Mat m)    = "Mat" <+> pretty m
+
+
+-- | Multiplication of 'Order's.
+--   (Corresponds to sequential composition.)
+
+-- I think this funny pattern matching is because overlapping patterns
+-- are producing a warning and thus an error (strict compilation settings)
+(.*.) :: (?cutoff :: CutOff) => Order -> Order -> Order
+Unknown    .*. _           = Unknown
+(Mat m)    .*. Unknown     = Unknown
+(Decr _ k) .*. Unknown     = Unknown
+(Decr u k) .*. (Decr u' l) = decr (u || u') (k + l)  -- if one is usable, so is the composition
+(Decr _ 0) .*. (Mat m)     = Mat m
+(Decr u k) .*. (Mat m)     = (Decr u k) .*. (collapse m)
+(Mat m1)   .*. (Mat m2)
+  | okM m1 m2              = Mat $ mul orderSemiring m1 m2
+  | otherwise              = (collapse m1) .*. (collapse m2)
+(Mat m)   .*. (Decr _ 0)   = Mat m
+(Mat m)   .*. (Decr u k)   = (collapse m) .*. (Decr u k)
+
+-- | collapse @m@
+--
+-- We assume that @m@ codes a permutation:  each row has at most one column
+-- that is not @Unknown@.
+--
+-- To collapse a matrix into a single value, we take the best value of
+-- each column and multiply them.  That means if one column is all @Unknown@,
+-- i.e., no argument relates to that parameter, then the collapsed value
+-- is also @Unknown@.
+--
+-- This makes order multiplication associative.
+
+collapse :: (?cutoff :: CutOff) => Matrix Int Order -> Order
+collapse m = case toLists $ Matrix.transpose m of
+  [] -> __IMPOSSIBLE__   -- This can never happen if order matrices are generated by the smart constructor
+  m' -> foldl1 (.*.) $ map (foldl1 maxO) m'
+
+collapseO :: (?cutoff :: CutOff) => Order -> Order
+collapseO (Mat m) = collapse m
+collapseO o       = o
+
+-- | Can two matrices be multplied together?
+okM :: Matrix Int Order -> Matrix Int Order -> Bool
+okM m1 m2 = rows (size m2) == cols (size m1)
+
+-- | The supremum of a (possibly empty) list of 'Order's.
+--   More information (i.e., more decrease) is bigger.
+--   'Unknown' is no information, thus, smallest.
+supremum :: (?cutoff :: CutOff) => [Order] -> Order
+supremum = foldr maxO Unknown
+
+-- | @('Order', 'maxO', '.*.')@ forms a semiring,
+--   with 'Unknown' as zero and 'Le' as one.
+
+maxO :: (?cutoff :: CutOff) => Order -> Order -> Order
+maxO o1 o2 = case (o1,o2) of
+    -- NOTE: strictly speaking the maximum does not exists
+    -- which is better, an unusable decrease by 2 or a usable decrease by 1?
+    -- We give the usable information priority if it is a decrease.
+  (Decr False _, Decr True  l) | l > 0 -> o2
+  (Decr True  k, Decr False _) | k > 0 -> o1
+  (Decr u k, Decr u' l) -> if l > k then o2 else o1
+  (Unknown, _)     -> o2
+  (_, Unknown)     -> o1
+  (Mat m1, Mat m2) -> Mat (Matrix.add maxO m1 m2)
+  (Mat m, _)       -> maxO (collapse m) o2
+  (_, Mat m)       -> maxO o1 (collapse m)
+
+-- | The infimum of a (non empty) list of 'Order's.
+--   Gets the worst information.
+--  'Unknown' is the least element, thus, dominant.
+infimum :: (?cutoff :: CutOff) => [Order] -> Order
+infimum (o:l) = List.foldl' minO o l
+infimum []    = __IMPOSSIBLE__
+
+-- | Pick the worst information.
+minO :: (?cutoff :: CutOff) => Order -> Order -> Order
+minO o1 o2 = case (o1,o2) of
+  (Unknown, _)           -> Unknown
+  (_, Unknown)           -> Unknown
+  -- different usability:
+  -- We pick the unusable one if it is not a decrease or
+  -- decreases not more than the usable one.
+  (Decr False k, Decr True  l) -> if k <= 0 || k <= l then o1 else o2
+  (Decr True  k, Decr False l) -> if l <= 0 || l <= k then o2 else o1
+  -- same usability:
+  (Decr u k, Decr _ l) -> Decr u (min k l)
+  (Mat m1, Mat m2)
+    | size m1 == size m2 -> Mat $ Matrix.intersectWith minO m1 m2
+    | otherwise          -> minO (collapse m1) (collapse m2)
+  (Mat m1, _)            -> minO (collapse m1) o2
+  (_, Mat m2)            -> minO o1 (collapse m2)
+
+
+-- | We use a record for semiring instead of a type class
+--   since implicit arguments cannot occur in instance constraints,
+--   like @instance (?cutoff :: Int) => SemiRing Order@.
+
+orderSemiring :: (?cutoff :: CutOff) => Semiring Order
+orderSemiring = Semiring.Semiring
+  { Semiring.add  = maxO
+  , Semiring.mul  = (.*.)
+  , Semiring.zero = Unknown
+  -- , Semiring.one  = Le
+  }
diff --git a/src/full/Agda/Termination/RecCheck.hs b/src/full/Agda/Termination/RecCheck.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/RecCheck.hs
@@ -0,0 +1,169 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{- | Checking for recursion:
+
+   - We detect truly (co)recursive definitions by computing the
+     dependency graph and checking for cycles.
+
+   - This is inexpensive and let us skip the termination check
+     when there's no (co)recursion
+
+   Original contribution by Andrea Vezzosi (sanzhiyan).
+   This implementation by Andreas.
+-}
+
+
+module Agda.Termination.RecCheck
+    ( MutualNames
+    , recursive
+    , anyDefs
+    )
+ where
+
+import Control.Monad (forM)
+import Data.Foldable
+import Data.Graph
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import qualified Data.Map as Map
+import qualified Data.Map.Strict as MapS
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Defs
+import Agda.Syntax.Common.Pretty  (prettyShow)
+
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.Impossible
+
+-- | The mutual block we are checking.
+--
+--   The functions are numbered according to their order of appearance
+--   in this set.
+
+type MutualNames = Set QName
+
+-- | We compute for each clause the set of potentially recursive names.
+type NamesPerClause = IntMap (Set QName)
+
+-- | Given a list of formally mutually recursive functions,
+--   check for actual recursive calls in the bodies of these functions.
+--   Returns the actually recursive functions as strongly connected components.
+--
+--   As a side effect, update the 'clauseRecursive' field in the
+--   clauses belonging to the given functions.
+recursive :: Set QName -> TCM [MutualNames]
+recursive names = do
+  let names' = toList names
+  -- For each function, get names per clause and total.
+  (perClauses, nss) <- unzip <$> mapM (recDef (`Set.member` names)) names'
+  -- Create graph suitable for stronglyConnComp.
+  -- Nodes are identical to node keys.
+  let graph  = zipWith (\ x ns -> (x, x, Set.toList ns)) names' nss
+  let sccs   = stronglyConnComp graph
+  let nonRec = mapMaybe (\case AcyclicSCC x -> Just x
+                               _            -> Nothing)
+                 sccs
+  let recs   = mapMaybe (\case CyclicSCC xs -> Just (Set.fromList xs)
+                               _            -> Nothing)
+                 sccs
+
+  reportSLn "rec.graph" 60 $ show graph
+
+  -- Mark all non-recursive functions and their clauses as such.
+  mapM_ markNonRecursive nonRec
+
+  -- Mark individual clauses of recursive functions:
+  --------------------------------------------------
+  -- Map names to clause numbers to sets of mentioned names.
+  let clMap = Map.fromListWith __IMPOSSIBLE__ $ zip names' perClauses
+  -- Walk through SCCs.
+  forM_ recs $ \ scc -> do
+    -- Does a set of names have an overlap with the current scc?
+    let overlap s = any (`Set.member` s) scc
+    -- Walk through members of SCC.
+    forM_ scc $ \ x -> do
+      -- Get the NamesPerClause for the current function x.
+      let perClause  = Map.findWithDefault __IMPOSSIBLE__ x clMap
+      -- A clause is recursive if its calls overlap with its scc.
+      let recClause i = overlap $ IntMap.findWithDefault __IMPOSSIBLE__ i perClause
+      markRecursive recClause x
+
+  -- Return recursive SCCs.
+  return recs
+
+-- | Mark a function as terminating and all its clauses as non-recursive.
+markNonRecursive :: QName -> TCM ()
+markNonRecursive q = modifySignature $ updateDefinition q $ updateTheDef $ \case
+  def@Function{} -> def
+   { funTerminates = Just True
+   , funClauses    = map (\ cl -> cl { clauseRecursive = Just False }) $ funClauses def
+   }
+  def@Record{} -> def
+   { recTerminates = Just True
+   }
+  def -> def
+
+-- | Mark all clauses of a function as recursive or non-recursive.
+markRecursive
+  :: (Int -> Bool)  -- ^ Which clauses are recursive?
+  -> QName -> TCM ()
+markRecursive f q = modifySignature $ updateDefinition q $ updateTheDef $ \case
+  def@Function{} -> def
+   { funClauses    = zipWith (\ i cl -> cl { clauseRecursive = Just (f i) }) [0..] $ funClauses def
+   }
+  def -> def
+
+-- | @recDef names name@ returns all definitions from @names@
+--   that are used in the type and body of @name@.
+recDef :: (QName -> Bool) -> QName -> TCM (NamesPerClause, Set QName)
+recDef include name = do
+  -- Retrieve definition
+  def <- getConstInfo name
+
+  -- Get names in type
+  ns1 <- anyDefs include (defType def)
+
+  -- Get names in body
+  (perClause, ns2) <- case theDef def of
+
+    Function{ funClauses = cls } -> do
+      perClause <- do
+        forM (zip [0..] cls) $ \ (i, cl) ->
+          (i,) <$> anyDefs include cl
+      return (IntMap.fromList perClause, mconcat $ map snd perClause)
+
+    Record{ recTel } -> do
+      ns <- anyDefs include recTel
+      return (IntMap.singleton 0 ns, ns)
+
+    _ -> return (mempty, mempty)
+
+  reportS "rec.graph" 20
+    [ "recDef " ++ prettyShow name
+    , "  names in the type: " ++ prettyShow ns1
+    , "  names in the def:  " ++ prettyShow ns2
+    ]
+  return (perClause, ns1 `mappend` ns2)
+
+-- | @anysDef names a@ returns all definitions from @names@
+--   that are used in @a@.
+anyDefs :: GetDefs a => (QName -> Bool) -> a -> TCM (Set QName)
+anyDefs include a = do
+  -- Prepare function to lookup metas outside of TCM
+  st <- useR stSolvedMetaStore
+  let lookup x = inst . mvInstantiation <$> MapS.lookup x st
+      -- we collect only those used definitions that are in @names@
+      emb d = if include d then Set.singleton d else Set.empty
+  -- get all the Defs that are in names
+  return $ getDefs' lookup emb a
+  where
+  -- TODO: Is it bad to ignore the lambdas?
+  inst (InstV i)                      = instBody i
+  inst Open                           = __IMPOSSIBLE__
+  inst OpenInstance                   = __IMPOSSIBLE__
+  inst BlockedConst{}                 = __IMPOSSIBLE__
+  inst PostponedTypeCheckingProblem{} = __IMPOSSIBLE__
diff --git a/src/full/Agda/Termination/Semiring.hs b/src/full/Agda/Termination/Semiring.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/Semiring.hs
@@ -0,0 +1,55 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Semirings.
+
+module Agda.Termination.Semiring
+  ( HasZero(..)
+  , Semiring(..)
+  , integerSemiring
+  , intSemiring
+  , boolSemiring
+  ) where
+
+
+
+-- | @HasZero@ is needed for sparse matrices, to tell which is the element
+--   that does not have to be stored.
+--   It is a cut-down version of @SemiRing@ which is definable
+--   without the implicit @?cutoff@.
+class Eq a => HasZero a where
+  zeroElement :: a
+
+-- | Semirings.
+
+data Semiring a = Semiring
+  { add  :: a -> a -> a  -- ^ Addition.
+  , mul  :: a -> a -> a  -- ^ Multiplication.
+  , zero :: a            -- ^ Zero.
+  -- The one is never used in matrix multiplication
+  -- , one  :: a            -- ^ One.
+  }
+
+------------------------------------------------------------------------
+-- Specific semirings
+
+-- | The standard semiring on 'Integer's.
+
+instance HasZero Integer where
+  zeroElement = 0
+
+integerSemiring :: Semiring Integer
+integerSemiring = Semiring { add = (+), mul = (*), zero = 0 } -- , one = 1 }
+
+-- | The standard semiring on 'Int's.
+
+instance HasZero Int where
+  zeroElement = 0
+
+intSemiring :: Semiring Int
+intSemiring = Semiring { add = (+), mul = (*), zero = 0 } -- , one = 1 }
+
+-- | The standard semiring on 'Bool's.
+
+boolSemiring :: Semiring Bool
+boolSemiring =
+  Semiring { add = (||), mul = (&&), zero = False } --, one = True }
diff --git a/src/full/Agda/Termination/SparseMatrix.hs b/src/full/Agda/Termination/SparseMatrix.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/SparseMatrix.hs
@@ -0,0 +1,450 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{- | Sparse matrices.
+
+We assume the matrices to be very sparse, so we just implement them as
+sorted association lists.
+
+Most operations are linear in the number of non-zero elements.
+
+An exception is transposition, which needs to sort the association
+list again; it has the complexity of sorting: @n log n@ where @n@ is
+the number of non-zero elements.
+
+Another exception is matrix multiplication, of course.
+
+ -}
+
+module Agda.Termination.SparseMatrix
+  ( -- * Basic data types
+    Matrix(Matrix)
+  , unM
+  -- , matrixInvariant  -- Moved to the internal test-suite
+  , Size(..)
+  , MIx (..)
+    -- * Generating and creating matrices
+  , fromLists
+  , fromIndexList
+  , toLists
+--  , Agda.Termination.Matrix.zipWith
+  -- , matrix  -- Moved to the internal test-suite
+    -- * Combining and querying matrices
+  , size
+  , square
+  , isEmpty
+  , isSingleton
+  , zipMatrices
+  , add
+  , intersectWith
+  , interAssocWith
+  , mul
+  , transpose
+  , Diagonal(..)
+  , toSparseRows
+  , supSize
+  , zipAssocWith
+    -- * Modifying matrices
+  , addRow
+  , addColumn
+  ) where
+
+import Data.Array
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Maybe
+
+
+import qualified Data.Foldable as Fold
+
+import qualified Text.PrettyPrint.Boxes as Boxes
+
+import Agda.Termination.Semiring (HasZero(..), Semiring)
+import qualified Agda.Termination.Semiring as Semiring
+
+
+import Agda.Utils.List
+import Agda.Utils.Maybe
+
+import Agda.Utils.PartialOrd
+import Agda.Syntax.Common.Pretty hiding (isEmpty)
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- * Basic data types
+------------------------------------------------------------------------
+
+-- | Size of a matrix.
+
+data Size i = Size
+  { rows :: i  -- ^ Number of rows,    @>= 0@.
+  , cols :: i  -- ^ Number of columns, @>= 0@.
+  }
+  deriving (Eq, Ord, Show)
+
+-- | Type of matrix indices (row, column).
+
+data MIx i = MIx
+  { row :: i  -- ^ Row index,   @1 <= row <= rows@.
+  , col :: i  -- ^ Column index @1 <= col <= cols@.
+  }
+  deriving (Eq, Ord, Show, Ix)
+
+-- UNUSED Liang-Ting Chen 2019-07-15
+---- | Convert a 'Size' to a set of bounds suitable for use with
+----   the matrices in this module.
+--
+--toBounds :: Num i => Size i -> (MIx i, MIx i)
+--toBounds sz = (MIx { row = 1, col = 1 }, MIx { row = rows sz, col = cols sz })
+
+-- | Type of matrices, parameterised on the type of values.
+--
+--   Sparse matrices are implemented as an ordered association list,
+--   mapping coordinates to values.
+
+data Matrix i b = Matrix
+  { size :: Size i        -- ^ Dimensions of the matrix.
+  , unM  :: [(MIx i, b)]  -- ^ Association of indices to values.
+  }
+  deriving (Eq, Ord, Functor, Foldable, Traversable)
+
+------------------------------------------------------------------------
+-- * Operations and query on matrix size.
+------------------------------------------------------------------------
+
+-- | 'True' iff the matrix is square.
+
+square :: Ix i => Matrix i b -> Bool
+square m = rows (size m) == cols (size m)
+
+-- | Returns 'True' iff the matrix is empty.
+
+isEmpty :: (Num i, Ix i) => Matrix i b -> Bool
+isEmpty m = rows sz <= 0 || cols sz <= 0
+  where sz = size m
+
+-- | Compute the matrix size of the union of two matrices.
+
+supSize :: Ord i => Matrix i a -> Matrix i b -> Size i
+supSize (Matrix (Size r1 c1) _) (Matrix (Size r2 c2) _) =
+  Size (max r1 r2) (max c1 c2)
+
+-- | Compute the matrix size of the intersection of two matrices.
+
+infSize :: Ord i => Matrix i a -> Matrix i b -> Size i
+infSize (Matrix (Size r1 c1) _) (Matrix (Size r2 c2) _) =
+  Size (min r1 r2) (min c1 c2)
+
+------------------------------------------------------------------------
+-- * Creating matrices and converting to lists.
+------------------------------------------------------------------------
+
+-- | Constructs a matrix from a list of @(index, value)@-pairs.
+--   @O(n)@ where @n@ is size of the list.
+--
+--   Precondition: indices are unique.
+
+fromIndexList :: (Ord i, HasZero b) => Size i -> [(MIx i, b)] -> Matrix i b
+fromIndexList sz = Matrix sz
+                 . List.sortBy (compare `on` fst)
+                 . filter ((zeroElement /=) . snd)
+
+-- | @'fromLists' sz rs@ constructs a matrix from a list of lists of
+--   values (a list of rows).
+--   @O(size)@ where @size = rows × cols@.
+--
+--   Precondition:
+--   @'length' rs '==' 'rows' sz@ and
+--   @'all' (('cols' sz '==') . 'length') rs@.
+
+fromLists :: (Ord i, Num i, Enum i, HasZero b) => Size i -> [[b]] -> Matrix i b
+fromLists sz bs = fromIndexList sz $ zip ([ MIx i j | i <- [1..rows sz]
+                                                    , j <- [1..cols sz]]) (concat bs)
+
+-- | Converts a sparse matrix to a sparse list of rows.
+--   @O(n)@ where @n@ is the number of non-zero entries of the matrix.
+--
+--   Only non-empty rows are generated.
+--
+
+toSparseRows :: (Eq i) => Matrix i b -> [(i,[(i,b)])]
+toSparseRows (Matrix _ []) = []
+toSparseRows (Matrix _ ((MIx i j, b) : m)) = aux i [(j,b)] m
+  where aux i' []  [] = []
+        aux i' row [] = [(i', reverse row)]
+        aux i' row ((MIx i j, b) : m)
+          | i' == i   = aux i' ((j,b):row) m
+          | otherwise = (i', reverse row) : aux i [(j,b)] m
+
+-- | Turn a sparse vector into a vector by inserting a fixed element
+--   at the missing positions.
+--   @O(size)@ where @size@ is the dimension of the vector.
+
+blowUpSparseVec :: (Integral i) => b -> i -> [(i,b)] -> [b]
+blowUpSparseVec zero n l = aux 1 l
+  where aux i []           = List.genericReplicate (n + 1 - i) zero
+        aux i l@((j,b):l')
+          | i > j || i > n = __IMPOSSIBLE__
+          | i == j         = b    : aux (i + 1) l'
+          | otherwise      = zero : aux (i + 1) l
+
+-- UNUSED Liang-Ting Chen 2019-07-15
+---- Older implementation without replicate.
+--blowUpSparseVec' :: (Ord i, Num i, Enum i) => b -> i -> [(i,b)] -> [b]
+--blowUpSparseVec' zero n l = aux 1 l
+--  where aux i [] | i > n = []
+--                 | otherwise = zero : aux (i+1) []
+--        aux i ((j,b):l) | i <= n && j == i = b : aux (succ i) l
+--        aux i ((j,b):l) | i <= n && j >= i = zero : aux (succ i) ((j,b):l)
+--        aux i l = __IMPOSSIBLE__
+--          -- error $ "blowUpSparseVec (n = " ++ show n ++ ") aux i=" ++ show i ++ " j=" ++ show (fst (head l)) ++ " length l = " ++ show (length l)
+--
+-- | Converts a matrix to a list of row lists.
+--   @O(size)@ where @size = rows × cols@.
+
+toLists :: (Integral i, HasZero b) => Matrix i b -> [[b]]
+toLists m@(Matrix size@(Size nrows ncols) _) =
+    blowUpSparseVec emptyRow nrows $
+      map (mapSnd (blowUpSparseVec zeroElement ncols)) $ toSparseRows m
+  where
+    emptyRow = List.genericReplicate ncols zeroElement
+
+------------------------------------------------------------------------
+-- * Combining and querying matrices
+------------------------------------------------------------------------
+
+-- | Returns 'Just b' iff it is a 1x1 matrix with just one entry 'b'.
+--   @O(1)@.
+
+isSingleton :: (Eq i, Num i, HasZero b) => Matrix i b -> Maybe b
+isSingleton (Matrix (Size 1 1) [(_,b)]) = Just b
+isSingleton (Matrix (Size 1 1) []     ) = Just zeroElement
+isSingleton (Matrix (Size 1 1) _      ) = __IMPOSSIBLE__
+isSingleton _ = Nothing
+
+-- | @'diagonal' m@ extracts the diagonal of @m@.
+--
+--   For non-square matrices, the length of the diagonal is
+--   the minimum of the dimensions of the matrix.
+
+class Diagonal m e | m -> e where
+  diagonal :: m -> [e]
+
+-- | Diagonal of sparse matrix.
+--
+--   @O(n)@ where @n@ is the number of non-zero elements in the matrix.
+
+instance (Integral i, HasZero b) => Diagonal (Matrix i b) b where
+  diagonal (Matrix (Size r c) m) =
+    blowUpSparseVec zeroElement (min r c) $
+      mapMaybe (\ (MIx i j, b) -> if i == j then Just (i, b) else Nothing) m
+
+-- | Transposable things.
+
+class Transpose a where
+  transpose :: a -> a
+
+-- | Size of transposed matrix.
+
+instance Transpose (Size i) where
+  transpose (Size n m) = Size m n
+
+-- | Transposing coordinates.
+
+instance Transpose (MIx i) where
+  transpose (MIx i j) = MIx j i
+
+-- | Matrix transposition.
+--
+--   @O(n log n)@ where @n@ is the number of non-zero elements in the matrix.
+
+instance Ord i => Transpose (Matrix i b) where
+  transpose (Matrix size m) =
+    Matrix (transpose size) $
+      List.sortBy (compare `on` fst) $
+        map (mapFst transpose) m
+
+
+-- | General pointwise combination function for association lists.
+--   @O(n1 + n2)@ where @ni@ is the number of non-zero element in matrix @i@.
+--
+--   In @zipAssocWith fs gs f g h l l'@,
+--
+--   @fs@ is possibly more efficient version of
+--   @'mapMaybe' (\ (i, a) -> (i,) <$> f a)@, and same for @gs@ and @g@.
+
+zipAssocWith :: (Ord i)
+  => ([(i,a)] -> [(i,c)]) -- ^ Only left map remaining.
+  -> ([(i,b)] -> [(i,c)]) -- ^ Only right map remaining.
+  -> (a -> Maybe c)       -- ^ Element only present in left map.
+  -> (b -> Maybe c)       -- ^ Element only present in right map.
+  -> (a -> b -> Maybe c)  -- ^ Element present in both maps.
+  -> [(i,a)] -> [(i,b)] -> [(i,c)]
+zipAssocWith fs gs f g h = merge
+  where
+    merge m1 [] = mapMaybe (\ (i, a) -> (i,) <$> f a) m1
+    merge [] m2 = mapMaybe (\ (i, b) -> (i,) <$> g b) m2
+    merge m1@((i,a):m1') m2@((j,b):m2') =
+      case compare i j of
+        LT -> mcons ((i,) <$> f a)   $ merge m1' m2
+        GT -> mcons ((j,) <$> g b)   $ merge m1  m2'
+        EQ -> mcons ((i,) <$> h a b) $ merge m1' m2'
+
+-- | Instance of 'zipAssocWith' which keeps longer assoc lists.
+--   @O(n1 + n2)@.
+
+unionAssocWith  :: (Ord i)
+  => (a -> Maybe c)       -- ^ Element only present in left map.
+  -> (b -> Maybe c)       -- ^ Element only present in right map.
+  -> (a -> b -> Maybe c)  -- ^ Element present in both maps.
+  -> [(i,a)] -> [(i,b)] -> [(i,c)]
+unionAssocWith f g h = zipAssocWith (map_ f) (map_ g) f g h
+  where
+    map_ f = mapMaybe (\ (i, a) -> (i,) <$> f a)
+
+-- | General pointwise combination function for sparse matrices.
+--   @O(n1 + n2)@.
+
+zipMatrices :: forall a b c i . (Ord i)
+  => (a -> c)       -- ^ Element only present in left matrix.
+  -> (b -> c)       -- ^ Element only present in right matrix.
+  -> (a -> b -> c)  -- ^ Element present in both matrices.
+  -> (c -> Bool)    -- ^ Result counts as zero?
+  -> Matrix i a -> Matrix i b -> Matrix i c
+zipMatrices f g h zero m1 m2 = Matrix (supSize m1 m2) $
+  unionAssocWith (drop0 . f) (drop0 . g) (\ a -> drop0 . h a) (unM m1) (unM m2)
+  where
+    drop0 = filterMaybe (not . zero)
+
+-- | @'add' (+) m1 m2@ adds @m1@ and @m2@, using @(+)@ to add values.
+--   @O(n1 + n2)@.
+--
+--   Returns a matrix of size @'supSize' m1 m2@.
+
+add :: (Ord i, HasZero a) => (a -> a -> a) -> Matrix i a -> Matrix i a -> Matrix i a
+add plus = zipMatrices id id plus (== zeroElement)
+
+-- | @'intersectWith' f m1 m2@ build the pointwise conjunction @m1@ and @m2@.
+--   Uses @f@ to combine non-zero values.
+--   @O(n1 + n2)@.
+--
+--   Returns a matrix of size @infSize m1 m2@.
+
+intersectWith :: (Ord i) => (a -> a -> a) -> Matrix i a -> Matrix i a -> Matrix i a
+intersectWith f m1 m2 = Matrix (infSize m1 m2) $ interAssocWith f (unM m1) (unM m2)
+
+-- | Association list intersection.
+--   @O(n1 + n2)@.
+--
+--   @interAssocWith f l l' = { (i, f a b) | (i,a) ∈ l and (i,b) ∈ l' }@
+--
+--   Used to combine sparse matrices, it might introduce zero elements
+--   if @f@ can return zero for non-zero arguments.
+
+interAssocWith :: (Ord i) => (a -> a -> a) -> [(i,a)] -> [(i,a)] -> [(i,a)]
+interAssocWith f [] m = []
+interAssocWith f l [] = []
+interAssocWith f l@((i,a):l') m@((j,b):m')
+    | i < j = interAssocWith f l' m
+    | i > j = interAssocWith f l m'
+    | otherwise = (i, f a b) : interAssocWith f l' m'
+
+-- | @'mul' semiring m1 m2@ multiplies matrices @m1@ and @m2@.
+--   Uses the operations of the semiring @semiring@ to perform the
+--   multiplication.
+--
+--   @O(n1 + n2 log n2 + Σ(i <= r1) Σ(j <= c2) d(i,j))@ where
+--   @r1@ is the number of non-empty rows in @m1@ and
+--   @c2@ is the number of non-empty columns in @m2@ and
+--   @d(i,j)@  is the bigger one of the following two quantifies:
+--   the length of sparse row @i@ in @m1@ and
+--   the length of sparse column @j@ in @m2@.
+--
+--   Given dimensions @m1 : r1 × c1@ and @m2 : r2 × c2@,
+--   a matrix of size @r1 × c2@ is returned.
+--   It is not necessary that @c1 == r2@, the matrices are implicitly
+--   patched with zeros to match up for multiplication.
+--   For sparse matrices, this patching is a no-op.
+
+mul :: (Ix i, Eq a)
+    => Semiring a -> Matrix i a -> Matrix i a -> Matrix i a
+mul semiring m1 m2 = Matrix (Size { rows = rows (size m1), cols = cols (size m2) }) $
+  [ (MIx i j, b)
+    | (i,v) <- toSparseRows m1
+    , (j,w) <- toSparseRows $ transpose m2
+    , let b = inner v w
+    , b /= zero
+  ]
+  where
+     zero  = Semiring.zero semiring
+     plus  = Semiring.add  semiring
+     times = Semiring.mul  semiring
+     inner v w = List.foldl' plus zero $
+                   map snd $ interAssocWith times v w
+
+-- | Pointwise comparison.
+--   Only matrices with the same dimension are comparable.
+instance (Ord i, PartialOrd a) => PartialOrd (Matrix i a) where
+  comparable m n
+    | size m /= size n = POAny
+    | otherwise        = Fold.fold $
+                           zipMatrices onlym onlyn both trivial m n
+    where
+      -- If an element is only in @m@, then its 'Unknown' in @n@
+      -- so it gotten better at best, in any case, not worse.
+      onlym o = POGT
+      -- If an element is only in @n@, then its 'Unknown' in @m@
+      -- so we have strictly less information.
+      onlyn o = POLT
+      both    = comparable
+      -- The zero element of the result sparse matrix is the
+      -- neutral element of the monoid.
+      trivial = (== mempty)
+
+------------------------------------------------------------------------
+-- Modifying matrices
+
+-- | @'addColumn' x m@ adds a new column to @m@, after the columns
+-- already existing in the matrix. All elements in the new column get
+-- set to @x@.
+
+addColumn :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i b
+addColumn x m | x == zeroElement = m { size = (size m) { cols = cols (size m) + 1 }}
+              | otherwise = __IMPOSSIBLE__
+
+-- | @'addRow' x m@ adds a new row to @m@, after the rows already
+-- existing in the matrix. All elements in the new row get set to @x@.
+
+addRow :: (Num i, HasZero b) => b -> Matrix i b -> Matrix i b
+addRow x m | x == zeroElement = m { size = (size m) { rows = rows (size m) + 1 }}
+           | otherwise = __IMPOSSIBLE__
+
+------------------------------------------------------------------------
+-- * Printing
+------------------------------------------------------------------------
+
+instance (Integral i, HasZero b, Show i, Show b) => Show (Matrix i b) where
+  showsPrec _ m =
+    showString "Agda.Termination.SparseMatrix.fromLists " . shows (size m) .
+    showString " " . shows (toLists m)
+
+instance (Integral i, HasZero b, Pretty b) =>
+         Pretty (Matrix i b) where
+--  pretty = vcat . map (hsep . map pretty) . toLists
+  pretty = vcat
+         . map text
+         . lines
+         . Boxes.render
+         . Boxes.hsep 1 Boxes.right
+         . map ( Boxes.vcat Boxes.right
+               . map ( Boxes.alignHoriz Boxes.right 4
+                     . Boxes.text . render . pretty
+                     )
+               )
+         . toLists
+         . transpose
+-- ADAPTED FROM:
+-- http://www.tedreed.info/programming/2012/06/02/how-to-use-textprettyprintboxes/
+-- print_table :: [[String]] -> IO ()
+-- print_table rows = printBox $ hsep 2 left (map (vcat left . map text) (transpose rows))
diff --git a/src/full/Agda/Termination/TermCheck.hs b/src/full/Agda/Termination/TermCheck.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/TermCheck.hs
@@ -0,0 +1,1514 @@
+{-# LANGUAGE GADTs                      #-}
+
+{-# LANGUAGE ImplicitParams             #-}
+{-# LANGUAGE NondecreasingIndentation   #-}
+
+{- Checking for Structural recursion
+   Authors: Andreas Abel, Nils Anders Danielsson, Ulf Norell,
+              Karl Mehltretter and others
+   Created: 2007-05-28
+   Source : TypeCheck.Rules.Decl
+ -}
+
+module Agda.Termination.TermCheck
+    ( termDecl
+    , termMutual
+    , Result
+    ) where
+
+import Prelude hiding ( null )
+
+import Control.Applicative  ( liftA2 )
+import Control.Monad        ( (<=<), filterM, forM, forM_, zipWithM )
+
+import Data.Foldable (toList)
+import qualified Data.List as List
+import Data.Monoid hiding ((<>))
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern as I
+import Agda.Syntax.Internal.Generic
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Translation.InternalToAbstract (NamedClause(..))
+
+import Agda.Termination.CutOff
+import Agda.Termination.Monad
+import Agda.Termination.CallGraph hiding (toList)
+import qualified Agda.Termination.CallGraph as CallGraph
+import Agda.Termination.CallMatrix hiding (toList)
+import Agda.Termination.Order     as Order
+import qualified Agda.Termination.SparseMatrix as Matrix
+import Agda.Termination.Termination (endos, idempotent)
+import qualified Agda.Termination.Termination  as Term
+import Agda.Termination.RecCheck
+
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Functions
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Forcing
+import Agda.TypeChecking.Records -- (isRecordConstructor, isInductiveRecord)
+import Agda.TypeChecking.Reduce (reduce, normalise, instantiate, instantiateFull, appDefE')
+import Agda.TypeChecking.SizedTypes
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import qualified Agda.Benchmarking as Benchmark
+import Agda.TypeChecking.Monad.Benchmark (billTo, billPureTo)
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad -- (mapM', forM', ifM, or2M, and2M)
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import qualified Agda.Utils.SmallSet as SmallSet
+import qualified Agda.Utils.VarSet as VarSet
+
+import Agda.Utils.Impossible
+
+-- | Call graph with call info for composed calls.
+
+type Calls = CallGraph CallPath
+
+-- | The result of termination checking a module.
+--   Must be a 'Monoid' and have 'Singleton'.
+
+type Result = [TerminationError]
+
+-- | Entry point: Termination check a single declaration.
+--
+--   Precondition: 'envMutualBlock' must be set correctly.
+
+termDecl :: A.Declaration -> TCM Result
+termDecl d = inTopContext $ termDecl' d
+
+
+-- | Termination check a single declaration
+--   (without necessarily ignoring @abstract@).
+
+termDecl' :: A.Declaration -> TCM Result
+termDecl' = \case
+    A.Axiom {}            -> return mempty
+    A.Field {}            -> return mempty
+    A.Primitive {}        -> return mempty
+    A.Mutual i ds         -> termMutual $ getNames ds
+    A.Section _ _ _ _ ds  -> termDecls ds
+        -- section structure can be ignored as we are termination checking
+        -- definitions lifted to the top-level
+    A.Apply {}            -> return mempty
+    A.Import {}           -> return mempty
+    A.Pragma {}           -> return mempty
+    A.Open {}             -> return mempty
+    A.PatternSynDef {}    -> return mempty
+    A.UnfoldingDecl{}     -> return mempty
+    A.Generalize {}       -> return mempty
+        -- open, pattern synonym and generalize defs are just artifacts from the concrete syntax
+    A.ScopedDecl scope ds -> {- withScope_ scope $ -} termDecls ds
+        -- scope is irrelevant as we are termination checking Syntax.Internal
+    A.RecSig{}            -> return mempty
+    A.RecDef _ x _ _ _ _ ds -> termMutual [x] <> termDecls ds
+        -- Andreas, 2022-10-23, issue #5823
+        -- Also check record types for termination.
+        -- They are unfolded during construction of unique inhabitants of eta-records.
+    -- These should all be wrapped in mutual blocks:
+    A.FunDef{}      -> __IMPOSSIBLE__
+    A.DataSig{}     -> __IMPOSSIBLE__
+    A.DataDef{}     -> __IMPOSSIBLE__
+    A.UnquoteDecl{} -> __IMPOSSIBLE__
+    A.UnquoteDef{}  -> __IMPOSSIBLE__
+    A.UnquoteData{} -> __IMPOSSIBLE__
+  where
+    termDecls ds = concat <$> mapM termDecl' ds
+
+    -- The mutual names mentioned in the abstract syntax
+    -- for symbols that need to be termination-checked.
+    getNames = concatMap getName
+    getName (A.FunDef i x cs)   = [x]
+    getName (A.RecDef _ x _ _ _ _ ds)   = x : getNames ds
+    getName (A.Mutual _ ds)             = getNames ds
+    getName (A.Section _ _ _ _ ds)      = getNames ds
+    getName (A.ScopedDecl _ ds)         = getNames ds
+    getName (A.UnquoteDecl _ _ xs _)    = xs
+    getName (A.UnquoteDef _ xs _)       = xs
+    getName _                           = []
+
+
+-- | Entry point: Termination check the current mutual block.
+
+termMutual
+  :: [QName]
+     -- ^ The function names defined in this block on top-level.
+     --   (For error-reporting only.)
+  -> TCM Result
+termMutual names0 = ifNotM (optTerminationCheck <$> pragmaOptions) (return mempty) $ {-else-}
+ inTopContext $ do
+
+  -- Get set of mutually defined names from the TCM.
+  -- This includes local and auxiliary functions introduced
+  -- during type-checking.
+  mid <- fromMaybe __IMPOSSIBLE__ <$> asksTC envMutualBlock
+  mutualBlock <- lookupMutualBlock mid
+  let allNames = Set.filter (not . isAbsurdLambdaName) $
+                 mutualNames mutualBlock
+      names    = if null names0 then allNames else Set.fromList names0
+      i        = mutualInfo mutualBlock
+
+  -- We set the range to avoid panics when printing error messages.
+  setCurrentRange i $ do
+
+  -- The following debug statement is part of a test case for Issue
+  -- #3590.
+  reportSLn "term.mutual.id" 40 $
+    "Termination checking mutual block " ++ show mid
+  reportSLn "term.mutual" 10 $ "Termination checking " ++ prettyShow allNames
+
+  -- NO_TERMINATION_CHECK
+  if (Info.mutualTerminationCheck i `elem` [ NoTerminationCheck, Terminating ]) then do
+      reportSLn "term.warn.yes" 10 $ "Skipping termination check for " ++ prettyShow names
+      forM_ allNames $ \ q -> setTerminates q True -- considered terminating!
+      return mempty
+  -- NON_TERMINATING
+  else if (Info.mutualTerminationCheck i == NonTerminating) then do
+      reportSLn "term.warn.yes" 10 $ "Considering as non-terminating: " ++ prettyShow names
+      forM_ allNames $ \ q -> setTerminates q False
+      return mempty
+  else do
+    sccs <- do
+      -- Andreas, 2016-10-01 issue #2231
+      -- Recursivity checker has to see through abstract definitions!
+      ignoreAbstractMode $ do
+        billTo [Benchmark.Termination, Benchmark.RecCheck] $ recursive allNames
+      -- -- Andreas, 2017-03-24, use positivity info to skip non-recursive functions
+      -- skip = ignoreAbstractMode $ allM allNames $ \ x -> do
+      --   null <$> getMutual x
+      -- PROBLEMS with test/Succeed/AbstractCoinduction.agda
+
+    -- Trivially terminating (non-recursive)?
+    when (null sccs) $
+      reportSLn "term.warn.yes" 10 $ "Trivially terminating: " ++ prettyShow names
+
+    -- Actual termination checking needed: go through SCCs.
+    concat <$> do
+     forM sccs $ \ allNames -> do
+
+     -- Set the mutual names in the termination environment.
+     let namesSCC = Set.filter (`Set.member` allNames) names
+     let setNames e = e
+           { terMutual    = allNames
+           , terUserNames = namesSCC
+           }
+         runTerm cont = runTerDefault $ do
+           cutoff <- terGetCutOff
+           reportSLn "term.top" 10 $ "Termination checking " ++ prettyShow namesSCC ++
+             " with cutoff=" ++ show cutoff ++ "..."
+           terLocal setNames cont
+
+     -- New check currently only makes a difference for copatterns and record types.
+     -- Since it is slow, only invoke it if
+     -- any of the definitions uses copatterns or is a record type.
+     ifM (anyM allNames $ \ q -> usesCopatterns q `or2M` (isJust <$> isRecord q))
+         -- Then: New check, one after another.
+         (runTerm $ forM' allNames $ termFunction)
+         -- Else: Old check, all at once.
+         (runTerm $ termMutual')
+
+-- | @termMutual'@ checks all names of the current mutual block,
+--   henceforth called @allNames@, for termination.
+--
+--   @allNames@ is taken from 'Internal' syntax, it contains also
+--   the definitions created by the type checker (e.g., with-functions).
+
+termMutual' :: TerM Result
+termMutual' = do
+
+  -- collect all recursive calls in the block
+  allNames <- terGetMutual
+  let collect = forM' allNames termDef
+
+  -- first try to termination check ignoring the dot patterns
+  calls1 <- collect
+  reportCalls "no " calls1
+
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  r <- billToTerGraph $ Term.terminates calls1
+  r <-
+       -- Andrea: 22/04/2020.
+       -- With cubical we will always have a clause where the dot
+       -- patterns are instead replaced with a variable, so they
+       -- cannot be relied on for termination.
+       -- See issue #4606 for a counterexample involving HITs.
+       --
+       -- Without the presence of HITs I conjecture that dot patterns
+       -- could be turned into actual splits, because no-confusion
+       -- would make the other cases impossible, so I do not disable
+       -- this for --without-K entirely.
+       ifM (isJust . optCubical <$> pragmaOptions) (return r) {- else -} $
+       case r of
+         r@Right{} -> return r
+         Left{}    -> do
+           -- Try again, but include the dot patterns this time.
+           calls2 <- terSetUseDotPatterns True $ collect
+           reportCalls "" calls2
+           billToTerGraph $ Term.terminates calls2
+
+  -- @names@ is taken from the 'Abstract' syntax, so it contains only
+  -- the names the user has declared.  This is for error reporting.
+  names <- terGetUserNames
+  case r of
+
+    Left calls -> do
+      mapM_ (`setTerminates` False) allNames
+      return $ singleton $ terminationError names calls
+
+    Right{} -> do
+      liftTCM $ reportSLn "term.warn.yes" 2 $
+        prettyShow (names) ++ " does termination check"
+      mapM_ (`setTerminates` True) allNames
+      return mempty
+
+-- | Smart constructor for 'TerminationError'.
+--   Removes 'termErrFunctions' that are not mentioned in 'termErrCalls'.
+terminationError :: Set QName -> CallPath -> TerminationError
+terminationError names calls = TerminationError names' calls'
+  where
+  calls'    = callInfos calls
+  mentioned = map callInfoTarget calls'
+  names'    = filter (hasElem mentioned) $ toList names
+
+billToTerGraph :: a -> TerM a
+billToTerGraph a = liftTCM $ billPureTo [Benchmark.Termination, Benchmark.Graph] a
+
+-- | @reportCalls@ for debug printing.
+--
+--   Replays the call graph completion for debugging.
+
+reportCalls :: String -> Calls -> TerM ()
+reportCalls no calls = do
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+
+  -- We work in TCM exclusively.
+  liftTCM $ do
+
+    reportS "term.lex" 20
+      [ "Calls (" ++ no ++ "dot patterns): " ++ prettyShow calls
+      ]
+
+    -- Print the whole completion phase.
+    verboseS "term.matrices" 40 $ do
+      let header s = unlines
+            [ replicate n '='
+            , replicate k '=' ++ s ++ replicate k' '='
+            , replicate n '='
+            ]
+            where n  = 70
+                  r  = n - length s
+                  k  = r `div` 2
+                  k' = r - k
+      let report s cs = reportSDoc "term.matrices" 40 $ vcat
+            [ text   $ header s
+            , nest 2 $ pretty cs
+            ]
+          cs0     = calls
+          step cs = do
+            let (new, cs') = completionStep cs0 cs
+            report " New call matrices " new
+            return $ if null new then Left () else Right cs'
+      report " Initial call matrices " cs0
+      trampolineM step cs0
+
+    -- Print the result of completion.
+    let calls' = CallGraph.complete calls
+        idems = filter idempotent $ endos $ CallGraph.toList calls'
+    -- TODO
+    -- reportSDoc "term.behaviours" 20 $ vcat
+    --   [ text $ "Recursion behaviours (" ++ no ++ "dot patterns):"
+    --   , nest 2 $ return $ Term.prettyBehaviour calls'
+    --   ]
+    reportSDoc "term.matrices" 30 $ vcat
+      [ text $ "Idempotent call matrices (" ++ no ++ "dot patterns):\n"
+      , nest 2 $ vcat $ punctuate "\n" $ map pretty idems
+      ]
+    -- reportSDoc "term.matrices" 30 $ vcat
+    --   [ text $ "Other call matrices (" ++ no ++ "dot patterns):"
+    --   , nest 2 $ pretty $ CallGraph.fromList others
+    --   ]
+    return ()
+
+-- | @termFunction name@ checks @name@ for termination.
+-- If it passes the termination check it is marked as "terminates" in the signature.
+
+termFunction :: QName -> TerM Result
+termFunction name = inConcreteOrAbstractMode name $ \ def -> do
+
+  -- Function @name@ is henceforth referred to by its @index@
+  -- in the list of @allNames@ of the mutual block.
+
+  allNames <- terGetMutual
+  let index = fromMaybe __IMPOSSIBLE__ $ Set.lookupIndex name allNames
+
+  -- Retrieve the target type of the function to check.
+  -- #4256: Don't use typeOfConst (which instantiates type with module params), since termination
+  -- checking is running in the empty context, but with the current module unchanged.
+  target <- case theDef def of
+    -- We are termination-checking a record (calls to record will not be guarding):
+    Record{} -> return TargetRecord
+    -- We are termination-checking a definition:
+    _ -> typeEndsInDef (defType def) <&> \case
+           Just d  -> TargetDef d
+           Nothing -> TargetOther
+  reportTarget target
+  terSetTarget target $ do
+
+    -- Collect the recursive calls in the block which (transitively)
+    -- involve @name@,
+    -- taking the target of @name@ into account for computing guardedness.
+
+    let collect = (`trampolineM` (Set.singleton index, mempty, mempty)) $ \ (todo, done, calls) -> do
+          if null todo then return $ Left calls else do
+            -- Extract calls originating from indices in @todo@.
+            new <- forM' todo $ \ i ->
+              termDef $
+              if i < 0 || i >= Set.size allNames
+              then __IMPOSSIBLE__
+              else Set.elemAt i allNames
+            -- Mark those functions as processed and add the calls to the result.
+            let done'  = done `mappend` todo
+                calls' = new  `mappend` calls
+            -- Compute the new todo list:
+                todo' = CallGraph.targetNodes new Set.\\ done'
+            -- Jump the trampoline.
+            return $ Right (todo', done', calls')
+
+    -- First try to termination check ignoring the dot patterns
+    calls1 <- terSetUseDotPatterns False $ collect
+    reportCalls "no " calls1
+
+    r <- do
+     cutoff <- terGetCutOff
+     let ?cutoff = cutoff
+     r <- billToTerGraph $ Term.terminatesFilter (== index) calls1
+
+     -- Andrea: 22/04/2020.
+     -- With cubical we will always have a clause where the dot
+     -- patterns are instead replaced with a variable, so they
+     -- cannot be relied on for termination.
+     -- See issue #4606 for a counterexample involving HITs.
+     --
+     -- Without the presence of HITs I conjecture that dot patterns
+     -- could be turned into actual splits, because no-confusion
+     -- would make the other cases impossible, so I do not disable
+     -- this for --without-K entirely.
+     --
+     -- Andreas, 2022-03-21: The check for --cubical was missing here.
+     ifM (isJust . optCubical <$> pragmaOptions) (return r) {- else -} $ case r of
+       Right () -> return $ Right ()
+       Left{}   -> do
+         -- Try again, but include the dot patterns this time.
+         calls2 <- terSetUseDotPatterns True $ collect
+         reportCalls "" calls2
+         billToTerGraph $ Term.terminatesFilter (== index) calls2
+
+    names <- terGetUserNames
+    case mapLeft callInfos r of
+
+      Left calls -> do
+        -- Mark as non-terminating.
+        setTerminates name False
+
+        -- Functions must be terminating, records types need not...
+        case theDef def of
+
+          -- Records need not terminate, so we just put the error on the debug log.
+          Record{} -> do
+            reportSDoc "term.warn.no" 10 $ vcat $
+              hsep [ "Record type", prettyTCM name, "does not termination check.", "Problematic calls:" ] :
+              (map (nest 2 . prettyTCM) $ List.sortOn getRange calls)
+            mempty
+
+          -- Functions must terminate, so we report the error.
+          _ -> do
+            let err = TerminationError [name | name `elem` names] calls
+            return $ singleton err
+
+      Right () -> do
+        reportSLn "term.warn.yes" 2 $
+          prettyShow name ++ " does termination check"
+        setTerminates name True
+        return mempty
+   where
+     reportTarget :: MonadDebug m => Target -> m ()
+     reportTarget tgt = reportSLn "term.target" 20 $ ("  " ++) $
+       case tgt of
+         TargetRecord -> "termination checking a record type"
+         TargetDef q  -> unwords [ "target type ends in", prettyShow q ]
+         TargetOther  -> "target type not recognized"
+
+-- | To process the target type.
+typeEndsInDef :: MonadTCM tcm => Type -> tcm (Maybe QName)
+typeEndsInDef t = liftTCM $ do
+  TelV _ core <- telViewPath t
+  case unEl core of
+    Def d vs -> return $ Just d
+    _        -> return Nothing
+
+-- | Termination check a definition by pattern matching.
+--
+--   TODO: Refactor!
+--   As this function may be called twice,
+--   once disregarding dot patterns,
+--   the second time regarding dot patterns,
+--   it is better if we separated bare call extraction
+--   from computing the change in structural order.
+--   Only the latter depends on the choice whether we
+--   consider dot patterns or not.
+termDef :: QName -> TerM Calls
+termDef name = terSetCurrent name $ inConcreteOrAbstractMode name $ \ def -> do
+
+ -- Skip calls to record types unless we are checking a record type in the first place.
+ let isRecord_ = case theDef def of { Record{} -> True; _ -> False }
+ let notTargetRecord = terGetTarget <&> \case
+       TargetRecord -> False
+       _ -> True
+ ifM (pure isRecord_ `and2M` notTargetRecord) mempty {-else-} $ do
+
+  -- Retrieve definition
+  let t = defType def
+
+  liftTCM $ reportSDoc "term.def.fun" 5 $
+    sep [ "termination checking type of" <+> prettyTCM name
+        , nest 2 $ ":" <+> prettyTCM t
+        ]
+
+  termType t `mappend` do
+
+  liftTCM $ reportSDoc "term.def.fun" 5 $
+    sep [ "termination checking body of" <+> prettyTCM name
+        , nest 2 $ ":" <+> prettyTCM t
+        ]
+
+  -- If --without-K, we disregard all arguments (and result)
+  -- which are not of data or record type.
+
+  withoutKEnabled <- liftTCM withoutKOption
+  applyWhen withoutKEnabled (setMasks t) $ do
+
+    -- If the result should be disregarded, set all calls to unguarded.
+    applyWhenM terGetMaskResult terUnguarded $ do
+
+      case theDef def of
+        Function{ funClauses = cls  } -> forM' cls $ \ cl -> do
+          if hasDefP (namedClausePats cl) -- generated hcomp clause, should be safe.
+                                          -- TODO find proper strategy.
+            then return empty
+            else termClause cl
+
+        -- @record R pars : Set where field tel@
+        -- is treated like function @R pars = tel@.
+        Record{ recPars, recTel } -> termRecTel recPars recTel
+
+        _ -> return empty
+
+-- | Extract "calls" to the field types from a record constructor telescope.
+-- Does not extract from the parameters, but treats these as the "pattern variables"
+-- (the lhs of the "function").
+termRecTel :: Nat -> Telescope -> TerM Calls
+termRecTel npars tel = do
+  -- Set up the record parameters like function parameters.
+  let (pars, fields) = splitAt npars $ telToList tel
+  addContext pars $ do
+    ps <- mkPats npars
+    terSetPatterns ps $ terSetSizeDepth pars $ do
+      -- Treat the record fields like the body of a function.
+      extract $ telFromList fields
+  where
+  -- create n variable patterns
+  mkPats n  = zipWith mkPat (downFrom n) <$> getContextNames
+  mkPat i x = notMasked $ VarP defaultPatternInfo $ DBPatVar (prettyShow x) i
+
+-- | Collect calls in type signature @f : (x1:A1)...(xn:An) -> B@.
+--   It is treated as if there were the additional function clauses.
+--   @@
+--      f = A1
+--      f x1 = A2
+--      f x1 x2 = A3
+--      ...
+--      f x1 ... xn = B
+--   @@
+
+termType :: Type -> TerM Calls
+termType = return mempty
+-- termType = loop 0  -- Andreas, 2019-04-10 deactivate for backwards-compatibility in 2.6.0 #1556
+  where
+  loop n t = do
+    ps <- mkPats n
+    reportSDoc "term.type" 60 $ vcat
+      [ text $ "termType " ++ show n ++ " with " ++ show (length ps) ++ " patterns"
+      , nest 2 $ "looking at type " <+> prettyTCM t
+      ]
+    tel <- getContextTelescope  -- Andreas, 2018-11-15, issue #3394, forgotten initialization of terSizeDepth
+    terSetPatterns ps $ terSetSizeDepth tel $ do
+      ifNotPiType t {-then-} extract {-else-} $ \ dom absB -> do
+        extract dom `mappend` underAbstractionAbs dom absB (loop $! n + 1)
+
+  -- create n variable patterns
+  mkPats n  = zipWith mkPat (downFrom n) <$> getContextNames
+  mkPat i x = notMasked $ VarP defaultPatternInfo $ DBPatVar (prettyShow x) i
+
+-- | Mask arguments and result for termination checking
+--   according to type of function.
+--   Only arguments of types ending in data/record or Size are counted in.
+setMasks :: Type -> TerM a -> TerM a
+setMasks t cont = do
+  (ds, d) <- liftTCM $ do
+    TelV tel core <- telViewPath t
+    -- Check argument types
+    ds <- checkArgumentTypes tel
+    -- Check result types
+    d  <- addContext tel $ isNothing <.> isDataOrRecord . unEl $ core
+    when d $
+      reportSLn "term.mask" 20 $ "result type is not data or record type, ignoring guardedness for --without-K"
+    return (ds, d)
+  terSetMaskArgs (ds ++ repeat True) $ terSetMaskResult d $ cont
+
+  where
+    checkArgumentTypes :: Telescope -> TCM [Bool]
+    checkArgumentTypes EmptyTel = return []
+    checkArgumentTypes (ExtendTel dom atel) = do
+      TelV tel2 t <- telViewPath $ unDom dom
+      d <- addContext tel2 $
+        (isNothing <$> isDataOrRecord (unEl t)) `or2M` (isJust <$> isSizeType t)
+      when d $
+        reportSDoc "term.mask" 20 $ do
+          "argument type "
+            <+> prettyTCM t
+            <+> " is not data or record type, ignoring structural descent for --without-K"
+      underAbstraction dom atel $ \tel -> (d:) <$> checkArgumentTypes tel
+
+-- | Is the current target type among the given ones?
+
+targetElem :: [QName] -> TerM Bool
+targetElem ds = terGetTarget <&> \case
+  TargetDef d  -> d `elem` ds
+  TargetRecord -> False
+  TargetOther  -> False
+
+
+-- | Convert a term (from a dot pattern) to a DeBruijn pattern.
+--
+--   The term is first normalized and stripped of all non-coinductive projections.
+
+termToDBP :: Term -> TerM DeBruijnPattern
+termToDBP t =
+  termToPattern =<< do liftTCM $ stripAllProjections =<< normalise t
+
+-- | Convert a term (from a dot pattern) to a pattern for the purposes of the termination checker.
+--
+--   @SIZESUC@ is treated as a constructor.
+
+class TermToPattern a b where
+  termToPattern :: a -> TerM b
+
+  default termToPattern :: (TermToPattern a' b', Traversable f, a ~ f a', b ~ f b') => a -> TerM b
+  termToPattern = traverse termToPattern
+
+instance TermToPattern a b => TermToPattern [a] [b] where
+instance TermToPattern a b => TermToPattern (Arg a) (Arg b) where
+instance TermToPattern a b => TermToPattern (Named c a) (Named c b) where
+
+-- OVERLAPPING
+-- instance TermToPattern a b => TermToPattern a (Named c b) where
+--   termToPattern t = unnamed <$> termToPattern t
+
+instance TermToPattern Term DeBruijnPattern where
+  termToPattern t = liftTCM (constructorForm t) >>= \case
+    -- Constructors.
+    Con c _ args -> ifDotPatsOrRecord c $
+      ConP c noConPatternInfo . map (fmap unnamed) <$> termToPattern (fromMaybe __IMPOSSIBLE__ $ allApplyElims args)
+    Def s [Apply arg] -> ifDotPats $ do
+      suc <- terGetSizeSuc
+      if Just s == suc then ConP (ConHead s IsData Inductive []) noConPatternInfo . map (fmap unnamed) <$> termToPattern [arg]
+       else fallback
+    DontCare t  -> termToPattern t -- OR: __IMPOSSIBLE__  -- removed by stripAllProjections
+    -- Leaves.
+    Var i []    -> varP . (`DBPatVar` i) . prettyShow <$> nameOfBV i
+    Lit l       -> return $ litP l
+    Dummy s _   -> __IMPOSSIBLE_VERBOSE__ s
+    t           -> fallback
+    where
+    -- Andreas, 2022-06-14, issues #5953 and #4725
+    -- Recognize variable and record patterns in dot patterns regardless
+    -- of whether dot-pattern termination is on.
+    ifDotPats           = ifNotM terGetUseDotPatterns fallback
+    ifDotPatsOrRecord c = ifM (pure (IsData == conDataRecord c) `and2M` do not <$> terGetUseDotPatterns) fallback
+    fallback            = return $ dotP t
+
+-- | Masks all non-data/record type patterns if --without-K.
+--   See issue #1023.
+maskNonDataArgs :: [DeBruijnPattern] -> TerM [Masked DeBruijnPattern]
+maskNonDataArgs ps = zipWith mask ps <$> terGetMaskArgs
+  where
+    mask p@ProjP{} _ = Masked False p
+    mask p         d = Masked d     p
+
+-- | Drop elements of the list which correspond to arguments forced by
+-- the constructor with the given QName.
+mapForcedArguments :: QName -> [a] -> (IsForced -> a -> Maybe b) -> TerM [b]
+mapForcedArguments c xs k = do
+  forcedArgs <- getForcedArgs c
+  let go xs (p:ps) = do
+        let (f, xs') = nextIsForced xs
+        case k f p of
+          Just b  -> b:go xs' ps
+          Nothing -> go xs' ps
+      go _ [] = []
+  pure $ go forcedArgs xs
+
+-- | Extract recursive calls from one clause.
+termClause :: Clause -> TerM Calls
+termClause clause = do
+  Clause{ clauseTel = tel, namedClausePats = ps, clauseBody = body } <- etaExpandClause clause
+  liftTCM $ reportSDoc "term.check.clause" 25 $ vcat
+    [ "termClause"
+    , nest 2 $ "tel =" <+> prettyTCM tel
+    , nest 2 $ "ps  =" <+> do addContext tel $ prettyTCMPatternList ps
+    ]
+  forM' body $ \ v -> addContext tel $ do
+    -- TODO: combine the following two traversals, avoid full normalisation.
+    -- Parse dot patterns as patterns as far as possible.
+    ps <- postTraversePatternM parseDotP ps
+    -- Blank out coconstructors.
+    ps <- preTraversePatternM stripCoCon ps
+    -- Mask non-data arguments.
+    mdbpats <- maskNonDataArgs $ map namedArg ps
+    terSetPatterns mdbpats $ do
+      terSetSizeDepth tel $ do
+        reportBody v
+        extract v
+
+  where
+    parseDotP = \case
+      DotP o t -> termToDBP t
+      p        -> return p
+    stripCoCon = \case
+      ConP (ConHead c _ CoInductive _) _ _ -> return unusedVar
+      p -> return p
+    reportBody :: Term -> TerM ()
+    reportBody v = verboseS "term.check.clause" 6 $ do
+      f       <- terGetCurrent
+      pats    <- terGetPatterns
+      liftTCM $ reportSDoc "term.check.clause" 6 $ do
+        sep [ text ("termination checking clause of")
+                <+> prettyTCM f
+            , nest 2 $ "lhs:" <+> sep (map prettyTCM pats)
+            , nest 2 $ "rhs:" <+> prettyTCM v
+            ]
+
+
+-- | Extract recursive calls from expressions.
+class ExtractCalls a where
+  extract :: a -> TerM Calls
+
+instance ExtractCalls a => ExtractCalls (Abs a) where
+  extract (NoAbs _ a) = extract a
+  extract (Abs x a)   = addContext x $ terRaise $ extract a
+
+instance ExtractCalls a => ExtractCalls (Arg a) where
+  extract = extract . unArg
+
+instance ExtractCalls a => ExtractCalls (Dom a) where
+  extract = extract . unDom
+
+instance ExtractCalls a => ExtractCalls (Elim' a) where
+  extract Proj{}    = return empty
+  extract (Apply a) = extract $ unArg a
+  extract (IApply x y a) = extract (x,(y,a)) -- TODO Andrea: conservative
+
+instance ExtractCalls a => ExtractCalls [a] where
+  extract = mapM' extract
+
+instance (ExtractCalls a, ExtractCalls b) => ExtractCalls (a,b) where
+  extract (a, b) = CallGraph.union <$> extract a <*> extract b
+
+instance (ExtractCalls a, ExtractCalls b, ExtractCalls c) => ExtractCalls (a,b,c) where
+  extract (a, b, c) = extract (a, (b, c))
+
+-- | Sorts can contain arbitrary terms of type @Level@,
+--   so look for recursive calls also in sorts.
+--   Ideally, 'Sort' would not be its own datatype but just
+--   a subgrammar of 'Term', then we would not need this boilerplate.
+
+instance ExtractCalls Sort where
+  extract s = do
+    liftTCM $ do
+      reportSDoc "term.sort" 20 $
+        "extracting calls from sort" <+> prettyTCM s
+      reportSDoc "term.sort" 50 $
+        text ("s = " ++ show s)
+    case s of
+      Inf _ _    -> return empty
+      SizeUniv   -> return empty
+      LockUniv   -> return empty
+      LevelUniv  -> return empty
+      IntervalUniv -> return empty
+      Univ _ t       -> terUnguarded $ extract t  -- no guarded levels
+      PiSort a s1 s2 -> extract (a, s1, s2)
+      FunSort s1 s2 -> extract (s1, s2)
+      UnivSort s -> extract s
+      MetaS x es -> return empty
+      DefS d es  -> return empty
+      DummyS{}   -> return empty
+
+-- | Extract recursive calls from a type.
+
+instance ExtractCalls Type where
+  extract (El s t) = extract (s, t)
+
+instance ExtractCalls a => ExtractCalls (Tele a) where
+  extract = \case
+    EmptyTel        -> mempty
+    ExtendTel a tel -> extract a <> extract tel
+
+-- | Extract recursive calls from a constructor application.
+
+constructor
+  :: QName
+    -- ^ Constructor name.
+  -> Induction
+    -- ^ Should the constructor be treated as inductive or coinductive?
+  -> [(Arg Term, Bool)]
+    -- ^ All the arguments,
+    --   and for every argument a boolean which is 'True' iff the
+    --   argument should be viewed as preserving guardedness.
+  -> TerM Calls
+constructor c ind args = do
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  forM' args $ \ (arg, preserves) -> do
+    let g' = case (preserves, ind) of
+             (True,  Inductive)   -> id
+             (True,  CoInductive) -> (Order.lt .*.)
+             (False, _)           -> const Order.unknown
+    terModifyGuarded g' $ extract arg
+
+-- | Handles function applications @g es@.
+
+function :: QName -> Elims -> TerM Calls
+function g es0 = do
+
+    f       <- terGetCurrent
+    names   <- terGetMutual
+    guarded <- terGetGuarded
+
+    -- let gArgs = Def g es0
+    liftTCM $ reportSDoc "term.function" 30 $
+      "termination checking function call " <+> prettyTCM (Def g es0)
+
+    -- First, look for calls in the arguments of the call gArgs.
+
+    -- If the function is a projection but not for a coinductive record,
+    -- then preserve guardedness for its principal argument.
+    isProj <- isProjectionButNotCoinductive g
+    let unguards = repeat Order.unknown
+    let guards = applyWhen isProj (guarded :) unguards
+    -- Collect calls in the arguments of this call.
+    let args = map unArg $ argsFromElims es0
+    calls <- forM' (zip guards args) $ \ (guard, a) -> do
+      terSetGuarded guard $ extract a
+
+    -- Then, consider call gArgs itself.
+
+    liftTCM $ reportSDoc "term.found.call" 20 $
+      sep [ "found call from" <+> prettyTCM f
+          , nest 2 $ "to" <+> prettyTCM g
+          ]
+
+    -- insert this call into the call list
+    case Set.lookupIndex g names of
+
+       -- call leads outside the mutual block and can be ignored
+       Nothing   -> return calls
+
+       -- call is to one of the mutally recursive functions/record
+       Just gInd -> do
+         cutoff <- terGetCutOff
+         let ?cutoff = cutoff
+
+         -- Andreas, 2017-02-14, issue #2458:
+         -- If we have inlined with-functions, we could be illtyped,
+         -- hence, do not reduce anything.
+         -- Andreas, 2017-06-20 issue #2613:
+         -- We still need to reduce constructors, even when with-inlining happened.
+         es <- -- ifM terGetHaveInlinedWith (return es0) {-else-} $
+           liftTCM $ forM es0 $
+             -- 2017-09-09, re issue #2732
+             -- The eta-contraction that was here does not seem necessary to make structural order
+             -- comparison not having to worry about eta.
+             -- Maybe we thought an eta redex could come from a meta instantiation.
+             -- However, eta-contraction is already performed by instantiateFull.
+             -- See test/Succeed/Issue2732-termination.agda.
+             traverse reduceCon <=< instantiateFull
+
+           -- 2017-05-16, issue #2403: Argument normalization is too expensive,
+           -- even if we only expand non-recursive functions.
+           -- Argument normalization TURNED OFF.
+           -- liftTCM $ billTo [Benchmark.Termination, Benchmark.Reduce] $ do
+           --  -- Andreas, 2017-01-13, issue #2403, normalize arguments for the structural ordering.
+           --  -- Andreas, 2017-03-25, issue #2495, restrict this to non-recursive functions
+           --  -- otherwise, the termination checking may run forever.
+           --  reportSLn "term.reduce" 90 $ "normalizing call arguments"
+           --  modifyAllowedReductions (List.\\ [UnconfirmedReductions,RecursiveReductions]) $
+           --    forM es0 $ \ e -> do
+           --      reportSDoc "term.reduce" 95 $ "normalizing " <+> prettyTCM e
+           --      etaContract =<< normalise e
+
+         -- Compute the call matrix.
+
+         -- Andreas, 2014-03-26 only 6% of termination time for library test
+         -- spent on call matrix generation
+         (nrows, ncols, matrix) <- billTo [Benchmark.Termination, Benchmark.Compare] $
+           compareArgs es
+
+         -- Andreas, 2022-03-21, #5823:
+         -- If we are "calling" a record type we are guarded unless the origin
+         -- of the termination analysis is itself a record.
+         -- This is because we usually do not "unfold" record types into their
+         -- field telescope.  We only do so when trying to construct the
+         -- unique inhabitant of record type (singleton analysis).
+         -- In the latter case, a call to a record type is not guarding.
+         guarded' <- isRecord g >>= \case
+           Just{} -> terGetTarget >>= \case
+             TargetRecord
+               -> return guarded
+             _ -> return (guarded .*. Order.lt)
+                    -- guarding when we call a record and not termination checking a record
+           Nothing
+             -- only a delayed definition can be guarded
+             | Order.decreasing guarded
+               -> return Order.le
+             | otherwise
+               -> return guarded
+         liftTCM $ reportSLn "term.guardedness" 20 $
+           "composing with guardedness " ++ prettyShow guarded ++
+           " counting as " ++ prettyShow guarded'
+         let matrix' = composeGuardedness guarded' matrix
+
+         -- Andreas, 2013-04-26 FORBIDDINGLY expensive!
+         -- This PrettyTCM QName cost 50% of the termination time for std-lib!!
+         -- gPretty <-liftTCM $ billTo [Benchmark.Termination, Benchmark.Level] $
+         --   render <$> prettyTCM g
+
+         -- Andreas, 2013-05-19 as pointed out by Andrea Vezzosi,
+         -- printing the call eagerly is forbiddingly expensive.
+         -- So we build a closure such that we can print the call
+         -- whenever we really need to.
+         -- This saves 30s (12%) on the std-lib!
+         -- Andreas, 2015-01-21 Issue 1410: Go to the module where g is defined
+         -- otherwise its free variables with be prepended to the call
+         -- in the error message.
+         doc <- liftTCM $ withCurrentModule (qnameModule g) $ buildClosure $
+           Def g $ List.dropWhileEnd ((Inserted ==) . getOrigin) es0
+           -- Andreas, 2018-07-22, issue #3136
+           -- Dropping only inserted arguments at the end, since
+           -- dropping arguments in the middle might make the printer crash.
+           -- Def g $ filter ((/= Inserted) . getOrigin) es0
+           -- Andreas, 2017-01-05, issue #2376
+           -- Remove arguments inserted by etaExpandClause.
+
+         let src  = fromMaybe __IMPOSSIBLE__ $ Set.lookupIndex f names
+             tgt  = gInd
+             cm   = makeCM ncols nrows matrix'
+             info = CallPath $ singleton $
+                    CallInfo
+                      { callInfoTarget = g
+                      , callInfoCall   = doc
+                      }
+         verboseS "term.kept.call" 5 $ do
+           pats <- terGetPatterns
+           reportSDoc "term.kept.call" 5 $ vcat
+             [ "kept call from" <+> text (prettyShow f) <+> hsep (map prettyTCM pats)
+             , nest 2 $ "to" <+> text (prettyShow g) <+>
+                         hsep (map (parens . prettyTCM) args)
+             , nest 2 $ "call matrix (with guardedness): "
+             , nest 2 $ pretty cm
+             ]
+         return $ CallGraph.insert src tgt cm info calls
+
+  where
+    -- We have to reduce constructors in case they're reexported.
+    -- Andreas, Issue 1530: constructors have to be reduced deep inside terms,
+    -- thus, we need to use traverseTermM.
+    reduceCon :: Term -> TCM Term
+    reduceCon = traverseTermM $ \case
+      Con c ci vs -> (`applyE` vs) <$> reduce (Con c ci [])  -- make sure we don't reduce the arguments
+      t -> return t
+
+
+-- | Try to get rid of a function call targeting the current SCC
+--   using a non-recursive clause.
+--
+--   This can help copattern definitions of dependent records.
+tryReduceNonRecursiveClause
+  :: QName                 -- ^ Function
+  -> Elims                 -- ^ Arguments
+  -> (Term -> TerM Calls)  -- ^ Continue here if we managed to reduce.
+  -> TerM Calls            -- ^ Otherwise, continue here.
+  -> TerM Calls
+tryReduceNonRecursiveClause g es continue fallback = do
+  -- Andreas, 2020-02-06, re: issue #906
+  let v0 = Def g es
+  reportSDoc "term.reduce" 40 $ "Trying to reduce away call: " <+> prettyTCM v0
+
+  -- First, make sure the function is in the current SCC.
+  ifM (notElem g <$> terGetMutual) fallback {-else-} $ do
+  reportSLn "term.reduce" 40 $ "This call is in the current SCC!"
+
+  -- Then, collect its non-recursive clauses.
+  cls <- liftTCM $ getNonRecursiveClauses g
+  reportSLn "term.reduce" 40 $ unwords [ "Function has", show (length cls), "non-recursive exact clauses"]
+  reportSDoc "term.reduce" 80 $ vcat $ map (prettyTCM . NamedClause g True) cls
+  reportSLn  "term.reduce" 80 . ("allowed reductions = " ++) . show . SmallSet.elems
+    =<< asksTC envAllowedReductions
+
+  -- Finally, try to reduce with the non-recursive clauses (and no rewrite rules).
+  r <- liftTCM $ modifyAllowedReductions (SmallSet.delete UnconfirmedReductions) $
+    runReduceM $ appDefE' g v0 cls [] (map notReduced es)
+  case r of
+    NoReduction{}    -> fallback
+    YesReduction _ v -> do
+      reportSDoc "term.reduce" 30 $ vcat
+        [ "Termination checker: Successfully reduced away call:"
+        , nest 2 $ prettyTCM v0
+        ]
+      verboseS "term.reduce" 5 $ tick "termination-checker-reduced-nonrecursive-call"
+      continue v
+
+getNonRecursiveClauses :: QName -> TCM [Clause]
+getNonRecursiveClauses q =
+  filter (liftA2 (&&) nonrec exact) . defClauses <$> getConstInfo q
+  where
+  nonrec = maybe False not . clauseRecursive
+  exact  = fromMaybe False . clauseExact
+
+-- | Extract recursive calls from a term.
+
+instance ExtractCalls Term where
+  extract t = do
+    reportSDoc "term.check.term" 50 $ do
+      "looking for calls in" <+> prettyTCM t
+
+    -- Instantiate top-level MetaVar.
+    instantiate t >>= \case
+
+      -- Constructed value.
+      Con ConHead{conName = c, conDataRecord = dataOrRec} _ es -> do
+        let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+        -- A constructor preserves the guardedness of all its arguments.
+        -- Andreas, 2022-09-19, issue #6108:
+        -- A higher constructor does not.  So check if there is an @IApply@ amoung @es@.
+        let argsg = zip args $ repeat $ all isProperApplyElim es
+
+        -- If we encounter a coinductive record constructor
+        -- in a type mutual with the current target
+        -- then we count it as guarding.
+        let inductive   = return Inductive    -- not guarding, but preserving
+            coinductive = return CoInductive  -- guarding
+        -- ♯ is guarding
+        ind <- ifM ((Just c ==) <$> terGetSharp) coinductive $ {-else-} do
+          -- data constructors are not guarding
+          if dataOrRec == IsData then inductive else do
+          -- abstract constructors are not guarding
+          caseMaybeM (isRecordConstructor c) inductive $ \ (q, def) -> do
+            reportSLn "term.check.term" 50 $ "constructor " ++ prettyShow c ++ " has record type " ++ prettyShow q
+            -- inductive record constructors are not guarding
+            if recInduction def /= Just CoInductive then inductive else do
+            -- coinductive constructors unrelated to the mutually
+            -- constructed inhabitants of coinductive types are not guarding
+            ifM (targetElem . fromMaybe __IMPOSSIBLE__ $ recMutual def)
+               {-then-} coinductive
+               {-else-} inductive
+        constructor c ind argsg
+
+      -- Function, data, or record type.
+      Def g es -> tryReduceNonRecursiveClause g es extract $ function g es
+
+      -- Abstraction. Preserves guardedness.
+      Lam h b -> extract b
+
+      -- Neutral term. Destroys guardedness.
+      Var i es -> terUnguarded $ extract es
+
+      -- Dependent function space.
+      Pi a (Abs x b) ->
+        CallGraph.union <$>
+        extract a <*> do
+          a <- maskSizeLt a  -- OR: just do not add a to the context!
+          addContext (x, a) $ terRaise $ extract b
+
+      -- Non-dependent function space.
+      Pi a (NoAbs _ b) ->
+        CallGraph.union <$> extract a <*> extract b
+
+      -- Literal.
+      Lit l -> return empty
+
+      -- Sort.
+      Sort s -> extract s
+
+      -- Unsolved metas are not considered termination problems, there
+      -- will be a warning for them anyway.
+      MetaV x args -> return empty
+
+      -- Erased and not-yet-erased proof.
+      DontCare t -> extract t
+
+      -- Level.
+      Level l -> -- billTo [Benchmark.Termination, Benchmark.Level] $ do
+        -- Andreas, 2014-03-26 Benchmark discontinued, < 0.3% spent on levels.
+        extract l
+
+      -- Dummy.
+      Dummy{} -> return empty
+
+-- | Extract recursive calls from level expressions.
+
+instance ExtractCalls Level where
+  extract (Max n as) = extract as
+
+instance ExtractCalls PlusLevel where
+  extract (Plus n l) = extract l
+
+-- | Rewrite type @tel -> Size< u@ to @tel -> Size@.
+maskSizeLt :: MonadTCM tcm => Dom Type -> tcm (Dom Type)
+maskSizeLt !dom = liftTCM $ do
+  let a = unDom dom
+  (msize, msizelt) <- getBuiltinSize
+  case (msize, msizelt) of
+    (_ , Nothing) -> return dom
+    (Nothing, _)  -> __IMPOSSIBLE__
+    (Just size, Just sizelt) -> do
+      TelV tel c <- telView a
+      case a of
+        El s (Def d [v]) | d == sizelt -> return $
+          abstract tel (El s $ Def size []) <$ dom
+        _ -> return dom
+
+{- | @compareArgs es@
+
+     Compare the list of de Bruijn patterns (=parameters) @pats@
+     with a list of arguments @es@ and create a call maxtrix
+     with |es| rows and |pats| columns.
+
+     The guardedness is the number of projection patterns in @pats@
+     minus the number of projections in @es@.
+ -}
+compareArgs :: [Elim] -> TerM (Int, Int, [[Order]])
+compareArgs es = do
+  pats <- terGetPatterns
+  liftTCM $ reportSDoc "term.compareArgs" 90 $ vcat
+    [ text $ "comparing " ++ show (length es) ++ " args to " ++ show (length pats) ++ " patterns"
+    ]
+  -- apats <- annotatePatsWithUseSizeLt pats
+  -- reportSDoc "term.compare" 20 $
+  --   "annotated patterns = " <+> sep (map prettyTCM apats)
+  -- matrix <- forM es $ \ e -> forM apats $ \ (b, p) -> terSetUseSizeLt b $ compareElim e p
+  matrix <- withUsableVars pats $ forM es $ \ e -> forM pats $ \ p -> compareElim e p
+
+  -- Count the number of coinductive projection(pattern)s in caller and callee.
+  -- Only recursive coinductive projections are eligible (Issue 1209).
+  projsCaller <- length <$> do
+    filterM (isCoinductiveProjection True) $ mapMaybe (fmap (headAmbQ . snd) . isProjP . getMasked) pats
+  projsCallee <- length <$> do
+    filterM (isCoinductiveProjection True) $ mapMaybe (fmap snd . isProjElim) es
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  useGuardedness <- liftTCM guardednessOption
+  let guardedness =
+        if useGuardedness
+        then decr True $ projsCaller - projsCallee
+        else Order.le
+  liftTCM $ reportSDoc "term.guardedness" 30 $ sep
+    [ "compareArgs:"
+    , nest 2 $ text $ "projsCaller = " ++ prettyShow projsCaller
+    , nest 2 $ text $ "projsCallee = " ++ prettyShow projsCallee
+    , nest 2 $ text $ "guardedness of call: " ++ prettyShow guardedness
+    ]
+  return $ addGuardedness guardedness (size es, size pats, matrix)
+
+-- | Traverse patterns from left to right.
+--   When we come to a projection pattern,
+--   switch usage of SIZELT constraints:
+--   on, if coinductive,
+--   off, if inductive.
+--
+--   UNUSED
+--annotatePatsWithUseSizeLt :: [DeBruijnPattern] -> TerM [(Bool,DeBruijnPattern)]
+--annotatePatsWithUseSizeLt = loop where
+--  loop [] = return []
+--  loop (p@(ProjP _ q) : pats) = ((False,p) :) <$> do projUseSizeLt q $ loop pats
+--  loop (p : pats) = (\ b ps -> (b,p) : ps) <$> terGetUseSizeLt <*> loop pats
+
+
+-- | @compareElim e dbpat@
+
+compareElim :: Elim -> Masked DeBruijnPattern -> TerM Order
+compareElim e p = do
+  liftTCM $ do
+    reportSDoc "term.compare" 30 $ sep
+      [ "compareElim"
+      , nest 2 $ "e = " <> prettyTCM e
+      , nest 2 $ "p = " <> prettyTCM p
+      ]
+    reportSDoc "term.compare" 50 $ sep
+      [ nest 2 $ text $ "e = " ++ show e
+      , nest 2 $ text $ "p = " ++ show p
+      ]
+  case (e, getMasked p) of
+    (Proj _ d, ProjP _ d') -> do
+      d  <- getOriginalProjection d
+      d' <- getOriginalProjection d'
+      o  <- compareProj d d'
+      reportSDoc "term.compare" 30 $ sep
+        [ text $ "comparing callee projection " ++ prettyShow d
+        , text $ "against caller projection " ++ prettyShow d'
+        , text $ "yields order " ++ prettyShow o
+        ]
+      return o
+    (Proj{}, _)            -> return Order.unknown
+    (Apply{}, ProjP{})     -> return Order.unknown
+    (Apply arg, _)         -> compareTerm (unArg arg) p
+    -- TODO Andrea: making sense?
+    (IApply{}, ProjP{})  -> return Order.unknown
+    (IApply _ _ arg, _)    -> compareTerm arg p
+
+-- | In dependent records, the types of later fields may depend on the
+--   values of earlier fields.  Thus when defining an inhabitant of a
+--   dependent record type such as Σ by copattern matching,
+--   a recursive call eliminated by an earlier projection (proj₁) might
+--   occur in the definition at a later projection (proj₂).
+--   Thus, earlier projections are considered "smaller" when
+--   comparing copattern spines.  This is an ok approximation
+--   of the actual dependency order.
+--   See issues 906, 942.
+compareProj :: MonadTCM tcm => QName -> QName -> tcm Order
+compareProj d d'
+  | d == d' = return Order.le
+  | otherwise = liftTCM $ do
+      -- different projections
+      mr  <- getRecordOfField d
+      mr' <- getRecordOfField d'
+      case (mr, mr') of
+        (Just r, Just r') | r == r' -> do
+          -- of same record
+          def <- theDef <$> getConstInfo r
+          case def of
+            Record{ recFields = fs } -> do
+              fs <- return $ map unDom fs
+              case (List.find (d ==) fs, List.find (d' ==) fs) of
+                (Just i, Just i')
+                  -- earlier field is smaller
+                  | i < i'    -> return Order.lt
+                  | i == i'   -> do
+                     __IMPOSSIBLE__
+                  | otherwise -> return Order.unknown
+                _ -> __IMPOSSIBLE__
+            _ -> __IMPOSSIBLE__
+        _ -> return Order.unknown
+
+-- | 'makeCM' turns the result of 'compareArgs' into a proper call matrix
+makeCM :: Int -> Int -> [[Order]] -> CallMatrix
+makeCM ncols nrows matrix = CallMatrix $
+  Matrix.fromLists (Matrix.Size nrows ncols) matrix
+
+-- | 'addGuardedness' adds guardedness flag in the upper left corner
+-- (0,0).
+addGuardedness :: Order -> (Int, Int, [[Order]]) -> (Int, Int, [[Order]])
+addGuardedness o (nrows, ncols, m) =
+  (nrows + 1, ncols + 1,
+   (o : replicate ncols Order.unknown) : map (Order.unknown :) m)
+
+-- | Compose something with the upper-left corner of a call matrix
+composeGuardedness :: (?cutoff :: CutOff) => Order -> [[Order]] -> [[Order]]
+composeGuardedness o ((corner : row) : rows) = ((o .*. corner) : row) : rows
+composeGuardedness _ _ = __IMPOSSIBLE__
+
+-- | Stripping off a record constructor is not counted as decrease, in
+--   contrast to a data constructor.
+--   A record constructor increases/decreases by 0, a data constructor by 1.
+offsetFromConstructor :: HasConstInfo tcm => QName -> tcm Int
+offsetFromConstructor c =
+  ifM (isEtaOrCoinductiveRecordConstructor c) (return 0) (return 1)
+
+--UNUSED Liang-Ting 2019-07-16
+---- | Compute the proper subpatterns of a 'DeBruijnPattern'.
+--subPatterns :: DeBruijnPattern -> [DeBruijnPattern]
+--subPatterns = foldPattern $ \case
+--  ConP _ _ ps -> map namedArg ps
+--  DefP _ _ ps -> map namedArg ps -- TODO check semantics
+--  VarP _ _    -> mempty
+--  LitP _      -> mempty
+--  DotP _ _    -> mempty
+--  ProjP _ _   -> mempty
+--  IApplyP{}   -> mempty
+
+
+compareTerm :: Term -> Masked DeBruijnPattern -> TerM Order
+compareTerm t p = do
+--   reportSDoc "term.compare" 25 $
+--     " comparing term " <+> prettyTCM t <+>
+--     " to pattern " <+> prettyTCM p
+  t <- liftTCM $ stripAllProjections t
+  o <- compareTerm' t p
+  liftTCM $ reportSDoc "term.compare" 25 $
+    " comparing term " <+> prettyTCM t <+>
+    " to pattern " <+> prettyTCM p <+>
+    text (" results in " ++ prettyShow o)
+  return o
+
+
+-- | Remove all non-coinductive projections from an algebraic term
+--   (not going under binders).
+--   Also, remove 'DontCare's.
+--
+class StripAllProjections a where
+  stripAllProjections :: a -> TCM a
+
+instance StripAllProjections a => StripAllProjections (Arg a) where
+  stripAllProjections = traverse stripAllProjections
+
+instance StripAllProjections Elims where
+  stripAllProjections es =
+    case es of
+      []             -> return []
+      (Apply a : es) -> do
+        (:) <$> (Apply <$> stripAllProjections a) <*> stripAllProjections es
+      (IApply x y a : es) -> do
+        -- TODO Andrea: are we doind extra work?
+        (:) <$> (IApply <$> stripAllProjections x
+                        <*> stripAllProjections y
+                        <*> stripAllProjections a)
+            <*> stripAllProjections es
+      (Proj o p  : es) -> do
+        isP <- isProjectionButNotCoinductive p
+        applyUnless isP (Proj o p :) <$> stripAllProjections es
+
+instance StripAllProjections Args where
+  stripAllProjections = mapM stripAllProjections
+
+instance StripAllProjections Term where
+  stripAllProjections t = do
+    case t of
+      Var i es   -> Var i <$> stripAllProjections es
+      Con c ci ts -> do
+        -- Andreas, 2019-02-23, re #2613.  This is apparently not necessary:
+        -- c <- fromRightM (\ err -> return c) $ getConForm (conName c)
+        Con c ci <$> stripAllProjections ts
+      Def d es   -> Def d <$> stripAllProjections es
+      DontCare t -> stripAllProjections t
+      _ -> return t
+
+-- | Normalize outermost constructor name in a pattern.
+
+reduceConPattern :: DeBruijnPattern -> TCM DeBruijnPattern
+reduceConPattern = \case
+  ConP c i ps -> fromRightM (\ err -> return c) (getConForm (conName c)) <&> \ c' ->
+    ConP c' i ps
+  p -> return p
+
+-- | @compareTerm' t dbpat@
+
+compareTerm' :: Term -> Masked DeBruijnPattern -> TerM Order
+compareTerm' v mp@(Masked m p) = do
+  suc  <- terGetSizeSuc
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  v <- liftTCM (instantiate v)
+  p <- liftTCM $ reduceConPattern p
+  case (v, p) of
+
+    -- Andreas, 2013-11-20 do not drop projections,
+    -- in any case not coinductive ones!:
+    (Var i es, _) | Just{} <- allApplyElims es ->
+      compareVar i mp
+
+    (DontCare t, _) ->
+      compareTerm' t mp
+
+    -- Andreas, 2014-09-22, issue 1281:
+    -- For metas, termination checking should be optimistic.
+    -- If there is any instance of the meta making termination
+    -- checking succeed, then we should not fail.
+    -- Thus, we assume the meta will be instantiated with the
+    -- deepest variable in @p@.
+    -- For sized types, the depth is maximally
+    -- the number of SIZELT hypotheses one can have in a context.
+    (MetaV{}, p) -> Order.decr True . max (if m then 0 else patternDepth p) . pred <$>
+       terAsks _terSizeDepth
+
+    -- Successor on both sides cancel each other.
+    -- We ignore the mask for sizes.
+    (Def s [Apply t], ConP s' _ [p]) | s == conName s' && Just s == suc ->
+      compareTerm' (unArg t) (notMasked $ namedArg p)
+
+    -- Register also size increase.
+    (Def s [Apply t], p) | Just s == suc ->
+      -- Andreas, 2012-10-19 do not cut off here
+      increase 1 <$> compareTerm' (unArg t) mp
+
+    -- In all cases that do not concern sizes,
+    -- we cannot continue if pattern is masked.
+
+    _ | m -> return Order.unknown
+
+    (Lit l, LitP _ l')
+      | l == l'     -> return Order.le
+      | otherwise   -> return Order.unknown
+
+    (Lit l, _) -> do
+      v <- liftTCM $ constructorForm v
+      case v of
+        Lit{}       -> return Order.unknown
+        v           -> compareTerm' v mp
+
+    -- Andreas, 2011-04-19 give subterm priority over matrix order
+
+    (Con{}, ConP c _ ps) | any (isSubTerm v . namedArg) ps ->
+      decr True <$> offsetFromConstructor (conName c)
+
+    (Con c _ es, ConP c' _ ps) | conName c == conName c'->
+      let ts = fromMaybe __IMPOSSIBLE__ $ allApplyElims es in
+      compareConArgs ts ps
+
+    (Con _ _ [], _) -> return Order.le
+
+    -- new case for counting constructors / projections
+    -- register also increase
+    (Con c _ es, _) -> do
+      let ts = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      increase <$> offsetFromConstructor (conName c)
+               <*> (infimum <$> mapM (\ t -> compareTerm' (unArg t) mp) ts)
+
+    (t, p) -> return $ subTerm t p
+
+-- | @subTerm@ computes a size difference (Order)
+subTerm :: (?cutoff :: CutOff) => Term -> DeBruijnPattern -> Order
+subTerm t p = if equal t p then Order.le else properSubTerm t p
+  where
+    equal (Con c _ es) (ConP c' _ ps) =
+      let ts = fromMaybe __IMPOSSIBLE__ $ allApplyElims es in
+      and $ (conName c == conName c')
+          : (length ts == length ps)
+          : zipWith (\ t p -> equal (unArg t) (namedArg p)) ts ps
+    equal (Var i []) (VarP _ x) = i == dbPatVarIndex x
+    equal (Lit l)    (LitP _ l') = l == l'
+    -- Terms.
+    -- Checking for identity here is very fragile.
+    -- However, we cannot do much more, as we are not allowed to normalize t.
+    -- (It might diverge, and we are just in the process of termination checking.)
+    equal t         (DotP _ t') = t == t'
+    equal _ _ = False
+
+    properSubTerm t (ConP _ _ ps) =
+      setUsability True $ decrease 1 $ supremum $ map (subTerm t . namedArg) ps
+    properSubTerm _ _ = Order.unknown
+
+isSubTerm :: (?cutoff :: CutOff) => Term -> DeBruijnPattern -> Bool
+isSubTerm t p = nonIncreasing $ subTerm t p
+
+compareConArgs :: Args -> [NamedArg DeBruijnPattern] -> TerM Order
+compareConArgs ts ps = do
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  case compare (length ts) (length ps) of
+
+    -- We may assume |ps| >= |ts|, otherwise c ps would be of functional type
+    -- which is impossible.
+    GT -> __IMPOSSIBLE__
+
+    -- Andreas, 2022-08-31, issue #6059: doing anything smarter than
+    -- @unknown@ here can lead to non-termination.
+    LT -> return Order.unknown
+
+    EQ -> List.foldl' (Order..*.) Order.le <$>
+               zipWithM compareTerm' (map unArg ts) (map (notMasked . namedArg) ps)
+       -- corresponds to taking the size, not the height
+       -- allows examples like (x, y) < (Succ x, y)
+{- version which does an "order matrix"
+   -- Andreas, 2013-02-18 disabled because it is unclear
+   -- how to scale idempotency test to matrix-shaped orders (need thinking/researcH)
+   -- Trigges issue 787.
+        (_,_) -> do -- build "call matrix"
+          m <- mapM (\t -> mapM (compareTerm' suc (unArg t)) ps) ts
+          let m2 = makeCM (length ps) (length ts) m
+          return $ Order.orderMat (Order.mat m2)
+-}
+{- version which takes height
+--    if null ts then Order.Le
+--               else Order.infimum (zipWith compareTerm' (map unArg ts) ps)
+-}
+
+compareVar :: Nat -> Masked DeBruijnPattern -> TerM Order
+compareVar i (Masked m p) = do
+  suc    <- terGetSizeSuc
+  cutoff <- terGetCutOff
+  let ?cutoff = cutoff
+  let no = return Order.unknown
+  case p of
+    ProjP{}   -> no
+    IApplyP _ _ _ x  -> compareVarVar i (Masked m x)
+    LitP{}    -> no
+    DotP{}   -> no
+    VarP _ x  -> compareVarVar i (Masked m x)
+
+    ConP s _ [p] | Just (conName s) == suc ->
+      setUsability True . decrease 1 <$> compareVar i (notMasked $ namedArg p)
+
+    ConP c pi ps -> if m then no else setUsability True <$> do
+      let
+        dropit Forced _ = Nothing
+        dropit NotForced x = Just x
+      ps <- ifM (optForcedArgumentRecursion <$> pragmaOptions)
+        {- then -} (pure ps)
+        {- else -} (mapForcedArguments (conName c) ps dropit)
+      decrease <$> offsetFromConstructor (conName c)
+               <*> (Order.supremum <$> mapM (compareVar i . notMasked . namedArg) ps)
+    DefP _ c ps -> if m then no else setUsability True <$> do
+      decrease <$> offsetFromConstructor c
+               <*> (Order.supremum <$> mapM (compareVar i . notMasked . namedArg) ps)
+      -- This should be fine for c == hcomp
+
+-- | Compare two variables.
+--
+--   The first variable comes from a term, the second from a pattern.
+compareVarVar :: Nat -> Masked DBPatVar -> TerM Order
+compareVarVar i (Masked m x@(DBPatVar _ j))
+  | i == j = if not m then return Order.le else liftTCM $
+      -- If j is a size, we ignore the mask.
+      ifM (isJust <$> do isSizeType =<< reduce =<< typeOfBV j)
+        {- then -} (return Order.le)
+        {- else -} (return Order.unknown)
+  | otherwise = do
+      -- record usability of variable
+      u <- (i `VarSet.member`) <$> terGetUsableVars
+      -- Andreas, 2017-07-26, issue #2331.
+      -- The usability logic is refuted by bounded size quantification in terms.
+      -- Thus, it is switched off (the infrastructure remains in place for now).
+      if not u then return Order.unknown else do
+      -- Only if usable:
+      res <- isBounded i
+      case res of
+        BoundedNo  -> return Order.unknown
+        BoundedLt v -> setUsability u . decrease 1 <$> compareTerm' v (Masked m $ varP x)
diff --git a/src/full/Agda/Termination/Termination.hs b/src/full/Agda/Termination/Termination.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Termination/Termination.hs
@@ -0,0 +1,87 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ImplicitParams #-}
+
+-- | Termination checker, based on
+--     \"A Predicative Analysis of Structural Recursion\" by
+--     Andreas Abel and Thorsten Altenkirch (JFP'01),
+--   and
+--     \"The Size-Change Principle for Program Termination\" by
+--     Chin Soon Lee, Neil Jones, and Amir Ben-Amram (POPL'01).
+
+module Agda.Termination.Termination
+  ( terminates
+  , terminatesFilter
+  , endos
+  , idempotent
+  ) where
+
+import Agda.Termination.CutOff
+import Agda.Termination.CallGraph
+import Agda.Termination.CallMatrix hiding (toList)
+import qualified Agda.Termination.CallMatrix as CMSet
+import Agda.Termination.Order
+import Agda.Termination.SparseMatrix
+
+import Agda.Utils.Maybe
+
+
+
+-- | TODO: This comment seems to be partly out of date.
+--
+-- @'terminates' cs@ checks if the functions represented by @cs@
+-- terminate. The call graph @cs@ should have one entry ('Call') per
+-- recursive function application.
+--
+-- @'Right' perms@ is returned if the functions are size-change terminating.
+--
+-- If termination can not be established, then @'Left' problems@ is
+-- returned instead. Here @problems@ contains an
+-- indication of why termination cannot be established. See 'lexOrder'
+-- for further details.
+--
+-- Note that this function assumes that all data types are strictly
+-- positive.
+--
+-- The termination criterion is taken from Jones et al.
+-- In the completed call graph, each idempotent call-matrix
+-- from a function to itself must have a decreasing argument.
+-- Idempotency is wrt. matrix multiplication.
+--
+-- This criterion is strictly more liberal than searching for a
+-- lexicographic order (and easier to implement, but harder to justify).
+
+terminates :: (Monoid cinfo, ?cutoff :: CutOff) => CallGraph cinfo -> Either cinfo ()
+terminates cs = checkIdems $ endos $ toList $ complete cs
+
+terminatesFilter :: (Monoid cinfo, ?cutoff :: CutOff) =>
+  (Node -> Bool) -> CallGraph cinfo -> Either cinfo ()
+terminatesFilter f cs = checkIdems $ endos $ filter f' $ toList $ complete cs
+  where f' c = f (source c) && f (target c)
+
+endos :: [Call cinfo] -> [CallMatrixAug cinfo]
+endos cs = [ m | c <- cs, source c == target c
+               , m <- CMSet.toList $ callMatrixSet c
+           ]
+
+checkIdems :: (?cutoff :: CutOff) => [CallMatrixAug cinfo] -> Either cinfo ()
+checkIdems calls = caseMaybe (listToMaybe offending) (Right ()) $ Left . augCallInfo
+  where
+    -- Every idempotent call must have decrease, otherwise it offends us.
+    offending = filter (not . hasDecrease) $ filter idempotent calls
+
+-- UNUSED Liang-Ting 2019-07-15
+--checkIdem :: (?cutoff :: CutOff) => CallMatrixAug cinfo -> Bool
+--checkIdem c = if idempotent c then hasDecrease c else True
+
+-- | A call @c@ is idempotent if it is an endo (@'source' == 'target'@)
+--   of order 1.
+--   (Endo-calls of higher orders are e.g. argument permutations).
+--   We can test idempotency by self-composition.
+--   Self-composition @c >*< c@ should not make any parameter-argument relation
+--   worse.
+idempotent  :: (?cutoff :: CutOff) => CallMatrixAug cinfo -> Bool
+idempotent (CallMatrixAug m _) = (m >*< m) `notWorse` m
+
+hasDecrease :: CallMatrixAug cinfo -> Bool
+hasDecrease = any isDecr . diagonal
diff --git a/src/full/Agda/TheTypeChecker.hs b/src/full/Agda/TheTypeChecker.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TheTypeChecker.hs
@@ -0,0 +1,9 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TheTypeChecker
+  ( checkDecls, checkDecl, checkDeclCached
+  , inferExpr, checkExpr
+  ) where
+
+import Agda.TypeChecking.Rules.Decl
+import Agda.TypeChecking.Rules.Term
diff --git a/src/full/Agda/TypeChecking/Abstract.hs b/src/full/Agda/TypeChecking/Abstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Abstract.hs
@@ -0,0 +1,350 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Functions for abstracting terms over other terms.
+
+module Agda.TypeChecking.Abstract where
+
+import Control.Monad
+import Control.Monad.Except
+
+import Data.Function (on)
+import qualified Data.HashMap.Strict as HMap
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.CheckInternal
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Functor
+import Agda.Utils.List ( splitExactlyAt, dropEnd )
+import Agda.Utils.Impossible
+
+-- | @abstractType a v b[v] = b@ where @a : v@.
+abstractType :: Type -> Term -> Type -> TCM Type
+abstractType a v (El s b) = El (absTerm v s) <$> abstractTerm a v (sort s) b
+
+-- | @piAbstractTerm NotHidden v a b[v] = (w : a) -> b[w]@
+--   @piAbstractTerm Hidden    v a b[v] = {w : a} -> b[w]@
+piAbstractTerm :: ArgInfo -> Term -> Type -> Type -> TCM Type
+piAbstractTerm info v a b = do
+  fun <- mkPi (setArgInfo info $ defaultDom ("w", a)) <$> abstractType a v b
+  reportSDoc "tc.abstract" 50 $
+    sep [ "piAbstract" <+> sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM a ]
+        , nest 2 $ "from" <+> prettyTCM b
+        , nest 2 $ "-->" <+> prettyTCM fun ]
+  reportSDoc "tc.abstract" 70 $
+    sep [ "piAbstract" <+> sep [ (text . show) v <+> ":", nest 2 $ (text . show) a ]
+        , nest 2 $ "from" <+> (text . show) b
+        , nest 2 $ "-->" <+> (text . show) fun ]
+  return fun
+
+-- | @piAbstract (v, a) b[v] = (w : a) -> b[w]@
+--
+--   For the inspect idiom, it does something special:
+--   @piAbstract (v, a) b[v] = (w : a) {w' : Eq a w v} -> b[w]
+--
+--   For @rewrite@, it does something special:
+--   @piAbstract (prf, Eq a v v') b[v,prf] = (w : a) (w' : Eq a w v') -> b[w,w']@
+
+piAbstract :: Arg (Term, EqualityView) -> Type -> TCM Type
+piAbstract (Arg info (v, OtherType a)) b = piAbstractTerm info v a b
+piAbstract (Arg info (v, IdiomType a)) b = do
+  b  <- raise 1 <$> abstractType a v b
+  eq <- addContext ("w" :: String, defaultDom a) $ do
+    -- manufacture the type @w ≡ v@
+    eqName <- primEqualityName
+    eqTy <- defType <$> getConstInfo eqName
+    -- E.g. @eqTy = eqTel → Set a@ where @eqTel = {a : Level} {A : Set a} (x y : A)@.
+    TelV eqTel _ <- telView eqTy
+    tel  <- newTelMeta (telFromList $ dropEnd 2 $ telToList eqTel)
+    let eq = Def eqName $ map Apply
+                 $ map (setHiding Hidden) tel
+                 -- we write `v ≡ w` because this equality is typically used to
+                 -- get `v` to unfold to whatever pattern was used to refine `w`
+                 -- in a with-clause.
+                 -- If we were to write `w ≡ v`, we would often need to take the
+                 -- symmetric of the proof we get to make use of `rewrite`.
+                 ++ [ defaultArg (raise 1 v)
+                    , defaultArg (var 0)
+                    ]
+    sort <- newSortMeta
+    let ty = El sort eq
+    ty <$ checkType ty
+
+  pure $ mkPi (setHiding (getHiding info) $ defaultDom ("w", a))
+       $ mkPi (setHiding NotHidden        $ defaultDom ("eq", eq))
+       $ b
+piAbstract (Arg info (prf, EqualityViewType eqt@(EqualityTypeData _ _ _ (Arg _ a) v _))) b = do
+  s <- sortOf a
+  let prfTy :: Type
+      prfTy = equalityUnview eqt
+      vTy   = El s a
+  b <- abstractType prfTy prf b
+  b <- addContext ("w" :: String, defaultDom prfTy) $
+         abstractType (raise 1 vTy) (unArg $ raise 1 v) b
+  return . funType "lhs" vTy . funType "equality" eqTy' . swap01 $ b
+  where
+    funType str a = mkPi $ setArgInfo info $ defaultDom (str, a)
+    -- Abstract the lhs (@a@) of the equality only.
+    eqt1 :: EqualityTypeData
+    eqt1  = raise 1 eqt
+    eqTy' :: Type
+    eqTy' = equalityUnview $ eqt1{ _eqtLhs = _eqtLhs eqt1 $> var 0 }
+
+
+-- | @isPrefixOf u v = Just es@ if @v == u `applyE` es@.
+class IsPrefixOf a where
+  isPrefixOf :: a -> a -> Maybe Elims
+
+instance IsPrefixOf Elims where
+  isPrefixOf us vs = do
+    (vs1, vs2) <- splitExactlyAt (length us) vs
+    guard $ equalSy us vs1
+    return vs2
+
+instance IsPrefixOf Args where
+  isPrefixOf us vs = do
+    (vs1, vs2) <- splitExactlyAt (length us) vs
+    guard $ equalSy us vs1
+    return $ map Apply vs2
+
+instance IsPrefixOf Term where
+  isPrefixOf u v =
+    case (u, v) of
+      (Var   i us, Var   j vs) | i == j  -> us `isPrefixOf` vs
+      (Def   f us, Def   g vs) | f == g  -> us `isPrefixOf` vs
+      (Con c _ us, Con d _ vs) | c == d  -> us `isPrefixOf` vs
+      (MetaV x us, MetaV y vs) | x == y  -> us `isPrefixOf` vs
+      (u, v) -> guard (equalSy u v) >> return []
+
+-- Type-based abstraction. Needed if u is a constructor application (#745).
+abstractTerm :: Type -> Term -> Type -> Term -> TCM Term
+abstractTerm a u@Con{} b v = do
+  reportSDoc "tc.abstract" 50 $
+    sep [ "Abstracting"
+        , nest 2 $ sep [ prettyTCM u <+> ":", nest 2 $ prettyTCM a ]
+        , "over"
+        , nest 2 $ sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM b ] ]
+  reportSDoc "tc.abstract" 70 $
+    sep [ "Abstracting"
+        , nest 2 $ sep [ (text . show) u <+> ":", nest 2 $ (text . show) a ]
+        , "over"
+        , nest 2 $ sep [ (text . show) v <+> ":", nest 2 $ (text . show) b ] ]
+
+  hole <- qualify <$> currentModule <*> freshName_ ("hole" :: String)
+  noMutualBlock $ addConstant' hole defaultArgInfo hole a defaultAxiom
+
+  args <- map Apply <$> getContextArgs
+  let n = length args
+
+  let abstr b v = do
+        m <- getContextSize
+        let (a', u') = raise (m - n) (a, u)
+        case u' `isPrefixOf` v of
+          Nothing -> return v
+          Just es -> do -- Check that the types match.
+            s <- getTC
+            do  noConstraints $ equalType a' b
+                putTC s
+                return $ Def hole (raise (m - n) args ++ es)
+              `catchError` \ _ -> do
+                reportSDoc "tc.abstract.ill-typed" 50 $
+                  sep [ "Skipping ill-typed abstraction"
+                      , nest 2 $ sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM b ] ]
+                return v
+
+  -- #2763: This can fail if the user is with-abstracting incorrectly (for
+  -- instance, abstracting over a first component of a sigma without also
+  -- abstracting the second component). In this case we skip abstraction
+  -- altogether and let the type check of the final with-function type produce
+  -- the error message.
+  res <- catchError_ (checkInternal' (defaultAction { preAction = abstr }) v CmpLeq b) $ \ err -> do
+        reportSDoc "tc.abstract.ill-typed" 40 $
+          "Skipping typed abstraction over ill-typed term" <?> (prettyTCM v <?> (":" <+> prettyTCM b))
+        return v
+  reportSDoc "tc.abstract" 50 $ "Resulting abstraction" <?> prettyTCM res
+  modifySignature $ updateDefinitions $ HMap.delete hole
+  return $ absTerm (Def hole args) res
+
+abstractTerm _ u _ v = return $ absTerm u v -- Non-constructors can use untyped abstraction
+
+class AbsTerm a where
+  -- | @subst u . absTerm u == id@
+  absTerm :: Term -> a -> a
+
+instance AbsTerm Term where
+  absTerm u v | Just es <- u `isPrefixOf` v = Var 0 $ absT es
+              | otherwise                   =
+    case v of
+-- Andreas, 2013-10-20: the original impl. works only at base types
+--    v | u == v  -> Var 0 []  -- incomplete see succeed/WithOfFunctionType
+      Var i vs    -> Var (i + 1) $ absT vs
+      Lam h b     -> Lam h $ absT b
+      Def c vs    -> Def c $ absT vs
+      Con c ci vs -> Con c ci $ absT vs
+      Pi a b      -> uncurry Pi $ absT (a, b)
+      Lit l       -> Lit l
+      Level l     -> Level $ absT l
+      Sort s      -> Sort $ absT s
+      MetaV m vs  -> MetaV m $ absT vs
+      DontCare mv -> DontCare $ absT mv
+      Dummy s es   -> Dummy s $ absT es
+      where
+        absT :: AbsTerm b => b -> b
+        absT x = absTerm u x
+
+instance AbsTerm Type where
+  absTerm u (El s v) = El (absTerm u s) (absTerm u v)
+
+instance AbsTerm Sort where
+  absTerm u = \case
+    Univ u n   -> Univ u $ absS n
+    s@Inf{}    -> s
+    SizeUniv   -> SizeUniv
+    LockUniv   -> LockUniv
+    LevelUniv  -> LevelUniv
+    IntervalUniv -> IntervalUniv
+    PiSort a s1 s2 -> PiSort (absS a) (absS s1) (absS s2)
+    FunSort s1 s2 -> FunSort (absS s1) (absS s2)
+    UnivSort s -> UnivSort $ absS s
+    MetaS x es -> MetaS x $ absS es
+    DefS d es  -> DefS d $ absS es
+    s@DummyS{} -> s
+    where
+      absS :: AbsTerm b => b -> b
+      absS x = absTerm u x
+
+instance AbsTerm Level where
+  absTerm u (Max n as) = Max n $ absTerm u as
+
+instance AbsTerm PlusLevel where
+  absTerm u (Plus n l) = Plus n $ absTerm u l
+
+instance AbsTerm a => AbsTerm (Elim' a) where
+  absTerm = fmap . absTerm
+
+instance AbsTerm a => AbsTerm (Arg a) where
+  absTerm = fmap . absTerm
+
+instance AbsTerm a => AbsTerm (Dom a) where
+  absTerm = fmap . absTerm
+
+instance AbsTerm a => AbsTerm [a] where
+  absTerm = fmap . absTerm
+
+instance AbsTerm a => AbsTerm (Maybe a) where
+  absTerm = fmap . absTerm
+
+instance (TermSubst a, AbsTerm a) => AbsTerm (Abs a) where
+  absTerm u (NoAbs x v) = NoAbs x $ absTerm u v
+  absTerm u (Abs   x v) = Abs x $ swap01 $ absTerm (raise 1 u) v
+
+instance (AbsTerm a, AbsTerm b) => AbsTerm (a, b) where
+  absTerm u (x, y) = (absTerm u x, absTerm u y)
+
+-- | This swaps @var 0@ and @var 1@.
+swap01 :: TermSubst a => a -> a
+swap01 = applySubst $ var 1 :# liftS 1 (raiseS 1)
+
+
+-- ** Equality of terms for the sake of with-abstraction.
+
+-- The following could be parameterized by a record of flags
+-- what parts of the syntax tree should be ignored.
+-- For now, there is a fixed strategy.
+
+class EqualSy a where
+  equalSy :: a -> a -> Bool
+
+instance EqualSy a => EqualSy [a] where
+  equalSy us vs = and $ (length us == length vs) : zipWith equalSy us vs
+
+instance EqualSy Term where
+  equalSy = curry $ \case
+    (Var i   vs, Var i'   vs') -> i == i' && equalSy vs vs'
+    (Con c _ es, Con c' _ es') -> c == c' && equalSy es es'
+    (Def   f es, Def   f' es') -> f == f' && equalSy es es'
+    (MetaV x es, MetaV x' es') -> x == x' && equalSy es es'
+    (Lit   l   , Lit   l'    ) -> l == l'
+    (Lam   ai b, Lam   ai' b') -> equalSy ai ai' && equalSy b b'
+    (Level l   , Level l'    ) -> equalSy l l'
+    (Sort  s   , Sort  s'    ) -> equalSy s s'
+    (Pi    a b , Pi    a' b' ) -> equalSy a a' && equalSy b b'
+    (DontCare _, DontCare _  ) -> True
+       -- Irrelevant things are syntactically equal.
+    (Dummy{}   , _           ) -> __IMPOSSIBLE__
+    (_         , Dummy{}     ) -> __IMPOSSIBLE__
+    _ -> False
+
+instance EqualSy Level where
+  equalSy (Max n vs) (Max n' vs') = n == n' && equalSy vs vs'
+
+instance EqualSy PlusLevel where
+  equalSy (Plus n v) (Plus n' v') = n == n' && equalSy v v'
+
+instance EqualSy Sort where
+  equalSy = curry $ \case
+    (Univ u l  , Univ u' l'  ) -> u == u' && equalSy l l'
+    (Inf u m   , Inf u' n    ) -> u == u' && m == n
+    (SizeUniv  , SizeUniv    ) -> True
+    (LevelUniv , LevelUniv   ) -> True
+    (PiSort a b c, PiSort a' b' c') -> equalSy a a' && equalSy b b' && equalSy c c'
+    (FunSort a b, FunSort a' b') -> equalSy a a' && equalSy b b'
+    (UnivSort a, UnivSort a' ) -> equalSy a a'
+    (MetaS x es, MetaS x' es') -> x == x' && equalSy es es'
+    (DefS  d es, DefS  d' es') -> d == d' && equalSy es es'
+    (DummyS{}  , _           ) -> __IMPOSSIBLE__
+    (_         , DummyS{}    ) -> __IMPOSSIBLE__
+    _ -> False
+
+-- | Ignores sorts.
+instance EqualSy Type where
+  equalSy = equalSy `on` unEl
+
+instance EqualSy a => EqualSy (Elim' a) where
+  equalSy = curry $ \case
+    (Proj _ f, Proj _ f') -> f == f'
+    (Apply a, Apply a') -> equalSy a a'
+    (IApply u v r, IApply u' v' r') ->
+           equalSy u u'
+        && equalSy v v'
+        && equalSy r r'
+    _ -> False
+
+-- | Ignores 'absName'.
+instance (Subst a, EqualSy a) => EqualSy (Abs a) where
+  equalSy = curry $ \case
+    (NoAbs _x b, NoAbs _x' b') -> equalSy b b' -- no need to raise if both are NoAbs
+    (a         , a'          ) -> equalSy (absBody a) (absBody a')
+
+-- | Ignore origin and free variables.
+instance EqualSy ArgInfo where
+  equalSy (ArgInfo h m _o _fv a) (ArgInfo h' m' _o' _fv' a') =
+    h == h' && m == m' && a == a'
+
+-- | Ignore the tactic.
+instance EqualSy a => EqualSy (Dom a) where
+  equalSy d@(Dom ai x f _tac a) d'@(Dom ai' x' f' _tac' a') = and
+    [ x == x'
+    , f == f'
+    , equalSy ai ai'
+    , equalSy a a'
+    ]
+
+-- | Ignores irrelevant arguments and modality.
+--   (And, of course, origin and free variables).
+instance EqualSy a => EqualSy (Arg a) where
+  equalSy (Arg (ArgInfo h m _o _fv a) v) (Arg (ArgInfo h' m' _o' _fv' a') v') =
+    h == h' && (isIrrelevant m || isIrrelevant m' || equalSy v v')
+    -- Andreas, 2017-10-04, issue #2775,
+    -- ignore irrelevant arguments during with-abstraction.
+    -- 2019-07-05, issue #3889, don't ignore quantity during caching
+    -- this is why we let equalSy replace (==).
diff --git a/src/full/Agda/TypeChecking/CheckInternal.hs b/src/full/Agda/TypeChecking/CheckInternal.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CheckInternal.hs
@@ -0,0 +1,367 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- Initially authored by Andreas, 2013-10-22.
+
+-- | A bidirectional type checker for internal syntax.
+--
+--   Performs checking on unreduced terms.
+--   With the exception that projection-like function applications
+--   have to be reduced since they break bidirectionality.
+
+module Agda.TypeChecking.CheckInternal
+  ( MonadCheckInternal
+  , checkType, infer, inferSpine
+  , CheckInternal(..)
+  , Action(..), defaultAction, eraseUnusedAction
+  ) where
+
+import Control.Monad
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.ProjectionLike (elimView, ProjEliminator(..))
+import Agda.TypeChecking.Records (shouldBeProjectible)
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor (($>))
+import Agda.Utils.Maybe
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+import Agda.Interaction.Options
+
+-- * Bidirectional rechecker
+
+type MonadCheckInternal m = MonadConversion m
+
+{-# SPECIALIZE checkType :: Type -> TCM () #-}
+-- | Entry point for e.g. checking WithFunctionType.
+checkType :: (MonadCheckInternal m) => Type -> m ()
+checkType t = catchConstraint (CheckType t) $ inferInternal t
+
+-- | 'checkInternal' traverses the whole 'Term', and we can use this
+--   traversal to modify the term.
+data Action m = Action
+  { preAction  :: Type -> Term -> m Term
+    -- ^ Called on each subterm before the checker runs.
+  , postAction :: Type -> Term -> m Term
+    -- ^ Called on each subterm after the type checking.
+  , modalityAction :: Modality -> Modality -> Modality
+    -- ^ Called for each @ArgInfo@.
+    --   The first 'Modality' is from the type,
+    --   the second from the term.
+  , elimViewAction :: Term -> m Term
+    -- ^ Called for bringing projection-like funs in post-fix form
+  }
+
+-- | The default action is to not change the 'Term' at all.
+defaultAction :: PureTCM m => Action m
+--(MonadReduce m, MonadTCEnv m, HasConstInfo m) => Action m
+defaultAction = Action
+  { preAction       = \ _ -> return
+  , postAction      = \ _ -> return
+  , modalityAction  = \ _ -> id
+  , elimViewAction  = elimView EvenLone
+  }
+
+eraseUnusedAction :: Action TCM
+eraseUnusedAction = defaultAction { postAction = eraseUnused }
+  where
+    eraseUnused :: Type -> Term -> TCM Term
+    eraseUnused t = \case
+      Def f es -> do
+        pols <- getPolarity f
+        return $ Def f $ eraseIfNonvariant pols es
+      v        -> return v
+
+    eraseIfNonvariant :: [Polarity] -> Elims -> Elims
+    eraseIfNonvariant []                  es             = es
+    eraseIfNonvariant pols                []             = []
+    eraseIfNonvariant (Nonvariant : pols) (e : es) = (fmap dontCare e) : eraseIfNonvariant pols es
+    eraseIfNonvariant (_          : pols) (e : es) = e : eraseIfNonvariant pols es
+
+class CheckInternal a where
+  checkInternal' :: (MonadCheckInternal m) => Action m -> a -> Comparison -> TypeOf a -> m a
+
+  checkInternal :: (MonadCheckInternal m) => a -> Comparison -> TypeOf a -> m ()
+  checkInternal v cmp t = void $ checkInternal' defaultAction v cmp t
+
+  inferInternal' :: (MonadCheckInternal m, TypeOf a ~ ()) => Action m -> a -> m a
+  inferInternal' act v = checkInternal' act v CmpEq ()
+
+  inferInternal :: (MonadCheckInternal m, TypeOf a ~ ()) => a -> m ()
+  inferInternal v = checkInternal v CmpEq ()
+
+{-# SPECIALIZE checkInternal' :: Action TCM -> Term  -> Comparison -> TypeOf Term -> TCM Term #-}
+{-# SPECIALIZE checkInternal' :: Action TCM -> Type  -> Comparison -> TypeOf Type -> TCM Type #-}
+{-# SPECIALIZE checkInternal' :: Action TCM -> Elims -> Comparison -> TypeOf Type -> TCM Elims #-}
+{-# SPECIALIZE checkInternal  :: Term -> Comparison -> TypeOf Term -> TCM () #-}
+{-# SPECIALIZE checkInternal  :: Type -> Comparison -> TypeOf Type -> TCM () #-}
+
+instance CheckInternal Type where
+  checkInternal' action (El s t) cmp _ = do
+    t' <- checkInternal' action t cmp (sort s)
+    s' <- sortOf t'
+    compareSort cmp s' s
+    return (El s t')
+
+instance CheckInternal Term where
+  checkInternal' :: (MonadCheckInternal m) => Action m -> Term -> Comparison -> Type -> m Term
+  checkInternal' action v cmp t = verboseBracket "tc.check.internal" 20 "" $ do
+    reportSDoc "tc.check.internal" 20 $ sep
+      [ "checking internal "
+      , nest 2 $ sep [ prettyTCM v <+> ":"
+                    , nest 2 $ prettyTCM t ] ]
+    reportSDoc "tc.check.internal" 60 $ sep
+      [ "checking internal with DB indices"
+      , nest 2 $ sep [ pretty v <+> ":"
+                    , nest 2 $ pretty t ] ]
+    ctx <- getContextTelescope
+    unless (null ctx) $ reportSDoc "tc.check.internal" 30 $ sep
+      [ "In context"
+      , nest 2 $ sep [ prettyTCM ctx ] ]
+    -- Bring projection-like funs in post-fix form,
+    -- (even lone ones by default).
+    v <- elimViewAction action =<< preAction action t v
+    postAction action t =<< case v of
+      Var i es   -> do
+        d <- domOfBV i
+        n <- nameOfBV i
+
+        -- Lucas, 23-11-2022:
+        -- For now we only check if pure modalities are respected.
+        -- In the future we SHOULD also be doing the same checks for every modality, as in Rules/Applications.hs
+        -- (commented below)
+        -- but this will break stuff that is allowed right now
+
+        unless (usableCohesion d) $
+          typeError $ VariableIsOfUnusableCohesion n (getCohesion d)
+
+        reportSDoc "tc.check.internal" 30 $ fsep
+          [ "variable" , prettyTCM (var i) , "has type" , prettyTCM (unDom d)
+          , "and modality", pretty (getModality d) ]
+        checkSpine action (unDom d) (Var i) es cmp t
+      Def f es   -> do  -- f is not projection(-like)!
+        -- There is no "implicitely applied module telescope" at this stage, so no
+        -- need to check it for modal errors, everything is covered by the
+        -- variable rule!
+        a <- defType <$> getConstInfo f
+        checkSpine action a (Def f) es cmp t
+      MetaV x es -> do -- we assume meta instantiations to be well-typed
+        a <- metaType x
+        reportSDoc "tc.check.internal" 30 $ "metavariable" <+> prettyTCM x <+> "has type" <+> prettyTCM a
+        checkSpine action a (MetaV x) es cmp t
+      Con c ci vs -> do
+        -- We need to fully apply the constructor to make getConType work!
+        fullyApplyCon c vs t $ \ _d _dt _pars a vs' tel t -> do
+          Con c ci vs2 <- checkSpine action a (Con c ci) vs' cmp t
+          -- Strip away the extra arguments
+          return $ applySubst (strengthenS impossible (size tel))
+            $ Con c ci $ take (length vs) vs2
+      Lit l      -> do
+        lt <- litType l
+        compareType cmp lt t
+        return $ Lit l
+      Lam ai vb  -> do
+        (a, b) <- shouldBePiOrPath t
+        ai <- checkArgInfo action ai $ domInfo a
+        let name = suggests [ Suggestion vb , Suggestion b ]
+        addContext (name, a) $ do
+          Lam ai . Abs (absName vb) <$> checkInternal' action (absBody vb) cmp (absBody b)
+      Pi a b     -> do
+        s <- shouldBeSort t
+        reportSDoc "tc.check.internal" 30 $ "pi type should have sort" <+> prettyTCM s
+        when (s == SizeUniv) $ typeError $ FunctionTypeInSizeUniv v
+        experimental <- optExperimentalIrrelevance <$> pragmaOptions
+        let sa  = getSort a
+            sb  = getSort (unAbs b)
+            mkDom v = El sa v <$ a
+            mkRng v = fmap (v <$) b
+            -- Preserve NoAbs
+            goInside = case b of
+              Abs{}   -> addContext $ (absName b,) $
+                applyWhen experimental (mapRelevance irrToNonStrict) a
+              NoAbs{} -> id
+        a <- mkDom <$> checkInternal' action (unEl $ unDom a) CmpLeq (sort sa)
+        v' <- goInside $ Pi a . mkRng <$> checkInternal' action (unEl $ unAbs b) CmpLeq (sort sb)
+        s' <- sortOf v -- Issue #6205: do not use v' since it might not be valid syntax
+        compareSort cmp s' s
+        return v'
+      Sort s     -> do
+        reportSDoc "tc.check.internal" 30 $ "checking sort" <+> prettyTCM s
+        s <- inferInternal' action s
+        s' <- inferUnivSort s
+        s'' <- shouldBeSort t
+        compareSort cmp s' s''
+        return $ Sort s
+      Level l    -> do
+        l <- inferInternal' action l
+        lt <- levelType'
+        compareType cmp lt t
+        return $ Level l
+      DontCare v -> DontCare <$> checkInternal' action v cmp t
+      -- Jesper, 2023-02-23: these can appear because of eta-expansion of
+      -- records with irrelevant fields
+      Dummy s _ -> return v -- __IMPOSSIBLE_VERBOSE__ s
+
+-- | @checkArgInfo actual expected@.
+--
+--   The @expected@ 'ArgInfo' comes from the type.
+--   The @actual@ 'ArgInfo' comes from the term and can be updated
+--   by an action.
+checkArgInfo :: (MonadCheckInternal m) => Action m -> ArgInfo -> ArgInfo -> m ArgInfo
+checkArgInfo action ai ai' = do
+  checkHiding    (getHiding ai)     (getHiding ai')
+  mod <- checkModality action (getModality ai)  (getModality ai')
+  return $ setModality mod ai
+
+checkHiding :: (MonadCheckInternal m) => Hiding -> Hiding -> m ()
+checkHiding h h' = unless (sameHiding h h') $ typeError $ HidingMismatch h h'
+
+-- | @checkRelevance action term type@.
+--
+--   The @term@ 'Relevance' can be updated by the @action@.
+checkModality :: (MonadCheckInternal m) => Action m -> Modality -> Modality -> m Modality
+checkModality action mod mod' = do
+  let (r,r') = (getRelevance mod, getRelevance mod')
+      (q,q') = (getQuantity  mod, getQuantity  mod')
+  unless (sameModality mod mod') $ typeError $ if
+    | not (sameRelevance r r') -> RelevanceMismatch r r'
+    | not (sameQuantity q q')  -> QuantityMismatch  q q'
+    | otherwise -> __IMPOSSIBLE__ -- add more cases when adding new modalities
+  return $ modalityAction action mod' mod  -- Argument order for actions: @type@ @term@
+
+{-# SPECIALIZE infer :: Term -> TCM Type #-}
+-- | Infer type of a neutral term.
+infer :: (MonadCheckInternal m) => Term -> m Type
+infer u = do
+  reportSDoc "tc.check.internal" 20 $ "CheckInternal.infer" <+> prettyTCM u
+  case u of
+    Var i es -> do
+      a <- typeOfBV i
+      fst <$> inferSpine defaultAction a (Var i) es
+    Def f es -> do
+      whenJustM (isRelevantProjection f) $ \_ -> nonInferable
+      a <- defType <$> getConstInfo f
+      fst <$> inferSpine defaultAction a (Def f) es
+    MetaV x es -> do -- we assume meta instantiations to be well-typed
+      a <- metaType x
+      fst <$> inferSpine defaultAction a (MetaV x) es
+    _ -> nonInferable
+  where
+    nonInferable :: MonadDebug m => m a
+    nonInferable = __IMPOSSIBLE_VERBOSE__ $ unlines
+      [ "CheckInternal.infer: non-inferable term:"
+      , "  " ++ prettyShow u
+      ]
+
+instance CheckInternal Elims where
+  checkInternal' action es cmp (t , hd) = snd <$> inferSpine action t hd es
+
+{-# SPECIALIZE inferSpine :: Action TCM -> Type -> (Elims -> Term) -> Elims -> TCM (Type, Elims) #-}
+-- | @inferSpine action t hd es@ checks that spine @es@ eliminates
+--   value @hd []@ of type @t@ and returns the remaining type
+--   (target of elimination) and the transformed eliminations.
+inferSpine :: (MonadCheckInternal m) => Action m -> Type -> (Elims -> Term) -> Elims -> m (Type, Elims)
+inferSpine action t hd es = loop t hd id es
+  where
+  loop t hd acc = \case
+    [] -> return (t , acc [])
+    (e : es) -> do
+      let self = hd []
+      reportSDoc "tc.check.internal" 30 $ sep
+        [ "inferring spine: "
+        , "type t = " <+> prettyTCM t
+        , "self  = " <+> prettyTCM self
+        , "eliminated by e = " <+> prettyTCM e
+        ]
+      case e of
+        IApply x y r -> do
+          (a, b) <- shouldBePath t
+          r' <- checkInternal' action r CmpLeq (unDom a)
+          izero <- primIZero
+          ione  <- primIOne
+          x' <- checkInternal' action x CmpLeq (b `absApp` izero)
+          y' <- checkInternal' action y CmpLeq (b `absApp` ione)
+          let e' = IApply x' y' r'
+          loop (b `absApp` r) (hd . (e:)) (acc . (e':)) es
+        Apply (Arg ai v) -> do
+          (a, b) <- shouldBePi t
+          ai <- checkArgInfo action ai $ domInfo a
+          v' <- applyModalityToContext (getModality a) $ checkInternal' action v CmpLeq $ unDom a
+          let e' = Apply (Arg ai v')
+          loop (b `absApp` v) (hd . (e:)) (acc . (e':)) es
+        -- case: projection or projection-like
+        Proj o f -> do
+          t' <- shouldBeProjectible self t o f
+          loop t' (hd . (e:)) (acc . (e:)) es
+
+{-# SPECIALIZE checkSpine :: Action TCM -> Type -> (Elims -> Term) -> Elims -> Comparison -> Type -> TCM Term #-}
+checkSpine
+  :: (MonadCheckInternal m)
+  => Action m
+  -> Type       -- ^ Type of the head @self@.
+  -> (Elims -> Term) -- ^ The head @hd@.
+  -> Elims      -- ^ The eliminations @es@.
+  -> Comparison -- ^ Check (@CmpLeq@) or infer (@CmpEq@) the final type.
+  -> Type       -- ^ Expected type of the application @self es@.
+  -> m Term     -- ^ The application after modification by the @Action@.
+checkSpine action a hd es cmp t = do
+  reportSDoc "tc.check.internal" 20 $ sep
+    [ "checking spine "
+    , nest 2 $ sep [ parens (sep [ prettyTCM (hd []) <+> ":"
+                                 , nest 2 $ prettyTCM a ])
+                   , nest 4 $ prettyTCM es <+> ":"
+                   , nest 2 $ prettyTCM t ] ]
+  (t' , es') <- inferSpine action a hd es
+  coerceSize (compareType cmp) (hd es) t' t
+  return $ hd es'
+
+instance CheckInternal Sort where
+  checkInternal' action s cmp _ = case s of
+    Univ u l -> Univ u <$> inferInternal' action l
+    Inf u n  -> return $ Inf u n
+    SizeUniv -> return SizeUniv
+    LockUniv -> return LockUniv
+    LevelUniv -> return LevelUniv
+    IntervalUniv -> return IntervalUniv
+    PiSort dom s1 s2 -> do
+      let a = unDom dom
+      s1' <- inferInternal' action s1
+      a' <- checkInternal' action a CmpLeq $ sort s1'
+      let dom' = dom $> a'
+      s2' <- mapAbstraction (El s1' <$> dom') (inferInternal' action) s2
+      return $ PiSort dom' s1' s2'
+    FunSort s1 s2 -> do
+      s1' <- inferInternal' action s1
+      s2' <- inferInternal' action s2
+      return $ FunSort s1' s2'
+    UnivSort s -> UnivSort <$> inferInternal' action s
+    MetaS x es -> do -- we assume sort meta instantiations to be well-formed
+      a <- metaType x
+      MetaS x <$> checkInternal' action es cmp (a , Sort . MetaS x)
+    DefS d es -> do
+      a <- defType <$> getConstInfo d
+      DefS d <$> checkInternal' action es cmp (a , Sort . DefS d)
+    DummyS s -> __IMPOSSIBLE_VERBOSE__ s
+
+instance CheckInternal Level where
+  checkInternal' action (Max n ls) _ _ = Max n <$> mapM (inferInternal' action) ls
+
+instance CheckInternal PlusLevel where
+  checkInternal' action (Plus k l) _ _ = Plus k <$> checkLevelAtom l
+    where
+    checkLevelAtom l = do
+      lvl <- levelType'
+      checkInternal' action l CmpLeq lvl
diff --git a/src/full/Agda/TypeChecking/CheckInternal.hs-boot b/src/full/Agda/TypeChecking/CheckInternal.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CheckInternal.hs-boot
@@ -0,0 +1,52 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE KindSignatures #-}
+
+module Agda.TypeChecking.CheckInternal where
+
+import Control.Monad.Except
+import qualified Control.Monad.Fail as Fail
+
+import qualified Data.Kind as Hs
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Warnings
+
+type MonadCheckInternal m =
+  ( PureTCM m
+  , MonadConstraint m
+  , MonadMetaSolver m
+  , MonadError TCErr m
+  , MonadWarning m
+  , MonadStatistics m
+  , MonadFresh ProblemId m
+  , MonadFresh Int m
+  , Fail.MonadFail m
+  )
+
+data Action (m :: Hs.Type -> Hs.Type)
+
+defaultAction :: PureTCM m => Action m
+eraseUnusedAction :: Action TCM
+
+class CheckInternal a where
+  checkInternal' :: (MonadCheckInternal m) => Action m -> a -> Comparison -> TypeOf a -> m a
+
+  checkInternal :: (MonadCheckInternal m) => a -> Comparison -> TypeOf a -> m ()
+  checkInternal v cmp t = void $ checkInternal' defaultAction v cmp t
+
+  inferInternal' :: (MonadCheckInternal m, TypeOf a ~ ()) => Action m -> a -> m a
+  inferInternal' act v = checkInternal' act v CmpEq ()
+
+  inferInternal :: (MonadCheckInternal m, TypeOf a ~ ()) => a -> m ()
+  inferInternal v = checkInternal v CmpEq ()
+
+instance CheckInternal Term
+instance CheckInternal Type
+instance CheckInternal Sort
+instance CheckInternal Level
+instance CheckInternal Elims
+
+checkType :: (MonadCheckInternal m) => Type -> m ()
+infer :: (MonadCheckInternal m) => Term -> m Type
diff --git a/src/full/Agda/TypeChecking/CompiledClause.hs b/src/full/Agda/TypeChecking/CompiledClause.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CompiledClause.hs
@@ -0,0 +1,223 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Case trees.
+--
+--   After coverage checking, pattern matching is translated
+--   to case trees, i.e., a tree of successive case splits
+--   on one variable at a time.
+
+module Agda.TypeChecking.CompiledClause where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import qualified Data.Map as Map
+import Data.Map (Map)
+import Data.Semigroup hiding (Arg(..))
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+data WithArity c = WithArity { arity :: Int, content :: c }
+  deriving (Functor, Foldable, Traversable, Show, Generic)
+
+-- | Branches in a case tree.
+
+data Case c = Branches
+  { projPatterns   :: Bool
+    -- ^ We are constructing a record here (copatterns).
+    --   'conBranches' lists projections.
+  , conBranches    :: Map QName (WithArity c)
+    -- ^ Map from constructor (or projection) names to their arity
+    --   and the case subtree.  (Projections have arity 0.)
+  , etaBranch      :: Maybe (ConHead, WithArity c)
+    -- ^ Eta-expand with the given (eta record) constructor. If this is
+    --   present, there should not be any conBranches or litBranches.
+  , litBranches    :: Map Literal c
+    -- ^ Map from literal to case subtree.
+  , catchAllBranch :: Maybe c
+    -- ^ (Possibly additional) catch-all clause.
+  , fallThrough :: Maybe Bool
+    -- ^ (if True) In case of non-canonical argument use catchAllBranch.
+  , lazyMatch :: Bool
+    -- ^ Lazy pattern match. Requires single (non-copattern) branch with no lit
+    --   branches and no catch-all.
+  }
+  deriving (Functor, Foldable, Traversable, Show, Generic)
+
+-- | Case tree with bodies.
+
+data CompiledClauses' a
+  = Case (Arg Int) (Case (CompiledClauses' a))
+    -- ^ @Case n bs@ stands for a match on the @n@-th argument
+    -- (counting from zero) with @bs@ as the case branches.
+    -- If the @n@-th argument is a projection, we have only 'conBranches'
+    -- with arity 0.
+  | Done [Arg ArgName] a
+    -- ^ @Done xs b@ stands for the body @b@ where the @xs@ contains hiding
+    --   and name suggestions for the free variables. This is needed to build
+    --   lambdas on the right hand side for partial applications which can
+    --   still reduce.
+  | Fail [Arg ArgName]
+    -- ^ Absurd case. Add the free variables here as well so we can build correct
+    --   number of lambdas for strict backends. (#4280)
+  deriving (Functor, Traversable, Foldable, Show, Generic)
+
+type CompiledClauses = CompiledClauses' Term
+
+litCase :: Literal -> c -> Case c
+litCase l x = Branches False Map.empty Nothing (Map.singleton l x) Nothing (Just False) False
+
+conCase :: QName -> Bool -> WithArity c -> Case c
+conCase c b x = Branches False (Map.singleton c x) Nothing Map.empty Nothing (Just b) False
+
+etaCase :: ConHead -> WithArity c -> Case c
+etaCase c x = Branches False Map.empty (Just (c, x)) Map.empty Nothing (Just False) True
+
+projCase :: QName -> c -> Case c
+projCase c x = Branches True (Map.singleton c $ WithArity 0 x) Nothing Map.empty Nothing (Just False) False
+
+catchAll :: c -> Case c
+catchAll x = Branches False Map.empty Nothing Map.empty (Just x) (Just True) False
+
+-- | Check that the requirements on lazy matching (single inductive case) are
+--   met, and set lazy to False otherwise.
+checkLazyMatch :: Case c -> Case c
+checkLazyMatch b = b { lazyMatch = lazyMatch b && requirements }
+  where
+    requirements = and
+      [ null (catchAllBranch b)
+      , Map.size (conBranches b) <= 1
+      , null (litBranches b)
+      , not $ projPatterns b ]
+
+-- | Check whether a case tree has a catch-all clause.
+hasCatchAll :: CompiledClauses -> Bool
+hasCatchAll = getAny . loop
+  where
+  loop cc = case cc of
+    Fail{}    -> mempty
+    Done{}    -> mempty
+    Case _ br -> maybe (foldMap loop br) (const $ Any True) $ catchAllBranch br
+
+-- | Check whether a case tree has any projection patterns
+hasProjectionPatterns :: CompiledClauses -> Bool
+hasProjectionPatterns = getAny . loop
+  where
+  loop cc = case cc of
+    Fail{}    -> mempty
+    Done{}    -> mempty
+    Case _ br -> Any (projPatterns br) <> foldMap loop br
+
+instance Semigroup c => Semigroup (WithArity c) where
+  WithArity n1 c1 <> WithArity n2 c2
+    | n1 == n2  = WithArity n1 (c1 <> c2)
+    | otherwise = __IMPOSSIBLE__   -- arity must match!
+
+instance (Semigroup c, Monoid c) => Monoid (WithArity c) where
+  mempty  = WithArity __IMPOSSIBLE__ mempty
+  mappend = (<>)
+
+instance Semigroup m => Semigroup (Case m) where
+  Branches cop cs eta ls m b lazy <> Branches cop' cs' eta' ls' m' b' lazy' = checkLazyMatch $
+    Branches (cop || cop') -- for @projCase <> mempty@
+             (Map.unionWith (<>) cs cs')
+             (unionEta eta eta')
+             (Map.unionWith (<>) ls ls')
+             (m <> m')
+             (combine b b')
+             (lazy && lazy')
+   where
+     combine Nothing  b'        = b
+     combine b        Nothing   = b
+     combine (Just b) (Just b') = Just $ b && b'
+
+     unionEta Nothing b = b
+     unionEta b Nothing = b
+     unionEta Just{} Just{} = __IMPOSSIBLE__
+
+instance (Semigroup m, Monoid m) => Monoid (Case m) where
+  mempty  = empty
+  mappend = (<>)
+
+instance Null (Case m) where
+  empty = Branches False Map.empty Nothing Map.empty Nothing Nothing True
+  null (Branches _cop cs eta ls mcatch _b _lazy) = null cs && null eta && null ls && null mcatch
+
+-- * Pretty instances.
+
+instance Pretty a => Pretty (WithArity a) where
+  pretty = pretty . content
+
+instance Pretty a => Pretty (Case a) where
+  prettyPrec p (Branches _cop cs eta ls m b lazy) =
+    mparens (p > 0) $ prLazy lazy <+> vcat (prettyMap_ cs ++ prEta eta ++ prettyMap_ ls ++ prC m)
+    where
+      prLazy True  = "~"
+      prLazy False = empty
+      prC Nothing = []
+      prC (Just x) = ["_ ->" <+> pretty x]
+      prEta Nothing = []
+      prEta (Just (c, cc)) = [("eta" <+> pretty c <+> "->") <?> pretty cc]
+
+prettyMap_ :: (Pretty k, Pretty v) => Map k v -> [Doc]
+prettyMap_ = map prettyAssign . Map.toList
+
+instance Pretty CompiledClauses where
+  pretty (Done hs t) = ("done" <> pretty hs) <?> pretty t
+  pretty Fail{}      = "fail"
+  pretty (Case n bs) | projPatterns bs =
+    sep [ "record"
+        , nest 2 $ pretty bs
+        ]
+  pretty (Case n bs) =
+    text ("case " ++ prettyShow n ++ " of") <?> pretty bs
+
+-- * KillRange instances.
+
+instance KillRange c => KillRange (WithArity c) where
+  killRange = fmap killRange
+
+instance KillRange c => KillRange (Case c) where
+  killRange (Branches cop con eta lit all b lazy) = Branches cop
+    (killRangeMap con)
+    (killRange eta)
+    (killRangeMap lit)
+    (killRange all)
+    b lazy
+
+instance KillRange CompiledClauses where
+  killRange (Case i br) = killRangeN Case i br
+  killRange (Done xs v) = killRangeN Done xs v
+  killRange (Fail xs)   = killRangeN Fail xs
+
+-- * TermLike instances
+
+instance TermLike a => TermLike (WithArity a) where
+  traverseTermM = traverse . traverseTermM
+  foldTerm      = foldMap . foldTerm
+
+instance TermLike a => TermLike (Case a) where
+  traverseTermM = traverse . traverseTermM
+  foldTerm      = foldMap . foldTerm
+
+instance TermLike a => TermLike (CompiledClauses' a) where
+  traverseTermM = traverse . traverseTermM
+  foldTerm      = foldMap . foldTerm
+
+-- NFData instances
+
+instance NFData c => NFData (WithArity c)
+instance NFData a => NFData (Case a)
+instance NFData a => NFData (CompiledClauses' a)
diff --git a/src/full/Agda/TypeChecking/CompiledClause/Compile.hs b/src/full/Agda/TypeChecking/CompiledClause/Compile.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CompiledClause/Compile.hs
@@ -0,0 +1,428 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.CompiledClause.Compile where
+
+import Prelude hiding (null)
+
+import Control.Applicative
+import Control.Monad
+import Control.Monad.Trans.Identity
+
+import Data.Maybe
+import Data.List (partition)
+import qualified Data.Map as Map
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.RecordPatterns
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Free.Precompute
+import Agda.TypeChecking.Reduce
+
+import Agda.Utils.Functor
+import Agda.Utils.Maybe
+import Agda.Utils.List
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+data RunRecordPatternTranslation = RunRecordPatternTranslation | DontRunRecordPatternTranslation
+  deriving (Eq)
+
+compileClauses' :: RunRecordPatternTranslation -> [Clause] -> Maybe SplitTree -> TCM CompiledClauses
+compileClauses' recpat cs mSplitTree = do
+
+  -- Throw away the unreachable clauses (#2723).
+  let notUnreachable = (Just True /=) . clauseUnreachable
+  cs <- map unBruijn <$> normaliseProjP (filter notUnreachable cs)
+
+  let translate | recpat == RunRecordPatternTranslation = runIdentityT . translateCompiledClauses
+                | otherwise                             = return
+
+  translate $ caseMaybe mSplitTree (compile cs) $ \splitTree ->
+    compileWithSplitTree splitTree cs
+
+-- | Process function clauses into case tree.
+--   This involves:
+--   1. Coverage checking, generating a split tree.
+--   2. Translation of lhs record patterns into rhs uses of projection.
+--      Update the split tree.
+--   3. Generating a case tree from the split tree.
+--   Phases 1. and 2. are skipped if @Nothing@.
+compileClauses ::
+  Maybe (QName, Type) -- ^ Translate record patterns and coverage check with given type?
+  -> [Clause]
+  -> TCM (Maybe SplitTree, Bool, CompiledClauses)
+     -- ^ The 'Bool' indicates whether we turned a record expression into a copattern match.
+compileClauses mt cs = do
+  -- Construct clauses with pattern variables bound in left-to-right order.
+  -- Discard de Bruijn indices in patterns.
+  case mt of
+    Nothing -> (Nothing,False,) . compile . map unBruijn <$> normaliseProjP cs
+    Just (q, t)  -> do
+      splitTree <- coverageCheck q t cs
+
+      reportSDoc "tc.cc.tree" 20 $ vcat
+        [ "split tree of " <+> prettyTCM q <+> " from coverage check "
+        , return $ P.pretty splitTree
+        ]
+
+      -- The coverage checker might have added some clauses (#2288)!
+      -- Throw away the unreachable clauses (#2723).
+      let notUnreachable = (Just True /=) . clauseUnreachable
+      cs <- normaliseProjP =<< instantiateFull =<< filter notUnreachable . defClauses <$> getConstInfo q
+
+      let cls = map unBruijn cs
+
+      reportSDoc "tc.cc" 30 $ sep $ do
+        ("clauses patterns of " <+> prettyTCM q <+> " before compilation") : do
+          map (prettyTCM . map unArg . clPats) cls
+      reportSDoc "tc.cc" 50 $
+        "clauses of " <+> prettyTCM q <+> " before compilation" <?> pretty cs
+      let cc = compileWithSplitTree splitTree cls
+      reportSDoc "tc.cc" 20 $ sep
+        [ "compiled clauses of " <+> prettyTCM q <+> " (still containing record splits)"
+        , nest 2 $ return $ P.pretty cc
+        ]
+      (cc, becameCopatternLHS) <- runChangeT $ translateCompiledClauses cc
+      reportSDoc "tc.cc" 12 $ sep
+        [ "compiled clauses of " <+> prettyTCM q
+        , nest 2 $ return $ P.pretty cc
+        ]
+      return (Just splitTree, becameCopatternLHS, fmap precomputeFreeVars_ cc)
+
+-- | Stripped-down version of 'Agda.Syntax.Internal.Clause'
+--   used in clause compiler.
+data Cl = Cl
+  { clPats :: [Arg Pattern]
+      -- ^ Pattern variables are considered in left-to-right order.
+  , clBody :: Maybe Term
+  } deriving (Show)
+
+instance P.Pretty Cl where
+  pretty (Cl ps b) = P.prettyList ps P.<+> "->" P.<+> maybe "_|_" P.pretty b
+
+type Cls = [Cl]
+
+-- | Strip down a clause. Don't forget to apply the substitution to the dot
+--   patterns!
+unBruijn :: Clause -> Cl
+unBruijn c = Cl (applySubst sub $ (map . fmap) (fmap dbPatVarName . namedThing) $ namedClausePats c)
+                (applySubst sub $ clauseBody c)
+  where
+    sub = renamingR $ fromMaybe __IMPOSSIBLE__ (clausePerm c)
+
+compileWithSplitTree :: SplitTree -> Cls -> CompiledClauses
+compileWithSplitTree t cs = case t of
+  SplitAt i lz ts -> Case i $ compiles lz ts $ splitOn (natSize ts == 1) (unArg i) cs
+        -- if there is just one case, we force expansion of catch-alls
+        -- this is needed to generate a sound tree on which we can
+        -- collapse record pattern splits
+  SplittingDone n -> compile cs
+    -- after end of split tree, continue with left-to-right strategy
+  where
+    compiles :: LazySplit -> SplitTrees -> Case Cls -> Case CompiledClauses
+    compiles lz ts br@Branches{ projPatterns = cop
+                              , conBranches = cons
+                              , etaBranch   = Nothing
+                              , litBranches = lits
+                              , fallThrough = fT
+                              , catchAllBranch = catchAll
+                              , lazyMatch = lazy }
+      = br{ conBranches    = updCons cons
+          , etaBranch      = Nothing
+          , litBranches    = updLits lits
+          , fallThrough    = fT
+          , catchAllBranch = updCatchall catchAll
+          , lazyMatch      = lazy || lz == LazySplit
+          }
+      where
+        updCons = Map.mapWithKey $ \ c cl ->
+         caseMaybe (lookup (SplitCon c) ts) compile compileWithSplitTree <$> cl
+         -- When the split tree is finished, we continue with @compile@.
+        updLits = Map.mapWithKey $ \ l cl ->
+          caseMaybe (lookup (SplitLit l) ts) compile compileWithSplitTree cl
+        updCatchall = fmap $ caseMaybe (lookup SplitCatchall ts) compile compileWithSplitTree
+    compiles _ _ Branches{etaBranch = Just{}} = __IMPOSSIBLE__  -- we haven't inserted eta matches yet
+
+compile :: Cls -> CompiledClauses
+compile [] = Fail []
+compile cs = case nextSplit cs of
+  Just (isRecP, n) -> Case n $ compile <$> splitOn isRecP (unArg n) cs
+  Nothing -> case clBody c of
+    -- It's possible to get more than one clause here due to
+    -- catch-all expansion.
+    Just t  -> Done (map (fmap name) $ clPats c) t
+    Nothing -> Fail (map (fmap name) $ clPats c)
+  where
+    -- If there are more than one clauses, take the first one.
+    c = headWithDefault __IMPOSSIBLE__ cs
+    name (VarP _ x) = x
+    name (DotP _ _) = underscore
+    name ConP{}  = __IMPOSSIBLE__
+    name DefP{}  = __IMPOSSIBLE__
+    name LitP{}  = __IMPOSSIBLE__
+    name ProjP{} = __IMPOSSIBLE__
+    name (IApplyP _ _ _ x) = x
+
+-- | Get the index of the next argument we need to split on.
+--   This the number of the first pattern that does a (non-lazy) match in the first clause.
+--   Or the first lazy match where all clauses agree on the constructor, if there are no
+--   non-lazy matches.
+nextSplit :: Cls -> Maybe (Bool, Arg Int)
+nextSplit []             = __IMPOSSIBLE__
+nextSplit (Cl ps _ : cs) = findSplit nonLazy ps <|> findSplit allAgree ps
+  where
+    nonLazy _ (ConP _ cpi _) = not $ conPLazy cpi
+    nonLazy _ _              = True
+
+    findSplit okPat ps = listToMaybe (catMaybes $
+      zipWith (\ (Arg ai p) n -> (, Arg ai n) <$> properSplit p <* guard (okPat n p)) ps [0..])
+
+    allAgree i (ConP c _ _) = all ((== Just (conName c)) . getCon . map unArg . drop i . clPats) cs
+    allAgree _ _            = False
+
+    getCon (ConP c _ _ : _) = Just $ conName c
+    getCon _                = Nothing
+
+-- | Is is not a variable pattern?
+--   And if yes, is it a record pattern and/or a fallThrough one?
+properSplit :: Pattern' a -> Maybe Bool
+properSplit (ConP _ cpi _) = Just ((conPRecord cpi && patOrigin (conPInfo cpi) == PatORec) || conPFallThrough cpi)
+properSplit DefP{}    = Just False
+properSplit LitP{}    = Just False
+properSplit ProjP{}   = Just False
+properSplit IApplyP{} = Nothing
+properSplit VarP{}    = Nothing
+properSplit DotP{}    = Nothing
+
+-- | Is this a variable pattern?
+--
+--   Maintain invariant: @isVar = isNothing . properSplit@!
+isVar :: Pattern' a -> Bool
+isVar IApplyP{} = True
+isVar VarP{}    = True
+isVar DotP{}    = True
+isVar ConP{}    = False
+isVar DefP{}    = False
+isVar LitP{}    = False
+isVar ProjP{}   = False
+
+-- | @splitOn single n cs@ will force expansion of catch-alls
+--   if @single@.
+splitOn :: Bool -> Int -> Cls -> Case Cls
+splitOn single n cs = mconcat $ map (fmap (:[]) . splitC n) $
+  -- (\ cs -> trace ("splitting on " ++ show n ++ " after expandCatchAlls " ++ show single ++ ": " ++ prettyShow (P.prettyList cs)) cs) $
+    expandCatchAlls single n cs
+
+splitC :: Int -> Cl -> Case Cl
+splitC n (Cl ps b) = caseMaybe mp fallback $ \case
+  ProjP _ d   -> projCase d $ Cl (ps0 ++ ps1) b
+  IApplyP{}   -> fallback
+  ConP c i qs -> (conCase (conName c) (conPFallThrough i) $ WithArity (length qs) $
+                   Cl (ps0 ++ map (fmap namedThing) qs ++ ps1) b) { lazyMatch = conPLazy i }
+  DefP o q qs -> (conCase q False $ WithArity (length qs) $
+                   Cl (ps0 ++ map (fmap namedThing) qs ++ ps1) b) { lazyMatch = False }
+  LitP _ l    -> litCase l $ Cl (ps0 ++ ps1) b
+  VarP{}      -> fallback
+  DotP{}      -> fallback
+  where
+    (ps0, rest) = splitAt n ps
+    mp          = unArg <$> listToMaybe rest
+    ps1         = drop 1 rest
+    fallback    = catchAll $ Cl ps b
+
+-- | Expand catch-alls that appear before actual matches.
+--
+-- Example:
+--
+-- @
+--    true  y
+--    x     false
+--    false y
+-- @
+--
+-- will expand the catch-all @x@ to @false@.
+--
+-- Catch-alls need also to be expanded if
+-- they come before/after a record pattern, otherwise we get into
+-- trouble when we want to eliminate splits on records later.
+--
+-- Another example (see Issue 1650):
+-- @
+--   f (x, (y, z)) true  = a
+--   f _           false = b
+-- @
+-- Split tree:
+-- @
+--   0 (first argument of f)
+--    \- 1 (second component of the pair)
+--        \- 3 (last argument of f)
+--            \-- true  -> a
+--             \- false -> b
+-- @
+-- We would like to get the following case tree:
+-- @
+--   case 0 of
+--   _,_ -> case 1 of
+--          _,_ -> case 3 of true  -> a; false -> b
+--          _   -> case 3 of true  -> a; false -> b
+--   _          -> case 3 of true  -> a; false -> b
+-- @
+--
+-- Example from issue #2168:
+-- @
+--   f x     false = a
+--   f false       = \ _ -> b
+--   f x     true  = c
+-- @
+-- case tree:
+-- @
+--   f x y = case y of
+--     true  -> case x of
+--       true  -> c
+--       false -> b
+--     false -> a
+-- @
+--
+-- Example from issue #3628:
+-- @
+--   f i j k (i = i0)(k = i1) = base
+--   f i j k (j = i1)         = base
+-- @
+-- case tree:
+-- @
+--   f i j k o = case i of
+--     i0 -> case k of
+--             i1 -> base
+--             _  -> case j of
+--                     i1 -> base
+--     _  -> case j of
+--             i1 -> base
+-- @
+expandCatchAlls :: Bool -> Int -> Cls -> Cls
+expandCatchAlls single n cs =
+  case cs of
+    _ -- Andreas, 2013-03-22
+      -- if there is a single case (such as for record splits)
+      -- we force expansion
+      | single -> doExpand =<< cs
+
+      -- If all clauses have a variable at the nth argument, expansion
+      -- would have no effect
+      | all (isCatchAllNth . clPats) cs -> cs
+
+    c@(Cl ps b):cs
+      -- If the head clause does not have a catch-all pattern for the
+      -- nth argument, we can keep it at the head and do no expansion
+      | not (isCatchAllNth ps) -> c : expandCatchAlls False n cs
+
+      -- If there's a DefP clause for this argument later on, then it
+      -- should take priority over catch-all clauses, so we rotate them
+      -- out of the way.
+      -- DefP clauses are always inserted by the system and should
+      -- "defeat" user-written inexact patterns.
+      | (defps@(_:_), rest) <- partition isDefPNth (c:cs)
+      -> defps ++ expandCatchAlls False n rest
+
+      -- If the head clause *does* have an irrefutable pattern for the
+      -- nth argument, and there's nothing more important after, then we
+      -- duplicate the subsequent overlapping clauses with c's RHS
+      -- instead.
+      | otherwise -> map (expand c) expansions ++ c : expandCatchAlls False n cs
+    _ -> __IMPOSSIBLE__
+  where
+    -- In case there is only one branch in the split tree, we expand all
+    -- catch-alls for this position
+    -- The @expansions@ are collected from all the clauses @cs@ then.
+    -- Note: @expansions@ could be empty, so we keep the orignal clause.
+    doExpand c@(Cl ps _)
+      | exCatchAllNth ps = map (expand c) expansions ++ [c]
+      | otherwise = [c]
+
+    -- True if nth pattern is variable or there are less than n patterns.
+    isCatchAllNth ps = all (isVar . unArg) $ take 1 $ drop n ps
+
+    -- True if nth pattern exists and is variable.
+    exCatchAllNth ps = any (isVar . unArg) $ take 1 $ drop n ps
+
+    classify (LitP _ l)   = Left l
+    classify (ConP c _ _) = Right (Left c)
+    classify (DefP _ q _) = Right (Right q)
+    classify _            = __IMPOSSIBLE__
+
+    isDefPNth cl = case unArg <$> listToMaybe (drop n (clPats cl)) of
+      Just DefP{} -> True
+      _ -> False
+
+    -- All non-catch-all patterns following this one (at position n).
+    -- These are the cases the wildcard needs to be expanded into.
+    expansions = nubOn (classify . unArg . snd)
+               . mapMaybe (notVarNth . clPats)
+               $ cs
+    notVarNth
+      :: [Arg Pattern]
+      -> Maybe ([Arg Pattern]  -- First @n@ patterns.
+               , Arg Pattern)  -- @n+1@st pattern, not a variable
+    notVarNth ps = do
+      let (ps1, ps2) = splitAt n ps
+      p <- listToMaybe ps2
+      guard $ not $ isVar $ unArg p
+      return (ps1, p)
+
+    expand cl (qs, q) =
+      case unArg q of
+        ConP c mt qs' -> Cl (ps0 ++ [q $> ConP c mt conPArgs] ++ ps1)
+                            (substBody n' m (Con c ci (map Apply conArgs)) b)
+          where
+            ci       = fromConPatternInfo mt
+            m        = length qs'
+            -- replace all direct subpatterns of q by _
+            -- TODO Andrea: might need these to sometimes be IApply?
+            conPArgs = map (fmap ($> varP "_")) qs'
+            conArgs  = zipWith (\ q' i -> q' $> var i) qs' $ downFrom m
+        LitP i l -> Cl (ps0 ++ [q $> LitP i l] ++ ps1) (substBody n' 0 (Lit l) b)
+        DefP o d qs' -> Cl (ps0 ++ [q $> DefP o d conPArgs] ++ ps1)
+                            (substBody n' m (Def d (map Apply conArgs)) b)
+          where
+            m        = length qs'
+            -- replace all direct subpatterns of q by _
+            conPArgs = map (fmap ($> varP "_")) qs'
+            conArgs  = zipWith (\ q' i -> q' $> var i) qs' $ downFrom m
+        _ -> __IMPOSSIBLE__
+      where
+        -- Andreas, 2016-09-19 issue #2168
+        -- Due to varying function arity, some clauses might be eta-contracted.
+        -- Thus, we eta-expand them.
+        Cl ps b = ensureNPatterns (n + 1) (map getArgInfo $ qs ++ [q]) cl
+        -- The following pattern match cannot fail (by construction of @ps@).
+        (ps0, _:ps1) = splitAt n ps
+
+        n' = countPatternVars ps1
+
+-- | Make sure (by eta-expansion) that clause has arity at least @n@
+--   where @n@ is also the length of the provided list.
+ensureNPatterns :: Int -> [ArgInfo] -> Cl -> Cl
+ensureNPatterns n ais0 cl@(Cl ps b)
+  | m <= 0    = cl
+  | otherwise = Cl (ps ++ ps') (raise m b `apply` args)
+  where
+  k    = length ps
+  ais  = drop k ais0
+  -- m = Number of arguments to add
+  m    = n - k
+  ps'  = for ais $ \ ai -> Arg ai $ varP "_"
+  args = zipWith (\ i ai -> Arg ai $ var i) (downFrom m) ais
+
+substBody :: Subst a => Int -> Int -> SubstArg a -> a -> a
+substBody n m v = applySubst $ liftS n $ v :# raiseS m
+
+instance PrecomputeFreeVars a => PrecomputeFreeVars (CompiledClauses' a) where
diff --git a/src/full/Agda/TypeChecking/CompiledClause/Compile.hs-boot b/src/full/Agda/TypeChecking/CompiledClause/Compile.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CompiledClause/Compile.hs-boot
@@ -0,0 +1,10 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.CompiledClause.Compile where
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Monad.Base
+
+compileClauses :: Maybe (QName, Type) -> [Clause] -> TCM (Maybe SplitTree, Bool, CompiledClauses)
diff --git a/src/full/Agda/TypeChecking/CompiledClause/Match.hs b/src/full/Agda/TypeChecking/CompiledClause/Match.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CompiledClause/Match.hs
@@ -0,0 +1,208 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.CompiledClause.Match where
+
+import qualified Data.Map as Map
+
+import Agda.Interaction.Options (optRewriting)
+
+import Agda.Syntax.Internal
+import Agda.Syntax.Common
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Monad hiding (constructorForm)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Reduce.Monad as RedM
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.Utils.Impossible
+
+matchCompiled :: CompiledClauses -> MaybeReducedArgs -> ReduceM (Reduced (Blocked Args) Term)
+matchCompiled c args = do
+  r <- matchCompiledE c $ map (fmap Apply) args
+  case r of
+    YesReduction simpl v -> return $ YesReduction simpl v
+    NoReduction bes      -> return $ NoReduction $ fmap (map (fromMaybe __IMPOSSIBLE__ . isApplyElim)) bes
+
+-- | @matchCompiledE c es@ takes a function given by case tree @c@ and
+--   and a spine @es@ and tries to apply the function to @es@.
+matchCompiledE :: CompiledClauses -> MaybeReducedElims -> ReduceM (Reduced (Blocked Elims) Term)
+matchCompiledE c args = match' [(c, args, id)]
+
+-- | A stack entry is a triple consisting of
+--   1. the part of the case tree to continue matching,
+--   2. the current argument vector, and
+--   3. a patch function taking the current argument vector back
+--      to the original argument vector.
+type Frame = (CompiledClauses, MaybeReducedElims, Elims -> Elims)
+type Stack = [Frame]
+
+
+-- | @match'@ tries to solve the matching problems on the @Stack@.
+--   In each iteration, the top problem is removed and handled.
+--
+--   If the top problem was a @Done@, we succeed.
+--
+--   If the top problem was a @Case n@ and the @n@th argument of the problem
+--   is not a constructor or literal, we are stuck, thus, fail.
+--
+--   If we have a branch for the constructor/literal, we put it on the stack
+--   to continue.
+--   If we do not have a branch, we fall through to the next problem, which
+--   should be the corresponding catch-all branch.
+--
+--   An empty stack is an exception that can come only from an incomplete
+--   function definition.
+
+-- TODO: literal/constructor pattern conflict (for Nat)
+
+match' :: Stack -> ReduceM (Reduced (Blocked Elims) Term)
+match' ((c, es, patch) : stack) = do
+  let no blocking es = return $ NoReduction $ blocking $ patch $ map ignoreReduced es
+      yes t          = flip YesReduction t <$> asksTC envSimplification
+
+  do
+
+    case c of
+
+      -- impossible case
+      Fail{} -> no (NotBlocked AbsurdMatch) es
+
+      -- done matching
+      Done xs t
+        -- if the function was partially applied, return a lambda
+        | m < n     -> yes $ applySubst (toSubst es) $ foldr lam t (drop m xs)
+        -- otherwise, just apply instantiation to body
+        -- apply the result to any extra arguments
+        | otherwise -> yes $ applySubst (toSubst es0) t `applyE` map ignoreReduced es1
+        where
+          n              = length xs
+          m              = length es
+          -- at least the first @n@ elims must be @Apply@s, so we can
+          -- turn them into a subsitution
+          toSubst        = parallelS . reverse . map (unArg . fromMaybe __IMPOSSIBLE__ . isApplyElim . ignoreReduced)
+          (es0, es1)     = splitAt n es
+          lam x t        = Lam (argInfo x) (Abs (unArg x) t)
+
+      -- splitting on an eta-record constructor
+      Case (Arg _ n) Branches{etaBranch = Just (c, cc), catchAllBranch = ca} ->
+        case splitAt n es of
+          (_, []) -> no (NotBlocked Underapplied) es
+          (es0, MaybeRed _ e@(Apply (Arg _ v0)) : es1) ->
+              let projs = [ MaybeRed NotReduced $ Apply $ Arg ai $ relToDontCare ai $ v0 `applyE` [Proj ProjSystem f] | Arg ai f <- fs ]
+                  catchAllFrame stack = maybe stack (\c -> (c, es, patch) : stack) ca in
+              match' $ (content cc, es0 ++ projs ++ es1, patchEta) : catchAllFrame stack
+            where
+              fs = conFields c
+              patchEta es = patch (es0 ++ [e] ++ es1)
+                where (es0, es') = splitAt n es
+                      (_, es1)   = splitAt (length fs) es'
+          _ -> __IMPOSSIBLE__
+
+      -- splitting on the @n@th elimination
+      Case (Arg _ n) bs -> do
+        case splitAt n es of
+          -- if the @n@th elimination is not supplied, no match
+          (_, []) -> no (NotBlocked Underapplied) es
+          -- if the @n@th elimination is @e0@
+          (es0, MaybeRed red e0 : es1) -> do
+            -- get the reduced form of @e0@
+            eb :: Blocked Elim <- do
+                  case red of
+                    Reduced b  -> return $ e0 <$ b
+                    NotReduced -> unfoldCorecursionE e0
+            let e = ignoreBlocking eb
+                -- replace the @n@th argument by its reduced form
+                es' = es0 ++ [MaybeRed (Reduced $ () <$ eb) e] ++ es1
+                -- if a catch-all clause exists, put it on the stack
+                catchAllFrame stack = maybe stack (\c -> (c, es', patch) : stack) (catchAllBranch bs)
+                -- If our argument is @Lit l@, we push @litFrame l@ onto the stack.
+                litFrame l stack =
+                  case Map.lookup l (litBranches bs) of
+                    Nothing -> stack
+                    Just cc -> (cc, es0 ++ es1, patchLit) : stack
+                -- If our argument (or its constructor form) is @Con c ci vs@
+                -- we push @conFrame c vs@ onto the stack.
+                conFrame c ci vs stack = conFrame' (conName c) (Con c ci) vs stack
+                conFrame' q f vs stack =
+                  case Map.lookup q (conBranches bs) of
+                    Nothing -> stack
+                    Just cc -> ( content cc
+                               , es0 ++ map (MaybeRed NotReduced) vs ++ es1
+                               , patchCon f (length vs)
+                               ) : stack
+                -- If our argument is @Proj p@, we push @projFrame p@ onto the stack.
+                projFrame p stack =
+                  case Map.lookup p (conBranches bs) of
+                    Nothing -> stack
+                    Just cc -> (content cc, es0 ++ es1, patchLit) : stack
+                -- The new patch function restores the @n@th argument to @v@:
+                -- In case we matched a literal, just put @v@ back.
+                patchLit es = patch (es0 ++ [e] ++ es1)
+                  where (es0, es1) = splitAt n es
+                -- In case we matched constructor @c@ with @m@ arguments,
+                -- contract these @m@ arguments @vs@ to @Con c ci vs@.
+--                patchCon c ci m es = patch (es0 ++ [Con c ci vs <$ e] ++ es2)
+                patchCon f m es = patch (es0 ++ [f vs <$ e] ++ es2)
+                  where (es0, rest) = splitAt n es
+                        (es1, es2)  = splitAt m rest
+                        vs          = es1
+            -- zo <- do
+            --    mi <- getBuiltinName' builtinIZero
+            --    mo <- getBuiltinName' builtinIOne
+            --    return $ Set.fromList $ catMaybes [mi,mo]
+
+            fallThrough <- return $ (Just True ==) (fallThrough bs) && isJust (catchAllBranch bs)
+
+            let
+              isCon b =
+                case ignoreBlocking b of
+                 Apply a | c@Con{} <- unArg a -> Just c
+                 _                            -> Nothing
+            -- Now do the matching on the @n@ths argument:
+            case eb of
+              -- In case of a literal, try also its constructor form
+              NotBlocked _ (Apply (Arg info v@(Lit l))) -> performedSimplification $ do
+                cv <- constructorForm v
+                let cFrame stack = case cv of
+                      Con c ci vs -> conFrame c ci vs stack
+                      _        -> stack
+                match' $ litFrame l $ cFrame $ catchAllFrame stack
+
+              NotBlocked _ (Apply (Arg info v@(Def q vs))) | Just{} <- Map.lookup q (conBranches bs) -> performedSimplification $ do
+                match' $ conFrame' q (Def q) vs $ catchAllFrame $ stack
+
+              -- In case of a constructor, push the conFrame
+              b | Just (Con c ci vs) <- isCon b -> performedSimplification $
+                match' $ conFrame c ci vs $ catchAllFrame $ stack
+
+              -- In case of a projection, push the projFrame
+              NotBlocked _ (Proj _ p) -> performedSimplification $
+                match' $ projFrame p $ stack -- catchAllFrame $ stack
+                -- Issue #1986: no catch-all for copattern matching!
+
+              _ | fallThrough -> match' $ catchAllFrame $ stack
+
+              Blocked x _            -> no (Blocked x) es'
+
+              -- Otherwise, we are stuck.  If we were stuck before,
+              -- we keep the old reason, otherwise we give reason StuckOn here.
+              NotBlocked blocked e -> no (NotBlocked $ stuckOn e blocked) es'
+
+
+-- If we reach the empty stack, then pattern matching was incomplete
+match' [] = {- new line here since __IMPOSSIBLE__ does not like the ' in match' -}
+  caseMaybeM (asksTC envAppDef) __IMPOSSIBLE__ $ \ f -> do
+    pds <- getPartialDefs
+    if f `elem` pds
+    then return (NoReduction $ NotBlocked (MissingClauses f) [])
+    else do
+      ifM (optRewriting <$> pragmaOptions)
+      {-then-} (return (NoReduction $ NotBlocked ReallyNotBlocked [])) -- See #5396
+      {-else-} $ traceSLn "impossible" 10
+        ("Incomplete pattern matching when applying " ++ prettyShow f)
+        __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/CompiledClause/Match.hs-boot b/src/full/Agda/TypeChecking/CompiledClause/Match.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/CompiledClause/Match.hs-boot
@@ -0,0 +1,11 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.CompiledClause.Match where
+
+-- import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.CompiledClause
+
+matchCompiled :: CompiledClauses -> MaybeReducedArgs -> ReduceM (Reduced (Blocked Args) Term)
+matchCompiledE :: CompiledClauses -> MaybeReducedElims -> ReduceM (Reduced (Blocked [Elim]) Term)
diff --git a/src/full/Agda/TypeChecking/Constraints.hs b/src/full/Agda/TypeChecking/Constraints.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Constraints.hs
@@ -0,0 +1,346 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Constraints where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Except
+
+import qualified Data.List as List
+import qualified Data.Set as Set
+import Data.Either
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.InstanceArguments
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.LevelConstraints
+import Agda.TypeChecking.SizedTypes
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Warnings
+
+import Agda.TypeChecking.Irrelevance
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Application
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Data ( checkDataSort )
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Def
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Term
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars
+import {-# SOURCE #-} Agda.TypeChecking.Empty
+import {-# SOURCE #-} Agda.TypeChecking.Lock
+import {-# SOURCE #-} Agda.TypeChecking.CheckInternal ( checkType )
+
+import Agda.Utils.CallStack ( withCurrentCallStack )
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Utils.ProfileOptions as Profile
+
+import Agda.Utils.Impossible
+
+instance MonadConstraint TCM where
+  addConstraint             = addConstraintTCM
+  addAwakeConstraint        = addAwakeConstraint'
+  solveConstraint           = solveConstraintTCM
+  solveSomeAwakeConstraints = solveSomeAwakeConstraintsTCM
+  wakeConstraints           = wakeConstraintsTCM
+  stealConstraints          = stealConstraintsTCM
+  modifyAwakeConstraints    = modifyTC . mapAwakeConstraints
+  modifySleepingConstraints = modifyTC . mapSleepingConstraints
+
+addConstraintTCM :: Blocker -> Constraint -> TCM ()
+addConstraintTCM unblock c = do
+      pids <- asksTC envActiveProblems
+      reportSDoc "tc.constr.add" 20 $ hsep
+        [ "adding constraint"
+        , prettyTCM . PConstr pids unblock =<< buildClosure c
+        , "unblocker: " , prettyTCM unblock
+        ]
+      -- Jesper, 2022-10-22: We should never block on a meta that is
+      -- already solved.
+      forM_ (allBlockingMetas unblock) $ \ m ->
+        whenM (isInstantiatedMeta m) $ do
+          reportSDoc "tc.constr.add" 5 $ "Attempted to block on solved meta" <+> prettyTCM m
+          __IMPOSSIBLE__
+      -- Need to reduce to reveal possibly blocking metas
+      c <- reduce =<< instantiateFull c
+      caseMaybeM (simpl c) {-no-} (addConstraint' unblock c) $ {-yes-} \ cs -> do
+          reportSDoc "tc.constr.add" 20 $ "  simplified:" <+> prettyList (map prettyTCM cs)
+          mapM_ solveConstraint_ cs
+      -- The added constraint can cause instance constraints to be solved,
+      -- but only the constraints which aren’t blocked on an uninstantiated meta.
+      unless (isInstanceConstraint c) $
+         wakeConstraints' isWakeableInstanceConstraint
+    where
+      isWakeableInstanceConstraint :: ProblemConstraint -> WakeUp
+      isWakeableInstanceConstraint c =
+        case clValue $ theConstraint c of
+          FindInstance{}
+            | constraintUnblocker c == alwaysUnblock -> WakeUp
+          _ -> DontWakeUp Nothing
+
+      isLvl LevelCmp{} = True
+      isLvl _          = False
+
+      -- Try to simplify a level constraint
+      simpl :: Constraint -> TCM (Maybe [Constraint])
+      simpl c
+        | isLvl c = do
+          -- Get all level constraints.
+          lvlcs <- instantiateFull =<< do
+            List.filter (isLvl . clValue) . map theConstraint <$> getAllConstraints
+          unless (null lvlcs) $ do
+            reportSDoc "tc.constr.lvl" 40 $ vcat
+              [ "simplifying level constraint" <+> prettyTCM c
+              , nest 2 $ hang "using" 2 $ prettyTCM lvlcs
+              ]
+          -- Try to simplify @c@ using the other constraints.
+          return $ simplifyLevelConstraint c $ map clValue lvlcs
+        | otherwise = return Nothing
+
+wakeConstraintsTCM :: (ProblemConstraint-> WakeUp) -> TCM ()
+wakeConstraintsTCM wake = do
+  c <- useR stSleepingConstraints
+  let (wakeup, sleepin) = partitionEithers $ map checkWakeUp c
+  reportSLn "tc.constr.wake" 50 $
+    "waking up         " ++ show (List.map (Set.toList . constraintProblems) wakeup) ++ "\n" ++
+    "  still sleeping: " ++ show (List.map (Set.toList . constraintProblems) sleepin)
+  modifySleepingConstraints $ const sleepin
+  modifyAwakeConstraints (++ wakeup)
+  where
+    checkWakeUp c = case wake c of
+      WakeUp              -> Left c
+      DontWakeUp Nothing  -> Right c
+      DontWakeUp (Just u) -> Right c{ constraintUnblocker = u }
+
+-- | Add all constraints belonging to the given problem to the current problem(s).
+stealConstraintsTCM :: ProblemId -> TCM ()
+stealConstraintsTCM pid = do
+  current <- asksTC envActiveProblems
+  reportSLn "tc.constr.steal" 50 $ "problem " ++ show (Set.toList current) ++ " is stealing problem " ++ show pid ++ "'s constraints!"
+  -- Add current to any constraint in pid.
+  let rename pc@(PConstr pids u c) | Set.member pid pids = PConstr (Set.union current pids) u c
+                                   | otherwise           = pc
+  -- We should never steal from an active problem.
+  whenM (Set.member pid <$> asksTC envActiveProblems) __IMPOSSIBLE__
+  modifyAwakeConstraints    $ List.map rename
+  modifySleepingConstraints $ List.map rename
+
+
+{-# SPECIALIZE noConstraints :: TCM a -> TCM a #-}
+-- | Don't allow the argument to produce any blocking constraints.
+--
+-- WARNING: this does not mean that the given computation cannot
+-- constrain the solution space further.
+-- It can well do so, by solving metas.
+noConstraints
+  :: (MonadConstraint m, MonadWarning m, MonadError TCErr m, MonadFresh ProblemId m)
+  => m a -> m a
+noConstraints problem = do
+  (pid, x) <- newProblem problem
+  cs <- getConstraintsForProblem pid
+  unless (null cs) $ do
+    withCurrentCallStack $ \loc -> do
+      w <- warning'_ loc (UnsolvedConstraints cs)
+      typeError' loc $ NonFatalErrors [ w ]
+  return x
+
+-- | Run a computation that should succeeds without constraining
+--   the solution space, i.e., not add any information about meta-variables.
+nonConstraining ::
+  ( HasOptions m
+  , MonadConstraint m
+  , MonadDebug m
+  , MonadError TCErr m
+  , MonadFresh ProblemId m
+  , MonadTCEnv m
+  , MonadWarning m
+  ) => m a -> m a
+nonConstraining = dontAssignMetas . noConstraints
+
+{-# SPECIALIZE newProblem :: TCM a -> TCM (ProblemId, a) #-}
+-- | Create a fresh problem for the given action.
+newProblem
+  :: (MonadFresh ProblemId m, MonadConstraint m)
+  => m a -> m (ProblemId, a)
+newProblem action = do
+  pid <- fresh
+  -- Don't get distracted by other constraints while working on the problem
+  x <- nowSolvingConstraints $ solvingProblem pid action
+  -- Now we can check any woken constraints
+  solveAwakeConstraints
+  return (pid, x)
+
+{-# SPECIALIZE newProblem_ :: TCM a -> TCM ProblemId #-}
+newProblem_
+  :: (MonadFresh ProblemId m, MonadConstraint m)
+  => m a -> m ProblemId
+newProblem_ action = fst <$> newProblem action
+
+ifNoConstraints :: TCM a -> (a -> TCM b) -> (ProblemId -> a -> TCM b) -> TCM b
+ifNoConstraints check ifNo ifCs = do
+  (pid, x) <- newProblem check
+  ifM (isProblemSolved pid) (ifNo x) (ifCs pid x)
+
+ifNoConstraints_ :: TCM () -> TCM a -> (ProblemId -> TCM a) -> TCM a
+ifNoConstraints_ check ifNo ifCs = ifNoConstraints check (const ifNo) (\pid _ -> ifCs pid)
+
+-- | @guardConstraint c blocker@ tries to solve @blocker@ first.
+--   If successful without constraints, it moves on to solve @c@, otherwise it
+--   adds a @c@ to the constraint pool, blocked by the problem generated by @blocker@.
+guardConstraint :: Constraint -> TCM () -> TCM ()
+guardConstraint c blocker =
+  ifNoConstraints_ blocker (solveConstraint c) (\ pid -> addConstraint (unblockOnProblem pid) c)
+
+whenConstraints :: TCM () -> TCM () -> TCM ()
+whenConstraints action handler =
+  ifNoConstraints_ action (return ()) $ \pid -> do
+    stealConstraints pid
+    handler
+
+{-# SPECIALIZE wakeupConstraints :: MetaId -> TCM () #-}
+-- | Wake up the constraints depending on the given meta.
+wakeupConstraints :: MonadMetaSolver m => MetaId -> m ()
+wakeupConstraints x = do
+  wakeConstraints' (wakeIfBlockedOnMeta x . constraintUnblocker)
+  solveAwakeConstraints
+
+-- | Wake up all constraints not blocked on a problem.
+wakeupConstraints_ :: TCM ()
+wakeupConstraints_ = do
+  wakeConstraints' (wakeup . constraintUnblocker)
+  solveAwakeConstraints
+  where
+    wakeup u | Set.null $ allBlockingProblems u = WakeUp
+             | otherwise                        = DontWakeUp Nothing
+
+-- | Solve awake constraints matching the predicate. If the second argument is
+--   True solve constraints even if already 'isSolvingConstraints'.
+solveSomeAwakeConstraintsTCM :: (ProblemConstraint -> Bool) -> Bool -> TCM ()
+solveSomeAwakeConstraintsTCM solveThis force = do
+    whenProfile Profile.Constraints $ liftTCM $ tickMax "max-open-constraints" . List.genericLength =<< getAllConstraints
+    whenM ((force ||) . not <$> isSolvingConstraints) $ nowSolvingConstraints $ do
+     -- solveSizeConstraints -- Andreas, 2012-09-27 attacks size constrs too early
+     -- Ulf, 2016-12-06: Don't inherit problems here! Stored constraints
+     -- already contain all their dependencies.
+     locallyTC eActiveProblems (const Set.empty) solve
+  where
+    solve = do
+      reportSDoc "tc.constr.solve" 10 $ hsep [ "Solving awake constraints."
+                                             , text . show . length =<< getAwakeConstraints
+                                             , "remaining." ]
+      whenJustM (takeAwakeConstraint' solveThis) $ \ c -> do
+        withConstraint solveConstraint c
+        solve
+
+solveConstraintTCM :: Constraint -> TCM ()
+solveConstraintTCM c = do
+    whenProfile Profile.Constraints $ liftTCM $ tick "attempted-constraints"
+    verboseBracket "tc.constr.solve" 20 "solving constraint" $ do
+      pids <- asksTC envActiveProblems
+      reportSDoc "tc.constr.solve.constr" 20 $ text (show $ Set.toList pids) <+> prettyTCM c
+      solveConstraint_ c
+
+solveConstraint_ :: Constraint -> TCM ()
+solveConstraint_ (ValueCmp cmp a u v)       = compareAs cmp a u v
+solveConstraint_ (ValueCmpOnFace cmp p a u v) = compareTermOnFace cmp p a u v
+solveConstraint_ (ElimCmp cmp fs a e u v)   = compareElims cmp fs a e u v
+solveConstraint_ (SortCmp cmp s1 s2)        = compareSort cmp s1 s2
+solveConstraint_ (LevelCmp cmp a b)         = compareLevel cmp a b
+solveConstraint_ (IsEmpty r t)              = ensureEmptyType r t
+solveConstraint_ (CheckSizeLtSat t)         = checkSizeLtSat t
+solveConstraint_ (UnquoteTactic tac hole goal) = unquoteTactic tac hole goal
+solveConstraint_ (UnBlock m)                =   -- alwaysUnblock since these have their own unblocking logic (for now)
+  ifM (isFrozen m `or2M` (not <$> asksTC envAssignMetas)) (do
+        reportSDoc "tc.constr.unblock" 15 $ hsep ["not unblocking", prettyTCM m, "because",
+                                                  ifM (isFrozen m) "it's frozen" "meta assignments are turned off"]
+        addConstraint alwaysUnblock $ UnBlock m) $ do
+    inst <- lookupMetaInstantiation m
+    reportSDoc "tc.constr.unblock" 65 $ "unblocking a metavar yields the constraint:" <+> pretty inst
+    case inst of
+      BlockedConst t -> do
+        reportSDoc "tc.constr.blocked" 15 $
+          text ("blocked const " ++ prettyShow m ++ " :=") <+> prettyTCM t
+        assignTerm m [] t
+      PostponedTypeCheckingProblem cl -> enterClosure cl $ \prob -> do
+          tel <- getContextTelescope
+          v   <- liftTCM $ checkTypeCheckingProblem prob
+          assignTerm m (telToArgs tel) v
+      -- Andreas, 2009-02-09, the following were IMPOSSIBLE cases
+      -- somehow they pop up in the context of sized types
+      --
+      -- already solved metavariables: should only happen for size
+      -- metas (not sure why it does, Andreas?)
+      -- Andreas, 2017-07-11:
+      -- I think this is because the size solver instantiates
+      -- some metas with infinity but does not clean up the UnBlock constraints.
+      -- See also issue #2637.
+      -- Ulf, 2018-04-30: The size solver shouldn't touch blocked terms! They have
+      -- a twin meta that it's safe to solve.
+      InstV{} -> __IMPOSSIBLE__
+      -- Open (whatever that means)
+      Open -> __IMPOSSIBLE__
+      OpenInstance -> __IMPOSSIBLE__
+solveConstraint_ (FindInstance m cands) = findInstance m cands
+solveConstraint_ (CheckFunDef i q cs _err) = withoutCache $
+  -- re #3498: checking a fundef would normally be cached, but here it's
+  -- happening out of order so it would only corrupt the caching log.
+  checkFunDef i q cs
+solveConstraint_ (CheckLockedVars a b c d)   = checkLockedVars a b c d
+solveConstraint_ (HasBiggerSort a)      = hasBiggerSort a
+solveConstraint_ (HasPTSRule a b)       = hasPTSRule a b
+solveConstraint_ (CheckDataSort q s)    = checkDataSort q s
+solveConstraint_ (CheckMetaInst m)      = checkMetaInst m
+solveConstraint_ (CheckType t)          = checkType t
+solveConstraint_ (UsableAtModality cc ms mod t) = usableAtModality' ms cc mod t
+
+checkTypeCheckingProblem :: TypeCheckingProblem -> TCM Term
+checkTypeCheckingProblem = \case
+  CheckExpr cmp e t              -> checkExpr' cmp e t
+  CheckArgs cmp eh r args t0 t1 k -> checkArguments cmp eh r args t0 t1 k
+  CheckProjAppToKnownPrincipalArg cmp e o ds args t k v0 pt patm ->
+    checkProjAppToKnownPrincipalArg cmp e o ds args t k v0 pt patm
+  CheckLambda cmp args body target -> checkPostponedLambda cmp args body target
+  DoQuoteTerm cmp et t           -> doQuoteTerm cmp et t
+
+debugConstraints :: TCM ()
+debugConstraints = verboseS "tc.constr" 50 $ do
+  awake    <- useTC stAwakeConstraints
+  sleeping <- useTC stSleepingConstraints
+  reportSDoc "tc.constr" 50 $ vcat
+    [ "Current constraints"
+    , nest 2 $ vcat [ "awake " <+> vcat (map prettyTCM awake)
+                    , "asleep" <+> vcat (map prettyTCM sleeping) ] ]
+
+-- Update the blocker after some instantiation or pruning might have happened.
+updateBlocker :: (PureTCM m) => Blocker -> m Blocker
+updateBlocker = instantiate
+
+addAndUnblocker :: (PureTCM m, MonadBlock m) => Blocker -> m a -> m a
+addAndUnblocker u
+  | u == alwaysUnblock = id
+  | otherwise          = catchPatternErr $ \ u' -> do
+      u <- updateBlocker u
+      patternViolation (unblockOnBoth u u')
+
+addOrUnblocker :: (PureTCM m, MonadBlock m) => Blocker -> m a -> m a
+addOrUnblocker u
+  | u == neverUnblock = id
+  | otherwise         = catchPatternErr $ \ u' -> do
+      u <- updateBlocker u
+      patternViolation (unblockOnEither u u')
+
+-- Reduce a term and call the continuation. If the continuation is
+-- blocked, the whole call is blocked either on what blocked the reduction
+-- or on what blocked the continuation (using `blockedOnEither`).
+withReduced
+  :: (Reduce a, IsMeta a, PureTCM m, MonadBlock m)
+  => a -> (a -> m b) -> m b
+withReduced a cont = ifBlocked a (\b a' -> addOrUnblocker b $ cont a') (\_ a' -> cont a')
diff --git a/src/full/Agda/TypeChecking/Constraints.hs-boot b/src/full/Agda/TypeChecking/Constraints.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Constraints.hs-boot
@@ -0,0 +1,20 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Constraints where
+
+
+import Control.Monad.Except (MonadError)
+
+import Agda.Syntax.Internal (ProblemId)
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Constraints (MonadConstraint)
+import Agda.TypeChecking.Warnings (MonadWarning)
+
+instance MonadConstraint TCM where
+
+noConstraints          :: (MonadConstraint m, MonadWarning m, MonadError TCErr m, MonadFresh ProblemId m)
+                       => m a -> m a
+ifNoConstraints_       :: TCM () -> TCM a -> (ProblemId -> TCM a) -> TCM a
+ifNoConstraints        :: TCM a -> (a -> TCM b) -> (ProblemId -> a -> TCM b) -> TCM b
+guardConstraint        :: Constraint -> TCM () -> TCM ()
+debugConstraints       :: TCM ()
diff --git a/src/full/Agda/TypeChecking/Conversion.hs b/src/full/Agda/TypeChecking/Conversion.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Conversion.hs
@@ -0,0 +1,2202 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE NondecreasingIndentation #-}
+
+#if __GLASGOW_HASKELL__ >= 810
+{-# OPTIONS_GHC -fmax-pmcheck-models=390 #-} -- Andreas, 2023-05-12, limit determined by binary search
+#endif
+
+module Agda.TypeChecking.Conversion where
+
+import Control.Arrow (second)
+import Control.Monad
+import Control.Monad.Except
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import Data.Function (on)
+import Data.Semigroup ((<>))
+import Data.IntMap (IntMap)
+
+import qualified Data.List   as List
+import qualified Data.IntMap as IntMap
+import qualified Data.IntSet as IntSet
+import qualified Data.Set    as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Translation.InternalToAbstract (reify)
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.MetaVars.Occurs (killArgs,PruneResult(..),rigidVarsNotContainedIn)
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import qualified Agda.TypeChecking.SyntacticEquality as SynEq
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion.Pure (pureCompareAs, runPureConversion)
+import Agda.TypeChecking.Forcing (isForced, nextIsForced)
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Datatypes (getConType, getFullyAppliedConType)
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Injectivity
+import Agda.TypeChecking.Polarity
+import Agda.TypeChecking.SizedTypes
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Implicit (implicitArgs)
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.ProjectionLike
+import Agda.TypeChecking.Warnings (MonadWarning)
+import Agda.Interaction.Options
+
+import Agda.Utils.Functor
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Monad
+import Agda.Utils.Maybe
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Utils.ProfileOptions as Profile
+import Agda.Utils.BoolSet (BoolSet)
+import qualified Agda.Utils.BoolSet as BoolSet
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+import Agda.Utils.Unsafe ( unsafeComparePointers )
+
+import Agda.Utils.Impossible
+
+type MonadConversion m =
+  ( PureTCM m
+  , MonadConstraint m
+  , MonadMetaSolver m
+  , MonadError TCErr m
+  , MonadWarning m
+  , MonadStatistics m
+  , MonadFresh ProblemId m
+  , MonadFresh Int m
+  , MonadFail m
+  )
+
+-- | Try whether a computation runs without errors or new constraints
+--   (may create new metas, though).
+--   Restores state upon failure.
+tryConversion
+  :: (MonadConstraint m, MonadWarning m, MonadError TCErr m, MonadFresh ProblemId m)
+  => m () -> m Bool
+tryConversion = isJust <.> tryConversion'
+
+-- | Try whether a computation runs without errors or new constraints
+--   (may create new metas, though).
+--   Return 'Just' the result upon success.
+--   Return 'Nothing' and restore state upon failure.
+tryConversion'
+  :: (MonadConstraint m, MonadWarning m, MonadError TCErr m, MonadFresh ProblemId m)
+  => m a -> m (Maybe a)
+tryConversion' m = tryMaybe $ noConstraints m
+
+-- | Check if to lists of arguments are the same (and all variables).
+--   Precondition: the lists have the same length.
+sameVars :: Elims -> Elims -> Bool
+sameVars xs ys = and $ zipWith same xs ys
+    where
+        same (Apply (Arg _ (Var n []))) (Apply (Arg _ (Var m []))) = n == m
+        same _ _ = False
+
+-- | @intersectVars us vs@ checks whether all relevant elements in @us@ and @vs@
+--   are variables, and if yes, returns a prune list which says @True@ for
+--   arguments which are different and can be pruned.
+intersectVars :: Elims -> Elims -> Maybe [Bool]
+intersectVars = zipWithM areVars where
+    -- ignore irrelevant args
+    areVars (Apply u) v | isIrrelevant u = Just False -- do not prune
+    areVars (Apply (Arg _ (Var n []))) (Apply (Arg _ (Var m []))) = Just $ n /= m -- prune different vars
+    areVars _ _                                   = Nothing
+
+-- | @guardPointerEquality x y s m@ behaves as @m@ if @x@ and @y@ are equal as pointers,
+-- or does nothing otherwise.
+-- Use with care, see the documentation for 'unsafeComparePointers'
+guardPointerEquality :: MonadConversion m => a -> a -> String -> m () -> m ()
+guardPointerEquality u v profileSection action =
+  if unsafeComparePointers u v
+  then whenProfile Profile.Conversion $ tick profileSection
+  else action
+
+{-# SPECIALIZE equalTerm :: Type -> Term -> Term -> TCM () #-}
+equalTerm :: MonadConversion m => Type -> Term -> Term -> m ()
+equalTerm = compareTerm CmpEq
+
+{-# SPECIALIZE equalAtom :: CompareAs -> Term -> Term -> TCM () #-}
+equalAtom :: MonadConversion m => CompareAs -> Term -> Term -> m ()
+equalAtom = compareAtom CmpEq
+
+{-# SPECIALIZE equalType :: Type -> Type -> TCM () #-}
+equalType :: MonadConversion m => Type -> Type -> m ()
+equalType = compareType CmpEq
+
+{- Comparing in irrelevant context always succeeds.
+
+   However, we might want to dig for solutions of irrelevant metas.
+
+   To this end, we can just ignore errors during conversion checking.
+ -}
+
+-- convError ::  MonadTCM tcm => TypeError -> tcm a
+-- | Ignore errors in irrelevant context.
+convError :: TypeError -> TCM ()
+convError err =
+  ifM ((==) Irrelevant <$> viewTC eRelevance)
+    (return ())
+    (typeError err)
+
+
+-- | Type directed equality on values.
+--
+compareTerm :: forall m. MonadConversion m => Comparison -> Type -> Term -> Term -> m ()
+compareTerm cmp a u v = compareAs cmp (AsTermsOf a) u v
+
+
+{-# SPECIALIZE compareAs :: Comparison -> CompareAs -> Term -> Term -> TCM ()  #-}
+-- | Type directed equality on terms or types.
+compareAs :: forall m. MonadConversion m => Comparison -> CompareAs -> Term -> Term -> m ()
+  -- If one term is a meta, try to instantiate right away. This avoids unnecessary unfolding.
+  -- Andreas, 2012-02-14: This is UNSOUND for subtyping!
+compareAs cmp a u v = do
+  reportSDoc "tc.conv.term" 20 $ sep $
+    [ "compareTerm"
+    , nest 2 $ prettyTCM u <+> prettyTCM cmp <+> prettyTCM v
+    , nest 2 $ prettyTCM a
+    ]
+  whenProfile Profile.Conversion $ tick "compare"
+
+  -- OLD CODE, traverses the *full* terms u v at each step, even if they
+  -- are different somewhere.  Leads to infeasibility in issue 854.
+  -- (u, v) <- instantiateFull (u, v)
+  -- let equal = u == v
+
+  -- Check syntactic equality. This actually saves us quite a bit of work.
+  guardPointerEquality u v "pointer equality: terms" $ SynEq.checkSyntacticEquality u v
+    (\_ _ -> whenProfile Profile.Conversion $ tick "compare equal") $
+    \u v -> do
+      reportSDoc "tc.conv.term" 15 $ sep $
+        [ "compareTerm (not syntactically equal)"
+        , nest 2 $ prettyTCM u <+> prettyTCM cmp <+> prettyTCM v
+        , nest 2 $ prettyTCM a
+        ]
+      -- If we are at type Size, we cannot short-cut comparison
+      -- against metas by assignment.
+      -- Andreas, 2014-04-12: this looks incomplete.
+      -- It seems to assume we are never comparing
+      -- at function types into Size.
+      let fallback = compareAs' cmp a u v
+          unlessSubtyping :: m () -> m ()
+          unlessSubtyping cont =
+              if cmp == CmpEq then cont else do
+                -- Andreas, 2014-04-12 do not short cut if type is blocked.
+                ifBlocked a (\ _ _ -> fallback) {-else-} $ \ _ a -> do
+                  -- do not short circuit size comparison!
+                  caseMaybeM (isSizeType a) cont (\ _ -> fallback)
+
+          dir = fromCmp cmp
+          rid = flipCmp dir     -- The reverse direction.  Bad name, I know.
+      case (u, v) of
+        (MetaV x us, MetaV y vs)
+          | x /= y    -> unlessSubtyping $ solve1 `orelse` solve2 `orelse` fallback
+          | otherwise -> fallback
+          where
+            (solve1, solve2) | x > y     = (assign dir x us v, assign rid y vs u)
+                             | otherwise = (assign rid y vs u, assign dir x us v)
+        (MetaV x us, _) -> unlessSubtyping $ assign dir x us v `orelse` fallback
+        (_, MetaV y vs) -> unlessSubtyping $ assign rid y vs u `orelse` fallback
+        (Def f es, Def f' es') | f == f' ->
+          ifNotM (optFirstOrder <$> pragmaOptions) fallback $ {- else -} unlessSubtyping $ do
+          def <- getConstInfo f
+          -- We do not shortcut projection-likes,
+          -- Andreas, 2022-03-07, issue #5809:
+          -- but irrelevant projections since they are applied to their parameters.
+          -- Amy, 2023-01-04, issue #6415: and not
+          -- prim^unglue/prim^unglueU either! removing the unglue from a
+          -- transport/hcomp may cause an infinite loop.
+          cubicalProjs <- traverse getName' [builtin_unglue, builtin_unglueU]
+          let
+            notFirstOrder = isJust (isRelevantProjection_ def)
+                         || any (Just f ==) cubicalProjs
+          if notFirstOrder then fallback else do
+          pol <- getPolarity' cmp f
+          whenProfile Profile.Conversion $ tick "compare first-order shortcut"
+          compareElims pol [] (defType def) (Def f []) es es' `orelse` fallback
+        _               -> fallback
+  where
+    assign :: CompareDirection -> MetaId -> Elims -> Term -> m ()
+    assign dir x es v = do
+      -- Andreas, 2013-10-19 can only solve if no projections
+      reportSDoc "tc.conv.term.shortcut" 20 $ sep
+        [ "attempting shortcut"
+        , nest 2 $ prettyTCM (MetaV x es) <+> ":=" <+> prettyTCM v
+        ]
+      whenM (isInstantiatedMeta x) (patternViolation alwaysUnblock) -- Already instantiated, retry right away
+      whenProfile Profile.Conversion $ tick "compare meta shortcut"
+      assignE dir x es v a $ compareAsDir dir a
+      reportSDoc "tc.conv.term.shortcut" 50 $
+        "shortcut successful" $$ nest 2 ("result:" <+> (pretty =<< instantiate (MetaV x es)))
+      whenProfile Profile.Conversion $ tick "compare meta shortcut successful"
+    -- Should be ok with catchError_ but catchError is much safer since we don't
+    -- rethrow errors.
+    orelse :: m () -> m () -> m ()
+    orelse m h = catchError m (\_ -> h)
+
+-- | Try to assign meta.  If meta is projected, try to eta-expand
+--   and run conversion check again.
+assignE :: (MonadConversion m)
+        => CompareDirection -> MetaId -> Elims -> Term -> CompareAs -> (Term -> Term -> m ()) -> m ()
+assignE dir x es v a comp = do
+  whenProfile Profile.Conversion $ tick "compare meta"
+  case allApplyElims es of
+    Just vs -> assignV dir x vs v a
+    Nothing -> do
+      reportSDoc "tc.conv.assign" 30 $ sep
+        [ "assigning to projected meta "
+        , prettyTCM x <+> sep (map prettyTCM es) <+> text (":" ++ show dir) <+> prettyTCM v
+        ]
+      etaExpandMeta [Records] x
+      res <- isInstantiatedMeta' x
+      case res of
+        Just u  -> do
+          reportSDoc "tc.conv.assign" 30 $ sep
+            [ "seems like eta expansion instantiated meta "
+            , prettyTCM x <+> text  (":" ++ show dir) <+> prettyTCM u
+            ]
+          let w = u `applyE` es
+          comp w v
+        Nothing ->  do
+          reportSLn "tc.conv.assign" 30 "eta expansion did not instantiate meta"
+          patternViolation $ unblockOnMeta x -- nothing happened, give up
+
+compareAsDir :: MonadConversion m => CompareDirection -> CompareAs -> Term -> Term -> m ()
+compareAsDir dir a = dirToCmp (`compareAs'` a) dir
+
+compareAs' :: forall m. MonadConversion m => Comparison -> CompareAs -> Term -> Term -> m ()
+compareAs' cmp tt m n = case tt of
+  AsTermsOf a -> compareTerm' cmp a m n
+  AsSizes     -> compareSizes cmp m n
+  AsTypes     -> compareAtom cmp AsTypes m n
+
+compareTerm' :: forall m. MonadConversion m => Comparison -> Type -> Term -> Term -> m ()
+compareTerm' cmp a m n =
+  verboseBracket "tc.conv.term" 20 "compareTerm" $ do
+  (ba, a') <- reduceWithBlocker a
+  (catchConstraint (ValueCmp cmp (AsTermsOf a') m n) :: m () -> m ()) $ blockOnError ba $ do
+    reportSDoc "tc.conv.term" 30 $ fsep
+      [ "compareTerm", prettyTCM m, prettyTCM cmp, prettyTCM n, ":", prettyTCM a' ]
+    propIrr  <- isPropEnabled
+    isSize   <- isJust <$> isSizeType a'
+    (bs, s)  <- reduceWithBlocker $ getSort a'
+    mlvl     <- getBuiltin' builtinLevel
+    reportSDoc "tc.conv.term" 40 $ fsep
+      [ "compareTerm", prettyTCM m, prettyTCM cmp, prettyTCM n, ":", prettyTCM a'
+      , "at sort", prettyTCM s]
+    reportSDoc "tc.conv.level" 60 $ nest 2 $ sep
+      [ "a'   =" <+> pretty a'
+      , "mlvl =" <+> pretty mlvl
+      , text $ "(Just (unEl a') == mlvl) = " ++ show (Just (unEl a') == mlvl)
+      ]
+    blockOnError bs $ case s of
+      Prop{} | propIrr -> compareIrrelevant a' m n
+      _    | isSize   -> compareSizes cmp m n
+      _               -> case unEl a' of
+        a | Just a == mlvl -> do
+          a <- levelView m
+          b <- levelView n
+          equalLevel a b
+        a@Pi{}    -> equalFun s a m n
+        Lam _ _   -> do
+          reportSDoc "tc.conv.term.sort" 10 $ fsep
+            [ "compareTerm", prettyTCM m, prettyTCM cmp, prettyTCM n, ":", prettyTCM a'
+            , "at sort", prettyTCM s
+            ]
+          __IMPOSSIBLE__
+        Def r es  -> do
+          isrec <- isEtaRecord r
+          if isrec
+            then do
+              whenProfile Profile.Conversion $ tick "compare at eta record"
+              sig <- getSignature
+              let ps = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+              -- Andreas, 2010-10-11: allowing neutrals to be blocked things does not seem
+              -- to change Agda's behavior
+              --    isNeutral Blocked{}          = False
+                  isNeutral (NotBlocked _ Con{}) = return False
+              -- Andreas, 2013-09-18 / 2015-06-29: a Def by copatterns is
+              -- not neutral if it is blocked (there can be missing projections
+              -- to trigger a reduction.
+                  isNeutral (NotBlocked r (Def q _)) = do    -- Andreas, 2014-12-06 optimize this using r !!
+                    not <$> usesCopatterns q -- a def by copattern can reduce if projected
+                  isNeutral _                   = return True
+                  isMeta b = case ignoreBlocking b of
+                               MetaV{} -> True
+                               _       -> False
+
+              reportSDoc "tc.conv.term" 30 $ prettyTCM a <+> "is eta record type"
+              m <- reduceB m
+              mNeutral <- isNeutral m
+              n <- reduceB n
+              nNeutral <- isNeutral n
+              if | isMeta m || isMeta n -> do
+                     whenProfile Profile.Conversion $ tick "compare at eta-record: meta"
+                     compareAtom cmp (AsTermsOf a') (ignoreBlocking m) (ignoreBlocking n)
+                 | mNeutral && nNeutral -> do
+                     whenProfile Profile.Conversion $ tick "compare at eta-record: both neutral"
+                     -- Andreas 2011-03-23: (fixing issue 396)
+                     -- if we are dealing with a singleton record,
+                     -- we can succeed immediately
+                     let profUnitEta = whenProfile Profile.Conversion $ tick "compare at eta-record: both neutral at unit"
+                     ifM (isSingletonRecordModuloRelevance r ps) (profUnitEta) $ do
+                       -- do not eta-expand if comparing two neutrals
+                       compareAtom cmp (AsTermsOf a') (ignoreBlocking m) (ignoreBlocking n)
+                 | otherwise -> do
+                     whenProfile Profile.Conversion $ tick "compare at eta-record: eta-expanding"
+                     (tel, m') <- etaExpandRecord r ps $ ignoreBlocking m
+                     (_  , n') <- etaExpandRecord r ps $ ignoreBlocking n
+                     -- No subtyping on record terms
+                     c <- getRecordConstructor r
+                     -- Record constructors are covariant (see test/succeed/CovariantConstructors).
+                     compareArgs (repeat $ polFromCmp cmp) [] (telePi_ tel __DUMMY_TYPE__) (Con c ConOSystem []) m' n'
+
+            else (do pathview <- pathView a'
+                     equalPath pathview a' m n)
+        _ -> compareAtom cmp (AsTermsOf a') m n
+  where
+    -- equality at function type (accounts for eta)
+    equalFun :: (MonadConversion m) => Sort -> Term -> Term -> Term -> m ()
+    equalFun s a@(Pi dom b) m n | domIsFinite dom = do
+       mp <- fmap getPrimName <$> getBuiltin' builtinIsOne
+       let asFn = El s (Pi (dom { domIsFinite = False }) b)
+       case unEl $ unDom dom of
+          Def q [Apply phi]
+              | Just q == mp -> compareTermOnFace cmp (unArg phi) asFn m n
+          _                  -> equalFun s (unEl asFn) m n
+
+    equalFun _ (Pi dom@Dom{domInfo = info} b) m n = do
+        whenProfile Profile.Conversion $ tick "compare at function type"
+        let name = suggests [ Suggestion b , Suggestion m , Suggestion n ]
+        addContext (name, dom) $ compareTerm cmp (absBody b) m' n'
+      where
+        (m',n') = raise 1 (m,n) `apply` [Arg info $ var 0]
+
+    equalFun _ _ _ _ = __IMPOSSIBLE__
+
+    equalPath :: (MonadConversion m) => PathView -> Type -> Term -> Term -> m ()
+    equalPath (PathType s _ l a x y) _ m n = do
+        whenProfile Profile.Conversion $ tick "compare at path type"
+        let name = "i" :: String
+        interval <- el primInterval
+        let (m',n') = raise 1 (m, n) `applyE` [IApply (raise 1 $ unArg x) (raise 1 $ unArg y) (var 0)]
+        addContext (name, defaultDom interval) $ compareTerm cmp (El (raise 1 s) $ raise 1 (unArg a) `apply` [argN $ var 0]) m' n'
+    equalPath OType{} a' m n = cmpDef a' m n
+
+    cmpDef a'@(El s ty) m n = do
+       mI     <- getBuiltinName'   builtinInterval
+       mIsOne <- getBuiltinName'   builtinIsOne
+       mGlue  <- getPrimitiveName' builtinGlue
+       mHComp <- getPrimitiveName' builtinHComp
+       mSub   <- getBuiltinName' builtinSub
+       mUnglueU <- getPrimitiveTerm' builtin_unglueU
+       mSubIn   <- getBuiltin' builtinSubIn
+       case ty of
+         Def q es | Just q == mIsOne -> return ()
+         Def q es | Just q == mGlue, Just args@(l:_:a:phi:_) <- allApplyElims es -> do
+              aty <- el' (pure $ unArg l) (pure $ unArg a)
+              unglue <- prim_unglue
+              let mkUnglue m = apply unglue $ map (setHiding Hidden) args ++ [argN m]
+              reportSDoc "conv.glue" 20 $ prettyTCM (aty,mkUnglue m,mkUnglue n)
+
+              -- Amy, 2023-01-04: Here and in hcompu below we *used to*
+              -- also compare whatever the glued terms would evaluate to
+              -- on φ. This is very loopy (consider φ = f i or φ = i0:
+              -- both generate empty substitutions so get us back to
+              -- exactly the same conversion problem)!
+              --
+              -- But is there a reason to do this comparison? The
+              -- answer, it turns out, is no!
+              --
+              -- Suppose you had
+              --    Γ ⊢ x = glue [φ → t] xb : Glue T S
+              --    Γ ⊢ y = glue [φ → s] yb : Glue T S
+              --    Γ ⊢ xb = yb : T
+              -- Is there a need to check whether Γ φ ⊢ t = s : S? No!
+              -- That's because the typing rule for glue is something like
+              --   glue φ : (s : PartialP φ S) (t : T [ φ → s ]) → Glue T S
+              -- where the bracket notation stands for an "implicit
+              -- Sub"-type, i.e. Γ, φ ⊢ t = s (definitionally)
+              --
+              -- So if we have a glued element, and we have xb = yb, we
+              -- can be sure that
+              --   Γ , φ ⊢ t = xb = yb = s
+              --
+              -- But what about the general case, where we're not
+              -- looking at a literal glue? Well, eta for Glue
+              -- means x = glue [φ → x] (unglue x), so the logic above
+              -- still applies. On φ, for the reducts to agree, it's
+              -- enough for the bases to agree.
+
+              compareTerm cmp aty (mkUnglue m) (mkUnglue n)
+         Def q es | Just q == mHComp, Just (sl:s:args@[phi,u,u0]) <- allApplyElims es
+                  , Sort (Type lvl) <- unArg s
+                  , Just unglueU <- mUnglueU, Just subIn <- mSubIn
+                  -> do
+              let l = Level lvl
+              ty <- el' (pure $ l) (pure $ unArg u0)
+              let bA = subIn `apply` [sl,s,phi,u0]
+              let mkUnglue m = apply unglueU $ [argH l] ++ map (setHiding Hidden) [phi,u]  ++ [argH bA,argN m]
+              reportSDoc "conv.hcompU" 20 $ prettyTCM (ty,mkUnglue m,mkUnglue n)
+              compareTerm cmp ty (mkUnglue m) (mkUnglue n)
+         Def q es | Just q == mSub, Just args@(l:a:_) <- allApplyElims es -> do
+              ty <- el' (pure $ unArg l) (pure $ unArg a)
+              out <- primSubOut
+              let mkOut m = apply out $ map (setHiding Hidden) args ++ [argN m]
+              compareTerm cmp ty (mkOut m) (mkOut n)
+         Def q [] | Just q == mI -> compareInterval cmp a' m n
+         _ -> compareAtom cmp (AsTermsOf a') m n
+
+compareAtomDir :: MonadConversion m => CompareDirection -> CompareAs -> Term -> Term -> m ()
+compareAtomDir dir a = dirToCmp (`compareAtom` a) dir
+
+-- | Compute the head type of an elimination. For projection-like functions
+--   this requires inferring the type of the principal argument.
+computeElimHeadType :: MonadConversion m => QName -> Elims -> Elims -> m Type
+computeElimHeadType f [] es' = computeDefType f es'
+computeElimHeadType f es _   = computeDefType f es
+
+-- | Syntax directed equality on atomic values
+--
+compareAtom :: forall m. MonadConversion m => Comparison -> CompareAs -> Term -> Term -> m ()
+compareAtom cmp t m n =
+  verboseBracket "tc.conv.atom" 20 "compareAtom" $
+  -- if a PatternErr is thrown, rebuild constraint!
+  (catchConstraint (ValueCmp cmp t m n) :: m () -> m ()) $ do
+    reportSLn "tc.conv.atom.size" 50 $ "compareAtom term size:  " ++ show (termSize m, termSize n)
+    reportSDoc "tc.conv.atom" 50 $
+      "compareAtom" <+> fsep [ prettyTCM m <+> prettyTCM cmp
+                             , prettyTCM n
+                             , prettyTCM t
+                             ]
+    whenProfile Profile.Conversion $ tick "compare by reduction"
+    -- Are we currently defining mutual functions? Which?
+    currentMutuals <- maybe (pure Set.empty) (mutualNames <.> lookupMutualBlock) =<< asksTC envMutualBlock
+
+    -- Andreas: what happens if I cut out the eta expansion here?
+    -- Answer: Triggers issue 245, does not resolve 348
+    (mb',nb') <- do
+      mb' <- etaExpandBlocked =<< reduceB m
+      nb' <- etaExpandBlocked =<< reduceB n
+      return (mb', nb')
+    let blocker = unblockOnEither (getBlocker mb') (getBlocker nb')
+    reportSLn "tc.conv.atom.size" 50 $ "term size after reduce: " ++ show (termSize $ ignoreBlocking mb', termSize $ ignoreBlocking nb')
+
+    -- constructorForm changes literal to constructors
+    -- only needed if the other side is not a literal
+    (mb'', nb'') <- case (ignoreBlocking mb', ignoreBlocking nb') of
+      (Lit _, Lit _) -> return (mb', nb')
+      _ -> (,) <$> traverse constructorForm mb'
+               <*> traverse constructorForm nb'
+
+    mb <- traverse unLevel mb''
+    nb <- traverse unLevel nb''
+
+    cmpBlocked <- viewTC eCompareBlocked
+
+    let m = ignoreBlocking mb
+        n = ignoreBlocking nb
+
+        checkDefinitionalEquality = unlessM (pureCompareAs CmpEq t m n) notEqual
+
+        notEqual = typeError $ UnequalTerms cmp m n t
+
+        dir = fromCmp cmp
+        rid = flipCmp dir     -- The reverse direction.  Bad name, I know.
+
+        assign dir x es v = assignE dir x es v t $ compareAtomDir dir t
+
+    reportSDoc "tc.conv.atom" 30 $
+      "compareAtom" <+> fsep [ prettyTCM mb <+> prettyTCM cmp
+                             , prettyTCM nb
+                             , prettyTCM t
+                             ]
+    reportSDoc "tc.conv.atom" 80 $
+      "compareAtom" <+> fsep [ pretty mb <+> prettyTCM cmp
+                                  , pretty nb
+                                  , ":" <+> pretty t ]
+    case (mb, nb) of
+      -- equate two metas x and y.  if y is the younger meta,
+      -- try first y := x and then x := y
+      _ | MetaV x xArgs <- ignoreBlocking mb,   -- Can be either Blocked or NotBlocked depending on
+          MetaV y yArgs <- ignoreBlocking nb -> -- envCompareBlocked check above.
+        compareMetas cmp t x xArgs y yArgs
+
+      -- one side a meta
+      _ | MetaV x es <- ignoreBlocking mb -> assign dir x es n
+      _ | MetaV x es <- ignoreBlocking nb -> assign rid x es m
+      (Blocked{}, Blocked{}) | not cmpBlocked  -> checkDefinitionalEquality
+      (Blocked b _, _) | not cmpBlocked -> useInjectivity (fromCmp cmp) b t m n   -- The blocked term  goes first
+      (_, Blocked b _) | not cmpBlocked -> useInjectivity (flipCmp $ fromCmp cmp) b t n m
+      bs -> do
+        blockOnError blocker $ do
+        -- -- Andreas, 2013-10-20 put projection-like function
+        -- -- into the spine, to make compareElims work.
+        -- -- 'False' means: leave (Def f []) unchanged even for
+        -- -- proj-like funs.
+        -- m <- elimView False m
+        -- n <- elimView False n
+        -- Andreas, 2015-07-01, actually, don't put them into the spine.
+        -- Polarity cannot be communicated properly if projection-like
+        -- functions are post-fix.
+        case (m, n) of
+          (Pi{}, Pi{}) -> equalFun m n
+
+          (Sort s1, Sort s2) ->
+            ifM (optCumulativity <$> pragmaOptions)
+              (compareSort cmp s1 s2)
+              (equalSort s1 s2)
+
+          (Lit l1, Lit l2) | l1 == l2 -> return ()
+          (Var i es, Var i' es') | i == i' -> do
+              a <- typeOfBV i
+              -- Variables are invariant in their arguments
+              compareElims [] [] a (var i) es es'
+
+          -- The case of definition application:
+          (Def f es, Def f' es') -> do
+
+              -- 1. All absurd lambdas are equal.
+              unlessM (bothAbsurd f f') $ do
+
+              -- 2. If the heads are unequal, the only chance is subtyping between SIZE and SIZELT.
+              if f /= f' then trySizeUniv cmp t m n f es f' es' else do
+
+              -- 3. If the heads are equal:
+              -- 3a. If there are no arguments, we are done.
+              unless (null es && null es') $ do
+
+              -- 3b. If some cubical magic kicks in, we are done.
+              unlessM (compareEtaPrims f es es') $ do
+
+              -- 3c. Oh no, we actually have to work and compare the eliminations!
+               a <- computeElimHeadType f es es'
+               -- The polarity vector of projection-like functions
+               -- does not include the parameters.
+               pol <- getPolarity' cmp f
+               compareElims pol [] a (Def f []) es es'
+
+          -- Due to eta-expansion, these constructors are fully applied.
+          (Con x ci xArgs, Con y _ yArgs)
+              | x == y -> do
+                  -- Get the type of the constructor instantiated to the datatype parameters.
+                  a' <- case t of
+                    AsTermsOf a -> conType x a
+                    AsSizes   -> __IMPOSSIBLE__
+                    AsTypes   -> __IMPOSSIBLE__
+                  forcedArgs <- getForcedArgs $ conName x
+                  -- Constructors are covariant in their arguments
+                  -- (see test/succeed/CovariantConstructors).
+                  compareElims (repeat $ polFromCmp cmp) forcedArgs a' (Con x ci []) xArgs yArgs
+          _ -> notEqual
+    where
+        -- returns True in case we handled the comparison already.
+        compareEtaPrims :: MonadConversion m => QName -> Elims -> Elims -> m Bool
+        compareEtaPrims q es es' = do
+          munglue <- getPrimitiveName' builtin_unglue
+          munglueU <- getPrimitiveName' builtin_unglueU
+          msubout <- getPrimitiveName' builtinSubOut
+          case () of
+            _ | Just q == munglue -> compareUnglueApp q es es'
+            _ | Just q == munglueU -> compareUnglueUApp q es es'
+            _ | Just q == msubout -> compareSubApp q es es'
+            _                     -> return False
+        compareSubApp q es es' = do
+          let (as,bs) = splitAt 5 es; (as',bs') = splitAt 5 es'
+          case (allApplyElims as, allApplyElims as') of
+            (Just [a,bA,phi,u,x], Just [a',bA',phi',u',x']) -> do
+              tSub <- primSub
+              -- Andrea, 28-07-16:
+              -- comparing the types is most probably wasteful,
+              -- since b and b' should be neutral terms, but it's a
+              -- precondition for the compareAtom call to make
+              -- sense.
+              equalType (El (tmSSort $ unArg a) $ apply tSub $ a : map (setHiding NotHidden) [bA,phi,u])
+                        (El (tmSSort $ unArg a) $ apply tSub $ a : map (setHiding NotHidden) [bA',phi',u'])
+              compareAtom cmp (AsTermsOf $ El (tmSSort $ unArg a) $ apply tSub $ a : map (setHiding NotHidden) [bA,phi,u])
+                              (unArg x) (unArg x')
+              compareElims [] [] (El (tmSort (unArg a)) (unArg bA)) (Def q as) bs bs'
+              return True
+            _  -> return False
+        compareUnglueApp q es es' = do
+          let (as,bs) = splitAt 7 es; (as',bs') = splitAt 7 es'
+          case (allApplyElims as, allApplyElims as') of
+            (Just [la,lb,bA,phi,bT,e,b], Just [la',lb',bA',phi',bT',e',b']) -> do
+              tGlue <- getPrimitiveTerm builtinGlue
+              -- Andrea, 28-07-16:
+              -- comparing the types is most probably wasteful,
+              -- since b and b' should be neutral terms, but it's a
+              -- precondition for the compareAtom call to make
+              -- sense.
+              -- equalType (El (tmSort (unArg lb)) $ apply tGlue $ [la,lb] ++ map (setHiding NotHidden) [bA,phi,bT,e])
+              --           (El (tmSort (unArg lb')) $ apply tGlue $ [la',lb'] ++ map (setHiding NotHidden) [bA',phi',bT',e'])
+              compareAtom cmp (AsTermsOf $ El (tmSort (unArg lb)) $ apply tGlue $ [la,lb] ++ map (setHiding NotHidden) [bA,phi,bT,e])
+                              (unArg b) (unArg b')
+              compareElims [] [] (El (tmSort (unArg la)) (unArg bA)) (Def q as) bs bs'
+              return True
+            _  -> return False
+        compareUnglueUApp :: MonadConversion m => QName -> Elims -> Elims -> m Bool
+        compareUnglueUApp q es es' = do
+          let (as,bs) = splitAt 5 es; (as',bs') = splitAt 5 es'
+          case (allApplyElims as, allApplyElims as') of
+            (Just [la,phi,bT,bAS,b], Just [la',phi',bT',bA',b']) -> do
+              tHComp <- primHComp
+              tLSuc <- primLevelSuc
+              tSubOut <- primSubOut
+              iz <- primIZero
+              let lsuc t = tLSuc `apply` [argN t]
+                  s = tmSort $ unArg la
+                  sucla = lsuc <$> la
+              bA <- runNamesT [] $ do
+                [la,phi,bT,bAS] <- mapM (open . unArg) [la,phi,bT,bAS]
+                (pure tSubOut <#> (pure tLSuc <@> la) <#> (Sort . tmSort <$> la) <#> phi <#> (bT <@> primIZero) <@> bAS)
+              compareAtom cmp (AsTermsOf $ El (tmSort . unArg $ sucla) $ apply tHComp $ [sucla, argH (Sort s), phi] ++ [argH (unArg bT), argH bA])
+                              (unArg b) (unArg b')
+              compareElims [] [] (El s bA) (Def q as) bs bs'
+              return True
+            _  -> return False
+        -- Andreas, 2013-05-15 due to new postponement strategy, type can now be blocked
+        conType c t = do
+          t <- abortIfBlocked t
+          let impossible = do
+                reportSDoc "impossible" 10 $
+                  "expected data/record type, found " <+> prettyTCM t
+                reportSDoc "impossible" 70 $ nest 2 $ "raw =" <+> pretty t
+                -- __IMPOSSIBLE__
+                -- Andreas, 2013-10-20:  in case termination checking fails
+                -- we might get some unreduced types here.
+                -- In issue 921, this happens during the final attempt
+                -- to solve left-over constraints.
+                -- Thus, instead of crashing, just give up gracefully.
+                patternViolation neverUnblock
+          maybe impossible (return . snd) =<< getFullyAppliedConType c t
+        equalFun t1 t2 = case (t1, t2) of
+          (Pi dom1 b1, Pi dom2 b2) -> do
+            verboseBracket "tc.conv.fun" 15 "compare function types" $ do
+              reportSDoc "tc.conv.fun" 20 $ nest 2 $ vcat
+                [ "t1 =" <+> prettyTCM t1
+                , "t2 =" <+> prettyTCM t2
+                ]
+              compareDom cmp dom2 dom1 b1 b2 errH errR errQ errC errF $
+                compareType cmp (absBody b1) (absBody b2)
+            where
+            errH = typeError $ UnequalHiding t1 t2
+            errR = typeError $ UnequalRelevance cmp t1 t2
+            errQ = typeError $ UnequalQuantity  cmp t1 t2
+            errC = typeError $ UnequalCohesion cmp t1 t2
+            errF = typeError $ UnequalFiniteness cmp t1 t2
+          _ -> __IMPOSSIBLE__
+
+-- | Check whether @x xArgs `cmp` y yArgs@
+compareMetas :: MonadConversion m => Comparison -> CompareAs -> MetaId -> Elims -> MetaId -> Elims -> m ()
+compareMetas cmp t x xArgs y yArgs | x == y = blockOnError (unblockOnMeta x) $ do
+  cmpBlocked <- viewTC eCompareBlocked
+  let ok    = return ()
+      notOk = patternViolation neverUnblock
+      fallback = do
+        -- Fallback: check definitional equality
+        a <- metaType x
+        runPureConversion (compareElims [] [] a (MetaV x []) xArgs yArgs) >>= \case
+          Just{}  -> ok
+          Nothing -> notOk
+  if | cmpBlocked -> do
+         a <- metaType x
+         compareElims [] [] a (MetaV x []) xArgs yArgs
+     | otherwise -> case intersectVars xArgs yArgs of
+         -- all relevant arguments are variables
+         Just kills -> do
+           -- kills is a list with 'True' for each different var
+           killResult <- killArgs kills x
+           case killResult of
+             NothingToPrune   -> ok
+             PrunedEverything -> ok
+             PrunedNothing    -> fallback
+             PrunedSomething  -> fallback
+         -- not all relevant arguments are variables
+         Nothing -> fallback
+compareMetas cmp t x xArgs y yArgs = do
+  [p1, p2] <- mapM getMetaPriority [x,y]
+  let dir = fromCmp cmp
+      rid = flipCmp dir     -- The reverse direction.  Bad name, I know.
+      retry = patternViolation alwaysUnblock
+  -- First try the one with the highest priority. If that doesn't
+  -- work, try the low priority one.
+  let (solve1, solve2)
+        | (p1, x) > (p2, y) = (l1, r2)
+        | otherwise         = (r1, l2)
+        where l1 = assignE dir x xArgs (MetaV y yArgs) t $ \ _ _ -> retry
+              r1 = assignE rid y yArgs (MetaV x xArgs) t $ \ _ _ -> retry
+              -- Careful: the first attempt might prune the low
+              -- priority meta! (Issue #2978)
+              l2 = ifM (isInstantiatedMeta x) retry l1
+              r2 = ifM (isInstantiatedMeta y) retry r1
+
+  -- Unblock on both unblockers of solve1 and solve2
+  catchPatternErr (`addOrUnblocker` solve2) solve1
+
+-- | Check whether @a1 `cmp` a2@ and continue in context extended by @a1@.
+compareDom :: (MonadConversion m , Free c)
+  => Comparison -- ^ @cmp@ The comparison direction
+  -> Dom Type   -- ^ @a1@  The smaller domain.
+  -> Dom Type   -- ^ @a2@  The other domain.
+  -> Abs b      -- ^ @b1@  The smaller codomain.
+  -> Abs c      -- ^ @b2@  The bigger codomain.
+  -> m ()     -- ^ Continuation if mismatch in 'Hiding'.
+  -> m ()     -- ^ Continuation if mismatch in 'Relevance'.
+  -> m ()     -- ^ Continuation if mismatch in 'Quantity'.
+  -> m ()     -- ^ Continuation if mismatch in 'Cohesion'.
+  -> m ()     -- ^ Continuation if mismatch in 'annFinite'.
+  -> m ()     -- ^ Continuation if comparison is successful.
+  -> m ()
+compareDom cmp0
+  dom1@(Dom{domInfo = i1, unDom = a1})
+  dom2@(Dom{domInfo = i2, unDom = a2})
+  b1 b2 errH errR errQ errC errF cont = do
+  if | not $ sameHiding dom1 dom2 -> errH
+     | not $ (==)         (getRelevance dom1) (getRelevance dom2) -> errR
+     | not $ sameQuantity (getQuantity  dom1) (getQuantity  dom2) -> errQ
+     | not $ sameCohesion (getCohesion  dom1) (getCohesion  dom2) -> errC
+     | not $ domIsFinite dom1 == domIsFinite dom2 -> errF
+     | otherwise -> do
+      let r = max (getRelevance dom1) (getRelevance dom2)
+              -- take "most irrelevant"
+          dependent = (r /= Irrelevant) && isBinderUsed b2
+      pid <- newProblem_ $ compareType cmp0 a1 a2
+      dom <- if dependent
+             then (\ a -> dom1 {unDom = a}) <$> blockTypeOnProblem a1 pid
+             else return dom1
+        -- We only need to require a1 == a2 if b2 is dependent
+        -- If it's non-dependent it doesn't matter what we add to the context.
+      let name = suggests [ Suggestion b1 , Suggestion b2 ]
+      addContext (name, dom) $ cont
+      stealConstraints pid
+        -- Andreas, 2013-05-15 Now, comparison of codomains is not
+        -- blocked any more by getting stuck on domains.
+        -- Only the domain type in context will be blocked.
+        -- But see issue #1258.
+
+-- | When comparing argument spines (in compareElims) where the first arguments
+--   don't match, we keep going, substituting the anti-unification of the two
+--   terms in the telescope. More precisely:
+--
+--  @@
+--    (u = v : A)[pid]   w = antiUnify pid A u v   us = vs : Δ[w/x]
+--    -------------------------------------------------------------
+--                    u us = v vs : (x : A) Δ
+--  @@
+--
+--   The simplest case of anti-unification is to return a fresh metavariable
+--   (created by blockTermOnProblem), but if there's shared structure between
+--   the two terms we can expose that.
+--
+--   This is really a crutch that lets us get away with things that otherwise
+--   would require heterogenous conversion checking. See for instance issue
+--   #2384.
+antiUnify :: MonadConversion m => ProblemId -> Type -> Term -> Term -> m Term
+antiUnify pid a u v = do
+  SynEq.checkSyntacticEquality u v (\u _ -> return u) $ \u v -> do
+  (u, v) <- reduce (u, v)
+  reportSDoc "tc.conv.antiUnify" 30 $ vcat
+    [ "antiUnify"
+    , "a =" <+> prettyTCM a
+    , "u =" <+> prettyTCM u
+    , "v =" <+> prettyTCM v
+    ]
+  case (u, v) of
+    (Pi ua ub, Pi va vb) -> do
+      wa0 <- antiUnifyType pid (unDom ua) (unDom va)
+      let wa = wa0 <$ ua
+      wb <- addContext wa $ antiUnifyType pid (absBody ub) (absBody vb)
+      return $ Pi wa (mkAbs (absName ub) wb)
+    (Lam i u, Lam _ v) ->
+      reduce (unEl a) >>= \case
+        Pi a b -> Lam i . (mkAbs (absName u)) <$> addContext a (antiUnify pid (absBody b) (absBody u) (absBody v))
+        _      -> fallback
+    (Var i us, Var j vs) | i == j -> maybeGiveUp $ do
+      a <- typeOfBV i
+      antiUnifyElims pid a (var i) us vs
+    -- Andreas, 2017-07-27:
+    -- It seems that nothing guarantees here that the constructors are fully
+    -- applied!?  Thus, @a@ could be a function type and we need the robust
+    -- @getConType@ here.
+    -- (Note that @patternViolation@ swallows exceptions coming from @getConType@
+    -- thus, we would not see clearly if we used @getFullyAppliedConType@ instead.)
+    (Con x ci us, Con y _ vs) | x == y -> maybeGiveUp $ do
+      a <- maybe abort (return . snd) =<< getConType x a
+      antiUnifyElims pid a (Con x ci []) us vs
+    (Def f [], Def g []) | f == g -> return (Def f [])
+    (Def f us, Def g vs) | f == g, length us == length vs -> maybeGiveUp $ do
+      a <- computeElimHeadType f us vs
+      antiUnifyElims pid a (Def f []) us vs
+    _ -> fallback
+  where
+    maybeGiveUp = catchPatternErr $ \ _ -> fallback
+    abort = patternViolation neverUnblock -- caught by maybeGiveUp
+    fallback = blockTermOnProblem a u pid
+
+antiUnifyArgs :: MonadConversion m => ProblemId -> Dom Type -> Arg Term -> Arg Term -> m (Arg Term)
+antiUnifyArgs pid dom u v
+  | not (sameModality (getModality u) (getModality v))
+              = patternViolation neverUnblock
+  | otherwise = applyModalityToContext u $
+    ifM (isIrrelevantOrPropM dom)
+    {-then-} (return u)
+    {-else-} ((<$ u) <$> antiUnify pid (unDom dom) (unArg u) (unArg v))
+
+antiUnifyType :: MonadConversion m => ProblemId -> Type -> Type -> m Type
+antiUnifyType pid (El s a) (El _ b) = workOnTypes $ El s <$> antiUnify pid (sort s) a b
+
+antiUnifyElims :: MonadConversion m => ProblemId -> Type -> Term -> Elims -> Elims -> m Term
+antiUnifyElims pid a self [] [] = return self
+antiUnifyElims pid a self (Proj o f : es1) (Proj _ g : es2) | f == g = do
+  res <- projectTyped self a o f
+  case res of
+    Just (_, self, a) -> antiUnifyElims pid a self es1 es2
+    Nothing -> patternViolation neverUnblock -- can fail for projection like
+antiUnifyElims pid a self (Apply u : es1) (Apply v : es2) = do
+  reduce (unEl a) >>= \case
+    Pi a b -> do
+      w <- antiUnifyArgs pid a u v
+      antiUnifyElims pid (b `lazyAbsApp` unArg w) (apply self [w]) es1 es2
+    _ -> patternViolation neverUnblock
+antiUnifyElims _ _ _ _ _ = patternViolation neverUnblock -- trigger maybeGiveUp in antiUnify
+
+-- | @compareElims pols a v els1 els2@ performs type-directed equality on eliminator spines.
+--   @t@ is the type of the head @v@.
+compareElims :: forall m. MonadConversion m => [Polarity] -> [IsForced] -> Type -> Term -> [Elim] -> [Elim] -> m ()
+compareElims pols0 fors0 a v els01 els02 =
+  verboseBracket "tc.conv.elim" 20 "compareElims" $
+  (catchConstraint (ElimCmp pols0 fors0 a v els01 els02) :: m () -> m ()) $ do
+  let v1 = applyE v els01
+      v2 = applyE v els02
+      failure = typeError $ UnequalTerms CmpEq v1 v2 (AsTermsOf a)
+        -- Andreas, 2013-03-15 since one of the spines is empty, @a@
+        -- is the correct type here.
+  unless (null els01) $ do
+    reportSDoc "tc.conv.elim" 25 $ "compareElims" $$ do
+     nest 2 $ vcat
+      [ "a     =" <+> prettyTCM a
+      , "pols0 (truncated to 10) =" <+> hsep (map prettyTCM $ take 10 pols0)
+      , "fors0 (truncated to 10) =" <+> hsep (map prettyTCM $ take 10 fors0)
+      , "v     =" <+> prettyTCM v
+      , "els01 =" <+> prettyTCM els01
+      , "els02 =" <+> prettyTCM els02
+      ]
+  case (els01, els02) of
+    ([]         , []         ) -> return ()
+    ([]         , Proj{}:_   ) -> failure -- not impossible, see issue 821
+    (Proj{}  : _, []         ) -> failure -- could be x.p =?= x for projection p
+    ([]         , Apply{} : _) -> failure -- not impossible, see issue 878
+    (Apply{} : _, []         ) -> failure
+    ([]         , IApply{} : _) -> failure
+    (IApply{} : _, []         ) -> failure
+    (Apply{} : _, Proj{}  : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True -- NB: popped up in issue 889
+    (Proj{}  : _, Apply{} : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True -- but should be impossible (but again in issue 1467)
+    (IApply{} : _, Proj{}  : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True
+    (Proj{}  : _, IApply{} : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True
+    (IApply{} : _, Apply{}  : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True
+    (Apply{}  : _, IApply{} : _) -> __IMPOSSIBLE__ <$ solveAwakeConstraints' True
+    (e@(IApply x1 y1 r1) : els1, IApply x2 y2 r2 : els2) -> do
+      reportSDoc "tc.conv.elim" 25 $ "compareElims IApply"
+       -- Andrea: copying stuff from the Apply case..
+      let (pol, pols) = nextPolarity pols0
+      a  <- abortIfBlocked a
+      va <- pathView a
+      reportSDoc "tc.conv.elim.iapply" 60 $ "compareElims IApply" $$ do
+        nest 2 $ "va =" <+> text (show (isPathType va))
+      case va of
+        PathType s path l bA x y -> do
+          b <- primIntervalType
+          compareWithPol pol (flip compareTerm b)
+                              r1 r2
+          -- TODO: compare (x1,x2) and (y1,y2) ?
+          let r = r1 -- TODO Andrea:  do blocking
+          codom <- el' (pure . unArg $ l) ((pure . unArg $ bA) <@> pure r)
+          compareElims pols [] codom -- Path non-dependent (codom `lazyAbsApp` unArg arg)
+                            (applyE v [e]) els1 els2
+        -- We allow for functions (i : I) -> ... to also be heads of a IApply,
+        -- because @etaContract@ can produce such terms
+        OType t@(El _ Pi{}) -> compareElims pols0 fors0 t v (Apply (defaultArg r1) : els1) (Apply (defaultArg r2) : els2)
+
+        OType t -> patternViolation (unblockOnAnyMetaIn t) -- Can we get here? We know a is not blocked.
+
+    (Apply arg1 : els1, Apply arg2 : els2) ->
+      (verboseBracket "tc.conv.elim" 20 "compare Apply" :: m () -> m ()) $ do
+      reportSDoc "tc.conv.elim" 10 $ nest 2 $ vcat
+        [ "a    =" <+> prettyTCM a
+        , "v    =" <+> prettyTCM v
+        , "arg1 =" <+> prettyTCM arg1
+        , "arg2 =" <+> prettyTCM arg2
+        ]
+      reportSDoc "tc.conv.elim" 50 $ nest 2 $ vcat
+        [ "raw:"
+        , "a    =" <+> pretty a
+        , "v    =" <+> pretty v
+        , "arg1 =" <+> pretty arg1
+        , "arg2 =" <+> pretty arg2
+        ]
+      let (pol, pols) = nextPolarity pols0
+          (for, fors) = nextIsForced fors0
+      a <- abortIfBlocked a
+      reportSLn "tc.conv.elim" 40 $ "type is not blocked"
+      case unEl a of
+        (Pi (Dom{domInfo = info, unDom = b}) codom) -> do
+          reportSLn "tc.conv.elim" 40 $ "type is a function type"
+          mlvl <- tryMaybe primLevel
+          let freeInCoDom (Abs _ c) = 0 `freeInIgnoringSorts` c
+              freeInCoDom _         = False
+              dependent = (Just (unEl b) /= mlvl) && freeInCoDom codom
+                -- Level-polymorphism (x : Level) -> ... does not count as dependency here
+                   -- NB: we could drop the free variable test and still be sound.
+                   -- It is a trade-off between the administrative effort of
+                   -- creating a blocking and traversing a term for free variables.
+                   -- Apparently, it is believed that checking free vars is cheaper.
+                   -- Andreas, 2013-05-15
+
+-- NEW, Andreas, 2013-05-15
+
+          -- compare arg1 and arg2
+          pid <- newProblem_ $ applyModalityToContext info $
+              if isForced for then
+                reportSLn "tc.conv.elim" 40 $ "argument is forced"
+              else if isIrrelevant info then do
+                reportSLn "tc.conv.elim" 40 $ "argument is irrelevant"
+                compareIrrelevant b (unArg arg1) (unArg arg2)
+              else do
+                reportSLn "tc.conv.elim" 40 $ "argument has polarity " ++ show pol
+                compareWithPol pol (flip compareTerm b)
+                  (unArg arg1) (unArg arg2)
+          -- if comparison got stuck and function type is dependent, block arg
+          solved <- isProblemSolved pid
+          reportSLn "tc.conv.elim" 40 $ "solved = " ++ show solved
+          arg <- if dependent && not solved
+                 then applyModalityToContext info $ do
+                  reportSDoc "tc.conv.elims" 50 $ vcat $
+                    [ "Trying antiUnify:"
+                    , nest 2 $ "b    =" <+> prettyTCM b
+                    , nest 2 $ "arg1 =" <+> prettyTCM arg1
+                    , nest 2 $ "arg2 =" <+> prettyTCM arg2
+                    ]
+                  arg <- (arg1 $>) <$> antiUnify pid b (unArg arg1) (unArg arg2)
+                  reportSDoc "tc.conv.elims" 50 $ hang "Anti-unification:" 2 (prettyTCM arg)
+                  reportSDoc "tc.conv.elims" 70 $ nest 2 $ "raw:" <+> pretty arg
+                  return arg
+                 else return arg1
+          -- continue, possibly with blocked instantiation
+          compareElims pols fors (codom `lazyAbsApp` unArg arg) (apply v [arg]) els1 els2
+          -- any left over constraints of arg are associated to the comparison
+          reportSLn "tc.conv.elim" 40 $ "stealing constraints from problem " ++ show pid
+          stealConstraints pid
+          {- Stealing solves this issue:
+
+             Does not create enough blocked tc-problems,
+             see test/fail/DontPrune.
+             (There are remaining problems which do not show up as yellow.)
+             Need to find a way to associate pid also to result of compareElims.
+          -}
+        a -> do
+          reportSDoc "impossible" 10 $
+            "unexpected type when comparing apply eliminations " <+> prettyTCM a
+          reportSDoc "impossible" 50 $ "raw type:" <+> pretty a
+          patternViolation (unblockOnAnyMetaIn a)
+          -- Andreas, 2013-10-22
+          -- in case of disabled reductions (due to failing termination check)
+          -- we might get stuck, so do not crash, but fail gently.
+          -- __IMPOSSIBLE__
+
+    -- case: f == f' are projections
+    (Proj o f : els1, Proj _ f' : els2)
+      | f /= f'   -> typeError $ MismatchedProjectionsError f f'
+      | otherwise -> do
+        a   <- abortIfBlocked a
+        res <- projectTyped v a o f -- fails only if f is proj.like but parameters cannot be retrieved
+        case res of
+          Just (_, u, t) -> do
+            -- Andreas, 2015-07-01:
+            -- The arguments following the principal argument of a projection
+            -- are invariant.  (At least as long as we have no explicit polarity
+            -- annotations.)
+            compareElims [] [] t u els1 els2
+          Nothing -> do
+            reportSDoc "tc.conv.elims" 30 $ sep
+              [ text $ "projection " ++ prettyShow f
+              , text   "applied to value " <+> prettyTCM v
+              , text   "of unexpected type " <+> prettyTCM a
+              ]
+            patternViolation (unblockOnAnyMetaIn a)
+
+
+-- | "Compare" two terms in irrelevant position.  This always succeeds.
+--   However, we can dig for solutions of irrelevant metas in the
+--   terms we compare.
+--   (Certainly not the systematic solution, that'd be proof search...)
+compareIrrelevant :: MonadConversion m => Type -> Term -> Term -> m ()
+{- 2012-04-02 DontCare no longer present
+compareIrrelevant t (DontCare v) w = compareIrrelevant t v w
+compareIrrelevant t v (DontCare w) = compareIrrelevant t v w
+-}
+compareIrrelevant t v0 w0 = do
+  let v = stripDontCare v0
+      w = stripDontCare w0
+  reportSDoc "tc.conv.irr" 20 $ vcat
+    [ "compareIrrelevant"
+    , nest 2 $ "v =" <+> prettyTCM v
+    , nest 2 $ "w =" <+> prettyTCM w
+    ]
+  reportSDoc "tc.conv.irr" 50 $ vcat
+    [ nest 2 $ "v =" <+> pretty v
+    , nest 2 $ "w =" <+> pretty w
+    ]
+  whenProfile Profile.Conversion $ tick "compare irrelevant"
+  try v w $ try w v $ return ()
+  where
+    try (MetaV x es) w fallback = do
+      mi <- lookupMetaInstantiation x
+      mm <- lookupMetaModality x
+      let rel  = getRelevance mm
+          inst = case mi of
+                   InstV{} -> True
+                   _       -> False
+      reportSDoc "tc.conv.irr" 20 $ vcat
+        [ nest 2 $ text $ "rel  = " ++ show rel
+        , nest 2 $ "inst =" <+> pretty inst
+        ]
+      if not (isIrrelevant rel) || inst
+        then fallback
+        -- Andreas, 2016-08-08, issue #2131:
+        -- Mining for solutions for irrelevant metas is not definite.
+        -- Thus, in case of error, leave meta unsolved.
+        else assignE DirEq x es w (AsTermsOf t) (compareIrrelevant t) `catchError` \ _ -> fallback
+        -- the value of irrelevant or unused meta does not matter
+    try v w fallback = fallback
+
+compareWithPol :: MonadConversion m => Polarity -> (Comparison -> a -> a -> m ()) -> a -> a -> m ()
+compareWithPol Invariant     cmp x y = cmp CmpEq x y
+compareWithPol Covariant     cmp x y = cmp CmpLeq x y
+compareWithPol Contravariant cmp x y = cmp CmpLeq y x
+compareWithPol Nonvariant    cmp x y = return ()
+
+polFromCmp :: Comparison -> Polarity
+polFromCmp CmpLeq = Covariant
+polFromCmp CmpEq  = Invariant
+
+-- | Type-directed equality on argument lists
+--
+compareArgs :: MonadConversion m => [Polarity] -> [IsForced] -> Type -> Term -> Args -> Args -> m ()
+compareArgs pol for a v args1 args2 =
+  compareElims pol for a v (map Apply args1) (map Apply args2)
+
+---------------------------------------------------------------------------
+-- * Types
+---------------------------------------------------------------------------
+
+{-# SPECIALIZE compareType :: Comparison -> Type -> Type -> TCM () #-}
+-- | Equality on Types
+compareType :: MonadConversion m => Comparison -> Type -> Type -> m ()
+compareType cmp ty1@(El s1 a1) ty2@(El s2 a2) =
+    workOnTypes $
+    verboseBracket "tc.conv.type" 20 "compareType" $ do
+        reportSDoc "tc.conv.type" 50 $ vcat
+          [ "compareType" <+> sep [ prettyTCM ty1 <+> prettyTCM cmp
+                                       , prettyTCM ty2 ]
+          , hsep [ "   sorts:", prettyTCM s1, " and ", prettyTCM s2 ]
+          ]
+        compareAs cmp AsTypes a1 a2
+
+leqType :: MonadConversion m => Type -> Type -> m ()
+leqType = compareType CmpLeq
+
+{-# SPECIALIZE coerce :: Comparison -> Term -> Type -> Type -> TCM Term #-}
+-- | @coerce v a b@ coerces @v : a@ to type @b@, returning a @v' : b@
+--   with maybe extra hidden applications or hidden abstractions.
+--
+--   In principle, this function can host coercive subtyping, but
+--   currently it only tries to fix problems with hidden function types.
+--
+coerce :: (MonadConversion m, MonadTCM m) => Comparison -> Term -> Type -> Type -> m Term
+coerce cmp v t1 t2 = blockTerm t2 $ do
+  verboseS "tc.conv.coerce" 10 $ do
+    (a1,a2) <- reify (t1,t2)
+    let dbglvl = 30
+    reportSDoc "tc.conv.coerce" dbglvl $
+      "coerce" <+> vcat
+        [ "term      v  =" <+> prettyTCM v
+        , "from type t1 =" <+> prettyTCM a1
+        , "to type   t2 =" <+> prettyTCM a2
+        , "comparison   =" <+> prettyTCM cmp
+        ]
+    reportSDoc "tc.conv.coerce" 70 $
+      "coerce" <+> vcat
+        [ "term      v  =" <+> pretty v
+        , "from type t1 =" <+> pretty t1
+        , "to type   t2 =" <+> pretty t2
+        , "comparison   =" <+> pretty cmp
+        ]
+  -- v <$ do workOnTypes $ leqType t1 t2
+  -- take off hidden/instance domains from t1 and t2
+  TelV tel1 b1 <- telViewUpTo' (-1) notVisible t1
+  TelV tel2 b2 <- telViewUpTo' (-1) notVisible t2
+  let n = size tel1 - size tel2
+  -- the crude solution would be
+  --   v' = λ {tel2} → v {tel1}
+  -- however, that may introduce unneccessary many function types
+  -- If n  > 0 and b2 is not blocked, it is safe to
+  -- insert n many hidden args
+  if n <= 0 then fallback else do
+    ifBlocked b2 (\ _ _ -> fallback) $ \ _ _ -> do
+      (args, t1') <- implicitArgs n notVisible t1
+      let v' = v `apply` args
+      v' <$ coerceSize (compareType cmp) v' t1' t2
+  where
+    fallback = v <$ coerceSize (compareType cmp) v t1 t2
+
+{-# SPECIALIZE coerceSize :: (Type -> Type -> TCM ()) -> Term -> Type -> Type -> TCM () #-}
+-- | Account for situations like @k : (Size< j) <= (Size< k + 1)@
+--
+--   Actually, the semantics is
+--   @(Size<= k) ∩ (Size< j) ⊆ rhs@
+--   which gives a disjunctive constraint.  Mmmh, looks like stuff
+--   TODO.
+--
+--   For now, we do a cheap heuristics.
+--
+coerceSize :: MonadConversion m => (Type -> Type -> m ()) -> Term -> Type -> Type -> m ()
+coerceSize leqType v t1 t2 = verboseBracket "tc.conv.size.coerce" 45 "coerceSize" $
+  workOnTypes $ do
+    reportSDoc "tc.conv.size.coerce" 70 $
+      "coerceSize" <+> vcat
+        [ "term      v  =" <+> pretty v
+        , "from type t1 =" <+> pretty t1
+        , "to type   t2 =" <+> pretty t2
+        ]
+    let fallback = leqType t1 t2
+        done = caseMaybeM (isSizeType =<< reduce t1) fallback $ \ _ -> return ()
+    -- Andreas, 2015-07-22, Issue 1615:
+    -- If t1 is a meta and t2 a type like Size< v2, we need to make sure we do not miss
+    -- the constraint v < v2!
+    caseMaybeM (isSizeType =<< reduce t2) fallback $ \ b2 -> do
+      -- Andreas, 2017-01-20, issue #2329:
+      -- If v is not a size suitable for the solver, like a neutral term,
+      -- we can only rely on the type.
+      mv <- sizeMaxView v
+      if any (\case{ DOtherSize{} -> True; _ -> False }) mv then fallback else do
+      -- Andreas, 2015-02-11 do not instantiate metas here (triggers issue 1203).
+      unlessM (tryConversion $ dontAssignMetas $ leqType t1 t2) $ do
+        -- A (most probably weaker) alternative is to just check syn.eq.
+        -- ifM (snd <$> checkSyntacticEquality t1 t2) (return v) $ {- else -} do
+        reportSDoc "tc.conv.size.coerce" 20 $ "coercing to a size type"
+        case b2 of
+          -- @t2 = Size@.  We are done!
+          BoundedNo -> done
+          -- @t2 = Size< v2@
+          BoundedLt v2 -> do
+            sv2 <- sizeView v2
+            case sv2 of
+              SizeInf     -> done
+              OtherSize{} -> do
+                -- Andreas, 2014-06-16:
+                -- Issue 1203: For now, just treat v < v2 as suc v <= v2
+                -- TODO: Need proper < comparison
+                vinc <- sizeSuc 1 v
+                compareSizes CmpLeq vinc v2
+                done
+              -- @v2 = a2 + 1@: In this case, we can try @v <= a2@
+              SizeSuc a2 -> do
+                compareSizes CmpLeq v a2
+                done  -- to pass Issue 1136
+
+---------------------------------------------------------------------------
+-- * Sorts and levels
+---------------------------------------------------------------------------
+
+compareLevel :: MonadConversion m => Comparison -> Level -> Level -> m ()
+compareLevel CmpLeq u v = leqLevel u v
+compareLevel CmpEq  u v = equalLevel u v
+
+compareSort :: MonadConversion m => Comparison -> Sort -> Sort -> m ()
+compareSort CmpEq  = equalSort
+compareSort CmpLeq = leqSort
+
+-- | Check that the first sort is less or equal to the second.
+--
+--   We can put @SizeUniv@ below @Inf@, but otherwise, it is
+--   unrelated to the other universes.
+--
+leqSort :: forall m. MonadConversion m => Sort -> Sort -> m ()
+leqSort s1 s2 = do
+  reportSDoc "tc.conv.sort" 30 $
+    sep [ "leqSort"
+        , nest 2 $ fsep [ prettyTCM s1 <+> "=<"
+                        , prettyTCM s2 ]
+        ]
+  reportSDoc "tc.conv.sort" 60 $
+    sep [ "leqSort"
+        , nest 2 $ fsep [ pretty s1 <+> "=<"
+                        , pretty s2 ]
+        ]
+  whenProfile Profile.Conversion $ tick "compare sorts"
+
+  SynEq.checkSyntacticEquality s1 s2 (\_ _ -> return ()) $ \s1 s2 -> do
+
+    s1b <- reduceB s1
+    s2b <- reduceB s2
+
+    let (s1,s2) = (ignoreBlocking s1b , ignoreBlocking s2b)
+        blocker = unblockOnEither (getBlocker s1b) (getBlocker s2b)
+        postpone = patternViolation blocker
+
+    let postponeIfBlocked = catchPatternErr $ \blocker -> do
+          if | blocker == neverUnblock -> typeError $ NotLeqSort s1 s2
+             | otherwise -> do
+                 reportSDoc "tc.conv.sort" 30 $ vcat
+                   [ "Postponing constraint"
+                   , nest 2 $ fsep [ prettyTCM s1 <+> "=<"
+                                   , prettyTCM s2 ]
+                   ]
+                 reportSDoc "tc.conv.sort" 60 $ vcat
+                   [ "Postponing constraint"
+                   , nest 2 $ fsep [ pretty s1 <+> "=<"
+                                   , pretty s2 ]
+                   ]
+                 blocker <- updateBlocker blocker
+                 addConstraint blocker $ SortCmp CmpLeq s1 s2
+
+    propEnabled <- isPropEnabled
+    typeInTypeEnabled <- typeInType
+    omegaInOmegaEnabled <- optOmegaInOmega <$> pragmaOptions
+    let infInInf = typeInTypeEnabled || omegaInOmegaEnabled
+
+    let fvsRHS = (`IntSet.member` allFreeVars s2)
+    badRigid <- s1 `rigidVarsNotContainedIn` fvsRHS
+
+    postponeIfBlocked $ case (s1, s2) of
+      -- Andreas, 2018-09-03: crash on dummy sort
+      (DummyS s, _) -> impossibleSort s
+      (_, DummyS s) -> impossibleSort s
+
+      -- The most basic rule: @Set l =< Set l'@ iff @l =< l'@
+      -- Likewise for @Prop@
+      -- Likewise for @SSet@
+      -- @Prop l@ is below @Set l@
+      -- @Set l@ is below @SSet l@
+      -- @Prop l@ is below @SSet l@
+      (Univ u a, Univ u' b) -> if u <= u' then leqLevel a b else no
+
+      -- @Setωᵢ@ is above all small sorts
+      (Inf u m , Inf u' n) -> answer $ u <= u' && (m <= n || infInInf)
+      (Univ u _, Inf u' _) -> answer $ u <= u'
+      (Inf u _, Univ u' _) -> answer $ u == u' && typeInTypeEnabled
+
+      -- @LockUniv@, @LevelUniv@, @IntervalUniv@, @SizeUniv@, and @Prop0@ are bottom sorts.
+      -- So is @Set0@ if @Prop@ is not enabled.
+      (_       , LockUniv) -> equalSort s1 s2
+      (_       , LevelUniv) -> equalSort s1 s2
+      (_       , IntervalUniv) -> equalSort s1 s2
+      (_       , SizeUniv) -> equalSort s1 s2
+      (_       , Prop (Max 0 [])) -> equalSort s1 s2
+      (_       , Type (Max 0 []))
+        | not propEnabled  -> equalSort s1 s2
+
+      -- @SizeUniv@, @LockUniv@ and @LevelUniv@ are unrelated to any @Set l@ or @Prop l@
+      (SizeUniv, Univ{}  ) -> no
+      (SizeUniv , Inf{}  ) -> no
+      (LockUniv, Univ{}  ) -> no
+      (LockUniv , Inf{}  ) -> no
+      (LevelUniv, Univ{}  ) -> no
+      (LevelUniv , Inf{}  ) -> no
+
+      -- @IntervalUniv@ is below @SSet l@, but not @Set l@ or @Prop l@
+      (IntervalUniv, Type{}) -> no
+      (IntervalUniv, Prop{}) -> no
+      (IntervalUniv , Inf u _) -> answer $ univFibrancy u == IsStrict
+      (IntervalUniv , SSet b) -> leqLevel (ClosedLevel 0) b
+
+      -- If the first sort is a small sort that rigidly depends on a
+      -- variable and the second sort does not mention this variable,
+      -- the second sort must be at least @Setω@.
+      (_       , _       ) | Right (SmallSort f) <- sizeOfSort s1 , badRigid -> leqSort (Inf f 0) s2
+
+      -- PiSort, FunSort, UnivSort and MetaS might reduce once we instantiate
+      -- more metas, so we postpone.
+      (PiSort{}, _       ) -> postpone
+      (_       , PiSort{}) -> postpone
+      (FunSort{}, _      ) -> postpone
+      (_      , FunSort{}) -> postpone
+      (UnivSort{}, _     ) -> postpone
+      (_     , UnivSort{}) -> postpone
+      (MetaS{} , _       ) -> postpone
+      (_       , MetaS{} ) -> postpone
+
+      -- DefS are postulated sorts, so they do not reduce.
+      (DefS{} , _     ) -> no
+      (_      , DefS{}) -> no
+
+  where
+  no  = patternViolation neverUnblock
+  yes = return ()
+  answer = \case
+    True -> yes
+    False -> no
+  impossibleSort s = do
+    reportS "impossible" 10
+      [ "leqSort: found dummy sort with description:"
+      , s
+      ]
+    __IMPOSSIBLE__
+
+leqLevel :: MonadConversion m => Level -> Level -> m ()
+leqLevel a b = catchConstraint (LevelCmp CmpLeq a b) $ do
+      reportSDoc "tc.conv.level" 30 $
+        "compareLevel" <+>
+          sep [ prettyTCM a <+> "=<"
+              , prettyTCM b ]
+      whenProfile Profile.Conversion $ tick "compare levels"
+
+      (a, b) <- normalise (a, b)
+      SynEq.checkSyntacticEquality' a b
+        (\_ _ ->
+          reportSDoc "tc.conv.level" 60
+            "checkSyntacticEquality returns True") $ \a b -> do
+      reportSDoc "tc.conv.level" 60
+        "checkSyntacticEquality returns False"
+
+      let notok    = unlessM typeInType $ typeError $ NotLeqSort (Type a) (Type b)
+          postpone = patternViolation (unblockOnAnyMetaIn (a, b))
+
+          wrap m = m `catchError` \case
+            TypeError{} -> notok
+            err         -> throwError err
+
+      cumulativity <- optCumulativity <$> pragmaOptions
+      areWeComputingOverlap <- viewTC eConflComputingOverlap
+      reportSDoc "tc.conv.level" 40 $
+        "compareLevelView" <+>
+          sep [ prettyList_ $ fmap (pretty . unSingleLevel) $ levelMaxView a
+              , "=<"
+              , prettyList_ $ fmap (pretty . unSingleLevel) $ levelMaxView b
+              ]
+
+      -- Extra reduce on level atoms, but should be cheap since they are already reduced.
+      aB <- mapM reduceB a
+      bB <- mapM reduceB b
+
+      wrap $ case (levelMaxView aB, levelMaxView bB) of
+
+        -- 0 ≤ any
+        (SingleClosed 0 :| [] , _) -> return ()
+
+        -- any ≤ 0
+        (as , SingleClosed 0 :| []) ->
+          forM_ as $ \ a' -> equalLevel (unSingleLevel $ fmap ignoreBlocking a') (ClosedLevel 0)
+
+        -- closed ≤ closed
+        (SingleClosed m :| [], SingleClosed n :| []) -> unless (m <= n) notok
+
+        -- closed ≤ b
+        (SingleClosed m :| [] , _)
+          | m <= levelLowerBound b -> return ()
+
+        -- as ≤ neutral/closed
+        (as, bs)
+          | all neutralOrClosed bs , levelLowerBound a > levelLowerBound b -> notok
+
+        -- ⊔ as ≤ single
+        (as@(_ :| _ : _), b :| []) ->
+          forM_ as $ \ a' -> leqLevel (unSingleLevel $ ignoreBlocking <$> a')
+                                      (unSingleLevel $ ignoreBlocking <$> b)
+
+        -- reduce constants
+        (as, bs)
+          | let minN = min (fst $ levelPlusView a) (fst $ levelPlusView b)
+                a'   = fromMaybe __IMPOSSIBLE__ $ subLevel minN a
+                b'   = fromMaybe __IMPOSSIBLE__ $ subLevel minN b
+          , minN > 0 -> leqLevel a' b'
+
+        -- remove subsumed
+        -- Andreas, 2014-04-07: This is ok if we do not go back to equalLevel
+        (as, bs)
+          | (subsumed@(_:_) , as') <- List1.partition (isSubsumed . fmap ignoreBlocking) as
+          -> leqLevel (unSingleLevels $ (fmap . fmap) ignoreBlocking as') b
+          where
+            isSubsumed a = any (`subsumes` a) $ (fmap . fmap) ignoreBlocking bs
+
+            subsumes :: SingleLevel -> SingleLevel -> Bool
+            subsumes (SingleClosed m)        (SingleClosed n)        = m >= n
+            subsumes (SinglePlus (Plus m _)) (SingleClosed n)        = m >= n
+            subsumes (SinglePlus (Plus m a)) (SinglePlus (Plus n b)) = a == b && m >= n
+            subsumes _ _ = False
+
+        -- as ≤ _l x₁ .. xₙ ⊔ bs
+        -- We can solve _l := λ x₁ .. xₙ -> as ⊔ (_l' x₁ .. xₙ)
+        -- (where _l' is a new metavariable)
+        (as , bs)
+          | cumulativity
+          , not areWeComputingOverlap
+          , Just (mb@(MetaV x es) , bs') <- singleMetaView $ (map . fmap) ignoreBlocking (List1.toList bs)
+          , null bs' || noMetas (Level a , unSingleLevels bs') -> do
+            mv <- lookupLocalMeta x
+            -- Jesper, 2019-10-13: abort if this is an interaction
+            -- meta or a generalizable meta
+            abort <- (isJust <$> isInteractionMeta x) `or2M`
+                     ((== YesGeneralizeVar) <$> isGeneralizableMeta x)
+            if | abort -> postpone
+               | otherwise -> do
+                  x' <- case mvJudgement mv of
+                    IsSort{} -> __IMPOSSIBLE__
+                    HasType _ cmp t -> do
+                      TelV tel t' <- telView t
+                      newMeta Instantiable (mvInfo mv) normalMetaPriority (idP $ size tel) $ HasType () cmp t
+                  reportSDoc "tc.conv.level" 20 $ fsep
+                    [ "attempting to solve" , prettyTCM (MetaV x es) , "to the maximum of"
+                    , prettyTCM (Level a) , "and the fresh meta" , prettyTCM (MetaV x' es)
+                    ]
+                  equalLevel (atomicLevel mb) $ levelLub a (atomicLevel $ MetaV x' es)
+
+
+        -- Andreas, 2016-09-28: This simplification loses the solution lzero.
+        -- Thus, it is invalid.
+        -- See test/Succeed/LevelMetaLeqNeutralLevel.agda.
+        -- -- [a] ≤ [neutral]
+        -- ([a@(Plus n _)], [b@(Plus m NeutralLevel{})])
+        --   | m == n -> equalLevel' (Max [a]) (Max [b])
+        --   -- Andreas, 2014-04-07: This call to equalLevel is ok even if we removed
+        --   -- subsumed terms from the lhs.
+
+        -- anything else
+        _ | noMetas (a, b) -> notok
+          | otherwise      -> postpone
+      where
+        neutralOrClosed (SingleClosed _)                   = True
+        neutralOrClosed (SinglePlus (Plus _ NotBlocked{})) = True
+        neutralOrClosed _                                  = False
+
+        -- Is there exactly one @MetaV@ in the list of single levels?
+        singleMetaView :: [SingleLevel] -> Maybe (Term, [SingleLevel])
+        singleMetaView (SinglePlus (Plus 0 l@(MetaV m es)) : ls)
+          | all (not . isMetaLevel) ls = Just (l,ls)
+        singleMetaView (l : ls)
+          | not $ isMetaLevel l = second (l:) <$> singleMetaView ls
+        singleMetaView _ = Nothing
+
+        isMetaLevel :: SingleLevel -> Bool
+        isMetaLevel (SinglePlus (Plus _ MetaV{})) = True
+        isMetaLevel _                             = False
+
+{-# SPECIALIZE equalLevel :: Level -> Level -> TCM () #-}
+equalLevel :: forall m. MonadConversion m => Level -> Level -> m ()
+equalLevel a b = do
+  reportSDoc "tc.conv.level" 50 $ sep [ "equalLevel", nest 2 $ parens $ pretty a, nest 2 $ parens $ pretty b ]
+  whenProfile Profile.Conversion $ tick "compare levels"
+  -- Andreas, 2013-10-31 remove common terms (that don't contain metas!)
+  -- THAT's actually UNSOUND when metas are instantiated, because
+  --     max a b == max a c  does not imply  b == c
+  -- as <- return $ Set.fromList $ closed0 as
+  -- bs <- return $ Set.fromList $ closed0 bs
+  -- let cs = Set.filter (not . hasMeta) $ Set.intersection as bs
+  -- as <- return $ Set.toList $ as Set.\\ cs
+  -- bs <- return $ Set.toList $ bs Set.\\ cs
+
+  reportSDoc "tc.conv.level" 40 $
+    sep [ "equalLevel"
+        , vcat [ nest 2 $ sep [ prettyTCM a <+> "=="
+                              , prettyTCM b
+                              ]
+               ]
+        ]
+  reportSDoc "tc.conv.level" 80 $ sep [ "equalLevel", nest 2 $ parens $ pretty a, nest 2 $ parens $ pretty b ]
+
+  (a, b) <- normalise (a, b)
+
+  -- Jesper, 2014-02-02 remove terms that certainly do not contribute
+  -- to the maximum
+  let (a', b') = removeSubsumed a b
+
+  SynEq.checkSyntacticEquality' a' b'
+    (\_ _ ->
+      reportSDoc "tc.conv.level" 60
+        "checkSyntacticEquality returns True") $ \a b -> do
+
+  reportSDoc "tc.conv.level" 60 "checkSyntacticEquality returns False"
+
+  let notok    = unlessM typeInType notOk
+      notOk    = typeError $ UnequalLevel CmpEq a' b'
+      postpone = do
+        reportSDoc "tc.conv.level" 30 $ hang "postponing:" 2 $ hang (pretty a' <+> "==") 0 (pretty b')
+        blocker <- unblockOnAnyMetaIn <$> instantiateFull (a', b')
+        patternViolation blocker
+
+  reportSDoc "tc.conv.level" 50 $
+    sep [ "equalLevel (w/o subsumed)"
+        , vcat [ nest 2 $ sep [ prettyTCM a' <+> "=="
+                              , prettyTCM b'
+                              ]
+               ]
+        ]
+
+  let as  = levelMaxView a'
+      bs  = levelMaxView b'
+  reportSDoc "tc.conv.level" 50 $
+    sep [ text "equalLevel"
+        , vcat [ nest 2 $ sep [ prettyList_ $ fmap (prettyTCM . unSingleLevel) as
+                              , "=="
+                              , prettyList_ $ fmap (prettyTCM . unSingleLevel) bs
+                              ]
+               ]
+        ]
+
+  reportSDoc "tc.conv.level" 80 $
+    sep [ text "equalLevel"
+        , vcat [ nest 2 $ sep [ prettyList_ $ fmap (pretty . unSingleLevel) as
+                              , "=="
+                              , prettyList_ $ fmap (pretty . unSingleLevel) bs
+                              ]
+               ]
+        ]
+
+  -- Extra reduce on level atoms, but should be cheap since they are already reduced.
+  as <- (mapM . mapM) reduceB as
+  bs <- (mapM . mapM) reduceB bs
+
+  catchConstraint (LevelCmp CmpEq a b) $ case (as, bs) of
+
+        -- closed == closed
+        (SingleClosed m :| [], SingleClosed n :| [])
+          | m == n    -> return ()
+          | otherwise -> notok
+
+        -- closed == neutral
+        (SingleClosed m :| [] , bs) | any isNeutral bs -> notok
+        (as , SingleClosed n :| []) | any isNeutral as -> notok
+
+        -- closed == b
+        (SingleClosed m :| [] , _) | m < levelLowerBound b -> notok
+        (_ , SingleClosed n :| []) | n < levelLowerBound a -> notok
+
+        -- 0 == a ⊔ b
+        (SingleClosed 0 :| [] , bs@(_ :| _ : _)) ->
+          forM_ bs $ \ b' ->  equalLevel (ClosedLevel 0) (unSingleLevel $ ignoreBlocking <$> b')
+        (as@(_ :| _ : _) , SingleClosed 0 :| []) ->
+          forM_ as $ \ a' -> equalLevel (unSingleLevel $ ignoreBlocking <$> a') (ClosedLevel 0)
+
+        -- meta == any
+        (SinglePlus (Plus k a) :| [] , SinglePlus (Plus l b) :| [])
+          -- there is only a potential choice when k == l
+          | MetaV x as' <- ignoreBlocking a
+          , MetaV y bs' <- ignoreBlocking b
+          , k == l -> do
+              lvl <- levelType'
+              compareMetas CmpEq (AsTermsOf lvl) x as' y bs'
+        (SinglePlus (Plus k a) :| [] , _)
+          | MetaV x as' <- ignoreBlocking a
+          , Just b' <- subLevel k b -> meta x as' b'
+        (_ , SinglePlus (Plus l b) :| [])
+          | MetaV y bs' <- ignoreBlocking b
+          , Just a' <- subLevel l a -> meta y bs' a'
+
+        -- a' ⊔ b == b
+        _ | Just a' <- levelMaxDiff a b
+          , b /= ClosedLevel 0 -> leqLevel a' b
+
+        -- a == b' ⊔ a
+        _ | Just b' <- levelMaxDiff b a
+          , a /= ClosedLevel 0 -> leqLevel b' a
+
+        -- neutral/closed == neutral/closed
+        (as , bs)
+          | all isNeutralOrClosed (as <> bs)
+          -- Andreas, 2013-10-31: There could be metas in neutral levels (see Issue 930).
+          -- Should not we postpone there as well?  Yes!
+          , not (any hasMeta (as <> bs))
+          , length as == length bs -> do
+              reportSLn "tc.conv.level" 60 $ "equalLevel: all are neutral or closed"
+              List1.zipWithM_ ((===) `on` levelTm . unSingleLevel . fmap ignoreBlocking) as bs
+
+        -- more cases?
+        _ | noMetas (a , b) -> notok
+          | otherwise       -> postpone
+
+      where
+        a === b = unlessM typeInType $ do
+          lvl <- levelType'
+          equalAtom (AsTermsOf lvl) a b
+
+        -- perform assignment (MetaV x as) := b
+        meta x as b = do
+          reportSLn "tc.meta.level" 30 $ "Assigning meta level"
+          reportSDoc "tc.meta.level" 50 $ "meta" <+> sep [prettyList $ map pretty as, pretty b]
+          lvl <- levelType'
+          assignE DirEq x as (levelTm b) (AsTermsOf lvl) (===) -- fallback: check equality as atoms
+
+        isNeutral (SinglePlus (Plus _ NotBlocked{})) = True
+        isNeutral _                                  = False
+
+        isNeutralOrClosed (SingleClosed _)                   = True
+        isNeutralOrClosed (SinglePlus (Plus _ NotBlocked{})) = True
+        isNeutralOrClosed _                                  = False
+
+        hasMeta (SinglePlus (Plus _ Blocked{})) = True
+        hasMeta (SinglePlus (Plus _ a))         = isJust $ firstMeta $ ignoreBlocking a
+        hasMeta (SingleClosed _)                = False
+
+        removeSubsumed a b =
+          let as = List1.toList $ levelMaxView a
+              bs = List1.toList $ levelMaxView b
+              a' = unSingleLevels $ filter (not . (`isStrictlySubsumedBy` bs)) as
+              b' = unSingleLevels $ filter (not . (`isStrictlySubsumedBy` as)) bs
+          in (a',b')
+
+        x `isStrictlySubsumedBy` ys = any (`strictlySubsumes` x) ys
+
+        SingleClosed m        `strictlySubsumes` SingleClosed n        = m > n
+        SinglePlus (Plus m a) `strictlySubsumes` SingleClosed n        = m > n
+        SinglePlus (Plus m a) `strictlySubsumes` SinglePlus (Plus n b) = a == b && m > n
+        _                     `strictlySubsumes` _                     = False
+
+
+{-# SPECIALIZE equalSort :: Sort -> Sort -> TCM () #-}
+-- | Check that the first sort equal to the second.
+equalSort :: forall m. MonadConversion m => Sort -> Sort -> m ()
+equalSort s1 s2 = do
+  reportSDoc "tc.conv.sort" 30 $ sep
+    [ "equalSort"
+    , vcat [ nest 2 $ fsep [ prettyTCM s1 <+> "=="
+                           , prettyTCM s2 ]
+           ]
+    ]
+  reportSDoc "tc.conv.sort" 60 $ sep
+    [ "equalSort"
+    , vcat [ nest 2 $ fsep [ pretty s1 <+> "=="
+                           , pretty s2 ]
+           ]
+    ]
+  whenProfile Profile.Conversion $ tick "compare sorts"
+
+  guardPointerEquality s1 s2 "pointer equality: sorts" $
+    SynEq.checkSyntacticEquality s1 s2 (\_ _ -> return ()) $ \s1 s2 -> do
+
+    s1b <- reduceB s1
+    s2b <- reduceB s2
+
+    let (s1,s2) = (ignoreBlocking s1b, ignoreBlocking s2b)
+        blocker = unblockOnEither (getBlocker s1b) (getBlocker s2b)
+
+    let postponeIfBlocked = catchPatternErr $ \blocker -> do
+          if | blocker == neverUnblock -> typeError $ UnequalSorts s1 s2
+             | otherwise -> do
+                 reportSDoc "tc.conv.sort" 30 $ vcat
+                   [ "Postponing constraint"
+                   , nest 2 $ fsep [ prettyTCM s1 <+> "=="
+                                   , prettyTCM s2 ]
+                   ]
+                 -- Andreas, 2023-12-21, recomputing the blocker fixes issue #7034.
+                 blocker <- updateBlocker blocker
+                 addConstraint blocker $ SortCmp CmpEq s1 s2
+
+    propEnabled <- isPropEnabled
+    typeInTypeEnabled <- typeInType
+    omegaInOmegaEnabled <- optOmegaInOmega <$> pragmaOptions
+    let infInInf = typeInTypeEnabled || omegaInOmegaEnabled
+
+    postponeIfBlocked $ case (s1, s2) of
+
+            -- Andreas, 2018-09-03: crash on dummy sort
+            (DummyS s, _) -> impossibleSort s
+            (_, DummyS s) -> impossibleSort s
+
+            -- one side is a meta sort: try to instantiate
+            -- In case both sides are meta sorts, instantiate the
+            -- bigger (i.e. more recent) one.
+            (MetaS x es , MetaS y es') -> compareMetas CmpEq AsTypes x es y es'
+            (MetaS x es , _          ) -> meta x es s2
+            (_          , MetaS x es ) -> meta x es s1
+
+            -- diagonal cases for rigid sorts
+            (Univ u a   , Univ u' b  ) | u == u' -> equalLevel a b `catchInequalLevel` no
+            (SizeUniv   , SizeUniv   ) -> yes
+            (LockUniv   , LockUniv   ) -> yes
+            (LevelUniv  , LevelUniv  ) -> yes
+            (IntervalUniv , IntervalUniv) -> yes
+            (Inf u m    , Inf u' n   ) ->
+              if u == u' && (m == n || infInInf) then yes else no
+
+            -- if --type-in-type is enabled, Setωᵢ is equal to any Set ℓ (see #3439)
+            (Univ u _   , Inf  u' _  ) -> answer $ u == u' && typeInTypeEnabled
+            (Inf  u _   , Univ u' _  ) -> answer $ u == u' && typeInTypeEnabled
+
+            -- equating @PiSort a b@ to another sort
+            (s1 , PiSort a b c) -> piSortEquals propEnabled s1 a b c blocker
+            (PiSort a b c , s2) -> piSortEquals propEnabled s2 a b c blocker
+
+            -- equating @FunSort a b@ to another sort
+            (s1 , FunSort a b) -> funSortEquals propEnabled s1 a b blocker
+            (FunSort a b , s2) -> funSortEquals propEnabled s2 a b blocker
+
+            -- equating @UnivSort s@ to another sort
+            (s1          , UnivSort s2) -> univSortEquals propEnabled infInInf s1 s2 blocker
+            (UnivSort s1 , s2         ) -> univSortEquals propEnabled infInInf s2 s1 blocker
+
+            -- postulated sorts can only be equal if they have the same head
+            (DefS d es  , DefS d' es')
+              | d == d'                -> do
+                  pol <- getPolarity' CmpEq d
+                  a <- computeElimHeadType d es es'
+                  compareElims pol [] a (Def d []) es es'
+              | otherwise              -> no
+
+            -- any other combinations of sorts are not equal
+            (_          , _          ) -> no
+
+    where
+      yes = return ()
+      no  = patternViolation neverUnblock
+      answer = \case
+        True -> yes
+        False -> no
+
+      -- perform assignment (MetaS x es) := s
+      meta :: MetaId -> [Elim' Term] -> Sort -> m ()
+      meta x es s = do
+        reportSLn "tc.meta.sort" 30 $ "Assigning meta sort"
+        reportSDoc "tc.meta.sort" 50 $ "meta" <+> sep [pretty x, prettyList $ map pretty es, pretty s]
+        assignE DirEq x es (Sort s) AsTypes __IMPOSSIBLE__
+
+       -- Sorts that contain exactly one other kind of sorts.
+      invertibleSort :: Bool -> Univ -> Bool
+      invertibleSort propEnabled = \case
+        -- @SSetω(n+1)@ is the successor sort of exactly @SSetω(n)@.
+        USSet -> True
+        -- @Setω(n+1)@ is the successor sort of exactly @Setω(n)@ if we do not have @Prop@.
+        UType -> not propEnabled
+        -- @Prop@ sorts are not successor sorts.
+        UProp -> False
+
+      -- Equate a sort @s1@ to @univSort s2@
+      -- Precondition: @s1@ and @univSort s2@ are already reduced.
+      univSortEquals :: Bool -> Bool -> Sort -> Sort -> Blocker -> m ()
+      univSortEquals propEnabled infInInf s1 s2 blocker = do
+        reportSDoc "tc.conv.sort" 35 $ vcat
+          [ "univSortEquals"
+          , "  s1 =" <+> prettyTCM s1
+          , "  s2 =" <+> prettyTCM s2
+          ]
+        let postpone = patternViolation blocker
+        case s1 of
+          -- @Prop l@, @SizeUniv@ and @LevelUniv@ are not successor sorts.
+          Prop{}      -> no
+          Inf UProp _ -> no
+          SizeUniv{}  -> no
+          LevelUniv{} -> no
+          -- Neither are @LockUniv@ or @IntervalUniv@.
+          LockUniv{}     -> no
+          IntervalUniv{} -> no
+
+          -- @Set l1@ is the successor sort of either @Set l2@ or
+          -- @Prop l2@ where @l1 == lsuc l2@.
+          Type l1 -> do
+            levelUnivEnabled <- optLevelUniverse <$> pragmaOptions
+            guardedEnabled   <- optGuarded       <$> pragmaOptions
+               -- @s2@ is definitely not @Inf n@ or @SizeUniv@
+            if | Inf _ _n <- s2 -> __IMPOSSIBLE__
+               | SizeUniv <- s2 -> __IMPOSSIBLE__
+               -- The predecessor @s2@ is can also not be @SSet _@ or @IntervalUniv@
+               | Univ USSet _ <- s2 -> __IMPOSSIBLE__
+               | IntervalUniv <- s2 -> __IMPOSSIBLE__
+               -- If @Prop@ is not used, then @s2@ must be of the form @Set l2@,
+               -- except when l1 == 1, then it could also be @LockUniv@ or @LevelUniv@.
+               | not (propEnabled || guardedEnabled || levelUnivEnabled) -> do
+                   l2 <- case subLevel 1 l1 of
+                     Just l2 -> return l2
+                     Nothing -> do
+                       l2 <- newLevelMeta
+                       equalLevel l1 (levelSuc l2)
+                       return l2
+                   equalSort (Type l2) s2
+               -- Otherwise we postpone
+               | otherwise -> postpone
+          -- @SSetω(n+1)@ is the successor sort of exactly @SSetω(n)@.
+          -- @SSetω@ is the successor sort of exactly @SSetω@ if
+          -- --type-in-type or --omega-in-omega is enabled.
+          -- The same is only true for @Setω(n+1)@ if @Propω...@ are disabled.
+          -- @Setω@ is the successor sort of @Setω@ (type:type) or @SizeUniv@ (--sized-types).
+          Inf u 0 -> do
+              -- Compute the predecessor(s) of (S)Setω and return it if it is unique.
+              sizedTypesEnabled <- sizedTypesOption
+              -- guardedEnabled <- optGuarded <$> pragmaOptions
+              case concat
+                [ [ s1       | u /= UProp, infInInf ]
+                , [ dummy    | u == UType, infInInf, propEnabled, let dummy = Inf UProp 0 ]
+                    -- We enter a dummy into the solution set if --prop makes predecessor ambiguous.
+                , [ SizeUniv | u == UType, sizedTypesEnabled ]
+                -- , [ LockUniv | guardedEnabled ]  -- LockUniv is actually in Set₁, not Setω
+                ]
+                of
+                [ s ] -> equalSort s s2
+                []    -> no
+                _     -> postpone
+          Inf u n | n > 0, invertibleSort propEnabled u ->
+            equalSort (Inf u $ n - 1) s2
+
+          -- Anything else: postpone
+          _ -> postpone
+
+
+      -- Equate a sort @s@ to @piSort a s1 s2@
+      -- Precondition: @s@ and @piSort a s1 s2@ are already reduced.
+      piSortEquals :: Bool -> Sort -> Dom Term -> Sort -> Abs Sort -> Blocker -> m ()
+      piSortEquals propEnabled s a s1 NoAbs{} blocker = __IMPOSSIBLE__
+      piSortEquals propEnabled s a s1 s2Abs@(Abs x s2) blocker = do
+        let adom = El s1 <$> a
+        reportSDoc "tc.conv.sort" 35 $ vcat
+          [ "piSortEquals"
+          , "  s  =" <+> prettyTCM s
+          , "  a  =" <+> prettyTCM adom
+          , "  s1 =" <+> prettyTCM s1
+          , "  s2 =" <+> addContext (x,adom) (prettyTCM s2)
+          ]
+        let postpone = patternViolation blocker
+           -- If @s2@ is dependent, then @piSort a s1 s2@ computes to
+           -- @Setωi@. Hence, if @s@ is small, then @s2@
+           -- cannot be dependent.
+        if | isSmallSort s -> do
+               -- We force @s2@ to be non-dependent by unifying it with
+               -- a fresh meta that does not depend on @x : a@
+               s2' <- newSortMeta
+               addContext (x , adom) $ equalSort s2 (raise 1 s2')
+               funSortEquals propEnabled s s1 s2' blocker
+           -- Otherwise: postpone
+           | otherwise -> postpone
+
+      -- Equate a sort @s@ to @funSort s1 s2@
+      -- Precondition: @s@ and @funSort s1 s2@ are already reduced
+      funSortEquals :: Bool -> Sort -> Sort -> Sort -> Blocker -> m ()
+      funSortEquals propEnabled s0 s1 s2 blocker = do
+        reportSDoc "tc.conv.sort" 35 $ vcat
+          [ "funSortEquals"
+          , "  s0 =" <+> prettyTCM s0
+          , "  s1 =" <+> prettyTCM s1
+          , "  s2 =" <+> prettyTCM s2
+          ]
+        sizedTypesEnabled <- sizedTypesOption
+        cubicalEnabled <- isJust . optCubical <$> pragmaOptions
+        levelUnivEnabled <- optLevelUniverse <$> pragmaOptions
+        let postpone = patternViolation blocker
+            err :: m ()
+            err = typeError $ UnequalSorts s0 (FunSort s1 s2)
+        case s0 of
+          -- If @Setωᵢ == funSort s1 s2@, then either @s1@ or @s2@ must
+          -- be @Setωᵢ@.
+
+          Inf u n ->
+            case (sizeOfSort s1, sizeOfSort s2) of
+
+              -- Both sorts have to be <= n in size, and their fibrancy <= u
+              (Right (SizeOfSort u' n'), _)
+                | n' > n                           -> err
+                | univFibrancy u' > univFibrancy u -> err
+              (_, Right (SizeOfSort u' n'))
+                | n' > n                           -> err
+                | univFibrancy u' > univFibrancy u -> err
+              -- Unless SSet, the kind of the funSort is the kind of the codomain
+                | u /= USSet, u /= u'              -> err
+
+              -- One sort has to be at least the same size as n
+              (Right (SizeOfSort u1 n1), Right (SizeOfSort u2 n2))
+                | n1 < n, n2 < n                   -> err
+                | u /= funUniv u1 u2               -> err
+
+              -- If have the domain sort only
+              (Right (SizeOfSort u' n'), _)
+                | u' /= USSet, n' < n              -> equalSort s0 s2
+                | otherwise                        -> postpone
+
+              -- If we just have the codomain sort
+              (_, Right (SizeOfSort USSet n'))     -> postpone
+              (_, Right (SizeOfSort _     n'))
+                | n' < n, u == USSet               -> equalSort s1 s2
+                | n' < n, not propEnabled,
+                  -- issue #6648: with --level-universe we have PTS rule (LevelUniv,Set,Setω)
+                  not levelUnivEnabled || n > 0    -> equalSort (Inf UType n) s1
+                | otherwise                        -> postpone
+
+              _ -> postpone
+
+          -- If @Set l == funSort s1 s2@, then @s2@ must be of the
+          -- form @Set l2@. @s1@ can be one of @Set l1@, @Prop l1@,
+          -- @SizeUniv@, or @IUniv@.
+          Type l -> do
+            l2 <- forceUniv UType s2
+            -- We must have @l2 =< l@, this might help us to solve
+            -- more constraints (in particular when @l == 0@).
+            leqLevel l2 l
+            -- Jesper, 2022-10-22, #6211: the operations `forceUniv`
+            -- and `leqLevel` above might have instantiated some
+            -- metas, so we need to reduce s1 again to get an
+            -- up-to-date Blocker.
+            s1b <- reduceB s1
+            let s1 = ignoreBlocking s1b
+                blocker = getBlocker s1b
+            -- Jesper, 2019-12-27: SizeUniv is disabled at the moment.
+            if | {- sizedTypesEnabled || -} propEnabled || cubicalEnabled ->
+                case funSort' s1 (Type l2) of
+                   -- If the work we did makes the @funSort@ compute,
+                   -- continue working.
+                   Right s -> equalSort (Type l) s
+                   -- Otherwise: postpone
+                   Left{}  -> patternViolation blocker
+               -- If both Prop and sized types are disabled, only the
+               -- case @s1 == Set l1@ remains.
+               | otherwise -> do
+                   l1 <- forceUniv UType s1
+                   equalLevel l (levelLub l1 l2)
+
+          -- If @Prop l == funSort s1 s2@, then @s2@ must be of the
+          -- form @Prop l2@, and @s1@ can be one of @Set l1@, Prop
+          -- l1@, or @SizeUniv@.
+          Prop l -> do
+            l2 <- forceUniv UProp s2
+            leqLevel l2 l
+            s1b <- reduceB s1
+            let s1 = ignoreBlocking s1b
+                blocker = getBlocker s1b
+            case funSort' s1 (Prop l2) of
+                   -- If the work we did makes the @funSort@ compute,
+                   -- continue working.
+                   Right s -> equalSort (Prop l) s
+                   -- Otherwise: postpone
+                   Left _  -> patternViolation blocker
+
+          -- TODO: SSet l
+
+          -- We have @SizeUniv == funSort s1 s2@ iff @s2 == SizeUniv@
+          SizeUniv -> equalSort SizeUniv s2
+          LevelUniv -> equalSort LevelUniv s2
+          -- Anything else: postpone
+          _        -> postpone
+
+      forceUniv :: Univ -> Sort -> m Level
+      forceUniv u = \case
+        Univ u' l | u == u' -> return l
+        s -> do
+          l <- newLevelMeta
+          equalSort s (Univ u l)
+          return l
+
+      impossibleSort s = do
+        reportS "impossible" 10
+          [ "equalSort: found dummy sort with description:"
+          , s
+          ]
+        __IMPOSSIBLE__
+
+      catchInequalLevel m fail = m `catchError` \case
+        TypeError{} -> fail
+        err         -> throwError err
+
+
+forallFaceMaps
+  :: MonadConversion m
+  => Term
+  -> (IntMap Bool -> Blocker -> Term -> m a)
+  -> (IntMap Bool -> Substitution -> m a)
+  -> m [a]
+forallFaceMaps t kb k = do
+  reportSDoc "conv.forall" 20 $
+      fsep ["forallFaceMaps"
+           , prettyTCM t
+           ]
+  as <- decomposeInterval t
+  boolToI <- do
+    io <- primIOne
+    iz <- primIZero
+    return (\b -> if b then io else iz)
+  forM as $ \ (ms,ts) -> do
+   ifBlockeds ts (kb ms) $ \ _ _ -> do
+    let xs = map (second boolToI) $ IntMap.toAscList ms
+    cxt <- getContext
+    reportSDoc "conv.forall" 20 $
+      fsep ["substContextN"
+           , prettyTCM cxt
+           , prettyTCM xs
+           ]
+    (cxt',sigma) <- substContextN cxt xs
+    resolved <- forM xs (\ (i,t) -> (,) <$> lookupBV i <*> return (applySubst sigma t))
+    updateContext sigma (const cxt') $
+      addBindings resolved $ do
+        cl <- buildClosure ()
+        tel <- getContextTelescope
+        m <- currentModule
+        sub <- getModuleParameterSub m
+        reportSDoc "conv.forall" 30 $ vcat
+          [ text (replicate 10 '-')
+          , prettyTCM (envCurrentModule $ clEnv cl)
+          -- , prettyTCM (envLetBindings $ clEnv cl)
+          , prettyTCM tel -- (toTelescope $ envContext $ clEnv cl)
+          , prettyTCM sigma
+          , prettyTCM m
+          , prettyTCM sub
+          ]
+        k ms sigma
+  where
+    -- TODO Andrea: inefficient because we try to reduce the ts which we know are in whnf
+    ifBlockeds ts blocked unblocked = do
+      and <- getPrimitiveTerm PrimIMin
+      io  <- primIOne
+      let t = foldr (\ x r -> and `apply` [argN x,argN r]) io ts
+      ifBlocked t blocked unblocked
+    addBindings [] m = m
+    addBindings ((Dom{domInfo = info,unDom = (nm,ty)},t):bs) m = addLetBinding info Inserted nm t ty (addBindings bs m)
+
+    substContextN :: MonadConversion m => Context -> [(Int,Term)] -> m (Context , Substitution)
+    substContextN c [] = return (c, idS)
+    substContextN c ((i,t):xs) = do
+      (c', sigma) <- substContext i t c
+      (c'', sigma')  <- substContextN c' (map (subtract 1 -*- applySubst sigma) xs)
+      return (c'', applySubst sigma' sigma)
+
+
+    -- assumes the term can be typed in the shorter telescope
+    -- the terms we get from toFaceMaps are closed.
+    substContext :: MonadConversion m => Int -> Term -> Context -> m (Context , Substitution)
+    substContext i t [] = __IMPOSSIBLE__
+    substContext i t (x:xs) | i == 0 = return $ (xs , singletonS 0 t)
+    substContext i t (x:xs) | i > 0 = do
+                                  reportSDoc "conv.forall" 20 $
+                                    fsep ["substContext"
+                                        , text (show (i-1))
+                                        , prettyTCM t
+                                        , prettyTCM xs
+                                        ]
+                                  (c,sigma) <- substContext (i-1) t xs
+                                  let e = applySubst sigma x
+                                  return (e:c, liftS 1 sigma)
+    substContext i t (x:xs) = __IMPOSSIBLE__
+
+compareInterval :: MonadConversion m => Comparison -> Type -> Term -> Term -> m ()
+compareInterval cmp i t u = do
+  reportSDoc "tc.conv.interval" 15 $
+    sep [ "{ compareInterval" <+> prettyTCM t <+> "=" <+> prettyTCM u ]
+  whenProfile Profile.Conversion $ tick "compare at interval type"
+  tb <- reduceB t
+  ub <- reduceB u
+  let t = ignoreBlocking tb
+      u = ignoreBlocking ub
+  it <- decomposeInterval' t
+  iu <- decomposeInterval' u
+  case () of
+    _ | isBlocked tb || isBlocked ub -> do
+      -- in case of metas we wouldn't be able to make progress by how we deal with de morgan laws.
+      -- (because the constraints generated by decomposition are sufficient but not necessary).
+      -- but we could still prune/solve some metas by comparing the terms as atoms.
+      -- also if blocked we won't find the terms conclusively unequal(?) so compareAtom
+      -- won't report type errors when we should accept.
+      interval <- primIntervalType
+      compareAtom CmpEq (AsTermsOf interval) t u
+    _ | otherwise -> do
+      x <- leqInterval it iu
+      y <- leqInterval iu it
+      let final = isCanonical it && isCanonical iu
+      if x && y then reportSDoc "tc.conv.interval" 15 $ "Ok! }" else
+        if final then typeError $ UnequalTerms cmp t u (AsTermsOf i)
+                 else do
+                   reportSDoc "tc.conv.interval" 15 $ "Giving up! }"
+                   patternViolation (unblockOnAnyMetaIn (t, u))
+ where
+   isBlocked Blocked{}    = True
+   isBlocked NotBlocked{} = False
+
+
+type Conj = (IntMap BoolSet, [Term])
+
+isCanonical :: [Conj] -> Bool
+isCanonical = all (null . snd)
+
+-- | leqInterval r q = r ≤ q in the I lattice.
+-- (∨ r_i) ≤ (∨ q_j)  iff  ∀ i. ∃ j. r_i ≤ q_j
+leqInterval :: MonadConversion m => [Conj] -> [Conj] -> m Bool
+leqInterval r q =
+  and <$> forM r (\ r_i ->
+   or <$> forM q (\ q_j -> leqConj r_i q_j))  -- TODO shortcut
+
+-- | leqConj r q = r ≤ q in the I lattice, when r and q are conjuctions.
+-- ' (∧ r_i)   ≤ (∧ q_j)               iff
+-- ' (∧ r_i)   ∧ (∧ q_j)   = (∧ r_i)   iff
+-- ' {r_i | i} ∪ {q_j | j} = {r_i | i} iff
+-- ' {q_j | j} ⊆ {r_i | i}
+leqConj :: MonadConversion m => Conj -> Conj -> m Bool
+leqConj (rs, rst) (qs, qst) = do
+  if IntMap.isSubmapOfBy BoolSet.isSubsetOf qs rs
+    then do
+      interval <-
+        El IntervalUniv . fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinInterval
+      -- we don't want to generate new constraints here because
+      -- 1. in some situations the same constraint would get generated twice.
+      -- 2. unless things are completely accepted we are going to
+      --    throw patternViolation in compareInterval.
+      let eqT t u = tryConversion (compareAtom CmpEq (AsTermsOf interval) t u)
+      let listSubset ts us =
+            and <$> forM ts (\t -> or <$> forM us (\u -> eqT t u)) -- TODO shortcut
+      listSubset qst rst
+    else
+      return False
+
+-- | equalTermOnFace φ A u v = _ , φ ⊢ u = v : A
+equalTermOnFace :: MonadConversion m => Term -> Type -> Term -> Term -> m ()
+equalTermOnFace = compareTermOnFace CmpEq
+
+compareTermOnFace :: MonadConversion m => Comparison -> Term -> Type -> Term -> Term -> m ()
+compareTermOnFace = compareTermOnFace' (const compareTerm)
+
+compareTermOnFace'
+  :: MonadConversion m
+  => (Substitution -> Comparison -> Type -> Term -> Term -> m ())
+  -> Comparison -> Term -> Type -> Term -> Term -> m ()
+compareTermOnFace' k cmp phi ty u v = do
+  reportSDoc "tc.conv.face" 40 $
+    text "compareTermOnFace:" <+> pretty phi <+> "|-" <+> pretty u <+> "==" <+> pretty v <+> ":" <+> pretty ty
+  whenProfile Profile.Conversion $ tick "compare at face type"
+
+  phi <- reduce phi
+  _ <- forallFaceMaps phi postponed $ \ faces alpha ->
+      k alpha cmp (applySubst alpha ty) (applySubst alpha u) (applySubst alpha v)
+  return ()
+ where
+  postponed ms blocker psi = do
+    phi <- runNamesT [] $ do
+             imin <- cl $ getPrimitiveTerm PrimIMin
+             ineg <- cl $ getPrimitiveTerm PrimINeg
+             psi <- open psi
+             let phi = foldr (\ (i,b) r -> do i <- open (var i); pure imin <@> (if b then i else pure ineg <@> i) <@> r)
+                          psi (IntMap.toList ms) -- TODO Andrea: make a view?
+             phi
+    addConstraint blocker (ValueCmpOnFace cmp phi ty u v)
+
+---------------------------------------------------------------------------
+-- * Definitions
+---------------------------------------------------------------------------
+
+bothAbsurd :: MonadConversion m => QName -> QName -> m Bool
+bothAbsurd f f'
+  | isAbsurdLambdaName f, isAbsurdLambdaName f' = do
+      -- Double check we are really dealing with absurd lambdas:
+      -- Their functions should not have bodies.
+      def  <- getConstInfo f
+      def' <- getConstInfo f'
+      case (theDef def, theDef def') of
+        (Function{ funClauses = [Clause{ clauseBody = Nothing }] },
+         Function{ funClauses = [Clause{ clauseBody = Nothing }] }) -> return True
+        _ -> return False
+  | otherwise = return False
diff --git a/src/full/Agda/TypeChecking/Conversion.hs-boot b/src/full/Agda/TypeChecking/Conversion.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Conversion.hs-boot
@@ -0,0 +1,40 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Conversion where
+
+import Control.Monad.Except ( MonadError )
+import qualified Control.Monad.Fail as Fail
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Warnings
+
+type MonadConversion m =
+  ( PureTCM m
+  , MonadConstraint m
+  , MonadMetaSolver m
+  , MonadError TCErr m
+  , MonadWarning m
+  , MonadStatistics m
+  , MonadFresh ProblemId m
+  , MonadFresh Int m
+  , Fail.MonadFail m
+  )
+
+compareTerm  :: MonadConversion m => Comparison -> Type -> Term -> Term -> m ()
+compareAs    :: MonadConversion m => Comparison -> CompareAs -> Term -> Term -> m ()
+compareTermOnFace :: MonadConversion m => Comparison -> Term -> Type -> Term -> Term -> m ()
+compareAtom  :: MonadConversion m => Comparison -> CompareAs -> Term -> Term -> m ()
+compareArgs  :: MonadConversion m => [Polarity] -> [IsForced] -> Type -> Term -> Args -> Args -> m ()
+compareElims :: MonadConversion m => [Polarity] -> [IsForced] -> Type -> Term -> [Elim] -> [Elim] -> m ()
+compareType  :: MonadConversion m => Comparison -> Type -> Type -> m ()
+compareSort  :: MonadConversion m => Comparison -> Sort -> Sort -> m ()
+compareLevel :: MonadConversion m => Comparison -> Level -> Level -> m ()
+equalTerm    :: MonadConversion m => Type -> Term -> Term -> m ()
+equalTermOnFace :: MonadConversion m => Term -> Type -> Term -> Term -> m ()
+equalType    :: MonadConversion m => Type -> Type -> m ()
+equalSort    :: MonadConversion m => Sort -> Sort -> m ()
+equalLevel   :: MonadConversion m => Level -> Level -> m ()
+leqType      :: MonadConversion m => Type -> Type -> m ()
+leqLevel     :: MonadConversion m => Level -> Level -> m ()
+leqSort      :: MonadConversion m => Sort -> Sort -> m ()
diff --git a/src/full/Agda/TypeChecking/Conversion/Pure.hs b/src/full/Agda/TypeChecking/Conversion/Pure.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Conversion/Pure.hs
@@ -0,0 +1,178 @@
+
+module Agda.TypeChecking.Conversion.Pure where
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import Control.Monad.Except
+import Control.Monad.State
+
+import Data.String
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce (isBlocked)
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+
+import Agda.Utils.Impossible
+
+data FreshThings = FreshThings
+  { freshInt       :: Int
+  , freshProblemId :: ProblemId
+  , freshNameId    :: NameId
+  }
+
+newtype PureConversionT m a = PureConversionT
+  { unPureConversionT :: ExceptT TCErr (StateT FreshThings m) a }
+  deriving (Functor, Applicative, Monad, MonadError TCErr, MonadState FreshThings, PureTCM)
+
+{-# SPECIALIZE pureEqualTerm :: Type -> Term -> Term -> TCM Bool #-}
+pureEqualTerm
+  :: (PureTCM m, MonadBlock m)
+  => Type -> Term -> Term -> m Bool
+pureEqualTerm a u v =
+  isJust <$> runPureConversion (equalTerm a u v)
+
+{-# SPECIALIZE pureEqualType :: Type -> Type -> TCM Bool #-}
+pureEqualType
+  :: (PureTCM m, MonadBlock m)
+  => Type -> Type -> m Bool
+pureEqualType a b =
+  isJust <$> runPureConversion (equalType a b)
+
+{-# SPECIALIZE pureCompareAs :: Comparison -> CompareAs -> Term -> Term -> TCM Bool #-}
+pureCompareAs
+  :: (PureTCM m, MonadBlock m)
+  => Comparison -> CompareAs -> Term -> Term -> m Bool
+pureCompareAs cmp a u v =
+  isJust <$> runPureConversion (compareAs cmp a u v)
+
+{-# SPECIALIZE runPureConversion :: PureConversionT TCM a -> TCM (Maybe a) #-}
+runPureConversion
+  :: (MonadBlock m, PureTCM m)
+  => PureConversionT m a -> m (Maybe a)
+runPureConversion (PureConversionT m) = locallyTC eCompareBlocked (const True) $
+  verboseBracket "tc.conv.pure" 40 "runPureConversion" $ do
+  i <- useR stFreshInt
+  pid <- useR stFreshProblemId
+  nid <- useR stFreshNameId
+  let frsh = FreshThings i pid nid
+  result <- fst <$> runStateT (runExceptT m) frsh
+  case result of
+    Left (PatternErr block)
+     | block == neverUnblock -> do
+         debugResult "stuck"
+         return Nothing
+     | otherwise             -> do
+         debugResult $ "blocked on" <+> prettyTCM block
+         patternViolation block
+    Left TypeError{}   -> do
+      debugResult "type error"
+      return Nothing
+    Left Exception{}   -> __IMPOSSIBLE__
+    Left IOException{} -> __IMPOSSIBLE__
+    Right x            -> do
+      debugResult "success"
+      return $ Just x
+  where
+    debugResult msg = reportSDoc "tc.conv.pure" 40 $ "runPureConversion result: " <+> msg
+
+instance MonadTrans PureConversionT where
+  lift = PureConversionT . lift . lift
+
+deriving instance MonadFail       m => MonadFail       (PureConversionT m)
+deriving instance HasBuiltins     m => HasBuiltins     (PureConversionT m)
+deriving instance HasConstInfo    m => HasConstInfo    (PureConversionT m)
+deriving instance HasOptions      m => HasOptions      (PureConversionT m)
+deriving instance MonadTCEnv      m => MonadTCEnv      (PureConversionT m)
+deriving instance ReadTCState     m => ReadTCState     (PureConversionT m)
+deriving instance MonadReduce     m => MonadReduce     (PureConversionT m)
+deriving instance MonadAddContext m => MonadAddContext (PureConversionT m)
+deriving instance MonadDebug      m => MonadDebug      (PureConversionT m)
+
+instance (Monad m, Semigroup a) => Semigroup (PureConversionT m a) where
+  d1 <> d2 = (<>) <$> d1 <*> d2
+
+instance (IsString a, Monad m) => IsString (PureConversionT m a) where
+  fromString s = return (fromString s)
+
+instance Monad m => Null (PureConversionT m Doc) where
+  empty = return empty
+  null = __IMPOSSIBLE__
+
+instance Monad m => MonadBlock (PureConversionT m) where
+  patternViolation = throwError . PatternErr
+  catchPatternErr handle m = m `catchError` \case
+    PatternErr b -> handle b
+    err          -> throwError err
+
+
+instance (PureTCM m, MonadBlock m) => MonadConstraint (PureConversionT m) where
+  addConstraint u _ = patternViolation u
+  addAwakeConstraint u _ = patternViolation u
+  solveConstraint c = patternViolation alwaysUnblock  -- TODO: does this happen?
+  solveSomeAwakeConstraints _ _ = return ()
+  wakeConstraints _ = return ()
+  stealConstraints _ = return ()
+  modifyAwakeConstraints _ = patternViolation alwaysUnblock  -- TODO: does this happen?
+  modifySleepingConstraints _ = patternViolation alwaysUnblock  -- TODO: does this happen?
+
+instance (PureTCM m, MonadBlock m) => MonadMetaSolver (PureConversionT m) where
+  newMeta' _ _ _ _ _ _ = patternViolation alwaysUnblock  -- TODO: does this happen?
+  assignV _ m _ v _ = do
+    bv <- isBlocked v
+    let blocker = caseMaybe bv id unblockOnEither $ unblockOnMeta m
+    patternViolation blocker
+  assignTerm' m _ v = do
+    bv <- isBlocked v
+    let blocker = caseMaybe bv id unblockOnEither $ unblockOnMeta m
+    patternViolation blocker
+  etaExpandMeta _ _ = return ()
+  updateMetaVar _ _ = patternViolation alwaysUnblock  -- TODO: does this happen?
+  speculateMetas fallback m = m >>= \case
+    KeepMetas     -> return ()
+    RollBackMetas -> fallback
+
+instance (PureTCM m, MonadBlock m) => MonadInteractionPoints (PureConversionT m) where
+  freshInteractionId = patternViolation alwaysUnblock  -- TODO: does this happen?
+  modifyInteractionPoints _ = patternViolation alwaysUnblock  -- TODO: does this happen?
+
+-- This is a bogus instance that promptly forgets all concrete names,
+-- but we don't really care
+instance ReadTCState m => MonadStConcreteNames (PureConversionT m) where
+  runStConcreteNames m = do
+    concNames <- useR stConcreteNames
+    fst <$> runStateT m concNames
+
+instance (PureTCM m, MonadBlock m) => MonadWarning (PureConversionT m) where
+  addWarning w = case classifyWarning (tcWarning w) of
+    ErrorWarnings -> patternViolation neverUnblock
+    AllWarnings   -> return ()
+
+instance ReadTCState m => MonadStatistics (PureConversionT m) where
+  modifyCounter _ _ = return ()
+
+instance Monad m => MonadFresh ProblemId (PureConversionT m) where
+  fresh = do
+    i <- gets freshProblemId
+    modify $ \f -> f { freshProblemId = i + 1 }
+    return i
+
+instance Monad m => MonadFresh NameId (PureConversionT m) where
+  fresh = do
+    i <- gets freshNameId
+    modify $ \f -> f { freshNameId = succ i }
+    return i
+
+instance Monad m => MonadFresh Int (PureConversionT m) where
+  fresh = do
+    i <- gets freshInt
+    modify $ \f -> f { freshInt = i + 1 }
+    return i
diff --git a/src/full/Agda/TypeChecking/Coverage.hs b/src/full/Agda/TypeChecking/Coverage.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Coverage.hs
@@ -0,0 +1,1540 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# LANGUAGE TypeApplications #-}
+
+{-| Coverage checking, case splitting, and splitting for refine tactics.
+
+ -}
+
+module Agda.TypeChecking.Coverage
+  ( SplitClause(..), clauseToSplitClause, insertTrailingArgs
+  , Covering(..), splitClauses
+  , coverageCheck
+  , isCovered
+  , splitClauseWithAbsurd
+  , splitLast
+  , splitResult
+  , normaliseProjP
+  ) where
+
+import Prelude hiding (null, (!!))  -- do not use partial functions like !!
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans ( lift )
+
+import Data.Foldable (for_)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import qualified Agda.Benchmarking as Bench
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Internal hiding (DataOrRecord)
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Translation.InternalToAbstract (NamedClause(..))
+
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+import Agda.TypeChecking.Rules.LHS (DataOrRecord, checkSortOfSplitVar)
+import Agda.TypeChecking.Rules.LHS.Problem (allFlexVars)
+import Agda.TypeChecking.Rules.LHS.Unify
+import Agda.TypeChecking.Rules.Term (unquoteTactic)
+
+import Agda.TypeChecking.Coverage.Match
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Coverage.SplitClause
+import Agda.TypeChecking.Coverage.Cubical
+
+
+import Agda.TypeChecking.Conversion (tryConversion, equalType)
+import Agda.TypeChecking.Datatypes (getConForm)
+import {-# SOURCE #-} Agda.TypeChecking.Empty ( checkEmptyTel, isEmptyTel, isEmptyType )
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Warnings
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Control.Monad.State
+
+
+type CoverM = ExceptT SplitError TCM
+
+-- | Top-level function for checking pattern coverage.
+--
+--   Effects:
+--
+--   - Marks unreachable clauses as such in the signature.
+--
+--   - Adds missing instances clauses to the signature.
+--
+coverageCheck
+  :: QName     -- ^ Name @f@ of definition.
+  -> Type      -- ^ Absolute type (including the full parameter telescope).
+  -> [Clause]  -- ^ Clauses of @f@.  These are the very clauses of @f@ in the signature.
+  -> TCM SplitTree
+coverageCheck f t cs = do
+  reportSLn "tc.cover.top" 30 $ "entering coverageCheck for " ++ prettyShow f
+  reportSDoc "tc.cover.top" 75 $ "  of type (raw): " <+> (text . prettyShow) t
+  reportSDoc "tc.cover.top" 45 $ "  of type: " <+> prettyTCM t
+  TelV gamma a <- telViewUpTo (-1) t
+  reportSLn "tc.cover.top" 30 $ "coverageCheck: computed telView"
+
+  let -- n             = arity
+      -- xs            = variable patterns fitting lgamma
+      n            = size gamma
+      xs           =  map (setOrigin Inserted) $ teleNamedArgs gamma
+
+  reportSLn "tc.cover.top" 30 $ "coverageCheck: getDefFreeVars"
+
+      -- The initial module parameter substitutions need to be weakened by the
+      -- number of arguments that aren't module parameters.
+  fv           <- getDefFreeVars f
+
+  reportSLn "tc.cover.top" 30 $ "coverageCheck: getting checkpoints"
+
+  -- TODO: does this make sense? Why are we weakening by n - fv?
+  checkpoints <- applySubst (raiseS (n - fv)) <$> viewTC eCheckpoints
+
+      -- construct the initial split clause
+  let sc = SClause gamma xs idS checkpoints $ Just $ defaultDom a
+
+  reportSDoc "tc.cover.top" 10 $ do
+    let prCl cl = addContext (clauseTel cl) $
+                  prettyTCMPatternList $ namedClausePats cl
+    vcat
+      [ text $ "Coverage checking " ++ prettyShow f ++ " with patterns:"
+      , nest 2 $ vcat $ map prCl cs
+      ]
+
+  -- used = actually used clauses for cover
+  -- pss  = non-covered cases
+  CoverResult splitTree used pss qss noex <- cover f cs sc
+
+  -- Andreas, 2018-11-12, issue #378:
+  -- some indices in @used@ and @noex@ point outside of @cs@,
+  -- since missing hcomp clauses have been added during the course of @cover@.
+  -- We simply delete theses indices from @noex@.
+  noex <- return $ List.filter (< length cs) $ IntSet.toList noex
+
+  reportSDoc "tc.cover.top" 10 $ vcat
+    [ "cover computed!"
+    , text $ "used clauses: " ++ show used
+    , text $ "non-exact clauses: " ++ show noex
+    ]
+  reportSDoc "tc.cover.splittree" 10 $ vcat
+    [ "generated split tree for" <+> prettyTCM f
+    , text $ prettyShow splitTree
+    ]
+  reportSDoc "tc.cover.covering" 10 $ vcat
+    [ text $ "covering patterns for " ++ prettyShow f
+    , nest 2 $ vcat $ map (\ cl -> addContext (clauseTel cl) $ prettyTCMPatternList $ namedClausePats cl) qss
+    ]
+
+  -- Storing the covering clauses so that checkIApplyConfluence_ can
+  -- find them later.
+  -- Andreas, 2019-03-27, only needed when --cubical
+  -- Jesper, 2022-10-18, also needed for some backends, so keep when flag says so
+  opts <- pragmaOptions
+  when (isJust (optCubical opts) || optKeepCoveringClauses opts) $
+    modifySignature $ updateDefinition f $ updateTheDef $ updateCovering $ const qss
+
+
+  -- filter out the missing clauses that are absurd.
+  pss <- ifNotM (optInferAbsurdClauses <$> pragmaOptions) (pure pss) {-else-} $
+   flip filterM pss $ \(tel,ps) ->
+    -- Andreas, 2019-04-13, issue #3692: when adding missing absurd
+    -- clauses, also put the absurd pattern in.
+    caseEitherM (checkEmptyTel noRange tel) (\ _ -> return True) $ \ l -> do
+      -- Now, @l@ is the first type in @tel@ (counting from 0=leftmost)
+      -- which is empty.  Turn it into a de Bruijn index @i@.
+      let i = size tel - 1 - l
+      -- Build a substitution mapping this pattern variable to the absurd pattern.
+      let sub = inplaceS i $ absurdP i
+        -- ifNotM (isEmptyTel tel) (return True) $ do
+      -- Jesper, 2018-11-28, Issue #3407: if the clause is absurd,
+      -- add the appropriate absurd clause to the definition.
+      let cl = Clause { clauseLHSRange  = noRange
+                      , clauseFullRange = noRange
+                      , clauseTel       = tel
+                      , namedClausePats = applySubst sub ps
+                      , clauseBody      = Nothing
+                      , clauseType      = Nothing
+                      , clauseCatchall    = True       -- absurd clauses are safe as catch-all
+                      , clauseExact       = Just False
+                      , clauseRecursive   = Just False
+                      , clauseUnreachable = Just False
+                      , clauseEllipsis    = NoEllipsis
+                      , clauseWhereModule = Nothing
+                      }
+      reportSDoc "tc.cover.missing" 20 $ inTopContext $ do
+        sep [ "adding missing absurd clause"
+            , nest 2 $ prettyTCM $ QNamed f cl
+            ]
+      reportSDoc "tc.cover.missing" 80 $ inTopContext $ vcat
+        [ "l   = " <+> pretty l
+        , "i   = " <+> pretty i
+        , "cl  = " <+> pretty (QNamed f cl)
+        ]
+      addClauses f [cl]
+      return False
+
+  -- report a warning if there are uncovered cases,
+  unless (null pss) $ do
+    stLocalPartialDefs `modifyTCLens` Set.insert f
+    whenM ((YesCoverageCheck ==) <$> viewTC eCoverageCheck) $
+      setCurrentRange cs $ warning $ CoverageIssue f pss
+
+  -- Andreas, 2017-08-28, issue #2723:
+  -- Mark clauses as reachable or unreachable in the signature.
+  -- Andreas, 2020-11-19, issue #5065
+  -- Remember whether clauses are exact or not.
+  let (is0, cs1) = unzip $ for (zip [0..] cs) $ \ (i, cl) -> let
+          unreachable = i `IntSet.notMember` used
+          exact       = i `IntSet.notMember` (IntSet.fromList noex)
+        in (boolToMaybe unreachable i, cl
+             { clauseUnreachable = Just unreachable
+             , clauseExact       = Just exact
+             })
+  -- is = indices of unreachable clauses
+  let is = catMaybes is0
+  reportSDoc "tc.cover.top" 10 $ vcat
+    [ text $ "unreachable clauses: " ++ if null is then "(none)" else show is
+    ]
+  -- Replace the first clauses by @cs1@.  There might be more
+  -- added by @inferMissingClause@.
+  modifyFunClauses f $ \ cs0 -> cs1 ++ drop (length cs1) cs0
+
+  -- Warn if there are unreachable clauses and mark them as unreachable.
+  unless (null is) $ do
+    -- Warn about unreachable clauses.
+    let unreached = filter ((Just True ==) . clauseUnreachable) cs1
+    let ranges    = map clauseFullRange unreached
+    setCurrentRange ranges $ warning $ UnreachableClauses f ranges
+
+  -- Report a warning if there are clauses that are not preserved as
+  -- definitional equalities and --exact-split is enabled
+  -- and they are not labelled as CATCHALL.
+  let noexclauses = forMaybe noex $ \ i -> do
+        let cl = indexWithDefault __IMPOSSIBLE__ cs1 i
+        if clauseCatchall cl then Nothing else Just cl
+  unless (null noexclauses) $ do
+      setCurrentRange (map clauseLHSRange noexclauses) $
+        warning $ CoverageNoExactSplit f $ noexclauses
+  return splitTree
+
+-- | Top-level function for eliminating redundant clauses in the interactive
+--   case splitter
+isCovered :: QName -> [Clause] -> SplitClause -> TCM Bool
+isCovered f cs sc = do
+  reportSDoc "tc.cover.isCovered" 20 $ vcat
+    [ "isCovered"
+    , nest 2 $ vcat $
+      [ "f  = " <+> prettyTCM f
+      , "cs = " <+> vcat (map (nest 2 . prettyTCM . NamedClause f True) cs)
+      , "sc = " <+> prettyTCM sc
+      ]
+    ]
+  -- Jesper, 2019-10: introduce trailing arguments (see #3828)
+  (_ , sc') <- insertTrailingArgs True sc
+  CoverResult { coverMissingClauses = missing } <- cover f cs sc'
+  return $ null missing
+ -- Andreas, 2019-08-08 and 2020-02-11
+ -- If there is an error (e.g. unification error), don't report it
+ -- to the user.  Rather, assume the clause is not already covered.
+ `catchError` \ _ -> return False
+
+-- | @cover f cs (SClause _ _ ps _) = return (CoverResult splitTree used missing covering noex)@.
+--   checks that the list of clauses @cs@ covers the given split clause.
+--   Returns the @splitTree@, the @used@ clauses, @missing@ cases, the @covering@ clauses,
+--   and the non-exact clauses @noex@.
+--
+--   Effect: adds missing instance clauses for @f@ to signature.
+--
+cover :: QName -> [Clause] -> SplitClause ->
+         TCM CoverResult
+cover f cs sc@(SClause tel ps _ _ target) = updateRelevance $ do
+  reportSDoc "tc.cover.cover" 10 $ inTopContext $ vcat
+    [ "checking coverage of pattern:"
+    , nest 2 $ prettyTCM sc
+    , nest 2 $ "target sort =" <+> do addContext tel $ maybe (text "<none>") (prettyTCM . getSort . unDom) target
+    ]
+  reportSLn "tc.cover.cover" 80 $ "raw target =\n" ++ show target
+  verboseS  "tc.cover.matching" 20 $ do
+    reportSLn "tc.cover.matching" 20 $ "clauses when matching:"
+    forM_ cs $ \ c -> do
+      let gamma = clauseTel c
+          ps = namedClausePats c
+      reportSDoc "tc.cover.matching" 20 $ addContext gamma $
+          "ps   :" <+> prettyTCM (fmap namedArg ps)
+
+  match cs ps >>= \case
+    Yes (i,mps) -> do
+      reportSLn "tc.cover.cover" 10 $ "pattern covered by clause " ++ show i
+      reportSDoc "tc.cover.cover" 20 $ text "with mps = " <+> do addContext tel $ pretty mps
+      exact <- allM mps $ isTrivialPattern . snd
+      let cl0 = indexWithDefault __IMPOSSIBLE__ cs i
+      cl <- applyCl sc cl0 mps
+      return $ CoverResult
+        { coverSplitTree      = SplittingDone (size tel)
+        , coverUsedClauses    = singleton i
+        , coverMissingClauses = []
+        , coverPatterns       = [cl]
+        , coverNoExactClauses = if exact then empty else singleton i
+        }
+
+    No        ->  do
+      reportSLn "tc.cover" 20 $ "pattern is not covered"
+      let infer dom = isInstance dom || isJust (domTactic dom)
+      if maybe False infer target
+        then do
+          -- Ulf, 2016-10-31: For now we only infer instance clauses. It would
+          -- make sense to do it also for hidden, but since the value of a
+          -- hidden clause is expected to be forced by later clauses, it's too
+          -- late to add it now. If it was inferrable we would have gotten a
+          -- type error before getting to this point.
+          -- Ulf, 2019-11-21: Also @tactic clauses.
+          cl <- inferMissingClause f sc
+          return $ CoverResult (SplittingDone (size tel)) empty [] [cl] empty
+        else do
+          let ps' = fromSplitPatterns ps
+          return $ CoverResult (SplittingDone (size tel)) empty [(tel, ps')] [] empty
+
+    -- We need to split!
+    -- If all clauses have an unsplit copattern, we try that first.
+    Block res bs -> trySplitRes res (null bs) splitError $ do
+      when (null bs) __IMPOSSIBLE__
+      -- Otherwise, if there are variables to split, we try them
+      -- in the order determined by a split strategy.
+      reportSLn "tc.cover.strategy" 20 $ "blocking vars = " ++ prettyShow bs
+      -- xs is a non-empty lists of blocking variables
+      -- try splitting on one of them
+      xs <- splitStrategy bs tel
+      -- Andreas, 2017-10-08, issue #2594
+      -- First, try to find split order for complete coverage.
+      -- If this fails, try to at least carry out the splitting to the end.
+      continue xs NoAllowPartialCover $ \ _err -> do
+        continue xs YesAllowPartialCover $ \ err -> do
+          splitError err
+  where
+    -- Andreas, 2019-08-07, issue #3966
+    -- When we get a SplitError, tighten the error Range to the clauses
+    -- that are still candidates for covering the SplitClause.
+    splitError :: SplitError -> TCM a
+    splitError = withRangeOfCandidateClauses . typeError . SplitError
+
+    -- This repeats the matching, but since we are crashing anyway,
+    -- the extra work just to compute a better Range does not matter.
+    withRangeOfCandidateClauses :: TCM a -> TCM a
+    withRangeOfCandidateClauses cont = do
+      cands <- mapMaybe (uncurry notNo) . zip cs <$> mapM (matchClause ps) cs
+      setCurrentRange cands cont
+      where
+        notNo :: Clause -> Match a -> Maybe Clause
+        notNo c = \case
+          Yes{}   -> Just c
+          Block{} -> Just c
+          No{}    -> Nothing
+
+    -- Rename the variables in a telescope in accordance with their
+    -- first appearance in the given NAPs. This is done to preserve
+    -- variable names in IApplyConfluence error messages. Specifically,
+    -- consider e.g.
+    --
+    --  data T : Set where
+    --    x : T
+    --    p : Path (Path T x x) refl refl
+    --  f (p i j) = ...
+    --
+    -- When generating the covering clause corresponding to f's clause,
+    -- the names we have in scope are i and i₁, since those are the
+    -- names of both PathP binder arguments. (recall Path A x y = PathP (λ i → A) x y)
+    -- So if we tried to print (Var 0 []) in the context of
+    -- IApplyConfluence for that clause, what we see isn't j, it's i₁.
+    --
+    -- This function takes "name suggestions" from both variable
+    -- patterns and IApply co/patterns, and replaces any existing names
+    -- in the telescope by the name in that pattern.
+    renTeleFromNap :: SplitClause -> Clause -> Telescope
+    renTeleFromNap SClause{scTel = tel, scPats = sps} clause =
+      telFromList $ evalState (traverse upd (telToList tel)) (size - offset)
+      where
+        ps = namedClausePats clause
+        offset = 1 + length (fromSplitPatterns sps) - length ps
+        -- Fold a single pattern into a map of name suggestions:
+        -- In the running example above, we have
+        --    f (p i@1 j@0)
+        -- so the map that nameSuggest (p ...) returns is {0 → j, 1 → j}
+        nameSuggest :: DeBruijnPattern -> IntMap ArgName
+        nameSuggest ps = flip foldPattern ps $ \case
+          VarP _ i | dbPatVarName i /= "_" ->
+            IntMap.singleton (dbPatVarIndex i) (dbPatVarName i)
+          IApplyP _ _ _ i | dbPatVarName i /= "_" ->
+            IntMap.singleton (dbPatVarIndex i) (dbPatVarName i)
+          _ -> mempty
+
+        -- Suggestions from all patterns..
+        suggestions = foldMap (nameSuggest . namedThing . unArg) ps
+
+        -- The state will start counting from (length Γ - 1), which is
+        -- the *highest* variable index, i.e. the index of the variable
+        -- with level 0. Instead of doing a lot of de Bruijn arithmetic
+        -- + recursion, traverse handles iteration and the State handles
+        -- counting down.
+        size = length (telToList tel)
+
+        upd :: Dom (ArgName , Type) -> State Int (Dom (ArgName , Type))
+        upd dom = state $ \s -> do
+          case IntMap.lookup s suggestions of
+            Just nm' -> ( dom{ domName = Just (WithOrigin CaseSplit (unranged nm'))
+                             , unDom = (nm' , snd (unDom dom))
+                             } , s - 1)
+            Nothing -> (dom , s - 1)
+
+    applyCl :: SplitClause -> Clause -> [(Nat, SplitPattern)] -> TCM Clause
+    applyCl sc@SClause{scTel = pretel, scPats = sps} cl mps
+        | tel <- renTeleFromNap sc cl = addContext tel $ do
+        let ps = namedClausePats cl
+        reportSDoc "tc.cover.applyCl" 40 $ "applyCl"
+        reportSDoc "tc.cover.applyCl" 40 $ "pretel =" <+> pretty pretel
+        reportSDoc "tc.cover.applyCl" 40 $ "tel    =" <+> pretty tel
+        reportSDoc "tc.cover.applyCl" 40 $ "ps     =" <+> pretty ps
+        reportSDoc "tc.cover.applyCl" 40 $ "mps    =" <+> pretty mps
+        reportSDoc "tc.cover.applyCl" 40 $ "s      =" <+> pretty s
+        reportSDoc "tc.cover.applyCl" 40 $ "ps[s]  =" <+> pretty (s `applySubst` ps)
+
+        -- If a matching clause has fewer patterns than the split
+        -- clause we ought to copy over the extra ones.
+        -- e.g. if the user wrote:
+        --
+        --   bar : Bool -> Bool
+        --   bar false = false
+        --   bar = \ _ -> true
+        --
+        -- then for the second clause the @extra@ patterns will be @[true]@.
+
+        let extra = drop (length ps) $ fromSplitPatterns sps
+            n_extra = length extra
+
+        reportSDoc "tc.cover.applyCl" 40 $ "extra  =" <+> pretty extra
+
+        -- When we add the extra patterns we also update the type
+        -- and the body of the clause.
+
+        mtv <- (traverse . traverse) (telViewUpToPath n_extra) $ clauseType cl
+        let ty = (fmap . fmap) ((parallelS (reverse $ map namedArg extra) `composeS` liftS n_extra s `applyPatSubst`) . theCore) mtv
+
+        reportSDoc "tc.cover.applyCl" 40 $ "new ty =" <+> pretty ty
+
+        return $
+             Clause { clauseLHSRange  = clauseLHSRange cl
+                    , clauseFullRange = clauseFullRange cl
+                    , clauseTel       = tel
+                    , namedClausePats = (s `applySubst` ps) ++ extra
+                    , clauseBody      = (`applyE` patternsToElims extra) . (s `applyPatSubst`) <$> clauseBody cl
+                    , clauseType      = ty
+                    , clauseCatchall    = clauseCatchall cl
+                    , clauseExact       = clauseExact cl
+                    , clauseRecursive   = clauseRecursive cl
+                    , clauseUnreachable = clauseUnreachable cl
+                    , clauseEllipsis    = clauseEllipsis cl
+                    , clauseWhereModule = clauseWhereModule cl
+                    }
+      where
+      mps' =
+        Map.fromList $
+        map (mapSnd (namedArg . fromSplitPattern . defaultNamedArg)) mps
+      s = parallelS (for (case Map.lookupMax mps' of
+                            Nothing     -> []
+                            Just (i, _) -> [0..i]) $ \ i ->
+                     fromMaybe (deBruijnVar i) (Map.lookup i mps'))
+
+    updateRelevance :: TCM a -> TCM a
+    updateRelevance cont =
+      -- Don't do anything if there is no target type info.
+      caseMaybe target cont $ \ b -> do
+        -- TODO (2018-10-16): if proofs get erased in the compiler, also wake erased vars!
+        let m = getModality b
+        applyModalityToContext m cont
+
+    continue
+      :: [BlockingVar]
+      -> AllowPartialCover
+      -> (SplitError -> TCM CoverResult)
+      -> TCM CoverResult
+    continue xs allowPartialCover handle = do
+      r <- altM1 (\ x -> fmap (,x) <$> split Inductive allowPartialCover sc x) xs
+      case r of
+        Left err -> handle err
+        -- If we get the empty covering, we have reached an impossible case
+        -- and are done.
+        Right (Covering n [], _) ->
+         do
+          -- TODO Andrea: I guess an empty pattern is not part of the cover?
+          let qs = []
+          return $ CoverResult (SplittingDone (size tel)) empty [] qs empty
+        Right (Covering n scs', x) -> do
+          let scs = map (\(t,(sc,i)) -> (t,sc)) scs'
+
+          (results_trX, cs) <- createMissingIndexedClauses f n x sc scs' cs
+          (scs, cs, results_hc) <- do
+            let fallback = return (scs, cs, [])
+            caseMaybeM (getPrimitiveName' builtinHComp) fallback $ \ comp -> do
+            let isComp = \case
+                  SplitCon c -> comp == c
+                  _ -> False
+            caseMaybe (List.find (isComp . fst) scs) fallback $ \ (sp, newSc) -> do
+            (res,cs') <- createMissingHCompClause f n x sc newSc cs
+            let scs2 = filter (not . isComp . fst) scs
+            return (scs2,cs',res)
+          let results_extra = results_hc ++ results_trX
+              trees_extra = map (\(sp,cr) -> (sp, coverSplitTree cr)) results_extra
+
+          results <- (++ map snd (results_extra)) <$> mapM ((cover f cs) . snd) scs
+          let trees = map coverSplitTree      results
+              useds = map coverUsedClauses    results
+              psss  = map coverMissingClauses results
+              qsss  = map coverPatterns       results
+              noex  = map coverNoExactClauses results
+          -- Jesper, 2016-03-10  We need to remember which variables were
+          -- eta-expanded by the unifier in order to generate a correct split
+          -- tree (see Issue 1872).
+          reportSDoc "tc.cover.split.eta" 60 $ vcat
+            [ "etaRecordSplits"
+            , nest 2 $ vcat
+              [ "n   = " <+> text (show n)
+              , "scs = " <+> prettyTCM scs
+              , "ps  = " <+> prettyTCMPatternList (fromSplitPatterns ps)
+              ]
+            ]
+          let trees' = zipWith (etaRecordSplits (unArg n) ps) scs trees
+              tree   = SplitAt n StrictSplit (trees' ++ trees_extra) -- TODO: Lazy?
+          return $ CoverResult tree (IntSet.unions useds) (concat psss) (concat qsss) (IntSet.unions noex)
+
+    -- Try to split result
+    trySplitRes
+      :: BlockedOnResult                  -- Are we blocked on the result?
+      -> Bool                             -- Is this the last thing we try?
+      -> (SplitError -> TCM CoverResult)  -- Handler for 'SplitError'
+      -> TCM CoverResult                  -- Continuation
+      -> TCM CoverResult
+    -- not blocked on result: try regular splits
+    trySplitRes NotBlockedOnResult finalSplit splitError cont
+      | finalSplit = __IMPOSSIBLE__ -- there must be *some* reason we are blocked
+      | otherwise  = cont
+    -- blocked on arguments that are not yet introduced:
+
+    -- we must split on a variable so that the target type becomes a pi type
+    trySplitRes (BlockedOnApply IsApply) finalSplit splitError cont = do
+      -- Andreas, 2021-12-31, issue #5712.
+      -- If there is a tactic to solve the clause, we might not have inserted
+      -- trailing args (due to #5358).  Now we force it!
+      (tel, sc') <- insertTrailingArgs True sc
+      if null tel then
+        if finalSplit then __IMPOSSIBLE__ -- already ruled out by lhs checker
+        else cont
+      else cover f cs sc'
+
+    -- ...or it was an IApply pattern, so we might just need to introduce the variable now.
+    trySplitRes (BlockedOnApply IsIApply) finalSplit splitError cont
+       = do
+         caseMaybeM (splitResultPath f sc) fallback $ (cover f cs . snd) <=< insertTrailingArgs False
+      where
+        fallback | finalSplit = __IMPOSSIBLE__ -- already ruled out by lhs checker?
+                 | otherwise  = cont
+
+    -- blocked on result but there are catchalls:
+    -- try regular splits if there are any, or else throw an error,
+    -- this is nicer than continuing and reporting unreachable clauses
+    -- (see issue #2833)
+    trySplitRes (BlockedOnProj True) finalSplit splitError cont
+      | finalSplit = splitError CosplitCatchall
+      | otherwise  = cont
+    -- all clauses have an unsplit copattern: try to split
+    trySplitRes (BlockedOnProj False) finalSplit splitError cont = do
+      reportSLn "tc.cover" 20 $ "blocked by projection pattern"
+      -- forM is a monadic map over a Maybe here
+      mcov <- splitResultRecord f sc
+      case mcov of
+        Left err
+          | finalSplit -> splitError err
+          | otherwise  -> cont
+        Right (Covering n scs) -> do
+          -- If result splitting was successful, continue coverage checking.
+          (projs, results) <- unzip <$> do
+            mapM (traverseF $ cover f cs <=< (snd <.> insertTrailingArgs False)) (map (\(t,(sc,i)) -> (t,sc)) scs)
+            -- OR:
+            -- forM scs $ \ (proj, sc') -> (proj,) <$> do
+            --   cover f cs =<< do
+            --     snd <$> fixTarget sc'
+          let trees = map coverSplitTree results
+              useds = map coverUsedClauses results
+              psss  = map coverMissingClauses results
+              qsss  = map coverPatterns results
+              noex  = map coverNoExactClauses results
+              tree  = SplitAt n StrictSplit $ zip projs trees   -- TODO: Lazy?
+          return $ CoverResult tree (IntSet.unions useds) (concat psss) (concat qsss) (IntSet.unions noex)
+
+    gatherEtaSplits :: Int -> SplitClause
+                    -> [NamedArg SplitPattern] -> [NamedArg SplitPattern]
+    gatherEtaSplits n sc []
+       | n >= 0    = __IMPOSSIBLE__ -- we should have encountered the main
+                                    -- split by now already
+       | otherwise = []
+    gatherEtaSplits n sc (p:ps) = case namedArg p of
+      VarP _ x
+       | n == 0    -> case p' of -- this is the main split
+           VarP  _ _    -> p : gatherEtaSplits (-1) sc ps
+           DotP  _ _    -> __IMPOSSIBLE__
+           ConP  _ _ qs -> qs ++ gatherEtaSplits (-1) sc ps
+           LitP{}       -> gatherEtaSplits (-1) sc ps
+           ProjP{}      -> __IMPOSSIBLE__
+           IApplyP{}    -> __IMPOSSIBLE__
+           DefP  _ _ qs -> qs ++ gatherEtaSplits (-1) sc ps -- __IMPOSSIBLE__ -- Andrea: maybe?
+       | otherwise ->
+           updateNamedArg (\ _ -> p') p : gatherEtaSplits (n-1) sc ps
+        where p' = lookupS (scSubst sc) $ splitPatVarIndex x
+      IApplyP{}   ->
+           updateNamedArg (applySubst (scSubst sc)) p : gatherEtaSplits (n-1) sc ps
+      DotP  _ _    -> p : gatherEtaSplits (n-1) sc ps -- count dot patterns
+      ConP  _ _ qs -> gatherEtaSplits n sc (qs ++ ps)
+      DefP  _ _ qs -> gatherEtaSplits n sc (qs ++ ps)
+      LitP{}       -> gatherEtaSplits n sc ps
+      ProjP{}      -> gatherEtaSplits n sc ps
+
+    addEtaSplits :: Int -> [NamedArg SplitPattern] -> SplitTree -> SplitTree
+    addEtaSplits k []     t = t
+    addEtaSplits k (p:ps) t = case namedArg p of
+      VarP  _ _     -> addEtaSplits (k + 1) ps t
+      DotP  _ _     -> addEtaSplits (k + 1) ps t
+      ConP c cpi qs -> SplitAt (p $> k) LazySplit [(SplitCon (conName c) , addEtaSplits k (qs ++ ps) t)]
+      LitP{}        -> __IMPOSSIBLE__
+      ProjP{}       -> __IMPOSSIBLE__
+      DefP{}        -> __IMPOSSIBLE__ -- Andrea: maybe?
+      IApplyP{}     -> addEtaSplits (k + 1) ps t
+
+    etaRecordSplits :: Int -> [NamedArg SplitPattern] -> (SplitTag,SplitClause)
+                    -> SplitTree -> (SplitTag,SplitTree)
+    etaRecordSplits n ps (q , sc) t =
+      (q , addEtaSplits 0 (gatherEtaSplits n sc ps) t)
+
+
+-- | Append a instance clause to the clauses of a function.
+inferMissingClause
+  :: QName
+       -- ^ Function name.
+  -> SplitClause
+       -- ^ Clause to add.  Clause hiding (in 'clauseType') must be 'Instance'.
+   -> TCM Clause
+inferMissingClause f (SClause tel ps _ cps (Just t)) = setCurrentRange f $ do
+  reportSDoc "tc.cover.infer" 20 $ addContext tel $ "Trying to infer right-hand side of type" <+> prettyTCM t
+  rhs <-
+    addContext tel
+    $ locallyTC eCheckpoints (const cps)
+    $ checkpoint IdS    -- introduce a fresh checkpoint
+    $ case getHiding t of
+        _ | Just tac <- domTactic t -> do
+          reportSDoc "tc.cover.infer" 40 $ vcat
+            [ "@tactic rhs"
+            , nest 2 $ "target =" <+> pretty t ]
+          (_, v) <- newValueMeta DontRunMetaOccursCheck CmpLeq (unDom t)
+          v <$ unquoteTactic tac v (unDom t)
+        Instance{} -> snd <$> newInstanceMeta "" (unDom t)
+        Hidden     -> __IMPOSSIBLE__
+        NotHidden  -> __IMPOSSIBLE__
+  let cl = Clause { clauseLHSRange  = noRange
+                  , clauseFullRange = noRange
+                  , clauseTel       = tel
+                  , namedClausePats = fromSplitPatterns ps
+                  , clauseBody      = Just rhs
+                  , clauseType      = Just (argFromDom t)
+                  , clauseCatchall    = False
+                  , clauseExact       = Just True
+                  , clauseRecursive   = Nothing     -- could be recursive
+                  , clauseUnreachable = Just False  -- missing, thus, not unreachable
+                  , clauseEllipsis    = NoEllipsis
+                  , clauseWhereModule = Nothing
+                  }
+  addClauses f [cl]  -- Important: add at the end.
+  return cl
+inferMissingClause _ (SClause _ _ _ _ Nothing) = __IMPOSSIBLE__
+
+splitStrategy :: BlockingVars -> Telescope -> TCM BlockingVars
+splitStrategy bs tel = return $ updateLast setBlockingVarOverlap xs
+  -- Make sure we do not insists on precomputed coverage when
+  -- we make our last try to split.
+  -- Otherwise, we will not get a nice error message.
+  where
+    xs             = strict ++ lazy
+    (lazy, strict) = List.partition blockingVarLazy bs
+{- KEEP!
+--  Andreas, 2012-10-13
+--  The following split strategy which prefers all-constructor columns
+--  fails on test/fail/CoverStrategy
+    xs       = ys ++ zs
+    (ys, zs) = partition allConstructors bs
+    allConstructors :: BlockingVar -> Bool
+    allConstructors = isJust . snd
+-}
+
+
+-- | Check that a type is a non-irrelevant datatype or a record with
+-- named constructor. Unless the 'Induction' argument is 'CoInductive'
+-- the data type must be inductive.
+isDatatype :: (MonadTCM tcm, MonadError SplitError tcm) =>
+              Induction -> Dom Type ->
+              tcm (DataOrRecord, QName, Args, Args, [QName], Bool)
+isDatatype ind at = do
+  let t       = unDom at
+      throw f = throwError . f =<< do liftTCM $ buildClosure t
+  t' <- liftTCM $ reduce t
+  mInterval <- liftTCM $ getBuiltinName' builtinInterval
+  mIsOne <- liftTCM $ getBuiltinName' builtinIsOne
+  case unEl t' of
+    Def d [] | Just d == mInterval -> throw NotADatatype
+    Def d [Apply phi] | Just d == mIsOne -> do
+                xs <- liftTCM $ decomposeInterval =<< reduce (unArg phi)
+                if null xs
+                   then return $ (IsData, d, [phi], [], [], False)
+                   else throw NotADatatype
+    Def d es -> do
+      let ~(Just args) = allApplyElims es
+      def <- liftTCM $ theDef <$> getConstInfo d
+      case def of
+        Datatype{dataPars = np, dataCons = cs}
+          | otherwise -> do
+              let (ps, is) = splitAt np args
+              return (IsData, d, ps, is, cs, not $ null (dataPathCons def))
+        Record{recPars = np, recConHead = con, recInduction = i, recEtaEquality'}
+          | i == Just CoInductive && ind /= CoInductive ->
+              throw CoinductiveDatatype
+          | otherwise ->
+              return (IsRecord InductionAndEta { recordInduction=i, recordEtaEquality=recEtaEquality' }, d, args, [], [conName con], False)
+        _ -> throw NotADatatype
+    _ -> throw NotADatatype
+
+-- | Update the target type of the split clause after a case split.
+fixTargetType
+  :: Quantity  -- ^ The quantity of the thing that is split.
+  -> SplitTag -> SplitClause -> Dom Type -> TCM SplitClause
+fixTargetType q tag sc@SClause{ scTel = sctel, scSubst = sigma } target = do
+    reportSDoc "tc.cover.target" 20 $ sep
+      [ "split clause telescope: " <+> prettyTCM sctel
+      ]
+    reportSDoc "tc.cover.target" 60 $ sep
+      [ "substitution          : " <+> prettyTCM sigma
+      ]
+    reportSDoc "tc.cover.target" 60 $ sep
+      [ "target type before substitution:" <+> pretty target
+      , "             after substitution:" <+> pretty (applySplitPSubst sigma target)
+      ]
+
+    -- We update the target quantity to 0 for erased constructors, but
+    -- not if the match is made in an erased position, or if the
+    -- original constructor definition is not erased.
+    updQuant <- do
+      let erased = case q of
+            Quantity0{} -> True
+            Quantity1{} -> __IMPOSSIBLE__
+            Quantityω{} -> False
+      if erased then return id else case tag of
+        SplitCon c -> do
+          q <- getQuantity <$> getOriginalConstInfo c
+          case q of
+            Quantity0{} -> return $ mapQuantity (composeQuantity q)
+            Quantity1{} -> return id
+            Quantityω{} -> return id
+        SplitLit{} -> return id
+        SplitCatchall{} -> return id
+
+    return $ sc { scTarget = Just $ updQuant $ applySplitPSubst sigma target }
+
+
+-- | Add more patterns to split clause if the target type is a function type.
+--   Returns the domains of the function type (if any).
+insertTrailingArgs
+  :: Bool         -- ^ Force insertion even when there is a 'domTactic'?
+  -> SplitClause
+  -> TCM (Telescope, SplitClause)
+insertTrailingArgs force sc@SClause{ scTel = sctel, scPats = ps, scSubst = sigma, scCheckpoints = cps, scTarget = target } = do
+  let fallback = return (empty, sc)
+  caseMaybe target fallback $ \ a -> do
+    if isJust (domTactic a) && not force then fallback else do
+    (TelV tel b) <- addContext sctel $ telViewUpTo (-1) $ unDom a
+    reportSDoc "tc.cover.target" 15 $ sep
+      [ "target type telescope: " <+> do
+          addContext sctel $ prettyTCM tel
+      , "target type core     : " <+> do
+          addContext sctel $ addContext tel $ prettyTCM b
+      ]
+    let n         = size tel
+        -- Andreas, 2016-10-04 issue #2236
+        -- Need to set origin to "Inserted" to avoid printing of hidden patterns.
+        xs        = map (mapArgInfo hiddenInserted) $ teleNamedArgs tel
+        -- Compute new split clause
+        sctel'    = telFromList $ telToList (raise n sctel) ++ telToList tel
+        -- Dot patterns in @ps@ need to be raised!  (Issue 1298)
+        ps'       = applySubst (raiseS n) ps ++ xs
+        newTarget = Just $ (if not (null tel) then a{ domTactic = Nothing } else a) $> b
+        sc'       = SClause
+          { scTel    = sctel'
+          , scPats   = ps'
+          , scSubst  = wkS n $ sigma -- Should be wkS instead of liftS since
+                                     -- variables are only added to new tel.
+          , scCheckpoints        = applySubst (raiseS n) cps
+          , scTarget = newTarget
+          }
+    -- Separate debug printing to find cause of crash (Issue 1374)
+    reportSDoc "tc.cover.target" 30 $ sep
+      [ "new split clause telescope   : " <+> prettyTCM sctel'
+      ]
+    reportSDoc "tc.cover.target" 30 $ sep
+      [ "new split clause patterns    : " <+> do
+          addContext sctel' $ prettyTCMPatternList $ fromSplitPatterns ps'
+      ]
+    reportSDoc "tc.cover.target" 60 $ sep
+      [ "new split clause substitution: " <+> prettyTCM (scSubst sc')
+      ]
+    reportSDoc "tc.cover.target" 30 $ sep
+      [ "new split clause target      : " <+> do
+          addContext sctel' $ prettyTCM $ fromJust newTarget
+      ]
+    reportSDoc "tc.cover.target" 20 $ sep
+      [ "new split clause"
+      , prettyTCM sc'
+      ]
+    return $ if n == 0 then (empty, sc { scTarget = newTarget }) else (tel, sc')
+
+-- Andreas, 2017-01-18, issue #819, set visible arguments to UserWritten.
+-- Otherwise, they will be printed as _.
+hiddenInserted :: ArgInfo -> ArgInfo
+hiddenInserted ai
+  | visible ai = setOrigin UserWritten ai
+  | otherwise  = setOrigin Inserted ai
+
+
+-- | Checks if a type in this sort supports hcomp.
+--   currently all such types will have a Level.
+--   precondition: Sort in whnf and not blocked.
+hasHComp :: Sort -> Maybe Level
+hasHComp (Type l) = Just l
+hasHComp _        = Nothing
+
+
+computeHCompSplit  :: Telescope   -- ^ Telescope before split point.
+  -> PatVarName                   -- ^ Name of pattern variable at split point.
+  -> Telescope                    -- ^ Telescope after split point.
+  -> QName                        -- ^ Name of datatype to split at.
+  -> Args                         -- ^ Data type parameters.
+  -> Args                         -- ^ Data type indices.
+  -> Nat                          -- ^ Index of split variable.
+  -> Telescope                    -- ^ Telescope for the patterns.
+  -> [NamedArg SplitPattern]      -- ^ Patterns before doing the split.
+  -> Map CheckpointId Substitution -- ^ Current checkpoints
+  -- -> QName                        -- ^ Constructor to fit into hole.
+  -> CoverM (Maybe (SplitTag,SplitClause))   -- ^ New split clause if successful.
+computeHCompSplit delta1 n delta2 d pars ixs hix tel ps cps = do
+  withK   <- not . optCubicalCompatible <$> pragmaOptions
+  if withK then return Nothing else do
+    -- Get the type of the datatype
+  -- Δ1 ⊢ dtype
+  dsort <- liftTCM $ (parallelS (reverse $ map unArg pars) `applySubst`) . dataSort . theDef <$> getConstInfo d
+  hCompName <- fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinHComp
+  theHCompT <- defType <$> getConstInfo hCompName
+
+  -- TODO can dsort be blocked or not in whnf?
+  caseMaybe (hasHComp dsort) (return Nothing) $ \ dlvl' -> do
+  let
+    dlvl = Level dlvl'
+    dterm = Def d [] `apply` (pars ++ ixs)
+  -- Δ1 ⊢ gamma
+  TelV gamma _ <- lift $ telView (theHCompT `piApply` [setHiding Hidden $ defaultArg $ dlvl , defaultArg $ dterm])
+  case (delta1 `abstract` gamma,IdS) of
+    (delta1',rho0) -> do
+--      debugSubst "rho0" rho0
+
+      -- We have Δ₁' ⊢ ρ₀ : Δ₁Γ, so split it into the part for Δ₁ and the part for Γ
+      let (rho1,rho2) = splitS (size gamma) $ toSplitPSubst rho0
+
+      let defp = DefP defaultPatternInfo hCompName . map (setOrigin Inserted) $ -- should there be a different Origin here?
+                   map (fmap unnamed) [setHiding Hidden $ defaultArg $ applySubst rho1 $ DotP defaultPatternInfo $ dlvl
+                                      ,setHiding Hidden $ defaultArg $ applySubst rho1 $ DotP defaultPatternInfo $ dterm]
+                   ++ applySubst rho2 (teleNamedArgs gamma) -- rho0?
+      -- Compute final context and substitution
+      let rho3    = consS defp rho1            -- Δ₁' ⊢ ρ₃ : Δ₁(x:D)
+          delta2' = applySplitPSubst rho3 delta2  -- Δ₂' = Δ₂ρ₃
+          delta'  = delta1' `abstract` delta2' -- Δ'  = Δ₁'Δ₂'
+          rho     = liftS (size delta2) rho3   -- Δ' ⊢ ρ : Δ₁(x:D)Δ₂
+
+      -- debugTel "delta'" delta'
+      -- debugSubst "rho" rho
+      -- debugPs tel ps
+
+      -- Apply the substitution
+      let ps' = applySubst rho ps
+      -- debugPlugged delta' ps'
+
+      let cps' = applySplitPSubst rho cps
+
+      return $ Just . (SplitCon hCompName,) $ SClause delta' ps' rho cps' Nothing -- target fixed later
+
+
+-- | @computeNeighbourhood delta1 delta2 d pars ixs hix tel ps con@
+--
+--   @
+--      delta1   Telescope before split point
+--      n        Name of pattern variable at split point
+--      delta2   Telescope after split point
+--      d        Name of datatype to split at
+--      pars     Data type parameters
+--      ixs      Data type indices
+--      hix      Index of split variable
+--      tel      Telescope for patterns ps
+--      ps       Patterns before doing the split
+--      cps      Current module parameter checkpoints
+--      con      Constructor to fit into hole
+--   @
+--   @dtype == d pars ixs@
+computeNeighbourhood
+  :: Telescope                    -- ^ Telescope before split point.
+  -> PatVarName                   -- ^ Name of pattern variable at split point.
+  -> Telescope                    -- ^ Telescope after split point.
+  -> QName                        -- ^ Name of datatype to split at.
+  -> Args                         -- ^ Data type parameters.
+  -> Args                         -- ^ Data type indices.
+  -> Nat                          -- ^ Index of split variable.
+  -> Telescope                    -- ^ Telescope for the patterns.
+  -> [NamedArg SplitPattern]      -- ^ Patterns before doing the split.
+  -> Map CheckpointId Substitution -- ^ Current checkpoints
+  -> QName                        -- ^ Constructor to fit into hole.
+  -> CoverM (Maybe (SplitClause, IInfo))   -- ^ New split clause if successful.
+computeNeighbourhood delta1 n delta2 d pars ixs hix tel ps cps c = do
+
+  -- Get the type of the datatype
+  dtype <- liftTCM $ (`piApply` pars) . defType <$> getConstInfo d
+
+  -- Get the real constructor name
+  con <- liftTCM $ fromRight __IMPOSSIBLE__ <$> getConForm c
+  con <- return $ con { conName = c }  -- What if we restore the current name?
+                                       -- Andreas, 2013-11-29 changes nothing!
+
+  -- Get the type of the constructor
+  ctype <- liftTCM $ defType <$> getConInfo con
+
+  -- Lookup the type of the constructor at the given parameters
+  (gamma0, cixs, boundary) <- do
+    (TelV gamma0 (El _ d), boundary) <- liftTCM $ addContext delta1 $
+      telViewPathBoundaryP (ctype `piApply` pars)
+    let Def _ es = d
+        Just cixs = allApplyElims es
+    return (gamma0, cixs, boundary)
+
+  let (_, Dom{domInfo = info} : _) = splitAt (size tel - hix - 1) (telToList tel)
+
+  -- Andreas, 2012-02-25 preserve name suggestion for recursive arguments
+  -- of constructor
+
+  let preserve (x, t@(El _ (Def d' _))) | d == d' = (n, t)
+      preserve (x, t) = (x, t)
+      gamma  = (fmap . mapModality) (composeModality (getModality info)) $ telFromList . map (fmap preserve) . telToList $ gamma0
+      delta1Gamma = delta1 `abstract` gamma
+
+  debugInit con ctype d pars ixs cixs delta1 delta2 gamma tel ps hix
+
+  cforced <- defForced <$> getConstInfo c
+      -- Variables in Δ₁ are not forced, since the unifier takes care to not introduce forced
+      -- variables.
+  let forced = replicate (size delta1) NotForced ++ cforced
+      flex   = allFlexVars forced delta1Gamma -- All variables are flexible
+
+  -- Unify constructor target and given type (in Δ₁Γ)
+  let conIxs   = drop (size pars) cixs
+      givenIxs = raise (size gamma) ixs
+
+  -- Andrea 2019-07-17 propagate the Cohesion to the equation telescope
+  -- TODO: should we propagate the modality in general?
+  -- See also LHS checking.
+  dtype <- addContext delta1 $ do
+         let updCoh = composeCohesion (getCohesion info)
+         TelV dtel dt <- telView dtype
+         return $ abstract (mapCohesion updCoh <$> dtel) dt
+  dsort <- addContext delta1 $ reduce (getSort dtype)
+
+  let withKIfStrict = applyWhen (isStrictDataSort dsort) $ locallyTC eSplitOnStrict $ const True
+
+  -- Should we attempt to compute a left inverse for this clause? When
+  -- --cubical-compatible --flat-split is given, we don't generate a
+  -- left inverse (at all). This means that, when the coverage checker
+  -- gets to the clause this was in, it won't generate a (malformed!)
+  -- transpX clause for @♭ matching.
+  -- TODO(Amy): properly support transpX when @♭ stuff is in the
+  -- context.
+  let flatSplit = boolToMaybe (getCohesion info == Flat) SplitOnFlat
+
+  r <- withKIfStrict $ lift $
+         Bench.billTo [Bench.Coverage, Bench.UnifyIndices] $
+           unifyIndices' flatSplit
+             delta1Gamma
+             flex
+             (raise (size gamma) dtype)
+             conIxs
+             givenIxs
+
+  TelV eqTel _ <- telView $ (raise (size gamma) dtype)
+
+  let stuck b errs = do
+        debugCantSplit
+        throwError $ UnificationStuck b (conName con) (delta1 `abstract` gamma) conIxs givenIxs errs
+
+
+  case r of
+    NoUnify {} -> debugNoUnify $> Nothing
+
+    UnifyBlocked block -> stuck (Just block) []
+
+    UnifyStuck errs -> stuck Nothing errs
+
+    Unifies (delta1',rho0,eqs,tauInv) -> do
+
+      let unifyInfo | Type _ <- dsort     -- only types of sort Type l have trX constructors:
+                                          -- re #3733: update if we add transp for other sorts.
+                    , not $ null $ conIxs -- no point propagating this info if trivial?
+                    , Right (tau,leftInv) <- tauInv
+            = TheInfo $ UE delta1Gamma delta1' eqTel (map unArg conIxs) (map unArg givenIxs) rho0 tau leftInv
+                    | otherwise
+            = NoInfo
+
+      case tauInv of
+        Right{} -> return ()
+        Left SplitOnStrict -> return ()
+        Left x -> do
+          whenM (optCubicalCompatible <$> pragmaOptions) $ do
+            -- re #3733: TODO better error msg.
+            lift $ warning . UnsupportedIndexedMatch =<< prettyTCM x
+
+      debugSubst "rho0" rho0
+
+      let rho0' = toSplitPSubst rho0
+
+      -- We have Δ₁' ⊢ ρ₀ : Δ₁Γ, so split it into the part for Δ₁ and the part for Γ
+      let (rho1,rho2) = splitS (size gamma) $ rho0'
+
+      -- Andreas, 2015-05-01  I guess it is fine to use no @conPType@
+      -- as the result of splitting is never used further down the pipeline.
+      -- After splitting, Agda reloads the file.
+      -- Andreas, 2017-09-03, issue #2729: remember that pattern was generated by case split.
+      let cpi  = noConPatternInfo{ conPInfo = PatternInfo PatOSplit [] , conPRecord = True }
+          conp = ConP con cpi $ applySubst rho0' $
+                   map (mapArgInfo hiddenInserted) $ telePatterns' (tele2NamedArgs gamma0) gamma boundary
+          -- Andreas, 2016-09-08, issue #2166: use gamma0 for correct argument names
+
+      -- Compute final context and substitution
+      let rho3    = consS conp rho1            -- Δ₁' ⊢ ρ₃ : Δ₁(x:D)
+          delta2' = applySplitPSubst rho3 delta2  -- Δ₂' = Δ₂ρ₃
+          delta'  = delta1' `abstract` delta2' -- Δ'  = Δ₁'Δ₂'
+          rho     = liftS (size delta2) rho3   -- Δ' ⊢ ρ : Δ₁(x:D)Δ₂
+
+      debugTel "delta'" delta'
+      debugSubst "rho" rho
+      debugPs tel ps
+
+      -- Apply the substitution
+      let ps' = applySubst rho ps
+      debugPlugged delta' ps'
+
+      let cps'  = applySplitPSubst rho cps
+
+      return $ Just . (,unifyInfo) $ SClause delta' ps' rho cps' Nothing -- target fixed later
+
+  where
+    debugInit con ctype d pars ixs cixs delta1 delta2 gamma tel ps hix = liftTCM $ do
+      reportSDoc "tc.cover.split.con" 20 $ vcat
+        [ "computeNeighbourhood"
+        , nest 2 $ vcat
+          [ "context=" <+> (inTopContext . prettyTCM =<< getContextTelescope)
+          , "con    =" <+> prettyTCM con
+          , "ctype  =" <+> prettyTCM ctype
+          , "ps     =" <+> do inTopContext $ addContext tel $ prettyTCMPatternList $ fromSplitPatterns ps
+          , "d      =" <+> prettyTCM d
+          , "pars   =" <+> do prettyList $ map prettyTCM pars
+          , "ixs    =" <+> do addContext delta1 $ prettyList $ map prettyTCM ixs
+          , "cixs   =" <+> do addContext gamma  $ prettyList $ map prettyTCM cixs
+          , "delta1 =" <+> do inTopContext $ prettyTCM delta1
+          , "delta2 =" <+> do inTopContext $ addContext delta1 $ addContext n $ prettyTCM delta2
+          , "gamma  =" <+> do inTopContext $ addContext delta1 $ prettyTCM gamma
+          , "tel  =" <+> do inTopContext $ prettyTCM tel
+          , "hix    =" <+> text (show hix)
+          ]
+        ]
+      reportSDoc "tc.cover.split.con" 70 $ vcat
+        [ "computeNeighbourhood"
+        , nest 2 $ vcat
+          [ "context=" <+> (inTopContext . (text . show) =<< getContextTelescope)
+          , "con    =" <+> (text . show) con
+          , "ctype  =" <+> (text . show) ctype
+          , "ps     =" <+> (text . show) ps
+          , "d      =" <+> (text . show) d
+          , "pars   =" <+> (text . show) pars
+          , "ixs    =" <+> (text . show) ixs
+          , "cixs   =" <+> (text . show) cixs
+          , "delta1 =" <+> (text . show) delta1
+          , "delta2 =" <+> (text . show) delta2
+          , "gamma  =" <+> (text . show) gamma
+          , "hix    =" <+> text (show hix)
+          ]
+        ]
+
+    debugNoUnify =
+      liftTCM $ reportSLn "tc.cover.split.con" 20 "  Constructor impossible!"
+
+    debugCantSplit =
+      liftTCM $ reportSLn "tc.cover.split.con" 20 "  Bad split!"
+
+    debugSubst s sub =
+      liftTCM $ reportSDoc "tc.cover.split.con" 20 $ nest 2 $ vcat
+        [ text (s ++ " =") <+> prettyTCM sub
+        ]
+
+    debugTel s tel =
+      liftTCM $ reportSDoc "tc.cover.split.con" 20 $ nest 2 $ vcat
+        [ text (s ++ " =") <+> prettyTCM tel
+        ]
+
+    debugPs tel ps =
+      liftTCM $ reportSDoc "tc.cover.split.con" 20 $
+        inTopContext $ addContext tel $ nest 2 $ vcat
+          [ "ps     =" <+> prettyTCMPatternList (fromSplitPatterns ps)
+          ]
+
+    debugPlugged delta' ps' = do
+      liftTCM $ reportSDoc "tc.cover.split.con" 20 $
+        inTopContext $ addContext delta' $ nest 2 $ vcat
+          [ "ps'    =" <+> do prettyTCMPatternList $ fromSplitPatterns ps'
+          ]
+
+-- | Introduce trailing pattern variables?
+data InsertTrailing
+  = DoInsertTrailing
+  | DontInsertTrailing
+  deriving (Eq, Show)
+
+-- | Allow partial covering for split?
+data AllowPartialCover
+  = YesAllowPartialCover  -- To try to coverage-check incomplete splits.
+  | NoAllowPartialCover   -- Default.
+  deriving (Eq, Show)
+
+-- | Entry point from @Interaction.MakeCase@.
+splitClauseWithAbsurd :: SplitClause -> Nat -> TCM (Either SplitError (Either SplitClause Covering))
+splitClauseWithAbsurd c x =
+  split' CheckEmpty Inductive NoAllowPartialCover DontInsertTrailing c (BlockingVar x [] [] True False)
+  -- Andreas, 2016-05-03, issue 1950:
+  -- Do not introduce trailing pattern vars after split,
+  -- because this does not work for with-clauses.
+
+-- | Entry point from @TypeChecking.Empty@ and @Interaction.BasicOps@.
+--   @splitLast CoInductive@ is used in the @refine@ tactics.
+
+splitLast :: Induction -> Telescope -> [NamedArg DeBruijnPattern] -> TCM (Either SplitError Covering)
+splitLast ind tel ps = split ind NoAllowPartialCover sc (BlockingVar 0 [] [] True False)
+  where sc = SClause tel (toSplitPatterns ps) empty empty target
+        -- TODO 2ltt: allows (Empty_fib -> Empty_strict) which is not conservative
+        target = (Just $ defaultDom $ El (Prop (Max 0 [])) $ Dummy "splitLastTarget" [])
+
+-- | @split ind splitClause x = return res@
+--   splits @splitClause@ at pattern var @x@ (de Bruijn index).
+--
+--   Possible results @res@ are:
+--
+--   1. @Left err@:
+--      Splitting failed.
+--
+--   2. @Right covering@:
+--      A covering set of split clauses, one for each valid constructor.
+--      This could be the empty set (denoting an absurd clause).
+
+split :: Induction
+         -- ^ Coinductive constructors are allowed if this argument is
+         -- 'CoInductive'.
+      -> AllowPartialCover
+         -- ^ Don't fail if computed 'Covering' does not cover all constructors.
+      -> SplitClause
+      -> BlockingVar
+      -> TCM (Either SplitError Covering)
+split ind allowPartialCover sc x =
+  fmap blendInAbsurdClause <$> split' NoCheckEmpty ind allowPartialCover DoInsertTrailing sc x
+  where
+    n = lookupPatternVar sc $ blockingVarNo x
+    blendInAbsurdClause :: Either SplitClause Covering -> Covering
+    blendInAbsurdClause = fromRight (const $ Covering n [])
+
+-- | Convert a de Bruijn index relative to the clause telescope to a de Bruijn
+--   level. The result should be the argument position (counted from left,
+--   starting with 0) to split at (dot patterns included!).
+lookupPatternVar :: SplitClause -> Int -> Arg Nat
+lookupPatternVar SClause{ scTel = tel, scPats = pats } x = arg $>
+    if n < 0 then __IMPOSSIBLE__ else n
+  where n = if k < 0
+            then __IMPOSSIBLE__
+            else fromMaybe __IMPOSSIBLE__ $ permPicks perm !!! k
+        perm = fromMaybe __IMPOSSIBLE__ $ dbPatPerm $ fromSplitPatterns pats
+        k = size tel - x - 1
+        arg = indexWithDefault __IMPOSSIBLE__ (telVars (size tel) tel) k
+
+
+data CheckEmpty = CheckEmpty | NoCheckEmpty
+
+-- | @split' ind pc ft splitClause x = return res@
+--   splits @splitClause@ at pattern var @x@ (de Bruijn index).
+--
+--   Possible results @res@ are:
+--
+--   1. @Left err@:
+--      Splitting failed.
+--
+--   2. @Right (Left splitClause')@:
+--      Absurd clause (type of @x@ has 0 valid constructors).
+--
+--   3. @Right (Right covering)@:
+--      A covering set of split clauses, one for each valid constructor.
+
+split' :: CheckEmpty
+          -- ^ Use isEmptyType to check whether the type of the variable to
+          -- split on is empty. This switch is necessary to break the cycle
+          -- between split' and isEmptyType.
+       -> Induction
+          -- ^ Coinductive constructors are allowed if this argument is
+          -- 'CoInductive'.
+       -> AllowPartialCover
+          -- ^ Don't fail if computed 'Covering' does not cover all constructors.
+       -> InsertTrailing
+          -- ^ If 'DoInsertTrailing', introduce new trailing variable patterns.
+       -> SplitClause
+       -> BlockingVar
+       -> TCM (Either SplitError (Either SplitClause Covering))
+split' checkEmpty ind allowPartialCover inserttrailing
+       sc@(SClause tel ps _ cps target) (BlockingVar x pcons' plits overlap lazy) =
+ liftTCM $ runExceptT $ do
+  debugInit tel x ps cps
+
+  -- Split the telescope at the variable
+  -- t = type of the variable,  Δ₁ ⊢ t
+  (n, t, delta1, delta2) <- do
+    let (tel1, dom : tel2) = splitAt (size tel - x - 1) $ telToList tel
+    return (fst $ unDom dom, snd <$> dom, telFromList tel1, telFromList tel2)
+
+  -- Compute the neighbourhoods for the constructors
+  let computeNeighborhoods = do
+        -- Check that t is a datatype or a record
+        -- Andreas, 2010-09-21, isDatatype now directly throws an exception if it fails
+        -- cons = constructors of this datatype
+        (dr, d, pars, ixs, cons', isHIT) <- inContextOfT $ isDatatype ind t
+        isFib <- lift $ isFibrant t
+        cons <- case checkEmpty of
+          CheckEmpty   -> ifM (liftTCM $ inContextOfT $ isEmptyType $ unDom t) (pure []) (pure cons')
+          NoCheckEmpty -> pure cons'
+        mns  <- forM cons $ \ con -> fmap (SplitCon con,) <$>
+          computeNeighbourhood delta1 n delta2 d pars ixs x tel ps cps con
+        hcompsc <- if isFib && (isHIT || not (null ixs)) && not (null mns) && inserttrailing == DoInsertTrailing
+                   then computeHCompSplit delta1 n delta2 d pars ixs x tel ps cps
+                   else return Nothing
+        let ns = catMaybes mns
+        return ( dr
+               , not (null ixs) -- Is "d" indexed?
+               , length $ ns
+               , ns ++ catMaybes ([fmap (fmap (,NoInfo)) hcompsc | not $ null $ ns])
+               )
+
+      computeLitNeighborhoods = do
+        typeOk <- liftTCM $ do
+          t' <- litType $ headWithDefault {-'-} __IMPOSSIBLE__ plits
+          liftTCM $ dontAssignMetas $ tryConversion $ equalType (unDom t) t'
+        unless typeOk $ throwError . NotADatatype =<< do liftTCM $ buildClosure (unDom t)
+        ns <- forM plits $ \lit -> do
+          let delta2' = subst 0 (Lit lit) delta2
+              delta'  = delta1 `abstract` delta2'
+              rho     = liftS x $ consS (litP lit) idS
+              ps'     = applySubst rho ps
+              cps'    = applySplitPSubst rho cps
+          return (SplitLit lit , SClause delta' ps' rho cps' Nothing)
+        ca <- do
+          let delta' = tel -- telescope is unchanged for catchall branch
+              varp   = VarP (PatternInfo PatOSplit []) $ SplitPatVar
+                         { splitPatVarName   = underscore
+                         , splitPatVarIndex  = 0
+                         , splitExcludedLits = plits
+                         }
+              rho    = liftS x $ consS varp $ raiseS 1
+              ps'    = applySubst rho ps
+          return (SplitCatchall , SClause delta' ps' rho cps Nothing)
+
+        -- If Agda is changed so that the type of a literal can belong
+        -- to an inductive family (with at least one index), then the
+        -- following code should be changed (the constructor False
+        -- stands for "not indexed").
+        let ns' = map ((fmap (,NoInfo))) $ ns ++ [ ca ]
+        return (IsData, False, length ns', ns')
+
+  -- numMatching is the number of proper constructors matching, excluding hcomp.
+  -- for literals this considers the catchall clause as 1 extra constructor.
+  (dr, isIndexed, numMatching, ns) <- if null pcons' && not (null plits)
+        then computeLitNeighborhoods
+        else computeNeighborhoods
+
+  ns <- case target of
+    Just a  -> forM ns $ \ (con,(sc,info)) -> lift $ (con,) . (,info) <$>
+                 fixTargetType (getQuantity t) con sc a
+    Nothing -> return ns
+
+  ns <- case inserttrailing of
+    DontInsertTrailing -> return ns
+    DoInsertTrailing   -> lift $ forM ns $ \(con,(sc,info)) ->
+      (con,) . (,info) . snd <$> insertTrailingArgs False sc
+
+  mHCompName <- getPrimitiveName' builtinHComp
+  opts       <- pragmaOptions
+  let withoutK        = optWithoutK opts
+      erasedMatches   = optErasedMatches opts
+      isRecordWithEta = case dr of
+        IsData       -> False
+        IsRecord r ->
+          case theEtaEquality (recordEtaEquality r) of
+            YesEta{} -> True
+            NoEta{}  -> False
+
+  erased <- hasQuantity0 <$> viewTC eQuantity
+  reportSLn "tc.cover.split" 60 $ "We are in erased context = " ++ show erased
+  let erasedError reason =
+        throwError . ErasedDatatype reason =<<
+          do liftTCM $ inContextOfT $ buildClosure (unDom t)
+
+  case numMatching of
+    0  -> do
+      let absurdp = VarP (PatternInfo PatOAbsurd []) $ SplitPatVar underscore 0 []
+          rho = liftS x $ consS absurdp $ raiseS 1
+          ps' = applySubst rho ps
+      return $ Left $ SClause
+               { scTel  = tel
+               , scPats = ps'
+               , scSubst              = __IMPOSSIBLE__ -- not used
+               , scCheckpoints        = __IMPOSSIBLE__ -- not used
+               , scTarget             = Nothing
+               }
+
+    -- Andreas, 2018-10-17: If more than one constructor matches, we cannot erase.
+    n | n > 1 && not erased && not (usableQuantity t) ->
+      erasedError SeveralConstructors
+
+    -- If exactly one constructor matches and the K rule is turned
+    -- off, then we only allow erasure for non-indexed data/record
+    -- types (#4172). If the type is not a record type with
+    -- η-equality, then the flag --erased-matches must be active.
+    1 | not erased && not (usableQuantity t) && withoutK &&
+        (isIndexed || not isRecordWithEta && not erasedMatches) ->
+      erasedError (if isIndexed then NoK else NoErasedMatches)
+
+    _ -> do
+
+      -- Andreas, 2012-10-10 fail if precomputed constructor set does not cover
+      -- all the data type constructors
+      -- Andreas, 2017-10-08 ... unless partial covering is explicitly allowed.
+      let ptags = map (SplitCon . conName) pcons' ++ map SplitLit plits
+      -- clauses for hcomp will be automatically generated.
+      let inferred_tags = maybe Set.empty (Set.singleton . SplitCon) mHCompName
+      let all_tags = Set.fromList ptags `Set.union` inferred_tags
+
+      when (allowPartialCover == NoAllowPartialCover && not overlap) $
+        for_ ns $ \(tag, (sc, _)) -> do
+          unless (tag `Set.member` all_tags) $ do
+            isImpossibleClause <- liftTCM $ isEmptyTel $ scTel sc
+            unless isImpossibleClause $ do
+              liftTCM $ reportSDoc "tc.cover" 10 $ vcat
+                [ text "Missing case for" <+> prettyTCM tag
+                , nest 2 $ prettyTCM sc
+                ]
+              throwError (GenericSplitError "precomputed set of constructors does not cover all cases")
+
+      liftTCM $ inContextOfT $ checkSortOfSplitVar dr (unDom t) delta2 target
+      return $ Right $ Covering (lookupPatternVar sc x) ns
+
+  where
+    inContextOfT, inContextOfDelta2 :: (MonadTCM tcm, MonadAddContext tcm, MonadDebug tcm) => tcm a -> tcm a
+    inContextOfT      = addContext tel . escapeContext impossible (x + 1)
+    inContextOfDelta2 = addContext tel . escapeContext impossible x
+
+    -- Debug printing
+    debugInit tel x ps cps = liftTCM $ inTopContext $ do
+      reportSDoc "tc.cover.top" 10 $ vcat
+        [ "TypeChecking.Coverage.split': split"
+        , nest 2 $ vcat
+          [ "tel     =" <+> prettyTCM tel
+          , "x       =" <+> prettyTCM x
+          , "ps      =" <+> do addContext tel $ prettyTCMPatternList $ fromSplitPatterns ps
+          , "cps     =" <+> prettyTCM cps
+          ]
+        ]
+      reportSDoc "tc.cover.top" 60 $ vcat
+        [ "TypeChecking.Coverage.split': split"
+        , nest 2 $ vcat
+          [ "tel     =" <+> (text . show) tel
+          , "x       =" <+> (text . show) x
+          , "ps      =" <+> (text . show) ps
+          , "cps     =" <+> (text . show) cps
+          ]
+        ]
+
+    debugHoleAndType delta1 delta2 s ps t =
+      liftTCM $ reportSDoc "tc.cover.top" 10 $ nest 2 $ vcat $
+        [ "p      =" <+> text (patVarNameToString s)
+        , "ps     =" <+> prettyTCMPatternList ps
+        , "delta1 =" <+> prettyTCM delta1
+        , "delta2 =" <+> inContextOfDelta2 (prettyTCM delta2)
+        , "t      =" <+> inContextOfT (prettyTCM t)
+        ]
+
+
+-- | splitResult for MakeCase, tries to introduce IApply or ProjP copatterns
+splitResult :: QName -> SplitClause -> TCM (Either SplitError [SplitClause])
+splitResult f sc = do
+  caseMaybeM (splitResultPath f sc)
+             ((fmap . fmap) splitClauses $ splitResultRecord f sc)
+             (return . Right . (:[]))
+
+
+-- | Tries to split the result to introduce an IApply pattern.
+splitResultPath :: QName -> SplitClause -> TCM (Maybe SplitClause)
+splitResultPath f sc@(SClause tel ps _ _ target) = do
+  caseMaybe target (return Nothing) $ \ t -> do
+        caseMaybeM (isPath (unDom t)) (return Nothing) $ \ _ -> do
+               (TelV i b, boundary) <- telViewUpToPathBoundary' 1 (unDom t)
+               let tel' = abstract tel i
+                   rho  = raiseS 1
+                   ps' = applySubst rho (scPats sc) ++ telePatterns i boundary
+                   cps' = applySubst rho (scCheckpoints sc)
+                   target' = Just $ b <$ t
+               return . Just $ SClause tel' ps' idS cps' target'
+
+-- | @splitResultRecord f sc = return res@
+--
+--   If the target type of @sc@ is a record type, a covering set of
+--   split clauses is returned (@sc@ extended by all valid projection patterns),
+--   otherwise @res == Left _@.
+--   Note that the empty set of split clauses is returned if the record has no fields.
+splitResultRecord :: QName -> SplitClause -> TCM (Either SplitError Covering)
+splitResultRecord f sc@(SClause tel ps _ _ target) = do
+  reportSDoc "tc.cover.split" 10 $ vcat
+    [ "splitting result:"
+    , nest 2 $ "f      =" <+> prettyTCM f
+    , nest 2 $ "target =" <+> addContext tel (maybe empty prettyTCM target)
+    ]
+  -- if we want to split projections, but have no target type, we give up
+  let failure = return . Left
+  caseMaybe target (failure CosplitNoTarget) $ \ t -> do
+    isR <- addContext tel $ isRecordType $ unDom t
+    case isR of
+      Just (_r, vs, Record{ recFields = fs }) -> do
+        reportSDoc "tc.cover" 20 $ sep
+          [ text $ "we are of record type _r = " ++ prettyShow _r
+          , text   "applied to parameters vs =" <+> addContext tel (prettyTCM vs)
+          , text $ "and have fields       fs = " ++ prettyShow fs
+          ]
+        -- Andreas, 2018-06-09, issue #2170, we always have irrelevant projections
+        -- available on the lhs.
+        -- -- Andreas, 2018-03-19, issue #2971, check that we have a "strong" record type,
+        -- -- i.e., with all the projections.  Otherwise, we may not split.
+        -- ifNotM (strongRecord fs) (failure CosplitIrrelevantProjections) $ {-else-} do
+        let es = patternsToElims $ fromSplitPatterns ps
+        -- Note: module parameters are part of ps
+        let self  = defaultArg $ Def f [] `applyE` es
+            pargs = vs ++ [self]
+            fieldValues = for fs $ \ proj -> unArg self `applyE` [Proj ProjSystem (unDom proj)]
+        reportSDoc "tc.cover" 20 $ addContext tel $ sep
+          [ text   "we are              self =" <+> prettyTCM (unArg self)
+          , text   "            field values =" <+> prettyTCM fieldValues
+          ]
+        let n = defaultArg $ permRange $ fromMaybe __IMPOSSIBLE__ $ dbPatPerm $ fromSplitPatterns ps
+            -- Andreas & James, 2013-11-19 includes the dot patterns!
+            -- See test/succeed/CopatternsAndDotPatterns.agda for a case with dot patterns
+            -- and copatterns which fails for @n = size tel@ with a broken case tree.
+
+        -- Andreas, 2016-07-22 read the style of projections from the user's lips
+        projOrigin <- ifM (optPostfixProjections <$> pragmaOptions) (return ProjPostfix) (return ProjPrefix)
+        Right . Covering n <$> do
+          forM (zip fs $ List.inits fieldValues) $ \ (proj, prevFields) -> do
+            -- compute the new target
+            dType <- defType <$> do getConstInfo $ unDom proj -- WRONG: typeOfConst $ unArg proj
+            let -- Substitution for parameters and previous fields. Needs to be applied to potential
+                -- tactic in proj.
+                fieldSub = reverse (map unArg vs ++ prevFields) ++# EmptyS impossible
+                proj'    = applySubst fieldSub proj
+                -- type of projection instantiated at self
+                target' = Just $ proj' $> dType `piApply` pargs      -- Always visible (#2287)
+                projArg = fmap (Named Nothing . ProjP projOrigin) $ argFromDom $ setHiding NotHidden proj
+                sc' = sc { scPats   = scPats sc ++ [projArg]
+                         , scSubst  = idS
+                         , scTarget = target'
+                         }
+            reportSDoc "tc.cover.copattern" 40 $ vcat
+              [ "fieldSub for" <+> prettyTCM (unDom proj)
+              , nest 2 $ pretty fieldSub ]
+            return (SplitCon (unDom proj), (sc', NoInfo))
+      _ -> addContext tel $ do
+        buildClosure (unDom t) >>= failure . CosplitNoRecordType
+  -- Andreas, 2018-06-09, issue #2170: splitting with irrelevant fields is always fine!
+  -- where
+  -- -- A record type is strong if it has all the projections.
+  -- -- This is the case if --irrelevant-projections or no field is irrelevant.
+  -- -- TODO: what about shape irrelevance?
+  -- strongRecord :: [Arg QName] -> TCM Bool
+  -- strongRecord fs = (optIrrelevantProjections <$> pragmaOptions) `or2M`
+  --   (return $ not $ any isIrrelevant fs)
+
+
+-- * Boring instances
+
+-- | For debugging only.
+instance PrettyTCM SplitClause where
+  prettyTCM (SClause tel pats sigma cps target) = sep
+    [ "SplitClause"
+    , nest 2 $ vcat
+      [ "tel          =" <+> prettyTCM tel
+      , "pats         =" <+> sep (map (prettyTCM . namedArg) pats)
+      , "subst        =" <+> prettyTCM sigma
+      , "checkpoints  =" <+> prettyTCM cps
+      , "target       =" <+> do
+          caseMaybe target empty $ \ t -> do
+            addContext tel $ prettyTCM t
+      -- Triggers crash (see Issue 1374).
+      -- , "subst target = " <+> do
+      --     caseMaybe target empty $ \ t -> do
+      --       addContext tel $ prettyTCM $ applySubst sigma t
+      ]
+    ]
diff --git a/src/full/Agda/TypeChecking/Coverage/Cubical.hs b/src/full/Agda/TypeChecking/Coverage/Cubical.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Coverage/Cubical.hs
@@ -0,0 +1,1371 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Coverage.Cubical where
+
+import Prelude hiding (null, (!!))  -- do not use partial functions like !!
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans ( lift )
+
+import qualified Data.Set as Set
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Internal hiding (DataOrRecord)
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.TypeChecking.Constraints () -- instance MonadConstraint TCM
+import Agda.TypeChecking.Coverage.Match
+import Agda.TypeChecking.Coverage.SplitClause
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Datatypes (getDatatypeArgs)
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Telescope.Path
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.List1 ( pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+
+createMissingIndexedClauses :: QName
+                            -> Arg Nat
+                            -> BlockingVar
+                            -> SplitClause
+                            -> [(SplitTag,(SplitClause,IInfo))]
+                            -> [Clause]
+                            -> TCM ([(SplitTag,CoverResult)],[Clause])
+createMissingIndexedClauses f n x old_sc scs cs = do
+  reflId <- getName' builtinReflId
+  let infos = [(c,i) | (SplitCon c, (_,TheInfo i)) <- scs ]
+  case scs of
+    [(SplitCon c,(_newSc,i@TheInfo{}))] | Just c == reflId -> do
+      mc <- createMissingConIdClause f n x old_sc i
+      caseMaybe mc (return ([],cs)) $ \ ((sp,tree),cl) -> do
+      let res = CoverResult tree (IntSet.singleton (length cs)) [] [cl] IntSet.empty
+      return ([(sp,res)],snoc cs cl)
+    xs | info:_ <- infos -> do
+         reportSDoc "tc.cover.indexed" 20 $ text "size (xs,infos):" <+> pretty (size xs,size infos)
+         reportSDoc "tc.cover.indexed" 20 $ text "xs :" <+> pretty (map fst xs)
+
+         unless (size xs == 1 + size infos) $
+            reportSDoc "tc.cover.indexed" 20 $ text "missing some infos"
+            -- Andrea: what to do when we only managed to build a unification proof for some of the constructors?
+         Constructor{conData} <- theDef <$> getConstInfo (fst info)
+         Datatype{dataPars = pars, dataIxs = nixs, dataTranspIx} <- theDef <$> getConstInfo conData
+         hcomp <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinHComp
+         trX <- fromMaybe __IMPOSSIBLE__ <$> pure dataTranspIx
+         trX_cl <- createMissingTrXTrXClause trX f n x old_sc
+         hcomp_cl <- createMissingTrXHCompClause trX f n x old_sc
+         (trees,cls) <- fmap unzip . forM infos $ \ (c,i) -> do
+           cl <- createMissingTrXConClause trX f n x old_sc c i
+           return $ ((SplitCon c , SplittingDone (size $ clauseTel cl)) , cl)
+         let extra = [ (SplitCon trX, SplittingDone $ size $ clauseTel trX_cl)
+                                           , (SplitCon hcomp, SplittingDone $ size $ clauseTel hcomp_cl)
+                                           ]
+                 --  = [ (SplitCon trX, SplittingDone $ size $ clauseTel trX_cl) ]
+             extraCl = [trX_cl, hcomp_cl]
+                 --  = [trX_cl]
+         let clauses = cls ++ extraCl
+         let tree = SplitAt (n <&> (+ (pars + nixs + 1))) StrictSplit $
+                                           trees
+                                        ++ extra
+             res = CoverResult
+               { coverSplitTree      = tree
+               , coverUsedClauses    = let l = length cs in IntSet.fromAscList [l .. l + length clauses - 1]
+               , coverMissingClauses = []
+               , coverPatterns       = clauses
+               , coverNoExactClauses = IntSet.empty
+               }
+         reportSDoc "tc.cover.indexed" 20 $
+           "tree:" <+> pretty tree
+         addClauses f clauses
+         return ([(SplitCon trX, res)], cs ++ clauses)
+    xs | otherwise -> return ([], cs)
+
+covFillTele :: QName -> Abs Telescope -> Term -> Args -> Term -> TCM [Term]
+covFillTele func tel face d j = do
+  ed_f <- liftTCM $ runExceptT $ trFillTel tel face d j
+  case ed_f of
+    Right d_f -> pure $ map unArg d_f
+    Left failed_t -> enterClosure failed_t $ \failed_t -> addContext ("i" :: String, __DUMMY_DOM__) $ do
+      typeError . GenericDocError =<< vcat
+        [ "Could not generate a transport clause for" <+> prettyTCM func
+        , "because a term of type" <+> prettyTCM (unAbs failed_t)
+        , "lives in the sort" <+> prettyTCM (getSort (unAbs failed_t)) <+> "and thus can not be transported"
+        ]
+
+createMissingTrXTrXClause :: QName -- ^ trX
+                            -> QName -- ^ f defined
+                            -> Arg Nat
+                            -> BlockingVar
+                            -> SplitClause
+                            -> TCM Clause
+createMissingTrXTrXClause q_trX f n x old_sc = do
+  let
+   old_tel = scTel old_sc
+   old_ps = fromSplitPatterns $ scPats old_sc
+   old_t = fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+
+  reportSDoc "tc.cover.trx.trx" 20 $ "trX-trX clause for" <+> prettyTCM f
+  reportSDoc "tc.cover.trx.trx" 20 $ nest 2 $ vcat $
+    [ "old_tel:" <+> prettyTCM old_tel
+    , "old_ps :" <+> addContext old_tel (prettyTCM $ patternsToElims old_ps)
+    , "old_t  :" <+> addContext old_tel (prettyTCM old_t)
+    ]
+
+  -- TODO: redo comments, the strategy changed.
+  -- old_tel = Γ1, (x : D η v), Δ
+  -- α = boundary(old_ps)
+  -- Γ1, (x : D η v), Δ ⊢ f old_ps : old_t [ α ↦ (f old_ps)[α] ]
+
+  -- α' = boundary(old_ps[x = pat])
+  -- Γ1, φ : I, p : Path X(η) _ v, ψ : I, q : Path X(η) _ (p i0), x0 : D η (q i0) ⊢ pat := trX p φ (trX q ψ x0) : D η v
+
+  -- Ξ = Γ1, φ : I, p : Path X(η) _ v, ψ : I, q : Path X(η) _ (p i0), x0 : D η (q i0), Δ[x = pat]
+
+  -- Ξ ⊢ w1 := f old_ps[γ1,x = pat,δ] : old_t[γ1,x = pat,δ] -- the case we are defining. can only be used if specialized.
+
+  -- Ξ ⊢ rhs : old_t[γ1,x = pat,δ] [ α' ↦ w1[α']
+                                -- , φ  ↦ w1[φ = i1, p = refl]
+                                -- , ψ  ↦ w1[ψ = i1, q = refl]
+                                -- ]
+  -- Ξ ⊢ q2 := tr (i. Path X(η) (q i0) (p i)) φ q : Path X(η) (q i0) (p i1)
+  -- Ξ ⊢ pat_rec[0] = pat : D η v
+  -- Ξ ⊢ pat_rec[1] = trX q2 (φ ∧ ψ) x0 : D η v
+  -- Ξ ⊢ pat-rec[i] := trX (\ j → p (i ∨ j)) (i ∨ φ) (trX (q2_f i) (ψ ∧ (φ ∨ ~ i)) t)
+
+  -- Ξ ⊢ δ_f[1] = tr (i. Δ[γ1,x = pat_rec[i]]) (φ ∧ ψ) δ
+  -- Ξ ⊢ w0 := f old_ps[γ1,x = pat_rec[1] ,δ_f[1]] : old_t[γ1,x = pat_rec[1],δ_f[1]]
+  -- Ξ ⊢ rhs := tr (i. old_t[γ1,x = pat_rec[~i], δ_f[~i]]) (φ ∧ ψ) w0 -- TODO plus sides.
+
+  interval <- elInf primInterval
+  iz <- primIZero
+  io <- primIOne
+  tHComp <- primHComp
+  tNeg <- primINeg
+  let neg i = pure tNeg <@> i
+  let min i j = cl primIMin <@> i <@> j
+  let max i j = cl primIMax <@> i <@> j
+  let
+    old_tel = scTel old_sc
+    old_ps' = AbsN (teleNames old_tel) $ fromSplitPatterns $ scPats old_sc
+    old_ps = pure $ old_ps'
+    old_ty = pure $ AbsN (teleNames old_tel) $ fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+  -- old_tel = Γ(x: D η v)Δ
+  -- Γ1, (x : D η v)  ⊢ delta = (δ : Δ)
+    (gamma1x,delta') = splitTelescopeAt (size old_tel - blockingVarNo x) old_tel
+    delta = pure $ AbsN (teleNames gamma1x) $ delta'
+    gamma1_size = (size gamma1x - 1)
+    (gamma1,ExtendTel dType' _) = splitTelescopeAt gamma1_size gamma1x
+
+  old_sides <- forM old_ps' $ \ ps -> do
+    let vs = iApplyVars ps
+    let tm = Def f $ patternsToElims ps
+    xs <- forM vs $ \ v ->
+        -- have to reduce these under the appropriate substitutions, otherwise non-normalizing(?)
+          fmap (var v,) . reduce $ (inplaceS v iz `applySubst` tm, inplaceS v io `applySubst` tm)
+    return $ concatMap (\(v,(l,r)) -> [(tNeg `apply` [argN v],l),(v,r)]) xs
+  let
+    gamma1ArgNames = teleArgNames gamma1
+    deltaArgNames = teleArgNames delta'
+  (params,xTel,dT) <- addContext gamma1 $ do
+    Just (d, ps, _is) <- getDatatypeArgs . unDom =<< reduce dType'
+    def <- getConstInfo d
+    let dTy = defType def
+    let Datatype{dataSort = s} = theDef def
+    TelV tel _ <- telView dTy
+    let params = AbsN (teleNames gamma1) ps
+        xTel = AbsN (teleNames gamma1) (tel `apply` ps)
+
+    dT <- runNamesT [] $ do
+          s <- open $ AbsN (teleNames tel) s
+          bindNArg (teleArgNames gamma1) $ \ g1 -> do
+          bindNArg (teleArgNames $ unAbsN xTel) $ \ x -> do
+          params <- pure params `applyN` (fmap unArg <$> g1)
+          x      <- sequence x
+          s <- s `applyN` (map (pure . unArg) $ params ++ x)
+          pure $ El s $ Def d [] `apply` (params ++ x)
+    return $ (params, xTel,dT)
+
+  let
+    xTelI = pure $ expTelescope interval <$> xTel
+    xTelIArgNames = teleArgNames (unAbsN xTel) -- same names
+
+  -- Γ1, φ, p, ψ, q, x0 ⊢ pat := trX p φ (trX q ψ x0)
+  let trX' = bindNArg gamma1ArgNames $ \ g1 -> do
+             bindNArg ([defaultArg "phi"] ++ xTelIArgNames) $ \ phi_p -> do
+             bindNArg [defaultArg "x0"] $ \ x0 -> do
+             param_args <- fmap (map (setHiding Hidden . fmap (unnamed . dotP))) $
+               pure params `applyN` (fmap unArg <$> g1)
+             (phi:p) <- sequence phi_p
+             x0 <- sequence x0
+             pure $ DefP defaultPatternInfo q_trX $ param_args ++ p ++ [phi] ++ x0
+      trX = (fmap . fmap . fmap) patternToTerm <$> trX'
+  let pat' =
+            bindN (map unArg gamma1ArgNames) $ \ g1 -> do
+            bindN (map unArg $ ([defaultArg "phi"] ++ xTelIArgNames)) $ \ phi_p -> do
+            bindN (map unArg $ ([defaultArg "psi"] ++ xTelIArgNames)) $ \ psi_q -> do
+            bindN (map unArg $ [defaultArg "x0"]) $ \ x0 -> do
+            -- (phi:p) <- sequence phi_p
+            -- (psi:q) <- sequence psi_q
+            -- x0 <- sequence x0
+            let trX = trX' `applyN` g1
+            trX `applyN` phi_p `applyN` [trX `applyN` psi_q `applyN` x0]
+          --  pure $ trX $ p ++ [phi, defaultArg $ unnamed $ trX $ q ++ [psi] ++ x0]
+      pat = (fmap . fmap . fmap . fmap) patternToTerm <$> pat'
+  let deltaPat g1 phi p psi q x0 =
+        delta `applyN` (g1 ++ [pat `applyN` g1 `applyN` (phi:p) `applyN` (psi:q) `applyN` [x0]])
+  -- Ξ
+  cTel <- runNamesT [] $
+    abstractN (pure gamma1) $ \ g1 -> do
+    abstractT "φ" (pure interval) $ \ phi -> do
+    abstractN (xTelI `applyN` g1) $ \ p -> do
+    abstractT "ψ" (pure interval) $ \ psi -> do
+    abstractN (xTelI `applyN` g1) $ \ q -> do
+    abstractT "x0" (pure dT `applyN` g1 `applyN` (for q $ \ f -> f <@> pure iz)) $ \ x0 -> do
+    deltaPat g1 phi p psi q x0
+
+  ps_ty_rhs <- runNamesT [] $ do
+    bindN (map unArg gamma1ArgNames) $ \ g1 -> do
+    bind "φ" $ \ phi -> do
+    bindN (map unArg xTelIArgNames) $ \ p -> do
+    bind "ψ" $ \ psi -> do
+    bindN (map unArg xTelIArgNames) $ \ q -> do
+    bind "x0" $ \ x0 -> do
+    bindN (map unArg deltaArgNames) $ \ d -> do
+    let
+      ps :: NamesT TCM NAPs
+      ps = old_ps `applyN` (g1
+                          ++ [pat' `applyN` g1 `applyN` (phi:p) `applyN` (psi:q) `applyN` [x0]]
+                          ++ d)
+
+      rhsTy = old_ty `applyN` (g1
+                          ++ [pat `applyN` g1 `applyN` (phi:p) `applyN` (psi:q) `applyN` [x0]]
+                          ++ d)
+
+    xTel <- (open =<<) $ pure xTel `applyN` g1
+    q4_f <- (open =<<) $ bind "i" $ \ i -> lamTel $ bind "j" $ \ j -> do
+      ty <- bind "i" $ \ _ -> xTel
+      face <- max phi $ max (neg j) (neg i)
+      base <- map defaultArg <$> appTel (sequence q) j
+      u  <- liftM2 (,) (max j psi) $ bind "h" $ \ h -> do
+              appTel (sequence p) (min j (min h i))
+      Right xs <- lift $ runExceptT $ transpSysTel' False ty [u] face base
+      pure $ map unArg xs
+    -- Ξ ⊢ pat_rec[0] = pat : D η v
+    -- Ξ ⊢ pat_rec[1] = trX q4 (φ ∧ ψ) x0 : D η v
+    -- Ξ ⊢ pat-rec[i] := trX (\ j → p (i ∨ j)) (i ∨ φ) (trX (q4_f i) (ψ ∧ (φ ∨ ~ i)) t)
+    pat_rec <- (open =<<) $ bind "i" $ \ i -> do
+          p_conn <- (mapM open =<<) $ lamTel $ bind "i" $ \ j -> sequence p `appTel` max i j
+          q4_f' <- (mapM open =<<) $ absApp <$> q4_f <*> i
+          trX `applyN` g1 `applyN` (max i phi:p_conn)
+              `applyN` [trX `applyN` g1 `applyN` (min psi (max phi (neg i)):q4_f') `applyN` [x0]]
+
+    let mkBndry args = do
+            args1 <- (mapM open =<<) $ (absApp <$> args <*> pure io)
+            -- faces ought to be constant on "j"
+            faces <- pure (fmap (map fst) old_sides) `applyN` args1
+            us <- forM (mapM (map snd) old_sides) $ \ u -> do
+                  lam "j" $ \ j -> ilam "o" $ \ _ -> do
+                    args <- (mapM open =<<) $ (absApp <$> args <*> j)
+                    pure u `applyN` args
+            forM (zip faces us) $ \ (phi,u) -> liftM2 (,) (open phi) (open u)
+    let mkComp pr = bind "i" $ \ i -> do
+          d_f <- (open =<<) $ bind "j" $ \ j -> do
+            tel <- bind "j" $ \ j -> delta `applyN` (g1 ++ [pr `applyN` [i,j]])
+            face <- min phi psi `max` (min i (max phi psi))
+            j <- j
+            d <- map defaultArg <$> sequence d
+            lift $ covFillTele f tel face d j
+          let args = bind "j" $ \ j -> do
+                g1 <- sequence g1
+                x <- pr `applyN` [i,neg j]
+                ys <- absApp <$> d_f <*> neg j
+                pure $ g1 ++ x:ys
+          ty <- (open =<<) $ bind "j" $ \ j -> do
+               args <- (mapM open =<<) $ absApp <$> args <*> j
+               fmap unDom $ old_ty `applyN` args
+          let face = max i (min phi psi)
+          base <- (open =<<) $ do
+            args' <- (mapM open =<<) $ absApp <$> args <*> pure iz
+            fmap (Def f) $ (fmap patternsToElims <$> old_ps) `applyN` args'
+          sys <- mkBndry args
+          transpSys ty sys face base
+
+    -- Ξ ⊢ δ_f[1] = tr (i. Δ[γ1,x = pat_rec[i]]) (φ ∧ ψ) δ
+    -- Ξ ⊢ w0 := f old_ps[γ1,x = pat_rec[1] ,δ_f[1]] : old_t[γ1,x = pat_rec[1],δ_f[1]]
+    -- Ξ ⊢ rhs := tr (i. old_t[γ1,x = pat_rec[~i], δ_f[~i]]) (φ ∧ ψ) w0 -- TODO plus sides.
+    syspsi <- (open =<<) $ lam "i" $ \ i -> ilam "o" $ \ _ -> do
+      c <- mkComp $ bindN ["i","j"] $ \ [i,j] -> do
+        Abs n (data_ty,lines) <- bind "k" $ \ k -> do
+          let phi_k = max phi (neg k)
+          let p_k = for p $ \ p -> lam "h" $ \ h -> p <@> (min k h)
+          data_ty <- pure dT `applyN` g1 `applyN` (for p $ \ p -> p <@> k)
+          line1 <- trX `applyN` g1 `applyN` (phi_k:p_k) `applyN` [x0]
+
+          line2 <- trX `applyN` g1
+                       `applyN` (max phi_k j      : (for p_k $ \ p -> lam "h" $ \ h -> p <@> (max h j)))
+                       `applyN`
+                  [trX `applyN` g1
+                       `applyN` (max phi_k (neg j): (for p_k $ \ p -> lam "h" $ \ h -> p <@> (min h j)))
+                       `applyN` [x0]]
+          pure (data_ty,[line1,line2])
+        data_ty <- open $ Abs n data_ty
+        [line1,line2] <- mapM (open . Abs n) lines
+        let sys = [(neg i, lam "k" $ \ k -> ilam "o" $ \ _ -> absApp <$> line2 <*> k)
+                  ,(neg j `max` j `max` i `max` phi, lam "k" $ \ k -> ilam "o" $ \ _ -> absApp <$> line1 <*> k)
+                  ]
+        transpSys data_ty sys (pure iz) x0
+      absApp <$> pure c <*> i
+    sysphi <- (open =<<) $ lam "i" $ \ i -> ilam "o" $ \ o -> do
+      c <- mkComp $ bindN ["i","j"] $ \ _ij -> do
+        trX `applyN` g1 `applyN` (psi:q) `applyN` [x0]
+      absApp <$> pure c <*> i
+    syse <- mkBndry $ bind "j" $ \ _ -> sequence $ g1 ++ [absApp <$> pat_rec <*> pure iz] ++ d
+    let sys = syse ++ [(phi,sysphi)] ++ [(psi,syspsi)]
+    w0 <- (open =<<) $ do
+      let w = mkComp (bindN ["i","j"] $ \ [_i, j] -> absApp <$> pat_rec <*> j)
+      absApp <$> w <*> pure iz
+    let rhs = hcomp (unDom <$> rhsTy) sys w0
+    (,,) <$> ps <*> rhsTy <*> rhs
+  let (ps,ty,rhs) = unAbsN $ unAbs $ unAbsN $ unAbs $ unAbsN $ unAbs $ unAbsN $ ps_ty_rhs
+  reportSDoc "tc.cover.trx.trx" 20 $ "trX-trX clause for" <+> prettyTCM f
+  let c = Clause { clauseLHSRange  = noRange
+                 , clauseFullRange = noRange
+                 , clauseTel       = cTel
+                 , namedClausePats = ps
+                 , clauseBody      = Just rhs
+                 , clauseType      = Just $ Arg (getArgInfo ty) (unDom ty)
+                 , clauseCatchall    = False
+                 , clauseExact       = Nothing
+                 , clauseRecursive   = Just True
+                 , clauseUnreachable = Just False
+                 , clauseEllipsis    = NoEllipsis
+                 , clauseWhereModule = Nothing
+                 }
+  debugClause "tc.cover.trx.trx" c
+  return $ c
+createMissingTrXHCompClause :: QName
+                            -> QName
+                            -> Arg Nat
+                            -> BlockingVar
+                            -> SplitClause
+                            -> TCM Clause
+createMissingTrXHCompClause q_trX f n x old_sc = do
+  let
+   old_tel = scTel old_sc
+   old_ps = fromSplitPatterns $ scPats old_sc
+   old_t = fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+
+  reportSDoc "tc.cover.trx.hcomp" 20 $ "trX-hcomp clause for" <+> prettyTCM f
+  reportSDoc "tc.cover.trx.hcomp" 20 $ nest 2 $ vcat $
+    [ "old_tel:" <+> prettyTCM old_tel
+    , "old_ps :" <+> addContext old_tel (prettyTCM $ patternsToElims old_ps)
+    , "old_t  :" <+> addContext old_tel (prettyTCM old_t)
+    ]
+
+  -- old_tel = Γ1, (x : D η v), Δ
+  -- α = boundary(old_ps)
+  -- Γ1, (x : D η v), Δ ⊢ f old_ps : old_t [ α ↦ (f old_ps)[α] ]
+
+  -- α' = boundary(old_ps[x = pat])
+  -- Γ1, φ : I, p : Path X(η) _ v, ψ : I, u : I -> [ψ] → D η (p i0), u0 : D η (p i0) ⊢ pat := trX p φ (hcomp ψ u u0) : D η v
+
+  -- Ξ = Γ1, φ : I, p : Path X(η) _ v, ψ : I, u : ..., u0 : D η (p i0), Δ[x = pat]
+
+  -- Ξ ⊢ w1 := f old_ps[γ1,x = pat,δ] : old_t[γ1,x = pat,δ] -- the case we are defining. can only be used if specialized.
+
+  -- Ξ ⊢ rhs : old_t[γ1,x = pat,δ] [ α' ↦ w1[α']
+                                -- , φ  ↦ w1[φ = i1, p = refl]   = f old_ps[γ1,x = hcomp ψ u u0    ,δ]
+                                -- , ψ  ↦ w1[ψ = i1]             = f old_ps[γ1,x = trX p φ (u i1 _),δ]
+                                -- ]
+
+  -- Ξ ⊢ q2 := tr (i. Path X(η) (q i0) (p i)) φ q : Path X(η) (q i0) (p i1)
+  -- Ξ ⊢ pat_rec[0] = pat : D η v
+  -- Ξ ⊢ pat_rec[1] = trX q2 (φ ∧ ψ) x0 : D η v
+  -- Ξ ⊢ pat-rec[i] := trX (\ j → q (i ∨ j)) (i ∨ φ) (trX (q2_f i) (ψ ∧ (φ ∨ ~ i)) t)
+
+  -- Ξ ⊢ δ_f[1] = tr (i. Δ[γ1,x = pat_rec[i]]) (φ ∧ ψ) δ : Δ[γ1,x = pat_rec[1]]
+  -- Ξ ⊢ w0 := f old_ps[γ1,x = pat_rec[1] ,δ_f[1]] : old_t[γ1,x = pat_rec[1],δ_f[1]]
+  -- Ξ ⊢ rhs := tr (i. old_t[γ1,x = pat_rec[~i], δ_f[~i]]) (φ ∧ ψ) w0 -- TODO plus sides.
+
+  q_hcomp <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinHComp
+  let
+   old_tel = scTel old_sc
+   old_ps = fromSplitPatterns $ scPats old_sc
+   old_t = fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+
+  reportSDoc "tc.cover.trx.trx" 20 $ "trX-trX clause for" <+> prettyTCM f
+  reportSDoc "tc.cover.trx.trx" 20 $ nest 2 $ vcat $
+    [ "old_tel:" <+> prettyTCM old_tel
+    , "old_ps :" <+> addContext old_tel (prettyTCM $ patternsToElims old_ps)
+    , "old_t  :" <+> addContext old_tel (prettyTCM old_t)
+    ]
+
+  -- TODO: redo comments, the strategy changed.
+  -- old_tel = Γ1, (x : D η v), Δ
+  -- α = boundary(old_ps)
+  -- Γ1, (x : D η v), Δ ⊢ f old_ps : old_t [ α ↦ (f old_ps)[α] ]
+
+  -- α' = boundary(old_ps[x = pat])
+  -- Γ1, φ : I, p : Path X(η) _ v, ψ : I, q : Path X(η) _ (p i0), x0 : D η (q i0) ⊢ pat := trX p φ (trX q ψ x0) : D η v
+
+  -- Ξ = Γ1, φ : I, p : Path X(η) _ v, ψ : I, q : Path X(η) _ (p i0), x0 : D η (q i0), Δ[x = pat]
+
+  -- Ξ ⊢ w1 := f old_ps[γ1,x = pat,δ] : old_t[γ1,x = pat,δ] -- the case we are defining. can only be used if specialized.
+
+  -- Ξ ⊢ rhs : old_t[γ1,x = pat,δ] [ α' ↦ w1[α']
+                                -- , φ  ↦ w1[φ = i1, p = refl]
+                                -- , ψ  ↦ w1[ψ = i1, q = refl]
+                                -- ]
+  -- Ξ ⊢ q2 := tr (i. Path X(η) (q i0) (p i)) φ q : Path X(η) (q i0) (p i1)
+  -- Ξ ⊢ pat_rec[0] = pat : D η v
+  -- Ξ ⊢ pat_rec[1] = trX q2 (φ ∧ ψ) x0 : D η v
+  -- Ξ ⊢ pat-rec[i] := trX (\ j → p (i ∨ j)) (i ∨ φ) (trX (q2_f i) (ψ ∧ (φ ∨ ~ i)) t)
+
+  -- Ξ ⊢ δ_f[1] = tr (i. Δ[γ1,x = pat_rec[i]]) (φ ∧ ψ) δ
+  -- Ξ ⊢ w0 := f old_ps[γ1,x = pat_rec[1] ,δ_f[1]] : old_t[γ1,x = pat_rec[1],δ_f[1]]
+  -- Ξ ⊢ rhs := tr (i. old_t[γ1,x = pat_rec[~i], δ_f[~i]]) (φ ∧ ψ) w0 -- TODO plus sides.
+
+  interval <- elInf primInterval
+  iz <- primIZero
+  io <- primIOne
+  tHComp <- primHComp
+  tNeg <- primINeg
+  let neg i = pure tNeg <@> i
+  let min i j = cl primIMin <@> i <@> j
+  let max i j = cl primIMax <@> i <@> j
+  let
+    old_tel = scTel old_sc
+    old_ps' = AbsN (teleNames old_tel) $ fromSplitPatterns $ scPats old_sc
+    old_ps = pure $ old_ps'
+    old_ty = pure $ AbsN (teleNames old_tel) $ fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+  -- old_tel = Γ(x: D η v)Δ
+  -- Γ1, (x : D η v)  ⊢ delta = (δ : Δ)
+    (gamma1x,delta') = splitTelescopeAt (size old_tel - blockingVarNo x) old_tel
+    delta = pure $ AbsN (teleNames gamma1x) $ delta'
+    gamma1_size = (size gamma1x - 1)
+    (gamma1,ExtendTel dType' _) = splitTelescopeAt gamma1_size gamma1x
+
+  old_sides <- forM old_ps' $ \ ps -> do
+    let vs = iApplyVars ps
+    let tm = Def f $ patternsToElims ps
+    xs <- forM vs $ \ v ->
+        -- have to reduce these under the appropriate substitutions, otherwise non-normalizing(?)
+          fmap (var v,) . reduce $ (inplaceS v iz `applySubst` tm, inplaceS v io `applySubst` tm)
+    return $ concatMap (\(v,(l,r)) -> [(tNeg `apply` [argN v],l),(v,r)]) xs
+  let
+    gamma1ArgNames = teleArgNames gamma1
+    deltaArgNames = teleArgNames delta'
+  (params,xTel,dT) <- addContext gamma1 $ do
+    Just (d, ps, _is) <- getDatatypeArgs . unDom =<< reduce dType'
+    def <- getConstInfo d
+    let dTy = defType def
+    let Datatype{dataSort = s} = theDef def
+    TelV tel _ <- telView dTy
+    let params = AbsN (teleNames gamma1) ps
+        xTel = AbsN (teleNames gamma1) (tel `apply` ps)
+
+    dT <- runNamesT [] $ do
+          s <- open $ AbsN (teleNames tel) s
+          bindNArg (teleArgNames gamma1) $ \ g1 -> do
+          bindNArg (teleArgNames $ unAbsN xTel) $ \ x -> do
+          params <- pure params `applyN` (fmap unArg <$> g1)
+          x      <- sequence x
+          s <- s `applyN` (map (pure . unArg) $ params ++ x)
+          pure $ El s $ Def d [] `apply` (params ++ x)
+    return $ (params, xTel,dT)
+
+  let
+    xTelI = pure $ expTelescope interval <$> xTel
+    xTelIArgNames = teleArgNames (unAbsN xTel) -- same names
+
+  -- Γ1, φ, p, ψ, q, x0 ⊢ pat := trX p φ (trX q ψ x0)
+  let trX' = bindNArg gamma1ArgNames $ \ g1 -> do
+             bindNArg ([defaultArg "phi"] ++ xTelIArgNames) $ \ phi_p -> do
+             bindNArg [defaultArg "x0"] $ \ x0 -> do
+             param_args <- fmap (map (setHiding Hidden . fmap (unnamed . dotP))) $
+               pure params `applyN` (fmap unArg <$> g1)
+             (phi:p) <- sequence phi_p
+             x0 <- sequence x0
+             pure $ DefP defaultPatternInfo q_trX $ param_args ++ p ++ [phi] ++ x0
+      trX = (fmap . fmap . fmap) patternToTerm <$> trX'
+  let
+    hcompD' g1 v =
+        bindNArg [argH "psi",argN "u", argN "u0"] $ \ x0 -> do
+        x0 <- sequence x0
+        Just (LEl l t) <- (toLType =<<) $ pure dT `applyN` g1 `applyN` v
+        let ty = map (fmap (unnamed . dotP) . argH) [Level l,t]
+        pure $ DefP defaultPatternInfo q_hcomp $ ty ++ x0
+  hcompD <- runNamesT [] $
+            bindN (map unArg $ gamma1ArgNames) $ \ g1 -> do
+            bindN (teleNames $ unAbsN $ xTel) $ \ v -> do
+            fmap patternToTerm <$> hcompD' g1 v
+  let pat' =
+            bindN (map unArg gamma1ArgNames) $ \ g1 -> do
+            bindN1 (fmap unArg (defaultArg "phi" :| xTelIArgNames)) $ \ phi_p -> do
+            bindN ["psi","u","u0"] $ \ x0 -> do
+            let trX = trX' `applyN` g1
+            let p0 = for (List1.tail phi_p) $ \ p -> p <@> pure iz
+            trX `applyN` (List1.toList phi_p) `applyN` [hcompD' g1 p0 `applyN` x0]
+      pat = (fmap . fmap . fmap) patternToTerm <$> pat'
+  let deltaPat g1 phi p x0 =
+        delta `applyN` (g1 ++ [pat `applyN` g1 `applyN` (phi:p) `applyN` x0])
+  -- Ξ
+  cTel <- runNamesT [] $
+    abstractN (pure gamma1) $ \ g1 -> do
+    abstractT "φ" (pure interval) $ \ phi -> do
+    abstractN (xTelI `applyN` g1) $ \ p -> do
+    let p0 = for p $ \ p -> p <@> pure iz
+    let ty = pure dT `applyN` g1 `applyN` p0
+    abstractT "ψ" (pure interval) $ \ psi -> do
+    abstractT "u" (pure interval --> pPi' "o" psi (\ _ -> ty)) $ \ u -> do
+    abstractT "u0" ty $ \ u0 -> do
+    deltaPat g1 phi p [psi,u,u0]
+
+  ps_ty_rhs <- runNamesT [] $ do
+    bindN (map unArg gamma1ArgNames) $ \ g1 -> do
+    bind "φ" $ \ phi -> do
+    bindN (map unArg xTelIArgNames) $ \ p -> do
+    bind "ψ" $ \ psi -> do
+    bind "u" $ \ u -> do
+    bind "u0" $ \ u0 -> do
+    bindN (map unArg deltaArgNames) $ \ d -> do
+    let
+      x0 :: Vars TCM
+      x0 = [psi,u,u0]
+      ps :: NamesT TCM NAPs
+      ps = old_ps `applyN` (g1
+                          ++ [pat' `applyN` g1 `applyN` (phi:p) `applyN` x0]
+                          ++ d)
+
+      rhsTy = old_ty `applyN` (g1
+                          ++ [pat `applyN` g1 `applyN` (phi:p) `applyN` x0]
+                          ++ d)
+
+    xTel <- (open =<<) $ pure xTel `applyN` g1
+    -- Ξ ⊢ pat-rec[i] := trX .. (hfill ... (~ i))
+    pat_rec <- (open =<<) $ bind "i" $ \ i -> do
+          let tr x = trX `applyN` g1 `applyN` (phi:p) `applyN` [x]
+          let p0 = for p $ \ p -> p <@> pure iz
+          tr (hcomp (pure dT `applyN` g1 `applyN` p0)
+                    [(psi,lam "j" $ \ j -> u <@> (min j (neg i)))
+                    ,(i  ,lam "j" $ \ _ -> ilam "o" $ \ _ -> u0)]
+                    u0)
+    --   args : (i.old_tel)  -> ...
+    let mkBndry args = do
+            args1 <- (mapM open =<<) $ (absApp <$> args <*> pure io)
+            -- faces ought to be constant on "j"
+            faces <- pure (fmap (map fst) old_sides) `applyN` args1
+            us <- forM (mapM (map snd) old_sides) $ \ u -> do
+                  lam "j" $ \ j -> ilam "o" $ \ _ -> do
+                    args <- (mapM open =<<) $ (absApp <$> args <*> j)
+                    pure u `applyN` args
+            forM (zip faces us) $ \ (phi,u) -> liftM2 (,) (open phi) (open u)
+    rhs <- do
+      d_f <- (open =<<) $ bind "j" $ \ j -> do
+        tel <- bind "j" $ \ j -> delta `applyN` (g1 ++ [absApp <$> pat_rec <*> j])
+        let face = iz
+        j <- j
+        d <- map defaultArg <$> sequence d
+        lift $ covFillTele f tel face d j
+      let args = bind "j" $ \ j -> do
+            g1 <- sequence g1
+            x <- absApp <$> pat_rec <*> neg j
+            ys <- absApp <$> d_f <*> neg j
+            pure $ g1 ++ x:ys
+      ty <- (open =<<) $ bind "j" $ \ j -> do
+           args <- (mapM open =<<) $ absApp <$> args <*> j
+           fmap unDom $ old_ty `applyN` args
+      let face = pure iz
+      othersys <- (open =<<) $ lam "j" $ \ j -> ilam "o" $ \ _ -> do
+        args' <- (mapM open =<<) $ absApp <$> args <*> j
+        fmap (Def f) $ (fmap patternsToElims <$> old_ps) `applyN` args'
+      sys <- mkBndry args
+      let
+        -- we could specialize all of sysphi/syspsi/base to compute
+        -- away trX or the hcomp respectively, should lead to
+        -- smaller/more efficient terms.
+        --
+        -- we could also ditch sysphi completely,
+        -- as the computation rule for hcomp would achieve the same.
+        sysphi = othersys
+        syspsi = othersys
+      base <- (open =<<) $ do
+        args' <- (mapM open =<<) $ absApp <$> args <*> pure iz
+        fmap (Def f) $ (fmap patternsToElims <$> old_ps) `applyN` args'
+      transpSys ty ((phi,sysphi):(psi,syspsi):sys) face base
+    (,,) <$> ps <*> rhsTy <*> pure rhs
+  let (ps,ty,rhs) = unAbsN $ unAbs $ unAbs $ unAbs $ unAbsN $ unAbs $ unAbsN $ ps_ty_rhs
+  reportSDoc "tc.cover.trx.hcomp" 20 $ "trX-hcomp clause for" <+> prettyTCM f
+  let c = Clause { clauseLHSRange  = noRange
+                 , clauseFullRange = noRange
+                 , clauseTel       = cTel
+                 , namedClausePats = ps
+                 , clauseBody      = Just rhs
+                 , clauseType      = Just $ Arg (getArgInfo ty) (unDom ty)
+                 , clauseCatchall    = False
+                 , clauseExact       = Nothing
+                 , clauseRecursive   = Just True
+                 , clauseUnreachable = Just False
+                 , clauseEllipsis    = NoEllipsis
+                 , clauseWhereModule = Nothing
+                 }
+  debugClause "tc.cover.trx.hcomp" c
+  return c
+createMissingTrXConClause :: QName -- trX
+                            -> QName -- f defined
+                            -> Arg Nat
+                            -> BlockingVar
+                            -> SplitClause
+                            -> QName -- constructor name
+                            -> UnifyEquiv
+                            -> TCM Clause
+createMissingTrXConClause q_trX f n x old_sc c (UE gamma gamma' xTel u v rho tau leftInv) = do
+  reportSDoc "tc.cover.trxcon" 20 $ "trX-con clause for" <+> prettyTCM f <+> "with con" <+> prettyTCM c
+  reportSDoc "tc.cover.trxcon" 20 $ nest 2 $ vcat $
+    [ "gamma" <+> prettyTCM gamma
+    , "gamma'" <+> prettyTCM gamma'
+    , "xTel" <+> addContext gamma (prettyTCM xTel)
+    , "u"  <+> addContext gamma (prettyTCM u)
+    , "v"  <+> addContext gamma (prettyTCM v)
+    , "rho" <+> addContext gamma' (prettyTCM rho)
+    ]
+
+  Constructor{conSrcCon = chead} <- theDef <$> getConstInfo c
+
+  -- = TheInfo $ UE delta1' eqTel (map unArg conIxs) (map unArg givenIxs) rho0 tau leftInv
+
+  -- η : Params_D ⊢ c : (a : Args(η)) → D η (ξ(η,a))
+
+  -- scTel old_sc = Γ1, (x : D η v), Δ
+  -- Γ1, (x : D η v), Δ ⊢ f old_ps : old_t [α(γ1,x,δ) ↦ e(γ1,x,δ)]
+
+  -- Γ = Γ1, a : Args(η)
+  -- Γ ⊢ u = ξ(η,a)
+  -- Γ ⊢ c a : D η u
+
+  -- Γ' ⊢ ρ : Γ
+
+  -- Γ' ⊢ u[ρ] = v[ρ] : X(η)[ρ]
+
+  -- Γ' ⊢ c a[ρ] : (D η v)[ρ]
+
+  -- Γ' ⊢ ρx := ρ,x = c a[ρ] : Γ,(x : D η v)
+
+  -- Γ',Δ[ρx] ⊢ old_t[ρx]
+  -- Γ',Δ[ρx] ⊢ f old_ps[ρx] : old_t[ρx] [α[ρx] ↦ e[γ1,x,δ][ρx]]
+
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ τ : Γ'
+
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ [ρx][τ] = [ρ[τ], x = c a[ρ[τ]]] : Γ,(x : D η v)
+
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ leftInv : ρ[τ],i1,refl ≡ idS : Γ,(φ : I),(p : Path X(η) u v)
+
+  -- Γ,(φ : I),(p : Path X(η) u v)| (i : I) ⊢ leftInv i : Γ,(φ : I),(p : Path X(η) u v)
+
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ leftInv i0 = ρ[τ],i1,refl : Γ,(φ : I),(p : Path X(η) u v)
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ leftInv i1 = γ   ,φ ,p    : Γ,(φ : I),(p : Path X(η) u v)
+  --                                 leftInv[φ = i1][i] = idS
+
+  -- Γ,(φ : I),(p : Path X(η) u v),Δ[ρx][τ] ⊢ τ' = liftS |Δ[ρx]| τ : Γ',Δ[ρx]
+
+  -- Γ,(φ : I),(p : Path X(η) u v),Δ[ρx][τ] ⊢
+  --            w := f old_ps[γ1[ρ[τ]],x = c a[ρ[τ]],δ] : old_t[ρx][τ'] = old_t[γ1[ρ[τ]],x = c a[ρ[τ]],δ]
+
+  -- Γ,(φ : I),(p : Path X(η) u v),Δ[ρx][τ], α(γ1,x,δ)[ρx][τ'] ⊢ w = e(γ1,x,δ)[ρx][τ']
+
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ pat := trX p φ (c a) : D η v
+
+
+  -- Ξ := Γ,(φ : I),(p : Path X(η) u v),(δ : Δ[x = pat])
+
+  -- Ξ ⊢ δ_f[1] = trTel (i. Δ[γ1[leftInv (~ i)], pat[leftInv (~i)]]) φ δ : Δ[ρ[τ], x = c a[ρ[τ]]]
+
+  -- Ξ ⊢ w[δ_f[1]] : old_t[γ1[ρ[τ]],x = c a[ρ[τ]],δ_f[1]]
+  -- Ξ, α(γ1,x,δ)[ρx][τ'][δ = δ_f[1]] ⊢ w[δ_f[1]] = e(γ1,x,δ)[ρx][τ'][δ_f[1]]
+
+  -- Ξ, α(γ1[ρ[τ]],c a[ρ[τ]],δ_f[1]) ⊢ w[δ_f[1]] = e(γ1[ρ[τ]],c a[ρ[τ]],δ_f[1])
+
+  -- Recap:
+  -- Γ1, (x : D η v), Δ ⊢ f old_ps : old_t [α(γ1,x,δ) ↦ e(γ1,x,δ)]
+  -- Ξ := Γ,(φ : I),(p : Path X(η) u v),(δ : Δ[x = pat])
+  -- Ξ ⊢ δ_f[1] := trTel (i. Δ[γ1[leftInv (~ i)], pat[leftInv (~i)]]) φ δ : Δ[ρ[τ], x = c a[ρ[τ]]]
+  -- Γ,(φ : I),(p : Path X(η) u v),Δ[ρx][τ] ⊢
+  --            w := f old_ps[γ1[ρ[τ]],x = c a[ρ[τ]],δ] : old_t[ρx][τ'] = old_t[γ1[ρ[τ]],x = c a[ρ[τ]],δ]
+  -- Γ,(φ : I),(p : Path X(η) u v) ⊢ pat := trX p φ (c a) : D η v
+
+
+  -- Ξ ⊢ ?rhs : old_t[γ1,x = pat,δ] [α(γ1,pat,δ) ↦ e(γ1,pat,δ)
+  --                               ,φ           ↦ w
+  --                               ]
+
+  -- ?rhs := transp (i. old_t[γ1[leftInv i],x = pat[leftInv i], δ_f[~i]]) φ (w[δ_f[1]])
+
+  -- we shall consider α(γ1,pat,δ) = α(γ1[ρ[τ]],c a[ρ[τ]],δ_f[1])
+  -- also rather than (p : Path X(η) u v) we'll have (p : I -> X(η)), same as the type of trX.
+
+  iz <- primIZero
+  interval <- elInf primInterval
+  let
+      old_tel = scTel old_sc
+      old_ps = pure $ AbsN (teleNames old_tel) $ fromSplitPatterns $ scPats old_sc
+      old_ty = pure $ AbsN (teleNames old_tel) $ fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+  -- old_tel = Γ(x: D η v)Δ
+  -- Γ1, (x : D η v)  ⊢ delta = (δ : Δ)
+      (gamma1x,delta') = splitTelescopeAt (size old_tel - blockingVarNo x) old_tel
+  let
+    gammaArgNames = teleArgNames gamma
+    deltaArgNames = teleArgNames delta'
+  let
+    xTelI = pure $ AbsN (teleNames gamma) $ expTelescope interval xTel
+    delta = pure $ AbsN (teleNames gamma1x) $ delta'
+    gamma1_size = (size gamma1x - 1)
+    (gamma1,ExtendTel dType' _) = splitTelescopeAt gamma1_size gamma1x
+  params <- addContext gamma1 $ do
+    Just (_d, ps, _is) <- getDatatypeArgs . unDom =<< reduce dType'
+    return $ AbsN (teleNames gamma1) ps
+  -- Γ, φ , p ⊢ pat := trX p φ (c a)
+  let pat' =
+            bindNArg gammaArgNames $ \ g1_args -> do
+            bindNArg ([defaultArg "phi"] ++ teleArgNames xTel) $ \ phi_p -> do
+            let (g1,args) = splitAt gamma1_size g1_args
+            (phi:p) <- sequence phi_p
+            args <- sequence args
+            let cargs = defaultArg $ unnamed $ ConP chead noConPatternInfo args
+            -- Amy (2022-11-06): Set the parameters to quantity-0.
+            param_args <- fmap (map (setQuantity (Quantity0 Q0Inferred) . setHiding Hidden . fmap (unnamed . dotP))) $
+              pure params `applyN` take gamma1_size (fmap unArg <$> g1_args)
+            pure $ DefP defaultPatternInfo q_trX $ param_args ++ p ++ [phi,cargs]
+      pat = (fmap . fmap) patternToTerm <$> pat'
+      pat_left' = (fmap . fmap) (Abs "i" . (applySubst leftInv)) <$> pat
+      g1_left' = bindN (map unArg gammaArgNames) $ \ g1_args -> do
+                bindN (map unArg $ [defaultArg "phi"] ++ teleArgNames xTel) $ \ phi_p -> do
+                g1 <- sequence $ take gamma1_size g1_args :: NamesT TCM [Term]
+                pure $ Abs "i" (applySubst leftInv g1)
+
+  gamma <- return $ pure gamma
+  let deltaPat g1_args phi p =
+        delta `applyN` (take gamma1_size g1_args ++ [pat `applyN` g1_args `applyN` (phi:p)])
+  let neg i = cl primINeg <@> i
+  -- Ξ
+  cTel <- runNamesT [] $
+    abstractN gamma $ \ g1_args -> do
+    abstractT "φ" (pure interval) $ \ phi -> do
+    abstractN (xTelI `applyN` g1_args) $ \ p -> do
+    deltaPat g1_args phi p
+  ps_ty_rhs <- runNamesT [] $ do
+    bindN (map unArg gammaArgNames) $ \ g1_args -> do
+    bind "phi" $ \ phi -> do
+    bindN (teleNames xTel) $ \ p -> do
+    bindN (map unArg $ deltaArgNames) $ \ d -> do
+    let
+      g1_left = g1_left' `applyN` g1_args `applyN` (phi:p)
+      pat_left = pat_left' `applyN` g1_args `applyN` (phi:p)
+      g1 :: Vars TCM
+      g1 = take gamma1_size g1_args
+
+      args :: Vars TCM
+      args = drop gamma1_size g1_args
+
+      ps :: NamesT TCM NAPs
+      ps = old_ps `applyN` (g1 ++ [pat' `applyN` g1_args `applyN` (phi:p)] ++ d)
+
+      rhsTy = old_ty `applyN` (g1 ++ [pat `applyN` g1_args `applyN` (phi:p)] ++ d)
+
+    -- (i. Δ[γ1[leftInv (~ i)], pat[leftInv (~i)]])
+    delta_f <- (open =<<) $ bind "i" $ \ i -> do
+      let ni = neg i
+      dargs <- (mapM open =<<) $ do
+        xs <- absApp <$> g1_left <*> ni
+        y <- absApp <$> pat_left <*> ni
+        return $ xs ++ [y]
+      delta `applyN` dargs
+
+    --  trFillTel (i. Δ[γ1[leftInv (~ i)], pat[leftInv (~i)]]) φ δ
+    d_f <- (open =<<) $ bind "i" $ \ i -> do
+      delta_f <- delta_f
+      phi <- phi
+      d <- map defaultArg <$> sequence d
+      i <- i
+      lift $ covFillTele f delta_f phi d i
+
+    -- w = Def f (old_ps[g1_left[i],pat_left[i],d_f[~ i]])
+    w <- (open =<<) $ bind "i" $ \ i -> do
+      psargs <- (mapM open =<<) $ do
+        xs <- absApp <$> g1_left <*> i
+        y <- absApp <$> pat_left <*> i
+        zs <- absApp <$> d_f <*> neg i
+        return $ xs ++ [y] ++ zs
+      ps <- (fmap patternsToElims <$> old_ps) `applyN` psargs
+      pure $ Def f ps
+
+
+    -- (i. old_t[γ1[leftInv i],x = pat[leftInv i], δ_f[~i]])
+    ty <- (open =<<) $ bind "i" $ \ i -> do
+      tyargs <- (mapM open =<<) $ do
+        xs <- absApp <$> g1_left <*> i
+        y <- absApp <$> pat_left <*> i
+        zs <- absApp <$> d_f <*> neg i
+        return $ xs ++ [y] ++ zs
+      fmap unDom $ old_ty `applyN` tyargs
+
+    sys <- do
+      sides <- do
+        neg <- primINeg
+        io <- primIOne
+        vs <- iApplyVars <$> ps
+        tm <- w
+        xs <- forM vs $ \ v ->
+            -- have to reduce these under the appropriate substitutions, otherwise non-normalizing(?)
+              fmap (var v,) . reduce $ (inplaceS v iz `applySubst` tm, inplaceS v io `applySubst` tm)
+        return $ concatMap (\(v,(l,r)) -> [(neg `apply` [argN v],l),(v,r)]) xs
+      forM sides $ \ (psi,u') -> do
+        u' <- open u'
+        u <- lam "i" $ \ i -> ilam "o" $ \ o -> absApp <$> u' <*> i
+        (,) <$> open psi <*> open u
+
+    let rhs = transpSys ty sys phi (absApp <$> w <*> pure iz)
+
+    (,,) <$> ps <*> rhsTy <*> rhs
+
+  let (ps,ty,rhs) = unAbsN $ unAbsN $ unAbs $ unAbsN $ ps_ty_rhs
+  qs <- mapM (fmap (fromMaybe __IMPOSSIBLE__) . getName') [builtinINeg, builtinIMax, builtinIMin]
+  rhs <- addContext cTel $
+           locallyReduceDefs (OnlyReduceDefs (Set.fromList $ q_trX : qs)) $ normalise rhs
+  let cl = Clause { clauseLHSRange  = noRange
+                  , clauseFullRange = noRange
+                  , clauseTel       = cTel
+                  , namedClausePats = ps
+                  , clauseBody      = Just rhs
+                  , clauseType      = Just $ Arg (getArgInfo ty) (unDom ty)
+                  , clauseCatchall    = False
+                  , clauseExact       = Nothing
+                  , clauseRecursive   = Just True
+                  , clauseUnreachable = Just False
+                  , clauseEllipsis    = NoEllipsis
+                  , clauseWhereModule = Nothing
+                  }
+
+
+  debugClause "tc.cover.trxcon" cl
+
+  reportSDoc "tc.cover.trxcon" 20 $ vcat $
+    [ "clause:"
+    ,  nest 2 $ prettyTCM . QNamed f $ cl
+    ]
+
+  let mod =
+        setRelevance Irrelevant $  -- See #5611.
+        getModality $ fromMaybe __IMPOSSIBLE__ $ scTarget old_sc
+  -- we follow what `cover` does when updating the modality from the target.
+  applyModalityToContext mod $ do
+    unlessM (hasQuantity0 <$> viewTC eQuantity) $ do
+    reportSDoc "tc.cover.trxcon" 20 $ text "testing usable at mod: " <+> pretty mod
+    addContext cTel $ usableAtModality IndexedClause mod rhs
+
+  return cl
+
+-- | If given @TheInfo{}@ then assumes "x : Id u v" and
+--   returns both a @SplittingDone@ for conId, and the @Clause@ that covers it.
+createMissingConIdClause :: QName         -- ^ function being defined
+                         -> Arg Nat       -- ^ @covSplitArg@ index
+                         -> BlockingVar   -- ^ @x@ variable being split on.
+                         -> SplitClause   -- ^ clause before split
+                         -> IInfo         -- ^ info from unification
+                         -> TCM (Maybe ((SplitTag,SplitTree),Clause))
+createMissingConIdClause f _n x old_sc (TheInfo info) = setCurrentRange f $ do
+  let
+    -- iΓ'
+    itel = infoTel
+    -- with 3 params, reflId : Id A u u -- no arguments.
+    -- iΓ' ⊢ iρ : Γ
+    --
+    -- Δ = Γ,φ,(p : u ≡ v) ⊢ iτ : iΓ'
+    -- ρ = iρ
+    -- τ = iτ
+    irho = infoRho info
+    itau = infoTau info
+    ileftInv = infoLeftInv info
+  interval <- elInf primInterval
+  tTrans  <- primTrans
+  tComp  <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinComp
+  conId <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinConId
+  let bindSplit (tel1,tel2) = (tel1,AbsN (teleNames tel1) tel2)
+  let
+      old_tel = scTel old_sc
+
+  -- old_tel = Γ(x: Id A u v)Δ
+  -- Γ(x: Id A u v)Δ ⊢ old_t
+  -- Γ ⊢ hdelta = (x : Id A u v)(δ : Δ)
+      pair@(_gamma,_hdelta@(ExtendTel hdom delta)) = splitTelescopeAt (size old_tel - (blockingVarNo x + 1)) old_tel
+      (gamma,hdelta) = bindSplit pair
+      old_t  = AbsN (teleNames old_tel) $ fromJust $ scTarget old_sc
+      old_ps = AbsN (teleNames old_tel) $ patternsToElims $ fromSplitPatterns $ scPats old_sc
+      old_ps' = AbsN (teleNames old_tel) $ fromSplitPatterns $ scPats old_sc
+
+  params <- runNamesT [] $ do
+    hdelta <- open hdelta
+    bindN (teleNames gamma) $ \ args -> do
+       hdelta@(ExtendTel hdom _) <- applyN hdelta args
+       Def _Id es@[_,_,_,_] <- reduce $ unEl $ unDom hdom
+       return $ map unArg $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+  working_tel <- runNamesT [] $ do
+    hdelta <- open hdelta
+    params <- open params
+    abstractN (pure gamma) $ \ args -> do
+      pTel <- open =<< (lift $ pathTelescope (infoEqTel info) (map defaultArg $ infoEqLHS info) (map defaultArg $ infoEqRHS info))
+      abstractN (pure (telFromList [defaultDom ("phi",interval)] :: Telescope)) $ \ [phi] ->
+        abstractN pTel $ \ [p] -> do
+          [l,bA,x,y] <- mapM open =<< applyN params args
+          apply1 <$> applyN hdelta args <*> (cl primConId <#> l <#> bA <#> x <#> y <@> phi <@> p)
+  -- working_tel ⊢ i. γ[leftInv i]
+  (gamma_args_left :: Abs [Term], con_phi_p_left :: Abs Term) <- fmap (raise (size delta) . unAbsN) . runNamesT [] $ do
+    params <- open params
+    bindN (teleNames gamma ++ ["phi","p"]) $ \ args' -> do
+      let (args,[phi,p]) = splitAt (size gamma) args'
+      [l,bA,x,y] <- mapM open =<< applyN params args
+      gargs <- Abs "i" . applySubst ileftInv <$> sequence args
+      con_phi_p <- Abs "i" . applySubst ileftInv <$> do
+        (cl primConId <#> l <#> bA <#> x <#> y <@> phi <@> p)
+      return (gargs,con_phi_p)
+  ps <- fmap unAbsN . runNamesT [] $ do
+    old_ps' <- open $ old_ps'
+    params <- open params
+    bindN (teleNames working_tel) $ \ (wargs :: [NamesT TCM Term]) -> do
+      let (g,phi:p:d) = splitAt (size gamma) $ telePatterns working_tel []
+      params <- map (argH . unnamed . dotP) <$> applyN params (take (size gamma) wargs)
+      let x = DefP defaultPatternInfo conId $ params ++ [phi,p]
+      args <- open $ map namedArg g ++ [x] ++ map namedArg d
+      applyN' old_ps' args
+  -- tel = Γ',Δ[ρ,x = refl]
+  -- Γ' ⊢ ρ : Γ
+  -- Γ' ⊢ u[ρ] = v[ρ] : A[ρ]
+
+  -- Γ' ⊢ ρ,x=refl : Γ,(x : Id A u v)
+
+  -- Γ',Δ[ρ,x = refl] ⊢ old_t[ρ,x=refl] = Δ₂ -> t
+  -- Γ',Δ[ρ,x = refl] ⊢ f old_ps[ρ,x = refl] : old_t[ρ,x = refl]
+  -- Γ,(φ : I),(p : Path A u v) ⊢ τ : Γ'
+
+  -- Γ' ⊢ [ρ,x = refl u[ρ]] : Γ,(x : Id A u v)
+
+  -- Γ,(φ : I),(p : Path A u v) ⊢ [ρ,x = refl u[ρ]][τ] = [ρ[τ], x = refl u[ρ[τ]]] : Γ,(x : Id A u v)
+
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv : ρ[τ],i1,refl ≡ idS : Γ,(φ : I),(p : Path A u v)
+
+  -- Γ,(φ : I),(p : Path A u v)| (i : I) ⊢ leftInv i : Γ,(φ : I),(p : Path A u v)
+
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv i0 = ρ[τ],i1,refl : Γ,(φ : I),(p : Path A u v)
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv i1 = γ   ,φ ,p : Γ,(φ : I),(p : Path A u v)
+  --                      leftInv[φ = i1][i] = idS
+
+  -- Γ,(φ : I),(p : Path A u v),Δ[ρ,x = refl][τ] ⊢ τ' = liftS |Δ[ρ,x = refl]| τ : Γ',Δ[ρ,x = refl]
+
+  -- Γ,(φ : I),(p : Path A u v),Δ[ρ,x = refl][τ] ⊢
+  --            w = f old_ps[ρ[τ],x = refl u[ρ[τ]],δ] : old_t[ρ,x = refl][τ'] = old_t[ρ[τ],x = refl u[ρ[τ]],δ]
+
+  -- Γ,(φ : I),(p : Path A u v) | (i : I) ⊢ μ = ⟨φ,p⟩[leftInv (~i)] : (Id A u v)[γ[leftInv (~ i)]]
+  --                                     μ[0] = ⟨ φ             , p    ⟩
+  --                                     μ[1] = ⟨ 1             , refl ⟩
+
+  -- Γ,(φ : I),(p : Path A u v),(δ : Δ[x = ⟨ φ , p ⟩]) ⊢
+  --         δ_f[1] = vecTransp (i. Δ[γ[leftInv (~ i)], ⟨φ,p⟩[leftInv (~i)]]) φ δ : Δ[ρ[τ], x = refl u[ρ[τ]]]
+
+  -- Γ,(φ : I),(p : Path A u v),(δ : Δ[x = ⟨ φ , p ⟩]) ⊢ w[δ_f[1]] : old_t[ρ[τ],x = refl u[ρ[τ]],δ_f[1]]
+  -- Γ,(φ : I),(p : Path A u v),Δ[x = ⟨ φ , p ⟩] ⊢ rhs = transp (i. old_t[γ[leftInv i],x = ⟨φ,p⟩[leftInv i], δ_f[~i]]) φ (w[δ_f[1]]) : old_t[γ,x = ⟨ φ , p ⟩,δ]
+  let
+      getLevel t = do
+        s <- reduce $ getSort t
+        case s of
+          Type l -> pure (Level l)
+          s      -> do
+            reportSDoc "tc.cover.hcomp" 20 $ text "getLevel, s = " <+> prettyTCM s
+            typeError . GenericDocError =<<
+                    (text "The sort of" <+> prettyTCM t <+> text "should be of the form \"Set l\"")
+  (ty,rhs) <- addContext working_tel $ runNamesT [] $ do
+    let
+        raiseFrom :: Subst a => Telescope -> a -> a
+        raiseFrom tel x = raise (size working_tel - size tel) x
+        all_args = teleArgs working_tel :: Args
+        (gamma_args,phi:p:delta_args) = splitAt (size gamma) all_args
+    old_t <- open $ raiseFrom EmptyTel old_t
+    old_ps <- open $ raiseFrom EmptyTel old_ps
+    delta_args <- open delta_args
+    gamma_args_left <- open gamma_args_left
+    con_phi_p_left <- open con_phi_p_left
+    hdelta <- open $ raiseFrom gamma hdelta
+    delta_f <- bind "i" $ \ i -> do
+      apply1 <$> applyN' hdelta (lazyAbsApp <$> gamma_args_left <*> (cl primINeg <@> i)) <*> (lazyAbsApp <$> con_phi_p_left <*> (cl primINeg <@> i))
+    delta_f <- open delta_f
+    [phi,p] <- mapM (open . unArg) [phi,p]
+    delta_args_f <- bind "i" $ \ i -> do
+
+      m <- trFillTel' True <$> delta_f <*> phi <*> delta_args <*> i
+      either __IMPOSSIBLE__ id <$> (lift $ runExceptT m)
+    delta_args_f <- open delta_args_f
+    old_t_f <- (open =<<) $ bind "i" $ \ i -> do
+      g <- lazyAbsApp <$> gamma_args_left <*> i
+      x <- lazyAbsApp <$> con_phi_p_left <*> i
+      d <- lazyAbsApp <$> delta_args_f <*> (cl primINeg <@> i)
+      args <- open $ g ++ [x] ++ map unArg d
+      applyN' old_t args
+    w <- (open =<<) $ bind "i" $ \ i -> do
+      g <- lazyAbsApp <$> gamma_args_left <*> i
+      x <- lazyAbsApp <$> con_phi_p_left <*> i
+      d <- lazyAbsApp <$> delta_args_f <*> (cl primINeg <@> i)
+      args <- open $ g ++ [x] ++ map unArg d
+      Def f <$> applyN' old_ps args
+
+    ps <- open ps
+    max <- primIMax
+    iz <- primIZero
+    alphas <- (open =<<) $ do
+      vs <- iApplyVars <$> ps
+      neg <- primINeg
+      zero <- primIZero
+      return $ foldr (\ x r -> max `apply` [argN $ max `apply` [argN x, argN (neg `apply` [argN x])], argN r]) zero $ map var vs
+    sides <- (open =<<) $ do
+      neg <- primINeg
+      io <- primIOne
+      bind "i" $ \ i -> do
+        vs <- iApplyVars <$> ps
+        tm <- lazyAbsApp <$> w <*> i
+        xs <- forM vs $ \ v ->
+          -- have to reduce these under the appropriate substitutions, otherwise non-normalizing
+          fmap (var v,) . reduce $ (inplaceS v iz `applySubst` tm, inplaceS v io `applySubst` tm)
+        phiv <- fromMaybe __IMPOSSIBLE__ . deBruijnView <$> phi
+        -- extra assumption: phi |- w i = w 0, otherwise we need [ phi -> w 0 ] specifically
+        tm_phi <- reduce $ inplaceS phiv io `applySubst` tm
+        phi <- phi
+        return $ (phi,tm_phi) : concatMap (\(v,(l,r)) -> [(neg `apply` [argN v],l),(v,r)]) xs
+
+    let imax i j = apply max $ map argN [i,j]
+    tPOr <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPOr
+    let
+      pOr l ty phi psi u0 u1 = do
+          [phi,psi] <- mapM open [phi,psi]
+          pure tPOr <#> l
+                    <@> phi <@> psi
+                    <#> (ilam "o" $ \ _ -> ty) <@> noilam u0 <@> u1
+
+      noilam u = do
+         u <- open u
+         ilam "o" $ \ _ -> u
+
+      combine l ty [] = __IMPOSSIBLE__
+      combine l ty [(psi,u)] = noilam u
+      combine l ty ((psi,u):xs) = pOr l ty psi (foldr imax iz (map fst xs)) u (combine l ty xs)
+
+    let ty i = lazyAbsApp <$> old_t_f <*> i
+    l <- (open =<<) $ lam "i" $ \ i -> do
+           t <- unDom <$> ty i
+           lift $ getLevel t
+    ((,) <$> ty (cl primIOne) <*>) $ do
+         n <- length . unAbs <$> sides
+         -- TODO don't comp if the family and the sides "j. [ α ↦ u ]" are constant?
+         if n > 1 then
+           pure tComp <#> l <@> (lam "i" $ \ i -> unEl . unDom <$> ty i)
+                <@> (cl primIMax <@> phi <@> alphas)
+                <@> (lam "i" $ \ i -> combine (l <@> i) (unEl . unDom <$> ty i) =<< (lazyAbsApp <$> sides <*> i))
+                <@> (lazyAbsApp <$> w <*> primIZero)
+         else
+           pure tTrans <#> l <@> (lam "i" $ \ i -> unEl . unDom <$> ty i)
+                <@> phi
+                <@> (lazyAbsApp <$> w <*> primIZero)
+
+  reportSDoc "tc.cover.conid" 20 $ text "conid case for" <+> text (show f)
+  reportSDoc "tc.cover.conid" 20 $ text "tel =" <+> prettyTCM working_tel
+  reportSDoc "tc.cover.conid" 25 $ addContext working_tel $ prettyTCM rhs
+
+  let cl =   Clause { clauseLHSRange  = noRange
+                    , clauseFullRange = noRange
+                    , clauseTel       = working_tel
+                    , namedClausePats = ps
+                    , clauseBody      = Just $ rhs
+                    , clauseType      = Just $ Arg (domInfo ty) (unDom ty)
+                    , clauseCatchall    = False
+                    , clauseUnreachable = Just False  -- missing, thus, not unreachable
+                    , clauseRecursive   = Just False
+                    , clauseEllipsis    = NoEllipsis
+                    , clauseExact       = Nothing
+                    , clauseWhereModule = Nothing
+                    }
+  addClauses f [cl]
+  return $ Just ((SplitCon conId,SplittingDone (size working_tel)),cl)
+createMissingConIdClause f n x old_sc NoInfo = return Nothing
+
+
+{-
+  OLD leftInv case
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv : ρ[τ] ≡ wkS 2 : Γ
+  -- Γ,(φ : I),(p : Path A u v)(i : I) ⊢ leftInv i : Γ
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv i0 = ρ[τ] : Γ
+  -- Γ,(φ : I),(p : Path A u v) ⊢ leftInv i1 = wkS 2 : Γ
+  -- leftInv[φ = i1][i] = wkS 2
+
+  -- Γ,(φ : I),(p : Path A u v),Δ[ρ,x = refl][τ] ⊢ τ' = liftS |Δ[ρ,x = refl]| τ : Γ',Δ[ρ,x = refl]
+
+  -- Γ,(φ : I),(p : Path A u v),Δ[ρ,x = refl][τ] ⊢ w = f old_ps[ρ,x = refl][τ'] : old_t[ρ,x = refl][τ']
+
+  -- Γ,(φ : I),(p : Path A u v) | (i : I) ⊢ μ = ⟨ (φ ∨ ~ i) , (\ j → p (i ∧ j)) ⟩ : Id A u (p i) =?= (Id A u v)[leftInv (~ i)]
+                                  μ[0] = ⟨ 1 , (\ _ → u[ρ[τ]]) ⟩
+                                  μ[1] = ⟨ φ , p               ⟩
+  -- Γ,(φ : I),(p : Path A u v),(δ : Δ[x = ⟨ φ , p ⟩]) ⊢ vecTransp (i. Δ[leftInv (~ i),μ[i]]) φ δ : Δ[ρ[τ], x = refl u[ρ[τ]]]
+-}
+
+-- | Append an hcomp clause to the clauses of a function.
+createMissingHCompClause
+  :: QName
+       -- ^ Function name.
+  -> Arg Nat -- ^ index of hcomp pattern
+  -> BlockingVar -- ^ Blocking var that lead to hcomp split.
+  -> SplitClause -- ^ Clause before the hcomp split
+  -> SplitClause
+       -- ^ Clause to add.
+  -> [Clause]
+   -> TCM ([(SplitTag,CoverResult)], [Clause])
+createMissingHCompClause f n x old_sc (SClause tel ps _sigma' _cps (Just t)) cs = setCurrentRange f $ do
+  reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "Trying to create right-hand side of type" <+> prettyTCM t
+  reportSDoc "tc.cover.hcomp" 30 $ addContext tel $ text "ps = " <+> prettyTCMPatternList (fromSplitPatterns ps)
+  reportSDoc "tc.cover.hcomp" 30 $ text "tel = " <+> prettyTCM tel
+
+  io      <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIOne
+  iz      <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIZero
+  let
+    cannotCreate :: MonadTCError m => Doc -> Closure (Abs Type) -> m a
+    cannotCreate doc t = do
+      typeError . SplitError $ CannotCreateMissingClause f (tel,fromSplitPatterns ps) doc t
+  let old_ps = patternsToElims $ fromSplitPatterns $ scPats old_sc
+      old_t  = fromJust $ scTarget old_sc
+      old_tel = scTel old_sc
+      -- old_tel = Γ(x:H)Δ
+      -- Γ(x:H)Δ ⊢ old_t
+      -- vs = iApplyVars old_ps
+      -- [ α ⇒ b ] = [(i,f old_ps (i=0),f old_ps (i=1)) | i <- vs]
+
+      -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ]
+      -- Γ(x:H)Δ ⊢ f old_ps : old_t [ α ⇒ b ]
+      -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢ rhs_we_define : (old_t[ α ⇒ b ])(x = hcomp φ u u0)
+
+      -- Extra assumption:
+      -- tel = Γ,φ,u,u0,Δ(x = hcomp φ u u0),Δ'
+      -- ps = old_ps[x = hcomp φ u u0],ps'
+      -- with Δ' and ps' introduced by fixTarget.
+      -- So final clause will be:
+      -- tel ⊢ ps ↦ rhs_we_define{wkS ..} ps'
+      getLevel t = do
+        s <- reduce $ getSort t
+        case s of
+          Type l -> pure (Level l)
+          s      -> do
+            reportSDoc "tc.cover.hcomp" 20 $ text "getLevel, s = " <+> prettyTCM s
+            typeError . GenericDocError =<<
+                    (text "The sort of" <+> prettyTCM t <+> text "should be of the form \"Set l\"")
+
+      -- Γ ⊢ hdelta = (x : H)(δ : Δ)
+      (gamma,hdelta@(ExtendTel hdom delta)) = splitTelescopeAt (size old_tel - (blockingVarNo x + 1)) old_tel
+
+      -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢
+      (working_tel,_deltaEx) = splitTelescopeAt (size gamma + 3 + size delta) tel
+
+      -- Γ,φ,u,u0,(x:H)(δ : Δ) ⊢ rhoS : Γ(x:H)(δ : Δ)
+      {- rhoS = liftS (size hdelta) $ raiseS 3 -}
+      vs = iApplyVars (scPats old_sc)
+
+  -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ] = [(i,f old_ps (i=0),f old_ps (i=1)) | i <- vs]
+  alphab <- forM vs $ \ i -> do
+               let
+                 -- Γ(x:H)(δ : Δ) ⊢
+                 tm = Def f old_ps
+               -- TODO only reduce IApply _ _ (0/1), as to avoid termination problems
+               (l,r) <- reduce (inplaceS i iz `applySubst` tm, inplaceS i io `applySubst` tm)
+               return $ (var i, (l, r))
+
+
+
+  cl <- do
+    (ty,rhs) <- addContext working_tel $ do
+      -- Γ(x:H)Δ ⊢ g = f old_ps : old_t [ α ⇒ b ]
+      -- Γ(x:H)(δ : Δ) ⊢ [ α ⇒ b ]
+      -- Γ,φ,u,u0 ⊢ Δf = i.Δ[x = hfill φ u u0 i]
+      -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ δ_fill     = i.tFillTel (i. Δf[~i]) δ (~ i) : i.Δf[i]
+      -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ old_t_fill = i.old_t[x = hfill φ u u0 i, δ_fill[i]]
+      -- Γ,φ,u,u0,δ : Δ(x = hcomp φ u u0) ⊢ comp (\ i. old_t_fill[i])
+      --                 (\ i. [ φ ↦ g[x = hfill φ u u0 i,δ_fill[i]] = g[u i,δ_fill[i]]
+      --                         α ↦ b[x = hfill φ u u0 i,δ_fill[i]]
+      --                        ])
+      --                 (g[x = u0,δ_fill[0]]) : old_t[x = hcomp φ u u0,δ]
+
+      runNamesT [] $ do
+          tPOr <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPOr
+          tIMax <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIMax
+          tIMin <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIMin
+          tINeg <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinINeg
+          tHComp <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinHComp
+          tTrans <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinTrans
+          extra_ps <- open $ patternsToElims $ fromSplitPatterns $ drop (length old_ps) ps
+          let
+            ineg j = pure tINeg <@> j
+            imax i j = pure tIMax <@> i <@> j
+            trFillTel' a b c d = do
+              m <- trFillTel <$> a <*> b <*> c <*> d
+              x <- lift $ runExceptT m
+              case x of
+                Left bad_t -> cannotCreate "Cannot transport with type family:" bad_t
+                Right args -> return args
+          comp <- mkCompLazy "hcompClause"
+          let
+            hcomp la bA phi u u0 = pure tHComp <#> la <#> bA
+                                               <#> phi
+                                               <@> u
+                                               <@> u0
+
+            hfill la bA phi u u0 i = hcomp la bA
+                                               (pure tIMax <@> phi <@> (pure tINeg <@> i))
+                                               (lam "j" $ \ j -> pure tPOr <#> la <@> phi <@> (pure tINeg <@> i) <#> ilam "o" (\ _ -> bA)
+                                                     <@> ilam "o" (\ o -> u <@> (pure tIMin <@> i <@> j) <..> o)
+                                                     <@> ilam "o" (\ _ -> u0)
+                                                   )
+                                               u0
+          -- Γ,φ,u,u0,(δ : Δ(x = hcomp φ u u0)) ⊢ hcompS : Γ(x:H)(δ : Δ)
+          hcompS <- lift $ do
+            hdom <- pure $ raise 3 hdom
+            let
+              [phi,u,u0] = map (pure . var) [2,1,0]
+              htype = pure $ unEl . unDom $ hdom
+              lvl = getLevel $ unDom hdom
+            hc <- pure tHComp <#> lvl <#> htype
+                                      <#> phi
+                                      <@> u
+                                      <@> u0
+            return $ liftS (size delta) $ hc `consS` raiseS 3
+          -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ raise 3+|Δ| hdom
+          hdom <- pure $ raise (3 + size delta) hdom
+          htype <- open $ unEl . unDom $ hdom
+          lvl <- open =<< (lift . getLevel $ unDom hdom)
+
+          -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢
+          [phi,u,u0] <- mapM (open . raise (size delta) . var) [2,1,0]
+          -- Γ,x,Δ ⊢ f old_ps
+          -- Γ ⊢ abstract hdelta (f old_ps)
+          g <- open $ raise (3 + size delta) $ abstract hdelta (Def f old_ps)
+          old_t <- open $ raise (3 + size delta) $ abstract hdelta (unDom old_t)
+          let bapp a x = lazyAbsApp <$> a <*> x
+          (delta_fill :: NamesT TCM (Abs Args)) <- (open =<<) $ do
+            -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ x.Δ
+            delta <- open $ raise (3 + size delta) delta
+            -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ i.Δ(x = hfill phi u u0 (~ i))
+            deltaf <- open =<< bind "i" (\ i ->
+                           (delta `bapp` hfill lvl htype phi u u0 (ineg i)))
+            -- Γ,φ,u,u0,Δ(x = hcomp phi u u0) ⊢ Δ(x = hcomp phi u u0) = Δf[0]
+            args <- (open =<<) $ teleArgs <$> (lazyAbsApp <$> deltaf <*> pure iz)
+            bind "i" $ \ i -> addContext ("i" :: String) $ do -- for error messages.
+              -- Γ,φ,u,u0,Δ(x = hcomp phi u u0),(i:I) ⊢ ... : Δ(x = hfill phi u u0 i)
+              trFillTel' deltaf (pure iz) args (ineg i)
+          let
+            apply_delta_fill i f = apply <$> f <*> (delta_fill `bapp` i)
+            call v i = apply_delta_fill i $ g <@> v
+          ty <- do
+                return $ \ i -> do
+                    v <- hfill lvl htype phi u u0 i
+                    hd <- old_t
+                    args <- delta_fill `bapp` i
+                    lift $ piApplyM hd $ Arg (domInfo hdom) v : args
+          ty_level <- do
+            t <- bind "i" $ \ x -> ty x
+            s <- reduce $ getSort (absBody t)
+            reportSDoc "tc.cover.hcomp" 20 $ text "ty_level, s = " <+> prettyTCM s
+            case s of
+              Type l -> open =<< lam "i" (\ _ -> pure $ Level l)
+              _      -> do cl <- liftTCM (buildClosure t)
+                           liftTCM (cannotCreate "Cannot compose with type family:" cl)
+
+          let
+            pOr_ty i phi psi u0 u1 = pure tPOr <#> (ty_level <@> i)
+                                               <@> phi <@> psi
+                                               <#> ilam "o" (\ _ -> unEl <$> ty i) <@> u0 <@> u1
+          alpha <- do
+            vars <- mapM (open . applySubst hcompS . fst) alphab
+            return $ foldr (imax . (\ v -> v `imax` ineg v)) (pure iz) vars
+
+          -- Γ,φ,u,u0,Δ(x = hcomp φ u u0) ⊢ b : (i : I) → [α] -> old_t[x = hfill φ u u0 i,δ_fill[i]]
+          b <- do
+             sides <- forM alphab $ \ (psi,(side0,side1)) -> do
+                psi <- open $ hcompS `applySubst` psi
+
+                [side0, side1] <- mapM (open . raise (3 + size delta) . abstract hdelta) [side0, side1]
+                return $ (ineg psi `imax` psi, \ i -> pOr_ty i (ineg psi) psi (ilam "o" $ \ _ -> apply_delta_fill i $ side0 <@> hfill lvl htype phi u u0 i)
+                                                            (ilam "o" $ \ _ -> apply_delta_fill i $ side1 <@> hfill lvl htype phi u u0 i))
+             let recurse []           i = __IMPOSSIBLE__
+                 recurse [(psi,u)]    i = u i
+                 recurse ((psi,u):xs) i = pOr_ty i psi (foldr (imax . fst) (pure iz) xs) (u i) (recurse xs i)
+             return $ recurse sides
+
+          ((,) <$> ty (pure io) <*>) $ do
+            comp ty_level
+               (lam "i" $ fmap unEl . ty)
+                           (phi `imax` alpha)
+                           (lam "i" $ \ i ->
+                               let rhs = (ilam "o" $ \ o -> call (u <@> i <..> o) i)
+                               in if null alphab then rhs else
+                                   pOr_ty i phi alpha rhs (b i)
+                           )
+                           (call u0 (pure iz))
+    reportSDoc "tc.cover.hcomp" 20 $ text "old_tel =" <+> prettyTCM tel
+    let n = size tel - (size gamma + 3 + size delta)
+    reportSDoc "tc.cover.hcomp" 20 $ text "n =" <+> text (show n)
+    (TelV deltaEx t,bs) <- telViewUpToPathBoundary' n ty
+    rhs <- pure $ raise n rhs `applyE` teleElims deltaEx bs
+
+    cxt <- getContextTelescope
+    reportSDoc "tc.cover.hcomp" 30 $ text "cxt = " <+> prettyTCM cxt
+    reportSDoc "tc.cover.hcomp" 30 $ text "tel = " <+> prettyTCM tel
+    reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "t = " <+> prettyTCM t
+    reportSDoc "tc.cover.hcomp" 20 $ addContext tel $ text "rhs = " <+> prettyTCM rhs
+
+    return $ Clause { clauseLHSRange  = noRange
+                    , clauseFullRange = noRange
+                    , clauseTel       = tel
+                    , namedClausePats = fromSplitPatterns ps
+                    , clauseBody      = Just $ rhs
+                    , clauseType      = Just $ defaultArg t
+                    , clauseCatchall    = False
+                    , clauseExact       = Just True
+                    , clauseRecursive   = Nothing     -- TODO: can it be recursive?
+                    , clauseUnreachable = Just False  -- missing, thus, not unreachable
+                    , clauseEllipsis    = NoEllipsis
+                    , clauseWhereModule = Nothing
+                    }
+  addClauses f [cl]  -- Important: add at the end.
+  let result = CoverResult
+          { coverSplitTree      = SplittingDone (size (clauseTel cl))
+          , coverUsedClauses    = IntSet.singleton (length cs)
+          , coverMissingClauses = []
+          , coverPatterns       = [cl]
+          , coverNoExactClauses = IntSet.empty
+          }
+  hcompName <- fromMaybe __IMPOSSIBLE__ <$> getName' builtinHComp
+  return ([(SplitCon hcompName, result)], cs ++ [cl])
+createMissingHCompClause _ _ _ _ (SClause _ _ _ _ Nothing) _ = __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/Coverage/Match.hs b/src/full/Agda/TypeChecking/Coverage/Match.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Coverage/Match.hs
@@ -0,0 +1,511 @@
+
+{-| Given
+
+    1. the function clauses @cs@
+    2. the patterns @ps@ of the split clause
+
+we want to compute a variable index (in the split clause) to split on next.
+
+The matcher here checks whether the split clause is covered by one of
+the given clauses @cs@ or whether further splitting is needed (and
+when yes, where).
+-}
+
+module Agda.TypeChecking.Coverage.Match
+  ( Match(..), match, matchClause
+  , SplitPattern, SplitPatVar(..)
+  , fromSplitPattern, fromSplitPatterns, toSplitPatterns
+  , toSplitPSubst, applySplitPSubst
+  , isTrivialPattern
+  , BlockingVar(..), BlockingVars, BlockedOnResult(..)
+  , setBlockingVarOverlap
+  , ApplyOrIApply(..)
+  ) where
+
+import Prelude hiding ( null )
+
+import Data.DList (DList)
+import Data.Foldable (toList)
+import qualified Data.List as List
+import Data.Maybe (mapMaybe, fromMaybe)
+import Data.Semigroup ( Semigroup, (<>))
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty ( PrettyTCM(..) )
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( Pretty(..), text, (<+>), cat , prettyList_ )
+import Agda.Utils.Monad
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+-- | If matching is inconclusive (@Block@) we want to know which
+--   variables or projections are blocking the match.
+data Match a
+  = Yes a   -- ^ Matches unconditionally.
+  | No      -- ^ Definitely does not match.
+  | Block
+    { blockedOnResult :: BlockedOnResult
+      -- ^ @BlockedOnProj o@ if the clause has a result split.
+    , blockedOnVars :: BlockingVars
+      -- ^ @BlockingVar i cs ls o@ means variable @i@ is blocked on
+      -- constructors @cs@ and literals @ls@.
+    }
+  deriving (Functor)
+
+-- | Missing elimination blocking a match.
+data BlockedOnResult
+  = BlockedOnProj      -- ^ Blocked on unsplit projection.
+     { blockedOnResultOverlap :: Bool
+       -- ^ True if there are also matching clauses without an unsplit
+       -- copattern.
+     }
+  | BlockedOnApply     -- ^ Blocked on unintroduced argument.
+     { blockedOnResultIApply :: ApplyOrIApply
+       -- ^ Is the unintroduced argument an 'IApply' pattern?
+     }
+  | NotBlockedOnResult
+
+data ApplyOrIApply = IsApply | IsIApply
+
+-- | Variable blocking a match.
+data BlockingVar = BlockingVar
+  { blockingVarNo  :: Nat
+    -- ^ De Bruijn index of variable blocking the match.
+  , blockingVarCons :: [ConHead]
+    -- ^ Constructors in this position.
+  , blockingVarLits :: [Literal]
+    -- ^ Literals in this position.
+  , blockingVarOverlap :: Bool
+    -- ^ True if at least one clause has a variable pattern in this
+    --   position.
+  , blockingVarLazy :: Bool
+    -- ^ True if at least one clause has a lazy pattern in this position.
+  } deriving (Show)
+
+type BlockingVars = [BlockingVar]
+
+-- | Substitution of 'SplitPattern's for de Bruijn indices in covering
+--   clause to match 'SplitClause'.
+type SplitInstantiation = [(Nat,SplitPattern)]
+
+{-# SPECIALIZE match :: [Clause] -> [NamedArg SplitPattern] -> TCM (Match (Nat, SplitInstantiation)) #-}
+-- | Match the given patterns against a list of clauses.
+--
+-- If successful, return the index of the covering clause.
+--
+match :: PureTCM m
+      => [Clause]                           -- ^ Search for clause that covers the patterns.
+      -> [NamedArg SplitPattern]            -- ^ Patterns of the current 'SplitClause'.
+      -> m (Match (Nat, SplitInstantiation))
+match cs ps = foldr choice (return No) $ zipWith matchIt [0..] cs
+  where
+    matchIt :: PureTCM m
+            => Nat  -- Clause number.
+            -> Clause
+            -> m (Match (Nat, SplitInstantiation))
+    matchIt i c = fmap (\s -> (i, toList s)) <$> matchClause ps c
+
+-- | For each variable in the patterns of a split clause, we remember the
+--   de Bruijn-index and the literals excluded by previous matches.
+
+--  (See issue #708.)
+data SplitPatVar = SplitPatVar
+  { splitPatVarName   :: PatVarName
+  , splitPatVarIndex  :: Int
+  , splitExcludedLits :: [Literal]
+  } deriving (Show)
+
+instance Pretty SplitPatVar where
+  prettyPrec _ x =
+    text (patVarNameToString (splitPatVarName x)) <>
+    text ("@" ++ show (splitPatVarIndex x)) <>
+    ifNull (splitExcludedLits x) empty (\lits ->
+      "\\{" <> prettyList_ lits <> "}")
+
+instance PrettyTCM SplitPatVar where
+  prettyTCM = prettyTCM . var . splitPatVarIndex
+
+type SplitPattern = Pattern' SplitPatVar
+
+toSplitVar :: DBPatVar -> SplitPatVar
+toSplitVar x = SplitPatVar (dbPatVarName x) (dbPatVarIndex x) []
+
+fromSplitVar :: SplitPatVar -> DBPatVar
+fromSplitVar x = DBPatVar (splitPatVarName x) (splitPatVarIndex x)
+
+instance DeBruijn SplitPatVar where
+  deBruijnView x = deBruijnView (fromSplitVar x)
+  debruijnNamedVar n i = toSplitVar (debruijnNamedVar n i)
+
+toSplitPatterns :: [NamedArg DeBruijnPattern] -> [NamedArg SplitPattern]
+toSplitPatterns = (fmap . fmap . fmap . fmap) toSplitVar
+
+fromSplitPattern :: NamedArg SplitPattern -> NamedArg DeBruijnPattern
+fromSplitPattern = (fmap . fmap . fmap) fromSplitVar
+
+fromSplitPatterns :: [NamedArg SplitPattern] -> [NamedArg DeBruijnPattern]
+fromSplitPatterns = fmap fromSplitPattern
+
+type SplitPSubstitution = Substitution' SplitPattern
+
+toSplitPSubst :: PatternSubstitution -> SplitPSubstitution
+toSplitPSubst = (fmap . fmap) toSplitVar
+
+fromSplitPSubst :: SplitPSubstitution -> PatternSubstitution
+fromSplitPSubst = (fmap . fmap) fromSplitVar
+
+applySplitPSubst :: TermSubst a => SplitPSubstitution -> a -> a
+applySplitPSubst = applyPatSubst . fromSplitPSubst
+
+-- TODO: merge this instance and the one for DeBruijnPattern in
+-- Substitute.hs into one for Subst (Pattern' a) (Pattern' a).
+instance Subst SplitPattern where
+  type SubstArg SplitPattern = SplitPattern
+
+  applySubst IdS = id
+  applySubst rho = \case
+    VarP i x        ->
+      usePatternInfo i $
+      useName (splitPatVarName x) $
+      useExcludedLits (splitExcludedLits x) $
+      lookupS rho $ splitPatVarIndex x
+    DotP i u        -> DotP i $ applySplitPSubst rho u
+    ConP c ci ps    -> ConP c ci $ applySubst rho ps
+    DefP i q ps     -> DefP i q $ applySubst rho ps
+    p@LitP{}        -> p
+    p@ProjP{}       -> p
+    IApplyP i l r x ->
+      useEndPoints (applySplitPSubst rho l) (applySplitPSubst rho r) $
+      usePatternInfo i $
+      useName (splitPatVarName x) $
+      useExcludedLits (splitExcludedLits x) $
+      lookupS rho $ splitPatVarIndex x
+
+    where
+      -- see Subst for DeBruijnPattern
+      useEndPoints :: Term -> Term -> SplitPattern -> SplitPattern
+      useEndPoints l r (VarP o x)        = IApplyP o l r x
+      useEndPoints l r (IApplyP o _ _ x) = IApplyP o l r x
+      useEndPoints l r x                 = __IMPOSSIBLE__
+
+      useName :: PatVarName -> SplitPattern -> SplitPattern
+      useName n (VarP o x)
+        | isUnderscore (splitPatVarName x)
+        = VarP o $ x { splitPatVarName = n }
+      useName _ x = x
+
+      useExcludedLits :: [Literal] -> SplitPattern -> SplitPattern
+      useExcludedLits lits = \case
+        (VarP o x) -> VarP o $ x
+          { splitExcludedLits = lits ++ splitExcludedLits x }
+        p -> p
+
+
+{-# SPECIALIZE isTrivialPattern :: Pattern' a -> TCM Bool #-}
+-- | A pattern that matches anything (modulo eta).
+isTrivialPattern :: (HasConstInfo m) => Pattern' a -> m Bool
+isTrivialPattern = \case
+  VarP{}      -> return True
+  DotP{}      -> return True
+  ConP c i ps -> andM $ ((conPLazy i ||) <$> isEtaCon (conName c))
+                      : (map (isTrivialPattern . namedArg) ps)
+  DefP{}      -> return False
+  LitP{}      -> return False
+  ProjP{}     -> return False
+  IApplyP{}   -> return True
+
+-- | If matching succeeds, we return the instantiation of the clause pattern vector
+--   to obtain the split clause pattern vector.
+type MatchResult = Match (DList (Nat, SplitPattern))
+
+instance Pretty BlockingVar where
+  pretty (BlockingVar i cs ls o l) = cat
+    [ text ("variable " ++ show i)
+    , if null cs then empty else " blocked on constructors" <+> pretty cs
+    , if null ls then empty else " blocked on literals" <+> pretty ls
+    , if o then " (overlapping)" else empty
+    , if l then " (lazy)" else empty
+    ]
+
+yes :: Monad m => a -> m (Match a)
+yes = return . Yes
+
+no :: Monad m => m (Match a)
+no = return No
+
+blockedOnConstructor :: Monad m => Nat -> ConHead -> ConPatternInfo -> m (Match a)
+blockedOnConstructor i c ci = return $ Block NotBlockedOnResult [BlockingVar i [c] [] False $ conPLazy ci]
+
+blockedOnLiteral :: Monad m => Nat -> Literal -> m (Match a)
+blockedOnLiteral i l = return $ Block NotBlockedOnResult [BlockingVar i [] [l] False False]
+
+blockedOnProjection :: Monad m => m (Match a)
+blockedOnProjection = return $ Block (BlockedOnProj False) []
+
+blockedOnApplication :: Monad m => ApplyOrIApply -> m (Match a)
+blockedOnApplication b = return $ Block (BlockedOnApply b) []
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Lens for 'blockingVarCons'.
+--mapBlockingVarCons :: ([ConHead] -> [ConHead]) -> BlockingVar -> BlockingVar
+--mapBlockingVarCons f b = b { blockingVarCons = f (blockingVarCons b) }
+--
+---- | Lens for 'blockingVarLits'.
+--mapBlockingVarLits :: ([Literal] -> [Literal]) -> BlockingVar -> BlockingVar
+--mapBlockingVarLits f b = b { blockingVarLits = f (blockingVarLits b) }
+
+setBlockingVarOverlap :: BlockingVar -> BlockingVar
+setBlockingVarOverlap = \x -> x { blockingVarOverlap = True }
+
+overlapping :: BlockingVars -> BlockingVars
+overlapping = map setBlockingVarOverlap
+
+-- | Left dominant merge of blocking vars.
+zipBlockingVars :: BlockingVars -> BlockingVars -> BlockingVars
+zipBlockingVars xs ys = map upd xs
+  where
+    upd (BlockingVar x cons lits o l) = case List.find ((x ==) . blockingVarNo) ys of
+      Just (BlockingVar _ cons' lits' o' l') -> BlockingVar x (cons ++ cons') (lits ++ lits') (o || o') (l || l')
+      Nothing -> BlockingVar x cons lits True l
+
+setBlockedOnResultOverlap :: BlockedOnResult -> BlockedOnResult
+setBlockedOnResultOverlap b = case b of
+  BlockedOnProj{}      -> b { blockedOnResultOverlap = True }
+  BlockedOnApply{}     -> b
+  NotBlockedOnResult{} -> b
+
+anyBlockedOnResult :: BlockedOnResult -> BlockedOnResult -> BlockedOnResult
+anyBlockedOnResult b1 b2 = case (b1,b2) of
+  (NotBlockedOnResult , b2                ) -> b2
+  (b1                 , NotBlockedOnResult) -> b1
+  (_                  , _                 ) -> __IMPOSSIBLE__
+
+-- | Left dominant merge of `BlockedOnResult`.
+choiceBlockedOnResult :: BlockedOnResult -> BlockedOnResult -> BlockedOnResult
+choiceBlockedOnResult b1 b2 = case (b1,b2) of
+  (NotBlockedOnResult  , _                 ) -> NotBlockedOnResult
+  (BlockedOnProj o1    , BlockedOnProj o2  ) -> BlockedOnProj (o1 || o2)
+  (BlockedOnProj _     , _                 ) -> BlockedOnProj True
+  (BlockedOnApply b    , _                 ) -> BlockedOnApply b
+
+-- | @choice m m'@ combines the match results @m@ of a function clause
+--   with the (already combined) match results $m'$ of the later clauses.
+--   It is for skipping clauses that definitely do not match ('No').
+--   It is left-strict, to be used with @foldr@.
+--   If one clause unconditionally matches ('Yes') we do not look further.
+choice :: Monad m => m (Match a) -> m (Match a) -> m (Match a)
+choice m m' = m >>= \case
+  Yes a -> yes a
+  Block r xs -> m' >>= \case
+    Block s ys -> return $ Block (choiceBlockedOnResult r s) $ zipBlockingVars xs ys
+    Yes _      -> return $ Block (setBlockedOnResultOverlap r) $ overlapping xs
+    No         -> return $ Block r xs
+  No    -> m'
+
+{-# SPECIALIZE matchClause :: [NamedArg SplitPattern] -> Clause -> TCM MatchResult #-}
+matchClause
+  :: PureTCM m
+  => [NamedArg SplitPattern]
+     -- ^ Split clause patterns @qs@.
+  -> Clause
+     -- ^ Clause @c@ to cover split clause.
+  -> m MatchResult
+     -- ^ Result.
+     --   If 'Yes' the instantiation @rs@ such that @(namedClausePats c)[rs] == qs@.
+matchClause qs c = matchPats (namedClausePats c) qs
+
+{-# SPECIALIZE matchPats :: DeBruijn a => [NamedArg (Pattern' a)] -> [NamedArg SplitPattern] -> TCM MatchResult #-}
+-- | @matchPats ps qs@ checks whether a function clause with patterns
+--   @ps@ covers a split clause with patterns @qs@.
+--
+--   Issue #842 / #1986: This is accepted:
+--   @
+--     F : Bool -> Set1
+--     F true = Set
+--     F      = \ x -> Set
+--   @
+--   For the second clause, the split clause is @F false@,
+--   so there are more patterns in the split clause than
+--   in the considered clause.  These additional patterns
+--   are simply dropped by @zipWith@.  This will result
+--   in @mconcat []@ which is @Yes []@.
+
+matchPats
+  :: (PureTCM m, DeBruijn a)
+  => [NamedArg (Pattern' a)]
+     -- ^ Clause pattern vector @ps@ (to cover split clause pattern vector).
+  -> [NamedArg SplitPattern]
+     -- ^ Split clause pattern vector @qs@ (to be covered by clause pattern vector).
+  -> m MatchResult
+     -- ^ Result.
+     --   If 'Yes' the instantiation @rs@ such that @ps[rs] == qs@.
+matchPats [] [] = yes mempty
+matchPats (p:ps) (q:qs) =
+  matchPat (namedArg p) (namedArg q) `combine` matchPats ps qs
+
+-- Patterns left in split clause:
+-- Andreas, 2016-06-03, issue #1986:
+-- catch-all for copatterns is inconsistent as found by Ulf.
+-- Thus, if the split clause has copatterns left,
+-- the current (shorter) clause is not considered covering.
+matchPats [] qs@(_:_) = case mapMaybe isProjP qs of
+  [] -> yes mempty -- no proj. patterns left
+  _  -> no         -- proj. patterns left
+
+-- Patterns left in candidate clause:
+-- If the current clause has additional copatterns in
+-- comparison to the split clause, we should split on them.
+matchPats (p:ps) [] = case isProjP p of
+  Just{}  -> blockedOnProjection
+  Nothing -> blockedOnApplication (case namedArg p of IApplyP{} -> IsIApply; _ -> IsApply)
+
+-- | Combine results of checking whether function clause patterns
+--   covers split clause patterns.
+--
+--   'No' is dominant: if one function clause pattern is disjoint to
+--   the corresponding split clause pattern, then
+--   the whole clauses are disjoint.
+--
+--   'Yes' is neutral: for a match, all patterns have to match.
+--
+--   'Block' accumulates variables of the split clause
+--   that have to be instantiated (an projection names of copattern matches)
+--   to make the split clause an instance of the function clause.
+combine :: (Monad m, Semigroup a) => m (Match a) -> m (Match a) -> m (Match a)
+combine m m' = m >>= \case
+    Yes a -> m' >>= \case
+      Yes b -> yes (a <> b)
+      y     -> return y
+    No    -> no
+    x@(Block r xs) -> m' >>= \case
+      No    -> no
+      Block s ys -> return $ Block (anyBlockedOnResult r s) (xs ++ ys)
+      Yes{} -> return x
+
+{-# SPECIALIZE matchPat :: DeBruijn a => Pattern' a -> SplitPattern -> TCM MatchResult #-}
+-- | @matchPat p q@ checks whether a function clause pattern @p@
+--   covers a split clause pattern @q@.  There are three results:
+--
+--   1. @Yes rs@ means it covers, because @p@ is a variable pattern. @rs@ collects
+--      the instantiations of the variables in @p@ s.t. @p[rs] = q@.
+--
+--   2. @No@ means it does not cover.
+--
+--   3. @Block [x]@ means @p@ is a proper instance of @q@ and could become
+--      a cover if @q@ was split on variable @x@.
+
+matchPat
+  :: (PureTCM m, DeBruijn a)
+  => Pattern' a
+     -- ^ Clause pattern @p@ (to cover split clause pattern).
+  -> SplitPattern
+     -- ^ Split clause pattern @q@ (to be covered by clause pattern).
+  -> m MatchResult
+     -- ^ Result.
+     --   If 'Yes', also the instantiation @rs@ of the clause pattern variables
+     --   to produce the split clause pattern, @p[rs] = q@.
+matchPat p q = case p of
+
+  VarP _ x ->
+    yes $ singleton (fromMaybe __IMPOSSIBLE__ (deBruijnView x), q)
+
+  DotP{} -> yes mempty
+  -- Jesper, 2014-11-04: putting 'Yes [q]' here triggers issue 1333.
+  -- Not checking for trivial patterns should be safe here, as dot patterns are
+  -- guaranteed to match if the rest of the pattern does, so some extra splitting
+  -- on them doesn't change the reduction behaviour.
+
+  p@(LitP _ l) -> case q of
+    VarP _ x -> if l `elem` splitExcludedLits x
+                then no
+                else blockedOnLiteral (splitPatVarIndex x) l
+    _ -> isLitP q >>= \case
+      Just l' -> if l == l' then yes mempty else no
+      Nothing -> no
+
+  ProjP _ d -> case q of
+    ProjP _ d' -> do
+      d <- getOriginalProjection d
+      if d == d' then yes mempty else no
+    _          -> __IMPOSSIBLE__
+
+  IApplyP _ _ _ x ->
+    yes $ singleton (fromMaybe __IMPOSSIBLE__ (deBruijnView x), q)
+
+                           --    Issue #4179: If the inferred pattern is a literal
+                           -- v  we need to turn it into a constructor pattern.
+  ConP c ci ps -> unDotP q >>= unLitP >>= \case
+    VarP _ x -> blockedOnConstructor (splitPatVarIndex x) c ci
+    ConP c' i qs
+      | c == c'   -> matchPats ps qs
+      | otherwise -> no
+    DotP o t  -> no
+    DefP{}   -> no
+    LitP{}    -> __IMPOSSIBLE__  -- excluded by typing and unLitP
+    ProjP{}   -> __IMPOSSIBLE__  -- excluded by typing
+    IApplyP _ _ _ x -> blockedOnConstructor (splitPatVarIndex x) c ci
+
+  DefP o c ps -> unDotP q >>= \case
+    VarP _ x -> no
+    ConP c' i qs -> no
+    DotP o t  -> no
+    LitP{}    -> no
+    DefP o c' qs
+      | c == c'   -> matchPats ps qs
+      | otherwise -> no
+    ProjP{}   -> __IMPOSSIBLE__  -- excluded by typing
+    IApplyP _ _ _ x -> __IMPOSSIBLE__ -- blockedOnConstructor (splitPatVarIndex x) c
+
+{-# SPECIALIZE unDotP :: DeBruijn a => Pattern' a -> TCM (Pattern' a) #-}
+-- | Unfold one level of a dot pattern to a proper pattern if possible.
+unDotP :: (MonadReduce m, DeBruijn a) => Pattern' a -> m (Pattern' a)
+unDotP (DotP o v) = reduce v >>= \case
+  Var i [] -> return $ deBruijnVar i
+  Con c _ vs -> do
+    let ps = map (fmap $ unnamed . DotP o) $ fromMaybe __IMPOSSIBLE__ $ allApplyElims vs
+    return $ ConP c noConPatternInfo ps
+  Lit l -> return $ LitP (PatternInfo PatODot []) l
+  v     -> return $ dotP v
+unDotP p = return p
+
+{-# SPECIALIZE isLitP :: Pattern' a -> TCM (Maybe Literal) #-}
+isLitP :: PureTCM m => Pattern' a -> m (Maybe Literal)
+isLitP (LitP _ l) = return $ Just l
+isLitP (DotP _ u) = reduce u >>= \case
+  Lit l -> return $ Just l
+  _ -> return $ Nothing
+isLitP (ConP c ci []) = do
+  Con zero _ [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinZero
+  if c == zero
+    then return $ Just $ LitNat 0
+    else return Nothing
+isLitP (ConP c ci [a]) | visible a && isRelevant a = do
+  Con suc _ [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSuc
+  if c == suc
+    then fmap inc <$> isLitP (namedArg a)
+    else return Nothing
+  where
+    inc :: Literal -> Literal
+    inc (LitNat n) = LitNat $ n + 1
+    inc _ = __IMPOSSIBLE__
+isLitP _ = return Nothing
+
+{-# SPECIALIZE unLitP :: Pattern' a -> TCM (Pattern' a) #-}
+unLitP :: HasBuiltins m => Pattern' a -> m (Pattern' a)
+unLitP (LitP info l@(LitNat n)) | n >= 0 = do
+  Con c ci es <- constructorForm' (fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinZero)
+                                  (fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSuc)
+                                  (Lit l)
+  let toP (Apply (Arg i (Lit l))) = Arg i (LitP info l)
+      toP _ = __IMPOSSIBLE__
+      cpi   = noConPatternInfo { conPInfo = info }
+  return $ ConP c cpi $ map (fmap unnamed . toP) es
+unLitP p = return p
diff --git a/src/full/Agda/TypeChecking/Coverage/SplitClause.hs b/src/full/Agda/TypeChecking/Coverage/SplitClause.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Coverage/SplitClause.hs
@@ -0,0 +1,124 @@
+{-| SplitClause and CoverResult types.
+ -}
+
+module Agda.TypeChecking.Coverage.SplitClause where
+
+import Prelude hiding (null, (!!))  -- do not use partial functions like !!
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Syntax.Internal hiding (DataOrRecord)
+
+import Agda.TypeChecking.Coverage.Match
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Telescope.Path
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Warnings
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.WithDefault
+
+import Agda.Utils.Impossible
+
+
+data SplitClause = SClause
+  { scTel    :: Telescope
+    -- ^ Type of variables in @scPats@.
+  , scPats   :: [NamedArg SplitPattern]
+    -- ^ The patterns leading to the currently considered branch of
+    --   the split tree.
+  , scSubst  :: Substitution' SplitPattern
+    -- ^ Substitution from 'scTel' to old context.
+    --   Only needed directly after split on variable:
+    --   * To update 'scTarget'
+    --   * To rename other split variables when splitting on
+    --     multiple variables.
+    --   @scSubst@ is not ``transitive'', i.e., does not record
+    --   the substitution from the original context to 'scTel'
+    --   over a series of splits.  It is freshly computed
+    --   after each split by 'computeNeighborhood'; also
+    --   'splitResult', which does not split on a variable,
+    --   should reset it to the identity 'idS', lest it be
+    --   applied to 'scTarget' again, leading to Issue 1294.
+  , scCheckpoints :: Map CheckpointId Substitution
+    -- ^ We need to keep track of the module parameter checkpoints for the
+    -- clause for the purpose of inferring missing instance clauses.
+  , scTarget :: Maybe (Dom Type)
+    -- ^ The type of the rhs, living in context 'scTel'.
+    --   'fixTargetType' computes the new 'scTarget' by applying
+    --   substitution 'scSubst'.
+  }
+
+data UnifyEquiv = UE { infoTel0 :: Telescope          -- Γ0
+                     , infoTel :: Telescope           -- Γ'
+                     , infoEqTel :: Telescope         -- Γ0 ⊢ Δ
+                     , infoEqLHS :: [Term]            -- Γ0 ⊢ us : Δ
+                     , infoEqRHS :: [Term]            -- Γ0 ⊢ vs : Δ
+                     , infoRho :: PatternSubstitution -- Γ' ⊢ ρ : Γ0
+                                                      -- Γ = Γ0,(φ : I),(eqs : Paths Δ us vs)
+                                                      -- Γ' ⊢ ρ,i1,refls : Γ
+                     , infoTau :: Substitution        -- Γ  ⊢ τ           : Γ'
+                     , infoLeftInv :: Substitution    -- Γ | (i : I) ⊢ leftInv : Γ
+                     -- leftInv[i=0] = ρ[τ],i1s,refls
+                     -- leftInv[i=1] = idS
+                     }
+                  deriving Show
+
+data IInfo = TheInfo UnifyEquiv | NoInfo deriving Show
+
+-- | A @Covering@ is the result of splitting a 'SplitClause'.
+data Covering = Covering
+  { covSplitArg     :: Arg Nat
+     -- ^ De Bruijn level (counting dot patterns) of argument we split on.
+  , covSplitClauses :: [(SplitTag, (SplitClause, IInfo))]
+      -- ^ Covering clauses, indexed by constructor/literal these clauses share.
+  }
+
+-- | Project the split clauses out of a covering.
+splitClauses :: Covering -> [SplitClause]
+splitClauses (Covering _ qcs) = map (fst . snd) qcs
+
+-- | Create a split clause from a clause in internal syntax. Used by make-case.
+clauseToSplitClause :: Clause -> SplitClause
+clauseToSplitClause cl = SClause
+  { scTel    = clauseTel cl
+  , scPats   = toSplitPatterns $ namedClausePats cl
+  , scSubst  = idS  -- Andreas, 2014-07-15  TODO: Is this ok?
+  , scCheckpoints = Map.empty -- #2996: not __IMPOSSIBLE__ for debug printing
+  , scTarget = domFromArg <$> clauseType cl
+  }
+
+
+---------------------------------------------
+-- Record type for the results of @cover@
+---------------------------------------------
+
+data CoverResult = CoverResult
+  { coverSplitTree       :: SplitTree
+  , coverUsedClauses     :: IntSet -- Set Nat
+  , coverMissingClauses  :: [(Telescope, [NamedArg DeBruijnPattern])]
+  , coverPatterns        :: [Clause]
+  -- ^ The set of patterns used as cover.
+  , coverNoExactClauses  :: IntSet -- Set Nat
+  }
diff --git a/src/full/Agda/TypeChecking/Coverage/SplitTree.hs b/src/full/Agda/TypeChecking/Coverage/SplitTree.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Coverage/SplitTree.hs
@@ -0,0 +1,121 @@
+
+{-# OPTIONS_GHC -Wall #-}
+
+{-| Split tree for transforming pattern clauses into case trees.
+
+The coverage checker generates a split tree from the clauses.
+The clause compiler uses it to transform clauses to case trees.
+
+The initial problem is a set of clauses.  The root node designates
+on which argument to split and has subtrees for all the constructors.
+Splitting continues until there is only a single clause left at
+each leaf of the split tree.
+
+-}
+module Agda.TypeChecking.Coverage.SplitTree where
+
+import Control.DeepSeq
+
+import Data.Tree
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Pretty () --instance only
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Null
+
+import Agda.Utils.Impossible
+
+type SplitTree  = SplitTree'  SplitTag
+type SplitTrees = SplitTrees' SplitTag
+
+-- | Abstract case tree shape.
+data SplitTree' a
+  = -- | No more splits coming. We are at a single, all-variable
+    -- clause.
+    SplittingDone
+    { splitBindings :: Int       -- ^  The number of variables bound in the clause
+    }
+  | -- | A split is necessary.
+    SplitAt
+    { splitArg   :: Arg Int       -- ^ Arg. no to split at.
+    , splitLazy  :: LazySplit
+    , splitTrees :: SplitTrees' a -- ^ Sub split trees.
+    }
+  deriving (Show, Generic)
+
+data LazySplit = LazySplit | StrictSplit
+  deriving (Show, Eq, Ord, Generic)
+
+-- | Split tree branching.  A finite map from constructor names to splittrees
+--   A list representation seems appropriate, since we are expecting not
+--   so many constructors per data type, and there is no need for
+--   random access.
+type SplitTrees' a = [(a, SplitTree' a)]
+
+-- | Tag for labeling branches of a split tree. Each branch is associated to
+--   either a constructor or a literal, or is a catchall branch (currently
+--   only used for splitting on a literal type).
+data SplitTag
+  = SplitCon QName
+  | SplitLit Literal
+  | SplitCatchall
+  deriving (Show, Eq, Ord, Generic)
+
+instance Pretty SplitTag where
+  pretty (SplitCon c) = pretty c
+  pretty (SplitLit l)  = pretty l
+  pretty SplitCatchall = underscore
+
+-- * Printing a split tree
+
+data SplitTreeLabel a = SplitTreeLabel
+  { lblConstructorName :: Maybe a   -- ^ 'Nothing' for root of split tree
+  , lblSplitArg        :: Maybe (Arg Int)
+  , lblLazy            :: LazySplit
+  , lblBindings        :: Maybe Int
+  }
+instance Pretty a => Pretty (SplitTreeLabel a) where
+  pretty = \case
+    SplitTreeLabel Nothing Nothing   _  (Just n) -> text $ "done, " ++ prettyShow n ++ " bindings"
+    SplitTreeLabel Nothing (Just n)  lz Nothing  -> lzp lz <+> text ("split at " ++ prettyShow n)
+    SplitTreeLabel (Just q) Nothing  _  (Just n) -> pretty q <+> text ("-> done, " ++ prettyShow n ++ " bindings")
+    SplitTreeLabel (Just q) (Just n) lz Nothing  -> pretty q <+> text "->" <+> lzp lz <+> text ("split at " ++ prettyShow n)
+    _ -> __IMPOSSIBLE__
+    where lzp lz | lz == LazySplit = "lazy"
+                 | otherwise       = empty
+
+-- | Convert a split tree into a 'Data.Tree' (for printing).
+toTree :: SplitTree' a -> Tree (SplitTreeLabel a)
+toTree = \case
+  SplittingDone n -> Node (SplitTreeLabel Nothing Nothing StrictSplit (Just n)) []
+  SplitAt n lz ts    -> Node (SplitTreeLabel Nothing (Just n) lz Nothing) $ toTrees ts
+
+toTrees :: SplitTrees' a -> Forest (SplitTreeLabel a)
+toTrees = map (\ (c,t) -> setCons c $ toTree t)
+  where
+    setCons :: a -> Tree (SplitTreeLabel a) -> Tree (SplitTreeLabel a)
+    setCons c (Node l ts) = Node (l { lblConstructorName = Just c }) ts
+
+instance Pretty a => Pretty (SplitTree' a) where
+  pretty = text . drawTree . fmap prettyShow . toTree
+
+instance KillRange SplitTag where
+  killRange = \case
+    SplitCon c -> killRangeN SplitCon c
+    SplitLit l -> killRangeN SplitLit l
+    SplitCatchall -> SplitCatchall
+
+instance KillRange a => KillRange (SplitTree' a) where
+  killRange = \case
+    SplittingDone n -> SplittingDone n
+    SplitAt i lz ts -> killRangeN (SplitAt i lz) ts
+
+instance NFData a => NFData (SplitTree' a)
+instance NFData LazySplit
+instance NFData SplitTag
diff --git a/src/full/Agda/TypeChecking/Datatypes.hs b/src/full/Agda/TypeChecking/Datatypes.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Datatypes.hs
@@ -0,0 +1,313 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Datatypes where
+
+import Control.Monad        ( filterM )
+import Control.Monad.Except ( MonadError(..), ExceptT(..), runExceptT )
+
+import Data.Maybe (fromMaybe)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Pretty
+
+import Agda.Utils.Either
+import Agda.Utils.Functor        ( (<.>) )
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Constructors
+---------------------------------------------------------------------------
+
+-- | Get true constructor with record fields.
+getConHead :: (HasConstInfo m) => QName -> m (Either SigError ConHead)
+getConHead c = runExceptT $ do
+  def <- ExceptT $ getConstInfo' c
+  case theDef def of
+    Constructor { conSrcCon = c' } -> return c'
+    Record     { recConHead = c' } -> return c'
+    _ -> throwError $ SigUnknown $ prettyShow c ++ " is not a constructor"
+
+isConstructor :: (HasConstInfo m) => QName -> m Bool
+isConstructor q = isRight <$> getConHead q
+
+-- | Get true constructor with fields, expanding literals to constructors
+--   if possible.
+getConForm :: QName -> TCM (Either SigError ConHead)
+getConForm c = caseEitherM (getConHead c) (return . Left) $ \ ch -> do
+  Con con _ [] <- constructorForm (Con ch ConOCon [])
+  return $ Right con
+
+-- | Augment constructor with record fields (preserve constructor name).
+--   The true constructor might only surface via 'reduce'.
+getOrigConHead :: QName -> TCM (Either SigError ConHead)
+getOrigConHead c = mapRight (setConName c) <$> getConHead c
+
+-- | Get the name of the datatype constructed by a given constructor.
+--   Precondition: The argument must refer to a constructor
+{-# SPECIALIZE getConstructorData :: QName -> TCM QName #-}
+getConstructorData :: HasConstInfo m => QName -> m QName
+getConstructorData c = do
+  def <- getConstInfo c
+  case theDef def of
+    Constructor{conData = d} -> return d
+    _                        -> __IMPOSSIBLE__
+
+-- | Is the datatype of this constructor a Higher Inductive Type?
+--   Precondition: The argument must refer to a constructor of a datatype or record.
+consOfHIT :: HasConstInfo m => QName -> m Bool
+consOfHIT c = do
+  d <- getConstructorData c
+  def <- theDef <$> getConstInfo d
+  case def of
+    Datatype {dataPathCons = xs} -> return $ not $ null xs
+    Record{} -> return False
+    _  -> __IMPOSSIBLE__
+
+isPathCons :: HasConstInfo m => QName -> m Bool
+isPathCons c = do
+  d <- getConstructorData c
+  def <- theDef <$> getConstInfo d
+  case def of
+    Datatype {dataPathCons = xs} -> return $ c `elem` xs
+    Record{} -> return False
+    _  -> __IMPOSSIBLE__
+
+-- | @getFullyAppliedConType c t@ computes the constructor parameters
+--   from data type @t@ and returns them
+--   plus the instantiated type of constructor @c@.
+--
+--   @Nothing@ if @t@ is not a data/record type or does not have
+--   a constructor @c@.
+--
+--   Precondition: @t@ is reduced.
+getFullyAppliedConType
+  :: PureTCM m
+  => ConHead  -- ^ Constructor.
+  -> Type     -- ^ Reduced type of the fully applied constructor.
+  -> m (Maybe ((QName, Type, Args), Type))
+       -- ^ @Nothing@ if not data or record type.
+       --
+       --   @Just ((d, dt, pars), ct)@ otherwise, where
+       --     @d@    is the data or record type name,
+       --     @dt@   is the type of the data or record name,
+       --     @pars@ are the reconstructed parameters,
+       --     @ct@   is the type of the constructor instantiated to the parameters.
+getFullyAppliedConType c t = do
+  reportSLn "tc.getConType" 35 $ unwords $
+    [ "getFullyAppliedConType", prettyShow c, prettyShow t ]
+  c <- fromRight __IMPOSSIBLE__ <$> getConHead (conName c)
+  cdef <- getConstInfo $ conName c
+  let ctype = defType cdef
+      cdata = conData $ theDef cdef
+      npars = conPars $ theDef cdef
+  case unEl t of
+    Def d es | d == cdata -> do
+      reportSLn "tc.getConType" 35 $ unwords $
+        [ "getFullyAppliedConType: case Def", prettyShow d, prettyShow es ]
+      dt <- defType <$> getConstInfo d
+      let pars = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ take npars es
+      ctPars <- ctype `piApplyM` pars
+      return $ Just ((d, dt, pars), ctPars)
+    _ -> return Nothing
+
+-- | Make sure a constructor is fully applied and infer the type of the constructor.
+--   Raises a type error if the constructor does not belong to the given type.
+fullyApplyCon
+  :: (PureTCM m, MonadBlock m, MonadTCError m)
+  => ConHead -- ^ Constructor.
+  -> Elims    -- ^ Constructor arguments.
+  -> Type    -- ^ Type of the constructor application.
+  -> (QName -> Type -> Args -> Type -> Elims -> Telescope -> Type -> m a)
+       -- ^ Name of the data/record type,
+       --   type of the data/record type,
+       --   reconstructed parameters,
+       --   type of the constructor (applied to parameters),
+       --   full application arguments,
+       --   types of missing arguments (already added to context),
+       --   type of the full application.
+  -> m a
+fullyApplyCon c vs t ret = fullyApplyCon' c vs t ret $
+  typeError . DoesNotConstructAnElementOf (conName c)
+
+-- | Like @fullyApplyCon@, but calls the given fallback function if
+--   it encounters something other than a datatype.
+fullyApplyCon'
+  :: (PureTCM m, MonadBlock m)
+  => ConHead -- ^ Constructor.
+  -> Elims    -- ^ Constructor arguments.
+  -> Type    -- ^ Type of the constructor application.
+  -> (QName -> Type -> Args -> Type -> Elims -> Telescope -> Type -> m a) -- ^ See @fullyApplyCon@
+  -> (Type -> m a) -- ^ Fallback function
+  -> m a
+fullyApplyCon' c vs t0 ret err = do
+  reportSDoc "tc.getConType" 30 $ sep $
+    [ "fullyApplyCon': constructor "
+    , prettyTCM c
+    , " with arguments"
+    , prettyTCM vs
+    , " at type "
+    , prettyTCM t0
+    ]
+  (TelV tel t, boundary) <- telViewPathBoundaryP t0
+  -- The type of the constructor application may still be a function
+  -- type.  In this case, we introduce the domains @tel@ into the context
+  -- and apply the constructor to these fresh variables.
+  addContext tel $ do
+    reportSLn "tc.getConType" 35 $ "  target type: " ++ prettyShow t
+    t <- abortIfBlocked t
+    getFullyAppliedConType c t >>= \case
+      Nothing -> err t
+      Just ((d, dt, pars), a) ->
+        ret d dt pars a (raise (size tel) vs ++ teleElims tel boundary) tel t
+
+-- | @getConType c t@ computes the constructor parameters from type @t@
+--   and returns them plus the instantiated type of constructor @c@.
+--   This works also if @t@ is a function type ending in a data/record type;
+--   the term from which @c@ comes need not be fully applied
+--
+--   @Nothing@ if @t@ is not a data/record type or does not have
+--   a constructor @c@.
+getConType
+  :: (PureTCM m, MonadBlock m)
+  => ConHead  -- ^ Constructor.
+  -> Type     -- ^ Ending in data/record type.
+  -> m (Maybe ((QName, Type, Args), Type))
+       -- ^ @Nothing@ if not ends in data or record type.
+       --
+       --   @Just ((d, dt, pars), ct)@ otherwise, where
+       --     @d@    is the data or record type name,
+       --     @dt@   is the type of the data or record name,
+       --     @pars@ are the reconstructed parameters,
+       --     @ct@   is the type of the constructor instantiated to the parameters.
+getConType ch t = do
+  let c = conName ch
+  -- Optimization: if the constructor has no parameters, there
+  -- is no need to reduce the type.
+  npars <- getNumberOfParameters c
+  if | npars == Just 0 -> do
+      ctype <- defType <$> getConstInfo c
+      d  <- getConstructorData c
+      dtype <- defType <$> getConstInfo d
+      return $ Just ((d,dtype,[]),ctype)
+     | otherwise -> fullyApplyCon' ch [] t
+      (\d dt pars ct es tel a -> return $
+        -- Now @dt@, @pars@, and @ct@ live under @tel@,
+        -- so we need to remove the dependency on @tel@.
+        let escape = applySubst (strengthenS impossible (size tel)) in
+        Just $ escape ((d, dt, pars), ct))
+      (\_ -> return Nothing)
+
+data ConstructorInfo
+  = DataCon Arity
+      -- ^ Arity of the data constructor.
+  | RecordCon PatternOrCopattern HasEta
+      Arity
+      -- ^ Arity of the record constructor.
+      [Dom QName]
+      -- ^ List of field names. Has length 'Arity'.
+
+-- | Return the number of non-parameter arguments to a constructor (arity).
+--   In case of record constructors, also return the field names (plus other info).
+--
+getConstructorInfo :: HasConstInfo m => QName -> m ConstructorInfo
+getConstructorInfo c = fromMaybe __IMPOSSIBLE__ <$> getConstructorInfo' c
+
+getConstructorInfo' :: HasConstInfo m => QName -> m (Maybe ConstructorInfo)
+getConstructorInfo' c = do
+  (theDef <$> getConstInfo c) >>= \case
+    Constructor{ conData = d, conArity = n } -> Just <$> do
+      (theDef <$> getConstInfo d) >>= \case
+        r@Record{ recFields = fs } ->
+           return $ RecordCon (recPatternMatching r) (recEtaEquality r) n fs
+        Datatype{} ->
+           return $ DataCon n
+        _ -> __IMPOSSIBLE__
+    _ -> return Nothing
+
+---------------------------------------------------------------------------
+-- * Data types
+---------------------------------------------------------------------------
+
+-- | Check if a name refers to a datatype or a record with a named constructor.
+isDatatype :: QName -> TCM Bool
+isDatatype d = do
+  def <- getConstInfo d
+  case theDef def of
+    Datatype{}                   -> return True
+    Record{recNamedCon = namedC} -> return namedC
+    _                            -> return False
+
+-- | Check if a name refers to a datatype or a record.
+isDataOrRecordType :: QName -> TCM (Maybe DataOrRecord)
+isDataOrRecordType d = do
+  (theDef <$> getConstInfo d) >>= \case
+    Record{ recEtaEquality', recPatternMatching } -> return $ Just $ IsRecord $
+      case recPatternMatching of
+        -- If the user explicitly asked for @pattern@, pattern matching is allowed.
+        p@PatternMatching -> p
+        -- Otherwise, 'recEtaEquality' might allow pattern matching.
+        CopatternMatching ->
+          if patternMatchingAllowed recEtaEquality' then PatternMatching else CopatternMatching
+    Datatype{} -> return $ Just IsData
+    _          -> return $ Nothing
+
+-- | Precodition: 'Term' is 'reduce'd.
+isDataOrRecord :: Term -> TCM (Maybe (QName, DataOrRecord))
+isDataOrRecord = \case
+    Def d _ -> fmap (d,) <$> isDataOrRecordType d
+    _       -> return Nothing
+
+getNumberOfParameters :: HasConstInfo m => QName -> m (Maybe Nat)
+getNumberOfParameters d = do
+  def <- getConstInfo d
+  case theDef def of
+    Datatype{ dataPars = n }   -> return $ Just n
+    Record{ recPars = n }      -> return $ Just n
+    Constructor{ conPars = n } -> return $ Just n
+    _                          -> return Nothing
+
+-- | This is a simplified version of @isDatatype@ from @Coverage@,
+--   useful when we do not want to import the module.
+getDatatypeArgs :: HasConstInfo m => Type -> m (Maybe (QName, Args, Args))
+getDatatypeArgs t = do
+  case unEl t of
+    Def d es -> do
+      let ~(Just args) = allApplyElims es
+      def <- theDef <$> getConstInfo d
+      case def of
+        Datatype{dataPars = np} -> do
+          let !(ps, is) = splitAt np args
+          return $ Just (d,   ps, is)
+        Record{} -> do
+          return $ Just (d, args, [])
+        _ -> return Nothing
+    _ -> return Nothing
+
+getNotErasedConstructors :: QName -> TCM [QName]
+getNotErasedConstructors d = do
+  filterM (usableModality <.> getConstInfo) =<< getConstructors d
+
+-- | Precondition: Name is a data or record type.
+getConstructors :: QName -> TCM [QName]
+getConstructors d = fromMaybe __IMPOSSIBLE__ <$>
+  getConstructors' d
+
+-- | 'Nothing' if not data or record type name.
+getConstructors' :: QName -> TCM (Maybe [QName])
+getConstructors' d = getConstructors_ . theDef <$> getConstInfo d
+
+-- | 'Nothing' if not data or record definition.
+getConstructors_ :: Defn -> Maybe [QName]
+getConstructors_ = \case
+    Datatype{dataCons = cs} -> Just cs
+    Record{recConHead = h}  -> Just [conName h]
+    _                       -> Nothing
diff --git a/src/full/Agda/TypeChecking/Datatypes.hs-boot b/src/full/Agda/TypeChecking/Datatypes.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Datatypes.hs-boot
@@ -0,0 +1,9 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Datatypes where
+
+import Agda.TypeChecking.Monad.Signature
+import Agda.Syntax.Internal
+
+getConHead         :: HasConstInfo m => QName -> m (Either SigError ConHead)
+getConstructorData :: HasConstInfo m => QName -> m QName
diff --git a/src/full/Agda/TypeChecking/DeadCode.hs b/src/full/Agda/TypeChecking/DeadCode.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/DeadCode.hs
@@ -0,0 +1,179 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.DeadCode (eliminateDeadCode) where
+
+import Control.Monad ((<$!>))
+import Control.Monad.Trans
+
+import Data.Maybe
+import Data.Monoid (All(..))
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Map.Strict as MapS
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.HashMap.Strict as HMap
+
+import Agda.Interaction.Options
+
+import qualified Agda.Syntax.Abstract as A
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Names
+import Agda.Syntax.Scope.Base
+
+import qualified Agda.Benchmarking as Bench
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+
+import Agda.Utils.HashTable (HashTable)
+import qualified Agda.Utils.HashTable as HT
+
+-- | Run before serialisation to remove any definitions and
+-- meta-variables that are not reachable from the module's public
+-- interface.
+--
+-- Things that are reachable only from warnings are removed.
+
+eliminateDeadCode ::
+     Map ModuleName a
+       -- ^ Exported modules whose telescopes should not be mutilated by the dead-code removal.
+  -> BuiltinThings PrimFun
+  -> DisplayForms
+  -> Signature
+  -> LocalMetaStore
+  -> TCM (DisplayForms, Signature, RemoteMetaStore)
+eliminateDeadCode publicModules bs disp sig ms = Bench.billTo [Bench.DeadCode] $ do
+  !patsyn <- getPatternSyns
+  !public <- Set.mapMonotonic anameName . publicNames <$> getScope
+  !save   <- optSaveMetas <$> pragmaOptions
+  !defs   <- if save then return (sig ^. sigDefinitions)
+                     else Bench.billTo [Bench.DeadCode, Bench.DeadCodeInstantiateFull]
+                          (traverse (\x -> instantiateFull x) (sig ^. sigDefinitions))
+
+  -- #2921: Eliminating definitions with attached COMPILE pragmas results in
+  -- the pragmas not being checked. Simple solution: don't eliminate these.
+  -- #6022 (Andreas, 2022-09-30): Eliminating cubical primitives can lead to crashes.
+   -- Simple solution: retain all primitives (shouldn't be many).
+  let hasCompilePragma = not . MapS.null . defCompiledRep
+      isPrimitive = \case
+        Primitive{}     -> True
+        PrimitiveSort{} -> True
+        _ -> False
+      extraRootsFilter (name, def)
+        | hasCompilePragma def || isPrimitive (theDef def) = Just name
+        | otherwise = Nothing
+      extraRoots =
+        Set.fromList $ mapMaybe extraRootsFilter $ HMap.toList defs
+
+      rootSections = Map.elems $ (sig ^. sigSections) `Map.intersection` publicModules
+      rootNames = Set.union public extraRoots
+      rootMetas =
+        if not save then Set.empty else metasIn
+          ( bs
+          , sig ^. sigSections
+          , sig ^. sigRewriteRules
+          , HMap.filterWithKey (\x _ -> Set.member x rootNames) disp
+          )
+
+  (!rns, !rms) <- Bench.billTo [Bench.DeadCode, Bench.DeadCodeReachable] $ liftIO $
+                    reachableFrom rootSections rootNames rootMetas patsyn disp defs ms
+
+  let !dead  = Set.fromList (HMap.keys defs) `Set.difference` rns
+      !valid = getAll . namesIn' (All . (`Set.notMember` dead))  -- no used name is dead
+      !defs' = HMap.map ( \ d -> d { defDisplay = filter valid (defDisplay d) } )
+               $ HMap.filterWithKey (\ x _ -> Set.member x rns) defs
+      !disp' = HMap.filter (not . null) $ HMap.map (filter valid) disp
+      !ms'   = HMap.fromList $
+                mapMaybe
+                  (\(m, mv) ->
+                    if not (Set.member m rms)
+                    then Nothing
+                    else Just (m, remoteMetaVariable mv)) $
+                MapS.toList ms
+
+  reportSLn "tc.dead" 10 $
+    "Removed " ++ show (HMap.size defs - HMap.size defs') ++
+    " unused definitions and " ++ show (MapS.size ms - HMap.size ms') ++
+    " unused meta-variables."
+  reportSLn "tc.dead" 90 $ unlines $
+    "Removed the following definitions from the signature:" :
+    map (("- " ++) . prettyShow) (Set.toList dead)
+  let !sig' = set sigDefinitions defs' sig
+  return (disp', sig', ms')
+
+reachableFrom ::
+     [Section]      -- ^ Root modules.
+  -> Set QName      -- ^ Root names.
+  -> Set MetaId     -- ^ Root metas.
+  -> A.PatternSynDefns
+  -> DisplayForms
+  -> Definitions
+  -> LocalMetaStore
+  -> IO (Set QName, Set MetaId)
+reachableFrom sections ids ms psyns disp defs insts = do
+
+  !seenNames <- HT.empty :: IO (HashTable QName ())
+  !seenMetas <- HT.empty :: IO (HashTable MetaId ())
+
+  let goName :: QName -> IO ()
+      goName !x = HT.lookup seenNames x >>= \case
+        Just _ ->
+          pure ()
+        Nothing -> do
+          HT.insert seenNames x ()
+          go (HMap.lookup x defs)
+          go (PSyn <$!> MapS.lookup x psyns)
+          go (HMap.lookup x disp)
+
+      goMeta :: MetaId -> IO ()
+      goMeta !m = HT.lookup seenMetas m >>= \case
+        Just _ ->
+          pure ()
+        Nothing -> do
+          HT.insert seenMetas m ()
+          case MapS.lookup m insts of
+            Nothing -> pure ()
+            Just mv -> go (instBody (theInstantiation mv))
+
+      go :: NamesIn a => a -> IO ()
+      go = namesAndMetasIn' (either goName goMeta)
+      {-# INLINE go #-}
+
+  go sections
+  foldMap goName ids
+  foldMap goMeta ms
+  !ids' <- HT.keySet seenNames
+  !ms'  <- HT.keySet seenMetas
+  pure (ids', ms')
+
+
+-- | Returns the instantiation.
+--
+-- Precondition: The instantiation must be of the form @'InstV' inst@.
+
+theInstantiation :: MetaVariable -> Instantiation
+theInstantiation mv = case mvInstantiation mv of
+  InstV inst                     -> inst
+  Open{}                         -> __IMPOSSIBLE__
+  OpenInstance{}                 -> __IMPOSSIBLE__
+  BlockedConst{}                 -> __IMPOSSIBLE__
+  PostponedTypeCheckingProblem{} -> __IMPOSSIBLE__
+
+-- | Converts from 'MetaVariable' to 'RemoteMetaVariable'.
+--
+-- Precondition: The instantiation must be of the form @'InstV' inst@.
+
+remoteMetaVariable :: MetaVariable -> RemoteMetaVariable
+remoteMetaVariable mv = RemoteMetaVariable
+  { rmvInstantiation = theInstantiation mv
+  , rmvModality      = getModality mv
+  , rmvJudgement     = mvJudgement mv
+  }
diff --git a/src/full/Agda/TypeChecking/DisplayForm.hs b/src/full/Agda/TypeChecking/DisplayForm.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/DisplayForm.hs
@@ -0,0 +1,272 @@
+{-# LANGUAGE UndecidableInstances #-}  -- for Arg a => Elim' a
+
+-- | Tools for 'DisplayTerm' and 'DisplayForm'.
+
+module Agda.TypeChecking.DisplayForm (displayForm) where
+
+import Control.Monad
+import Control.Monad.Trans (lift)
+import Control.Monad.Trans.Maybe
+
+import Data.Monoid (All(..))
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Names
+import Agda.Syntax.Scope.Base (inverseScopeLookupName)
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Reduce (instantiate)
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+-- | Get the arities of all display forms for a name.
+displayFormArities :: (HasConstInfo m, ReadTCState m) => QName -> m [Int]
+displayFormArities q = map (length . dfPats . dget) <$> getDisplayForms q
+
+-- | Lift a local display form to an outer context. The substitution goes from the parent context to
+--   the context of the local display form (see Issue 958). Current only handles pure extensions of
+--   the parent context.
+liftLocalDisplayForm :: Substitution -> DisplayForm -> Maybe DisplayForm
+liftLocalDisplayForm IdS df = Just df
+liftLocalDisplayForm (Wk n IdS) (Display m lhs rhs) =
+  -- We lift a display form by turning matches on free variables into pattern variables, which can
+  -- be done by simply adding to the dfPatternVars field.
+  Just $ Display (n + m) lhs rhs
+liftLocalDisplayForm _ _ = Nothing
+
+type MonadDisplayForm m =
+  ( MonadReduce m
+  , ReadTCState m
+  , HasConstInfo m
+  , HasBuiltins m
+  , MonadDebug m
+  )
+
+-- | Find a matching display form for @q es@.
+--   In essence this tries to rewrite @q es@ with any
+--   display form @q ps --> dt@ and returns the instantiated
+--   @dt@ if successful.  First match wins.
+displayForm :: MonadDisplayForm m => QName -> Elims -> m (Maybe DisplayTerm)
+displayForm q es = do
+  -- Get display forms for name q.
+  odfs  <- getDisplayForms q
+  if (null odfs) then do
+    reportSLn "tc.display.top" 101 $ "no displayForm for " ++ prettyShow q
+    return Nothing
+  else do
+    -- Display debug info about the @Open@s.
+    unlessDebugPrinting $ reportSDoc "tc.display.top" 100 $ do
+      cps <- viewTC eCheckpoints
+      cxt <- getContextTelescope
+      return $ vcat
+        [ "displayForm for" <+> pretty q
+        , nest 2 $ "cxt =" <+> pretty cxt
+        , nest 2 $ "cps =" <+> vcat (map pretty (Map.toList cps))
+        , nest 2 $ "dfs =" <+> vcat (map pretty odfs) ]
+    -- Use only the display forms that can be opened in the current context.
+    dfs   <- catMaybes <$> mapM (tryGetOpen liftLocalDisplayForm) odfs
+    scope <- getScope
+    -- Keep the display forms that match the application @q es@.
+    ms <- do
+      ms <- mapM (runMaybeT . (`matchDisplayForm` es)) dfs
+      return [ m | Just (d, m) <- ms, wellScoped scope d ]
+    -- Not safe when printing non-terminating terms.
+    -- (nfdfs, us) <- normalise (dfs, es)
+    unlessDebugPrinting $ reportSDoc "tc.display.top" 100 $ return $ vcat
+      [ "name        :" <+> pretty q
+      , "displayForms:" <+> pretty dfs
+      , "arguments   :" <+> pretty es
+      , "matches     :" <+> pretty ms
+      , "result      :" <+> pretty (listToMaybe ms)
+      ]
+    -- Return the first display form that matches.
+    return $ listToMaybe ms
+  where
+    -- Look at the original display form, not the instantiated result when
+    -- checking if it's well-scoped. Otherwise we might pick up out of scope
+    -- identifiers coming from the source term.
+    wellScoped scope (Display _ _ d)
+      | isWithDisplay d = True
+      | otherwise       = getAll $ namesIn' (All . inScope scope) d  -- all names in d should be in scope
+
+    inScope scope x = not $ null $ inverseScopeLookupName x scope
+
+    isWithDisplay DWithApp{} = True
+    isWithDisplay _          = False
+
+-- | Match a 'DisplayForm' @q ps = v@ against @q es@.
+--   Return the 'DisplayTerm' @v[us]@ if the match was successful,
+--   i.e., @es / ps = Just us@.
+matchDisplayForm :: MonadDisplayForm m
+                 => DisplayForm -> Elims -> MaybeT m (DisplayForm, DisplayTerm)
+matchDisplayForm d@(Display n ps v) es
+  | length ps > length es = mzero
+  | otherwise             = do
+      let (es0, es1) = splitAt (length ps) es
+      mm <- match (Window 0 n) ps es0
+      us <- forM [0 .. n - 1] $ \ i -> do
+              -- #5294: Fail if we don't have bindings for all variables. This can
+              --        happen outside parameterised modules when some of the parameters
+              --        are not used in the lhs.
+              Just u <- return $ Map.lookup i mm
+              return u
+      return (d, substWithOrigin (parallelS $ map woThing us) us v `applyE` es1)
+
+type MatchResult = Map Int (WithOrigin Term)
+
+unionMatch :: Monad m => MatchResult -> MatchResult -> MaybeT m MatchResult
+unionMatch m1 m2
+  | null (Map.intersection m1 m2) = return $ Map.union m1 m2
+  | otherwise = mzero  -- Non-linear pattern, fail for now.
+
+unionsMatch :: Monad m => [MatchResult] -> MaybeT m MatchResult
+unionsMatch = foldM unionMatch Map.empty
+
+data Window = Window {dbLo, dbHi :: Nat}
+
+inWindow :: Window -> Nat -> Maybe Nat
+inWindow (Window lo hi) n | lo <= n, n < hi = Just (n - lo)
+                          | otherwise       = Nothing
+
+shiftWindow :: Window -> Window
+shiftWindow (Window lo hi) = Window (lo + 1) (hi + 1)
+
+-- | Class @Match@ for matching a term @p@ in the role of a pattern
+--   against a term @v@.
+--
+--   Free variables inside the window in @p@ are pattern variables and
+--   the result of matching is a map from pattern variables (shifted down to start at 0) to subterms
+--   of @v@.
+class Match a where
+  match :: MonadDisplayForm m => Window -> a -> a -> MaybeT m MatchResult
+
+instance Match a => Match [a] where
+  match n xs ys = unionsMatch =<< zipWithM (match n) xs ys
+
+instance Match a => Match (Arg a) where
+  match n p v = Map.map (setOrigin (getOrigin v)) <$> match n (unArg p) (unArg v)
+
+instance Match a => Match (Elim' a) where
+  match n p v =
+    case (p, v) of
+      (Proj _ f, Proj _ f') | f == f' -> return Map.empty
+      _ | Just a  <- isApplyElim p
+        , Just a' <- isApplyElim v    -> match n a a'
+      -- we do not care to differentiate between Apply and IApply for
+      -- printing.
+      _                               -> mzero
+
+instance Match Term where
+  match w p v = lift (instantiate v) >>= \ v -> case (unSpine p, unSpine v) of
+    (Var i [], v)    | Just j <- inWindow w i -> return $ Map.singleton j (WithOrigin Inserted v)
+    (Var i (_:_), v) | Just{} <- inWindow w i -> mzero  -- Higher-order pattern, fail for now.
+    (Var i ps, Var j vs) | i == j  -> match w ps vs
+    (Def c ps, Def d vs) | c == d  -> match w ps vs
+    (Con c _ ps, Con d _ vs) | c == d -> match w ps vs
+    (Lit l, Lit l')      | l == l' -> return Map.empty
+    (Lam h p, Lam h' v)  | h == h' -> match (shiftWindow w) (unAbs p) (unAbs v)
+    (p, v)               | p == v  -> return Map.empty  -- TODO: this is wrong (this is why we lifted the rhs before)
+    (p, Level l)                   -> match w p =<< reallyUnLevelView l
+    (Sort ps, Sort pv)             -> match w ps pv
+    (p, Sort (Type v))             -> match w p =<< reallyUnLevelView v
+    _                              -> mzero
+
+instance Match Sort where
+  match w p v = case (p, v) of
+    (Type pl, Type vl) -> match w pl vl
+    _ | p == v -> return Map.empty
+    _          -> mzero
+
+instance Match Level where
+  match w p v = do
+    p <- reallyUnLevelView p
+    v <- reallyUnLevelView v
+    match w p v
+
+-- | Substitute terms with origin into display terms,
+--   replacing variables along with their origins.
+--
+--   The purpose is to replace the pattern variables in a with-display form,
+--   and only on the top level of the lhs.  Thus, we are happy to fall back
+--   to ordinary substitution where it does not matter.
+--   This fixes issue #2590.
+
+class SubstWithOrigin a where
+  substWithOrigin :: Substitution -> [WithOrigin Term] -> a -> a
+
+instance SubstWithOrigin a => SubstWithOrigin [a] where
+  substWithOrigin rho ots = map (substWithOrigin rho ots)
+
+instance (SubstWithOrigin a, SubstWithOrigin (Arg a)) => SubstWithOrigin (Elim' a) where
+  substWithOrigin rho ots (Apply arg) = Apply $ substWithOrigin rho ots arg
+  substWithOrigin rho ots e@Proj{}    = e
+  substWithOrigin rho ots (IApply u v w) = IApply
+    (substWithOrigin rho ots u)
+    (substWithOrigin rho ots v)
+    (substWithOrigin rho ots w)
+
+
+
+instance SubstWithOrigin (Arg Term) where
+  substWithOrigin rho ots (Arg ai v) =
+    case v of
+      -- pattern variable: replace origin if better
+      Var x [] -> case ots !!! x of
+        Just (WithOrigin o u) -> Arg (mapOrigin (replaceOrigin o) ai) u
+        Nothing -> Arg ai $ applySubst rho v -- Issue #2717, not __IMPOSSIBLE__
+      -- constructor: recurse
+      Con c ci args -> Arg ai $ Con c ci $ substWithOrigin rho ots args
+      -- def: recurse
+      Def q es -> Arg ai $ Def q $ substWithOrigin rho ots es
+      -- otherwise: fall back to ordinary substitution
+      _ -> Arg ai $ applySubst rho v
+    where
+      replaceOrigin _ UserWritten = UserWritten
+      replaceOrigin o _           = o
+
+instance SubstWithOrigin Term where
+  substWithOrigin rho ots v =
+    case v of
+      -- constructor: recurse
+      Con c ci args -> Con c ci $ substWithOrigin rho ots args
+      -- def: recurse
+      Def q es -> Def q $ substWithOrigin rho ots es
+      -- otherwise: fall back to oridinary substitution
+      _ -> applySubst rho v
+
+-- Do not go into dot pattern, otherwise interaction test #231 fails
+instance SubstWithOrigin DisplayTerm where
+  substWithOrigin rho ots =
+    \case
+      DTerm' v es    -> DTerm' (substWithOrigin rho ots v) $ substWithOrigin rho ots es
+      DDot'  v es    -> DDot'  (substWithOrigin rho ots v) $ substWithOrigin rho ots es
+      DDef q es      -> DDef q    $ substWithOrigin rho ots es
+      DCon c ci args -> DCon c ci $ substWithOrigin rho ots args
+      DWithApp t ts es -> DWithApp
+        (substWithOrigin rho ots t)
+        (substWithOrigin rho ots ts)
+        (substWithOrigin rho ots es)
+
+-- Do not go into dot pattern, otherwise interaction test #231 fails
+instance SubstWithOrigin (Arg DisplayTerm) where
+  substWithOrigin rho ots (Arg ai dt) =
+    case dt of
+      DTerm' v es    -> substWithOrigin rho ots (Arg ai v) <&> (`DTerm'` substWithOrigin rho ots es)
+      DDot'  v es    -> Arg ai $ DDot' (applySubst rho v)  $ substWithOrigin rho ots es
+      DDef q es      -> Arg ai $ DDef q    $ substWithOrigin rho ots es
+      DCon c ci args -> Arg ai $ DCon c ci $ substWithOrigin rho ots args
+      DWithApp t ts es -> Arg ai $ DWithApp
+        (substWithOrigin rho ots t)
+        (substWithOrigin rho ots ts)
+        (substWithOrigin rho ots es)
diff --git a/src/full/Agda/TypeChecking/DropArgs.hs b/src/full/Agda/TypeChecking/DropArgs.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/DropArgs.hs
@@ -0,0 +1,80 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.DropArgs where
+
+import Control.Arrow (second)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Substitute
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage.SplitTree
+
+import Agda.Utils.Functor
+import Agda.Utils.Permutation
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Dropping initial arguments to create a projection-like function
+---------------------------------------------------------------------------
+
+-- | When making a function projection-like, we drop the first @n@
+--   arguments.
+class DropArgs a where
+  dropArgs :: Int -> a -> a
+
+instance DropArgs a => DropArgs (Maybe a) where
+  dropArgs n = fmap (dropArgs n)
+
+-- | NOTE: This creates telescopes with unbound de Bruijn indices.
+instance DropArgs Telescope where
+  dropArgs n tel = telFromList $ drop n $ telToList tel
+
+instance DropArgs Permutation where
+  dropArgs n (Perm m p) = Perm (m - n) $ map (subtract n) $ drop n p
+
+-- | NOTE: does not work for recursive functions.
+instance DropArgs Clause where
+  dropArgs n cl =
+      cl{ -- Andreas, 2012-09-25: just dropping the front of telescope
+          -- makes it ill-formed (unbound indices)
+          -- we should let the telescope intact!?
+          -- Ulf, 2016-06-23: Indeed. After parameter refinement it's even
+          -- worse: the module parameters we want to drop aren't necessarily
+          -- the first things in the telescope.
+          namedClausePats = drop n $ namedClausePats cl
+          -- BUG: need to drop also from recursive calls!!
+        }
+
+instance DropArgs FunctionInverse where
+  dropArgs n finv = fmap (dropArgs n) finv
+
+-- | Use for dropping initial lambdas in clause bodies.
+--   NOTE: does not reduce term, need lambdas to be present.
+instance DropArgs Term where
+  dropArgs 0 = id
+  dropArgs n = \case
+    Lam h b -> dropArgs (n - 1) (absBody b)
+    _       -> __IMPOSSIBLE__
+
+-- | To drop the first @n@ arguments in a compiled clause,
+--   we reduce the split argument indices by @n@ and
+--   drop @n@ arguments from the bodies.
+--   NOTE: this only works for non-recursive functions, we
+--   are not dropping arguments to recursive calls in bodies.
+instance DropArgs CompiledClauses where
+  dropArgs n cc = case cc of
+    Case i br | unArg i < n   -> __IMPOSSIBLE__
+              | otherwise     -> Case (i <&> \ j -> j - n) $ fmap (dropArgs n) br
+    Done xs t | length xs < n -> __IMPOSSIBLE__
+              | otherwise     -> Done (drop n xs) t
+    Fail xs   | length xs < n -> __IMPOSSIBLE__
+              | otherwise     -> Fail (drop n xs)
+
+instance DropArgs SplitTree where
+  dropArgs n (SplittingDone m) = SplittingDone (m - n)
+  dropArgs n (SplitAt i lz ts) = SplitAt (subtract n <$> i) lz $ map (second $ dropArgs n) ts
diff --git a/src/full/Agda/TypeChecking/Empty.hs b/src/full/Agda/TypeChecking/Empty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Empty.hs
@@ -0,0 +1,115 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Empty
+  ( isEmptyType
+  , isEmptyTel
+  , ensureEmptyType
+  , checkEmptyTel
+  ) where
+
+import Control.Monad        ( void )
+import Control.Monad.Except ( MonadError(..) )
+
+import Data.Semigroup
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Coverage
+import Agda.TypeChecking.Coverage.Match ( fromSplitPatterns )
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce ( instantiateFull )
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Either
+import Agda.Utils.List
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible
+
+data ErrorNonEmpty
+  = Fail               -- ^ Generic failure
+  | FailBecause TCErr  -- ^ Failure with informative error
+  | DontKnow Blocker   -- ^ Emptyness check blocked
+
+instance Semigroup ErrorNonEmpty where
+  DontKnow u1     <> DontKnow u2  = DontKnow $ unblockOnBoth u1 u2  -- Both must unblock for this to proceed
+  e@DontKnow{}    <> _            = e
+  _               <> e@DontKnow{} = e
+  FailBecause err <> _            = FailBecause err
+  Fail            <> err          = err
+
+instance Monoid ErrorNonEmpty where
+  mempty  = Fail
+  mappend = (Data.Semigroup.<>)
+
+-- | Ensure that a type is empty.
+--   This check may be postponed as emptiness constraint.
+ensureEmptyType
+  :: Range -- ^ Range of the absurd pattern.
+  -> Type  -- ^ Type that should be empty (empty data type or iterated product of such).
+  -> TCM ()
+ensureEmptyType r t = caseEitherM (checkEmptyType r t) failure return
+  where
+  failure (DontKnow u)      = addConstraint u $ IsEmpty r t
+  failure (FailBecause err) = throwError err
+  failure Fail              = typeError $ ShouldBeEmpty t []
+
+-- | Check whether a type is empty.
+isEmptyType :: Type -> TCM Bool
+isEmptyType ty = isRight <$> checkEmptyType noRange ty
+
+-- | Check whether some type in a telescope is empty.
+isEmptyTel :: Telescope -> TCM Bool
+isEmptyTel tel = isRight <$> checkEmptyTel noRange tel
+
+-- Either the type is possibly non-empty (Left err) or it is really empty
+-- (Right ()).
+checkEmptyType :: Range -> Type -> TCM (Either ErrorNonEmpty ())
+checkEmptyType range t = do
+  mr <- tryRecordType t
+  case mr of
+
+    -- If t is blocked or a meta, we cannot decide emptiness now.  Postpone.
+    Left (Blocked b t) -> return $ Left (DontKnow b)
+
+    -- If t is not a record type, try to split
+    Left (NotBlocked nb t) -> do
+      -- from the current context xs:ts, create a pattern list
+      -- xs _ : ts t and try to split on _ (the last variable)
+      tel0 <- getContextTelescope
+      let gamma = telToList tel0 ++ [domFromArg $ defaultArg (underscore, t)]
+          tel   = telFromList gamma
+          ps    = teleNamedArgs tel
+
+      dontAssignMetas $ do
+        r <- splitLast Inductive tel ps
+        case r of
+          Left UnificationStuck{} -> do
+            blocker <- unblockOnAnyMetaIn <$> instantiateFull tel -- TODO Jesper: get proper blocking information from unification
+            return $ Left $ DontKnow blocker
+          Left _                  -> return $ Left Fail
+          Right cov -> do
+            let ps = map (namedArg . lastWithDefault __IMPOSSIBLE__ . fromSplitPatterns . scPats) $ splitClauses cov
+            if (null ps) then return (Right ()) else
+              Left . FailBecause <$> do typeError_ $ ShouldBeEmpty t ps
+
+    -- If t is a record type, see if any of the field types is empty
+    Right (r, pars, def) -> do
+      if | NoEta{} <- recEtaEquality def -> return $ Left Fail
+         | otherwise -> void <$> do checkEmptyTel range $ recTel def `apply` pars
+
+-- | Check whether one of the types in the given telescope is constructor-less
+--   and if yes, return its index in the telescope (0 = leftmost).
+checkEmptyTel :: Range -> Telescope -> TCM (Either ErrorNonEmpty Int)
+checkEmptyTel r = loop 0
+  where
+  loop i EmptyTel            = return $ Left Fail
+  loop i (ExtendTel dom tel) = orEitherM
+    [ (i <$) <$> checkEmptyType r (unDom dom)
+    , underAbstraction dom tel $ loop (succ i)
+    ]
diff --git a/src/full/Agda/TypeChecking/Empty.hs-boot b/src/full/Agda/TypeChecking/Empty.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Empty.hs-boot
@@ -0,0 +1,20 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Empty
+  ( isEmptyType
+  , isEmptyTel
+  , ensureEmptyType
+  , checkEmptyTel
+  ) where
+
+import Agda.TypeChecking.Monad (TCM)
+import Agda.Syntax.Internal (Type, Telescope)
+import Agda.Syntax.Position (Range)
+
+data ErrorNonEmpty
+
+isEmptyType :: Type      -> TCM Bool
+isEmptyTel  :: Telescope -> TCM Bool
+
+ensureEmptyType :: Range -> Type -> TCM ()
+checkEmptyTel   :: Range -> Telescope -> TCM (Either ErrorNonEmpty Int)
diff --git a/src/full/Agda/TypeChecking/Errors.hs b/src/full/Agda/TypeChecking/Errors.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Errors.hs
@@ -0,0 +1,1892 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.TypeChecking.Errors
+  ( renderError
+  , prettyError
+  , tcErrString
+  , prettyTCWarnings'
+  , prettyTCWarnings
+  , tcWarningsToError
+  , applyFlagsToTCWarningsPreserving
+  , applyFlagsToTCWarnings
+  , getAllUnsolvedWarnings
+  , getAllWarningsPreserving
+  , getAllWarnings
+  , getAllWarningsOfTCErr
+  , dropTopLevelModule
+  , topLevelModuleDropper
+  , stringTCErr
+  , explainWhyInScope
+  , Verbalize(verbalize)
+  ) where
+
+import Prelude hiding ( null, foldl )
+
+import qualified Control.Exception as E
+import Control.Monad ((>=>), (<=<))
+import Control.Monad.Except
+
+import qualified Data.CaseInsensitive as CaseInsens
+import Data.Foldable (foldl)
+import Data.Function (on)
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import Data.List (sortBy, dropWhileEnd, intercalate)
+import qualified Data.List as List
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Text.PrettyPrint.Boxes as Boxes
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Definitions (notSoNiceDeclarations)
+import Agda.Syntax.Concrete.Pretty (prettyHiding, prettyRelevance)
+import Agda.Syntax.Notation
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Scope.Monad (isDatatypeModule)
+import Agda.Syntax.Scope.Base
+
+import Agda.TypeChecking.Monad (typeOfConst)
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Closure
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.SizedTypes ( sizeType )
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Pretty.Call
+import Agda.TypeChecking.Pretty.Warning
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Reduce (instantiate)
+
+import Agda.Utils.FileName
+import Agda.Utils.Float  ( toStringWithoutDotZero )
+import Agda.Utils.Function
+import Agda.Utils.Functor( for )
+import Agda.Utils.List   ( initLast, lastMaybe )
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( prettyShow, render )
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Top level function
+---------------------------------------------------------------------------
+
+{-# SPECIALIZE renderError :: TCErr -> TCM String #-}
+renderError :: MonadTCM tcm => TCErr -> tcm String
+renderError = fmap show . prettyError
+
+{-# SPECIALIZE prettyError :: TCErr -> TCM Doc #-}
+prettyError :: MonadTCM tcm => TCErr -> tcm Doc
+prettyError = liftTCM . flip renderError' [] where
+  renderError' :: TCErr -> [TCErr] -> TCM Doc
+  renderError' err errs
+    | length errs > 3 = fsep (
+        pwords "total panic: error when printing error from printing error from printing error." ++
+        pwords "I give up! Approximations of errors (original error last):" )
+        $$ vcat (map (text . tcErrString) errs)
+    | otherwise = applyUnless (null errs) ("panic: error when printing error!" $$) $ do
+        (prettyTCM err $$ vcat (map (text . ("when printing error " ++) . tcErrString) errs))
+        `catchError` \ err' -> renderError' err' (err:errs)
+
+---------------------------------------------------------------------------
+-- * Helpers
+---------------------------------------------------------------------------
+
+panic :: Monad m => String -> m Doc
+panic s = fwords $ "Panic: " ++ s
+
+nameWithBinding :: MonadPretty m => QName -> m Doc
+nameWithBinding q =
+  (prettyTCM q <+> "bound at") <?> prettyTCM r
+  where
+    r = nameBindingSite $ qnameName q
+
+tcErrString :: TCErr -> String
+tcErrString err = prettyShow (getRange err) ++ " " ++ case err of
+  TypeError _ _ cl  -> errorString $ clValue cl
+  Exception r s     -> prettyShow r ++ " " ++ show s
+  IOException _ r e -> prettyShow r ++ " " ++ E.displayException e
+  PatternErr{}      -> "PatternErr"
+
+stringTCErr :: String -> TCErr
+stringTCErr = Exception noRange . P.text
+
+errorString :: TypeError -> String
+errorString err = case err of
+  AmbiguousModule{}                        -> "AmbiguousModule"
+  AmbiguousName{}                          -> "AmbiguousName"
+  AmbiguousField{}                         -> "AmbiguousField"
+  AmbiguousParseForApplication{}           -> "AmbiguousParseForApplication"
+  AmbiguousParseForLHS{}                   -> "AmbiguousParseForLHS"
+  AmbiguousProjection{}                    -> "AmbiguousProjection"
+  AmbiguousOverloadedProjection{}          -> "AmbiguousOverloadedProjection"
+  AmbiguousConstructor{}                   -> "AmbiguousConstructor"
+--  AmbiguousParseForPatternSynonym{}        -> "AmbiguousParseForPatternSynonym"
+  AmbiguousTopLevelModuleName {}           -> "AmbiguousTopLevelModuleName"
+  BadArgumentsToPatternSynonym{}           -> "BadArgumentsToPatternSynonym"
+  TooFewArgumentsToPatternSynonym{}        -> "TooFewArgumentsToPatternSynonym"
+  CannotResolveAmbiguousPatternSynonym{}   -> "CannotResolveAmbiguousPatternSynonym"
+  UnboundVariablesInPatternSynonym{}       -> "UnboundVariablesInPatternSynonym"
+  BothWithAndRHS                           -> "BothWithAndRHS"
+  BuiltinInParameterisedModule{}           -> "BuiltinInParameterisedModule"
+  BuiltinMustBeConstructor{}               -> "BuiltinMustBeConstructor"
+  ClashingDefinition{}                     -> "ClashingDefinition"
+  ClashingFileNamesFor{}                   -> "ClashingFileNamesFor"
+  ClashingImport{}                         -> "ClashingImport"
+  ClashingModule{}                         -> "ClashingModule"
+  ClashingModuleImport{}                   -> "ClashingModuleImport"
+  CompilationError{}                       -> "CompilationError"
+  ConstructorPatternInWrongDatatype{}      -> "ConstructorPatternInWrongDatatype"
+  CyclicModuleDependency{}                 -> "CyclicModuleDependency"
+  DataMustEndInSort{}                      -> "DataMustEndInSort"
+-- UNUSED:    DataTooManyParameters{}                  -> "DataTooManyParameters"
+  CantResolveOverloadedConstructorsTargetingSameDatatype{} -> "CantResolveOverloadedConstructorsTargetingSameDatatype"
+  DoesNotConstructAnElementOf{}            -> "DoesNotConstructAnElementOf"
+  DuplicateBuiltinBinding{}                -> "DuplicateBuiltinBinding"
+  DuplicateConstructors{}                  -> "DuplicateConstructors"
+  DuplicateFields{}                        -> "DuplicateFields"
+  DuplicateImports{}                       -> "DuplicateImports"
+  FieldOutsideRecord                       -> "FieldOutsideRecord"
+  FileNotFound{}                           -> "FileNotFound"
+  GenericError{}                           -> "GenericError"
+  GenericDocError{}                        -> "GenericDocError"
+  InstanceNoCandidate{}                    -> "InstanceNoCandidate"
+  IllformedProjectionPatternAbstract{}     -> "IllformedProjectionPatternAbstract"
+  IllformedProjectionPatternConcrete{}     -> "IllformedProjectionPatternConcrete"
+  CannotEliminateWithPattern{}             -> "CannotEliminateWithPattern"
+  CannotEliminateWithProjection{}          -> "CannotEliminateWithProjection"
+  IllegalDeclarationInDataDefinition{}     -> "IllegalDeclarationInDataDefinition"
+  IllegalLetInTelescope{}                  -> "IllegalLetInTelescope"
+  IllegalPatternInTelescope{}              -> "IllegalPatternInTelescope"
+-- UNUSED:  IncompletePatternMatching{}              -> "IncompletePatternMatching"
+  InternalError{}                          -> "InternalError"
+  InvalidPattern{}                         -> "InvalidPattern"
+  LocalVsImportedModuleClash{}             -> "LocalVsImportedModuleClash"
+  MetaCannotDependOn{}                     -> "MetaCannotDependOn"
+  MetaOccursInItself{}                     -> "MetaOccursInItself"
+  MetaIrrelevantSolution{}                 -> "MetaIrrelevantSolution"
+  MetaErasedSolution{}                     -> "MetaErasedSolution"
+  ModuleArityMismatch{}                    -> "ModuleArityMismatch"
+  ModuleDefinedInOtherFile {}              -> "ModuleDefinedInOtherFile"
+  ModuleNameUnexpected{}                   -> "ModuleNameUnexpected"
+  ModuleNameDoesntMatchFileName {}         -> "ModuleNameDoesntMatchFileName"
+  NeedOptionCopatterns{}                   -> "NeedOptionCopatterns"
+  NeedOptionRewriting{}                    -> "NeedOptionRewriting"
+  NeedOptionProp{}                         -> "NeedOptionProp"
+  NeedOptionTwoLevel{}                     -> "NeedOptionTwoLevel"
+  GeneralizeNotSupportedHere{}             -> "GeneralizeNotSupportedHere"
+  GeneralizeCyclicDependency{}             -> "GeneralizeCyclicDependency"
+  GeneralizeUnsolvedMeta{}                 -> "GeneralizeUnsolvedMeta"
+  GeneralizedVarInLetOpenedModule{}        -> "GeneralizedVarInLetOpenedModule"
+  MultipleFixityDecls{}                    -> "MultipleFixityDecls"
+  MultiplePolarityPragmas{}                -> "MultiplePolarityPragmas"
+  NoBindingForBuiltin{}                    -> "NoBindingForBuiltin"
+  NoBindingForPrimitive{}                  -> "NoBindingForPrimitive"
+  NoParseForApplication{}                  -> "NoParseForApplication"
+  NoParseForLHS{}                          -> "NoParseForLHS"
+--  NoParseForPatternSynonym{}               -> "NoParseForPatternSynonym"
+  NoRHSRequiresAbsurdPattern{}             -> "NoRHSRequiresAbsurdPattern"
+  NoSuchBuiltinName{}                      -> "NoSuchBuiltinName"
+  NoSuchModule{}                           -> "NoSuchModule"
+  DuplicatePrimitiveBinding{}              -> "DuplicatePrimitiveBinding"
+  NoSuchPrimitiveFunction{}                -> "NoSuchPrimitiveFunction"
+  WrongArgInfoForPrimitive{}               -> "WrongArgInfoForPrimitive"
+  NotAModuleExpr{}                         -> "NotAModuleExpr"
+  NotAProperTerm                           -> "NotAProperTerm"
+  InvalidType{}                            -> "InvalidType"
+  InvalidTypeSort{}                        -> "InvalidTypeSort"
+  FunctionTypeInSizeUniv{}                 -> "FunctionTypeInSizeUniv"
+  NotAValidLetBinding{}                    -> "NotAValidLetBinding"
+  NotValidBeforeField{}                    -> "NotValidBeforeField"
+  NotAnExpression{}                        -> "NotAnExpression"
+  NotImplemented{}                         -> "NotImplemented"
+  NotSupported{}                           -> "NotSupported"
+  AbstractConstructorNotInScope{}          -> "AbstractConstructorNotInScope"
+  NotInScope{}                             -> "NotInScope"
+  NotLeqSort{}                             -> "NotLeqSort"
+  NothingAppliedToHiddenArg{}              -> "NothingAppliedToHiddenArg"
+  NothingAppliedToInstanceArg{}            -> "NothingAppliedToInstanceArg"
+  OverlappingProjects {}                   -> "OverlappingProjects"
+  OperatorInformation {}                   -> "OperatorInformation"
+  PropMustBeSingleton                      -> "PropMustBeSingleton"
+  RepeatedVariablesInPattern{}             -> "RepeatedVariablesInPattern"
+  ShadowedModule{}                         -> "ShadowedModule"
+  ShouldBeASort{}                          -> "ShouldBeASort"
+  ShouldBeApplicationOf{}                  -> "ShouldBeApplicationOf"
+  ShouldBeAppliedToTheDatatypeParameters{} -> "ShouldBeAppliedToTheDatatypeParameters"
+  ShouldBeEmpty{}                          -> "ShouldBeEmpty"
+  ShouldBePi{}                             -> "ShouldBePi"
+  ShouldBePath{}                           -> "ShouldBePath"
+  ShouldBeRecordType{}                     -> "ShouldBeRecordType"
+  ShouldBeRecordPattern{}                  -> "ShouldBeRecordPattern"
+  NotAProjectionPattern{}                  -> "NotAProjectionPattern"
+  ShouldEndInApplicationOfTheDatatype{}    -> "ShouldEndInApplicationOfTheDatatype"
+  SplitError{}                             -> "SplitError"
+  ImpossibleConstructor{}                  -> "ImpossibleConstructor"
+  TooManyFields{}                          -> "TooManyFields"
+  TooManyPolarities{}                      -> "TooManyPolarities"
+  SplitOnIrrelevant{}                      -> "SplitOnIrrelevant"
+  SplitOnUnusableCohesion{}                -> "SplitOnUnusableCohesion"
+  -- UNUSED: -- SplitOnErased{}                          -> "SplitOnErased"
+  SplitOnNonVariable{}                     -> "SplitOnNonVariable"
+  SplitOnNonEtaRecord{}                    -> "SplitOnNonEtaRecord"
+  SplitOnAbstract{}                        -> "SplitOnAbstract"
+  SplitOnUnchecked{}                       -> "SplitOnUnchecked"
+  SplitOnPartial{}                         -> "SplitOnPartial"
+  SplitInProp{}                            -> "SplitInProp"
+  DefinitionIsIrrelevant{}                 -> "DefinitionIsIrrelevant"
+  DefinitionIsErased{}                     -> "DefinitionIsErased"
+  VariableIsIrrelevant{}                   -> "VariableIsIrrelevant"
+  VariableIsErased{}                       -> "VariableIsErased"
+  VariableIsOfUnusableCohesion{}           -> "VariableIsOfUnusableCohesion"
+  UnequalBecauseOfUniverseConflict{}       -> "UnequalBecauseOfUniverseConflict"
+  UnequalRelevance{}                       -> "UnequalRelevance"
+  UnequalQuantity{}                        -> "UnequalQuantity"
+  UnequalCohesion{}                        -> "UnequalCohesion"
+  UnequalFiniteness{}                      -> "UnequalFiniteness"
+  UnequalHiding{}                          -> "UnequalHiding"
+  UnequalLevel{}                           -> "UnequalLevel"
+  UnequalSorts{}                           -> "UnequalSorts"
+  UnequalTerms{}                           -> "UnequalTerms"
+  UnequalTypes{}                           -> "UnequalTypes"
+--  UnequalTelescopes{}                      -> "UnequalTelescopes" -- UNUSED
+  WithOnFreeVariable{}                     -> "WithOnFreeVariable"
+  UnexpectedWithPatterns{}                 -> "UnexpectedWithPatterns"
+  UninstantiatedDotPattern{}               -> "UninstantiatedDotPattern"
+  ForcedConstructorNotInstantiated{}       -> "ForcedConstructorNotInstantiated"
+  SolvedButOpenHoles{}                     -> "SolvedButOpenHoles"
+  UnusedVariableInPatternSynonym           -> "UnusedVariableInPatternSynonym"
+  UnquoteFailed{}                          -> "UnquoteFailed"
+  DeBruijnIndexOutOfScope{}                -> "DeBruijnIndexOutOfScope"
+  WithClausePatternMismatch{}              -> "WithClausePatternMismatch"
+  WrongHidingInApplication{}               -> "WrongHidingInApplication"
+  WrongHidingInLHS{}                       -> "WrongHidingInLHS"
+  WrongHidingInLambda{}                    -> "WrongHidingInLambda"
+  WrongHidingInProjection{}                -> "WrongHidingInProjection"
+  IllegalHidingInPostfixProjection{}       -> "IllegalHidingInPostfixProjection"
+  WrongIrrelevanceInLambda{}               -> "WrongIrrelevanceInLambda"
+  WrongQuantityInLambda{}                  -> "WrongQuantityInLambda"
+  WrongCohesionInLambda{}                  -> "WrongCohesionInLambda"
+  WrongNamedArgument{}                     -> "WrongNamedArgument"
+  WrongNumberOfConstructorArguments{}      -> "WrongNumberOfConstructorArguments"
+  QuantityMismatch{}                       -> "QuantityMismatch"
+  HidingMismatch{}                         -> "HidingMismatch"
+  RelevanceMismatch{}                      -> "RelevanceMismatch"
+  NonFatalErrors{}                         -> "NonFatalErrors"
+  InstanceSearchDepthExhausted{}           -> "InstanceSearchDepthExhausted"
+  TriedToCopyConstrainedPrim{}             -> "TriedToCopyConstrainedPrim"
+  SortOfSplitVarError{}                    -> "SortOfSplitVarError"
+  ReferencesFutureVariables{}              -> "ReferencesFutureVariables"
+  DoesNotMentionTicks{}                    -> "DoesNotMentionTicks"
+  MismatchedProjectionsError{}             -> "MismatchedProjectionsError"
+  AttributeKindNotEnabled{}                -> "AttributeKindNotEnabled"
+  InvalidProjectionParameter{}             -> "InvalidProjectionParameter"
+  TacticAttributeNotAllowed{}              -> "TacticAttributeNotAllowed"
+  CannotRewriteByNonEquation{}             -> "CannotRewriteByNonEquation"
+  MacroResultTypeMismatch{}                -> "MacroResultTypeMismatch"
+  NamedWhereModuleInRefinedContext{}       -> "NamedWhereModuleInRefinedContext"
+  CubicalPrimitiveNotFullyApplied{}        -> "CubicalPrimitiveNotFullyApplied"
+  TooManyArgumentsToLeveledSort{}          -> "TooManyArgumentsToLeveledSort"
+  TooManyArgumentsToUnivOmega{}            -> "TooManyArgumentsToUnivOmega"
+  IllTypedPatternAfterWithAbstraction{}    -> "IllTypedPatternAfterWithAbstraction"
+  ComatchingDisabledForRecord{}            -> "ComatchingDisabledForRecord"
+  BuiltinMustBeIsOne{}                     -> "BuiltinMustBeIsOne"
+  IllegalRewriteRule{}                     -> "IllegalRewriteRule"
+  IncorrectTypeForRewriteRelation{}        -> "IncorrectTypeForRewriteRelation"
+  UnexpectedParameter{}                    -> "UnexpectedParameter"
+  NoParameterOfName{}                      -> "NoParameterOfName"
+  UnexpectedModalityAnnotationInParameter{} -> "UnexpectedModalityAnnotationInParameter"
+  SortDoesNotAdmitDataDefinitions{}        -> "SortDoesNotAdmitDataDefinitions"
+  SortCannotDependOnItsIndex{}             -> "SortCannotDependOnItsIndex"
+  ExpectedBindingForParameter{}            -> "ExpectedBindingForParameter"
+  UnexpectedTypeSignatureForParameter{}    -> "UnexpectedTypeSignatureForParameter"
+
+instance PrettyTCM TCErr where
+  prettyTCM err = case err of
+    -- Gallais, 2016-05-14
+    -- Given where `NonFatalErrors` are created, we know for a
+    -- fact that ̀ws` is non-empty.
+    TypeError loc _ Closure{ clValue = NonFatalErrors ws } -> do
+      reportSLn "error" 2 $ "Error raised at " ++ prettyShow loc
+      foldr1 ($$) $ fmap prettyTCM ws
+    -- Andreas, 2014-03-23
+    -- This use of withTCState seems ok since we do not collect
+    -- Benchmark info during printing errors.
+    TypeError loc s e -> withTCState (const s) $ do
+      reportSLn "error" 2 $ "Error raised at " ++ prettyShow loc
+      sayWhen (envRange $ clEnv e) (envCall $ clEnv e) $ prettyTCM e
+    Exception r s     -> sayWhere r $ return s
+    IOException _ r e -> sayWhere r $ fwords $ show e
+    PatternErr{}      -> sayWhere err $ panic "uncaught pattern violation"
+
+-- | Drops given amount of leading components of the qualified name.
+dropTopLevelModule' :: Int -> QName -> QName
+dropTopLevelModule' k (QName (MName ns) n) = QName (MName (drop k ns)) n
+
+-- | Drops the filename component of the qualified name.
+dropTopLevelModule :: MonadPretty m => QName -> m QName
+dropTopLevelModule q = ($ q) <$> topLevelModuleDropper
+
+-- | Produces a function which drops the filename component of the qualified name.
+topLevelModuleDropper :: (MonadDebug m, MonadTCEnv m, ReadTCState m) => m (QName -> QName)
+topLevelModuleDropper =
+  caseMaybeM currentTopLevelModule
+    (return id)
+    (return . dropTopLevelModule' . size)
+
+prettyDisamb :: MonadPretty m => (QName -> Maybe (Range' SrcFile)) -> QName -> m Doc
+prettyDisamb f x = do
+  let d  = pretty =<< dropTopLevelModule x
+  caseMaybe (f x) d $ \ r -> d <+> ("(introduced at " <> prettyTCM r <> ")")
+
+-- | Print the last range in 'qnameModule'.
+prettyDisambProj :: MonadPretty m => QName -> m Doc
+prettyDisambProj = prettyDisamb $ lastMaybe . filter (noRange /=) . map nameBindingSite . mnameToList . qnameModule
+
+--   Print the range in 'qnameName'. This fixes the bad error message in #4130.
+prettyDisambCons :: MonadPretty m => QName -> m Doc
+prettyDisambCons = prettyDisamb $ Just . nameBindingSite . qnameName
+
+instance PrettyTCM TypeError where
+  prettyTCM err = case err of
+    InternalError s -> panic s
+
+    NotImplemented s -> fwords $ "Not implemented: " ++ s
+
+    NotSupported s -> fwords $ "Not supported: " ++ s
+
+    CompilationError s -> sep [fwords "Compilation error:", text s]
+
+    GenericError s -> fwords s
+
+    GenericDocError d -> return d
+
+    PropMustBeSingleton -> fwords
+      "Datatypes in Prop must have at most one constructor when proof irrelevance is enabled"
+
+    DataMustEndInSort t -> fsep $
+      pwords "The type of a datatype must end in a sort."
+      ++ [prettyTCM t] ++ pwords "isn't a sort."
+
+{- UNUSED:
+    DataTooManyParameters -> fsep $ pwords "Too many parameters given to data type."
+-}
+
+    ShouldEndInApplicationOfTheDatatype t -> fsep $
+      pwords "The target of a constructor must be the datatype applied to its parameters,"
+      ++ [prettyTCM t] ++ pwords "isn't"
+
+    ShouldBeAppliedToTheDatatypeParameters s t -> fsep $
+      pwords "The target of the constructor should be" ++ [prettyTCM s] ++
+      pwords "instead of" ++ [prettyTCM t]
+
+    ShouldBeApplicationOf t q -> fsep $
+      pwords "The pattern constructs an element of" ++ [prettyTCM q] ++
+      pwords "which is not the right datatype"
+
+    ShouldBeRecordType t -> fsep $
+      pwords "Expected non-abstract record type, found " ++ [prettyTCM t]
+
+    ShouldBeRecordPattern p -> fsep $
+      pwords "Expected record pattern" -- ", found " ++ [prettyTCM p]
+
+    NotAProjectionPattern p -> fsep $
+      pwords "Not a valid projection for a copattern: " ++ [ prettyA p ]
+
+    WrongHidingInLHS -> fwords "Unexpected implicit argument"
+
+    WrongHidingInLambda t ->
+      fwords "Found an implicit lambda where an explicit lambda was expected"
+
+    WrongHidingInProjection d ->
+      sep [ "Wrong hiding used for projection " , prettyTCM d ]
+
+
+    IllegalHidingInPostfixProjection arg -> fsep $
+      pwords "Illegal hiding in postfix projection " ++
+      [pretty arg]
+
+    WrongIrrelevanceInLambda ->
+      fwords "Found a non-strict lambda where a irrelevant lambda was expected"
+
+    WrongQuantityInLambda ->
+      fwords "Incorrect quantity annotation in lambda"
+
+    WrongCohesionInLambda ->
+      fwords "Incorrect cohesion annotation in lambda"
+
+    WrongNamedArgument a xs0 -> fsep $
+      pwords "Function does not accept argument "
+      ++ [prettyTCM a] -- ++ pwords " (wrong argument name)"
+      ++ [parens $ fsep $ text "possible arguments:" : map pretty xs | not (null xs)]
+      where
+      xs = filter (not . isNoName) xs0
+
+    WrongHidingInApplication t ->
+      fwords "Found an implicit application where an explicit application was expected"
+
+    HidingMismatch h h' -> fwords $
+      "Expected " ++ verbalize (Indefinite h') ++ " argument, but found " ++
+      verbalize (Indefinite h) ++ " argument"
+
+    RelevanceMismatch r r' -> fwords $
+      "Expected " ++ verbalize (Indefinite r') ++ " argument, but found " ++
+      verbalize (Indefinite r) ++ " argument"
+
+    QuantityMismatch q q' -> fwords $
+      "Expected " ++ verbalize (Indefinite q') ++ " argument, but found " ++
+      verbalize (Indefinite q) ++ " argument"
+
+    UninstantiatedDotPattern e -> fsep $
+      pwords "Failed to infer the value of dotted pattern"
+
+    ForcedConstructorNotInstantiated p -> fsep $
+      pwords "Failed to infer that constructor pattern "
+      ++ [prettyA p] ++ pwords " is forced"
+
+    IllformedProjectionPatternAbstract p -> fsep $
+      pwords "Ill-formed projection pattern " ++ [prettyA p]
+
+    IllformedProjectionPatternConcrete p -> fsep $
+      pwords "Ill-formed projection pattern" ++ [pretty p]
+
+    CannotEliminateWithPattern b p a -> do
+      let isProj = isJust (isProjP p)
+      fsep $
+        pwords "Cannot eliminate type" ++ prettyTCM a : if
+         | isProj -> pwords "with projection pattern" ++ [prettyA p]
+         | A.ProjP _ _ f <- namedArg p -> pwords "with pattern" ++ [prettyA p] ++
+             pwords "(suggestion: write" ++ [".(" <> prettyA (A.Proj ProjPrefix f) <> ")"] ++ pwords "for a dot pattern," ++
+             pwords "or remove the braces for a postfix projection)"
+         | otherwise ->
+             "with" : text (kindOfPattern (namedArg p)) : "pattern" : prettyA p :
+             pwords "(did you supply too many arguments?)"
+      where
+      kindOfPattern = \case
+        A.VarP{}    -> "variable"
+        A.ConP{}    -> "constructor"
+        A.ProjP{}   -> __IMPOSSIBLE__
+        A.DefP{}    -> __IMPOSSIBLE__
+        A.WildP{}   -> "wildcard"
+        A.DotP{}    -> "dot"
+        A.AbsurdP{} -> "absurd"
+        A.LitP{}    -> "literal"
+        A.RecP{}    -> "record"
+        A.WithP{}   -> "with"
+        A.EqualP{}  -> "equality"
+        A.AsP _ _ p -> kindOfPattern p
+        A.PatternSynP{} -> __IMPOSSIBLE__
+        A.AnnP _ _ p -> kindOfPattern p
+
+    CannotEliminateWithProjection ty isAmbiguous projection -> sep
+        [ "Cannot eliminate type "
+        , prettyTCM (unArg ty)
+        , " with projection "
+        , if isAmbiguous then
+            text $ prettyShow projection
+          else
+            prettyTCM projection
+        ]
+
+    WrongNumberOfConstructorArguments c expect given -> fsep $
+      pwords "The constructor" ++ [prettyTCM c] ++
+      pwords "expects" ++ [prettyTCM expect] ++
+      pwords "arguments (including hidden ones), but has been given"
+      ++ [prettyTCM given] ++ pwords "(including hidden ones)"
+
+    CantResolveOverloadedConstructorsTargetingSameDatatype d cs -> fsep $
+      pwords "Can't resolve overloaded constructors targeting the same datatype"
+      ++ [parens (prettyTCM (qnameToConcrete d)) <> colon]
+      ++ map pretty (List1.toList cs)
+
+    DoesNotConstructAnElementOf c t -> fsep $
+      pwords "The constructor" ++ [prettyTCM c] ++
+      pwords "does not construct an element of" ++ [prettyTCM t]
+
+    ConstructorPatternInWrongDatatype c d -> fsep $
+      [prettyTCM c] ++ pwords "is not a constructor of the datatype"
+      ++ [prettyTCM d]
+
+    ShadowedModule x [] -> __IMPOSSIBLE__
+
+    ShadowedModule x ms@(m0 : _) -> do
+      -- Clash! Concrete module name x already points to the abstract names ms.
+      (r, m) <- do
+        -- Andreas, 2017-07-28, issue #719.
+        -- First, we try to find whether one of the abstract names @ms@ points back to @x@
+        scope <- getScope
+        -- Get all pairs (y,m) such that y points to some m ∈ ms.
+        let xms0 = ms >>= \ m -> map (,m) $ inverseScopeLookupModule m scope
+        reportSLn "scope.clash.error" 30 $ "candidates = " ++ prettyShow xms0
+
+        -- Try to find x (which will have a different Range, if it has one (#2649)).
+        let xms = filter ((\ y -> not (null $ getRange y) && y == C.QName x) . fst) xms0
+        reportSLn "scope.class.error" 30 $ "filtered candidates = " ++ prettyShow xms
+
+        -- If we found a copy of x with non-empty range, great!
+        ifJust (listToMaybe xms) (\ (x', m) -> return (getRange x', m)) $ {-else-} do
+
+        -- If that failed, we pick the first m from ms which has a nameBindingSite.
+        let rms = ms >>= \ m -> map (,m) $
+              filter (noRange /=) $ map nameBindingSite $ reverse $ mnameToList m
+              -- Andreas, 2017-07-25, issue #2649
+              -- Take the first nameBindingSite we can get hold of.
+        reportSLn "scope.class.error" 30 $ "rangeful clashing modules = " ++ prettyShow rms
+
+        -- If even this fails, we pick the first m and give no range.
+        return $ fromMaybe (noRange, m0) $ listToMaybe rms
+
+      fsep $
+        pwords "Duplicate definition of module" ++ [prettyTCM x <> "."] ++
+        pwords "Previous definition of" ++ [help m] ++ pwords "module" ++ [prettyTCM x] ++
+        pwords "at" ++ [prettyTCM r]
+      where
+        help :: MonadPretty m => ModuleName -> m Doc
+        help m = caseMaybeM (isDatatypeModule m) empty $ \case
+          IsDataModule   -> "(datatype)"
+          IsRecordModule -> "(record)"
+
+    ModuleArityMismatch m EmptyTel args -> fsep $
+      pwords "The module" ++ [prettyTCM m] ++
+      pwords "is not parameterized, but is being applied to arguments"
+
+    ModuleArityMismatch m tel@(ExtendTel _ _) args -> fsep $
+      pwords "The arguments to " ++ [prettyTCM m] ++ pwords "do not fit the telescope" ++
+      [prettyTCM tel]
+
+    ShouldBeEmpty t [] -> fsep $
+       prettyTCM t : pwords "should be empty, but that's not obvious to me"
+
+    ShouldBeEmpty t ps -> fsep (
+      prettyTCM t :
+      pwords "should be empty, but the following constructor patterns are valid:"
+      ) $$ nest 2 (vcat $ map (prettyPat 0) ps)
+
+    ShouldBeASort t -> fsep $
+      prettyTCM t : pwords "should be a sort, but it isn't"
+
+    ShouldBePi t -> fsep $
+      prettyTCM t : pwords "should be a function type, but it isn't"
+
+    ShouldBePath t -> fsep $
+      prettyTCM t : pwords "should be a Path or PathP type, but it isn't"
+
+    NotAProperTerm -> fwords "Found a malformed term"
+
+    InvalidTypeSort s -> fsep $ prettyTCM s : pwords "is not a valid sort"
+    InvalidType v -> fsep $ prettyTCM v : pwords "is not a valid type"
+
+    FunctionTypeInSizeUniv v -> fsep $
+      pwords "Functions may not return sizes, thus, function type " ++
+      [ prettyTCM v ] ++ pwords " is illegal"
+
+    SplitOnIrrelevant t -> fsep $
+      pwords "Cannot pattern match against" ++ [text $ verbalize $ getRelevance t] ++
+      pwords "argument of type" ++ [prettyTCM $ unDom t]
+
+    SplitOnUnusableCohesion t -> fsep $
+      pwords "Cannot pattern match against" ++ [text $ verbalize $ getCohesion t] ++
+      pwords "argument of type" ++ [prettyTCM $ unDom t]
+
+    -- UNUSED:
+    -- SplitOnErased t -> fsep $
+    --   pwords "Cannot pattern match against" ++ [text $ verbalize $ getQuantity t] ++
+    --   pwords "argument of type" ++ [prettyTCM $ unDom t]
+
+    SplitOnNonVariable v t -> fsep $
+      pwords "Cannot pattern match because the (refined) argument " ++
+      [ prettyTCM v ] ++ pwords " is not a variable."
+
+    SplitOnNonEtaRecord q -> fsep $ concat
+      [ pwords "Pattern matching on no-eta record type"
+      , [ prettyTCM q, parens ("defined at" <+> prettyTCM r) ]
+      , pwords "is not allowed"
+      , [ parens "to activate, add declaration `pattern` to record definition" ]
+      ]
+      where r = nameBindingSite $ qnameName q
+
+    SplitOnAbstract d ->
+      "Cannot split on abstract data type" <+> prettyTCM d
+
+    SplitOnUnchecked d ->
+      "Cannot split on data type" <+> prettyTCM d <+> "whose definition has not yet been checked"
+
+    SplitOnPartial dom -> vcat
+      [ "Splitting on partial elements is only allowed at the type Partial, but the domain here is", nest 2 $ prettyTCM $ unDom dom ]
+
+    SplitInProp dr -> fsep
+      [ text "Cannot split on"
+      , text $ kindOfData dr
+      , text "in Prop unless target is in Prop"
+      ]
+      where
+        kindOfData :: DataOrRecordE -> String
+        kindOfData IsData                                                          = "datatype"
+        kindOfData (IsRecord InductionAndEta {recordInduction=Nothing})            = "record type"
+        kindOfData (IsRecord InductionAndEta {recordInduction=(Just Inductive)})   =  "inductive record type"
+        kindOfData (IsRecord InductionAndEta {recordInduction=(Just CoInductive)}) = "coinductive record type"
+
+
+    DefinitionIsIrrelevant x -> fsep $
+      "Identifier" : prettyTCM x : pwords "is declared irrelevant, so it cannot be used here"
+
+    DefinitionIsErased x -> fsep $
+      "Identifier" : prettyTCM x : pwords "is declared erased, so it cannot be used here"
+
+    VariableIsIrrelevant x -> fsep $
+      "Variable" : prettyTCM (nameConcrete x) : pwords "is declared irrelevant, so it cannot be used here"
+
+    VariableIsErased x -> fsep $
+      "Variable" : prettyTCM (nameConcrete x) : pwords "is declared erased, so it cannot be used here"
+
+    VariableIsOfUnusableCohesion x c -> fsep
+      ["Variable", prettyTCM (nameConcrete x), "is declared", text (show c), "so it cannot be used here"]
+
+    UnequalBecauseOfUniverseConflict cmp s t -> fsep $
+      [prettyTCM s, notCmp cmp, prettyTCM t, "because this would result in an invalid use of Setω" ]
+
+    UnequalTerms cmp s t a -> case (s,t) of
+      (Sort s1      , Sort s2      )
+        | CmpEq  <- cmp              -> prettyTCM $ UnequalSorts s1 s2
+        | CmpLeq <- cmp              -> prettyTCM $ NotLeqSort s1 s2
+      (Sort MetaS{} , t            ) -> prettyTCM $ ShouldBeASort $ El __IMPOSSIBLE__ t
+      (s            , Sort MetaS{} ) -> prettyTCM $ ShouldBeASort $ El __IMPOSSIBLE__ s
+      (Sort DefS{}  , t            ) -> prettyTCM $ ShouldBeASort $ El __IMPOSSIBLE__ t
+      (s            , Sort DefS{}  ) -> prettyTCM $ ShouldBeASort $ El __IMPOSSIBLE__ s
+      (_            , _            ) -> do
+        (d1, d2, d) <- prettyInEqual s t
+        fsep $ concat $
+          [ [return d1, notCmp cmp, return d2]
+          , case a of
+                AsTermsOf t -> pwords "of type" ++ [prettyTCM t]
+                AsSizes     -> pwords "of type" ++ [prettyTCM =<< sizeType]
+                AsTypes     -> []
+          , [return d]
+          ]
+
+    UnequalLevel cmp s t -> fsep $
+      [prettyTCM s, notCmp cmp, prettyTCM t]
+
+-- UnequalTelescopes is UNUSED
+--   UnequalTelescopes cmp a b -> fsep $
+--     [prettyTCM a, notCmp cmp, prettyTCM b]
+
+    UnequalTypes cmp a b -> prettyUnequal a (notCmp cmp) b
+--              fsep $ [prettyTCM a, notCmp cmp, prettyTCM b]
+
+    UnequalRelevance cmp a b -> fsep $
+      [prettyTCM a, notCmp cmp, prettyTCM b] ++
+      pwords "because one is a relevant function type and the other is an irrelevant function type"
+
+    UnequalQuantity cmp a b -> fsep $
+      [prettyTCM a, notCmp cmp, prettyTCM b] ++
+      pwords "because one is a non-erased function type and the other is an erased function type"
+
+    UnequalCohesion cmp a b -> fsep $
+      [prettyTCM a, notCmp cmp, prettyTCM b] ++
+      pwords "because one is a non-flat function type and the other is a flat function type"
+      -- FUTURE Cohesion: update message if/when introducing sharp.
+
+    UnequalFiniteness cmp a b -> fsep $
+      [prettyTCM a, notCmp cmp, prettyTCM b] ++
+      pwords "because one is a type of partial elements and the other is a function type"
+      -- FUTURE Cohesion: update message if/when introducing sharp.
+
+    UnequalHiding a b -> fsep $
+      [prettyTCM a, "!=", prettyTCM b] ++
+      pwords "because one is an implicit function type and the other is an explicit function type"
+
+    UnequalSorts s1 s2 -> fsep $
+      [prettyTCM s1, "!=", prettyTCM s2]
+
+    NotLeqSort s1 s2 -> fsep $
+      [prettyTCM s1] ++ pwords "is not less or equal than" ++ [prettyTCM s2]
+
+    TooManyFields r missing xs -> prettyTooManyFields r missing xs
+
+    DuplicateConstructors xs -> fsep $
+      pwords "Duplicate" ++ constructors xs ++ punctuate comma (map pretty xs) ++
+      pwords "in datatype"
+      where
+      constructors ys = P.singPlural ys [text "constructor"] [text "constructors"]
+
+    DuplicateFields xs -> prettyDuplicateFields xs
+
+    WithOnFreeVariable e v -> do
+      de <- prettyA e
+      dv <- prettyTCM v
+      if show de == show dv
+        then fsep $
+          pwords "Cannot `with` on variable" ++ [return dv] ++
+          pwords " bound in a module telescope (or patterns of a parent clause)"
+        else fsep $
+          pwords "Cannot `with` on expression" ++ [return de] ++ pwords "which reduces to variable" ++ [return dv] ++
+          pwords " bound in a module telescope (or patterns of a parent clause)"
+
+    UnexpectedWithPatterns ps -> fsep $
+      pwords "Unexpected with patterns" ++ punctuate " |" (map prettyA ps)
+
+    WithClausePatternMismatch p q -> fsep $
+      pwords "With clause pattern " ++ [prettyA p] ++
+      pwords " is not an instance of its parent pattern " ++ [P.fsep <$> prettyTCMPatterns [q]]
+
+    -- The following error is caught and reraised as GenericDocError in Occurs.hs
+    MetaCannotDependOn m {- ps -} i -> fsep $
+      pwords "The metavariable" ++ [prettyTCM $ MetaV m []] ++
+      pwords "cannot depend on" ++ [pvar i] ++
+      [] -- pwords "because it" ++ deps
+        where
+          pvar = prettyTCM . I.var
+          -- deps = case map pvar ps of
+          --   []  -> pwords "does not depend on any variables"
+          --   [x] -> pwords "only depends on the variable" ++ [x]
+          --   xs  -> pwords "only depends on the variables" ++ punctuate comma xs
+
+    -- The following error is caught and reraised as GenericDocError in Occurs.hs
+    MetaOccursInItself m -> fsep $
+      pwords "Cannot construct infinite solution of metavariable" ++ [prettyTCM $ MetaV m []]
+
+    -- The following error is caught and reraised as GenericDocError in Occurs.hs
+    MetaIrrelevantSolution m _ -> fsep $
+      pwords "Cannot instantiate the metavariable because (part of) the" ++
+      pwords "solution was created in an irrelevant context."
+
+    -- The following error is caught and reraised as GenericDocError in Occurs.hs
+    MetaErasedSolution m _ -> fsep $
+      pwords "Cannot instantiate the metavariable because (part of) the" ++
+      pwords "solution was created in an erased context."
+
+    BuiltinMustBeConstructor s e -> fsep $
+      [prettyA e] ++ pwords "must be a constructor in the binding to builtin" ++ [pretty s]
+
+    NoSuchBuiltinName s -> fsep $
+      pwords "There is no built-in thing called" ++ [pretty s]
+
+    DuplicateBuiltinBinding b x y -> fsep $
+      pwords "Duplicate binding for built-in thing" ++ [pretty b <> comma] ++
+      pwords "previous binding to" ++ [prettyTCM x]
+
+    NoBindingForBuiltin x
+      | x `elem` [builtinZero, builtinSuc] -> fsep $
+        pwords "No binding for builtin " ++ [pretty x <> comma] ++
+        pwords ("use {-# BUILTIN " ++ getBuiltinId builtinNat ++ " name #-} to bind builtin natural " ++
+                "numbers to the type 'name'")
+      | otherwise -> fsep $
+        pwords "No binding for builtin thing" ++ [pretty x <> comma] ++
+        pwords ("use {-# BUILTIN " ++ getBuiltinId x ++ " name #-} to bind it to 'name'")
+
+    NoBindingForPrimitive x -> fsep $
+      pwords "Missing binding for" ++
+      [pretty x] ++
+      pwords "primitive."
+
+    DuplicatePrimitiveBinding b x y -> fsep $
+      pwords "Duplicate binding for primitive thing" ++ [pretty b <> comma] ++
+      pwords "previous binding to" ++ [prettyTCM x]
+
+    NoSuchPrimitiveFunction x -> fsep $
+      pwords "There is no primitive function called" ++ [text x]
+
+    WrongArgInfoForPrimitive x got expect ->
+      vcat [ fsep $ pwords "Wrong definition properties for primitive" ++ [pretty x]
+           , nest 2 $ text $ "Got:      " ++ intercalate ", " gs
+           , nest 2 $ text $ "Expected: " ++ intercalate ", " es ]
+      where
+        (gs, es) = unzip [ p | p@(g, e) <- zip (things got) (things expect), g /= e ]
+        things i = [verbalize $ getHiding i,
+                    "at modality " ++ verbalize (getModality i)]
+
+    BuiltinInParameterisedModule x -> fwords $
+      "The BUILTIN pragma cannot appear inside a bound context " ++
+      "(for instance, in a parameterised module or as a local declaration)"
+
+    IllegalDeclarationInDataDefinition ds -> vcat
+      [ "Illegal declaration in data type definition"
+      , nest 2 $ vcat $ map pretty ds
+      ]
+
+    IllegalLetInTelescope tb -> fsep $
+      -- pwords "The binding" ++
+      pretty tb :
+      pwords " is not allowed in a telescope here."
+
+    IllegalPatternInTelescope bd -> fsep $
+      pretty bd :
+      pwords " is not allowed in a telescope here."
+
+    NoRHSRequiresAbsurdPattern ps -> fwords $
+      "The right-hand side can only be omitted if there " ++
+      "is an absurd pattern, () or {}, in the left-hand side."
+
+    LocalVsImportedModuleClash m -> fsep $
+      pwords "The module" ++ [prettyTCM m] ++
+      pwords "can refer to either a local module or an imported module"
+
+    SolvedButOpenHoles -> fsep $
+      pwords "Module cannot be imported since it has open interaction points" ++
+      pwords "(consider adding {-# OPTIONS --allow-unsolved-metas #-} to this module)"
+
+    CyclicModuleDependency ms ->
+      fsep (pwords "cyclic module dependency:")
+      $$ nest 2 (vcat $ map pretty ms)
+
+    FileNotFound x files ->
+      fsep ( pwords "Failed to find source of module" ++ [pretty x] ++
+             pwords "in any of the following locations:"
+           ) $$ nest 2 (vcat $ map (text . filePath) files)
+
+    OverlappingProjects f m1 m2
+      | canon d1 == canon d2 -> fsep $ concat
+          [ pwords "Case mismatch when accessing file"
+          , [ text $ filePath f ]
+          , pwords "through module name"
+          , [ pure d2 ]
+          ]
+      | otherwise -> fsep
+           ( pwords "The file" ++ [text (filePath f)] ++
+             pwords "can be accessed via several project roots. Both" ++
+             [ pure d1 ] ++ pwords "and" ++ [ pure d2 ] ++
+             pwords "point to this file."
+           )
+      where
+      canon = CaseInsens.mk . P.render
+      d1 = P.pretty m1
+      d2 = P.pretty m2
+
+    AmbiguousTopLevelModuleName x files ->
+      fsep ( pwords "Ambiguous module name. The module name" ++
+             [pretty x] ++
+             pwords "could refer to any of the following files:"
+           ) $$ nest 2 (vcat $ map (text . filePath) files)
+
+    AmbiguousProjection d disambs -> vcat
+      [ "Ambiguous projection " <> prettyTCM d <> "."
+      , "It could refer to any of"
+      , nest 2 $ vcat $ (map prettyDisambProj disambs)
+      ]
+
+    AmbiguousOverloadedProjection ds reason -> do
+      let nameRaw = pretty $ A.nameConcrete $ A.qnameName $ List1.head ds
+      vcat
+        [ fsep
+          [ text "Cannot resolve overloaded projection"
+          , nameRaw
+          , text "because"
+          , pure reason
+          ]
+        , nest 2 $ text "candidates in scope:"
+        , vcat $ for ds $ \ d -> do
+            t <- typeOfConst d
+            text "-" <+> nest 2 (nameRaw <+> text ":" <+> prettyTCM t)
+        ]
+
+    AmbiguousConstructor c disambs -> vcat
+      [ "Ambiguous constructor " <> pretty (qnameName c) <> "."
+      , "It could refer to any of"
+      , nest 2 $ vcat $ map prettyDisambCons disambs
+      ]
+
+    ClashingFileNamesFor x files ->
+      fsep ( pwords "Multiple possible sources for module"
+             ++ [prettyTCM x] ++ pwords "found:"
+           ) $$ nest 2 (vcat $ map (text . filePath) files)
+
+    ModuleDefinedInOtherFile mod file file' -> fsep $
+      pwords "You tried to load" ++ [text (filePath file)] ++
+      pwords "which defines the module" ++ [pretty mod <> "."] ++
+      pwords "However, according to the include path this module should" ++
+      pwords "be defined in" ++ [text (filePath file') <> "."]
+
+    ModuleNameUnexpected given expected
+      | canon dGiven == canon dExpected -> fsep $ concat
+          [ pwords "Case mismatch between the actual module name"
+          , [ pure dGiven ]
+          , pwords "and the expected module name"
+          , [ pure dExpected ]
+          ]
+      | otherwise -> fsep $ concat
+          [ pwords "The name of the top level module does not match the file name. The module"
+          , [ pure dGiven ]
+          , pwords "should probably be named"
+          , [ pure dExpected ]
+          ]
+      where
+      canon = CaseInsens.mk . P.render
+      dGiven    = P.pretty given
+      dExpected = P.pretty expected
+
+
+    ModuleNameDoesntMatchFileName given files ->
+      fsep (pwords "The name of the top level module does not match the file name. The module" ++
+           [ pretty given ] ++ pwords "should be defined in one of the following files:")
+      $$ nest 2 (vcat $ map (text . filePath) files)
+
+    BothWithAndRHS -> fsep $ pwords "Unexpected right hand side"
+
+    AbstractConstructorNotInScope q -> fsep $
+      [ "Constructor"
+      , prettyTCM q
+      ] ++ pwords "is abstract, thus, not in scope here"
+
+    NotInScope xs ->
+      -- using the warning version to avoid code duplication
+      prettyWarning (NotInScopeW xs)
+
+    NoSuchModule x -> fsep $ pwords "No module" ++ [pretty x] ++ pwords "in scope"
+
+    AmbiguousName x reason -> vcat
+      [ fsep $ pwords "Ambiguous name" ++ [pretty x <> "."] ++
+               pwords "It could refer to any one of"
+      , nest 2 $ vcat $ fmap nameWithBinding $ ambiguousNamesInReason reason
+      , explainWhyInScope $ whyInScopeDataFromAmbiguousNameReason x reason
+      ]
+
+    AmbiguousModule x ys -> vcat
+      [ fsep $ pwords "Ambiguous module name" ++ [pretty x <> "."] ++
+               pwords "It could refer to any one of"
+      , nest 2 $ vcat $ fmap help ys
+      , fwords "(hint: Use C-c C-w (in Emacs) if you want to know why)"
+      ]
+      where
+        help :: MonadPretty m => ModuleName -> m Doc
+        help m = do
+          anno <- caseMaybeM (isDatatypeModule m) (return empty) $ \case
+            IsDataModule   -> return $ "(datatype module)"
+            IsRecordModule -> return $ "(record module)"
+          sep [prettyTCM m, anno ]
+
+    AmbiguousField field modules -> vcat $
+      "Ambiguity: the field" <+> prettyTCM field
+        <+> "appears in the following modules: " : map prettyTCM modules
+
+    ClashingDefinition x y suggestion -> fsep $
+      pwords "Multiple definitions of" ++ [pretty x <> "."] ++
+      pwords "Previous definition at"
+      ++ [prettyTCM $ nameBindingSite $ qnameName y] ++
+      caseMaybe suggestion [] (\d ->
+        [  "Perhaps you meant to write "
+        $$ nest 2 ("'" <> pretty (notSoNiceDeclarations d) <> "'")
+        $$ ("at" <+> (pretty . envRange =<< askTC)) <> "?"
+        $$ "In data definitions separate from data declaration, the ':' and type must be omitted."
+        ])
+
+    ClashingModule m1 m2 -> fsep $
+      pwords "The modules" ++ [prettyTCM m1, "and", prettyTCM m2]
+      ++ pwords "clash."
+
+    ClashingImport x y -> fsep $
+      pwords "Import clash between" ++ [pretty x, "and", prettyTCM y]
+
+    ClashingModuleImport x y -> fsep $
+      pwords "Module import clash between" ++ [pretty x, "and", prettyTCM y]
+
+    DuplicateImports m xs -> fsep $
+      pwords "Ambiguous imports from module" ++ [pretty m] ++ pwords "for" ++
+      punctuate comma (map pretty xs)
+
+    NotAModuleExpr e -> fsep $
+      pwords "The right-hand side of a module definition must have the form 'M e1 .. en'" ++
+      pwords "where M is a module name. The expression"
+      ++ [pretty e, "doesn't."]
+
+    FieldOutsideRecord -> fsep $
+      pwords "Field appearing outside record declaration."
+
+    InvalidPattern p -> fsep $
+      pretty p : pwords "is not a valid pattern"
+
+    RepeatedVariablesInPattern xs -> fsep $
+      pwords "Repeated variables in pattern:" ++ map pretty xs
+
+    NotAnExpression e -> fsep $
+      pretty e : pwords "is not a valid expression."
+
+    NotAValidLetBinding nd -> fwords $
+      "Not a valid let-declaration"
+
+    NotValidBeforeField nd -> fwords $
+      "This declaration is illegal in a record before the last field"
+
+    NothingAppliedToHiddenArg e -> fsep $
+      [pretty e] ++ pwords "cannot appear by itself. It needs to be the argument to" ++
+      pwords "a function expecting an implicit argument."
+
+    NothingAppliedToInstanceArg e -> fsep $
+      [pretty e] ++ pwords "cannot appear by itself. It needs to be the argument to" ++
+      pwords "a function expecting an instance argument."
+
+    NoParseForApplication es -> fsep (
+      pwords "Could not parse the application" ++ [pretty $ C.RawApp noRange es])
+
+    AmbiguousParseForApplication es es' -> fsep (
+      pwords "Don't know how to parse" ++ [pretty_es <> "."] ++
+      pwords "Could mean any one of:"
+      ) $$ nest 2 (vcat $ fmap pretty' es')
+      where
+        pretty_es :: MonadPretty m => m Doc
+        pretty_es = pretty $ C.RawApp noRange es
+
+        pretty' :: MonadPretty m => C.Expr -> m Doc
+        pretty' e = do
+          p1 <- pretty_es
+          p2 <- pretty e
+          if render p1 == render p2 then unambiguous e else return p2
+
+        unambiguous :: MonadPretty m => C.Expr -> m Doc
+        unambiguous e@(C.OpApp r op _ xs)
+          | all (isOrdinary . namedArg) xs =
+            pretty $
+              foldl (C.App r) (C.Ident op) $
+                (fmap . fmap . fmap) fromOrdinary xs
+          | any (isPlaceholder . namedArg) xs =
+              pretty e <+> "(section)"
+        unambiguous e = pretty e
+
+        isOrdinary :: MaybePlaceholder (C.OpApp e) -> Bool
+        isOrdinary (NoPlaceholder _ (C.Ordinary _)) = True
+        isOrdinary _                                = False
+
+        fromOrdinary :: MaybePlaceholder (C.OpApp e) -> e
+        fromOrdinary (NoPlaceholder _ (C.Ordinary e)) = e
+        fromOrdinary _                                = __IMPOSSIBLE__
+
+        isPlaceholder :: MaybePlaceholder a -> Bool
+        isPlaceholder Placeholder{}   = True
+        isPlaceholder NoPlaceholder{} = False
+
+    BadArgumentsToPatternSynonym x -> fsep $
+      pwords "Bad arguments to pattern synonym " ++ [prettyTCM $ headAmbQ x]
+
+    TooFewArgumentsToPatternSynonym x -> fsep $
+      pwords "Too few arguments to pattern synonym " ++ [prettyTCM $ headAmbQ x]
+
+    CannotResolveAmbiguousPatternSynonym defs -> vcat
+      [ fsep $ pwords "Cannot resolve overloaded pattern synonym" ++ [prettyTCM x <> comma] ++
+               pwords "since candidates have different shapes:"
+      , nest 2 $ vcat $ fmap prDef defs
+      , fsep $ pwords "(hint: overloaded pattern synonyms must be equal up to variable and constructor names)"
+      ]
+      where
+        (x, _) = List1.head defs
+        prDef (x, (xs, p)) = prettyA (A.PatternSynDef x (map (fmap BindName) xs) p) <?> ("at" <+> pretty r)
+          where r = nameBindingSite $ qnameName x
+
+    UnusedVariableInPatternSynonym -> fsep $
+      pwords "Unused variable in pattern synonym."
+
+    UnboundVariablesInPatternSynonym xs -> fsep $
+      pwords "Unbound variables in pattern synonym: " ++
+      [sep (map prettyA xs)]
+
+    NoParseForLHS lhsOrPatSyn errs p -> vcat
+      [ fsep $ pwords "Could not parse the" ++ prettyLhsOrPatSyn ++ [pretty p]
+      , prettyErrs
+      ]
+      where
+      prettyLhsOrPatSyn = pwords $ case lhsOrPatSyn of
+        IsLHS    -> "left-hand side"
+        IsPatSyn -> "pattern synonym"
+      prettyErrs = case errs of
+        []     -> empty
+        p0 : _ -> fsep $ pwords "Problematic expression:" ++ [pretty p0]
+
+{- UNUSED
+    NoParseForPatternSynonym p -> fsep $
+      pwords "Could not parse the pattern synonym" ++ [pretty p]
+-}
+
+    AmbiguousParseForLHS lhsOrPatSyn p ps -> do
+      d <- pretty p
+      vcat $
+        [ fsep $
+            pwords "Don't know how to parse" ++ [pure d <> "."] ++
+            pwords "Could mean any one of:"
+        ]
+          ++
+        map (nest 2 . pretty' d) ps
+      where
+        pretty' :: MonadPretty m => Doc -> C.Pattern -> m Doc
+        pretty' d1 p' = do
+          d2 <- pretty p'
+          if render d1 == render d2 then pretty $ unambiguousP p' else return d2
+
+        -- the entire pattern is shown, not just the ambiguous part,
+        -- so we need to dig in order to find the OpAppP's.
+        unambiguousP :: C.Pattern -> C.Pattern
+        unambiguousP (C.AppP x y)         = C.AppP (unambiguousP x) $ (fmap.fmap) unambiguousP y
+        unambiguousP (C.HiddenP r x)      = C.HiddenP r $ fmap unambiguousP x
+        unambiguousP (C.InstanceP r x)    = C.InstanceP r $ fmap unambiguousP x
+        unambiguousP (C.ParenP r x)       = C.ParenP r $ unambiguousP x
+        unambiguousP (C.AsP r n x)        = C.AsP r n $ unambiguousP x
+        unambiguousP (C.OpAppP r op _ xs) = foldl C.AppP (C.IdentP True op) xs
+        unambiguousP e                    = e
+
+    OperatorInformation sects err ->
+      prettyTCM err
+        $+$
+      fsep (pwords "Operators used in the grammar:")
+        $$
+      nest 2
+        (if null sects then "None" else
+         vcat (map text $
+               lines $
+               Boxes.render $
+               (\(col1, col2, col3) ->
+                   Boxes.hsep 1 Boxes.top $
+                   map (Boxes.vcat Boxes.left) [col1, col2, col3]) $
+               unzip3 $
+               map prettySect $
+               sortBy (compare `on` prettyShow . notaName . sectNotation) $
+               filter (not . closedWithoutHoles) sects))
+      where
+      trimLeft  = dropWhile isAHole
+      trimRight = dropWhileEnd isAHole
+
+      closedWithoutHoles sect =
+        sectKind sect == NonfixNotation
+          &&
+        null [ () | HolePart{} <- trimLeft $ trimRight $
+                                    notation (sectNotation sect) ]
+
+      prettyName n = Boxes.text $
+        P.render (P.pretty n) ++
+        " (" ++ P.render (P.pretty (nameBindingSite n)) ++ ")"
+
+      prettySect sect =
+        ( Boxes.text (P.render (P.pretty section))
+            Boxes.//
+          strut
+        , Boxes.text
+            ("(" ++
+             kind ++ " " ++
+             (if notaIsOperator nota
+              then "operator"
+              else "notation") ++
+             (if sectIsSection sect
+              then " section"
+              else "") ++
+             (case sectLevel sect of
+                Nothing          -> ""
+                Just Unrelated   -> ", unrelated"
+                Just (Related l) -> ", level " ++ toStringWithoutDotZero l) ++
+             ")")
+            Boxes.//
+          strut
+        , "["
+            Boxes.<>
+          Boxes.vcat Boxes.left
+            (map (\n -> prettyName n Boxes.<> ",") names ++
+             [prettyName name Boxes.<> "]"])
+        )
+        where
+        nota    = sectNotation sect
+        section = qualifyFirstIdPart
+                    (foldr (\x s -> C.nameToRawName x ++ "." ++ s)
+                           ""
+                           (List1.init (C.qnameParts (notaName nota))))
+                    (spacesBetweenAdjacentIds $
+                     trim (notation nota))
+
+        qualifyFirstIdPart _ []              = []
+        qualifyFirstIdPart q (IdPart x : ps) = IdPart (fmap (q ++) x) : ps
+        qualifyFirstIdPart q (p : ps)        = p : qualifyFirstIdPart q ps
+
+        spacesBetweenAdjacentIds (IdPart x : ps@(IdPart _ : _)) =
+          IdPart x : IdPart (unranged " ") : spacesBetweenAdjacentIds ps
+        spacesBetweenAdjacentIds (p : ps) =
+          p : spacesBetweenAdjacentIds ps
+        spacesBetweenAdjacentIds [] = []
+
+        trim = case sectKind sect of
+          InfixNotation   -> trimLeft . trimRight
+          PrefixNotation  -> trimRight
+          PostfixNotation -> trimLeft
+          NonfixNotation  -> id
+          NoNotation      -> __IMPOSSIBLE__
+
+        (names, name) = fromMaybe __IMPOSSIBLE__ $ initLast $ Set.toList $ notaNames nota
+
+        strut = Boxes.emptyBox (length names) 0
+
+        kind = case sectKind sect of
+          PrefixNotation  -> "prefix"
+          PostfixNotation -> "postfix"
+          NonfixNotation  -> "closed"
+          NoNotation      -> __IMPOSSIBLE__
+          InfixNotation   ->
+            case fixityAssoc $ notaFixity nota of
+              NonAssoc   -> "infix"
+              LeftAssoc  -> "infixl"
+              RightAssoc -> "infixr"
+
+{- UNUSED
+    AmbiguousParseForPatternSynonym p ps -> fsep (
+      pwords "Don't know how to parse" ++ [pretty p <> "."] ++
+      pwords "Could mean any one of:"
+      ) $$ nest 2 (vcat $ map pretty ps)
+-}
+
+{- UNUSED
+    IncompletePatternMatching v args -> fsep $
+      pwords "Incomplete pattern matching for" ++ [prettyTCM v <> "."] ++
+      pwords "No match for" ++ map prettyTCM args
+-}
+
+    SplitError e -> prettyTCM e
+
+    ImpossibleConstructor c neg -> fsep $
+      pwords "The case for the constructor " ++ [prettyTCM c] ++
+      pwords " is impossible" ++ [prettyTCM neg] ++
+      pwords "Possible solution: remove the clause, or use an absurd pattern ()."
+
+    TooManyPolarities x n -> fsep $
+      pwords "Too many polarities given in the POLARITY pragma for" ++
+      [prettyTCM x] ++
+      pwords "(at most" ++ [text (show n)] ++ pwords "allowed)."
+
+    InstanceNoCandidate t errs -> vcat $
+      [ fsep $ pwords "No instance of type" ++ [prettyTCM t] ++ pwords "was found in scope."
+      , vcat $ map prCand errs ]
+      where
+        prCand (term, err) =
+          text "-" <+>
+            vcat [ prettyTCM term <?> text "was ruled out because"
+                 , prettyTCM err ]
+
+    UnquoteFailed e -> case e of
+      BadVisibility msg arg -> fsep $
+        pwords $ "Unable to unquote the argument. It should be `" ++ msg ++ "'."
+
+      ConInsteadOfDef x def con -> fsep $
+        pwords ("Use " ++ con ++ " instead of " ++ def ++ " for constructor") ++
+        [prettyTCM x]
+
+      DefInsteadOfCon x def con -> fsep $
+        pwords ("Use " ++ def ++ " instead of " ++ con ++ " for non-constructor")
+        ++ [prettyTCM x]
+
+      NonCanonical kind t ->
+        fwords ("Cannot unquote non-canonical " ++ kind)
+        $$ nest 2 (prettyTCM t)
+
+      BlockedOnMeta _ m -> fsep $
+        pwords $ "Unquote failed because of unsolved meta variables."
+
+      UnquotePanic err -> __IMPOSSIBLE__
+
+    DeBruijnIndexOutOfScope i EmptyTel [] -> fsep $
+        pwords $ "de Bruijn index " ++ show i ++ " is not in scope in the empty context"
+    DeBruijnIndexOutOfScope i cxt names ->
+        sep [ text ("de Bruijn index " ++ show i ++ " is not in scope in the context")
+            , inTopContext $ addContext ("_" :: String) $ prettyTCM cxt' ]
+      where
+        cxt' = cxt `abstract` raise (size cxt) (nameCxt names)
+        nameCxt :: [Name] -> I.Telescope
+        nameCxt [] = EmptyTel
+        nameCxt (x : xs) = ExtendTel (defaultDom (El __DUMMY_SORT__ $ I.var 0)) $
+          NoAbs (P.prettyShow x) $ nameCxt xs
+
+    NeedOptionCopatterns -> fsep $
+      pwords "Option --copatterns needed to enable destructor patterns"
+
+    NeedOptionRewriting  -> fsep $
+      pwords "Option --rewriting needed to add and use rewrite rules"
+
+    NeedOptionProp       -> fsep $
+      pwords "Universe Prop is disabled (use options --prop and --no-prop to enable/disable Prop)"
+
+    NeedOptionTwoLevel   -> fsep $
+      pwords "Universe SSet is disabled (use option --two-level to enable SSet)"
+
+    GeneralizeNotSupportedHere x -> fsep $
+      pwords $ "Generalizable variable " ++ prettyShow x ++ " is not supported here"
+
+    GeneralizeCyclicDependency -> fsep $
+      pwords "Cyclic dependency between generalized variables"
+
+    GeneralizeUnsolvedMeta -> fsep $
+      pwords "Unsolved meta not generalized"
+
+    GeneralizedVarInLetOpenedModule x -> fsep $
+      pwords "Cannot use generalized variable from let-opened module: " ++
+      [prettyTCM x]
+
+    MultipleFixityDecls xs ->
+      sep [ fsep $ pwords "Multiple fixity or syntax declarations for"
+          , vcat $ map f xs
+          ]
+      where
+        f (x, fs) = (pretty x <> ": ") <+> fsep (map pretty fs)
+
+    MultiplePolarityPragmas xs -> fsep $
+      pwords "Multiple polarity pragmas for" ++ map pretty xs
+
+    NonFatalErrors ws -> foldr1 ($$) $ fmap prettyTCM ws
+
+    InstanceSearchDepthExhausted c a d -> fsep $
+      pwords ("Instance search depth exhausted (max depth: " ++ show d ++ ") for candidate") ++
+      [hang (prettyTCM c <+> ":") 2 (prettyTCM a)]
+
+    TriedToCopyConstrainedPrim q -> fsep $
+      pwords "Cannot create a module containing a copy of" ++ [prettyTCM q]
+
+    SortOfSplitVarError _ doc -> return doc
+
+    ReferencesFutureVariables term (disallowed :| _) lock leftmost
+      | disallowed == leftmost
+      -> fsep $ pwords "The lock variable"
+             ++ pure (prettyTCM =<< nameOfBV disallowed)
+             ++ pwords "can not appear simultaneously in the \"later\" term"
+             ++ pure (prettyTCM term)
+             ++ pwords "and in the lock term"
+             ++ pure (prettyTCM lock <> ".")
+
+    ReferencesFutureVariables term (disallowed :| rest) lock leftmost -> do
+      explain <- (/=) <$> prettyTCM lock <*> (prettyTCM =<< nameOfBV leftmost)
+      let
+        name = prettyTCM =<< nameOfBV leftmost
+        mod = case getLock lock of
+          IsLock LockOLock -> "@lock"
+          IsLock LockOTick -> "@tick"
+          _ -> __IMPOSSIBLE__
+      vcat $ concat
+        [ pure . fsep $ concat
+          [ pwords "The variable", pure (prettyTCM =<< nameOfBV disallowed), pwords "can not be mentioned here,"
+          , pwords "since it was not introduced before the variable", pure (name <> ".")
+          ]
+        , [ fsep ( pwords "Variables introduced after"
+                ++ pure name
+                ++ pwords "can not be used, since that is the leftmost" ++ pure mod ++ pwords "variable in the locking term"
+                ++ pure (prettyTCM lock <> "."))
+          | explain
+          ]
+        , [ fsep ( pwords "The following"
+                  ++ P.singPlural rest (pwords "variable is") (pwords "variables are")
+                  ++ pwords "not allowed here, either:"
+                  ++ punctuate comma (map (prettyTCM <=< nameOfBV) rest))
+          | not (null rest)
+          ]
+        ]
+
+    DoesNotMentionTicks term ty lock ->
+      let
+        mod = case getLock lock of
+          IsLock LockOLock -> "@lock"
+          IsLock LockOTick -> "@tick"
+          _ -> __IMPOSSIBLE__
+      in
+        vcat
+        [ fsep $
+            pwords "The term"
+            ++ [prettyTCM lock <> ","]
+            ++ pwords "given as an argument to the guarded value"
+        , nest 2 (prettyTCM term <+> ":" <+> prettyTCM ty)
+        , fsep (pwords ("can not be used as a " ++ mod ++ " argument, since it does not mention any " ++ mod ++ " variables."))
+        ]
+
+    MismatchedProjectionsError left right -> fsep $
+      pwords "The projections" ++ [prettyTCM left] ++
+      pwords "and" ++ [prettyTCM right] ++
+      pwords "do not match"
+
+    AttributeKindNotEnabled kind opt s -> fsep $
+      [text kind] ++
+      pwords "attributes have not been enabled (use" ++
+      [text opt] ++
+      pwords "to enable them):" ++
+      [text s]
+
+    InvalidProjectionParameter arg -> fsep $
+      pwords "Invalid projection parameter " ++
+      [prettyA arg]
+
+    TacticAttributeNotAllowed -> fsep $
+      pwords "The @tactic attribute is not allowed here"
+
+    CannotRewriteByNonEquation t ->
+      "Cannot rewrite by equation of type" <+> prettyTCM t
+
+    MacroResultTypeMismatch expectedType ->
+      sep [ "Result type of a macro must be", nest 2 $ prettyTCM expectedType ]
+
+    NamedWhereModuleInRefinedContext args names -> do
+      let pr x v = text (x ++ " =") <+> prettyTCM v
+      vcat
+        [ fsep (pwords $ "Named where-modules are not allowed when module parameters have been refined by pattern matching. " ++
+                          "See https://github.com/agda/agda/issues/2897.")
+        , text $ "In this case the module parameter" ++
+                  (if not (null args) then "s have" else " has") ++
+                  " been refined to"
+        , nest 2 $ vcat (zipWith pr names args) ]
+
+    CubicalPrimitiveNotFullyApplied c ->
+      prettyTCM c <+> "must be fully applied"
+
+    TooManyArgumentsToLeveledSort q -> fsep $
+      [ prettyTCM q , "cannot be applied to more than one argument" ]
+
+    TooManyArgumentsToUnivOmega q -> fsep $
+      [ prettyTCM q , "cannot be applied to an argument" ]
+
+    IllTypedPatternAfterWithAbstraction p -> vcat
+      [ "Ill-typed pattern after with abstraction: " <+> prettyA p
+      , "(perhaps you can replace it by `_`?)"
+      ]
+
+    ComatchingDisabledForRecord recName ->
+      "Copattern matching is disabled for record" <+> prettyTCM recName
+
+    BuiltinMustBeIsOne builtin ->
+      prettyTCM builtin <+> " is not IsOne."
+
+    IllegalRewriteRule q reason -> case reason of
+      LHSNotDefOrConstr -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since the left-hand side is neither a defined symbol nor a constructor" ]
+      VariablesNotBoundByLHS xs -> hsep
+        [ prettyTCM q
+        , " is not a legal rewrite rule, since the following variables are not bound by the left hand side: "
+        , prettyList_ (map (prettyTCM . var) $ IntSet.toList xs)
+        ]
+      VariablesBoundMoreThanOnce xs -> do
+        (prettyTCM q
+          <+> " is not a legal rewrite rule, since the following parameters are bound more than once on the left hand side: "
+          <+> hsep (List.intersperse "," $ map (prettyTCM . var) $ IntSet.toList xs))
+          <> ". Perhaps you can use a postulate instead of a constructor as the head symbol?"
+      LHSReducesTo v v' -> fsep
+        [ prettyTCM q <+> " is not a legal rewrite rule, since the left-hand side "
+        , prettyTCM v <+> " reduces to " <+> prettyTCM v' ]
+      HeadSymbolIsProjection f -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since the head symbol"
+        , prettyTCM f , "is a projection"
+        ]
+      HeadSymbolIsProjectionLikeFunction f -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since the head symbol"
+        , hd , "is a projection-like function."
+        , "You can turn off the projection-like optimization for", hd
+        , "with the pragma {-# NOT_PROJECTION_LIKE", hd, "#-}"
+        , "or globally with the flag --no-projection-like"
+        ]
+        where hd = prettyTCM f
+      HeadSymbolNotPostulateFunctionConstructor f -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since the head symbol"
+        , prettyTCM f , "is not a postulate, a function, or a constructor"
+        ]
+      HeadSymbolDefContainsMetas f -> hsep
+        [ prettyTCM q , "is not a legal rewrite rule, since the definition of the head symbol"
+        , prettyTCM f , "contains unsolved metavariables and confluence checking is enabled."
+        ]
+      ConstructorParamsNotGeneral c vs -> vcat
+        [ prettyTCM q <+> text " is not a legal rewrite rule, since the constructor parameters are not fully general:"
+        , nest 2 $ text "Constructor: " <+> prettyTCM c
+        , nest 2 $ text "Parameters: " <+> prettyList (map prettyTCM vs)
+        ]
+      ContainsUnsolvedMetaVariables ms -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since"
+        , "it contains the unsolved meta variable(s)", prettyList_ (map prettyTCM $ Set.toList ms)
+        ]
+      BlockedOnProblems ps -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since"
+        , "it is blocked on problem(s)", prettyList_ (map prettyTCM $ Set.toList ps)
+        ]
+      RequiresDefinitions qs -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule, since"
+        , "it requires the definition(s) of", prettyList_ (map prettyTCM $ Set.toList qs)
+        ]
+      DoesNotTargetRewriteRelation -> hsep
+        [ prettyTCM q , " does not target rewrite relation" ]
+      BeforeFunctionDefinition -> hsep
+        [ "Rewrite rule from function "
+        , prettyTCM q
+        , " cannot be added before the function definition"
+        ]
+      EmptyReason -> hsep
+        [ prettyTCM q , " is not a legal rewrite rule" ]
+
+    IncorrectTypeForRewriteRelation v reason -> case reason of
+      ShouldAcceptAtLeastTwoArguments -> sep
+        [ prettyTCM v <+> " does not have the right type for a rewriting relation"
+        , "because it should accept at least two arguments"
+        ]
+      FinalTwoArgumentsNotVisible -> sep
+        [ prettyTCM v <+> " does not have the right type for a rewriting relation"
+        , "because its two final arguments are not both visible."
+        ]
+      TypeDoesNotEndInSort core tel -> sep
+        [ prettyTCM v <+> " does not have the right type for a rewriting relation"
+        , "because its type does not end in a sort, but in "
+          <+> do inTopContext $ addContext tel $ prettyTCM core
+        ]
+
+    UnexpectedParameter par -> do
+      text "Unexpected parameter" <+> prettyA par
+
+    NoParameterOfName x -> do
+      text ("No parameter of name " ++ x)
+
+    UnexpectedModalityAnnotationInParameter par -> do
+      text "Unexpected modality/relevance annotation in" <+> prettyA par
+
+    SortDoesNotAdmitDataDefinitions name s ->fsep
+      [ "The universe"
+      , prettyTCM s
+      , "of"
+      , prettyTCM name
+      , "does not admit data or record declarations"
+      ]
+
+    SortCannotDependOnItsIndex name t -> fsep
+      [ "The sort of" <+> prettyTCM name
+      , "cannot depend on its indices in the type"
+      , prettyTCM t
+      ]
+
+    ExpectedBindingForParameter a b -> sep
+      [ "Expected binding for parameter"
+      , text (absName b) <+> text ":" <+> prettyTCM (unDom a)
+      ]
+
+    UnexpectedTypeSignatureForParameter xs -> do
+      let s | length xs > 1 = "s"
+            | otherwise     = ""
+      text ("Unexpected type signature for parameter" ++ s) <+> sep (fmap prettyA xs)
+
+    where
+    mpar n args
+      | n > 0 && not (null args) = parens
+      | otherwise                = id
+
+    prettyArg :: MonadPretty m => Arg (I.Pattern' a) -> m Doc
+    prettyArg (Arg info x) = case getHiding info of
+      Hidden     -> braces $ prettyPat 0 x
+      Instance{} -> dbraces $ prettyPat 0 x
+      NotHidden  -> prettyPat 1 x
+
+    prettyPat :: MonadPretty m => Integer -> (I.Pattern' a) -> m Doc
+    prettyPat _ (I.VarP _ _) = "_"
+    prettyPat _ (I.DotP _ _) = "._"
+    prettyPat n (I.ConP c _ args) =
+      mpar n args $
+        prettyTCM c <+> fsep (map (prettyArg . fmap namedThing) args)
+    prettyPat n (I.DefP o q args) =
+      mpar n args $
+        prettyTCM q <+> fsep (map (prettyArg . fmap namedThing) args)
+    prettyPat _ (I.LitP _ l) = prettyTCM l
+    prettyPat _ (I.ProjP _ p) = "." <> prettyTCM p
+    prettyPat _ (I.IApplyP _ _ _ _) = "_"
+
+notCmp :: MonadPretty m => Comparison -> m Doc
+notCmp cmp = "!" <> prettyTCM cmp
+
+-- | Print two terms that are supposedly unequal.
+--   If they print to the same identifier, add some explanation
+--   why they are different nevertheless.
+prettyInEqual :: MonadPretty m => Term -> Term -> m (Doc, Doc, Doc)
+prettyInEqual t1 t2 = do
+  d1 <- prettyTCM t1
+  d2 <- prettyTCM t2
+  (d1, d2,) <$> do
+     -- if printed differently, no extra explanation needed
+    if P.render d1 /= P.render d2 then empty else do
+      (v1, v2) <- instantiate (t1, t2)
+      case (v1, v2) of
+        (I.Var i1 _, I.Var i2 _)
+          | i1 == i2  -> generic -- possible, see issue 1826
+          | otherwise -> varVar i1 i2
+        (I.Def{}, I.Con{}) -> __IMPOSSIBLE__  -- ambiguous identifiers
+        (I.Con{}, I.Def{}) -> __IMPOSSIBLE__
+        (I.Var{}, I.Def{}) -> varDef
+        (I.Def{}, I.Var{}) -> varDef
+        (I.Var{}, I.Con{}) -> varCon
+        (I.Con{}, I.Var{}) -> varCon
+        (I.Def x _, I.Def y _)
+          | isExtendedLambdaName x, isExtendedLambdaName y -> extLamExtLam x y
+        _                  -> empty
+  where
+    varDef, varCon, generic :: MonadPretty m => m Doc
+    varDef = parens $ fwords "because one is a variable and one a defined identifier"
+    varCon = parens $ fwords "because one is a variable and one a constructor"
+    generic = parens $ fwords $ "although these terms are looking the same, " ++
+      "they contain different but identically rendered identifiers somewhere"
+    varVar :: MonadPretty m => Int -> Int -> m Doc
+    varVar i j = parens $ fwords $
+                   "because one has de Bruijn index " ++ show i
+                   ++ " and the other " ++ show j
+
+    extLamExtLam :: MonadPretty m => QName -> QName -> m Doc
+    extLamExtLam a b = vcat
+      [ fwords "Because they are distinct extended lambdas: one is defined at"
+      , "  " <+> pretty (nameBindingSite (qnameName a))
+      , fwords "and the other at"
+      , "  " <+> (pretty (nameBindingSite (qnameName b)) <> ",")
+      , fwords "so they have different internal representations."
+      ]
+
+class PrettyUnequal a where
+  prettyUnequal :: MonadPretty m => a -> m Doc -> a -> m Doc
+
+instance PrettyUnequal Term where
+  prettyUnequal t1 ncmp t2 = do
+    (d1, d2, d) <- prettyInEqual t1 t2
+    fsep $ return d1 : ncmp : return d2 : return d : []
+
+instance PrettyUnequal I.Type where
+  prettyUnequal t1 ncmp t2 = prettyUnequal (unEl t1) ncmp (unEl t2)
+
+instance PrettyTCM SplitError where
+  prettyTCM :: forall m. MonadPretty m => SplitError -> m Doc
+  prettyTCM err = case err of
+    NotADatatype t -> enterClosure t $ \ t -> fsep $
+      pwords "Cannot split on argument of non-datatype" ++ [prettyTCM t]
+
+    BlockedType b t -> enterClosure t $ \ t -> fsep $
+      pwords "Cannot split on argument of unresolved type" ++ [prettyTCM t]
+
+    ErasedDatatype reason t -> enterClosure t $ \ t -> fsep $
+      pwords "Cannot branch on erased argument of datatype" ++
+      [prettyTCM t] ++
+      case reason of
+        NoErasedMatches ->
+          pwords "because the option --erased-matches is not active"
+        NoK ->
+          pwords "because the K rule is turned off"
+        SeveralConstructors ->
+          []
+
+    CoinductiveDatatype t -> enterClosure t $ \ t -> fsep $
+      pwords "Cannot pattern match on the coinductive type" ++ [prettyTCM t]
+
+{- UNUSED
+    NoRecordConstructor t -> fsep $
+      pwords "Cannot pattern match on record" ++ [prettyTCM t] ++
+      pwords "because it has no constructor"
+ -}
+
+    UnificationStuck b c tel cIxs gIxs errs
+      | length cIxs /= length gIxs -> __IMPOSSIBLE__
+      | otherwise                  -> vcat . concat $
+        [ [ fsep . concat $
+            [ pwords "I'm not sure if there should be a case for the constructor"
+            , [prettyTCM c <> ","]
+            , pwords "because I get stuck when trying to solve the following"
+            , pwords "unification problems (inferred index ≟ expected index):"
+            ]
+          ]
+        , zipWith prEq cIxs gIxs
+        , if null errs then [] else
+            fsep ( pwords "Possible" ++ pwords (P.singPlural errs "reason" "reasons") ++
+                     pwords "why unification failed:" ) :
+            map (nest 2 . prettyTCM) errs
+        ]
+      where
+        -- Andreas, 2019-08-08, issue #3943
+        -- To not print hidden indices just as {_}, we strip the Arg and print
+        -- the hiding information manually.
+        prEq :: Arg Term -> Arg Term -> m Doc
+        prEq cIx gIx = addContext tel $ nest 2 $ hsep [ pr cIx , "≟" , pr gIx ]
+        pr arg = prettyRelevance arg . prettyHiding arg id <$> prettyTCM (unArg arg)
+
+    CosplitCatchall -> fsep $
+      pwords "Cannot split into projections because not all clauses have a projection copattern"
+
+    CosplitNoTarget -> fsep $
+      pwords "Cannot split into projections because target type is unknown"
+
+    CosplitNoRecordType t -> enterClosure t $ \t -> fsep $
+      pwords "Cannot split into projections because the target type "
+      ++ [prettyTCM t] ++ pwords " is not a record type"
+
+    CannotCreateMissingClause f cl msg t -> fsep (
+      pwords "Cannot generate inferred clause for" ++ [prettyTCM f <> "."] ++
+      pwords "Case to handle:") $$ nest 2 (vcat $ [display cl])
+                                $$ ((pure msg <+> enterClosure t displayAbs) <> ".")
+        where
+        displayAbs :: Abs I.Type -> m Doc
+        displayAbs (Abs x t) = addContext x $ prettyTCM t
+        displayAbs (NoAbs x t) = prettyTCM t
+        display (tel, ps) = prettyTCM $ NamedClause f True $
+          empty { clauseTel = tel, namedClausePats = ps }
+
+
+    GenericSplitError s -> fsep $ pwords "Split failed:" ++ pwords s
+
+instance PrettyTCM NegativeUnification where
+  prettyTCM err = case err of
+    UnifyConflict tel u v -> addContext tel $ vcat $
+      [ fsep $ pwords "because unification ended with a conflicting equation "
+      , nest 2 $ prettyTCM u <+> "≟" <+> prettyTCM v
+      ]
+
+    UnifyCycle tel i u -> addContext tel $ vcat $
+      [ fsep $ pwords "because unification ended with a cyclic equation "
+      , nest 2 $ prettyTCM (var i) <+> "≟" <+> prettyTCM u
+      ]
+
+instance PrettyTCM UnificationFailure where
+  prettyTCM err = case err of
+    UnifyIndicesNotVars tel a u v ixs -> addContext tel $ fsep $
+      pwords "Cannot apply injectivity to the equation" ++ [prettyTCM u] ++
+      pwords "=" ++ [prettyTCM v] ++ pwords "of type" ++ [prettyTCM a] ++
+      pwords "because I cannot generalize over the indices" ++
+      [prettyList (map prettyTCM ixs) <> "."]
+
+    UnifyRecursiveEq tel a i u -> addContext tel $ fsep $
+      pwords "Cannot solve variable " ++ [prettyTCM (var i)] ++
+      pwords " of type " ++ [prettyTCM a] ++
+      pwords " with solution " ++ [prettyTCM u] ++
+      pwords " because the variable occurs in the solution," ++
+      pwords " or in the type of one of the variables in the solution."
+
+    UnifyReflexiveEq tel a u -> addContext tel $ fsep $
+      pwords "Cannot eliminate reflexive equation" ++ [prettyTCM u] ++
+      pwords "=" ++ [prettyTCM u] ++ pwords "of type" ++ [prettyTCM a] ++
+      pwords "because K has been disabled."
+
+    UnifyUnusableModality tel a i u mod -> addContext tel $ fsep $
+      pwords "Cannot solve variable " ++ [prettyTCM (var i)] ++
+      pwords "of type " ++ [prettyTCM a] ++
+      pwords "with solution " ++ [prettyTCM u] ++
+      pwords "because the solution cannot be used at" ++
+             [ text (verbalize $ getRelevance mod) <> ","
+             , text $ verbalize $ getQuantity mod ] ++
+      pwords "modality"
+
+
+
+explainWhyInScope :: forall m. MonadPretty m => WhyInScopeData -> m Doc
+explainWhyInScope (WhyInScopeData y _ Nothing [] []) = text (prettyShow  y ++ " is not in scope.")
+explainWhyInScope (WhyInScopeData y _ v xs ms) = vcat
+  [ text (prettyShow y ++ " is in scope as")
+  , nest 2 $ vcat [variable v xs, modules ms]
+  ]
+  where
+    -- variable :: Maybe _ -> [_] -> m Doc
+    variable Nothing vs = names vs
+    variable (Just x) vs
+      | null vs   = asVar
+      | otherwise = vcat
+         [ sep [ asVar, nest 2 $ shadowing x]
+         , nest 2 $ names vs
+         ]
+      where
+        asVar :: m Doc
+        asVar = do
+          "* a variable bound at" <+> prettyTCM (nameBindingSite $ localVar x)
+        shadowing :: LocalVar -> m Doc
+        shadowing (LocalVar _ _ [])    = "shadowing"
+        shadowing _ = "in conflict with"
+    names   = vcat . map pName
+    modules = vcat . map pMod
+
+    pKind = \case
+      ConName                  -> "constructor"
+      CoConName                -> "coinductive constructor"
+      FldName                  -> "record field"
+      PatternSynName           -> "pattern synonym"
+      GeneralizeName           -> "generalizable variable"
+      DisallowedGeneralizeName -> "generalizable variable from let open"
+      MacroName                -> "macro name"
+      QuotableName             -> "quotable name"
+      -- previously DefName:
+      DataName                 -> "data type"
+      RecName                  -> "record type"
+      AxiomName                -> "postulate"
+      PrimName                 -> "primitive function"
+      FunName                  -> "defined name"
+      OtherDefName             -> "defined name"
+
+    pName :: AbstractName -> m Doc
+    pName a = sep
+      [ "* a"
+        <+> pKind (anameKind a)
+        <+> text (prettyShow $ anameName a)
+      , nest 2 $ "brought into scope by"
+      ] $$
+      nest 2 (pWhy (nameBindingSite $ qnameName $ anameName a) (anameLineage a))
+    pMod :: AbstractModule -> m Doc
+    pMod  a = sep
+      [ "* a module" <+> text (prettyShow $ amodName a)
+      , nest 2 $ "brought into scope by"
+      ] $$
+      nest 2 (pWhy (nameBindingSite $ qnameName $ mnameToQName $ amodName a) (amodLineage a))
+
+    pWhy :: Range -> WhyInScope -> m Doc
+    pWhy r Defined = "- its definition at" <+> prettyTCM r
+    pWhy r (Opened (C.QName x) w) | isNoName x = pWhy r w
+    pWhy r (Opened m w) =
+      "- the opening of"
+      <+> prettyTCM m
+      <+> "at"
+      <+> prettyTCM (getRange m)
+      $$
+      pWhy r w
+    pWhy r (Applied m w) =
+      "- the application of"
+      <+> prettyTCM m
+      <+> "at"
+      <+> prettyTCM (getRange m)
+      $$
+      pWhy r w
+
+
+
+---------------------------------------------------------------------------
+-- * Natural language
+---------------------------------------------------------------------------
+
+class Verbalize a where
+  verbalize :: a -> String
+
+instance Verbalize Hiding where
+  verbalize = hidingToString
+
+instance Verbalize Relevance where
+  verbalize r =
+    case r of
+      Relevant   -> "relevant"
+      Irrelevant -> "irrelevant"
+      NonStrict  -> "shape-irrelevant"
+
+instance Verbalize Quantity where
+  verbalize = \case
+    Quantity0{} -> "erased"
+    Quantity1{} -> "linear"
+    Quantityω{} -> "unrestricted"
+
+instance Verbalize Cohesion where
+  verbalize r =
+    case r of
+      Flat       -> "flat"
+      Continuous -> "continuous"
+      Squash     -> "squashed"
+
+instance Verbalize Modality where
+  verbalize mod | mod == defaultModality = "default"
+  verbalize (Modality rel qnt coh) = intercalate ", " $
+    [ verbalize rel | rel /= defaultRelevance ] ++
+    [ verbalize qnt | qnt /= defaultQuantity ] ++
+    [ verbalize coh | coh /= defaultCohesion ]
+
+-- | Indefinite article.
+data Indefinite a = Indefinite a
+
+instance Verbalize a => Verbalize (Indefinite a) where
+  verbalize (Indefinite a) =
+    case verbalize a of
+      "" -> ""
+      w@(c:cs) | c `elem` ['a','e','i','o'] -> "an " ++ w
+               | otherwise                  -> "a " ++ w
+      -- Aarne Ranta would whip me if he saw this.
diff --git a/src/full/Agda/TypeChecking/Errors.hs-boot b/src/full/Agda/TypeChecking/Errors.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Errors.hs-boot
@@ -0,0 +1,14 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Errors where
+
+import Agda.Syntax.Abstract.Name
+
+import Agda.TypeChecking.Monad.Base
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Debug (MonadDebug)
+
+-- Misplaced SPECIALISE pragma:
+-- {-# SPECIALIZE renderError :: TCErr -> TCM String #-}
+renderError :: MonadTCM tcm => TCErr -> tcm String
+
+topLevelModuleDropper :: (MonadDebug m, MonadTCEnv m, ReadTCState m) => m (QName -> QName)
diff --git a/src/full/Agda/TypeChecking/EtaContract.hs b/src/full/Agda/TypeChecking/EtaContract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/EtaContract.hs
@@ -0,0 +1,123 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Compute eta short normal forms.
+module Agda.TypeChecking.EtaContract where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce.Monad () --instance only
+import {-# SOURCE #-} Agda.TypeChecking.Records
+import {-# SOURCE #-} Agda.TypeChecking.Datatypes
+
+import Agda.Utils.Monad
+import Agda.Utils.List (initLast)
+
+import Agda.Utils.Impossible
+
+-- TODO: move to Agda.Syntax.Internal.SomeThing
+data BinAppView = App Term (Arg Term)
+                | NoApp Term
+
+binAppView :: Term -> BinAppView
+binAppView t = case t of
+  Var i xs   -> appE (Var i) xs
+  Def c xs   -> appE (Def c) xs
+  -- Andreas, 2013-09-17: do not eta-contract when body is (record) constructor
+  -- like in \ x -> s , x!  (See interaction/DoNotEtaContractFunIntoRecord)
+  -- (Cf. also issue 889 (fixed differently).)
+  -- At least record constructors should be fully applied where possible!
+  -- TODO: also for ordinary constructors (\ x -> suc x  vs.  suc)?
+  Con c ci xs
+    | IsData <- conDataRecord c
+             -> appE (Con c ci) xs
+    | otherwise
+             -> noApp
+  Lit _      -> noApp
+  Level _    -> noApp   -- could be an application, but let's not eta contract levels
+  Lam _ _    -> noApp
+  Pi _ _     -> noApp
+  Sort _     -> noApp
+  MetaV _ _  -> noApp
+  DontCare _ -> noApp
+  Dummy{}    -> __IMPOSSIBLE__
+  where
+    noApp = NoApp t
+    appE f es0 | Just (es, Apply v) <- initLast es0 = App (f es) v
+    appE _ _ = noApp
+
+-- | Contracts all eta-redexes it sees without reducing.
+{-# SPECIALIZE etaContract :: TermLike a => a -> TCM a #-}
+{-# SPECIALIZE etaContract :: TermLike a => a -> ReduceM a #-}
+etaContract :: (MonadTCEnv m, HasConstInfo m, HasOptions m, TermLike a) => a -> m a
+etaContract = traverseTermM etaOnce
+
+{-# SPECIALIZE etaOnce :: Term -> TCM Term #-}
+{-# SPECIALIZE etaOnce :: Term -> ReduceM Term #-}
+etaOnce :: (MonadTCEnv m, HasConstInfo m, HasOptions m) => Term -> m Term
+etaOnce = \case
+  -- Andreas, 2012-11-18: this call to reportSDoc seems to cost me 2%
+  -- performance on the std-lib
+  -- reportSDoc "tc.eta" 70 $ "eta-contracting" <+> prettyTCM v
+  Lam i (Abs x b) -> etaLam i x b  -- NoAbs can't be eta'd
+
+  -- Andreas, 2012-12-18:  Abstract definitions could contain
+  -- abstract records whose constructors are not in scope.
+  -- To be able to eta-contract them, we ignore abstract.
+  Con c ci es -> etaCon c ci es etaContractRecord
+
+  v -> return v
+
+-- | If record constructor, call eta-contraction function.
+etaCon :: (MonadTCEnv m, HasConstInfo m, HasOptions m)
+  => ConHead  -- ^ Constructor name @c@.
+  -> ConInfo  -- ^ Constructor info @ci@.
+  -> Elims     -- ^ Constructor arguments @args@.
+  -> (QName -> ConHead -> ConInfo -> Args -> m Term)
+              -- ^ Eta-contraction workhorse, gets also name of record type.
+  -> m Term   -- ^ Returns @Con c ci args@ or its eta-contraction.
+etaCon c ci es cont = ignoreAbstractMode $ do
+  let fallback = return $ Con c ci es
+  -- reportSDoc "tc.eta" 20 $ "eta-contracting record" <+> prettyTCM t
+  r <- getConstructorData $ conName c -- fails in ConcreteMode if c is abstract
+  ifNotM (isEtaRecord r) fallback $ {-else-} do
+    -- reportSDoc "tc.eta" 20 $ "eta-contracting record" <+> prettyTCM t
+    let Just args = allApplyElims es
+    cont r c ci args
+
+-- | Try to contract a lambda-abstraction @Lam i (Abs x b)@.
+etaLam :: (MonadTCEnv m, HasConstInfo m, HasOptions m)
+  => ArgInfo  -- ^ Info @i@ of the 'Lam'.
+  -> ArgName  -- ^ Name @x@ of the abstraction.
+  -> Term     -- ^ Body ('Term') @b@ of the 'Abs'.
+  -> m Term   -- ^ @Lam i (Abs x b)@, eta-contracted if possible.
+etaLam i x b = do
+    let fallback = return $ Lam i $ Abs x b
+    case binAppView b of
+      App u (Arg info v) -> do
+        tyty <- typeInType
+        if isVar0 tyty v
+        -- Andreas, 2017-02-20 issue #2464
+        -- Contracting with any irrelevant argument breaks subject reduction.
+        -- E.g. \ .x -> f .(subst P eq x)  can in general not be contracted to f.
+        -- -- (isIrrelevant info || isVar0 tyty v)
+             && sameHiding i info
+             && sameModality i info
+             && not (freeIn 0 u)
+           then return $ strengthen impossible u
+           else fallback
+      _ -> fallback
+  where
+    isVar0 _ (Var 0 [])               = True
+    -- Andreas, 2016-01-08 If --type-in-type, all levels are equal.
+    -- Jesper, 2019-10-15 issue #3073
+    -- Contracting level arguments is not sound unless the domain type
+    -- is in fact @Level@, e.g. @\(A : Set) → F lzero@ should not be
+    -- eta-contracted to @F@.
+    -- isVar0 True Level{}               = True
+    isVar0 tyty (Level (Max 0 [Plus 0 l])) = isVar0 tyty l
+    isVar0 _ _ = False
diff --git a/src/full/Agda/TypeChecking/Forcing.hs b/src/full/Agda/TypeChecking/Forcing.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Forcing.hs
@@ -0,0 +1,174 @@
+
+{-| A constructor argument is forced if it appears as pattern variable
+in an index of the target.
+
+For instance @x@ is forced in @sing@ and @n@ is forced in @zero@ and @suc@:
+
+@
+  data Sing {a}{A : Set a} : A -> Set where
+    sing : (x : A) -> Sing x
+
+  data Fin : Nat -> Set where
+    zero : (n : Nat) -> Fin (suc n)
+    suc  : (n : Nat) (i : Fin n) -> Fin (suc n)
+@
+
+At runtime, forced constructor arguments may be erased as they can be
+recovered from dot patterns.  For instance,
+@
+  unsing : {A : Set} (x : A) -> Sing x -> A
+  unsing .x (sing x) = x
+@
+can become
+@
+  unsing x sing = x
+@
+and
+@
+  proj : (n : Nat) (i : Fin n) -> Nat
+  proj .(suc n) (zero n) = n
+  proj .(suc n) (suc n i) = n
+@
+becomes
+@
+  proj (suc n) zero    = n
+  proj (suc n) (suc i) = n
+@
+
+This module implements the analysis of which constructor arguments are forced. The process of moving
+the binding site of forced arguments is implemented in the unifier (see the Solution step of
+Agda.TypeChecking.Rules.LHS.Unify.unifyStep).
+
+Forcing is a concept from pattern matching and thus builds on the
+concept of equality (I) used there (closed terms, extensional) which is
+different from the equality (II) used in conversion checking and the
+constraint solver (open terms, intensional).
+
+Up to issue 1441 (Feb 2015), the forcing analysis here relied on the
+wrong equality (II), considering type constructors as injective.  This is
+unsound for program extraction, but ok if forcing is only used to decide which
+arguments to skip during conversion checking.
+
+From now on, forcing uses equality (I) and does not search for forced
+variables under type constructors.  This may lose some savings during
+conversion checking.  If this turns out to be a problem, the old
+forcing could be brought back, using a new modality @Skip@ to indicate
+that this is a relevant argument but still can be skipped during
+conversion checking as it is forced by equality (II).
+
+-}
+
+module Agda.TypeChecking.Forcing
+  ( computeForcingAnnotations,
+    isForced,
+    nextIsForced ) where
+
+import Data.Bifunctor
+import Data.DList (DList)
+import qualified Data.DList as DL
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.Monoid -- for (<>) in GHC 8.0.2
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.List
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- | Given the type of a constructor (excluding the parameters),
+--   decide which arguments are forced.
+--   Precondition: the type is of the form @Γ → D vs@ and the @vs@
+--   are in normal form.
+computeForcingAnnotations :: QName -> Type -> TCM [IsForced]
+computeForcingAnnotations c t =
+  ifNotM (optForcing <$> pragmaOptions {-then-}) (return []) $ {-else-} do
+    -- Andreas, 2015-03-10  Normalization prevents Issue 1454.
+    -- t <- normalise t
+    -- Andreas, 2015-03-28  Issue 1469: Normalization too costly.
+    -- Instantiation also fixes Issue 1454.
+    -- Note that normalization of s0 below does not help.
+    t <- instantiateFull t
+    -- Ulf, 2018-01-28 (#2919): We do need to reduce the target type enough to
+    -- get to the actual data type.
+    -- Also #2947: The type might reduce to a pi type.
+    TelV tel (El _ a) <- telViewPath t
+    let vs = case a of
+          Def _ us -> us
+          _        -> __IMPOSSIBLE__
+        n = size tel
+        xs :: [(Modality, Nat)]
+        xs = DL.toList $ forcedVariables vs
+        xs' :: IntMap [Modality]
+        xs' = IntMap.map DL.toList $ IntMap.fromListWith (<>) $
+              map (\(m, i) -> (i, DL.singleton m)) xs
+        -- #2819: We can only mark an argument as forced if it appears in the
+        -- type with a relevance below (i.e. more relevant) than the one of the
+        -- constructor argument. Otherwise we can't actually get the value from
+        -- the type. Also the argument shouldn't be irrelevant, since in that
+        -- case it isn't really forced.
+        isForced :: Modality -> Nat -> Bool
+        isForced m i =
+               (hasQuantity0 m || noUserQuantity m)
+            && (getRelevance m /= Irrelevant)
+            && case IntMap.lookup i xs' of
+                 Nothing -> False
+                 Just ms -> any (`moreUsableModality` m) ms
+        forcedArgs =
+          [ if isForced m i then Forced else NotForced
+          | (i, m) <- zip (downFrom n) $ map getModality (telToList tel)
+          ]
+    reportS "tc.force" 60
+      [ "Forcing analysis for " ++ prettyShow c
+      , "  xs          = " ++ show (map snd xs)
+      , "  forcedArgs  = " ++ show forcedArgs
+      ]
+    return forcedArgs
+
+-- | Compute the pattern variables of a term or term-like thing.
+class ForcedVariables a where
+  forcedVariables :: a -> DList (Modality, Nat)
+
+  default forcedVariables ::
+    (ForcedVariables b, Foldable t, a ~ t b) =>
+    a -> DList (Modality, Nat)
+  forcedVariables = foldMap forcedVariables
+
+instance ForcedVariables a => ForcedVariables [a] where
+
+-- Note that the 'a' does not include the 'Arg' in 'Apply'.
+instance ForcedVariables a => ForcedVariables (Elim' a) where
+  forcedVariables (Apply x) = forcedVariables x
+  forcedVariables IApply{}  = mempty  -- No forced variables in path applications
+  forcedVariables Proj{}    = mempty
+
+instance ForcedVariables a => ForcedVariables (Arg a) where
+  forcedVariables x =
+    fmap (first (composeModality m)) (forcedVariables (unArg x))
+    where m = getModality x
+
+-- | Assumes that the term is in normal form.
+instance ForcedVariables Term where
+  forcedVariables = \case
+    Var i []   -> DL.singleton (unitModality, i)
+    Con _ _ vs -> forcedVariables vs
+    _          -> mempty
+
+isForced :: IsForced -> Bool
+isForced Forced    = True
+isForced NotForced = False
+
+nextIsForced :: [IsForced] -> (IsForced, [IsForced])
+nextIsForced []     = (NotForced, [])
+nextIsForced (f:fs) = (f, fs)
diff --git a/src/full/Agda/TypeChecking/Free.hs b/src/full/Agda/TypeChecking/Free.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Free.hs
@@ -0,0 +1,321 @@
+{-# LANGUAGE UndecidableInstances       #-} -- Due to underdetermined var in IsVarSet multi-param typeclass
+
+-- | Computing the free variables of a term.
+--
+-- The distinction between rigid and strongly rigid occurrences comes from:
+--   Jason C. Reed, PhD thesis, 2009, page 96 (see also his LFMTP 2009 paper)
+--
+-- The main idea is that x = t(x) is unsolvable if x occurs strongly rigidly
+-- in t.  It might have a solution if the occurrence is not strongly rigid, e.g.
+--
+--   x = \f -> suc (f (x (\ y -> k)))  has  x = \f -> suc (f (suc k))
+--
+-- [Jason C. Reed, PhD thesis, page 106]
+--
+-- Under coinductive constructors, occurrences are never strongly rigid.
+-- Also, function types and lambdas do not establish strong rigidity.
+-- Only inductive constructors do so.
+-- (See issue 1271).
+--
+-- If you need the occurrence information for all free variables, you can use
+-- @freeVars@ which has amoungst others this instance
+-- @
+--    freeVars :: Term -> VarMap
+-- @
+-- From @VarMap@, specific information can be extracted, e.g.,
+-- @
+--    relevantVars :: VarMap -> VarSet
+--    relevantVars = filterVarMap isRelevant
+-- @
+--
+-- To just check the status of a single free variable, there are more
+-- efficient methods, e.g.,
+-- @
+--    freeIn :: Nat -> Term -> Bool
+-- @
+--
+-- Tailored optimized variable checks can be implemented as semimodules to 'VarOcc',
+-- see, for example, 'VarCounts' or 'SingleFlexRig'.
+
+module Agda.TypeChecking.Free
+    ( VarCounts(..)
+    , Free
+    , IsVarSet(..)
+    , IgnoreSorts(..)
+    , freeVars, freeVars', filterVarMap, filterVarMapToList
+    , runFree, rigidVars, stronglyRigidVars, unguardedVars, allVars
+    , flexibleVars
+    , allFreeVars
+    , allRelevantVars, allRelevantVarsIgnoring
+    , freeVarsIgnore
+    , freeIn, freeInIgnoringSorts, isBinderUsed
+    , relevantIn, relevantInIgnoringSortAnn
+    , FlexRig'(..), FlexRig
+    , LensFlexRig(..), isFlexible, isUnguarded, isStronglyRigid, isWeaklyRigid
+    , VarOcc'(..), VarOcc
+    , varOccurrenceIn
+    , flexRigOccurrenceIn
+    , closed
+    , MetaSet
+    , insertMetaSet, foldrMetaSet, metaSetToBlocker
+    ) where
+
+import Prelude hiding (null)
+
+import Data.Semigroup ( Semigroup, (<>), Any(..), All(..) )
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+
+import qualified Agda.Benchmarking as Bench
+
+import Agda.Syntax.Common hiding (Arg, NamedArg)
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Free.Lazy
+  -- ( Free(..) , FreeEnv(..), initFreeEnv
+  -- , FlexRig, FlexRig'(..)
+  -- , VarOcc(..), topVarOcc, TheVarMap, theVarMap, IgnoreSorts(..), Variable, SingleVar
+  -- , MetaSet, insertMetaSet, foldrMetaSet
+  -- , IsVarSet(..), runFreeM
+  -- )
+
+import Agda.Utils.Singleton
+
+---------------------------------------------------------------------------
+-- * Simple variable set implementations.
+
+type VarSet = IntSet
+
+-- In most cases we don't care about the VarOcc.
+
+instance IsVarSet () VarSet where withVarOcc _ = id
+instance IsVarSet () [Int]  where withVarOcc _ = id
+instance IsVarSet () Any    where withVarOcc _ = id
+instance IsVarSet () All    where withVarOcc _ = id
+
+---------------------------------------------------------------------------
+-- * Plain variable occurrence counting.
+
+newtype VarCounts = VarCounts { varCounts :: IntMap Int }
+
+instance Semigroup VarCounts where
+  VarCounts fv1 <> VarCounts fv2 = VarCounts (IntMap.unionWith (+) fv1 fv2)
+
+instance Monoid VarCounts where
+  mempty = VarCounts IntMap.empty
+  mappend = (<>)
+
+instance IsVarSet () VarCounts where
+  withVarOcc _ = id
+
+instance Singleton Variable VarCounts where
+  singleton i = VarCounts $ IntMap.singleton i 1
+
+---------------------------------------------------------------------------
+-- * Collecting free variables (generic).
+
+-- | Collect all free variables together with information about their occurrence.
+--
+-- Doesn't go inside solved metas, but collects the variables from a
+-- metavariable application @X ts@ as @flexibleVars@.
+{-# SPECIALIZE freeVars :: Free a => a -> VarMap #-}
+freeVars :: (IsVarSet a c, Singleton Variable c, Free t) => t -> c
+freeVars = freeVarsIgnore IgnoreNot
+
+freeVarsIgnore :: (IsVarSet a c, Singleton Variable c, Free t) =>
+                  IgnoreSorts -> t -> c
+freeVarsIgnore = runFree singleton
+
+-- Specialization to typical monoids
+{-# SPECIALIZE runFree :: Free a => SingleVar Any      -> IgnoreSorts -> a -> Any #-}
+-- Specialization to Term
+{-# SPECIALIZE runFree :: SingleVar Any      -> IgnoreSorts -> Term -> Any #-}
+
+-- | Compute free variables.
+runFree :: (IsVarSet a c, Free t) => SingleVar c -> IgnoreSorts -> t -> c
+runFree single i t = -- bench $  -- Benchmarking is expensive (4% on std-lib)
+  runFreeM single i (freeVars' t)
+  where
+  bench = Bench.billToPure [ Bench.Typing , Bench.Free ]
+
+---------------------------------------------------------------------------
+-- * Occurrence computation for a single variable.
+
+-- ** Full free occurrence info for a single variable.
+
+-- | Get the full occurrence information of a free variable.
+varOccurrenceIn :: Free a => Nat -> a -> Maybe VarOcc
+varOccurrenceIn = varOccurrenceIn' IgnoreNot
+
+varOccurrenceIn' :: Free a => IgnoreSorts -> Nat -> a -> Maybe VarOcc
+varOccurrenceIn' ig x t = theSingleVarOcc $ runFree sg ig t
+  where
+  sg y = if x == y then oneSingleVarOcc else mempty
+
+-- | "Collection" just keeping track of the occurrence of a single variable.
+--   'Nothing' means variable does not occur freely.
+newtype SingleVarOcc = SingleVarOcc { theSingleVarOcc :: Maybe VarOcc }
+
+oneSingleVarOcc :: SingleVarOcc
+oneSingleVarOcc = SingleVarOcc $ Just $ oneVarOcc
+
+-- | Hereditary Semigroup instance for 'Maybe'.
+--   (The default instance for 'Maybe' may not be the hereditary one.)
+instance Semigroup SingleVarOcc where
+  SingleVarOcc Nothing <> s = s
+  s <> SingleVarOcc Nothing = s
+  SingleVarOcc (Just o) <> SingleVarOcc (Just o') = SingleVarOcc $ Just $ o <> o'
+
+instance Monoid SingleVarOcc where
+  mempty = SingleVarOcc Nothing
+  mappend = (<>)
+
+instance IsVarSet MetaSet SingleVarOcc where
+  withVarOcc o = SingleVarOcc . fmap (composeVarOcc o) . theSingleVarOcc
+
+-- ** Flexible /rigid occurrence info for a single variable.
+
+-- | Get the full occurrence information of a free variable.
+flexRigOccurrenceIn :: Free a => Nat -> a -> Maybe FlexRig
+flexRigOccurrenceIn = flexRigOccurrenceIn' IgnoreNot
+
+flexRigOccurrenceIn' :: Free a => IgnoreSorts -> Nat -> a -> Maybe FlexRig
+flexRigOccurrenceIn' ig x t = theSingleFlexRig $ runFree sg ig t
+  where
+  sg y = if x == y then oneSingleFlexRig else mempty
+
+-- | "Collection" just keeping track of the occurrence of a single variable.
+--   'Nothing' means variable does not occur freely.
+newtype SingleFlexRig = SingleFlexRig { theSingleFlexRig :: Maybe FlexRig }
+
+oneSingleFlexRig :: SingleFlexRig
+oneSingleFlexRig = SingleFlexRig $ Just $ oneFlexRig
+
+-- | Hereditary Semigroup instance for 'Maybe'.
+--   (The default instance for 'Maybe' may not be the hereditary one.)
+instance Semigroup SingleFlexRig where
+  SingleFlexRig Nothing <> s = s
+  s <> SingleFlexRig Nothing = s
+  SingleFlexRig (Just o) <> SingleFlexRig (Just o') = SingleFlexRig $ Just $ addFlexRig o o'
+
+instance Monoid SingleFlexRig where
+  mempty = SingleFlexRig Nothing
+  mappend = (<>)
+
+instance IsVarSet MetaSet SingleFlexRig where
+  withVarOcc o = SingleFlexRig . fmap (composeFlexRig $ varFlexRig o) . theSingleFlexRig
+
+-- ** Plain free occurrence.
+
+-- | Check if a variable is free, possibly ignoring sorts.
+freeIn' :: Free a => IgnoreSorts -> Nat -> a -> Bool
+freeIn' ig x t = getAny $ runFree (Any . (x ==)) ig t
+
+{-# SPECIALIZE freeIn :: Nat -> Term -> Bool #-}
+freeIn :: Free a => Nat -> a -> Bool
+freeIn = freeIn' IgnoreNot
+
+freeInIgnoringSorts :: Free a => Nat -> a -> Bool
+freeInIgnoringSorts = freeIn' IgnoreAll
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+--freeInIgnoringSortAnn :: Free a => Nat -> a -> Bool
+--freeInIgnoringSortAnn = freeIn' IgnoreInAnnotations
+
+-- | Is the variable bound by the abstraction actually used?
+isBinderUsed :: Free a => Abs a -> Bool
+isBinderUsed NoAbs{}   = False
+isBinderUsed (Abs _ x) = 0 `freeIn` x
+
+-- ** Relevant free occurrence.
+
+newtype RelevantIn c = RelevantIn {getRelevantIn :: c}
+  deriving (Semigroup, Monoid)
+
+instance IsVarSet a c => IsVarSet a (RelevantIn c) where  -- UndecidableInstances
+  withVarOcc o x
+    | isIrrelevant o = mempty
+    | otherwise = RelevantIn $ withVarOcc o $ getRelevantIn x
+
+relevantIn' :: Free t => IgnoreSorts -> Nat -> t -> Bool
+relevantIn' ig x t = getAny . getRelevantIn $ runFree (RelevantIn . Any . (x ==)) ig t
+
+relevantInIgnoringSortAnn :: Free t => Nat -> t -> Bool
+relevantInIgnoringSortAnn = relevantIn' IgnoreInAnnotations
+
+relevantIn :: Free t => Nat -> t -> Bool
+relevantIn = relevantIn' IgnoreAll
+
+---------------------------------------------------------------------------
+-- * Occurrences of all free variables.
+
+-- | Is the term entirely closed (no free variables)?
+closed :: Free t => t -> Bool
+closed t = getAll $ runFree (const $ All False) IgnoreNot t
+
+-- | Collect all free variables.
+allFreeVars :: Free t => t -> VarSet
+allFreeVars = runFree IntSet.singleton IgnoreNot
+
+-- | Collect all relevant free variables, possibly ignoring sorts.
+allRelevantVarsIgnoring :: Free t => IgnoreSorts -> t -> VarSet
+allRelevantVarsIgnoring ig = getRelevantIn . runFree (RelevantIn . IntSet.singleton) ig
+
+-- | Collect all relevant free variables, excluding the "unused" ones.
+allRelevantVars :: Free t => t -> VarSet
+allRelevantVars = allRelevantVarsIgnoring IgnoreNot
+
+---------------------------------------------------------------------------
+-- * Backwards-compatible interface to 'freeVars'.
+
+filterVarMap :: (VarOcc -> Bool) -> VarMap -> VarSet
+filterVarMap f = IntMap.keysSet . IntMap.filter f . theVarMap
+
+filterVarMapToList :: (VarOcc -> Bool) -> VarMap -> [Variable]
+filterVarMapToList f = map fst . filter (f . snd) . IntMap.toList . theVarMap
+
+-- | Variables under only and at least one inductive constructor(s).
+stronglyRigidVars :: VarMap -> VarSet
+stronglyRigidVars = filterVarMap $ \case
+  VarOcc StronglyRigid _ -> True
+  _ -> False
+
+-- | Variables at top or only under inductive record constructors
+--   λs and Πs.
+--   The purpose of recording these separately is that they
+--   can still become strongly rigid if put under a constructor
+--   whereas weakly rigid ones stay weakly rigid.
+unguardedVars :: VarMap -> VarSet
+unguardedVars = filterVarMap $ \case
+  VarOcc Unguarded _ -> True
+  _ -> False
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+---- | Ordinary rigid variables, e.g., in arguments of variables or functions.
+--weaklyRigidVars :: VarMap -> VarSet
+--weaklyRigidVars = filterVarMap $ \case
+--  VarOcc WeaklyRigid _ -> True
+--  _ -> False
+
+-- | Rigid variables: either strongly rigid, unguarded, or weakly rigid.
+rigidVars :: VarMap -> VarSet
+rigidVars = filterVarMap $ \case
+  VarOcc o _ -> o `elem` [ WeaklyRigid, Unguarded, StronglyRigid ]
+
+-- | Variables occuring in arguments of metas.
+--  These are only potentially free, depending how the meta variable is instantiated.
+--  The set contains the id's of the meta variables that this variable is an argument to.
+flexibleVars :: VarMap -> IntMap MetaSet
+flexibleVars (VarMap m) = (`IntMap.mapMaybe` m) $ \case
+ VarOcc (Flexible ms) _ -> Just ms
+ _ -> Nothing
+
+---- | Variables in irrelevant arguments and under a @DontCare@, i.e.,
+----   in irrelevant positions.
+--irrelevantVars :: VarMap -> VarSet
+--irrelevantVars = filterVarMap isIrrelevant
+
+allVars :: VarMap -> VarSet
+allVars = IntMap.keysSet . theVarMap
diff --git a/src/full/Agda/TypeChecking/Free/Lazy.hs b/src/full/Agda/TypeChecking/Free/Lazy.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Free/Lazy.hs
@@ -0,0 +1,612 @@
+
+-- | Computing the free variables of a term lazily.
+--
+-- We implement a reduce (traversal into monoid) over internal syntax
+-- for a generic collection (monoid with singletons).  This should allow
+-- a more efficient test for the presence of a particular variable.
+--
+-- Worst-case complexity does not change (i.e. the case when a variable
+-- does not occur), but best case-complexity does matter.  For instance,
+-- see 'Agda.TypeChecking.Substitute.mkAbs': each time we construct
+-- a dependent function type, we check whether it is actually dependent.
+--
+-- The distinction between rigid and strongly rigid occurrences comes from:
+--   Jason C. Reed, PhD thesis, 2009, page 96 (see also his LFMTP 2009 paper)
+--
+-- The main idea is that x = t(x) is unsolvable if x occurs strongly rigidly
+-- in t.  It might have a solution if the occurrence is not strongly rigid, e.g.
+--
+--   x = \f -> suc (f (x (\ y -> k)))  has  x = \f -> suc (f (suc k))
+--
+-- [Jason C. Reed, PhD thesis, page 106]
+--
+-- Under coinductive constructors, occurrences are never strongly rigid.
+-- Also, function types and lambdas do not establish strong rigidity.
+-- Only inductive constructors do so.
+-- (See issue 1271).
+--
+-- For further reading on semirings and semimodules for variable occurrence,
+-- see e.g. Conor McBrides "I got plenty of nuttin'" (Wadlerfest 2016).
+-- There, he treats the "quantity" dimension of variable occurrences.
+--
+-- The semiring has an additive operation for combining occurrences of subterms,
+-- and a multiplicative operation of representing function composition.  E.g.
+-- if variable @x@ appears @o@ in term @u@, but @u@ appears in context @q@ in
+-- term @t@ then occurrence of variable @x@ coming from @u@ is accounted for
+-- as @q o@ in @t@.
+--
+-- Consider example @(λ{ x → (x,x)}) y@:
+--
+--   * Variable @x@ occurs once unguarded in @x@.
+--
+--   * It occurs twice unguarded in the aggregation @x@ @x@
+--
+--   * Inductive constructor @,@ turns this into two strictly rigid occurrences.
+--
+--     If @,@ is a record constructor, then we stay unguarded.
+--
+--   * The function @({λ x → (x,x)})@ provides a context for variable @y@.
+--     This context can be described as weakly rigid with quantity two.
+--
+--   * The final occurrence of @y@ is obtained as composing the context with
+--     the occurrence of @y@ in itself (which is the unit for composition).
+--     Thus, @y@ occurs weakly rigid with quantity two.
+--
+-- It is not a given that the context can be described in the same way
+-- as the variable occurrence.  However, for quantity it is the case
+-- and we obtain a semiring of occurrences with 0, 1, and even ω, which
+-- is an absorptive element for addition.
+
+module Agda.TypeChecking.Free.Lazy where
+
+import Control.Applicative hiding (empty)
+import Control.Monad        ( guard )
+import Control.Monad.Reader ( MonadReader(..), asks, ReaderT, Reader, runReader )
+
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as HashSet
+import Data.Semigroup ( Semigroup, (<>) )
+import qualified Data.Set as Set
+import Data.Set (Set)
+
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Semigroup
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+---------------------------------------------------------------------------
+-- * Set of meta variables.
+
+-- | A set of meta variables.  Forms a monoid under union.
+
+newtype MetaSet = MetaSet { theMetaSet :: HashSet MetaId }
+  deriving (Eq, Show, Null, Semigroup, Monoid)
+
+instance Singleton MetaId MetaSet where
+  singleton = MetaSet . singleton
+
+insertMetaSet :: MetaId -> MetaSet -> MetaSet
+insertMetaSet m (MetaSet ms) = MetaSet $ HashSet.insert m ms
+
+foldrMetaSet :: (MetaId -> a -> a) -> a -> MetaSet -> a
+foldrMetaSet f e ms = HashSet.foldr f e $ theMetaSet ms
+
+metaSetToBlocker :: MetaSet -> Blocker
+metaSetToBlocker ms = unblockOnAny $ foldrMetaSet (Set.insert . unblockOnMeta) Set.empty ms
+
+---------------------------------------------------------------------------
+-- * Flexible and rigid occurrences (semigroup)
+
+-- | Depending on the surrounding context of a variable,
+--   it's occurrence can be classified as flexible or rigid,
+--   with finer distinctions.
+--
+--   The constructors are listed in increasing order (wrt. information content).
+data FlexRig' a
+  = Flexible a        -- ^ In arguments of metas.
+                      --   The set of metas is used by ''Agda.TypeChecking.Rewriting.NonLinMatch''
+                      --   to generate the right blocking information.
+                      --   The semantics is that the status of a variable occurrence may change
+                      --   if one of the metas in the set gets solved.  We may say the occurrence
+                      --   is tainted by the meta variables in the set.
+  | WeaklyRigid       -- ^ In arguments to variables and definitions.
+  | Unguarded         -- ^ In top position, or only under inductive record constructors (unit).
+  | StronglyRigid     -- ^ Under at least one and only inductive constructors.
+  deriving (Eq, Show, Functor, Foldable)
+
+type FlexRig = FlexRig' MetaSet
+
+class LensFlexRig o a | o -> a where
+  lensFlexRig :: Lens' o (FlexRig' a)
+
+instance LensFlexRig (FlexRig' a) a where
+  lensFlexRig = id
+
+isFlexible :: LensFlexRig o a => o -> Bool
+isFlexible o = case o ^. lensFlexRig of
+  Flexible {} -> True
+  _ -> False
+
+isUnguarded :: LensFlexRig o a => o -> Bool
+isUnguarded o = case o ^. lensFlexRig of
+  Unguarded -> True
+  _ -> False
+
+isWeaklyRigid :: LensFlexRig o a => o -> Bool
+isWeaklyRigid o = case o ^. lensFlexRig of
+   WeaklyRigid -> True
+   _ -> False
+
+isStronglyRigid :: LensFlexRig o a => o -> Bool
+isStronglyRigid o = case o ^. lensFlexRig of
+  StronglyRigid -> True
+  _ -> False
+
+-- | 'FlexRig' aggregation (additive operation of the semiring).
+--   For combining occurrences of the same variable in subterms.
+--   This is a refinement of the 'max' operation for 'FlexRig'
+--   which would work if 'Flexible' did not have the 'MetaSet' as an argument.
+--   Now, to aggregate two 'Flexible' occurrences, we union the involved 'MetaSet's.
+
+addFlexRig :: Semigroup a => FlexRig' a -> FlexRig' a -> FlexRig' a
+addFlexRig = curry $ \case
+  -- StronglyRigid is dominant
+  (StronglyRigid, _) -> StronglyRigid
+  (_, StronglyRigid) -> StronglyRigid
+  -- Next is Unguarded
+  (Unguarded, _) -> Unguarded
+  (_, Unguarded) -> Unguarded
+  -- Then WeaklyRigid
+  (WeaklyRigid, _) -> WeaklyRigid
+  (_, WeaklyRigid) -> WeaklyRigid
+  -- Least is Flexible.  We union the meta sets, as the variable
+  -- is tainted by all of the involved meta variable.
+  (Flexible ms1, Flexible ms2) -> Flexible $ ms1 <> ms2
+
+-- | Unit for 'addFlexRig'.
+zeroFlexRig :: Monoid a => FlexRig' a
+zeroFlexRig = Flexible mempty
+
+-- | Absorptive for 'addFlexRig'.
+omegaFlexRig :: FlexRig' a
+omegaFlexRig = StronglyRigid
+
+-- | 'FlexRig' composition (multiplicative operation of the semiring).
+--   For accumulating the context of a variable.
+--
+--   'Flexible' is dominant.  Once we are under a meta, we are flexible
+--   regardless what else comes.  We taint all variable occurrences
+--   under a meta by this meta.
+--
+--   'WeaklyRigid' is next in strength.  Destroys strong rigidity.
+--
+--   'StronglyRigid' is still dominant over 'Unguarded'.
+--
+--   'Unguarded' is the unit.  It is the top (identity) context.
+--
+composeFlexRig :: Semigroup a => FlexRig' a -> FlexRig' a -> FlexRig' a
+composeFlexRig = curry $ \case
+    (Flexible ms1, Flexible ms2) -> Flexible $ ms1 <> ms2
+    (Flexible ms1, _) -> Flexible ms1
+    (_, Flexible ms2) -> Flexible ms2
+    (WeaklyRigid, _) -> WeaklyRigid
+    (_, WeaklyRigid) -> WeaklyRigid
+    (StronglyRigid, _) -> StronglyRigid
+    (_, StronglyRigid) -> StronglyRigid
+    (Unguarded, Unguarded) -> Unguarded
+
+-- | Unit for 'composeFlexRig'.
+oneFlexRig :: FlexRig' a
+oneFlexRig = Unguarded
+
+---------------------------------------------------------------------------
+-- * Multi-dimensional feature vector for variable occurrence (semigroup)
+
+-- | Occurrence of free variables is classified by several dimensions.
+--   Currently, we have 'FlexRig' and 'Modality'.
+data VarOcc' a = VarOcc
+  { varFlexRig   :: FlexRig' a
+  , varModality  :: Modality
+  }
+  deriving (Show)
+type VarOcc = VarOcc' MetaSet
+
+-- | Equality up to origin.
+instance Eq a => Eq (VarOcc' a) where
+  VarOcc fr m == VarOcc fr' m' = fr == fr' && sameModality m m'
+
+instance LensModality (VarOcc' a) where
+  getModality = varModality
+  mapModality f (VarOcc x r) = VarOcc x $ f r
+
+instance LensRelevance (VarOcc' a) where
+instance LensQuantity (VarOcc' a) where
+
+-- | Access to 'varFlexRig' in 'VarOcc'.
+instance LensFlexRig (VarOcc' a) a where
+  lensFlexRig f (VarOcc fr m) = f fr <&> \ fr' -> VarOcc fr' m
+-- lensFlexRig :: Lens' (VarOcc' a) (FlexRig' a)
+-- lensFlexRig f (VarOcc fr m) = f fr <&> \ fr' -> VarOcc fr' m
+
+
+-- | The default way of aggregating free variable info from subterms is by adding
+--   the variable occurrences.  For instance, if we have a pair @(t₁,t₂)@ then
+--   and @t₁@ has @o₁@ the occurrences of a variable @x@
+--   and @t₂@ has @o₂@ the occurrences of the same variable, then
+--   @(t₁,t₂)@ has @mappend o₁ o₂@ occurrences of that variable.
+--
+--   From counting 'Quantity', we extrapolate this to 'FlexRig' and 'Relevance':
+--   we care most about about 'StronglyRigid' 'Relevant' occurrences.
+--   E.g., if @t₁@ has a 'StronglyRigid' occurrence and @t₂@ a 'Flexible' occurrence,
+--   then @(t₁,t₂)@ still has a 'StronglyRigid' occurrence.
+--   Analogously, @Relevant@ occurrences count most, as we wish e.g. to forbid
+--   relevant occurrences of variables that are declared to be irrelevant.
+--
+--   'VarOcc' forms a semiring, and this monoid is the addition of the semiring.
+
+instance Semigroup a => Semigroup (VarOcc' a) where
+  VarOcc o m <> VarOcc o' m' = VarOcc (addFlexRig o o') (addModality m m')
+
+-- | The neutral element for variable occurrence aggregation is least serious
+--   occurrence: flexible, irrelevant.
+--   This is also the absorptive element for 'composeVarOcc', if we ignore
+--   the 'MetaSet' in 'Flexible'.
+instance (Semigroup a, Monoid a) => Monoid (VarOcc' a) where
+  mempty  = VarOcc (Flexible mempty) zeroModality
+  mappend = (<>)
+
+-- | The absorptive element of variable occurrence under aggregation:
+--   strongly rigid, relevant.
+topVarOcc :: VarOcc' a
+topVarOcc = VarOcc StronglyRigid topModality
+
+-- | First argument is the outer occurrence (context) and second is the inner.
+--   This multiplicative operation is to modify an occurrence under a context.
+composeVarOcc :: Semigroup a => VarOcc' a -> VarOcc' a -> VarOcc' a
+composeVarOcc (VarOcc o m) (VarOcc o' m') = VarOcc (composeFlexRig o o') (composeModality m m')
+  -- We use the multipicative modality monoid (composition).
+
+oneVarOcc :: VarOcc' a
+oneVarOcc = VarOcc Unguarded unitModality
+
+---------------------------------------------------------------------------
+-- * Storing variable occurrences (semimodule).
+
+-- | Any representation @c@ of a set of variables need to be able to be modified by
+--   a variable occurrence. This is to ensure that free variable analysis is
+--   compositional. For instance, it should be possible to compute `fv (v [u/x])`
+--   from `fv v` and `fv u`.
+--
+--   In algebraic terminology, a variable set @a@ needs to be (almost) a left semimodule
+--   to the semiring 'VarOcc'.
+class (Singleton MetaId a, Semigroup a, Monoid a, Semigroup c, Monoid c) => IsVarSet a c | c -> a where
+  -- | Laws
+  --    * Respects monoid operations:
+  --      ```
+  --        withVarOcc o mempty   == mempty
+  --        withVarOcc o (x <> y) == withVarOcc o x <> withVarOcc o y
+  --      ```
+  --    * Respects VarOcc composition:
+  --      ```
+  --        withVarOcc oneVarOcc             = id
+  --        withVarOcc (composeVarOcc o1 o2) = withVarOcc o1 . withVarOcc o2
+  --      ```
+  --    * Respects VarOcc aggregation:
+  --      ```
+  --        withVarOcc (o1 <> o2) x = withVarOcc o1 x <> withVarOcc o2 x
+  --      ```
+  --      Since the corresponding unit law may fail,
+  --      ```
+  --        withVarOcc mempty x = mempty
+  --      ```
+  --      it is not quite a semimodule.
+  withVarOcc :: VarOcc' a -> c -> c
+
+-- | Representation of a variable set as map from de Bruijn indices
+--   to 'VarOcc'.
+type TheVarMap' a = IntMap (VarOcc' a)
+newtype VarMap' a = VarMap { theVarMap :: TheVarMap' a }
+  deriving (Eq, Show)
+
+type TheVarMap = TheVarMap' MetaSet
+type    VarMap =    VarMap' MetaSet
+
+-- | A "set"-style 'Singleton' instance with default/initial variable occurrence.
+instance Singleton Variable (VarMap' a) where
+  singleton i = VarMap $ IntMap.singleton i oneVarOcc
+
+mapVarMap :: (TheVarMap' a -> TheVarMap' b) -> VarMap' a -> VarMap' b
+mapVarMap f = VarMap . f . theVarMap
+
+lookupVarMap :: Variable -> VarMap' a -> Maybe (VarOcc' a)
+lookupVarMap i = IntMap.lookup i . theVarMap
+
+-- Andreas & Jesper, 2018-05-11, issue #3052:
+
+-- | Proper monoid instance for @VarMap@ rather than inheriting the broken one from IntMap.
+--   We combine two occurrences of a variable using 'mappend'.
+instance Semigroup a => Semigroup (VarMap' a) where
+  VarMap m <> VarMap m' = VarMap $ IntMap.unionWith (<>) m m'
+
+instance Semigroup a => Monoid (VarMap' a) where
+  mempty  = VarMap IntMap.empty
+  mappend = (<>)
+  mconcat = VarMap . IntMap.unionsWith (<>) . map theVarMap
+  -- mconcat = VarMap . IntMap.unionsWith mappend . coerce   -- ghc 8.6.5 does not seem to like this coerce
+
+instance (Singleton MetaId a, Semigroup a, Monoid a) => IsVarSet a (VarMap' a) where
+  withVarOcc o = mapVarMap $ fmap $ composeVarOcc o
+
+
+---------------------------------------------------------------------------
+-- * Simple flexible/rigid variable collection.
+
+-- | Keep track of 'FlexRig' for every variable, but forget the involved meta vars.
+type TheFlexRigMap = IntMap (FlexRig' ())
+newtype FlexRigMap = FlexRigMap { theFlexRigMap :: TheFlexRigMap }
+  deriving (Show, Singleton (Variable, FlexRig' ()))
+
+mapFlexRigMap :: (TheFlexRigMap -> TheFlexRigMap) -> FlexRigMap -> FlexRigMap
+mapFlexRigMap f = FlexRigMap . f . theFlexRigMap
+
+instance Semigroup FlexRigMap where
+  FlexRigMap m <> FlexRigMap m' = FlexRigMap $ IntMap.unionWith addFlexRig m m'
+
+instance Monoid FlexRigMap where
+  mempty  = FlexRigMap IntMap.empty
+  mappend = (<>)
+  mconcat = FlexRigMap . IntMap.unionsWith addFlexRig . map theFlexRigMap
+
+-- | Compose everything with the 'varFlexRig' part of the 'VarOcc'.
+instance IsVarSet () FlexRigMap where
+  withVarOcc o = mapFlexRigMap $ fmap $ composeFlexRig $ () <$ varFlexRig o
+
+instance Singleton MetaId () where
+  singleton _ = ()
+
+---------------------------------------------------------------------------
+-- * Environment for collecting free variables.
+
+-- | Where should we skip sorts in free variable analysis?
+
+data IgnoreSorts
+  = IgnoreNot            -- ^ Do not skip.
+  | IgnoreInAnnotations  -- ^ Skip when annotation to a type.
+  | IgnoreAll            -- ^ Skip unconditionally.
+  deriving (Eq, Show)
+
+-- | The current context.
+
+data FreeEnv' a b c = FreeEnv
+  { feExtra     :: !b
+    -- ^ Additional context, e.g., whether to ignore free variables in sorts.
+  , feFlexRig   :: !(FlexRig' a)
+    -- ^ Are we flexible or rigid?
+  , feModality  :: !Modality
+    -- ^ What is the current relevance and quantity?
+  , feSingleton :: Maybe Variable -> c
+    -- ^ Method to return a single variable.
+  }
+
+type Variable    = Int
+type SingleVar c = Variable -> c
+
+type FreeEnv c = FreeEnv' MetaSet IgnoreSorts c
+
+-- | Ignore free variables in sorts.
+feIgnoreSorts :: FreeEnv' a IgnoreSorts c -> IgnoreSorts
+feIgnoreSorts = feExtra
+
+instance LensFlexRig (FreeEnv' a b c) a where
+  lensFlexRig f e = f (feFlexRig e) <&> \ fr -> e { feFlexRig = fr }
+
+instance LensModality (FreeEnv' a b c) where
+  getModality = feModality
+  mapModality f e = e { feModality = f (feModality e) }
+
+instance LensRelevance (FreeEnv' a b c) where
+instance LensQuantity (FreeEnv' a b c) where
+
+-- | The initial context.
+
+initFreeEnv :: Monoid c => b -> SingleVar c -> FreeEnv' a b c
+initFreeEnv e sing = FreeEnv
+  { feExtra       = e
+  , feFlexRig     = Unguarded
+  , feModality    = unitModality      -- multiplicative monoid
+  , feSingleton   = maybe mempty sing
+  }
+
+type FreeT a b m c = ReaderT (FreeEnv' a b c) m c
+type FreeM a c = Reader (FreeEnv' a IgnoreSorts c) c
+
+-- | Run function for FreeM.
+runFreeM :: IsVarSet a c => SingleVar c -> IgnoreSorts -> FreeM a c -> c
+runFreeM single i m = runReader m $ initFreeEnv i single
+
+instance (Functor m, Applicative m, Monad m, Semigroup c, Monoid c) => Monoid (FreeT a b m c) where
+  mempty  = pure mempty
+  mappend = (<>)
+  mconcat = mconcat <.> sequence
+
+-- | Base case: a variable.
+variable :: (Monad m, IsVarSet a c) => Int -> FreeT a b m c
+variable n = do
+  o <- asks feFlexRig
+  r <- asks feModality
+  s <- asks feSingleton
+  return $ withVarOcc (VarOcc o r) (s $ Just n)
+
+-- | Subtract, but return Nothing if result is negative.
+subVar :: Int -> Maybe Variable -> Maybe Variable
+-- subVar n x = x >>= \ i -> (i - n) <$ guard (n <= i)
+subVar n x = do
+  i <- x
+  guard $ i >= n
+  return $ i - n
+
+-- | Going under a binder.
+underBinder :: MonadReader (FreeEnv' a b c) m => m z -> m z
+underBinder = underBinder' 1
+
+-- | Going under @n@ binders.
+underBinder' :: MonadReader (FreeEnv' a b c) m => Nat -> m z -> m z
+underBinder' n = local $ \ e -> e { feSingleton = feSingleton e . subVar n }
+
+-- | Changing the 'Modality'.
+underModality :: (MonadReader r m, LensModality r, LensModality o) => o -> m z -> m z
+underModality = local . mapModality . composeModality . getModality
+
+-- | Changing the 'Relevance'.
+underRelevance :: (MonadReader r m, LensRelevance r, LensRelevance o) => o -> m z -> m z
+underRelevance = local . mapRelevance . composeRelevance . getRelevance
+
+-- | In the given computation the 'Quantity' is locally scaled using
+-- the 'Quantity' of the first argument.
+underQuantity ::
+  (MonadReader r m, LensQuantity r, LensQuantity o) => o -> m a -> m a
+underQuantity = local . mapQuantity . composeQuantity . getQuantity
+
+-- | Changing the 'FlexRig' context.
+underFlexRig :: (MonadReader r m, LensFlexRig r a, Semigroup a, LensFlexRig o a) => o -> m z -> m z
+underFlexRig = local . over lensFlexRig . composeFlexRig . view lensFlexRig
+
+-- | What happens to the variables occurring under a constructor?
+underConstructor :: (MonadReader r m, LensFlexRig r a, Semigroup a) => ConHead -> Elims -> m z -> m z
+underConstructor (ConHead _c _d i fs) es =
+  case i of
+    -- Coinductive (record) constructors admit infinite cycles:
+    CoInductive -> underFlexRig WeaklyRigid
+    -- Inductive constructors do not admit infinite cycles:
+    Inductive   | natSize es == natSize fs -> underFlexRig StronglyRigid
+                | otherwise                -> underFlexRig WeaklyRigid
+    -- Jesper, 2020-10-22: Issue #4995: treat occurrences in non-fully
+    -- applied constructors as weakly rigid.
+    -- Ulf, 2019-10-18: Now the termination checker treats inductive recursive records
+    -- the same as datatypes, so absense of infinite cycles can be proven in Agda, and thus
+    -- the unifier is allowed to do it too. Test case: test/Succeed/Issue1271a.agda
+    -- WAS:
+    -- -- Inductive record constructors do not admit infinite cycles,
+    -- -- but this cannot be proven inside Agda.
+    -- -- Thus, unification should not prove it either.
+
+---------------------------------------------------------------------------
+-- * Recursively collecting free variables.
+
+-- | Gather free variables in a collection.
+class Free t where
+  -- Misplaced SPECIALIZE pragma:
+  -- {-# SPECIALIZE freeVars' :: a -> FreeM Any #-}
+  -- So you cannot specialize all instances in one go. :(
+  freeVars' :: IsVarSet a c => t -> FreeM a c
+
+  default freeVars' :: (t ~ f b, Foldable f, Free b) => IsVarSet a c => t -> FreeM a c
+  freeVars' = foldMap freeVars'
+
+
+instance Free Term where
+  -- SPECIALIZE instance does not work as well, see
+  -- https://ghc.haskell.org/trac/ghc/ticket/10434#ticket
+  -- {-# SPECIALIZE instance Free Term All #-}
+  -- {-# SPECIALIZE freeVars' :: Term -> FreeM Any #-}
+  -- {-# SPECIALIZE freeVars' :: Term -> FreeM All #-}
+  -- {-# SPECIALIZE freeVars' :: Term -> FreeM VarSet #-}
+  freeVars' t = case unSpine t of -- #4484: unSpine to avoid projected variables being treated as StronglyRigid
+    Var n ts     -> variable n `mappend` do underFlexRig WeaklyRigid $ freeVars' ts
+    -- λ is not considered guarding, as
+    -- we cannot prove that x ≡ λy.x is impossible.
+    Lam _ t      -> underFlexRig WeaklyRigid $ freeVars' t
+    Lit _        -> mempty
+    Def _ ts     -> underFlexRig WeaklyRigid $ freeVars' ts  -- because we are not in TCM
+      -- we cannot query whether we are dealing with a data/record (strongly r.)
+      -- or a definition by pattern matching (weakly rigid)
+      -- thus, we approximate, losing that x = List x is unsolvable
+    Con c _ ts   -> underConstructor c ts $ freeVars' ts
+    -- Pi is not guarding, since we cannot prove that A ≡ B → A is impossible.
+    -- Even as we do not permit infinite type expressions,
+    -- we cannot prove their absence (as Set is not inductive).
+    -- Also, this is incompatible with univalence (HoTT).
+    Pi a b       -> freeVars' (a,b)
+    Sort s       -> freeVars' s
+    Level l      -> freeVars' l
+    MetaV m ts   -> underFlexRig (Flexible $ singleton m) $ freeVars' ts
+    DontCare mt  -> underModality (Modality Irrelevant unitQuantity unitCohesion) $ freeVars' mt
+    Dummy{}      -> mempty
+
+instance Free t => Free (Type' t) where
+  freeVars' (El s t) =
+    ifM (asks ((IgnoreNot ==) . feIgnoreSorts))
+      {- then -} (freeVars' (s, t))
+      {- else -} (freeVars' t)
+
+instance Free Sort where
+  freeVars' s =
+    ifM (asks ((IgnoreAll ==) . feIgnoreSorts)) mempty $ {- else -}
+    case s of
+      Univ _ a   -> freeVars' a
+      Inf _ _    -> mempty
+      SizeUniv   -> mempty
+      LockUniv   -> mempty
+      LevelUniv  -> mempty
+      IntervalUniv -> mempty
+      PiSort a s1 s2 -> underFlexRig (Flexible mempty) (freeVars' $ unDom a) `mappend`
+                        underFlexRig WeaklyRigid (freeVars' (s1, s2))
+      FunSort s1 s2 -> freeVars' s1 `mappend` freeVars' s2
+      UnivSort s -> underFlexRig WeaklyRigid $ freeVars' s
+      MetaS x es -> underFlexRig (Flexible $ singleton x) $ freeVars' es
+      DefS _ es  -> underFlexRig WeaklyRigid $ freeVars' es
+      DummyS{}   -> mempty
+
+instance Free Level where
+  freeVars' (Max _ as) = freeVars' as
+
+instance Free t => Free (PlusLevel' t) where
+  freeVars' (Plus _ l)    = freeVars' l
+
+instance Free t => Free [t]            where
+instance Free t => Free (Maybe t)      where
+instance Free t => Free (WithHiding t) where
+instance Free t => Free (Named nm t)
+
+instance (Free t, Free u) => Free (t, u) where
+  freeVars' (t, u) = freeVars' t `mappend` freeVars' u
+
+instance (Free t, Free u, Free v) => Free (t, u, v) where
+  freeVars' (t, u, v) = freeVars' t `mappend` freeVars' u `mappend` freeVars' v
+
+instance Free t => Free (Elim' t) where
+  freeVars' (Apply t) = freeVars' t
+  freeVars' (Proj{} ) = mempty
+  freeVars' (IApply x y r) = freeVars' (x,y,r)
+
+instance Free t => Free (Arg t) where
+  freeVars' t = underModality (getModality t) $ freeVars' $ unArg t
+
+instance Free t => Free (Dom t) where
+  freeVars' d = freeVars' (domTactic d, unDom d)
+
+instance Free t => Free (Abs t) where
+  freeVars' (Abs   _ b) = underBinder $ freeVars' b
+  freeVars' (NoAbs _ b) = freeVars' b
+
+instance Free t => Free (Tele t) where
+  freeVars' EmptyTel          = mempty
+  freeVars' (ExtendTel t tel) = freeVars' (t, tel)
+
+instance Free Clause where
+  freeVars' cl = underBinder' (size $ clauseTel cl) $ freeVars' $ clauseBody cl
+
+instance Free EqualityView where
+  freeVars' = \case
+    OtherType t -> freeVars' t
+    IdiomType t -> freeVars' t
+    EqualityType s _eq l t a b -> freeVars' (s, l, [t, a, b])
diff --git a/src/full/Agda/TypeChecking/Free/Precompute.hs b/src/full/Agda/TypeChecking/Free/Precompute.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Free/Precompute.hs
@@ -0,0 +1,115 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Precompute free variables in a term (and store in 'ArgInfo').
+module Agda.TypeChecking.Free.Precompute
+  ( PrecomputeFreeVars, precomputeFreeVars
+  , precomputedFreeVars, precomputeFreeVars_ ) where
+
+import Control.Monad.Writer
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+
+
+type FV = Writer IntSet
+
+precomputeFreeVars_ :: PrecomputeFreeVars a => a -> a
+precomputeFreeVars_ = fst . runWriter . precomputeFreeVars
+
+precomputedFreeVars :: PrecomputeFreeVars a => a -> IntSet
+precomputedFreeVars = snd . runWriter . precomputeFreeVars
+
+class PrecomputeFreeVars a where
+  precomputeFreeVars :: a -> FV a
+
+  default precomputeFreeVars :: (Traversable c, PrecomputeFreeVars x, a ~ c x) => a -> FV a
+  precomputeFreeVars = traverse precomputeFreeVars
+
+-- The instances where things actually happen: Arg, Abs and Term.
+
+maybePrecomputed :: PrecomputeFreeVars a => ArgInfo -> a -> FV (ArgInfo, a)
+maybePrecomputed i x =
+  case getFreeVariables i of
+    KnownFVs fv -> (i, x) <$ tell fv
+    UnknownFVs -> do
+      (x', fv) <- listen $ precomputeFreeVars x
+      return (setFreeVariables (KnownFVs fv) i, x')
+
+instance PrecomputeFreeVars a => PrecomputeFreeVars (Arg a) where
+  precomputeFreeVars arg@(Arg i x) = uncurry Arg <$> maybePrecomputed i x
+
+-- Note that we don't store free variables in the Dom. The reason is that the
+-- ArgInfo in the Dom tends to get reused during type checking for the argument
+-- of that domain type, and it would be tedious and error prone to ensure that
+-- we don't accidentally inherit also the free variables. Moreover we don't
+-- really need the free variables of the Dom.
+instance PrecomputeFreeVars a => PrecomputeFreeVars (Dom a) where
+
+instance PrecomputeFreeVars a => PrecomputeFreeVars (Abs a) where
+  precomputeFreeVars (NoAbs x b) = NoAbs x <$> precomputeFreeVars b
+  precomputeFreeVars (Abs x b) =
+    censor (IntSet.map (subtract 1) . IntSet.delete 0) $
+      Abs x <$> precomputeFreeVars b
+
+instance PrecomputeFreeVars Term where
+  precomputeFreeVars t =
+    case t of
+      Var x es -> do
+        tell (IntSet.singleton x)
+        Var x <$> precomputeFreeVars es
+      Lam i b    -> Lam i      <$> precomputeFreeVars b
+      Lit{}      -> pure t
+      Def f es   -> Def f      <$> precomputeFreeVars es
+      Con c i es -> Con c i    <$> precomputeFreeVars es
+      Pi a b     -> uncurry Pi <$> precomputeFreeVars (a, b)
+      Sort s     -> Sort       <$> precomputeFreeVars s
+      Level l    -> Level      <$> precomputeFreeVars l
+      MetaV x es -> MetaV x    <$> precomputeFreeVars es
+      DontCare t -> DontCare   <$> precomputeFreeVars t
+      Dummy{}    -> pure t
+
+-- The other instances are boilerplate.
+
+instance PrecomputeFreeVars Sort where
+  precomputeFreeVars s =
+    case s of
+      Univ u a   -> Univ u <$> precomputeFreeVars a
+      Inf _ _    -> pure s
+      SizeUniv   -> pure s
+      LockUniv   -> pure s
+      LevelUniv  -> pure s
+      IntervalUniv -> pure s
+      PiSort a s1 s2 -> PiSort <$> precomputeFreeVars a <*> precomputeFreeVars s1 <*> precomputeFreeVars s2
+      FunSort s1 s2 -> uncurry FunSort <$> precomputeFreeVars (s1, s2)
+      UnivSort s -> UnivSort <$> precomputeFreeVars s
+      MetaS x es -> MetaS x <$> precomputeFreeVars es
+      DefS d es  -> DefS d <$> precomputeFreeVars es
+      DummyS{}   -> pure s
+
+instance PrecomputeFreeVars Level where
+  precomputeFreeVars (Max n ls) = Max n <$> precomputeFreeVars ls
+
+instance PrecomputeFreeVars PlusLevel where
+  precomputeFreeVars (Plus n l) = Plus n <$> precomputeFreeVars l
+
+instance PrecomputeFreeVars Type where
+  precomputeFreeVars (El s t) = uncurry El <$> precomputeFreeVars (s, t)
+
+-- Note: don't use default instance, since that bypasses the 'Arg' in 'Apply'.
+instance PrecomputeFreeVars a => PrecomputeFreeVars (Elim' a) where
+  precomputeFreeVars e =
+    case e of
+      Apply x      -> Apply <$> precomputeFreeVars x
+      IApply a x y -> IApply <$> precomputeFreeVars a <*> precomputeFreeVars x <*> precomputeFreeVars y
+      Proj{}       -> pure e
+
+-- The very boilerplate instances
+
+instance PrecomputeFreeVars a => PrecomputeFreeVars [a] where
+instance PrecomputeFreeVars a => PrecomputeFreeVars (Maybe a) where
+
+instance (PrecomputeFreeVars a, PrecomputeFreeVars b) => PrecomputeFreeVars (a, b) where
+  precomputeFreeVars (x, y) = (,) <$> precomputeFreeVars x <*> precomputeFreeVars y
diff --git a/src/full/Agda/TypeChecking/Free/Reduce.hs b/src/full/Agda/TypeChecking/Free/Reduce.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Free/Reduce.hs
@@ -0,0 +1,189 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Free variable check that reduces the subject to make certain variables not
+--   free. Used when pruning metavariables in Agda.TypeChecking.MetaVars.Occurs.
+module Agda.TypeChecking.Free.Reduce
+  ( ForceNotFree
+  , forceNotFree
+  , reallyFree
+  , IsFree(..)
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad.Reader
+import Control.Monad.State
+
+import qualified Data.IntMap as IntMap
+import Data.IntMap (IntMap)
+import qualified Data.IntSet as IntSet
+import Data.IntSet (IntSet)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Free.Precompute
+
+import Agda.Utils.Monad
+import Agda.Utils.Null
+
+-- | A variable can either not occur (`NotFree`) or it does occur
+--   (`MaybeFree`).  In the latter case, the occurrence may disappear
+--   depending on the instantiation of some set of metas.
+data IsFree
+  = MaybeFree MetaSet
+  | NotFree
+  deriving (Eq, Show)
+
+-- | Try to enforce a set of variables not occurring in a given
+--   type. Returns a possibly reduced version of the type and for each
+--   of the given variables whether it is either not free, or
+--   maybe free depending on some metavariables.
+forceNotFree :: (ForceNotFree a, Reduce a, MonadReduce m)
+             => IntSet -> a -> m (IntMap IsFree, a)
+forceNotFree xs a = do
+  -- Initially, all variables are marked as `NotFree`. This is changed
+  -- to `MaybeFree` when we find an occurrence.
+  let mxs = IntMap.fromSet (const NotFree) xs
+  (a, mxs) <- runStateT (runReaderT (forceNotFreeR $ precomputeFreeVars_ a) mempty) mxs
+  return (mxs, a)
+
+-- | Checks if the given term contains any free variables that are in
+--   the given set of variables, possibly reducing the term in the
+--   process.  Returns `Right Nothing` if there are such variables,
+--   `Right (Just v')` if there are none (where v' is the possibly
+--   reduced version of the given term) or `Left b` if the problem is
+--   blocked on a meta.
+reallyFree :: (MonadReduce m, Reduce a, ForceNotFree a)
+           => IntSet -> a -> m (Either Blocked_ (Maybe a))
+reallyFree xs v = do
+  (mxs , v') <- forceNotFree xs v
+  case IntMap.foldr pickFree NotFree mxs of
+    MaybeFree ms
+      | null ms   -> return $ Right Nothing
+      | otherwise -> return $ Left $ Blocked blocker ()
+      where blocker = metaSetToBlocker ms
+    NotFree -> return $ Right (Just v')
+
+  where
+    -- Check if any of the variables occur freely.
+    -- Prefer occurrences that do not depend on any metas.
+    pickFree :: IsFree -> IsFree -> IsFree
+    pickFree f1@(MaybeFree ms1) f2
+      | null ms1  = f1
+    pickFree f1@(MaybeFree ms1) f2@(MaybeFree ms2)
+      | null ms2  = f2
+      | otherwise = f1
+    pickFree f1@(MaybeFree ms1) NotFree = f1
+    pickFree NotFree f2 = f2
+
+type MonadFreeRed m =
+  ( MonadReader MetaSet m
+  , MonadState (IntMap IsFree) m
+  , MonadReduce m
+  )
+
+class (PrecomputeFreeVars a, Subst a) => ForceNotFree a where
+  -- Reduce the argument if necessary, to make as many as possible of
+  -- the variables in the state not free. Updates the state, marking
+  -- the variables that couldn't be make not free as `MaybeFree`. By
+  -- updating the state as soon as a variable can not be reduced away,
+  -- we avoid trying to get rid of it in other places.
+  forceNotFree' :: (MonadFreeRed m) => a -> m a
+
+-- Return the set of variables for which there is still hope that they
+-- may not occur.
+varsToForceNotFree :: (MonadFreeRed m) => m IntSet
+varsToForceNotFree = gets (IntMap.keysSet . (IntMap.filter (== NotFree)))
+
+-- Reduce the argument if there are offending free variables. Doesn't call the
+-- continuation when no reduction is required.
+reduceIfFreeVars :: (Reduce a, ForceNotFree a, MonadFreeRed m)
+                 => (a -> m a) -> a -> m a
+reduceIfFreeVars k a = do
+  xs <- varsToForceNotFree
+  let fvs     = precomputedFreeVars a
+      notfree = IntSet.disjoint xs fvs
+  if notfree
+    then return a
+    else k . precomputeFreeVars_ =<< reduce a
+
+-- Careful not to define forceNotFree' = forceNotFreeR since that would loop.
+forceNotFreeR :: (Reduce a, ForceNotFree a, MonadFreeRed m)
+              => a -> m a
+forceNotFreeR = reduceIfFreeVars forceNotFree'
+
+instance (Reduce a, ForceNotFree a) => ForceNotFree (Arg a) where
+  -- Precomputed free variables are stored in the Arg so reduceIf outside the
+  -- traverse.
+  forceNotFree' = reduceIfFreeVars (traverse forceNotFree')
+
+instance (Reduce a, ForceNotFree a, TermSubst a) => ForceNotFree (Dom a) where
+  forceNotFree' = traverse forceNotFreeR
+
+instance (Reduce a, ForceNotFree a) => ForceNotFree (Abs a) where
+  -- Reduction stops at abstractions (lambda/pi) so do reduceIf/forceNotFreeR here.
+  forceNotFree' a@NoAbs{} = traverse forceNotFreeR a
+  forceNotFree' a@Abs{} =
+    -- Shift variables up when going under the abstraction and back down when
+    -- coming out of it. Since we never add new indices to the state
+    -- there's no danger of getting negative indices.
+    reduceIfFreeVars (bracket_ (modify $ IntMap.mapKeys succ) (\ _ -> modify $ IntMap.mapKeys pred) .
+                      traverse forceNotFree') a
+
+instance ForceNotFree a => ForceNotFree [a] where
+  forceNotFree' = traverse forceNotFree'
+
+instance (Reduce a, ForceNotFree a) => ForceNotFree (Elim' a) where
+  -- There's an Arg inside Elim' which stores precomputed free vars, so let's
+  -- not skip over that.
+  forceNotFree' (Apply arg)    = Apply <$> forceNotFree' arg
+  forceNotFree' e@Proj{}       = return e
+  forceNotFree' (IApply x y r) = IApply <$> forceNotFreeR x <*> forceNotFreeR y <*> forceNotFreeR r
+
+instance ForceNotFree Type where
+  forceNotFree' (El s t) = El <$> forceNotFree' s <*> forceNotFree' t
+
+instance ForceNotFree Term where
+  forceNotFree' = \case
+    Var x es   -> do
+      metas <- ask
+      modify $ IntMap.adjust (const $ MaybeFree metas) x
+      Var x <$> forceNotFree' es
+    Def f es   -> Def f    <$> forceNotFree' es
+    Con c h es -> Con c h  <$> forceNotFree' es
+    MetaV x es -> local (insertMetaSet x) $
+                  MetaV x  <$> forceNotFree' es
+    Lam h b    -> Lam h    <$> forceNotFree' b
+    Pi a b     -> Pi       <$> forceNotFree' a <*> forceNotFree' b  -- Dom and Abs do reduceIf so not needed here
+    Sort s     -> Sort     <$> forceNotFree' s
+    Level l    -> Level    <$> forceNotFree' l
+    DontCare t -> DontCare <$> forceNotFreeR t  -- Reduction stops at DontCare so reduceIf
+    t@Lit{}    -> return t
+    t@Dummy{}  -> return t
+
+instance ForceNotFree Level where
+  forceNotFree' (Max m as) = Max m <$> forceNotFree' as
+
+instance ForceNotFree PlusLevel where
+  forceNotFree' (Plus k a) = Plus k <$> forceNotFree' a
+
+instance ForceNotFree Sort where
+  -- Reduce for sorts already goes under all sort constructors, so we can get
+  -- away without forceNotFreeR here.
+  forceNotFree' = \case
+    Univ u l     -> Univ u <$> forceNotFree' l
+    PiSort a b c -> PiSort <$> forceNotFree' a <*> forceNotFree' b <*> forceNotFree' c
+    FunSort a b -> FunSort <$> forceNotFree' a <*> forceNotFree' b
+    UnivSort s -> UnivSort <$> forceNotFree' s
+    MetaS x es -> MetaS x  <$> forceNotFree' es
+    DefS d es  -> DefS d   <$> forceNotFree' es
+    s@(Inf _ _)-> return s
+    s@SizeUniv -> return s
+    s@LockUniv -> return s
+    s@LevelUniv -> return s
+    s@IntervalUniv -> return s
+    s@DummyS{} -> return s
diff --git a/src/full/Agda/TypeChecking/Functions.hs b/src/full/Agda/TypeChecking/Functions.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Functions.hs
@@ -0,0 +1,101 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Functions
+  ( etaExpandClause
+  , getDef
+  ) where
+
+import Control.Arrow ( first )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Impossible
+import Agda.Utils.Functor ( ($>) )
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Monad
+import Agda.Utils.Size
+
+
+-- | Expand a clause to the maximal arity, by inserting variable
+--   patterns and applying the body to variables.
+
+--  Fixes issue #2376.
+--  Replaces 'introHiddenLambdas'.
+--  See, e.g., test/Succeed/SizedTypesExtendedLambda.agda.
+
+--  This is used instead of special treatment of lambdas
+--  (which was unsound: Issue #121)
+
+etaExpandClause :: MonadTCM tcm => Clause -> tcm Clause
+etaExpandClause clause = liftTCM $ do
+  case clause of
+    Clause _  _  ctel ps _           Nothing  _ _ _ _ _ _ -> return clause
+    Clause _  _  ctel ps Nothing     (Just t) _ _ _ _ _ _ -> return clause
+    Clause rl rf ctel ps (Just body) (Just t) catchall exact recursive unreachable ell wm -> do
+
+      -- Get the telescope to expand the clause with.
+      TelV tel0 t' <- addContext ctel $ telView $ unArg t
+
+      -- If the rhs has lambdas, harvest the names of the bound variables.
+      let xs   = peekLambdas body
+      let ltel = useNames xs $ telToList tel0
+      let tel  = telFromList ltel
+      let n    = size tel
+      unless (n == size tel0) __IMPOSSIBLE__  -- useNames should not drop anything
+      -- Join with lhs telescope, extend patterns and apply body.
+      -- NB: no need to raise ctel!
+      let ctel' = telFromList $ telToList ctel ++ ltel
+          ps'   = raise n ps ++ teleNamedArgs tel
+          body' = raise n body `apply` teleArgs tel
+      reportSDoc "term.clause.expand" 30 $ inTopContext $ vcat
+        [ "etaExpandClause"
+        , "  body    = " <+> addContext ctel' (prettyTCM body)
+        , "  xs      = " <+> text (prettyShow xs)
+        , "  new tel = " <+> prettyTCM ctel'
+        ]
+      return $ Clause rl rf ctel' ps' (Just body') (Just (t $> t')) catchall exact recursive unreachable ell wm
+  where
+    -- Get all initial lambdas of the body.
+    peekLambdas :: Term -> [Arg ArgName]
+    peekLambdas v =
+      case v of
+        Lam info b -> Arg info (absName b) : peekLambdas (unAbs b)
+        _ -> []
+
+    -- Use the names of the first argument, and set the Origin all other
+    -- parts of the telescope to Inserted.
+    -- The first list of arguments is a subset of the telescope.
+    -- Thus, if compared pointwise, if the hiding does not match,
+    -- it means we skipped an element of the telescope.
+    useNames :: [Arg ArgName] -> ListTel -> ListTel
+    useNames []     tel       = map (setOrigin Inserted) tel
+    -- Andrea: we can have more Lam's than Pi's, because they might be for Path
+    -- Andreas, 2017-03-24: the following case is not IMPOSSIBLE when positivity checking comes before termination checking, see examples/tactics/ac/AC.agda
+    useNames (_:_)  []        = []
+    useNames (x:xs) (dom:tel)
+      | sameHiding x dom =
+          -- set the ArgName of the dom
+          fmap (first $ const $ unArg x) dom : useNames xs tel
+      | otherwise =
+          setOrigin Inserted dom : useNames (x:xs) tel
+
+-- | Get the name of defined symbol of the head normal form of a term.
+--   Returns 'Nothing' if no such head exists.
+
+getDef :: Term -> TCM (Maybe QName)
+getDef t = reduce t >>= \case
+  Def d _    -> return $ Just d
+  Lam _ v    -> underAbstraction_ v getDef
+  Level v    -> getDef =<< reallyUnLevelView v
+  DontCare v -> getDef v
+  _          -> return Nothing
diff --git a/src/full/Agda/TypeChecking/Generalize.hs b/src/full/Agda/TypeChecking/Generalize.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Generalize.hs
@@ -0,0 +1,1020 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-|
+
+This module implements the type checking part of generalisable variables. When we get here we have
+a type checking problem for a type (or telescope) containing a known set of generalisable variables
+and we need to produce a well typed type (or telescope) with the correct generalisations. For instance,
+given
+
+@
+variable
+  A  : Set
+  n  : Nat
+  xs : Vec A n
+
+foo : SomeType xs
+@
+
+generalisation should produce @{A : Set} {n : Nat} {xs : Vec A n} → SomeType xs@ for the type of
+@foo@.
+
+The functions `generalizeType` and `generalizeTelescope` don't have access to the abstract syntax to
+be type checked (@SomeType xs@ in the example). Instead they are provided a type checking action
+that delivers a `Type` or a `Telescope`. The challenge is setting up a context in which @SomeType
+xs@ can be type checked successfully by this action, without knowing what the telescope of
+generalised variables will be. Once we have computed this telescope the result needs to be
+transformed into a well typed type abstracted over it.
+
+__At no point are we allowed to cheat!__ Any transformation between well typed terms needs to be done
+by well typed substitutions.
+
+The key idea is to run the type checking action in the context of a single variable of an unknown
+type. Once we know what variables to generalise over this type is instantiated to a fresh record
+type with a field for each generalised variable. Turning the result of action into something valid
+in the context of the generalised variables is then a simple substitution unpacking the record
+variable.
+
+In more detail, generalisation proceeds as follows:
+
+- Add a variable @genTel@ of an unknown type to the context (`withGenRecVar`).
+
+@
+  (genTel : _GenTel)
+@
+
+- Create metavariables for the generalisable variables appearing in the problem and their
+  dependencies (`createGenValues`). In the example this would be
+
+@
+  (genTel : _GenTel) ⊢
+    _A  : Set
+    _n  : Nat
+    _xs : Vec _A _n
+@
+
+- Run the type checking action (`createMetasAndTypeCheck`), binding the mentioned generalisable
+  variables to the corresponding newly created metavariables. This binding is stored in
+  `eGeneralizedVars` and picked up in `Agda.TypeChecking.Rules.Application.inferDef`
+
+@
+  (genTel : _GenTel) ⊢ SomeType (_xs genTel)
+@
+
+- Compute the telescope of generalised variables (`computeGeneralization`). This is done by taking
+  the unconstrained metavariables created by `createGenValues` or created during the type checking
+  action and sorting them into a well formed telescope.
+
+@
+  {A : Set} {n : Nat} {xs : Vec A n}
+@
+
+- Create a record type @GeneralizeTel@ whose fields are the generalised variables and instantiate
+  the type of @genTel@ to it (`createGenRecordType`).
+
+@
+  record GeneralizeTel : Set₁ where
+    constructor mkGeneralizeTel
+    field
+      A  : Set
+      n  : Nat
+      xs : Vec A n
+@
+
+- Solve the metavariables with their corresponding projections from @genTel@.
+
+@
+  _A  := λ genTel → genTel .A
+  _n  := λ genTel → genTel .n
+  _xs := λ genTel → genTel .xs
+@
+
+- Build the unpacking substitution (`unpackSub`) that maps terms in @(genTel : GeneralizeTel)@ to
+  terms in the context of the generalised variables by substituting a record value for @genTel@.
+
+@
+  {A : Set} {n : Nat} {xs : Vec A n} ⊢ [mkGeneralizeTel A n xs / genTel] : (genTel : GeneralizeTel)
+@
+
+- Build the final result by applying the unpacking substitution to the result of the type checking
+  action and abstracting over the generalised telescope.
+
+@
+  {A : Set} {n : Nat} {xs : Vec A n} → SomeType (_xs (mkGeneralizeTel A n xs)) ==
+  {A : Set} {n : Nat} {xs : Vec A n} → SomeType xs
+@
+
+- In case of `generalizeType` return the resulting pi type.
+- In case of `generalizeTelescope` enter the resulting context, applying the unpacking substitution
+  to let bindings (TODO #6916: and also module applications!) created in the telescope, and call the
+  continuation.
+
+-}
+
+module Agda.TypeChecking.Generalize
+  ( generalizeType
+  , generalizeType'
+  , generalizeTelescope ) where
+
+import Prelude hiding (null)
+
+import Control.Arrow ((&&&), first)
+import Control.Monad
+import Control.Monad.Except
+
+import qualified Data.IntSet as IntSet
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Map.Strict as MapS
+import Data.List (partition, sortBy)
+import Data.Monoid
+import Data.Function (on)
+
+import Agda.Interaction.Options.Base
+
+import Agda.Syntax.Common
+import Agda.Syntax.Common.Pretty (prettyShow, singPlural)
+import Agda.Syntax.Concrete.Name (LensInScope(..))
+import Agda.Syntax.Position
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Scope.Monad (bindVariable, outsideLocalVars)
+import Agda.Syntax.Scope.Base (BindingSource(..))
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.InstanceArguments (postponeInstanceConstraints)
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+
+import Agda.Benchmarking (Phase(Typing, Generalize))
+import Agda.Utils.Benchmark
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+import Agda.Utils.List (downFrom, hasElem)
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Size
+import Agda.Utils.Permutation
+
+-- | Generalize a telescope over a set of generalizable variables.
+generalizeTelescope :: Map QName Name -> (forall a. (Telescope -> TCM a) -> TCM a) -> ([Maybe Name] -> Telescope -> TCM a) -> TCM a
+generalizeTelescope vars typecheckAction ret | Map.null vars = typecheckAction (ret [])
+generalizeTelescope vars typecheckAction ret = billTo [Typing, Generalize] $ withGenRecVar $ \ genRecMeta -> do
+  let s = Map.keysSet vars
+  ((cxtNames, tel, letbinds), namedMetas, allmetas) <-
+    createMetasAndTypeCheck s $ typecheckAction $ \ tel -> do
+      cxt <- take (size tel) <$> getContext
+      lbs <- getLetBindings -- This gives let-bindings valid in the current context
+      return (map (fst . unDom) cxt, tel, lbs)
+
+  reportSDoc "tc.generalize.metas" 60 $ vcat
+    [ "open metas =" <+> (text . show . fmap ((miNameSuggestion &&& miGeneralizable) . mvInfo)) (openMetas $ allmetas)
+    ]
+  -- Translate the QName to the corresponding bound variable
+  (genTel, genTelNames, sub) <- computeGeneralization genRecMeta namedMetas allmetas
+
+  let boundVar q = fromMaybe __IMPOSSIBLE__ $ Map.lookup q vars
+      genTelVars = (map . fmap) boundVar genTelNames
+
+  tel' <- applySubst sub <$> instantiateFull tel
+
+  -- This is not so nice. When changing the context from Γ (r : R) to Γ Δ we need to do this at the
+  -- level of contexts (as a Context -> Context function), so we repeat the name logic here. Take
+  -- care to preserve the name of named generalized variables.
+  let setName name d = first (const name) <$> d
+      cxtEntry (mname, d) = do
+          name <- maybe (setNotInScope <$> freshName_ s) return mname
+          return $ setName name d
+        where s  = fst $ unDom d
+      dropCxt err = updateContext (strengthenS err 1) (drop 1)
+  genTelCxt <- dropCxt __IMPOSSIBLE__ $ mapM cxtEntry $ reverse $ zip genTelVars $ telToList genTel
+
+  -- For the explicit module telescope we get the names from the typecheck
+  -- action.
+  let newTelCxt = zipWith setName cxtNames $ reverse $ telToList tel'
+
+  -- We are in context Γ (r : R) and should call the continuation in context Γ Δ Θρ passing it Δ Θρ
+  -- We have
+  --   Γ (r : R) ⊢ Θ            Θ = tel
+  --   Γ ⊢ Δ                    Δ = genTel
+  --   Γ Δ ⊢ ρ : Γ (r : R)      ρ = sub
+  --   Γ ⊢ Δ Θρ                 Θρ = tel'
+  -- And we shouldn't forget about the let-bindings (#3470)
+  --   Γ (r : R) Θ ⊢ letbinds
+  --   Γ Δ Θρ      ⊢ letbinds' = letbinds(lift |Θ| ρ)
+  -- And modules created in the telescope (#6916)
+  --   TODO
+  letbinds' <- applySubst (liftS (size tel) sub) <$> instantiateFull letbinds
+  let addLet (x, LetBinding o v dom) = addLetBinding' o x v dom
+
+  updateContext sub ((genTelCxt ++) . drop 1) $
+    updateContext (raiseS (size tel')) (newTelCxt ++) $
+      foldr addLet (ret genTelVars $ abstract genTel tel') letbinds'
+
+
+-- | Generalize a type over a set of (used) generalizable variables.
+generalizeType :: Set QName -> TCM Type -> TCM ([Maybe QName], Type)
+generalizeType s typecheckAction = do
+  (ns, t, _) <- generalizeType' s $ (,()) <$> typecheckAction
+  return (ns, t)
+
+-- | Allow returning additional information from the type checking action.
+generalizeType' :: Set QName -> TCM (Type, a) -> TCM ([Maybe QName], Type, a)
+generalizeType' s typecheckAction = billTo [Typing, Generalize] $ withGenRecVar $ \ genRecMeta -> do
+
+  ((t, userdata), namedMetas, allmetas) <- createMetasAndTypeCheck s typecheckAction
+
+  reportSDoc "tc.generalize.metas" 60 $ vcat
+    [ "open metas =" <+> (text . show . fmap ((miNameSuggestion &&& miGeneralizable) . mvInfo)) (openMetas $ allmetas)
+    ]
+
+  (genTel, genTelNames, sub) <- computeGeneralization genRecMeta namedMetas allmetas
+
+  t' <- abstract genTel . applySubst sub <$> instantiateFull t
+
+  reportSDoc "tc.generalize" 40 $ vcat
+    [ "generalized"
+    , nest 2 $ "t =" <+> escapeContext impossible 1 (prettyTCM t') ]
+
+  return (genTelNames, t', userdata)
+
+-- | Create metas for the generalizable variables and run the type check action.
+createMetasAndTypeCheck ::
+  Set QName -> TCM a -> TCM (a, Map MetaId QName, LocalMetaStores)
+createMetasAndTypeCheck s typecheckAction = do
+  ((namedMetas, x), allmetas) <- metasCreatedBy $ do
+    (metamap, genvals) <- createGenValues s
+    x <- locallyTC eGeneralizedVars (const genvals) typecheckAction
+    return (metamap, x)
+  return (x, namedMetas, allmetas)
+
+-- | Add a placeholder variable that will be substituted with a record value packing up all the
+--   generalized variables.
+withGenRecVar :: (Type -> TCM a) -> TCM a
+withGenRecVar ret = do
+  -- Create a meta type (in Set₀) for the telescope record. It won't
+  -- necessarily fit in Set₀, but since it's only used locally the sort
+  -- shouldn't matter. Another option would be to put it in Setω, which is a
+  -- bit more honest, but this leads to performance problems (see #3306).
+  genRecMeta <- newTypeMeta (mkType 0)
+  addContext (defaultDom ("genTel" :: String, genRecMeta)) $ ret genRecMeta
+
+-- | Compute the generalized telescope from metas created when checking the *thing* (type or telescope) to be
+--   generalized. Called in the context extended with the telescope record variable (whose type is
+--   the first argument). Returns the telescope of generalized variables and a substitution from
+--   this telescope to the current context.
+computeGeneralization
+  :: Type
+       -- ^ The metavariable to be instantiated with record type containing
+       --   as fields the variables generalized in the *thing*.
+  -> Map MetaId name
+       -- ^ Metas created from an occurrence of a @variable@. (The original free variables.)
+       --   E.g. if you have
+       --   @
+       --     variable  l : Level; A : Set l
+       --     postulate f : A → A
+       --   @
+       --   then @A@ would be in this @Map@, but not @l@.
+  -> LocalMetaStores
+       -- ^ The metas created when type-checking the *thing*.
+  -> TCM (Telescope, [Maybe name], Substitution)
+       -- ^ The telescope together with binder name (left-to-right order),
+       --   and substitution from this telescope to the current context.
+computeGeneralization genRecMeta nameMap allmetas = postponeInstanceConstraints $ do
+
+  reportSDoc "tc.generalize" 10 $ "computing generalization for type" <+> prettyTCM genRecMeta
+
+  -- Pair metas with their metaInfo
+  let mvs :: [(MetaId, MetaVariable)]
+      mvs = MapS.assocs (openMetas allmetas) ++
+            MapS.assocs (solvedMetas allmetas)
+
+  -- Issue 4727: filter out metavariables that were created before the
+  -- current checkpoint, since they are too old to be generalized.
+  -- TODO: make metasCreatedBy smarter so it doesn't see pruned
+  -- versions of old metas as new metas.
+  cp <- viewTC eCurrentCheckpoint
+  let isFreshMeta :: MonadReduce m => MetaVariable -> m Bool
+      isFreshMeta mv = enterClosure mv $ \ _ -> isJust <$> checkpointSubstitution' cp
+  mvs :: [(MetaId, MetaVariable)] <- filterM (isFreshMeta . snd) mvs
+
+  cs <- (++) <$> useTC stAwakeConstraints
+             <*> useTC stSleepingConstraints
+
+  reportSDoc "tc.generalize" 50 $ "current constraints:" <?> vcat (map prettyTCM cs)
+
+  constrainedMetas <- Set.unions <$> mapM (constraintMetas . clValue . theConstraint) cs
+
+  reportSDoc "tc.generalize" 30 $ nest 2 $
+    "constrainedMetas     = " <+> prettyList_ (map prettyTCM $ Set.toList constrainedMetas)
+
+  let isConstrained x = Set.member x constrainedMetas
+      -- Note: Always generalize named metas even if they are constrained. We
+      -- freeze them so they won't be instantiated by the constraint, and we do
+      -- want the nice error from checking the constraint after generalization.
+      -- See #3276.
+      isGeneralizable (x, mv) = Map.member x nameMap ||
+                                not (isConstrained x) && NoGeneralize /= unArg (miGeneralizable (mvInfo mv))
+      isSort = isSortMeta_ . snd
+      isOpen = isOpenMeta . mvInstantiation . snd
+
+  -- Split the generalizable metas in open and closed
+  let (generalizable, nongeneralizable)         = partition isGeneralizable mvs
+      (generalizableOpen', generalizableClosed) = partition isOpen generalizable
+      (openSortMetas, generalizableOpen)        = partition isSort generalizableOpen'
+      nongeneralizableOpen                      = filter isOpen nongeneralizable
+
+  reportSDoc "tc.generalize" 30 $ nest 2 $ vcat
+    [ "generalizable        = " <+> prettyList_ (map (prettyTCM . fst) generalizable)
+    , "generalizableOpen    = " <+> prettyList_ (map (prettyTCM . fst) generalizableOpen)
+    , "openSortMetas        = " <+> prettyList_ (map (prettyTCM . fst) openSortMetas)
+    ]
+
+  -- Issue 3301: We can't generalize over sorts
+  unlessNull openSortMetas $ \ ms ->
+    warning $ CantGeneralizeOverSorts $ map fst ms
+
+  -- Any meta in the solution of a generalizable meta should be generalized over (if possible).
+  cp <- viewTC eCurrentCheckpoint
+  let canGeneralize x | isConstrained x = return False
+      canGeneralize x = do
+          mv   <- lookupLocalMeta x
+          msub <- enterClosure mv $ \ _ ->
+                    checkpointSubstitution' cp
+          let sameContext =
+                -- We can only generalize if the metavariable takes the context variables of the
+                -- current context as arguments. This happens either when the context of the meta
+                -- is the same as the current context and there is no pruning, or the meta context
+                -- is a weakening but the extra variables have been pruned.
+                -- It would be possible to generalize also in the case when some context variables
+                -- (other than genTel) have been pruned, but it's hard to construct an example
+                -- where this actually happens.
+                case (msub, mvPermutation mv) of
+                  (Just IdS, Perm m xs)        -> xs == [0 .. m - 1]
+                  (Just (Wk n IdS), Perm m xs) -> xs == [0 .. m - n - 1]
+                  _                            -> False
+          unless sameContext $ reportSDoc "tc.generalize" 20 $ do
+            ty <- getMetaType x
+            let Perm m xs = mvPermutation mv
+            vcat
+              [ text "Don't know how to generalize over"
+              , nest 2 $ prettyTCM x <+> text ":" <+> prettyTCM ty
+              , text "in context"
+              , nest 2 $ inTopContext . prettyTCM =<< getContextTelescope
+              , text "permutation:" <+> text (show (m, xs))
+              , text "subst:" <+> pretty msub ]
+          return sameContext
+
+  inherited :: Set MetaId <- Set.unions <$> forM generalizableClosed \ (x, mv) ->
+    case mvInstantiation mv of
+      InstV inst -> do
+        parentName <- getMetaNameSuggestion x
+        metas <- filterM canGeneralize . Set.toList .
+                 allMetas Set.singleton =<<
+                 instantiateFull (instBody inst)
+        unless (null metas) $
+          reportSDoc "tc.generalize" 40 $
+            hcat ["Inherited metas from ", prettyTCM x, ":"] <?> prettyList_ (map prettyTCM metas)
+        -- #4291: Override existing meta name suggestion.
+        -- Don't suggest names for explicitly named generalizable metas.
+        case filter (`Map.notMember` nameMap) metas of
+          -- If we solved the parent with a new meta use the parent name for that.
+          [m] | MetaV{} <- instBody inst -> setMetaNameSuggestion m parentName
+          -- Otherwise suffix with a number.
+          ms -> zipWithM_ (\ i m -> setMetaNameSuggestion m (parentName ++ "." ++ show i)) [1..] ms
+        return $ Set.fromList metas
+      _ -> __IMPOSSIBLE__
+
+  let (alsoGeneralize, reallyDontGeneralize) = partition (`Set.member` inherited) $ map fst nongeneralizableOpen
+      generalizeOver   = map fst generalizableOpen ++ alsoGeneralize
+      shouldGeneralize = (generalizeOver `hasElem`)
+
+  reportSDoc "tc.generalize" 30 $ nest 2 $ vcat
+    [ "alsoGeneralize       = " <+> prettyList_ (map prettyTCM alsoGeneralize)
+    , "reallyDontGeneralize = " <+> prettyList_ (map prettyTCM reallyDontGeneralize)
+    ]
+
+  reportSDoc "tc.generalize" 10 $ "we're generalizing over" <+> prettyList_ (map prettyTCM generalizeOver)
+
+  -- Sort metas in dependency order. Include open metas that we are not
+  -- generalizing over, since they will need to be pruned appropriately (see
+  -- Issue 3672).
+  allSortedMetas <- fromMaybeM (typeError GeneralizeCyclicDependency) $
+    dependencySortMetas (generalizeOver ++ reallyDontGeneralize ++ map fst openSortMetas)
+  let sortedMetas = filter shouldGeneralize allSortedMetas
+
+  let dropCxt err = updateContext (strengthenS err 1) (drop 1)
+
+  -- Create the pre-record type (we don't yet know the types of the fields)
+  (genRecName, genRecCon, genRecFields) <- dropCxt __IMPOSSIBLE__ $
+      createGenRecordType genRecMeta sortedMetas
+
+  reportSDoc "tc.generalize" 30 $ vcat $
+    [ "created genRecordType"
+    , nest 2 $ "genRecName   = " <+> prettyTCM genRecName
+    , nest 2 $ "genRecCon    = " <+> prettyTCM genRecCon
+    , nest 2 $ "genRecFields = " <+> prettyList_ (map prettyTCM genRecFields)
+    ]
+
+  -- Solve the generalizable metas. Each generalizable meta is solved by projecting the
+  -- corresponding field from the genTel record.
+  cxtTel <- getContextTelescope
+  let solve m field = do
+        reportSDoc "tc.generalize" 30 $ "solving generalized meta" <+>
+          prettyTCM m <+> ":=" <+> prettyTCM (Var 0 [Proj ProjSystem field])
+        -- m should not be instantiated, but if we don't check constraints
+        -- properly it could be (#3666 and #3667). Fail hard instead of
+        -- generating bogus types.
+        whenM (isInstantiatedMeta m) __IMPOSSIBLE__
+        assignTerm' m (telToArgs cxtTel) $ Var 0 [Proj ProjSystem field]
+  zipWithM_ solve sortedMetas genRecFields
+
+  -- Record the named variables in the telescope
+  let telNames = map (`Map.lookup` nameMap) sortedMetas
+
+  -- Build the telescope of generalized metas
+  teleTypes <- do
+    args <- getContextArgs
+    concat <$> forM sortedMetas \ m -> do
+      mv <- lookupLocalMeta m
+      let info =
+            (hideOrKeepInstance $
+            getArgInfo $ miGeneralizable $ mvInfo mv) { argInfoOrigin = Generalization }
+          HasType{ jMetaType = t } = mvJudgement mv
+          perm = mvPermutation mv
+      t' <- piApplyM t $ permute (takeP (length args) perm) args
+      return [(Arg info $ miNameSuggestion $ mvInfo mv, t')]
+  let genTel = buildGeneralizeTel genRecCon teleTypes
+
+  reportSDoc "tc.generalize" 40 $ vcat
+    [ text "teleTypes =" <+> prettyTCM teleTypes
+    , text "genTel    =" <+> prettyTCM genTel
+    ]
+
+  -- Now we need to prune the unsolved metas to make sure they respect the new
+  -- dependencies (#3672). Also update interaction points to point to pruned metas.
+  let inscope (ii, InteractionPoint{ipMeta = Just x})
+        | MapS.member x (openMetas allmetas) ||
+          MapS.member x (solvedMetas allmetas) =
+          Just (x, ii)
+      inscope _ = Nothing
+  ips <- Map.fromDistinctAscList . mapMaybe inscope . fst . BiMap.toDistinctAscendingLists <$> useTC stInteractionPoints
+  pruneUnsolvedMetas genRecName genRecCon genTel genRecFields ips shouldGeneralize allSortedMetas
+
+  -- Fill in the missing details of the telescope record.
+  dropCxt __IMPOSSIBLE__ $ fillInGenRecordDetails genRecName genRecCon genRecFields genRecMeta genTel
+
+  -- Now abstract over the telescope. We need to apply the substitution that subsitutes a record
+  -- value packing up the generalized variables for the genTel variable.
+  let sub = unpackSub genRecCon (map (argInfo . fst) teleTypes) (length teleTypes)
+
+  -- Instantiate all fresh meta-variables to get rid of
+  -- __DUMMY_TERM__.
+  genTel <- flip instantiateWhen genTel $ \m -> do
+    mv <- lookupMeta m
+    case mv of
+      Nothing         -> __IMPOSSIBLE__
+      Just Left{}     -> return False
+      Just (Right mv) -> isFreshMeta mv
+
+  return (genTel, telNames, sub)
+
+-- | Prune unsolved metas (#3672). The input includes also the generalized metas and is sorted in
+-- dependency order. The telescope is the generalized telescope.
+pruneUnsolvedMetas :: QName -> ConHead -> Telescope -> [QName] -> Map MetaId InteractionId -> (MetaId -> Bool) -> [MetaId] -> TCM ()
+pruneUnsolvedMetas genRecName genRecCon genTel genRecFields interactionPoints isGeneralized metas
+  | all isGeneralized metas = return ()
+  | otherwise               = prune [] genTel metas
+  where
+    prune _ _ [] = return ()
+    prune cxt tel (x : xs) | not (isGeneralized x) = do
+      -- If x is a blocked term we shouldn't instantiate it.
+      whenM (not <$> isBlockedTerm x) $ do
+        x <- if null tel then return x else prePrune x
+        pruneMeta (telFromList $ reverse cxt) x
+      prune cxt tel xs
+    prune cxt (ExtendTel a tel) (x : xs) = prune (fmap (x,) a : cxt) (unAbs tel) xs
+      where x = absName tel
+    prune _ _ _ = __IMPOSSIBLE__
+
+    sub = unpackSub genRecCon $ map getArgInfo $ telToList genTel
+
+    prepruneErrorRefinedContext = prepruneError $
+      "Failed to generalize because some of the generalized variables depend on an " ++
+      "unsolved meta created in a refined context (not a simple extension of the context where " ++
+      "generalization happens)."
+
+    prepruneErrorCyclicDependencies = prepruneError $
+      "Failed to generalize due to circular dependencies between the generalized " ++
+      "variables and an unsolved meta."
+
+    prepruneErrorFailedToInstantiate = prepruneError $
+      "Failed to generalize because the generalized variables depend on an unsolved meta " ++
+      "that could not be lifted outside the generalization."
+
+    prepruneError :: String -> MetaId -> TCM a
+    prepruneError msg x = do
+      r <- getMetaRange x
+      genericDocError =<<
+        (fwords (msg ++ " The problematic unsolved meta is") $$
+                 (nest 2 $ prettyTCM (MetaV x []) <+> "at" <+> pretty r)
+        )
+
+    -- If one of the fields depend on this meta, we have to make sure that this meta doesn't depend
+    -- on any variables introduced after the genRec. See test/Fail/Issue3672b.agda for a test case.
+    prePrune x = do
+      cp <- viewTC eCurrentCheckpoint
+      mv <- lookupLocalMeta x
+      (i, _A) <- enterClosure mv $ \ _ -> do
+        δ <- checkpointSubstitution cp
+        _A <- case mvJudgement mv of
+                IsSort{}  -> return Nothing
+                HasType{} -> Just <$> getMetaTypeInContext x
+        case δ of
+          Wk n IdS -> return (n, _A)
+          IdS      -> return (0, _A)
+          _        -> prepruneErrorRefinedContext x
+      if i == 0 then return x else do
+        reportSDoc "tc.generalize.prune.pre" 40 $ vcat
+          [ "prepruning"
+          , nest 2 $ pretty x <+> ":" <+> pretty (jMetaType $ mvJudgement mv)
+          , nest 2 $ "|Δ| =" <+> pshow i ]
+
+        -- We have
+        --   Γ (r : GenRec)            current context
+        --   Γ (r : GenRec) Δ ⊢ x : A  with |Δ| = i
+        -- and we need to get rid of the dependency on Δ.
+
+        -- We can only do this if A does not depend on Δ, so check this first.
+        case IntSet.minView (allFreeVars _A) of
+          Just (j, _) | j < i -> prepruneErrorCyclicDependencies x
+          _                   -> return ()
+
+        -- If it doesn't we can strenghten it to the current context (this is done by
+        -- newMetaFromOld).
+        --   Γ (r : GenRec) ⊢ ρ : Γ (r : GenRec) Δ
+        let ρ  = strengthenS impossible i
+            ρ' = raiseS i
+
+        (y, u) <- newMetaFromOld mv ρ _A
+
+        let uρ' = applySubst ρ' u
+
+        reportSDoc "tc.generalize.prune.pre" 40 $ nest 2 $ vcat
+          [ "u    =" <+> pretty u
+          , "uρ⁻¹ =" <+> pretty uρ' ]
+
+        -- To solve it we enter the context of x again
+        enterClosure mv $ \ _ -> do
+          -- v is x applied to the context variables
+          v <- case _A of
+                 Nothing -> Sort . MetaS x . map Apply <$> getMetaContextArgs mv
+                 Just{}  -> MetaV x . map Apply <$> getMetaContextArgs mv
+          noConstraints (doPrune x mv _A v uρ') `catchError` \ _ -> prepruneErrorFailedToInstantiate x
+          setInteractionPoint x y
+          return y
+
+    pruneMeta _Θ x = do
+      cp <- viewTC eCurrentCheckpoint
+      mv <- lookupLocalMeta x
+      -- The reason we are doing all this inside the closure of x is so that if x is an interaction
+      -- meta we get the right context for the pruned interaction meta.
+      enterClosure mv $ \ _ ->
+        -- If we can't find the generalized record, it's already been pruned and we don't have to do
+        -- anything.
+        whenJustM (findGenRec mv) $ \ i -> do
+
+        reportSDoc "tc.generalize.prune" 30 $ vcat
+          [ "pruning"
+          , nest 2 $ inTopContext $ prettyTCM (mvJudgement mv)
+          , nest 2 $ "GenRecTel is var" <+> pretty i ]
+
+        _ΓrΔ <- getContextTelescope
+        let (_Γ, _Δ) = (telFromList gs, telFromList ds)
+              where (gs, _ : ds) = splitAt (size _ΓrΔ - i - 1) (telToList _ΓrΔ)
+
+        -- Get the type of x. By doing this here we let the checkpoint machinery sort out the
+        _A <- case mvJudgement mv of
+                IsSort{}  -> return Nothing
+                HasType{} -> Just <$> getMetaTypeInContext x
+
+        -- We have
+        --   Γ  (r : GenTel) Δ         current context
+        --   Γ₀ (r : GenTel)           top context
+        --   Γ₀ ⊢ Θ                    prefix of the generalized telescope currently in scope
+        --   Γ (r : GenTel) Δ ⊢ x : A  the meta to prune
+
+        -- Get the substitution from the point of generalization to the current context. This always
+        -- succeeds since if the meta depends on GenTel it must have been created inside the
+        -- generalization:
+        --   Γ (r : GenTel) Δ ⊢ δ : Γ₀ (r : GenTel)
+        δ <- checkpointSubstitution cp
+
+        -- v is x applied to the context variables
+        v <- case _A of
+               Nothing -> Sort . MetaS x . map Apply <$> getMetaContextArgs mv
+               Just{}  -> MetaV x . map Apply <$> getMetaContextArgs mv
+
+        -- Now ultimately we want to create the fresh meta in the context
+        --   Γ Θγ Δσ where Γ    ⊢ γ : Γ₀
+        --                 Γ Θγ ⊢ σ : Γ (r : GenTel)
+        -- σ is the unpacking substitution (which is polymorphic in Γ)
+        let σ   = sub (size _Θ)
+            --    Γ <- Γ (r : GenTel) Δ <- Γ₀ (r : GenTel) <- Γ₀
+            γ   = strengthenS impossible (i + 1) `composeS` δ `composeS` raiseS 1
+            _Θγ = applySubst γ _Θ
+            _Δσ = applySubst σ _Δ
+
+        -- The substitution into the new context is simply lifting σ over Δ:
+        --   Γ Θγ Δσ ⊢ lift i σ : Γ (r : GenTel) Δ
+        let ρ  = liftS i σ
+            -- We also need ρ⁻¹, which is a lot easier to construct.
+            ρ' = liftS i $ [ Var 0 [Proj ProjSystem fld] | fld <- reverse $ take (size _Θ) $ genRecFields ] ++# raiseS 1
+
+        reportSDoc "tc.generalize.prune" 30 $ nest 2 $ vcat
+          [ "Γ   =" <+> pretty _Γ
+          , "Θ   =" <+> pretty _Θ
+          , "Δ   =" <+> pretty _Δ
+          , "σ   =" <+> pretty σ
+          , "γ   =" <+> pretty γ
+          , "δ   =" <+> pretty δ
+          , "ρ   =" <+> pretty ρ
+          , "ρ⁻¹ =" <+> pretty ρ'
+          , "Θγ  =" <+> pretty _Θγ
+          , "Δσ  =" <+> pretty _Δσ
+          , "_A  =" <+> pretty _A
+          ]
+
+        -- When updating the context we also need to pick names for the variables. Get them from the
+        -- current context and generate fresh ones for the generalized variables in Θ.
+        (newCxt, rΘ) <- do
+          (rΔ, _ : rΓ) <- splitAt i <$> getContext
+          let setName = traverse $ \ (s, ty) -> (,ty) <$> freshName_ s
+          rΘ <- mapM setName $ reverse $ telToList _Θγ
+          let rΔσ = zipWith (\ name dom -> first (const name) <$> dom)
+                            (map (fst . unDom) rΔ)
+                            (reverse $ telToList _Δσ)
+          return (rΔσ ++ rΘ ++ rΓ, rΘ)
+
+        -- Now we can enter the new context and create our meta variable.
+        (y, u) <- updateContext ρ (const newCxt) $ localScope $ do
+
+          -- First, we add the named variables to the scope, to allow
+          -- them to be used in holes (#3341). These should go outside Δ (#3735).
+          outsideLocalVars i $ addNamedVariablesToScope rΘ
+
+          -- Now we can create the new meta
+          newMetaFromOld mv ρ _A
+
+        -- Finally we solve x := yρ⁻¹. The reason for solving it this way instead of xρ := y is that
+        -- ρ contains dummy terms for the variables that are not in scope.
+        -- If x has been instantiated by some constraint unblocked by previous pruning or
+        -- generalization, use equalTerm instead of assigning to x. If this fails (see
+        -- test/Fail/Issue3655b.agda for a test case), we need to give an error. This can happen if
+        -- there are dependencies between generalized variables that are hidden by constraints and
+        -- the dependency sorting happens to pick the wrong order. For instance, if we have
+        --    α : Nat   (unsolved meta)
+        --    t : F α   (named variable)
+        --    n : Nat   (named variable)
+        -- and a constraint F α == F n, where F does some pattern matching preventing the constraint
+        -- to be solved when n is still a meta. If t appears before n in the type these will be sorted
+        -- as α, t, n, but we will solve α := n before we get to the pruning here. It's good that we
+        -- solve first though, because that means we can give a more informative error message than
+        -- the "Cannot instantiate..." we would otherwise get.
+        let uρ' = applySubst ρ' u
+        reportSDoc "tc.generalize.prune" 80 $ vcat
+          [ "solving"
+          , nest 2 $ sep [ pretty v   <+> "=="
+                         , pretty uρ' <+> ":"
+                         , pretty _A ] ]
+        noConstraints (doPrune x mv _A v uρ') `catchError` niceError x v
+
+        reportSDoc "tc.generalize.prune" 80 $ vcat
+          [ "solved"
+          , nest 2 $ "v    =" <+> (pretty =<< instantiateFull v)
+          , nest 2 $ "uρ⁻¹ =" <+> (pretty =<< instantiateFull uρ') ]
+
+        setInteractionPoint x y
+
+    findGenRec :: MetaVariable -> TCM (Maybe Int)
+    findGenRec mv = do
+      cxt <- instantiateFull =<< getContext
+      let n         = length cxt
+          notPruned = IntSet.fromList $
+                      permute (takeP n $ mvPermutation mv) $
+                      downFrom n
+      case [ i
+           | (i, Dom{unDom = (_, El _ (Def q _))}) <- zip [0..] cxt
+           , q == genRecName
+           , i `IntSet.member` notPruned
+           ] of
+        []    -> return Nothing
+        _:_:_ -> __IMPOSSIBLE__
+        [i]   -> return (Just i)
+                                                    -- Nothing if sort meta
+    newMetaFromOld :: MetaVariable -> Substitution -> Maybe Type -> TCM (MetaId, Term)
+    newMetaFromOld mv ρ mA = setCurrentRange mv $
+      case mA of
+        Nothing -> do
+          s@(MetaS y _) <- newSortMeta
+          return (y, Sort s)
+        Just _A -> do
+          let _Aρ = applySubst ρ _A
+          newNamedValueMeta DontRunMetaOccursCheck
+                            (miNameSuggestion $ mvInfo mv)
+                            (jComparison $ mvJudgement mv) _Aρ
+
+    -- If x is a hole, update the hole to point to y instead.
+    setInteractionPoint x y =
+      whenJust (Map.lookup x interactionPoints) (`connectInteractionPoint` y)
+
+    doPrune :: MetaId -> MetaVariable -> Maybe Type -> Term -> Term -> TCM ()
+    doPrune x mv mt v u =
+      case mt of
+        _ | isOpen -> assign DirEq x (getArgs v) u $ maybe AsTypes AsTermsOf mt
+        Nothing    -> equalSort (unwrapSort v) (unwrapSort u)
+        Just t     -> equalTerm t v u
+      where
+        isOpen = isOpenMeta $ mvInstantiation mv
+        getArgs = \case
+            Sort (MetaS _ es) -> fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+            MetaV _ es        -> fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+            _                 -> __IMPOSSIBLE__
+        unwrapSort (Sort s) = s
+        unwrapSort _        = __IMPOSSIBLE__
+
+    niceError x u err = do
+      u <- instantiateFull u
+      let err' = case err of
+                   TypeError{tcErrClosErr = cl} ->
+                     -- Remove the 'when' part from the error since it's most like the same as ours.
+                     err{ tcErrClosErr = cl{ clEnv = (clEnv cl) { envCall = Nothing } } }
+                   _ -> err
+          telList = telToList genTel
+          names   = map (fst . unDom) telList
+          late    = map (fst . unDom) $ filter (getAny . allMetas (Any . (== x))) telList
+          projs (Proj _ q)
+            | q `elem` genRecFields = Set.fromList $ catMaybes [getGeneralizedFieldName q]
+          projs _                 = Set.empty
+          early = Set.toList $ flip foldTerm u $ \ case
+                  Var _ es   -> foldMap projs es
+                  Def _ es   -> foldMap projs es
+                  MetaV _ es -> foldMap projs es
+                  _          -> Set.empty
+          commas []       = __IMPOSSIBLE__
+          commas [x]      = x
+          commas [x, y]   = x ++ ", and " ++ y
+          commas (x : xs) = x ++ ", " ++ commas xs
+          cause = "There were unsolved constraints that obscured the " ++
+                  "dependencies between the generalized variables."
+          solution = "The most reliable solution is to provide enough information to make the dependencies " ++
+                     "clear, but simply mentioning the variables in the right order should also work."
+          order = sep [ fwords "Dependency analysis suggested this (likely incorrect) order:",
+                        nest 2 $ fwords (unwords names) ]
+          guess = unwords
+            [ "After constraint solving it looks like", commas late
+            , singPlural late (++ "s") id "actually depend"
+            , "on", commas early
+            ]
+      genericDocError =<< vcat
+        [ fwords $ "Variable generalization failed."
+        , nest 2 $ sep ["- Probable cause", nest 4 $ fwords cause]
+        , nest 2 $ sep ["- Suggestion", nest 4 $ fwords solution]
+        , nest 2 $ sep $ ["- Further information"
+                         , nest 2 $ "-" <+> order ] ++
+                         [ nest 2 $ "-" <+> fwords guess | not (null late), not (null early) ] ++
+                         [ nest 2 $ "-" <+> sep [ fwords "The dependency I error is", prettyTCM err' ] ]
+        ]
+
+    addNamedVariablesToScope cxt =
+      forM_ cxt $ \ Dom{ unDom = (x, _) } -> do
+        -- Recognize named variables by lack of '.' (TODO: hacky!)
+        reportSLn "tc.generalize.eta.scope" 40 $ "Adding (or not) " ++ prettyShow (nameConcrete x) ++ " to the scope"
+        when ('.' `notElem` prettyShow (nameConcrete x)) $ do
+          reportSLn "tc.generalize.eta.scope" 40 "  (added)"
+          bindVariable LambdaBound (nameConcrete x) x
+
+-- | Create a substition from a context where the i first record fields are variables to a context
+--   where you have a single variable of the record type. Packs up the field variables in a record
+--   constructor and pads with __DUMMY_TERM__s for the missing fields. Important that you apply this
+--   to terms that only projects the defined fields from the record variable.
+--   Used with partial record values when building the telescope of generalized variables in which
+--   case we have done the dependency analysis that guarantees it is safe.
+unpackSub :: ConHead -> [ArgInfo] -> Int -> Substitution
+unpackSub con infos i = recSub
+  where
+    ar = length infos
+    appl info v = Apply (Arg info v)
+    recVal = Con con ConOSystem $ zipWith appl infos $ [var j | j <- [i - 1, i - 2..0]] ++ replicate (ar - i) __DUMMY_TERM__
+
+    -- want: Γ Δᵢ ⊢ recSub i : Γ (r : R)
+    -- have:
+    -- Γ Δᵢ ⊢ recVal i :# σ : Θ (r : R),  if Γ Δᵢ ⊢ σ : Θ
+    -- Γ Δᵢ ⊢ WkS i IdS : Γ
+    recSub = recVal :# Wk i IdS
+
+-- | Takes the list of types
+--    A₁ []
+--    A₂ [r.f₁]
+--    A₃ [r.f₂, r.f₃]
+--    ...
+--   And builds the telescope
+--    (x₁ : A₁ [ r := c _       .. _ ])
+--    (x₂ : A₂ [ r := c x₁ _    .. _ ])
+--    (x₃ : A₃ [ r := c x₁ x₂ _ .. _ ])
+--    ...
+buildGeneralizeTel :: ConHead -> [(Arg MetaNameSuggestion, Type)] -> Telescope
+buildGeneralizeTel con xs = go 0 xs
+  where
+    infos = map (argInfo . fst) xs
+    recSub i = unpackSub con infos i
+    go _ [] = EmptyTel
+    go i ((name, ty) : xs) = ExtendTel (dom ty') $ Abs (unArg name) $ go (i + 1) xs
+      where ty' = applySubst (recSub i) ty
+            dom = defaultNamedArgDom (getArgInfo name) (unArg name)
+
+-- | Create metas for all used generalizable variables and their dependencies.
+createGenValues :: Set QName -> TCM (Map MetaId QName, Map QName GeneralizedValue)
+createGenValues s = do
+  genvals <- locallyTC eGeneralizeMetas (const YesGeneralizeVar) $
+               mapM createGenValue $ sortBy (compare `on` getRange) $ Set.toList s
+  let metaMap = Map.fromListWith __IMPOSSIBLE__ [ (m, x) | (x, m, _) <- genvals ]
+      nameMap = Map.fromListWith __IMPOSSIBLE__ [ (x, v) | (x, _, v) <- genvals ]
+  return (metaMap, nameMap)
+
+-- | Create a generalisable meta for a generalisable variable.
+createGenValue :: QName -> TCM (QName, MetaId, GeneralizedValue)
+createGenValue x = setCurrentRange x $ do
+  cp  <- viewTC eCurrentCheckpoint
+  def <- instantiateDef =<< getConstInfo x
+                   -- Only prefix of generalizable arguments (for now?)
+  let nGen       = case defArgGeneralizable def of
+                     NoGeneralizableArgs     -> 0
+                     SomeGeneralizableArgs n -> n
+      ty         = defType def
+      TelV tel _ = telView' ty
+      -- Generalizable variables are never explicit, so if they're given as
+      -- explicit we default to hidden.
+      hideExplicit arg | visible arg = hide arg
+                       | otherwise   = arg
+      argTel     = telFromList $ map hideExplicit $ take nGen $ telToList tel
+
+  args <- newTelMeta argTel
+  metaType <- piApplyM ty args
+
+  let name     = prettyShow (nameConcrete $ qnameName x)
+  (m, term) <- newNamedValueMeta DontRunMetaOccursCheck name CmpLeq metaType
+
+  -- Freeze the meta to prevent named generalizable metas from being
+  -- instantiated, and set the quantity of the meta to the declared
+  -- quantity of the generalisable variable.
+  updateMetaVar m $ \ mv ->
+    setModality (getModality (defArgInfo def)) $
+    mv { mvFrozen = Frozen }
+
+  -- Set up names of arg metas
+  forM_ (zip3 [1..] (map unArg args) (telToList argTel)) $ \ case
+    (i, MetaV m _, Dom{unDom = (x, _)}) -> do
+      let suf "_" = show i
+          suf ""  = show i
+          suf x   = x
+      setMetaNameSuggestion m (name ++ "." ++ suf x)
+    _ -> return ()  -- eta expanded
+
+  -- Update the ArgInfos for the named meta. The argument metas are
+  -- created with the correct ArgInfo.
+  setMetaGeneralizableArgInfo m $ hideExplicit (defArgInfo def)
+
+  reportSDoc "tc.generalize" 50 $ vcat
+    [ "created metas for generalized variable" <+> prettyTCM x
+    , nest 2 $ "top  =" <+> prettyTCM term
+    , nest 2 $ "args =" <+> prettyTCM args ]
+
+  case term of
+    MetaV{} -> return ()
+    _       -> genericDocError =<< ("Cannot generalize over" <+> prettyTCM x <+> "of eta-expandable type") <?>
+                                    prettyTCM metaType
+  return (x, m, GeneralizedValue{ genvalCheckpoint = cp
+                                , genvalTerm       = term
+                                , genvalType       = metaType })
+
+-- | Create a not-yet correct record type for the generalized telescope. It's not yet correct since
+--   we haven't computed the telescope yet, and we need the record type to do it.
+createGenRecordType :: Type -> [MetaId] -> TCM (QName, ConHead, [QName])
+createGenRecordType genRecMeta@(El genRecSort _) sortedMetas = do
+  current <- currentModule
+  let freshQName s = qualify current <$> freshName_ (s :: String)
+      mkFieldName  = freshQName . (generalizedFieldName ++) <=< getMetaNameSuggestion
+  genRecFields <- mapM (defaultDom <.> mkFieldName) sortedMetas
+  genRecName   <- freshQName "GeneralizeTel"
+  genRecCon    <- freshQName "mkGeneralizeTel" <&> \ con -> ConHead
+                  { conName      = con
+                  , conDataRecord= IsRecord CopatternMatching
+                  , conInductive = Inductive
+                  , conFields    = map argFromDom genRecFields
+                  }
+  projIx <- succ . size <$> getContext
+  erasure <- optErasure <$> pragmaOptions
+  inTopContext $ forM_ (zip sortedMetas genRecFields) $ \ (meta, fld) -> do
+    fieldTy <- getMetaType meta
+    let field = unDom fld
+    addConstant' field (getArgInfo fld) field fieldTy $
+      let proj = Projection { projProper   = Just genRecName
+                            , projOrig     = field
+                            , projFromType = defaultArg genRecName
+                            , projIndex    = projIx
+                            , projLams     = ProjLams [defaultArg "gtel"] } in
+      Function { funClauses      = []
+               , funCompiled     = Nothing
+               , funSplitTree    = Nothing
+               , funTreeless     = Nothing
+               , funInv          = NotInjective
+               , funMutual       = Just []
+               , funAbstr        = ConcreteDef
+               , funProjection   = Right proj
+               , funErasure      = erasure
+               , funFlags        = Set.empty
+               , funTerminates   = Just True
+               , funExtLam       = Nothing
+               , funWith         = Nothing
+               , funCovering     = []
+               , funIsKanOp      = Nothing
+               , funOpaque       = TransparentDef
+               }
+  addConstant' (conName genRecCon) defaultArgInfo (conName genRecCon) __DUMMY_TYPE__ $ -- Filled in later
+    Constructor { conPars   = 0
+                , conArity  = length genRecFields
+                , conSrcCon = genRecCon
+                , conData   = genRecName
+                , conAbstr  = ConcreteDef
+                , conComp   = emptyCompKit
+                , conProj   = Nothing
+                , conForced = []
+                , conErased = Nothing
+                , conErasure = erasure
+                , conInline  = False
+                }
+  let dummyTel 0 = EmptyTel
+      dummyTel n = ExtendTel (defaultDom __DUMMY_TYPE__) $ Abs "_" $ dummyTel (n - 1)
+  addConstant' genRecName defaultArgInfo genRecName (sort genRecSort) $
+    Record { recPars         = 0
+           , recClause       = Nothing
+           , recConHead      = genRecCon
+           , recNamedCon     = False
+           , recFields       = genRecFields
+           , recTel          = dummyTel (length genRecFields) -- Filled in later
+           , recMutual       = Just []
+           , recEtaEquality' = Inferred YesEta
+           , recPatternMatching = CopatternMatching
+           , recInduction    = Nothing
+           , recTerminates   = Just True    -- not recursive
+           , recAbstr        = ConcreteDef
+           , recComp         = emptyCompKit
+           }
+  reportSDoc "tc.generalize" 20 $ vcat
+    [ text "created genRec" <+> prettyList_ (map (text . prettyShow . unDom) genRecFields) ]
+  reportSDoc "tc.generalize" 80 $ vcat
+    [ text "created genRec" <+> text (prettyShow genRecFields) ]
+  -- Solve the genRecMeta
+  args <- getContextArgs
+  let genRecTy = El genRecSort $ Def genRecName $ map Apply args
+  noConstraints $ equalType genRecTy genRecMeta
+  return (genRecName, genRecCon, map unDom genRecFields)
+
+-- | Once we have the generalized telescope we can fill in the missing details of the record type.
+fillInGenRecordDetails :: QName -> ConHead -> [QName] -> Type -> Telescope -> TCM ()
+fillInGenRecordDetails name con fields recTy fieldTel = do
+  cxtTel <- fmap hideAndRelParams <$> getContextTelescope
+  let fullTel = cxtTel `abstract` fieldTel
+  -- Field types
+  let mkFieldTypes [] EmptyTel = []
+      mkFieldTypes (fld : flds) (ExtendTel ty ftel) =
+          abstract cxtTel (El s $ Pi (defaultDom recTy) (Abs "r" $ unDom ty)) :
+          mkFieldTypes flds (absApp ftel proj)
+        where
+          s = mkPiSort (defaultDom recTy) (Abs "r" $ unDom ty)
+          proj = Var 0 [Proj ProjSystem fld]
+      mkFieldTypes _ _ = __IMPOSSIBLE__
+  let fieldTypes = mkFieldTypes fields (raise 1 fieldTel)
+  reportSDoc "tc.generalize" 40 $ text "Field types:" <+> inTopContext (nest 2 $ vcat $ map prettyTCM fieldTypes)
+  zipWithM_ setType fields fieldTypes
+  -- Constructor type
+  let conType = fullTel `abstract` raise (size fieldTel) recTy
+  reportSDoc "tc.generalize" 40 $ text "Final genRecCon type:" <+> inTopContext (prettyTCM conType)
+  setType (conName con) conType
+  -- Record telescope: Includes both parameters and fields.
+  modifyGlobalDefinition name $ set (lensTheDef . lensRecord . lensRecTel) fullTel
+  where
+    setType q ty = modifyGlobalDefinition q $ \ d -> d { defType = ty }
diff --git a/src/full/Agda/TypeChecking/IApplyConfluence.hs b/src/full/Agda/TypeChecking/IApplyConfluence.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/IApplyConfluence.hs
@@ -0,0 +1,240 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.IApplyConfluence where
+
+import Prelude hiding (null, (!!))  -- do not use partial functions like !!
+
+import Control.Monad
+import Control.Monad.Except
+
+import Data.Bifunctor (first, second)
+import Data.DList (DList)
+import Data.Foldable (toList)
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.Interaction.Options
+
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Telescope.Path
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Maybe
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Impossible
+import Agda.Utils.Functor
+
+
+checkIApplyConfluence_ :: QName -> TCM ()
+checkIApplyConfluence_ f = whenM (isJust . optCubical <$> pragmaOptions) $ do
+  -- Andreas, 2019-03-27, iapply confluence should only be checked
+  -- when --cubical or --erased-cubical is active. See
+  -- test/Succeed/CheckIApplyConfluence.agda.
+  -- We cannot reach the following crash point unless
+  -- --cubical/--erased-cubical is active.
+  __CRASH_WHEN__ "tc.cover.iapply.confluence.crash" 666
+  reportSDoc "tc.cover.iapply" 10 $ text "Checking IApply confluence of" <+> pretty f
+  inConcreteOrAbstractMode f $ \ d -> do
+  case theDef d of
+    Function{funClauses = cls', funCovering = cls} -> do
+      reportSDoc "tc.cover.iapply" 10 $ text "length cls =" <+> pretty (length cls)
+      when (null cls && any (not . null . iApplyVars . namedClausePats) cls') $
+        __IMPOSSIBLE__
+      unlessM (optKeepCoveringClauses <$> pragmaOptions) $
+        modifySignature $ updateDefinition f $ updateTheDef
+          $ updateCovering (const [])
+
+      traceCall (CheckFunDefCall (getRange f) f [] False) $
+        forM_ cls $ checkIApplyConfluence f
+    _ -> return ()
+
+-- | @checkIApplyConfluence f (Clause {namedClausePats = ps})@ checks that @f ps@
+-- reduces in a way that agrees with @IApply@ reductions.
+checkIApplyConfluence :: QName -> Clause -> TCM ()
+checkIApplyConfluence f cl = case cl of
+      Clause {clauseBody = Nothing} -> return ()
+      Clause {clauseType = Nothing} -> __IMPOSSIBLE__
+      -- Inserted clause, will respect boundaries whenever the
+      -- user-written clauses do. Saves a ton of work!
+      Clause {namedClausePats = ps} | hasDefP ps -> pure ()
+      cl@Clause { clauseTel = clTel
+                , namedClausePats = ps
+                , clauseType = Just t
+                , clauseBody = Just body
+                } -> setCurrentRange (clauseLHSRange cl) $ do
+          let
+            trhs = unArg t
+          oldCall <- asksTC envCall
+          reportSDoc "tc.cover.iapply" 40 $ "tel =" <+> prettyTCM clTel
+          reportSDoc "tc.cover.iapply" 40 $ "ps =" <+> pretty ps
+          ps <- normaliseProjP ps
+          forM_ (iApplyVars ps) $ \ i -> do
+            unview <- intervalUnview'
+            let phi = unview $ IMax (argN $ unview (INeg $ argN $ var i)) $ argN $ var i
+            let es = patternsToElims ps
+            let lhs = Def f es
+
+            reportSDoc "tc.cover.iapply" 40 $ text "clause:" <+> pretty ps <+> "->" <+> pretty body
+            reportSDoc "tc.cover.iapply" 20 $ "body =" <+> prettyTCM body
+            inTopContext $ reportSDoc "tc.cover.iapply" 20 $ "Γ =" <+> prettyTCM clTel
+
+            let
+              k :: Substitution -> Comparison -> Type -> Term -> Term -> TCM ()
+              -- TODO (Amy, 2023-07-08): Simplifying the LHS of a
+              -- generated clause in its context is loopy, see #6722
+              k phi cmp ty u v | hasDefP ps = compareTerm cmp ty u v
+              k phi cmp ty u v = do
+                u_e   <- simplify u
+                -- Issue #6725: Print these terms in their own TC state.
+                -- If printing the values before entering the conversion
+                -- checker is too expensive then we could save the TC
+                -- state and print them when erroring instead, but that
+                -- might cause space leaks.
+                (u_p, v_p) <- (,) <$> prettyTCM u_e <*> (prettyTCM =<< simplify v)
+
+                let
+                  -- Make note of the context (literally): we're
+                  -- checking that this specific clause in f is
+                  -- confluent with IApply reductions. That way if we
+                  -- can tell the user what the endpoints are.
+                  why = CheckIApplyConfluence
+                    (getRange cl) f
+                    (applySubst phi lhs)
+                    u_e v ty
+
+                  -- But if the conversion checking failed really early, we drop the extra
+                  -- information. In that case, it's just noise.
+                  maybeDropCall e@(TypeError loc s err)
+                    | UnequalTerms _ u' v' _ <- clValue err =
+                      -- Issue #6725: restore the TC state from the
+                      -- error before dealing with the stored terms.
+                      withTCState (const s) $ enterClosure err $ \e' -> do
+                        u' <- prettyTCM =<< simplify u'
+                        v' <- prettyTCM =<< simplify v'
+
+                        -- Specifically, we compare how the things are pretty-printed, to avoid
+                        -- double-printing, rather than a more refined heuristic, since the
+                        -- “failure case” here is *at worst* accidentally reminding the user of how
+                        -- IApplyConfluence works.
+                        if (u_p == u' && v_p == v')
+                          then localTC (\e -> e { envCall = oldCall }) $ typeError e'
+                          else throwError e
+                  maybeDropCall x = throwError x
+
+                -- Note: Any postponed constraint with this call *will* have the extra
+                -- information. This is a feature: if the constraint is woken up later,
+                -- then it's probably a good idea to remind the user of what's going on,
+                -- instead of presenting a mysterious error.
+                traceCall why (compareTerm cmp ty u v `catchError` maybeDropCall)
+
+            addContext clTel $ compareTermOnFace' k CmpEq phi trhs lhs body
+
+-- | current context is of the form Γ.Δ
+unifyElims :: Args
+              -- ^ variables to keep   Γ ⊢ x_n .. x_0 : Γ
+           -> Args
+              -- ^ variables to solve  Γ.Δ ⊢ ts : Γ
+           -> (Substitution -> [(Term,Term)] -> TCM a)
+              -- Γ.Δ' ⊢ σ : Γ.Δ
+              -- Γ.Δ' new current context.
+              -- Γ.Δ' ⊢ [(x = u)]
+              -- Γ.Δ', [(x = u)] ⊢ id_g = ts[σ] : Γ
+           -> TCM a
+unifyElims vs ts k = do
+  dom <- getContext
+  let (binds' , eqs' ) = candidate (map unArg vs) (map unArg ts)
+      (binds'', eqss') =
+        unzip $
+        map (\(j, tts) -> case toList tts of
+                t : ts -> ((j, t), map (, var j) ts)
+                []     -> __IMPOSSIBLE__) $
+        IntMap.toList $ IntMap.fromListWith (<>) binds'
+      cod'  = codomain s (IntSet.fromList $ map fst binds'')
+      cod   = cod' dom
+      svs   = size vs
+      binds = IntMap.fromList $
+              map (second (raise (size cod - svs))) binds''
+      eqs   = map (first  (raise (size dom - svs))) $
+              eqs' ++ concat eqss'
+      s     = bindS binds
+  updateContext s cod' $ k s (s `applySubst` eqs)
+  where
+  candidate :: [Term] -> [Term] -> ([(Nat, DList Term)], [(Term, Term)])
+  candidate is ts = case (is, ts) of
+    (i : is, Var j [] : ts) -> first ((j, singleton i) :) $
+                               candidate is ts
+    (i : is, t : ts)        -> second ((i, t) :) $
+                               candidate is ts
+    ([],     [])            -> ([], [])
+    _                       -> __IMPOSSIBLE__
+
+  bindS binds = parallelS $
+    case IntMap.lookupMax binds of
+      Nothing       -> []
+      Just (max, _) -> for [0 .. max] $ \i ->
+        fromMaybe (deBruijnVar i) (IntMap.lookup i binds)
+
+  codomain
+    :: Substitution
+    -> IntSet  -- Support.
+    -> Context -> Context
+  codomain s vs =
+    mapMaybe (\(i, c) -> if i `IntSet.member` vs
+                         then Nothing
+                         else Just c) .
+    zipWith (\i c -> (i, dropS (i + 1) s `applySubst` c)) [0..]
+
+-- | Like @unifyElims@ but @Γ@ is from the meta's @MetaInfo@ and
+-- the context extension @Δ@ is taken from the @Closure@.
+unifyElimsMeta :: MetaId -> Args -> Closure Constraint -> ([(Term,Term)] -> Constraint -> TCM a) -> TCM a
+unifyElimsMeta m es_m cl k = ifM (isNothing . optCubical <$> pragmaOptions) (enterClosure cl $ k []) $ do
+                  mv <- lookupLocalMeta m
+                  enterClosure (getMetaInfo mv) $ \ _ -> do -- mTel ⊢
+                  ty <- metaType m
+                  mTel0 <- getContextTelescope
+                  unless (size mTel0 == size es_m) $ reportSDoc "tc.iapply.ip.meta" 20 $ "funny number of elims" <+> text (show (size mTel0, size es_m))
+                  unless (size mTel0 <= size es_m) $ __IMPOSSIBLE__ -- meta has at least enough arguments to fill its creation context.
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "ty: " <+> prettyTCM ty
+
+                  -- if we have more arguments we extend the telescope accordingly.
+                  TelV mTel1 _ <- telViewUpToPath (size es_m) ty
+                  addContext (mTel1 `apply` teleArgs mTel0) $ do
+                  mTel <- getContextTelescope
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "mTel: " <+> prettyTCM mTel
+
+                  es_m <- return $ take (size mTel) es_m
+                  -- invariant: size mTel == size es_m
+
+                  (c,cxt) <- enterClosure cl $ \ c -> (c,) <$> getContextTelescope
+                  reportSDoc "tc.iapply.ip.meta" 20 $ prettyTCM cxt
+
+                  addContext cxt $ do
+
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "es_m" <+> prettyTCM es_m
+
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "trying unifyElims"
+
+                  unifyElims (teleArgs mTel) es_m $ \ sigma eqs -> do
+
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "gotten a substitution"
+
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "sigma:" <+> prettyTCM sigma
+                  reportSDoc "tc.iapply.ip.meta" 20 $ "sigma:" <+> pretty sigma
+
+                  k eqs (sigma `applySubst` c)
diff --git a/src/full/Agda/TypeChecking/Implicit.hs b/src/full/Agda/TypeChecking/Implicit.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Implicit.hs
@@ -0,0 +1,229 @@
+{-# LANGUAGE PatternSynonyms #-}
+
+{-| Functions for inserting implicit arguments at the right places.
+-}
+module Agda.TypeChecking.Implicit where
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.IO.Class
+
+import Agda.Syntax.Position (beginningOf, getRange)
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract (Binder, mkBinder_)
+import Agda.Syntax.Internal as I
+
+import Agda.TypeChecking.Irrelevance
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Term (unquoteTactic)
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Tuple
+
+-- Cut and paste from insertImplicitPatternsT:
+
+-- | Insert implicit binders in a list of binders, but not at the end.
+insertImplicitBindersT
+  :: (PureTCM m, MonadError TCErr m, MonadFresh NameId m, MonadTrace m)
+  => [NamedArg Binder]     -- ^ Should be non-empty, otherwise nothing happens.
+  -> Type                  -- ^ Function type eliminated by arguments given by binders.
+  -> m [NamedArg Binder] -- ^ Padded binders.
+insertImplicitBindersT = \case
+  []     -> \ _ -> return []
+  b : bs -> List1.toList <.> insertImplicitBindersT1 (b :| bs)
+
+-- | Insert implicit binders in a list of binders, but not at the end.
+insertImplicitBindersT1
+  :: (PureTCM m, MonadError TCErr m, MonadFresh NameId m, MonadTrace m)
+  => List1 (NamedArg Binder)        -- ^ Non-empty.
+  -> Type                           -- ^ Function type eliminated by arguments given by binders.
+  -> m (List1 (NamedArg Binder))  -- ^ Padded binders.
+insertImplicitBindersT1 bs@(b :| _) a = setCurrentRange b $ do
+  TelV tel ty0 <- telViewUpTo' (-1) (not . visible) a
+  reportSDoc "tc.term.lambda.imp" 20 $
+    vcat [ "insertImplicitBindersT"
+         , nest 2 $ "bs  = " <+> do
+             brackets $ fsep $ punctuate comma $ fmap prettyA bs
+         , nest 2 $ "tel = " <+> prettyTCM tel
+         , nest 2 $ "ty  = " <+> addContext tel (prettyTCM ty0)
+         ]
+  reportSDoc "tc.term.lambda.imp" 70 $
+    vcat [ "insertImplicitBindersT"
+         , nest 2 $ "bs  = " <+> (text . show . List1.toList) bs
+         , nest 2 $ "tel = " <+> (text . show) tel
+         , nest 2 $ "ty  = " <+> (text . show) ty0
+         ]
+  hs <- insImp b tel
+  -- Continue with implicit binders inserted before @b@.
+  let bs0@(b1 :| bs1) = List1.prependList hs bs
+  reduce a >>= piOrPath >>= \case
+    -- If @a@ is a function (or path) type, continue inserting after @b1@.
+    Left (_, ty) -> (b1 :|) <$> insertImplicitBindersT bs1 (absBody ty)
+    -- Otherwise, we are done.
+    Right{}      -> return bs0
+  where
+  insImp b EmptyTel = return []
+  insImp b tel = case insertImplicit b $ telToList tel of
+    BadImplicits   -> typeError WrongHidingInLHS
+    NoSuchName x   -> typeError WrongHidingInLHS
+    ImpInsert doms -> mapM implicitArg doms
+      where
+      implicitArg d = setOrigin Inserted . unnamedArg (domInfo d) . mkBinder_ <$> do
+        freshNoName $ beginningOf $ getRange b
+
+-- | @implicitArgs n expand t@ generates up to @n@ implicit argument
+--   metas (unbounded if @n<0@), as long as @t@ is a function type
+--   and @expand@ holds on the hiding info of its domain.
+
+implicitArgs
+  :: (PureTCM m, MonadMetaSolver m, MonadTCM m)
+  => Int               -- ^ @n@, the maximum number of implicts to be inserted.
+  -> (Hiding -> Bool)  -- ^ @expand@, the predicate to test whether we should keep inserting.
+  -> Type              -- ^ The (function) type @t@ we are eliminating.
+  -> m (Args, Type)  -- ^ The eliminating arguments and the remaining type.
+implicitArgs n expand t = mapFst (map (fmap namedThing)) <$> do
+  implicitNamedArgs n (\ h x -> expand h) t
+
+-- | @implicitNamedArgs n expand t@ generates up to @n@ named implicit arguments
+--   metas (unbounded if @n<0@), as long as @t@ is a function type
+--   and @expand@ holds on the hiding and name info of its domain.
+
+implicitNamedArgs
+  :: (PureTCM m, MonadMetaSolver m, MonadTCM m)
+  => Int                          -- ^ @n@, the maximum number of implicts to be inserted.
+  -> (Hiding -> ArgName -> Bool)  -- ^ @expand@, the predicate to test whether we should keep inserting.
+  -> Type                         -- ^ The (function) type @t@ we are eliminating.
+  -> m (NamedArgs, Type)        -- ^ The eliminating arguments and the remaining type.
+implicitNamedArgs 0 expand t0 = return ([], t0)
+implicitNamedArgs n expand t0 = do
+    t0' <- reduce t0
+    reportSDoc "tc.term.args" 30 $ "implicitNamedArgs" <+> prettyTCM t0'
+    reportSDoc "tc.term.args" 80 $ "implicitNamedArgs" <+> text (show t0')
+    case unEl t0' of
+      Pi dom@Dom{domInfo = info, domTactic = tac, unDom = a} b
+        | let x = bareNameWithDefault "_" dom, expand (getHiding info) x -> do
+          info' <- if hidden info then return info else do
+            reportSDoc "tc.term.args.ifs" 15 $
+              "inserting instance meta for type" <+> prettyTCM a
+            reportSDoc "tc.term.args.ifs" 40 $ nest 2 $ vcat
+              [ "x      = " <+> text (show x)
+              , "hiding = " <+> text (show $ getHiding info)
+              ]
+
+            return $ makeInstance info
+          (_, v) <- newMetaArg info' x CmpLeq a
+          whenJust tac $ \ tac -> liftTCM $
+            applyModalityToContext info $ unquoteTactic tac v a
+          let narg = Arg info (Named (Just $ WithOrigin Inserted $ unranged x) v)
+          mapFst (narg :) <$> implicitNamedArgs (n-1) expand (absApp b v)
+      _ -> return ([], t0')
+
+-- | Create a metavariable according to the 'Hiding' info.
+
+newMetaArg
+  :: (PureTCM m, MonadMetaSolver m)
+  => ArgInfo    -- ^ Kind/relevance of meta.
+  -> ArgName    -- ^ Name suggestion for meta.
+  -> Comparison -- ^ Check (@CmpLeq@) or infer (@CmpEq@) the type.
+  -> Type       -- ^ Type of meta.
+  -> m (MetaId, Term)  -- ^ The created meta as id and as term.
+newMetaArg info x cmp a = do
+  prp <- runBlocked $ isPropM a
+  let irrelevantIfProp =
+        applyWhen (prp == Right True) $ applyRelevanceToContext Irrelevant
+  applyModalityToContext info $ irrelevantIfProp $
+    newMeta (getHiding info) (argNameToString x) a
+  where
+    newMeta :: MonadMetaSolver m => Hiding -> String -> Type -> m (MetaId, Term)
+    newMeta Instance{} n = newInstanceMeta n
+    newMeta Hidden     n = newNamedValueMeta RunMetaOccursCheck n cmp
+    newMeta NotHidden  n = newNamedValueMeta RunMetaOccursCheck n cmp
+
+-- | Create a questionmark according to the 'Hiding' info.
+
+newInteractionMetaArg
+  :: ArgInfo    -- ^ Kind/relevance of meta.
+  -> ArgName    -- ^ Name suggestion for meta.
+  -> Comparison -- ^ Check (@CmpLeq@) or infer (@CmpEq@) the type.
+  -> Type       -- ^ Type of meta.
+  -> TCM (MetaId, Term)  -- ^ The created meta as id and as term.
+newInteractionMetaArg info x cmp a = do
+  applyModalityToContext info $
+    newMeta (getHiding info) (argNameToString x) a
+  where
+    newMeta :: Hiding -> String -> Type -> TCM (MetaId, Term)
+    newMeta Instance{} n = newInstanceMeta n
+    newMeta Hidden     n = newNamedValueMeta' RunMetaOccursCheck n cmp
+    newMeta NotHidden  n = newNamedValueMeta' RunMetaOccursCheck n cmp
+
+---------------------------------------------------------------------------
+
+-- | Possible results of 'insertImplicit'.
+data ImplicitInsertion
+      = ImpInsert [Dom ()] -- ^ Success: this many implicits have to be inserted (list can be empty).
+      | BadImplicits       -- ^ Error: hidden argument where there should have been a non-hidden argument.
+      | NoSuchName ArgName -- ^ Error: bad named argument.
+  deriving (Show)
+
+pattern NoInsertNeeded :: ImplicitInsertion
+pattern NoInsertNeeded = ImpInsert []
+
+-- | If the next given argument is @a@ and the expected arguments are @ts@
+--   @insertImplicit' a ts@ returns the prefix of @ts@ that precedes @a@.
+--
+--   If @a@ is named but this name does not appear in @ts@, the 'NoSuchName' exception is thrown.
+--
+insertImplicit
+  :: NamedArg e  -- ^ Next given argument @a@.
+  -> [Dom a]     -- ^ Expected arguments @ts@.
+  -> ImplicitInsertion
+insertImplicit a doms = insertImplicit' a $
+  for doms $ \ dom ->
+    dom $> bareNameWithDefault "_" dom
+
+-- | If the next given argument is @a@ and the expected arguments are @ts@
+--   @insertImplicit' a ts@ returns the prefix of @ts@ that precedes @a@.
+--
+--   If @a@ is named but this name does not appear in @ts@, the 'NoSuchName' exception is thrown.
+--
+insertImplicit'
+  :: NamedArg e     -- ^ Next given argument @a@.
+  -> [Dom ArgName]  -- ^ Expected arguments @ts@.
+  -> ImplicitInsertion
+insertImplicit' _ [] = BadImplicits
+insertImplicit' a ts
+
+  -- If @a@ is visible, then take the non-visible prefix of @ts@.
+  | visible a = ImpInsert $ takeWhile notVisible $ map void ts
+
+  -- If @a@ is named, take prefix of @ts@ until the name of @a@ (with correct hiding).
+  -- If the name is not found, throw exception 'NoSuchName'.
+  | Just x <- bareNameOf a = maybe (NoSuchName x) ImpInsert $
+      takeHiddenUntil (\ t -> x == unDom t && sameHiding a t) ts
+
+  -- If @a@ is neither visible nor named, take prefix of @ts@ with different hiding than @a@.
+  | otherwise = maybe BadImplicits ImpInsert $
+      takeHiddenUntil (sameHiding a) ts
+
+    where
+    -- @takeHiddenUntil p ts@ returns the 'getHiding' of the prefix of @ts@
+    -- until @p@ holds or a visible argument is encountered.
+    -- If @p@ never holds, 'Nothing' is returned.
+    --
+    --   Precondition: @p@ should imply @not . visible@.
+    takeHiddenUntil :: (Dom ArgName -> Bool) -> [Dom ArgName] -> Maybe [Dom ()]
+    takeHiddenUntil p ts =
+      case ts2 of
+        []      -> Nothing  -- Predicate was never true
+        (t : _) -> if visible t then Nothing else Just $ map void ts1
+      where
+      (ts1, ts2) = break (\ t -> p t || visible t) ts
diff --git a/src/full/Agda/TypeChecking/Injectivity.hs b/src/full/Agda/TypeChecking/Injectivity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Injectivity.hs
@@ -0,0 +1,507 @@
+{- |
+
+"Injectivity", or more precisely, "constructor headedness", is a
+property of functions defined by pattern matching that helps us solve
+constraints involving blocked applications of such functions.
+"Blocked" shall mean here that pattern matching is blocked on a meta
+variable, and constructor headedness lets us learn more about that
+meta variable.
+
+Consider the simple example:
+@
+  isZero : Nat -> Bool
+  isZero zero    = true
+  isZero (suc n) = false
+@
+This function is constructor-headed, meaning that all rhss are headed
+by a distinct constructor.  Thus, on a constraint like
+@
+  isZero ?X = false : Bool
+@
+involving an application of @isZero@ that is blocked on meta variable @?X@,
+we can exploit injectivity and learn that @?X = suc ?Y@ for a new
+meta-variable @?Y@.
+
+Which functions qualify for injectivity?
+
+1. The function needs to have at least one non-absurd clause that has
+a proper match, meaning that the function can actually be blocked on a
+meta.  Proper matches are these patterns:
+
+  - data constructor (@ConP@, but not record constructor)
+  - literal (@LitP@)
+  - HIT-patterns (@DefP@)
+
+Projection patterns (@ProjP@) are excluded because metas cannot occupy their place!
+
+2. All the clauses that satisfy (1.) need to be headed by a distinct constructor.
+
+-}
+
+module Agda.TypeChecking.Injectivity where
+
+import Control.Applicative
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Fail
+import Control.Monad.State
+import Control.Monad.Reader
+import Control.Monad.Trans.Maybe
+
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.Maybe
+import Data.Traversable hiding (for)
+import Data.Semigroup ((<>))
+import Data.Foldable (fold)
+
+import qualified Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Irrelevance (isIrrelevantOrPropM)
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope.Path
+import Agda.TypeChecking.Reduce
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Polarity
+import Agda.TypeChecking.Warnings
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import qualified Agda.Utils.ProfileOptions as Profile
+
+import Agda.Utils.Impossible
+
+headSymbol :: Term -> TCM (Maybe TermHead)
+headSymbol v = do -- ignoreAbstractMode $ do
+  -- Andreas, 2013-02-18 ignoreAbstractMode leads to information leakage
+
+  v <- constructorForm =<< ignoreBlocking <$> reduceHead v
+  case v of
+    Def f _ -> do
+      let yes = return $ Just $ ConsHead f
+          no  = return $ Nothing
+      def <- theDef <$> do ignoreAbstractMode $ getConstInfo f
+        -- Andreas, 2013-02-18
+        -- if we do not ignoreAbstractMode here, abstract Functions get turned
+        -- into Axioms, but we want to distinguish these.
+      case def of
+        Datatype{}  -> yes
+        Record{}    -> yes
+        DataOrRecSig{} -> yes
+        Axiom{}     -> do
+          reportSLn "tc.inj.axiom" 50 $ "headSymbol: " ++ prettyShow f ++ " is an Axiom."
+          -- Don't treat axioms in the current mutual block
+          -- as constructors (they might have definitions we
+          -- don't know about yet).
+          caseMaybeM (asksTC envMutualBlock) yes $ \ mb -> do
+            fs <- mutualNames <$> lookupMutualBlock mb
+            if Set.member f fs then no else yes
+        Function{}    -> no
+        Primitive{}   -> no
+        PrimitiveSort{} -> no
+        GeneralizableVar{} -> __IMPOSSIBLE__
+        Constructor{} -> __IMPOSSIBLE__
+        AbstractDefn{}-> __IMPOSSIBLE__
+    -- Andreas, 2019-07-10, issue #3900: canonicalName needs ignoreAbstractMode
+    Con c _ _ -> ignoreAbstractMode $ do
+                 q <- canonicalName (conName c)
+                 ifM (isPathCons q) (return Nothing) $
+                     {- else -}     return $ Just $ ConsHead q
+    Sort _  -> return (Just SortHead)
+    Pi _ _  -> return (Just PiHead)
+    Var i [] -> return (Just $ VarHead i) -- Only naked variables. Otherwise substituting a neutral term is not guaranteed to stay neutral.
+    Lit _   -> return Nothing -- TODO: LitHead (for literals with no constructorForm)
+    Lam{}   -> return Nothing
+    Var{}   -> return Nothing
+    Level{} -> return Nothing
+    MetaV{} -> return Nothing
+    DontCare{} -> return Nothing
+    Dummy s _ -> __IMPOSSIBLE_VERBOSE__ s
+
+-- | Is this a matchable definition, or constructor, which reduces based
+-- on interval substitutions?
+isUnstableDef :: PureTCM m => QName -> m Bool
+isUnstableDef qn = do
+  defn <- getConstInfo qn
+  prims <- traverse getPrimitiveName'
+    [ builtinHComp
+    , builtinComp
+    , builtinTrans
+    , builtinGlue
+    , builtin_glue
+    , builtin_glueU ]
+  case theDef defn of
+    _ | any (Just qn ==) prims -> pure True
+    Function{funIsKanOp = Just _} -> pure True
+    _ -> pure False
+
+
+-- | Do a full whnf and treat neutral terms as rigid. Used on the arguments to
+--   an injective functions and to the right-hand side. Only returns
+--   heads which are stable under interval substitution, i.e. NOT path
+--   constructors or generated hcomp/transp!
+headSymbol'
+  :: (PureTCM m, MonadError TCErr m)
+  => Term -> m (Maybe TermHead)
+headSymbol' v = do
+  v <- traverse constructorForm =<< reduceB v
+  case v of
+    Blocked{} -> return Nothing
+    NotBlocked _ v -> case v of
+      Def g _    ->
+        ifM (isUnstableDef g)
+          (pure Nothing)
+          (pure . Just $ ConsHead g)
+      Con c _ _  -> do
+        q <- canonicalName (conName c)
+        ifM (isPathCons q)
+          (pure Nothing)
+          (return $ Just $ ConsHead q)
+      Var i _    -> return $ Just (VarHead i)
+      Sort _     -> return $ Just SortHead
+      Pi _ _     -> return $ Just PiHead
+      Lit _      -> return Nothing
+      Lam{}      -> return Nothing
+      Level{}    -> return Nothing
+      DontCare{} -> return Nothing
+      MetaV{}    -> __IMPOSSIBLE__
+      Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+-- | Does deBruijn variable i correspond to a top-level argument, and if so
+--   which one (index from the left).
+topLevelArg :: Clause -> Int -> Maybe TermHead
+topLevelArg Clause{ namedClausePats = ps } i =
+  case [ n | (n, VarP _ (DBPatVar _ j)) <- zip [0..] $ map namedArg ps, i == j ] of
+    []    -> Nothing
+    [n]   -> Just (VarHead n)
+    _:_:_ -> __IMPOSSIBLE__
+
+-- | Join a list of inversion maps.
+joinHeadMaps :: [InversionMap c] -> InversionMap c
+joinHeadMaps = Map.unionsWith (<>)
+
+-- | Update the heads of an inversion map.
+updateHeads :: Monad m => (TermHead -> [c] -> m TermHead) -> InversionMap c -> m (InversionMap c)
+updateHeads f m = joinHeadMaps <$> mapM f' (Map.toList m)
+  where f' (h, c) = (`Map.singleton` c) <$> f h c
+
+checkInjectivity :: QName -> [Clause] -> TCM FunctionInverse
+checkInjectivity f cs0
+  | not (any properlyMatchingClause cs) = do
+      reportSLn "tc.inj.check.pointless" 35 $
+        "Injectivity of " ++ prettyShow (A.qnameToConcrete f) ++ " would be pointless."
+      return NotInjective
+  | otherwise = checkInjectivity' f cs
+  where
+    -- We can filter out absurd clauses.
+    cs = filter (isJust . clauseBody) cs0
+    -- We cannot filter out clauses that have no proper match, because
+    -- these could be catch-all clauses.
+    -- However, we need at least one proper match to get injectivity started.
+    properlyMatchingClause =
+      any (properlyMatching' False False . namedArg) . namedClausePats
+
+-- | Precondition: all the given clauses are non-absurd and contain a proper match.
+checkInjectivity' :: QName -> [Clause] -> TCM FunctionInverse
+checkInjectivity' f cs = fromMaybe NotInjective <.> runMaybeT $ do
+  reportSLn "tc.inj.check" 40 $ "Checking injectivity of " ++ prettyShow f
+
+  let varToArg :: Clause -> TermHead -> MaybeT TCM TermHead
+      varToArg c (VarHead i) = MaybeT $ return $ topLevelArg c i
+      varToArg _ h           = return h
+
+  -- We don't need to consider absurd clauses
+  let computeHead c | hasDefP (namedClausePats c) = return []
+      -- hasDefP clauses are skipped, these matter only for --cubical, in which case the function will behave as NotInjective.
+      computeHead c@Clause{ clauseBody = Just body , clauseType = Just tbody } = addContext (clauseTel c) $ do
+        maybeIrr <- fromRight (const True) <.> runBlocked $ isIrrelevantOrPropM tbody
+        -- We treat ordinary clauses with IApply copatterns as *immediately*
+        -- failing the injectivity check. Consider e.g.
+        --   foo x = T
+        --   foo (y i) = Glue U λ { (i = i0) → T , _ ; (i = i1) → T , _ }
+        -- seeing foo α = Glue ... and inverting it to α = y β loses solutions. E.g. if we
+        -- later had some other α = x, now we're screwed, x ≠ y β. But if we had postponed
+        -- originally we'd just compare T = Glue ... which has a chance of going through.
+        let ivars = iApplyVars (namedClausePats c)
+        guard (null ivars)
+        h <- if maybeIrr then return UnknownHead else
+          varToArg c =<< do
+            lift $ fromMaybe UnknownHead <$> do
+              headSymbol body
+        return [Map.singleton h [c]]
+      computeHead _ = return []
+
+  hdMap <- joinHeadMaps . concat <$> mapM computeHead cs
+
+  case Map.lookup UnknownHead hdMap of
+    Just (_:_:_) -> empty -- More than one unknown head: we can't really do anything in that case.
+    _            -> return ()
+
+  reportSLn  "tc.inj.check" 20 $ prettyShow f ++ " is potentially injective."
+  reportSDoc "tc.inj.check" 30 $ nest 2 $ vcat $
+    for (Map.toList hdMap) $ \ (h, uc) ->
+      text (prettyShow h) <+> "-->" <+>
+      case uc of
+        [c] -> prettyTCM $ map namedArg $ namedClausePats c
+        _   -> "(multiple clauses)"
+  return $ Inverse hdMap
+
+-- | If a clause is over-applied we can't trust the head (Issue 2944). For
+--   instance, the clause might be `f ps = u , v` and the actual call `f vs
+--   .fst`. In this case the head will be the head of `u` rather than `_,_`.
+checkOverapplication
+  :: forall m. (HasConstInfo m)
+  => Elims -> InversionMap Clause -> m (InversionMap Clause)
+checkOverapplication es = updateHeads overapplied
+  where
+    overapplied :: TermHead -> [Clause] -> m TermHead
+    overapplied h cs | all (not . isOverapplied) cs = return h
+    overapplied h cs = ifM (isSuperRigid h) (return h) (return UnknownHead)
+
+    -- A super-rigid head is one that can't be eliminated. Crucially, this is
+    -- applied after instantiateVars, so VarHeads are really bound variables.
+    isSuperRigid SortHead     = return True
+    isSuperRigid PiHead       = return True
+    isSuperRigid VarHead{}    = return True
+    isSuperRigid UnknownHead  = return True -- or False, doesn't matter
+    isSuperRigid (ConsHead q) = do
+      def <- getConstInfo q
+      return $ case theDef def of
+        Axiom{}        -> True
+        DataOrRecSig{} -> True
+        AbstractDefn{} -> True
+        Function{}     -> False
+        Datatype{}     -> True
+        Record{}       -> True
+        Constructor{conSrcCon = ConHead{ conDataRecord = d, conFields = fs }}
+                       -> d == IsData || null fs   -- Record constructors can be eliminated by projections
+        Primitive{}    -> False
+        PrimitiveSort{} -> __IMPOSSIBLE__
+        GeneralizableVar{} -> __IMPOSSIBLE__
+
+
+    isOverapplied Clause{ namedClausePats = ps } = length es > length ps
+
+-- | Turn variable heads, referring to top-level argument positions, into
+--   proper heads. These might still be `VarHead`, but in that case they refer to
+--   deBruijn variables. Checks that the instantiated heads are still rigid and
+--   distinct.
+instantiateVarHeads
+  :: forall m c. (PureTCM m, MonadError TCErr m)
+  => QName -> Elims -> InversionMap c -> m (Maybe (InversionMap c))
+instantiateVarHeads f es m = runMaybeT $ updateHeads (const . instHead) m
+  where
+    instHead :: TermHead -> MaybeT m TermHead
+    instHead h@(VarHead i)
+      | Just (Apply arg) <- es !!! i = MaybeT $ headSymbol' (unArg arg)
+      | otherwise = empty   -- impossible?
+    instHead h = return h
+
+-- | Argument should be in weak head normal form.
+functionInverse
+  :: (PureTCM m, MonadError TCErr m)
+  => Term -> m InvView
+functionInverse = \case
+  Def f es -> do
+    inv <- defInverse <$> getConstInfo f
+    cubical <- optCubical <$> pragmaOptions
+    case inv of
+      NotInjective -> return NoInv
+      Inverse m -> maybe NoInv (Inv f es) <$> (traverse (checkOverapplication es) =<< instantiateVarHeads f es m)
+        -- NB: Invertible functions are never classified as
+        --     projection-like, so this is fine, we are not
+        --     missing parameters.  (Andreas, 2013-11-01)
+  _ -> return NoInv
+
+data InvView = Inv QName [Elim] (InversionMap Clause)
+             | NoInv
+
+-- | Precondition: The first term must be blocked on the given meta and the second must be neutral.
+useInjectivity :: MonadConversion m => CompareDirection -> Blocker -> CompareAs -> Term -> Term -> m ()
+useInjectivity dir blocker ty blk neu = locallyTC eInjectivityDepth succ $ do
+  inv <- functionInverse blk
+  -- Injectivity might cause non-termination for unsatisfiable constraints
+  -- (#431, #3067). Look at the number of active problems and the injectivity
+  -- depth to detect this.
+  nProblems <- Set.size <$> viewTC eActiveProblems
+  injDepth  <- viewTC eInjectivityDepth
+  let depth = max nProblems injDepth
+  maxDepth  <- maxInversionDepth
+  case inv of
+    NoInv            -> fallback  -- not invertible
+    Inv f blkArgs hdMap
+      | depth > maxDepth -> warning (InversionDepthReached f) >> fallback
+      | otherwise -> do
+      reportSDoc "tc.inj.use" 30 $ fsep $
+        pwords "useInjectivity on" ++
+        [ prettyTCM blk, prettyTCM cmp, prettyTCM neu, prettyTCM ty]
+      whenProfile Profile.Conversion $ tick "compare by reduction: injectivity"
+      let canReduceToSelf = Map.member (ConsHead f) hdMap || Map.member UnknownHead hdMap
+      case neu of
+        -- f us == f vs  <=>  us == vs
+        -- Crucially, this relies on `f vs` being neutral and only works
+        -- if `f` is not a possible head for `f us`.
+        Def f' neuArgs | f == f', not canReduceToSelf -> do
+          fTy <- defType <$> getConstInfo f
+          reportSDoc "tc.inj.use" 20 $ vcat
+            [ fsep (pwords "comparing application of injective function" ++ [prettyTCM f] ++
+                  pwords "at")
+            , nest 2 $ fsep $ punctuate comma $ map prettyTCM blkArgs
+            , nest 2 $ fsep $ punctuate comma $ map prettyTCM neuArgs
+            , nest 2 $ "and type" <+> prettyTCM fTy
+            ]
+          fs  <- getForcedArgs f
+          pol <- getPolarity' cmp f
+          reportSDoc "tc.inj.invert.success" 20 $ hsep ["Successful spine comparison of", prettyTCM f]
+          whenProfile Profile.Conversion $ tick "compare by reduction: injectivity successful"
+          app (compareElims pol fs fTy (Def f [])) blkArgs neuArgs
+
+        -- f us == c vs
+        --    Find the clause unique clause `f ps` with head `c` and unify
+        --    us == ps  with fresh metas for the pattern variables of ps.
+        --    If there's no such clause we can safely throw an error.
+        _ -> headSymbol' neu >>= \ case
+          Nothing -> do
+            reportSDoc "tc.inj.use" 20 $ fsep $
+              pwords "no head symbol found for" ++ [prettyTCM neu] ++ pwords ", so not inverting"
+            fallback
+          Just (ConsHead f') | f == f', canReduceToSelf -> do
+            reportSDoc "tc.inj.use" 20 $ fsep $
+              pwords "head symbol" ++ [prettyTCM f'] ++ pwords "can reduce to self, so not inverting"
+            fallback
+                                    -- We can't invert in this case, since we can't
+                                    -- tell the difference between a solution that makes
+                                    -- the blocked term neutral and one that makes progress.
+          Just hd -> invertFunction cmp blk inv hd fallback err success
+            where err = typeError $ app (\ u v -> UnequalTerms cmp u v ty) blk neu
+  where
+    fallback     = addConstraint blocker $ app (ValueCmp cmp ty) blk neu
+    success blk' = app (compareAs cmp ty) blk' neu
+
+    cmpApp :: (Comparison, (a -> a -> b) -> a -> a -> b)
+    cmpApp = case dir of
+      DirEq -> (CmpEq, id)
+      DirLeq -> (CmpLeq, id)
+      DirGeq -> (CmpLeq, flip)
+    (cmp, app) = cmpApp
+
+-- | The second argument should be a blocked application and the third argument
+--   the inverse of the applied function.
+invertFunction
+  :: MonadConversion m
+  => Comparison -> Term -> InvView -> TermHead -> m () -> m () -> (Term -> m ()) -> m ()
+invertFunction _ _ NoInv _ fallback _ _ = fallback
+invertFunction cmp blk (Inv f blkArgs hdMap) hd fallback err success = do
+    fTy <- defType <$> getConstInfo f
+    reportSDoc "tc.inj.use" 20 $ vcat
+      [ "inverting injective function" <?> hsep [prettyTCM f, ":", prettyTCM fTy]
+      , "for" <?> pretty hd
+      , nest 2 $ "args =" <+> prettyList (map prettyTCM blkArgs)
+      ]                         -- Clauses with unknown heads are also possible candidates
+    case fromMaybe [] $ Map.lookup hd hdMap <> Map.lookup UnknownHead hdMap of
+      [] -> err
+      _:_:_ -> fallback
+      [cl@Clause{ clauseTel  = tel }] -> speculateMetas fallback $ do
+          let ps   = clausePats cl
+              perm = fromMaybe __IMPOSSIBLE__ $ clausePerm cl
+          -- These are what dot patterns should be instantiated at
+          ms <- map unArg <$> newTelMeta tel
+          reportSDoc "tc.inj.invert" 20 $ vcat
+            [ "meta patterns" <+> prettyList (map prettyTCM ms)
+            , "  perm =" <+> text (show perm)
+            , "  tel  =" <+> prettyTCM tel
+            , "  ps   =" <+> prettyList (map (text . prettyShow) ps)
+            ]
+          -- and this is the order the variables occur in the patterns
+          let msAux = permute (invertP __IMPOSSIBLE__ $ compactP perm) ms
+          let sub   = parallelS (reverse ms)
+          margs <- runReaderT (evalStateT (mapM metaElim ps) msAux) sub
+          reportSDoc "tc.inj.invert" 20 $ vcat
+            [ "inversion"
+            , nest 2 $ vcat
+              [ "lhs  =" <+> prettyTCM margs
+              , "rhs  =" <+> prettyTCM blkArgs
+              , "type =" <+> prettyTCM fTy
+              ]
+            ]
+          -- Since we do not care for the value of non-variant metas here,
+          -- we can treat 'Nonvariant' as 'Invariant'.
+          -- That ensures these metas do not remain unsolved.
+          pol <- purgeNonvariant <$> getPolarity' cmp f
+          fs  <- getForcedArgs f
+          -- The clause might not give as many patterns as there
+          -- are arguments (point-free style definitions).
+          let blkArgs' = take (length margs) blkArgs
+          compareElims pol fs fTy (Def f []) margs blkArgs'
+
+          -- Check that we made progress.
+          r <- liftReduce $ unfoldDefinitionStep (Def f []) f blkArgs
+          case r of
+            YesReduction _ blk' -> do
+              reportSDoc "tc.inj.invert.success" 20 $ hsep ["Successful inversion of", prettyTCM f, "at", pretty hd]
+              KeepMetas <$ success blk'
+            NoReduction{}       -> do
+              reportSDoc "tc.inj.invert" 30 $ vcat
+                [ "aborting inversion;" <+> prettyTCM blk
+                , "does not reduce"
+                ]
+              return RollBackMetas
+  where
+    nextMeta :: (MonadState [Term] m, MonadFail m) => m Term
+    nextMeta = do
+      m : ms <- get
+      put ms
+      return m
+
+    dotP :: MonadReader Substitution m => Term -> m Term
+    dotP v = do
+      sub <- ask
+      return $ applySubst sub v
+
+    metaElim
+      :: (MonadState [Term] m, MonadReader Substitution m, HasConstInfo m, MonadFail m)
+      => Arg DeBruijnPattern -> m Elim
+    metaElim (Arg _ (ProjP o p))  = Proj o <$> getOriginalProjection p
+    metaElim (Arg info p)         = Apply . Arg info <$> metaPat p
+
+    metaArgs
+      :: (MonadState [Term] m, MonadReader Substitution m, MonadFail m)
+      => [NamedArg DeBruijnPattern] -> m Args
+    metaArgs args = mapM (traverse $ metaPat . namedThing) args
+
+    metaPat
+      :: (MonadState [Term] m, MonadReader Substitution m, MonadFail m)
+      => DeBruijnPattern -> m Term
+    metaPat (DotP _ v)       = dotP v
+    metaPat (VarP _ _)       = nextMeta
+    metaPat (IApplyP{})      = nextMeta
+    metaPat (ConP c mt args) = Con c (fromConPatternInfo mt) . map Apply <$> metaArgs args
+    metaPat (DefP o q args)  = Def q . map Apply <$> metaArgs args
+    metaPat (LitP _ l)       = return $ Lit l
+    metaPat ProjP{}          = __IMPOSSIBLE__
+
+forcePiUsingInjectivity :: Type -> TCM Type
+forcePiUsingInjectivity t = reduceB t >>= \ case
+    Blocked _ blkTy -> do
+      let blk = unEl blkTy
+      inv <- functionInverse blk
+      blkTy <$ invertFunction CmpEq blk inv PiHead fallback err success
+    NotBlocked _ t -> return t
+  where
+    fallback  = return ()
+    err       = typeError (ShouldBePi t)
+    success _ = return ()
diff --git a/src/full/Agda/TypeChecking/Inlining.hs b/src/full/Agda/TypeChecking/Inlining.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Inlining.hs
@@ -0,0 +1,30 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Logic for deciding which functions should be automatically inlined.
+module Agda.TypeChecking.Inlining (autoInline) where
+
+import qualified Data.IntMap as IntMap
+
+import Agda.Interaction.Options
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Free
+import Agda.Utils.Lens
+
+-- | Mark a definition to be inlined if it satisfies the inlining criterion.
+autoInline :: Defn -> TCM Defn
+autoInline defn = do
+  inlining <- optAutoInline <$> pragmaOptions
+  if | inlining, shouldInline defn -> return $ set funInline True defn
+     | otherwise                   -> return defn
+
+shouldInline :: Defn -> Bool
+shouldInline Function{funCompiled = Just cc} = shouldInline' cc
+shouldInline _ = False
+
+-- Only auto-inline simple definitions (no pattern matching) where no variable
+-- is used more than once, and some variables are not used at all.
+shouldInline' :: CompiledClauses -> Bool
+shouldInline' (Done xs body) = all (< 2) counts && length counts < length xs
+  where counts = IntMap.elems $ varCounts $ freeVars body
+shouldInline' _ = False
diff --git a/src/full/Agda/TypeChecking/InstanceArguments.hs b/src/full/Agda/TypeChecking/InstanceArguments.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/InstanceArguments.hs
@@ -0,0 +1,636 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.InstanceArguments
+  ( findInstance
+  , isInstanceConstraint
+  , solveAwakeInstanceConstraints
+  , shouldPostponeInstanceSearch
+  , postponeInstanceConstraints
+  , getInstanceCandidates
+  ) where
+
+import Control.Monad        ( forM )
+import Control.Monad.Except ( ExceptT(..), runExceptT, MonadError(..) )
+import Control.Monad.Trans  ( lift )
+
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import qualified Data.List as List
+import Data.Function (on)
+import Data.Monoid hiding ((<>))
+import Data.Foldable (foldrM)
+
+import Agda.Interaction.Options (optQualifiedInstances)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Name (isQualified)
+import Agda.Syntax.Position
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Scope.Base (isNameInScope, inverseScopeLookupName', AllowAmbiguousNames(..))
+
+import Agda.TypeChecking.Conversion.Pure (pureEqualTerm)
+import Agda.TypeChecking.Errors () --instance only
+import Agda.TypeChecking.Implicit (implicitArgs)
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import {-# SOURCE #-} Agda.TypeChecking.Constraints
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+
+import qualified Agda.Benchmarking as Benchmark
+import Agda.TypeChecking.Monad.Benchmark (billTo)
+
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Null (empty)
+
+import Agda.Utils.Impossible
+
+-- | Compute a list of instance candidates.
+--   'Nothing' if target type or any context type is a meta, error if
+--   type is not eligible for instance search.
+initialInstanceCandidates :: Type -> TCM (Either Blocker [Candidate])
+initialInstanceCandidates t = do
+  (_ , otn) <- getOutputTypeName t
+  case otn of
+    NoOutputTypeName -> typeError $ GenericError $
+      "Instance search can only be used to find elements in a named type"
+    OutputTypeNameNotYetKnown b -> do
+      reportSDoc "tc.instance.cands" 30 $ "Instance type is not yet known. "
+      return (Left b)
+    OutputTypeVisiblePi -> typeError $ GenericError $
+      "Instance search cannot be used to find elements in an explicit function type"
+    OutputTypeVar    -> do
+      reportSDoc "tc.instance.cands" 30 $ "Instance type is a variable. "
+      runBlocked getContextVars
+    OutputTypeName n -> do
+      reportSDoc "tc.instance.cands" 30 $ "Found instance type head: " <+> prettyTCM n
+      runBlocked getContextVars >>= \case
+        Left b -> return $ Left b
+        Right ctxVars -> Right . (ctxVars ++) <$> getScopeDefs n
+  where
+    -- get a list of variables with their type, relative to current context
+    getContextVars :: BlockT TCM [Candidate]
+    getContextVars = do
+      ctx <- getContext
+      reportSDoc "tc.instance.cands" 40 $ hang "Getting candidates from context" 2 (inTopContext $ prettyTCM $ PrettyContext ctx)
+          -- Context variables with their types lifted to live in the full context
+      let varsAndRaisedTypes = [ (var i, raise (i + 1) t) | (i, t) <- zip [0..] ctx ]
+          vars = [ Candidate LocalCandidate x t (isOverlappable info)
+                 | (x, Dom{domInfo = info, unDom = (_, t)}) <- varsAndRaisedTypes
+                 , isInstance info
+                 ]
+
+      -- {{}}-fields of variables are also candidates
+      let cxtAndTypes = [ (LocalCandidate, x, t) | (x, Dom{unDom = (_, t)}) <- varsAndRaisedTypes ]
+      fields <- concat <$> mapM instanceFields (reverse cxtAndTypes)
+      reportSDoc "tc.instance.fields" 30 $
+        if null fields then "no instance field candidates" else
+          "instance field candidates" $$ do
+            nest 2 $ vcat
+              [ sep [ (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":"
+                    , nest 2 $ prettyTCM t
+                    ]
+              | c@(Candidate q v t overlap) <- fields
+              ]
+
+      -- get let bindings
+      env <- asksTC envLetBindings
+      env <- mapM (traverse getOpen) $ Map.toList env
+      let lets = [ Candidate LocalCandidate v t False
+                 | (_, LetBinding _ v Dom{domInfo = info, unDom = t}) <- env
+                 , isInstance info
+                 , usableModality info
+                 ]
+      return $ vars ++ fields ++ lets
+
+    etaExpand :: (MonadTCM m, PureTCM m)
+              => Bool -> Type -> m (Maybe (QName, Args))
+    etaExpand etaOnce t =
+      isEtaRecordType t >>= \case
+        Nothing | etaOnce -> do
+          isRecordType t >>= \case
+            Nothing         -> return Nothing
+            Just (r, vs, _) -> do
+              m <- currentModule
+              -- Are we inside the record module? If so it's safe and desirable
+              -- to eta-expand once (issue #2320).
+              if qnameToList0 r `List.isPrefixOf` mnameToList m
+                then return (Just (r, vs))
+                else return Nothing
+        r -> return r
+
+    instanceFields :: (CandidateKind,Term,Type) -> BlockT TCM [Candidate]
+    instanceFields = instanceFields' True
+
+    instanceFields' :: Bool -> (CandidateKind,Term,Type) -> BlockT TCM [Candidate]
+    instanceFields' etaOnce (q, v, t) =
+      ifBlocked t (\ m _ -> patternViolation m) $ \ _ t -> do
+      caseMaybeM (etaExpand etaOnce t) (return []) $ \ (r, pars) -> do
+        (tel, args) <- lift $ forceEtaExpandRecord r pars v
+        let types = map unDom $ applySubst (parallelS $ reverse $ map unArg args) (flattenTel tel)
+        fmap concat $ forM (zip args types) $ \ (arg, t) ->
+          ([ Candidate LocalCandidate (unArg arg) t (isOverlappable arg)
+           | isInstance arg ] ++) <$>
+          instanceFields' False (LocalCandidate, unArg arg, t)
+
+    getScopeDefs :: QName -> TCM [Candidate]
+    getScopeDefs n = do
+      instanceDefs <- getInstanceDefs
+      rel          <- viewTC eRelevance
+      let qs = maybe [] Set.toList $ Map.lookup n instanceDefs
+      catMaybes <$> mapM (candidate rel) qs
+
+    candidate :: Relevance -> QName -> TCM (Maybe Candidate)
+    candidate rel q = ifNotM (isNameInScope q <$> getScope) (return Nothing) $ do
+      -- Jesper, 2020-03-16: When using --no-qualified-instances,
+      -- filter out instances that are only in scope under a qualified
+      -- name.
+      filterQualified $ do
+      -- Andreas, 2012-07-07:
+      -- we try to get the info for q
+      -- while opening a module, q may be in scope but not in the signature
+      -- in this case, we just ignore q (issue 674)
+      flip catchError handle $ do
+        def <- getConstInfo q
+        if not (getRelevance def `moreRelevant` rel) then return Nothing else do
+          -- Andreas, 2017-01-14: instantiateDef is a bit of an overkill
+          -- if we anyway get the freeVarsToApply
+          -- WAS: t <- defType <$> instantiateDef def
+          args <- freeVarsToApply q
+          let t = defType def `piApply` args
+              rel = getRelevance $ defArgInfo def
+          let v = case theDef def of
+               -- drop parameters if it's a projection function...
+               Function{ funProjection = Right p } -> projDropParsApply p ProjSystem rel args
+               -- Andreas, 2014-08-19: constructors cannot be declared as
+               -- instances (at least as of now).
+               -- I do not understand why the Constructor case is not impossible.
+               -- Ulf, 2014-08-20: constructors are always instances.
+               Constructor{ conSrcCon = c }       -> Con c ConOSystem []
+               _                                  -> Def q $ map Apply args
+          return $ Just $ Candidate (GlobalCandidate q) v t False
+      where
+        -- unbound constant throws an internal error
+        handle (TypeError _ _ (Closure {clValue = InternalError _})) = return Nothing
+        handle err                                                   = throwError err
+
+        filterQualified :: TCM (Maybe Candidate) -> TCM (Maybe Candidate)
+        filterQualified m = ifM (optQualifiedInstances <$> pragmaOptions) m $ do
+          qc <- inverseScopeLookupName' AmbiguousAnything q <$> getScope
+          let isQual = maybe True isQualified $ listToMaybe qc
+          reportSDoc "tc.instance.qualified" 30 $
+            if isQual then
+              "dropping qualified instance" <+> prettyTCM q
+            else
+              "keeping instance" <+> prettyTCM q <+>
+              "since it is in scope as" <+> prettyTCM qc
+          if isQual then return Nothing else m
+
+
+-- | @findInstance m (v,a)s@ tries to instantiate on of the types @a@s
+--   of the candidate terms @v@s to the type @t@ of the metavariable @m@.
+--   If successful, meta @m@ is solved with the instantiation of @v@.
+--   If unsuccessful, the constraint is regenerated, with possibly reduced
+--   candidate set.
+--   The list of candidates is equal to @Nothing@ when the type of the meta
+--   wasn't known when the constraint was generated. In that case, try to find
+--   its type again.
+findInstance :: MetaId -> Maybe [Candidate] -> TCM ()
+findInstance m Nothing = do
+  -- Andreas, 2015-02-07: New metas should be created with range of the
+  -- current instance meta, thus, we set the range.
+  mv <- lookupLocalMeta m
+  setCurrentRange mv $ do
+    reportSLn "tc.instance" 20 $ "The type of the FindInstance constraint isn't known, trying to find it again."
+    t <- instantiate =<< getMetaTypeInContext m
+    reportSLn "tc.instance" 70 $ "findInstance 1: t: " ++ prettyShow t
+
+    -- Issue #2577: If the target is a function type the arguments are
+    -- potential candidates, so we add them to the context to make
+    -- initialInstanceCandidates pick them up.
+    TelV tel t <- telViewUpTo' (-1) notVisible t
+    cands <- addContext tel $ initialInstanceCandidates t
+    case cands of
+      Left unblock -> do
+        reportSLn "tc.instance" 20 "Can't figure out target of instance goal. Postponing constraint."
+        addConstraint unblock $ FindInstance m Nothing
+      Right cs -> findInstance m (Just cs)
+
+findInstance m (Just cands) =                          -- Note: if no blocking meta variable this will not unblock until the end of the mutual block
+  whenJustM (findInstance' m cands) $ (\ (cands, b) -> addConstraint b $ FindInstance m $ Just cands)
+
+-- | Entry point for `tcGetInstances` primitive
+getInstanceCandidates :: MetaId -> TCM (Either Blocker [Candidate])
+getInstanceCandidates m = wrapper where
+  wrapper = do
+    mv <- lookupLocalMeta m
+    setCurrentRange mv $ do
+      t <- instantiate =<< getMetaTypeInContext m
+      TelV tel t' <- telViewUpTo' (-1) notVisible t
+      addContext tel $ runExceptT (worker t')
+
+  worker :: Type -> ExceptT Blocker TCM [Candidate]
+  worker t' = do
+    cands <- ExceptT (initialInstanceCandidates t')
+    cands <- lift (checkCandidates m t' cands) <&> \case
+      Nothing         -> cands
+      Just (_, cands) -> fst <$> cands
+    cands <- lift (foldrM insertCandidate [] cands)
+    reportSDoc "tc.instance.sort" 20 $ nest 2 $ vcat
+      [ "sorted candidates"
+      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":" <+> prettyTCM t
+             | c@(Candidate q v t overlap) <- cands ] ]
+    pure cands
+
+-- | @'doesCandidateSpecialise' c1 c2@ checks whether the instance candidate @c1@
+-- /specialises/ the instance candidate @c2@, i.e., whether the type of
+-- @c2@ is a substitution instance of @c1@'s type.
+-- Only the final return type of the instances is considered: the
+-- presence of unsolvable instance arguments in the types of @c1@ or
+-- @c2@ does not affect the results of 'doesCandidateSpecialise'.
+doesCandidateSpecialise :: Candidate -> Candidate -> TCM Bool
+doesCandidateSpecialise c1@Candidate{candidateType = t1} c2@Candidate{candidateType = t2} = do
+  -- We compare
+  --    c1 : ∀ {Γ} → T
+  -- against
+  --    c2 : ∀ {Δ} → S
+  -- by moving to the context Γ ⊢, so that any variables in T's type are
+  -- "rigid", but *instantiating* S[?/Δ], so its variables are
+  -- "flexible"; then calling the conversion checker.
+
+  let
+    handle _ = do
+      reportSDoc "tc.instance.sort" 30 $ nest 2 "=> NOT specialisation"
+      pure False
+
+    wrap = flip catchError handle
+          -- Turn failures into returning false
+         . localTCState
+         -- Discard any changes to the TC state (metas from
+         -- instantiating t2, recursive instance constraints, etc)
+         . postponeInstanceConstraints
+         -- Don't spend any time looking for instances in the contexts
+
+  TelV tel t1 <- telView t1
+  addContext tel $ wrap $ do
+    (args, t2) <- implicitArgs (-1) (\h -> notVisible h) t2
+
+    reportSDoc "tc.instance.sort" 30 $ "Does" <+> prettyTCM c1 <+> "specialise" <+> (prettyTCM c2 <> "?")
+    reportSDoc "tc.instance.sort" 60 $ vcat
+      [ "Comparing candidate"
+      , nest 2 (prettyTCM c1 <+> colon <+> prettyTCM t1)
+      , "vs"
+      , nest 2 (prettyTCM c2 <+> colon <+> prettyTCM t2)
+      ]
+
+    leqType t2 t1
+    reportSDoc "tc.instance.sort" 30 $ nest 2 "=> IS specialisation"
+    pure True
+
+insertCandidate :: Candidate -> [Candidate] -> TCM [Candidate]
+insertCandidate x []     = pure [x]
+insertCandidate x (y:xs) = doesCandidateSpecialise x y >>= \case
+  True  -> pure (x:y:xs)
+  False -> (y:) <$> insertCandidate x xs
+
+-- | Result says whether we need to add constraint, and if so, the set of
+--   remaining candidates and an eventual blocking metavariable.
+findInstance' :: MetaId -> [Candidate] -> TCM (Maybe ([Candidate], Blocker))
+findInstance' m cands = ifM (isFrozen m) (do
+    reportSLn "tc.instance" 20 "Refusing to solve frozen instance meta."
+    return (Just (cands, neverUnblock))) $ do
+  ifM shouldPostponeInstanceSearch (do
+    reportSLn "tc.instance" 20 "Postponing possibly recursive instance search."
+    return $ Just (cands, neverUnblock)) $ billTo [Benchmark.Typing, Benchmark.InstanceSearch] $ do
+  -- Andreas, 2015-02-07: New metas should be created with range of the
+  -- current instance meta, thus, we set the range.
+  mv <- lookupLocalMeta m
+  setCurrentRange mv $ do
+      reportSLn "tc.instance" 15 $
+        "findInstance 2: constraint: " ++ prettyShow m ++ "; candidates left: " ++ show (length cands)
+      reportSDoc "tc.instance" 60 $ nest 2 $ vcat
+        [ sep [ (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":"
+              , nest 2 $ prettyTCM t ] | c@(Candidate q v t overlap) <- cands ]
+      reportSDoc "tc.instance" 70 $ "raw" $$ do
+       nest 2 $ vcat
+        [ sep [ (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":"
+              , nest 2 $ pretty t ] | c@(Candidate q v t overlap) <- cands ]
+      t <- getMetaTypeInContext m
+      reportSLn "tc.instance" 70 $ "findInstance 2: t: " ++ prettyShow t
+      insidePi t $ \ t -> do
+      reportSDoc "tc.instance" 15 $ "findInstance 3: t =" <+> prettyTCM t
+      reportSLn "tc.instance" 70 $ "findInstance 3: t: " ++ prettyShow t
+
+      mcands <-
+        -- Temporarily remove other instance constraints to avoid
+        -- redundant solution attempts
+        holdConstraints (const isInstanceProblemConstraint) $
+        checkCandidates m t cands
+
+      debugConstraints
+      case mcands of
+
+        Just ([(_, err)], []) -> do
+          reportSDoc "tc.instance" 15 $
+            "findInstance 5: the only viable candidate failed..."
+          throwError err
+        Just (errs, []) -> do
+          if null errs then reportSDoc "tc.instance" 15 $ "findInstance 5: no viable candidate found..."
+                       else reportSDoc "tc.instance" 15 $ "findInstance 5: all viable candidates failed..."
+          -- #3676: Sort the candidates based on the size of the range for the errors and
+          --        set the range of the full error to the range of the most precise candidate
+          --        error.
+          let sortedErrs = List.sortBy (compare `on` precision) errs
+                where precision (_, err) = maybe infinity iLength $ rangeToInterval $ getRange err
+                      infinity = 1000000000
+          setCurrentRange (take 1 $ map snd sortedErrs) $
+            typeError $ InstanceNoCandidate t [ (candidateTerm c, err) | (c, err) <- sortedErrs ]
+
+        Just (_, [(c@(Candidate q term t' _), v)]) -> do
+
+          reportSDoc "tc.instance" 15 $ vcat
+            [ "instance search: attempting"
+            , nest 2 $ prettyTCM m <+> ":=" <+> prettyTCM v
+            ]
+          reportSDoc "tc.instance" 70 $ nest 2 $
+            "candidate v = " <+> pretty v
+          ctxElims <- map Apply <$> getContextArgs
+          equalTerm t (MetaV m ctxElims) v
+
+          reportSDoc "tc.instance" 15 $ vcat
+            [ "findInstance 5: solved by instance search using the only candidate"
+            , nest 2 $ prettyTCM c <+> "=" <+> prettyTCM term
+            , "of type " <+> prettyTCM t'
+            , "for type" <+> prettyTCM t
+            ]
+
+          -- If we actually solved the constraints we should wake up any held
+          -- instance constraints, to make sure we don't forget about them.
+          wakeupInstanceConstraints
+          return Nothing  -- We’re done
+
+        _ -> do
+          let cs = maybe cands (map fst . snd) mcands -- keep the current candidates if Nothing
+          reportSDoc "tc.instance" 15 $
+            text ("findInstance 5: refined candidates: ") <+>
+            prettyTCM (List.map candidateTerm cs)
+          return (Just (cs, neverUnblock))
+
+insidePi :: Type -> (Type -> TCM a) -> TCM a
+insidePi t ret = reduce (unEl t) >>= \case
+    Pi a b     -> addContext (absName b, a) $ insidePi (absBody b) ret
+    Def{}      -> ret t
+    Var{}      -> ret t
+    Sort{}     -> __IMPOSSIBLE__
+    Con{}      -> __IMPOSSIBLE__
+    Lam{}      -> __IMPOSSIBLE__
+    Lit{}      -> __IMPOSSIBLE__
+    Level{}    -> __IMPOSSIBLE__
+    MetaV{}    -> __IMPOSSIBLE__
+    DontCare{} -> __IMPOSSIBLE__
+    Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+-- | Apply the computation to every argument in turn by reseting the state every
+--   time. Return the list of the arguments giving the result True.
+--
+--   If the resulting list contains exactly one element, then the state is the
+--   same as the one obtained after running the corresponding computation. In
+--   all the other cases, the state is reset.
+--
+--   Also returns the candidates that pass type checking but fails constraints,
+--   so that the error messages can be reported if there are no successful
+--   candidates.
+filterResetingState :: MetaId -> [Candidate] -> (Candidate -> TCM YesNo) -> TCM ([(Candidate, TCErr)], [(Candidate, Term)])
+filterResetingState m cands f = do
+  ctxArgs  <- getContextArgs
+  let ctxElims = map Apply ctxArgs
+  result <- mapM (\c -> do bs <- localTCStateSaving (f c); return (c, bs)) cands
+
+  -- Check that there aren't any hard failures
+  case [ err | (_, (HellNo err, _)) <- result ] of
+    err : _ -> throwError err
+    []      -> return ()
+
+  -- c : Candidate
+  -- r : YesNo
+  -- a : Type         (fully instantiated)
+  -- s : TCState
+  let result' = [ (c, v, s) | (c, (r, s)) <- result, v <- maybeToList (fromYes r) ]
+  result'' <- dropSameCandidates m result'
+  case result'' of
+    [(c, v, s)] -> ([], [(c,v)]) <$ putTC s
+    _           -> do
+      let bad  = [ (c, err) | (c, (NoBecause err, _)) <- result ]
+          good = [ (c, v) | (c, v, _) <- result'' ]
+      return (bad, good)
+
+-- Drop all candidates which are judgmentally equal to the first one.
+-- This is sufficient to reduce the list to a singleton should all be equal.
+dropSameCandidates :: MetaId -> [(Candidate, Term, a)] -> TCM [(Candidate, Term, a)]
+dropSameCandidates m cands0 = verboseBracket "tc.instance" 30 "dropSameCandidates" $ do
+  !nextMeta    <- nextLocalMeta
+  isRemoteMeta <- isRemoteMeta
+  -- Does "it" contain any fresh meta-variables?
+  let freshMetas =
+        getAny .
+        allMetas (\m -> Any (not (isRemoteMeta m || m < nextMeta)))
+
+  -- Take overlappable candidates into account
+  let cands =
+        case List.partition (\ (c, _, _) -> candidateOverlappable c) cands0 of
+          (cand : _, []) -> [cand]  -- only overlappable candidates: pick the first one
+          _              -> cands0  -- otherwise require equality
+
+  reportSDoc "tc.instance" 50 $ vcat
+    [ "valid candidates:"
+    , nest 2 $ vcat [ if freshMetas v then "(redacted)" else
+                      sep [ prettyTCM v ]
+                    | (_, v, _) <- cands ] ]
+  rel <- getRelevance <$> lookupMetaModality m
+  case cands of
+    []            -> return cands
+    cvd : _ | isIrrelevant rel -> do
+      reportSLn "tc.instance" 30 "dropSameCandidates: Meta is irrelevant so any candidate will do."
+      return [cvd]
+    cvd@(_, v, _) : vas
+      | freshMetas v -> do
+          reportSLn "tc.instance" 30 "dropSameCandidates: Solution of instance meta has fresh metas so we don't filter equal candidates yet"
+          return (cvd : vas)
+      | otherwise -> (cvd :) <$> dropWhileM equal vas
+      where
+        equal :: (Candidate, Term, a) -> TCM Bool
+        equal (_, v', _)
+            | freshMetas v' = return False  -- If there are fresh metas we can't compare
+            | otherwise     =
+          verboseBracket "tc.instance" 30 "dropSameCandidates: " $ do
+          reportSDoc "tc.instance" 30 $ sep [ prettyTCM v <+> "==", nest 2 $ prettyTCM v' ]
+          a <- uncurry piApplyM =<< ((,) <$> getMetaType m <*> getContextArgs)
+          runBlocked (pureEqualTerm a v v') <&> \case
+            Left{}  -> False
+            Right b -> b
+
+data YesNo = Yes Term | No | NoBecause TCErr | HellNo TCErr
+  deriving (Show)
+
+fromYes :: YesNo -> Maybe Term
+fromYes (Yes t) = Just t
+fromYes _       = Nothing
+
+-- | Given a meta @m@ of type @t@ and a list of candidates @cands@,
+-- @checkCandidates m t cands@ returns a refined list of valid candidates and
+-- candidates that failed some constraints.
+checkCandidates :: MetaId -> Type -> [Candidate] -> TCM (Maybe ([(Candidate, TCErr)], [(Candidate, Term)]))
+checkCandidates m t cands =
+  verboseBracket "tc.instance.candidates" 20 ("checkCandidates " ++ prettyShow m) $
+  ifM (anyMetaTypes cands) (return Nothing) $ Just <$> do
+    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ "target:" <+> prettyTCM t
+    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ vcat
+      [ "candidates"
+      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":" <+> prettyTCM t
+             | c@(Candidate q v t overlap) <- cands ] ]
+    cands' <- filterResetingState m cands (checkCandidateForMeta m t)
+    reportSDoc "tc.instance.candidates" 20 $ nest 2 $ vcat
+      [ "valid candidates"
+      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM c <+> ":" <+> prettyTCM t
+             | c@(Candidate q v t overlap) <- map fst (snd cands') ] ]
+    reportSDoc "tc.instance.candidates" 60 $ nest 2 $ vcat
+      [ "valid candidates"
+      , vcat [ "-" <+> (if overlap then "overlap" else empty) <+> prettyTCM v <+> ":" <+> prettyTCM t
+             | c@(Candidate q v t overlap) <- map fst (snd cands') ] ]
+    return cands'
+  where
+    anyMetaTypes :: [Candidate] -> TCM Bool
+    anyMetaTypes [] = return False
+    anyMetaTypes (Candidate _ _ a _ : cands) = do
+      a <- instantiate a
+      case unEl a of
+        MetaV{} -> return True
+        _       -> anyMetaTypes cands
+
+    checkDepth :: Term -> Type -> TCM YesNo -> TCM YesNo
+    checkDepth c a k = locallyTC eInstanceDepth succ $ do
+      d        <- viewTC eInstanceDepth
+      maxDepth <- maxInstanceSearchDepth
+      when (d > maxDepth) $ typeError $ InstanceSearchDepthExhausted c a maxDepth
+      k
+
+    checkCandidateForMeta :: MetaId -> Type -> Candidate -> TCM YesNo
+    checkCandidateForMeta m t (Candidate q term t' _) = checkDepth term t' $ do
+      -- Andreas, 2015-02-07: New metas should be created with range of the
+      -- current instance meta, thus, we set the range.
+      mv <- lookupLocalMeta m
+      setCurrentRange mv $ runCandidateCheck $
+        verboseBracket "tc.instance" 20 ("checkCandidateForMeta " ++ prettyShow m) $ do
+          reportSDoc "tc.instance" 20 $ vcat
+            [ "checkCandidateForMeta"
+            , "  t    =" <+> prettyTCM t
+            , "  t'   =" <+> prettyTCM t'
+            , "  term =" <+> prettyTCM term
+            ]
+          reportSDoc "tc.instance" 70 $ vcat
+            [ "  t    =" <+> pretty t
+            , "  t'   =" <+> pretty t'
+            , "  term =" <+> pretty term
+            ]
+          debugConstraints
+
+          -- Apply hidden and instance arguments (in case of
+          -- --overlapping-instances, this performs recursive
+          -- inst. search!).
+          (args, t'') <- implicitArgs (-1) (\h -> notVisible h) t'
+
+          reportSDoc "tc.instance" 20 $
+            "instance search: checking" <+> prettyTCM t'' <+> "<=" <+> prettyTCM t
+          reportSDoc "tc.instance" 70 $ vcat
+            [ "instance search: checking (raw)"
+            , nest 4 $ pretty t''
+            , nest 2 $ "<="
+            , nest 4 $ pretty t
+            ]
+          leqType t'' t
+          debugConstraints
+
+          flip catchError (return . NoBecause) $ do
+            -- make a pass over constraints, to detect cases where
+            -- some are made unsolvable by the type comparison, but
+            -- don't do this for FindInstance's to prevent loops.
+            solveAwakeConstraints' True
+            -- We need instantiateFull here to remove 'local' metas
+            v <- instantiateFull =<< (term `applyDroppingParameters` args)
+            reportSDoc "tc.instance" 15 $
+              sep [ ("instance search: found solution for" <+> prettyTCM m) <> ":"
+                  , nest 2 $ prettyTCM v ]
+            return $ Yes v
+      where
+        runCandidateCheck = flip catchError handle . nowConsideringInstance
+
+        hardFailure :: TCErr -> Bool
+        hardFailure (TypeError _ _ err) =
+          case clValue err of
+            InstanceSearchDepthExhausted{} -> True
+            _                              -> False
+        hardFailure _ = False
+
+        handle :: TCErr -> TCM YesNo
+        handle err
+          | hardFailure err = return $ HellNo err
+          | otherwise       = do
+              reportSDoc "tc.instance" 50 $ "candidate failed type check:" <+> prettyTCM err
+              return No
+
+
+nowConsideringInstance :: (ReadTCState m) => m a -> m a
+nowConsideringInstance = locallyTCState stConsideringInstance $ const True
+
+isInstanceProblemConstraint :: ProblemConstraint -> Bool
+isInstanceProblemConstraint = isInstanceConstraint . clValue . theConstraint
+
+wakeupInstanceConstraints :: TCM ()
+wakeupInstanceConstraints =
+  unlessM shouldPostponeInstanceSearch $ do
+    wakeConstraints (wakeUpWhen_ isInstanceProblemConstraint)
+    solveAwakeInstanceConstraints
+
+solveAwakeInstanceConstraints :: TCM ()
+solveAwakeInstanceConstraints =
+  solveSomeAwakeConstraints isInstanceProblemConstraint False
+
+postponeInstanceConstraints :: TCM a -> TCM a
+postponeInstanceConstraints m =
+  locallyTCState stPostponeInstanceSearch (const True) m <* wakeupInstanceConstraints
+
+-- | To preserve the invariant that a constructor is not applied to its
+--   parameter arguments, we explicitly check whether function term
+--   we are applying to arguments is a unapplied constructor.
+--   In this case we drop the first 'conPars' arguments.
+--   See Issue670a.
+--   Andreas, 2013-11-07 Also do this for projections, see Issue670b.
+applyDroppingParameters :: Term -> Args -> TCM Term
+applyDroppingParameters t vs = do
+  let fallback = return $ t `apply` vs
+  case t of
+    Con c ci [] -> do
+      def <- theDef <$> getConInfo c
+      case def of
+        Constructor {conPars = n} -> return $ Con c ci (map Apply $ drop n vs)
+        _ -> __IMPOSSIBLE__
+    Def f [] -> do
+      -- Andreas, 2022-03-07, issue #5809: don't drop parameters of irrelevant projections.
+      mp <- isRelevantProjection f
+      case mp of
+        Just Projection{projIndex = n} -> do
+          case drop n vs of
+            []     -> return t
+            u : us -> (`apply` us) <$> applyDef ProjPrefix f u
+        _ -> fallback
+    _ -> fallback
diff --git a/src/full/Agda/TypeChecking/Irrelevance.hs b/src/full/Agda/TypeChecking/Irrelevance.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Irrelevance.hs
@@ -0,0 +1,427 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+{-| Compile-time irrelevance.
+
+In type theory with compile-time irrelevance à la Pfenning (LiCS 2001),
+variables in the context are annotated with relevance attributes.
+@@
+  Γ = r₁x₁:A₁, ..., rⱼxⱼ:Aⱼ
+@@
+To handle irrelevant projections, we also record the current relevance
+attribute in the judgement.  For instance, this attribute is equal to
+to 'Irrelevant' if we are in an irrelevant position, like an
+irrelevant argument.
+@@
+  Γ ⊢r t : A
+@@
+Only relevant variables can be used:
+@@
+
+  (Relevant x : A) ∈ Γ
+  --------------------
+  Γ  ⊢r  x  :  A
+@@
+Irrelevant global declarations can only be used if @r = Irrelevant@.
+
+When we enter a @r'@-relevant function argument, we compose the @r@ with @r'@
+and (left-)divide the attributes in the context by @r'@.
+@@
+  Γ  ⊢r  t  :  (r' x : A) → B      r' \ Γ  ⊢(r'·r)  u  :  A
+  ---------------------------------------------------------
+  Γ  ⊢r  t u  :  B[u/x]
+@@
+No surprises for abstraction:
+@@
+
+  Γ, (r' x : A)  ⊢r  :  B
+  -----------------------------
+  Γ  ⊢r  λxt  :  (r' x : A) → B
+@@
+
+This is different for runtime irrelevance (erasure) which is ``flat'',
+meaning that once one is in an irrelevant context, all new assumptions will
+be usable, since they are turned relevant once entering the context.
+See Conor McBride (WadlerFest 2016), for a type system in this spirit:
+
+We use such a rule for runtime-irrelevance:
+@@
+  Γ, (q \ q') x : A  ⊢q  t  :  B
+  ------------------------------
+  Γ  ⊢q  λxt  :  (q' x : A) → B
+@@
+
+Conor's system is however set up differently, with a very different
+variable rule:
+
+@@
+
+  (q x : A) ∈ Γ
+  --------------
+  Γ  ⊢q  x  :  A
+
+  Γ, (q·p) x : A  ⊢q  t  :  B
+  -----------------------------
+  Γ  ⊢q  λxt  :  (p x : A) → B
+
+  Γ  ⊢q  t  :  (p x : A) → B       Γ'  ⊢qp  u  :  A
+  -------------------------------------------------
+  Γ + Γ'  ⊢q  t u  :  B[u/x]
+@@
+
+
+-}
+
+module Agda.TypeChecking.Irrelevance where
+
+import Control.Monad.Except
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Concrete.Pretty
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute.Class
+
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+-- | Check whether something can be used in a position of the given relevance.
+--
+--   This is a substitute for double-checking that only makes sure
+--   relevances are correct.  See issue #2640.
+--
+--   Used in unifier (@ unifyStep Solution{}@).
+--
+--   At the moment, this implements McBride-style irrelevance,
+--   where Pfenning-style would be the most accurate thing.
+--   However, these two notions only differ how they handle
+--   bound variables in a term.  Here, we are only concerned
+--   in the free variables, used meta-variables, and used
+--   (irrelevant) definitions.
+--
+class UsableRelevance a where
+  usableRel
+    :: (ReadTCState m, HasConstInfo m, MonadTCEnv m, MonadAddContext m, MonadDebug m)
+    => Relevance -> a -> m Bool
+
+instance UsableRelevance Term where
+  usableRel rel = \case
+    Var i vs -> do
+      irel <- getRelevance <$> domOfBV i
+      let ok = irel `moreRelevant` rel
+      reportSDoc "tc.irr" 50 $
+        "Variable" <+> prettyTCM (var i) <+>
+        text ("has relevance " ++ show irel ++ ", which is " ++
+              (if ok then "" else "NOT ") ++ "more relevant than " ++ show rel)
+      return ok `and2M` usableRel rel vs
+    Def f vs -> do
+      frel <- relOfConst f
+      return (frel `moreRelevant` rel) `and2M` usableRel rel vs
+    Con c _ vs -> usableRel rel vs
+    Lit l    -> return True
+    Lam _ v  -> usableRel rel v
+    Pi a b   -> usableRel rel (a,b)
+    Sort s   -> usableRel rel s
+    Level l  -> return True
+    MetaV m vs -> do
+      mrel <- getRelevance <$> lookupMetaModality m
+      return (mrel `moreRelevant` rel) `and2M` usableRel rel vs
+    DontCare v -> usableRel rel v -- TODO: allow irrelevant things to be used in DontCare position?
+    Dummy{}  -> return True
+
+instance UsableRelevance a => UsableRelevance (Type' a) where
+  usableRel rel (El _ t) = usableRel rel t
+
+instance UsableRelevance Sort where
+  usableRel rel = \case
+    Univ _ l -> usableRel rel l
+    Inf _ _ -> return True
+    SizeUniv -> return True
+    LockUniv -> return True
+    LevelUniv -> return True
+    IntervalUniv -> return True
+    PiSort a s1 s2 -> usableRel rel (a,s1,s2)
+    FunSort s1 s2 -> usableRel rel (s1,s2)
+    UnivSort s -> usableRel rel s
+    MetaS x es -> usableRel rel es
+    DefS d es  -> usableRel rel $ Def d es
+    DummyS{} -> return True
+
+instance UsableRelevance Level where
+  usableRel rel (Max _ ls) = usableRel rel ls
+
+instance UsableRelevance PlusLevel where
+  usableRel rel (Plus _ l) = usableRel rel l
+
+instance UsableRelevance a => UsableRelevance [a] where
+  usableRel rel = andM . map (usableRel rel)
+
+instance (UsableRelevance a, UsableRelevance b) => UsableRelevance (a,b) where
+  usableRel rel (a,b) = usableRel rel a `and2M` usableRel rel b
+
+instance (UsableRelevance a, UsableRelevance b, UsableRelevance c) => UsableRelevance (a,b,c) where
+  usableRel rel (a,b,c) = usableRel rel a `and2M` usableRel rel b `and2M` usableRel rel c
+
+instance UsableRelevance a => UsableRelevance (Elim' a) where
+  usableRel rel (Apply a) = usableRel rel a
+  usableRel rel (Proj _ p) = do
+    prel <- relOfConst p
+    return $ prel `moreRelevant` rel
+  usableRel rel (IApply x y v) = usableRel rel v
+
+instance UsableRelevance a => UsableRelevance (Arg a) where
+  usableRel rel (Arg info u) =
+    let rel' = getRelevance info
+    in  usableRel (rel `composeRelevance` rel') u
+
+instance UsableRelevance a => UsableRelevance (Dom a) where
+  usableRel rel Dom{unDom = u} = usableRel rel u
+
+instance (Subst a, UsableRelevance a) => UsableRelevance (Abs a) where
+  usableRel rel abs = underAbstraction_ abs $ \u -> usableRel rel u
+
+-- | Check whether something can be used in a position of the given modality.
+--
+--   This is a substitute for double-checking that only makes sure
+--   modalities are correct.  See issue #2640.
+--
+--   Used in unifier (@ unifyStep Solution{}@).
+--
+--   This uses McBride-style modality checking.
+--   It does not differ from Pfenning-style if we
+--   are only interested in the modality of the
+--   free variables, used meta-variables, and used
+--   definitions.
+--
+class UsableModality a where
+  usableMod
+    :: (ReadTCState m, HasConstInfo m, MonadTCEnv m, MonadAddContext m, MonadDebug m, MonadReduce m, MonadError Blocker m)
+    => Modality -> a -> m Bool
+
+instance UsableModality Term where
+  usableMod mod u = do
+   case u of
+    Var i vs -> do
+      imod <- getModality <$> domOfBV i
+      let ok = imod `moreUsableModality` mod
+      reportSDoc "tc.irr" 50 $
+        "Variable" <+> prettyTCM (var i) <+>
+        text ("has modality " ++ show imod ++ ", which is a " ++
+              (if ok then "" else "NOT ") ++ "more usable modality than " ++ show mod)
+      return ok `and2M` usableMod mod vs
+    Def f vs -> do
+      fmod <- modalityOfConst f
+      -- Pure modalities don't matter here, only positional ones, hence remove
+      -- them from the equation.
+      let ok = setCohesion Flat fmod `moreUsableModality` mod
+      reportSDoc "tc.irr" 50 $
+        "Definition" <+> prettyTCM (Def f []) <+>
+        text ("has modality " ++ show fmod ++ ", which is a " ++
+              (if ok then "" else "NOT ") ++ "more usable modality than " ++ show mod)
+      return ok `and2M` usableMod mod vs
+    Con c o vs -> do
+      cmod <- modalityOfConst (conName c)
+      let ok = cmod `moreUsableModality` mod
+      reportSDoc "tc.irr" 50 $
+        "The constructor" <+> prettyTCM (Con c o []) <+>
+        text ("has the modality " ++ show cmod ++ ", which is " ++
+              (if ok then "" else "NOT ") ++
+              "more usable than the modality " ++ show mod ++ ".")
+      return ok `and2M` usableMod mod vs
+    Lit l    -> return True
+    Lam info v  -> usableModAbs info mod v
+    -- Even if Pi contains Type, here we check it as a constructor for terms in the universe.
+    Pi a b   -> usableMod domMod (unEl $ unDom a) `and2M` usableModAbs (getArgInfo a) mod (unEl <$> b)
+      where
+        domMod = mapQuantity (composeQuantity $ getQuantity a) $
+                 mapCohesion (composeCohesion $ getCohesion a) mod
+    -- Andrea 15/10/2020 not updating these cases yet, but they are quite suspicious,
+    -- do we have special typing rules for Sort and Level?
+    Sort s   -> usableMod mod s
+    Level l  -> return True
+    MetaV m vs -> do
+      mmod <- lookupMetaModality m
+      let ok = mmod `moreUsableModality` mod
+      reportSDoc "tc.irr" 50 $
+        "Metavariable" <+> prettyTCM (MetaV m []) <+>
+        text ("has modality " ++ show mmod ++ ", which is a " ++
+              (if ok then "" else "NOT ") ++ "more usable modality than " ++ show mod)
+      (return ok `and2M` usableMod mod vs) `or2M` do
+        u <- instantiate u
+        caseMaybe (isMeta u) (usableMod mod u) $ \ m -> throwError (UnblockOnMeta m)
+    DontCare v -> usableMod mod v
+    Dummy{}  -> return True
+
+usableModAbs :: (Subst a, MonadAddContext m, UsableModality a,
+                       ReadTCState m, HasConstInfo m, MonadReduce m, MonadError Blocker m) =>
+                      ArgInfo -> Modality -> Abs a -> m Bool
+usableModAbs info mod abs = underAbstraction (setArgInfo info $ __DUMMY_DOM__) abs $ \ u -> usableMod mod u
+
+instance UsableRelevance a => UsableModality (Type' a) where
+  usableMod mod (El _ t) = usableRel (getRelevance mod) t
+
+instance UsableModality Sort where
+  usableMod mod s = usableRel (getRelevance mod) s
+
+instance UsableModality Level where
+  usableMod mod (Max _ ls) = usableRel (getRelevance mod) ls
+
+-- instance UsableModality PlusLevel where
+--   usableMod mod ClosedLevel{} = return True
+--   usableMod mod (Plus _ l)    = usableMod mod l
+
+instance UsableModality a => UsableModality [a] where
+  usableMod mod = andM . map (usableMod mod)
+
+instance (UsableModality a, UsableModality b) => UsableModality (a,b) where
+  usableMod mod (a,b) = usableMod mod a `and2M` usableMod mod b
+
+instance UsableModality a => UsableModality (Elim' a) where
+  usableMod mod (Apply a) = usableMod mod a
+  usableMod mod (Proj _ p) = do
+    pmod <- modalityOfConst p
+    return $ pmod `moreUsableModality` mod
+  usableMod mod (IApply x y v) = usableMod mod v
+
+instance UsableModality a => UsableModality (Arg a) where
+  usableMod mod (Arg info u) =
+    let mod' = getModality info
+    in  usableMod (mod `composeModality` mod') u
+
+instance UsableModality a => UsableModality (Dom a) where
+  usableMod mod Dom{unDom = u} = usableMod mod u
+
+usableAtModality'
+  :: MonadConstraint TCM
+  -- Note: This weird-looking constraint is to trick GHC into accepting
+  -- that an instance of MonadConstraint TCM will exist, even if we
+  -- can't import the module in which it is defined.
+  => Maybe Sort -> WhyCheckModality -> Modality -> Term -> TCM ()
+usableAtModality' ms why mod t =
+  catchConstraint (UsableAtModality why ms mod t) $ do
+    whenM (maybe (pure True) isFibrant ms) $ do
+      res <- runExceptT $ usableMod mod t
+      case res of
+        Right b -> unless b $
+          typeError . GenericDocError =<< formatWhy
+        Left blocker -> patternViolation blocker
+  where
+    formatWhy = do
+      compatible <- optCubicalCompatible <$> pragmaOptions
+      cubical <- isJust . optCubical <$> pragmaOptions
+      let
+        context
+          | cubical    = "in Cubical Agda,"
+          | compatible = "to maintain compatibility with Cubical Agda,"
+          | otherwise  = "when --without-K is enabled,"
+
+        explanation what
+          | cubical || compatible =
+            [ ""
+            , fsep ( "Note:":pwords context
+                  ++ pwords what ++ pwords "must be usable at the modality"
+                  ++ pwords "in which the function was defined, since it will be"
+                  ++ pwords "used for computing transports"
+                  )
+            , ""
+            ]
+          | otherwise = []
+
+      case why of
+        IndexedClause ->
+          vcat $
+            ( fsep ( pwords "This clause has target type"
+                  ++ [prettyTCM t]
+                  ++ pwords "which is not usable at the required modality"
+                  ++ [pure (attributesForModality mod) <> "."]
+                   )
+            : explanation "the target type")
+
+        -- Arguments sometimes need to be transported too:
+        IndexedClauseArg forced the_arg ->
+          vcat $
+            ( fsep (pwords "The argument" ++ [prettyTCM the_arg] ++ pwords "has type")
+            : nest 2 (prettyTCM t)
+            : fsep ( pwords "which is not usable at the required modality"
+                  ++ [pure (attributesForModality mod) <> "."] )
+            : explanation "this argument's type")
+
+        -- Note: if a generated clause is modality-incorrect, that's a
+        -- bug in the LHS modality check
+        GeneratedClause ->
+          __IMPOSSIBLE_VERBOSE__ . show =<<
+                   prettyTCM t
+              <+> "is not usable at the required modality"
+              <+> pure (attributesForModality mod)
+        _ -> prettyTCM t <+> "is not usable at the required modality"
+         <+> pure (attributesForModality mod)
+
+
+usableAtModality :: MonadConstraint TCM => WhyCheckModality -> Modality -> Term -> TCM ()
+usableAtModality = usableAtModality' Nothing
+
+
+-- * Propositions
+
+-- | Is a type a proposition?  (Needs reduction.)
+
+isPropM
+  :: (LensSort a, PrettyTCM a, PureTCM m, MonadBlock m)
+  => a -> m Bool
+isPropM a = do
+  traceSDoc "tc.prop" 80 ("Is " <+> prettyTCM a <+> "of sort" <+> prettyTCM (getSort a) <+> "in Prop?") $ do
+  abortIfBlocked (getSort a) <&> \case
+    Prop{} -> True
+    _      -> False
+
+{-# SPECIALIZE isIrrelevantOrPropM :: Dom Type -> TCM Bool #-}
+isIrrelevantOrPropM
+  :: (LensRelevance a, LensSort a, PrettyTCM a, PureTCM m, MonadBlock m)
+  => a -> m Bool
+isIrrelevantOrPropM x = return (isIrrelevant x) `or2M` isPropM x
+
+-- * Fibrant types
+
+-- | Is a type fibrant (i.e. Type, Prop)?
+
+isFibrant
+  :: (LensSort a, PureTCM m, MonadBlock m)
+  => a -> m Bool
+isFibrant a = abortIfBlocked (getSort a) <&> \case
+  Univ u _   -> univFibrancy u == IsFibrant
+  Inf u _    -> univFibrancy u == IsFibrant
+  SizeUniv{} -> False
+  LockUniv{} -> False
+  LevelUniv{}  -> False
+  IntervalUniv{} -> False
+  PiSort{}   -> False
+  FunSort{}  -> False
+  UnivSort{} -> False
+  MetaS{}    -> False
+  DefS{}     -> False
+  DummyS{}   -> False
+
+
+-- | Cofibrant types are those that could be the domain of a fibrant
+--   pi type. (Notion by C. Sattler).
+isCoFibrantSort :: (LensSort a, PureTCM m, MonadBlock m) => a -> m Bool
+isCoFibrantSort a = abortIfBlocked (getSort a) <&> \case
+  Univ u _   -> univFibrancy u == IsFibrant
+  Inf u _    -> univFibrancy u == IsFibrant
+  SizeUniv{} -> False
+  LockUniv{} -> True
+  LevelUniv{}  -> False
+  IntervalUniv{} -> True
+  PiSort{}   -> False
+  FunSort{}  -> False
+  UnivSort{} -> False
+  MetaS{}    -> False
+  DefS{}     -> False
+  DummyS{}   -> False
diff --git a/src/full/Agda/TypeChecking/Irrelevance.hs-boot b/src/full/Agda/TypeChecking/Irrelevance.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Irrelevance.hs-boot
@@ -0,0 +1,13 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Irrelevance where
+
+import Agda.Syntax.Internal (LensSort)
+
+import Agda.TypeChecking.Monad.Base (MonadBlock)
+import {-# SOURCE #-} Agda.TypeChecking.Pretty (PrettyTCM)
+import Agda.TypeChecking.Monad.Pure (PureTCM)
+
+isPropM
+  :: (LensSort a, PrettyTCM a, PureTCM m, MonadBlock m)
+  => a -> m Bool
diff --git a/src/full/Agda/TypeChecking/Level.hs b/src/full/Agda/TypeChecking/Level.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Level.hs
@@ -0,0 +1,268 @@
+
+module Agda.TypeChecking.Level where
+
+import Data.Maybe
+import qualified Data.List as List
+import Data.Traversable (Traversable)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Free.Lazy
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Reduce
+
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import Agda.Utils.Maybe ( caseMaybeM, allJustM )
+import Agda.Utils.Monad ( tryMaybe )
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+data LevelKit = LevelKit
+  { lvlType  :: Term
+  , lvlSuc   :: Term -> Term
+  , lvlMax   :: Term -> Term -> Term
+  , lvlZero  :: Term
+  , typeName :: QName
+  , sucName  :: QName
+  , maxName  :: QName
+  , zeroName :: QName
+  }
+
+{-# SPECIALIZE levelType :: TCM Type #-}
+-- | Get the 'primLevel' as a 'Type'.  Aborts if any of the level BUILTINs is undefined.
+levelType :: (HasBuiltins m, MonadTCError m) => m Type
+levelType =
+  El LevelUniv . lvlType <$> requireLevels
+  -- Andreas, 2022-10-11, issue #6168
+  -- It seems superfluous to require all level builtins here,
+  -- but since we are in MonadTCError here, this is our chance to make sure
+  -- that all level builtins are defined.
+  -- Otherwise, we might run into an __IMPOSSIBLE__ later,
+  -- e.g. if only BUILTIN LEVEL was defined by reallyUnLevelView requires all builtins.
+
+{-# SPECIALIZE levelType' :: TCM Type #-}
+-- | Get the 'primLevel' as a 'Type'.  Unsafe, crashes if the BUILTIN LEVEL is undefined.
+levelType' :: (HasBuiltins m) => m Type
+levelType' =
+  El LevelUniv . fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevel
+
+{-# SPECIALIZE isLevelType :: Type -> TCM Bool #-}
+isLevelType :: PureTCM m => Type -> m Bool
+isLevelType a = reduce (unEl a) >>= \case
+  Def f [] -> do
+    Def lvl [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevel
+    return $ f == lvl
+  _ -> return False
+
+{-# SPECIALIZE builtinLevelKit :: TCM LevelKit #-}
+{-# SPECIALIZE builtinLevelKit :: ReduceM LevelKit #-}
+builtinLevelKit :: (HasBuiltins m) => m LevelKit
+builtinLevelKit = do
+    level@(Def l [])     <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevel
+    zero@(Def z [])      <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelZero
+    suc@(Def s [])       <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelSuc
+    max@(Def m [])       <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelMax
+    return $ LevelKit
+      { lvlType  = level
+      , lvlSuc   = \ a -> suc `apply1` a
+      , lvlMax   = \ a b -> max `applys` [a, b]
+      , lvlZero  = zero
+      , typeName = l
+      , sucName  = s
+      , maxName  = m
+      , zeroName = z
+      }
+
+{-# SPECIALIZE requireLevels :: TCM LevelKit #-}
+-- | Raises an error if no level kit is available.
+requireLevels :: (HasBuiltins m, MonadTCError m) => m LevelKit
+requireLevels = do
+    level@(Def l [])     <- getBuiltin builtinLevel
+    zero@(Def z [])      <- getBuiltin builtinLevelZero
+    suc@(Def s [])       <- getBuiltin builtinLevelSuc
+    max@(Def m [])       <- getBuiltin builtinLevelMax
+    return $ LevelKit
+      { lvlType  = level
+      , lvlSuc   = \ a -> suc `apply1` a
+      , lvlMax   = \ a b -> max `applys` [a, b]
+      , lvlZero  = zero
+      , typeName = l
+      , sucName  = s
+      , maxName  = m
+      , zeroName = z
+      }
+
+-- | Checks whether level kit is fully available.
+haveLevels :: HasBuiltins m => m Bool
+haveLevels = caseMaybeM (allJustM $ map getBuiltin' levelBuiltins)
+    (return False)
+    (\ _bs -> return True)
+  where
+  levelBuiltins =
+    [ builtinLevelUniv
+    , builtinLevel
+    , builtinLevelZero
+    , builtinLevelSuc
+    , builtinLevelMax
+    ]
+
+{-# SPECIALIZE unLevel :: Term -> TCM Term #-}
+{-# SPECIALIZE unLevel :: Term -> ReduceM Term #-}
+unLevel :: (HasBuiltins m) => Term -> m Term
+unLevel (Level l)  = reallyUnLevelView l
+unLevel v = return v
+
+{-# SPECIALIZE reallyUnLevelView :: Level -> TCM Term #-}
+{-# SPECIALIZE reallyUnLevelView :: Level -> ReduceM Term #-}
+reallyUnLevelView :: (HasBuiltins m) => Level -> m Term
+reallyUnLevelView nv = (`unlevelWithKit` nv) <$> builtinLevelKit
+
+unlevelWithKit :: LevelKit -> Level -> Term
+unlevelWithKit LevelKit{ lvlZero = zer, lvlSuc = suc, lvlMax = max } = \case
+  Max m []  -> unConstV zer suc m
+  Max 0 [a] -> unPlusV suc a
+  Max m as  -> foldl1 max $ [ unConstV zer suc m | m > 0 ] ++ map (unPlusV suc) as
+
+unConstV :: Term -> (Term -> Term) -> Integer -> Term
+unConstV zer suc n = foldr ($) zer (List.genericReplicate n suc)
+
+unPlusV :: (Term -> Term) -> PlusLevel -> Term
+unPlusV suc (Plus n a) = foldr ($) a (List.genericReplicate n suc)
+
+maybePrimCon :: TCM Term -> TCM (Maybe ConHead)
+maybePrimCon prim = tryMaybe $ do
+    Con c ci [] <- prim
+    return c
+
+maybePrimDef :: TCM Term -> TCM (Maybe QName)
+maybePrimDef prim = tryMaybe $ do
+    Def f [] <- prim
+    return f
+
+{-# SPECIALIZE levelView :: Term -> TCM Level #-}
+levelView :: PureTCM m => Term -> m Level
+levelView a = do
+  reportSLn "tc.level.view" 50 $ "{ levelView " ++ show a
+  v <- levelView' a
+  reportSLn "tc.level.view" 50 $ "  view: " ++ show v ++ "}"
+  return v
+
+{-# SPECIALIZE levelView' :: Term -> TCM Level #-}
+levelView' :: PureTCM m => Term -> m Level
+levelView' a = do
+  Def lzero [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelZero
+  Def lsuc  [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelSuc
+  Def lmax  [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevelMax
+  let view a = do
+        ba <- reduceB a
+        case ignoreBlocking ba of
+          Level l -> return l
+          Def s [Apply arg]
+            | s == lsuc  -> levelSuc <$> view (unArg arg)
+          Def z []
+            | z == lzero -> return $ ClosedLevel 0
+          Def m [Apply arg1, Apply arg2]
+            | m == lmax  -> levelLub <$> view (unArg arg1) <*> view (unArg arg2)
+          l              -> return $ atomicLevel l
+  view a
+
+-- | Given a level @l@, find the maximum constant @n@ such that @l = n + l'@
+levelPlusView :: Level -> (Integer, Level)
+levelPlusView (Max 0 []) = (0 , Max 0 [])
+levelPlusView (Max 0 as@(_:_)) = (minN , Max 0 (map sub as))
+  where
+    minN = minimum [ n | Plus n _ <- as ]
+    sub (Plus n a) = Plus (n - minN) a
+levelPlusView (Max n as) = (minN , Max (n - minN) (map sub as))
+  where
+    minN = minimum $ n : [ n' | Plus n' _ <- as ]
+    sub (Plus n' a) = Plus (n' - minN) a
+
+-- | Given a level @l@, find the biggest constant @n@ such that @n <= l@
+levelLowerBound :: Level -> Integer
+levelLowerBound (Max m as) = maximum $ m : [n | Plus n _ <- as]
+
+-- | Given a constant @n@ and a level @l@, find the level @l'@ such
+--   that @l = n + l'@ (or Nothing if there is no such level).
+--   Operates on levels in canonical form.
+subLevel :: Integer -> Level -> Maybe Level
+subLevel n (Max m ls) = Max <$> m' <*> traverse subPlus ls
+  where
+    m' :: Maybe Integer
+    m' | m == 0, not (null ls) = Just 0
+       | otherwise             = sub m
+
+    -- General purpose function.
+    nonNeg :: Integer -> Maybe Integer
+    nonNeg j | j >= 0 = Just j
+             | otherwise = Nothing
+
+    sub :: Integer -> Maybe Integer
+    sub = nonNeg . subtract n
+
+    subPlus :: PlusLevel -> Maybe PlusLevel
+    subPlus (Plus j l) = Plus <$> sub j <*> Just l
+
+-- | Given two levels @a@ and @b@, try to decompose the first one as
+-- @a = a' ⊔ b@ (for the minimal value of @a'@).
+levelMaxDiff :: Level -> Level -> Maybe Level
+levelMaxDiff (Max m as) (Max n bs) = Max <$> diffC m n <*> diffP as bs
+  where
+    diffC :: Integer -> Integer -> Maybe Integer
+    diffC m n
+      | m == n    = Just 0
+      | m > n     = Just m
+      | otherwise = Nothing
+
+    diffP :: [PlusLevel] -> [PlusLevel] -> Maybe [PlusLevel]
+    diffP as     []     = Just as
+    diffP []     bs     = Nothing
+    diffP (a@(Plus m x) : as) (b@(Plus n y) : bs)
+      | x == y = if
+        | m == n    -> diffP as bs
+        | m > n     -> (Plus m x:) <$> diffP as bs
+        | otherwise -> Nothing
+      | otherwise = (a:) <$> diffP as (b:bs)
+
+-- | A @SingleLevel@ is a @Level@ that cannot be further decomposed as
+--   a maximum @a ⊔ b@.
+data SingleLevel' t = SingleClosed Integer | SinglePlus (PlusLevel' t)
+  deriving (Show, Functor, Foldable, Traversable)
+
+type SingleLevel = SingleLevel' Term
+
+deriving instance Eq SingleLevel
+
+unSingleLevel :: SingleLevel' t -> Level' t
+unSingleLevel (SingleClosed m) = Max m []
+unSingleLevel (SinglePlus a)   = Max 0 [a]
+
+-- | Return the maximum of the given @SingleLevel@s
+unSingleLevels :: [SingleLevel] -> Level
+unSingleLevels ls = levelMax n as
+  where
+    n = maximum $ 0 : [m | SingleClosed m <- ls]
+    as = [a | SinglePlus a <- ls]
+
+levelMaxView :: Level' t -> List1 (SingleLevel' t)
+levelMaxView (Max n [])     = singleton $ SingleClosed n
+levelMaxView (Max 0 (a:as)) = SinglePlus a :| map SinglePlus as
+levelMaxView (Max n as)     = SingleClosed n :| map SinglePlus as
+
+singleLevelView :: Level' t -> Maybe (SingleLevel' t)
+singleLevelView l = case levelMaxView l of
+  s :| [] -> Just s
+  _       -> Nothing
+
+instance Subst t => Subst (SingleLevel' t) where
+  type SubstArg (SingleLevel' t) = SubstArg t
+
+  applySubst sub (SingleClosed m) = SingleClosed m
+  applySubst sub (SinglePlus a)   = SinglePlus $ applySubst sub a
+
+instance Free t => Free (SingleLevel' t) where
+  freeVars' (SingleClosed m) = mempty
+  freeVars' (SinglePlus a)   = freeVars' a
diff --git a/src/full/Agda/TypeChecking/Level.hs-boot b/src/full/Agda/TypeChecking/Level.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Level.hs-boot
@@ -0,0 +1,8 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Level where
+
+import Agda.TypeChecking.Monad.Builtin (HasBuiltins)
+import Agda.Syntax.Internal
+
+reallyUnLevelView :: (HasBuiltins m) => Level -> m Term
diff --git a/src/full/Agda/TypeChecking/Level/Solve.hs b/src/full/Agda/TypeChecking/Level/Solve.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Level/Solve.hs
@@ -0,0 +1,71 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ScopedTypeVariables #-}
+
+module Agda.TypeChecking.Level.Solve where
+
+import Control.Monad
+import Control.Monad.Except
+
+import qualified Data.Map.Strict as MapS
+import Data.Maybe
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.MetaVars.Mention
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Functor
+import Agda.Utils.Monad
+
+-- | Run the given action. At the end take all new metavariables of
+--   type level for which the only constraints are upper bounds on the
+--   level, and instantiate them to the lowest level.
+defaultOpenLevelsToZero :: (PureTCM m, MonadMetaSolver m) => m a -> m a
+defaultOpenLevelsToZero f = ifNotM (optCumulativity <$> pragmaOptions) f $ do
+  (result, newMetas) <- metasCreatedBy f
+  defaultLevelsToZero (openMetas newMetas)
+  return result
+
+defaultLevelsToZero ::
+  forall m. (PureTCM m, MonadMetaSolver m) => LocalMetaStore -> m ()
+defaultLevelsToZero xs = loop =<< openLevelMetas (MapS.keys xs)
+  where
+    loop :: [MetaId] -> m ()
+    loop xs = do
+      let isOpen x = isOpenMeta <$> lookupMetaInstantiation x
+      xs <- filterM isOpen xs
+      allMetaTypes <- getOpenMetas >>= traverse metaType
+      let notInTypeOfMeta x = not $ mentionsMeta x allMetaTypes
+      progress <- forM xs $ \x -> do
+        cs <- filter (mentionsMeta x) <$> getAllConstraints
+        if | notInTypeOfMeta x , all (`isUpperBoundFor` x) cs -> do
+               m <- lookupMeta x
+               TelV tel t <- telView =<< metaType x
+               addContext tel $ assignV DirEq x (teleArgs tel) (Level $ ClosedLevel 0) (AsTermsOf t)
+               return True
+             `catchError` \_ -> return False
+           | otherwise -> return False
+
+      when (or progress) $ (loop xs)
+
+    openLevelMetas :: [MetaId] -> m [MetaId]
+    openLevelMetas xs = filterM (isNothing <.> isInteractionMeta) xs
+      >>= filterM (fmap (== NoGeneralize) . isGeneralizableMeta)
+      >>= filterM isLevelMeta
+
+    isLevelMeta :: MetaId -> m Bool
+    isLevelMeta x = do
+      TelV tel t <- telView =<< metaType x
+      addContext tel $ isLevelType t
+
+    isUpperBoundFor :: ProblemConstraint -> MetaId -> Bool
+    isUpperBoundFor c x = case clValue (theConstraint c) of
+      LevelCmp CmpLeq l u -> not $ mentionsMeta x u
+      _                   -> False
diff --git a/src/full/Agda/TypeChecking/LevelConstraints.hs b/src/full/Agda/TypeChecking/LevelConstraints.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/LevelConstraints.hs
@@ -0,0 +1,89 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.LevelConstraints ( simplifyLevelConstraint ) where
+
+import qualified Data.List as List
+import Data.Maybe
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Level
+
+import Agda.Utils.Impossible
+import Agda.Utils.List (nubOn)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Update
+
+-- | @simplifyLevelConstraint c cs@ turns an @c@ into an equality
+--   constraint if it is an inequality constraint and the reverse
+--   inequality is contained in @cs@.
+--
+--   The constraints don't necessarily have to live in the same context, but
+--   they do need to be universally quanitfied over the context. This function
+--   takes care of renaming variables when checking for matches.
+simplifyLevelConstraint
+  :: Constraint          -- ^ Constraint @c@ to simplify.
+  -> [Constraint]        -- ^ Other constraints, enable simplification.
+  -> Maybe [Constraint]  -- ^ @Just@: list of constraints equal to the original @c@.
+                         --   @Nothing@: no simplification possible.
+simplifyLevelConstraint c others = do
+    cs <- inequalities c
+    case runChange $ mapM simpl cs of
+      (cs', True) -> Just cs'
+      (_,  False) -> Nothing
+
+  where
+    simpl :: Leq -> Change (Constraint)
+    simpl (a :=< b)
+      | any (matchLeq (b :=< a)) leqs = dirty  $ LevelCmp CmpEq  (unSingleLevel a) (unSingleLevel b)
+      | otherwise                     = return $ LevelCmp CmpLeq (unSingleLevel a) (unSingleLevel b)
+    leqs = concat $ mapMaybe inequalities others
+
+data Leq = SingleLevel :=< SingleLevel
+  deriving (Show, Eq)
+
+-- | Check if two inequality constraints are the same up to variable renaming.
+matchLeq :: Leq -> Leq -> Bool
+matchLeq (a :=< b) (c :=< d)
+  | length xs == length ys = (a, b) == applySubst rho (c, d)
+  | otherwise              = False
+  where
+    free :: Free a => a -> [Int]
+    free = nubOn id . runFree (:[]) IgnoreNot  -- Note: use a list to preserve order of variables
+    xs  = free (a, b)
+    ys  = free (c, d)
+    rho = mkSub $ List.sort $ zip ys xs
+    mkSub = go 0
+      where
+        go _ [] = IdS
+        go y ren0@((y', x) : ren)
+          | y == y'   = Var x [] :# go (y + 1) ren
+          | otherwise = strengthenS' impossible 1 $ go (y + 1) ren0
+
+-- | Turn a level constraint into a list of inequalities between
+--   single levels, if possible.
+
+inequalities :: Constraint -> Maybe [Leq]
+
+inequalities (LevelCmp CmpLeq a b)
+  | Just b' <- singleLevelView b = Just $ map (:=< b') $ List1.toList $ levelMaxView a
+  -- Andreas, 2016-09-28
+  -- Why was this most natural case missing?
+  -- See test/Succeed/LevelLeqGeq.agda for where it is useful!
+
+-- These are very special cases only, in no way complete:
+-- E.g.: a = a ⊔ b ⊔ c --> b ≤ a & c ≤ a
+
+inequalities (LevelCmp CmpEq a b)
+  | Just a' <- singleLevelView a =
+  case List1.break (== a') (levelMaxView b) of
+    (bs0, _ : bs1) -> Just [ b' :=< a' | b' <- bs0 ++ bs1 ]
+    _              -> Nothing
+
+inequalities (LevelCmp CmpEq a b)
+  | Just b' <- singleLevelView b =
+  case List1.break (== b') (levelMaxView a) of
+    (as0, _ : as1) -> Just [ a' :=< b' | a' <- as0 ++ as1 ]
+    _              -> Nothing
+inequalities _ = Nothing
diff --git a/src/full/Agda/TypeChecking/Lock.hs b/src/full/Agda/TypeChecking/Lock.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Lock.hs
@@ -0,0 +1,147 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Lock
+  ( isTimeless
+  , checkLockedVars
+  , checkEarlierThan
+  )
+where
+
+import Control.Monad            ( filterM, forM, forM_ )
+
+import qualified Data.IntMap as IMap
+import qualified Data.IntSet as ISet
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Constraints () -- instance MonadConstraint TCM
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute.Class
+import Agda.TypeChecking.Free
+
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.VarSet as VSet
+import Agda.Utils.Functor
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Size
+
+checkLockedVars
+  :: Term
+     -- ^ term to check
+  -> Type
+     -- ^ its type
+  -> Arg Term
+     -- ^ the lock
+  -> Type
+     -- ^ type of the lock
+  -> TCM ()
+checkLockedVars t ty lk lk_ty = catchConstraint (CheckLockedVars t ty lk lk_ty) $ do
+  -- Have to instantiate the lock, otherwise we might block on it even
+  -- after it's been solved (e.g.: it's an interaction point, see #6528)
+  -- Update (Andreas, 2023-10-23, issue #6913): need even full instantiation.
+  -- Since @lk@ is typically just a variable, 'instantiateFull' is not expensive here.
+  -- In #6913 it was a postulate applied to a meta, thus, 'instantiate' was not enough.
+  lk <- instantiateFull lk
+  reportSDoc "tc.term.lock" 40 $ "Checking locked vars.."
+  reportSDoc "tc.term.lock" 50 $ nest 2 $ vcat
+     [ text "t     = " <+> pretty t
+     , text "ty    = " <+> pretty ty
+     , text "lk    = " <+> pretty lk
+     , text "lk_ty = " <+> pretty lk_ty
+     ]
+
+  -- Strategy: compute allowed variables, check that @t@ doesn't use more.
+  mi <- getLockVar (unArg lk)
+  caseMaybe mi (typeError (DoesNotMentionTicks t ty lk)) $ \ i -> do
+
+  cxt <- getContext
+  let toCheck = zip [0..] $ zipWith raise [1..] (take i cxt)
+
+  let fv = freeVarsIgnore IgnoreInAnnotations (t,ty)
+  let
+    rigid = rigidVars fv
+    -- flexible = IMap.keysSet $ flexibleVars fv
+    termVars = allVars fv -- ISet.union rigid flexible
+    earlierVars = ISet.fromList [i + 1 .. size cxt - 1]
+  if termVars `ISet.isSubsetOf` earlierVars then return () else do
+
+  checked <- fmap catMaybes . forM toCheck $ \ (j,dom) -> do
+    ifM (isTimeless (snd . unDom $ dom))
+        (return $ Just j)
+        (return $ Nothing)
+
+  let allowedVars = ISet.union earlierVars (ISet.fromList checked)
+
+  if termVars `ISet.isSubsetOf` allowedVars then return () else do
+  let
+    illegalVars = rigid ISet.\\ allowedVars
+    -- flexVars = flexibleVars fv
+    -- blockingMetas = map (`lookupVarMap` flexVars) (ISet.toList $ termVars ISet.\\ allowedVars)
+  if ISet.null illegalVars then  -- only flexible vars are infringing
+    -- TODO: be more precise about which metas
+    -- flexVars = flexibleVars fv
+    -- blockingMetas = map (`lookupVarMap` flexVars) (ISet.toList $ termVars ISet.\\ allowedVars)
+    patternViolation alwaysUnblock
+  else
+    typeError $ ReferencesFutureVariables t (List1.fromList (ISet.toList illegalVars)) lk i
+    -- List1.fromList is guarded by not (null illegalVars)
+
+
+-- | Precondition: 'Term' is fully instantiated.
+getLockVar :: Term -> TCMT IO (Maybe Int)
+getLockVar lk = do
+  let
+    fv = freeVarsIgnore IgnoreInAnnotations lk
+    flex = flexibleVars fv
+
+    isLock i = fmap (getLock . domInfo) (lookupBV i) <&> \case
+      IsLock{} -> True
+      IsNotLock{} -> False
+
+  unless (IMap.null flex) $ do
+    let metas = Set.unions $ map (foldrMetaSet Set.insert Set.empty) $ IMap.elems flex
+    patternViolation $ unblockOnAnyMeta metas
+      -- Andreas, 2023-10-23, issue #6913:
+      -- We should not block on solved metas, so we need @lk@ to be fully instantiated,
+      -- otherwise it may mention solved metas which end up here.
+
+  is <- filterM isLock $ ISet.toList $ rigidVars fv
+
+  -- Out of the lock variables that appear in @lk@ the one in the
+  -- left-most position in the context is what will determine the
+  -- available context for the head.
+  let mi | Prelude.null is   = Nothing
+         | otherwise = Just $ maximum is
+
+  pure mi
+
+isTimeless :: Type -> TCM Bool
+isTimeless t = do
+  t <- abortIfBlocked t
+  timeless <- mapM getName' [builtinInterval, builtinIsOne]
+  case unEl t of
+    Def q _ | Just q `elem` timeless -> return True
+    _                                -> return False
+
+notAllowedVarsError :: Term -> [Int] -> TCM b
+notAllowedVarsError lk is = do
+        typeError . GenericDocError =<<
+         ("The following vars are not allowed in a later value applied to"
+          <+> prettyTCM lk <+> ":" <+> prettyTCM (map var $ is))
+
+checkEarlierThan :: Term -> VSet.VarSet -> TCM ()
+checkEarlierThan lk fvs = do
+  mv <- getLockVar lk
+  caseMaybe mv (return ()) $ \ i -> do
+    let problems = filter (<= i) $ VSet.toList fvs
+    forM_ problems $ \ j -> do
+      ty <- typeOfBV j
+      unlessM (isTimeless ty) $
+        notAllowedVarsError lk [j]
diff --git a/src/full/Agda/TypeChecking/Lock.hs-boot b/src/full/Agda/TypeChecking/Lock.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Lock.hs-boot
@@ -0,0 +1,37 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+module Agda.TypeChecking.Lock where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+-- import Agda.TypeChecking.Monad.Context
+-- import Agda.TypeChecking.Pretty
+-- import Agda.TypeChecking.Reduce
+-- import Agda.TypeChecking.Substitute.Class
+-- import Agda.TypeChecking.Telescope
+-- import Agda.TypeChecking.Free
+
+-- import Agda.Utils.Function
+-- import Agda.Utils.Lens
+-- import Agda.Utils.Maybe
+-- import Agda.Utils.Monad
+-- import Agda.Utils.Size
+
+-- #include "undefined.h"
+-- import Agda.Utils.Impossible
+
+
+
+checkLockedVars
+  :: Term
+     -- ^ term to check
+  -> Type
+     -- ^ its type
+  -> Arg Term
+     -- ^ the lock
+  -> Type
+     -- ^ type of the lock
+  -> TCM ()
diff --git a/src/full/Agda/TypeChecking/MetaVars.hs b/src/full/Agda/TypeChecking/MetaVars.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/MetaVars.hs
@@ -0,0 +1,1940 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# LANGUAGE GADTs #-}
+
+module Agda.TypeChecking.MetaVars where
+
+import Prelude hiding (null)
+
+import Control.Monad        ( foldM, forM, forM_, liftM2, void, guard )
+import Control.Monad.Except ( MonadError(..), ExceptT, runExceptT )
+import Control.Monad.Trans  ( lift )
+import Control.Monad.Trans.Maybe
+
+import Data.Function (on)
+import qualified Data.IntSet as IntSet
+import qualified Data.IntMap as IntMap
+import qualified Data.List as List
+import qualified Data.Map.Strict as MapS
+import qualified Data.Set as Set
+import qualified Data.Foldable as Fold
+import qualified Data.Traversable as Trav
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Abstract.Name as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Position (getRange)
+
+import Agda.TypeChecking.Monad
+-- import Agda.TypeChecking.Monad.Builtin
+-- import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Substitute
+import qualified Agda.TypeChecking.SyntacticEquality as SynEq
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Lock
+import Agda.TypeChecking.Level (levelType)
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.EtaContract
+import Agda.TypeChecking.SizedTypes (boundedSizeMetaHook, isSizeProblem)
+import {-# SOURCE #-} Agda.TypeChecking.CheckInternal
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+
+-- import Agda.TypeChecking.CheckInternal
+-- import {-# SOURCE #-} Agda.TypeChecking.CheckInternal (checkInternal)
+import Agda.TypeChecking.MetaVars.Occurs
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Function
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty (Pretty, prettyShow, render)
+import qualified Agda.Utils.ProfileOptions as Profile
+import Agda.Utils.Singleton
+import qualified Agda.Utils.Graph.TopSort as Graph
+import Agda.Utils.VarSet (VarSet)
+import qualified Agda.Utils.VarSet as VarSet
+
+import Agda.Utils.Impossible
+
+instance MonadMetaSolver TCM where
+  newMeta' = newMetaTCM'
+  assignV dir x args v t = assignWrapper dir x (map Apply args) v $ assign dir x args v t
+  assignTerm' = assignTermTCM'
+  etaExpandMeta = etaExpandMetaTCM
+  updateMetaVar = updateMetaVarTCM
+
+  -- Right now we roll back the full state when aborting.
+  -- TODO: only roll back the metavariables
+  speculateMetas fallback m = do
+    (a, s) <- localTCStateSaving m
+    case a of
+      KeepMetas     -> putTC s
+      RollBackMetas -> fallback
+
+-- | Find position of a value in a list.
+--   Used to change metavar argument indices during assignment.
+--
+--   @reverse@ is necessary because we are directly abstracting over the list.
+--
+findIdx :: Eq a => [a] -> a -> Maybe Int
+findIdx vs v = List.elemIndex v (reverse vs)
+
+-- | Does the given local meta-variable have a twin meta-variable?
+
+hasTwinMeta :: MetaId -> TCM Bool
+hasTwinMeta x = do
+    m <- lookupLocalMeta x
+    return $ isJust $ mvTwin m
+
+-- | Check whether a meta variable is a place holder for a blocked term.
+isBlockedTerm :: MetaId -> TCM Bool
+isBlockedTerm x = do
+    reportSLn "tc.meta.blocked" 12 $ "is " ++ prettyShow x ++ " a blocked term? "
+    i <- lookupMetaInstantiation x
+    let r = case i of
+            BlockedConst{}                 -> True
+            PostponedTypeCheckingProblem{} -> True
+            InstV{}                        -> False
+            Open{}                         -> False
+            OpenInstance{}                 -> False
+    reportSLn "tc.meta.blocked" 12 $
+      if r then "  yes, because " ++ prettyShow i else "  no"
+    return r
+
+isEtaExpandable :: [MetaKind] -> MetaId -> TCM Bool
+isEtaExpandable kinds x = do
+    i <- lookupMetaInstantiation x
+    return $ case i of
+      Open{}                         -> True
+      OpenInstance{}                 -> Records `notElem` kinds
+      InstV{}                        -> False
+      BlockedConst{}                 -> False
+      PostponedTypeCheckingProblem{} -> False
+
+-- * Performing the assignment
+
+-- | Performing the meta variable assignment.
+--
+--   The instantiation should not be an 'InstV' and the 'MetaId'
+--   should point to something 'Open' or a 'BlockedConst'.
+--   Further, the meta variable may not be 'Frozen'.
+assignTerm :: MonadMetaSolver m => MetaId -> [Arg ArgName] -> Term -> m ()
+assignTerm x tel v = do
+     -- verify (new) invariants
+    whenM (isFrozen x) __IMPOSSIBLE__
+    assignTerm' x tel v
+
+-- | Skip frozen check.  Used for eta expanding frozen metas.
+assignTermTCM' :: MetaId -> [Arg ArgName] -> Term -> TCM ()
+assignTermTCM' x tel v = do
+    reportSDoc "tc.meta.assign" 70 $ vcat
+      [ "assignTerm" <+> prettyTCM x <+> " := " <+> prettyTCM v
+      , nest 2 $ "tel =" <+> prettyList_ (map (text . unArg) tel)
+      ]
+     -- verify (new) invariants
+    whenM (not <$> asksTC envAssignMetas) __IMPOSSIBLE__
+
+    whenProfile Profile.Metas $ liftTCM $ return () {-tickMax "max-open-metas" . (fromIntegral . size) =<< getOpenMetas-}
+    updateMetaVarTCM x $ \ mv ->
+      mv { mvInstantiation = InstV $ Instantiation
+             { instTel = tel
+             , instBody = v
+             -- Andreas, 2022-04-28, issue #5875:
+             -- Can't killRange the meta-solution, since this will destroy
+             -- ranges of termination errors (and potentially other passes
+             -- that run on internal syntax)!
+             -- , instBody = killRange v
+             }
+         }
+    etaExpandListeners x
+    wakeupConstraints x
+    reportSLn "tc.meta.assign" 20 $ "completed assignment of " ++ prettyShow x
+
+-- * Creating meta variables.
+
+-- | Create a sort meta that cannot be instantiated with 'Inf' (Setω).
+newSortMetaBelowInf :: TCM Sort
+newSortMetaBelowInf = do
+  x <- newSortMeta
+  hasBiggerSort x
+  return x
+
+{-# SPECIALIZE newSortMeta :: TCM Sort #-}
+-- | Create a sort meta that may be instantiated with 'Inf' (Setω).
+newSortMeta :: MonadMetaSolver m => m Sort
+newSortMeta =
+  ifM hasUniversePolymorphism (newSortMetaCtx =<< getContextArgs)
+  -- else (no universe polymorphism)
+  $ do i   <- createMetaInfo
+       let j = IsSort () __DUMMY_TYPE__
+       x   <- newMeta Instantiable i normalMetaPriority (idP 0) j
+       reportSDoc "tc.meta.new" 50 $
+         "new sort meta" <+> prettyTCM x
+       return $ MetaS x []
+
+-- | Create a sort meta that may be instantiated with 'Inf' (Setω).
+newSortMetaCtx :: MonadMetaSolver m => Args -> m Sort
+newSortMetaCtx vs = do
+    i   <- createMetaInfo
+    tel <- getContextTelescope
+    let t = telePi_ tel __DUMMY_TYPE__
+    x   <- newMeta Instantiable i normalMetaPriority (idP $ size tel) $ IsSort () t
+    reportSDoc "tc.meta.new" 50 $
+      "new sort meta" <+> prettyTCM x <+> ":" <+> prettyTCM t
+    return $ MetaS x $ map Apply vs
+
+newTypeMeta' :: Comparison -> Sort -> TCM Type
+newTypeMeta' cmp s = El s . snd <$> newValueMeta RunMetaOccursCheck cmp (sort s)
+
+newTypeMeta :: Sort -> TCM Type
+newTypeMeta = newTypeMeta' CmpLeq
+
+newTypeMeta_ ::  TCM Type
+newTypeMeta_  = newTypeMeta' CmpEq =<< (workOnTypes $ newSortMeta)
+-- TODO: (this could be made work with new uni-poly)
+-- Andreas, 2011-04-27: If a type meta gets solved, than we do not have to check
+-- that it has a sort.  The sort comes from the solution.
+-- newTypeMeta_  = newTypeMeta Inf
+
+{-# SPECIALIZE newLevelMeta :: TCM Level #-}
+newLevelMeta :: MonadMetaSolver m => m Level
+newLevelMeta = do
+  (x, v) <- newValueMeta RunMetaOccursCheck CmpEq =<< levelType
+  return $ case v of
+    Level l    -> l
+    _          -> atomicLevel v
+
+{-# SPECIALIZE newInstanceMeta :: MetaNameSuggestion -> Type -> TCM (MetaId, Term) #-}
+-- | @newInstanceMeta s t cands@ creates a new instance metavariable
+--   of type the output type of @t@ with name suggestion @s@.
+newInstanceMeta
+  :: MonadMetaSolver m
+  => MetaNameSuggestion -> Type -> m (MetaId, Term)
+newInstanceMeta s t = do
+  vs  <- getContextArgs
+  ctx <- getContextTelescope
+  newInstanceMetaCtx s (telePi_ ctx t) vs
+
+newInstanceMetaCtx
+  :: MonadMetaSolver m
+  => MetaNameSuggestion -> Type -> Args -> m (MetaId, Term)
+newInstanceMetaCtx s t vs = do
+  reportSDoc "tc.meta.new" 50 $ fsep
+    [ "new instance meta:"
+    , nest 2 $ prettyTCM vs <+> "|-"
+    ]
+  -- Andreas, 2017-10-04, issue #2753: no metaOccurs check for instance metas
+  i0 <- createMetaInfo' DontRunMetaOccursCheck
+  let i = i0 { miNameSuggestion = s }
+  TelV tel _ <- telView t
+  let perm = idP (size tel)
+  x <- newMeta' OpenInstance Instantiable i normalMetaPriority perm (HasType () CmpLeq t)
+  reportSDoc "tc.meta.new" 50 $ fsep
+    [ nest 2 $ pretty x <+> ":" <+> prettyTCM t
+    ]
+  let c = FindInstance x Nothing
+  addAwakeConstraint alwaysUnblock c
+  etaExpandMetaSafe x
+  return (x, MetaV x $ map Apply vs)
+
+-- | Create a new value meta with specific dependencies, possibly η-expanding in the process.
+newNamedValueMeta :: MonadMetaSolver m => RunMetaOccursCheck -> MetaNameSuggestion -> Comparison -> Type -> m (MetaId, Term)
+newNamedValueMeta b s cmp t = do
+  (x, v) <- newValueMeta b cmp t
+  setMetaNameSuggestion x s
+  return (x, v)
+
+-- | Create a new value meta with specific dependencies without η-expanding.
+newNamedValueMeta' :: MonadMetaSolver m => RunMetaOccursCheck -> MetaNameSuggestion -> Comparison -> Type -> m (MetaId, Term)
+newNamedValueMeta' b s cmp t = do
+  (x, v) <- newValueMeta' b cmp t
+  setMetaNameSuggestion x s
+  return (x, v)
+
+{-# SPECIALIZE newValueMeta :: RunMetaOccursCheck -> Comparison -> Type -> TCM (MetaId, Term) #-}
+-- | Create a new metavariable, possibly η-expanding in the process.
+newValueMeta :: MonadMetaSolver m => RunMetaOccursCheck -> Comparison -> Type -> m (MetaId, Term)
+newValueMeta b cmp t = do
+  vs  <- getContextArgs
+  tel <- getContextTelescope
+  newValueMetaCtx Instantiable b cmp t tel (idP $ size tel) vs
+
+newValueMetaCtx
+  :: MonadMetaSolver m
+  => Frozen -> RunMetaOccursCheck -> Comparison -> Type -> Telescope -> Permutation -> Args -> m (MetaId, Term)
+newValueMetaCtx frozen b cmp t tel perm ctx =
+  mapSndM instantiateFull =<< newValueMetaCtx' frozen b cmp t tel perm ctx
+
+{-# SPECIALIZE newValueMeta' :: RunMetaOccursCheck -> Comparison -> Type -> TCM (MetaId, Term) #-}
+-- | Create a new value meta without η-expanding.
+newValueMeta'
+  :: MonadMetaSolver m
+  => RunMetaOccursCheck -> Comparison -> Type -> m (MetaId, Term)
+newValueMeta' b cmp t = do
+  vs  <- getContextArgs
+  tel <- getContextTelescope
+  newValueMetaCtx' Instantiable b cmp t tel (idP $ size tel) vs
+
+newValueMetaCtx'
+  :: MonadMetaSolver m
+  => Frozen -> RunMetaOccursCheck -> Comparison -> Type -> Telescope -> Permutation -> Args -> m (MetaId, Term)
+newValueMetaCtx' frozen b cmp a tel perm vs = do
+  i <- createMetaInfo' b
+  let t     = telePi_ tel a
+  x <- newMeta frozen i normalMetaPriority perm (HasType () cmp t)
+  modality <- currentModality
+  reportSDoc "tc.meta.new" 50 $ fsep
+    [ text $ "new meta (" ++ show (i ^. lensIsAbstract) ++ "):"
+    , nest 2 $ prettyTCM vs <+> "|-"
+    , nest 2 $ pretty x <+> ":" <+> pretty modality <+> prettyTCM t
+    ]
+  etaExpandMetaSafe x
+  -- Andreas, 2012-09-24: for Metas X : Size< u add constraint X+1 <= u
+  let u = MetaV x $ map Apply vs
+  boundedSizeMetaHook u tel a
+  return (x, u)
+
+newTelMeta :: MonadMetaSolver m => Telescope -> m Args
+newTelMeta tel = newArgsMeta (abstract tel $ __DUMMY_TYPE__)
+
+type Condition = Dom Type -> Abs Type -> Bool
+
+trueCondition :: Condition
+trueCondition _ _ = True
+
+{-# SPECIALIZE newArgsMeta :: Type -> TCM Args #-}
+newArgsMeta :: MonadMetaSolver m => Type -> m Args
+newArgsMeta = newArgsMeta' trueCondition
+
+{-# SPECIALIZE newArgsMeta' :: Condition -> Type -> TCM Args #-}
+newArgsMeta' :: MonadMetaSolver m => Condition -> Type -> m Args
+newArgsMeta' condition t = do
+  args <- getContextArgs
+  tel  <- getContextTelescope
+  newArgsMetaCtx' Instantiable condition t tel (idP $ size tel) args
+
+newArgsMetaCtx :: Type -> Telescope -> Permutation -> Args -> TCM Args
+newArgsMetaCtx = newArgsMetaCtx' Instantiable trueCondition
+
+newArgsMetaCtx''
+  :: MonadMetaSolver m
+  => MetaNameSuggestion -> Frozen -> Condition -> Type -> Telescope -> Permutation -> Args -> m Args
+newArgsMetaCtx'' pref frozen condition (El s tm) tel perm ctx = do
+  tm <- reduce tm
+  case tm of
+    Pi dom@(Dom{domInfo = info, unDom = a}) codom | condition dom codom -> do
+      let mod  = getModality info
+          -- Issue #3031: It's not enough to applyModalityToContext, since most (all?)
+          -- of the context lives in tel. Don't forget the arguments in ctx.
+          tel' = telFromList $
+                 map (mod `inverseApplyModalityButNotQuantity`) $
+                 telToList tel
+          ctx' = map (mod `inverseApplyModalityButNotQuantity`) ctx
+      (m, u) <- applyModalityToContext info $
+                 newValueMetaCtx frozen RunMetaOccursCheck CmpLeq a tel' perm ctx'
+      -- Jesper, 2021-05-05: When creating a metavariable from a
+      -- generalizable variable, we must set the modality at which it
+      -- will be generalized.  Don't do this for other metavariables,
+      -- as they should keep the defaul modality (see #5363).
+      whenM ((== YesGeneralizeVar) <$> viewTC eGeneralizeMetas) $
+        setMetaGeneralizableArgInfo m $ hideOrKeepInstance info
+      setMetaNameSuggestion m (suffixNameSuggestion pref (absName codom))
+      args <- newArgsMetaCtx'' pref frozen condition (codom `absApp` u) tel perm ctx
+      return $ Arg info u : args
+    _  -> return []
+
+newArgsMetaCtx'
+  :: MonadMetaSolver m
+  => Frozen -> Condition -> Type -> Telescope -> Permutation -> Args -> m Args
+newArgsMetaCtx' = newArgsMetaCtx'' mempty
+
+-- | Create a metavariable of record type. This is actually one metavariable
+--   for each field.
+newRecordMeta :: QName -> Args -> TCM Term
+newRecordMeta r pars = do
+  args <- getContextArgs
+  tel  <- getContextTelescope
+  newRecordMetaCtx mempty Instantiable r pars tel (idP $ size tel) args
+
+newRecordMetaCtx
+  :: MetaNameSuggestion
+  -- ^ Name suggestion to be used as a /prefix/ of the name suggestions
+  -- for the metas that represent each field
+  -> Frozen  -- ^ Should the meta be created frozen?
+  -> QName   -- ^ Name of record type
+  -> Args    -- ^ Parameters of record type.
+  -> Telescope -> Permutation -> Args -> TCM Term
+newRecordMetaCtx pref frozen r pars tel perm ctx = do
+  ftel   <- flip apply pars <$> getRecordFieldTypes r
+  fields <- newArgsMetaCtx'' pref frozen trueCondition
+              (telePi_ ftel __DUMMY_TYPE__) tel perm ctx
+  con    <- getRecordConstructor r
+  return $ Con con ConOSystem (map Apply fields)
+
+newQuestionMark :: InteractionId -> Comparison -> Type -> TCM (MetaId, Term)
+newQuestionMark ii cmp = newQuestionMark' (newValueMeta' RunMetaOccursCheck) ii cmp
+
+
+-- Since we are type-checking some code twice, e.g., record declarations
+-- for the sake of the record constructor type and then again for the sake
+-- of the record module (issue #434), we may encounter an interaction point
+-- for which we already have a meta.  In this case, we want to reuse the meta.
+-- Otherwise we get two meta for one interaction point which are not connected,
+-- and e.g. Agda might solve one in some way
+-- and the user the other in some other way...
+--
+-- New reference: Andreas, 2021-07-21, issues #5478 and #5463
+-- Old reference: Andreas, 2016-07-29, issue 1720-2
+-- See also: issue #2257
+newQuestionMark'
+  :: (Comparison -> Type -> TCM (MetaId, Term))
+  -> InteractionId -> Comparison -> Type -> TCM (MetaId, Term)
+newQuestionMark' new ii cmp t = lookupInteractionMeta ii >>= \case
+
+  -- Case: new meta.
+  Nothing -> do
+    -- Do not run check for recursive occurrence of meta in definitions,
+    -- because we want to give the recursive solution interactively (Issue 589)
+    (x, m) <- new cmp t
+    connectInteractionPoint ii x
+    return (x, m)
+
+  -- Case: existing meta.
+  Just x -> do
+    -- Get the context Γ in which the meta was created.
+    MetaVar
+      { mvInfo = MetaInfo{ miClosRange = Closure{ clEnv = TCEnv{ envContext = gamma }}}
+      , mvPermutation = p
+      } <- fromMaybe __IMPOSSIBLE__ <$> lookupLocalMeta' x
+    -- Get the current context Δ.
+    delta <- getContext
+    -- A bit hazardous:
+    -- we base our decisions on the names of the context entries.
+    -- Ideally, Agda would organize contexts in ancestry trees
+    -- with substitutions to move between parent and child.
+    let glen = length gamma
+    let dlen = length delta
+    let gxs  = map (fst . unDom) gamma
+    let dxs  = map (fst . unDom) delta
+    reportSDoc "tc.interaction" 20 $ vcat
+      [ "reusing meta"
+      , nest 2 $ "creation context:" <+> pretty gxs
+      , nest 2 $ "reusage  context:" <+> pretty dxs
+      ]
+
+    -- When checking a record declaration (e.g. Σ), creation context Γ
+    -- might be of the forms Γ₀,Γ₁ or Γ₀,fst,Γ₁ or Γ₀,fst,snd,Γ₁ whereas
+    -- Δ is of the form Γ₀,r,Γ₁,{Δ₂} for record variable r.
+    -- So first find the record variable in Δ.
+    rev_args <- case List.findIndex nameIsRecordName dxs of
+
+      -- Case: no record variable in the context.
+      -- Test whether Δ is an extension of Γ.
+      Nothing -> do
+        unless (gxs `List.isSuffixOf` dxs) $ do
+          reportSDoc "impossible" 10 $ vcat
+            [ "expecting meta-creation context"
+            , nest 2 $ pretty gxs
+            , "to be a suffix of the meta-reuse context"
+            , nest 2 $ pretty dxs
+            ]
+          reportSDoc "impossible" 70 $ vcat
+            [ "expecting meta-creation context"
+            , nest 2 $ (text . show) gxs
+            , "to be a suffix of the meta-reuse context"
+            , nest 2 $ (text . show) dxs
+            ]
+          __IMPOSSIBLE__
+        -- Apply the meta to |Γ| arguments from Δ.
+        return $ map var [dlen - glen .. dlen - 1]
+
+      -- Case: record variable in the context.
+      Just k -> do
+        -- Verify that the contexts relate as expected.
+        let g0len = length dxs - k - 1
+        -- Find out the Δ₂ and Γ₁ parts.
+        -- However, as they do not share common ancestry, the @nameId@s differ,
+        -- so we consider only the original concrete names.
+        -- This is a bit risky... blame goes to #434.
+        let gys = map nameCanonical gxs
+        let dys = map nameCanonical dxs
+        let (d2len, g1len) = findOverlap (take k dys) gys
+        reportSDoc "tc.interaction" 30 $ vcat $ map (nest 2)
+          [ "glen  =" <+> pretty glen
+          , "g0len =" <+> pretty g0len
+          , "g1len =" <+> pretty g1len
+          , "d2len =" <+> pretty d2len
+          ]
+        -- The Γ₀ part should match.
+        unless (drop (glen - g0len) gxs == drop (k + 1) dxs) $ do
+          reportSDoc "impossible" 10 $ vcat
+            [ "expecting meta-creation context (with fields instead of record var)"
+            , nest 2 $ pretty gxs
+            , "to share ancestry (suffix) with the meta-reuse context (with record var)"
+            , nest 2 $ pretty dxs
+            ]
+          __IMPOSSIBLE__
+        -- The Γ₁ part should match.
+        unless ( ((==) `on` take g1len) gys (drop d2len dys) ) $ do
+          reportSDoc "impossible" 10 $ vcat
+            [ "expecting meta-creation context (with fields instead of record var)"
+            , nest 2 $ pretty gxs
+            , "to be an expansion of the meta-reuse context (with record var)"
+            , nest 2 $ pretty dxs
+            ]
+          __IMPOSSIBLE__
+        let (vs1, v : vs0) = splitAt g1len $ map var [d2len..dlen-1]
+        -- We need to expand the record var @v@ into the correct number of fields.
+        let numFields = glen - g1len - g0len
+        if numFields <= 0 then return $ vs1 ++ vs0 else do
+          -- Get the record type.
+          let t = snd . unDom . fromMaybe __IMPOSSIBLE__ $ delta !!! k
+          -- Get the record field names.
+          fs <- getRecordTypeFields t
+          -- Field arguments to the original meta are projections from the record var.
+          let vfs = map ((\ x -> v `applyE` [Proj ProjSystem x]) . unDom) fs
+          -- These are the final args to the original meta:
+          return $ vs1 ++ reverse (take numFields vfs) ++ vs0
+
+    -- Use ArgInfo from Γ.
+    let args = reverse $ zipWith (<$) rev_args $ map argFromDom gamma
+    -- Take the permutation into account (see TC.Monad.MetaVars.getMetaContextArgs).
+    let vs = permute (takeP (length args) p) args
+    reportSDoc "tc.interaction" 20 $ vcat
+      [ "meta reuse arguments:" <+> prettyTCM vs ]
+    return (x, MetaV x $ map Apply vs)
+
+{-# SPECIALIZE blockTerm :: Type -> TCM Term -> TCM Term #-}
+-- | Construct a blocked constant if there are constraints.
+blockTerm
+  :: (MonadMetaSolver m, MonadConstraint m, MonadFresh Nat m, MonadFresh ProblemId m)
+  => Type -> m Term -> m Term
+blockTerm t blocker = do
+  (pid, v) <- newProblem blocker
+  blockTermOnProblem t v pid
+
+{-# SPECIALIZE blockTermOnProblem :: Type -> Term -> ProblemId -> TCM Term #-}
+blockTermOnProblem
+  :: (MonadMetaSolver m, MonadFresh Nat m)
+  => Type -> Term -> ProblemId -> m Term
+blockTermOnProblem t v pid = do
+  -- Andreas, 2012-09-27 do not block on unsolved size constraints
+  solved <- isProblemSolved pid
+  ifM (return solved `or2M` isSizeProblem pid)
+      (v <$ reportSLn "tc.meta.blocked" 20 ("Not blocking because " ++ show pid ++ " is " ++
+                                            if solved then "solved" else "a size problem")) $ do
+    i   <- createMetaInfo
+    es  <- map Apply <$> getContextArgs
+    tel <- getContextTelescope
+    x   <- newMeta' (BlockedConst $ abstract tel v)
+                    Instantiable
+                    i
+                    lowMetaPriority
+                    (idP $ size tel)
+                    (HasType () CmpLeq $ telePi_ tel t)
+                    -- we don't instantiate blocked terms
+    inTopContext $ addConstraint (unblockOnProblem pid) (UnBlock x)
+    reportSDoc "tc.meta.blocked" 20 $ vcat
+      [ "blocked" <+> prettyTCM x <+> ":=" <+> inTopContext
+        (prettyTCM $ abstract tel v)
+      , "     by" <+> (prettyTCM =<< getConstraintsForProblem pid)
+      ]
+    inst <- isInstantiatedMeta x
+    if inst
+      then instantiate (MetaV x es)
+      else do
+        -- We don't return the blocked term instead create a fresh metavariable
+        -- that we compare against the blocked term once it's unblocked. This way
+        -- blocked terms can be instantiated before they are unblocked, thus making
+        -- constraint solving a bit more robust against instantiation order.
+        -- Andreas, 2015-05-22: DontRunMetaOccursCheck to avoid Issue585-17.
+        (m', v) <- newValueMeta DontRunMetaOccursCheck CmpLeq t
+        reportSDoc "tc.meta.blocked" 30
+          $   "setting twin of"
+          <+> prettyTCM m'
+          <+> "to be"
+          <+> prettyTCM x
+        updateMetaVar m' (\mv -> mv { mvTwin = Just x })
+        i   <- fresh
+        -- This constraint is woken up when unblocking, so it doesn't need a problem id.
+        cmp <- buildProblemConstraint_ (unblockOnMeta x) (ValueCmp CmpEq (AsTermsOf t) v (MetaV x es))
+        reportSDoc "tc.constr.add" 20 $ "adding constraint" <+> prettyTCM cmp
+        listenToMeta (CheckConstraint i cmp) x
+        return v
+
+{-# SPECIALIZE blockTypeOnProblem :: Type -> ProblemId -> TCM Type #-}
+blockTypeOnProblem
+  :: (MonadMetaSolver m, MonadFresh Nat m)
+  => Type -> ProblemId -> m Type
+blockTypeOnProblem (El s a) pid = El s <$> blockTermOnProblem (sort s) a pid
+
+-- | @unblockedTester t@ returns a 'Blocker' for @t@.
+--
+--   Auxiliary function used when creating a postponed type checking problem.
+unblockedTester :: Type -> TCM Blocker
+unblockedTester t = ifBlocked t (\ b _ -> return b) (\ _ _ -> return alwaysUnblock)
+
+-- | Create a postponed type checking problem @e : t@ that waits for type @t@
+--   to unblock (become instantiated or its constraints resolved).
+postponeTypeCheckingProblem_ :: TypeCheckingProblem -> TCM Term
+postponeTypeCheckingProblem_ p = do
+  postponeTypeCheckingProblem p =<< unblock p
+  where
+    unblock (CheckExpr _ _ t)         = unblockedTester t
+    unblock (CheckArgs _ _ _ _ t _ _) = unblockedTester t  -- The type of the head of the application.
+    unblock (CheckProjAppToKnownPrincipalArg _ _ _ _ _ _ _ _ t _) = unblockedTester t -- The type of the principal argument
+    unblock (CheckLambda _ _ _ t)     = unblockedTester t
+    unblock (DoQuoteTerm _ _ _)       = __IMPOSSIBLE__     -- also quoteTerm problems
+
+-- | Create a postponed type checking problem @e : t@ that waits for conditon
+--   @unblock@.  A new meta is created in the current context that has as
+--   instantiation the postponed type checking problem.  An 'UnBlock' constraint
+--   is added for this meta, which links to this meta.
+postponeTypeCheckingProblem :: TypeCheckingProblem -> Blocker -> TCM Term
+postponeTypeCheckingProblem p unblock | unblock == alwaysUnblock = do
+  reportSDoc "impossible" 2 $ "Postponed without blocker:" <?> prettyTCM p
+  __IMPOSSIBLE__
+postponeTypeCheckingProblem p unblock = do
+  i   <- createMetaInfo' DontRunMetaOccursCheck
+  tel <- getContextTelescope
+  cl  <- buildClosure p
+  let t = problemType p
+  m   <- newMeta' (PostponedTypeCheckingProblem cl)
+                  Instantiable i normalMetaPriority (idP (size tel))
+         $ HasType () CmpLeq $ telePi_ tel t
+  inTopContext $ reportSDoc "tc.meta.postponed" 20 $ vcat
+    [ "new meta" <+> prettyTCM m <+> ":" <+> prettyTCM (telePi_ tel t)
+    , "for postponed typechecking problem" <+> prettyTCM p
+    ]
+
+  -- Create the meta that we actually return
+  -- Andreas, 2012-03-15
+  -- This is an alias to the pptc meta, in order to allow pruning (issue 468)
+  -- and instantiation.
+  -- Since this meta's solution comes from user code, we do not need
+  -- to run the extended occurs check (metaOccurs) to exclude
+  -- non-terminating solutions.
+  es  <- map Apply <$> getContextArgs
+  (_, v) <- newValueMeta DontRunMetaOccursCheck CmpLeq t
+  cmp <- buildProblemConstraint_ (unblockOnMeta m) (ValueCmp CmpEq (AsTermsOf t) v (MetaV m es))
+  reportSDoc "tc.constr.add" 20 $ "adding constraint" <+> prettyTCM cmp
+  i   <- liftTCM fresh
+  listenToMeta (CheckConstraint i cmp) m
+  addConstraint unblock (UnBlock m)
+  return v
+
+-- | Type of the term that is produced by solving the 'TypeCheckingProblem'.
+problemType :: TypeCheckingProblem -> Type
+problemType (CheckExpr _ _ t         ) = t
+problemType (CheckArgs _ _ _ _ _ t _ ) = t  -- The target type of the application.
+problemType (CheckProjAppToKnownPrincipalArg _ _ _ _ _ t _ _ _ _) = t -- The target type of the application
+problemType (CheckLambda _ _ _ t     ) = t
+problemType (DoQuoteTerm _ _ t)        = t
+
+-- | Eta-expand a local meta-variable, if it is of the specified kind.
+--   Don't do anything if the meta-variable is a blocked term.
+etaExpandMetaTCM :: [MetaKind] -> MetaId -> TCM ()
+etaExpandMetaTCM kinds m = whenM ((not <$> isFrozen m) `and2M` asksTC envAssignMetas `and2M` isEtaExpandable kinds m) $ do
+  verboseBracket "tc.meta.eta" 20 ("etaExpandMeta " ++ prettyShow m) $ do
+    let waitFor b = do
+          reportSDoc "tc.meta.eta" 20 $ do
+            "postponing eta-expansion of meta variable" <+>
+              prettyTCM m <+>
+              "which is blocked by" <+> prettyTCM b
+          mapM_ (listenToMeta (EtaExpand m)) $ allBlockingMetas b
+        dontExpand = do
+          reportSDoc "tc.meta.eta" 20 $ do
+            "we do not expand meta variable" <+> prettyTCM m <+>
+              text ("(requested was expansion of " ++ show kinds ++ ")")
+    meta <- lookupLocalMeta m
+    case mvJudgement meta of
+      IsSort{} -> dontExpand
+      HasType _ cmp a -> do
+
+        reportSDoc "tc.meta.eta" 40 $ sep
+          [ text "considering eta-expansion at type "
+          , prettyTCM a
+          , text " raw: "
+          , pretty a
+          ]
+
+        TelV tel b <- telView a
+        reportSDoc "tc.meta.eta" 40 $ sep
+          [ text "considering eta-expansion at type"
+          , addContext tel (prettyTCM b)
+          , text "under telescope"
+          , prettyTCM tel
+          ]
+
+        -- Eta expanding metas with a domFinite will just make sure
+        -- they go unsolved: conversion will compare them at the
+        -- different cases for the domain, so it will not find the
+        -- solution for the whole meta.
+        if any domIsFinite (flattenTel tel) then dontExpand else do
+
+        -- Issue #3774: continue with the right context for b
+        addContext tel $ do
+
+        -- if the target type @b@ of @m@ is a meta variable @x@ itself
+        -- (@NonBlocked (MetaV{})@),
+        -- or it is blocked by a meta-variable @x@ (@Blocked@), we cannot
+        -- eta expand now, we have to postpone this.  Once @x@ is
+        -- instantiated, we can continue eta-expanding m.  This is realized
+        -- by adding @m@ to the listeners of @x@.
+        ifBlocked (unEl b) (\ x _ -> waitFor x) $ \ _ t -> case t of
+          lvl@(Def r es) ->
+            ifM (isEtaRecord r) {- then -} (do
+              let ps = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+              let expand = do
+                    u <- withMetaInfo' meta $
+                      newRecordMetaCtx (miNameSuggestion (mvInfo meta))
+                        (mvFrozen meta) r ps tel (idP $ size tel) $ teleArgs tel
+                    -- Andreas, 2019-03-18, AIM XXIX, issue #3597
+                    -- When meta is frozen instantiate it with in-turn frozen metas.
+                    inTopContext $ do
+                      reportSDoc "tc.meta.eta" 15 $ sep
+                          [ "eta expanding: " <+> pretty m <+> " --> "
+                          , nest 2 $ prettyTCM u
+                          ]
+                      -- Andreas, 2012-03-29: No need for occurrence check etc.
+                      -- we directly assign the solution for the meta
+                      -- 2012-05-23: We also bypass the check for frozen.
+                      noConstraints $ assignTerm' m (telToArgs tel) u  -- should never produce any constraints
+              if Records `elem` kinds then
+                expand
+               else if (SingletonRecords `elem` kinds) then
+                catchPatternErr (\x -> waitFor x) $ do
+                 ifM (isSingletonRecord r ps) expand dontExpand
+                else dontExpand
+            ) $ {- else -} ifM (andM [ return $ Levels `elem` kinds
+                            , typeInType
+                            , (Just lvl ==) <$> getBuiltin' builtinLevel
+                            ]) (do
+              reportSLn "tc.meta.eta" 20 $ "Expanding level meta to 0 (type-in-type)"
+              -- Andreas, 2012-03-30: No need for occurrence check etc.
+              -- we directly assign the solution for the meta
+              noConstraints $ assignTerm m (telToArgs tel) $ Level $ ClosedLevel 0
+           ) $ {- else -} dontExpand
+          _ -> dontExpand
+
+-- | Eta expand blocking metavariables of record type, and reduce the
+-- blocked thing.
+
+etaExpandBlocked :: (MonadReduce m, MonadMetaSolver m, IsMeta t, Reduce t)
+                 => Blocked t -> m (Blocked t)
+etaExpandBlocked t@NotBlocked{} = return t
+etaExpandBlocked t@(Blocked _ v) | Just{} <- isMeta v = return t
+etaExpandBlocked (Blocked b t)  = do
+  reportSDoc "tc.meta.eta" 30 $ "Eta expanding blockers" <+> pretty b
+  mapM_ (etaExpandMeta [Records]) $ allBlockingMetas b
+  t <- reduceB t
+  case t of
+    Blocked b' _ | b /= b' -> etaExpandBlocked t
+    _                      -> return t
+
+{-# SPECIALIZE assignWrapper :: CompareDirection -> MetaId -> Elims -> Term -> TCM () -> TCM () #-}
+assignWrapper :: (MonadMetaSolver m, MonadConstraint m, MonadError TCErr m, MonadDebug m, HasOptions m)
+              => CompareDirection -> MetaId -> Elims -> Term -> m () -> m ()
+assignWrapper dir x es v doAssign = do
+  ifNotM (asksTC envAssignMetas) dontAssign $ {- else -} do
+    reportSDoc "tc.meta.assign" 10 $ do
+      "term" <+> prettyTCM (MetaV x es) <+> text (":" ++ prettyShow dir) <+> prettyTCM v
+    nowSolvingConstraints doAssign `finally` solveAwakeConstraints
+
+  where dontAssign = do
+          reportSLn "tc.meta.assign" 10 "don't assign metas"
+          patternViolation alwaysUnblock  -- retry again when we are allowed to instantiate metas
+
+-- | Miller pattern unification:
+--
+--   @assign dir x vs v a@ solves problem @x vs <=(dir) v : a@ for meta @x@
+--   if @vs@ are distinct variables (linearity check)
+--   and @v@ depends only on these variables
+--   and does not contain @x@ itself (occurs check).
+--
+--   This is the basic story, but we have added some features:
+--
+--   1. Pruning.
+--   2. Benign cases of non-linearity.
+--   3. @vs@ may contain record patterns.
+--
+--   For a reference to some of these extensions, read
+--   Andreas Abel and Brigitte Pientka's TLCA 2011 paper.
+
+assign :: CompareDirection -> MetaId -> Args -> Term -> CompareAs -> TCM ()
+assign dir x args v target = addOrUnblocker (unblockOnMeta x) $ do
+
+  mvar <- lookupLocalMeta x  -- information associated with meta x
+  let t = jMetaType $ mvJudgement mvar
+
+  -- Andreas, 2011-05-20 TODO!
+  -- full normalization  (which also happens during occurs check)
+  -- is too expensive! (see Issue 415)
+  -- need to do something cheaper, especially if
+  -- we are dealing with a Miller pattern that can be solved
+  -- immediately!
+  -- Ulf, 2011-08-25 DONE!
+  -- Just instantiating the top-level meta, which is cheaper. The occurs
+  -- check will first try without unfolding any definitions (treating
+  -- arguments to definitions as flexible), if that fails it tries again
+  -- with full unfolding.
+  reportSDoc "tc.meta.assign" 25 $ "v = " <+> prettyTCM v
+  v <- instantiate v
+  reportSDoc "tc.meta.assign" 25 $ "v = " <+> prettyTCM v
+  reportSDoc "tc.meta.assign" 45 $
+    "MetaVars.assign: assigning meta " <+> prettyTCM (MetaV x []) <+>
+    " with args " <+> prettyList_ (map (prettyTCM . unArg) args) <+>
+    " to " <+> prettyTCM v
+  reportSDoc "tc.meta.assign" 45 $
+    "MetaVars.assign: type of meta: " <+> prettyTCM t
+
+  reportSDoc "tc.meta.assign" 75 $
+    text "MetaVars.assign: assigning meta  " <> pretty x <> text "  with args  " <> pretty args <> text "  to  " <> pretty v
+
+  let
+    boundary v = do
+      cubical <- optCubical <$> pragmaOptions
+      isip <- isInteractionMetaB x args
+      case (,) <$> cubical <*> isip of
+        Just (_, (x, ip, args)) -> tryAddBoundary dir x ip args v target
+        _ -> pure ()
+
+  case (v, mvJudgement mvar) of
+      (Sort s, HasType{}) -> hasBiggerSort s
+      _                   -> return ()
+
+  -- Jesper, 2019-09-13: When --no-sort-comparison is enabled,
+  -- we equate the sort of the solution with the sort of the
+  -- metavariable, in order to solve metavariables in sorts.
+  -- Jesper, 2020-04-22: We do this before any of the other steps
+  -- because comparing the sorts might lead to some metavariables
+  -- being solved, which can help with pruning (see #4615).
+  -- Jesper, 2020-08-25: --no-sort-comparison is now the default
+  -- behaviour.
+  --
+  -- Under most circumstances, the conversion checker guarantees that
+  -- the solution for the meta has the correct type, so there is no
+  -- need to check anything. However, there are two circumstances in
+  -- which we do need to check the type of the solution:
+  --
+  -- 1. When comparing two types they are not guaranteed to have the
+  --    same sort.
+  --
+  -- 2. When --cumulativity is enabled the same can happen when
+  --    comparing two terms at a sort type.
+
+  cumulativity <- optCumulativity <$> pragmaOptions
+
+  let checkSolutionSort cmp s v = do
+        s' <- sortOf v
+        reportSDoc "tc.meta.assign" 40 $
+          "Instantiating sort" <+> prettyTCM s <+>
+          "to sort" <+> prettyTCM s' <+> "of solution" <+> prettyTCM v
+        traceCall (CheckMetaSolution (getRange mvar) x (sort s) v) $
+          compareSort cmp s' s
+
+  case (target , mvJudgement mvar) of
+    -- Case 1 (comparing term to meta as types)
+    (AsTypes{}   , HasType _ cmp0 t) -> do
+        let cmp   = if cumulativity then cmp0 else CmpEq
+            abort = patternViolation =<< updateBlocker (unblockOnAnyMetaIn t) -- TODO: make piApplyM' compute unblocker
+        t' <- piApplyM' abort t args
+        s <- shouldBeSort t'
+        checkSolutionSort cmp s v
+
+    -- Case 2 (comparing term to type-level meta as terms, with --cumulativity)
+    (AsTermsOf{} , HasType _ cmp t)
+      | cumulativity -> do
+          let abort = patternViolation =<< updateBlocker (unblockOnAnyMetaIn t)
+          t' <- piApplyM' abort t args
+          TelV tel t'' <- telView t'
+          addContext tel $ ifNotSort t'' (return ()) $ \s -> do
+            let v' = raise (size tel) v `apply` teleArgs tel
+            checkSolutionSort cmp s v'
+
+    (AsTypes{}   , IsSort{}       ) -> return ()
+    (AsTermsOf{} , _              ) -> return ()
+    (AsSizes{}   , _              ) -> return ()  -- TODO: should we do something similar for sizes?
+
+
+
+  -- We don't instantiate frozen mvars
+  when (mvFrozen mvar == Frozen) $ do
+    reportSLn "tc.meta.assign" 25 $ "aborting: meta is frozen!"
+    -- IApplyConfluence can contribute boundary conditions to frozen metas
+    boundary v
+    patternViolation neverUnblock
+
+  -- We never get blocked terms here anymore. TODO: we actually do. why?
+  whenM (isBlockedTerm x) $ do
+    reportSLn "tc.meta.assign" 25 $ "aborting: meta is a blocked term!"
+    patternViolation (unblockOnMeta x)
+
+  -- Andreas, 2010-10-15 I want to see whether rhs is blocked
+  reportSLn "tc.meta.assign" 50 $ "MetaVars.assign: I want to see whether rhs is blocked"
+  reportSDoc "tc.meta.assign" 25 $ do
+    v0 <- reduceB v
+    case v0 of
+      Blocked m0 _ -> "r.h.s. blocked on:" <+> prettyTCM m0
+      NotBlocked{} -> "r.h.s. not blocked"
+  reportSDoc "tc.meta.assign" 25 $ "v = " <+> prettyTCM v
+
+  -- Turn the assignment problem @_X args >= SizeLt u@ into
+  -- @_X args = SizeLt (_Y args@ and constraint
+  -- @_Y args >= u@.
+  subtypingForSizeLt dir x mvar t args v $ \ v -> do
+
+    reportSDoc "tc.meta.assign" 25 $ "v = " <+> prettyTCM v
+    reportSDoc "tc.meta.assign.proj" 45 $ do
+      cxt <- getContextTelescope
+      vcat
+        [ "context before projection expansion"
+        , nest 2 $ inTopContext $ prettyTCM cxt
+        ]
+
+    -- Normalise and eta contract the arguments to the meta. These are
+    -- usually small, and simplifying might let us instantiate more metas.
+    -- Also, try to expand away projected vars in meta args.
+
+    expandProjectedVars args (v, target) $ \ args (v, target) -> do
+
+      reportSDoc "tc.meta.assign.proj" 45 $ do
+        cxt <- getContextTelescope
+        vcat
+          [ "context after projection expansion"
+          , nest 2 $ inTopContext $ prettyTCM cxt
+          ]
+
+      -- Andreas, 2019-11-16, issue #4159:
+      -- We would like to save the work we put into expanding projected variables.
+      -- However, the Conversion checker speculatively tries some assignment
+      -- in some places (e.g. shortcut) and relies on an exception to be thrown
+      -- to try other alternatives next.
+      -- If we catch the exception here, this (brittle) mechanism will be broken.
+      -- Maybe one possibility would be to rethrow the exception with the
+      -- new constraint.  Then, further up, it could be decided whether
+      -- to discard the new constraint and do something different,
+      -- or add the new constraint when postponing.
+
+      -- BEGIN attempt #4159
+      -- let constraint = case v of
+      --       -- Sort s -> dirToCmp SortCmp dir (MetaS x $ map Apply args) s
+      --       _      -> dirToCmp (\ cmp -> ValueCmp cmp target) dir (MetaV x $ map Apply args) v
+      -- reportSDoc "tc.meta.assign.catch" 40 $ sep
+      --   [ "assign: catching constraint:"
+      --   , prettyTCM constraint
+      --   ]
+      -- -- reportSDoc "tc.meta.assign.catch" 60 $ sep
+      -- --   [ "assign: catching constraint:"
+      -- --   , pretty constraint
+      -- --   ]
+      -- reportSDoc "tc.meta.assign.catch" 80 $ sep
+      --   [ "assign: catching constraint (raw):"
+      --   , (text . show) constraint
+      --   ]
+      -- catchConstraint constraint $ do
+      -- END attempt #4159
+
+
+      -- Andreas, 2011-04-21 do the occurs check first
+      -- e.g. _1 x (suc x) = suc (_2 x y)
+      -- even though the lhs is not a pattern, we can prune the y from _2
+
+      let
+                vars        = freeVars args
+                relVL       = filterVarMapToList isRelevant  vars
+                nonstrictVL = filterVarMapToList isNonStrict vars
+                irrVL       = filterVarMapToList (liftM2 (&&) isIrrelevant isUnguarded) vars
+            -- Andreas, 2011-10-06 only irrelevant vars that are direct
+            -- arguments to the meta, hence, can be abstracted over, may
+            -- appear on the rhs.  (test/fail/Issue483b)
+            -- Update 2011-03-27: Also irr. vars under record constructors.
+            -- Andreas, 2019-06-25:  The reason is that when solving
+            -- @X args = v@ we drop all irrelevant arguments that
+            -- are not variables (after flattening of record constructors).
+            -- (See isVarOrIrrelevant in inverseSubst.)
+            -- Thus, the occurs-check needs to ensure only these variables
+            -- are mentioned on the rhs.
+            -- In the terminology of free variable analysis, the retained
+            -- irrelevant variables are exactly the Unguarded ones.
+            -- Jesper, 2019-10-15: This is actually wrong since it
+            -- will lead to pruning of metas that should not be
+            -- pruned, see #4136.
+
+      reportSDoc "tc.meta.assign" 20 $
+          let pr (Var n []) = text (show n)
+              pr (Def c []) = prettyTCM c
+              pr _          = ".."
+          in vcat
+               [ "mvar args:" <+> sep (map (pr . unArg) args)
+               , "fvars lhs (rel):" <+> sep (map (text . show) relVL)
+               , "fvars lhs (nonstrict):" <+> sep (map (text . show) nonstrictVL)
+               , "fvars lhs (irr):" <+> sep (map (text . show) irrVL)
+               ]
+
+      -- Check that the x doesn't occur in the right hand side.
+      -- Prune mvars on rhs such that they can only depend on lhs vars.
+      -- Herein, distinguish relevant and irrelevant vars,
+      -- since when abstracting irrelevant lhs vars, they may only occur
+      -- irrelevantly on rhs.
+      -- v <- liftTCM $ occursCheck x (relVL, nonstrictVL, irrVL) v
+      v <- liftTCM $ occursCheck x vars v
+
+      reportSLn "tc.meta.assign" 15 "passed occursCheck"
+      reportSDoc "tc.meta.assign" 25 $ "v = " <+> prettyTCM v
+      verboseS "tc.meta.assign" 30 $ do
+        let n = termSize v
+        when (n > 200) $ reportSDoc "tc.meta.assign" 30 $
+          sep [ "size" <+> text (show n)
+--              , nest 2 $ "type" <+> prettyTCM t
+              , nest 2 $ "term" <+> prettyTCM v
+              ]
+
+      -- Check linearity of @ids@
+      -- Andreas, 2010-09-24: Herein, ignore the variables which are not
+      -- free in v
+      -- Ulf, 2011-09-22: we need to respect irrelevant vars as well, otherwise
+      -- we'll build solutions where the irrelevant terms are not valid
+      let fvs = allFreeVars v
+      reportSDoc "tc.meta.assign" 20 $
+        "fvars rhs:" <+> sep (map (text . show) $ VarSet.toList fvs)
+
+      -- Check that the arguments are variables
+      mids <- do
+        res <- runExceptT $ inverseSubst' (const False) args
+        case res of
+          -- all args are variables
+          Right ids -> do
+            reportSDoc "tc.meta.assign" 60 $
+              "inverseSubst returns:" <+> sep (map pretty ids)
+            reportSDoc "tc.meta.assign" 50 $
+              "inverseSubst returns:" <+> sep (map prettyTCM ids)
+            let boundVars = VarSet.fromList $ map fst ids
+            if fvs `VarSet.isSubsetOf` boundVars
+              then return $ Just ids
+              else return Nothing
+          -- we have proper values as arguments which could be cased on
+          -- here, we cannot prune, since offending vars could be eliminated
+          Left (CantInvert tm) -> Nothing <$ boundary v
+          -- we have non-variables, but these are not eliminateable
+          Left NeutralArg  -> Just <$> attemptPruning x args fvs
+          -- we have a projected variable which could not be eta-expanded away:
+          -- same as neutral
+          Left ProjVar{}   -> Just <$> attemptPruning x args fvs
+
+      case mids of  -- vv Ulf 2014-07-13: actually not needed after all: attemptInertRHSImprovement x args v
+        Nothing  -> patternViolation =<< updateBlocker (unblockOnAnyMetaIn v)  -- TODO: more precise
+        Just ids -> do
+          -- Check linearity
+          ids <- do
+            res <- runExceptT $ checkLinearity {- (`VarSet.member` fvs) -} ids
+            case res of
+              -- case: linear
+              Right ids -> return ids
+              -- case: non-linear variables that could possibly be pruned
+              -- If pruning fails we need to unblock on any meta in the rhs, since they might get
+              -- rid of the dependency on the non-linear variable. TODO: be more precise (all metas
+              -- using non-linear variables need to be solved).
+              Left ()   -> do
+                block <- updateBlocker $ unblockOnAnyMetaIn v
+                addOrUnblocker block $ attemptPruning x args fvs
+
+          -- Check ids is time respecting.
+          () <- do
+            let idvars = map (mapSnd allFreeVars) ids
+            -- earlierThan α v := v "arrives" before α
+            let earlierThan l j = j > l
+            TelV tel' _ <- telViewUpToPath (length args) t
+            forM_ ids $ \(i,u) -> do
+              d <- lookupBV i
+              case getLock (getArgInfo d) of
+                IsNotLock -> pure ()
+                IsLock{} -> do
+                let us = IntSet.unions $ map snd $ filter (earlierThan i . fst) idvars
+                -- us Earlier than u
+                addContext tel' $ checkEarlierThan u us
+                  `catchError` \case
+                     TypeError{} -> patternViolation (unblockOnMeta x) -- If the earlier check hard-fails we need to
+                     err         -> throwError err                     -- solve this meta in some other way.
+
+          let n = length args
+          TelV tel' _ <- telViewUpToPath n t
+
+          -- Check subtyping constraints on the context variables.
+
+          -- Intuition: suppose @_X : (x : A) → B@, then to turn
+          --   @
+          --     Γ(x : A') ⊢ _X x =?= v : B'@
+          --   @
+          -- into
+          --   @
+          --     Γ ⊢ _X =?= λ x → v
+          --   @
+          -- we need to check that @A <: A'@ (due to contravariance).
+          let sigma = parallelS $ reverse $ map unArg args
+          hasSubtyping <- optCumulativity <$> pragmaOptions
+          when hasSubtyping $ forM_ ids $ \(i , u) -> do
+            -- @u@ is a (projected) variable, so we can infer its type
+            a  <- applySubst sigma <$> addContext tel' (infer u)
+            a' <- typeOfBV i
+            checkSubtypeIsEqual a' a
+              `catchError` \case
+                TypeError{} -> patternViolation (unblockOnMeta x) -- If the subtype check hard-fails we need to
+                err         -> throwError err                     -- solve this meta in some other way.
+
+          -- Solve.
+          m <- getContextSize
+          assignMeta' m x t n ids v
+  where
+    -- Try to remove meta arguments from lhs that mention variables not occurring on rhs.
+    attemptPruning
+      :: MetaId  -- Meta-variable (lhs)
+      -> Args    -- Meta arguments (lhs)
+      -> FVs     -- Variables occuring on the rhs
+      -> TCM a
+    attemptPruning x args fvs = do
+      -- non-linear lhs: we cannot solve, but prune
+      killResult <- prune x args $ (`VarSet.member` fvs)
+      let success = killResult `elem` [PrunedSomething,PrunedEverything]
+      reportSDoc "tc.meta.assign" 10 $
+        "pruning" <+> prettyTCM x <+> do text $ if success then "succeeded" else "failed"
+      blocker <- if
+        | success   -> return alwaysUnblock  -- If pruning succeeded we want to retry right away
+        | otherwise -> unblockOnAnyMetaIn . MetaV x . map Apply <$> instantiateFull args
+             -- TODO: could be more precise: only unblock on metas
+             --       applied to offending variables
+      patternViolation blocker
+
+-- | Is the given metavariable application secretly an interaction point
+-- application? Ugly.
+isInteractionMetaB
+  :: forall m. (ReadTCState m, MonadReduce m, MonadPretty m)
+  => MetaId
+  -> Args
+  -> m (Maybe (MetaId, InteractionId, Args))
+isInteractionMetaB mid args =
+  runMaybeT $ here mid args `mplus` do
+    -- If the meta isn't literally an interaction point it might still
+    -- be instantiable to an interaction point, as long as we ignore
+    -- blocking
+    lift (instantiateBlockingFull (MetaV mid (Apply <$> args))) >>= there
+  where
+    here mid args = do
+      iid <- MaybeT (isInteractionMeta mid)
+      pure (mid, iid, args)
+
+    instantiateBlockingFull = locallyTCState stInstantiateBlocking (const True) . instantiateFull
+
+    there :: Term -> MaybeT m (MetaId, InteractionId, Args)
+    there (MetaV m args) = do
+      iid  <- MaybeT (isInteractionMeta m)
+      args <- MaybeT (pure (allApplyElims args))
+      pure (m, iid, args)
+    -- It might be the case that the inner meta (the interaction point)
+    -- exists in a larger context, so instantiating the outer meta (the
+    -- original argument) will produce lambdas.
+    --
+    -- Since the boundary code runs in the inner, larger context, we can
+    -- peel off the lambdas without running afoul of the scope.
+    there (Lam _ as) = there (absApp as (var 0))
+    there _ = mzero
+
+{- UNUSED
+-- | When faced with @_X us == D vs@ for an inert D we can solve this by
+--   @_X xs := D _Ys@ with new constraints @_Yi us == vi@. This is important
+--   for instance arguments, where knowing the head D might enable progress.
+attemptInertRHSImprovement :: MetaId -> Args -> Term -> TCM ()
+attemptInertRHSImprovement m args v = do
+  reportSDoc "tc.meta.inert" 30 $ vcat
+    [ "attempting inert rhs improvement"
+    , nest 2 $ sep [ prettyTCM (MetaV m $ map Apply args) <+> "=="
+                   , prettyTCM v ] ]
+  -- Check that the right-hand side has the form D vs, for some inert constant D.
+  -- Returns the type of D and a function to build an application of D.
+  (a, mkRHS) <- ensureInert v
+  -- Check that all arguments to the meta are neutral and does not have head D.
+  -- If there are non-neutral arguments there could be solutions to the meta
+  -- that computes over these arguments. If D is an argument to the meta we get
+  -- multiple solutions (for instance: _M Nat == Nat can be solved by both
+  -- _M := \ x -> x and _M := \ x -> Nat).
+  mapM_ (ensureNeutral (mkRHS []) . unArg) args
+  tel <- theTel <$> (telView =<< getMetaType m)
+  -- When attempting shortcut meta solutions, metas aren't necessarily fully
+  -- eta expanded. If this is the case we skip inert improvement.
+  when (length args < size tel) $ do
+    reportSDoc "tc.meta.inert" 30 $ "not fully applied"
+    patternViolation
+  -- Solve the meta with _M := \ xs -> D (_Y1 xs) .. (_Yn xs), for fresh metas
+  -- _Yi.
+  metaArgs <- inTopContext $ addContext tel $ newArgsMeta a
+  let varArgs = map Apply $ reverse $ zipWith (\i a -> var i <$ a) [0..] (reverse args)
+      sol     = mkRHS metaArgs
+      argTel  = map ("x" <$) args
+  reportSDoc "tc.meta.inert" 30 $ nest 2 $ vcat
+    [ "a       =" <+> prettyTCM a
+    , "tel     =" <+> prettyTCM tel
+    , "metas   =" <+> prettyList (map prettyTCM metaArgs)
+    , "sol     =" <+> prettyTCM sol
+    ]
+  assignTerm m argTel sol
+  patternViolation  -- throwing a pattern violation here lets the constraint
+                    -- machinery worry about restarting the comparison.
+  where
+    ensureInert :: Term -> TCM (Type, Args -> Term)
+    ensureInert v = do
+      let notInert = do
+            reportSDoc "tc.meta.inert" 30 $ nest 2 $ "not inert:" <+> prettyTCM v
+            patternViolation
+          toArgs elims =
+            case allApplyElims elims of
+              Nothing -> do
+                reportSDoc "tc.meta.inert" 30 $ nest 2 $ "can't do projections from inert"
+                patternViolation
+              Just args -> return args
+      case v of
+        Var x elims -> (, Var x . map Apply) <$> typeOfBV x
+        Con c ci args  -> notInert -- (, Con c ci) <$> defType <$> getConstInfo (conName c)
+        Def f elims -> do
+          def <- getConstInfo f
+          let good = return (defType def, Def f . map Apply)
+          case theDef def of
+            Axiom{}       -> good
+            Datatype{}    -> good
+            Record{}      -> good
+            Function{}    -> notInert
+            Primitive{}   -> notInert
+            Constructor{} -> __IMPOSSIBLE__
+
+        Pi{}       -> notInert -- this is actually inert but improving doesn't buy us anything for Pi
+        Lam{}      -> notInert
+        Sort{}     -> notInert
+        Lit{}      -> notInert
+        Level{}    -> notInert
+        MetaV{}    -> notInert
+        DontCare{} -> notInert
+
+    ensureNeutral :: Term -> Term -> TCM ()
+    ensureNeutral rhs v = do
+      b <- reduceB v
+      let notNeutral v = do
+            reportSDoc "tc.meta.inert" 30 $ nest 2 $ "not neutral:" <+> prettyTCM v
+            patternViolation
+          checkRHS arg
+            | arg == rhs = do
+              reportSDoc "tc.meta.inert" 30 $ nest 2 $ "argument shares head with RHS:" <+> prettyTCM arg
+              patternViolation
+            | otherwise  = return ()
+      case b of
+        Blocked{}      -> notNeutral v
+        NotBlocked r v ->                      -- Andrea(s) 2014-12-06 can r be useful?
+          case v of
+            Var x _    -> checkRHS (Var x [])
+            Def f _    -> checkRHS (Def f [])
+            Pi{}       -> return ()
+            Sort{}     -> return ()
+            Level{}    -> return ()
+            Lit{}      -> notNeutral v
+            DontCare{} -> notNeutral v
+            Con{}      -> notNeutral v
+            Lam{}      -> notNeutral v
+            MetaV{}    -> __IMPOSSIBLE__
+-- END UNUSED -}
+
+-- | @assignMeta m x t ids u@ solves @x ids = u@ for meta @x@ of type @t@,
+--   where term @u@ lives in a context of length @m@.
+--   Precondition: @ids@ is linear.
+assignMeta :: Int -> MetaId -> Type -> [Int] -> Term -> TCM ()
+assignMeta m x t ids v = do
+  let n    = length ids
+      cand = List.sort $ zip ids $ map var $ downFrom n
+  assignMeta' m x t n cand v
+
+-- | @assignMeta' m x t ids u@ solves @x = [ids]u@ for meta @x@ of type @t@,
+--   where term @u@ lives in a context of length @m@,
+--   and @ids@ is a partial substitution.
+assignMeta' :: Int -> MetaId -> Type -> Int -> SubstCand -> Term -> TCM ()
+assignMeta' m x t n ids v = do
+  -- we are linear, so we can solve!
+  reportSDoc "tc.meta.assign" 25 $
+      "preparing to instantiate: " <+> prettyTCM v
+
+  -- Rename the variables in v to make it suitable for abstraction over ids.
+  -- Basically, if
+  --   Γ   = a b c d e
+  --   ids = d b e
+  -- then
+  --   v' = (λ a b c d e. v) _ 1 _ 2 0
+  --
+  -- Andreas, 2013-10-25 Solve using substitutions:
+  -- Convert assocList @ids@ (which is sorted) into substitution,
+  -- filling in __IMPOSSIBLE__ for the missing terms, e.g.
+  -- [(0,0),(1,2),(3,1)] --> [0, 2, __IMP__, 1, __IMP__]
+  -- ALT 1: O(m * size ids), serves as specification
+  -- let ivs = [fromMaybe __IMPOSSIBLE__ $ lookup i ids | i <- [0..m-1]]
+  -- ALT 2: O(m)
+  let assocToList i = \case
+        _           | i >= m -> []
+        ((j,u) : l) | i == j -> Just u  : assocToList (i + 1) l
+        l                    -> Nothing : assocToList (i + 1) l
+      ivs = assocToList 0 ids
+      rho = prependS impossible ivs $ raiseS n
+      v'  = applySubst rho v
+
+  -- Metas are top-level so we do the assignment at top-level.
+  inTopContext $ do
+    -- Andreas, 2011-04-18 to work with irrelevant parameters
+    -- we need to construct tel' from the type of the meta variable
+    -- (no longer from ids which may not be the complete variable list
+    -- any more)
+    reportSDoc "tc.meta.assign" 15 $ "type of meta =" <+> prettyTCM t
+
+    (telv@(TelV tel' a), bs) <- telViewUpToPathBoundary n t
+    reportSDoc "tc.meta.assign" 30 $ "tel'  =" <+> prettyTCM tel'
+    reportSDoc "tc.meta.assign" 30 $ "#args =" <+> text (show n)
+    -- Andreas, 2013-09-17 (AIM XVIII): if t does not provide enough
+    -- types for the arguments, it might be blocked by a meta;
+    -- then we give up. (Issue 903)
+    when (size tel' < n) $ do
+      a <- abortIfBlocked a
+      reportSDoc "impossible" 10 $ "not enough pis, but not blocked?" <?> pretty a
+      __IMPOSSIBLE__   -- If we get here it was _not_ blocked by a meta!
+
+    -- Perform the assignment (and wake constraints).
+
+    let vsol = abstract tel' v'
+
+    -- Andreas, 2013-10-25 double check solution before assigning
+    whenM (optDoubleCheck  <$> pragmaOptions) $ do
+      m <- lookupLocalMeta x
+      reportSDoc "tc.meta.check" 30 $ "double checking solution"
+      catchConstraint (CheckMetaInst x) $
+        addContext tel' $ checkSolutionForMeta x m v' a
+
+    reportSDoc "tc.meta.assign" 10 $
+      "solving" <+> prettyTCM x <+> ":=" <+> prettyTCM vsol
+
+    v' <- blockOnBoundary telv bs v'
+
+    assignTerm x (telToArgs tel') v'
+  where
+    blockOnBoundary :: TelView -> Boundary -> Term -> TCM Term
+    blockOnBoundary telv         [] v = return v
+    blockOnBoundary (TelV tel t) bs v = addContext tel $
+      blockTerm t $ do
+        neg <- primINeg
+        forM_ bs $ \ (r,(x,y)) -> do
+          equalTermOnFace (neg `apply1` r) t x v
+          equalTermOnFace r  t y v
+        return v
+
+-- | Check that the instantiation of the given metavariable fits the
+--   type of the metavariable. If the metavariable is not yet
+--   instantiated, add a constraint to check the instantiation later.
+checkMetaInst :: MetaId -> TCM ()
+checkMetaInst x = do
+  m <- lookupLocalMeta x
+  let postpone = addConstraint (unblockOnMeta x) $ CheckMetaInst x
+  case mvInstantiation m of
+    BlockedConst{} -> postpone
+    PostponedTypeCheckingProblem{} -> postpone
+    Open{} -> postpone
+    OpenInstance{} -> postpone
+    InstV inst -> do
+      let n = size (instTel inst)
+          t = jMetaType $ mvJudgement m
+      (telv@(TelV tel a),bs) <- telViewUpToPathBoundary n t
+      catchConstraint (CheckMetaInst x) $ addContext tel $
+        checkSolutionForMeta x m (instBody inst) a
+
+-- | Check that the instantiation of the metavariable with the given
+--   term is well-typed.
+checkSolutionForMeta :: MetaId -> MetaVariable -> Term -> Type -> TCM ()
+checkSolutionForMeta x m v a = do
+  reportSDoc "tc.meta.check" 30 $ "checking solution for meta" <+> prettyTCM x
+  case mvJudgement m of
+    HasType{ jComparison = cmp } -> do
+      reportSDoc "tc.meta.check" 30 $ nest 2 $
+        prettyTCM x <+> " : " <+> prettyTCM a <+> ":=" <+> prettyTCM v
+      reportSDoc "tc.meta.check" 50 $ nest 2 $ do
+        ctx <- getContext
+        inTopContext $ "in context: " <+> prettyTCM (PrettyContext ctx)
+      traceCall (CheckMetaSolution (getRange m) x a v) $
+        checkInternal v cmp a
+    IsSort{}  -> void $ do
+      reportSDoc "tc.meta.check" 30 $ nest 2 $
+        prettyTCM x <+> ":=" <+> prettyTCM v <+> " is a sort"
+      s <- shouldBeSort (El __DUMMY_SORT__ v)
+      traceCall (CheckMetaSolution (getRange m) x (sort (univSort s)) (Sort s)) $
+        inferInternal s
+
+-- | Given two types @a@ and @b@ with @a <: b@, check that @a == b@.
+checkSubtypeIsEqual :: Type -> Type -> TCM ()
+checkSubtypeIsEqual a b = do
+  reportSDoc "tc.meta.subtype" 30 $
+    "checking that subtype" <+> prettyTCM a <+>
+    "of" <+> prettyTCM b <+> "is actually equal."
+  SynEq.checkSyntacticEquality a b (\_ _ -> return ()) $ \a b -> do
+    cumulativity <- optCumulativity <$> pragmaOptions
+    abortIfBlocked (unEl b) >>= \case
+      Sort sb -> abortIfBlocked (unEl a) >>= \case
+        Sort sa | cumulativity -> equalSort sa sb
+                             | otherwise    -> return ()
+        Dummy{} -> return () -- TODO: this shouldn't happen but
+                             -- currently does because of generalized
+                             -- metas being created in a dummy context
+        a -> patternViolation =<< updateBlocker (unblockOnAnyMetaIn a) -- TODO: can this happen?
+      Pi b1 b2 -> abortIfBlocked (unEl a) >>= \case
+        Pi a1 a2
+          | getRelevance a1 /= getRelevance b1 -> patternViolation neverUnblock -- Can we recover from this?
+          | getQuantity  a1 /= getQuantity  b1 -> patternViolation neverUnblock
+          | getCohesion  a1 /= getCohesion  b1 -> patternViolation neverUnblock
+          | otherwise -> do
+              checkSubtypeIsEqual (unDom b1) (unDom a1)
+              underAbstractionAbs a1 a2 $ \a2' -> checkSubtypeIsEqual a2' (absBody b2)
+        Dummy{} -> return () -- TODO: this shouldn't happen but
+                             -- currently does because of generalized
+                             -- metas being created in a dummy context
+        a -> patternViolation =<< updateBlocker (unblockOnAnyMetaIn a)
+      -- TODO: check subtyping for Size< types
+      _ -> return ()
+
+
+-- | Turn the assignment problem @_X args <= SizeLt u@ into
+-- @_X args = SizeLt (_Y args)@ and constraint
+-- @_Y args <= u@.
+subtypingForSizeLt
+  :: CompareDirection -- ^ @dir@
+  -> MetaId           -- ^ The local meta-variable @x@.
+  -> MetaVariable     -- ^ Its associated information @mvar <- lookupLocalMeta x@.
+  -> Type             -- ^ Its type @t = jMetaType $ mvJudgement mvar@
+  -> Args             -- ^ Its arguments.
+  -> Term             -- ^ Its to-be-assigned value @v@, such that @x args `dir` v@.
+  -> (Term -> TCM ()) -- ^ Continuation taking its possibly assigned value.
+  -> TCM ()
+subtypingForSizeLt DirEq x mvar t args v cont = cont v
+subtypingForSizeLt dir   x mvar t args v cont = do
+  let fallback = cont v
+  -- Check whether we have built-ins SIZE and SIZELT
+  (mSize, mSizeLt) <- getBuiltinSize
+  caseMaybe mSize   fallback $ \ qSize   -> do
+    caseMaybe mSizeLt fallback $ \ qSizeLt -> do
+      -- Check whether v is a SIZELT
+      v <- reduce v
+      case v of
+        Def q [Apply (Arg ai u)] | q == qSizeLt -> do
+          -- Clone the meta into a new size meta @y@.
+          -- To this end, we swap the target of t for Size.
+          TelV tel _ <- telView t
+          let size = sizeType_ qSize
+              t'   = telePi tel size
+          y <- newMeta Instantiable (mvInfo mvar) (mvPriority mvar) (mvPermutation mvar)
+                       (HasType __IMPOSSIBLE__ CmpLeq t')
+          -- Note: no eta-expansion of new meta possible/necessary.
+          -- Add the size constraint @y args `dir` u@.
+          let yArgs = MetaV y $ map Apply args
+          addConstraint (unblockOnMeta y) $ dirToCmp (`ValueCmp` AsSizes) dir yArgs u
+          -- We continue with the new assignment problem, and install
+          -- an exception handler, since we created a meta and a constraint,
+          -- so we cannot fall back to the original handler.
+          let xArgs = MetaV x $ map Apply args
+              v'    = Def qSizeLt [Apply $ Arg ai yArgs]
+              c     = dirToCmp (`ValueCmp` (AsTermsOf sizeUniv)) dir xArgs v'
+          catchConstraint c $ cont v'
+        _ -> fallback
+
+-- | Eta-expand bound variables like @z@ in @X (fst z)@.
+expandProjectedVars
+  :: ( Pretty a, PrettyTCM a, NoProjectedVar a
+     -- , Normalise a, TermLike a, Subst Term a
+     , ReduceAndEtaContract a
+     , PrettyTCM b, TermSubst b
+     )
+  => a  -- ^ Meta variable arguments.
+  -> b  -- ^ Right hand side.
+  -> (a -> b -> TCM c)
+  -> TCM c
+expandProjectedVars args v ret = loop (args, v) where
+  loop (args, v) = do
+    reportSDoc "tc.meta.assign.proj" 45 $ "meta args: " <+> prettyTCM args
+    args <- callByName $ reduceAndEtaContract args
+    reportSDoc "tc.meta.assign.proj" 45 $ "norm args: " <+> prettyTCM args
+    reportSDoc "tc.meta.assign.proj" 85 $ "norm args: " <+> pretty args
+    let done = ret args v
+    case noProjectedVar args of
+      Right ()              -> do
+        reportSDoc "tc.meta.assign.proj" 40 $
+          "no projected var found in args: " <+> prettyTCM args
+        done
+      Left (ProjectedVar i _) -> etaExpandProjectedVar i (args, v) done loop
+
+-- | Eta-expand a de Bruijn index of record type in context and passed term(s).
+etaExpandProjectedVar :: (PrettyTCM a, TermSubst a) => Int -> a -> TCM c -> (a -> TCM c) -> TCM c
+etaExpandProjectedVar i v fail succeed = do
+  reportSDoc "tc.meta.assign.proj" 40 $
+    "trying to expand projected variable" <+> prettyTCM (var i)
+  caseMaybeM (etaExpandBoundVar i) fail $ \ (delta, sigma, tau) -> do
+    reportSDoc "tc.meta.assign.proj" 25 $
+      "eta-expanding var " <+> prettyTCM (var i) <+>
+      " in terms " <+> prettyTCM v
+    unsafeInTopContext $ addContext delta $
+      succeed $ applySubst tau v
+
+-- | Check whether one of the meta args is a projected var.
+class NoProjectedVar a where
+  noProjectedVar :: a -> Either ProjectedVar ()
+
+  default noProjectedVar
+    :: (NoProjectedVar b, Foldable t, t b ~ a)
+    => a -> Either ProjectedVar ()
+  noProjectedVar = Fold.mapM_ noProjectedVar
+
+instance NoProjectedVar a => NoProjectedVar (Arg a)
+instance NoProjectedVar a => NoProjectedVar [a]
+
+instance NoProjectedVar Term where
+  noProjectedVar = \case
+      Var i es
+        | qs@(_:_) <- takeWhileJust id $ map isProjElim es
+        -> Left $ ProjectedVar i qs
+      -- Andreas, 2015-09-12 Issue #1316:
+      -- Also look in inductive record constructors
+      Con (ConHead _ IsRecord{} Inductive _) _ es
+        | Just vs <- allApplyElims es
+        -> noProjectedVar vs
+      _ -> return ()
+
+-- | Normalize just far enough to be able to eta-contract maximally.
+class (TermLike a, TermSubst a, Reduce a) => ReduceAndEtaContract a where
+  reduceAndEtaContract :: a -> TCM a
+
+  default reduceAndEtaContract
+    :: (Traversable f, TermLike b, Subst b, Reduce b, ReduceAndEtaContract b, f b ~ a)
+    => a -> TCM a
+  reduceAndEtaContract = Trav.mapM reduceAndEtaContract
+
+instance ReduceAndEtaContract a => ReduceAndEtaContract [a]
+instance ReduceAndEtaContract a => ReduceAndEtaContract (Arg a)
+
+instance ReduceAndEtaContract Term where
+  reduceAndEtaContract u = do
+    reduce u >>= \case
+      -- In case of lambda or record constructor, it makes sense to
+      -- reduce further.
+      Lam ai (Abs x b) -> etaLam ai x =<< reduceAndEtaContract b
+      Con c ci es -> etaCon c ci es $ \ r c ci args -> do
+        args <- reduceAndEtaContract args
+        etaContractRecord r c ci args
+      v -> return v
+
+{- UNUSED, BUT KEEP!
+-- Wrong attempt at expanding bound variables.
+-- The following code curries meta instead.
+
+-- | @etaExpandProjectedVar mvar x t n qs@
+--
+--   @mvar@ is the meta var info.
+--   @x@ is the meta variable we are trying to solve for.
+--   @t@ is its type.
+--   @n@ is the number of the meta arg we want to curry (starting at 0).
+--   @qs@ is the projection path along which we curry.
+--
+etaExpandProjectedVar :: MetaVariable -> MetaId -> Type -> Int -> [QName] -> TCM a
+etaExpandProjectedVar mvar x t n qs = inTopContext $ do
+  (_, uncurry, t') <- curryAt t n
+  let TelV tel a = telView' t'
+      perm       = idP (size tel)
+  y <- newMeta (mvInfo mvar) (mvPriority mvar) perm (HasType __IMPOSSIBLE__ t')
+  assignTerm' x (uncurry $ MetaV y [])
+  patternViolation
+-}
+
+{-
+  -- first, strip the leading n domains (which remain unchanged)
+  TelV gamma core <- telViewUpTo n t
+  case unEl core of
+    -- There should be at least one domain left
+    Pi (Dom ai a) b -> do
+      -- Eta-expand @dom@ along @qs@ into a telescope @tel@, computing a substitution.
+      -- For now, we only eta-expand once.
+      -- This might trigger another call to @etaExpandProjectedVar@ later.
+      -- A more efficient version does all the eta-expansions at once here.
+      (r, pars, def) <- fromMaybe __IMPOSSIBLE__ <$> isRecordType a
+      unless (recEtaEquality def) __IMPOSSIBLE__
+      let tel = recTel def `apply` pars
+          m   = size tel
+          v   = Con (recConHead def) $ map var $ downFrom m
+          b'  = raise m b `absApp` v
+          fs  = recFields def
+          vs  = zipWith (\ f i -> Var i [Proj f]) fs $ downFrom m
+          -- v = c (n-1) ... 1 0
+      (tel, u) <- etaExpandAtRecordType a $ var 0
+      -- TODO: compose argInfo ai with tel.
+      -- Substitute into @b@.
+      -- Abstract over @tel@.
+      -- Abstract over @gamma@.
+      -- Create new meta.
+      -- Solve old meta, using substitution.
+      patternViolation
+    _ -> __IMPOSSIBLE__
+-}
+
+type FVs = VarSet
+type SubstCand = [(Int,Term)] -- ^ a possibly non-deterministic substitution
+
+-- | Turn non-det substitution into proper substitution, if possible.
+--   Otherwise, raise the error.
+checkLinearity :: SubstCand -> ExceptT () TCM SubstCand
+checkLinearity ids = do
+  -- see issue #920
+  List1.toList <$> mapM makeLinear (List1.groupOn fst ids)
+  where
+    -- Non-determinism can be healed if type is singleton. [Issue 593]
+    -- (Same as for irrelevance.)
+    makeLinear :: List1 (Int, Term) -> ExceptT () TCM (Int, Term)
+    makeLinear (p       :| []) = return p
+    makeLinear (p@(i,t) :| _ ) =
+      ifM ((Right True ==) <$> do lift . runBlocked . isSingletonTypeModuloRelevance =<< typeOfBV i)
+        (return p)
+        (throwError ())
+
+-- Intermediate result in the following function
+type Res = [(Arg Nat, Term)]
+
+-- | Exceptions raised when substitution cannot be inverted.
+data InvertExcept
+  = CantInvert Term           -- ^ Cannot recover.
+  | NeutralArg                -- ^ A potentially neutral arg: can't invert, but can try pruning.
+  | ProjVar ProjectedVar      -- ^ Try to eta-expand var to remove projs.
+
+-- | Check that arguments @args@ to a metavar are in pattern fragment.
+--   Assumes all arguments already in whnf and eta-reduced.
+--   Parameters are represented as @Var@s so @checkArgs@ really
+--   checks that all args are @Var@s and returns the "substitution"
+--   to be applied to the rhs of the equation to solve.
+--   (If @args@ is considered a substitution, its inverse is returned.)
+--
+--   The returned list might not be ordered.
+--   Linearity, i.e., whether the substitution is deterministic,
+--   has to be checked separately.
+--
+inverseSubst' :: (Term -> Bool) -> Args -> ExceptT InvertExcept TCM SubstCand
+inverseSubst' skip args = map (mapFst unArg) <$> loop (zip args terms)
+  where
+  loop  = foldM isVarOrIrrelevant []
+  terms = map var (downFrom (size args))
+  failure c = do
+    lift $ reportSDoc "tc.meta.assign" 15 $ vcat
+      [ "not all arguments are variables: " <+> prettyTCM args
+      , "  aborting assignment" ]
+    throwError (CantInvert c)
+  neutralArg = throwError NeutralArg
+
+  isVarOrIrrelevant :: Res -> (Arg Term, Term) -> ExceptT InvertExcept TCM Res
+  isVarOrIrrelevant vars (Arg info v, t) = do
+    let irr | isIrrelevant info = True
+            | DontCare{} <- v   = True
+            | otherwise         = False
+    ineg <- getPrimitiveName' builtinINeg
+    case stripDontCare v of
+      -- i := x
+      Var i [] -> return $ (Arg info i, t) `cons` vars
+
+      -- π i := x  try to eta-expand projection π away!
+      Var i es | Just qs <- mapM isProjElim es ->
+        throwError $ ProjVar $ ProjectedVar i qs
+
+      -- (i, j) := x  becomes  [i := fst x, j := snd x]
+      -- Andreas, 2013-09-17 but only if constructor is fully applied
+      tm@(Con c ci es) -> do
+        let fallback
+             | isIrrelevant info = return vars
+             | skip tm           = return vars
+             | otherwise         = failure tm
+        irrProj <- optIrrelevantProjections <$> pragmaOptions
+        lift (isRecordConstructor $ conName c) >>= \case
+          Just (_, r@Record{ recFields = fs })
+            | YesEta <- recEtaEquality r  -- Andreas, 2019-11-10, issue #4185: only for eta-records
+            , length fs == length es
+            , hasQuantity0 info || all usableQuantity fs     -- Andreas, 2019-11-12/17, issue #4168b
+            , irrProj || all isRelevant fs -> do
+              let aux (Arg _ v) Dom{domInfo = info', unDom = f} =
+                    (Arg ai v,) $ t `applyE` [Proj ProjSystem f]
+                    where
+                    ai = ArgInfo
+                      { argInfoHiding   = min (getHiding info) (getHiding info')
+                      , argInfoModality = Modality
+                        { modRelevance  = max (getRelevance info) (getRelevance info')
+                        , modQuantity   = max (getQuantity  info) (getQuantity  info')
+                        , modCohesion   = max (getCohesion  info) (getCohesion  info')
+                        }
+                      , argInfoOrigin   = min (getOrigin info) (getOrigin info')
+                      , argInfoFreeVariables = unknownFreeVariables
+                      , argInfoAnnotation    = argInfoAnnotation info'
+                      }
+                  vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+              res <- loop $ zipWith aux vs fs
+              return $ res `append` vars
+            | otherwise -> fallback
+          _ -> fallback
+
+      -- An irrelevant argument which is not an irrefutable pattern is dropped
+      _ | irr -> return vars
+
+      -- Distinguish args that can be eliminated (Con,Lit,Lam,unsure) ==> failure
+      -- from those that can only put somewhere as a whole ==> neutralArg
+      Var{}      -> neutralArg
+
+      -- primINeg i := x becomes i := primINeg x
+      -- (primINeg is a definitional involution)
+      Def qn es | Just [Arg _ (Var i [])] <- allApplyElims es, Just qn == ineg ->
+        pure $ (Arg info i, Def qn [Apply (defaultArg t)]) `cons` vars
+
+      Def{}      -> neutralArg  -- Note that this Def{} is in normal form and might be prunable.
+      t@Lam{}    -> failure t
+      t@Lit{}    -> failure t
+      t@MetaV{}  -> failure t
+      Pi{}       -> neutralArg
+      Sort{}     -> neutralArg
+      Level{}    -> neutralArg
+      DontCare{} -> __IMPOSSIBLE__ -- Ruled out by stripDontCare
+      Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+  -- managing an assoc list where duplicate indizes cannot be irrelevant vars
+  append :: Res -> Res -> Res
+  append res vars = foldr cons vars res
+
+  -- adding an irrelevant entry only if not present
+  cons :: (Arg Nat, Term) -> Res -> Res
+  cons a@(Arg ai i, t) vars
+    | isIrrelevant ai = applyUnless (any ((i ==) . unArg . fst) vars) (a :) vars
+    | otherwise       = a :  -- adding a relevant entry
+        -- filter out duplicate irrelevants
+        filter (not . (\ a@(Arg info j, t) -> isIrrelevant info && i == j)) vars
+
+-- | If the given metavariable application represents a face, return:
+--
+--    * The metavariable information;
+--    * The actual face, as an assignment of booleans to variables;
+--
+--    * The substitution candidate resulting from @inverseSubst'@. This
+--    is guaranteed to be linear and deterministic.
+--
+--    * The actual substitution, mapping from the constraint context to
+--    the metavariable's context.
+--
+--  Put concisely, a face constraint is an equation in the pattern
+--  fragment modulo the presence of endpoints (@i0@ and @i1@) in the
+--  telescope. In more detail, a face constraint has the form
+--
+--    @?0 Δ (i = i0) (j = i0) Γ (k = i1) Θ (l = i0) = t@
+--
+--  where all the greek letters consist entirely of distinct bound
+--  variables (and, of course, arbitrarily many endpoints are allowed
+--  between each substitution fragment).
+isFaceConstraint
+  :: MetaId
+  -> Args
+  -> TCM (Maybe (MetaVariable, IntMap.IntMap Bool, SubstCand, Substitution))
+isFaceConstraint mid args = runMaybeT $ do
+  iv   <- intervalView'
+  mvar <- lookupLocalMeta mid  -- information associated with meta x
+  -- Make sure that this is actually an interaction point:
+  (_, _, _) <- MaybeT $ isInteractionMetaB mid args
+
+  let
+    t = jMetaType $ mvJudgement mvar
+    n = length args
+
+    isEndpoint tm = isJust (fin (defaultArg tm) 0)
+
+    fin (Arg _ tm) i = case iv tm of
+      IOne  -> Just (i, True)
+      IZero -> Just (i, False)
+      _     -> Nothing
+
+  -- The logic here is essentially the same as for actually solving the
+  -- meta.. We just return the pieces instead of doing the assignment.
+  -- We must check the "face condition" (the relaxed pattern condition)
+  -- and check linearity of the substitution candidate, otherwise the
+  -- equation can't be inverted into a face constraint.
+  sub <- MaybeT $ either (const Nothing) Just <$> runExceptT (inverseSubst' isEndpoint args)
+  ids <- MaybeT $ either (const Nothing) Just <$> runExceptT (checkLinearity sub)
+
+  m           <- getContextSize
+  TelV tel' _ <- telViewUpToPath n t
+  tel''       <- enterClosure mvar $ \_ -> getContextTelescope
+
+  let
+    assocToList i = \case
+      _           | i >= m -> []
+      ((j,u) : l) | i == j -> Just u  : assocToList (i + 1) l
+      l                    -> Nothing : assocToList (i + 1) l
+    ivs = assocToList 0 ids
+    rho = prependS impossible ivs $ raiseS n
+
+    over  = size tel' - size tel''
+    endps = IntMap.fromList $ catMaybes $ zipWith (\a i -> fin a (i - over)) args (downFrom n)
+
+  reportSDoc "tc.ip.boundary" 45 $ vcat
+    [ "ivs   =" <+> prettyTCM ivs
+    , "tel'  =" <+> prettyTCM tel'
+    , "tel'' =" <+> prettyTCM tel''
+    , "ids   =" <+> prettyTCM ids
+    , "sub   =" <+> prettyTCM sub
+    , "endps =" <+> pretty endps
+    ]
+
+  guard (not (IntMap.null endps))
+  -- Can happen when the metavariable's context does not yet know about
+  -- an interval variable it will be applied to later, eg in the partial
+  -- argument to hcomp:
+  guard (all (>= 0) (IntMap.keys endps))
+  -- In that case we fail here — when the user writes some more
+  -- patterns, they'll become positive
+  pure (mvar, endps, ids, rho)
+
+-- | Record a "face" equation onto an interaction point into the actual
+-- interaction point boundary. Takes all the same arguments as
+-- @assignMeta'@.
+tryAddBoundary :: CompareDirection -> MetaId -> InteractionId -> Args -> Term -> CompareAs -> TCM ()
+tryAddBoundary dir x iid args v target = do
+  reportSDoc "tc.ip.boundary" 30 $ vcat
+    [ "boundary: looking at equational constraint"
+    , prettyTCM (MetaV x (Apply <$> args)) <+> "=?" <+> prettyTCM v
+    ]
+  iv   <- intervalView'
+  mvar <- lookupLocalMeta x  -- information associated with meta x
+
+  let
+    t = jMetaType $ mvJudgement mvar
+    n = length args
+    rhsv = allFreeVars v
+
+    allVars :: SubstCand -> Bool
+    allVars sub = rhsv `VarSet.isSubsetOf` VarSet.fromList (map fst sub)
+
+  TelV tel' _ <- telViewUpToPath n t
+
+  void . runMaybeT $ do
+    -- Make sure we're looking at a face constraint:
+    (_, endps, ids, rho) <- MaybeT $ isFaceConstraint x args
+    -- And that the non-endpoint parts of the 'Args' cover the free
+    -- variables of the RHS:
+    guard (allVars ids)
+
+    -- ρ is a substitution from the "constraint context" (the context
+    -- we're in) to the metavariable's context. moreover, v[ρ] is
+    -- well-scoped in the meta's context.
+    let v' = abstract tel' $ applySubst rho v
+    -- We store the boundary faces directly as lambdas for simplicity.
+
+    enterClosure mvar $ \_ -> do
+      reportSDoc "tc.ip.boundary" 30 $ vcat
+        [ "recovered interaction point boundary"
+        , "  endps =" <+> pretty endps
+        , "  rho   =" <+> pretty rho
+        , "  t     =" <+> inTopContext (prettyTCM t)
+        , "  v'    =" <+> inTopContext (prettyTCM v')
+        ]
+
+      let
+        -- Always store the constraint with the smaller termSize:
+        upd (IPBoundary m) = case MapS.lookup endps m of
+          Just t -> if termSize t < termSize v'
+            then IPBoundary m
+            else IPBoundary $ MapS.insert endps v' m
+          Nothing -> IPBoundary $ MapS.insert endps v' m
+        f ip = ip{ ipBoundary = upd (ipBoundary ip) }
+
+      lift $ modifyInteractionPoints (BiMap.adjust f iid)
+
+-- | Turn open metas into postulates.
+--
+--   Preconditions:
+--
+--   1. We are 'inTopContext'.
+--
+--   2. 'envCurrentModule' is set to the top-level module.
+--
+openMetasToPostulates :: TCM ()
+openMetasToPostulates = do
+  m <- asksTC envCurrentModule
+
+  -- Go through all open metas.
+  ms <- MapS.assocs <$> useTC stOpenMetaStore
+  forM_ ms $ \ (x, mv) -> do
+    let t = dummyTypeToOmega $ jMetaType $ mvJudgement mv
+
+    -- Create a name for the new postulate.
+    let r = clValue $ miClosRange $ mvInfo mv
+    s' <- render <$> prettyTCM x -- Using _ is a bad idea, as it prints as prefix op
+    let s = "unsolved#meta." ++ filter (/= '_') s'
+    n <- freshName r s
+    let q = A.QName m n
+
+    -- Debug.
+    reportSDoc "meta.postulate" 20 $ vcat
+      [ text ("Turning " ++ if isSortMeta_ mv then "sort" else "value" ++ " meta ")
+          <+> prettyTCM x <+> " into postulate."
+      , nest 2 $ vcat
+        [ "Name: " <+> prettyTCM q
+        , "Type: " <+> prettyTCM t
+        ]
+      ]
+
+    -- Add the new postulate to the signature.
+    addConstant' q defaultArgInfo q t defaultAxiom
+
+    -- Solve the meta.
+    let inst = InstV $ Instantiation
+                 { instTel = [], instBody = Def q [] }
+    updateMetaVar x $ \ mv0 -> mv0 { mvInstantiation = inst }
+    return ()
+  where
+    -- Unsolved sort metas can have a type ending in a Dummy if they are allowed to be instantiated
+    -- to Setω. This will crash the serializer (issue #3730). To avoid this we replace dummy type
+    -- codomains by Setω.
+    dummyTypeToOmega t =
+      case telView' t of
+        TelV tel (El _ Dummy{}) -> abstract tel (sort $ Inf UType 0)
+        _ -> t
+
+-- | Sort metas in dependency order.
+dependencySortMetas :: [MetaId] -> TCM (Maybe [MetaId])
+dependencySortMetas metas = do
+  metaGraph <- concat <$> do
+    forM metas $ \ m -> do
+      deps <- allMetas (\m' -> if m' `Set.member` metas'
+                               then singleton m'
+                               else mempty) <$>
+                getType m
+      return [ (m, m') | m' <- Set.toList deps ]
+
+  return $ Graph.topSort metas' metaGraph
+
+  where
+    metas' = Set.fromList metas
+
+    -- Sort metas don't have types, but we still want to sort them.
+    getType m = do
+      j <- lookupMetaJudgement m
+      case j of
+        IsSort{}                 -> return Nothing
+        HasType{ jMetaType = t } -> Just <$> instantiateFull t
diff --git a/src/full/Agda/TypeChecking/MetaVars.hs-boot b/src/full/Agda/TypeChecking/MetaVars.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/MetaVars.hs-boot
@@ -0,0 +1,27 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.MetaVars where
+
+import Agda.Syntax.Common           ( Arg )
+import Agda.Syntax.Internal         ( MetaId, Term, Type, Args, Dom, Abs, Telescope, Sort, Substitution )
+import Agda.TypeChecking.Monad.Base ( TCM, RunMetaOccursCheck, Comparison, CompareAs, CompareDirection, MetaVariable )
+import Agda.TypeChecking.Monad.MetaVars (MonadMetaSolver)
+import Data.IntMap (IntMap)
+
+instance MonadMetaSolver TCM
+
+type Condition = Dom Type -> Abs Type -> Bool
+type SubstCand = [(Int,Term)]
+
+newArgsMeta'      :: MonadMetaSolver m => Condition -> Type -> m Args
+newArgsMeta       :: MonadMetaSolver m => Type -> m Args
+assignTerm        :: MonadMetaSolver m => MetaId -> [Arg String] -> Term -> m ()
+assign            :: CompareDirection -> MetaId -> Args -> Term -> CompareAs -> TCM ()
+newInstanceMeta   :: MonadMetaSolver m => String -> Type -> m (MetaId, Term)
+newValueMeta      :: MonadMetaSolver m => RunMetaOccursCheck -> Comparison -> Type -> m (MetaId, Term)
+newNamedValueMeta :: MonadMetaSolver m => RunMetaOccursCheck -> String -> Comparison -> Type -> m (MetaId, Term)
+newNamedValueMeta':: MonadMetaSolver m => RunMetaOccursCheck -> String -> Comparison -> Type -> m (MetaId, Term)
+newTelMeta        :: MonadMetaSolver m => Telescope -> m Args
+newSortMeta       :: MonadMetaSolver m => m Sort
+checkMetaInst     :: MetaId -> TCM ()
+isFaceConstraint  :: MetaId -> Args -> TCM (Maybe (MetaVariable, IntMap Bool, SubstCand, Substitution))
diff --git a/src/full/Agda/TypeChecking/MetaVars/Mention.hs b/src/full/Agda/TypeChecking/MetaVars/Mention.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/MetaVars/Mention.hs
@@ -0,0 +1,138 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.MetaVars.Mention where
+
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as HashSet
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+
+class MentionsMeta t where
+  mentionsMetas :: HashSet MetaId -> t -> Bool
+
+mentionsMeta :: MentionsMeta t => MetaId -> t -> Bool
+mentionsMeta = mentionsMetas . HashSet.singleton
+
+instance MentionsMeta Term where
+  mentionsMetas xs = \case
+    Var _ args   -> mm args
+    Lam _ b      -> mm b
+    Lit{}        -> False
+    Def _ args   -> mm args
+    Con _ _ args -> mm args
+    Pi a b       -> mm (a, b)
+    Sort s       -> mm s
+    Level l      -> mm l
+    Dummy{}      -> False
+    DontCare v   -> False   -- we don't have to look inside don't cares when deciding to wake constraints
+    MetaV y args -> HashSet.member y xs || mm args   -- TODO: we really only have to look one level deep at meta args
+    where
+      mm :: forall t. MentionsMeta t => t -> Bool
+      mm = mentionsMetas xs
+
+instance MentionsMeta Level where
+  mentionsMetas xs (Max _ as) = mentionsMetas xs as
+
+instance MentionsMeta PlusLevel where
+  mentionsMetas xs (Plus _ a) = mentionsMetas xs a
+
+instance MentionsMeta Blocker where
+  mentionsMetas xs (UnblockOnAll bs)  = mentionsMetas xs $ Set.toList bs
+  mentionsMetas xs (UnblockOnAny bs)  = mentionsMetas xs $ Set.toList bs
+  mentionsMetas xs (UnblockOnMeta x)  = HashSet.member x xs
+  mentionsMetas xs UnblockOnProblem{} = False
+  mentionsMetas xs UnblockOnDef{}     = False
+
+instance MentionsMeta Type where
+    mentionsMetas xs (El s t) = mentionsMetas xs (s, t)
+
+instance MentionsMeta Sort where
+  mentionsMetas xs = \case
+    Univ _ l   -> mentionsMetas xs l
+    Inf _ _    -> False
+    SizeUniv   -> False
+    LockUniv   -> False
+    LevelUniv  -> False
+    IntervalUniv -> False
+    PiSort a s1 s2 -> mentionsMetas xs (a, s1, s2)
+    FunSort s1 s2 -> mentionsMetas xs (s1, s2)
+    UnivSort s -> mentionsMetas xs s
+    MetaS m es -> HashSet.member m xs || mentionsMetas xs es
+    DefS d es  -> mentionsMetas xs es
+    DummyS{}   -> False
+
+instance MentionsMeta t => MentionsMeta (Abs t) where
+  mentionsMetas xs = mentionsMetas xs . unAbs
+
+instance MentionsMeta t => MentionsMeta (Arg t) where
+  mentionsMetas xs a | isIrrelevant a = False
+  -- we don't have to look inside irrelevant arguments when deciding to wake constraints
+  mentionsMetas xs a = mentionsMetas xs (unArg a)
+
+instance MentionsMeta t => MentionsMeta (Dom t) where
+  mentionsMetas xs = mentionsMetas xs . unDom
+
+instance MentionsMeta t => MentionsMeta [t] where
+  mentionsMetas xs = any (mentionsMetas xs)
+
+instance MentionsMeta t => MentionsMeta (Maybe t) where
+  mentionsMetas xs = maybe False (mentionsMetas xs)
+
+instance (MentionsMeta a, MentionsMeta b) => MentionsMeta (a, b) where
+  mentionsMetas xs (a, b) = mentionsMetas xs a || mentionsMetas xs b
+
+instance (MentionsMeta a, MentionsMeta b, MentionsMeta c) => MentionsMeta (a, b, c) where
+  mentionsMetas xs (a, b, c) = mentionsMetas xs a || mentionsMetas xs b || mentionsMetas xs c
+
+instance MentionsMeta a => MentionsMeta (Closure a) where
+  mentionsMetas xs cl = mentionsMetas xs (clValue cl)
+
+instance MentionsMeta Elim where
+  mentionsMetas xs Proj{} = False
+  mentionsMetas xs (Apply v) = mentionsMetas xs v
+  mentionsMetas xs (IApply y0 y1 v) = mentionsMetas xs (y0,y1,v)
+
+instance MentionsMeta a => MentionsMeta (Tele a) where
+  mentionsMetas xs EmptyTel = False
+  mentionsMetas xs (ExtendTel a b) = mentionsMetas xs (a, b)
+
+instance MentionsMeta ProblemConstraint where
+  mentionsMetas xs = mentionsMetas xs . theConstraint
+
+instance MentionsMeta Constraint where
+  mentionsMetas xs = \case
+    ValueCmp _ t u v    -> mm (t, u, v)
+    ValueCmpOnFace _ p t u v    -> mm ((p,t), u, v)
+    ElimCmp _ _ t v as bs -> mm ((t, v), (as, bs))
+    LevelCmp _ u v      -> mm (u, v)
+    SortCmp _ a b       -> mm (a, b)
+    UnBlock _           -> True   -- this might be a postponed typechecking
+                                  -- problem and we don't have a handle on
+                                  -- what metas it depends on
+    FindInstance{}      -> True   -- this needs to be woken up for any meta
+    IsEmpty r t         -> mm t
+    CheckSizeLtSat t    -> mm t
+    CheckFunDef{}       -> True   -- not sure what metas this depends on
+    HasBiggerSort a     -> mm a
+    HasPTSRule a b      -> mm (a, b)
+    UnquoteTactic tac hole goal -> False
+    CheckDataSort q s   -> mm s
+    CheckMetaInst m     -> True   -- TODO
+    CheckType t         -> mm t
+    CheckLockedVars a b c d -> mm ((a, b), (c, d))
+    UsableAtModality _ ms mod t -> mm (ms, t)
+    where
+      mm :: forall t. MentionsMeta t => t -> Bool
+      mm = mentionsMetas xs
+
+instance MentionsMeta CompareAs where
+  mentionsMetas xs = \case
+    AsTermsOf a -> mentionsMetas xs a
+    AsSizes -> False
+    AsTypes -> False
+
+-- instance (Ord k, MentionsMeta e) => MentionsMeta (Map k e) where
+--   mentionsMeta = traverse mentionsMeta
diff --git a/src/full/Agda/TypeChecking/MetaVars/Occurs.hs b/src/full/Agda/TypeChecking/MetaVars/Occurs.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/MetaVars/Occurs.hs
@@ -0,0 +1,1115 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation  #-}
+
+{- | The occurs check for unification.  Does pruning on the fly.
+
+  When hitting a meta variable:
+
+  - Compute flex/rigid for its arguments.
+  - Compare to allowed variables.
+  - Mark arguments with rigid occurrences of disallowed variables for deletion.
+  - Attempt to delete marked arguments.
+  - We don't need to check for success, we can just continue occurs checking.
+-}
+
+module Agda.TypeChecking.MetaVars.Occurs where
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Reader
+
+import Data.Foldable (traverse_)
+import Data.Functor
+import Data.Monoid
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.IntMap as IntMap
+import qualified Data.IntSet as IntSet
+import Data.IntSet (IntSet)
+
+import qualified Agda.Benchmarking as Bench
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Free.Lazy
+import Agda.TypeChecking.Free.Reduce
+import Agda.TypeChecking.ProjectionLike
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Records
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars
+import Agda.Interaction.Options (optFirstOrder)
+
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Lens
+import Agda.Utils.List (downFrom)
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * MetaOccursCheck: going into definitions to exclude cyclic solutions
+
+{- To address issue 585 (meta var occurrences in mutual defs)
+
+data B : Set where
+  inn : A -> B
+
+out : B -> A
+out (inn a) = a
+
+postulate
+  P : (y : A) (z : Unit -> B) → Set
+  p : (x : Unit -> B) → P (out (x unit)) x
+
+mutual
+  d : Unit -> B
+  d unit = inn _           -- Y
+
+  g : P (out (d unit)) d
+  g = p _             -- X
+
+-- Agda solves  d unit = inn (out (d unit))
+--
+-- out (X unit) = out (d unit) = out (inn Y) = Y
+-- X = d
+
+When doing the occurs check on d, we need to look at the definition of
+d to discover that it mentions X.
+
+To this end, we extend the state by names of definitions that have to
+be checked when they occur.  At the beginning, this is initialized
+with the names in the current mutual block.  Each time we encounter a
+name in the list during occurs check, we delete it (if check is
+successful).  This way, we do not duplicate work.
+
+-}
+
+modifyOccursCheckDefs :: (Set QName -> Set QName) -> TCM ()
+modifyOccursCheckDefs f = stOccursCheckDefs `modifyTCLens` f
+
+-- | Set the names of definitions to be looked at
+--   to the defs in the current mutual block.
+initOccursCheck :: MetaVariable -> TCM ()
+initOccursCheck mv = modifyOccursCheckDefs . const =<<
+  if (miMetaOccursCheck (mvInfo mv) == DontRunMetaOccursCheck)
+   then do
+     reportSLn "tc.meta.occurs" 20 $
+       "initOccursCheck: we do not look into definitions"
+     return Set.empty
+   else do
+     reportSLn "tc.meta.occurs" 20 $
+       "initOccursCheck: we look into the following definitions:"
+     mb <- asksTC envMutualBlock
+     case mb of
+       Nothing -> do
+         reportSLn "tc.meta.occurs" 20 $ "(none)"
+         return Set.empty
+       Just b  -> do
+         ds <- mutualNames <$> lookupMutualBlock b
+         reportSDoc "tc.meta.occurs" 20 $ sep $ map prettyTCM $ Set.toList ds
+         return ds
+
+
+-- | Is a def in the list of stuff to be checked?
+defNeedsChecking :: QName -> TCM Bool
+defNeedsChecking d = Set.member d <$> useTC stOccursCheckDefs
+
+-- | Remove a def from the list of defs to be looked at.
+tallyDef :: QName -> TCM ()
+tallyDef d = modifyOccursCheckDefs $ Set.delete d
+
+---------------------------------------------------------------------------
+-- * OccursM monad and its services
+
+-- | Extra environment for the occurs check.  (Complements 'FreeEnv'.)
+data OccursExtra = OccursExtra
+  { occUnfold  :: UnfoldStrategy
+  , occVars    :: VarMap          -- ^ The allowed variables with their variance.
+  , occMeta    :: MetaId          -- ^ The meta we want to solve.
+  , occCxtSize :: Nat             -- ^ The size of the typing context upon invocation.
+  }
+
+type OccursCtx  = FreeEnv' () OccursExtra AllowedVar
+type OccursM    = ReaderT OccursCtx TCM
+
+-- ** Modality handling.
+
+-- | The passed modality is the one of the current context.
+type AllowedVar = Modality -> All
+
+instance IsVarSet () AllowedVar where
+  withVarOcc o f = f . composeModality (getModality o)
+
+-- | Check whether a free variable is allowed in the context as
+--   specified by the modality.
+variableCheck :: VarMap -> Maybe Variable -> AllowedVar
+variableCheck xs mi q = All $
+  -- Bound variables are always allowed to occur:
+  caseMaybe mi True $ \ i ->
+    -- Free variables not listed in @xs@ are forbidden:
+    caseMaybe (lookupVarMap i xs) False $ \ o ->
+      -- For listed variables it holds:
+      -- The ascribed modality @o@ must be submodality of the
+      -- modality @q@ of the current context.
+      -- E.g. irrelevant variables (ascribed, lhs) can only
+      -- be used in irrelevant position (rhs).
+      getModality o `moreUsableModality` q
+
+-- | Occurs check fails if a defined name is not available
+--   since it was declared in irrelevant or erased context.
+definitionCheck :: QName -> OccursM ()
+definitionCheck d = do
+  cxt <- ask
+  let irr = isIrrelevant cxt
+      er  = hasQuantity0 cxt
+      m   = occMeta $ feExtra cxt
+  -- Anything goes if we are both irrelevant and erased.
+  -- Otherwise, have to check the modality of the defined name.
+  unless (irr && er) $ getConstInfo' d >>= \case
+   Left _ -> do
+    -- Andreas, 2021-07-29.
+    -- The definition is not in scope.
+    -- This shouldn't happen, but does so in issue #5492.
+    -- Let's bail out...
+    patternViolation' alwaysUnblock 35 $
+      unwords ["occursCheck: definition", prettyShow d, "not in scope" ]
+   Right def -> do
+    let dmod = getModality def
+    unless (irr || usableRelevance dmod) $ do
+      reportSDoc "tc.meta.occurs" 35 $ hsep
+        [ "occursCheck: definition"
+        , prettyTCM d
+        , "has relevance"
+        , text . show $ getRelevance dmod
+        ]
+      abort neverUnblock $ MetaIrrelevantSolution m $ Def d []
+    unless (er || usableQuantity dmod) $ do
+      reportSDoc "tc.meta.occurs" 35 $ hsep
+        [ "occursCheck: definition"
+        , prettyTCM d
+        , "has quantity"
+        , text . show $ getQuantity dmod
+        ]
+      abort neverUnblock $ MetaErasedSolution m $ Def d []
+
+metaCheck :: MetaId -> OccursM MetaId
+metaCheck m = do
+  cxt <- ask
+  let rel = getRelevance cxt
+      qnt = getQuantity cxt
+      m0  = occMeta $ feExtra cxt
+
+  -- Check for loop
+  --   don't fail hard on this, since we might still be on the top-level
+  --   after some killing (Issue 442)
+  --
+  -- Andreas, 2013-02-18  Issue 795 demonstrates that a recursive
+  -- occurrence of a meta could be solved by the identity.
+  --   ? (Q A) = Q (? A)
+  -- So, do not throw an error.
+  -- I guess the error was there from times when occurrence check
+  -- was done after the "lhs=linear variables" check, but now
+  -- occurrence check comes first.
+  -- WAS:
+  -- when (m == m') $ if ctx == Top then patternViolation else
+  --   abort ctx $ MetaOccursInItself m'
+  when (m == m0) $ patternViolation' neverUnblock 50 $ "occursCheck failed: Found " ++ prettyShow m
+
+  mv <- lookupLocalMeta m
+  let mmod = getModality mv
+      mmod' = setRelevance rel $ setQuantity qnt $ mmod
+  if (mmod `moreUsableModality` mmod') then return m else do
+    reportSDoc "tc.meta.occurs" 35 $ hsep
+      [ "occursCheck: meta variable"
+      , prettyTCM m
+      , "has relevance"
+      , text . show $ getRelevance mmod
+      , "and quantity"
+      , text . show $ getQuantity mmod
+      ]
+    allowAssign <- asksTC envAssignMetas
+    -- Jesper, 2020-11-10: if we encounter a metavariable that is
+    -- unusable because of its modality (e.g. irrelevant or erased) we
+    -- try to *promote* the meta to the required modality, by creating
+    -- a new meta with that modality and solving the old one with
+    -- it. Don't do this if the meta occurs in a flexible or unguarded
+    -- position:
+    -- - If it is in a flexible position, it could disappear when
+    --   another meta is solved, so promotion is maybe not necessary.
+    -- - If it is in a top-level position, we can instead solve the
+    --   equation by instantiating the other way around, so promotion
+    --   is not necessary.
+
+    -- Actually, this is not the case anymore, no new meta is created and
+    -- instead the metavar itself gets modified with the new modality.
+    let fail reason = do
+          reportSDoc "tc.meta.occurs" 20 $ "Meta occurs check found bad relevance"
+          reportSDoc "tc.meta.occurs" 20 $ "aborting because" <+> reason
+          patternViolation $ unblockOnMeta m
+    when (mvFrozen mv == Frozen)             $ fail "meta is frozen"
+    unless (isOpenMeta $ mvInstantiation mv) $ fail "meta is already solved"
+    unlessM (asksTC envAssignMetas)          $ fail "assigning metas is not allowed here"
+    -- Jesper, 2023-09-03, issue #6759: When --lossy-unification is enabled,
+    -- we already lose the guarantee that we only throw an error when a
+    -- problem is really unsolvable in favor of taking the "obvious" solution.
+    -- In this case the "obvious" solution is to promote the meta even if
+    -- it is in a flexible position, so that is what we do.
+    whenM (pure (isFlexible cxt) `and2M` (not . optFirstOrder <$> pragmaOptions))
+                                             $ fail "occurrence is flexible"
+    when (isUnguarded cxt)                   $ fail "occurrence is unguarded"
+
+    reportSDoc "tc.meta.occurs" 20 $ "Promoting meta" <+> prettyTCM m <+> "to modality" <+> prettyTCM mmod'
+    -- The meta gets updated here
+    updateMetaVar m $ \ mv -> mv { mvInfo = setModality mmod' $ mvInfo mv }
+    etaExpandListeners m
+    wakeupConstraints m
+    return m
+
+-- | Construct a test whether a de Bruijn index is allowed
+--   or needs to be pruned.
+allowedVars :: OccursM (Nat -> Bool)
+allowedVars = do
+  -- @n@ is the number of binders we have stepped under.
+  n  <- liftM2 (-) getContextSize (asks (occCxtSize . feExtra))
+  xs <- asks (theVarMap . occVars . feExtra)
+  -- Bound variables are allowed, and those mentioned in occVars.
+  return $ \ i -> i < n || (i - n) `IntMap.member` xs
+
+-- ** Unfolding during occurs check.
+
+-- | Unfold definitions during occurs check?
+--   This effectively runs the occurs check on the normal form.
+data UnfoldStrategy = YesUnfold | NoUnfold
+  deriving (Eq, Show)
+
+defArgs :: OccursM a -> OccursM a
+defArgs m = asks (occUnfold . feExtra) >>= \case
+  NoUnfold  -> flexibly m
+  YesUnfold -> weakly m
+
+-- | For a path constructor `c : ... -> Path D a b`, we have that e.g. `c es i0` reduces to `a`.
+--   So we have to consider its arguments as flexible when we do not actually unfold.
+conArgs :: Elims -> OccursM a -> OccursM a
+conArgs es m = asks (occUnfold . feExtra) >>= \case
+  YesUnfold -> m
+  NoUnfold | null [ () | IApply{} <- es ]
+            -> m
+  NoUnfold  -> flexibly m
+
+unfoldB :: (Instantiate t, Reduce t) => t -> OccursM (Blocked t)
+unfoldB v = do
+  unfold <- asks $ occUnfold . feExtra
+  rel    <- asks feModality
+  case unfold of
+    YesUnfold | not (isIrrelevant rel) -> reduceB v
+    _                                  -> notBlocked <$> instantiate v
+
+unfold :: (Instantiate t, Reduce t) => t -> OccursM t
+unfold v = asks (occUnfold . feExtra) >>= \case
+  NoUnfold  -> instantiate v
+  YesUnfold -> reduce v
+
+-- ** Managing rigidiy during occurs check.
+
+-- | Leave the strongly rigid position.
+weakly :: OccursM a -> OccursM a
+weakly = local $ over lensFlexRig $ composeFlexRig WeaklyRigid
+
+strongly :: OccursM a -> OccursM a
+strongly = local $ over lensFlexRig $ \case
+  WeaklyRigid -> StronglyRigid
+  Unguarded   -> StronglyRigid
+  ctx -> ctx
+
+flexibly :: OccursM a -> OccursM a
+flexibly = local $ set lensFlexRig $ Flexible ()
+
+-- ** Error throwing during occurs check.
+
+patternViolation' :: MonadTCM m => Blocker -> Int -> String -> m a
+patternViolation' unblock n err = liftTCM $ do
+  reportSLn "tc.meta.occurs" n err
+  patternViolation unblock
+
+abort :: Blocker -> TypeError -> OccursM a
+abort unblock err = do
+  ctx <- ask
+  lift $ do
+    if | isIrrelevant ctx                    -> soft
+       | StronglyRigid <- ctx ^. lensFlexRig -> hard
+       | otherwise -> soft
+  where
+  hard = typeError err -- here, throw an uncatchable error (unsolvable constraint)
+  soft = patternViolation' unblock 70 (show err) -- throws a PatternErr, which leads to delayed constraint
+
+---------------------------------------------------------------------------
+-- * Implementation of the occurs check.
+
+-- | Extended occurs check.
+class Occurs t where
+  occurs :: t -> OccursM t
+  metaOccurs :: MetaId -> t -> TCM ()  -- raise exception if meta occurs in t
+
+  default metaOccurs :: (Foldable f, Occurs a, f a ~ t) => MetaId -> t -> TCM ()
+  metaOccurs = traverse_ . metaOccurs
+
+occurs_ :: (Occurs t, TypeOf t ~ ()) => t -> OccursM t
+occurs_ t = occurs t
+
+metaOccurs2 :: (Occurs a, Occurs b) => MetaId -> a -> b -> TCM ()
+metaOccurs2 m x y = metaOccurs m x >> metaOccurs m y
+
+metaOccurs3 :: (Occurs a, Occurs b, Occurs c) => MetaId -> a -> b -> c -> TCM ()
+metaOccurs3 m x y z = metaOccurs m x >> metaOccurs m y >> metaOccurs m z
+
+-- | When assigning @m xs := v@, check that @m@ does not occur in @v@
+--   and that the free variables of @v@ are contained in @xs@.
+occursCheck
+  :: MetaId -> VarMap -> Term -> TCM Term
+occursCheck m xs v = Bench.billTo [ Bench.Typing, Bench.OccursCheck ] $ do
+  mv <- lookupLocalMeta m
+  n  <- getContextSize
+  reportSDoc "tc.meta.occurs" 65 $ "occursCheck" <+> pretty m <+> text (show xs)
+  let initEnv unf = FreeEnv
+        {  feExtra = OccursExtra
+          { occUnfold  = unf
+          , occVars    = xs
+          , occMeta    = m
+          , occCxtSize = n
+          }
+        , feFlexRig   = StronglyRigid -- ? Unguarded
+        , feModality  = getModality mv
+        , feSingleton = variableCheck xs
+        }
+  initOccursCheck mv
+  nicerErrorMessage $ do
+    -- First try without normalising the term
+    (occurs v `runReaderT` initEnv NoUnfold) `catchError` \err -> do
+      -- If first run is inconclusive, try again with normalization
+      -- (unless metavariable is irrelevant, in which case the
+      -- constraint will anyway be dropped)
+      case err of
+        PatternErr{} | not (isIrrelevant $ getModality mv) -> do
+          initOccursCheck mv
+          occurs v `runReaderT` initEnv YesUnfold
+        _ -> throwError err
+
+  where
+    -- Produce nicer error messages
+    nicerErrorMessage :: TCM a -> TCM a
+    nicerErrorMessage f = f `catchError` \ err -> case err of
+      TypeError _ _ cl -> case clValue cl of
+        MetaOccursInItself{} ->
+          typeError . GenericDocError =<<
+            fsep [ text "Refuse to construct infinite term by instantiating"
+                 , prettyTCM m
+                 , "to"
+                 , prettyTCM =<< instantiateFull v
+                 ]
+        MetaCannotDependOn _ i ->
+          ifM (isSortMeta m `and2M` (not <$> hasUniversePolymorphism))
+          ( typeError . GenericDocError =<<
+            fsep [ text "Cannot instantiate the metavariable"
+                 , prettyTCM m
+                 , "to"
+                 , prettyTCM v
+                 , "since universe polymorphism is disabled"
+                 ]
+          ) {- else -}
+          ( typeError . GenericDocError =<<
+              fsep [ text "Cannot instantiate the metavariable"
+                   , prettyTCM m
+                   , "to solution"
+                   , prettyTCM v
+                   , "since it contains the variable"
+                   , enterClosure cl $ \_ -> prettyTCM (Var i [])
+                   , "which is not in scope of the metavariable"
+                   ]
+            )
+        MetaIrrelevantSolution _ _ ->
+          typeError . GenericDocError =<<
+            fsep [ text "Cannot instantiate the metavariable"
+                 , prettyTCM m
+                 , "to solution"
+                 , prettyTCM v
+                 , "since (part of) the solution was created in an irrelevant context"
+                 ]
+        MetaErasedSolution _ _ ->
+          typeError . GenericDocError =<<
+            fsep [ text "Cannot instantiate the metavariable"
+                 , prettyTCM m
+                 , "to solution"
+                 , prettyTCM v
+                 , "since (part of) the solution was created in an erased context"
+                 ]
+        _ -> throwError err
+      _ -> throwError err
+
+instance Occurs Term where
+  occurs v = do
+    vb  <- unfoldB v
+    let block = getBlocker vb
+        -- On a failure, we should retry when any meta that is blocking
+        -- the term is solved.
+        flexIfBlocked = if
+          -- In the metavariable case we should not yet become flexible
+          -- because otherwise pruning won't fire.
+          | MetaV{} <- ignoreBlocking vb -> addOrUnblocker block
+          | block /= neverUnblock -> flexibly . addOrUnblocker block
+          -- Re #3594, do not fail hard when Underapplied:
+          -- the occurrence could be computed away after eta expansion.
+          | NotBlocked{blockingStatus = Underapplied} <- vb -> flexibly
+          | otherwise -> id
+    v <- reduceProjectionLike $ ignoreBlocking vb
+    flexIfBlocked $ do
+        ctx <- ask
+        let m = occMeta . feExtra $ ctx
+        reportSDoc "tc.meta.occurs" 45 $
+          text ("occursCheck " ++ prettyShow m ++ " (" ++ show (feFlexRig ctx) ++ ") of ") <+> prettyTCM v
+        reportSDoc "tc.meta.occurs" 70 $
+          nest 2 $ pretty v
+        case v of
+          Var i es   -> do
+            allowed <- getAll . ($ unitModality) <$> variable i
+            if allowed then Var i <$> weakly (occurs es) else do
+              -- if the offending variable is of singleton type,
+              -- eta-expand it away
+              reportSDoc "tc.meta.occurs" 35 $ "offending variable: " <+> prettyTCM (var i)
+              t <-  typeOfBV i
+              reportSDoc "tc.meta.occurs" 35 $ nest 2 $ "of type " <+> prettyTCM t
+              isST <- typeLevelReductions $ isSingletonType t
+              reportSDoc "tc.meta.occurs" 35 $ nest 2 $ "(after singleton test)"
+              case isST of
+                -- not a singleton type
+                Nothing ->
+                  -- #4480: Only hard fail if the variable is not in scope. Wrong modality/relevance
+                  -- could potentially be salvaged by eta expansion.
+                  ifM (($ i) <$> allowedVars) -- vv TODO: neverUnblock is not correct! What could trigger this eta expansion though?
+                      (patternViolation' neverUnblock 70 $ "Disallowed var " ++ show i ++ " due to modality/relevance")
+                      (strongly $ abort neverUnblock $ MetaCannotDependOn m i)
+                -- is a singleton type with unique inhabitant sv
+                (Just sv) -> return $ sv `applyE` es
+          Lam h f     -> do
+            Lam h <$> occurs f
+          Level l     -> Level <$> occurs_ l
+          Lit l       -> return v
+          Dummy{}     -> return v
+          DontCare v  -> dontCare <$> do
+            onlyReduceTypes $ underRelevance Irrelevant $ occurs v
+          Def d es    -> do
+            definitionCheck d
+            Def d <$> occDef d es
+          Con c ci vs -> do
+            definitionCheck (conName c)
+            Con c ci <$> conArgs vs (occurs vs)  -- if strongly rigid, remain so, except with unreduced IApply arguments.
+          Pi a b      -> Pi <$> occurs_ a <*> occurs b
+          Sort s      -> Sort <$> do underRelevance NonStrict $ occurs_ s
+          MetaV m' es -> do
+            m' <- metaCheck m'
+            -- The arguments of a meta are in a flexible position
+            (MetaV m' <$> do flexibly $ occurs es) `catchError` \ err -> do
+                ctx <- ask
+                reportSDoc "tc.meta.kill" 25 $ vcat
+                  [ text $ "error during flexible occurs check, we are " ++ show (ctx ^. lensFlexRig)
+                  , text $ show err
+                  ]
+                case err of
+                  -- On pattern violations try to remove offending
+                  -- flexible occurrences (if not already in a flexible context)
+                  PatternErr{} | not (isFlexible ctx) -> do
+                    reportSLn "tc.meta.kill" 20 $
+                      "oops, pattern violation for " ++ prettyShow m'
+                    -- Andreas, 2014-03-02, see issue 1070:
+                    -- Do not prune when meta is projected!
+                    caseMaybe (allApplyElims es) (throwError err) $ \ vs -> do
+                      killResult <- lift . prune m' vs =<< allowedVars
+                      if (killResult == PrunedEverything) then do
+                        -- after successful pruning, restart occurs check
+                        reportSDoc "tc.meta.prune" 40 $ "Pruned everything"
+                        v' <- instantiate (MetaV m' es)
+                        occurs v'
+                      else throwError err
+                  _ -> throwError err
+          where
+            -- a data or record type constructor propagates strong occurrences
+            -- since e.g. x = List x is unsolvable
+            occDef d vs = do
+              m   <- asks (occMeta . feExtra)
+              lift $ metaOccurs m d
+              ifM (liftTCM $ isJust <$> isDataOrRecordType d)
+                {-then-} (occurs vs)
+                {-else-} (defArgs $ occurs vs)
+
+  metaOccurs m v = do
+    v <- instantiate v
+    case v of
+      Var i vs   -> metaOccurs m vs
+      Lam h f    -> metaOccurs m f
+      Level l    -> metaOccurs m l
+      Lit l      -> return ()
+      Dummy{}    -> return ()
+      DontCare v -> metaOccurs m v
+      Def d vs   -> metaOccurs2 m d vs
+      Con c _ vs -> metaOccurs m vs
+      Pi a b     -> metaOccurs2 m a b
+      Sort s     -> metaOccurs m s              -- vv m is already an unblocker
+      MetaV m' vs | m == m'   -> patternViolation' neverUnblock 50 $ "Found occurrence of " ++ prettyShow m
+                  | otherwise -> addOrUnblocker (unblockOnMeta m') $ metaOccurs m vs
+
+instance Occurs QName where
+  occurs d = __IMPOSSIBLE__
+
+  metaOccurs m d = whenM (defNeedsChecking d) $ do
+    tallyDef d
+    reportSDoc "tc.meta.occurs" 30 $ "Checking for occurrences in " <+> prettyTCM d
+    metaOccursQName m d
+
+metaOccursQName :: MetaId -> QName -> TCM ()
+metaOccursQName m x = metaOccurs m . theDef =<< do
+  ignoreAbstractMode $ getConstInfo x
+  -- Andreas, 2019-05-03, issue #3742:
+  -- ignoreAbstractMode necessary, as abstract
+  -- constructors are also called up.
+
+instance Occurs Defn where
+  occurs def = __IMPOSSIBLE__
+
+  metaOccurs m Axiom{}                      = return ()
+  metaOccurs m DataOrRecSig{}               = return ()
+  metaOccurs m Function{ funClauses = cls } = traverse_ (metaOccurs m) cls
+  -- since a datatype is isomorphic to the sum of its constructor types
+  -- we check the constructor types
+  metaOccurs m Datatype{ dataCons = cs }    = mapM_ (metaOccursQName m) cs
+  metaOccurs m Record{ recConHead = c }     = metaOccursQName m $ conName c
+  metaOccurs m Constructor{}                = return ()
+  metaOccurs m Primitive{}                  = return ()
+  metaOccurs m PrimitiveSort{}              = __IMPOSSIBLE__
+  metaOccurs m AbstractDefn{}               = __IMPOSSIBLE__
+  metaOccurs m GeneralizableVar{}           = __IMPOSSIBLE__
+
+instance Occurs Clause where
+  occurs cl = __IMPOSSIBLE__
+
+  metaOccurs m cl = whenJust (clauseBody cl) $ metaOccurs m
+
+instance Occurs Level where
+  occurs (Max n as) = Max n <$> traverse occurs_ as
+
+  metaOccurs m (Max _ as) =
+    addOrUnblocker (unblockOnAnyMetaIn as) $ traverse_ (metaOccurs m) as
+    -- TODO: Should only be blocking metas in as. But any meta that can
+    --       let the Max make progress needs to be included. For instance,
+    --       _1 ⊔ _2 = _1 should unblock on _2, even though _1 is the meta
+    --       failing occurs check.
+
+instance Occurs PlusLevel where
+  occurs (Plus n l) = do
+    Plus n <$> occurs l
+
+  metaOccurs m (Plus n l) = metaOccurs m l
+
+instance Occurs Type where
+  occurs (El s v) = El <$> occurs_ s <*> occurs v
+
+  metaOccurs m (El s v) = metaOccurs2 m s v
+
+instance Occurs Sort where
+  occurs s = do
+    unfold s >>= \case
+      PiSort a s1 s2 -> do
+        s1' <- flexibly $ occurs_ s1
+        a'  <- (a $>) <$> do flexibly $ occurs (unDom a)
+        s2' <- mapAbstraction (El s1' <$> a') (flexibly . underBinder . occurs_) s2
+        return $ PiSort a' s1' s2'
+      FunSort s1 s2 -> FunSort <$> flexibly (occurs_ s1) <*> flexibly (occurs_ s2)
+      Univ u a   -> Univ u <$> occurs_ a
+      s@Inf{}    -> return s
+      s@SizeUniv -> return s
+      s@LockUniv -> return s
+      s@LevelUniv -> return s
+      s@IntervalUniv -> return s
+      UnivSort s -> UnivSort <$> do flexibly $ occurs_ s
+      MetaS x es -> do
+        MetaV x es <- occurs (MetaV x es)
+        return $ MetaS x es
+      DefS x es -> do
+        Def x es <- occurs (Def x es)
+        return $ DefS x es
+      DummyS{}   -> return s
+
+  metaOccurs m s = do
+    s <- instantiate s
+    case s of
+      PiSort a s1 s2 -> do
+        metaOccurs m a
+        metaOccurs m s1
+        metaOccurs m (absBody s2)
+      FunSort s1 s2 -> metaOccurs2 m s1 s2
+      Univ _ a   -> metaOccurs m a
+      Inf _ _    -> return ()
+      SizeUniv   -> return ()
+      LockUniv   -> return ()
+      LevelUniv  -> return ()
+      IntervalUniv -> return ()
+      UnivSort s -> metaOccurs m s
+      MetaS x es -> metaOccurs m $ MetaV x es
+      DefS d es  -> metaOccurs m $ Def d es
+      DummyS{}   -> return ()
+
+instance Occurs Elims where
+  occurs []     = return []
+  occurs (e:es) = do
+    reportSDoc "tc.meta.occurs.elim" 45 $ "occurs" <+> prettyTCM e
+    reportSDoc "tc.meta.occurs.elim" 70 $ "occurs" <+> pretty e
+    e' <- case e of
+      (Proj o f)     -> do
+        definitionCheck f
+        return e
+      (Apply u)      -> do
+        u' <- occurs u
+        return (Apply u')
+      (IApply x y u) -> do
+        x' <- occurs x
+        y' <- occurs y
+        u' <- occurs u
+        return (IApply x' y' u')
+    (e':) <$> occurs es
+
+  metaOccurs m es = forM_ es $ \case
+    Proj{} -> return ()
+    Apply a -> metaOccurs m a
+    IApply x y a -> metaOccurs3 m x y a
+
+instance Occurs (Abs Term) where
+  occurs (NoAbs s x) = NoAbs s <$> occurs x
+  occurs x = mapAbstraction_ (\body -> underBinder $ occurs body) x
+
+  metaOccurs m (Abs   _ x) = metaOccurs m x
+  metaOccurs m (NoAbs _ x) = metaOccurs m x
+
+instance Occurs (Abs Type) where
+  occurs (NoAbs s x) = NoAbs s <$> occurs_ x
+  occurs x = mapAbstraction_ (\body -> underBinder $ occurs_ body) x
+
+  metaOccurs m (Abs   _ x) = metaOccurs m x
+  metaOccurs m (NoAbs _ x) = metaOccurs m x
+
+instance Occurs a => Occurs (Arg a) where
+  occurs (Arg info v) = Arg info <$> do
+    applyWhen (isIrrelevant info) onlyReduceTypes $
+      underModality info $ occurs v
+  metaOccurs m = metaOccurs m . unArg
+
+instance Occurs a => Occurs (Dom a) where
+  occurs :: Occurs a => Dom a -> OccursM (Dom a)
+  occurs (Dom info n f t x) =
+    Dom info n f t <$> underQuantity info (occurs x)
+
+---------------------------------------------------------------------------
+-- * Pruning: getting rid of flexible occurrences.
+
+-- | @prune m' vs xs@ attempts to remove all arguments from @vs@ whose
+--   free variables are not contained in @xs@.
+--   If successful, @m'@ is solved by the new, pruned meta variable and we
+--   return @True@ else @False@.
+--
+--   Issue 1147:
+--   If any of the meta args @vs@ is matchable, e.g., is a constructor term,
+--   we cannot prune, because the offending variables could be removed by
+--   reduction for a suitable instantiation of the meta variable.
+prune
+  :: (PureTCM m, MonadMetaSolver m)
+  => MetaId         -- ^ Meta to prune.
+  -> Args           -- ^ Arguments to meta variable.
+  -> (Nat -> Bool)  -- ^ Test for allowed variable (de Bruijn index).
+  -> m PruneResult
+prune m' vs xs = do
+  caseEitherM (runExceptT $ mapM ((hasBadRigid xs) . unArg) vs)
+    (const $ return PrunedNothing) $ \ kills -> do
+    reportSDoc "tc.meta.kill" 10 $ vcat
+      [ "attempting kills"
+      , nest 2 $ vcat
+        [ "m'    =" <+> pretty m'
+        -- , "xs    =" <+> prettyList (map (prettyTCM . var) xs)  -- no longer printable
+        , "vs    =" <+> prettyList (map prettyTCM vs)
+        , "kills =" <+> text (show kills)
+        ]
+      ]
+    killArgs kills m'
+
+-- | @hasBadRigid xs v = Just True@ iff one of the rigid variables in @v@ is not in @xs@.
+--   Actually we can only prune if a bad variable is in the head. See issue 458.
+--   Or in a non-eliminateable position (see succeed/PruningNonMillerPattern).
+--
+--   @hasBadRigid xs v = Nothing@ means that
+--   we cannot prune at all as one of the meta args is matchable.
+--   (See issue 1147.)
+hasBadRigid
+  :: PureTCM m
+  => (Nat -> Bool)      -- ^ Test for allowed variable (de Bruijn index).
+  -> Term               -- ^ Argument of meta variable.
+  -> ExceptT () m Bool  -- ^ Exception if argument is matchable.
+hasBadRigid xs t = do
+  -- We fail if we encounter a matchable argument.
+  let failure = throwError ()
+  tb <- reduceB t
+  let t = ignoreBlocking tb
+  case t of
+    Var x _      -> return $ not $ xs x
+    -- Issue 1153: A lambda has to be considered matchable.
+    -- Lam _ v    -> hasBadRigid (0 : map (+1) xs) (absBody v)
+    Lam _ v      -> failure
+    DontCare v   -> hasBadRigid xs v
+    -- The following types of arguments cannot be eliminated by a pattern
+    -- match: data, record, Pi, levels, sorts
+    -- Thus, their offending rigid variables are bad.
+    v@(Def f es) -> ifNotM (isNeutral tb f es) failure $ {- else -} do
+      lift $ es `rigidVarsNotContainedIn` xs
+    -- Andreas, 2012-05-03: There is room for further improvement.
+    -- We could also consider a defined f which is not blocked by a meta.
+    Pi a b       -> lift $ (a,b) `rigidVarsNotContainedIn` xs
+    Level v      -> lift $ v `rigidVarsNotContainedIn` xs
+    Sort s       -> lift $ s `rigidVarsNotContainedIn` xs
+    -- Since constructors can be eliminated by pattern-matching,
+    -- offending variables under a constructor could be removed by
+    -- the right instantiation of the meta variable.
+    -- Thus, they are not rigid.
+    Con c _ es | Just args <- allApplyElims es -> do
+      ifM (isEtaCon (conName c))
+        -- in case of a record con, we can in principle prune
+        -- (but not this argument; the meta could become a projection!)
+        (and <$> mapM (hasBadRigid xs . unArg) args)  -- not andM, we need to force the exceptions!
+        failure
+    Con c _ es | otherwise -> failure
+    Lit{}        -> failure -- matchable
+    MetaV{}      -> failure -- potentially matchable
+    Dummy{}      -> return False
+
+-- | Check whether a term @Def f es@ is finally stuck.
+--   Currently, we give only a crude approximation.
+isNeutral :: (HasConstInfo m) => Blocked t -> QName -> Elims -> m Bool
+isNeutral b f es = do
+  let yes = return True
+      no  = return False
+  def <- getConstInfo f
+  if not (null $ defMatchable def) then no else do
+  case theDef def of
+    AbstractDefn{} -> yes
+    Axiom{}    -> yes
+    Datatype{} -> yes
+    Record{}   -> yes
+    Function{} -> case b of
+      NotBlocked StuckOn{}   _ -> yes
+      NotBlocked AbsurdMatch _ -> yes
+      _                        -> no
+    GeneralizableVar{} -> __IMPOSSIBLE__
+    _          -> no
+
+-- | Check whether any of the variables (given as de Bruijn indices)
+--   occurs *definitely* in the term in a rigid position.
+--   Reduces the term successively to remove variables in dead subterms.
+--   This fixes issue 1386.
+rigidVarsNotContainedIn
+  :: (PureTCM m, AnyRigid a)
+  => a
+  -> (Nat -> Bool)   -- ^ Test for allowed variable (de Bruijn index).
+  -> m Bool
+rigidVarsNotContainedIn v is = do
+  n0 <- getContextSize
+  let -- allowed variables as de Bruijn levels
+      levels = is . (n0-1 -)
+      -- test if index is forbidden by converting it to level
+      test i = do
+        n <- getContextSize
+        -- get de Bruijn level for i
+        let l = n-1 - i
+            -- If l >= n0 then it is a bound variable and can be
+            -- ignored.  Otherwise, it has to be in the allowed levels.
+            forbidden = l < n0 && not (levels l)
+        when forbidden $
+          reportSLn "tc.meta.kill" 20 $
+            "found forbidden de Bruijn level " ++ show l
+        return forbidden
+  anyRigid test v
+
+-- | Collect the *definitely* rigid variables in a monoid.
+--   We need to successively reduce the expression to do this.
+
+class AnyRigid a where
+  anyRigid :: (PureTCM tcm)
+           => (Nat -> tcm Bool) -> a -> tcm Bool
+
+instance AnyRigid Term where
+  anyRigid f t = do
+    b <- reduceB t
+    case ignoreBlocking b of
+      -- Upon entry, we are in rigid position, thus,
+      -- bound variables are rigid ones.
+      Var i es   -> f i `or2M` anyRigid f es
+      Lam _ t    -> anyRigid f t
+      Lit{}      -> return False
+      Def _ es   -> case b of
+        -- If the definition is blocked by a meta, its arguments
+        -- may be in flexible positions.
+        Blocked{}                   -> return False
+        -- If the definition is incomplete, arguments might disappear
+        -- by reductions that come with more clauses, thus, these
+        -- arguments are not rigid.
+        NotBlocked (MissingClauses _) _ -> return False
+        -- _        -> mempty -- breaks: ImproveInertRHS, Issue442, PruneRecord, PruningNonMillerPattern
+        _        -> anyRigid f es
+      Con _ _ ts -> anyRigid f ts
+      Pi a b     -> anyRigid f (a,b)
+      Sort s     -> anyRigid f s
+      Level l    -> anyRigid f l
+      MetaV{}    -> return False
+      DontCare{} -> return False
+      Dummy{}    -> return False
+
+instance AnyRigid Type where
+  anyRigid f (El s t) = anyRigid f (s,t)
+
+instance AnyRigid Sort where
+  anyRigid f s =
+    case s of
+      Univ _ l   -> anyRigid f l
+      Inf _ _    -> return False
+      SizeUniv   -> return False
+      LockUniv   -> return False
+      LevelUniv  -> return False
+      IntervalUniv -> return False
+      PiSort a s1 s2 -> return False
+      FunSort s1 s2 -> return False
+      UnivSort s -> anyRigid f s
+      MetaS{}    -> return False
+      DefS{}     -> return False
+      DummyS{}   -> return False
+
+instance AnyRigid Level where
+  anyRigid f (Max _ ls) = anyRigid f ls
+
+instance AnyRigid PlusLevel where
+  anyRigid f (Plus _ l)    = anyRigid f l
+
+instance (Subst a, AnyRigid a) => AnyRigid (Abs a) where
+  anyRigid f b = underAbstraction_ b $ anyRigid f
+
+instance AnyRigid a => AnyRigid (Arg a) where
+  anyRigid f a =
+    case getRelevance a of
+      -- Irrelevant arguments are definitionally equal to
+      -- values, so the variables there are not considered
+      -- "definitely rigid".
+      Irrelevant -> return False
+      _          -> anyRigid f $ unArg a
+
+instance AnyRigid a => AnyRigid (Dom a) where
+  anyRigid f dom = anyRigid f $ unDom dom
+
+instance AnyRigid a => AnyRigid (Elim' a) where
+  anyRigid f (Apply a)      = anyRigid f a
+  anyRigid f (IApply x y a) = anyRigid f (x,(y,a))
+  anyRigid f Proj{}         = return False
+
+instance AnyRigid a => AnyRigid [a] where
+  anyRigid f xs = anyM xs $ anyRigid f
+
+instance (AnyRigid a, AnyRigid b) => AnyRigid (a,b) where
+  anyRigid f (a,b) = anyRigid f a `or2M` anyRigid f b
+
+
+data PruneResult
+  = NothingToPrune   -- ^ the kill list is empty or only @False@s
+  | PrunedNothing    -- ^ there is no possible kill (because of type dep.)
+  | PrunedSomething  -- ^ managed to kill some args in the list
+  | PrunedEverything -- ^ all prescribed kills where performed
+    deriving (Eq, Show)
+
+-- | @killArgs [k1,...,kn] X@ prunes argument @i@ from metavar @X@ if @ki==True@.
+--   Pruning is carried out whenever > 0 arguments can be pruned.
+killArgs :: (MonadMetaSolver m) => [Bool] -> MetaId -> m PruneResult
+killArgs kills _
+  | not (or kills) = return NothingToPrune  -- nothing to kill
+killArgs kills m = do
+  mv <- lookupLocalMeta m
+  allowAssign <- asksTC envAssignMetas
+  if mvFrozen mv == Frozen || not allowAssign then return PrunedNothing else do
+      -- Andreas 2011-04-26, we allow pruning in MetaV and MetaS
+      let a = jMetaType $ mvJudgement mv
+      TelV tel b <- telView' <$> instantiateFull a
+      let args         = zip (telToList tel) (kills ++ repeat False)
+      (kills', a') <- killedType args b
+      dbg kills' a a'
+      -- If there is any prunable argument, perform the pruning
+      if not (any unArg kills') then return PrunedNothing else do
+        addContext tel $ performKill kills' m a'
+        -- Only successful if all occurrences were killed
+        -- Andreas, 2011-05-09 more precisely, check that at least
+        -- the in 'kills' prescribed kills were carried out
+        return $ if (and $ zipWith implies kills $ map unArg kills')
+                   then PrunedEverything
+                   else PrunedSomething
+  where
+    implies :: Bool -> Bool -> Bool
+    implies False _ = True
+    implies True  x = x
+    dbg kills' a a' =
+      reportSDoc "tc.meta.kill" 10 $ vcat
+        [ "after kill analysis"
+        , nest 2 $ vcat
+          [ "metavar =" <+> prettyTCM m
+          , "kills   =" <+> text (show kills)
+          , "kills'  =" <+> prettyList (map prettyTCM kills')
+          , "oldType =" <+> prettyTCM a
+          , "newType =" <+> prettyTCM a'
+          ]
+        ]
+
+-- | @killedType [((x1,a1),k1)..((xn,an),kn)] b = ([k'1..k'n],t')@
+--   (ignoring @Dom@).  Let @t' = (xs:as) -> b@.
+--   Invariant: @k'i == True@ iff @ki == True@ and pruning the @i@th argument from
+--   type @b@ is possible without creating unbound variables.
+--   @t'@ is type @t@ after pruning all @k'i==True@.
+killedType :: (MonadReduce m) => [(Dom (ArgName, Type), Bool)] -> Type -> m ([Arg Bool], Type)
+killedType args b = do
+
+  let n = length args
+  let iargs = zip (downFrom n) args
+
+  -- Turn list of bools into an IntSet containing the variables we want to kill
+  -- (indices relative to b).
+  let tokill = IntSet.fromList [ i | (i, (_, True)) <- iargs ]
+
+  -- First, check the free variables of b to see if they prevent any kills.
+  (tokill, b) <- reallyNotFreeIn tokill b
+
+  -- Then recurse over the telescope (right-to-left), building up the final type.
+  (killed, b) <- go (reverse $ map fst args) tokill b
+
+  -- Turn the IntSet of killed variables into the list of Arg Bool's to return.
+  let kills = [ Arg (getArgInfo dom) (IntSet.member i killed)
+              | (i, (dom, _)) <- iargs ]
+  return (kills, b)
+  where
+    down = IntSet.map pred
+    up   = IntSet.map succ
+
+    -- go Δ xs B
+    -- Invariants:
+    --   - Δ ⊢ B
+    --   - Δ is represented as a list in right-to-left order
+    --   - xs are deBruijn indices into Δ
+    --   - xs ∩ FV(B) = Ø
+    -- Result: (ys, Δ' → B')
+    --    where Δ' ⊆ Δ  (possibly reduced to remove dependencies, see #3177)
+    --          ys ⊆ xs are the variables that were dropped from Δ
+    --          B' = strengthen ys B
+    go :: (MonadReduce m) => [Dom (ArgName, Type)] -> IntSet -> Type -> m (IntSet, Type)
+    go [] xs b | IntSet.null xs = return (xs, b)
+               | otherwise      = __IMPOSSIBLE__
+    go (arg : args) xs b  -- go (Δ (x : A)) xs B, (x = deBruijn index 0)
+      | IntSet.member 0 xs = do
+          -- Case x ∈ xs. We know x ∉ FV(B), so we can safely drop x from the
+          -- telescope. Drop x from xs (and shift indices) and recurse with
+          -- `strengthen x B`.
+          let ys = down (IntSet.delete 0 xs)
+          (ys, b) <- go args ys $ strengthen impossible b
+          -- We need to return a set of killed variables relative to Δ (x : A), so
+          -- shift ys and add x back in.
+          return (IntSet.insert 0 $ up ys, b)
+      | otherwise = do
+          -- Case x ∉ xs. We either can't or don't want to get rid of x. In
+          -- this case we have to check A for potential dependencies preventing
+          -- us from killing variables in xs.
+          let xs'       = down xs -- Shift to make relative to Δ ⊢ A
+              (name, a) = unDom arg
+          (ys, a) <- reallyNotFreeIn xs' a
+          -- Recurse on Δ, ys, and (x : A') → B, where A reduces to A' and ys ⊆ xs'
+          -- not free in A'. We already know ys not free in B.
+          (zs, b) <- go args ys $ mkPi ((name, a) <$ arg) b
+          -- Shift back up to make it relative to Δ (x : A) again.
+          return (up zs, b)
+
+reallyNotFreeIn :: (MonadReduce m) => IntSet -> Type -> m (IntSet, Type)
+reallyNotFreeIn xs a | IntSet.null xs = return (xs, a) -- Shortcut
+reallyNotFreeIn xs a = do
+  let fvs      = freeVars a
+      anywhere = allVars fvs
+      rigid    = IntSet.unions [stronglyRigidVars fvs, unguardedVars fvs]
+      nonrigid = IntSet.difference anywhere rigid
+      hasNo    = IntSet.disjoint xs
+  if hasNo nonrigid
+    then
+       -- No non-rigid occurrences. We can't do anything about the rigid
+       -- occurrences so drop those and leave `a` untouched.
+       return (IntSet.difference xs rigid, a)
+    else do
+      -- If there are non-rigid occurrences we need to reduce a to see if
+      -- we can get rid of them (#3177).
+      (fvs, a) <- forceNotFree (IntSet.difference xs rigid) a
+      let xs = IntMap.keysSet $ IntMap.filter (== NotFree) fvs
+      return (xs, a)
+
+-- | Instantiate a meta variable with a new one that only takes
+--   the arguments which are not pruneable.
+performKill
+  :: MonadMetaSolver m
+  => [Arg Bool]    -- ^ Arguments to old meta var in left to right order
+                   --   with @Bool@ indicating whether they can be pruned.
+  -> MetaId        -- ^ The old meta var to receive pruning.
+  -> Type          -- ^ The pruned type of the new meta var.
+  -> m ()
+performKill kills m a = do
+  mv <- lookupLocalMeta m
+  when (mvFrozen mv == Frozen) __IMPOSSIBLE__
+  -- Arity of the old meta.
+  let n = size kills
+  -- The permutation of the new meta picks the arguments
+  -- which are not pruned in left to right order
+  -- (de Bruijn level order).
+  let perm = Perm n
+             [ i | (i, Arg _ False) <- zip [0..] kills ]
+      -- The permutation for the old meta might range over a prefix of the arguments
+      oldPerm = liftP (max 0 $ n - m) p
+        where p = mvPermutation mv
+              m = size p
+      judg = case mvJudgement mv of
+        HasType{ jComparison = cmp } -> HasType __IMPOSSIBLE__ cmp a
+        IsSort{}  -> IsSort  __IMPOSSIBLE__ a
+  m' <- newMeta Instantiable (mvInfo mv) (mvPriority mv) (composeP perm oldPerm) judg
+  -- Andreas, 2010-10-15 eta expand new meta variable if necessary
+  etaExpandMetaSafe m'
+  let -- Arguments to new meta (de Bruijn indices)
+      -- in left to right order.
+      vars = [ Arg info (var i)
+             | (i, Arg info False) <- zip (downFrom n) kills ]
+      u       = MetaV m' $ map Apply vars
+      -- Arguments to the old meta (just arg infos and name hints)
+      -- in left to right order.
+      tel     = map ("v" <$) kills
+  dbg m' u
+  assignTerm m tel u  -- m tel := u
+  where
+    dbg m' u = reportSDoc "tc.meta.kill" 10 $ vcat
+      [ "actual killing"
+      , nest 2 $ vcat
+        [ "new meta:" <+> pretty m'
+        , "kills   :" <+> prettyList_ (map (text . show . unArg) kills)
+        , "inst    :" <+> pretty m <+> ":=" <+> prettyTCM u
+        ]
+      ]
diff --git a/src/full/Agda/TypeChecking/Modalities.hs b/src/full/Agda/TypeChecking/Modalities.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Modalities.hs
@@ -0,0 +1,104 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Modalities
+  ( checkModality'
+  , checkModality
+  , checkModalityArgs
+  ) where
+
+import Control.Applicative ((<|>))
+import Control.Monad
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Free.Lazy
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+-- | The second argument is the definition of the first.
+--   Returns 'Nothing' if ok, otherwise the error message.
+checkRelevance' :: (MonadConversion m) => QName -> Definition -> m (Maybe TypeError)
+checkRelevance' x def = do
+  case getRelevance def of
+    Relevant -> return Nothing -- relevance functions can be used in any context.
+    drel -> do
+      -- Andreas,, 2018-06-09, issue #2170
+      -- irrelevant projections are only allowed if --irrelevant-projections
+      ifM (return (isJust $ isProjection_ $ theDef def) `and2M`
+           (not . optIrrelevantProjections <$> pragmaOptions)) {-then-} needIrrProj {-else-} $ do
+        rel <- viewTC eRelevance
+        reportSDoc "tc.irr" 50 $ vcat
+          [ "declaration relevance =" <+> text (show drel)
+          , "context     relevance =" <+> text (show rel)
+          ]
+        return $ boolToMaybe (not $ drel `moreRelevant` rel) $ DefinitionIsIrrelevant x
+  where
+  needIrrProj = Just . GenericDocError <$> do
+    sep [ "Projection " , prettyTCM x, " is irrelevant."
+        , " Turn on option --irrelevant-projections to use it (unsafe)."
+        ]
+
+-- | The second argument is the definition of the first.
+--   Returns 'Nothing' if ok, otherwise the error message.
+checkQuantity' :: (MonadConversion m) => QName -> Definition -> m (Maybe TypeError)
+checkQuantity' x def = do
+  case getQuantity def of
+    dq@Quantityω{} -> do
+      reportSDoc "tc.irr" 50 $ vcat
+        [ "declaration quantity =" <+> text (show dq)
+        -- , "context     quantity =" <+> text (show q)
+        ]
+      return Nothing -- Abundant definitions can be used in any context.
+    dq -> do
+      q <- viewTC eQuantity
+      reportSDoc "tc.irr" 50 $ vcat
+        [ "declaration quantity =" <+> text (show dq)
+        , "context     quantity =" <+> text (show q)
+        ]
+      return $ boolToMaybe (not $ dq `moreQuantity` q) $ DefinitionIsErased x
+
+-- | The second argument is the definition of the first.
+checkModality' :: (MonadConversion m) => QName -> Definition -> m (Maybe TypeError)
+checkModality' x def = do
+  relOk <- checkRelevance' x def
+  qtyOk <- checkQuantity' x def
+  return $ relOk <|> qtyOk
+
+-- | The second argument is the definition of the first.
+checkModality :: (MonadConversion m) => QName -> Definition -> m ()
+checkModality x def = checkModality' x def >>= mapM_ typeError
+
+-- | Checks that the given implicitely inserted arguments, are used in a modally
+--   correct way.
+checkModalityArgs :: (MonadConversion m) => Definition -> Args -> m ()
+checkModalityArgs d vs = do
+  let
+    vmap :: VarMap
+    vmap = freeVars vs
+
+  -- we iterate over all vars in the context and their ArgInfo,
+  -- checking for each that "vs" uses them as allowed.
+  as <- getContextArgs
+  forM_ as $ \ (Arg avail t) -> do
+    let m = do
+          v <- deBruijnView t
+          varModality <$> lookupVarMap v vmap
+    whenJust m $ \ used -> do
+        unless (getCohesion avail `moreCohesion` getCohesion used) $
+           genericDocError =<< fsep
+             [ "Telescope variable" <+> prettyTCM t
+             , "is indirectly being used in the" <+> text (verbalize (getModality used)) <+> "modality"
+             , "but only available as in the" <+> text (verbalize (getModality avail)) <+> "modality"
+             , "when inserting into the top-level"
+             , pretty (defName d) <+> ":" <+> prettyTCM (defType d)
+             ]
diff --git a/src/full/Agda/TypeChecking/Monad.hs b/src/full/Agda/TypeChecking/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad.hs
@@ -0,0 +1,45 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad
+    ( module Agda.TypeChecking.Monad.Base
+    , module Agda.TypeChecking.Monad.Builtin
+    , module Agda.TypeChecking.Monad.Closure
+    , module Agda.TypeChecking.Monad.Constraints
+    , module Agda.TypeChecking.Monad.Context
+    , module Agda.TypeChecking.Monad.Debug
+    , module Agda.TypeChecking.Monad.Env
+    , module Agda.TypeChecking.Monad.Imports
+    , module Agda.TypeChecking.Monad.MetaVars
+    , module Agda.TypeChecking.Monad.Modality
+    , module Agda.TypeChecking.Monad.Mutual
+    , module Agda.TypeChecking.Monad.Open
+    , module Agda.TypeChecking.Monad.Options
+    , module Agda.TypeChecking.Monad.Pure
+    , module Agda.TypeChecking.Monad.Signature
+    , module Agda.TypeChecking.Monad.SizedTypes
+    , module Agda.TypeChecking.Monad.State
+    , module Agda.TypeChecking.Monad.Statistics
+    , module Agda.TypeChecking.Monad.Trace
+    , module Agda.TypeChecking.Monad.Caching
+    ) where
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Closure
+import Agda.TypeChecking.Monad.Constraints
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Env
+import Agda.TypeChecking.Monad.Imports
+import Agda.TypeChecking.Monad.MetaVars
+import Agda.TypeChecking.Monad.Modality
+import Agda.TypeChecking.Monad.Mutual
+import Agda.TypeChecking.Monad.Options
+import Agda.TypeChecking.Monad.Open
+import Agda.TypeChecking.Monad.Pure
+import Agda.TypeChecking.Monad.Signature
+import Agda.TypeChecking.Monad.SizedTypes
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Monad.Statistics
+import Agda.TypeChecking.Monad.Trace
+import Agda.TypeChecking.Monad.Caching
diff --git a/src/full/Agda/TypeChecking/Monad/Base.hs b/src/full/Agda/TypeChecking/Monad/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Base.hs
@@ -0,0 +1,5821 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE RecursiveDo #-}
+-- {-# LANGUAGE UndecidableInstances #-}  -- ghc >= 8.2, GeneralizedNewtypeDeriving MonadTransControl BlockT
+
+module Agda.TypeChecking.Monad.Base
+  ( module Agda.TypeChecking.Monad.Base
+  , HasOptions (..)
+  , RecordFieldWarning
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Applicative hiding (empty)
+import qualified Control.Concurrent as C
+import Control.DeepSeq
+import qualified Control.Exception as E
+
+import qualified Control.Monad.Fail as Fail
+
+import Control.Monad                ( void )
+import Control.Monad.Except
+import Control.Monad.Fix
+import Control.Monad.IO.Class       ( MonadIO(..) )
+import Control.Monad.State          ( MonadState(..), modify, StateT(..), runStateT )
+import Control.Monad.Reader         ( MonadReader(..), ReaderT(..), runReaderT )
+import Control.Monad.Writer         ( WriterT )
+import Control.Monad.Trans          ( MonadTrans(..), lift )
+import Control.Monad.Trans.Control  ( MonadTransControl(..), liftThrough )
+import Control.Monad.Trans.Identity ( IdentityT(..), runIdentityT )
+import Control.Monad.Trans.Maybe    ( MaybeT(..) )
+
+import Control.Parallel             ( pseq )
+
+import Data.Array (Ix)
+import Data.DList (DList)
+import Data.Function (on)
+import Data.Int
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Maybe
+import Data.Map (Map)
+import qualified Data.Map as Map -- hiding (singleton, null, empty)
+import Data.Sequence (Seq)
+import Data.Set (Set, toList, fromList)
+import qualified Data.Set as Set -- hiding (singleton, null, empty)
+import Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as HMap
+import qualified Data.HashSet as HashSet
+import Data.Hashable
+import Data.HashSet (HashSet)
+import Data.Semigroup ( Semigroup, (<>)) --, Any(..) )
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.String
+import Data.Text (Text)
+import qualified Data.Text.Lazy as TL
+
+import Data.IORef
+
+import GHC.Generics (Generic)
+
+import Agda.Benchmarking (Benchmark, Phase)
+
+import {-# SOURCE #-} Agda.Compiler.Treeless.Pretty () -- Instances only
+import Agda.Syntax.Common
+import Agda.Syntax.Builtin (SomeBuiltin, BuiltinId, PrimitiveId)
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Concrete.Definitions
+  (NiceDeclaration, DeclarationWarning, declarationWarningName)
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Internal.Generic (TermLike(..))
+import Agda.Syntax.Parser (ParseWarning)
+import Agda.Syntax.Parser.Monad (parseWarningName)
+import Agda.Syntax.TopLevelModuleName
+  (RawTopLevelModuleName, TopLevelModuleName)
+import Agda.Syntax.Treeless (Compiled)
+import Agda.Syntax.Notation
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+import qualified Agda.Syntax.Info as Info
+
+import qualified Agda.TypeChecking.Monad.Base.Warning as W
+import           Agda.TypeChecking.Monad.Base.Warning (RecordFieldWarning)
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Free.Lazy (Free(freeVars'), underBinder', underBinder)
+
+-- Args, defined in Agda.Syntax.Treeless and exported from Agda.Compiler.Backend
+-- conflicts with Args, defined in Agda.Syntax.Internal and also imported here.
+-- This only matters when interpreted in ghci, which sees all of the module's
+-- exported symbols, not just the ones defined in the `.hs-boot`. See the
+-- comment in ../../Compiler/Backend.hs-boot
+import {-# SOURCE #-} Agda.Compiler.Backend hiding (Args)
+
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Warnings
+import {-# SOURCE #-} Agda.Interaction.Response
+  (InteractionOutputCallback, defaultInteractionOutputCallback)
+import Agda.Interaction.Highlighting.Precise
+  (HighlightingInfo, NameKind)
+import Agda.Interaction.Library
+
+import Agda.Utils.Benchmark (MonadBench(..))
+import Agda.Utils.BiMap (BiMap, HasTag(..))
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.CallStack ( CallStack, HasCallStack, withCallerCallStack )
+import Agda.Utils.FileName
+import Agda.Utils.Functor
+import Agda.Utils.Hash
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.ListT
+import Agda.Utils.List1 (List1, pattern (:|))
+import Agda.Utils.List2 (List2, pattern List2)
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.SmallSet (SmallSet)
+import qualified Agda.Utils.SmallSet as SmallSet
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Type checking state
+---------------------------------------------------------------------------
+
+data TCState = TCSt
+  { stPreScopeState   :: !PreScopeState
+    -- ^ The state which is frozen after scope checking.
+  , stPostScopeState  :: !PostScopeState
+    -- ^ The state which is modified after scope checking.
+  , stPersistentState :: !PersistentTCState
+    -- ^ State which is forever, like a diamond.
+  }
+  deriving Generic
+
+class Monad m => ReadTCState m where
+  getTCState :: m TCState
+  locallyTCState :: Lens' TCState a -> (a -> a) -> m b -> m b
+
+  withTCState :: (TCState -> TCState) -> m a -> m a
+  withTCState = locallyTCState id
+
+  default getTCState :: (MonadTrans t, ReadTCState n, t n ~ m) => m TCState
+  getTCState = lift getTCState
+
+  default locallyTCState
+    :: (MonadTransControl t, ReadTCState n, t n ~ m)
+    => Lens' TCState a -> (a -> a) -> m b -> m b
+  locallyTCState l = liftThrough . locallyTCState l
+
+instance ReadTCState m => ReadTCState (ListT m) where
+  locallyTCState l = mapListT . locallyTCState l
+
+instance ReadTCState m => ReadTCState (ChangeT m)
+instance ReadTCState m => ReadTCState (ExceptT err m)
+instance ReadTCState m => ReadTCState (IdentityT m)
+instance ReadTCState m => ReadTCState (MaybeT m)
+instance ReadTCState m => ReadTCState (ReaderT r m)
+instance ReadTCState m => ReadTCState (StateT s m)
+instance (Monoid w, ReadTCState m) => ReadTCState (WriterT w m)
+
+
+instance Show TCState where
+  show _ = "TCSt{}"
+
+data PreScopeState = PreScopeState
+  { stPreTokens             :: !HighlightingInfo
+    -- ^ Highlighting info for tokens and Happy parser warnings (but
+    -- not for those tokens/warnings for which highlighting exists in
+    -- 'stPostSyntaxInfo').
+  , stPreImports            :: !Signature  -- XX populated by scope checker
+    -- ^ Imported declared identifiers.
+    --   Those most not be serialized!
+  , stPreImportedModules    :: !(Set TopLevelModuleName)
+      -- Andreas, 2023-08-05, issue #6750, don't make this a 'HashSet'
+      -- because then the order of its @toList@ is undefined,
+      -- leading to undefined deserialization order.
+    -- ^ The top-level modules imported by the current module.
+  , stPreModuleToSource     :: !ModuleToSource   -- imports
+  , stPreVisitedModules     :: !VisitedModules   -- imports
+  , stPreScope              :: !ScopeInfo
+    -- generated by scope checker, current file:
+    -- which modules you have, public definitions, current file, maps concrete names to abstract names.
+  , stPrePatternSyns        :: !A.PatternSynDefns
+    -- ^ Pattern synonyms of the current file.  Serialized.
+  , stPrePatternSynImports  :: !A.PatternSynDefns
+    -- ^ Imported pattern synonyms.  Must not be serialized!
+  , stPreGeneralizedVars    :: !(Strict.Maybe (Set QName))
+    -- ^ Collected generalizable variables; used during scope checking of terms
+  , stPrePragmaOptions      :: !PragmaOptions
+    -- ^ Options applying to the current file. @OPTIONS@
+    -- pragmas only affect this field.
+  , stPreImportedBuiltins   :: !(BuiltinThings PrimFun)
+  , stPreImportedDisplayForms :: !DisplayForms
+    -- ^ Display forms added by someone else to imported identifiers
+  , stPreImportedInstanceDefs :: !InstanceTable
+  , stPreForeignCode        :: !(Map BackendName ForeignCodeStack)
+    -- ^ @{-\# FOREIGN \#-}@ code that should be included in the compiled output.
+    -- Does not include code for imported modules.
+  , stPreFreshInteractionId :: !InteractionId
+  , stPreImportedUserWarnings :: !(Map A.QName Text)
+    -- ^ Imported @UserWarning@s, not to be stored in the @Interface@
+  , stPreLocalUserWarnings    :: !(Map A.QName Text)
+    -- ^ Locally defined @UserWarning@s, to be stored in the @Interface@
+  , stPreWarningOnImport      :: !(Strict.Maybe Text)
+    -- ^ Whether the current module should raise a warning when opened
+  , stPreImportedPartialDefs :: !(Set QName)
+    -- ^ Imported partial definitions, not to be stored in the @Interface@
+  , stPreProjectConfigs :: !(Map FilePath ProjectConfig)
+    -- ^ Map from directories to paths of closest enclosing .agda-lib
+    --   files (or @Nothing@ if there are none).
+  , stPreAgdaLibFiles   :: !(Map FilePath AgdaLibFile)
+    -- ^ Contents of .agda-lib files that have already been parsed.
+  , stPreImportedMetaStore :: !RemoteMetaStore
+    -- ^ Used for meta-variables from other modules.
+  , stPreCopiedNames       :: !(HashMap A.QName A.QName)
+    -- ^ Associates a copied name (the key) to its original name (the
+    -- value). Computed by the scope checker, used to compute opaque
+    -- blocks.
+  , stPreNameCopies        :: !(HashMap A.QName (HashSet A.QName))
+    -- ^ Associates an original name (the key) to all its copies (the
+    -- value). Computed by the scope checker, used to compute opaque
+    -- blocks.
+  }
+  deriving Generic
+
+-- | Name disambiguation for the sake of highlighting.
+data DisambiguatedName = DisambiguatedName NameKind A.QName
+  deriving Generic
+type DisambiguatedNames = IntMap DisambiguatedName
+
+type ConcreteNames = Map Name [C.Name]
+
+data PostScopeState = PostScopeState
+  { stPostSyntaxInfo          :: !HighlightingInfo
+    -- ^ Highlighting info.
+  , stPostDisambiguatedNames  :: !DisambiguatedNames
+    -- ^ Disambiguation carried out by the type checker.
+    --   Maps position of first name character to disambiguated @'A.QName'@
+    --   for each @'A.AmbiguousQName'@ already passed by the type checker.
+  , stPostOpenMetaStore       :: !LocalMetaStore
+    -- ^ Used for open meta-variables.
+  , stPostSolvedMetaStore     :: !LocalMetaStore
+    -- ^ Used for local, instantiated meta-variables.
+  , stPostInteractionPoints   :: !InteractionPoints -- scope checker first
+  , stPostAwakeConstraints    :: !Constraints
+  , stPostSleepingConstraints :: !Constraints
+  , stPostDirty               :: !Bool -- local
+    -- ^ Dirty when a constraint is added, used to prevent pointer update.
+    -- Currently unused.
+  , stPostOccursCheckDefs     :: !(Set QName) -- local
+    -- ^ Definitions to be considered during occurs check.
+    --   Initialized to the current mutual block before the check.
+    --   During occurs check, we remove definitions from this set
+    --   as soon we have checked them.
+  , stPostSignature           :: !Signature
+    -- ^ Declared identifiers of the current file.
+    --   These will be serialized after successful type checking.
+  , stPostModuleCheckpoints   :: !(Map ModuleName CheckpointId)
+    -- ^ For each module remember the checkpoint corresponding to the orignal
+    --   context of the module parameters.
+  , stPostImportsDisplayForms :: !DisplayForms
+    -- ^ Display forms we add for imported identifiers
+  , stPostCurrentModule       ::
+      !(Maybe (ModuleName, TopLevelModuleName))
+    -- ^ The current module is available after it has been type
+    -- checked.
+  , stPostInstanceDefs        :: !TempInstanceTable
+  , stPostConcreteNames       :: !ConcreteNames
+    -- ^ Map keeping track of concrete names assigned to each abstract name
+    --   (can be more than one name in case the first one is shadowed)
+  , stPostUsedNames           :: !(Map RawName (DList RawName))
+    -- ^ Map keeping track for each name root (= name w/o numeric
+    -- suffixes) what names with the same root have been used during a
+    -- TC computation. This information is used to build the
+    -- @ShadowingNames@ map.
+  , stPostShadowingNames      :: !(Map Name (DList RawName))
+    -- ^ Map keeping track for each (abstract) name the list of all
+    -- (raw) names that it could maybe be shadowed by.
+  , stPostStatistics          :: !Statistics
+    -- ^ Counters to collect various statistics about meta variables etc.
+    --   Only for current file.
+  , stPostTCWarnings          :: ![TCWarning]
+  , stPostMutualBlocks        :: !(Map MutualId MutualBlock)
+  , stPostLocalBuiltins       :: !(BuiltinThings PrimFun)
+  , stPostFreshMetaId         :: !MetaId
+  , stPostFreshMutualId       :: !MutualId
+  , stPostFreshProblemId      :: !ProblemId
+  , stPostFreshCheckpointId   :: !CheckpointId
+  , stPostFreshInt            :: !Int
+  , stPostFreshNameId         :: !NameId
+  , stPostFreshOpaqueId       :: !OpaqueId
+  , stPostAreWeCaching        :: !Bool
+  , stPostPostponeInstanceSearch :: !Bool
+  , stPostConsideringInstance :: !Bool
+  , stPostInstantiateBlocking :: !Bool
+    -- ^ Should we instantiate away blocking metas?
+    --   This can produce ill-typed terms but they are often more readable. See issue #3606.
+    --   Best set to True only for calls to pretty*/reify to limit unwanted reductions.
+  , stPostLocalPartialDefs    :: !(Set QName)
+    -- ^ Local partial definitions, to be stored in the @Interface@
+  , stPostOpaqueBlocks        :: Map OpaqueId OpaqueBlock
+    -- ^ Associates opaque identifiers to their actual blocks.
+  , stPostOpaqueIds           :: Map QName OpaqueId
+    -- ^ Associates each opaque QName to the block it was defined in.
+  }
+  deriving (Generic)
+
+-- | A mutual block of names in the signature.
+data MutualBlock = MutualBlock
+  { mutualInfo  :: Info.MutualInfo
+    -- ^ The original info of the mutual block.
+  , mutualNames :: Set QName
+  } deriving (Show, Eq, Generic)
+
+instance Null MutualBlock where
+  empty = MutualBlock empty empty
+
+-- | A part of the state which is not reverted when an error is thrown
+-- or the state is reset.
+data PersistentTCState = PersistentTCSt
+  { stDecodedModules    :: !DecodedModules
+  , stPersistentTopLevelModuleNames ::
+      !(BiMap RawTopLevelModuleName ModuleNameHash)
+    -- ^ Module name hashes for top-level module names (and vice
+    -- versa).
+  , stPersistentOptions :: CommandLineOptions
+  , stInteractionOutputCallback  :: InteractionOutputCallback
+    -- ^ Callback function to call when there is a response
+    --   to give to the interactive frontend.
+    --   See the documentation of 'InteractionOutputCallback'.
+  , stBenchmark         :: !Benchmark
+    -- ^ Structure to track how much CPU time was spent on which Agda phase.
+    --   Needs to be a strict field to avoid space leaks!
+  , stAccumStatistics   :: !Statistics
+    -- ^ Should be strict field.
+  , stPersistLoadedFileCache :: !(Strict.Maybe LoadedFileCache)
+    -- ^ Cached typechecking state from the last loaded file.
+    --   Should be @Nothing@ when checking imports.
+  , stPersistBackends   :: [Backend]
+    -- ^ Current backends with their options
+  }
+  deriving Generic
+
+data LoadedFileCache = LoadedFileCache
+  { lfcCached  :: !CachedTypeCheckLog
+  , lfcCurrent :: !CurrentTypeCheckLog
+  }
+  deriving Generic
+
+-- | A log of what the type checker does and states after the action is
+-- completed.  The cached version is stored first executed action first.
+type CachedTypeCheckLog = [(TypeCheckAction, PostScopeState)]
+
+-- | Like 'CachedTypeCheckLog', but storing the log for an ongoing type
+-- checking of a module.  Stored in reverse order (last performed action
+-- first).
+type CurrentTypeCheckLog = [(TypeCheckAction, PostScopeState)]
+
+-- | A complete log for a module will look like this:
+--
+--   * 'Pragmas'
+--
+--   * 'EnterSection', entering the main module.
+--
+--   * 'Decl'/'EnterSection'/'LeaveSection', for declarations and nested
+--     modules
+--
+--   * 'LeaveSection', leaving the main module.
+data TypeCheckAction
+  = EnterSection !Erased !ModuleName !A.Telescope
+  | LeaveSection !ModuleName
+  | Decl !A.Declaration
+    -- ^ Never a Section or ScopeDecl
+  | Pragmas !PragmaOptions
+  deriving (Generic)
+
+-- | Empty persistent state.
+
+initPersistentState :: PersistentTCState
+initPersistentState = PersistentTCSt
+  { stPersistentOptions         = defaultOptions
+  , stPersistentTopLevelModuleNames = empty
+  , stDecodedModules            = Map.empty
+  , stInteractionOutputCallback = defaultInteractionOutputCallback
+  , stBenchmark                 = empty
+  , stAccumStatistics           = Map.empty
+  , stPersistLoadedFileCache    = empty
+  , stPersistBackends           = []
+  }
+
+-- | An initial 'MetaId'.
+
+initialMetaId :: MetaId
+initialMetaId = MetaId
+  { metaId     = 0
+  , metaModule = noModuleNameHash
+  }
+
+-- | Empty state of type checker.
+
+initPreScopeState :: PreScopeState
+initPreScopeState = PreScopeState
+  { stPreTokens               = mempty
+  , stPreImports              = emptySignature
+  , stPreImportedModules      = empty
+  , stPreModuleToSource       = Map.empty
+  , stPreVisitedModules       = Map.empty
+  , stPreScope                = emptyScopeInfo
+  , stPrePatternSyns          = Map.empty
+  , stPrePatternSynImports    = Map.empty
+  , stPreGeneralizedVars      = mempty
+  , stPrePragmaOptions        = defaultInteractionOptions
+  , stPreImportedBuiltins     = Map.empty
+  , stPreImportedDisplayForms = HMap.empty
+  , stPreImportedInstanceDefs = Map.empty
+  , stPreForeignCode          = Map.empty
+  , stPreFreshInteractionId   = 0
+  , stPreImportedUserWarnings = Map.empty
+  , stPreLocalUserWarnings    = Map.empty
+  , stPreWarningOnImport      = empty
+  , stPreImportedPartialDefs  = Set.empty
+  , stPreProjectConfigs       = Map.empty
+  , stPreAgdaLibFiles         = Map.empty
+  , stPreImportedMetaStore    = HMap.empty
+  , stPreCopiedNames          = HMap.empty
+  , stPreNameCopies           = HMap.empty
+  }
+
+initPostScopeState :: PostScopeState
+initPostScopeState = PostScopeState
+  { stPostSyntaxInfo           = mempty
+  , stPostDisambiguatedNames   = IntMap.empty
+  , stPostOpenMetaStore        = Map.empty
+  , stPostSolvedMetaStore      = Map.empty
+  , stPostInteractionPoints    = empty
+  , stPostAwakeConstraints     = []
+  , stPostSleepingConstraints  = []
+  , stPostDirty                = False
+  , stPostOccursCheckDefs      = Set.empty
+  , stPostSignature            = emptySignature
+  , stPostModuleCheckpoints    = Map.empty
+  , stPostImportsDisplayForms  = HMap.empty
+  , stPostCurrentModule        = empty
+  , stPostInstanceDefs         = (Map.empty , Set.empty)
+  , stPostConcreteNames        = Map.empty
+  , stPostUsedNames            = Map.empty
+  , stPostShadowingNames       = Map.empty
+  , stPostStatistics           = Map.empty
+  , stPostTCWarnings           = []
+  , stPostMutualBlocks         = Map.empty
+  , stPostLocalBuiltins        = Map.empty
+  , stPostFreshMetaId          = initialMetaId
+  , stPostFreshMutualId        = 0
+  , stPostFreshProblemId       = 1
+  , stPostFreshCheckpointId    = 1
+  , stPostFreshInt             = 0
+  , stPostFreshNameId          = NameId 0 noModuleNameHash
+  , stPostFreshOpaqueId        = OpaqueId 0 noModuleNameHash
+  , stPostAreWeCaching         = False
+  , stPostPostponeInstanceSearch = False
+  , stPostConsideringInstance  = False
+  , stPostInstantiateBlocking  = False
+  , stPostLocalPartialDefs     = Set.empty
+  , stPostOpaqueBlocks         = Map.empty
+  , stPostOpaqueIds            = Map.empty
+  }
+
+initState :: TCState
+initState = TCSt
+  { stPreScopeState   = initPreScopeState
+  , stPostScopeState  = initPostScopeState
+  , stPersistentState = initPersistentState
+  }
+
+-- * st-prefixed lenses
+------------------------------------------------------------------------
+
+stTokens :: Lens' TCState HighlightingInfo
+stTokens f s =
+  f (stPreTokens (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreTokens = x}}
+
+stImports :: Lens' TCState Signature
+stImports f s =
+  f (stPreImports (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImports = x}}
+
+stImportedModules ::
+  Lens' TCState (Set TopLevelModuleName)
+stImportedModules f s =
+  f (stPreImportedModules (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedModules = x}}
+
+stModuleToSource :: Lens' TCState ModuleToSource
+stModuleToSource f s =
+  f (stPreModuleToSource (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreModuleToSource = x}}
+
+stVisitedModules :: Lens' TCState VisitedModules
+stVisitedModules f s =
+  f (stPreVisitedModules (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreVisitedModules = x}}
+
+stScope :: Lens' TCState ScopeInfo
+stScope f s =
+  f (stPreScope (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreScope = x}}
+
+stPatternSyns :: Lens' TCState A.PatternSynDefns
+stPatternSyns f s =
+  f (stPrePatternSyns (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPrePatternSyns = x}}
+
+stPatternSynImports :: Lens' TCState A.PatternSynDefns
+stPatternSynImports f s =
+  f (stPrePatternSynImports (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPrePatternSynImports = x}}
+
+stGeneralizedVars :: Lens' TCState (Maybe (Set QName))
+stGeneralizedVars f s =
+  f (Strict.toLazy $ stPreGeneralizedVars (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreGeneralizedVars = Strict.toStrict x}}
+
+stPragmaOptions :: Lens' TCState PragmaOptions
+stPragmaOptions f s =
+  f (stPrePragmaOptions (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPrePragmaOptions = x}}
+
+stImportedBuiltins :: Lens' TCState (BuiltinThings PrimFun)
+stImportedBuiltins f s =
+  f (stPreImportedBuiltins (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedBuiltins = x}}
+
+stForeignCode :: Lens' TCState (Map BackendName ForeignCodeStack)
+stForeignCode f s =
+  f (stPreForeignCode (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreForeignCode = x}}
+
+stFreshInteractionId :: Lens' TCState InteractionId
+stFreshInteractionId f s =
+  f (stPreFreshInteractionId (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreFreshInteractionId = x}}
+
+stImportedUserWarnings :: Lens' TCState (Map A.QName Text)
+stImportedUserWarnings f s =
+  f (stPreImportedUserWarnings (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedUserWarnings = x}}
+
+stLocalUserWarnings :: Lens' TCState (Map A.QName Text)
+stLocalUserWarnings f s =
+  f (stPreLocalUserWarnings (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreLocalUserWarnings = x}}
+
+getUserWarnings :: ReadTCState m => m (Map A.QName Text)
+getUserWarnings = do
+  iuw <- useR stImportedUserWarnings
+  luw <- useR stLocalUserWarnings
+  return $ iuw `Map.union` luw
+
+stWarningOnImport :: Lens' TCState (Maybe Text)
+stWarningOnImport f s =
+  f (Strict.toLazy $ stPreWarningOnImport (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreWarningOnImport = Strict.toStrict x}}
+
+stImportedPartialDefs :: Lens' TCState (Set QName)
+stImportedPartialDefs f s =
+  f (stPreImportedPartialDefs (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedPartialDefs = x}}
+
+stLocalPartialDefs :: Lens' TCState (Set QName)
+stLocalPartialDefs f s =
+  f (stPostLocalPartialDefs (stPostScopeState s)) <&>
+  \ x -> s {stPostScopeState = (stPostScopeState s) {stPostLocalPartialDefs = x}}
+
+getPartialDefs :: ReadTCState m => m (Set QName)
+getPartialDefs = do
+  ipd <- useR stImportedPartialDefs
+  lpd <- useR stLocalPartialDefs
+  return $ ipd `Set.union` lpd
+
+stLoadedFileCache :: Lens' TCState (Maybe LoadedFileCache)
+stLoadedFileCache f s =
+  f (Strict.toLazy $ stPersistLoadedFileCache (stPersistentState s)) <&>
+  \x -> s {stPersistentState = (stPersistentState s) {stPersistLoadedFileCache = Strict.toStrict x}}
+
+stBackends :: Lens' TCState [Backend]
+stBackends f s =
+  f (stPersistBackends (stPersistentState s)) <&>
+  \x -> s {stPersistentState = (stPersistentState s) {stPersistBackends = x}}
+
+stProjectConfigs :: Lens' TCState (Map FilePath ProjectConfig)
+stProjectConfigs f s =
+  f (stPreProjectConfigs (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreProjectConfigs = x}}
+
+stAgdaLibFiles :: Lens' TCState (Map FilePath AgdaLibFile)
+stAgdaLibFiles f s =
+  f (stPreAgdaLibFiles (stPreScopeState s)) <&>
+  \ x -> s {stPreScopeState = (stPreScopeState s) {stPreAgdaLibFiles = x}}
+
+stTopLevelModuleNames ::
+  Lens' TCState (BiMap RawTopLevelModuleName ModuleNameHash)
+stTopLevelModuleNames f s =
+  f (stPersistentTopLevelModuleNames (stPersistentState s)) <&>
+  \ x -> s {stPersistentState =
+              (stPersistentState s) {stPersistentTopLevelModuleNames = x}}
+
+stImportedMetaStore :: Lens' TCState RemoteMetaStore
+stImportedMetaStore f s =
+  f (stPreImportedMetaStore (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedMetaStore = x}}
+
+stCopiedNames :: Lens' TCState (HashMap QName QName)
+stCopiedNames f s =
+  f (stPreCopiedNames (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreCopiedNames = x}}
+
+stNameCopies :: Lens' TCState (HashMap QName (HashSet QName))
+stNameCopies f s =
+  f (stPreNameCopies (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreNameCopies = x}}
+
+stFreshNameId :: Lens' TCState NameId
+stFreshNameId f s =
+  f (stPostFreshNameId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshNameId = x}}
+
+stFreshOpaqueId :: Lens' TCState OpaqueId
+stFreshOpaqueId f s =
+  f (stPostFreshOpaqueId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshOpaqueId = x}}
+
+stOpaqueBlocks :: Lens' TCState (Map OpaqueId OpaqueBlock)
+stOpaqueBlocks f s =
+  f (stPostOpaqueBlocks (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostOpaqueBlocks = x}}
+
+stOpaqueIds :: Lens' TCState (Map QName OpaqueId)
+stOpaqueIds f s =
+  f (stPostOpaqueIds (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostOpaqueIds = x}}
+
+stSyntaxInfo :: Lens' TCState HighlightingInfo
+stSyntaxInfo f s =
+  f (stPostSyntaxInfo (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostSyntaxInfo = x}}
+
+stDisambiguatedNames :: Lens' TCState DisambiguatedNames
+stDisambiguatedNames f s =
+  f (stPostDisambiguatedNames (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostDisambiguatedNames = x}}
+
+stOpenMetaStore :: Lens' TCState LocalMetaStore
+stOpenMetaStore f s =
+  f (stPostOpenMetaStore (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostOpenMetaStore = x}}
+
+stSolvedMetaStore :: Lens' TCState LocalMetaStore
+stSolvedMetaStore f s =
+  f (stPostSolvedMetaStore (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostSolvedMetaStore = x}}
+
+stInteractionPoints :: Lens' TCState InteractionPoints
+stInteractionPoints f s =
+  f (stPostInteractionPoints (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostInteractionPoints = x}}
+
+stAwakeConstraints :: Lens' TCState Constraints
+stAwakeConstraints f s =
+  f (stPostAwakeConstraints (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostAwakeConstraints = x}}
+
+stSleepingConstraints :: Lens' TCState Constraints
+stSleepingConstraints f s =
+  f (stPostSleepingConstraints (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostSleepingConstraints = x}}
+
+stDirty :: Lens' TCState Bool
+stDirty f s =
+  f (stPostDirty (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostDirty = x}}
+
+stOccursCheckDefs :: Lens' TCState (Set QName)
+stOccursCheckDefs f s =
+  f (stPostOccursCheckDefs (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostOccursCheckDefs = x}}
+
+stSignature :: Lens' TCState Signature
+stSignature f s =
+  f (stPostSignature (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostSignature = x}}
+
+stModuleCheckpoints :: Lens' TCState (Map ModuleName CheckpointId)
+stModuleCheckpoints f s =
+  f (stPostModuleCheckpoints (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostModuleCheckpoints = x}}
+
+stImportsDisplayForms :: Lens' TCState DisplayForms
+stImportsDisplayForms f s =
+  f (stPostImportsDisplayForms (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostImportsDisplayForms = x}}
+
+stImportedDisplayForms :: Lens' TCState DisplayForms
+stImportedDisplayForms f s =
+  f (stPreImportedDisplayForms (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedDisplayForms = x}}
+
+-- | Note that the lens is \"strict\".
+
+stCurrentModule ::
+  Lens' TCState (Maybe (ModuleName, TopLevelModuleName))
+stCurrentModule f s =
+  f (stPostCurrentModule (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState =
+             (stPostScopeState s)
+               {stPostCurrentModule = case x of
+                  Nothing         -> Nothing
+                  Just (!m, !top) -> Just (m, top)}}
+
+stImportedInstanceDefs :: Lens' TCState InstanceTable
+stImportedInstanceDefs f s =
+  f (stPreImportedInstanceDefs (stPreScopeState s)) <&>
+  \x -> s {stPreScopeState = (stPreScopeState s) {stPreImportedInstanceDefs = x}}
+
+stInstanceDefs :: Lens' TCState TempInstanceTable
+stInstanceDefs f s =
+  f (stPostInstanceDefs (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostInstanceDefs = x}}
+
+stConcreteNames :: Lens' TCState ConcreteNames
+stConcreteNames f s =
+  f (stPostConcreteNames (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostConcreteNames = x}}
+
+stUsedNames :: Lens' TCState (Map RawName (DList RawName))
+stUsedNames f s =
+  f (stPostUsedNames (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostUsedNames = x}}
+
+stShadowingNames :: Lens' TCState (Map Name (DList RawName))
+stShadowingNames f s =
+  f (stPostShadowingNames (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostShadowingNames = x}}
+
+stStatistics :: Lens' TCState Statistics
+stStatistics f s =
+  f (stPostStatistics (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostStatistics = x}}
+
+stTCWarnings :: Lens' TCState [TCWarning]
+stTCWarnings f s =
+  f (stPostTCWarnings (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostTCWarnings = x}}
+
+stMutualBlocks :: Lens' TCState (Map MutualId MutualBlock)
+stMutualBlocks f s =
+  f (stPostMutualBlocks (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostMutualBlocks = x}}
+
+stLocalBuiltins :: Lens' TCState (BuiltinThings PrimFun)
+stLocalBuiltins f s =
+  f (stPostLocalBuiltins (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostLocalBuiltins = x}}
+
+stFreshMetaId :: Lens' TCState MetaId
+stFreshMetaId f s =
+  f (stPostFreshMetaId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshMetaId = x}}
+
+stFreshMutualId :: Lens' TCState MutualId
+stFreshMutualId f s =
+  f (stPostFreshMutualId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshMutualId = x}}
+
+stFreshProblemId :: Lens' TCState ProblemId
+stFreshProblemId f s =
+  f (stPostFreshProblemId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshProblemId = x}}
+
+stFreshCheckpointId :: Lens' TCState CheckpointId
+stFreshCheckpointId f s =
+  f (stPostFreshCheckpointId (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshCheckpointId = x}}
+
+stFreshInt :: Lens' TCState Int
+stFreshInt f s =
+  f (stPostFreshInt (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostFreshInt = x}}
+
+-- use @areWeCaching@ from the Caching module instead.
+stAreWeCaching :: Lens' TCState Bool
+stAreWeCaching f s =
+  f (stPostAreWeCaching (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostAreWeCaching = x}}
+
+stPostponeInstanceSearch :: Lens' TCState Bool
+stPostponeInstanceSearch f s =
+  f (stPostPostponeInstanceSearch (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostPostponeInstanceSearch = x}}
+
+stConsideringInstance :: Lens' TCState Bool
+stConsideringInstance f s =
+  f (stPostConsideringInstance (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostConsideringInstance = x}}
+
+stInstantiateBlocking :: Lens' TCState Bool
+stInstantiateBlocking f s =
+  f (stPostInstantiateBlocking (stPostScopeState s)) <&>
+  \x -> s {stPostScopeState = (stPostScopeState s) {stPostInstantiateBlocking = x}}
+
+stBuiltinThings :: TCState -> BuiltinThings PrimFun
+stBuiltinThings s = Map.unionWith unionBuiltin (s ^. stLocalBuiltins) (s ^. stImportedBuiltins)
+
+-- | Union two 'Builtin's.  Only defined for 'BuiltinRewriteRelations'.
+unionBuiltin :: Builtin a -> Builtin a -> Builtin a
+unionBuiltin = curry $ \case
+  (BuiltinRewriteRelations xs, BuiltinRewriteRelations ys) -> BuiltinRewriteRelations $ xs <> ys
+  _ -> __IMPOSSIBLE__
+
+
+-- * Fresh things
+------------------------------------------------------------------------
+
+class Enum i => HasFresh i where
+    freshLens :: Lens' TCState i
+    nextFresh' :: i -> i
+    nextFresh' = succ
+
+{-# INLINE nextFresh #-}
+nextFresh :: HasFresh i => TCState -> (i, TCState)
+nextFresh s =
+  let !c = s ^. freshLens
+      !next = set freshLens (nextFresh' c) s
+  in (c, next)
+
+class Monad m => MonadFresh i m where
+  fresh :: m i
+
+  default fresh :: (MonadTrans t, MonadFresh i n, t n ~ m) => m i
+  fresh = lift fresh
+
+instance MonadFresh i m => MonadFresh i (ReaderT r m)
+instance MonadFresh i m => MonadFresh i (StateT s m)
+instance MonadFresh i m => MonadFresh i (ListT m)
+instance MonadFresh i m => MonadFresh i (IdentityT m)
+
+instance HasFresh i => MonadFresh i TCM where
+  fresh = do
+        !s <- getTC
+        let (!c , !s') = nextFresh s
+        putTC s'
+        return c
+  {-# INLINE fresh #-}
+
+instance HasFresh MetaId where
+  freshLens = stFreshMetaId
+
+instance HasFresh MutualId where
+  freshLens = stFreshMutualId
+
+instance HasFresh InteractionId where
+  freshLens = stFreshInteractionId
+
+instance HasFresh NameId where
+  freshLens = stFreshNameId
+  -- nextFresh increments the current fresh name by 2 so @NameId@s used
+  -- before caching starts do not overlap with the ones used after.
+  nextFresh' = succ . succ
+
+instance HasFresh OpaqueId where
+  freshLens = stFreshOpaqueId
+
+instance HasFresh Int where
+  freshLens = stFreshInt
+
+instance HasFresh ProblemId where
+  freshLens = stFreshProblemId
+
+newtype CheckpointId = CheckpointId Int
+  deriving (Eq, Ord, Enum, Real, Integral, Num, NFData)
+
+instance Show CheckpointId where
+  show (CheckpointId n) = show n
+
+instance Pretty CheckpointId where
+  pretty (CheckpointId n) = pretty n
+
+instance HasFresh CheckpointId where
+  freshLens = stFreshCheckpointId
+
+freshName :: MonadFresh NameId m => Range -> String -> m Name
+freshName r s = do
+  i <- fresh
+  return $ mkName r i s
+
+freshNoName :: MonadFresh NameId m => Range -> m Name
+freshNoName r =
+    do  i <- fresh
+        return $ makeName i (C.NoName noRange i) r noFixity' False
+
+freshNoName_ :: MonadFresh NameId m => m Name
+freshNoName_ = freshNoName noRange
+
+freshRecordName :: MonadFresh NameId m => m Name
+freshRecordName = do
+  i <- fresh
+  return $ makeName i (C.setNotInScope $ C.simpleName "r") noRange noFixity' True
+
+-- | Create a fresh name from @a@.
+class FreshName a where
+  freshName_ :: MonadFresh NameId m => a -> m Name
+
+instance FreshName (Range, String) where
+  freshName_ = uncurry freshName
+
+instance FreshName String where
+  freshName_ = freshName noRange
+
+instance FreshName Range where
+  freshName_ = freshNoName
+
+instance FreshName () where
+  freshName_ () = freshNoName_
+
+---------------------------------------------------------------------------
+-- ** Managing file names
+---------------------------------------------------------------------------
+
+-- | Maps top-level module names to the corresponding source file
+-- names.
+
+type ModuleToSource = Map TopLevelModuleName AbsolutePath
+
+---------------------------------------------------------------------------
+-- ** Associating concrete names to an abstract name
+---------------------------------------------------------------------------
+
+-- | A monad that has read and write access to the stConcreteNames
+--   part of the TCState. Basically, this is a synonym for `MonadState
+--   ConcreteNames m` (which cannot be used directly because of the
+--   limitations of Haskell's typeclass system).
+class Monad m => MonadStConcreteNames m where
+  runStConcreteNames :: StateT ConcreteNames m a -> m a
+
+  useConcreteNames :: m ConcreteNames
+  useConcreteNames = runStConcreteNames get
+
+  modifyConcreteNames :: (ConcreteNames -> ConcreteNames) -> m ()
+  modifyConcreteNames = runStConcreteNames . modify
+
+instance MonadStConcreteNames TCM where
+  runStConcreteNames m = stateTCLensM stConcreteNames $ runStateT m
+
+instance MonadStConcreteNames m => MonadStConcreteNames (IdentityT m) where
+  runStConcreteNames m = IdentityT $ runStConcreteNames $ StateT $ runIdentityT . runStateT m
+
+instance MonadStConcreteNames m => MonadStConcreteNames (ReaderT r m) where
+  runStConcreteNames m = ReaderT $ runStConcreteNames . StateT . flip (runReaderT . runStateT m)
+
+instance MonadStConcreteNames m => MonadStConcreteNames (StateT s m) where
+  runStConcreteNames m = StateT $ \s -> runStConcreteNames $ StateT $ \ns -> do
+    ((x,ns'),s') <- runStateT (runStateT m ns) s
+    return ((x,s'),ns')
+
+---------------------------------------------------------------------------
+-- ** Interface
+---------------------------------------------------------------------------
+
+
+-- | Distinguishes between type-checked and scope-checked interfaces
+--   when stored in the map of `VisitedModules`.
+data ModuleCheckMode
+  = ModuleScopeChecked
+  | ModuleTypeChecked
+  deriving (Eq, Ord, Bounded, Enum, Show, Generic)
+
+
+data ModuleInfo = ModuleInfo
+  { miInterface  :: Interface
+  , miWarnings   :: [TCWarning]
+    -- ^ Warnings were encountered when the module was type checked.
+    --   These might include warnings not stored in the interface itself,
+    --   specifically unsolved interaction metas.
+    --   See "Agda.Interaction.Imports"
+  , miPrimitive  :: Bool
+    -- ^ 'True' if the module is a primitive module, which should always
+    -- be importable.
+  , miMode       :: ModuleCheckMode
+    -- ^ The `ModuleCheckMode` used to create the `Interface`
+  }
+  deriving Generic
+
+type VisitedModules = Map TopLevelModuleName ModuleInfo
+type DecodedModules = Map TopLevelModuleName ModuleInfo
+
+data ForeignCode = ForeignCode Range String
+  deriving (Show, Generic)
+
+-- | Foreign code fragments are stored in reversed order to support efficient appending:
+--   head points to the latest pragma in module.
+newtype ForeignCodeStack = ForeignCodeStack
+  { getForeignCodeStack :: [ForeignCode]
+  } deriving (Show, Generic, NFData)
+
+data Interface = Interface
+  { iSourceHash      :: Hash
+    -- ^ Hash of the source code.
+  , iSource          :: TL.Text
+    -- ^ The source code. The source code is stored so that the HTML
+    -- and LaTeX backends can generate their output without having to
+    -- re-read the (possibly out of date) source code.
+  , iFileType        :: FileType
+    -- ^ Source file type, determined from the file extension
+  , iImportedModules :: [(TopLevelModuleName, Hash)]
+    -- ^ Imported modules and their hashes.
+  , iModuleName      :: ModuleName
+    -- ^ Module name of this interface.
+  , iTopLevelModuleName :: TopLevelModuleName
+    -- ^ The module's top-level module name.
+  , iScope           :: Map ModuleName Scope
+    -- ^ Scope defined by this module.
+    --
+    --   Andreas, AIM XX: Too avoid duplicate serialization, this field is
+    --   not serialized, so if you deserialize an interface, @iScope@
+    --   will be empty.
+    --   But 'constructIScope' constructs 'iScope' from 'iInsideScope'.
+  , iInsideScope     :: ScopeInfo
+    -- ^ Scope after we loaded this interface.
+    --   Used in 'Agda.Interaction.BasicOps.AtTopLevel'
+    --   and     'Agda.Interaction.CommandLine.interactionLoop'.
+  , iSignature       :: Signature
+  , iMetaBindings    :: RemoteMetaStore
+    -- ^ Instantiations for meta-variables that come from this module.
+  , iDisplayForms    :: DisplayForms
+    -- ^ Display forms added for imported identifiers.
+  , iUserWarnings    :: Map A.QName Text
+    -- ^ User warnings for imported identifiers
+  , iImportWarning   :: Maybe Text
+    -- ^ Whether this module should raise a warning when imported
+  , iBuiltin         :: BuiltinThings (PrimitiveId, QName)
+  , iForeignCode     :: Map BackendName ForeignCodeStack
+  , iHighlighting    :: HighlightingInfo
+  , iDefaultPragmaOptions :: [OptionsPragma]
+    -- ^ Pragma options set in library files.
+  , iFilePragmaOptions    :: [OptionsPragma]
+    -- ^ Pragma options set in the file.
+  , iOptionsUsed     :: PragmaOptions
+    -- ^ Options/features used when checking the file (can be different
+    --   from options set directly in the file).
+  , iPatternSyns     :: A.PatternSynDefns
+  , iWarnings        :: [TCWarning]
+  , iPartialDefs     :: Set QName
+  , iOpaqueBlocks    :: Map OpaqueId OpaqueBlock
+  , iOpaqueNames     :: Map QName OpaqueId
+  }
+  deriving (Show, Generic)
+
+instance Pretty Interface where
+  pretty (Interface
+            sourceH source fileT importedM moduleN topModN scope insideS
+            signature metas display userwarn importwarn builtin
+            foreignCode highlighting libPragmaO filePragmaO oUsed
+            patternS warnings partialdefs oblocks onames) =
+
+    hang "Interface" 2 $ vcat
+      [ "source hash:"         <+> (pretty . show) sourceH
+      , "source:"              $$  nest 2 (text $ TL.unpack source)
+      , "file type:"           <+> (pretty . show) fileT
+      , "imported modules:"    <+> (pretty . show) importedM
+      , "module name:"         <+> pretty moduleN
+      , "top-level module name:" <+> pretty topModN
+      , "scope:"               <+> (pretty . show) scope
+      , "inside scope:"        <+> (pretty . show) insideS
+      , "signature:"           <+> (pretty . show) signature
+      , "meta-variables:"      <+> (pretty . show) metas
+      , "display:"             <+> (pretty . show) display
+      , "user warnings:"       <+> (pretty . show) userwarn
+      , "import warning:"      <+> (pretty . show) importwarn
+      , "builtin:"             <+> (pretty . show) builtin
+      , "Foreign code:"        <+> (pretty . show) foreignCode
+      , "highlighting:"        <+> (pretty . show) highlighting
+      , "library pragma options:" <+> (pretty . show) libPragmaO
+      , "file pragma options:" <+> (pretty . show) filePragmaO
+      , "options used:"        <+> (pretty . show) oUsed
+      , "pattern syns:"        <+> (pretty . show) patternS
+      , "warnings:"            <+> (pretty . show) warnings
+      , "partial definitions:" <+> (pretty . show) partialdefs
+      , "opaque blocks:"       <+> pretty oblocks
+      , "opaque names"         <+> pretty onames
+      ]
+
+-- | Combines the source hash and the (full) hashes of the imported modules.
+iFullHash :: Interface -> Hash
+iFullHash i = combineHashes $ iSourceHash i : List.map snd (iImportedModules i)
+
+-- | A lens for the 'iSignature' field of the 'Interface' type.
+
+intSignature :: Lens' Interface Signature
+intSignature f i = f (iSignature i) <&> \s -> i { iSignature = s }
+
+---------------------------------------------------------------------------
+-- ** Closure
+---------------------------------------------------------------------------
+
+data Closure a = Closure
+  { clSignature        :: Signature
+  , clEnv              :: TCEnv
+  , clScope            :: ScopeInfo
+  , clModuleCheckpoints :: Map ModuleName CheckpointId
+  , clValue            :: a
+  }
+    deriving (Functor, Foldable, Generic)
+
+instance Show a => Show (Closure a) where
+  show cl = "Closure { clValue = " ++ show (clValue cl) ++ " }"
+
+instance HasRange a => HasRange (Closure a) where
+  getRange = getRange . clValue
+
+class LensClosure b a | b -> a where
+  lensClosure :: Lens' b (Closure a)
+
+instance LensClosure (Closure a) a where
+  lensClosure = id
+
+instance LensTCEnv (Closure a) where
+  lensTCEnv f cl = (f $! clEnv cl) <&> \ env -> cl { clEnv = env }
+
+{-# SPECIALIZE buildClosure :: a -> TCM (Closure a)  #-}
+buildClosure :: (MonadTCEnv m, ReadTCState m) => a -> m (Closure a)
+buildClosure x = do
+    env   <- askTC
+    sig   <- useR stSignature
+    scope <- useR stScope
+    cps   <- useR stModuleCheckpoints
+    return $ Closure sig env scope cps x
+
+---------------------------------------------------------------------------
+-- ** Constraints
+---------------------------------------------------------------------------
+
+type Constraints = [ProblemConstraint]
+
+data ProblemConstraint = PConstr
+  { constraintProblems  :: Set ProblemId
+  , constraintUnblocker :: Blocker
+  , theConstraint       :: Closure Constraint
+  }
+  deriving (Show, Generic)
+
+instance HasRange ProblemConstraint where
+  getRange = getRange . theConstraint
+
+-- | Why are we performing a modality check?
+data WhyCheckModality
+  = ConstructorType
+  -- ^ Because --without-K is enabled, so the types of data constructors
+  -- must be usable at the context's modality.
+  | IndexedClause
+  -- ^ Because --without-K is enabled, so the result type of clauses
+  -- must be usable at the context's modality.
+  | IndexedClauseArg Name Name
+  -- ^ Because --without-K is enabled, so any argument (second name)
+  -- which mentions a dotted argument (first name) must have a type
+  -- which is usable at the context's modality.
+  | GeneratedClause
+  -- ^ Because we double-check the --cubical-compatible clauses. This is
+  -- an internal error!
+  deriving (Show, Generic)
+
+data Constraint
+  = ValueCmp Comparison CompareAs Term Term
+  | ValueCmpOnFace Comparison Term Type Term Term
+  | ElimCmp [Polarity] [IsForced] Type Term [Elim] [Elim]
+  | SortCmp Comparison Sort Sort
+  | LevelCmp Comparison Level Level
+--  | ShortCut MetaId Term Type
+--    -- ^ A delayed instantiation.  Replaces @ValueCmp@ in 'postponeTypeCheckingProblem'.
+  | HasBiggerSort Sort
+  | HasPTSRule (Dom Type) (Abs Sort)
+  | CheckDataSort QName Sort
+    -- ^ Check that the sort 'Sort' of data type 'QName' admits data/record types.
+    -- E.g., sorts @IUniv@, @SizeUniv@ etc. do not admit such constructions.
+    -- See 'Agda.TypeChecking.Rules.Data.checkDataSort'.
+  | CheckMetaInst MetaId
+  | CheckType Type
+  | UnBlock MetaId
+    -- ^ Meta created for a term blocked by a postponed type checking problem or unsolved
+    --   constraints. The 'MetaInstantiation' for the meta (when unsolved) is either 'BlockedConst'
+    --   or 'PostponedTypeCheckingProblem'.
+  | IsEmpty Range Type
+    -- ^ The range is the one of the absurd pattern.
+  | CheckSizeLtSat Term
+    -- ^ Check that the 'Term' is either not a SIZELT or a non-empty SIZELT.
+  | FindInstance MetaId (Maybe [Candidate])
+    -- ^ the first argument is the instance argument and the second one is the list of candidates
+    --   (or Nothing if we haven’t determined the list of candidates yet)
+  | CheckFunDef A.DefInfo QName [A.Clause] TCErr
+    -- ^ Last argument is the error causing us to postpone.
+  | UnquoteTactic Term Term Type   -- ^ First argument is computation and the others are hole and goal type
+  | CheckLockedVars Term Type (Arg Term) Type     -- ^ @CheckLockedVars t ty lk lk_ty@ with @t : ty@, @lk : lk_ty@ and @t lk@ well-typed.
+  | UsableAtModality WhyCheckModality (Maybe Sort) Modality Term
+    -- ^ Is the term usable at the given modality?
+    -- This check should run if the @Sort@ is @Nothing@ or @isFibrant@.
+  deriving (Show, Generic)
+
+instance HasRange Constraint where
+  getRange (IsEmpty r t) = r
+  getRange _ = noRange
+{- no Range instances for Term, Type, Elm, Tele, Sort, Level, MetaId
+  getRange (ValueCmp cmp a u v) = getRange (a,u,v)
+  getRange (ElimCmp pol a v es es') = getRange (a,v,es,es')
+  getRange (TelCmp a b cmp tel tel') = getRange (a,b,tel,tel')
+  getRange (SortCmp cmp s s') = getRange (s,s')
+  getRange (LevelCmp cmp l l') = getRange (l,l')
+  getRange (UnBlock x) = getRange x
+  getRange (FindInstance x cands) = getRange x
+-}
+
+instance Free Constraint where
+  freeVars' c =
+    case c of
+      ValueCmp _ t u v      -> freeVars' (t, (u, v))
+      ValueCmpOnFace _ p t u v -> freeVars' (p, (t, (u, v)))
+      ElimCmp _ _ t u es es'  -> freeVars' ((t, u), (es, es'))
+      SortCmp _ s s'        -> freeVars' (s, s')
+      LevelCmp _ l l'       -> freeVars' (l, l')
+      UnBlock _             -> mempty
+      IsEmpty _ t           -> freeVars' t
+      CheckSizeLtSat u      -> freeVars' u
+      FindInstance _ cs     -> freeVars' cs
+      CheckFunDef{}         -> mempty
+      HasBiggerSort s       -> freeVars' s
+      HasPTSRule a s        -> freeVars' (a , s)
+      CheckLockedVars a b c d -> freeVars' ((a,b),(c,d))
+      UnquoteTactic t h g   -> freeVars' (t, (h, g))
+      CheckDataSort _ s     -> freeVars' s
+      CheckMetaInst m       -> mempty
+      CheckType t           -> freeVars' t
+      UsableAtModality _ ms mod t -> freeVars' (ms, t)
+
+instance TermLike Constraint where
+  foldTerm f = \case
+      ValueCmp _ t u v       -> foldTerm f (t, u, v)
+      ValueCmpOnFace _ p t u v -> foldTerm f (p, t, u, v)
+      ElimCmp _ _ t u es es' -> foldTerm f (t, u, es, es')
+      LevelCmp _ l l'        -> foldTerm f (Level l, Level l')  -- Note wrapping as term, to ensure f gets to act on l and l'
+      IsEmpty _ t            -> foldTerm f t
+      CheckSizeLtSat u       -> foldTerm f u
+      UnquoteTactic t h g    -> foldTerm f (t, h, g)
+      SortCmp _ s1 s2        -> foldTerm f (Sort s1, Sort s2)   -- Same as LevelCmp case
+      UnBlock _              -> mempty
+      CheckLockedVars a b c d -> foldTerm f (a, b, c, d)
+      FindInstance _ _       -> mempty
+      CheckFunDef{}          -> mempty
+      HasBiggerSort s        -> foldTerm f s
+      HasPTSRule a s         -> foldTerm f (a, Sort <$> s)
+      CheckDataSort _ s      -> foldTerm f s
+      CheckMetaInst m        -> mempty
+      CheckType t            -> foldTerm f t
+      UsableAtModality _ ms m t   -> foldTerm f (Sort <$> ms, t)
+
+  traverseTermM f c = __IMPOSSIBLE__ -- Not yet implemented
+
+instance AllMetas Constraint
+
+data Comparison = CmpEq | CmpLeq
+  deriving (Eq, Show, Generic)
+
+instance Pretty Comparison where
+  pretty CmpEq  = "="
+  pretty CmpLeq = "=<"
+
+-- | An extension of 'Comparison' to @>=@.
+data CompareDirection = DirEq | DirLeq | DirGeq
+  deriving (Eq, Show)
+
+instance Pretty CompareDirection where
+  pretty = text . \case
+    DirEq  -> "="
+    DirLeq -> "=<"
+    DirGeq -> ">="
+
+-- | Embed 'Comparison' into 'CompareDirection'.
+fromCmp :: Comparison -> CompareDirection
+fromCmp CmpEq  = DirEq
+fromCmp CmpLeq = DirLeq
+
+-- | Flip the direction of comparison.
+flipCmp :: CompareDirection -> CompareDirection
+flipCmp DirEq  = DirEq
+flipCmp DirLeq = DirGeq
+flipCmp DirGeq = DirLeq
+
+-- | Turn a 'Comparison' function into a 'CompareDirection' function.
+--
+--   Property: @dirToCmp f (fromCmp cmp) = f cmp@
+dirToCmp :: (Comparison -> a -> a -> c) -> CompareDirection -> a -> a -> c
+dirToCmp cont DirEq  = cont CmpEq
+dirToCmp cont DirLeq = cont CmpLeq
+dirToCmp cont DirGeq = flip $ cont CmpLeq
+
+-- | We can either compare two terms at a given type, or compare two
+--   types without knowing (or caring about) their sorts.
+data CompareAs
+  = AsTermsOf Type -- ^ @Type@ should not be @Size@.
+                   --   But currently, we do not rely on this invariant.
+  | AsSizes        -- ^ Replaces @AsTermsOf Size@.
+  | AsTypes
+  deriving (Show, Generic)
+
+instance Free CompareAs where
+  freeVars' (AsTermsOf a) = freeVars' a
+  freeVars' AsSizes       = mempty
+  freeVars' AsTypes       = mempty
+
+instance TermLike CompareAs where
+  foldTerm f (AsTermsOf a) = foldTerm f a
+  foldTerm f AsSizes       = mempty
+  foldTerm f AsTypes       = mempty
+
+  traverseTermM f = \case
+    AsTermsOf a -> AsTermsOf <$> traverseTermM f a
+    AsSizes     -> return AsSizes
+    AsTypes     -> return AsTypes
+
+instance AllMetas CompareAs
+
+instance Pretty CompareAs where
+  pretty (AsTermsOf a) = ":" <+> pretty a
+  pretty AsSizes       = ":" <+> text "Size"
+  pretty AsTypes       = empty
+
+---------------------------------------------------------------------------
+-- * Open things
+---------------------------------------------------------------------------
+
+-- | A thing tagged with the context it came from. Also keeps the substitution from previous
+--   checkpoints. This lets us handle the case when an open thing was created in a context that we
+--   have since exited. Remember which module it's from to make sure we don't get confused by
+--   checkpoints from other files.
+data Open a = OpenThing { openThingCheckpoint    :: CheckpointId
+                        , openThingCheckpointMap :: Map CheckpointId Substitution
+                        , openThingModule        :: ModuleNameHash
+                        , openThing              :: a }
+    deriving (Show, Functor, Foldable, Traversable, Generic)
+
+instance Decoration Open where
+  traverseF f (OpenThing cp env m x) = OpenThing cp env m <$> f x
+
+instance Pretty a => Pretty (Open a) where
+  prettyPrec p (OpenThing cp env _ x) = mparens (p > 9) $
+    "OpenThing" <+> pretty cp <+> pretty (Map.toList env) <?> prettyPrec 10 x
+
+---------------------------------------------------------------------------
+-- * Judgements
+--
+-- Used exclusively for typing of meta variables.
+---------------------------------------------------------------------------
+
+-- | Parametrized since it is used without MetaId when creating a new meta.
+data Judgement a
+  = HasType
+    { jMetaId     :: a
+    , jComparison :: Comparison -- ^ are we checking (@CmpLeq@) or inferring (@CmpEq@) the type?
+    , jMetaType   :: Type
+    }
+  | IsSort
+    { jMetaId   :: a
+    , jMetaType :: Type -- Andreas, 2011-04-26: type needed for higher-order sort metas
+    }
+  deriving (Show, Generic)
+
+instance Pretty a => Pretty (Judgement a) where
+    pretty (HasType a cmp t) = hsep [ pretty a, ":"    , pretty t ]
+    pretty (IsSort  a t)     = hsep [ pretty a, ":sort", pretty t ]
+
+-----------------------------------------------------------------------------
+-- ** Generalizable variables
+-----------------------------------------------------------------------------
+
+data DoGeneralize
+  = YesGeneralizeVar  -- ^ Generalize because it is a generalizable variable.
+  | YesGeneralizeMeta -- ^ Generalize because it is a metavariable and
+                      --   we're currently checking the type of a generalizable variable
+                      --   (this should get the default modality).
+  | NoGeneralize      -- ^ Don't generalize.
+  deriving (Eq, Ord, Show, Generic)
+
+-- | The value of a generalizable variable. This is created to be a
+--   generalizable meta before checking the type to be generalized.
+data GeneralizedValue = GeneralizedValue
+  { genvalCheckpoint :: CheckpointId
+  , genvalTerm       :: Term
+  , genvalType       :: Type
+  } deriving (Show, Generic)
+
+---------------------------------------------------------------------------
+-- ** Meta variables
+---------------------------------------------------------------------------
+
+-- | Information about local meta-variables.
+
+data MetaVariable =
+        MetaVar { mvInfo          :: MetaInfo
+                , mvPriority      :: MetaPriority -- ^ some metavariables are more eager to be instantiated
+                , mvPermutation   :: Permutation
+                  -- ^ a metavariable doesn't have to depend on all variables
+                  --   in the context, this "permutation" will throw away the
+                  --   ones it does not depend on
+                , mvJudgement     :: Judgement MetaId
+                , mvInstantiation :: MetaInstantiation
+                , mvListeners     :: Set Listener -- ^ meta variables scheduled for eta-expansion but blocked by this one
+                , mvFrozen        :: Frozen -- ^ are we past the point where we can instantiate this meta variable?
+                , mvTwin          :: Maybe MetaId
+                  -- ^ @Just m@ means that this meta-variable will be
+                  -- equated to @m@ when the latter is unblocked. See
+                  -- 'Agda.TypeChecking.MetaVars.blockTermOnProblem'.
+                }
+  deriving Generic
+
+data Listener = EtaExpand MetaId
+              | CheckConstraint Nat ProblemConstraint
+  deriving Generic
+
+instance Eq Listener where
+  EtaExpand       x   == EtaExpand       y   = x == y
+  CheckConstraint x _ == CheckConstraint y _ = x == y
+  _ == _ = False
+
+instance Ord Listener where
+  EtaExpand       x   `compare` EtaExpand       y   = x `compare` y
+  CheckConstraint x _ `compare` CheckConstraint y _ = x `compare` y
+  EtaExpand{} `compare` CheckConstraint{} = LT
+  CheckConstraint{} `compare` EtaExpand{} = GT
+
+-- | Frozen meta variable cannot be instantiated by unification.
+--   This serves to prevent the completion of a definition by its use
+--   outside of the current block.
+--   (See issues 118, 288, 399).
+data Frozen
+  = Frozen        -- ^ Do not instantiate.
+  | Instantiable
+    deriving (Eq, Show, Generic)
+
+data MetaInstantiation
+        = InstV Instantiation -- ^ solved
+        | Open                -- ^ unsolved
+        | OpenInstance        -- ^ open, to be instantiated by instance search
+        | BlockedConst Term   -- ^ solution blocked by unsolved constraints
+        | PostponedTypeCheckingProblem (Closure TypeCheckingProblem)
+  deriving Generic
+
+-- | Meta-variable instantiations.
+
+data Instantiation = Instantiation
+  { instTel :: [Arg String]
+    -- ^ The solution is abstracted over these free variables.
+  , instBody :: Term
+    -- ^ The body of the solution.
+  }
+  deriving (Show, Generic)
+
+-- | Information about remote meta-variables.
+--
+-- Remote meta-variables are meta-variables originating in other
+-- modules. These meta-variables are always instantiated. We do not
+-- retain all the information about a local meta-variable when
+-- creating an interface:
+--
+-- * The 'mvPriority' field is not needed, because the meta-variable
+--   cannot be instantiated.
+-- * The 'mvFrozen' field is not needed, because there is no point in
+--   freezing instantiated meta-variables.
+-- * The 'mvListeners' field is not needed, because no meta-variable
+--   should be listening to this one.
+-- * The 'mvTwin' field is not needed, because the meta-variable has
+--   already been instantiated.
+-- * The 'mvPermutation' is currently removed, but could be retained
+--   if it turns out to be useful for something.
+-- * The only part of the 'mvInfo' field that is kept is the
+--   'miModality' field. The 'miMetaOccursCheck' and 'miGeneralizable'
+--   fields are omitted, because the meta-variable has already been
+--   instantiated. The 'Range' that is part of the 'miClosRange' field
+--   and the 'miNameSuggestion' field are omitted because instantiated
+--   meta-variables are typically not presented to users. Finally the
+--   'Closure' part of the 'miClosRange' field is omitted because it
+--   can be large (at least if we ignore potential sharing).
+
+data RemoteMetaVariable = RemoteMetaVariable
+  { rmvInstantiation :: Instantiation
+  , rmvModality      :: Modality
+  , rmvJudgement     :: Judgement MetaId
+  }
+  deriving (Show, Generic)
+
+-- | Solving a 'CheckArgs' constraint may or may not check the target type. If
+--   it did, it returns a handle to any unsolved constraints.
+data CheckedTarget = CheckedTarget (Maybe ProblemId)
+                   | NotCheckedTarget
+
+data PrincipalArgTypeMetas = PrincipalArgTypeMetas
+  { patmMetas     :: Args -- ^ metas created for hidden and instance arguments
+                          --   in the principal argument's type
+  , patmRemainder :: Type -- ^ principal argument's type, stripped of hidden and
+                          --   instance arguments
+  }
+  deriving Generic
+
+data TypeCheckingProblem
+  = CheckExpr Comparison A.Expr Type
+  | CheckArgs Comparison ExpandHidden Range [NamedArg A.Expr] Type Type (ArgsCheckState CheckedTarget -> TCM Term)
+  | CheckProjAppToKnownPrincipalArg Comparison A.Expr ProjOrigin (List1 QName) A.Args Type Int Term Type PrincipalArgTypeMetas
+  | CheckLambda Comparison (Arg (List1 (WithHiding Name), Maybe Type)) A.Expr Type
+    -- ^ @(λ (xs : t₀) → e) : t@
+    --   This is not an instance of 'CheckExpr' as the domain type
+    --   has already been checked.
+    --   For example, when checking
+    --     @(λ (x y : Fin _) → e) : (x : Fin n) → ?@
+    --   we want to postpone @(λ (y : Fin n) → e) : ?@ where @Fin n@
+    --   is a 'Type' rather than an 'A.Expr'.
+  | DoQuoteTerm Comparison Term Type -- ^ Quote the given term and check type against `Term`
+  deriving Generic
+
+instance Pretty MetaInstantiation where
+  pretty = \case
+    Open                                     -> "Open"
+    OpenInstance                             -> "OpenInstance"
+    PostponedTypeCheckingProblem{}           -> "PostponedTypeCheckingProblem (...)"
+    BlockedConst t                           -> hsep [ "BlockedConst", parens (pretty t) ]
+    InstV Instantiation{ instTel, instBody } -> hsep [ "InstV", pretty instTel, parens (pretty instBody) ]
+
+-- | Meta variable priority:
+--   When we have an equation between meta-variables, which one
+--   should be instantiated?
+--
+--   Higher value means higher priority to be instantiated.
+newtype MetaPriority = MetaPriority Int
+    deriving (Eq, Ord, Show, NFData)
+
+data RunMetaOccursCheck
+  = RunMetaOccursCheck
+  | DontRunMetaOccursCheck
+  deriving (Eq, Ord, Show, Generic)
+
+-- | @MetaInfo@ is cloned from one meta to the next during pruning.
+data MetaInfo = MetaInfo
+  { miClosRange       :: Closure Range -- TODO: Not so nice. But we want both to have the environment of the meta (Closure) and its range.
+  , miModality        :: Modality           -- ^ Instantiable with irrelevant/erased solution?
+  , miMetaOccursCheck :: RunMetaOccursCheck -- ^ Run the extended occurs check that goes in definitions?
+  , miNameSuggestion  :: MetaNameSuggestion
+    -- ^ Used for printing.
+    --   @Just x@ if meta-variable comes from omitted argument with name @x@.
+  , miGeneralizable   :: Arg DoGeneralize
+    -- ^ Should this meta be generalized if unsolved? If so, at what ArgInfo?
+  }
+  deriving Generic
+
+instance LensModality MetaInfo where
+  getModality = miModality
+  setModality mod mi = mi { miModality = mod }
+  mapModality f mi = mi { miModality = f $ miModality mi }
+
+instance LensQuantity MetaInfo where
+  getQuantity   = getQuantity . getModality
+  mapQuantity f = mapModality (mapQuantity f)
+
+instance LensRelevance MetaInfo where
+  mapRelevance f = mapModality (mapRelevance f)
+
+-- | Name suggestion for meta variable.  Empty string means no suggestion.
+type MetaNameSuggestion = String
+
+-- | For printing, we couple a meta with its name suggestion.
+data NamedMeta = NamedMeta
+  { nmSuggestion :: MetaNameSuggestion
+  , nmid         :: MetaId
+  }
+
+-- | Append an 'ArgName' to a 'MetaNameSuggestion', for computing the
+-- name suggestions of eta-expansion metas. If the 'MetaNameSuggestion'
+-- is empty or an underscore, the field name is taken as the suggestion.
+suffixNameSuggestion :: MetaNameSuggestion -> ArgName -> MetaNameSuggestion
+suffixNameSuggestion "_"    field = field
+suffixNameSuggestion ""     field = field
+suffixNameSuggestion record field = record ++ "." ++ field
+
+instance Pretty NamedMeta where
+  pretty (NamedMeta "" x) = pretty x
+  pretty (NamedMeta "_" x) = pretty x
+  pretty (NamedMeta s  x) = text $ "_" ++ s ++ prettyShow x
+
+-- | Used for meta-variables from the current module.
+
+type LocalMetaStore = Map MetaId MetaVariable
+
+{-# SPECIALIZE Map.insert :: MetaId -> v -> Map MetaId v -> Map MetaId v #-}
+{-# SPECIALIZE Map.lookup :: MetaId -> Map MetaId v -> Maybe v #-}
+
+-- | Used for meta-variables from other modules (and in 'Interface's).
+
+type RemoteMetaStore = HashMap MetaId RemoteMetaVariable
+
+instance HasRange MetaInfo where
+  getRange = clValue . miClosRange
+
+instance HasRange MetaVariable where
+    getRange m = getRange $ getMetaInfo m
+
+instance SetRange MetaInfo where
+  setRange r m = m { miClosRange = (miClosRange m) { clValue = r }}
+
+instance SetRange MetaVariable where
+  setRange r m = m { mvInfo = setRange r (mvInfo m) }
+
+instance LensModality MetaVariable where
+  getModality = getModality . mvInfo
+  setModality mod mv = mv { mvInfo = setModality mod $ mvInfo mv }
+  mapModality f mv = mv { mvInfo = mapModality f $ mvInfo mv }
+
+instance LensRelevance MetaVariable where
+  setRelevance mod mv = mv { mvInfo = setRelevance mod $ mvInfo mv }
+
+instance LensQuantity MetaVariable where
+  getQuantity   = getQuantity . getModality
+  mapQuantity f = mapModality (mapQuantity f)
+
+instance LensModality RemoteMetaVariable where
+  getModality      = rmvModality
+  mapModality f mv = mv { rmvModality = f $ rmvModality mv }
+
+instance LensRelevance RemoteMetaVariable where
+  mapRelevance f = mapModality (mapRelevance f)
+
+instance LensQuantity RemoteMetaVariable where
+  mapQuantity f = mapModality (mapQuantity f)
+
+normalMetaPriority :: MetaPriority
+normalMetaPriority = MetaPriority 0
+
+lowMetaPriority :: MetaPriority
+lowMetaPriority = MetaPriority (-10)
+
+highMetaPriority :: MetaPriority
+highMetaPriority = MetaPriority 10
+
+getMetaInfo :: MetaVariable -> Closure Range
+getMetaInfo = miClosRange . mvInfo
+
+getMetaScope :: MetaVariable -> ScopeInfo
+getMetaScope m = clScope $ getMetaInfo m
+
+getMetaEnv :: MetaVariable -> TCEnv
+getMetaEnv m = clEnv $ getMetaInfo m
+
+getMetaSig :: MetaVariable -> Signature
+getMetaSig m = clSignature $ getMetaInfo m
+
+-- Lenses
+
+metaFrozen :: Lens' MetaVariable Frozen
+metaFrozen f mv = f (mvFrozen mv) <&> \ x -> mv { mvFrozen = x }
+
+_mvInfo :: Lens' MetaVariable MetaInfo
+_mvInfo f mv = (f $! mvInfo mv) <&> \ mi -> mv { mvInfo = mi }
+
+-- Lenses onto Closure Range
+
+instance LensClosure MetaInfo Range where
+  lensClosure f mi = (f $! miClosRange mi) <&> \ cl -> mi { miClosRange = cl }
+
+instance LensClosure MetaVariable Range where
+  lensClosure = _mvInfo . lensClosure
+
+-- Lenses onto IsAbstract
+
+instance LensIsAbstract TCEnv where
+  lensIsAbstract f env =
+     -- Andreas, 2019-08-19
+     -- Using $! to prevent space leaks like #1829.
+     -- This can crash when trying to get IsAbstract from IgnoreAbstractMode.
+    (f $! fromMaybe __IMPOSSIBLE__ (aModeToDef $ envAbstractMode env))
+    <&> \ a -> env { envAbstractMode = aDefToMode a }
+
+instance LensIsAbstract (Closure a) where
+  lensIsAbstract = lensTCEnv . lensIsAbstract
+
+instance LensIsAbstract MetaInfo where
+  lensIsAbstract = lensClosure . lensIsAbstract
+
+instance LensIsOpaque TCEnv where
+  lensIsOpaque f env =
+    (f $! case envCurrentOpaqueId env of { Just x -> OpaqueDef x ; Nothing -> TransparentDef })
+    <&> \case { OpaqueDef x    -> env { envCurrentOpaqueId = Just x }
+              ; TransparentDef -> env { envCurrentOpaqueId = Nothing }
+              }
+
+---------------------------------------------------------------------------
+-- ** Interaction meta variables
+---------------------------------------------------------------------------
+
+-- | Interaction points are created by the scope checker who sets the range.
+--   The meta variable is created by the type checker and then hooked up to the
+--   interaction point.
+data InteractionPoint = InteractionPoint
+  { ipRange    :: Range        -- ^ The position of the interaction point.
+  , ipMeta     :: Maybe MetaId -- ^ The meta variable, if any, holding the type etc.
+  , ipSolved   :: Bool         -- ^ Has this interaction point already been solved?
+  , ipClause   :: IPClause
+    -- ^ The clause of the interaction point (if any).
+    --   Used for case splitting.
+  , ipBoundary :: IPBoundary
+  }
+  deriving Generic
+
+instance Eq InteractionPoint where (==) = (==) `on` ipMeta
+
+instance HasTag InteractionPoint where
+  type Tag InteractionPoint = MetaId
+  tag = ipMeta
+
+-- | Data structure managing the interaction points.
+--
+--   We never remove interaction points from this map, only set their
+--   'ipSolved' to @True@.  (Issue #2368)
+type InteractionPoints = BiMap InteractionId InteractionPoint
+
+-- | Flag to indicate whether the meta is overapplied in the
+--   constraint.  A meta is overapplied if it has more arguments than
+--   the size of the telescope in its creation environment
+--   (as stored in MetaInfo).
+data Overapplied = Overapplied | NotOverapplied
+  deriving (Eq, Show, Generic)
+
+-- | Datatype representing a single boundary condition:
+--   x_0 = u_0, ... ,x_n = u_n ⊢ t = ?n es
+data IPFace' t = IPFace'
+  { faceEqns :: [(t, t)]
+  , faceRHS  :: t
+  }
+
+newtype IPBoundary' t = IPBoundary
+  { getBoundary :: Map (IntMap Bool) t
+  }
+  deriving (Show, Functor, Foldable, Traversable, Generic)
+
+type IPBoundary = IPBoundary' Term
+
+-- | Which clause is an interaction point located in?
+data IPClause = IPClause
+  { ipcQName    :: QName              -- ^ The name of the function.
+  , ipcClauseNo :: Int                -- ^ The number of the clause of this function.
+  , ipcType     :: Type               -- ^ The type of the function
+  , ipcWithSub  :: Maybe Substitution -- ^ Module parameter substitution
+  , ipcClause   :: A.SpineClause      -- ^ The original AST clause.
+  , ipcClosure  :: Closure ()         -- ^ Environment for rechecking the clause.
+  }
+  | IPNoClause -- ^ The interaction point is not in the rhs of a clause.
+  deriving (Generic)
+
+instance Eq IPClause where
+  IPNoClause           == IPNoClause             = True
+  IPClause x i _ _ _ _ == IPClause x' i' _ _ _ _ = x == x' && i == i'
+  _                    == _                      = False
+
+---------------------------------------------------------------------------
+-- ** Signature
+---------------------------------------------------------------------------
+
+data Signature = Sig
+      { _sigSections    :: Sections
+      , _sigDefinitions :: Definitions
+      , _sigRewriteRules:: RewriteRuleMap  -- ^ The rewrite rules defined in this file.
+      }
+  deriving (Show, Generic)
+
+sigSections :: Lens' Signature Sections
+sigSections f s =
+  f (_sigSections s) <&>
+  \x -> s {_sigSections = x}
+
+sigDefinitions :: Lens' Signature Definitions
+sigDefinitions f s =
+  f (_sigDefinitions s) <&>
+  \x -> s {_sigDefinitions = x}
+
+sigRewriteRules :: Lens' Signature RewriteRuleMap
+sigRewriteRules f s =
+  f (_sigRewriteRules s) <&>
+  \x -> s {_sigRewriteRules = x}
+
+type Sections    = Map ModuleName Section
+type Definitions = HashMap QName Definition
+type RewriteRuleMap = HashMap QName RewriteRules
+type DisplayForms = HashMap QName [LocalDisplayForm]
+
+-- 2023-21-30, András: see issue 6927
+#if __GLASGOW_HASKELL__ >= 900
+{-# SPECIALIZE HMap.insert :: QName -> v -> HashMap QName v -> HashMap QName v #-}
+#endif
+{-# SPECIALIZE HMap.lookup :: QName -> HashMap QName v -> Maybe v #-}
+
+newtype Section = Section { _secTelescope :: Telescope }
+  deriving (Show, NFData)
+
+instance Pretty Section where
+  pretty = pretty . _secTelescope
+
+secTelescope :: Lens' Section Telescope
+secTelescope f s =
+  f (_secTelescope s) <&>
+  \x -> s {_secTelescope = x}
+
+emptySignature :: Signature
+emptySignature = Sig Map.empty HMap.empty HMap.empty
+
+-- | A @DisplayForm@ is in essence a rewrite rule @q ts --> dt@ for a defined symbol (could be a
+--   constructor as well) @q@. The right hand side is a 'DisplayTerm' which is used to 'reify' to a
+--   more readable 'Abstract.Syntax'.
+--
+--   The patterns @ts@ are just terms, but the first @dfPatternVars@ variables are pattern variables
+--   that matches any term.
+data DisplayForm = Display
+  { dfPatternVars :: Nat
+    -- ^ Number @n@ of pattern variables in 'dfPats'.
+  , dfPats :: Elims
+    -- ^ Left hand side patterns, the @n@ first free variables are pattern variables,
+    --   any variables above @n@ are fixed and only match that particular variable. This
+    --   happens when you have display forms inside parameterised modules that match on the module
+    --   parameters. The 'ArgInfo' is ignored in these patterns.
+  , dfRHS :: DisplayTerm
+    -- ^ Right hand side.
+  }
+  deriving (Show, Generic)
+
+type LocalDisplayForm = Open DisplayForm
+
+-- | A structured presentation of a 'Term' for reification into
+--   'Abstract.Syntax'.
+data DisplayTerm
+  = DWithApp DisplayTerm [DisplayTerm] Elims
+    -- ^ @(f vs | ws) es@.
+    --   The first 'DisplayTerm' is the parent function @f@ with its args @vs@.
+    --   The list of 'DisplayTerm's are the with expressions @ws@.
+    --   The 'Elims' are additional arguments @es@
+    --   (possible in case the with-application is of function type)
+    --   or projections (if it is of record type).
+  | DCon ConHead ConInfo [Arg DisplayTerm]
+    -- ^ @c vs@.
+  | DDef QName [Elim' DisplayTerm]
+    -- ^ @d vs@.
+  | DDot' Term Elims
+    -- ^ @.(v es)@.  See 'DTerm''.
+  | DTerm' Term Elims
+    -- ^ @v es@.
+    --   This is a frozen elimination that is not always safe to run,
+    --   because display forms may be ill-typed.
+    --   (See issue #6476.)
+  deriving (Show, Generic)
+
+pattern DDot :: Term -> DisplayTerm
+pattern DDot v = DDot' v []
+
+pattern DTerm :: Term -> DisplayTerm
+pattern DTerm v = DTerm' v []
+
+instance Free DisplayForm where
+  freeVars' (Display n ps t) = underBinder (freeVars' ps) `mappend` underBinder' n (freeVars' t)
+
+instance Free DisplayTerm where
+  freeVars' (DWithApp t ws es) = freeVars' (t, (ws, es))
+  freeVars' (DCon _ _ vs)      = freeVars' vs
+  freeVars' (DDef _ es)        = freeVars' es
+  freeVars' (DDot' v es)       = freeVars' (v, es)
+  freeVars' (DTerm' v es)      = freeVars' (v, es)
+
+instance Pretty DisplayTerm where
+  prettyPrec p v =
+    case v of
+      DTerm v           -> prettyPrec p v
+      DTerm' v es       -> prettyPrec 9 v `pApp` es
+      DDot v            -> "." <> prettyPrec 10 v
+      DDot' v es        -> "." <> parens (prettyPrec 9 v `pAp` es)
+      DDef f es        -> pretty f `pApp` es
+      DCon c _ vs      -> pretty (conName c) `pApp` map Apply vs
+      DWithApp h ws es ->
+        mparens (p > 0)
+          (sep [ pretty h
+              , nest 2 $ fsep [ "|" <+> pretty w | w <- ws ] ])
+        `pApp` es
+    where
+      pApp :: Pretty el => Doc -> [el] -> Doc
+      pApp d els = mparens (not (null els) && p > 9) $ pAp d els
+      pAp :: Pretty el => Doc -> [el] -> Doc
+      pAp d els = sep [d, nest 2 $ fsep (map (prettyPrec 10) els)]
+
+instance Pretty DisplayForm where
+  prettyPrec p (Display fv lhs rhs) = mparens (p > 9) $
+    "Display" <?> fsep [ pshow fv, prettyPrec 10 lhs, prettyPrec 10 rhs ]
+
+-- | By default, we have no display form.
+defaultDisplayForm :: QName -> [LocalDisplayForm]
+defaultDisplayForm c = []
+
+-- | Non-linear (non-constructor) first-order pattern.
+data NLPat
+  = PVar !Int [Arg Int]
+    -- ^ Matches anything (modulo non-linearity) that only contains bound
+    --   variables that occur in the given arguments.
+  | PDef QName PElims
+    -- ^ Matches @f es@
+  | PLam ArgInfo (Abs NLPat)
+    -- ^ Matches @λ x → t@
+  | PPi (Dom NLPType) (Abs NLPType)
+    -- ^ Matches @(x : A) → B@
+  | PSort NLPSort
+    -- ^ Matches a sort of the given shape.
+  | PBoundVar {-# UNPACK #-} !Int PElims
+    -- ^ Matches @x es@ where x is a lambda-bound variable
+  | PTerm Term
+    -- ^ Matches the term modulo β (ideally βη).
+  deriving (Show, Generic)
+type PElims = [Elim' NLPat]
+
+type instance TypeOf NLPat = Type
+type instance TypeOf [Elim' NLPat] = (Type, Elims -> Term)
+
+instance TermLike NLPat where
+  traverseTermM f = \case
+    p@PVar{}       -> return p
+    PDef d ps      -> PDef d <$> traverseTermM f ps
+    PLam i p       -> PLam i <$> traverseTermM f p
+    PPi a b        -> PPi <$> traverseTermM f a <*> traverseTermM f b
+    PSort s        -> PSort <$> traverseTermM f s
+    PBoundVar i ps -> PBoundVar i <$> traverseTermM f ps
+    PTerm t        -> PTerm <$> f t
+
+  foldTerm f t = case t of
+    PVar{}         -> mempty
+    PDef d ps      -> foldTerm f ps
+    PLam i p       -> foldTerm f p
+    PPi a b        -> foldTerm f (a, b)
+    PSort s        -> foldTerm f s
+    PBoundVar i ps -> foldTerm f ps
+    PTerm t        -> foldTerm f t
+
+instance AllMetas NLPat
+
+data NLPType = NLPType
+  { nlpTypeSort :: NLPSort
+  , nlpTypeUnEl :: NLPat
+  } deriving (Show, Generic)
+
+instance TermLike NLPType where
+  traverseTermM f (NLPType s t) = NLPType <$> traverseTermM f s <*> traverseTermM f t
+
+  foldTerm f (NLPType s t) = foldTerm f (s, t)
+
+instance AllMetas NLPType
+
+data NLPSort
+  = PUniv Univ NLPat
+  | PInf Univ Integer
+  | PSizeUniv
+  | PLockUniv
+  | PLevelUniv
+  | PIntervalUniv
+  deriving (Show, Generic)
+
+pattern PType, PProp, PSSet :: NLPat -> NLPSort
+pattern PType p = PUniv UType p
+pattern PProp p = PUniv UProp p
+pattern PSSet p = PUniv USSet p
+
+{-# COMPLETE
+  PType, PSSet, PProp, PInf,
+  PSizeUniv, PLockUniv, PLevelUniv, PIntervalUniv #-}
+
+instance TermLike NLPSort where
+  traverseTermM f = \case
+    PUniv u p         -> PUniv u <$> traverseTermM f p
+    s@PInf{}          -> return s
+    s@PSizeUniv{}     -> return s
+    s@PLockUniv{}     -> return s
+    s@PLevelUniv{}    -> return s
+    s@PIntervalUniv{} -> return s
+
+  foldTerm f t = case t of
+    PUniv _ p         -> foldTerm f p
+    s@PInf{}          -> mempty
+    s@PSizeUniv{}     -> mempty
+    s@PLockUniv{}     -> mempty
+    s@PLevelUniv{}    -> mempty
+    s@PIntervalUniv{} -> mempty
+
+instance AllMetas NLPSort
+
+type RewriteRules = [RewriteRule]
+
+-- | Rewrite rules can be added independently from function clauses.
+data RewriteRule = RewriteRule
+  { rewName    :: QName      -- ^ Name of rewrite rule @q : Γ → f ps ≡ rhs@
+                             --   where @≡@ is the rewrite relation.
+  , rewContext :: Telescope  -- ^ @Γ@.
+  , rewHead    :: QName      -- ^ @f@.
+  , rewPats    :: PElims     -- ^ @Γ ⊢ f ps : t@.
+  , rewRHS     :: Term       -- ^ @Γ ⊢ rhs : t@.
+  , rewType    :: Type       -- ^ @Γ ⊢ t@.
+  , rewFromClause :: Bool    -- ^ Was this rewrite rule created from a clause in the definition of the function?
+  }
+    deriving (Show, Generic)
+
+data Definition = Defn
+  { defArgInfo        :: ArgInfo -- ^ Hiding should not be used.
+  , defName           :: QName   -- ^ The canonical name, used e.g. in compilation.
+  , defType           :: Type    -- ^ Type of the lifted definition.
+  , defPolarity       :: [Polarity]
+    -- ^ Variance information on arguments of the definition.
+    --   Does not include info for dropped parameters to
+    --   projection(-like) functions and constructors.
+  , defArgOccurrences :: [Occurrence]
+    -- ^ Positivity information on arguments of the definition.
+    --   Does not include info for dropped parameters to
+    --   projection(-like) functions and constructors.
+
+    --   Sometimes Agda looks up 'Occurrence's in these lists based on
+    --   their position, so one might consider replacing the list
+    --   with, say, an 'IntMap'. However, presumably these lists tend
+    --   to be short, in which case 'IntMap's could be slower than
+    --   lists. For instance, at one point the longest list
+    --   encountered for the standard library (in serialised
+    --   interfaces) had length 27. Distribution:
+    --
+    --   Length, number of lists
+    --   -----------------------
+    --
+    --    0, 2444
+    --    1,  721
+    --    2,  433
+    --    3,  668
+    --    4,  602
+    --    5,  624
+    --    6,  626
+    --    7,  484
+    --    8,  375
+    --    9,  264
+    --   10,  305
+    --   11,  188
+    --   12,  171
+    --   13,  108
+    --   14,   84
+    --   15,   80
+    --   16,   38
+    --   17,   23
+    --   18,   16
+    --   19,    8
+    --   20,    7
+    --   21,    5
+    --   22,    2
+    --   23,    3
+    --   27,    1
+
+  , defArgGeneralizable :: NumGeneralizableArgs
+    -- ^ For a generalized variable, shows how many arguments should be generalised.
+  , defGeneralizedParams :: [Maybe Name]
+    -- ^ Gives the name of the (bound variable) parameter for named generalized
+    --   parameters. This is needed to bring it into scope when type checking
+    --   the data/record definition corresponding to a type with generalized
+    --   parameters.
+  , defDisplay        :: [LocalDisplayForm]
+  , defMutual         :: MutualId
+  , defCompiledRep    :: CompiledRepresentation
+  , defInstance       :: Maybe QName
+    -- ^ @Just q@ when this definition is an instance of class q
+  , defCopy           :: Bool
+    -- ^ Has this function been created by a module
+                         -- instantiation?
+  , defMatchable      :: Set QName
+    -- ^ The set of symbols with rewrite rules that match against this symbol
+  , defNoCompilation  :: Bool
+    -- ^ should compilers skip this? Used for e.g. cubical's comp
+  , defInjective      :: Bool
+    -- ^ Should the def be treated as injective by the pattern matching unifier?
+  , defCopatternLHS   :: Bool
+    -- ^ Is this a function defined by copatterns?
+  , defBlocked        :: Blocked_
+    -- ^ What blocking tag to use when we cannot reduce this def?
+    --   Used when checking a function definition is blocked on a meta
+    --   in the type.
+  , defLanguage       :: !Language
+    -- ^ The language used for the definition.
+  , theDef            :: Defn
+  }
+    deriving (Show, Generic)
+
+instance LensArgInfo Definition where
+  getArgInfo = defArgInfo
+  mapArgInfo f def = def { defArgInfo = f $ defArgInfo def }
+
+instance LensModality  Definition where
+instance LensQuantity  Definition where
+instance LensRelevance Definition where
+
+data NumGeneralizableArgs
+  = NoGeneralizableArgs
+  | SomeGeneralizableArgs !Int
+    -- ^ When lambda-lifting new args are generalizable if
+    --   'SomeGeneralizableArgs', also when the number is zero.
+  deriving Show
+
+lensTheDef :: Lens' Definition Defn
+lensTheDef f d = f (theDef d) <&> \ df -> d { theDef = df }
+
+-- | Create a definition with sensible defaults.
+defaultDefn ::
+  ArgInfo -> QName -> Type -> Language -> Defn -> Definition
+defaultDefn info x t lang def = Defn
+  { defArgInfo        = info
+  , defName           = x
+  , defType           = t
+  , defPolarity       = []
+  , defArgOccurrences = []
+  , defArgGeneralizable = NoGeneralizableArgs
+  , defGeneralizedParams = []
+  , defDisplay        = defaultDisplayForm x
+  , defMutual         = 0
+  , defCompiledRep    = noCompiledRep
+  , defInstance       = Nothing
+  , defCopy           = False
+  , defMatchable      = Set.empty
+  , defNoCompilation  = False
+  , defInjective      = False
+  , defCopatternLHS   = False
+  , defBlocked        = NotBlocked ReallyNotBlocked ()
+  , defLanguage       = lang
+  , theDef            = def
+  }
+
+-- | Polarity for equality and subtype checking.
+data Polarity
+  = Covariant      -- ^ monotone
+  | Contravariant  -- ^ antitone
+  | Invariant      -- ^ no information (mixed variance)
+  | Nonvariant     -- ^ constant
+  deriving (Show, Eq, Generic)
+
+instance Pretty Polarity where
+  pretty = text . \case
+    Covariant     -> "+"
+    Contravariant -> "-"
+    Invariant     -> "*"
+    Nonvariant    -> "_"
+
+-- | Information about whether an argument is forced by the type of a function.
+data IsForced
+  = Forced
+  | NotForced
+  deriving (Show, Eq, Generic)
+
+-- | The backends are responsible for parsing their own pragmas.
+data CompilerPragma = CompilerPragma Range String
+  deriving (Show, Eq, Generic)
+
+instance HasRange CompilerPragma where
+  getRange (CompilerPragma r _) = r
+
+type BackendName    = String
+
+jsBackendName, ghcBackendName :: BackendName
+jsBackendName  = "JS"
+ghcBackendName = "GHC"
+
+type CompiledRepresentation = Map BackendName [CompilerPragma]
+
+noCompiledRep :: CompiledRepresentation
+noCompiledRep = Map.empty
+
+-- A face represented as a list of equality constraints.
+-- (r,False) ↦ (r = i0)
+-- (r,True ) ↦ (r = i1)
+type Face = [(Term,Bool)]
+
+-- | An alternative representation of partial elements in a telescope:
+--   Γ ⊢ λ Δ. [φ₁ u₁, ... , φₙ uₙ] : Δ → PartialP (∨_ᵢ φᵢ) T
+--   see cubicaltt paper (however we do not store the type T).
+data System = System
+  { systemTel :: Telescope
+    -- ^ the telescope Δ, binding vars for the clauses, Γ ⊢ Δ
+  , systemClauses :: [(Face,Term)]
+    -- ^ a system [φ₁ u₁, ... , φₙ uₙ] where Γ, Δ ⊢ φᵢ and Γ, Δ, φᵢ ⊢ uᵢ
+  } deriving (Show, Generic)
+
+-- | Additional information for extended lambdas.
+data ExtLamInfo = ExtLamInfo
+  { extLamModule    :: ModuleName
+    -- ^ For complicated reasons the scope checker decides the QName of a
+    --   pattern lambda, and thus its module. We really need to decide the
+    --   module during type checking though, since if the lambda appears in a
+    --   refined context the module picked by the scope checker has very much
+    --   the wrong parameters.
+  , extLamAbsurd :: Bool
+    -- ^ Was this definition created from an absurd lambda @λ ()@?
+  , extLamSys :: !(Strict.Maybe System)
+  } deriving (Show, Generic)
+
+modifySystem :: (System -> System) -> ExtLamInfo -> ExtLamInfo
+modifySystem f e = let !e' = e { extLamSys = f <$> extLamSys e } in e'
+
+-- | Additional information for projection 'Function's.
+data Projection = Projection
+  { projProper    :: Maybe QName
+    -- ^ @Nothing@ if only projection-like, @Just r@ if record projection.
+    --   The @r@ is the name of the record type projected from.
+    --   This field is updated by module application.
+  , projOrig      :: QName
+    -- ^ The original projection name
+    --   (current name could be from module application).
+  , projFromType  :: Arg QName
+    -- ^ Type projected from. Original record type if @projProper = Just{}@.
+    --   Also stores @ArgInfo@ of the principal argument.
+    --   This field is unchanged by module application.
+  , projIndex     :: Int
+    -- ^ Index of the record argument.
+    --   Start counting with 1, because 0 means that
+    --   it is already applied to the record value.
+    --   This can happen in module instantiation, but
+    --   then either the record value is @var 0@, or @funProjection == Nothing@.
+  , projLams :: ProjLams
+    -- ^ Term @t@ to be be applied to record parameters and record value.
+    --   The parameters will be dropped.
+    --   In case of a proper projection, a postfix projection application
+    --   will be created: @t = \ pars r -> r .p@
+    --   (Invariant: the number of abstractions equals 'projIndex'.)
+    --   In case of a projection-like function, just the function symbol
+    --   is returned as 'Def':  @t = \ pars -> f@.
+  } deriving (Show, Generic)
+
+-- | Abstractions to build projection function (dropping parameters).
+newtype ProjLams = ProjLams { getProjLams :: [Arg ArgName] }
+  deriving (Show, Null, Generic)
+
+-- | Building the projection function (which drops the parameters).
+projDropPars :: Projection -> ProjOrigin -> Term
+-- Proper projections:
+projDropPars (Projection Just{} d _ _ lams) o =
+  case initLast $ getProjLams lams of
+    Nothing -> Def d []
+    Just (pars, Arg i y) ->
+      let core = Lam i $ Abs y $ Var 0 [Proj o d] in
+      List.foldr (\ (Arg ai x) -> Lam ai . NoAbs x) core pars
+-- Projection-like functions:
+projDropPars (Projection Nothing d _ _ lams) o =
+  List.foldr (\ (Arg ai x) -> Lam ai . NoAbs x) (Def d []) $
+    initWithDefault __IMPOSSIBLE__ $ getProjLams lams
+
+-- | The info of the principal (record) argument.
+projArgInfo :: Projection -> ArgInfo
+projArgInfo (Projection _ _ _ _ lams) =
+  maybe __IMPOSSIBLE__ getArgInfo $ lastMaybe $ getProjLams lams
+
+-- | Should a record type admit eta-equality?
+data EtaEquality
+  = Specified { theEtaEquality :: !HasEta }  -- ^ User specifed 'eta-equality' or 'no-eta-equality'.
+  | Inferred  { theEtaEquality :: !HasEta }  -- ^ Positivity checker inferred whether eta is safe.
+  deriving (Show, Eq, Generic)
+
+instance PatternMatchingAllowed EtaEquality where
+  patternMatchingAllowed = patternMatchingAllowed . theEtaEquality
+
+instance CopatternMatchingAllowed EtaEquality where
+  copatternMatchingAllowed = copatternMatchingAllowed . theEtaEquality
+
+-- | Make sure we do not overwrite a user specification.
+setEtaEquality :: EtaEquality -> HasEta -> EtaEquality
+setEtaEquality e@Specified{} _ = e
+setEtaEquality _ b = Inferred b
+
+data FunctionFlag
+  = FunStatic  -- ^ Should calls to this function be normalised at compile-time?
+  | FunInline  -- ^ Should calls to this function be inlined by the compiler?
+  | FunMacro   -- ^ Is this function a macro?
+  deriving (Eq, Ord, Enum, Show, Generic)
+
+data CompKit = CompKit
+  { nameOfHComp :: Maybe QName
+  , nameOfTransp :: Maybe QName
+  }
+  deriving (Eq, Ord, Show, Generic)
+
+emptyCompKit :: CompKit
+emptyCompKit = CompKit Nothing Nothing
+
+defaultAxiom :: Defn
+defaultAxiom = Axiom False
+
+constTranspAxiom :: Defn
+constTranspAxiom = Axiom True
+
+data Defn
+  = AxiomDefn AxiomData
+      -- ^ Postulate.
+  | DataOrRecSigDefn DataOrRecSigData
+      -- ^ Data or record type signature that doesn't yet have a definition.
+  | GeneralizableVar
+      -- ^ Generalizable variable (introduced in `generalize` block).
+  | AbstractDefn Defn
+      -- ^ Returned by 'getConstInfo' if definition is abstract.
+  | FunctionDefn FunctionData
+  | DatatypeDefn DatatypeData
+  | RecordDefn RecordData
+  | ConstructorDefn ConstructorData
+  | PrimitiveDefn PrimitiveData
+      -- ^ Primitive or builtin functions.
+  | PrimitiveSortDefn PrimitiveSortData
+    deriving (Show, Generic)
+
+{-# COMPLETE
+  Axiom, DataOrRecSig, GeneralizableVar, AbstractDefn,
+  Function, Datatype, Record, Constructor, Primitive, PrimitiveSort #-}
+
+data AxiomData = AxiomData
+  { _axiomConstTransp :: Bool
+    -- ^ Can transp for this postulate be constant?
+    --   Set to @True@ for bultins like String.
+  } deriving (Show, Generic)
+
+pattern Axiom :: Bool -> Defn
+pattern Axiom{ axiomConstTransp } = AxiomDefn (AxiomData axiomConstTransp)
+
+data DataOrRecSigData = DataOrRecSigData
+  { _datarecPars :: Int
+  } deriving (Show, Generic)
+
+pattern DataOrRecSig :: Int -> Defn
+pattern DataOrRecSig{ datarecPars } = DataOrRecSigDefn (DataOrRecSigData datarecPars)
+
+-- | Indicates the reason behind a function having not been marked
+-- projection-like.
+data ProjectionLikenessMissing
+  = MaybeProjection
+    -- ^ Projection-likeness analysis has not run on this function yet.
+    -- It may do so in the future.
+  | NeverProjection
+    -- ^ The user has requested that this function be not be marked
+    -- projection-like. The analysis may already have run on this
+    -- function, but the results have been discarded, and it will not be
+    -- run again.
+  deriving (Show, Generic, Enum, Bounded)
+
+data FunctionData = FunctionData
+  { _funClauses        :: [Clause]
+  , _funCompiled       :: Maybe CompiledClauses
+      -- ^ 'Nothing' while function is still type-checked.
+      --   @Just cc@ after type and coverage checking and
+      --   translation to case trees.
+  , _funSplitTree      :: Maybe SplitTree
+      -- ^ The split tree constructed by the coverage
+      --   checker. Needed to re-compile the clauses after
+      --   forcing translation.
+  , _funTreeless       :: Maybe Compiled
+      -- ^ Intermediate representation for compiler backends.
+  , _funCovering       :: [Clause]
+      -- ^ Covering clauses computed by coverage checking.
+      --   Erased by (IApply) confluence checking(?)
+  , _funInv            :: FunctionInverse
+  , _funMutual         :: Maybe [QName]
+      -- ^ Mutually recursive functions, @data@s and @record@s.
+      --   Does include this function.
+      --   Empty list if not recursive.
+      --   @Nothing@ if not yet computed (by positivity checker).
+  , _funAbstr          :: IsAbstract
+  , _funProjection     :: Either ProjectionLikenessMissing Projection
+      -- ^ Is it a record projection?
+      --   If yes, then return the name of the record type and index of
+      --   the record argument.  Start counting with 1, because 0 means that
+      --   it is already applied to the record. (Can happen in module
+      --   instantiation.) This information is used in the termination
+      --   checker.
+  , _funErasure :: !Bool
+    -- ^ Was @--erasure@ in effect when the function was defined?
+    -- (This can affect the type of a projection.)
+  , _funFlags          :: Set FunctionFlag
+  , _funTerminates     :: Maybe Bool
+      -- ^ Has this function been termination checked?  Did it pass?
+  , _funExtLam         :: Maybe ExtLamInfo
+      -- ^ Is this function generated from an extended lambda?
+      --   If yes, then return the number of hidden and non-hidden lambda-lifted arguments.
+  , _funWith           :: Maybe QName
+      -- ^ Is this a generated with-function?
+      --   If yes, then what's the name of the parent function?
+  , _funIsKanOp        :: Maybe QName
+      -- ^ Is this a helper for one of the Kan operations (transp,
+      -- hcomp) on data types/records? If so, for which data type?
+  , _funOpaque         :: IsOpaque
+      -- ^ Is this function opaque? If so, and we're not in an opaque
+      -- block that includes this function('s name), it will be treated
+      -- abstractly.
+  } deriving (Show, Generic)
+
+pattern Function
+  :: [Clause]
+  -> Maybe CompiledClauses
+  -> Maybe SplitTree
+  -> Maybe Compiled
+  -> [Clause]
+  -> FunctionInverse
+  -> Maybe [QName]
+  -> IsAbstract
+  -> Either ProjectionLikenessMissing Projection
+  -> Bool
+  -> Set FunctionFlag
+  -> Maybe Bool
+  -> Maybe ExtLamInfo
+  -> Maybe QName
+  -> Maybe QName
+  -> IsOpaque
+  -> Defn
+pattern Function
+  { funClauses
+  , funCompiled
+  , funSplitTree
+  , funTreeless
+  , funCovering
+  , funInv
+  , funMutual
+  , funAbstr
+  , funProjection
+  , funErasure
+  , funFlags
+  , funTerminates
+  , funExtLam
+  , funWith
+  , funIsKanOp
+  , funOpaque
+  } = FunctionDefn (FunctionData
+    funClauses
+    funCompiled
+    funSplitTree
+    funTreeless
+    funCovering
+    funInv
+    funMutual
+    funAbstr
+    funProjection
+    funErasure
+    funFlags
+    funTerminates
+    funExtLam
+    funWith
+    funIsKanOp
+    funOpaque
+  )
+
+data DatatypeData = DatatypeData
+  { _dataPars           :: Nat
+      -- ^ Number of parameters.
+  , _dataIxs            :: Nat
+      -- ^ Number of indices.
+  , _dataClause         :: Maybe Clause
+      -- ^ This might be in an instantiated module.
+  , _dataCons           :: [QName]
+      -- ^ Constructor names, ordered according to the order of their definition.
+  , _dataSort           :: Sort
+  , _dataMutual         :: Maybe [QName]
+      -- ^ Mutually recursive functions, @data@s and @record@s.
+      --   Does include this data type.
+      --   Empty if not recursive.
+      --   @Nothing@ if not yet computed (by positivity checker).
+  , _dataAbstr          :: IsAbstract
+  , _dataPathCons       :: [QName]
+      -- ^ Path constructor names (subset of @dataCons@).
+  , _dataTranspIx       :: Maybe QName
+      -- ^ If indexed datatype, name of the "index transport" function.
+  , _dataTransp         :: Maybe QName
+      -- ^ Transport function, should be available for all datatypes in supported sorts.
+  } deriving (Show, Generic)
+
+pattern Datatype
+  :: Nat
+  -> Nat
+  -> (Maybe Clause)
+  -> [QName]
+  -> Sort
+  -> Maybe [QName]
+  -> IsAbstract
+  -> [QName]
+  -> Maybe QName
+  -> Maybe QName
+  -> Defn
+
+pattern Datatype
+  { dataPars
+  , dataIxs
+  , dataClause
+  , dataCons
+  , dataSort
+  , dataMutual
+  , dataAbstr
+  , dataPathCons
+  , dataTranspIx
+  , dataTransp
+  } = DatatypeDefn (DatatypeData
+    dataPars
+    dataIxs
+    dataClause
+    dataCons
+    dataSort
+    dataMutual
+    dataAbstr
+    dataPathCons
+    dataTranspIx
+    dataTransp
+  )
+
+data RecordData = RecordData
+  { _recPars           :: Nat
+      -- ^ Number of parameters.
+  , _recClause         :: Maybe Clause
+      -- ^ Was this record type created by a module application?
+      --   If yes, the clause is its definition (linking back to the original record type).
+  , _recConHead        :: ConHead
+      -- ^ Constructor name and fields.
+  , _recNamedCon       :: Bool
+      -- ^ Does this record have a @constructor@?
+  , _recFields         :: [Dom QName]
+      -- ^ The record field names.
+  , _recTel            :: Telescope
+      -- ^ The record field telescope. (Includes record parameters.)
+      --   Note: @TelV recTel _ == telView' recConType@.
+      --   Thus, @recTel@ is redundant.
+  , _recMutual         :: Maybe [QName]
+      -- ^ Mutually recursive functions, @data@s and @record@s.
+      --   Does include this record.
+      --   Empty if not recursive.
+      --   @Nothing@ if not yet computed (by positivity checker).
+  , _recEtaEquality'    :: EtaEquality
+      -- ^ Eta-expand at this record type?
+      --   @False@ for unguarded recursive records and coinductive records
+      --   unless the user specifies otherwise.
+  , _recPatternMatching :: PatternOrCopattern
+      -- ^ In case eta-equality is off, do we allow pattern matching on the
+      --   constructor or construction by copattern matching?
+      --   Having both loses subject reduction, see issue #4560.
+      --   After positivity checking, this field is obsolete, part of 'EtaEquality'.
+  , _recInduction      :: Maybe Induction
+      -- ^ 'Inductive' or 'CoInductive'?  Matters only for recursive records.
+      --   'Nothing' means that the user did not specify it, which is an error
+      --   for recursive records.
+  , _recTerminates     :: Maybe Bool
+      -- ^ 'Just True' means that unfolding of the recursive record terminates,
+      --   'Just False' means that we have no evidence for termination,
+      --   and 'Nothing' means we have not run the termination checker yet.
+  , _recAbstr          :: IsAbstract
+  , _recComp           :: CompKit
+  } deriving (Show, Generic)
+
+pattern Record
+  :: Nat
+  -> Maybe Clause
+  -> ConHead
+  -> Bool
+  -> [Dom QName]
+  -> Telescope
+  -> Maybe [QName]
+  -> EtaEquality
+  -> PatternOrCopattern
+  -> Maybe Induction
+  -> Maybe Bool
+  -> IsAbstract
+  -> CompKit
+  -> Defn
+
+pattern Record
+  { recPars
+  , recClause
+  , recConHead
+  , recNamedCon
+  , recFields
+  , recTel
+  , recMutual
+  , recEtaEquality'
+  , recPatternMatching
+  , recInduction
+  , recTerminates
+  , recAbstr
+  , recComp
+  } = RecordDefn (RecordData
+    recPars
+    recClause
+    recConHead
+    recNamedCon
+    recFields
+    recTel
+    recMutual
+    recEtaEquality'
+    recPatternMatching
+    recInduction
+    recTerminates
+    recAbstr
+    recComp
+  )
+
+data ConstructorData = ConstructorData
+  { _conPars   :: Int
+      -- ^ Number of parameters.
+  , _conArity  :: Int
+      -- ^ Number of arguments (excluding parameters).
+  , _conSrcCon :: ConHead
+      -- ^ Name of (original) constructor and fields. (This might be in a module instance.)
+  , _conData   :: QName
+      -- ^ Name of datatype or record type.
+  , _conAbstr  :: IsAbstract
+  , _conComp   :: CompKit
+      -- ^ Cubical composition.
+  , _conProj   :: Maybe [QName]
+      -- ^ Projections. 'Nothing' if not yet computed.
+  , _conForced :: [IsForced]
+      -- ^ Which arguments are forced (i.e. determined by the type of the constructor)?
+      --   Either this list is empty (if the forcing analysis isn't run), or its length is @conArity@.
+  , _conErased :: Maybe [Bool]
+      -- ^ Which arguments are erased at runtime (computed during compilation to treeless)?
+      --   'True' means erased, 'False' means retained.
+      --   'Nothing' if no erasure analysis has been performed yet.
+      --   The length of the list is @conArity@.
+  , _conErasure :: !Bool
+      -- ^ Was @--erasure@ in effect when the constructor was defined?
+      --   (This can affect the constructor's type.)
+  , _conInline :: !Bool
+      -- ^ Shall we translate the constructor on the root of the rhs into copattern matching on the lhs?
+      --   Activated by INLINE pragma.
+  } deriving (Show, Generic)
+
+pattern Constructor
+  :: Int
+  -> Int
+  -> ConHead
+  -> QName
+  -> IsAbstract
+  -> CompKit
+  -> Maybe [QName]
+  -> [IsForced]
+  -> Maybe [Bool]
+  -> Bool
+  -> Bool
+  -> Defn
+pattern Constructor
+  { conPars
+  , conArity
+  , conSrcCon
+  , conData
+  , conAbstr
+  , conComp
+  , conProj
+  , conForced
+  , conErased
+  , conErasure
+  , conInline
+  } = ConstructorDefn (ConstructorData
+    conPars
+    conArity
+    conSrcCon
+    conData
+    conAbstr
+    conComp
+    conProj
+    conForced
+    conErased
+    conErasure
+    conInline
+  )
+
+data PrimitiveData = PrimitiveData
+  { _primAbstr    :: IsAbstract
+  , _primName     :: PrimitiveId
+  , _primClauses  :: [Clause]
+      -- ^ 'null' for primitive functions, @not null@ for builtin functions.
+  , _primInv      :: FunctionInverse
+      -- ^ Builtin functions can have inverses. For instance, natural number addition.
+  , _primCompiled :: Maybe CompiledClauses
+      -- ^ 'Nothing' for primitive functions,
+      --   @'Just' something@ for builtin functions.
+  , _primOpaque   :: IsOpaque
+      -- ^ Primitives can also live in opaque blocks.
+  } deriving (Show, Generic)
+
+pattern Primitive
+  :: IsAbstract
+  -> PrimitiveId
+  -> [Clause]
+  -> FunctionInverse
+  -> Maybe CompiledClauses
+  -> IsOpaque
+  -> Defn
+pattern Primitive
+  { primAbstr
+  , primName
+  , primClauses
+  , primInv
+  , primCompiled
+  , primOpaque
+  } = PrimitiveDefn (PrimitiveData
+    primAbstr
+    primName
+    primClauses
+    primInv
+    primCompiled
+    primOpaque
+  )
+
+data PrimitiveSortData = PrimitiveSortData
+  { _primSortName :: BuiltinSort
+  , _primSortSort :: Sort
+  } deriving (Show, Generic)
+
+pattern PrimitiveSort
+  :: BuiltinSort
+  -> Sort
+  -> Defn
+pattern PrimitiveSort
+  { primSortName
+  , primSortSort
+  } = PrimitiveSortDefn (PrimitiveSortData
+    primSortName
+    primSortSort
+  )
+
+-- TODO: lenses for all Defn variants
+
+lensFunction :: Lens' Defn FunctionData
+lensFunction f = \case
+  FunctionDefn d -> FunctionDefn <$> f d
+  _ -> __IMPOSSIBLE__
+
+lensConstructor :: Lens' Defn ConstructorData
+lensConstructor f = \case
+  ConstructorDefn d -> ConstructorDefn <$> f d
+  _ -> __IMPOSSIBLE__
+
+lensRecord :: Lens' Defn RecordData
+lensRecord f = \case
+  RecordDefn d -> RecordDefn <$> f d
+  _ -> __IMPOSSIBLE__
+
+-- Lenses for Record
+
+lensRecTel :: Lens' RecordData Telescope
+lensRecTel f r =
+  f (_recTel r) <&> \ tel -> r { _recTel = tel }
+
+-- Pretty printing definitions
+
+instance Pretty Definition where
+  pretty Defn{..} =
+    "Defn {" <?> vcat
+      [ "defArgInfo        =" <?> pshow defArgInfo
+      , "defName           =" <?> pretty defName
+      , "defType           =" <?> pretty defType
+      , "defPolarity       =" <?> pshow defPolarity
+      , "defArgOccurrences =" <?> pshow defArgOccurrences
+      , "defGeneralizedParams =" <?> pshow defGeneralizedParams
+      , "defDisplay        =" <?> pretty defDisplay
+      , "defMutual         =" <?> pshow defMutual
+      , "defCompiledRep    =" <?> pshow defCompiledRep
+      , "defInstance       =" <?> pshow defInstance
+      , "defCopy           =" <?> pshow defCopy
+      , "defMatchable      =" <?> pshow (Set.toList defMatchable)
+      , "defInjective      =" <?> pshow defInjective
+      , "defCopatternLHS   =" <?> pshow defCopatternLHS
+      , "theDef            =" <?> pretty theDef ] <+> "}"
+
+instance Pretty Defn where
+  pretty = \case
+    AxiomDefn _         -> "Axiom"
+    DataOrRecSigDefn d  -> pretty d
+    GeneralizableVar    -> "GeneralizableVar"
+    AbstractDefn def    -> "AbstractDefn" <?> parens (pretty def)
+    FunctionDefn d      -> pretty d
+    DatatypeDefn d      -> pretty d
+    RecordDefn d        -> pretty d
+    ConstructorDefn d   -> pretty d
+    PrimitiveDefn d     -> pretty d
+    PrimitiveSortDefn d -> pretty d
+
+instance Pretty DataOrRecSigData where
+  pretty (DataOrRecSigData n) = "DataOrRecSig" <+> pretty n
+
+instance Pretty ProjectionLikenessMissing where
+  pretty MaybeProjection = "MaybeProjection"
+  pretty NeverProjection = "NeverProjection"
+
+instance Pretty FunctionData where
+  pretty (FunctionData
+      funClauses
+      funCompiled
+      funSplitTree
+      funTreeless
+      _funCovering
+      funInv
+      funMutual
+      funAbstr
+      funProjection
+      funErasure
+      funFlags
+      funTerminates
+      _funExtLam
+      funWith
+      funIsKanOp
+      funOpaque
+    ) =
+    "Function {" <?> vcat
+      [ "funClauses      =" <?> vcat (map pretty funClauses)
+      , "funCompiled     =" <?> pretty funCompiled
+      , "funSplitTree    =" <?> pretty funSplitTree
+      , "funTreeless     =" <?> pretty funTreeless
+      , "funInv          =" <?> pretty funInv
+      , "funMutual       =" <?> pshow funMutual
+      , "funAbstr        =" <?> pshow funAbstr
+      , "funProjection   =" <?> pretty funProjection
+      , "funErasure      =" <?> pretty funErasure
+      , "funFlags        =" <?> pshow funFlags
+      , "funTerminates   =" <?> pshow funTerminates
+      , "funWith         =" <?> pretty funWith
+      , "funIsKanOp      =" <?> pretty funIsKanOp
+      , "funOpaque       =" <?> pshow funOpaque
+      ] <?> "}"
+
+instance Pretty DatatypeData where
+  pretty (DatatypeData
+      dataPars
+      dataIxs
+      dataClause
+      dataCons
+      dataSort
+      dataMutual
+      _dataAbstr
+      _dataPathCons
+      _dataTranspIx
+      _dataTransp
+    ) =
+    "Datatype {" <?> vcat
+      [ "dataPars       =" <?> pshow dataPars
+      , "dataIxs        =" <?> pshow dataIxs
+      , "dataClause     =" <?> pretty dataClause
+      , "dataCons       =" <?> pshow dataCons
+      , "dataSort       =" <?> pretty dataSort
+      , "dataMutual     =" <?> pshow dataMutual
+      , "dataAbstr      =" <?> pshow dataAbstr
+      ] <?> "}"
+
+instance Pretty RecordData where
+  pretty (RecordData
+      recPars
+      recClause
+      recConHead
+      recNamedCon
+      recFields
+      recTel
+      recMutual
+      recEtaEquality'
+      _recPatternMatching
+      recInduction
+      _recTerminates
+      recAbstr
+      _recComp
+    ) =
+    "Record {" <?> vcat
+      [ "recPars         =" <?> pshow recPars
+      , "recClause       =" <?> pretty recClause
+      , "recConHead      =" <?> pretty recConHead
+      , "recNamedCon     =" <?> pretty recNamedCon
+      , "recFields       =" <?> pretty recFields
+      , "recTel          =" <?> pretty recTel
+      , "recMutual       =" <?> pshow recMutual
+      , "recEtaEquality' =" <?> pshow recEtaEquality'
+      , "recInduction    =" <?> pshow recInduction
+      , "recAbstr        =" <?> pshow recAbstr
+      ] <?> "}"
+
+instance Pretty ConstructorData where
+  pretty (ConstructorData
+      conPars
+      conArity
+      conSrcCon
+      conData
+      conAbstr
+      _conComp
+      _conProj
+      _conForced
+      conErased
+      conErasure
+      conInline
+    ) =
+    "Constructor {" <?> vcat
+      [ "conPars    =" <?> pshow conPars
+      , "conArity   =" <?> pshow conArity
+      , "conSrcCon  =" <?> pretty conSrcCon
+      , "conData    =" <?> pretty conData
+      , "conAbstr   =" <?> pshow conAbstr
+      , "conErased  =" <?> pshow conErased
+      , "conErasure =" <?> pshow conErasure
+      , "conInline  =" <?> pshow conInline
+      ] <?> "}"
+
+instance Pretty PrimitiveData where
+  pretty (PrimitiveData
+      primAbstr
+      primName
+      primClauses
+      _primInv
+      primCompiled
+      primOpaque
+      ) =
+    "Primitive {" <?> vcat
+      [ "primAbstr    =" <?> pshow primAbstr
+      , "primName     =" <?> pshow primName
+      , "primClauses  =" <?> pshow primClauses
+      , "primCompiled =" <?> pshow primCompiled
+      , "primOpaque   =" <?> pshow primOpaque
+      ] <?> "}"
+
+instance Pretty PrimitiveSortData where
+  pretty (PrimitiveSortData primSortName primSortSort) =
+    "PrimitiveSort {" <?> vcat
+      [ "primSortName =" <?> pshow primSortName
+      , "primSortSort =" <?> pshow primSortSort
+      ] <?> "}"
+
+instance Pretty Projection where
+  pretty Projection{..} =
+    "Projection {" <?> vcat
+      [ "projProper   =" <?> pretty projProper
+      , "projOrig     =" <?> pretty projOrig
+      , "projFromType =" <?> pretty projFromType
+      , "projIndex    =" <?> pshow projIndex
+      , "projLams     =" <?> pretty projLams
+      ]
+
+instance Pretty c => Pretty (FunctionInverse' c) where
+  pretty NotInjective = "NotInjective"
+  pretty (Inverse inv) = "Inverse" <?>
+    vcat [ pretty h <+> "->" <?> pretty cs
+         | (h, cs) <- Map.toList inv ]
+
+instance Pretty ProjLams where
+  pretty (ProjLams args) = pretty args
+
+-- | Is the record type recursive?
+recRecursive :: Defn -> Bool
+recRecursive (Record { recMutual = Just qs }) = not $ null qs
+recRecursive _ = __IMPOSSIBLE__
+
+recEtaEquality :: Defn -> HasEta
+recEtaEquality = theEtaEquality . recEtaEquality'
+
+-- | A template for creating 'Function' definitions, with sensible
+-- defaults.
+emptyFunctionData :: HasOptions m => m FunctionData
+emptyFunctionData = do
+  erasure <- optErasure <$> pragmaOptions
+  return $ FunctionData
+    { _funClauses     = []
+    , _funCompiled    = Nothing
+    , _funSplitTree   = Nothing
+    , _funTreeless    = Nothing
+    , _funInv         = NotInjective
+    , _funMutual      = Nothing
+    , _funAbstr       = ConcreteDef
+    , _funProjection  = Left MaybeProjection
+    , _funErasure     = erasure
+    , _funFlags       = Set.empty
+    , _funTerminates  = Nothing
+    , _funExtLam      = Nothing
+    , _funWith        = Nothing
+    , _funCovering    = []
+    , _funIsKanOp     = Nothing
+    , _funOpaque      = TransparentDef
+    }
+
+emptyFunction :: HasOptions m => m Defn
+emptyFunction = FunctionDefn <$> emptyFunctionData
+
+funFlag :: FunctionFlag -> Lens' Defn Bool
+funFlag flag f def@Function{ funFlags = flags } =
+  f (Set.member flag flags) <&>
+  \ b -> def{ funFlags = (if b then Set.insert else Set.delete) flag flags }
+funFlag _ f def = f False $> def
+
+funStatic, funInline, funMacro :: Lens' Defn Bool
+funStatic       = funFlag FunStatic
+funInline       = funFlag FunInline
+funMacro        = funFlag FunMacro
+
+isMacro :: Defn -> Bool
+isMacro = (^. funMacro)
+
+-- | Checking whether we are dealing with a function yet to be defined.
+isEmptyFunction :: Defn -> Bool
+isEmptyFunction def =
+  case def of
+    Function { funClauses = [] } -> True
+    _ -> False
+
+isCopatternLHS :: [Clause] -> Bool
+isCopatternLHS = List.any (List.any (isJust . A.isProjP) . namedClausePats)
+
+recCon :: Defn -> QName
+recCon Record{ recConHead } = conName recConHead
+recCon _ = __IMPOSSIBLE__
+
+defIsRecord :: Defn -> Bool
+defIsRecord Record{} = True
+defIsRecord _        = False
+
+defIsDataOrRecord :: Defn -> Bool
+defIsDataOrRecord Record{}   = True
+defIsDataOrRecord Datatype{} = True
+defIsDataOrRecord _          = False
+
+defConstructors :: Defn -> [QName]
+defConstructors Datatype{dataCons = cs} = cs
+defConstructors Record{recConHead = c} = [conName c]
+defConstructors _ = __IMPOSSIBLE__
+
+newtype Fields = Fields [(C.Name, Type)]
+  deriving Null
+
+-- | Did we encounter a simplifying reduction?
+--   In terms of CIC, that would be a iota-reduction.
+--   In terms of Agda, this is a constructor or literal
+--   pattern that matched.
+--   Just beta-reduction (substitution) or delta-reduction
+--   (unfolding of definitions) does not count as simplifying?
+
+data Simplification = YesSimplification | NoSimplification
+  deriving (Eq, Show, Generic)
+
+instance Null Simplification where
+  empty = NoSimplification
+  null  = (== NoSimplification)
+
+instance Semigroup Simplification where
+  YesSimplification <> _ = YesSimplification
+  NoSimplification  <> s = s
+
+instance Monoid Simplification where
+  mempty = NoSimplification
+  mappend = (<>)
+
+data Reduced no yes
+  = NoReduction no
+  | YesReduction Simplification yes
+  deriving Functor
+
+redReturn :: a -> ReduceM (Reduced a' a)
+redReturn = return . YesReduction YesSimplification
+
+-- | Conceptually: @redBind m f k = either (return . Left . f) k =<< m@
+
+redBind :: ReduceM (Reduced a a') -> (a -> b) ->
+           (a' -> ReduceM (Reduced b b')) -> ReduceM (Reduced b b')
+redBind ma f k = do
+  r <- ma
+  case r of
+    NoReduction x    -> return $ NoReduction $ f x
+    YesReduction _ y -> k y
+
+-- | Three cases: 1. not reduced, 2. reduced, but blocked, 3. reduced, not blocked.
+data IsReduced
+  = NotReduced
+  | Reduced    (Blocked ())
+
+data MaybeReduced a = MaybeRed
+  { isReduced     :: IsReduced
+  , ignoreReduced :: a
+  }
+  deriving (Functor)
+
+instance IsProjElim e => IsProjElim (MaybeReduced e) where
+  isProjElim = isProjElim . ignoreReduced
+
+type MaybeReducedArgs = [MaybeReduced (Arg Term)]
+type MaybeReducedElims = [MaybeReduced Elim]
+
+notReduced :: a -> MaybeReduced a
+notReduced x = MaybeRed NotReduced x
+
+reduced :: Blocked (Arg Term) -> MaybeReduced (Arg Term)
+reduced b = MaybeRed (Reduced $ () <$ b) $ ignoreBlocking b
+
+-- | Controlling 'reduce'.
+data AllowedReduction
+  = ProjectionReductions     -- ^ (Projection and) projection-like functions may be reduced.
+  | InlineReductions         -- ^ Functions marked INLINE may be reduced.
+  | CopatternReductions      -- ^ Copattern definitions may be reduced.
+  | FunctionReductions       -- ^ Non-recursive functions and primitives may be reduced.
+  | RecursiveReductions      -- ^ Even recursive functions may be reduced.
+  | LevelReductions          -- ^ Reduce @'Level'@ terms.
+  | TypeLevelReductions      -- ^ Allow @allReductions@ in types, even
+                             --   if not allowed at term level (used
+                             --   by confluence checker)
+  | UnconfirmedReductions    -- ^ Functions whose termination has not (yet) been confirmed.
+  | NonTerminatingReductions -- ^ Functions that have failed termination checking.
+  deriving (Show, Eq, Ord, Enum, Bounded, Ix, Generic)
+
+instance SmallSet.SmallSetElement AllowedReduction
+
+type AllowedReductions = SmallSet AllowedReduction
+
+-- | Not quite all reductions (skip non-terminating reductions)
+allReductions :: AllowedReductions
+allReductions = SmallSet.delete NonTerminatingReductions reallyAllReductions
+
+reallyAllReductions :: AllowedReductions
+reallyAllReductions = SmallSet.total
+
+data ReduceDefs
+  = OnlyReduceDefs (Set QName)
+  | DontReduceDefs (Set QName)
+  deriving Generic
+
+reduceAllDefs :: ReduceDefs
+reduceAllDefs = DontReduceDefs empty
+
+locallyReduceDefs :: MonadTCEnv m => ReduceDefs -> m a -> m a
+locallyReduceDefs = locallyTC eReduceDefs . const
+
+locallyReduceAllDefs :: MonadTCEnv m => m a -> m a
+locallyReduceAllDefs = locallyReduceDefs reduceAllDefs
+
+shouldReduceDef :: (MonadTCEnv m) => QName -> m Bool
+shouldReduceDef f = asksTC envReduceDefs <&> \case
+  OnlyReduceDefs defs -> f `Set.member` defs
+  DontReduceDefs defs -> not $ f `Set.member` defs
+
+toReduceDefs :: (Bool, [QName]) -> ReduceDefs
+toReduceDefs (True,  ns) = OnlyReduceDefs (Data.Set.fromList ns)
+toReduceDefs (False, ns) = DontReduceDefs (Data.Set.fromList ns)
+
+fromReduceDefs :: ReduceDefs -> (Bool, [QName])
+fromReduceDefs (OnlyReduceDefs ns) = (True,  toList ns)
+fromReduceDefs (DontReduceDefs ns) = (False, toList ns)
+
+locallyReconstructed :: MonadTCEnv m => m a -> m a
+locallyReconstructed = locallyTC eReconstructed . const $ True
+
+isReconstructed :: (MonadTCEnv m) => m Bool
+isReconstructed = asksTC envReconstructed
+
+-- | Primitives
+
+data PrimitiveImpl = PrimImpl Type PrimFun
+
+data PrimFun = PrimFun
+  { primFunName           :: QName
+  , primFunArity          :: Arity
+  , primFunArgOccurrences :: [Occurrence]
+    -- ^ See 'defArgOccurrences'.
+  , primFunImplementation :: [Arg Term] -> Int -> ReduceM (Reduced MaybeReducedArgs Term)
+  }
+  deriving Generic
+
+primFun :: QName -> Arity -> ([Arg Term] -> ReduceM (Reduced MaybeReducedArgs Term)) -> PrimFun
+primFun q ar imp = PrimFun q ar [] (\args _ -> imp args)
+
+defClauses :: Definition -> [Clause]
+defClauses Defn{theDef = Function{funClauses = cs}}        = cs
+defClauses Defn{theDef = Primitive{primClauses = cs}}      = cs
+defClauses Defn{theDef = Datatype{dataClause = Just c}}    = [c]
+defClauses Defn{theDef = Record{recClause = Just c}}       = [c]
+defClauses _                                               = []
+
+defCompiled :: Definition -> Maybe CompiledClauses
+defCompiled Defn{theDef = Function {funCompiled  = mcc}} = mcc
+defCompiled Defn{theDef = Primitive{primCompiled = mcc}} = mcc
+defCompiled _ = Nothing
+
+defParameters :: Definition -> Maybe Nat
+defParameters Defn{theDef = Datatype{dataPars = n}} = Just n
+defParameters Defn{theDef = Record  {recPars  = n}} = Just n
+defParameters _                                     = Nothing
+
+defInverse :: Definition -> FunctionInverse
+defInverse Defn{theDef = Function { funInv  = inv }} = inv
+defInverse Defn{theDef = Primitive{ primInv = inv }} = inv
+defInverse _                                         = NotInjective
+
+defCompilerPragmas :: BackendName -> Definition -> [CompilerPragma]
+defCompilerPragmas b = reverse . fromMaybe [] . Map.lookup b . defCompiledRep
+  -- reversed because we add new pragmas to the front of the list
+
+-- | Has the definition failed the termination checker?
+defNonterminating :: Definition -> Bool
+defNonterminating Defn{theDef = Function{funTerminates = Just False}} = True
+defNonterminating _                                                   = False
+
+-- | Has the definition not termination checked or did the check fail?
+defTerminationUnconfirmed :: Definition -> Bool
+defTerminationUnconfirmed Defn{theDef = Function{funTerminates = Just True}} = False
+defTerminationUnconfirmed Defn{theDef = Function{funTerminates = _        }} = True
+defTerminationUnconfirmed _ = False
+
+defAbstract :: Definition -> IsAbstract
+defAbstract d = case theDef d of
+    Axiom{}                   -> ConcreteDef
+    DataOrRecSig{}            -> ConcreteDef
+    GeneralizableVar{}        -> ConcreteDef
+    AbstractDefn{}            -> AbstractDef
+    Function{funAbstr = a}    -> a
+    Datatype{dataAbstr = a}   -> a
+    Record{recAbstr = a}      -> a
+    Constructor{conAbstr = a} -> a
+    Primitive{primAbstr = a}  -> a
+    PrimitiveSort{}           -> ConcreteDef
+
+defOpaque :: Definition -> IsOpaque
+defOpaque d = case theDef d of
+    -- These two can be opaque:
+    Function{funOpaque=o}     -> o
+    Primitive{primOpaque=o}   -> o
+
+    -- Doesn't matter whether or not it's opaque:
+    Axiom{}                   -> TransparentDef
+    -- Concreteness is orthogonal to opacity:
+    AbstractDefn{}            -> TransparentDef
+
+    -- None of these are supported in opaque blocks:
+    DataOrRecSig{}            -> TransparentDef
+    GeneralizableVar{}        -> TransparentDef
+    Datatype{}                -> TransparentDef
+    Record{}                  -> TransparentDef
+    Constructor{}             -> TransparentDef
+    PrimitiveSort{}           -> TransparentDef
+
+defForced :: Definition -> [IsForced]
+defForced d = case theDef d of
+    Constructor{conForced = fs} -> fs
+    Axiom{}                     -> []
+    DataOrRecSig{}              -> []
+    GeneralizableVar{}          -> []
+    AbstractDefn{}              -> []
+    Function{}                  -> []
+    Datatype{}                  -> []
+    Record{}                    -> []
+    Primitive{}                 -> []
+    PrimitiveSort{}             -> []
+
+---------------------------------------------------------------------------
+-- ** Injectivity
+---------------------------------------------------------------------------
+
+type FunctionInverse = FunctionInverse' Clause
+type InversionMap c = Map TermHead [c]
+
+data FunctionInverse' c
+  = NotInjective
+  | Inverse (InversionMap c)
+  deriving (Show, Functor, Generic)
+
+data TermHead = SortHead
+              | PiHead
+              | ConsHead QName
+              | VarHead Nat
+              | UnknownHead
+  deriving (Eq, Ord, Show, Generic)
+
+instance Pretty TermHead where
+  pretty = \ case
+    SortHead    -> "SortHead"
+    PiHead      -> "PiHead"
+    ConsHead q  -> "ConsHead" <+> pretty q
+    VarHead i   -> text ("VarHead " ++ show i)
+    UnknownHead -> "UnknownHead"
+
+---------------------------------------------------------------------------
+-- ** Mutual blocks
+---------------------------------------------------------------------------
+
+newtype MutualId = MutId Int32
+  deriving (Eq, Ord, Show, Num, Enum, NFData)
+
+---------------------------------------------------------------------------
+-- ** Statistics
+---------------------------------------------------------------------------
+
+type Statistics = Map String Integer
+
+---------------------------------------------------------------------------
+-- ** Trace
+---------------------------------------------------------------------------
+
+data Call
+  = CheckClause Type A.SpineClause
+  | CheckLHS A.SpineLHS
+  | CheckPattern A.Pattern Telescope Type
+  | CheckPatternLinearityType C.Name
+  | CheckPatternLinearityValue C.Name
+  | CheckLetBinding A.LetBinding
+  | InferExpr A.Expr
+  | CheckExprCall Comparison A.Expr Type
+  | CheckDotPattern A.Expr Term
+  | CheckProjection Range QName Type
+  | IsTypeCall Comparison A.Expr Sort
+  | IsType_ A.Expr
+  | InferVar Name
+  | InferDef QName
+  | CheckArguments Range [NamedArg A.Expr] Type (Maybe Type)
+  | CheckMetaSolution Range MetaId Type Term
+  | CheckTargetType Range Type Type
+  | CheckDataDef Range QName [A.LamBinding] [A.Constructor]
+  | CheckRecDef Range QName [A.LamBinding] [A.Constructor]
+  | CheckConstructor QName Telescope Sort A.Constructor
+  | CheckConArgFitsIn QName Bool Type Sort
+  | CheckFunDefCall Range QName [A.Clause] Bool
+    -- ^ Highlight (interactively) if and only if the boolean is 'True'.
+  | CheckPragma Range A.Pragma
+  | CheckPrimitive Range QName A.Expr
+  | CheckIsEmpty Range Type
+  | CheckConfluence QName QName
+  | CheckModuleParameters ModuleName A.Telescope
+  | CheckWithFunctionType Type
+  | CheckSectionApplication Range Erased ModuleName A.ModuleApplication
+  | CheckNamedWhere ModuleName
+  -- | Checking a clause for confluence with endpoint reductions. Always
+  -- @φ ⊢ f vs = rhs@ for now, but we store the simplifications of
+    -- @f vs[φ]@ and @rhs[φ]@.
+  | CheckIApplyConfluence
+      Range  -- ^ Clause range
+      QName  -- ^ Function name
+      Term   -- ^ (As-is) Function applied to the patterns in this clause
+      Term   -- ^ (Simplified) Function applied to the patterns in this clause
+      Term   -- ^ (Simplified) clause RHS
+      Type   -- ^ (Simplified) clause type
+  | ScopeCheckExpr C.Expr
+  | ScopeCheckDeclaration NiceDeclaration
+  | ScopeCheckLHS C.QName C.Pattern
+  | NoHighlighting
+  | ModuleContents  -- ^ Interaction command: show module contents.
+  | SetRange Range  -- ^ used by 'setCurrentRange'
+  deriving Generic
+
+instance Pretty Call where
+    pretty CheckClause{}             = "CheckClause"
+    pretty CheckLHS{}                = "CheckLHS"
+    pretty CheckPattern{}            = "CheckPattern"
+    pretty CheckPatternLinearityType{}  = "CheckPatternLinearityType"
+    pretty CheckPatternLinearityValue{} = "CheckPatternLinearityValue"
+    pretty InferExpr{}               = "InferExpr"
+    pretty CheckExprCall{}           = "CheckExprCall"
+    pretty CheckLetBinding{}         = "CheckLetBinding"
+    pretty CheckProjection{}         = "CheckProjection"
+    pretty IsTypeCall{}              = "IsTypeCall"
+    pretty IsType_{}                 = "IsType_"
+    pretty InferVar{}                = "InferVar"
+    pretty InferDef{}                = "InferDef"
+    pretty CheckArguments{}          = "CheckArguments"
+    pretty CheckMetaSolution{}       = "CheckMetaSolution"
+    pretty CheckTargetType{}         = "CheckTargetType"
+    pretty CheckDataDef{}            = "CheckDataDef"
+    pretty CheckRecDef{}             = "CheckRecDef"
+    pretty CheckConstructor{}        = "CheckConstructor"
+    pretty CheckConArgFitsIn{}       = "CheckConArgFitsIn"
+    pretty CheckFunDefCall{}         = "CheckFunDefCall"
+    pretty CheckPragma{}             = "CheckPragma"
+    pretty CheckPrimitive{}          = "CheckPrimitive"
+    pretty CheckModuleParameters{}   = "CheckModuleParameters"
+    pretty CheckWithFunctionType{}   = "CheckWithFunctionType"
+    pretty CheckNamedWhere{}         = "CheckNamedWhere"
+    pretty ScopeCheckExpr{}          = "ScopeCheckExpr"
+    pretty ScopeCheckDeclaration{}   = "ScopeCheckDeclaration"
+    pretty ScopeCheckLHS{}           = "ScopeCheckLHS"
+    pretty CheckDotPattern{}         = "CheckDotPattern"
+    pretty SetRange{}                = "SetRange"
+    pretty CheckSectionApplication{} = "CheckSectionApplication"
+    pretty CheckIsEmpty{}            = "CheckIsEmpty"
+    pretty CheckConfluence{}         = "CheckConfluence"
+    pretty NoHighlighting{}          = "NoHighlighting"
+    pretty ModuleContents{}          = "ModuleContents"
+    pretty CheckIApplyConfluence{}   = "ModuleContents"
+
+instance HasRange Call where
+    getRange (CheckClause _ c)                   = getRange c
+    getRange (CheckLHS lhs)                      = getRange lhs
+    getRange (CheckPattern p _ _)                = getRange p
+    getRange (CheckPatternLinearityType x)       = getRange x
+    getRange (CheckPatternLinearityValue x)      = getRange x
+    getRange (InferExpr e)                       = getRange e
+    getRange (CheckExprCall _ e _)               = getRange e
+    getRange (CheckLetBinding b)                 = getRange b
+    getRange (CheckProjection r _ _)             = r
+    getRange (IsTypeCall cmp e s)                = getRange e
+    getRange (IsType_ e)                         = getRange e
+    getRange (InferVar x)                        = getRange x
+    getRange (InferDef f)                        = getRange f
+    getRange (CheckArguments r _ _ _)            = r
+    getRange (CheckMetaSolution r _ _ _)         = r
+    getRange (CheckTargetType r _ _)             = r
+    getRange (CheckDataDef i _ _ _)              = getRange i
+    getRange (CheckRecDef i _ _ _)               = getRange i
+    getRange (CheckConstructor _ _ _ c)          = getRange c
+    getRange (CheckConArgFitsIn c _ _ _)         = getRange c
+    getRange (CheckFunDefCall i _ _ _)           = getRange i
+    getRange (CheckPragma r _)                   = r
+    getRange (CheckPrimitive i _ _)              = getRange i
+    getRange (CheckModuleParameters _ tel)       = getRange tel
+    getRange CheckWithFunctionType{}             = noRange
+    getRange (CheckNamedWhere m)                 = getRange m
+    getRange (ScopeCheckExpr e)                  = getRange e
+    getRange (ScopeCheckDeclaration d)           = getRange d
+    getRange (ScopeCheckLHS _ p)                 = getRange p
+    getRange (CheckDotPattern e _)               = getRange e
+    getRange (SetRange r)                        = r
+    getRange (CheckSectionApplication r _ _ _)   = r
+    getRange (CheckIsEmpty r _)                  = r
+    getRange (CheckConfluence rule1 rule2)       = max (getRange rule1) (getRange rule2)
+    getRange NoHighlighting                      = noRange
+    getRange ModuleContents                      = noRange
+    getRange (CheckIApplyConfluence e _ _ _ _ _) = getRange e
+
+---------------------------------------------------------------------------
+-- ** Instance table
+---------------------------------------------------------------------------
+
+-- | The instance table is a @Map@ associating to every name of
+--   record/data type/postulate its list of instances
+type InstanceTable = Map QName (Set QName)
+
+-- | When typechecking something of the following form:
+--
+--     instance
+--       x : _
+--       x = y
+--
+--   it's not yet known where to add @x@, so we add it to a list of
+--   unresolved instances and we'll deal with it later.
+type TempInstanceTable = (InstanceTable , Set QName)
+
+---------------------------------------------------------------------------
+-- ** Builtin things
+---------------------------------------------------------------------------
+
+data BuiltinSort
+  = SortUniv Univ
+  | SortOmega Univ
+  | SortIntervalUniv
+  | SortLevelUniv
+  deriving (Show, Eq, Generic)
+
+pattern SortProp, SortSet, SortStrictSet, SortPropOmega, SortSetOmega, SortStrictSetOmega :: BuiltinSort
+pattern SortProp           = SortUniv  UProp
+pattern SortSet            = SortUniv  UType
+pattern SortStrictSet      = SortUniv  USSet
+pattern SortPropOmega      = SortOmega UProp
+pattern SortSetOmega       = SortOmega UType
+pattern SortStrictSetOmega = SortOmega USSet
+
+{-# COMPLETE
+  SortProp, SortSet, SortStrictSet,
+  SortPropOmega, SortSetOmega, SortStrictSetOmega,
+  SortIntervalUniv, SortLevelUniv #-}
+
+data BuiltinDescriptor
+  = BuiltinData (TCM Type) [BuiltinId]
+  | BuiltinDataCons (TCM Type)
+  | BuiltinPrim PrimitiveId (Term -> TCM ())
+  | BuiltinSort BuiltinSort
+  | BuiltinPostulate Relevance (TCM Type)
+  | BuiltinUnknown (Maybe (TCM Type)) (Term -> Type -> TCM ())
+    -- ^ Builtin of any kind.
+    --   Type can be checked (@Just t@) or inferred (@Nothing@).
+    --   The second argument is the hook for the verification function.
+
+data BuiltinInfo =
+   BuiltinInfo { builtinName :: BuiltinId
+               , builtinDesc :: BuiltinDescriptor }
+
+type BuiltinThings pf = Map SomeBuiltin (Builtin pf)
+
+data Builtin pf
+        = Builtin Term
+        | Prim pf
+        | BuiltinRewriteRelations (Set QName)
+            -- ^ @BUILTIN REWRITE@.  We can have several rewrite relations.
+    deriving (Show, Functor, Foldable, Traversable, Generic)
+
+---------------------------------------------------------------------------
+-- * Highlighting levels
+---------------------------------------------------------------------------
+
+-- | How much highlighting should be sent to the user interface?
+
+data HighlightingLevel
+  = None
+  | NonInteractive
+  | Interactive
+    -- ^ This includes both non-interactive highlighting and
+    -- interactive highlighting of the expression that is currently
+    -- being type-checked.
+    deriving (Eq, Ord, Show, Read, Generic)
+
+-- | How should highlighting be sent to the user interface?
+
+data HighlightingMethod
+  = Direct
+    -- ^ Via stdout.
+  | Indirect
+    -- ^ Both via files and via stdout.
+    deriving (Eq, Show, Read, Generic)
+
+-- | @ifTopLevelAndHighlightingLevelIs l b m@ runs @m@ when we're
+-- type-checking the top-level module (or before we've started doing
+-- this) and either the highlighting level is /at least/ @l@ or @b@ is
+-- 'True'.
+
+ifTopLevelAndHighlightingLevelIsOr ::
+  MonadTCEnv tcm => HighlightingLevel -> Bool -> tcm () -> tcm ()
+ifTopLevelAndHighlightingLevelIsOr l b m = do
+  e <- askTC
+  when (envHighlightingLevel e >= l || b) $
+    case (envImportPath e) of
+      -- Below the main module.
+      (_:_:_) -> pure ()
+      -- In or before the top-level module.
+      _ -> m
+
+-- | @ifTopLevelAndHighlightingLevelIs l m@ runs @m@ when we're
+-- type-checking the top-level module (or before we've started doing
+-- this) and the highlighting level is /at least/ @l@.
+
+ifTopLevelAndHighlightingLevelIs ::
+  MonadTCEnv tcm => HighlightingLevel -> tcm () -> tcm ()
+ifTopLevelAndHighlightingLevelIs l =
+  ifTopLevelAndHighlightingLevelIsOr l False
+
+---------------------------------------------------------------------------
+-- * Type checking environment
+---------------------------------------------------------------------------
+
+data TCEnv =
+    TCEnv { envContext             :: Context
+          , envLetBindings         :: LetBindings
+          , envCurrentModule       :: ModuleName
+          , envCurrentPath         :: Maybe AbsolutePath
+            -- ^ The path to the file that is currently being
+            -- type-checked.  'Nothing' if we do not have a file
+            -- (like in interactive mode see @CommandLine@).
+          , envAnonymousModules    :: [(ModuleName, Nat)] -- ^ anonymous modules and their number of free variables
+          , envImportPath          :: [TopLevelModuleName]
+            -- ^ The module stack with the entry being the top-level module as
+            --   Agda chases modules. It will be empty if there is no main
+            --   module, will have a single entry for the top level module, or
+            --   more when descending past the main module. This is used to
+            --   detect import cycles and in some cases highlighting behavior.
+            --   The level of a given module is not necessarily the same as the
+            --   length, in the module dependency graph, of the shortest path
+            --   from the top-level module; it depends on in which order Agda
+            --   chooses to chase dependencies.
+          , envMutualBlock         :: Maybe MutualId -- ^ the current (if any) mutual block
+          , envTerminationCheck    :: TerminationCheck ()  -- ^ are we inside the scope of a termination pragma
+          , envCoverageCheck       :: CoverageCheck        -- ^ are we inside the scope of a coverage pragma
+          , envMakeCase            :: Bool                 -- ^ are we inside a make-case (if so, ignore forcing analysis in unifier)
+          , envSolvingConstraints  :: Bool
+                -- ^ Are we currently in the process of solving active constraints?
+          , envCheckingWhere       :: Bool
+                -- ^ Have we stepped into the where-declarations of a clause?
+                --   Everything under a @where@ will be checked with this flag on.
+          , envWorkingOnTypes      :: Bool
+                -- ^ Are we working on types? Turned on by 'workOnTypes'.
+          , envAssignMetas         :: Bool
+            -- ^ Are we allowed to assign metas?
+          , envActiveProblems      :: Set ProblemId
+          , envAbstractMode        :: AbstractMode
+                -- ^ When checking the typesignature of a public definition
+                --   or the body of a non-abstract definition this is true.
+                --   To prevent information about abstract things leaking
+                --   outside the module.
+          , envRelevance           :: Relevance
+                -- ^ Are we checking an irrelevant argument? (=@Irrelevant@)
+                -- Then top-level irrelevant declarations are enabled.
+                -- Other value: @Relevant@, then only relevant decls. are available.
+          , envQuantity            :: Quantity
+                -- ^ Are we checking a runtime-irrelevant thing? (='Quantity0')
+                -- Then runtime-irrelevant things are usable.
+          , envHardCompileTimeMode :: Bool
+                -- ^ Is the \"hard\" compile-time mode enabled? In
+                -- this mode the quantity component of the environment
+                -- is always zero, and every new definition is treated
+                -- as erased.
+          , envSplitOnStrict       :: Bool
+                -- ^ Are we currently case-splitting on a strict
+                --   datatype (i.e. in SSet)? If yes, the
+                --   pattern-matching unifier will solve reflexive
+                --   equations even --without-K.
+          , envDisplayFormsEnabled :: Bool
+                -- ^ Sometimes we want to disable display forms.
+          , envFoldLetBindings :: Bool
+                -- ^ Fold let-bindings when printing terms (default: True)
+          , envRange :: Range
+          , envHighlightingRange :: Range
+                -- ^ Interactive highlighting uses this range rather
+                --   than 'envRange'.
+          , envClause :: IPClause
+                -- ^ What is the current clause we are type-checking?
+                --   Will be recorded in interaction points in this clause.
+          , envCall  :: Maybe (Closure Call)
+                -- ^ what we're doing at the moment
+          , envHighlightingLevel  :: HighlightingLevel
+                -- ^ Set to 'None' when imported modules are
+                --   type-checked.
+          , envHighlightingMethod :: HighlightingMethod
+          , envExpandLast :: ExpandHidden
+                -- ^ When type-checking an alias f=e, we do not want
+                -- to insert hidden arguments in the end, because
+                -- these will become unsolved metas.
+          , envAppDef :: Maybe QName
+                -- ^ We are reducing an application of this function.
+                -- (For tracking of incomplete matches.)
+          , envSimplification :: Simplification
+                -- ^ Did we encounter a simplification (proper match)
+                --   during the current reduction process?
+          , envAllowedReductions :: AllowedReductions
+          , envReduceDefs :: ReduceDefs
+          , envReconstructed :: Bool
+          , envInjectivityDepth :: Int
+                -- ^ Injectivity can cause non-termination for unsolvable contraints
+                --   (#431, #3067). Keep a limit on the nesting depth of injectivity
+                --   uses.
+          , envCompareBlocked :: Bool
+                -- ^ When @True@, the conversion checker will consider
+                --   all term constructors as injective, including
+                --   blocked function applications and metas. Warning:
+                --   this should only be used when not assigning any
+                --   metas (e.g. when @envAssignMetas@ is @False@ or
+                --   when running @pureEqualTerms@) or else we get
+                --   non-unique meta solutions.
+          , envPrintDomainFreePi :: Bool
+                -- ^ When @True@, types will be omitted from printed pi types if they
+                --   can be inferred.
+          , envPrintMetasBare :: Bool
+                -- ^ When @True@, throw away meta numbers and meta elims.
+                --   This is used for reifying terms for feeding into the
+                --   user's source code, e.g., for the interaction tactics @solveAll@.
+          , envInsideDotPattern :: Bool
+                -- ^ Used by the scope checker to make sure that certain forms
+                --   of expressions are not used inside dot patterns: extended
+                --   lambdas and let-expressions.
+          , envUnquoteFlags :: UnquoteFlags
+          , envInstanceDepth :: !Int
+                -- ^ Until we get a termination checker for instance search (#1743) we
+                --   limit the search depth to ensure termination.
+          , envIsDebugPrinting :: Bool
+          , envPrintingPatternLambdas :: [QName]
+                -- ^ #3004: pattern lambdas with copatterns may refer to themselves. We
+                --   don't have a good story for what to do in this case, but at least
+                --   printing shouldn't loop. Here we keep track of which pattern lambdas
+                --   we are currently in the process of printing.
+          , envCallByNeed :: Bool
+                -- ^ Use call-by-need evaluation for reductions.
+          , envCurrentCheckpoint :: CheckpointId
+                -- ^ Checkpoints track the evolution of the context as we go
+                -- under binders or refine it by pattern matching.
+          , envCheckpoints :: Map CheckpointId Substitution
+                -- ^ Keeps the substitution from each previous checkpoint to
+                --   the current context.
+          , envGeneralizeMetas :: DoGeneralize
+                -- ^ Should new metas generalized over.
+          , envGeneralizedVars :: Map QName GeneralizedValue
+                -- ^ Values for used generalizable variables.
+          , envActiveBackendName :: Maybe BackendName
+                -- ^ Is some backend active at the moment, and if yes, which?
+                --   NB: we only store the 'BackendName' here, otherwise
+                --   @instance Data TCEnv@ is not derivable.
+                --   The actual backend can be obtained from the name via 'stBackends'.
+          , envConflComputingOverlap :: Bool
+                -- ^ Are we currently computing the overlap between
+                --   two rewrite rules for the purpose of confluence checking?
+          , envCurrentlyElaborating :: Bool
+                -- ^ Are we currently in the process of executing an
+                --   elaborate-and-give interactive command?
+          , envSyntacticEqualityFuel :: !(Strict.Maybe Int)
+                -- ^ If this counter is 'Strict.Nothing', then
+                -- syntactic equality checking is unrestricted. If it
+                -- is zero, then syntactic equality checking is not
+                -- run at all. If it is a positive number, then
+                -- syntactic equality checking is allowed to run, but
+                -- the counter is decreased in the failure
+                -- continuation of
+                -- 'Agda.TypeChecking.SyntacticEquality.checkSyntacticEquality'.
+          , envCurrentOpaqueId :: !(Maybe OpaqueId)
+                -- ^ Unique identifier of the opaque block we are
+                -- currently under, if any. Used by the scope checker
+                -- (to associate definitions to blocks), and by the type
+                -- checker (for unfolding control).
+          }
+    deriving (Generic)
+
+initEnv :: TCEnv
+initEnv = TCEnv { envContext             = []
+                , envLetBindings         = Map.empty
+                , envCurrentModule       = noModuleName
+                , envCurrentPath         = Nothing
+                , envAnonymousModules    = []
+                , envImportPath          = []
+                , envMutualBlock         = Nothing
+                , envTerminationCheck    = TerminationCheck
+                , envCoverageCheck       = YesCoverageCheck
+                , envMakeCase            = False
+                , envSolvingConstraints  = False
+                , envCheckingWhere       = False
+                , envActiveProblems      = Set.empty
+                , envWorkingOnTypes      = False
+                , envAssignMetas         = True
+                , envAbstractMode        = ConcreteMode
+  -- Andreas, 2013-02-21:  This was 'AbstractMode' until now.
+  -- However, top-level checks for mutual blocks, such as
+  -- constructor-headedness, should not be able to look into
+  -- abstract definitions unless abstract themselves.
+  -- (See also discussion on issue 796.)
+  -- The initial mode should be 'ConcreteMode', ensuring you
+  -- can only look into abstract things in an abstract
+  -- definition (which sets 'AbstractMode').
+                , envRelevance              = unitRelevance
+                , envQuantity               = unitQuantity
+                , envHardCompileTimeMode    = False
+                , envSplitOnStrict          = False
+                , envDisplayFormsEnabled    = True
+                , envFoldLetBindings        = True
+                , envRange                  = noRange
+                , envHighlightingRange      = noRange
+                , envClause                 = IPNoClause
+                , envCall                   = Nothing
+                , envHighlightingLevel      = None
+                , envHighlightingMethod     = Indirect
+                , envExpandLast             = ExpandLast
+                , envAppDef                 = Nothing
+                , envSimplification         = NoSimplification
+                , envAllowedReductions      = allReductions
+                , envReduceDefs             = reduceAllDefs
+                , envReconstructed          = False
+                , envInjectivityDepth       = 0
+                , envCompareBlocked         = False
+                , envPrintDomainFreePi      = False
+                , envPrintMetasBare         = False
+                , envInsideDotPattern       = False
+                , envUnquoteFlags           = defaultUnquoteFlags
+                , envInstanceDepth          = 0
+                , envIsDebugPrinting        = False
+                , envPrintingPatternLambdas = []
+                , envCallByNeed             = True
+                , envCurrentCheckpoint      = 0
+                , envCheckpoints            = Map.singleton 0 IdS
+                , envGeneralizeMetas        = NoGeneralize
+                , envGeneralizedVars        = Map.empty
+                , envActiveBackendName      = Nothing
+                , envConflComputingOverlap  = False
+                , envCurrentlyElaborating   = False
+                , envSyntacticEqualityFuel  = Strict.Nothing
+                , envCurrentOpaqueId        = Nothing
+                }
+
+class LensTCEnv a where
+  lensTCEnv :: Lens' a TCEnv
+
+instance LensTCEnv TCEnv where
+  lensTCEnv = id
+
+data UnquoteFlags = UnquoteFlags
+  { _unquoteNormalise :: Bool }
+  deriving Generic
+
+defaultUnquoteFlags :: UnquoteFlags
+defaultUnquoteFlags = UnquoteFlags
+  { _unquoteNormalise = False }
+
+unquoteNormalise :: Lens' UnquoteFlags Bool
+unquoteNormalise f e = f (_unquoteNormalise e) <&> \ x -> e { _unquoteNormalise = x }
+
+eUnquoteNormalise :: Lens' TCEnv Bool
+eUnquoteNormalise = eUnquoteFlags . unquoteNormalise
+
+-- * e-prefixed lenses
+------------------------------------------------------------------------
+
+eContext :: Lens' TCEnv Context
+eContext f e = f (envContext e) <&> \ x -> e { envContext = x }
+
+eLetBindings :: Lens' TCEnv LetBindings
+eLetBindings f e = f (envLetBindings e) <&> \ x -> e { envLetBindings = x }
+
+eCurrentModule :: Lens' TCEnv ModuleName
+eCurrentModule f e = f (envCurrentModule e) <&> \ x -> e { envCurrentModule = x }
+
+eCurrentPath :: Lens' TCEnv (Maybe AbsolutePath)
+eCurrentPath f e = f (envCurrentPath e) <&> \ x -> e { envCurrentPath = x }
+
+eAnonymousModules :: Lens' TCEnv [(ModuleName, Nat)]
+eAnonymousModules f e = f (envAnonymousModules e) <&> \ x -> e { envAnonymousModules = x }
+
+eImportPath :: Lens' TCEnv [TopLevelModuleName]
+eImportPath f e = f (envImportPath e) <&> \ x -> e { envImportPath = x }
+
+eMutualBlock :: Lens' TCEnv (Maybe MutualId)
+eMutualBlock f e = f (envMutualBlock e) <&> \ x -> e { envMutualBlock = x }
+
+eTerminationCheck :: Lens' TCEnv (TerminationCheck ())
+eTerminationCheck f e = f (envTerminationCheck e) <&> \ x -> e { envTerminationCheck = x }
+
+eCoverageCheck :: Lens' TCEnv CoverageCheck
+eCoverageCheck f e = f (envCoverageCheck e) <&> \ x -> e { envCoverageCheck = x }
+
+eMakeCase :: Lens' TCEnv Bool
+eMakeCase f e = f (envMakeCase e) <&> \ x -> e { envMakeCase = x }
+
+eSolvingConstraints :: Lens' TCEnv Bool
+eSolvingConstraints f e = f (envSolvingConstraints e) <&> \ x -> e { envSolvingConstraints = x }
+
+eCheckingWhere :: Lens' TCEnv Bool
+eCheckingWhere f e = f (envCheckingWhere e) <&> \ x -> e { envCheckingWhere = x }
+
+eWorkingOnTypes :: Lens' TCEnv Bool
+eWorkingOnTypes f e = f (envWorkingOnTypes e) <&> \ x -> e { envWorkingOnTypes = x }
+
+eAssignMetas :: Lens' TCEnv Bool
+eAssignMetas f e = f (envAssignMetas e) <&> \ x -> e { envAssignMetas = x }
+
+eActiveProblems :: Lens' TCEnv (Set ProblemId)
+eActiveProblems f e = f (envActiveProblems e) <&> \ x -> e { envActiveProblems = x }
+
+eAbstractMode :: Lens' TCEnv AbstractMode
+eAbstractMode f e = f (envAbstractMode e) <&> \ x -> e { envAbstractMode = x }
+
+eRelevance :: Lens' TCEnv Relevance
+eRelevance f e = f (envRelevance e) <&> \x -> e { envRelevance = x }
+
+-- | Note that this lens does not satisfy all lens laws: If hard
+-- compile-time mode is enabled, then quantities other than zero are
+-- replaced by '__IMPOSSIBLE__'.
+
+eQuantity :: Lens' TCEnv Quantity
+eQuantity f e =
+  if envHardCompileTimeMode e
+  then f (check (envQuantity e)) <&>
+       \x -> e { envQuantity = check x }
+  else f (envQuantity e) <&> \x -> e { envQuantity = x }
+  where
+  check q
+    | hasQuantity0 q = q
+    | otherwise      = __IMPOSSIBLE__
+
+eHardCompileTimeMode :: Lens' TCEnv Bool
+eHardCompileTimeMode f e = f (envHardCompileTimeMode e) <&> \x -> e { envHardCompileTimeMode = x }
+
+eSplitOnStrict :: Lens' TCEnv Bool
+eSplitOnStrict f e = f (envSplitOnStrict e) <&> \ x -> e { envSplitOnStrict = x }
+
+eDisplayFormsEnabled :: Lens' TCEnv Bool
+eDisplayFormsEnabled f e = f (envDisplayFormsEnabled e) <&> \ x -> e { envDisplayFormsEnabled = x }
+
+eFoldLetBindings :: Lens' TCEnv Bool
+eFoldLetBindings f e = f (envFoldLetBindings e) <&> \ x -> e { envFoldLetBindings = x }
+
+eRange :: Lens' TCEnv Range
+eRange f e = f (envRange e) <&> \ x -> e { envRange = x }
+
+eHighlightingRange :: Lens' TCEnv Range
+eHighlightingRange f e = f (envHighlightingRange e) <&> \ x -> e { envHighlightingRange = x }
+
+eCall :: Lens' TCEnv (Maybe (Closure Call))
+eCall f e = f (envCall e) <&> \ x -> e { envCall = x }
+
+eHighlightingLevel :: Lens' TCEnv HighlightingLevel
+eHighlightingLevel f e = f (envHighlightingLevel e) <&> \ x -> e { envHighlightingLevel = x }
+
+eHighlightingMethod :: Lens' TCEnv HighlightingMethod
+eHighlightingMethod f e = f (envHighlightingMethod e) <&> \ x -> e { envHighlightingMethod = x }
+
+eExpandLast :: Lens' TCEnv ExpandHidden
+eExpandLast f e = f (envExpandLast e) <&> \ x -> e { envExpandLast = x }
+
+eExpandLastBool :: Lens' TCEnv Bool
+eExpandLastBool f e = f (isExpandLast $ envExpandLast e) <&> \ x -> e { envExpandLast = toExpandLast x }
+
+eAppDef :: Lens' TCEnv (Maybe QName)
+eAppDef f e = f (envAppDef e) <&> \ x -> e { envAppDef = x }
+
+eSimplification :: Lens' TCEnv Simplification
+eSimplification f e = f (envSimplification e) <&> \ x -> e { envSimplification = x }
+
+eAllowedReductions :: Lens' TCEnv AllowedReductions
+eAllowedReductions f e = f (envAllowedReductions e) <&> \ x -> e { envAllowedReductions = x }
+
+eReduceDefs :: Lens' TCEnv ReduceDefs
+eReduceDefs f e = f (envReduceDefs e) <&> \ x -> e { envReduceDefs = x }
+
+eReduceDefsPair :: Lens' TCEnv (Bool, [QName])
+eReduceDefsPair f e = f (fromReduceDefs $ envReduceDefs e) <&> \ x -> e { envReduceDefs = toReduceDefs x }
+
+eReconstructed :: Lens' TCEnv Bool
+eReconstructed f e = f (envReconstructed e) <&> \ x -> e { envReconstructed = x }
+
+eInjectivityDepth :: Lens' TCEnv Int
+eInjectivityDepth f e = f (envInjectivityDepth e) <&> \ x -> e { envInjectivityDepth = x }
+
+eCompareBlocked :: Lens' TCEnv Bool
+eCompareBlocked f e = f (envCompareBlocked e) <&> \ x -> e { envCompareBlocked = x }
+
+ePrintDomainFreePi :: Lens' TCEnv Bool
+ePrintDomainFreePi f e = f (envPrintDomainFreePi e) <&> \ x -> e { envPrintDomainFreePi = x }
+
+ePrintMetasBare :: Lens' TCEnv Bool
+ePrintMetasBare f e = f (envPrintMetasBare e) <&> \ x -> e { envPrintMetasBare = x }
+
+eInsideDotPattern :: Lens' TCEnv Bool
+eInsideDotPattern f e = f (envInsideDotPattern e) <&> \ x -> e { envInsideDotPattern = x }
+
+eUnquoteFlags :: Lens' TCEnv UnquoteFlags
+eUnquoteFlags f e = f (envUnquoteFlags e) <&> \ x -> e { envUnquoteFlags = x }
+
+eInstanceDepth :: Lens' TCEnv Int
+eInstanceDepth f e = f (envInstanceDepth e) <&> \ x -> e { envInstanceDepth = x }
+
+eIsDebugPrinting :: Lens' TCEnv Bool
+eIsDebugPrinting f e = f (envIsDebugPrinting e) <&> \ x -> e { envIsDebugPrinting = x }
+
+ePrintingPatternLambdas :: Lens' TCEnv [QName]
+ePrintingPatternLambdas f e = f (envPrintingPatternLambdas e) <&> \ x -> e { envPrintingPatternLambdas = x }
+
+eCallByNeed :: Lens' TCEnv Bool
+eCallByNeed f e = f (envCallByNeed e) <&> \ x -> e { envCallByNeed = x }
+
+eCurrentCheckpoint :: Lens' TCEnv CheckpointId
+eCurrentCheckpoint f e = f (envCurrentCheckpoint e) <&> \ x -> e { envCurrentCheckpoint = x }
+
+eCheckpoints :: Lens' TCEnv (Map CheckpointId Substitution)
+eCheckpoints f e = f (envCheckpoints e) <&> \ x -> e { envCheckpoints = x }
+
+eGeneralizeMetas :: Lens' TCEnv DoGeneralize
+eGeneralizeMetas f e = f (envGeneralizeMetas e) <&> \ x -> e { envGeneralizeMetas = x }
+
+eGeneralizedVars :: Lens' TCEnv (Map QName GeneralizedValue)
+eGeneralizedVars f e = f (envGeneralizedVars e) <&> \ x -> e { envGeneralizedVars = x }
+
+eActiveBackendName :: Lens' TCEnv (Maybe BackendName)
+eActiveBackendName f e = f (envActiveBackendName e) <&> \ x -> e { envActiveBackendName = x }
+
+eConflComputingOverlap :: Lens' TCEnv Bool
+eConflComputingOverlap f e = f (envConflComputingOverlap e) <&> \ x -> e { envConflComputingOverlap = x }
+
+eCurrentlyElaborating :: Lens' TCEnv Bool
+eCurrentlyElaborating f e = f (envCurrentlyElaborating e) <&> \ x -> e { envCurrentlyElaborating = x }
+
+{-# SPECIALISE currentModality :: TCM Modality #-}
+-- | The current modality.
+--   Note that the returned cohesion component is always 'unitCohesion'.
+currentModality :: MonadTCEnv m => m Modality
+currentModality = do
+  r <- viewTC eRelevance
+  q <- viewTC eQuantity
+  return Modality
+    { modRelevance = r
+    , modQuantity  = q
+    , modCohesion  = unitCohesion
+    }
+
+---------------------------------------------------------------------------
+-- ** Context
+---------------------------------------------------------------------------
+
+-- | The @Context@ is a stack of 'ContextEntry's.
+type Context      = [ContextEntry]
+type ContextEntry = Dom (Name, Type)
+
+---------------------------------------------------------------------------
+-- ** Let bindings
+---------------------------------------------------------------------------
+
+type LetBindings = Map Name (Open LetBinding)
+
+data LetBinding = LetBinding { letOrigin :: Origin
+                             , letTerm   :: Term
+                             , letType   :: Dom Type
+                             }
+  deriving (Show, Generic)
+
+onLetBindingType :: (Dom Type -> Dom Type) -> LetBinding -> LetBinding
+onLetBindingType f b = b { letType = f $ letType b }
+
+---------------------------------------------------------------------------
+-- ** Abstract mode
+---------------------------------------------------------------------------
+
+data AbstractMode
+  = AbstractMode        -- ^ Abstract things in the current module can be accessed.
+  | ConcreteMode        -- ^ No abstract things can be accessed.
+  | IgnoreAbstractMode  -- ^ All abstract things can be accessed.
+  deriving (Show, Eq, Generic)
+
+aDefToMode :: IsAbstract -> AbstractMode
+aDefToMode AbstractDef = AbstractMode
+aDefToMode ConcreteDef = ConcreteMode
+
+aModeToDef :: AbstractMode -> Maybe IsAbstract
+aModeToDef AbstractMode = Just AbstractDef
+aModeToDef ConcreteMode = Just ConcreteDef
+aModeToDef _ = Nothing
+
+---------------------------------------------------------------------------
+-- ** Opaque blocks
+---------------------------------------------------------------------------
+
+-- | A block of opaque definitions.
+data OpaqueBlock = OpaqueBlock
+  { opaqueId        :: {-# UNPACK #-} !OpaqueId
+    -- ^ Unique identifier for this block.
+  , opaqueUnfolding :: HashSet QName
+    -- ^ Set of names we are allowed to unfold. After scope-checking,
+    -- this set should be transitively closed.
+  , opaqueDecls     :: HashSet QName
+    -- ^ Declarations contained in this abstract block.
+  , opaqueParent    :: Maybe OpaqueId
+    -- ^ Pointer to an enclosing opaque block, if one exists.
+  , opaqueRange     :: Range
+    -- ^ Where is this opaque block?
+  } deriving (Show, Generic)
+
+instance Pretty OpaqueBlock where
+  pretty (OpaqueBlock _ uf ds p _) = vcat
+    $ [ "opaque (extends " <> pretty p <> ") {"
+      , nest 2 "unfolds"
+      ]
+    ++ [ nest 4 (pretty n <> ",") | n <- List.sort $ HashSet.toList uf ]
+         -- Andreas, 2023-08-10, https://github.com/agda/agda/pull/6628#discussion_r1285078454
+         -- The HashSet.toList is non-deterministic, order may depend on version of @hashable@.
+         -- Thus, we sort the list, so that the output isn't dependent on the specific build.
+    ++ [ nest 2 "declares" ]
+    ++ [ nest 4 (pretty n <+> ": _") | n <- List.sort $ HashSet.toList ds ]
+    ++ [ "}" ]
+
+instance Eq OpaqueBlock where
+  xs == ys = opaqueId xs == opaqueId ys
+
+instance Hashable OpaqueBlock where
+  hashWithSalt s = hashWithSalt s . opaqueId
+
+---------------------------------------------------------------------------
+-- ** Insertion of implicit arguments
+---------------------------------------------------------------------------
+
+data ExpandHidden
+  = ExpandLast      -- ^ Add implicit arguments in the end until type is no longer hidden 'Pi'.
+  | DontExpandLast  -- ^ Do not append implicit arguments.
+  | ReallyDontExpandLast -- ^ Makes 'doExpandLast' have no effect. Used to avoid implicit insertion of arguments to metavariables.
+  deriving (Eq, Generic)
+
+isExpandLast :: ExpandHidden -> Bool
+isExpandLast ExpandLast           = True
+isExpandLast DontExpandLast       = False
+isExpandLast ReallyDontExpandLast = False
+
+isDontExpandLast :: ExpandHidden -> Bool
+isDontExpandLast = not . isExpandLast
+
+toExpandLast :: Bool -> ExpandHidden
+toExpandLast True  = ExpandLast
+toExpandLast False = DontExpandLast
+
+data CandidateKind
+  = LocalCandidate
+  | GlobalCandidate QName
+  deriving (Show, Generic)
+
+-- | A candidate solution for an instance meta is a term with its type.
+--   It may be the case that the candidate is not fully applied yet or
+--   of the wrong type, hence the need for the type.
+data Candidate  = Candidate { candidateKind :: CandidateKind
+                            , candidateTerm :: Term
+                            , candidateType :: Type
+                            , candidateOverlappable :: Bool
+                            }
+  deriving (Show, Generic)
+
+instance Free Candidate where
+  freeVars' (Candidate _ t u _) = freeVars' (t, u)
+
+
+---------------------------------------------------------------------------
+-- ** Checking arguments
+---------------------------------------------------------------------------
+
+data ArgsCheckState a = ACState
+       { acRanges :: [Maybe Range]
+         -- ^ Ranges of checked arguments, where present.
+         -- e.g. inserted implicits have no correponding abstract syntax.
+       , acElims  :: Elims
+         -- ^ Checked and inserted arguments so far.
+       , acConstraints :: [Maybe (Abs Constraint)]
+         -- ^ Constraints for the head so far,
+         -- i.e. before applying the correponding elim.
+       , acType   :: Type
+         -- ^ Type for the rest of the application.
+       , acData   :: a
+       }
+  deriving (Show)
+
+
+---------------------------------------------------------------------------
+-- * Type checking warnings (aka non-fatal errors)
+---------------------------------------------------------------------------
+
+-- | A non-fatal error is an error which does not prevent us from
+-- checking the document further and interacting with the user.
+
+data Warning
+  = NicifierIssue            DeclarationWarning
+  | TerminationIssue         [TerminationError]
+  | UnreachableClauses       QName [Range]
+  -- ^ `UnreachableClauses f rs` means that the clauses in `f` whose ranges are rs
+  --   are unreachable
+  | CoverageIssue            QName [(Telescope, [NamedArg DeBruijnPattern])]
+  -- ^ `CoverageIssue f pss` means that `pss` are not covered in `f`
+  | CoverageNoExactSplit     QName [Clause]
+  | InlineNoExactSplit       QName Clause
+    -- ^ 'Clause' was turned into copattern matching clause(s) by an @{-# INLINE constructor #-}@
+    --   and thus is not a definitional equality any more.
+  | NotStrictlyPositive      QName (Seq OccursWhere)
+
+  | UnsolvedMetaVariables    [Range]  -- ^ Do not use directly with 'warning'
+  | UnsolvedInteractionMetas [Range]  -- ^ Do not use directly with 'warning'
+  | UnsolvedConstraints      Constraints
+    -- ^ Do not use directly with 'warning'
+  | InteractionMetaBoundaries [Range]
+    -- ^ Do not use directly with 'warning'
+
+  | CantGeneralizeOverSorts [MetaId]
+  | AbsurdPatternRequiresNoRHS [NamedArg DeBruijnPattern]
+  | OldBuiltin               BuiltinId BuiltinId
+    -- ^ In `OldBuiltin old new`, the BUILTIN old has been replaced by new
+  | EmptyRewritePragma
+    -- ^ If the user wrote just @{-\# REWRITE \#-}@.
+  | EmptyWhere
+    -- ^ An empty @where@ block is dead code.
+  | IllformedAsClause String
+    -- ^ If the user wrote something other than an unqualified name
+    --   in the @as@ clause of an @import@ statement.
+    --   The 'String' gives optionally extra explanation.
+  | InvalidCharacterLiteral Char
+    -- ^ A character literal Agda does not support, e.g. surrogate code points.
+  | ClashesViaRenaming NameOrModule [C.Name]
+    -- ^ If a `renaming' import directive introduces a name or module name clash
+    --   in the exported names of a module.
+    --   (See issue #4154.)
+  | UselessPatternDeclarationForRecord String
+    -- ^ The 'pattern' declaration is useless in the presence
+    --   of either @coinductive@ or @eta-equality@.
+    --   Content of 'String' is "coinductive" or "eta", resp.
+  | UselessPragma Range Doc
+    -- ^ Warning when pragma is useless and thus ignored.
+    --   'Range' is for dead code highlighting.
+  | UselessPublic
+    -- ^ If the user opens a module public before the module header.
+    --   (See issue #2377.)
+  | UselessHiding [C.ImportedName]
+    -- ^ Names in `hiding` directive that don't hide anything
+    --   imported by a `using` directive.
+  | UselessInline            QName
+  | WrongInstanceDeclaration
+  | InstanceWithExplicitArg  QName
+  -- ^ An instance was declared with an implicit argument, which means it
+  --   will never actually be considered by instance search.
+  | InstanceNoOutputTypeName Doc
+  -- ^ The type of an instance argument doesn't end in a named or
+  -- variable type, so it will never be considered by instance search.
+  | InstanceArgWithExplicitArg Doc
+  -- ^ As InstanceWithExplicitArg, but for local bindings rather than
+  --   top-level instances.
+  | InversionDepthReached    QName
+  -- ^ The --inversion-max-depth was reached.
+  | NoGuardednessFlag        QName
+  -- ^ A coinductive record was declared but neither --guardedness nor
+  --   --sized-types is enabled.
+
+  -- Generic warnings for one-off things
+  | GenericWarning           Doc
+    -- ^ Harmless generic warning (not an error)
+
+  -- Safe flag errors
+  | SafeFlagPostulate C.Name
+  | SafeFlagPragma [String]                -- ^ Unsafe OPTIONS.
+  | SafeFlagWithoutKFlagPrimEraseEquality
+  | WithoutKFlagPrimEraseEquality
+  | OptionWarning            OptionWarning
+  | ParseWarning             ParseWarning
+  | LibraryWarning           LibWarning
+  | DeprecationWarning String String String
+    -- ^ `DeprecationWarning old new version`:
+    --   `old` is deprecated, use `new` instead. This will be an error in Agda `version`.
+  | UserWarning Text
+    -- ^ User-defined warning (e.g. to mention that a name is deprecated)
+  | DuplicateUsing (List1 C.ImportedName)
+    -- ^ Duplicate mentions of the same name in @using@ directive(s).
+  | FixityInRenamingModule (List1 Range)
+    -- ^ Fixity of modules cannot be changed via renaming (since modules have no fixity).
+  | ModuleDoesntExport C.QName [C.Name] [C.Name] [C.ImportedName]
+    -- ^ Some imported names are not actually exported by the source module.
+    --   The second argument is the names that could be exported.
+    --   The third  argument is the module names that could be exported.
+  | InfectiveImport Doc
+    -- ^ Importing a file using an infective option into one which doesn't
+  | CoInfectiveImport Doc
+    -- ^ Importing a file not using a coinfective option from one which does
+  | RewriteNonConfluent Term Term Term Doc
+    -- ^ Confluence checker found critical pair and equality checking
+    --   resulted in a type error
+  | RewriteMaybeNonConfluent Term Term [Doc]
+    -- ^ Confluence checker got stuck on computing overlap between two
+    --   rewrite rules
+  | RewriteAmbiguousRules Term Term Term
+    -- ^ The global confluence checker found a term @u@ that reduces
+    --   to both @v1@ and @v2@ and there is no rule to resolve the
+    --   ambiguity.
+  | RewriteMissingRule Term Term Term
+    -- ^ The global confluence checker found a term @u@ that reduces
+    --   to @v@, but @v@ does not reduce to @rho(u)@.
+  | PragmaCompileErased BackendName QName
+    -- ^ COMPILE directive for an erased symbol
+  | NotInScopeW [C.QName]
+    -- ^ Out of scope error we can recover from
+  | UnsupportedIndexedMatch Doc
+    -- ^ Was not able to compute a full equivalence when splitting.
+  | AsPatternShadowsConstructorOrPatternSynonym Bool
+    -- ^ The as-name in an as-pattern may not shadow a constructor (@False@)
+    --   or pattern synonym name (@True@),
+    --   because this can be confusing to read.
+  | PatternShadowsConstructor C.Name A.QName
+    -- ^ A pattern variable has the name of a constructor
+    --   (data constructor or matchable record constructor).
+  | PlentyInHardCompileTimeMode QωOrigin
+    -- ^ Explicit use of @@ω@ or @@plenty@ in hard compile-time mode.
+  | RecordFieldWarning RecordFieldWarning
+  | NotAffectedByOpaque
+  | UnfoldTransparentName QName
+  | UselessOpaque
+
+  -- Cubical
+  | FaceConstraintCannotBeHidden ArgInfo
+    -- ^ Face constraint patterns @(i = 0)@ must be visible arguments.
+  | FaceConstraintCannotBeNamed NamedName
+    -- ^ Face constraint patterns @(i = 0)@ must be unnamed arguments.
+
+  -- Not source code related
+  | DuplicateInterfaceFiles AbsolutePath AbsolutePath
+    -- ^ `DuplicateInterfaceFiles selectedInterfaceFile ignoredInterfaceFile`
+  deriving (Show, Generic)
+
+recordFieldWarningToError :: RecordFieldWarning -> TypeError
+recordFieldWarningToError = \case
+  W.DuplicateFields    xrs -> DuplicateFields    $ map fst xrs
+  W.TooManyFields q ys xrs -> TooManyFields q ys $ map fst xrs
+
+warningName :: Warning -> WarningName
+warningName = \case
+  -- special cases
+  NicifierIssue dw             -> declarationWarningName dw
+  OptionWarning ow             -> optionWarningName ow
+  ParseWarning pw              -> parseWarningName pw
+  LibraryWarning lw            -> libraryWarningName lw
+  -- scope- and type-checking errors
+  AsPatternShadowsConstructorOrPatternSynonym{} -> AsPatternShadowsConstructorOrPatternSynonym_
+  PatternShadowsConstructor{}  -> PatternShadowsConstructor_
+  AbsurdPatternRequiresNoRHS{} -> AbsurdPatternRequiresNoRHS_
+  CantGeneralizeOverSorts{}    -> CantGeneralizeOverSorts_
+  CoverageIssue{}              -> CoverageIssue_
+  CoverageNoExactSplit{}       -> CoverageNoExactSplit_
+  InlineNoExactSplit{}         -> InlineNoExactSplit_
+  DeprecationWarning{}         -> DeprecationWarning_
+  EmptyRewritePragma           -> EmptyRewritePragma_
+  EmptyWhere                   -> EmptyWhere_
+  IllformedAsClause{}          -> IllformedAsClause_
+  WrongInstanceDeclaration{}   -> WrongInstanceDeclaration_
+  InstanceWithExplicitArg{}    -> InstanceWithExplicitArg_
+  InstanceNoOutputTypeName{}   -> InstanceNoOutputTypeName_
+  InstanceArgWithExplicitArg{} -> InstanceArgWithExplicitArg_
+  DuplicateUsing{}             -> DuplicateUsing_
+  FixityInRenamingModule{}     -> FixityInRenamingModule_
+  InvalidCharacterLiteral{}    -> InvalidCharacterLiteral_
+  UselessPragma{}              -> UselessPragma_
+  GenericWarning{}             -> GenericWarning_
+  InversionDepthReached{}      -> InversionDepthReached_
+  InteractionMetaBoundaries{}  -> InteractionMetaBoundaries_{}
+  ModuleDoesntExport{}         -> ModuleDoesntExport_
+  NoGuardednessFlag{}          -> NoGuardednessFlag_
+  NotInScopeW{}                -> NotInScope_
+  NotStrictlyPositive{}        -> NotStrictlyPositive_
+  UnsupportedIndexedMatch{}    -> UnsupportedIndexedMatch_
+  OldBuiltin{}                 -> OldBuiltin_
+  SafeFlagPostulate{}          -> SafeFlagPostulate_
+  SafeFlagPragma{}             -> SafeFlagPragma_
+  SafeFlagWithoutKFlagPrimEraseEquality -> SafeFlagWithoutKFlagPrimEraseEquality_
+  WithoutKFlagPrimEraseEquality -> WithoutKFlagPrimEraseEquality_
+  TerminationIssue{}           -> TerminationIssue_
+  UnreachableClauses{}         -> UnreachableClauses_
+  UnsolvedInteractionMetas{}   -> UnsolvedInteractionMetas_
+  UnsolvedConstraints{}        -> UnsolvedConstraints_
+  UnsolvedMetaVariables{}      -> UnsolvedMetaVariables_
+  UselessHiding{}              -> UselessHiding_
+  UselessInline{}              -> UselessInline_
+  UselessPublic{}              -> UselessPublic_
+  UselessPatternDeclarationForRecord{} -> UselessPatternDeclarationForRecord_
+  ClashesViaRenaming{}         -> ClashesViaRenaming_
+  UserWarning{}                -> UserWarning_
+  InfectiveImport{}            -> InfectiveImport_
+  CoInfectiveImport{}          -> CoInfectiveImport_
+  RewriteNonConfluent{}        -> RewriteNonConfluent_
+  RewriteMaybeNonConfluent{}   -> RewriteMaybeNonConfluent_
+  RewriteAmbiguousRules{}      -> RewriteAmbiguousRules_
+  RewriteMissingRule{}         -> RewriteMissingRule_
+  PragmaCompileErased{}        -> PragmaCompileErased_
+  PlentyInHardCompileTimeMode{}
+                               -> PlentyInHardCompileTimeMode_
+  -- record field warnings
+  RecordFieldWarning w -> case w of
+    W.DuplicateFields{}   -> DuplicateFields_
+    W.TooManyFields{}     -> TooManyFields_
+
+  NotAffectedByOpaque{}   -> NotAffectedByOpaque_
+  UselessOpaque{}         -> UselessOpaque_
+  UnfoldTransparentName{} -> UnfoldTransparentName_
+
+  -- Cubical
+  FaceConstraintCannotBeHidden{} -> FaceConstraintCannotBeHidden_
+  FaceConstraintCannotBeNamed{}  -> FaceConstraintCannotBeNamed_
+
+  -- Not source code related
+  DuplicateInterfaceFiles{}      -> DuplicateInterfaceFiles_
+
+-- Indicates wether changes in the source code can silence or influence the
+-- warning.
+isSourceCodeWarning :: WarningName -> Bool
+isSourceCodeWarning DuplicateInterfaceFiles_{} = False
+isSourceCodeWarning _ = True
+
+data TCWarning
+  = TCWarning
+    { tcWarningLocation :: CallStack
+        -- ^ Location in the internal Agda source code location where the error raised
+    , tcWarningRange    :: Range
+        -- ^ Range where the warning was raised
+    , tcWarning         :: Warning
+        -- ^ The warning itself
+    , tcWarningPrintedWarning :: Doc
+        -- ^ The warning printed in the state and environment where it was raised
+    , tcWarningCached :: Bool
+        -- ^ Should the warning be affected by caching.
+    }
+  deriving (Show, Generic)
+
+tcWarningOrigin :: TCWarning -> SrcFile
+tcWarningOrigin = rangeFile . tcWarningRange
+
+instance HasRange TCWarning where
+  getRange = tcWarningRange
+
+-- used for merging lists of warnings
+instance Eq TCWarning where
+  (==) = (==) `on` tcWarningPrintedWarning
+
+---------------------------------------------------------------------------
+-- * Type checking errors
+---------------------------------------------------------------------------
+
+-- | Information about a call.
+
+data CallInfo = CallInfo
+  { callInfoTarget :: QName
+    -- ^ Target function name.  (Contains its range.)
+  , callInfoCall :: Closure Term
+    -- ^ To be formatted representation of the call.
+  } deriving (Show, Generic)
+    -- no Eq, Ord instances: too expensive! (see issues 851, 852)
+
+instance HasRange CallInfo where
+  getRange = getRange . callInfoTarget
+
+-- | We only 'show' the name of the callee.
+instance Pretty CallInfo where pretty = pretty . callInfoTarget
+
+-- | Information about a mutual block which did not pass the
+-- termination checker.
+
+data TerminationError = TerminationError
+  { termErrFunctions :: [QName]
+    -- ^ The functions which failed to check. (May not include
+    -- automatically generated functions.)
+  , termErrCalls :: [CallInfo]
+    -- ^ The problematic call sites.
+  } deriving (Show, Generic)
+
+-- | The reason for an 'ErasedDatatype' error.
+
+data ErasedDatatypeReason
+  = SeveralConstructors
+    -- ^ There are several constructors.
+  | NoErasedMatches
+    -- ^ The flag @--erased-matches@ is not used.
+  | NoK
+    -- ^ The K rule is not activated.
+  deriving (Show, Generic)
+
+-- | Error when splitting a pattern variable into possible constructor patterns.
+data SplitError
+  = NotADatatype        (Closure Type)  -- ^ Neither data type nor record.
+  | BlockedType Blocker (Closure Type)  -- ^ Type could not be sufficiently reduced.
+  | ErasedDatatype ErasedDatatypeReason (Closure Type)
+                                        -- ^ Data type, but in erased position.
+  | CoinductiveDatatype (Closure Type)  -- ^ Split on codata not allowed.
+  -- UNUSED, but keep!
+  -- -- | NoRecordConstructor Type  -- ^ record type, but no constructor
+  | UnificationStuck
+    { cantSplitBlocker  :: Maybe Blocker -- ^ Blocking metavariable (if any)
+    , cantSplitConName  :: QName        -- ^ Constructor.
+    , cantSplitTel      :: Telescope    -- ^ Context for indices.
+    , cantSplitConIdx   :: Args         -- ^ Inferred indices (from type of constructor).
+    , cantSplitGivenIdx :: Args         -- ^ Expected indices (from checking pattern).
+    , cantSplitFailures :: [UnificationFailure] -- ^ Reason(s) why unification got stuck.
+    }
+  | CosplitCatchall
+      -- ^ Copattern split with a catchall
+  | CosplitNoTarget
+      -- ^ We do not know the target type of the clause.
+  | CosplitNoRecordType (Closure Type)
+      -- ^ Target type is not a record type.
+  | CannotCreateMissingClause QName (Telescope,[NamedArg DeBruijnPattern]) Doc (Closure (Abs Type))
+
+  | GenericSplitError String
+  deriving (Show, Generic)
+
+data NegativeUnification
+  = UnifyConflict Telescope Term Term
+  | UnifyCycle Telescope Int Term
+  deriving (Show, Generic)
+
+data UnificationFailure
+  = UnifyIndicesNotVars Telescope Type Term Term Args -- ^ Failed to apply injectivity to constructor of indexed datatype
+  | UnifyRecursiveEq Telescope Type Int Term          -- ^ Can't solve equation because variable occurs in (type of) lhs
+  | UnifyReflexiveEq Telescope Type Term              -- ^ Can't solve reflexive equation because --without-K is enabled
+  | UnifyUnusableModality Telescope Type Int Term Modality  -- ^ Can't solve equation because solution modality is less "usable"
+  deriving (Show, Generic)
+
+data UnquoteError
+  = BadVisibility String (Arg I.Term)
+  | ConInsteadOfDef QName String String
+  | DefInsteadOfCon QName String String
+  | NonCanonical String I.Term
+  | BlockedOnMeta TCState Blocker
+  | UnquotePanic String
+  deriving (Show, Generic)
+
+data TypeError
+        = InternalError String
+        | NotImplemented String
+        | NotSupported String
+        | CompilationError String
+        | PropMustBeSingleton
+        | DataMustEndInSort Term
+{- UNUSED
+        | DataTooManyParameters
+            -- ^ In @data D xs where@ the number of parameters @xs@ does not fit the
+            --   the parameters given in the forward declaraion @data D Gamma : T@.
+-}
+        | ShouldEndInApplicationOfTheDatatype Type
+            -- ^ The target of a constructor isn't an application of its
+            -- datatype. The 'Type' records what it does target.
+        | ShouldBeAppliedToTheDatatypeParameters Term Term
+            -- ^ The target of a constructor isn't its datatype applied to
+            --   something that isn't the parameters. First term is the correct
+            --   target and the second term is the actual target.
+        | ShouldBeApplicationOf Type QName
+            -- ^ Expected a type to be an application of a particular datatype.
+        | ConstructorPatternInWrongDatatype QName QName -- ^ constructor, datatype
+        | CantResolveOverloadedConstructorsTargetingSameDatatype QName (List1 QName)
+          -- ^ Datatype, constructors.
+        | DoesNotConstructAnElementOf QName Type -- ^ constructor, type
+        | WrongHidingInLHS
+            -- ^ The left hand side of a function definition has a hidden argument
+            --   where a non-hidden was expected.
+        | WrongHidingInLambda Type
+            -- ^ Expected a non-hidden function and found a hidden lambda.
+        | WrongHidingInApplication Type
+            -- ^ A function is applied to a hidden argument where a non-hidden was expected.
+        | WrongHidingInProjection QName
+        | IllegalHidingInPostfixProjection (NamedArg C.Expr)
+        | WrongNamedArgument (NamedArg A.Expr) [NamedName]
+            -- ^ A function is applied to a hidden named argument it does not have.
+            -- The list contains names of possible hidden arguments at this point.
+        | WrongIrrelevanceInLambda
+            -- ^ Wrong user-given relevance annotation in lambda.
+        | WrongQuantityInLambda
+            -- ^ Wrong user-given quantity annotation in lambda.
+        | WrongCohesionInLambda
+            -- ^ Wrong user-given cohesion annotation in lambda.
+        | QuantityMismatch Quantity Quantity
+            -- ^ The given quantity does not correspond to the expected quantity.
+        | HidingMismatch Hiding Hiding
+            -- ^ The given hiding does not correspond to the expected hiding.
+        | RelevanceMismatch Relevance Relevance
+            -- ^ The given relevance does not correspond to the expected relevane.
+        | UninstantiatedDotPattern A.Expr
+        | ForcedConstructorNotInstantiated A.Pattern
+        | IllformedProjectionPatternAbstract A.Pattern
+        | IllformedProjectionPatternConcrete C.Pattern
+        | CannotEliminateWithPattern (Maybe Blocker) (NamedArg A.Pattern) Type
+        | CannotEliminateWithProjection (Arg Type) Bool QName
+        | WrongNumberOfConstructorArguments QName Nat Nat
+        | ShouldBeEmpty Type [DeBruijnPattern]
+        | ShouldBeASort Type
+            -- ^ The given type should have been a sort.
+        | ShouldBePi Type
+            -- ^ The given type should have been a pi.
+        | ShouldBePath Type
+        | ShouldBeRecordType Type
+        | ShouldBeRecordPattern DeBruijnPattern
+        | NotAProjectionPattern (NamedArg A.Pattern)
+        | NotAProperTerm
+        | InvalidTypeSort Sort
+            -- ^ This sort is not a type expression.
+        | InvalidType Term
+            -- ^ This term is not a type expression.
+        | FunctionTypeInSizeUniv Term
+            -- ^ This term, a function type constructor, lives in
+            --   @SizeUniv@, which is not allowed.
+        | SplitOnIrrelevant (Dom Type)
+        | SplitOnUnusableCohesion (Dom Type)
+        -- UNUSED: -- | SplitOnErased (Dom Type)
+        | SplitOnNonVariable Term Type
+        | SplitOnNonEtaRecord QName
+        | SplitOnAbstract QName
+        | SplitOnUnchecked QName
+        | SplitOnPartial (Dom Type)
+        | SplitInProp DataOrRecordE
+        | DefinitionIsIrrelevant QName
+        | DefinitionIsErased QName
+        | VariableIsIrrelevant Name
+        | VariableIsErased Name
+        | VariableIsOfUnusableCohesion Name Cohesion
+        | UnequalLevel Comparison Level Level
+        | UnequalTerms Comparison Term Term CompareAs
+        | UnequalTypes Comparison Type Type
+--      | UnequalTelescopes Comparison Telescope Telescope -- UNUSED
+        | UnequalRelevance Comparison Term Term
+            -- ^ The two function types have different relevance.
+        | UnequalQuantity Comparison Term Term
+            -- ^ The two function types have different relevance.
+        | UnequalCohesion Comparison Term Term
+            -- ^ The two function types have different cohesion.
+        | UnequalFiniteness Comparison Term Term
+            -- ^ One of the function types has a finite domain (i.e. is a @Partia@l@) and the other isonot.
+        | UnequalHiding Term Term
+            -- ^ The two function types have different hiding.
+        | UnequalSorts Sort Sort
+        | UnequalBecauseOfUniverseConflict Comparison Term Term
+        | NotLeqSort Sort Sort
+        | MetaCannotDependOn MetaId Nat
+            -- ^ The arguments are the meta variable and the parameter that it wants to depend on.
+        | MetaOccursInItself MetaId
+        | MetaIrrelevantSolution MetaId Term
+        | MetaErasedSolution MetaId Term
+        | GenericError String
+        | GenericDocError Doc
+        | SortOfSplitVarError (Maybe Blocker) Doc
+          -- ^ the meta is what we might be blocked on.
+        | BuiltinMustBeConstructor BuiltinId A.Expr
+        | NoSuchBuiltinName String
+        | DuplicateBuiltinBinding BuiltinId Term Term
+        | NoBindingForBuiltin BuiltinId
+        | NoBindingForPrimitive PrimitiveId
+        | NoSuchPrimitiveFunction String
+        | DuplicatePrimitiveBinding PrimitiveId QName QName
+        | WrongArgInfoForPrimitive PrimitiveId ArgInfo ArgInfo
+        | ShadowedModule C.Name [A.ModuleName]
+        | BuiltinInParameterisedModule BuiltinId
+        | IllegalDeclarationInDataDefinition [C.Declaration]
+            -- ^ The declaration list comes from a single 'C.NiceDeclaration'.
+        | IllegalLetInTelescope C.TypedBinding
+        | IllegalPatternInTelescope C.Binder
+        | NoRHSRequiresAbsurdPattern [NamedArg A.Pattern]
+        | TooManyFields QName [C.Name] [C.Name]
+          -- ^ Record type, fields not supplied by user, non-fields but supplied.
+        | DuplicateFields [C.Name]
+        | DuplicateConstructors [C.Name]
+        | WithOnFreeVariable A.Expr Term
+        | UnexpectedWithPatterns [A.Pattern]
+        | WithClausePatternMismatch A.Pattern (NamedArg DeBruijnPattern)
+        | IllTypedPatternAfterWithAbstraction A.Pattern
+        | FieldOutsideRecord
+        | ModuleArityMismatch A.ModuleName Telescope [NamedArg A.Expr]
+        | GeneralizeCyclicDependency
+        | GeneralizeUnsolvedMeta
+        | ReferencesFutureVariables Term (List1.NonEmpty Int) (Arg Term) Int
+          -- ^ The first term references the given list of variables,
+          -- which are in "the future" with respect to the given lock
+          -- (and its leftmost variable)
+        | DoesNotMentionTicks Term Type (Arg Term)
+          -- ^ Arguments: later term, its type, lock term. The lock term
+          -- does not mention any @lock variables.
+        | MismatchedProjectionsError QName QName
+        | AttributeKindNotEnabled String String String
+        | InvalidProjectionParameter (NamedArg A.Expr)
+        | TacticAttributeNotAllowed
+        | CannotRewriteByNonEquation Type
+        | MacroResultTypeMismatch Type
+        | NamedWhereModuleInRefinedContext [Term] [String]
+        | CubicalPrimitiveNotFullyApplied QName
+        | TooManyArgumentsToLeveledSort QName
+        | TooManyArgumentsToUnivOmega QName
+        | ComatchingDisabledForRecord QName
+        | BuiltinMustBeIsOne Term
+        | IllegalRewriteRule QName IllegalRewriteRuleReason
+        | IncorrectTypeForRewriteRelation Term IncorrectTypeForRewriteRelationReason
+    -- Data errors
+        | UnexpectedParameter A.LamBinding
+        | NoParameterOfName ArgName
+        | UnexpectedModalityAnnotationInParameter A.LamBinding
+        | ExpectedBindingForParameter (Dom Type) (Abs Type)
+        | UnexpectedTypeSignatureForParameter (List1 (NamedArg A.Binder))
+        | SortDoesNotAdmitDataDefinitions QName Sort
+        | SortCannotDependOnItsIndex QName Type
+    -- Coverage errors
+-- UNUSED:        | IncompletePatternMatching Term [Elim] -- can only happen if coverage checking is switched off
+        | SplitError SplitError
+        | ImpossibleConstructor QName NegativeUnification
+    -- Positivity errors
+        | TooManyPolarities QName Int
+    -- Import errors
+        | LocalVsImportedModuleClash ModuleName
+        | SolvedButOpenHoles
+          -- ^ Some interaction points (holes) have not been filled by user.
+          --   There are not 'UnsolvedMetas' since unification solved them.
+          --   This is an error, since interaction points are never filled
+          --   without user interaction.
+        | CyclicModuleDependency [TopLevelModuleName]
+        | FileNotFound TopLevelModuleName [AbsolutePath]
+        | OverlappingProjects AbsolutePath TopLevelModuleName TopLevelModuleName
+        | AmbiguousTopLevelModuleName TopLevelModuleName [AbsolutePath]
+        | ModuleNameUnexpected TopLevelModuleName TopLevelModuleName
+          -- ^ Found module name, expected module name.
+        | ModuleNameDoesntMatchFileName TopLevelModuleName [AbsolutePath]
+        | ClashingFileNamesFor ModuleName [AbsolutePath]
+        | ModuleDefinedInOtherFile TopLevelModuleName AbsolutePath AbsolutePath
+          -- ^ Module name, file from which it was loaded, file which
+          -- the include path says contains the module.
+    -- Scope errors
+        | BothWithAndRHS
+        | AbstractConstructorNotInScope A.QName
+        | NotInScope [C.QName]
+        | NoSuchModule C.QName
+        | AmbiguousName C.QName AmbiguousNameReason
+        | AmbiguousModule C.QName (List1 A.ModuleName)
+        | AmbiguousField C.Name [A.ModuleName]
+        | AmbiguousConstructor QName [QName]
+        | ClashingDefinition C.QName A.QName (Maybe NiceDeclaration)
+        | ClashingModule A.ModuleName A.ModuleName
+        | ClashingImport C.Name A.QName
+        | ClashingModuleImport C.Name A.ModuleName
+        | DuplicateImports C.QName [C.ImportedName]
+        | InvalidPattern C.Pattern
+        | RepeatedVariablesInPattern [C.Name]
+        | GeneralizeNotSupportedHere A.QName
+        | GeneralizedVarInLetOpenedModule A.QName
+        | MultipleFixityDecls [(C.Name, [Fixity'])]
+        | MultiplePolarityPragmas [C.Name]
+    -- Concrete to Abstract errors
+        | NotAModuleExpr C.Expr
+            -- ^ The expr was used in the right hand side of an implicit module
+            --   definition, but it wasn't of the form @m Delta@.
+        | NotAnExpression C.Expr
+        | NotAValidLetBinding NiceDeclaration
+        | NotValidBeforeField NiceDeclaration
+        | NothingAppliedToHiddenArg C.Expr
+        | NothingAppliedToInstanceArg C.Expr
+    -- Pattern synonym errors
+        | BadArgumentsToPatternSynonym A.AmbiguousQName
+        | TooFewArgumentsToPatternSynonym A.AmbiguousQName
+        | CannotResolveAmbiguousPatternSynonym (List1 (A.QName, A.PatternSynDefn))
+        | UnusedVariableInPatternSynonym
+        | UnboundVariablesInPatternSynonym [A.Name]
+    -- Operator errors
+        | NoParseForApplication (List2 C.Expr)
+        | AmbiguousParseForApplication (List2 C.Expr) (List1 C.Expr)
+        | NoParseForLHS LHSOrPatSyn [C.Pattern] C.Pattern
+            -- ^ The list contains patterns that failed to be interpreted.
+            --   If it is non-empty, the first entry could be printed as error hint.
+        | AmbiguousParseForLHS LHSOrPatSyn C.Pattern [C.Pattern]
+            -- ^ Pattern and its possible interpretations.
+        | AmbiguousProjection QName [QName]
+        | AmbiguousOverloadedProjection (List1 QName) Doc
+        | OperatorInformation [NotationSection] TypeError
+{- UNUSED
+        | NoParseForPatternSynonym C.Pattern
+        | AmbiguousParseForPatternSynonym C.Pattern [C.Pattern]
+-}
+    -- Usage errors
+    -- Instance search errors
+        | InstanceNoCandidate Type [(Term, TCErr)]
+    -- Reflection errors
+        | UnquoteFailed UnquoteError
+        | DeBruijnIndexOutOfScope Nat Telescope [Name]
+    -- Language option errors
+        | NeedOptionCopatterns
+        | NeedOptionRewriting
+        | NeedOptionProp
+        | NeedOptionTwoLevel
+    -- Failure associated to warnings
+        | NonFatalErrors [TCWarning]
+    -- Instance search errors
+        | InstanceSearchDepthExhausted Term Type Int
+        | TriedToCopyConstrainedPrim QName
+          deriving (Show, Generic)
+
+type DataOrRecordE = DataOrRecord' InductionAndEta
+
+data InductionAndEta = InductionAndEta
+  { recordInduction   :: Maybe Induction
+  , recordEtaEquality :: EtaEquality
+  } deriving (Show, Generic)
+
+-- Reason, why rewrite rule is invalid
+data IllegalRewriteRuleReason
+  = LHSNotDefOrConstr
+  | VariablesNotBoundByLHS IntSet
+  | VariablesBoundMoreThanOnce IntSet
+  | LHSReducesTo Term Term
+  | HeadSymbolIsProjection QName
+  | HeadSymbolIsProjectionLikeFunction QName
+  | HeadSymbolNotPostulateFunctionConstructor QName
+  | HeadSymbolDefContainsMetas QName
+  | ConstructorParamsNotGeneral ConHead Args
+  | ContainsUnsolvedMetaVariables (Set MetaId)
+  | BlockedOnProblems (Set ProblemId)
+  | RequiresDefinitions (Set QName)
+  | DoesNotTargetRewriteRelation
+  | BeforeFunctionDefinition
+  | EmptyReason
+    deriving (Show, Generic)
+
+-- Reason, why type for rewrite rule is incorrect
+data IncorrectTypeForRewriteRelationReason
+  = ShouldAcceptAtLeastTwoArguments
+  | FinalTwoArgumentsNotVisible
+  | TypeDoesNotEndInSort Type Telescope
+    deriving (Show, Generic)
+
+-- | Distinguish error message when parsing lhs or pattern synonym, resp.
+data LHSOrPatSyn = IsLHS | IsPatSyn
+  deriving (Eq, Show, Generic)
+
+-- | Type-checking errors.
+
+data TCErr
+  = TypeError
+    { tcErrLocation :: CallStack
+       -- ^ Location in the internal Agda source code where the error was raised
+    , tcErrState    :: TCState
+        -- ^ The state in which the error was raised.
+    , tcErrClosErr  :: Closure TypeError
+        -- ^ The environment in which the error as raised plus the error.
+    }
+  | Exception Range Doc
+  | IOException TCState Range E.IOException
+    -- ^ The first argument is the state in which the error was
+    -- raised.
+  | PatternErr Blocker
+      -- ^ The exception which is usually caught.
+      --   Raised for pattern violations during unification ('assignV')
+      --   but also in other situations where we want to backtrack.
+      --   Contains an unblocker to control when the computation should
+      --   be retried.
+
+instance Show TCErr where
+  show (TypeError _ _ e)   = prettyShow (envRange $ clEnv e) ++ ": " ++ show (clValue e)
+  show (Exception r d)     = prettyShow r ++ ": " ++ render d
+  show (IOException _ r e) = prettyShow r ++ ": " ++
+                             E.displayException e
+  show PatternErr{}        = "Pattern violation (you shouldn't see this)"
+
+instance HasRange TCErr where
+  getRange (TypeError _ _ cl)  = envRange $ clEnv cl
+  getRange (Exception r _)     = r
+  getRange (IOException s r _) = r
+  getRange PatternErr{}        = noRange
+
+instance E.Exception TCErr
+
+-----------------------------------------------------------------------------
+-- * Accessing options
+-----------------------------------------------------------------------------
+
+instance MonadIO m => HasOptions (TCMT m) where
+  pragmaOptions = useTC stPragmaOptions
+  {-# INLINE pragmaOptions #-}
+
+  commandLineOptions = do
+    p  <- useTC stPragmaOptions
+    cl <- stPersistentOptions . stPersistentState <$> getTC
+    return $ cl { optPragmaOptions = p }
+  {-# SPECIALIZE commandLineOptions :: TCM CommandLineOptions #-}
+
+-- HasOptions lifts through monad transformers
+-- (see default signatures in the HasOptions class).
+
+sizedTypesOption :: HasOptions m => m Bool
+sizedTypesOption = optSizedTypes <$> pragmaOptions
+{-# INLINE sizedTypesOption #-}
+
+guardednessOption :: HasOptions m => m Bool
+guardednessOption = optGuardedness <$> pragmaOptions
+{-# INLINE guardednessOption #-}
+
+withoutKOption :: HasOptions m => m Bool
+withoutKOption = optWithoutK <$> pragmaOptions
+{-# INLINE withoutKOption #-}
+
+cubicalCompatibleOption :: HasOptions m => m Bool
+cubicalCompatibleOption = optCubicalCompatible <$> pragmaOptions
+{-# INLINE cubicalCompatibleOption #-}
+
+enableCaching :: HasOptions m => m Bool
+enableCaching = optCaching <$> pragmaOptions
+{-# INLINE enableCaching #-}
+
+-----------------------------------------------------------------------------
+-- * The reduce monad
+-----------------------------------------------------------------------------
+
+-- | Environment of the reduce monad.
+data ReduceEnv = ReduceEnv
+  { redEnv  :: TCEnv    -- ^ Read only access to environment.
+  , redSt   :: TCState  -- ^ Read only access to state (signature, metas...).
+  , redPred :: Maybe (MetaId -> ReduceM Bool)
+    -- ^ An optional predicate that is used by 'instantiate'' and
+    -- 'instantiateFull'': meta-variables are only instantiated if
+    -- they satisfy this predicate.
+  }
+
+mapRedEnv :: (TCEnv -> TCEnv) -> ReduceEnv -> ReduceEnv
+mapRedEnv f s = s { redEnv = f (redEnv s) }
+{-# INLINE mapRedEnv #-}
+
+mapRedSt :: (TCState -> TCState) -> ReduceEnv -> ReduceEnv
+mapRedSt f s = s { redSt = f (redSt s) }
+{-# INLINE mapRedSt #-}
+
+mapRedEnvSt :: (TCEnv -> TCEnv) -> (TCState -> TCState) -> ReduceEnv
+            -> ReduceEnv
+mapRedEnvSt f g (ReduceEnv e s p) = ReduceEnv (f e) (g s) p
+{-# INLINE mapRedEnvSt #-}
+
+-- Lenses
+reduceEnv :: Lens' ReduceEnv TCEnv
+reduceEnv f s = f (redEnv s) <&> \ e -> s { redEnv = e }
+{-# INLINE reduceEnv #-}
+
+reduceSt :: Lens' ReduceEnv TCState
+reduceSt f s = f (redSt s) <&> \ e -> s { redSt = e }
+{-# INLINE reduceSt #-}
+
+newtype ReduceM a = ReduceM { unReduceM :: ReduceEnv -> a }
+--  deriving (Functor, Applicative, Monad)
+
+
+onReduceEnv :: (ReduceEnv -> ReduceEnv) -> ReduceM a -> ReduceM a
+onReduceEnv f (ReduceM m) = ReduceM (m . f)
+{-# INLINE onReduceEnv #-}
+
+fmapReduce :: (a -> b) -> ReduceM a -> ReduceM b
+fmapReduce f (ReduceM m) = ReduceM $ \ e -> f $! m e
+{-# INLINE fmapReduce #-}
+
+-- Andreas, 2021-05-12, issue #5379:
+-- It seems more stable to force to evaluate @mf <*> ma@
+-- from left to right, for the sake of printing
+-- debug messages in order.
+apReduce :: ReduceM (a -> b) -> ReduceM a -> ReduceM b
+apReduce (ReduceM f) (ReduceM x) = ReduceM $ \ e ->
+  let g = f e
+      a = x e
+  in  g `pseq` a `pseq` g a
+{-# INLINE apReduce #-}
+
+
+-- Andreas, 2021-05-12, issue #5379
+-- Since the MonadDebug instance of ReduceM is implemented via
+-- unsafePerformIO, we need to force results that later
+-- computations do not depend on, otherwise we lose debug messages.
+thenReduce :: ReduceM a -> ReduceM b -> ReduceM b
+thenReduce (ReduceM x) (ReduceM y) = ReduceM $ \ e -> x e `pseq` y e
+{-# INLINE thenReduce #-}
+
+
+-- Andreas, 2021-05-14:
+-- `seq` does not force evaluation order, the optimizier is allowed to replace
+-- @
+--    a `seq` b`
+-- @
+-- by:
+-- @
+--    b `seq` a `seq` b
+-- @
+-- see https://hackage.haskell.org/package/parallel/docs/Control-Parallel.html
+--
+-- In contrast, `pseq` is only strict in its first argument, so such a permutation
+-- is forbidden.
+-- If we want to ensure that debug messages are printed before exceptions are
+-- propagated, we need to use `pseq`, as in:
+-- @
+--    unsafePerformIO (putStrLn "Black hawk is going down...") `pseq` throw HitByRPG
+-- @
+beforeReduce :: ReduceM a -> ReduceM b -> ReduceM a
+beforeReduce (ReduceM x) (ReduceM y) = ReduceM $ \ e ->
+  let a = x e
+  in  a `pseq` y e `pseq` a
+{-# INLINE beforeReduce #-}
+
+bindReduce :: ReduceM a -> (a -> ReduceM b) -> ReduceM b
+bindReduce (ReduceM m) f = ReduceM $ \ e -> unReduceM (f $! m e) e
+{-# INLINE bindReduce #-}
+
+instance Functor ReduceM where
+  fmap = fmapReduce
+
+instance Applicative ReduceM where
+  pure x = ReduceM (const x)
+  (<*>) = apReduce
+  (*>)  = thenReduce
+  (<*)  = beforeReduce
+
+instance Monad ReduceM where
+  return = pure
+  (>>=) = bindReduce
+  (>>) = (*>)
+
+instance Fail.MonadFail ReduceM where
+  fail = error
+
+instance ReadTCState ReduceM where
+  getTCState = ReduceM redSt
+  locallyTCState l f = onReduceEnv $ mapRedSt $ over l f
+
+runReduceM :: ReduceM a -> TCM a
+runReduceM m = TCM $ \ r e -> do
+  s <- readIORef r
+  E.evaluate $ unReduceM m $ ReduceEnv e s Nothing
+  -- Andreas, 2021-05-13, issue #5379
+  -- This was the following, which is apparently not strict enough
+  -- to force all unsafePerformIOs...
+  -- runReduceM m = do
+  --   e <- askTC
+  --   s <- getTC
+  --   return $! unReduceM m (ReduceEnv e s)
+
+runReduceF :: (a -> ReduceM b) -> TCM (a -> b)
+runReduceF f = do
+  e <- askTC
+  s <- getTC
+  return $ \x -> unReduceM (f x) (ReduceEnv e s Nothing)
+
+instance MonadTCEnv ReduceM where
+  askTC   = ReduceM redEnv
+  localTC = onReduceEnv . mapRedEnv
+
+-- Andrea comments (https://github.com/agda/agda/issues/1829#issuecomment-522312084):
+--
+--   useR forces the result of projecting the lens,
+--   this usually prevents retaining the whole structure when we only need a field.
+--
+-- This fixes (or contributes to the fix of) the space leak issue #1829 (caching).
+useR :: (ReadTCState m) => Lens' TCState a -> m a
+useR l = do
+  !x <- getTCState <&> (^. l)
+  return x
+{-# INLINE useR #-}
+
+askR :: ReduceM ReduceEnv
+askR = ReduceM ask
+{-# INLINE askR #-}
+
+localR :: (ReduceEnv -> ReduceEnv) -> ReduceM a -> ReduceM a
+localR f = ReduceM . local f . unReduceM
+{-# INLINE localR #-}
+
+instance HasOptions ReduceM where
+  pragmaOptions      = useR stPragmaOptions
+  commandLineOptions = do
+    p  <- useR stPragmaOptions
+    cl <- stPersistentOptions . stPersistentState <$> getTCState
+    return $ cl{ optPragmaOptions = p }
+
+class ( Applicative m
+      , MonadTCEnv m
+      , ReadTCState m
+      , HasOptions m
+      ) => MonadReduce m where
+  liftReduce :: ReduceM a -> m a
+
+  default liftReduce :: (MonadTrans t, MonadReduce n, t n ~ m) => ReduceM a -> m a
+  liftReduce = lift . liftReduce
+
+instance MonadReduce ReduceM where
+  liftReduce = id
+
+instance MonadReduce m => MonadReduce (ChangeT m)
+instance MonadReduce m => MonadReduce (ExceptT err m)
+instance MonadReduce m => MonadReduce (IdentityT m)
+instance MonadReduce m => MonadReduce (ListT m)
+instance MonadReduce m => MonadReduce (MaybeT m)
+instance MonadReduce m => MonadReduce (ReaderT r m)
+instance MonadReduce m => MonadReduce (StateT w m)
+instance (Monoid w, MonadReduce m) => MonadReduce (WriterT w m)
+instance MonadReduce m => MonadReduce (BlockT m)
+
+---------------------------------------------------------------------------
+-- * Monad with read-only 'TCEnv'
+---------------------------------------------------------------------------
+
+-- | @MonadTCEnv@ made into its own dedicated service class.
+--   This allows us to use 'MonadReader' for 'ReaderT' extensions of @TCM@.
+class Monad m => MonadTCEnv m where
+  askTC   :: m TCEnv
+  localTC :: (TCEnv -> TCEnv) -> m a -> m a
+
+  default askTC :: (MonadTrans t, MonadTCEnv n, t n ~ m) => m TCEnv
+  askTC = lift askTC
+
+  default localTC
+    :: (MonadTransControl t, MonadTCEnv n, t n ~ m)
+    =>  (TCEnv -> TCEnv) -> m a -> m a
+  localTC = liftThrough . localTC
+
+instance MonadTCEnv m => MonadTCEnv (ChangeT m)
+instance MonadTCEnv m => MonadTCEnv (ExceptT err m)
+instance MonadTCEnv m => MonadTCEnv (IdentityT m)
+instance MonadTCEnv m => MonadTCEnv (MaybeT m)
+instance MonadTCEnv m => MonadTCEnv (ReaderT r m)
+instance MonadTCEnv m => MonadTCEnv (StateT s m)
+instance (Monoid w, MonadTCEnv m) => MonadTCEnv (WriterT w m)
+
+instance MonadTCEnv m => MonadTCEnv (ListT m) where
+  localTC = mapListT . localTC
+
+{-# INLINE asksTC #-}
+asksTC :: MonadTCEnv m => (TCEnv -> a) -> m a
+asksTC f = f <$> askTC
+
+{-# INLINE viewTC #-}
+viewTC :: MonadTCEnv m => Lens' TCEnv a -> m a
+viewTC l = asksTC (^. l)
+
+{-# INLINE locallyTC #-}
+-- | Modify the lens-indicated part of the @TCEnv@ in a subcomputation.
+locallyTC :: MonadTCEnv m => Lens' TCEnv a -> (a -> a) -> m b -> m b
+locallyTC l = localTC . over l
+
+---------------------------------------------------------------------------
+-- * Monad with mutable 'TCState'
+---------------------------------------------------------------------------
+
+-- | @MonadTCState@ made into its own dedicated service class.
+--   This allows us to use 'MonadState' for 'StateT' extensions of @TCM@.
+class Monad m => MonadTCState m where
+  getTC :: m TCState
+  putTC :: TCState -> m ()
+  modifyTC :: (TCState -> TCState) -> m ()
+
+  default getTC :: (MonadTrans t, MonadTCState n, t n ~ m) => m TCState
+  getTC = lift getTC
+
+  default putTC :: (MonadTrans t, MonadTCState n, t n ~ m) => TCState -> m ()
+  putTC = lift . putTC
+
+  default modifyTC :: (MonadTrans t, MonadTCState n, t n ~ m) => (TCState -> TCState) -> m ()
+  modifyTC = lift . modifyTC
+
+instance MonadTCState m => MonadTCState (MaybeT m)
+instance MonadTCState m => MonadTCState (ListT m)
+instance MonadTCState m => MonadTCState (ExceptT err m)
+instance MonadTCState m => MonadTCState (ReaderT r m)
+instance MonadTCState m => MonadTCState (StateT s m)
+instance MonadTCState m => MonadTCState (ChangeT m)
+instance MonadTCState m => MonadTCState (IdentityT m)
+instance (Monoid w, MonadTCState m) => MonadTCState (WriterT w m)
+
+{-# INLINE getsTC #-}
+-- ** @TCState@ accessors (no lenses)
+getsTC :: ReadTCState m => (TCState -> a) -> m a
+getsTC f = f <$> getTCState
+
+{-# INLINE modifyTC' #-}
+-- | A variant of 'modifyTC' in which the computation is strict in the
+-- new state.
+modifyTC' :: MonadTCState m => (TCState -> TCState) -> m ()
+modifyTC' f = do
+  s' <- getTC
+  putTC $! f s'
+
+-- SEE TC.Monad.State
+-- -- | Restore the 'TCState' after computation.
+-- localTCState :: MonadTCState m => m a -> m a
+-- localTCState = bracket_ getTC putTC
+
+-- ** @TCState@ accessors via lenses
+
+{-# INLINE useTC #-}
+useTC :: ReadTCState m => Lens' TCState a -> m a
+useTC l = do
+  !x <- getsTC (^. l)
+  return x
+
+infix 4 `setTCLens`
+
+{-# INLINE setTCLens #-}
+-- | Overwrite the part of the 'TCState' focused on by the lens.
+setTCLens :: MonadTCState m => Lens' TCState a -> a -> m ()
+setTCLens l = modifyTC . set l
+
+{-# INLINE setTCLens' #-}
+-- | Overwrite the part of the 'TCState' focused on by the lens
+-- (strictly).
+setTCLens' :: MonadTCState m => Lens' TCState a -> a -> m ()
+setTCLens' l = modifyTC' . set l
+
+{-# INLINE modifyTCLens #-}
+-- | Modify the part of the 'TCState' focused on by the lens.
+modifyTCLens :: MonadTCState m => Lens' TCState a -> (a -> a) -> m ()
+modifyTCLens l = modifyTC . over l
+
+{-# INLINE modifyTCLens' #-}
+-- | Modify the part of the 'TCState' focused on by the lens
+-- (strictly).
+modifyTCLens' :: MonadTCState m => Lens' TCState a -> (a -> a) -> m ()
+modifyTCLens' l = modifyTC' . over l
+
+{-# INLINE modifyTCLensM #-}
+-- | Modify a part of the state monadically.
+modifyTCLensM :: MonadTCState m => Lens' TCState a -> (a -> m a) -> m ()
+modifyTCLensM l f = putTC =<< l f =<< getTC
+
+{-# INLINE stateTCLens #-}
+-- | Modify the part of the 'TCState' focused on by the lens, and return some result.
+stateTCLens :: MonadTCState m => Lens' TCState a -> (a -> (r , a)) -> m r
+stateTCLens l f = stateTCLensM l $ return . f
+
+{-# INLINE stateTCLensM #-}
+-- | Modify a part of the state monadically, and return some result.
+stateTCLensM :: MonadTCState m => Lens' TCState a -> (a -> m (r , a)) -> m r
+stateTCLensM l f = do
+  s <- getTC
+  (result , x) <- f $ s ^. l
+  putTC $ set l x s
+  return result
+
+
+---------------------------------------------------------------------------
+-- ** Monad with capability to block a computation
+---------------------------------------------------------------------------
+
+class Monad m => MonadBlock m where
+
+  -- | `patternViolation b` aborts the current computation
+  patternViolation :: Blocker -> m a
+
+  default patternViolation :: (MonadTrans t, MonadBlock n, m ~ t n) => Blocker -> m a
+  patternViolation = lift . patternViolation
+
+  -- | `catchPatternErr handle m` runs m, handling pattern violations
+  --    with `handle` (doesn't roll back the state)
+  catchPatternErr :: (Blocker -> m a) -> m a -> m a
+
+newtype BlockT m a = BlockT { unBlockT :: ExceptT Blocker m a }
+  deriving ( Functor, Applicative, Monad, MonadTrans -- , MonadTransControl -- requires GHC >= 8.2
+           , MonadIO, Fail.MonadFail
+           , ReadTCState, HasOptions
+           , MonadTCEnv, MonadTCState, MonadTCM
+           )
+
+instance Monad m => MonadBlock (BlockT m) where
+  patternViolation = BlockT . throwError
+  catchPatternErr h f = BlockT $ catchError (unBlockT f) (unBlockT . h)
+
+instance Monad m => MonadBlock (ExceptT TCErr m) where
+  patternViolation = throwError . PatternErr
+  catchPatternErr h f = catchError f $ \case
+    PatternErr b -> h b
+    err          -> throwError err
+
+runBlocked :: Monad m => BlockT m a -> m (Either Blocker a)
+runBlocked = runExceptT . unBlockT
+{-# INLINE runBlocked #-}
+
+instance MonadBlock m => MonadBlock (MaybeT m) where
+  catchPatternErr h m = MaybeT $ catchPatternErr (runMaybeT . h) $ runMaybeT m
+
+instance MonadBlock m => MonadBlock (ReaderT e m) where
+  catchPatternErr h m = ReaderT $ \ e ->
+    let run = flip runReaderT e in catchPatternErr (run . h) (run m)
+
+---------------------------------------------------------------------------
+-- * Type checking monad transformer
+---------------------------------------------------------------------------
+
+-- | The type checking monad transformer.
+-- Adds readonly 'TCEnv' and mutable 'TCState'.
+newtype TCMT m a = TCM { unTCM :: IORef TCState -> TCEnv -> m a }
+
+-- | Type checking monad.
+type TCM = TCMT IO
+
+{-# SPECIALIZE INLINE mapTCMT :: (forall a. IO a -> IO a) -> TCM a -> TCM a #-}
+mapTCMT :: (forall a. m a -> n a) -> TCMT m a -> TCMT n a
+mapTCMT f (TCM m) = TCM $ \ s e -> f (m s e)
+
+pureTCM :: MonadIO m => (TCState -> TCEnv -> a) -> TCMT m a
+pureTCM f = TCM $ \ r e -> do
+  s <- liftIO $ readIORef r
+  return (f s e)
+{-# INLINE pureTCM #-}
+
+-- One goal of the definitions and pragmas below is to inline the
+-- monad operations as much as possible. This doesn't seem to have a
+-- large effect on the performance of the normal executable, but (at
+-- least on one machine/configuration) it has a massive effect on the
+-- performance of the profiling executable [1], and reduces the time
+-- attributed to bind from over 90% to about 25%.
+--
+-- [1] When compiled with -auto-all and run with -p: roughly 750%
+-- faster for one example.
+
+returnTCMT :: Applicative m => a -> TCMT m a
+returnTCMT = \x -> TCM $ \_ _ -> pure x
+{-# INLINE returnTCMT #-}
+
+bindTCMT :: Monad m => TCMT m a -> (a -> TCMT m b) -> TCMT m b
+bindTCMT = \(TCM m) k -> TCM $ \r e -> m r e >>= \x -> unTCM (k x) r e
+{-# INLINE bindTCMT #-}
+
+thenTCMT :: Applicative m => TCMT m a -> TCMT m b -> TCMT m b
+thenTCMT = \(TCM m1) (TCM m2) -> TCM $ \r e -> m1 r e *> m2 r e
+{-# INLINE thenTCMT #-}
+
+instance Functor m => Functor (TCMT m) where
+  fmap = fmapTCMT; {-# INLINE fmap #-}
+
+fmapTCMT :: Functor m => (a -> b) -> TCMT m a -> TCMT m b
+fmapTCMT = \f (TCM m) -> TCM $ \r e -> fmap f (m r e)
+{-# INLINE fmapTCMT #-}
+
+instance Applicative m => Applicative (TCMT m) where
+  pure  = returnTCMT; {-# INLINE pure #-}
+  (<*>) = apTCMT; {-# INLINE (<*>) #-}
+
+apTCMT :: Applicative m => TCMT m (a -> b) -> TCMT m a -> TCMT m b
+apTCMT = \(TCM mf) (TCM m) -> TCM $ \r e -> mf r e <*> m r e
+{-# INLINE apTCMT #-}
+
+instance MonadTrans TCMT where
+    lift m = TCM $ \_ _ -> m; {-# INLINE lift #-}
+
+-- We want a special monad implementation of fail.
+-- Andreas, 2022-02-02, issue #5659:
+-- @transformers-0.6@ requires exactly a @Monad@ superclass constraint here
+-- if we want @instance MonadTrans TCMT@.
+instance Monad m => Monad (TCMT m) where
+    return = pure; {-# INLINE return #-}
+    (>>=)  = bindTCMT; {-# INLINE (>>=) #-}
+    (>>)   = (*>); {-# INLINE (>>) #-}
+
+instance MonadIO m => Fail.MonadFail (TCMT m) where
+  fail = internalError
+
+instance MonadIO m => MonadIO (TCMT m) where
+  liftIO m = TCM $ \ s env -> do
+    liftIO $ wrap s (envRange env) $ do
+      x <- m
+      x `seq` return x
+    where
+      wrap s r m = E.catch m $ \ err -> do
+        s <- readIORef s
+        E.throwIO $ IOException s r err
+
+instance ( MonadFix m
+         ) => MonadFix (TCMT m) where
+  mfix f = TCM $ \s env -> mdo
+    x <- unTCM (f x) s env
+    return x
+
+instance MonadIO m => MonadTCEnv (TCMT m) where
+  askTC             = TCM $ \ _ e -> return e; {-# INLINE askTC #-}
+  localTC f (TCM m) = TCM $ \ s e -> m s (f e); {-# INLINE localTC #-}
+
+instance MonadIO m => MonadTCState (TCMT m) where
+  getTC   = TCM $ \ r _e -> liftIO (readIORef r); {-# INLINE getTC #-}
+  putTC s = TCM $ \ r _e -> liftIO (writeIORef r s); {-# INLINE putTC #-}
+  modifyTC f = putTC . f =<< getTC; {-# INLINE modifyTC #-}
+
+instance MonadIO m => ReadTCState (TCMT m) where
+  getTCState = getTC; {-# INLINE getTCState #-}
+  locallyTCState l f = bracket_ (useTC l <* modifyTCLens l f) (setTCLens l); {-# INLINE locallyTCState #-}
+
+instance MonadBlock TCM where
+  patternViolation b = throwError (PatternErr b)
+  catchPatternErr handle v =
+       catchError_ v $ \err ->
+       case err of
+            -- Not putting s (which should really be the what's already there) makes things go
+            -- a lot slower (+20% total time on standard library). How is that possible??
+            -- The problem is most likely that there are internal catchErrors which forgets the
+            -- state. catchError should preserve the state on pattern violations.
+           PatternErr u -> handle u
+           _            -> throwError err
+
+
+instance MonadError TCErr TCM where
+  throwError = liftIO . E.throwIO
+  catchError m h = TCM $ \ r e -> do  -- now we are in the IO monad
+    oldState <- readIORef r
+    unTCM m r e `E.catch` \err -> do
+      -- Reset the state, but do not forget changes to the persistent
+      -- component. Not for pattern violations.
+      case err of
+        PatternErr{} -> return ()
+        _            ->
+          liftIO $ do
+            newState <- readIORef r
+            writeIORef r $ oldState { stPersistentState = stPersistentState newState }
+      unTCM (h err) r e
+
+-- | Like 'catchError', but resets the state completely before running the handler.
+--   This means it also loses changes to the 'stPersistentState'.
+--
+--   The intended use is to catch internal errors during debug printing.
+--   In debug printing, we are not expecting state changes.
+instance CatchImpossible TCM where
+  catchImpossibleJust f m h = TCM $ \ r e -> do
+    -- save the state
+    s <- readIORef r
+    catchImpossibleJust f (unTCM m r e) $ \ err -> do
+      writeIORef r s
+      unTCM (h err) r e
+
+instance MonadIO m => MonadReduce (TCMT m) where
+  liftReduce = liftTCM . runReduceM; {-# INLINE liftReduce #-}
+
+instance (IsString a, MonadIO m) => IsString (TCMT m a) where
+  fromString s = return (fromString s)
+
+-- | Strict (non-shortcut) semigroup.
+--
+--   Note that there might be a lazy alternative, e.g.,
+--   for TCM All we might want 'Agda.Utils.Monad.and2M' as concatenation,
+--   to shortcut conjunction in case we already have 'False'.
+--
+instance {-# OVERLAPPABLE #-} (MonadIO m, Semigroup a) => Semigroup (TCMT m a) where
+  (<>) = liftA2 (<>)
+
+-- | Strict (non-shortcut) monoid.
+instance {-# OVERLAPPABLE #-} (MonadIO m, Semigroup a, Monoid a) => Monoid (TCMT m a) where
+  mempty  = pure mempty
+  mappend = (<>)
+  mconcat = mconcat <.> sequence
+
+instance {-# OVERLAPPABLE #-} (MonadIO m, Null a) => Null (TCMT m a) where
+  empty = return empty
+  null  = __IMPOSSIBLE__
+
+-- | Preserve the state of the failing computation.
+catchError_ :: TCM a -> (TCErr -> TCM a) -> TCM a
+catchError_ m h = TCM $ \r e ->
+  unTCM m r e
+  `E.catch` \err -> unTCM (h err) r e
+
+-- | Execute a finalizer even when an exception is thrown.
+--   Does not catch any errors.
+--   In case both the regular computation and the finalizer
+--   throw an exception, the one of the finalizer is propagated.
+finally_ :: TCM a -> TCM b -> TCM a
+finally_ m f = do
+    x <- m `catchError_` \ err -> f >> throwError err
+    _ <- f
+    return x
+
+-- | Embedding a TCM computation.
+
+class ( Applicative tcm, MonadIO tcm
+      , MonadTCEnv tcm
+      , MonadTCState tcm
+      , HasOptions tcm
+      ) => MonadTCM tcm where
+    liftTCM :: TCM a -> tcm a
+
+    default liftTCM :: (MonadTCM m, MonadTrans t, tcm ~ t m) => TCM a -> tcm a
+    liftTCM = lift . liftTCM
+    {-# INLINE liftTCM #-}
+
+{-# RULES "liftTCM/id" liftTCM = id #-}
+instance MonadIO m => MonadTCM (TCMT m) where
+    liftTCM = mapTCMT liftIO
+    {-# INLINE liftTCM #-}
+
+instance MonadTCM tcm => MonadTCM (ChangeT tcm)
+instance MonadTCM tcm => MonadTCM (ExceptT err tcm)
+instance MonadTCM tcm => MonadTCM (IdentityT tcm)
+instance MonadTCM tcm => MonadTCM (ListT tcm)
+instance MonadTCM tcm => MonadTCM (MaybeT tcm)
+instance MonadTCM tcm => MonadTCM (ReaderT r tcm)
+instance MonadTCM tcm => MonadTCM (StateT s tcm)
+instance (Monoid w, MonadTCM tcm) => MonadTCM (WriterT w tcm)
+
+-- | We store benchmark statistics in an IORef.
+--   This enables benchmarking pure computation, see
+--   "Agda.Benchmarking".
+instance MonadBench TCM where
+  type BenchPhase TCM = Phase
+  getBenchmark = liftIO $ getBenchmark
+  putBenchmark = liftIO . putBenchmark
+  finally = finally_
+
+instance Null (TCM Doc) where
+  empty = return empty
+  null = __IMPOSSIBLE__
+
+internalError :: (HasCallStack, MonadTCM tcm) => String -> tcm a
+internalError s = withCallerCallStack $ \ loc ->
+  liftTCM $ typeError' loc $ InternalError s
+
+-- | The constraints needed for 'typeError' and similar.
+type MonadTCError m = (MonadTCEnv m, ReadTCState m, MonadError TCErr m)
+
+-- | Utility function for 1-arg constructed type errors.
+-- Note that the @HasCallStack@ constraint is on the *resulting* function.
+locatedTypeError :: MonadTCError m => (a -> TypeError) -> (HasCallStack => a -> m b)
+locatedTypeError f e = withCallerCallStack (flip typeError' (f e))
+
+genericError :: (HasCallStack, MonadTCError m) => String -> m a
+genericError = locatedTypeError GenericError
+
+{-# SPECIALIZE genericDocError :: Doc -> TCM a #-}
+genericDocError :: (HasCallStack, MonadTCError m) => Doc -> m a
+genericDocError = locatedTypeError GenericDocError
+
+{-# SPECIALIZE typeError' :: CallStack -> TypeError -> TCM a #-}
+typeError' :: MonadTCError m => CallStack -> TypeError -> m a
+typeError' loc err = throwError =<< typeError'_ loc err
+
+{-# SPECIALIZE typeError :: HasCallStack => TypeError -> TCM a #-}
+typeError :: (HasCallStack, MonadTCError m) => TypeError -> m a
+typeError err = withCallerCallStack $ \loc -> throwError =<< typeError'_ loc err
+
+{-# SPECIALIZE typeError'_ :: CallStack -> TypeError -> TCM TCErr #-}
+typeError'_ :: (MonadTCEnv m, ReadTCState m) => CallStack -> TypeError -> m TCErr
+typeError'_ loc err = TypeError loc <$> getTCState <*> buildClosure err
+
+{-# SPECIALIZE typeError_ :: HasCallStack => TypeError -> TCM TCErr #-}
+typeError_ :: (HasCallStack, MonadTCEnv m, ReadTCState m) => TypeError -> m TCErr
+typeError_ = withCallerCallStack . flip typeError'_
+
+-- | Running the type checking monad (most general form).
+{-# SPECIALIZE runTCM :: TCEnv -> TCState -> TCM a -> IO (a, TCState) #-}
+runTCM :: MonadIO m => TCEnv -> TCState -> TCMT m a -> m (a, TCState)
+runTCM e s m = do
+  r <- liftIO $ newIORef s
+  a <- unTCM m r e
+  s <- liftIO $ readIORef r
+  return (a, s)
+
+-- | Running the type checking monad on toplevel (with initial state).
+runTCMTop :: TCM a -> IO (Either TCErr a)
+runTCMTop m = (Right <$> runTCMTop' m) `E.catch` (return . Left)
+
+runTCMTop' :: MonadIO m => TCMT m a -> m a
+runTCMTop' m = do
+  r <- liftIO $ newIORef initState
+  unTCM m r initEnv
+
+-- | 'runSafeTCM' runs a safe 'TCM' action (a 'TCM' action which
+--   cannot fail, except that it might raise 'IOException's) in the
+--   initial environment.
+
+runSafeTCM :: TCM a -> TCState -> IO (a, TCState)
+runSafeTCM m st =
+  runTCM initEnv st m `E.catch` \(e :: TCErr) -> case e of
+    IOException _ _ err -> E.throwIO err
+    _                   -> __IMPOSSIBLE__
+
+-- | Runs the given computation in a separate thread, with /a copy/ of
+-- the current state and environment.
+--
+-- Note that Agda sometimes uses actual, mutable state. If the
+-- computation given to @forkTCM@ tries to /modify/ this state, then
+-- bad things can happen, because accesses are not mutually exclusive.
+-- The @forkTCM@ function has been added mainly to allow the thread to
+-- /read/ (a snapshot of) the current state in a convenient way.
+--
+-- Note also that exceptions which are raised in the thread are not
+-- propagated to the parent, so the thread should not do anything
+-- important.
+
+forkTCM :: TCM a -> TCM ()
+forkTCM m = do
+  s <- getTC
+  e <- askTC
+  liftIO $ void $ C.forkIO $ void $ runTCM e s m
+
+---------------------------------------------------------------------------
+-- * Names for generated definitions
+---------------------------------------------------------------------------
+
+-- | Base name for patterns in telescopes
+patternInTeleName :: String
+patternInTeleName = ".patternInTele"
+
+-- | Base name for extended lambda patterns
+extendedLambdaName :: String
+extendedLambdaName = ".extendedlambda"
+
+-- | Check whether we have an definition from an extended lambda.
+isExtendedLambdaName :: A.QName -> Bool
+isExtendedLambdaName = (extendedLambdaName `List.isPrefixOf`) . prettyShow . nameConcrete . qnameName
+
+-- | Name of absurdLambda definitions.
+absurdLambdaName :: String
+absurdLambdaName = ".absurdlambda"
+
+-- | Check whether we have an definition from an absurd lambda.
+isAbsurdLambdaName :: QName -> Bool
+isAbsurdLambdaName = (absurdLambdaName ==) . prettyShow . qnameName
+
+-- | Base name for generalized variable projections
+generalizedFieldName :: String
+generalizedFieldName = ".generalizedField-"
+
+-- | Check whether we have a generalized variable field
+getGeneralizedFieldName :: A.QName -> Maybe String
+getGeneralizedFieldName q
+  | generalizedFieldName `List.isPrefixOf` strName = Just (drop (length generalizedFieldName) strName)
+  | otherwise                                      = Nothing
+  where strName = prettyShow $ nameConcrete $ qnameName q
+
+---------------------------------------------------------------------------
+-- * KillRange instances
+---------------------------------------------------------------------------
+
+instance KillRange Signature where
+  killRange (Sig secs defs rews) = killRangeN Sig secs defs rews
+
+instance KillRange Sections where
+  killRange = fmap killRange
+
+instance KillRange Definitions where
+  killRange = fmap killRange
+
+instance KillRange RewriteRuleMap where
+  killRange = fmap killRange
+
+instance KillRange Section where
+  killRange (Section tel) = killRangeN Section tel
+
+instance KillRange Definition where
+  killRange (Defn ai name t pols occs gens gpars displ mut compiled inst copy ma nc inj copat blk lang def) =
+    killRangeN Defn ai name t pols occs gens gpars displ mut compiled inst copy ma nc inj copat blk lang def
+    -- TODO clarify: Keep the range in the defName field?
+
+instance KillRange NumGeneralizableArgs where
+  killRange = id
+
+instance KillRange NLPat where
+  killRange (PVar x y) = killRangeN PVar x y
+  killRange (PDef x y) = killRangeN PDef x y
+  killRange (PLam x y) = killRangeN PLam x y
+  killRange (PPi x y)  = killRangeN PPi x y
+  killRange (PSort x)  = killRangeN PSort x
+  killRange (PBoundVar x y) = killRangeN PBoundVar x y
+  killRange (PTerm x)  = killRangeN PTerm x
+
+instance KillRange NLPType where
+  killRange (NLPType s a) = killRangeN NLPType s a
+
+instance KillRange NLPSort where
+  killRange (PUniv u l) = killRangeN (PUniv u) l
+  killRange s@(PInf f n) = s
+  killRange PSizeUniv = PSizeUniv
+  killRange PLockUniv = PLockUniv
+  killRange PLevelUniv = PLevelUniv
+  killRange PIntervalUniv = PIntervalUniv
+
+instance KillRange RewriteRule where
+  killRange (RewriteRule q gamma f es rhs t c) =
+    killRangeN RewriteRule q gamma f es rhs t c
+
+instance KillRange CompiledRepresentation where
+  killRange = id
+
+
+instance KillRange EtaEquality where
+  killRange = id
+
+instance KillRange System where
+  killRange (System tel sys) = System (killRange tel) (killRange sys)
+
+instance KillRange ExtLamInfo where
+  killRange (ExtLamInfo m b sys) = killRangeN ExtLamInfo m b sys
+
+instance KillRange FunctionFlag where
+  killRange = id
+
+instance KillRange CompKit where
+  killRange = id
+
+instance KillRange ProjectionLikenessMissing where
+  killRange = id
+
+instance KillRange BuiltinSort where
+  killRange = id
+
+instance KillRange Defn where
+  killRange def =
+    case def of
+      Axiom a -> Axiom a
+      DataOrRecSig n -> DataOrRecSig n
+      GeneralizableVar -> GeneralizableVar
+      AbstractDefn{} -> __IMPOSSIBLE__ -- only returned by 'getConstInfo'!
+      Function a b c d e f g h i j k l m n o p ->
+        killRangeN Function a b c d e f g h i j k l m n o p
+      Datatype a b c d e f g h i j   -> killRangeN Datatype a b c d e f g h i j
+      Record a b c d e f g h i j k l m -> killRangeN Record a b c d e f g h i j k l m
+      Constructor a b c d e f g h i j k -> killRangeN Constructor a b c d e f g h i j k
+      Primitive a b c d e f          -> killRangeN Primitive a b c d e f
+      PrimitiveSort a b              -> killRangeN PrimitiveSort a b
+
+instance KillRange MutualId where
+  killRange = id
+
+instance KillRange c => KillRange (FunctionInverse' c) where
+  killRange NotInjective = NotInjective
+  killRange (Inverse m)  = Inverse $ killRangeMap m
+
+instance KillRange TermHead where
+  killRange SortHead     = SortHead
+  killRange PiHead       = PiHead
+  killRange (ConsHead q) = ConsHead $ killRange q
+  killRange h@VarHead{}  = h
+  killRange UnknownHead  = UnknownHead
+
+instance KillRange Projection where
+  killRange (Projection a b c d e) = killRangeN Projection a b c d e
+
+instance KillRange ProjLams where
+  killRange = id
+
+instance KillRange a => KillRange (Open a) where
+  killRange = fmap killRange
+
+instance KillRange DisplayForm where
+  killRange (Display n es dt) = killRangeN Display n es dt
+
+instance KillRange Polarity where
+  killRange = id
+
+instance KillRange IsForced where
+  killRange = id
+
+instance KillRange DoGeneralize where
+  killRange = id
+
+instance KillRange DisplayTerm where
+  killRange dt =
+    case dt of
+      DWithApp dt dts es -> killRangeN DWithApp dt dts es
+      DCon q ci dts      -> killRangeN DCon q ci dts
+      DDef q dts         -> killRangeN DDef q dts
+      DDot' v es         -> killRangeN DDot' v es
+      DTerm' v es        -> killRangeN DTerm' v es
+
+instance KillRange a => KillRange (Closure a) where
+  killRange = id
+
+---------------------------------------------------------------------------
+-- NFData instances
+---------------------------------------------------------------------------
+
+instance NFData NumGeneralizableArgs where
+  rnf NoGeneralizableArgs       = ()
+  rnf (SomeGeneralizableArgs _) = ()
+
+instance NFData TCErr where
+  rnf (TypeError a b c)   = rnf a `seq` rnf b `seq` rnf c
+  rnf (Exception a b)     = rnf a `seq` rnf b
+  rnf (IOException a b c) = rnf a `seq` rnf b `seq` rnf (c == c)
+                            -- At the time of writing there is no
+                            -- NFData instance for E.IOException.
+  rnf (PatternErr a)      = rnf a
+
+-- | This instance could be optimised, some things are guaranteed to
+-- be forced.
+
+instance NFData PreScopeState
+
+-- | This instance could be optimised, some things are guaranteed to
+-- be forced.
+
+instance NFData PostScopeState
+
+instance NFData TCState
+instance NFData DisambiguatedName
+instance NFData MutualBlock
+instance NFData OpaqueBlock
+instance NFData (BiMap RawTopLevelModuleName ModuleNameHash)
+instance NFData PersistentTCState
+instance NFData LoadedFileCache
+instance NFData TypeCheckAction
+instance NFData ModuleCheckMode
+instance NFData ModuleInfo
+instance NFData ForeignCode
+instance NFData Interface
+instance NFData a => NFData (Closure a)
+instance NFData ProblemConstraint
+instance NFData WhyCheckModality
+instance NFData Constraint
+instance NFData Signature
+instance NFData Comparison
+instance NFData CompareAs
+instance NFData a => NFData (Open a)
+instance NFData a => NFData (Judgement a)
+instance NFData DoGeneralize
+instance NFData GeneralizedValue
+instance NFData MetaVariable
+instance NFData Listener
+instance NFData MetaInstantiation
+instance NFData Instantiation
+instance NFData RemoteMetaVariable
+instance NFData Frozen
+instance NFData PrincipalArgTypeMetas
+instance NFData TypeCheckingProblem
+instance NFData RunMetaOccursCheck
+instance NFData MetaInfo
+instance NFData InteractionPoint
+instance NFData InteractionPoints
+instance NFData Overapplied
+instance NFData t => NFData (IPBoundary' t)
+instance NFData IPClause
+instance NFData DisplayForm
+instance NFData DisplayTerm
+instance NFData NLPat
+instance NFData NLPType
+instance NFData NLPSort
+instance NFData RewriteRule
+instance NFData Definition
+instance NFData Polarity
+instance NFData IsForced
+instance NFData Projection
+instance NFData ProjLams
+instance NFData CompilerPragma
+instance NFData System
+instance NFData ExtLamInfo
+instance NFData EtaEquality
+instance NFData FunctionFlag
+instance NFData CompKit
+instance NFData AxiomData
+instance NFData DataOrRecSigData
+instance NFData ProjectionLikenessMissing
+instance NFData FunctionData
+instance NFData DatatypeData
+instance NFData RecordData
+instance NFData ConstructorData
+instance NFData PrimitiveData
+instance NFData PrimitiveSortData
+instance NFData Defn
+instance NFData Simplification
+instance NFData AllowedReduction
+instance NFData ReduceDefs
+instance NFData PrimFun
+instance NFData c => NFData (FunctionInverse' c)
+instance NFData TermHead
+instance NFData Call
+instance NFData BuiltinSort
+instance NFData pf => NFData (Builtin pf)
+instance NFData HighlightingLevel
+instance NFData HighlightingMethod
+instance NFData TCEnv
+instance NFData LetBinding
+instance NFData UnquoteFlags
+instance NFData AbstractMode
+instance NFData ExpandHidden
+instance NFData CandidateKind
+instance NFData Candidate
+instance NFData Warning
+instance NFData RecordFieldWarning
+instance NFData TCWarning
+instance NFData CallInfo
+instance NFData TerminationError
+instance NFData ErasedDatatypeReason
+instance NFData SplitError
+instance NFData NegativeUnification
+instance NFData UnificationFailure
+instance NFData UnquoteError
+instance NFData TypeError
+instance NFData LHSOrPatSyn
+instance NFData DataOrRecordE
+instance NFData InductionAndEta
+instance NFData IllegalRewriteRuleReason
+instance NFData IncorrectTypeForRewriteRelationReason
diff --git a/src/full/Agda/TypeChecking/Monad/Base.hs-boot b/src/full/Agda/TypeChecking/Monad/Base.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Base.hs-boot
@@ -0,0 +1,51 @@
+{-# LANGUAGE CPP #-}
+
+module Agda.TypeChecking.Monad.Base where
+
+import Control.Monad.IO.Class (MonadIO)
+import Data.IORef (IORef)
+import Data.Map (Map)
+
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+import Agda.Utils.FileName (AbsolutePath)
+
+data Warning
+
+data TCErr
+data TCWarning
+data NamedMeta
+data HighlightingMethod
+instance Show HighlightingMethod
+instance Read HighlightingMethod
+
+data HighlightingLevel
+instance Show HighlightingLevel
+instance Read HighlightingLevel
+
+
+data TCEnv
+data TCState
+newtype TCMT m a = TCM { unTCM :: IORef TCState -> TCEnv -> m a }
+
+instance Applicative m => Applicative (TCMT m)
+instance Functor m => Functor (TCMT m)
+instance MonadIO m => MonadIO (TCMT m)
+
+#if __GLASGOW_HASKELL__ < 806
+instance MonadIO m => Monad (TCMT m) where
+#else
+-- Andreas, 2022-02-02, issue #5659:
+-- @transformers-0.6@ requires exactly a @Monad@ superclass constraint here
+-- if we want @instance MonadTrans TCMT@.
+instance Monad m => Monad (TCMT m) where
+#endif
+
+type TCM = TCMT IO
+
+type ModuleToSource = Map TopLevelModuleName AbsolutePath
+
+type BackendName = String
+
+data Comparison
+data Polarity
+data IPFace' a
diff --git a/src/full/Agda/TypeChecking/Monad/Base/Warning.hs b/src/full/Agda/TypeChecking/Monad/Base/Warning.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Base/Warning.hs
@@ -0,0 +1,17 @@
+-- | Types related to warnings raised by Agda.
+
+module Agda.TypeChecking.Monad.Base.Warning where
+
+import           GHC.Generics               (Generic)
+
+import           Agda.Syntax.Abstract.Name
+import           Agda.Syntax.Position       (Range)
+import qualified Agda.Syntax.Concrete.Name  as C
+
+data RecordFieldWarning
+  = DuplicateFields [(C.Name, Range)]
+      -- ^ Each redundant field comes with a range of associated dead code.
+  | TooManyFields QName [C.Name] [(C.Name, Range)]
+      -- ^ Record type, fields not supplied by user, non-fields but supplied.
+      --   The redundant fields come with a range of associated dead code.
+  deriving (Show, Generic)
diff --git a/src/full/Agda/TypeChecking/Monad/Benchmark.hs b/src/full/Agda/TypeChecking/Monad/Benchmark.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Benchmark.hs
@@ -0,0 +1,76 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Measure CPU time for individual phases of the Agda pipeline.
+
+module Agda.TypeChecking.Monad.Benchmark
+  ( module Agda.Benchmarking
+  , B.MonadBench
+  , B.BenchPhase
+  , B.getBenchmark
+  , updateBenchmarkingStatus
+  , B.billTo, B.billPureTo, B.billToCPS
+  , B.reset
+  , print
+  ) where
+
+import Prelude hiding (print)
+
+import Agda.Benchmarking
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug
+
+import qualified Agda.Utils.Benchmark as B
+
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Utils.ProfileOptions as Profile
+
+-- | When profile options are set or changed, we need to turn benchmarking on or off.
+updateBenchmarkingStatus :: TCM ()
+-- {-# SPECIALIZE updateBenchmarkingStatus :: TCM () #-}
+-- updateBenchmarkingStatus :: (HasOptions m, MonadBench a m) => m ()
+updateBenchmarkingStatus =
+  B.setBenchmarking =<< benchmarking
+
+-- | Check whether benchmarking is activated.
+{-# SPECIALIZE benchmarking :: TCM (B.BenchmarkOn Phase) #-}
+benchmarking :: MonadTCM tcm => tcm (B.BenchmarkOn Phase)
+benchmarking = liftTCM $
+  ifM (hasProfileOption Profile.Internal)    (pure $ B.BenchmarkSome isInternalAccount) $
+  ifM (hasProfileOption Profile.Definitions) (pure $ B.BenchmarkSome isDefAccount) $
+  ifM (hasProfileOption Profile.Modules)     (pure $ B.BenchmarkSome isModuleAccount) $
+  pure B.BenchmarkOff
+
+-- | Prints the accumulated benchmark results. Does nothing if
+--   no benchmark profiling is enabled.
+print :: MonadTCM tcm => tcm ()
+print = liftTCM $ whenM (B.isBenchmarkOn [] <$> benchmarking) $ do
+  b <- B.getBenchmark
+  -- Andreas, 2017-07-29, issue #2602:
+  -- The following line messes up the AgdaInfo buffer,
+  -- thus, as Fredrik Forsberg suggest, I restore the original
+  -- line for release 2.5.3 until a fix is found.
+  -- reportSLn "" 0 $ prettyShow b
+  -- Ulf, 2020-03-04: Using benchmarkLevel here means that it only prints if internal benchmarking
+  -- is turned on, effectively making module/definition benchmarking impossible (since internal
+  -- takes precedence). It needs to be > 1 to avoid triggering #2602 though. Also use
+  -- displayDebugMessage instead of reportSLn to avoid requiring -v profile:2.
+  displayDebugMessage "profile" 2 $ prettyShow b
+
+-- -- | Bill a computation to a specific account.
+-- {-# SPECIALIZE billTo :: Account -> TCM a -> TCM a #-}
+-- billTo :: MonadTCM tcm => Account -> tcm a -> tcm a
+-- billTo account = lift1TCM $ B.billTo account
+   -- Andreas, 2015-05-23
+   -- FAILS as lift1TCM :: (TCM a -> TCM b) -> tcm a -> tcm b
+   -- cannot be implemented lazily in general.
+   -- With `lazily` I mean that embedded IO computations in @tcm a@ are
+   -- not executed, but passed on to @TCM a -> TCM b@ unevaluated.
+   -- If they are treated strictly, then the whole benchmarking is inaccurate
+   -- of course, as the computation is done before the clock is started.
+
+-- -- | Bill a pure computation to a specific account.
+-- {-# SPECIALIZE billPureTo :: Account -> a -> TCM a #-}
+-- billPureTo :: MonadTCM tcm => Account -> a -> tcm a
+-- billPureTo k a = billTo k $ return a
diff --git a/src/full/Agda/TypeChecking/Monad/Builtin.hs b/src/full/Agda/TypeChecking/Monad/Builtin.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Builtin.hs
@@ -0,0 +1,813 @@
+
+module Agda.TypeChecking.Monad.Builtin
+  ( module Agda.TypeChecking.Monad.Builtin
+  , module Agda.Syntax.Builtin  -- The names are defined here.
+  ) where
+
+import qualified Control.Monad.Fail as Fail
+
+import Control.Monad                ( liftM2, void )
+import Control.Monad.Except
+import Control.Monad.IO.Class       ( MonadIO(..) )
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Identity (IdentityT)
+import Control.Monad.Trans.Maybe
+import Control.Monad.Writer
+
+import Data.Function ( on )
+import qualified Data.Map as Map
+import Data.Set (Set)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+import Agda.Syntax.Builtin
+import Agda.Syntax.Internal as I
+import Agda.TypeChecking.Monad.Base
+-- import Agda.TypeChecking.Functions  -- LEADS TO IMPORT CYCLE
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.ListT
+import Agda.Utils.Monad
+import Agda.Utils.Maybe
+import Agda.Utils.Singleton
+import Agda.Utils.Tuple
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+class ( Functor m
+      , Applicative m
+      , Fail.MonadFail m
+      ) => HasBuiltins m where
+  getBuiltinThing :: SomeBuiltin -> m (Maybe (Builtin PrimFun))
+
+  default getBuiltinThing :: (MonadTrans t, HasBuiltins n, t n ~ m) => SomeBuiltin -> m (Maybe (Builtin PrimFun))
+  getBuiltinThing = lift . getBuiltinThing
+
+instance HasBuiltins m => HasBuiltins (ChangeT m)
+instance HasBuiltins m => HasBuiltins (ExceptT e m)
+instance HasBuiltins m => HasBuiltins (IdentityT m)
+instance HasBuiltins m => HasBuiltins (ListT m)
+instance HasBuiltins m => HasBuiltins (MaybeT m)
+instance HasBuiltins m => HasBuiltins (ReaderT e m)
+instance HasBuiltins m => HasBuiltins (StateT s m)
+instance (HasBuiltins m, Monoid w) => HasBuiltins (WriterT w m)
+
+deriving instance HasBuiltins m => HasBuiltins (BlockT m)
+
+instance MonadIO m => HasBuiltins (TCMT m) where
+  getBuiltinThing b =
+    liftM2 (unionMaybeWith unionBuiltin)
+      (Map.lookup b <$> useTC stLocalBuiltins)
+      (Map.lookup b <$> useTC stImportedBuiltins)
+{-# SPECIALIZE getBuiltinThing :: SomeBuiltin -> TCM (Maybe (Builtin PrimFun)) #-}
+
+
+-- | The trivial implementation of 'HasBuiltins', using a constant 'TCState'.
+--
+-- This may be used instead of 'TCMT'/'ReduceM' where builtins must be accessed
+-- in a pure context.
+newtype BuiltinAccess a = BuiltinAccess { unBuiltinAccess :: TCState -> a }
+  deriving (Functor, Applicative, Monad)
+
+instance Fail.MonadFail BuiltinAccess where
+  fail msg = BuiltinAccess $ \_ -> error msg
+
+instance HasBuiltins BuiltinAccess where
+  getBuiltinThing b = BuiltinAccess $ \state ->
+    unionMaybeWith unionBuiltin
+      (Map.lookup b $ state ^. stLocalBuiltins)
+      (Map.lookup b $ state ^. stImportedBuiltins)
+
+-- | Run a 'BuiltinAccess' monad.
+runBuiltinAccess :: TCState -> BuiltinAccess a -> a
+runBuiltinAccess s m = unBuiltinAccess m s
+
+
+-- If Agda is changed so that the type of a literal can belong to an
+-- inductive family (with at least one index), then the implementation
+-- of split' in Agda.TypeChecking.Coverage should be changed.
+
+litType
+  :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+  => Literal -> m Type
+litType = \case
+  LitNat n    -> do
+    _ <- primZero
+    when (n > 0) $ void $ primSuc
+    el <$> primNat
+  LitWord64 _ -> el <$> primWord64
+  LitFloat _  -> el <$> primFloat
+  LitChar _   -> el <$> primChar
+  LitString _ -> el <$> primString
+  LitQName _  -> el <$> primQName
+  LitMeta _ _ -> el <$> primAgdaMeta
+  where
+    el t = El (mkType 0) t
+
+setBuiltinThings :: BuiltinThings PrimFun -> TCM ()
+setBuiltinThings b = stLocalBuiltins `setTCLens` b
+
+bindBuiltinName :: BuiltinId -> Term -> TCM ()
+bindBuiltinName b x = do
+  builtin <- getBuiltinThing b'
+  case builtin of
+    Just (Builtin y) -> typeError $ DuplicateBuiltinBinding b y x
+    Just Prim{}      -> typeError $ __IMPOSSIBLE__
+    Just BuiltinRewriteRelations{} -> __IMPOSSIBLE__
+    Nothing          -> stLocalBuiltins `modifyTCLens` Map.insert b' (Builtin x)
+  where b' = BuiltinName b
+
+bindPrimitive :: PrimitiveId -> PrimFun -> TCM ()
+bindPrimitive b pf = do
+  builtin <- getBuiltinThing b'
+  case builtin of
+    Just (Builtin _) -> typeError $ NoSuchPrimitiveFunction (getBuiltinId b)
+    Just (Prim x)    -> typeError $ (DuplicatePrimitiveBinding b `on` primFunName) x pf
+    Just BuiltinRewriteRelations{} -> __IMPOSSIBLE__
+    Nothing          -> stLocalBuiltins `modifyTCLens` Map.insert b' (Prim pf)
+  where b' = PrimitiveName b
+
+-- | Add one (more) relation symbol to the rewrite relations.
+bindBuiltinRewriteRelation :: QName -> TCM ()
+bindBuiltinRewriteRelation x =
+  stLocalBuiltins `modifyTCLens`
+    Map.insertWith unionBuiltin (BuiltinName builtinRewrite) (BuiltinRewriteRelations $ singleton x)
+
+-- | Get the currently registered rewrite relation symbols.
+getBuiltinRewriteRelations :: HasBuiltins m => m (Maybe (Set QName))
+getBuiltinRewriteRelations = fmap rels <$> getBuiltinThing (BuiltinName builtinRewrite)
+  where
+  rels = \case
+    BuiltinRewriteRelations xs -> xs
+    Prim{}    -> __IMPOSSIBLE__
+    Builtin{} -> __IMPOSSIBLE__
+
+{-# INLINABLE getBuiltin #-}
+getBuiltin :: (HasBuiltins m, MonadTCError m)
+           => BuiltinId -> m Term
+getBuiltin x =
+  fromMaybeM (typeError $ NoBindingForBuiltin x) $ getBuiltin' x
+
+{-# INLINABLE getBuiltin' #-}
+getBuiltin' :: HasBuiltins m => BuiltinId -> m (Maybe Term)
+getBuiltin' x = (getBuiltin =<<) <$> getBuiltinThing (BuiltinName x) where
+  getBuiltin BuiltinRewriteRelations{} = __IMPOSSIBLE__
+  getBuiltin (Builtin t)               = Just $ killRange t
+  getBuiltin _                         = Nothing
+
+{-# INLINABLE getPrimitive' #-}
+getPrimitive' :: HasBuiltins m => PrimitiveId -> m (Maybe PrimFun)
+getPrimitive' x = (getPrim =<<) <$> getBuiltinThing (PrimitiveName x)
+  where
+    getPrim (Prim pf) = return pf
+    getPrim BuiltinRewriteRelations{} = __IMPOSSIBLE__
+    getPrim _         = Nothing
+
+{-# INLINABLE getPrimitive #-}
+getPrimitive :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+             => PrimitiveId -> m PrimFun
+getPrimitive x =
+  fromMaybeM (typeError . NoSuchPrimitiveFunction $ getBuiltinId x) $ getPrimitive' x
+
+getPrimitiveTerm :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+                 => PrimitiveId -> m Term
+getPrimitiveTerm x = (`Def` []) . primFunName <$> getPrimitive x
+
+
+getPrimitiveTerm' :: HasBuiltins m => PrimitiveId -> m (Maybe Term)
+getPrimitiveTerm' x = fmap (`Def` []) <$> getPrimitiveName' x
+
+getTerm' :: (HasBuiltins m, IsBuiltin a) => a -> m (Maybe Term)
+getTerm' = go . someBuiltin where
+  go (BuiltinName x)   = getBuiltin' x
+  go (PrimitiveName x) = getPrimitiveTerm' x
+
+getName' :: (HasBuiltins m, IsBuiltin a) => a -> m (Maybe QName)
+getName' = go . someBuiltin where
+  go (BuiltinName x)   = getBuiltinName' x
+  go (PrimitiveName x) = getPrimitiveName' x
+
+-- | @getTerm use name@ looks up @name@ as a primitive or builtin, and
+-- throws an error otherwise.
+-- The @use@ argument describes how the name is used for the sake of
+-- the error message.
+getTerm :: (HasBuiltins m, IsBuiltin a) => String -> a -> m Term
+getTerm use name = flip fromMaybeM (getTerm' name) $
+  return $! throwImpossible (ImpMissingDefinitions [getBuiltinId name] use)
+
+
+-- | Rewrite a literal to constructor form if possible.
+constructorForm :: HasBuiltins m => Term -> m Term
+constructorForm v = do
+  let pZero = fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinZero
+      pSuc  = fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSuc
+  constructorForm' pZero pSuc v
+
+{-# INLINABLE constructorForm' #-}
+{-# SPECIALIZE constructorForm' :: TCM Term -> TCM Term -> Term -> TCM Term #-}
+constructorForm' :: Applicative m => m Term -> m Term -> Term -> m Term
+constructorForm' pZero pSuc v =
+  case v of
+    Lit (LitNat n)
+      | n == 0    -> pZero
+      | n > 0     -> (`apply1` Lit (LitNat $ n - 1)) <$> pSuc
+      | otherwise -> pure v
+    _ -> pure v
+
+---------------------------------------------------------------------------
+-- * The names of built-in things
+---------------------------------------------------------------------------
+
+primInteger, primIntegerPos, primIntegerNegSuc,
+    primFloat, primChar, primString, primUnit, primUnitUnit, primBool, primTrue, primFalse,
+    primSigma,
+    primList, primNil, primCons, primIO, primNat, primSuc, primZero, primMaybe, primNothing, primJust,
+    primPath, primPathP, primIntervalUniv, primInterval, primIZero, primIOne, primPartial, primPartialP,
+    primIMin, primIMax, primINeg,
+    primIsOne, primItIsOne, primIsOne1, primIsOne2, primIsOneEmpty,
+    primSub, primSubIn, primSubOut,
+    primTrans, primHComp,
+    primId, primConId, primIdElim,
+    primEquiv, primEquivFun, primEquivProof,
+    primTranspProof,
+    primGlue, prim_glue, prim_unglue,
+    prim_glueU, prim_unglueU,
+    primFaceForall,
+    primNatPlus, primNatMinus, primNatTimes, primNatDivSucAux, primNatModSucAux,
+    primNatEquality, primNatLess,
+    -- Machine words
+    primWord64,
+    primSizeUniv, primSize, primSizeLt, primSizeSuc, primSizeInf, primSizeMax,
+    primInf, primSharp, primFlat,
+    primEquality, primRefl,
+    primLevel, primLevelZero, primLevelSuc, primLevelMax,
+    primLockUniv,
+    primLevelUniv,
+    primProp, primSet, primStrictSet, primPropOmega, primSetOmega, primSSetOmega,
+    primFromNat, primFromNeg, primFromString,
+    -- builtins for reflection:
+    primQName, primArgInfo, primArgArgInfo, primArg, primArgArg, primAbs, primAbsAbs, primAgdaTerm, primAgdaTermVar,
+    primAgdaTermLam, primAgdaTermExtLam, primAgdaTermDef, primAgdaTermCon, primAgdaTermPi,
+    primAgdaTermSort, primAgdaTermLit, primAgdaTermUnsupported, primAgdaTermMeta,
+    primAgdaErrorPart, primAgdaErrorPartString, primAgdaErrorPartTerm, primAgdaErrorPartPatt, primAgdaErrorPartName,
+    primHiding, primHidden, primInstance, primVisible,
+    primRelevance, primRelevant, primIrrelevant,
+    primQuantity, primQuantity0, primQuantityω,
+    primModality, primModalityConstructor,
+    primAssoc, primAssocLeft, primAssocRight, primAssocNon,
+    primPrecedence, primPrecRelated, primPrecUnrelated,
+    primFixity, primFixityFixity,
+    primAgdaLiteral, primAgdaLitNat, primAgdaLitWord64, primAgdaLitFloat, primAgdaLitString, primAgdaLitChar, primAgdaLitQName, primAgdaLitMeta,
+    primAgdaSort, primAgdaSortSet, primAgdaSortLit, primAgdaSortProp, primAgdaSortPropLit, primAgdaSortInf, primAgdaSortUnsupported,
+    primAgdaDefinition, primAgdaDefinitionFunDef, primAgdaDefinitionDataDef, primAgdaDefinitionRecordDef,
+    primAgdaDefinitionPostulate, primAgdaDefinitionPrimitive, primAgdaDefinitionDataConstructor,
+    primAgdaClause, primAgdaClauseClause, primAgdaClauseAbsurd,
+    primAgdaPattern, primAgdaPatCon, primAgdaPatVar, primAgdaPatDot,
+    primAgdaPatLit, primAgdaPatProj,
+    primAgdaPatAbsurd,
+    primAgdaMeta,
+    primAgdaBlocker, primAgdaBlockerAny, primAgdaBlockerAll, primAgdaBlockerMeta,
+    primAgdaTCM, primAgdaTCMReturn, primAgdaTCMBind, primAgdaTCMUnify,
+    primAgdaTCMTypeError, primAgdaTCMInferType, primAgdaTCMCheckType,
+    primAgdaTCMNormalise, primAgdaTCMReduce,
+    primAgdaTCMCatchError, primAgdaTCMGetContext, primAgdaTCMExtendContext, primAgdaTCMInContext,
+    primAgdaTCMFreshName, primAgdaTCMDeclareDef, primAgdaTCMDeclarePostulate, primAgdaTCMDeclareData, primAgdaTCMDefineData, primAgdaTCMDefineFun,
+    primAgdaTCMGetType, primAgdaTCMGetDefinition,
+    primAgdaTCMQuoteTerm, primAgdaTCMUnquoteTerm, primAgdaTCMQuoteOmegaTerm,
+    primAgdaTCMCommit, primAgdaTCMIsMacro, primAgdaTCMBlock,
+    primAgdaTCMFormatErrorParts, primAgdaTCMDebugPrint,
+    primAgdaTCMWithNormalisation, primAgdaTCMWithReconstructed,
+    primAgdaTCMWithExpandLast, primAgdaTCMWithReduceDefs,
+    primAgdaTCMAskNormalisation, primAgdaTCMAskReconstructed,
+    primAgdaTCMAskExpandLast, primAgdaTCMAskReduceDefs,
+    primAgdaTCMNoConstraints,
+    primAgdaTCMRunSpeculative,
+    primAgdaTCMExec,
+    primAgdaTCMGetInstances,
+    primAgdaTCMPragmaForeign,
+    primAgdaTCMPragmaCompile
+    :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) => m Term
+
+primInteger                           = getBuiltin builtinInteger
+primIntegerPos                        = getBuiltin builtinIntegerPos
+primIntegerNegSuc                     = getBuiltin builtinIntegerNegSuc
+primFloat                             = getBuiltin builtinFloat
+primChar                              = getBuiltin builtinChar
+primString                            = getBuiltin builtinString
+primBool                              = getBuiltin builtinBool
+primSigma                             = getBuiltin builtinSigma
+primUnit                              = getBuiltin builtinUnit
+primUnitUnit                          = getBuiltin builtinUnitUnit
+primTrue                              = getBuiltin builtinTrue
+primFalse                             = getBuiltin builtinFalse
+primList                              = getBuiltin builtinList
+primNil                               = getBuiltin builtinNil
+primCons                              = getBuiltin builtinCons
+primMaybe                             = getBuiltin builtinMaybe
+primNothing                           = getBuiltin builtinNothing
+primJust                              = getBuiltin builtinJust
+primIO                                = getBuiltin builtinIO
+primId                                = getBuiltin builtinId
+primConId                             = getPrimitiveTerm builtinConId
+primIdElim                            = getPrimitiveTerm builtinIdElim
+primPath                              = getBuiltin builtinPath
+primPathP                             = getBuiltin builtinPathP
+primIntervalUniv                      = getBuiltin builtinIntervalUniv
+primInterval                          = getBuiltin builtinInterval
+primIZero                             = getBuiltin builtinIZero
+primIOne                              = getBuiltin builtinIOne
+primIMin                              = getPrimitiveTerm builtinIMin
+primIMax                              = getPrimitiveTerm builtinIMax
+primINeg                              = getPrimitiveTerm builtinINeg
+primPartial                           = getPrimitiveTerm PrimPartial
+primPartialP                          = getPrimitiveTerm PrimPartialP
+primIsOne                             = getBuiltin builtinIsOne
+primItIsOne                           = getBuiltin builtinItIsOne
+primTrans                             = getPrimitiveTerm builtinTrans
+primHComp                             = getPrimitiveTerm builtinHComp
+primEquiv                             = getBuiltin builtinEquiv
+primEquivFun                          = getBuiltin builtinEquivFun
+primEquivProof                        = getBuiltin builtinEquivProof
+primTranspProof                       = getBuiltin builtinTranspProof
+prim_glueU                            = getPrimitiveTerm builtin_glueU
+prim_unglueU                          = getPrimitiveTerm builtin_unglueU
+primGlue                              = getPrimitiveTerm builtinGlue
+prim_glue                             = getPrimitiveTerm builtin_glue
+prim_unglue                           = getPrimitiveTerm builtin_unglue
+primFaceForall                        = getPrimitiveTerm builtinFaceForall
+primIsOne1                            = getBuiltin builtinIsOne1
+primIsOne2                            = getBuiltin builtinIsOne2
+primIsOneEmpty                        = getBuiltin builtinIsOneEmpty
+primSub                               = getBuiltin builtinSub
+primSubIn                             = getBuiltin builtinSubIn
+primSubOut                            = getPrimitiveTerm builtinSubOut
+primNat                               = getBuiltin builtinNat
+primSuc                               = getBuiltin builtinSuc
+primZero                              = getBuiltin builtinZero
+primNatPlus                           = getBuiltin builtinNatPlus
+primNatMinus                          = getBuiltin builtinNatMinus
+primNatTimes                          = getBuiltin builtinNatTimes
+primNatDivSucAux                      = getBuiltin builtinNatDivSucAux
+primNatModSucAux                      = getBuiltin builtinNatModSucAux
+primNatEquality                       = getBuiltin builtinNatEquals
+primNatLess                           = getBuiltin builtinNatLess
+primWord64                            = getBuiltin builtinWord64
+primSizeUniv                          = getBuiltin builtinSizeUniv
+primSize                              = getBuiltin builtinSize
+primSizeLt                            = getBuiltin builtinSizeLt
+primSizeSuc                           = getBuiltin builtinSizeSuc
+primSizeInf                           = getBuiltin builtinSizeInf
+primSizeMax                           = getBuiltin builtinSizeMax
+primInf                               = getBuiltin builtinInf
+primSharp                             = getBuiltin builtinSharp
+primFlat                              = getBuiltin builtinFlat
+primEquality                          = getBuiltin builtinEquality
+primRefl                              = getBuiltin builtinRefl
+primLevel                             = getBuiltin builtinLevel
+primLevelZero                         = getBuiltin builtinLevelZero
+primLevelSuc                          = getBuiltin builtinLevelSuc
+primLevelMax                          = getBuiltin builtinLevelMax
+primProp                              = getBuiltin builtinProp
+primSet                               = getBuiltin builtinSet
+primStrictSet                         = getBuiltin builtinStrictSet
+primPropOmega                         = getBuiltin builtinPropOmega
+primSetOmega                          = getBuiltin builtinSetOmega
+primSSetOmega                         = getBuiltin builtinSSetOmega
+primLockUniv                          = getPrimitiveTerm builtinLockUniv
+primLevelUniv                         = getBuiltin builtinLevelUniv
+primFromNat                           = getBuiltin builtinFromNat
+primFromNeg                           = getBuiltin builtinFromNeg
+primFromString                        = getBuiltin builtinFromString
+primQName                             = getBuiltin builtinQName
+primArg                               = getBuiltin builtinArg
+primArgArg                            = getBuiltin builtinArgArg
+primAbs                               = getBuiltin builtinAbs
+primAbsAbs                            = getBuiltin builtinAbsAbs
+primAgdaSort                          = getBuiltin builtinAgdaSort
+primHiding                            = getBuiltin builtinHiding
+primHidden                            = getBuiltin builtinHidden
+primInstance                          = getBuiltin builtinInstance
+primVisible                           = getBuiltin builtinVisible
+primRelevance                         = getBuiltin builtinRelevance
+primRelevant                          = getBuiltin builtinRelevant
+primIrrelevant                        = getBuiltin builtinIrrelevant
+primQuantity                          = getBuiltin builtinQuantity
+primQuantity0                         = getBuiltin builtinQuantity0
+primQuantityω                         = getBuiltin builtinQuantityω
+primModality                          = getBuiltin builtinModality
+primModalityConstructor               = getBuiltin builtinModalityConstructor
+primAssoc                             = getBuiltin builtinAssoc
+primAssocLeft                         = getBuiltin builtinAssocLeft
+primAssocRight                        = getBuiltin builtinAssocRight
+primAssocNon                          = getBuiltin builtinAssocNon
+primPrecedence                        = getBuiltin builtinPrecedence
+primPrecRelated                       = getBuiltin builtinPrecRelated
+primPrecUnrelated                     = getBuiltin builtinPrecUnrelated
+primFixity                            = getBuiltin builtinFixity
+primFixityFixity                      = getBuiltin builtinFixityFixity
+primAgdaBlocker                       = getBuiltin builtinAgdaBlocker
+primAgdaBlockerAny                    = getBuiltin builtinAgdaBlockerAny
+primAgdaBlockerAll                    = getBuiltin builtinAgdaBlockerAll
+primAgdaBlockerMeta                   = getBuiltin builtinAgdaBlockerMeta
+primArgInfo                           = getBuiltin builtinArgInfo
+primArgArgInfo                        = getBuiltin builtinArgArgInfo
+primAgdaSortSet                       = getBuiltin builtinAgdaSortSet
+primAgdaSortLit                       = getBuiltin builtinAgdaSortLit
+primAgdaSortProp                      = getBuiltin builtinAgdaSortProp
+primAgdaSortPropLit                   = getBuiltin builtinAgdaSortPropLit
+primAgdaSortInf                       = getBuiltin builtinAgdaSortInf
+primAgdaSortUnsupported               = getBuiltin builtinAgdaSortUnsupported
+primAgdaTerm                          = getBuiltin builtinAgdaTerm
+primAgdaTermVar                       = getBuiltin builtinAgdaTermVar
+primAgdaTermLam                       = getBuiltin builtinAgdaTermLam
+primAgdaTermExtLam                    = getBuiltin builtinAgdaTermExtLam
+primAgdaTermDef                       = getBuiltin builtinAgdaTermDef
+primAgdaTermCon                       = getBuiltin builtinAgdaTermCon
+primAgdaTermPi                        = getBuiltin builtinAgdaTermPi
+primAgdaTermSort                      = getBuiltin builtinAgdaTermSort
+primAgdaTermLit                       = getBuiltin builtinAgdaTermLit
+primAgdaTermUnsupported               = getBuiltin builtinAgdaTermUnsupported
+primAgdaTermMeta                      = getBuiltin builtinAgdaTermMeta
+primAgdaErrorPart                     = getBuiltin builtinAgdaErrorPart
+primAgdaErrorPartString               = getBuiltin builtinAgdaErrorPartString
+primAgdaErrorPartTerm                 = getBuiltin builtinAgdaErrorPartTerm
+primAgdaErrorPartPatt                 = getBuiltin builtinAgdaErrorPartPatt
+primAgdaErrorPartName                 = getBuiltin builtinAgdaErrorPartName
+primAgdaLiteral                       = getBuiltin builtinAgdaLiteral
+primAgdaLitNat                        = getBuiltin builtinAgdaLitNat
+primAgdaLitWord64                     = getBuiltin builtinAgdaLitWord64
+primAgdaLitFloat                      = getBuiltin builtinAgdaLitFloat
+primAgdaLitChar                       = getBuiltin builtinAgdaLitChar
+primAgdaLitString                     = getBuiltin builtinAgdaLitString
+primAgdaLitQName                      = getBuiltin builtinAgdaLitQName
+primAgdaLitMeta                       = getBuiltin builtinAgdaLitMeta
+primAgdaPattern                       = getBuiltin builtinAgdaPattern
+primAgdaPatCon                        = getBuiltin builtinAgdaPatCon
+primAgdaPatVar                        = getBuiltin builtinAgdaPatVar
+primAgdaPatDot                        = getBuiltin builtinAgdaPatDot
+primAgdaPatLit                        = getBuiltin builtinAgdaPatLit
+primAgdaPatProj                       = getBuiltin builtinAgdaPatProj
+primAgdaPatAbsurd                     = getBuiltin builtinAgdaPatAbsurd
+primAgdaClause                        = getBuiltin builtinAgdaClause
+primAgdaClauseClause                  = getBuiltin builtinAgdaClauseClause
+primAgdaClauseAbsurd                  = getBuiltin builtinAgdaClauseAbsurd
+primAgdaDefinitionFunDef              = getBuiltin builtinAgdaDefinitionFunDef
+primAgdaDefinitionDataDef             = getBuiltin builtinAgdaDefinitionDataDef
+primAgdaDefinitionRecordDef           = getBuiltin builtinAgdaDefinitionRecordDef
+primAgdaDefinitionDataConstructor     = getBuiltin builtinAgdaDefinitionDataConstructor
+primAgdaDefinitionPostulate           = getBuiltin builtinAgdaDefinitionPostulate
+primAgdaDefinitionPrimitive           = getBuiltin builtinAgdaDefinitionPrimitive
+primAgdaDefinition                    = getBuiltin builtinAgdaDefinition
+primAgdaMeta                          = getBuiltin builtinAgdaMeta
+primAgdaTCM                           = getBuiltin builtinAgdaTCM
+primAgdaTCMReturn                     = getBuiltin builtinAgdaTCMReturn
+primAgdaTCMBind                       = getBuiltin builtinAgdaTCMBind
+primAgdaTCMUnify                      = getBuiltin builtinAgdaTCMUnify
+primAgdaTCMTypeError                  = getBuiltin builtinAgdaTCMTypeError
+primAgdaTCMInferType                  = getBuiltin builtinAgdaTCMInferType
+primAgdaTCMCheckType                  = getBuiltin builtinAgdaTCMCheckType
+primAgdaTCMNormalise                  = getBuiltin builtinAgdaTCMNormalise
+primAgdaTCMReduce                     = getBuiltin builtinAgdaTCMReduce
+primAgdaTCMCatchError                 = getBuiltin builtinAgdaTCMCatchError
+primAgdaTCMGetContext                 = getBuiltin builtinAgdaTCMGetContext
+primAgdaTCMExtendContext              = getBuiltin builtinAgdaTCMExtendContext
+primAgdaTCMInContext                  = getBuiltin builtinAgdaTCMInContext
+primAgdaTCMFreshName                  = getBuiltin builtinAgdaTCMFreshName
+primAgdaTCMDeclareDef                 = getBuiltin builtinAgdaTCMDeclareDef
+primAgdaTCMDeclarePostulate           = getBuiltin builtinAgdaTCMDeclarePostulate
+primAgdaTCMDeclareData                = getBuiltin builtinAgdaTCMDeclareData
+primAgdaTCMDefineData                 = getBuiltin builtinAgdaTCMDefineData
+primAgdaTCMDefineFun                  = getBuiltin builtinAgdaTCMDefineFun
+primAgdaTCMGetType                    = getBuiltin builtinAgdaTCMGetType
+primAgdaTCMGetDefinition              = getBuiltin builtinAgdaTCMGetDefinition
+primAgdaTCMQuoteTerm                  = getBuiltin builtinAgdaTCMQuoteTerm
+primAgdaTCMQuoteOmegaTerm             = getBuiltin builtinAgdaTCMQuoteOmegaTerm
+primAgdaTCMUnquoteTerm                = getBuiltin builtinAgdaTCMUnquoteTerm
+primAgdaTCMBlock                      = getBuiltin builtinAgdaTCMBlock
+primAgdaTCMCommit                     = getBuiltin builtinAgdaTCMCommit
+primAgdaTCMIsMacro                    = getBuiltin builtinAgdaTCMIsMacro
+primAgdaTCMWithNormalisation          = getBuiltin builtinAgdaTCMWithNormalisation
+primAgdaTCMWithReconstructed          = getBuiltin builtinAgdaTCMWithReconstructed
+primAgdaTCMWithExpandLast             = getBuiltin builtinAgdaTCMWithExpandLast
+primAgdaTCMWithReduceDefs             = getBuiltin builtinAgdaTCMWithReduceDefs
+primAgdaTCMAskNormalisation           = getBuiltin builtinAgdaTCMAskNormalisation
+primAgdaTCMAskReconstructed           = getBuiltin builtinAgdaTCMAskReconstructed
+primAgdaTCMAskExpandLast              = getBuiltin builtinAgdaTCMAskExpandLast
+primAgdaTCMAskReduceDefs              = getBuiltin builtinAgdaTCMAskReduceDefs
+primAgdaTCMFormatErrorParts           = getBuiltin builtinAgdaTCMFormatErrorParts
+primAgdaTCMDebugPrint                 = getBuiltin builtinAgdaTCMDebugPrint
+primAgdaTCMNoConstraints              = getBuiltin builtinAgdaTCMNoConstraints
+primAgdaTCMRunSpeculative             = getBuiltin builtinAgdaTCMRunSpeculative
+primAgdaTCMExec                       = getBuiltin builtinAgdaTCMExec
+primAgdaTCMGetInstances               = getBuiltin builtinAgdaTCMGetInstances
+primAgdaTCMPragmaForeign              = getBuiltin builtinAgdaTCMPragmaForeign
+primAgdaTCMPragmaCompile              = getBuiltin builtinAgdaTCMPragmaCompile
+
+-- | The coinductive primitives.
+
+data CoinductionKit = CoinductionKit
+  { nameOfInf   :: QName
+  , nameOfSharp :: QName
+  , nameOfFlat  :: QName
+  }
+
+-- | Tries to build a 'CoinductionKit'.
+
+coinductionKit' :: TCM CoinductionKit
+coinductionKit' = do
+  Def inf   _ <- primInf
+  Def sharp _ <- primSharp
+  Def flat  _ <- primFlat
+  return $ CoinductionKit
+    { nameOfInf   = inf
+    , nameOfSharp = sharp
+    , nameOfFlat  = flat
+    }
+
+coinductionKit :: TCM (Maybe CoinductionKit)
+coinductionKit = tryMaybe coinductionKit'
+
+-- | Sort primitives.
+
+data SortKit = SortKit
+  { nameOfUniv   :: UnivSize -> Univ -> QName
+  , isNameOfUniv :: QName -> Maybe (UnivSize, Univ)
+  }
+
+mkSortKit :: QName -> QName -> QName -> QName -> QName -> QName -> SortKit
+mkSortKit prop set sset propomega setomega ssetomega = SortKit
+  { nameOfUniv = curry $ \case
+      (USmall , UProp) -> prop
+      (USmall , UType) -> set
+      (USmall , USSet) -> sset
+      (ULarge , UProp) -> propomega
+      (ULarge , UType) -> setomega
+      (ULarge , USSet) -> ssetomega
+  , isNameOfUniv = \ x -> if
+      | x == prop      -> Just (USmall , UProp)
+      | x == set       -> Just (USmall , UType)
+      | x == sset      -> Just (USmall , USSet)
+      | x == propomega -> Just (ULarge , UProp)
+      | x == setomega  -> Just (ULarge , UType)
+      | x == ssetomega -> Just (ULarge , USSet)
+      | otherwise -> Nothing
+  }
+
+-- | Compute a 'SortKit' in an environment that supports failures.
+--
+-- When 'optLoadPrimitives' is set to 'False', 'sortKit' is a fallible operation,
+-- so for the uses of 'sortKit' in fallible contexts (e.g. 'TCM'),
+-- we report a type error rather than exploding.
+sortKit :: (HasBuiltins m, MonadTCError m, HasOptions m) => m SortKit
+sortKit = do
+  Def prop     _  <- getBuiltin builtinProp
+  Def set      _  <- getBuiltin builtinSet
+  Def sset     _  <- getBuiltin builtinStrictSet
+  Def propomega _ <- getBuiltin builtinPropOmega
+  Def setomega _  <- getBuiltin builtinSetOmega
+  Def ssetomega _ <- getBuiltin builtinSSetOmega
+  return $ mkSortKit prop set sset propomega setomega ssetomega
+
+-- | Compute a 'SortKit' in contexts that do not support failure (e.g.
+-- 'Reify'). This should only be used when we are sure that the
+-- primitive sorts have been bound, i.e. because it is "after" type
+-- checking.
+infallibleSortKit :: HasBuiltins m => m SortKit
+infallibleSortKit = do
+  Def prop     _  <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinProp
+  Def set      _  <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSet
+  Def sset     _  <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinStrictSet
+  Def propomega _ <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinPropOmega
+  Def setomega _  <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSetOmega
+  Def ssetomega _ <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSSetOmega
+  return $ mkSortKit prop set sset propomega setomega ssetomega
+
+------------------------------------------------------------------------
+-- * Path equality
+------------------------------------------------------------------------
+
+getPrimName :: Term -> QName
+getPrimName ty = do
+  let lamV (Lam i b)  = mapFst (getHiding i :) $ lamV (unAbs b)
+      lamV (Pi _ b)   = lamV (unEl $ unAbs b)
+      lamV v          = ([], v)
+  case lamV ty of
+            (_, Def path _) -> path
+            (_, Con nm _ _)   -> conName nm
+            (_, Var 0 [Proj _ l]) -> l
+            (_, t)          -> __IMPOSSIBLE__
+
+getBuiltinName' :: HasBuiltins m => BuiltinId -> m (Maybe QName)
+getBuiltinName' n = fmap getPrimName <$> getBuiltin' n
+
+getPrimitiveName' :: HasBuiltins m => PrimitiveId -> m (Maybe QName)
+getPrimitiveName' n = fmap primFunName <$> getPrimitive' n
+
+isPrimitive :: HasBuiltins m => PrimitiveId -> QName -> m Bool
+isPrimitive n q = (Just q ==) <$> getPrimitiveName' n
+
+intervalSort :: Sort
+intervalSort = IntervalUniv
+
+{-# SPECIALIZE intervalView' :: TCM (Term -> IntervalView) #-}
+{-# INLINABLE intervalView' #-}
+intervalView' :: HasBuiltins m => m (Term -> IntervalView)
+intervalView' = do
+  iz <- getBuiltinName' builtinIZero
+  io <- getBuiltinName' builtinIOne
+  imax <- getPrimitiveName' builtinIMax
+  imin <- getPrimitiveName' builtinIMin
+  ineg <- getPrimitiveName' builtinINeg
+  return $ \ t ->
+    case t of
+      Def q es ->
+        case es of
+          [Apply x,Apply y] | Just q == imin -> IMin x y
+          [Apply x,Apply y] | Just q == imax -> IMax x y
+          [Apply x]         | Just q == ineg -> INeg x
+          _                 -> OTerm t
+      Con q _ [] | Just (conName q) == iz -> IZero
+                 | Just (conName q) == io -> IOne
+      _ -> OTerm t
+
+{-# INLINE intervalView #-}
+intervalView :: HasBuiltins m => Term -> m IntervalView
+intervalView t = do
+  f <- intervalView'
+  return (f t)
+
+intervalUnview :: HasBuiltins m => IntervalView -> m Term
+intervalUnview t = do
+  f <- intervalUnview'
+  return (f t)
+
+{-# SPECIALIZE intervalUnview' :: TCM (IntervalView -> Term) #-}
+intervalUnview' :: HasBuiltins m => m (IntervalView -> Term)
+intervalUnview' = do
+  iz <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinIZero -- should it be a type error instead?
+  io <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinIOne
+  imin <- (`Def` []) . fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinIMin
+  imax <- (`Def` []) . fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinIMax
+  ineg <- (`Def` []) . fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinINeg
+  return $ \ v -> case v of
+             IZero -> iz
+             IOne  -> io
+             IMin x y -> apply imin [x,y]
+             IMax x y -> apply imax [x,y]
+             INeg x   -> apply ineg [x]
+             OTerm t -> t
+
+------------------------------------------------------------------------
+-- * Path equality
+------------------------------------------------------------------------
+
+-- | Check whether the type is actually an path (lhs ≡ rhs)
+--   and extract lhs, rhs, and their type.
+--
+--   Precondition: type is reduced.
+
+{-# INLINE pathView #-}
+pathView :: HasBuiltins m => Type -> m PathView
+pathView t0 = do
+  view <- pathView'
+  return $ view t0
+
+{-# SPECIALIZE pathView' :: TCM (Type -> PathView)  #-}
+pathView' :: HasBuiltins m => m (Type -> PathView)
+pathView' = do
+ mpath  <- getBuiltinName' builtinPath
+ mpathp <- getBuiltinName' builtinPathP
+ return $ \ t0@(El s t) ->
+  case t of
+    Def path' [ Apply level , Apply typ , Apply lhs , Apply rhs ]
+      | Just path' == mpath, Just path <- mpathp -> PathType s path level (lam_i <$> typ) lhs rhs
+      where lam_i = Lam defaultArgInfo . NoAbs "_"
+    Def path' [ Apply level , Apply typ , Apply lhs , Apply rhs ]
+      | Just path' == mpathp, Just path <- mpathp -> PathType s path level typ lhs rhs
+    _ -> OType t0
+
+{-# SPECIALIZE idViewAsPath :: Type -> TCM PathView  #-}
+-- | Non dependent Path
+idViewAsPath :: HasBuiltins m => Type -> m PathView
+idViewAsPath t0@(El s t) = do
+  mid <- fmap getPrimName <$> getBuiltin' builtinId
+  mpath <- fmap getPrimName <$> getBuiltin' builtinPath
+  case mid of
+   Just path | isJust mpath -> case t of
+    Def path' [ Apply level , Apply typ , Apply lhs , Apply rhs ]
+      | path' == path -> return $ PathType s (fromJust mpath) level typ lhs rhs
+    _ -> return $ OType t0
+   _ -> return $ OType t0
+
+boldPathView :: Type -> PathView
+boldPathView t0@(El s t) = do
+  case t of
+    Def path' [ Apply level , Apply typ , Apply lhs , Apply rhs ]
+      -> PathType s path' level typ lhs rhs
+    _ -> OType t0
+
+-- | Revert the 'PathView'.
+--
+--   Postcondition: type is reduced.
+
+pathUnview :: PathView -> Type
+pathUnview (OType t) = t
+pathUnview (PathType s path l t lhs rhs) =
+  El s $ Def path $ map Apply [l, t, lhs, rhs]
+
+------------------------------------------------------------------------
+-- * Swan's Id Equality
+------------------------------------------------------------------------
+
+{-# INLINABLE conidView' #-}
+-- f x (< phi , p > : Id A x _) = Just (phi,p)
+conidView' :: HasBuiltins m => m (Term -> Term -> Maybe (Arg Term,Arg Term))
+conidView' = do
+  mn <- sequence <$> mapM getName' [someBuiltin builtinReflId, someBuiltin builtinConId]
+  mio <- getTerm' builtinIOne
+  let fallback = return $ \ _ _ -> Nothing
+  caseMaybe mn fallback $ \ [refl,conid] ->
+   caseMaybe mio fallback $ \ io -> return $ \ x t ->
+    case t of
+      Con h _ [] | conName h == refl -> Just (defaultArg io,defaultArg (Lam defaultArgInfo $ NoAbs "_" $ x))
+      Def d es | Just [l,a,x,y,phi,p] <- allApplyElims es, d == conid -> Just (phi, p)
+      _ -> Nothing
+
+------------------------------------------------------------------------
+-- * Builtin equality
+------------------------------------------------------------------------
+
+-- | Get the name of the equality type.
+primEqualityName :: TCM QName
+-- primEqualityName = getDef =<< primEquality  -- LEADS TO IMPORT CYCLE
+primEqualityName = do
+  eq <- primEquality
+  -- Andreas, 2014-05-17 moved this here from TC.Rules.Def
+  -- Don't know why up to 2 hidden lambdas need to be stripped,
+  -- but I left the code in place.
+  -- Maybe it was intended that equality could be declared
+  -- in three different ways:
+  -- 1. universe and type polymorphic
+  -- 2. type polymorphic only
+  -- 3. monomorphic.
+  let lamV (Lam i b)  = mapFst (getHiding i :) $ lamV (unAbs b)
+      lamV v          = ([], v)
+  return $ case lamV eq of
+    (_, Def equality _) -> equality
+    _                   -> __IMPOSSIBLE__
+
+-- | Check whether the type is actually an equality (lhs ≡ rhs)
+--   and extract lhs, rhs, and their type.
+--
+--   Precondition: type is reduced.
+
+equalityView :: Type -> TCM EqualityView
+equalityView t0@(El s t) = do
+  equality <- primEqualityName
+  case t of
+    Def equality' es | equality' == equality -> do
+      let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      let n = length vs
+      unless (n >= 3) __IMPOSSIBLE__
+      let (pars, [ typ , lhs, rhs ]) = splitAt (n-3) vs
+      return $ EqualityType s equality pars typ lhs rhs
+    _ -> return $ OtherType t0
+
+-- | Revert the 'EqualityView'.
+--
+--   Postcondition: type is reduced.
+
+class EqualityUnview a where
+  equalityUnview :: a -> Type
+
+instance EqualityUnview EqualityView where
+  equalityUnview = \case
+    OtherType t -> t
+    IdiomType t -> t
+    EqualityViewType eqt -> equalityUnview eqt
+
+instance EqualityUnview EqualityTypeData where
+  equalityUnview (EqualityTypeData s equality l t lhs rhs) =
+    El s $ Def equality $ map Apply (l ++ [t, lhs, rhs])
+
+-- | Primitives with typechecking constrants.
+constrainedPrims :: [PrimitiveId]
+constrainedPrims =
+  [ builtinConId
+  , builtinPOr
+  , builtinComp
+  , builtinHComp
+  , builtinTrans
+  , builtin_glue
+  , builtin_glueU
+  ]
+
+getNameOfConstrained :: HasBuiltins m => PrimitiveId -> m (Maybe QName)
+getNameOfConstrained s = do
+  unless (s `elem` constrainedPrims) __IMPOSSIBLE__
+  getName' s
diff --git a/src/full/Agda/TypeChecking/Monad/Builtin.hs-boot b/src/full/Agda/TypeChecking/Monad/Builtin.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Builtin.hs-boot
@@ -0,0 +1,27 @@
+
+module Agda.TypeChecking.Monad.Builtin where
+
+import Control.Monad.IO.Class       ( MonadIO )
+import Control.Monad.Reader         ( ReaderT )
+import Control.Monad.State          ( StateT )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Trans          ( MonadTrans, lift )
+
+import qualified Control.Monad.Fail as Fail
+
+import Agda.TypeChecking.Monad.Base (TCMT, Builtin, PrimFun)
+import Agda.Syntax.Builtin (SomeBuiltin)
+
+class ( Functor m
+      , Applicative m
+      , Fail.MonadFail m
+      ) => HasBuiltins m where
+  getBuiltinThing :: SomeBuiltin -> m (Maybe (Builtin PrimFun))
+  default getBuiltinThing :: (MonadTrans t, HasBuiltins n, t n ~ m) => SomeBuiltin -> m (Maybe (Builtin PrimFun))
+  getBuiltinThing = lift . getBuiltinThing
+
+instance HasBuiltins m => HasBuiltins (IdentityT m)
+instance HasBuiltins m => HasBuiltins (ReaderT e m)
+instance HasBuiltins m => HasBuiltins (StateT s m)
+
+instance MonadIO m => HasBuiltins (TCMT m)
diff --git a/src/full/Agda/TypeChecking/Monad/Caching.hs b/src/full/Agda/TypeChecking/Monad/Caching.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Caching.hs
@@ -0,0 +1,156 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Caching
+  ( -- * Log reading/writing operations
+    writeToCurrentLog
+  , readFromCachedLog
+  , cleanCachedLog
+  , cacheCurrentLog
+
+    -- * Activating/deactivating
+  , activateLoadedFileCache
+  , cachingStarts
+  , areWeCaching
+  , localCache, withoutCache
+
+    -- * Restoring the 'PostScopeState'
+  , restorePostScopeState
+  ) where
+
+import Agda.Syntax.Common
+
+import Agda.Interaction.Options
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+import Agda.Utils.Null (empty)
+
+import Agda.Utils.Impossible
+
+-- | To be called before any write or restore calls.
+{-# SPECIALIZE cachingStarts :: TCM () #-}
+cachingStarts :: (MonadDebug m, MonadTCState m, ReadTCState m) => m ()
+cachingStarts = do
+    NameId _ m <- useTC stFreshNameId
+    stFreshNameId `setTCLens` NameId 1 m
+    stFreshOpaqueId `setTCLens` OpaqueId 1 m
+    stAreWeCaching `setTCLens` True
+    validateCache m -- fixes issue #4835
+    where
+      validateCache m = (localCache readFromCachedLog) >>= \case
+        Just (_ , s) -> do
+          let
+            NameId _ m' = stPostFreshNameId s
+            OpaqueId _ m'' = stPostFreshOpaqueId s
+            stale = or [ m' /= m, m'' /= m ]
+          when stale cleanCachedLog
+        _ -> return ()
+
+areWeCaching :: (ReadTCState m) => m Bool
+areWeCaching = useR stAreWeCaching
+
+-- | Writes a 'TypeCheckAction' to the current log, using the current
+-- 'PostScopeState'
+{-# SPECIALIZE writeToCurrentLog :: TypeCheckAction -> TCM () #-}
+writeToCurrentLog :: (MonadDebug m, MonadTCState m, ReadTCState m) => TypeCheckAction -> m ()
+writeToCurrentLog !d = do
+  reportSLn "cache" 10 $ "cachePostScopeState"
+  !l <- getsTC stPostScopeState
+  modifyCache $ fmap $ \lfc -> lfc{ lfcCurrent = (d, l) : lfcCurrent lfc}
+
+{-# SPECIALIZE restorePostScopeState :: PostScopeState -> TCM () #-}
+restorePostScopeState :: (MonadDebug m, MonadTCState m) => PostScopeState -> m ()
+restorePostScopeState pss = do
+  reportSLn "cache" 10 $ "restorePostScopeState"
+  modifyTC $ \s ->
+    let ipoints = s ^. stInteractionPoints
+        ws = s ^. stTCWarnings
+        pss' = pss{stPostInteractionPoints = stPostInteractionPoints pss `mergeIPMap` ipoints
+                  ,stPostTCWarnings = stPostTCWarnings pss `mergeWarnings` ws
+                  ,stPostOpaqueBlocks = s ^. stOpaqueBlocks
+                  ,stPostOpaqueIds = s ^. stOpaqueIds
+                  }
+    in  s{stPostScopeState = pss'}
+  where
+    mergeIPMap lm sm = BiMap.mapWithKey (\k v -> maybe v (`mergeIP` v) (BiMap.lookup k lm)) sm
+    -- see #1338 on why we need to use the new ranges.
+    mergeIP li si = li { ipRange = ipRange si }
+
+    mergeWarnings loading current = [ w | w <- current, not $ tcWarningCached w ]
+                                 ++ [ w | w <- loading,       tcWarningCached w ]
+
+{-# SPECIALIZE modifyCache :: (Maybe LoadedFileCache -> Maybe LoadedFileCache) -> TCM () #-}
+modifyCache
+  :: MonadTCState m
+  => (Maybe LoadedFileCache -> Maybe LoadedFileCache)
+  -> m ()
+modifyCache = modifyTCLens stLoadedFileCache
+
+{-# SPECIALIZE getCache :: TCM (Maybe LoadedFileCache) #-}
+getCache :: ReadTCState m => m (Maybe LoadedFileCache)
+getCache = useTC stLoadedFileCache
+
+{-# SPECIALIZE putCache :: Maybe LoadedFileCache -> TCM () #-}
+putCache :: MonadTCState m => Maybe LoadedFileCache -> m ()
+putCache = setTCLens stLoadedFileCache
+
+-- | Runs the action and restores the current cache at the end of it.
+{-# SPECIALIZE localCache :: TCM a -> TCM a #-}
+localCache :: (MonadTCState m, ReadTCState m) => m a -> m a
+localCache = bracket_ getCache putCache
+
+-- | Runs the action without cache and restores the current cache at
+-- the end of it.
+{-# SPECIALIZE withoutCache :: TCM a -> TCM a #-}
+withoutCache :: (MonadTCState m, ReadTCState m) => m a -> m a
+withoutCache m = localCache $ do
+    putCache empty
+    m
+
+-- | Reads the next entry in the cached type check log, if present.
+{-# SPECIALIZE readFromCachedLog :: TCM (Maybe (TypeCheckAction, PostScopeState)) #-}
+readFromCachedLog :: (MonadDebug m, MonadTCState m, ReadTCState m) => m (Maybe (TypeCheckAction, PostScopeState))
+readFromCachedLog = do
+  reportSLn "cache" 10 $ "getCachedTypeCheckAction"
+  getCache >>= \case
+    Just lfc | (entry : entries) <- lfcCached lfc -> do
+      putCache $ Just lfc{lfcCached = entries}
+      return (Just entry)
+    _ -> do
+      return Nothing
+
+-- | Empties the "to read" CachedState. To be used when it gets invalid.
+{-# SPECIALIZE cleanCachedLog :: TCM () #-}
+cleanCachedLog :: (MonadDebug m, MonadTCState m) => m ()
+cleanCachedLog = do
+  reportSLn "cache" 10 $ "cleanCachedLog"
+  modifyCache $ fmap $ \lfc -> lfc{lfcCached = []}
+
+-- | Makes sure that the 'stLoadedFileCache' is 'Just', with a clean
+-- current log. Crashes is 'stLoadedFileCache' is already active with a
+-- dirty log.  Should be called when we start typechecking the current
+-- file.
+{-# SPECIALIZE activateLoadedFileCache :: TCM () #-}
+activateLoadedFileCache :: (HasOptions m, MonadDebug m, MonadTCState m) => m ()
+activateLoadedFileCache = do
+  reportSLn "cache" 10 $ "activateLoadedFileCache"
+
+  whenM (optGHCiInteraction <$> commandLineOptions) $
+    whenM enableCaching $ do
+      modifyCache $ \case
+         Nothing                          -> Just $ LoadedFileCache [] []
+         Just lfc | null (lfcCurrent lfc) -> Just lfc
+         _                                -> __IMPOSSIBLE__
+
+-- | Caches the current type check log.  Discardes the old cache.  Does
+-- nothing if caching is inactive.
+{-# SPECIALIZE cacheCurrentLog :: TCM () #-}
+cacheCurrentLog :: (MonadDebug m, MonadTCState m) => m ()
+cacheCurrentLog = do
+  reportSLn "cache" 10 $ "cacheCurrentTypeCheckLog"
+  modifyCache $ fmap $ \lfc ->
+    lfc{lfcCached = reverse (lfcCurrent lfc), lfcCurrent = []}
diff --git a/src/full/Agda/TypeChecking/Monad/Closure.hs b/src/full/Agda/TypeChecking/Monad/Closure.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Closure.hs
@@ -0,0 +1,29 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Closure where
+
+import Control.Monad
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Env
+import Agda.TypeChecking.Monad.State
+
+import Agda.Utils.Lens
+
+{-# INLINE enterClosure #-}
+enterClosure :: (MonadTCEnv m, ReadTCState m, LensClosure c a)
+             => c -> (a -> m b) -> m b
+enterClosure c k | Closure _sig env scope cps x <- c ^. lensClosure = do
+  isDbg <- viewTC eIsDebugPrinting
+  withScope_ scope
+    $ locallyTCState stModuleCheckpoints (const cps)
+    $ withEnv env{ envIsDebugPrinting = isDbg }
+    $ k x
+
+{-# INLINE withClosure  #-}
+withClosure :: (MonadTCEnv m, ReadTCState m) => Closure a -> (a -> m b) -> m (Closure b)
+withClosure cl k = enterClosure cl $ k >=> buildClosure
+
+{-# INLINE mapClosure  #-}
+mapClosure :: (MonadTCEnv m, ReadTCState m) => (a -> m b) -> Closure a -> m (Closure b)
+mapClosure = flip withClosure
diff --git a/src/full/Agda/TypeChecking/Monad/Constraints.hs b/src/full/Agda/TypeChecking/Monad/Constraints.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Constraints.hs
@@ -0,0 +1,247 @@
+
+module Agda.TypeChecking.Monad.Constraints where
+
+import Control.Arrow ((&&&))
+import Control.Monad.Except
+import Control.Monad.Reader
+
+import qualified Data.Foldable as Fold
+import qualified Data.List as List
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Semigroup ((<>))
+
+import Agda.Interaction.Options.Base
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Closure
+import Agda.TypeChecking.Monad.Debug
+
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+
+solvingProblem :: MonadConstraint m => ProblemId -> m a -> m a
+solvingProblem pid = solvingProblems (Set.singleton pid)
+
+solvingProblems :: MonadConstraint m => Set ProblemId -> m a -> m a
+solvingProblems pids m = verboseBracket "tc.constr.solve" 50 ("working on problems " ++ show (Set.toList pids)) $ do
+  x <- localTC (\e -> e { envActiveProblems = pids `Set.union` envActiveProblems e }) m
+  Fold.forM_ pids $ \ pid -> do
+    ifNotM (isProblemSolved pid)
+        (reportSLn "tc.constr.solve" 50 $ "problem " ++ show pid ++ " was not solved.")
+      $ {- else -} do
+        reportSLn "tc.constr.solve" 50 $ "problem " ++ show pid ++ " was solved!"
+        wakeConstraints (wakeIfBlockedOnProblem pid . constraintUnblocker)
+  return x
+
+isProblemSolved :: (MonadTCEnv m, ReadTCState m) => ProblemId -> m Bool
+isProblemSolved pid =
+  and2M (not . Set.member pid <$> asksTC envActiveProblems)
+        (not . any (Set.member pid . constraintProblems) <$> getAllConstraints)
+
+{-# SPECIALIZE getConstraintsForProblem :: ProblemId -> TCM Constraints #-}
+getConstraintsForProblem :: ReadTCState m => ProblemId -> m Constraints
+getConstraintsForProblem pid = List.filter (Set.member pid . constraintProblems) <$> getAllConstraints
+
+-- | Get the awake constraints
+getAwakeConstraints :: ReadTCState m => m Constraints
+getAwakeConstraints = useR stAwakeConstraints
+
+-- danger...
+dropConstraints :: MonadConstraint m => (ProblemConstraint -> Bool) -> m ()
+dropConstraints crit = do
+  let filt = List.filter $ not . crit
+  modifySleepingConstraints filt
+  modifyAwakeConstraints    filt
+
+-- | Takes out all constraints matching given filter.
+--   Danger!  The taken constraints need to be solved or put back at some point.
+takeConstraints :: MonadConstraint m => (ProblemConstraint -> Bool) -> m Constraints
+takeConstraints f = do
+  (takeAwake , keepAwake ) <- List.partition f <$> useTC stAwakeConstraints
+  (takeAsleep, keepAsleep) <- List.partition f <$> useTC stSleepingConstraints
+  modifyAwakeConstraints    $ const keepAwake
+  modifySleepingConstraints $ const keepAsleep
+  return $ takeAwake ++ takeAsleep
+
+putConstraintsToSleep :: MonadConstraint m => (ProblemConstraint -> Bool) -> m ()
+putConstraintsToSleep sleepy = do
+  awakeOnes <- useR stAwakeConstraints
+  let (gotoSleep, stayAwake) = List.partition sleepy awakeOnes
+  modifySleepingConstraints $ (++ gotoSleep)
+  modifyAwakeConstraints    $ const stayAwake
+
+putAllConstraintsToSleep :: MonadConstraint m => m ()
+putAllConstraintsToSleep = putConstraintsToSleep (const True)
+
+data ConstraintStatus = AwakeConstraint | SleepingConstraint
+  deriving (Eq, Show)
+
+-- | Suspend constraints matching the predicate during the execution of the
+--   second argument. Caution: held sleeping constraints will not be woken up
+--   by events that would normally trigger a wakeup call.
+holdConstraints :: (ConstraintStatus -> ProblemConstraint -> Bool) -> TCM a -> TCM a
+holdConstraints p m = do
+  (holdAwake, stillAwake)   <- List.partition (p AwakeConstraint)    <$> useTC stAwakeConstraints
+  (holdAsleep, stillAsleep) <- List.partition (p SleepingConstraint) <$> useTC stSleepingConstraints
+  stAwakeConstraints    `setTCLens` stillAwake
+  stSleepingConstraints `setTCLens` stillAsleep
+  let restore = do
+        stAwakeConstraints    `modifyTCLens` (holdAwake ++)
+        stSleepingConstraints `modifyTCLens` (holdAsleep ++)
+  catchError (m <* restore) (\ err -> restore *> throwError err)
+
+takeAwakeConstraint :: MonadConstraint m => m (Maybe ProblemConstraint)
+takeAwakeConstraint = takeAwakeConstraint' (const True)
+
+takeAwakeConstraint'
+  :: MonadConstraint m
+  => (ProblemConstraint -> Bool) -> m (Maybe ProblemConstraint)
+takeAwakeConstraint' p = do
+  cs <- getAwakeConstraints
+  case break p cs of
+    (_, [])       -> return Nothing
+    (cs0, c : cs) -> do
+      modifyAwakeConstraints $ const (cs0 ++ cs)
+      return $ Just c
+
+getAllConstraints :: ReadTCState m => m Constraints
+getAllConstraints = do
+  s <- getTCState
+  return $ s ^. stAwakeConstraints ++ s ^. stSleepingConstraints
+
+withConstraint :: MonadConstraint m => (Constraint -> m a) -> ProblemConstraint -> m a
+withConstraint f (PConstr pids _ c) = do
+  -- We should preserve the problem stack and the isSolvingConstraint flag
+  (pids', isSolving) <- asksTC $ envActiveProblems &&& envSolvingConstraints
+  enterClosure c $ \c ->
+    localTC (\e -> e { envActiveProblems = pids', envSolvingConstraints = isSolving }) $
+    solvingProblems pids (f c)
+
+buildProblemConstraint
+  :: (MonadTCEnv m, ReadTCState m)
+  => Set ProblemId -> Blocker -> Constraint -> m ProblemConstraint
+buildProblemConstraint pids unblock c = PConstr pids unblock <$> buildClosure c
+
+buildProblemConstraint_
+  :: (MonadTCEnv m, ReadTCState m)
+  => Blocker -> Constraint -> m ProblemConstraint
+buildProblemConstraint_ = buildProblemConstraint Set.empty
+
+buildConstraint :: Blocker -> Constraint -> TCM ProblemConstraint
+buildConstraint unblock c = do
+  pids <- asksTC envActiveProblems
+  buildProblemConstraint pids unblock c
+
+-- | Monad service class containing methods for adding and solving
+--   constraints
+class ( MonadTCEnv m
+      , ReadTCState m
+      , MonadError TCErr m
+      , MonadBlock m
+      , HasOptions m
+      , MonadDebug m
+      ) => MonadConstraint m where
+  -- | Unconditionally add the constraint.
+  addConstraint :: Blocker -> Constraint -> m ()
+
+  -- | Add constraint as awake constraint.
+  addAwakeConstraint :: Blocker -> Constraint -> m ()
+
+  solveConstraint :: Constraint -> m ()
+
+  -- | Solve awake constraints matching the predicate. If the second argument is
+  --   True solve constraints even if already 'isSolvingConstraints'.
+  solveSomeAwakeConstraints :: (ProblemConstraint -> Bool) -> Bool -> m ()
+
+  wakeConstraints :: (ProblemConstraint-> WakeUp) -> m ()
+
+  stealConstraints :: ProblemId -> m ()
+
+  modifyAwakeConstraints :: (Constraints -> Constraints) -> m ()
+
+  modifySleepingConstraints  :: (Constraints -> Constraints) -> m ()
+
+instance MonadConstraint m => MonadConstraint (ReaderT e m) where
+  addConstraint             = (lift .) . addConstraint
+  addAwakeConstraint        = (lift .) . addAwakeConstraint
+  solveConstraint           = lift . solveConstraint
+  solveSomeAwakeConstraints = (lift .) . solveSomeAwakeConstraints
+  stealConstraints          = lift . stealConstraints
+  modifyAwakeConstraints    = lift . modifyAwakeConstraints
+  modifySleepingConstraints = lift . modifySleepingConstraints
+  wakeConstraints = lift . wakeConstraints
+
+-- | Add new a constraint
+addConstraint' :: Blocker -> Constraint -> TCM ()
+addConstraint' = addConstraintTo stSleepingConstraints
+
+addAwakeConstraint' :: Blocker -> Constraint -> TCM ()
+addAwakeConstraint' = addConstraintTo stAwakeConstraints
+
+addConstraintTo :: Lens' TCState Constraints -> Blocker -> Constraint -> TCM ()
+addConstraintTo bucket unblock c = do
+    pc <- build
+    stDirty `setTCLens` True
+    bucket `modifyTCLens` (pc :)
+  where
+    build | isBlocking c = buildConstraint unblock c
+          | otherwise    = buildProblemConstraint_ unblock c
+    isBlocking = \case
+      SortCmp{}        -> False
+      LevelCmp{}       -> False
+      FindInstance{}   -> False
+      HasBiggerSort{}  -> False
+      HasPTSRule{}     -> False
+      CheckDataSort{}  -> False
+      ValueCmp{}       -> True
+      ValueCmpOnFace{} -> True
+      ElimCmp{}        -> True
+      UnBlock{}        -> True
+      IsEmpty{}        -> True
+      CheckSizeLtSat{} -> True
+      CheckFunDef{}    -> True
+      UnquoteTactic{}  -> True
+      CheckMetaInst{}  -> True
+      CheckType{}      -> True
+      CheckLockedVars{} -> True
+      UsableAtModality{} -> True
+
+-- | Start solving constraints
+nowSolvingConstraints :: MonadTCEnv m => m a -> m a
+nowSolvingConstraints = localTC $ \e -> e { envSolvingConstraints = True }
+
+isSolvingConstraints :: MonadTCEnv m => m Bool
+isSolvingConstraints = asksTC envSolvingConstraints
+
+-- | Add constraint if the action raises a pattern violation
+catchConstraint :: MonadConstraint m => Constraint -> m () -> m ()
+catchConstraint c = catchPatternErr $ \ unblock -> addConstraint unblock c
+
+isInstanceConstraint :: Constraint -> Bool
+isInstanceConstraint FindInstance{} = True
+isInstanceConstraint _              = False
+
+shouldPostponeInstanceSearch :: (ReadTCState m, HasOptions m) => m Bool
+shouldPostponeInstanceSearch =
+  and2M ((^. stConsideringInstance) <$> getTCState)
+        (not . optOverlappingInstances <$> pragmaOptions)
+  `or2M` ((^. stPostponeInstanceSearch) <$> getTCState)
+
+-- | Wake constraints matching the given predicate (and aren't instance
+--   constraints if 'shouldPostponeInstanceSearch').
+wakeConstraints' :: MonadConstraint m => (ProblemConstraint -> WakeUp) -> m ()
+wakeConstraints' p = do
+  skipInstance <- shouldPostponeInstanceSearch
+  let skip c = skipInstance && isInstanceConstraint (clValue $ theConstraint c)
+  wakeConstraints $ wakeUpWhen (not . skip) p
+
+---------------------------------------------------------------------------
+-- * Lenses
+---------------------------------------------------------------------------
+
+mapAwakeConstraints :: (Constraints -> Constraints) -> TCState -> TCState
+mapAwakeConstraints = over stAwakeConstraints
+
+mapSleepingConstraints :: (Constraints -> Constraints) -> TCState -> TCState
+mapSleepingConstraints = over stSleepingConstraints
diff --git a/src/full/Agda/TypeChecking/Monad/Context.hs b/src/full/Agda/TypeChecking/Monad/Context.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Context.hs
@@ -0,0 +1,537 @@
+
+module Agda.TypeChecking.Monad.Context where
+
+import Data.Text (Text)
+import qualified Data.Text as T
+
+import Control.Monad                ( (<=<), forM, when )
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Control  ( MonadTransControl(..), liftThrough )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Trans.Maybe
+import Control.Monad.Writer         ( WriterT )
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import qualified Data.DList as DL
+import Data.Foldable
+import qualified Data.List as List
+import qualified Data.Map as Map
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Concrete.Name (NameInScope(..), LensInScope(..), nameRoot, nameToRawName)
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Monad.Open
+import Agda.TypeChecking.Monad.State
+
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List ((!!!), downFrom)
+import Agda.Utils.ListT
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+-- * Modifying the context
+
+-- | Modify a 'Context' in a computation.  Warning: does not update
+--   the checkpoints. Use @updateContext@ instead.
+{-# INLINE unsafeModifyContext #-}
+unsafeModifyContext :: MonadTCEnv tcm => (Context -> Context) -> tcm a -> tcm a
+unsafeModifyContext f = localTC $ \e -> e { envContext = f $ envContext e }
+
+{-# INLINE modifyContextInfo #-}
+-- | Modify the 'Dom' part of context entries.
+modifyContextInfo :: MonadTCEnv tcm => (forall e. Dom e -> Dom e) -> tcm a -> tcm a
+modifyContextInfo f = unsafeModifyContext $ map f
+
+-- | Change to top (=empty) context. Resets the checkpoints.
+{-# SPECIALIZE inTopContext :: TCM a -> TCM a #-}
+inTopContext :: (MonadTCEnv tcm, ReadTCState tcm) => tcm a -> tcm a
+inTopContext cont =
+  unsafeModifyContext (const [])
+        $ locallyTC eCurrentCheckpoint (const 0)
+        $ locallyTC eCheckpoints (const $ Map.singleton 0 IdS)
+        $ locallyTCState stModuleCheckpoints (const Map.empty)
+        $ locallyScope scopeLocals (const [])
+        $ locallyTC eLetBindings (const Map.empty)
+        $ cont
+
+-- | Change to top (=empty) context, but don't update the checkpoints. Totally
+--   not safe!
+{-# SPECIALIZE unsafeInTopContext :: TCM a -> TCM a #-}
+unsafeInTopContext :: (MonadTCEnv m, ReadTCState m) => m a -> m a
+unsafeInTopContext cont =
+  locallyScope scopeLocals (const []) $
+    unsafeModifyContext (const []) cont
+
+-- | Delete the last @n@ bindings from the context.
+--
+--   Doesn't update checkpoints! Use `escapeContext` or `updateContext
+--   rho (drop n)` instead, for an appropriate substitution `rho`.
+{-# SPECIALIZE unsafeEscapeContext :: Int -> TCM a -> TCM a #-}
+unsafeEscapeContext :: MonadTCM tcm => Int -> tcm a -> tcm a
+unsafeEscapeContext n = unsafeModifyContext $ drop n
+
+{-# SPECIALIZE escapeContext :: Impossible -> Int -> TCM a -> TCM a #-}
+-- | Delete the last @n@ bindings from the context. Any occurrences of
+-- these variables are replaced with the given @err@.
+escapeContext :: MonadAddContext m => Impossible -> Int -> m a -> m a
+escapeContext err n = updateContext (strengthenS err n) $ drop n
+
+-- * Manipulating checkpoints --
+
+{-# SPECIALIZE checkpoint :: Substitution -> TCM a -> TCM a #-}
+-- | Add a new checkpoint. Do not use directly!
+checkpoint
+  :: (MonadDebug tcm, MonadTCM tcm, MonadFresh CheckpointId tcm, ReadTCState tcm)
+  => Substitution -> tcm a -> tcm a
+checkpoint sub k = do
+  unlessDebugPrinting $ reportSLn "tc.cxt.checkpoint" 105 $ "New checkpoint {"
+  old     <- viewTC eCurrentCheckpoint
+  oldMods <- useTC  stModuleCheckpoints
+  chkpt <- fresh
+  unlessDebugPrinting $ verboseS "tc.cxt.checkpoint" 105 $ do
+    cxt <- getContextTelescope
+    cps <- viewTC eCheckpoints
+    let cps' = Map.insert chkpt IdS $ fmap (applySubst sub) cps
+        prCps cps = vcat [ pshow c <+> ": " <+> pretty s | (c, s) <- Map.toList cps ]
+    reportSDoc "tc.cxt.checkpoint" 105 $ return $ nest 2 $ vcat
+      [ "old =" <+> pshow old
+      , "new =" <+> pshow chkpt
+      , "sub =" <+> pretty sub
+      , "cxt =" <+> pretty cxt
+      , "old substs =" <+> prCps cps
+      , "new substs =" <?> prCps cps'
+      ]
+  x <- flip localTC k $ \ env -> env
+    { envCurrentCheckpoint = chkpt
+    , envCheckpoints       = Map.insert chkpt IdS $
+                              fmap (applySubst sub) (envCheckpoints env)
+    }
+  newMods <- useTC stModuleCheckpoints
+  -- Set the checkpoint for introduced modules to the old checkpoint when the
+  -- new one goes out of scope. #2897: This isn't actually sound for modules
+  -- created under refined parent parameters, but as long as those modules
+  -- aren't named we shouldn't look at the checkpoint. The right thing to do
+  -- would be to not store these modules in the checkpoint map, but todo..
+  stModuleCheckpoints `setTCLens` Map.union oldMods (old <$ newMods)
+  unlessDebugPrinting $ reportSLn "tc.cxt.checkpoint" 105 "}"
+  return x
+
+-- | Get the substitution from the context at a given checkpoint to the current context.
+checkpointSubstitution :: MonadTCEnv tcm => CheckpointId -> tcm Substitution
+checkpointSubstitution = maybe __IMPOSSIBLE__ return <=< checkpointSubstitution'
+
+-- | Get the substitution from the context at a given checkpoint to the current context.
+checkpointSubstitution' :: MonadTCEnv tcm => CheckpointId -> tcm (Maybe Substitution)
+checkpointSubstitution' chkpt = viewTC (eCheckpoints . key chkpt)
+
+-- | Get substitution @Γ ⊢ ρ : Γm@ where @Γ@ is the current context
+--   and @Γm@ is the module parameter telescope of module @m@.
+--
+--   Returns @Nothing@ in case the we don't have a checkpoint for @m@.
+getModuleParameterSub :: (MonadTCEnv m, ReadTCState m) => ModuleName -> m (Maybe Substitution)
+getModuleParameterSub m = do
+  mcp <- (^. stModuleCheckpoints . key m) <$> getTCState
+  traverse checkpointSubstitution mcp
+
+
+-- * Adding to the context
+
+class MonadTCEnv m => MonadAddContext m where
+  -- | @addCtx x arg cont@ add a variable to the context.
+  --
+  --   Chooses an unused 'Name'.
+  --
+  --   Warning: Does not update module parameter substitution!
+  addCtx :: Name -> Dom Type -> m a -> m a
+
+  -- | Add a let bound variable to the context
+  addLetBinding' :: Origin -> Name -> Term -> Dom Type -> m a -> m a
+
+  -- | Update the context.
+  --   Requires a substitution that transports things living in the old context
+  --   to the new.
+  updateContext :: Substitution -> (Context -> Context) -> m a -> m a
+
+  withFreshName :: Range -> ArgName -> (Name -> m a) -> m a
+
+  default addCtx
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Name -> Dom Type -> m a -> m a
+  addCtx x a = liftThrough $ addCtx x a
+
+  default addLetBinding'
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Origin -> Name -> Term -> Dom Type -> m a -> m a
+  addLetBinding' o x u a = liftThrough $ addLetBinding' o x u a
+
+  default updateContext
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Substitution -> (Context -> Context) -> m a -> m a
+  updateContext sub f = liftThrough $ updateContext sub f
+
+  default withFreshName
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Range -> ArgName -> (Name -> m a) -> m a
+  withFreshName r x cont = do
+    st <- liftWith $ \ run -> do
+      withFreshName r x $ run . cont
+    restoreT $ return st
+
+{-# INLINE defaultAddCtx #-}
+-- | Default implementation of addCtx in terms of updateContext
+defaultAddCtx :: MonadAddContext m => Name -> Dom Type -> m a -> m a
+defaultAddCtx x a ret =
+  updateContext (raiseS 1) (((x,) <$> a) :) ret
+
+withFreshName_ :: (MonadAddContext m) => ArgName -> (Name -> m a) -> m a
+withFreshName_ = withFreshName noRange
+
+instance MonadAddContext m => MonadAddContext (ChangeT m)
+instance MonadAddContext m => MonadAddContext (ExceptT e m)
+instance MonadAddContext m => MonadAddContext (IdentityT m)
+instance MonadAddContext m => MonadAddContext (MaybeT m)
+instance MonadAddContext m => MonadAddContext (ReaderT r m)
+instance MonadAddContext m => MonadAddContext (StateT r m)
+instance (Monoid w, MonadAddContext m) => MonadAddContext (WriterT w m)
+deriving instance MonadAddContext m => MonadAddContext (BlockT m)
+
+instance MonadAddContext m => MonadAddContext (ListT m) where
+  addCtx x a             = liftListT $ addCtx x a
+  addLetBinding' o x u a = liftListT $ addLetBinding' o x u a
+  updateContext sub f    = liftListT $ updateContext sub f
+  withFreshName r x cont = ListT $ withFreshName r x $ runListT . cont
+
+-- | Run the given TCM action, and register the given variable as
+--   being shadowed by all the names with the same root that are added
+--   to the context during this TCM action.
+withShadowingNameTCM :: Name -> TCM b -> TCM b
+withShadowingNameTCM x f = do
+  reportSDoc "tc.cxt.shadowing" 80 $ pure $ "registered" <+> pretty x <+> "for shadowing"
+  when (isInScope x == InScope) $ tellUsedName x
+  (result , useds) <- listenUsedNames f
+  reportSDoc "tc.cxt.shadowing" 90 $ pure $ "all used names: " <+> text (show useds)
+  tellShadowing x useds
+  return result
+
+    where
+      listenUsedNames f = do
+        origUsedNames <- useTC stUsedNames
+        setTCLens stUsedNames Map.empty
+        result <- f
+        newUsedNames <- useTC stUsedNames
+        setTCLens stUsedNames $ Map.unionWith (<>) origUsedNames newUsedNames
+        return (result , newUsedNames)
+
+      tellUsedName x = do
+        let concreteX = nameConcrete x
+            rawX      = nameToRawName concreteX
+            rootX     = nameRoot concreteX
+        modifyTCLens (stUsedNames . key rootX) $
+          Just . (rawX `DL.cons`) . fold
+
+      tellShadowing x useds = case Map.lookup (nameRoot $ nameConcrete x) useds of
+        Just shadows -> do
+          reportSDoc "tc.cxt.shadowing" 80 $ pure $
+            "names shadowing" <+> pretty x <+> ": " <+>
+            prettyList_ (map pretty $ toList shadows)
+          modifyTCLens stShadowingNames $ Map.insertWith (<>) x shadows
+        Nothing      -> return ()
+
+instance MonadAddContext TCM where
+  addCtx x a ret = applyUnless (isNoName x) (withShadowingNameTCM x) $
+    defaultAddCtx x a ret
+
+  addLetBinding' o x u a ret = applyUnless (isNoName x) (withShadowingNameTCM x) $
+    defaultAddLetBinding' o x u a ret
+
+  updateContext sub f = unsafeModifyContext f . checkpoint sub
+
+  withFreshName r x m = freshName r x >>= m
+
+addRecordNameContext
+  :: (MonadAddContext m, MonadFresh NameId m)
+  => Dom Type -> m b -> m b
+addRecordNameContext dom ret = do
+  x <- setNotInScope <$> freshRecordName
+  addCtx x dom ret
+
+-- | Various specializations of @addCtx@.
+class AddContext b where
+  addContext :: (MonadAddContext m) => b -> m a -> m a
+  contextSize :: b -> Nat
+
+-- | Wrapper to tell 'addContext' not to mark names as
+--   'NotInScope'. Used when adding a user-provided, but already type
+--   checked, telescope to the context.
+newtype KeepNames a = KeepNames a
+
+instance {-# OVERLAPPABLE #-} AddContext a => AddContext [a] where
+  addContext = flip (foldr addContext); {-# INLINABLE addContext #-}
+  contextSize = sum . map contextSize
+
+instance AddContext (Name, Dom Type) where
+  addContext = uncurry addCtx; {-# INLINE addContext #-}
+  contextSize _ = 1
+{-# SPECIALIZE addContext :: (Name, Dom Type) -> TCM a -> TCM a #-}
+
+instance AddContext (Dom (Name, Type)) where
+  addContext = addContext . distributeF
+  contextSize _ = 1
+
+instance AddContext (Dom (String, Type)) where
+  addContext = addContext . distributeF
+  contextSize _ = 1
+
+instance AddContext ([Name], Dom Type) where
+  addContext (xs, dom) = addContext (bindsToTel' id xs dom)
+  contextSize (xs, _) = length xs
+
+instance AddContext (List1 Name, Dom Type) where
+  addContext (xs, dom) = addContext (bindsToTel'1 id xs dom)
+  contextSize (xs, _) = length xs
+
+instance AddContext ([WithHiding Name], Dom Type) where
+  addContext ([]    , dom) = id
+  addContext (x : xs, dom) = addContext (x :| xs, dom)
+  contextSize (xs, _) = length xs
+
+instance AddContext (List1 (WithHiding Name), Dom Type) where
+  addContext (WithHiding h x :| xs, dom) =
+    addContext (x , mapHiding (mappend h) dom) .
+    addContext (xs, raise 1 dom)
+  contextSize (xs, _) = length xs
+
+instance AddContext ([Arg Name], Type) where
+  addContext (xs, t) = addContext ((map . fmap) unnamed xs :: [NamedArg Name], t)
+  contextSize (xs, _) = length xs
+
+instance AddContext (List1 (Arg Name), Type) where
+  addContext (xs, t) = addContext ((fmap . fmap) unnamed xs :: List1 (NamedArg Name), t)
+  contextSize (xs, _) = length xs
+
+instance AddContext ([NamedArg Name], Type) where
+  addContext ([], _)     = id
+  addContext (x : xs, t) = addContext (x :| xs, t)
+  contextSize (xs, _) = length xs
+
+instance AddContext (List1 (NamedArg Name), Type) where
+  addContext (x :| xs, t) =
+    addContext (namedArg x, t <$ domFromNamedArgName x) .
+    addContext (xs, raise 1 t)
+  contextSize (xs, _) = length xs
+
+instance AddContext (String, Dom Type) where
+  addContext (s, dom) ret =
+    withFreshName noRange s $ \x -> addCtx (setNotInScope x) dom ret
+  contextSize _ = 1
+{-# SPECIALIZE addContext :: (String, Dom Type) -> TCM a -> TCM a #-}
+
+instance AddContext (Text, Dom Type) where
+  addContext (s, dom) ret = addContext (T.unpack s, dom) ret
+  contextSize _ = 1
+{-# SPECIALIZE addContext :: (Text, Dom Type) -> TCM a -> TCM a #-}
+
+instance AddContext (KeepNames String, Dom Type) where
+  addContext (KeepNames s, dom) ret =
+    withFreshName noRange s $ \ x -> addCtx x dom ret
+  contextSize _ = 1
+{-# SPECIALIZE addContext :: (KeepNames String, Dom Type) -> TCM a -> TCM a #-}
+
+instance AddContext (Dom Type) where
+  addContext dom = addContext ("_" :: String, dom)
+  contextSize _ = 1
+
+instance AddContext Name where
+  addContext x = addContext (x, __DUMMY_DOM__)
+  contextSize _ = 1
+
+instance {-# OVERLAPPING #-} AddContext String where
+  addContext s = addContext (s, __DUMMY_DOM__)
+  contextSize _ = 1
+
+instance AddContext (KeepNames Telescope) where
+  addContext (KeepNames tel) ret = loop tel where
+    loop EmptyTel          = ret
+    loop (ExtendTel t tel) = underAbstraction' KeepNames t tel loop
+  contextSize (KeepNames tel) = size tel
+{-# SPECIALIZE addContext :: KeepNames Telescope -> TCM a -> TCM a #-}
+
+instance AddContext Telescope where
+  addContext tel ret = loop tel where
+    loop EmptyTel          = ret
+    loop (ExtendTel t tel) = underAbstraction' id t tel loop
+  contextSize = size
+{-# SPECIALIZE addContext :: Telescope -> TCM a -> TCM a #-}
+
+-- | Go under an abstraction.  Do not extend context in case of 'NoAbs'.
+{-# SPECIALIZE underAbstraction :: Subst a => Dom Type -> Abs a -> (a -> TCM b) -> TCM b #-}
+underAbstraction :: (Subst a, MonadAddContext m) => Dom Type -> Abs a -> (a -> m b) -> m b
+underAbstraction = underAbstraction' id
+
+underAbstraction' :: (Subst a, MonadAddContext m, AddContext (name, Dom Type)) =>
+                     (String -> name) -> Dom Type -> Abs a -> (a -> m b) -> m b
+underAbstraction' _ _ (NoAbs _ v) k = k v
+underAbstraction' wrap t a k = underAbstractionAbs' wrap t a k
+
+-- | Go under an abstraction, treating 'NoAbs' as 'Abs'.
+underAbstractionAbs :: (Subst a, MonadAddContext m) => Dom Type -> Abs a -> (a -> m b) -> m b
+underAbstractionAbs = underAbstractionAbs' id
+
+underAbstractionAbs'
+  :: (Subst a, MonadAddContext m, AddContext (name, Dom Type))
+  => (String -> name) -> Dom Type -> Abs a -> (a -> m b) -> m b
+underAbstractionAbs' wrap t a k = addContext (wrap $ realName $ absName a, t) $ k $ absBody a
+  where
+    realName s = if isNoName s then "x" else argNameToString s
+
+-- | Go under an abstract without worrying about the type to add to the context.
+{-# SPECIALIZE underAbstraction_ :: Subst a => Abs a -> (a -> TCM b) -> TCM b #-}
+underAbstraction_ :: (Subst a, MonadAddContext m) => Abs a -> (a -> m b) -> m b
+underAbstraction_ = underAbstraction __DUMMY_DOM__
+
+-- | Map a monadic function on the thing under the abstraction, adding
+--   the abstracted variable to the context.
+mapAbstraction
+  :: (Subst a, Subst b, MonadAddContext m)
+  => Dom Type -> (a -> m b) -> Abs a -> m (Abs b)
+mapAbstraction dom f x = (x $>) <$> underAbstraction dom x f
+
+mapAbstraction_
+  :: (Subst a, Subst b, MonadAddContext m)
+  => (a -> m b) -> Abs a -> m (Abs b)
+mapAbstraction_ = mapAbstraction __DUMMY_DOM__
+
+{-# SPECIALIZE getLetBindings :: TCM [(Name, LetBinding)] #-}
+getLetBindings :: MonadTCEnv tcm => tcm [(Name, LetBinding)]
+getLetBindings = do
+  bs <- asksTC envLetBindings
+  forM (Map.toList bs) $ \ (n, o) -> (,) n <$> getOpen o
+
+-- | Add a let bound variable
+{-# SPECIALIZE addLetBinding' :: Origin -> Name -> Term -> Dom Type -> TCM a -> TCM a #-}
+defaultAddLetBinding' :: (ReadTCState m, MonadTCEnv m) => Origin -> Name -> Term -> Dom Type -> m a -> m a
+defaultAddLetBinding' o x v t ret = do
+    vt <- makeOpen $ LetBinding o v t
+    flip localTC ret $ \e -> e { envLetBindings = Map.insert x vt $ envLetBindings e }
+
+-- | Add a let bound variable
+{-# SPECIALIZE addLetBinding :: ArgInfo -> Origin -> Name -> Term -> Type -> TCM a -> TCM a #-}
+addLetBinding :: MonadAddContext m => ArgInfo -> Origin -> Name -> Term -> Type -> m a -> m a
+addLetBinding info o x v t0 ret = addLetBinding' o x v (defaultArgDom info t0) ret
+
+
+{-# SPECIALIZE removeLetBinding :: Name -> TCM a -> TCM a #-}
+-- | Remove a let bound variable.
+removeLetBinding :: MonadTCEnv m => Name -> m a -> m a
+removeLetBinding x = localTC $ \ e -> e { envLetBindings = Map.delete x (envLetBindings e) }
+
+{-# SPECIALIZE removeLetBindingsFrom :: Name -> TCM a -> TCM a #-}
+-- | Remove a let bound variable and all let bindings introduced after it. For instance before
+--   printing its body to avoid folding the binding itself, or using bindings defined later.
+--   Relies on the invariant that names introduced later are sorted after earlier names.
+removeLetBindingsFrom :: MonadTCEnv m => Name -> m a -> m a
+removeLetBindingsFrom x = localTC $ \ e -> e { envLetBindings = fst $ Map.split x (envLetBindings e) }
+
+-- * Querying the context
+
+-- | Get the current context.
+{-# SPECIALIZE getContext :: TCM Context #-}
+getContext :: MonadTCEnv m => m Context
+getContext = asksTC envContext
+
+-- | Get the size of the current context.
+{-# SPECIALIZE getContextSize :: TCM Nat #-}
+getContextSize :: (Applicative m, MonadTCEnv m) => m Nat
+getContextSize = length <$> asksTC envContext
+
+-- | Generate @[var (n - 1), ..., var 0]@ for all declarations in the context.
+{-# SPECIALIZE getContextArgs :: TCM Args #-}
+getContextArgs :: (Applicative m, MonadTCEnv m) => m Args
+getContextArgs = reverse . zipWith mkArg [0..] <$> getContext
+  where mkArg i dom = var i <$ argFromDom dom
+
+-- | Generate @[var (n - 1), ..., var 0]@ for all declarations in the context.
+{-# SPECIALIZE getContextTerms :: TCM [Term] #-}
+getContextTerms :: (Applicative m, MonadTCEnv m) => m [Term]
+getContextTerms = map var . downFrom <$> getContextSize
+
+-- | Get the current context as a 'Telescope'.
+{-# SPECIALIZE getContextTelescope :: TCM Telescope #-}
+getContextTelescope :: (Applicative m, MonadTCEnv m) => m Telescope
+getContextTelescope = telFromList' nameToArgName . reverse <$> getContext
+
+-- | Get the names of all declarations in the context.
+{-# SPECIALIZE getContextNames :: TCM [Name] #-}
+getContextNames :: (Applicative m, MonadTCEnv m) => m [Name]
+getContextNames = map (fst . unDom) <$> getContext
+
+-- | get type of bound variable (i.e. deBruijn index)
+--
+{-# SPECIALIZE lookupBV' :: Nat -> TCM (Maybe ContextEntry) #-}
+lookupBV' :: MonadTCEnv m => Nat -> m (Maybe ContextEntry)
+lookupBV' n = do
+  ctx <- getContext
+  return $ raise (n + 1) <$> ctx !!! n
+
+{-# SPECIALIZE lookupBV :: Nat -> TCM (Dom (Name, Type)) #-}
+lookupBV :: (MonadFail m, MonadTCEnv m) => Nat -> m (Dom (Name, Type))
+lookupBV n = do
+  let failure = do
+        ctx <- getContext
+        fail $ "de Bruijn index out of scope: " ++ show n ++
+               " in context " ++ prettyShow (map (fst . unDom) ctx)
+  maybeM failure return $ lookupBV' n
+
+{-# SPECIALIZE domOfBV :: Nat -> TCM (Dom Type) #-}
+domOfBV :: (Applicative m, MonadFail m, MonadTCEnv m) => Nat -> m (Dom Type)
+domOfBV n = fmap snd <$> lookupBV n
+
+{-# SPECIALIZE typeOfBV :: Nat -> TCM Type #-}
+typeOfBV :: (Applicative m, MonadFail m, MonadTCEnv m) => Nat -> m Type
+typeOfBV i = unDom <$> domOfBV i
+
+{-# SPECIALIZE nameOfBV' :: Nat -> TCM (Maybe Name) #-}
+nameOfBV' :: (Applicative m, MonadFail m, MonadTCEnv m) => Nat -> m (Maybe Name)
+nameOfBV' n = fmap (fst . unDom) <$> lookupBV' n
+
+{-# SPECIALIZE nameOfBV :: Nat -> TCM Name #-}
+nameOfBV :: (Applicative m, MonadFail m, MonadTCEnv m) => Nat -> m Name
+nameOfBV n = fst . unDom <$> lookupBV n
+
+-- | Get the term corresponding to a named variable. If it is a lambda bound
+--   variable the deBruijn index is returned and if it is a let bound variable
+--   its definition is returned.
+{-# SPECIALIZE getVarInfo :: Name -> TCM (Term, Dom Type) #-}
+getVarInfo :: (MonadFail m, MonadTCEnv m) => Name -> m (Term, Dom Type)
+getVarInfo x =
+    do  ctx <- getContext
+        def <- asksTC envLetBindings
+        case List.findIndex ((== x) . fst . unDom) ctx of
+            Just n -> do
+                t <- domOfBV n
+                return (var n, t)
+            _       ->
+                case Map.lookup x def of
+                    Just vt -> do
+                      LetBinding _ v t <- getOpen vt
+                      return (v, t)
+                    _       -> fail $ "unbound variable " ++ prettyShow (nameConcrete x) ++
+                                " (id: " ++ prettyShow (nameId x) ++ ")"
diff --git a/src/full/Agda/TypeChecking/Monad/Context.hs-boot b/src/full/Agda/TypeChecking/Monad/Context.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Context.hs-boot
@@ -0,0 +1,50 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Context where
+
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Control  ( MonadTransControl(..), liftThrough )
+import Control.Monad.Trans.Identity ( IdentityT )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.TypeChecking.Monad.Base
+
+checkpointSubstitution :: MonadTCEnv tcm => CheckpointId -> tcm Substitution
+
+class MonadTCEnv m => MonadAddContext m where
+  addCtx :: Name -> Dom Type -> m a -> m a
+  addLetBinding' :: Origin -> Name -> Term -> Dom Type -> m a -> m a
+  updateContext :: Substitution -> (Context -> Context) -> m a -> m a
+  withFreshName :: Range -> ArgName -> (Name -> m a) -> m a
+
+  default addCtx
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Name -> Dom Type -> m a -> m a
+  addCtx x a = liftThrough $ addCtx x a
+
+  default addLetBinding'
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Origin -> Name -> Term -> Dom Type -> m a -> m a
+  addLetBinding' o x u a = liftThrough $ addLetBinding' o x u a
+
+  default updateContext
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Substitution -> (Context -> Context) -> m a -> m a
+  updateContext sub f = liftThrough $ updateContext sub f
+
+  default withFreshName
+    :: (MonadAddContext n, MonadTransControl t, t n ~ m)
+    => Range -> ArgName -> (Name -> m a) -> m a
+  withFreshName r x cont = do
+    st <- liftWith $ \ run -> do
+      withFreshName r x $ run . cont
+    restoreT $ return st
+
+instance MonadAddContext m => MonadAddContext (IdentityT m) where
+instance MonadAddContext m => MonadAddContext (ReaderT r m) where
+instance MonadAddContext m => MonadAddContext (StateT r m) where
+
+instance MonadAddContext TCM
diff --git a/src/full/Agda/TypeChecking/Monad/Debug.hs b/src/full/Agda/TypeChecking/Monad/Debug.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Debug.hs
@@ -0,0 +1,442 @@
+{-# LANGUAGE CPP #-}
+
+module Agda.TypeChecking.Monad.Debug
+  ( module Agda.TypeChecking.Monad.Debug
+  , Verbosity, VerboseKey, VerboseLevel
+  ) where
+
+import qualified Control.Exception as E
+import qualified Control.DeepSeq as DeepSeq (force)
+
+import Control.Applicative          ( liftA2 )
+import Control.Monad.IO.Class       ( MonadIO(..) )
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Control  ( MonadTransControl(..), liftThrough )
+import Control.Monad.Trans.Maybe
+import Control.Monad.Trans.Identity
+import Control.Monad.Writer
+
+import Data.Maybe
+import Data.Time                    ( getCurrentTime, getCurrentTimeZone, utcToLocalTime )
+import Data.Time.Format.ISO8601.Compat ( iso8601Show )
+  -- This is also exported from Data.Time.Format.ISO8601, but only from time >= 1.9
+
+import {-# SOURCE #-} Agda.TypeChecking.Errors
+import Agda.TypeChecking.Monad.Base
+
+import Agda.Interaction.Options
+import {-# SOURCE #-} Agda.Interaction.Response (Response(..))
+
+import Agda.Utils.CallStack ( HasCallStack, withCallerCallStack )
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.ListT
+import Agda.Utils.Maybe
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.ProfileOptions
+import Agda.Utils.Update
+import qualified Agda.Utils.Trie as Trie
+
+import Agda.Utils.Impossible
+
+class (Functor m, Applicative m, Monad m) => MonadDebug m where
+
+  formatDebugMessage :: VerboseKey -> VerboseLevel -> TCM Doc -> m String
+  traceDebugMessage  :: VerboseKey -> VerboseLevel -> String -> m a -> m a
+
+  -- | Print brackets around debug messages issued by a computation.
+  verboseBracket     :: VerboseKey -> VerboseLevel -> String -> m a -> m a
+
+  getVerbosity       :: m Verbosity
+  getProfileOptions  :: m ProfileOptions
+
+  -- | Check whether we are currently debug printing.
+  isDebugPrinting    :: m Bool
+
+  -- | Flag in a computation that we are currently debug printing.
+  nowDebugPrinting   :: m a -> m a
+
+  -- default implementation of transformed debug monad
+
+  default formatDebugMessage
+    :: (MonadTrans t, MonadDebug n, m ~ t n)
+    => VerboseKey -> VerboseLevel -> TCM Doc -> m String
+  formatDebugMessage k n d = lift $ formatDebugMessage k n d
+
+  default traceDebugMessage
+    :: (MonadTransControl t, MonadDebug n, m ~ t n)
+    => VerboseKey -> VerboseLevel -> String -> m a -> m a
+  traceDebugMessage k n s = liftThrough $ traceDebugMessage k n s
+
+#ifdef DEBUG
+  default verboseBracket
+    :: (MonadTransControl t, MonadDebug n, m ~ t n)
+    => VerboseKey -> VerboseLevel -> String -> m a -> m a
+  verboseBracket k n s = liftThrough $ verboseBracket k n s
+#else
+  default verboseBracket
+    :: (MonadTransControl t, MonadDebug n, m ~ t n)
+    => VerboseKey -> VerboseLevel -> String -> m a -> m a
+  verboseBracket k n s ma = ma
+  {-# INLINE verboseBracket #-}
+#endif
+
+  default getVerbosity
+    :: (MonadTrans t, MonadDebug n, m ~ t n)
+    => m Verbosity
+  getVerbosity = lift getVerbosity
+
+  default getProfileOptions
+    :: (MonadTrans t, MonadDebug n, m ~ t n)
+    => m ProfileOptions
+  getProfileOptions = lift getProfileOptions
+
+  default isDebugPrinting
+    :: (MonadTrans t, MonadDebug n, m ~ t n)
+    => m Bool
+  isDebugPrinting = lift isDebugPrinting
+
+  default nowDebugPrinting
+    :: (MonadTransControl t, MonadDebug n, m ~ t n)
+    => m a -> m a
+  nowDebugPrinting = liftThrough nowDebugPrinting
+
+-- Default implementations (working around the restriction to only
+-- have one default signature).
+
+defaultGetVerbosity :: HasOptions m => m Verbosity
+defaultGetVerbosity = optVerbose <$> pragmaOptions
+
+defaultGetProfileOptions :: HasOptions m => m ProfileOptions
+defaultGetProfileOptions = optProfiling <$> pragmaOptions
+
+defaultIsDebugPrinting :: MonadTCEnv m => m Bool
+defaultIsDebugPrinting = asksTC envIsDebugPrinting
+
+defaultNowDebugPrinting :: MonadTCEnv m => m a -> m a
+defaultNowDebugPrinting = locallyTC eIsDebugPrinting $ const True
+
+-- | Print a debug message if switched on.
+displayDebugMessage :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m ()
+displayDebugMessage k n s = traceDebugMessage k n s $ return ()
+
+-- | During printing, catch internal errors of kind 'Impossible' and print them.
+catchAndPrintImpossible
+  :: (CatchImpossible m, Monad m)
+  => VerboseKey -> VerboseLevel -> m String -> m String
+catchAndPrintImpossible k n m = catchImpossibleJust catchMe m $ \ imposs -> do
+  return $ render $ vcat
+    [ text $ "Debug printing " ++ k ++ ":" ++ show n ++ " failed due to exception:"
+    , vcat $ map (nest 2 . text) $ lines $ show imposs
+    ]
+  where
+  -- Exception filter: Catch only the 'Impossible' exception during debug printing.
+  catchMe :: Impossible -> Maybe Impossible
+  catchMe = filterMaybe $ \case
+    Impossible{}            -> True
+    Unreachable{}           -> False
+    ImpMissingDefinitions{} -> False
+
+instance MonadDebug TCM where
+
+  traceDebugMessage k n s cont = do
+    -- Andreas, 2019-08-20, issue #4016:
+    -- Force any lazy 'Impossible' exceptions to the surface and handle them.
+    s  <- liftIO . catchAndPrintImpossible k n . E.evaluate . DeepSeq.force $ s
+    cb <- getsTC $ stInteractionOutputCallback . stPersistentState
+
+    -- Andreas, 2022-06-15, prefix with time stamp if `-v debug.time:100`:
+    msg <- ifNotM (hasVerbosity "debug.time" 100) {-then-} (return s) {-else-} $ do
+      now <- liftIO $ trailingZeros . iso8601Show <$> liftA2 utcToLocalTime getCurrentTimeZone getCurrentTime
+      return $ concat [ now, ": ", s ]
+
+    cb $ Resp_RunningInfo n msg
+    cont
+    where
+    -- Surprisingly, iso8601Show gives us _up to_ 6 fractional digits (microseconds),
+    -- but not exactly 6.  https://github.com/haskell/time/issues/211
+    -- So we need to do the padding ourselves.
+    -- yyyy-mm-ddThh:mm:ss.ssssss
+    -- 12345678901234567890123456
+    trailingZeros = take 26 . (++ repeat '0')
+
+  formatDebugMessage k n d = catchAndPrintImpossible k n $ do
+    render <$> d `catchError` \ err -> do
+      renderError err <&> \ s -> vcat
+        [ sep $ map text
+          [ "Printing debug message"
+          , k  ++ ":" ++ show n
+          , "failed due to error:"
+          ]
+        , nest 2 $ text s
+        ]
+
+#ifdef DEBUG
+  verboseBracket k n s = applyWhenVerboseS k n $ \ m -> do
+    openVerboseBracket k n s
+    (m <* closeVerboseBracket k n) `catchError` \ e -> do
+      closeVerboseBracketException k n
+      throwError e
+#else
+  verboseBracket k n s ma = ma
+  {-# INLINE verboseBracket #-}
+#endif
+
+  getVerbosity      = defaultGetVerbosity
+  getProfileOptions = defaultGetProfileOptions
+  isDebugPrinting   = defaultIsDebugPrinting
+  nowDebugPrinting  = defaultNowDebugPrinting
+
+-- MonadTrans default instances
+
+deriving instance MonadDebug m => MonadDebug (BlockT m)  -- ghc <= 8.0, GeneralizedNewtypeDeriving
+instance MonadDebug m => MonadDebug (ChangeT m)
+instance MonadDebug m => MonadDebug (ExceptT e m)
+instance MonadDebug m => MonadDebug (MaybeT m)
+instance MonadDebug m => MonadDebug (ReaderT r m)
+instance MonadDebug m => MonadDebug (StateT s m)
+instance (MonadDebug m, Monoid w) => MonadDebug (WriterT w m)
+instance MonadDebug m => MonadDebug (IdentityT m)
+
+-- We are lacking MonadTransControl ListT
+
+instance MonadDebug m => MonadDebug (ListT m) where
+  traceDebugMessage k n s = liftListT $ traceDebugMessage k n s
+  verboseBracket    k n s = liftListT $ verboseBracket k n s
+  nowDebugPrinting        = liftListT nowDebugPrinting
+
+-- | Debug print some lines if the verbosity level for the given
+--   'VerboseKey' is at least 'VerboseLevel'.
+--
+-- Note: In the presence of @OverloadedStrings@, just
+-- @@
+--   reportS key level "Literate string"
+-- @@
+-- gives an @Ambiguous type variable@ error in @GHC@.
+-- Use the legacy functions 'reportSLn' and 'reportSDoc' instead then.
+--
+class ReportS a where
+  reportS :: MonadDebug m => VerboseKey -> VerboseLevel -> a -> m ()
+
+instance ReportS (TCM Doc) where reportS = reportSDoc
+instance ReportS String    where reportS = reportSLn
+
+instance ReportS [TCM Doc] where reportS k n = reportSDoc k n . fmap vcat . sequence
+instance ReportS [String]  where reportS k n = reportSLn  k n . unlines
+instance ReportS [Doc]     where reportS k n = reportSLn  k n . render . vcat
+instance ReportS Doc       where reportS k n = reportSLn  k n . render
+
+#ifdef DEBUG
+
+-- | Conditionally println debug string.
+{-# SPECIALIZE reportSLn :: VerboseKey -> VerboseLevel -> String -> TCM () #-}
+reportSLn :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m ()
+reportSLn k n s = verboseS k n $ displayDebugMessage k n $ s ++ "\n"
+
+#else
+
+{-# INLINE reportSLn #-}
+reportSLn :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m ()
+reportSLn _ _ _ = pure ()
+
+#endif
+
+-- | Conditionally println debug string. Works regardless of the debug flag.
+{-# SPECIALIZE reportSLn :: VerboseKey -> VerboseLevel -> String -> TCM () #-}
+alwaysReportSLn :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m ()
+alwaysReportSLn k n s = verboseS k n $ displayDebugMessage k n $ s ++ "\n"
+
+
+__IMPOSSIBLE_VERBOSE__ :: (HasCallStack, MonadDebug m) => String -> m a
+__IMPOSSIBLE_VERBOSE__ s = do
+  -- Andreas, 2023-07-19, issue #6728 is fixed by manually inlining reportSLn here.
+  -- reportSLn "impossible" 10 s
+  -- It seems like GHC 9.6 optimization does otherwise something that throws
+  -- away the debug message.
+  let k = "impossible"
+  let n = 10
+  verboseS k n $ displayDebugMessage k n $ s ++ "\n"
+
+  throwImpossible err
+  where
+    -- Create the "Impossible" error using *our* caller as the call site.
+    err = withCallerCallStack Impossible
+
+#ifdef DEBUG
+
+-- | Conditionally render debug 'Doc' and print it.
+{-# SPECIALIZE reportSDoc :: VerboseKey -> VerboseLevel -> TCM Doc -> TCM () #-}
+reportSDoc :: MonadDebug m => VerboseKey -> VerboseLevel -> TCM Doc -> m ()
+reportSDoc k n d = verboseS k n $ do
+  displayDebugMessage k n . (++ "\n") =<< formatDebugMessage k n (locallyTC eIsDebugPrinting (const True) d)
+
+-- | Debug print the result of a computation.
+reportResult :: MonadDebug m => VerboseKey -> VerboseLevel -> (a -> TCM Doc) -> m a -> m a
+reportResult k n debug action = do
+  x <- action
+  x <$ reportSDoc k n (debug x)
+
+#else
+
+-- | Conditionally render debug 'Doc' and print it.
+{-# INLINE reportSDoc #-}
+reportSDoc :: MonadDebug m => VerboseKey -> VerboseLevel -> TCM Doc -> m ()
+reportSDoc _ _ _ = pure ()
+
+-- | Debug print the result of a computation.
+{-# INLINE reportResult #-}
+reportResult :: MonadDebug m => VerboseKey -> VerboseLevel -> (a -> TCM Doc) -> m a -> m a
+reportResult _ _ _ action = action
+
+#endif
+
+-- | Conditionally render debug 'Doc' and print it. Works regardless of the debug flag.
+{-# SPECIALIZE reportSDoc :: VerboseKey -> VerboseLevel -> TCM Doc -> TCM () #-}
+alwaysReportSDoc :: MonadDebug m => VerboseKey -> VerboseLevel -> TCM Doc -> m ()
+alwaysReportSDoc k n d = verboseS k n $ do
+  displayDebugMessage k n . (++ "\n") =<< formatDebugMessage k n (locallyTC eIsDebugPrinting (const True) d)
+
+unlessDebugPrinting :: MonadDebug m => m () -> m ()
+unlessDebugPrinting = unlessM isDebugPrinting
+
+-- | Debug print some lines if the verbosity level for the given
+--   'VerboseKey' is at least 'VerboseLevel'.
+--
+-- Note: In the presence of @OverloadedStrings@, just
+-- @@
+--   traceS key level "Literate string"
+-- @@
+-- gives an @Ambiguous type variable@ error in @GHC@.
+-- Use the legacy functions 'traceSLn' and 'traceSDoc' instead then.
+--
+class TraceS a where
+  traceS :: MonadDebug m => VerboseKey -> VerboseLevel -> a -> m c -> m c
+
+instance TraceS (TCM Doc) where traceS = traceSDoc
+instance TraceS String    where traceS = traceSLn
+
+instance TraceS [TCM Doc] where traceS k n = traceSDoc k n . fmap vcat . sequence
+instance TraceS [String]  where traceS k n = traceSLn  k n . unlines
+instance TraceS [Doc]     where traceS k n = traceSLn  k n . render . vcat
+instance TraceS Doc       where traceS k n = traceSLn  k n . render
+
+
+#ifdef DEBUG
+
+traceSLn :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m a -> m a
+traceSLn k n s = applyWhenVerboseS k n $ traceDebugMessage k n $ s ++ "\n"
+
+-- | Conditionally render debug 'Doc', print it, and then continue.
+traceSDoc :: MonadDebug m => VerboseKey -> VerboseLevel -> TCM Doc -> m a -> m a
+traceSDoc k n d = applyWhenVerboseS k n $ \cont -> do
+  s <- formatDebugMessage k n $ locallyTC eIsDebugPrinting (const True) d
+  traceDebugMessage k n (s ++ "\n") cont
+
+#else
+
+{-# INLINE traceSLn #-}
+traceSLn :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m a -> m a
+traceSLn _ _ _ action = action
+
+-- | Conditionally render debug 'Doc', print it, and then continue.
+{-# INLINE traceSDoc #-}
+traceSDoc :: MonadDebug m => VerboseKey -> VerboseLevel -> TCM Doc -> m a -> m a
+traceSDoc _ _ _ action = action
+
+#endif
+
+
+openVerboseBracket :: MonadDebug m => VerboseKey -> VerboseLevel -> String -> m ()
+openVerboseBracket k n s = displayDebugMessage k n $ "{ " ++ s ++ "\n"
+
+closeVerboseBracket :: MonadDebug m => VerboseKey -> VerboseLevel -> m ()
+closeVerboseBracket k n = displayDebugMessage k n "}\n"
+
+closeVerboseBracketException :: MonadDebug m => VerboseKey -> VerboseLevel -> m ()
+closeVerboseBracketException k n = displayDebugMessage k n "} (exception)\n"
+
+
+------------------------------------------------------------------------
+-- Verbosity
+
+-- Invariant (which we may or may not currently break): Debug
+-- printouts use one of the following functions:
+--
+--   reportS
+--   reportSLn
+--   reportSDoc
+
+-- | Check whether a certain verbosity level is activated.
+--
+--   Precondition: The level must be non-negative.
+{-# SPECIALIZE hasVerbosity :: VerboseKey -> VerboseLevel -> TCM Bool #-}
+hasVerbosity :: MonadDebug m => VerboseKey -> VerboseLevel -> m Bool
+hasVerbosity k n = do
+  t <- getVerbosity
+  return $ case t of
+    Strict.Nothing -> n <= 1
+    Strict.Just t
+      -- This code is not executed if no debug flags have been given.
+      | t == Trie.singleton [] 0 ->
+        -- A special case for "-v0".
+        n <= 0
+      | otherwise ->
+        let ks = parseVerboseKey k
+            m  = lastWithDefault 0 $ Trie.lookupPath ks t
+        in n <= m
+
+-- | Check whether a certain verbosity level is activated (exact match).
+
+{-# SPECIALIZE hasExactVerbosity :: VerboseKey -> VerboseLevel -> TCM Bool #-}
+hasExactVerbosity :: MonadDebug m => VerboseKey -> VerboseLevel -> m Bool
+hasExactVerbosity k n = do
+  t <- getVerbosity
+  return $ case t of
+    Strict.Nothing -> n == 1
+    Strict.Just t
+      -- This code is not executed if no debug flags have been given.
+      | t == Trie.singleton [] 0 ->
+        -- A special case for "-v0".
+        n == 0
+      | otherwise ->
+        Just n == Trie.lookup (parseVerboseKey k) t
+
+-- | Run a computation if a certain verbosity level is activated (exact match).
+
+{-# SPECIALIZE whenExactVerbosity :: VerboseKey -> VerboseLevel -> TCM () -> TCM () #-}
+whenExactVerbosity :: MonadDebug m => VerboseKey -> VerboseLevel -> m () -> m ()
+whenExactVerbosity k n = whenM $ hasExactVerbosity k n
+
+__CRASH_WHEN__ :: (HasCallStack, MonadTCM m, MonadDebug m) => VerboseKey -> VerboseLevel -> m ()
+__CRASH_WHEN__ k n = whenExactVerbosity k n (throwImpossible err)
+  where
+    -- Create the "Unreachable" error using *our* caller as the call site.
+    err = withCallerCallStack Unreachable
+
+-- | Run a computation if a certain verbosity level is activated.
+--
+--   Precondition: The level must be non-negative.
+{-# SPECIALIZE verboseS :: VerboseKey -> VerboseLevel -> TCM () -> TCM () #-}
+-- {-# SPECIALIZE verboseS :: MonadIO m => VerboseKey -> VerboseLevel -> TCMT m () -> TCMT m () #-} -- RULE left-hand side too complicated to desugar
+-- {-# SPECIALIZE verboseS :: MonadTCM tcm => VerboseKey -> VerboseLevel -> tcm () -> tcm () #-}
+verboseS :: MonadDebug m => VerboseKey -> VerboseLevel -> m () -> m ()
+verboseS k n action = whenM (hasVerbosity k n) $ nowDebugPrinting action
+
+-- | Apply a function if a certain verbosity level is activated.
+--
+--   Precondition: The level must be non-negative.
+applyWhenVerboseS :: MonadDebug m => VerboseKey -> VerboseLevel -> (m a -> m a) -> m a -> m a
+applyWhenVerboseS k n f a = ifM (hasVerbosity k n) (f a) a
+
+-- | Check whether a certain profile option is activated.
+{-# SPECIALIZE hasProfileOption :: ProfileOption -> TCM Bool #-}
+hasProfileOption :: MonadDebug m => ProfileOption -> m Bool
+hasProfileOption opt = containsProfileOption opt <$> getProfileOptions
+
+-- | Run some code when the given profiling option is active.
+whenProfile :: MonadDebug m => ProfileOption -> m () -> m ()
+whenProfile opt = whenM (hasProfileOption opt)
diff --git a/src/full/Agda/TypeChecking/Monad/Debug.hs-boot b/src/full/Agda/TypeChecking/Monad/Debug.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Debug.hs-boot
@@ -0,0 +1,7 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Debug where
+
+import Data.Kind (Type)
+
+class MonadDebug (m :: Type -> Type)
diff --git a/src/full/Agda/TypeChecking/Monad/Env.hs b/src/full/Agda/TypeChecking/Monad/Env.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Env.hs
@@ -0,0 +1,144 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Env where
+
+import qualified Data.List as List
+
+import Data.Maybe (fromMaybe)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract.Name
+
+import Agda.TypeChecking.Monad.Base
+
+import Agda.Utils.FileName
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+
+-- | Get the name of the current module, if any.
+{-# SPECIALIZE currentModule :: TCM ModuleName #-}
+{-# SPECIALIZE currentModule :: ReduceM ModuleName #-}
+currentModule :: MonadTCEnv m => m ModuleName
+currentModule = asksTC envCurrentModule
+
+-- | Set the name of the current module.
+withCurrentModule :: (MonadTCEnv m) => ModuleName -> m a -> m a
+withCurrentModule m =
+    localTC $ \ e -> e { envCurrentModule = m }
+
+-- | Get the path of the currently checked file
+getCurrentPath :: MonadTCEnv m => m AbsolutePath
+getCurrentPath = fromMaybe __IMPOSSIBLE__ <$> asksTC envCurrentPath
+
+-- | Get the number of variables bound by anonymous modules.
+{-# SPECIALIZE getAnonymousVariables :: ModuleName -> TCM Nat #-}
+{-# SPECIALIZE getAnonymousVariables :: ModuleName -> ReduceM Nat #-}
+getAnonymousVariables :: MonadTCEnv m => ModuleName -> m Nat
+getAnonymousVariables m = do
+  ms <- asksTC envAnonymousModules
+  return $ sum [ n | (m', n) <- ms, mnameToList m' `List.isPrefixOf` mnameToList m ]
+
+-- | Add variables bound by an anonymous module.
+withAnonymousModule :: ModuleName -> Nat -> TCM a -> TCM a
+withAnonymousModule m n =
+  localTC $ \ e -> e { envAnonymousModules = (m, n) : envAnonymousModules e }
+
+-- | Set the current environment to the given
+withEnv :: MonadTCEnv m => TCEnv -> m a -> m a
+withEnv env = localTC $ \ env0 -> env
+  -- Keep persistent settings
+  { envPrintMetasBare         = envPrintMetasBare env0
+  }
+
+-- | Get the current environment
+getEnv :: TCM TCEnv
+getEnv = askTC
+
+-- | Set highlighting level
+withHighlightingLevel :: HighlightingLevel -> TCM a -> TCM a
+withHighlightingLevel h = localTC $ \ e -> e { envHighlightingLevel = h }
+
+-- | Restore setting for 'ExpandLast' to default.
+doExpandLast :: TCM a -> TCM a
+doExpandLast = localTC $ \ e -> e { envExpandLast = setExpand (envExpandLast e) }
+  where
+    setExpand ReallyDontExpandLast = ReallyDontExpandLast
+    setExpand _                    = ExpandLast
+
+dontExpandLast :: TCM a -> TCM a
+dontExpandLast = localTC $ \ e -> e { envExpandLast = DontExpandLast }
+
+reallyDontExpandLast :: TCM a -> TCM a
+reallyDontExpandLast = localTC $ \ e -> e { envExpandLast = ReallyDontExpandLast }
+
+-- | If the reduced did a proper match (constructor or literal pattern),
+--   then record this as simplification step.
+{-# SPECIALIZE performedSimplification :: TCM a -> TCM a #-}
+performedSimplification :: MonadTCEnv m => m a -> m a
+performedSimplification = localTC $ \ e -> e { envSimplification = YesSimplification }
+
+{-# SPECIALIZE performedSimplification' :: Simplification -> TCM a -> TCM a #-}
+performedSimplification' :: MonadTCEnv m => Simplification -> m a -> m a
+performedSimplification' simpl = localTC $ \ e -> e { envSimplification = simpl `mappend` envSimplification e }
+
+getSimplification :: MonadTCEnv m => m Simplification
+getSimplification = asksTC envSimplification
+
+-- * Controlling reduction.
+
+-- | Lens for 'AllowedReductions'.
+updateAllowedReductions :: (AllowedReductions -> AllowedReductions) -> TCEnv -> TCEnv
+updateAllowedReductions f e = e { envAllowedReductions = f (envAllowedReductions e) }
+
+modifyAllowedReductions :: MonadTCEnv m => (AllowedReductions -> AllowedReductions) -> m a -> m a
+modifyAllowedReductions = localTC . updateAllowedReductions
+
+putAllowedReductions :: MonadTCEnv m => AllowedReductions -> m a -> m a
+putAllowedReductions = modifyAllowedReductions . const
+
+-- | Reduce @Def f vs@ only if @f@ is a projection.
+onlyReduceProjections :: MonadTCEnv m => m a -> m a
+onlyReduceProjections = modifyAllowedReductions $ SmallSet.intersection $
+  SmallSet.singleton ProjectionReductions
+
+-- | Allow all reductions except for non-terminating functions (default).
+allowAllReductions :: MonadTCEnv m => m a -> m a
+allowAllReductions = putAllowedReductions allReductions
+
+-- | Allow all reductions including non-terminating functions.
+allowNonTerminatingReductions :: MonadTCEnv m => m a -> m a
+allowNonTerminatingReductions = putAllowedReductions reallyAllReductions
+
+-- | Allow all reductions when reducing types. Otherwise only allow
+--   inlined functions to be unfolded.
+onlyReduceTypes :: MonadTCEnv m => m a -> m a
+onlyReduceTypes = modifyAllowedReductions $ SmallSet.intersection $
+  SmallSet.fromList [TypeLevelReductions, InlineReductions]
+
+-- | Update allowed reductions when working on types
+typeLevelReductions :: MonadTCEnv m => m a -> m a
+typeLevelReductions = modifyAllowedReductions $ \reds -> if
+  | TypeLevelReductions `SmallSet.member` reds ->
+      if NonTerminatingReductions `SmallSet.member` reds
+       then reallyAllReductions
+       else allReductions
+  | otherwise -> reds
+
+-- * Concerning 'envInsideDotPattern'
+
+insideDotPattern :: TCM a -> TCM a
+insideDotPattern = localTC $ \ e -> e { envInsideDotPattern = True }
+
+isInsideDotPattern :: TCM Bool
+isInsideDotPattern = asksTC envInsideDotPattern
+
+-- | Don't use call-by-need evaluation for the given computation.
+callByName :: TCM a -> TCM a
+callByName = localTC $ \ e -> e { envCallByNeed = False }
+
+-- | Don't fold let bindings when printing. This is a bit crude since it disables any folding of let
+--   bindings at all. In many cases it's better to use `removeLetBinding` before printing to drop
+--   the let bindings that should not be folded.
+dontFoldLetBindings :: MonadTCEnv m => m a -> m a
+dontFoldLetBindings = localTC $ \ e -> e { envFoldLetBindings = False }
diff --git a/src/full/Agda/TypeChecking/Monad/Imports.hs b/src/full/Agda/TypeChecking/Monad/Imports.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Imports.hs
@@ -0,0 +1,107 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Imports
+  ( addImport
+  , addImportCycleCheck
+  , checkForImportCycle
+  , dropDecodedModule
+  , getDecodedModule
+  , getDecodedModules
+  , getImportPath
+  , getPrettyVisitedModules
+  , getVisitedModule
+  , getVisitedModules
+  , setDecodedModules
+  , setVisitedModules
+  , storeDecodedModule
+  , visitModule
+  , withImportPath
+  ) where
+
+import Control.Arrow   ( (***) )
+import Control.Monad   ( when )
+
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+
+import Agda.Syntax.TopLevelModuleName
+import Agda.TypeChecking.Monad.Base
+
+import Agda.Utils.List ( caseListM )
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+addImport :: TopLevelModuleName -> TCM ()
+addImport top = modifyTCLens' stImportedModules $ Set.insert top
+
+addImportCycleCheck :: TopLevelModuleName -> TCM a -> TCM a
+addImportCycleCheck m =
+    localTC $ \e -> e { envImportPath = m : envImportPath e }
+
+getImportPath :: TCM [TopLevelModuleName]
+getImportPath = asksTC envImportPath
+
+visitModule :: ModuleInfo -> TCM ()
+visitModule mi =
+  modifyTCLens stVisitedModules $
+    Map.insert (iTopLevelModuleName $ miInterface mi) mi
+
+setVisitedModules :: VisitedModules -> TCM ()
+setVisitedModules ms = setTCLens stVisitedModules ms
+
+getVisitedModules :: ReadTCState m => m VisitedModules
+getVisitedModules = useTC stVisitedModules
+
+getPrettyVisitedModules :: ReadTCState m => m Doc
+getPrettyVisitedModules = do
+  visited <-  fmap (uncurry (<>) . (pretty *** (prettyCheckMode . miMode))) . Map.toList
+          <$> getVisitedModules
+  return $ hcat $ punctuate ", " visited
+  where
+  prettyCheckMode :: ModuleCheckMode -> Doc
+  prettyCheckMode ModuleTypeChecked                  = ""
+  prettyCheckMode ModuleScopeChecked                 = " (scope only)"
+
+getVisitedModule :: ReadTCState m
+                 => TopLevelModuleName
+                 -> m (Maybe ModuleInfo)
+getVisitedModule x = Map.lookup x <$> useTC stVisitedModules
+
+getDecodedModules :: TCM DecodedModules
+getDecodedModules = stDecodedModules . stPersistentState <$> getTC
+
+setDecodedModules :: DecodedModules -> TCM ()
+setDecodedModules ms = modifyTC $ \s ->
+  s { stPersistentState = (stPersistentState s) { stDecodedModules = ms } }
+
+getDecodedModule :: TopLevelModuleName -> TCM (Maybe ModuleInfo)
+getDecodedModule x = Map.lookup x . stDecodedModules . stPersistentState <$> getTC
+
+storeDecodedModule :: ModuleInfo -> TCM ()
+storeDecodedModule mi = modifyTC $ \s ->
+  s { stPersistentState =
+        (stPersistentState s) { stDecodedModules =
+          Map.insert (iTopLevelModuleName $ miInterface mi) mi $
+            stDecodedModules (stPersistentState s)
+        }
+  }
+
+dropDecodedModule :: TopLevelModuleName -> TCM ()
+dropDecodedModule x = modifyTC $ \s ->
+  s { stPersistentState =
+        (stPersistentState s) { stDecodedModules =
+                                  Map.delete x $ stDecodedModules $ stPersistentState s
+                              }
+  }
+
+withImportPath :: [TopLevelModuleName] -> TCM a -> TCM a
+withImportPath path = localTC $ \e -> e { envImportPath = path }
+
+-- | Assumes that the first module in the import path is the module we are
+--   worried about.
+checkForImportCycle :: TCM ()
+checkForImportCycle = do
+  caseListM getImportPath __IMPOSSIBLE__ $ \ m ms -> do
+    when (m `elem` ms) $ typeError $ CyclicModuleDependency
+                                   $ dropWhile (/= m) $ reverse (m:ms)
diff --git a/src/full/Agda/TypeChecking/Monad/MetaVars.hs b/src/full/Agda/TypeChecking/Monad/MetaVars.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/MetaVars.hs
@@ -0,0 +1,857 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Monad.MetaVars where
+
+import Prelude hiding (null)
+
+import Control.Monad                ( (<=<), forM_, guard )
+import Control.Monad.Except         ( MonadError )
+import Control.Monad.State          ( StateT, execStateT, get, put )
+import Control.Monad.Trans          ( MonadTrans, lift )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Reader         ( ReaderT(ReaderT), runReaderT )
+import Control.Monad.Writer         ( WriterT, execWriterT, tell )
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import qualified Data.HashMap.Strict as HMap
+import qualified Data.List as List
+import qualified Data.Map.Strict as MapS
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Foldable as Fold
+
+import GHC.Stack (HasCallStack)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin (HasBuiltins)
+import Agda.TypeChecking.Monad.Trace
+import Agda.TypeChecking.Monad.Closure
+import Agda.TypeChecking.Monad.Constraints (MonadConstraint(..))
+import Agda.TypeChecking.Monad.Debug
+  (MonadDebug, reportSLn, __IMPOSSIBLE_VERBOSE__)
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Signature (HasConstInfo)
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Substitute
+import {-# SOURCE #-} Agda.TypeChecking.Telescope
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Functor ((<.>))
+import Agda.Utils.Lens
+import Agda.Utils.List (nubOn)
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Tuple
+import qualified Agda.Utils.Maybe.Strict as Strict
+
+import Agda.Utils.Impossible
+
+-- | Various kinds of metavariables.
+
+data MetaKind =
+    Records
+    -- ^ Meta variables of record type.
+  | SingletonRecords
+    -- ^ Meta variables of \"hereditarily singleton\" record type.
+  | Levels
+    -- ^ Meta variables of level type, if type-in-type is activated.
+  deriving (Eq, Enum, Bounded, Show)
+
+-- | All possible metavariable kinds.
+
+allMetaKinds :: [MetaKind]
+allMetaKinds = [minBound .. maxBound]
+
+data KeepMetas = KeepMetas | RollBackMetas
+
+-- | Monad service class for creating, solving and eta-expanding of
+--   metavariables.
+class ( MonadConstraint m
+      , MonadReduce m
+      , MonadAddContext m
+      , MonadTCEnv m
+      , ReadTCState m
+      , HasBuiltins m
+      , HasConstInfo m
+      , MonadDebug m
+      ) => MonadMetaSolver m where
+  -- | Generate a new meta variable with some instantiation given.
+  --   For instance, the instantiation could be a 'PostponedTypeCheckingProblem'.
+  newMeta' :: MetaInstantiation -> Frozen -> MetaInfo -> MetaPriority -> Permutation ->
+              Judgement a -> m MetaId
+
+  -- * Solve constraint @x vs = v@.
+
+  -- | Assign to an open metavar which may not be frozen.
+  --   First check that metavar args are in pattern fragment.
+  --     Then do extended occurs check on given thing.
+  --
+  --   Assignment is aborted by throwing a @PatternErr@ via a call to
+  --   @patternViolation@.  This error is caught by @catchConstraint@
+  --   during equality checking (@compareAtom@) and leads to
+  --   restoration of the original constraints.
+  assignV :: CompareDirection -> MetaId -> Args -> Term -> CompareAs -> m ()
+
+  -- | Directly instantiate the metavariable. Skip pattern check,
+  -- occurs check and frozen check. Used for eta expanding frozen
+  -- metas.
+  assignTerm' :: MonadMetaSolver m => MetaId -> [Arg ArgName] -> Term -> m ()
+
+  -- | Eta-expand a local meta-variable, if it is of the specified
+  -- kind. Don't do anything if the meta-variable is a blocked term.
+  etaExpandMeta :: [MetaKind] -> MetaId -> m ()
+
+  -- | Update the status of the metavariable
+  updateMetaVar :: MetaId -> (MetaVariable -> MetaVariable) -> m ()
+
+  -- | 'speculateMetas fallback m' speculatively runs 'm', but if the
+  --    result is 'RollBackMetas' any changes to metavariables are
+  --    rolled back and 'fallback' is run instead.
+  speculateMetas :: m () -> m KeepMetas -> m ()
+
+instance MonadMetaSolver m => MonadMetaSolver (ReaderT r m) where
+  newMeta' inst f i p perm j = lift $ newMeta' inst f i p perm j
+  assignV dir m us v cmp = lift $ assignV dir m us v cmp
+  assignTerm' m us v = lift $ assignTerm' m us v
+  etaExpandMeta k m = lift $ etaExpandMeta k m
+  updateMetaVar m f = lift $ updateMetaVar m f
+  speculateMetas fallback m = ReaderT $ \x -> speculateMetas (runReaderT fallback x) (runReaderT m x)
+
+-- | Switch off assignment of metas.
+dontAssignMetas :: (MonadTCEnv m, HasOptions m, MonadDebug m) => m a -> m a
+dontAssignMetas cont = do
+  reportSLn "tc.meta" 45 $ "don't assign metas"
+  localTC (\ env -> env { envAssignMetas = False }) cont
+
+-- | Is the meta-variable from another top-level module?
+
+isRemoteMeta :: ReadTCState m => m (MetaId -> Bool)
+isRemoteMeta = do
+  h <- currentModuleNameHash
+  return (\m -> h /= metaModule m)
+
+-- | If another meta-variable is created, then it will get this
+-- 'MetaId' (unless the state is changed too much, for instance by
+-- 'setTopLevelModule').
+
+nextLocalMeta :: ReadTCState m => m MetaId
+nextLocalMeta = useR stFreshMetaId
+
+-- | Pairs of local meta-stores.
+
+data LocalMetaStores = LocalMetaStores
+  { openMetas :: LocalMetaStore
+    -- ^ A 'MetaStore' containing open meta-variables.
+  , solvedMetas :: LocalMetaStore
+    -- ^ A 'MetaStore' containing instantiated meta-variables.
+  }
+
+-- | Run a computation and record which new metas it created.
+metasCreatedBy ::
+  forall m a. ReadTCState m => m a -> m (a, LocalMetaStores)
+metasCreatedBy m = do
+  !nextMeta <- nextLocalMeta
+  a         <- m
+  os        <- created stOpenMetaStore   nextMeta
+  ss        <- created stSolvedMetaStore nextMeta
+  return (a, LocalMetaStores { openMetas = os, solvedMetas = ss })
+  where
+  created :: Lens' TCState LocalMetaStore -> MetaId -> m LocalMetaStore
+  created store next = do
+    ms <- useTC store
+    return $ case MapS.splitLookup next ms of
+      (_, Nothing, ms) -> ms
+      (_, Just m,  ms) -> MapS.insert next m ms
+
+-- | Find information about the given local meta-variable, if any.
+
+lookupLocalMeta' :: ReadTCState m => MetaId -> m (Maybe MetaVariable)
+lookupLocalMeta' m = do
+  mv <- lkup <$> useR stSolvedMetaStore
+  case mv of
+    mv@Just{} -> return mv
+    Nothing   -> lkup <$> useR stOpenMetaStore
+  where
+  lkup = MapS.lookup m
+
+-- | Find information about the given local meta-variable.
+
+lookupLocalMeta ::
+  (HasCallStack, MonadDebug m, ReadTCState m) =>
+  MetaId -> m MetaVariable
+lookupLocalMeta m =
+  fromMaybeM (__IMPOSSIBLE_VERBOSE__ err) $ lookupLocalMeta' m
+  where
+  err = "no such local meta-variable " ++ prettyShow m
+
+-- | Find information about the (local or remote) meta-variable, if
+-- any.
+--
+-- If no meta-variable is found, then the reason could be that the
+-- dead-code elimination
+-- ('Agda.TypeChecking.DeadCode.eliminateDeadCode') failed to find the
+-- meta-variable, perhaps because some 'NamesIn' instance is
+-- incorrectly defined.
+
+{-# SPECIALIZE lookupMeta :: MetaId -> TCM (Maybe (Either RemoteMetaVariable MetaVariable)) #-}
+lookupMeta ::
+  ReadTCState m =>
+  MetaId -> m (Maybe (Either RemoteMetaVariable MetaVariable))
+lookupMeta m = do
+  mv <- lookupLocalMeta' m
+  case mv of
+    Just mv -> return (Just (Right mv))
+    Nothing -> fmap Left . HMap.lookup m <$> useR stImportedMetaStore
+
+-- | Find the meta-variable's instantiation.
+
+{-# SPECIALIZE lookupMetaInstantiation :: MetaId -> TCM MetaInstantiation #-}
+lookupMetaInstantiation ::
+  ReadTCState m => MetaId -> m MetaInstantiation
+lookupMetaInstantiation m = do
+  mi <- lookupMeta m
+  case mi of
+    Just (Left mv)  -> return (InstV $ rmvInstantiation mv)
+    Just (Right mv) -> return (mvInstantiation mv)
+    Nothing         -> __IMPOSSIBLE__
+
+-- | Find the meta-variable's judgement.
+
+lookupMetaJudgement :: ReadTCState m => MetaId -> m (Judgement MetaId)
+lookupMetaJudgement m = do
+  mi <- lookupMeta m
+  case mi of
+    Just (Left mv)  -> return (rmvJudgement mv)
+    Just (Right mv) -> return (mvJudgement mv)
+    Nothing         -> __IMPOSSIBLE__
+
+-- | Find the meta-variable's modality.
+
+lookupMetaModality :: ReadTCState m => MetaId -> m Modality
+lookupMetaModality m = do
+  mi <- lookupMeta m
+  case mi of
+    Just (Left mv)  -> return (rmvModality mv)
+    Just (Right mv) -> return (getModality mv)
+    Nothing         -> __IMPOSSIBLE__
+
+{-# INLINE metaType #-}
+-- | The type of a term or sort meta-variable.
+metaType :: ReadTCState m => MetaId -> m Type
+metaType x = jMetaType <$> lookupMetaJudgement x
+
+-- | Update the information associated with a local meta-variable.
+updateMetaVarTCM ::
+  HasCallStack => MetaId -> (MetaVariable -> MetaVariable) -> TCM ()
+updateMetaVarTCM m f = do
+  mv <- lookupLocalMeta' m
+  case mv of
+    Nothing -> do
+      mv <- lookupMeta m
+      case mv of
+        Nothing -> __IMPOSSIBLE_VERBOSE__
+                     ("Meta-variable not found: " ++ prettyShow m)
+        Just{}  -> __IMPOSSIBLE_VERBOSE__
+                     ("Attempt to update remote meta-variable: " ++
+                      prettyShow m)
+    Just mv -> do
+      let mv'    = f mv
+          insert = (`modifyTCLens` MapS.insert m mv')
+          delete = (`modifyTCLens` MapS.delete m)
+      case ( isOpenMeta (mvInstantiation mv)
+           , isOpenMeta (mvInstantiation mv')
+           ) of
+        (True,  True)  -> insert stOpenMetaStore
+        (False, False) -> insert stSolvedMetaStore
+        (True,  False) -> do
+          delete stOpenMetaStore
+          insert stSolvedMetaStore
+        (False, True)  -> __IMPOSSIBLE__
+
+-- | Insert a new meta-variable with associated information into the
+-- local meta store.
+insertMetaVar :: MetaId -> MetaVariable -> TCM ()
+insertMetaVar m mv
+  | isOpenMeta (mvInstantiation mv) = insert stOpenMetaStore
+  | otherwise                       = insert stSolvedMetaStore
+  where
+  insert = (`modifyTCLens` MapS.insert m mv)
+
+{-# INLINE getMetaPriority #-}
+-- | Returns the 'MetaPriority' of the given local meta-variable.
+getMetaPriority ::
+  (HasCallStack, MonadDebug m, ReadTCState m) =>
+  MetaId -> m MetaPriority
+getMetaPriority = mvPriority <.> lookupLocalMeta
+
+isSortMeta :: ReadTCState m => MetaId -> m Bool
+isSortMeta m = isSortJudgement <$> lookupMetaJudgement m
+
+isSortMeta_ :: MetaVariable -> Bool
+isSortMeta_ mv = isSortJudgement (mvJudgement mv)
+
+isSortJudgement :: Judgement a -> Bool
+isSortJudgement HasType{} = False
+isSortJudgement IsSort{}  = True
+
+{-# SPECIALIZE getMetaType :: MetaId -> TCM Type #-}
+getMetaType :: ReadTCState m => MetaId -> m Type
+getMetaType m = do
+  j <- lookupMetaJudgement m
+  return $ case j of
+    HasType{ jMetaType = t } -> t
+    IsSort{}  -> __IMPOSSIBLE__
+
+{-# SPECIALIZE getMetaContextArgs :: MetaVariable -> TCM Args #-}
+-- | Compute the context variables that a local meta-variable should
+-- be applied to, accounting for pruning.
+getMetaContextArgs :: MonadTCEnv m => MetaVariable -> m Args
+getMetaContextArgs MetaVar{ mvPermutation = p } = do
+  args <- getContextArgs
+  return $ permute (takeP (length args) p) args
+
+{-# SPECIALIZE getMetaTypeInContext :: MetaId -> TCM Type #-}
+-- | Given a local meta-variable, return the type applied to the
+-- current context.
+getMetaTypeInContext ::
+  (HasBuiltins m, HasCallStack, MonadDebug m, MonadReduce m,
+   MonadTCEnv m, ReadTCState m) =>
+  MetaId -> m Type
+getMetaTypeInContext m = do
+  mv@MetaVar{ mvJudgement = j } <- lookupLocalMeta m
+  case j of
+    HasType{ jMetaType = t } -> piApplyM t =<< getMetaContextArgs mv
+    IsSort{}                 -> __IMPOSSIBLE__
+
+{-# SPECIALIZE isGeneralizableMeta :: MetaId -> TCM DoGeneralize #-}
+-- | Is it a local meta-variable that might be generalized?
+isGeneralizableMeta ::
+  (HasCallStack, MonadDebug m, ReadTCState m) =>
+  MetaId -> m DoGeneralize
+isGeneralizableMeta x =
+  unArg . miGeneralizable . mvInfo <$> lookupLocalMeta x
+
+-- | Check whether all metas are instantiated.
+--   Precondition: argument is a meta (in some form) or a list of metas.
+class IsInstantiatedMeta a where
+  isInstantiatedMeta :: (MonadFail m, ReadTCState m) => a -> m Bool
+
+{-# SPECIALIZE isInstantiatedMeta :: Term -> TCM Bool #-}
+{-# SPECIALIZE isInstantiatedMeta :: Type -> TCM Bool #-}
+
+instance IsInstantiatedMeta MetaId where
+  isInstantiatedMeta m = isJust <$> isInstantiatedMeta' m
+
+instance IsInstantiatedMeta Term where
+  isInstantiatedMeta = loop where
+   loop v =
+    case v of
+      MetaV x _  -> isInstantiatedMeta x
+      DontCare v -> loop v
+      Level l    -> isInstantiatedMeta l
+      Lam _ b    -> isInstantiatedMeta b
+      Con _ _ es | Just vs <- allApplyElims es -> isInstantiatedMeta vs
+      _          -> __IMPOSSIBLE__
+
+instance IsInstantiatedMeta Level where
+  isInstantiatedMeta (Max n ls) | n == 0 = isInstantiatedMeta ls
+  isInstantiatedMeta _ = __IMPOSSIBLE__
+
+instance IsInstantiatedMeta PlusLevel where
+  isInstantiatedMeta (Plus n l) | n == 0 = isInstantiatedMeta l
+  isInstantiatedMeta _ = __IMPOSSIBLE__
+
+instance IsInstantiatedMeta a => IsInstantiatedMeta [a] where
+  isInstantiatedMeta = andM . map isInstantiatedMeta
+
+instance IsInstantiatedMeta a => IsInstantiatedMeta (Maybe a) where
+  isInstantiatedMeta = isInstantiatedMeta . maybeToList
+
+instance IsInstantiatedMeta a => IsInstantiatedMeta (Arg a) where
+  isInstantiatedMeta = isInstantiatedMeta . unArg
+
+-- | Does not worry about raising.
+instance IsInstantiatedMeta a => IsInstantiatedMeta (Abs a) where
+  isInstantiatedMeta = isInstantiatedMeta . unAbs
+
+{-# SPECIALIZE isInstantiatedMeta' :: MetaId -> TCM (Maybe Term) #-}
+isInstantiatedMeta' :: (MonadFail m, ReadTCState m) => MetaId -> m (Maybe Term)
+isInstantiatedMeta' m = do
+  inst <- lookupMetaInstantiation m
+  return $ case inst of
+    InstV inst -> Just $ foldr mkLam (instBody inst) (instTel inst)
+    _          -> Nothing
+
+-- | Returns all metavariables in a constraint. Slightly complicated by the
+--   fact that blocked terms are represented by two meta variables. To find the
+--   second one we need to look up the meta listeners for the one in the
+--   UnBlock constraint.
+--   This is used for the purpose of deciding if a metavariable is constrained or if it can be
+--   generalized over (see Agda.TypeChecking.Generalize).
+constraintMetas :: Constraint -> TCM (Set MetaId)
+constraintMetas = \case
+    -- We don't use allMetas here since some constraints should not stop us from generalizing. For
+    -- instance CheckSizeLtSat (see #3694). We also have to check meta listeners to get metas of
+    -- UnBlock constraints.
+    -- #5147: Don't count metas in the type of a constraint. For instance the constraint u = v : t
+    -- should not stop us from generalize metas in t, since we could never solve those metas based
+    -- on that constraint alone.
+      ValueCmp _ _ u v         -> return $ allMetas Set.singleton (u, v)
+      ValueCmpOnFace _ p _ u v -> return $ allMetas Set.singleton (p, u, v)
+      ElimCmp _ _ _ _ es es'   -> return $ allMetas Set.singleton (es, es')
+      LevelCmp _ l l'          -> return $ allMetas Set.singleton (Level l, Level l')
+      UnquoteTactic t h g      -> return $ allMetas Set.singleton (t, h, g)
+      SortCmp _ s1 s2          -> return $ allMetas Set.singleton (Sort s1, Sort s2)
+      UnBlock x                -> Set.insert x . Set.unions <$> (mapM listenerMetas =<< getMetaListeners x)
+      FindInstance x _         ->
+        -- #5093: We should not generalize over metas bound by instance constraints.
+        -- We keep instance constraints even if the meta is solved, to check that it could indeed
+        -- be filled by instance search. If it's solved, look in the solution.
+        caseMaybeM (isInstantiatedMeta' x) (return $ Set.singleton x) $ return . allMetas Set.singleton
+      IsEmpty{}                -> return mempty
+      CheckFunDef{}            -> return mempty
+      CheckSizeLtSat{}         -> return mempty
+      HasBiggerSort{}          -> return mempty
+      HasPTSRule{}             -> return mempty
+      CheckDataSort{}          -> return mempty
+      CheckMetaInst x          -> return mempty
+      CheckType t              -> return $ allMetas Set.singleton t
+      CheckLockedVars a b c d  -> return $ allMetas Set.singleton (a, b, c, d)
+      UsableAtModality{}       -> return mempty
+  where
+    -- For blocked constant twin variables
+    listenerMetas EtaExpand{}           = return Set.empty
+    listenerMetas (CheckConstraint _ c) = constraintMetas (clValue $ theConstraint c)
+
+-- | Create 'MetaInfo' in the current environment.
+createMetaInfo :: (MonadTCEnv m, ReadTCState m) => m MetaInfo
+createMetaInfo = createMetaInfo' RunMetaOccursCheck
+
+createMetaInfo'
+  :: (MonadTCEnv m, ReadTCState m)
+  => RunMetaOccursCheck -> m MetaInfo
+createMetaInfo' b = do
+  r        <- getCurrentRange
+  cl       <- buildClosure r
+  gen      <- viewTC eGeneralizeMetas
+  modality <- currentModality
+  return MetaInfo
+    { miClosRange       = cl
+    , miModality        = modality
+    , miMetaOccursCheck = b
+    , miNameSuggestion  = ""
+    , miGeneralizable   = defaultArg gen
+                          -- The ArgInfo is set to the right value in
+                          -- the newArgsMetaCtx' function.
+    }
+
+setValueMetaName :: MonadMetaSolver m => Term -> MetaNameSuggestion -> m ()
+setValueMetaName v s = do
+  case v of
+    MetaV mi _ -> setMetaNameSuggestion mi s
+    u          -> do
+      reportSLn "tc.meta.name" 70 $
+        "cannot set meta name; newMeta returns " ++ show u
+      return ()
+
+getMetaNameSuggestion ::
+  (HasCallStack, MonadDebug m, ReadTCState m) =>
+  MetaId -> m MetaNameSuggestion
+getMetaNameSuggestion mi =
+  miNameSuggestion . mvInfo <$> lookupLocalMeta mi
+
+setMetaNameSuggestion :: MonadMetaSolver m => MetaId -> MetaNameSuggestion -> m ()
+setMetaNameSuggestion mi s = unless (null s || isUnderscore s) $ do
+  reportSLn "tc.meta.name" 20 $
+    "setting name of meta " ++ prettyShow mi ++ " to " ++ s
+  updateMetaVar mi $ \ mvar ->
+    mvar { mvInfo = (mvInfo mvar) { miNameSuggestion = s }}
+
+-- | Change the ArgInfo that will be used when generalizing over this
+-- local meta-variable.
+setMetaGeneralizableArgInfo :: MonadMetaSolver m => MetaId -> ArgInfo -> m ()
+setMetaGeneralizableArgInfo m i = updateMetaVar m $ \ mv ->
+  mv { mvInfo = (mvInfo mv)
+        { miGeneralizable = setArgInfo i (miGeneralizable (mvInfo mv)) } }
+
+updateMetaVarRange :: MonadMetaSolver m => MetaId -> Range -> m ()
+updateMetaVarRange mi r = updateMetaVar mi (setRange r)
+
+setMetaOccursCheck :: MonadMetaSolver m => MetaId -> RunMetaOccursCheck -> m ()
+setMetaOccursCheck mi b = updateMetaVar mi $ \ mvar ->
+  mvar { mvInfo = (mvInfo mvar) { miMetaOccursCheck = b } }
+
+-- * Query and manipulate interaction points.
+
+class (MonadTCEnv m, ReadTCState m) => MonadInteractionPoints m where
+  freshInteractionId :: m InteractionId
+  default freshInteractionId
+    :: (MonadTrans t, MonadInteractionPoints n, t n ~ m)
+    => m InteractionId
+  freshInteractionId = lift freshInteractionId
+
+  modifyInteractionPoints :: (InteractionPoints -> InteractionPoints) -> m ()
+  default modifyInteractionPoints
+    :: (MonadTrans t, MonadInteractionPoints n, t n ~ m)
+    => (InteractionPoints -> InteractionPoints) -> m ()
+  modifyInteractionPoints = lift . modifyInteractionPoints
+
+instance MonadInteractionPoints m => MonadInteractionPoints (IdentityT m)
+instance MonadInteractionPoints m => MonadInteractionPoints (ReaderT r m)
+instance MonadInteractionPoints m => MonadInteractionPoints (StateT s m)
+
+instance MonadInteractionPoints TCM where
+  freshInteractionId = fresh
+  modifyInteractionPoints f = stInteractionPoints `modifyTCLens` f
+
+-- | Register an interaction point during scope checking.
+--   If there is no interaction id yet, create one.
+registerInteractionPoint
+  :: forall m. MonadInteractionPoints m
+  => Bool -> Range -> Maybe Nat -> m InteractionId
+registerInteractionPoint preciseRange r maybeId = do
+  m <- useR stInteractionPoints
+  -- If we're given an interaction id we shouldn't look up by range.
+  -- This is important when doing 'refine', since all interaction points
+  -- created by the refine gets the same range.
+  if not preciseRange || isJust maybeId then continue m else do
+    -- If the range does not come from a file, it is not
+    -- precise, so ignore it.
+    Strict.caseMaybe (rangeFile r) (continue m) $ \ _ -> do
+    -- First, try to find the interaction point by Range.
+    caseMaybe (findInteractionPoint_ r m) (continue m) {-else-} return
+ where
+ continue :: InteractionPoints -> m InteractionId
+ continue m = do
+  -- We did not find an interaction id with the same Range, so let's create one!
+  ii <- case maybeId of
+    Just i  -> return $ InteractionId i
+    Nothing -> freshInteractionId
+  let ip = InteractionPoint { ipRange = r, ipMeta = Nothing, ipSolved = False, ipClause = IPNoClause, ipBoundary = IPBoundary mempty }
+  case BiMap.insertLookupWithKey (\ key new old -> old) ii ip m of
+    -- If the interaction point is already present, we keep the old ip.
+    -- However, it needs to be at the same range as the new one.
+    (Just ip0, _)
+       | ipRange ip /= ipRange ip0 -> __IMPOSSIBLE__
+       | otherwise                 -> return ii
+    (Nothing, m') -> do
+      modifyInteractionPoints (const m')
+      return ii
+
+-- | Find an interaction point by 'Range' by searching the whole map.
+--   Issue 3000: Don't consider solved interaction points.
+--
+--   O(n): linear in the number of registered interaction points.
+
+findInteractionPoint_ :: Range -> InteractionPoints -> Maybe InteractionId
+findInteractionPoint_ r m = do
+  guard $ not $ null r
+  listToMaybe $ mapMaybe sameRange $ BiMap.toList m
+  where
+    sameRange :: (InteractionId, InteractionPoint) -> Maybe InteractionId
+    sameRange (ii, InteractionPoint r' _ False _ _) | r == r' = Just ii
+    sameRange _ = Nothing
+
+{-# INLINABLE connectInteractionPoint #-}
+-- | Hook up a local meta-variable to an interaction point.
+connectInteractionPoint
+  :: MonadInteractionPoints m
+  => InteractionId -> MetaId -> m ()
+connectInteractionPoint ii mi = do
+  ipCl <- asksTC envClause
+  m <- useR stInteractionPoints
+  let ip = InteractionPoint { ipRange = __IMPOSSIBLE__, ipMeta = Just mi, ipSolved = False, ipClause = ipCl, ipBoundary = IPBoundary mempty }
+  -- The interaction point needs to be present already, we just set the meta.
+  case BiMap.insertLookupWithKey (\ key new old -> new { ipRange = ipRange old }) ii ip m of
+    (Nothing, _) -> __IMPOSSIBLE__
+    (Just _, m') -> modifyInteractionPoints $ const m'
+
+-- | Mark an interaction point as solved.
+removeInteractionPoint :: MonadInteractionPoints m => InteractionId -> m ()
+removeInteractionPoint ii =
+  modifyInteractionPoints $ BiMap.update (\ ip -> Just ip{ ipSolved = True }) ii
+
+-- | Get a list of interaction ids.
+{-# SPECIALIZE getInteractionPoints :: TCM [InteractionId] #-}
+getInteractionPoints :: ReadTCState m => m [InteractionId]
+getInteractionPoints = BiMap.keys <$> useR stInteractionPoints
+
+-- | Get all metas that correspond to unsolved interaction ids.
+getInteractionMetas :: ReadTCState m => m [MetaId]
+getInteractionMetas =
+  mapMaybe ipMeta . filter (not . ipSolved) . BiMap.elems <$> useR stInteractionPoints
+
+getUniqueMetasRanges ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => [MetaId] -> m [Range]
+getUniqueMetasRanges = fmap (nubOn id) . mapM getMetaRange
+
+getUnsolvedMetas ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => m [Range]
+getUnsolvedMetas = do
+  openMetas            <- getOpenMetas
+  interactionMetas     <- getInteractionMetas
+  getUniqueMetasRanges (openMetas List.\\ interactionMetas)
+
+getUnsolvedInteractionMetas ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => m [Range]
+getUnsolvedInteractionMetas = getUniqueMetasRanges =<< getInteractionMetas
+
+-- | Get all metas that correspond to unsolved interaction ids.
+getInteractionIdsAndMetas :: ReadTCState m => m [(InteractionId,MetaId)]
+getInteractionIdsAndMetas =
+  mapMaybe f . filter (not . ipSolved . snd) . BiMap.toList <$> useR stInteractionPoints
+  where f (ii, ip) = (ii,) <$> ipMeta ip
+
+-- | Does the meta variable correspond to an interaction point?
+--
+--   Time: @O(log n)@ where @n@ is the number of interaction metas.
+isInteractionMeta :: ReadTCState m => MetaId -> m (Maybe InteractionId)
+isInteractionMeta x = BiMap.invLookup x <$> useR stInteractionPoints
+
+-- | Get the information associated to an interaction point.
+{-# SPECIALIZE lookupInteractionPoint :: InteractionId -> TCM InteractionPoint #-}
+lookupInteractionPoint
+  :: (MonadFail m, ReadTCState m, MonadError TCErr m)
+  => InteractionId -> m InteractionPoint
+lookupInteractionPoint ii =
+  fromMaybeM err $ BiMap.lookup ii <$> useR stInteractionPoints
+  where
+    err  = fail $ "no such interaction point: " ++ show ii
+
+{-# SPECIALIZE lookupInteractionId :: InteractionId -> TCM MetaId #-}
+-- | Get 'MetaId' for an interaction point.
+--   Precondition: interaction point is connected.
+lookupInteractionId
+  :: (MonadFail m, ReadTCState m, MonadError TCErr m, MonadTCEnv m)
+  => InteractionId -> m MetaId
+lookupInteractionId ii = fromMaybeM err2 $ ipMeta <$> lookupInteractionPoint ii
+  where
+    err2 = typeError $ GenericError $ "No type nor action available for hole " ++ prettyShow ii ++ ". Possible cause: the hole has not been reached during type checking (do you see yellow?)"
+
+-- | Check whether an interaction id is already associated with a meta variable.
+lookupInteractionMeta :: ReadTCState m => InteractionId -> m (Maybe MetaId)
+lookupInteractionMeta ii = lookupInteractionMeta_ ii <$> useR stInteractionPoints
+
+lookupInteractionMeta_ :: InteractionId -> InteractionPoints -> Maybe MetaId
+lookupInteractionMeta_ ii m = ipMeta =<< BiMap.lookup ii m
+
+-- | Generate new meta variable.
+newMeta :: MonadMetaSolver m => Frozen -> MetaInfo -> MetaPriority -> Permutation -> Judgement a -> m MetaId
+newMeta = newMeta' Open
+
+-- | Generate a new meta variable with some instantiation given.
+--   For instance, the instantiation could be a 'PostponedTypeCheckingProblem'.
+newMetaTCM' :: MetaInstantiation -> Frozen -> MetaInfo -> MetaPriority -> Permutation ->
+               Judgement a -> TCM MetaId
+newMetaTCM' inst frozen mi p perm j = do
+  x <- fresh
+  let j' = j { jMetaId = x }  -- fill the identifier part of the judgement
+      mv = MetaVar{ mvInfo             = mi
+                  , mvPriority         = p
+                  , mvPermutation      = perm
+                  , mvJudgement        = j'
+                  , mvInstantiation    = inst
+                  , mvListeners        = Set.empty
+                  , mvFrozen           = frozen
+                  , mvTwin             = Nothing
+                  }
+  -- printing not available (import cycle)
+  -- reportSDoc "tc.meta.new" 50 $ "new meta" <+> prettyTCM j'
+  insertMetaVar x mv
+  return x
+
+-- | Get the 'Range' for an interaction point.
+{-# SPECIALIZE getInteractionRange :: InteractionId -> TCM Range #-}
+getInteractionRange
+  :: (MonadInteractionPoints m, MonadFail m, MonadError TCErr m)
+  => InteractionId -> m Range
+getInteractionRange = ipRange <.> lookupInteractionPoint
+
+-- | Get the 'Range' for a local meta-variable.
+getMetaRange ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => MetaId -> m Range
+getMetaRange = getRange <.> lookupLocalMeta
+
+getInteractionScope ::
+  (MonadDebug m, MonadFail m, ReadTCState m, MonadError TCErr m,
+   MonadTCEnv m) =>
+  InteractionId -> m ScopeInfo
+getInteractionScope =
+  getMetaScope <.> lookupLocalMeta <=< lookupInteractionId
+
+withMetaInfo' :: (MonadTCEnv m, ReadTCState m, MonadTrace m) => MetaVariable -> m a -> m a
+withMetaInfo' mv = withMetaInfo (miClosRange $ mvInfo mv)
+
+withMetaInfo :: (MonadTCEnv m, ReadTCState m, MonadTrace m) => Closure Range -> m a -> m a
+withMetaInfo mI cont = enterClosure mI $ \ r ->
+  setCurrentRange r cont
+
+withInteractionId ::
+  (MonadDebug m, MonadFail m, ReadTCState m, MonadError TCErr m,
+   MonadTCEnv m, MonadTrace m) =>
+  InteractionId -> m a -> m a
+withInteractionId i ret = do
+  m <- lookupInteractionId i
+  withMetaId m ret
+
+withMetaId ::
+  (HasCallStack, MonadDebug m, MonadTCEnv m, MonadTrace m,
+   ReadTCState m) =>
+  MetaId -> m a -> m a
+withMetaId m ret = do
+  mv <- lookupLocalMeta m
+  withMetaInfo' mv ret
+
+getOpenMetas :: ReadTCState m => m [MetaId]
+getOpenMetas = MapS.keys <$> useR stOpenMetaStore
+
+isOpenMeta :: MetaInstantiation -> Bool
+isOpenMeta Open                           = True
+isOpenMeta OpenInstance                   = True
+isOpenMeta BlockedConst{}                 = True
+isOpenMeta PostponedTypeCheckingProblem{} = True
+isOpenMeta InstV{}                        = False
+
+-- | @listenToMeta l m@: register @l@ as a listener to @m@. This is done
+--   when the type of l is blocked by @m@.
+listenToMeta :: MonadMetaSolver m => Listener -> MetaId -> m ()
+listenToMeta l m =
+  updateMetaVar m $ \mv -> mv { mvListeners = Set.insert l $ mvListeners mv }
+
+-- | Unregister a listener.
+unlistenToMeta :: MonadMetaSolver m => Listener -> MetaId -> m ()
+unlistenToMeta l m =
+  updateMetaVar m $ \mv -> mv { mvListeners = Set.delete l $ mvListeners mv }
+
+-- | Get the listeners for a local meta-variable.
+getMetaListeners ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => MetaId -> m [Listener]
+getMetaListeners m = Set.toList . mvListeners <$> lookupLocalMeta m
+
+clearMetaListeners :: MonadMetaSolver m => MetaId -> m ()
+clearMetaListeners m =
+  updateMetaVar m $ \mv -> mv { mvListeners = Set.empty }
+
+-- | Do safe eta-expansions for meta (@SingletonRecords,Levels@).
+etaExpandMetaSafe :: (MonadMetaSolver m) => MetaId -> m ()
+etaExpandMetaSafe = etaExpandMeta [SingletonRecords,Levels]
+
+-- | Eta expand metavariables listening on the current meta.
+etaExpandListeners :: MonadMetaSolver m => MetaId -> m ()
+etaExpandListeners m = do
+  ls <- getMetaListeners m
+  clearMetaListeners m  -- we don't really have to do this
+  mapM_ wakeupListener ls
+
+-- | Wake up a meta listener and let it do its thing
+wakeupListener :: MonadMetaSolver m => Listener -> m ()
+  -- Andreas 2010-10-15: do not expand record mvars, lazyness needed for irrelevance
+wakeupListener (EtaExpand x)         = etaExpandMetaSafe x
+wakeupListener (CheckConstraint _ c) = do
+  --reportSDoc "tc.meta.blocked" 20 $ "waking boxed constraint" <+> prettyTCM c
+  modifyAwakeConstraints (c:)
+  solveAwakeConstraints
+
+solveAwakeConstraints :: (MonadConstraint m) => m ()
+solveAwakeConstraints = solveAwakeConstraints' False
+
+solveAwakeConstraints' :: (MonadConstraint m) => Bool -> m ()
+solveAwakeConstraints' = solveSomeAwakeConstraints (const True)
+
+---------------------------------------------------------------------------
+-- * Freezing and unfreezing metas.
+---------------------------------------------------------------------------
+
+{-# SPECIALIZE freezeMetas :: LocalMetaStore -> TCM (Set MetaId) #-}
+-- | Freeze the given meta-variables (but only if they are open) and
+-- return those that were not already frozen.
+freezeMetas :: forall m. MonadTCState m => LocalMetaStore -> m (Set MetaId)
+freezeMetas ms =
+  execWriterT $
+  modifyTCLensM stOpenMetaStore $
+  execStateT (mapM_ freeze $ MapS.keys ms)
+  where
+  freeze :: MetaId -> StateT LocalMetaStore (WriterT (Set MetaId) m) ()
+  freeze m = do
+    store <- get
+    case MapS.lookup m store of
+      Just mvar
+        | mvFrozen mvar /= Frozen -> do
+          lift $ tell (Set.singleton m)
+          put $ MapS.insert m (mvar { mvFrozen = Frozen }) store
+        | otherwise -> return ()
+      Nothing -> return ()
+
+-- | Thaw all open meta variables.
+unfreezeMetas :: TCM ()
+unfreezeMetas = stOpenMetaStore `modifyTCLens` MapS.map unfreeze
+  where
+  unfreeze :: MetaVariable -> MetaVariable
+  unfreeze mvar = mvar { mvFrozen = Instantiable }
+
+{-# SPECIALIZE isFrozen :: MetaId -> TCM Bool #-}
+isFrozen ::
+  (HasCallStack, MonadDebug m, ReadTCState m) => MetaId -> m Bool
+isFrozen x = do
+  mvar <- lookupLocalMeta x
+  return $ mvFrozen mvar == Frozen
+
+withFrozenMetas ::
+    (MonadMetaSolver m, MonadTCState m)
+  => m a -> m a
+withFrozenMetas act = do
+  openMetas <- useR stOpenMetaStore
+  frozenMetas <- freezeMetas openMetas
+  result <- act
+  forM_ frozenMetas $ \m ->
+    updateMetaVar m $ \ mv -> mv { mvFrozen = Instantiable }
+  return result
+
+-- | Unfreeze a meta and its type if this is a meta again.
+--   Does not unfreeze deep occurrences of meta-variables or remote
+--   meta-variables.
+class UnFreezeMeta a where
+  unfreezeMeta :: MonadMetaSolver m => a -> m ()
+
+instance UnFreezeMeta MetaId where
+  unfreezeMeta x = unlessM (($ x) <$> isRemoteMeta) $ do
+    updateMetaVar x $ \ mv -> mv { mvFrozen = Instantiable }
+    unfreezeMeta =<< metaType x
+{-# SPECIALIZE unfreezeMeta :: MetaId -> TCM () #-}
+
+instance UnFreezeMeta Type where
+  unfreezeMeta (El s t) = unfreezeMeta s >> unfreezeMeta t
+
+instance UnFreezeMeta Term where
+  unfreezeMeta (MetaV x _)   = unfreezeMeta x
+  unfreezeMeta (Sort s)      = unfreezeMeta s
+  unfreezeMeta (Level l)     = unfreezeMeta l
+  unfreezeMeta (DontCare t)  = unfreezeMeta t
+  unfreezeMeta (Lam _ v)     = unfreezeMeta v
+  unfreezeMeta _             = return ()
+
+instance UnFreezeMeta Sort where
+  unfreezeMeta (MetaS x _)   = unfreezeMeta x
+  unfreezeMeta _             = return ()
+
+instance UnFreezeMeta Level where
+  unfreezeMeta (Max _ ls)      = unfreezeMeta ls
+
+instance UnFreezeMeta PlusLevel where
+  unfreezeMeta (Plus _ a)    = unfreezeMeta a
+
+instance UnFreezeMeta a => UnFreezeMeta [a] where
+  unfreezeMeta = mapM_ unfreezeMeta
+
+instance UnFreezeMeta a => UnFreezeMeta (Abs a) where
+  unfreezeMeta = Fold.mapM_ unfreezeMeta
diff --git a/src/full/Agda/TypeChecking/Monad/MetaVars.hs-boot b/src/full/Agda/TypeChecking/Monad/MetaVars.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/MetaVars.hs-boot
@@ -0,0 +1,32 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.MetaVars where
+
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Identity ( IdentityT )
+
+import Agda.Syntax.Common (InteractionId, MetaId)
+import Agda.TypeChecking.Monad.Base
+
+class (MonadTCEnv m, ReadTCState m) => MonadInteractionPoints m where
+  freshInteractionId :: m InteractionId
+  modifyInteractionPoints :: (InteractionPoints -> InteractionPoints) -> m ()
+
+  default freshInteractionId
+    :: (MonadTrans t, MonadInteractionPoints n, t n ~ m)
+    => m InteractionId
+  freshInteractionId = lift freshInteractionId
+
+  default modifyInteractionPoints
+    :: (MonadTrans t, MonadInteractionPoints n, t n ~ m)
+    => (InteractionPoints -> InteractionPoints) -> m ()
+  modifyInteractionPoints = lift . modifyInteractionPoints
+
+instance MonadInteractionPoints m => MonadInteractionPoints (IdentityT m)
+instance MonadInteractionPoints m => MonadInteractionPoints (ReaderT r m)
+instance MonadInteractionPoints m => MonadInteractionPoints (StateT s m)
+
+instance MonadInteractionPoints TCM
+
+isInteractionMeta :: ReadTCState m => MetaId -> m (Maybe InteractionId)
diff --git a/src/full/Agda/TypeChecking/Monad/Modality.hs b/src/full/Agda/TypeChecking/Monad/Modality.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Modality.hs
@@ -0,0 +1,202 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{- | Modality.
+
+Agda has support for several modalities, namely:
+
+ * 'Cohesion'
+ * 'Quantity'
+ * 'Relevance'
+
+In order to type check such modalities, we must store the current modality in
+the typing context. This module provides functions to update the context based
+on a given modality.
+
+See "Agda.TypeChecking.Irrelevance".
+-}
+
+module Agda.TypeChecking.Monad.Modality where
+
+import qualified Data.Map as Map
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Env
+
+import Agda.Utils.Function
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+
+-- | data 'Relevance'
+--   see "Agda.Syntax.Common".
+
+-- * Operations on 'Dom'.
+
+-- | Prepare parts of a parameter telescope for abstraction in constructors
+--   and projections.
+hideAndRelParams :: (LensHiding a, LensRelevance a) => a -> a
+hideAndRelParams = hideOrKeepInstance . mapRelevance nonStrictToIrr
+
+-- * Operations on 'Context'.
+
+-- | Modify the context whenever going from the l.h.s. (term side)
+--   of the typing judgement to the r.h.s. (type side).
+workOnTypes :: (MonadTCEnv m, HasOptions m, MonadDebug m)
+            => m a -> m a
+workOnTypes cont = do
+  allowed <- optExperimentalIrrelevance <$> pragmaOptions
+  verboseBracket "tc.irr" 60 "workOnTypes" $ workOnTypes' allowed cont
+
+-- | Internal workhorse, expects value of --experimental-irrelevance flag
+--   as argument.
+workOnTypes' :: (MonadTCEnv m) => Bool -> m a -> m a
+workOnTypes' experimental
+  = applyWhen experimental (modifyContextInfo $ mapRelevance irrToNonStrict)
+  . applyQuantityToJudgement zeroQuantity
+  . typeLevelReductions
+  . localTC (\ e -> e { envWorkingOnTypes = True })
+
+-- | (Conditionally) wake up irrelevant variables and make them relevant.
+--   For instance,
+--   in an irrelevant function argument otherwise irrelevant variables
+--   may be used, so they are awoken before type checking the argument.
+--
+--   Also allow the use of irrelevant definitions.
+applyRelevanceToContext :: (MonadTCEnv tcm, LensRelevance r) => r -> tcm a -> tcm a
+applyRelevanceToContext thing =
+  case getRelevance thing of
+    Relevant -> id
+    rel      -> applyRelevanceToContextOnly   rel
+              . applyRelevanceToJudgementOnly rel
+
+-- | (Conditionally) wake up irrelevant variables and make them relevant.
+--   For instance,
+--   in an irrelevant function argument otherwise irrelevant variables
+--   may be used, so they are awoken before type checking the argument.
+--
+--   Precondition: @Relevance /= Relevant@
+applyRelevanceToContextOnly :: (MonadTCEnv tcm) => Relevance -> tcm a -> tcm a
+applyRelevanceToContextOnly rel = localTC
+  $ over eContext     (map $ inverseApplyRelevance rel)
+  . over eLetBindings (Map.map . fmap . onLetBindingType $ inverseApplyRelevance rel)
+
+-- | Apply relevance @rel@ the the relevance annotation of the (typing/equality)
+--   judgement.  This is part of the work done when going into a @rel@-context.
+--
+--   Precondition: @Relevance /= Relevant@
+applyRelevanceToJudgementOnly :: (MonadTCEnv tcm) => Relevance -> tcm a -> tcm a
+applyRelevanceToJudgementOnly = localTC . over eRelevance . composeRelevance
+
+-- | Like 'applyRelevanceToContext', but only act on context if
+--   @--irrelevant-projections@.
+--   See issue #2170.
+applyRelevanceToContextFunBody :: (MonadTCM tcm, LensRelevance r) => r -> tcm a -> tcm a
+applyRelevanceToContextFunBody thing cont =
+  case getRelevance thing of
+    Relevant -> cont
+    rel -> applyWhenM (optIrrelevantProjections <$> pragmaOptions)
+      (applyRelevanceToContextOnly rel) $    -- enable local irr. defs only when option
+      applyRelevanceToJudgementOnly rel cont -- enable global irr. defs alway
+
+-- | Apply the quantity to the quantity annotation of the
+-- (typing/equality) judgement.
+--
+-- Precondition: The quantity must not be @'Quantity1' something@.
+applyQuantityToJudgement ::
+  (MonadTCEnv tcm, LensQuantity q) => q -> tcm a -> tcm a
+applyQuantityToJudgement =
+  localTC . over eQuantity . composeQuantity . getQuantity
+
+-- | Apply inverse composition with the given cohesion to the typing context.
+applyCohesionToContext :: (MonadTCEnv tcm, LensCohesion m) => m -> tcm a -> tcm a
+applyCohesionToContext thing =
+  case getCohesion thing of
+    m | m == unitCohesion -> id
+      | otherwise         -> applyCohesionToContextOnly   m
+                             -- Cohesion does not apply to the judgment.
+
+applyCohesionToContextOnly :: (MonadTCEnv tcm) => Cohesion -> tcm a -> tcm a
+applyCohesionToContextOnly q = localTC
+  $ over eContext     (map $ inverseApplyCohesion q)
+  . over eLetBindings (Map.map . fmap . onLetBindingType $ inverseApplyCohesion q)
+
+-- | Can we split on arguments of the given cohesion?
+splittableCohesion :: (HasOptions m, LensCohesion a) => a -> m Bool
+splittableCohesion a = do
+  let c = getCohesion a
+  pure (usableCohesion c) `and2M` (pure (c /= Flat) `or2M` do optFlatSplit <$> pragmaOptions)
+
+
+{-# SPECIALIZE applyModalityToContext :: Modality -> TCM a -> TCM a #-}
+-- | (Conditionally) wake up irrelevant variables and make them relevant.
+--   For instance,
+--   in an irrelevant function argument otherwise irrelevant variables
+--   may be used, so they are awoken before type checking the argument.
+--
+--   Also allow the use of irrelevant definitions.
+--
+--   This function might also do something for other modalities.
+applyModalityToContext :: (MonadTCEnv tcm, LensModality m) => m -> tcm a -> tcm a
+applyModalityToContext thing =
+  case getModality thing of
+    m | m == unitModality -> id
+      | otherwise         -> applyModalityToContextOnly   m
+                           . applyModalityToJudgementOnly m
+
+-- | (Conditionally) wake up irrelevant variables and make them relevant.
+--   For instance,
+--   in an irrelevant function argument otherwise irrelevant variables
+--   may be used, so they are awoken before type checking the
+--   argument.
+--
+--   This function might also do something for other modalities, but
+--   not for quantities.
+--
+--   Precondition: @Modality /= Relevant@
+applyModalityToContextOnly :: (MonadTCEnv tcm) => Modality -> tcm a -> tcm a
+applyModalityToContextOnly m = localTC
+  $ over eContext (map $ inverseApplyModalityButNotQuantity m)
+  . over eLetBindings
+      (Map.map . fmap . onLetBindingType $ inverseApplyModalityButNotQuantity m)
+
+-- | Apply the relevance and quantity components of the modality to
+-- the modality annotation of the (typing/equality) judgement.
+--
+-- Precondition: The relevance component must not be 'Relevant'.
+applyModalityToJudgementOnly :: (MonadTCEnv tcm) => Modality -> tcm a -> tcm a
+applyModalityToJudgementOnly m =
+  localTC $ over eRelevance (composeRelevance (getRelevance m)) .
+            over eQuantity  (composeQuantity  (getQuantity m))
+
+-- | Like 'applyModalityToContext', but only act on context (for Relevance) if
+--   @--irrelevant-projections@.
+--   See issue #2170.
+applyModalityToContextFunBody :: (MonadTCM tcm, LensModality r) => r -> tcm a -> tcm a
+applyModalityToContextFunBody thing cont = do
+    ifM (optIrrelevantProjections <$> pragmaOptions)
+      {-then-} (applyModalityToContext m cont)                -- enable global irr. defs always
+      {-else-} (applyRelevanceToContextFunBody (getRelevance m)
+               $ applyCohesionToContext (getCohesion m)
+               $ applyQuantityToJudgement (getQuantity m) cont) -- enable local irr. defs only when option
+  where
+    m = getModality thing
+
+-- | Wake up irrelevant variables and make them relevant. This is used
+--   when type checking terms in a hole, in which case you want to be able to
+--   (for instance) infer the type of an irrelevant variable. In the course
+--   of type checking an irrelevant function argument 'applyRelevanceToContext'
+--   is used instead, which also sets the context relevance to 'Irrelevant'.
+--   This is not the right thing to do when type checking interactively in a
+--   hole since it also marks all metas created during type checking as
+--   irrelevant (issue #2568).
+--
+--   Also set the current quantity to 0.
+wakeIrrelevantVars :: (MonadTCEnv tcm) => tcm a -> tcm a
+wakeIrrelevantVars
+  = applyRelevanceToContextOnly Irrelevant
+  . applyQuantityToJudgement zeroQuantity
diff --git a/src/full/Agda/TypeChecking/Monad/Mutual.hs b/src/full/Agda/TypeChecking/Monad/Mutual.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Mutual.hs
@@ -0,0 +1,80 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Mutual where
+
+import Prelude hiding (null)
+
+
+
+
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+
+import Agda.Syntax.Info as Info
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.State
+
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( prettyShow )
+
+noMutualBlock :: TCM a -> TCM a
+noMutualBlock = localTC $ \e -> e { envMutualBlock = Nothing }
+
+-- | Pass the current mutual block id
+--   or create a new mutual block if we are not already inside on.
+inMutualBlock :: (MutualId -> TCM a) -> TCM a
+inMutualBlock m = do
+  mi <- asksTC envMutualBlock
+  case mi of
+    Nothing -> do
+      i <- fresh
+      localTC (\ e -> e { envMutualBlock = Just i }) $ m i
+    -- Don't create a new mutual block if we're already inside one.
+    Just i -> m i
+
+-- | Set the mutual block info for a block,
+--   possibly overwriting the existing one.
+
+setMutualBlockInfo :: MutualId -> Info.MutualInfo -> TCM ()
+setMutualBlockInfo mi info = stMutualBlocks `modifyTCLens` Map.alter f mi
+  where
+  f Nothing                   = Just $ MutualBlock info empty
+  f (Just (MutualBlock _ xs)) = Just $ MutualBlock info xs
+
+-- | Set the mutual block info for a block if non-existing.
+
+insertMutualBlockInfo :: MutualId -> Info.MutualInfo -> TCM ()
+insertMutualBlockInfo mi info = stMutualBlocks `modifyTCLens` Map.alter f mi
+  where
+  f Nothing = Just $ MutualBlock info empty
+  f (Just mb@(MutualBlock info0 xs))
+    | null info0 = Just $ MutualBlock info xs
+    | otherwise  = Just mb
+
+-- | Set the mutual block for a definition.
+
+setMutualBlock :: MutualId -> QName -> TCM ()
+setMutualBlock i x = do
+  stMutualBlocks `modifyTCLens` Map.alter f i
+  stSignature    `modifyTCLens` updateDefinition x (\ defn -> defn { defMutual = i })
+  where
+  f Nothing                    = Just $ MutualBlock empty $ Set.singleton x
+  f (Just (MutualBlock mi xs)) = Just $ MutualBlock mi $ Set.insert x xs
+
+-- | Get the current mutual block, if any, otherwise a fresh mutual
+-- block is returned.
+currentOrFreshMutualBlock :: TCM MutualId
+currentOrFreshMutualBlock = maybe fresh return =<< asksTC envMutualBlock
+
+lookupMutualBlock :: ReadTCState tcm => MutualId -> tcm MutualBlock
+lookupMutualBlock mi = Map.findWithDefault empty mi <$> useTC stMutualBlocks
+   -- can be empty if we ask for the current mutual block and there is none
+
+-- | Reverse lookup of a mutual block id for a name.
+mutualBlockOf :: QName -> TCM MutualId
+mutualBlockOf x = do
+  mb <- Map.toList <$> useTC stMutualBlocks
+  case filter (Set.member x . mutualNames . snd) mb of
+    (i, _) : _ -> return i
+    _          -> fail $ "No mutual block for " ++ prettyShow x
diff --git a/src/full/Agda/TypeChecking/Monad/Open.hs b/src/full/Agda/TypeChecking/Monad/Open.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Open.hs
@@ -0,0 +1,69 @@
+
+module Agda.TypeChecking.Monad.Open
+        ( makeOpen
+        , getOpen
+        , tryGetOpen
+        , isClosed
+        ) where
+
+import Control.Applicative
+import Control.Monad.Trans
+import Control.Monad.Trans.Maybe
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.State (currentModuleNameHash)
+
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Context
+
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+
+-- | Create an open term in the current context.
+makeOpen :: (ReadTCState m, MonadTCEnv m) => a -> m (Open a)
+makeOpen x = do
+    cp  <- viewTC eCurrentCheckpoint
+    env <- viewTC eCheckpoints
+    m   <- currentModuleNameHash
+    return $ OpenThing cp env m x
+
+-- | Extract the value from an open term. The checkpoint at which it was
+--   created must be in scope.
+getOpen :: (TermSubst a, MonadTCEnv m) => Open a -> m a
+getOpen (OpenThing cp _ _ x) = do
+  sub <- checkpointSubstitution cp
+  return $ applySubst sub x
+
+-- | Extract the value from an open term. If the checkpoint is no longer in scope use the provided
+--   function to pull the object to the most recent common checkpoint. The function is given the
+--   substitution from the common ancestor to the checkpoint of the thing.
+tryGetOpen :: (TermSubst a, ReadTCState m, MonadTCEnv m) => (Substitution -> a -> Maybe a) -> Open a -> m (Maybe a)
+tryGetOpen extract open = do
+  OpenThing cp env _ x <- restrict open -- Strip the env if from another module
+  runMaybeT $ do
+      (`applySubst` x) <$> (liftMaybe =<< viewTC (eCheckpoints . key cp))
+    <|> do  -- Checkpoint no longer in scope
+      curEnv <- lift $ viewTC eCheckpoints
+      parent <- findParent env curEnv
+      let Just subToOld = Map.lookup parent env
+          Just subToCur = Map.lookup parent curEnv
+      (applySubst subToCur) <$> liftMaybe (extract subToOld x)
+  where
+    -- If this comes from a different file, the checkpoints refer to checkpoints in that file and
+    -- not in the current file. To avoid confusing them we set the checkpoint to -1 and only keep
+    -- checkpoint 0 (which is shared between files) in the environment.
+    restrict o@(OpenThing cp env m x) = do
+      cur <- currentModuleNameHash
+      if m == cur then return o
+                  else return $ OpenThing (-1) (Map.filterWithKey (\ k _ -> k == 0) env) m x
+
+    findParent m1 m2 = case Map.lookupMax (Map.intersection m1 m2) of
+      Nothing       -> empty
+      Just (max, _) -> return max
+
+-- | An 'Open' is closed if it has checkpoint 0.
+isClosed :: Open a -> Bool
+isClosed (OpenThing cp _ _ _) = cp == 0
diff --git a/src/full/Agda/TypeChecking/Monad/Options.hs b/src/full/Agda/TypeChecking/Monad/Options.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Options.hs
@@ -0,0 +1,455 @@
+
+module Agda.TypeChecking.Monad.Options where
+
+import Prelude hiding (null)
+
+import Control.Monad          ( unless, when )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Writer
+
+import qualified Data.Graph as Graph
+import Data.List (sort)
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import System.Directory
+import System.FilePath
+
+import Agda.Syntax.Common
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Monad.Debug (reportSDoc)
+import Agda.TypeChecking.Warnings
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Imports
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Monad.Benchmark
+import Agda.TypeChecking.Monad.Trace
+
+import Agda.Interaction.FindFile
+import Agda.Interaction.Options
+import qualified Agda.Interaction.Options.Lenses as Lens
+import Agda.Interaction.Library
+import Agda.Interaction.Library.Base (libAbove, libFile)
+
+import Agda.Utils.FileName
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as G
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+import Agda.Utils.WithDefault
+
+import Agda.Utils.Impossible
+
+-- | Sets the pragma options.
+--   Checks for unsafe combinations.
+setPragmaOptions :: PragmaOptions -> TCM ()
+setPragmaOptions opts = do
+  -- Check for unsafe pragma options if @--safe@ is on.
+  when (Lens.getSafeMode opts) $
+    unlessNull (unsafePragmaOptions opts) $ \ unsafe ->
+      warning $ SafeFlagPragma unsafe
+
+  stPragmaOptions `setTCLens` opts
+  updateBenchmarkingStatus
+
+-- | Sets the command line options (both persistent and pragma options
+-- are updated).
+--
+-- Relative include directories are made absolute with respect to the
+-- current working directory. If the include directories have changed
+-- then the state is reset (partly, see 'setIncludeDirs').
+--
+-- An empty list of relative include directories (@'Left' []@) is
+-- interpreted as @["."]@.
+setCommandLineOptions :: CommandLineOptions -> TCM ()
+setCommandLineOptions opts = do
+  root <- liftIO (absolute =<< getCurrentDirectory)
+  setCommandLineOptions' root opts
+
+setCommandLineOptions'
+  :: AbsolutePath
+     -- ^ The base directory of relative paths.
+  -> CommandLineOptions
+  -> TCM ()
+setCommandLineOptions' root opts = do
+  -- Andreas, 2022-11-19: removed a call to checkOpts which did nothing.
+      incs <- case optAbsoluteIncludePaths opts of
+        [] -> do
+          opts' <- setLibraryPaths root opts
+          let incs = optIncludePaths opts'
+          setIncludeDirs incs root
+          getIncludeDirs
+        incs -> return incs
+      modifyTC $ Lens.setCommandLineOptions opts{ optAbsoluteIncludePaths = incs }
+      setPragmaOptions (optPragmaOptions opts)
+      updateBenchmarkingStatus
+
+libToTCM :: LibM a -> TCM a
+libToTCM m = do
+  cachedConfs <- useTC stProjectConfigs
+  cachedLibs  <- useTC stAgdaLibFiles
+
+  ((z, warns), (cachedConfs', cachedLibs')) <- liftIO $
+    (`runStateT` (cachedConfs, cachedLibs)) $ runWriterT $ runExceptT m
+
+  modifyTCLens stProjectConfigs $ const cachedConfs'
+  modifyTCLens stAgdaLibFiles   $ const cachedLibs'
+
+  unless (null warns) $ warnings $ map LibraryWarning warns
+  case z of
+    Left s  -> typeError $ GenericDocError s
+    Right x -> return x
+
+-- | Returns the library files for a given file.
+--
+-- Nothing is returned if 'optUseLibs' is 'False'.
+--
+-- An error is raised if 'optUseLibs' is 'True' and a library file is
+-- located too far down the directory hierarchy (see
+-- 'checkLibraryFileNotTooFarDown').
+
+getAgdaLibFiles
+  :: AbsolutePath        -- ^ The file name.
+  -> TopLevelModuleName  -- ^ The top-level module name.
+  -> TCM [AgdaLibFile]
+getAgdaLibFiles f m = do
+  ls <- getAgdaLibFilesWithoutTopLevelModuleName f
+  mapM_ (checkLibraryFileNotTooFarDown m) ls
+  return ls
+
+-- | Returns potential library files for a file without a known
+-- top-level module name.
+--
+-- Once the top-level module name is known one can use
+-- 'checkLibraryFileNotTooFarDown' to check that the potential library
+-- files were not located too far down the directory hierarchy.
+--
+-- Nothing is returned if 'optUseLibs' is 'False'.
+
+getAgdaLibFilesWithoutTopLevelModuleName
+  :: AbsolutePath  -- ^ The file.
+  -> TCM [AgdaLibFile]
+getAgdaLibFilesWithoutTopLevelModuleName f = do
+  useLibs <- optUseLibs <$> commandLineOptions
+  if | useLibs   -> libToTCM $ mkLibM [] $ getAgdaLibFiles' root
+     | otherwise -> return []
+  where
+  root = takeDirectory $ filePath f
+
+-- | Checks that a library file for the module @A.B.C@ (say) in the
+-- directory @dir/A/B@ is located at least two directories above the
+-- file (not in @dir/A@ or @dir/A/B@).
+
+checkLibraryFileNotTooFarDown ::
+  TopLevelModuleName ->
+  AgdaLibFile ->
+  TCM ()
+checkLibraryFileNotTooFarDown m lib =
+  when (lib ^. libAbove < size m - 1) $ typeError $ GenericError $
+    "A .agda-lib file for " ++ prettyShow m ++
+    " must not be located in the directory " ++
+    takeDirectory (lib ^. libFile)
+
+-- | Returns the library options for a given file.
+
+getLibraryOptions
+  :: AbsolutePath        -- ^ The file name.
+  -> TopLevelModuleName  -- ^ The top-level module name.
+  -> TCM [OptionsPragma]
+getLibraryOptions f m = map _libPragmas <$> getAgdaLibFiles f m
+
+setLibraryPaths
+  :: AbsolutePath
+     -- ^ The base directory of relative paths.
+  -> CommandLineOptions
+  -> TCM CommandLineOptions
+setLibraryPaths root o =
+  setLibraryIncludes =<< addDefaultLibraries root o
+
+setLibraryIncludes :: CommandLineOptions -> TCM CommandLineOptions
+setLibraryIncludes o
+  | not (optUseLibs o) = pure o
+  | otherwise = do
+    let libs = optLibraries o
+    installed <- libToTCM $ getInstalledLibraries (optOverrideLibrariesFile o)
+    paths     <- libToTCM $ libraryIncludePaths (optOverrideLibrariesFile o) installed libs
+    return o{ optIncludePaths = paths ++ optIncludePaths o }
+
+addDefaultLibraries
+  :: AbsolutePath
+     -- ^ The base directory of relative paths.
+  -> CommandLineOptions
+  -> TCM CommandLineOptions
+addDefaultLibraries root o
+  | not (null $ optLibraries o) || not (optUseLibs o) = pure o
+  | otherwise = do
+  (libs, incs) <- libToTCM $ getDefaultLibraries (filePath root) (optDefaultLibs o)
+  return o{ optIncludePaths = incs ++ optIncludePaths o, optLibraries = libs }
+
+-- This function is only called when an interactor exists
+-- (i.e. when Agda actually does something).
+addTrustedExecutables
+  :: CommandLineOptions
+  -> TCM CommandLineOptions
+addTrustedExecutables o = do
+  trustedExes <- libToTCM $ getTrustedExecutables
+  -- Wen, 2020-06-03
+  -- Replace the map wholesale instead of computing the union because this function
+  -- should never be called more than once, and doing so either has the same result
+  -- or is a security risk.
+  return o{ optTrustedExecutables = trustedExes }
+
+setOptionsFromPragma :: OptionsPragma -> TCM ()
+setOptionsFromPragma ps = setCurrentRange (pragmaRange ps) $ do
+    opts <- commandLineOptions
+    let (z, warns) = runOptM (parsePragmaOptions ps opts)
+    mapM_ (warning . OptionWarning) warns
+    case z of
+      Left err    -> typeError $ GenericError err
+      Right opts' -> setPragmaOptions opts'
+
+-- | Disable display forms.
+enableDisplayForms :: MonadTCEnv m => m a -> m a
+enableDisplayForms =
+  localTC $ \e -> e { envDisplayFormsEnabled = True }
+
+-- | Disable display forms.
+disableDisplayForms :: MonadTCEnv m => m a -> m a
+disableDisplayForms =
+  localTC $ \e -> e { envDisplayFormsEnabled = False }
+
+-- | Check if display forms are enabled.
+displayFormsEnabled :: MonadTCEnv m => m Bool
+displayFormsEnabled = asksTC envDisplayFormsEnabled
+
+-- | Gets the include directories.
+--
+-- Precondition: 'optAbsoluteIncludePaths' must be nonempty (i.e.
+-- 'setCommandLineOptions' must have run).
+
+getIncludeDirs :: HasOptions m => m [AbsolutePath]
+getIncludeDirs = do
+  incs <- optAbsoluteIncludePaths <$> commandLineOptions
+  case incs of
+    [] -> __IMPOSSIBLE__
+    _  -> return incs
+
+-- | Makes the given directories absolute and stores them as include
+-- directories.
+--
+-- If the include directories change, then the state is reset
+-- (completely, except for the include directories and some other
+-- things).
+--
+-- An empty list is interpreted as @["."]@.
+
+setIncludeDirs :: [FilePath]    -- ^ New include directories.
+               -> AbsolutePath  -- ^ The base directory of relative paths.
+               -> TCM ()
+setIncludeDirs incs root = do
+  -- save the previous include dirs
+  oldIncs <- getsTC Lens.getAbsoluteIncludePaths
+
+  -- Add the current dir if no include path is given
+  incs <- return $ if null incs then ["."] else incs
+  -- Make paths absolute
+  incs <- return $  map (mkAbsolute . (filePath root </>)) incs
+
+  -- Andreas, 2013-10-30  Add default include dir
+      -- NB: This is an absolute file name, but
+      -- Agda.Utils.FilePath wants to check absoluteness anyway.
+  primdir <- liftIO $ mkAbsolute <$> getPrimitiveLibDir
+      -- We add the default dir at the end, since it is then
+      -- printed last in error messages.
+      -- Might also be useful to overwrite default imports...
+  incs <- return $ nubOn id $ incs ++ [primdir]
+
+  reportSDoc "setIncludeDirs" 10 $ return $ vcat
+    [ "Old include directories:"
+    , nest 2 $ vcat $ map pretty oldIncs
+    , "New include directories:"
+    , nest 2 $ vcat $ map pretty incs
+    ]
+
+  -- Check whether the include dirs have changed.  If yes, reset state.
+  -- Andreas, 2013-10-30 comments:
+  -- The logic, namely using the include-dirs variable as a driver
+  -- for the interaction, qualifies for a code-obfuscation contest.
+  -- I guess one Boolean more in the state cost 10.000 EUR at the time
+  -- of this implementation...
+  --
+  -- Andreas, perhaps you have misunderstood something: If the include
+  -- directories have changed and we do not reset the decoded modules,
+  -- then we might (depending on how the rest of the code works) end
+  -- up in a situation in which we use the contents of the file
+  -- "old-path/M.agda", when the user actually meant
+  -- "new-path/M.agda".
+  when (sort oldIncs /= sort incs) $ do
+    ho <- getInteractionOutputCallback
+    tcWarnings <- useTC stTCWarnings -- restore already generated warnings
+    projectConfs <- useTC stProjectConfigs  -- restore cached project configs & .agda-lib
+    agdaLibFiles <- useTC stAgdaLibFiles    -- files, since they use absolute paths
+    decodedModules <- getDecodedModules
+    (keptDecodedModules, modFile) <- modulesToKeep incs decodedModules
+    resetAllState
+    setTCLens stTCWarnings tcWarnings
+    setTCLens stProjectConfigs projectConfs
+    setTCLens stAgdaLibFiles agdaLibFiles
+    setInteractionOutputCallback ho
+    setDecodedModules keptDecodedModules
+    setTCLens stModuleToSource modFile
+
+  Lens.putAbsoluteIncludePaths incs
+  where
+  -- A decoded module is kept if its top-level module name is resolved
+  -- to the same absolute path using the old and the new include
+  -- directories, and the same applies to all dependencies.
+  --
+  -- File system accesses are cached using the ModuleToSource data
+  -- structure: For the old include directories this should mean that
+  -- the file system is not accessed, but the file system is accessed
+  -- for the new include directories, and certain changes to the file
+  -- system could lead to interfaces being discarded. A new
+  -- ModuleToSource structure, constructed using the new include
+  -- directories, is returned.
+  modulesToKeep
+    :: [AbsolutePath]  -- New include directories.
+    -> DecodedModules  -- Old decoded modules.
+    -> TCM (DecodedModules, ModuleToSource)
+  modulesToKeep incs old = process Map.empty Map.empty modules
+    where
+    -- A graph with one node per module in old, and an edge from m to
+    -- n if the module corresponding to m imports the module
+    -- corresponding to n.
+    dependencyGraph :: G.Graph TopLevelModuleName ()
+    dependencyGraph =
+      G.fromNodes
+        [ iTopLevelModuleName $ miInterface m
+        | m <- Map.elems old
+        ]
+        `G.union`
+      G.fromEdges
+        [ G.Edge
+            { source = iTopLevelModuleName $ miInterface m
+            , target = d
+            , label = ()
+            }
+        | m      <- Map.elems old
+        , (d, _) <- iImportedModules $ miInterface m
+        ]
+
+    -- All the modules from old, sorted so that all of a module's
+    -- dependencies precede it in the list.
+    modules :: [ModuleInfo]
+    modules =
+      map (\case
+              Graph.CyclicSCC{} ->
+                -- Agda does not allow cycles in the dependency graph.
+                __IMPOSSIBLE__
+              Graph.AcyclicSCC m ->
+                case Map.lookup m old of
+                  Just m  -> m
+                  Nothing -> __IMPOSSIBLE__) $
+      G.sccs' dependencyGraph
+
+    process ::
+      Map TopLevelModuleName ModuleInfo -> ModuleToSource ->
+      [ModuleInfo] -> TCM (DecodedModules, ModuleToSource)
+    process !keep !modFile [] = return
+      ( Map.fromList $
+        Map.toList keep
+      , modFile
+      )
+    process keep modFile (m : ms) = do
+      let deps     = map fst $ iImportedModules $ miInterface m
+          depsKept = all (`Map.member` keep) deps
+      (keep, modFile) <-
+        if not depsKept then return (keep, modFile) else do
+        let t = iTopLevelModuleName $ miInterface m
+        oldF            <- findFile' t
+        (newF, modFile) <- liftIO $ findFile'' incs t modFile
+        return $ case (oldF, newF) of
+          (Right f1, Right f2) | f1 == f2 ->
+            (Map.insert t m keep, modFile)
+          _ -> (keep, modFile)
+      process keep modFile ms
+
+isPropEnabled :: HasOptions m => m Bool
+isPropEnabled = optProp <$> pragmaOptions
+
+isLevelUniverseEnabled :: HasOptions m => m Bool
+isLevelUniverseEnabled = optLevelUniverse <$> pragmaOptions
+
+isTwoLevelEnabled :: HasOptions m => m Bool
+isTwoLevelEnabled = optTwoLevel <$> pragmaOptions
+
+{-# SPECIALIZE hasUniversePolymorphism :: TCM Bool #-}
+hasUniversePolymorphism :: HasOptions m => m Bool
+hasUniversePolymorphism = optUniversePolymorphism <$> pragmaOptions
+
+showImplicitArguments :: HasOptions m => m Bool
+showImplicitArguments = optShowImplicit <$> pragmaOptions
+
+showGeneralizedArguments :: HasOptions m => m Bool
+showGeneralizedArguments = (\opt -> optShowGeneralized opt) <$> pragmaOptions
+
+showIrrelevantArguments :: HasOptions m => m Bool
+showIrrelevantArguments = optShowIrrelevant <$> pragmaOptions
+
+showIdentitySubstitutions :: HasOptions m => m Bool
+showIdentitySubstitutions = optShowIdentitySubstitutions <$> pragmaOptions
+
+-- | Switch on printing of implicit and irrelevant arguments.
+--   E.g. for reification in with-function generation.
+--
+--   Restores all 'PragmaOptions' after completion.
+--   Thus, do not attempt to make persistent 'PragmaOptions'
+--   changes in a `withShowAllArguments` bracket.
+
+withShowAllArguments :: ReadTCState m => m a -> m a
+withShowAllArguments = withShowAllArguments' True
+
+withShowAllArguments' :: ReadTCState m => Bool -> m a -> m a
+withShowAllArguments' yes = withPragmaOptions $ \ opts ->
+  opts { _optShowImplicit = Value yes, _optShowIrrelevant = Value yes }
+
+withoutPrintingGeneralization :: ReadTCState m => m a -> m a
+withoutPrintingGeneralization = withPragmaOptions $ \ opts ->
+  opts { _optShowGeneralized = Value False }
+
+-- | Change 'PragmaOptions' for a computation and restore afterwards.
+withPragmaOptions :: ReadTCState m => (PragmaOptions -> PragmaOptions) -> m a -> m a
+withPragmaOptions = locallyTCState stPragmaOptions
+
+positivityCheckEnabled :: HasOptions m => m Bool
+positivityCheckEnabled = optPositivityCheck <$> pragmaOptions
+
+{-# SPECIALIZE typeInType :: TCM Bool #-}
+typeInType :: HasOptions m => m Bool
+typeInType = not . optUniverseCheck <$> pragmaOptions
+
+etaEnabled :: HasOptions m => m Bool
+etaEnabled = optEta <$> pragmaOptions
+
+maxInstanceSearchDepth :: HasOptions m => m Int
+maxInstanceSearchDepth = optInstanceSearchDepth <$> pragmaOptions
+
+maxInversionDepth :: HasOptions m => m Int
+maxInversionDepth = optInversionMaxDepth <$> pragmaOptions
+
+-- | Returns the 'Language' currently in effect.
+
+getLanguage :: HasOptions m => m Language
+getLanguage = do
+  opts <- pragmaOptions
+  return $
+    if not (optWithoutK opts) then WithK else
+    case optCubical opts of
+      Just variant -> Cubical variant
+      Nothing      -> WithoutK
diff --git a/src/full/Agda/TypeChecking/Monad/Options.hs-boot b/src/full/Agda/TypeChecking/Monad/Options.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Options.hs-boot
@@ -0,0 +1,11 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Options where
+
+import Agda.Interaction.Library.Base
+import Agda.Interaction.Options.HasOptions
+import Agda.TypeChecking.Monad.Base
+import Agda.Utils.FileName
+
+libToTCM       :: LibM a -> TCM a
+getIncludeDirs :: HasOptions m => m [AbsolutePath]
diff --git a/src/full/Agda/TypeChecking/Monad/Pure.hs b/src/full/Agda/TypeChecking/Monad/Pure.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Pure.hs
@@ -0,0 +1,45 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | A typeclass collecting all 'pure' typechecking operations
+-- | (i.e. ones that do not modify the typechecking state, throw or
+-- | catch errors, or do IO other than debug printing).
+
+
+module Agda.TypeChecking.Monad.Pure where
+
+import Control.Monad.Except ( ExceptT )
+import Control.Monad.Trans.Maybe ( MaybeT )
+import Control.Monad.Reader ( ReaderT )
+import Control.Monad.State ( StateT )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Writer ( WriterT )
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Signature
+
+import Agda.Utils.ListT
+import Agda.Utils.Update
+
+class
+  ( HasBuiltins m
+  , HasConstInfo m
+  , MonadAddContext m
+  , MonadDebug m
+  , MonadReduce m
+  , MonadTCEnv m
+  , ReadTCState m
+  ) => PureTCM m where
+
+instance PureTCM TCM where
+instance PureTCM m => PureTCM (BlockT m)
+instance PureTCM m => PureTCM (ChangeT m)
+instance PureTCM m => PureTCM (ExceptT e m)
+instance PureTCM m => PureTCM (IdentityT m)
+instance PureTCM m => PureTCM (ListT m)
+instance PureTCM m => PureTCM (MaybeT m)
+instance PureTCM m => PureTCM (ReaderT r m)
+instance (PureTCM m, Monoid w) => PureTCM (WriterT w m)
+instance PureTCM m => PureTCM (StateT s m)
diff --git a/src/full/Agda/TypeChecking/Monad/Pure.hs-boot b/src/full/Agda/TypeChecking/Monad/Pure.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Pure.hs-boot
@@ -0,0 +1,30 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Pure where
+
+import Control.Monad.Reader ( ReaderT )
+import Control.Monad.State ( StateT )
+import Control.Monad.Trans.Identity ( IdentityT )
+import Control.Monad.Writer ( WriterT )
+
+import Agda.TypeChecking.Monad.Base
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Builtin
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Signature
+
+class
+  ( HasBuiltins m
+  , HasConstInfo m
+  , MonadAddContext m
+  , MonadDebug m
+  , MonadReduce m
+  , MonadTCEnv m
+  , ReadTCState m
+  ) => PureTCM m where
+
+instance PureTCM TCM where
+instance PureTCM m => PureTCM (IdentityT m)
+instance PureTCM m => PureTCM (ReaderT r m)
+instance (PureTCM m, Monoid w) => PureTCM (WriterT w m)
+instance PureTCM m => PureTCM (StateT s m)
diff --git a/src/full/Agda/TypeChecking/Monad/Signature.hs b/src/full/Agda/TypeChecking/Monad/Signature.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Signature.hs
@@ -0,0 +1,1409 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Monad.Signature where
+
+import Prelude hiding (null)
+
+import qualified Control.Monad.Fail as Fail
+
+import Control.Arrow                 ( first, second )
+import Control.Monad.Except          ( ExceptT )
+import Control.Monad.State           ( StateT  )
+import Control.Monad.Reader          ( ReaderT )
+import Control.Monad.Writer          ( WriterT )
+import Control.Monad.Trans.Maybe     ( MaybeT  )
+import Control.Monad.Trans.Identity  ( IdentityT )
+import Control.Monad.Trans           ( MonadTrans, lift )
+
+import Data.Foldable (for_)
+import qualified Data.List as List
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+import qualified Data.HashMap.Strict as HMap
+import Data.Maybe
+import Data.Semigroup ((<>))
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Abstract (Ren, ScopeCopyInfo(..))
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Names
+import Agda.Syntax.Position
+import Agda.Syntax.Treeless (Compiled(..), TTerm, ArgUsage)
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Constraints
+import Agda.TypeChecking.Monad.Env
+import Agda.TypeChecking.Monad.Mutual
+import Agda.TypeChecking.Monad.Open
+import Agda.TypeChecking.Monad.Options
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Monad.Trace
+import Agda.TypeChecking.DropArgs
+import Agda.TypeChecking.Warnings
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage.SplitTree
+import {-# SOURCE #-} Agda.TypeChecking.CompiledClause.Compile
+import {-# SOURCE #-} Agda.TypeChecking.Polarity
+import {-# SOURCE #-} Agda.TypeChecking.Pretty
+import {-# SOURCE #-} Agda.TypeChecking.ProjectionLike
+import {-# SOURCE #-} Agda.TypeChecking.Reduce
+import {-# SOURCE #-} Agda.TypeChecking.Opacity
+
+import {-# SOURCE #-} Agda.Compiler.Treeless.Erase
+import {-# SOURCE #-} Agda.Compiler.Builtin
+
+import Agda.Utils.CallStack.Base
+import Agda.Utils.Either
+import Agda.Utils.Function ( applyWhen )
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.ListT
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (Doc, prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+-- | If the first argument is @'Erased' something@, then hard
+-- compile-time mode is enabled when the continuation is run.
+
+setHardCompileTimeModeIfErased
+  :: Erased
+  -> TCM a
+     -- ^ Continuation.
+  -> TCM a
+setHardCompileTimeModeIfErased erased =
+  localTC
+    $ applyWhen (isErased erased) (set eHardCompileTimeMode True)
+    . over eQuantity (`composeQuantity` asQuantity erased)
+
+-- | If the quantity is \"erased\", then hard compile-time mode is
+-- enabled when the continuation is run.
+--
+-- Precondition: The quantity must not be @'Quantity1' something@.
+
+setHardCompileTimeModeIfErased'
+  :: LensQuantity q
+  => q
+     -- ^ The quantity.
+  -> TCM a
+     -- ^ Continuation.
+  -> TCM a
+setHardCompileTimeModeIfErased' =
+  setHardCompileTimeModeIfErased .
+    fromMaybe __IMPOSSIBLE__ . erasedFromQuantity . getQuantity
+
+-- | Use run-time mode in the continuation unless the current mode is
+-- the hard compile-time mode.
+
+setRunTimeModeUnlessInHardCompileTimeMode
+  :: TCM a
+     -- ^ Continuation.
+  -> TCM a
+setRunTimeModeUnlessInHardCompileTimeMode c =
+  ifM (viewTC eHardCompileTimeMode) c $
+  localTC (over eQuantity $ mapQuantity (`addQuantity` topQuantity)) c
+
+-- | Use hard compile-time mode in the continuation if the first
+-- argument is @'Erased' something@. Use run-time mode if the first
+-- argument is @'NotErased' something@ and the current mode is not
+-- hard compile-time mode.
+
+setModeUnlessInHardCompileTimeMode
+  :: Erased
+  -> TCM a
+     -- ^ Continuation.
+  -> TCM a
+setModeUnlessInHardCompileTimeMode erased c = case erased of
+  Erased{}    -> setHardCompileTimeModeIfErased erased c
+  NotErased{} -> do
+    warnForPlentyInHardCompileTimeMode erased
+    setRunTimeModeUnlessInHardCompileTimeMode c
+
+-- | Warn if the user explicitly wrote @@ω@ or @@plenty@ but the
+-- current mode is the hard compile-time mode.
+
+warnForPlentyInHardCompileTimeMode :: Erased -> TCM ()
+warnForPlentyInHardCompileTimeMode = \case
+  Erased{}    -> return ()
+  NotErased o -> do
+    let warn = warning $ PlentyInHardCompileTimeMode o
+    hard <- viewTC eHardCompileTimeMode
+    if not hard then return () else case o of
+      QωInferred{} -> return ()
+      Qω{}         -> warn
+      QωPlenty{}   -> warn
+
+-- | Add a constant to the signature. Lifts the definition to top level.
+addConstant :: QName -> Definition -> TCM ()
+addConstant q d = do
+  reportSDoc "tc.signature" 20 $ "adding constant " <+> pretty q <+> " to signature"
+
+  -- Every constant that gets added to the signature in hard
+  -- compile-time mode is treated as erased.
+  hard <- viewTC eHardCompileTimeMode
+  d    <- if not hard then return d else do
+    case erasedFromQuantity (getQuantity d) of
+      Nothing     -> __IMPOSSIBLE__
+      Just erased -> do
+        warnForPlentyInHardCompileTimeMode erased
+        return $ mapQuantity (zeroQuantity `composeQuantity`) d
+
+  tel <- getContextTelescope
+  let tel' = replaceEmptyName "r" $ killRange $ case theDef d of
+              Constructor{} -> fmap hideOrKeepInstance tel
+              Function{ funProjection = Right Projection{ projProper = Just{}, projIndex = n } } ->
+                let fallback = fmap hideOrKeepInstance tel in
+                if n > 0 then fallback else
+                -- if the record value is part of the telescope, its hiding should left unchanged
+                  case initLast $ telToList tel of
+                    Nothing -> fallback
+                    Just (doms, dom) -> telFromList $ fmap hideOrKeepInstance doms ++ [dom]
+              _ -> tel
+  let d' = abstract tel' $ d { defName = q }
+  reportSDoc "tc.signature" 60 $ "lambda-lifted definition =" <?> pretty d'
+  modifySignature $ updateDefinitions $ HMap.insertWith (+++) q d'
+  i <- currentOrFreshMutualBlock
+  setMutualBlock i q
+  where
+    new +++ old = new { defDisplay = defDisplay new ++ defDisplay old
+                      , defInstance = defInstance new `mplus` defInstance old }
+
+-- | A combination of 'addConstant' and 'defaultDefn'. The 'Language'
+-- does not need to be supplied.
+
+addConstant' ::
+  QName -> ArgInfo -> QName -> Type -> Defn -> TCM ()
+addConstant' q info x t def = do
+  lang <- getLanguage
+  addConstant q $ defaultDefn info x t lang def
+
+-- | Set termination info of a defined function symbol.
+setTerminates :: MonadTCState m => QName -> Bool -> m ()
+setTerminates q b = modifySignature $ updateDefinition q $ updateTheDef $ \case
+    def@Function{} -> def { funTerminates = Just b }
+    def@Record{}   -> def { recTerminates = Just b }
+    def -> def
+
+-- | Set CompiledClauses of a defined function symbol.
+setCompiledClauses :: QName -> CompiledClauses -> TCM ()
+setCompiledClauses q cc = modifySignature $ updateDefinition q $ updateTheDef $ setT
+  where
+    setT def@Function{} = def { funCompiled = Just cc }
+    setT def            = def
+
+-- | Set SplitTree of a defined function symbol.
+setSplitTree :: QName -> SplitTree -> TCM ()
+setSplitTree q st = modifySignature $ updateDefinition q $ updateTheDef $ setT
+  where
+    setT def@Function{} = def { funSplitTree = Just st }
+    setT def            = def
+
+-- | Modify the clauses of a function.
+modifyFunClauses :: QName -> ([Clause] -> [Clause]) -> TCM ()
+modifyFunClauses q f =
+  modifySignature $ updateDefinition q $ updateTheDef $ updateFunClauses f
+
+-- | Lifts clauses to the top-level and adds them to definition.
+--   Also adjusts the 'funCopatternLHS' field if necessary.
+addClauses :: (MonadConstraint m, MonadTCState m) => QName -> [Clause] -> m ()
+addClauses q cls = do
+  tel <- getContextTelescope
+  modifySignature $ updateDefinition q $
+    updateTheDef (updateFunClauses (++ abstract tel cls))
+    . updateDefCopatternLHS (|| isCopatternLHS cls)
+
+  -- Jesper, 2022-10-13: unblock any constraints that were
+  -- waiting for more clauses of this function
+  wakeConstraints' $ wakeIfBlockedOnDef q . constraintUnblocker
+
+mkPragma :: String -> TCM CompilerPragma
+mkPragma s = CompilerPragma <$> getCurrentRange <*> pure s
+
+-- | Add a compiler pragma `{-\# COMPILE <backend> <name> <text> \#-}`
+addPragma :: BackendName -> QName -> String -> TCM ()
+addPragma b q s = ifM erased
+  {- then -} (warning $ PragmaCompileErased b q)
+  {- else -} $ do
+    pragma <- mkPragma s
+    modifySignature $ updateDefinition q $ addCompilerPragma b pragma
+
+  where
+
+  erased :: TCM Bool
+  erased = do
+    def <- theDef <$> getConstInfo q
+    case def of
+      -- If we have a defined symbol, we check whether it is erasable
+      Function{} ->
+        locallyTC      eActiveBackendName (const $ Just b) $
+        locallyTCState stBackends         (const $ builtinBackends) $
+        isErasable q
+     -- Otherwise (Axiom, Datatype, Record type, etc.) we keep it
+      _ -> pure False
+
+getUniqueCompilerPragma :: BackendName -> QName -> TCM (Maybe CompilerPragma)
+getUniqueCompilerPragma backend q = do
+  ps <- defCompilerPragmas backend <$> getConstInfo q
+  case ps of
+    []  -> return Nothing
+    [p] -> return $ Just p
+    (_:p1:_) ->
+      setCurrentRange p1 $
+            genericDocError =<< do
+                  hang (text ("Conflicting " ++ backend ++ " pragmas for") <+> pretty q <+> "at") 2 $
+                       vcat [ "-" <+> pretty (getRange p) | p <- ps ]
+
+setFunctionFlag :: FunctionFlag -> Bool -> QName -> TCM ()
+setFunctionFlag flag val q = modifyGlobalDefinition q $ set (lensTheDef . funFlag flag) val
+
+markStatic :: QName -> TCM ()
+markStatic = setFunctionFlag FunStatic True
+
+markInline :: Bool -> QName -> TCM ()
+markInline b = setFunctionFlag FunInline b
+
+markInjective :: QName -> TCM ()
+markInjective q = modifyGlobalDefinition q $ \def -> def { defInjective = True }
+
+unionSignatures :: [Signature] -> Signature
+unionSignatures ss = foldr unionSignature emptySignature ss
+  where
+    unionSignature (Sig a b c) (Sig a' b' c') =
+      Sig (Map.union a a')
+          (HMap.union b b')              -- definitions are unique (in at most one module)
+          (HMap.unionWith mappend c c')  -- rewrite rules are accumulated
+
+-- | Add a section to the signature.
+--
+--   The current context will be stored as the cumulative module parameters
+--   for this section.
+addSection :: ModuleName -> TCM ()
+addSection m = do
+  tel <- getContextTelescope
+  let sec = Section tel
+  -- Make sure we do not overwrite an existing section!
+  whenJustM (getSection m) $ \ sec' -> do
+    -- At least not with different content!
+    if (sec == sec') then do
+      -- Andreas, 2015-12-02: test/Succeed/Issue1701II.agda
+      -- reports a "redundantly adding existing section".
+      reportSDoc "tc.section" 10 $ "warning: redundantly adding existing section" <+> pretty m
+      reportSDoc "tc.section" 60 $ "with content" <+> pretty sec
+    else do
+      reportSDoc "impossible" 10 $ "overwriting existing section" <+> pretty m
+      reportSDoc "impossible" 60 $ "of content  " <+> pretty sec'
+      reportSDoc "impossible" 60 $ "with content" <+> pretty sec
+      __IMPOSSIBLE__
+  -- Add the new section.
+  setModuleCheckpoint m
+  modifySignature $ over sigSections $ Map.insert m sec
+
+-- | Sets the checkpoint for the given module to the current checkpoint.
+setModuleCheckpoint :: ModuleName -> TCM ()
+setModuleCheckpoint m = do
+  chkpt <- viewTC eCurrentCheckpoint
+  stModuleCheckpoints `modifyTCLens` Map.insert m chkpt
+
+-- | Get a section.
+--
+--   Why Maybe? The reason is that we look up all prefixes of a module to
+--   compute number of parameters, and for hierarchical top-level modules,
+--   A.B.C say, A and A.B do not exist.
+{-# SPECIALIZE getSection :: ModuleName -> TCM (Maybe Section) #-}
+{-# SPECIALIZE getSection :: ModuleName -> ReduceM (Maybe Section) #-}
+getSection :: (Functor m, ReadTCState m) => ModuleName -> m (Maybe Section)
+getSection m = do
+  sig  <- (^. stSignature . sigSections) <$> getTCState
+  isig <- (^. stImports   . sigSections) <$> getTCState
+  return $ Map.lookup m sig `mplus` Map.lookup m isig
+
+-- | Lookup a section telescope.
+--
+--   If it doesn't exist, like in hierarchical top-level modules,
+--   the section telescope is empty.
+{-# SPECIALIZE lookupSection :: ModuleName -> TCM Telescope #-}
+{-# SPECIALIZE lookupSection :: ModuleName -> ReduceM Telescope #-}
+lookupSection :: (Functor m, ReadTCState m) => ModuleName -> m Telescope
+lookupSection m = maybe EmptyTel (^. secTelescope) <$> getSection m
+
+-- | Add display forms for a name @f@ copied by a module application. Essentially if @f@ can reduce to
+--
+-- @
+-- λ xs → A.B.C.f vs
+-- @
+--
+-- by unfolding module application copies (`defCopy`), then we add a display form
+--
+-- @
+-- A.B.C.f vs ==> f xs
+-- @
+addDisplayForms :: QName -> TCM ()
+addDisplayForms x = do
+  reportSDoc "tc.display.section" 20 $ "Computing display forms for" <+> pretty x
+  def <- getConstInfo x
+  let v = case theDef def of
+             Constructor{conSrcCon = h} -> Con h{ conName = x } ConOSystem []
+             _                          -> Def x []
+
+  -- Compute all unfoldings of x by repeatedly calling reduceDefCopy
+  vs <- unfoldings x v
+  reportSDoc "tc.display.section" 20 $ nest 2 $ vcat
+    [ "unfoldings:" <?> vcat [ "-" <+> pretty v | v <- vs ] ]
+
+  -- Turn unfoldings into display forms
+  npars <- subtract (projectionArgs def) <$> getContextSize
+  let dfs = map (displayForm npars v) vs
+  reportSDoc "tc.display.section" 20 $ nest 2 $ vcat
+    [ "displayForms:" <?> vcat [ "-" <+> (pretty y <+> "-->" <?> pretty df) | (y, df) <- dfs ] ]
+
+  -- and add them
+  mapM_ (uncurry addDisplayForm) dfs
+  where
+
+    -- To get display forms for projections we need to unSpine here.
+    view :: Term -> ([Arg ArgName], Term)
+    view = second unSpine . lamView
+
+    -- Given an unfolding `top = λ xs → y es` generate a display form
+    -- `y es ==> top xs`. The first `npars` variables in `xs` are module parameters
+    -- and should not be pattern variables, but matched literally.
+    displayForm :: Nat -> Term -> Term -> (QName, DisplayForm)
+    displayForm npars top v =
+      case view v of
+        (xs, Def y es)   -> (y,)         $ mkDisplay xs es
+        (xs, Con h i es) -> (conName h,) $ mkDisplay xs es
+        _ -> __IMPOSSIBLE__
+      where
+        mkDisplay xs es = Display (n - npars) es $ DTerm $ top `apply` args
+          -- Andreas, 2023-01-26, #6476:
+          -- I think this @apply@ is safe (rather than @DTerm' top (map Apply args)@).
+          where
+            n    = length xs
+            args = zipWith (\ x i -> var i <$ x) xs (downFrom n)
+
+    -- Unfold a single defCopy.
+    unfoldOnce :: Term -> TCM (Reduced () Term)
+    unfoldOnce v = case view v of
+      (xs, Def f es)   -> (fmap . fmap) (unlamView xs) (reduceDefCopyTCM f es)
+      (xs, Con c i es) -> (fmap . fmap) (unlamView xs) (reduceDefCopyTCM (conName c) es)
+      _                -> pure $ NoReduction ()
+
+    -- Compute all reduceDefCopy unfoldings of `x`. Stop when we hit a non-copy.
+    unfoldings :: QName -> Term -> TCM [Term]
+    unfoldings x v = unfoldOnce v >>= \ case
+      NoReduction{}     -> return []
+      YesReduction _ v' -> do
+        let headSymbol = case snd $ view v' of
+              Def y _   -> Just y
+              Con y _ _ -> Just (conName y)
+              _         -> Nothing
+        case headSymbol of
+          Nothing -> return []
+          Just y | x == y -> do
+            -- This should never happen, but if it does, getting an __IMPOSSIBLE__ is much better
+            -- than looping.
+            reportSDoc "impossible" 10 $ nest 2 $ vcat
+              [ "reduceDefCopy said YesReduction but the head symbol is the same!?"
+              , nest 2 $ "v  =" <+> pretty v
+              , nest 2 $ "v' =" <+> pretty v'
+              ]
+            __IMPOSSIBLE__
+          Just y -> do
+            ifM (defCopy <$> getConstInfo y)
+                ((v' :) <$> unfoldings y v')  -- another copy so keep going
+                (return [v'])                 -- not a copy, we stop
+
+-- | Module application (followed by module parameter abstraction).
+applySection
+  :: ModuleName     -- ^ Name of new module defined by the module macro.
+  -> Telescope      -- ^ Parameters of new module.
+  -> ModuleName     -- ^ Name of old module applied to arguments.
+  -> Args           -- ^ Arguments of module application.
+  -> ScopeCopyInfo  -- ^ Imported names and modules
+  -> TCM ()
+applySection new ptel old ts ScopeCopyInfo{ renModules = rm, renNames = rd } = do
+  rd <- closeConstructors rd
+  applySection' new ptel old ts ScopeCopyInfo{ renModules = rm, renNames = rd }
+  where
+    -- If a datatype is being copied, all its constructors need to be copied,
+    -- and if a constructor is copied its datatype needs to be.
+    closeConstructors :: Ren QName -> TCM (Ren QName)
+    closeConstructors rd = do
+        ds <- nubOn id . catMaybes <$> traverse constructorData (Map.keys rd)
+        cs <- nubOn id . concat    <$> traverse dataConstructors (Map.keys rd)
+        new <- Map.unionsWith (<>) <$> traverse rename (ds ++ cs)
+        reportSDoc "tc.mod.apply.complete" 30 $
+          "also copying: " <+> pretty new
+        return $ Map.unionWith (<>) new rd
+      where
+        rename :: QName -> TCM (Ren QName)
+        rename x
+          | x `Map.member` rd = pure mempty
+          | otherwise =
+              Map.singleton x . pure . qnameFromList . singleton <$> freshName_ (prettyShow $ qnameName x)
+
+        constructorData :: QName -> TCM (Maybe QName)
+        constructorData x = do
+          (theDef <$> getConstInfo x) <&> \case
+            Constructor{ conData = d } -> Just d
+            _                          -> Nothing
+
+        dataConstructors :: QName -> TCM [QName]
+        dataConstructors x = do
+          (theDef <$> getConstInfo x) <&> \case
+            Datatype{ dataCons = cs } -> cs
+            Record{ recConHead = h }  -> [conName h]
+            _                         -> []
+
+applySection' :: ModuleName -> Telescope -> ModuleName -> Args -> ScopeCopyInfo -> TCM ()
+applySection' new ptel old ts ScopeCopyInfo{ renNames = rd, renModules = rm } = do
+  do
+    noCopyList <- catMaybes <$> mapM getName' constrainedPrims
+    for_ (Map.keys rd) $ \ q ->
+      when (q `elem` noCopyList) $ typeError (TriedToCopyConstrainedPrim q)
+
+  reportSDoc "tc.mod.apply" 10 $ vcat
+    [ "applySection"
+    , "new  =" <+> pretty new
+    , "ptel =" <+> pretty ptel
+    , "old  =" <+> pretty old
+    , "ts   =" <+> pretty ts
+    ]
+  _ <- Map.traverseWithKey (traverse . copyDef ts) rd
+  _ <- Map.traverseWithKey (traverse . copySec ts) rm
+  computePolarity (Map.elems rd >>= List1.toList)
+  where
+    -- Andreas, 2013-10-29
+    -- Here, if the name x is not imported, it persists as
+    -- old, possibly out-of-scope name.
+    -- This old name may used by the case split tactic, leading to
+    -- names that cannot be printed properly.
+    -- I guess it would make sense to mark non-imported names
+    -- as such (out-of-scope) and let splitting fail if it would
+    -- produce out-of-scope constructors.
+    --
+    -- Taking 'List1.head' because 'Module.Data.cons' and 'Module.cons' are
+    -- equivalent valid names and either can be used.
+    copyName x = maybe x List1.head (Map.lookup x rd)
+
+    argsToUse x = do
+      let m = commonParentModule old x
+      reportSDoc "tc.mod.apply" 80 $ "Common prefix: " <+> pretty m
+      size <$> lookupSection m
+
+    copyDef :: Args -> QName -> QName -> TCM ()
+    copyDef ts x y = do
+      def <- getConstInfo x
+      np  <- argsToUse (qnameModule x)
+      -- Issue #3083: We need to use the hiding from the telescope of the
+      -- original module. This can be different than the hiding for the common
+      -- parent in the case of record modules.
+      hidings <- map getHiding . telToList <$> lookupSection (qnameModule x)
+      let ts' = zipWith setHiding hidings ts
+      commonTel <- lookupSection (commonParentModule old $ qnameModule x)
+      reportSDoc "tc.mod.apply" 80 $ vcat
+        [ "copyDef" <+> pretty x <+> "->" <+> pretty y
+        , "ts' = " <+> pretty ts' ]
+      -- The module telescope had been divided by some μ, so the corresponding
+      -- top level definition had type μ \ Γ → B, so if we have a substitution
+      -- Δ → Γ we actually want to apply μ \ - to it, so the new top-level
+      -- definition we get will have signature μ \ Δ → B.  This is only valid
+      -- for pure modality systems though.
+      let ai = defArgInfo def
+          m = unitModality { modCohesion = getCohesion ai }
+      localTC (over eContext (map (mapModality (m `inverseComposeModality`)))) $
+        copyDef' ts' np def
+      where
+        copyDef' ts np d = do
+          reportSDoc "tc.mod.apply" 60 $ "making new def for" <+> pretty y <+> "from" <+> pretty x <+> "with" <+> text (show np) <+> "args" <+> text (show $ defAbstract d)
+          reportSDoc "tc.mod.apply" 80 $ vcat
+            [ "args = " <+> text (show ts')
+            , "old type = " <+> pretty (defType d) ]
+          reportSDoc "tc.mod.apply" 80 $
+            "new type = " <+> pretty t
+          addConstant y =<< nd y
+          makeProjection y
+          -- Issue1238: the copied def should be an 'instance' if the original
+          -- def is one. Skip constructors since the original constructor will
+          -- still work as an instance.
+          -- Issue5583: Don't skip constructures, because the original constructor doesn't always
+          -- work. For instance if it's only available in an anonymous module generated by
+          -- `open import M args`.
+          whenJust inst $ \ c -> addNamedInstance y c
+          -- Set display form for the old name if it's not a constructor.
+{- BREAKS fail/Issue478
+          -- Andreas, 2012-10-20 and if we are not an anonymous module
+          -- unless (isAnonymousModuleName new || isCon || not (null ptel)) $ do
+-}
+          -- BREAKS fail/Issue1643a
+          -- -- Andreas, 2015-09-09 Issue 1643:
+          -- -- Do not add a display form for a bare module alias.
+          -- when (not isCon && null ptel && not (null ts)) $ do
+          when (null ptel) $ do
+            addDisplayForms y
+          where
+            ts' = take np ts
+            t   = defType d `piApply` ts'
+            pol = defPolarity d `apply` ts'
+            occ = defArgOccurrences d `apply` ts'
+            gen = defArgGeneralizable d `apply` ts'
+            inst = defInstance d
+            -- the name is set by the addConstant function
+            nd :: QName -> TCM Definition
+            nd y = do
+              -- The arguments may use some feature of the current
+              -- language.
+              lang <- getLanguage
+              for def $ \ df -> Defn
+                    { defArgInfo        = defArgInfo d
+                    , defName           = y
+                    , defType           = t
+                    , defPolarity       = pol
+                    , defArgOccurrences = occ
+                    , defArgGeneralizable = gen
+                    , defGeneralizedParams = [] -- This is only needed for type checking data/record defs so no need to copy it.
+                    , defDisplay        = []
+                    , defMutual         = -1   -- TODO: mutual block?
+                    , defCompiledRep    = noCompiledRep
+                    , defInstance       = inst
+                    , defCopy           = True
+                    , defMatchable      = Set.empty
+                    , defNoCompilation  = defNoCompilation d
+                    , defInjective      = False
+                    , defCopatternLHS   = isCopatternLHS [cl]
+                    , defBlocked        = defBlocked d
+                    , defLanguage       =
+                      case defLanguage d of
+                        -- Note that Cubical Agda code can be imported
+                        -- when --erased-cubical is used.
+                        l@(Cubical CFull) -> l
+                        Cubical CErased   -> lang
+                        WithoutK          -> lang
+                        WithK             -> lang
+                    , theDef            = df }
+            oldDef = theDef d
+            isCon  = case oldDef of { Constructor{} -> True ; _ -> False }
+            mutual = case oldDef of { Function{funMutual = m} -> m              ; _ -> Nothing }
+            extlam = case oldDef of { Function{funExtLam = e} -> e              ; _ -> Nothing }
+            with   = case oldDef of { Function{funWith = w}   -> copyName <$> w ; _ -> Nothing }
+            -- Andreas, 2015-05-11, to fix issue 1413:
+            -- Even if we apply the record argument (must be @var 0@), we stay a projection.
+            -- This is because we may abstract the record argument later again.
+            -- See succeed/ProjectionNotNormalized.agda
+            isVar0 t = case unArg t of Var 0 [] -> True; _ -> False
+            proj :: Either ProjectionLikenessMissing Projection
+            proj   = case oldDef of
+              Function{funProjection = Right p@Projection{projIndex = n}}
+                | size ts' < n || (size ts' == n && maybe True isVar0 (lastMaybe ts'))
+                -> Right p { projIndex = n - size ts'
+                           , projLams  = projLams p `apply` ts'
+                           , projProper= copyName <$> projProper p
+                           }
+              -- Preserve no-projection-likeness flag if it exists, and
+              -- it's set to @Left _@. For future reference: The match
+              -- on left can't be simplified or it accidentally
+              -- circumvents the guard above.
+              Function{funProjection = Left projl} -> Left projl
+              _ -> Left MaybeProjection
+            def =
+              case oldDef of
+                Constructor{ conPars = np, conData = d } -> return $
+                  oldDef { conPars = np - size ts'
+                         , conData = copyName d
+                         }
+                Datatype{ dataPars = np, dataCons = cs } -> return $
+                  oldDef { dataPars   = np - size ts'
+                         , dataClause = Just cl
+                         , dataCons   = map copyName cs
+                         }
+                Record{ recPars = np, recTel = tel } -> return $
+                  oldDef { recPars    = np - size ts'
+                         , recClause  = Just cl
+                         , recTel     = apply tel ts'
+                         }
+                GeneralizableVar -> return GeneralizableVar
+                _ -> do
+                  (mst, _, cc) <- compileClauses Nothing [cl] -- Andreas, 2012-10-07 non need for record pattern translation
+                  fun          <- emptyFunctionData
+                  let newDef =
+                        set funMacro  (oldDef ^. funMacro) $
+                        set funStatic (oldDef ^. funStatic) $
+                        set funInline True $
+                        FunctionDefn fun
+                        { _funClauses        = [cl]
+                        , _funCompiled       = Just cc
+                        , _funSplitTree      = mst
+                        , _funMutual         = mutual
+                        , _funProjection     = proj
+                        , _funTerminates     = Just True
+                        , _funExtLam         = extlam
+                        , _funWith           = with
+                        }
+                  reportSDoc "tc.mod.apply" 80 $ ("new def for" <+> pretty x) <?> pretty newDef
+                  return newDef
+
+            cl = Clause { clauseLHSRange    = getRange $ defClauses d
+                        , clauseFullRange   = getRange $ defClauses d
+                        , clauseTel         = EmptyTel
+                        , namedClausePats   = []
+                        , clauseBody        = Just $ dropArgs pars $ case oldDef of
+                            Function{funProjection = Right p} -> projDropParsApply p ProjSystem rel ts'
+                            _ -> Def x $ map Apply ts'
+                        , clauseType        = Just $ defaultArg t
+                        , clauseCatchall    = False
+                        , clauseExact       = Just True
+                        , clauseRecursive   = Just False -- definitely not recursive
+                        , clauseUnreachable = Just False -- definitely not unreachable
+                        , clauseEllipsis    = NoEllipsis
+                        , clauseWhereModule = Nothing
+                        }
+              where
+                -- The number of remaining parameters. We need to drop the
+                -- lambdas corresponding to these from the clause body above.
+                pars = max 0 $ either (const 0) (pred . projIndex) proj
+                rel  = getRelevance $ defArgInfo d
+
+    {- Example
+
+    module Top Θ where
+      module A Γ where
+        module M Φ where
+      module B Δ where
+        module N Ψ where
+          module O Ψ' where
+        open A public     -- introduces only M --> A.M into the *scope*
+    module C Ξ = Top.B ts
+
+    new section C
+      tel = Ξ.(Θ.Δ)[ts]
+
+    calls
+      1. copySec ts Top.A.M C.M
+      2. copySec ts Top.B.N C.N
+      3. copySec ts Top.B.N.O C.N.O
+    with
+      old = Top.B
+
+    For 1.
+      Common prefix is: Top
+      totalArgs = |Θ|   (section Top)
+      tel       = Θ.Γ.Φ (section Top.A.M)
+      ts'       = take totalArgs ts
+      Θ₂        = drop totalArgs Θ
+      new section C.M
+        tel =  Θ₂.Γ.Φ[ts']
+    -}
+    copySec :: Args -> ModuleName -> ModuleName -> TCM ()
+    copySec ts x y = do
+      totalArgs <- argsToUse x
+      tel       <- lookupSection x
+      let sectionTel =  apply tel $ take totalArgs ts
+      reportSDoc "tc.mod.apply" 80 $ "Copying section" <+> pretty x <+> "to" <+> pretty y
+      reportSDoc "tc.mod.apply" 80 $ "  ts           = " <+> mconcat (List.intersperse "; " (map pretty ts))
+      reportSDoc "tc.mod.apply" 80 $ "  totalArgs    = " <+> text (show totalArgs)
+      reportSDoc "tc.mod.apply" 80 $ "  tel          = " <+> text (unwords (map (fst . unDom) $ telToList tel))  -- only names
+      reportSDoc "tc.mod.apply" 80 $ "  sectionTel   = " <+> text (unwords (map (fst . unDom) $ telToList ptel)) -- only names
+      addContext sectionTel $ addSection y
+
+-- | Add a display form to a definition (could be in this or imported signature).
+addDisplayForm :: QName -> DisplayForm -> TCM ()
+addDisplayForm x df = do
+  d <- makeOpen df
+  let add = updateDefinition x $ \ def -> def{ defDisplay = d : defDisplay def }
+  ifM (isLocal x)
+    {-then-} (modifySignature add)
+    {-else-} (stImportsDisplayForms `modifyTCLens` HMap.insertWith (++) x [d])
+  whenM (hasLoopingDisplayForm x) $
+    typeError . GenericDocError =<< do "Cannot add recursive display form for" <+> pretty x
+
+isLocal :: ReadTCState m => QName -> m Bool
+isLocal x = HMap.member x <$> useR (stSignature . sigDefinitions)
+
+getDisplayForms :: (HasConstInfo m, ReadTCState m) => QName -> m [LocalDisplayForm]
+getDisplayForms q = do
+  ds  <- either (const []) defDisplay <$> getConstInfo' q
+  ds1 <- HMap.lookupDefault [] q <$> useR stImportsDisplayForms
+  ds2 <- HMap.lookupDefault [] q <$> useR stImportedDisplayForms
+  ifM (isLocal q) (return $ ds ++ ds1 ++ ds2)
+                  (return $ ds1 ++ ds ++ ds2)
+
+-- | Find all names used (recursively) by display forms of a given name.
+chaseDisplayForms :: QName -> TCM (Set QName)
+chaseDisplayForms q = go Set.empty [q]
+  where
+    go :: Set QName        -- Accumulator.
+       -> [QName]          -- Work list.  TODO: make work set to avoid duplicate chasing?
+       -> TCM (Set QName)
+    go used []       = pure used
+    go used (q : qs) = do
+      let rhs (Display _ _ e) = e   -- Only look at names in the right-hand side (#1870)
+      let notYetUsed x = if x `Set.member` used then Set.empty else Set.singleton x
+      ds <- namesIn' notYetUsed . map (rhs . dget)
+            <$> (getDisplayForms q `catchError_` \ _ -> pure [])  -- might be a pattern synonym
+      go (Set.union ds used) (Set.toList ds ++ qs)
+
+-- | Check if a display form is looping.
+hasLoopingDisplayForm :: QName -> TCM Bool
+hasLoopingDisplayForm q = Set.member q <$> chaseDisplayForms q
+
+canonicalName :: HasConstInfo m => QName -> m QName
+canonicalName x = do
+  def <- theDef <$> getConstInfo x
+  case def of
+    Constructor{conSrcCon = c}                                -> return $ conName c
+    Record{recClause = Just (Clause{ clauseBody = body })}    -> can body
+    Datatype{dataClause = Just (Clause{ clauseBody = body })} -> can body
+    _                                                         -> return x
+  where
+    can body = canonicalName $ extract $ fromMaybe __IMPOSSIBLE__ body
+    extract (Def x _)  = x
+    extract _          = __IMPOSSIBLE__
+
+sameDef :: HasConstInfo m => QName -> QName -> m (Maybe QName)
+sameDef d1 d2 = do
+  c1 <- canonicalName d1
+  c2 <- canonicalName d2
+  if (c1 == c2) then return $ Just c1 else return Nothing
+
+-- | Does the given constructor come from a single-constructor type?
+--
+-- Precondition: The name has to refer to a constructor.
+singleConstructorType :: QName -> TCM Bool
+singleConstructorType q = do
+  d <- theDef <$> getConstInfo q
+  case d of
+    Record {}                   -> return True
+    Constructor { conData = d } -> do
+      di <- theDef <$> getConstInfo d
+      return $ case di of
+        Record {}                  -> True
+        Datatype { dataCons = cs } -> natSize cs == 1
+        _                          -> __IMPOSSIBLE__
+    _ -> __IMPOSSIBLE__
+
+-- | Signature lookup errors.
+data SigError
+  = SigUnknown String -- ^ The name is not in the signature; default error message.
+  | SigAbstract       -- ^ The name is not available, since it is abstract.
+  | SigCubicalNotErasure
+    -- ^ The name is not available because it was defined in Cubical
+    -- Agda, but the current language is Erased Cubical Agda, and
+    -- @--erasure@ is not active.
+
+-- | Generates an error message corresponding to
+-- 'SigCubicalNotErasure' for a given 'QName'.
+notSoPrettySigCubicalNotErasure :: QName -> String
+notSoPrettySigCubicalNotErasure q =
+  "The name " ++ prettyShow q ++ " which was defined in Cubical " ++
+  "Agda can only be used in Erased Cubical Agda if the option " ++
+  "--erasure is used"
+
+-- | Generates an error message corresponding to
+-- 'SigCubicalNotErasure' for a given 'QName'.
+prettySigCubicalNotErasure :: MonadPretty m => QName -> m Doc
+prettySigCubicalNotErasure q = fsep $
+  pwords "The name" ++
+  [prettyTCM q] ++
+  pwords "which was defined in Cubical Agda can only be used in" ++
+  pwords "Erased Cubical Agda if the option --erasure is used"
+
+-- | An eliminator for 'SigError'. All constructors except for
+-- 'SigAbstract' are assumed to be impossible.
+sigError :: (HasCallStack, MonadDebug m) => m a -> SigError -> m a
+sigError a = \case
+  SigUnknown s         -> __IMPOSSIBLE_VERBOSE__ s
+  SigAbstract          -> a
+  SigCubicalNotErasure -> __IMPOSSIBLE__
+
+class ( Functor m
+      , Applicative m
+      , Fail.MonadFail m
+      , HasOptions m
+      , MonadDebug m
+      , MonadTCEnv m
+      ) => HasConstInfo m where
+  -- | Lookup the definition of a name. The result is a closed thing, all free
+  --   variables have been abstracted over.
+  getConstInfo :: QName -> m Definition
+  getConstInfo q = getConstInfo' q >>= \case
+      Right d -> return d
+      Left (SigUnknown err) -> __IMPOSSIBLE_VERBOSE__ err
+      Left SigAbstract      -> __IMPOSSIBLE_VERBOSE__ $
+        "Abstract, thus, not in scope: " ++ prettyShow q
+      Left SigCubicalNotErasure -> __IMPOSSIBLE_VERBOSE__ $
+        notSoPrettySigCubicalNotErasure q
+
+  -- | Version that reports exceptions:
+  getConstInfo' :: QName -> m (Either SigError Definition)
+  -- getConstInfo' q = Right <$> getConstInfo q -- conflicts with default signature
+
+  -- | Lookup the rewrite rules with the given head symbol.
+  getRewriteRulesFor :: QName -> m RewriteRules
+
+  -- Lifting HasConstInfo through monad transformers:
+
+  default getConstInfo'
+    :: (HasConstInfo n, MonadTrans t, m ~ t n)
+    => QName -> m (Either SigError Definition)
+  getConstInfo' = lift . getConstInfo'
+
+  default getRewriteRulesFor
+    :: (HasConstInfo n, MonadTrans t, m ~ t n)
+    => QName -> m RewriteRules
+  getRewriteRulesFor = lift . getRewriteRulesFor
+
+{-# SPECIALIZE getConstInfo :: QName -> TCM Definition #-}
+
+{-# SPECIALIZE getOriginalConstInfo :: QName -> TCM Definition #-}
+-- | The computation 'getConstInfo' sometimes tweaks the returned
+-- 'Definition', depending on the current 'Language' and the
+-- 'Language' of the 'Definition'. This variant of 'getConstInfo' does
+-- not perform any tweaks.
+getOriginalConstInfo ::
+  (ReadTCState m, HasConstInfo m) => QName -> m Definition
+getOriginalConstInfo q = do
+  def  <- getConstInfo q
+  lang <- getLanguage
+  case (lang, defLanguage def) of
+    (Cubical CErased, Cubical CFull) ->
+      locallyTCState
+        (stPragmaOptions . lensOptCubical)
+        (const $ Just CFull)
+        (getConstInfo q)
+    _ -> return def
+
+defaultGetRewriteRulesFor :: (ReadTCState m, MonadTCEnv m) => QName -> m RewriteRules
+defaultGetRewriteRulesFor q = ifNotM (shouldReduceDef q) (return []) $ do
+  st <- getTCState
+  let sig = st ^. stSignature
+      imp = st ^. stImports
+      look s = HMap.lookup q $ s ^. sigRewriteRules
+  return $ mconcat $ catMaybes [look sig, look imp]
+
+-- | Get the original name of the projection
+--   (the current one could be from a module application).
+getOriginalProjection :: HasConstInfo m => QName -> m QName
+getOriginalProjection q = projOrig . fromMaybe __IMPOSSIBLE__ <$> isProjection q
+
+instance HasConstInfo (TCMT IO) where
+  getRewriteRulesFor = defaultGetRewriteRulesFor
+  getConstInfo' q = do
+    st  <- getTC
+    env <- askTC
+    defaultGetConstInfo st env q
+  getConstInfo q = getConstInfo' q >>= \case
+      Right d -> return d
+      Left (SigUnknown err)     -> fail err
+      Left SigAbstract          -> notInScopeError $ qnameToConcrete q
+      Left SigCubicalNotErasure ->
+        typeError . GenericDocError =<< prettySigCubicalNotErasure q
+
+defaultGetConstInfo
+  :: (HasOptions m, MonadDebug m, MonadTCEnv m)
+  => TCState -> TCEnv -> QName -> m (Either SigError Definition)
+defaultGetConstInfo st env q = do
+    let defs  = st ^. stSignature . sigDefinitions
+        idefs = st ^. stImports   . sigDefinitions
+    case catMaybes [HMap.lookup q defs, HMap.lookup q idefs] of
+        []  -> return $ Left $ SigUnknown $ "Unbound name: " ++ prettyShow q ++ showQNameId q
+        [d] -> checkErasureFixQuantity d >>= \case
+                 Left err -> return (Left err)
+                 Right d  -> mkAbs env d
+        ds  -> __IMPOSSIBLE_VERBOSE__ $ "Ambiguous name: " ++ prettyShow q
+    where
+      mkAbs env d
+        -- Apply the reducibility rules (abstract, opaque) to check
+        -- whether the definition should be hidden behind an
+        -- 'AbstractDef'.
+        | not (isAccessibleDef env st d{defName = q'}) =
+          case alwaysMakeAbstract d of
+            Just d      -> return $ Right d
+            Nothing     -> return $ Left SigAbstract
+              -- the above can happen since the scope checker is a bit sloppy with 'abstract'
+        | otherwise = return $ Right d
+        where
+          q' = case theDef d of
+            -- Hack to make abstract constructors work properly. The constructors
+            -- live in a module with the same name as the datatype, but for 'abstract'
+            -- purposes they're considered to be in the same module as the datatype.
+            Constructor{} -> dropLastModule q
+            _             -> q
+
+          dropLastModule q@QName{ qnameModule = m } =
+            q{ qnameModule = mnameFromList $
+                 initWithDefault __IMPOSSIBLE__ $ mnameToList m
+             }
+
+      -- Names defined in Cubical Agda may only be used in Erased
+      -- Cubical Agda if --erasure is used. In that case they are (to
+      -- a large degree) treated as erased.
+      checkErasureFixQuantity d = do
+        current <- getLanguage
+        if defLanguage d == Cubical CFull &&
+           current == Cubical CErased
+        then do
+          erasure <- optErasure <$> pragmaOptions
+          return $
+            if erasure
+            then Right $ setQuantity zeroQuantity d
+            else Left SigCubicalNotErasure
+        else return $ Right d
+
+-- HasConstInfo lifts through monad transformers
+-- (see default signatures in HasConstInfo class).
+
+instance HasConstInfo m => HasConstInfo (ChangeT m)
+instance HasConstInfo m => HasConstInfo (ExceptT err m)
+instance HasConstInfo m => HasConstInfo (IdentityT m)
+instance HasConstInfo m => HasConstInfo (ListT m)
+instance HasConstInfo m => HasConstInfo (MaybeT m)
+instance HasConstInfo m => HasConstInfo (ReaderT r m)
+instance HasConstInfo m => HasConstInfo (StateT s m)
+instance (Monoid w, HasConstInfo m) => HasConstInfo (WriterT w m)
+instance HasConstInfo m => HasConstInfo (BlockT m)
+
+{-# INLINE getConInfo #-}
+getConInfo :: HasConstInfo m => ConHead -> m Definition
+getConInfo = getConstInfo . conName
+
+-- | Look up the polarity of a definition.
+getPolarity :: HasConstInfo m => QName -> m [Polarity]
+getPolarity q = defPolarity <$> getConstInfo q
+
+-- | Look up polarity of a definition and compose with polarity
+--   represented by 'Comparison'.
+getPolarity' :: HasConstInfo m => Comparison -> QName -> m [Polarity]
+getPolarity' CmpEq  q = map (composePol Invariant) <$> getPolarity q -- return []
+getPolarity' CmpLeq q = getPolarity q -- composition with Covariant is identity
+
+-- | Set the polarity of a definition.
+setPolarity :: (MonadTCState m, MonadDebug m) => QName -> [Polarity] -> m ()
+setPolarity q pol = do
+  reportSDoc "tc.polarity.set" 20 $
+    "Setting polarity of" <+> pretty q <+> "to" <+> pretty pol <> "."
+  modifySignature $ updateDefinition q $ updateDefPolarity $ const pol
+
+-- | Look up the forced arguments of a definition.
+getForcedArgs :: HasConstInfo m => QName -> m [IsForced]
+getForcedArgs q = defForced <$> getConstInfo q
+
+-- | Get argument occurrence info for argument @i@ of definition @d@ (never fails).
+getArgOccurrence :: QName -> Nat -> TCM Occurrence
+getArgOccurrence d i = do
+  def <- getConstInfo d
+  return $! case theDef def of
+    Constructor{} -> StrictPos
+    _             -> fromMaybe Mixed $ defArgOccurrences def !!! i
+
+-- | Sets the 'defArgOccurrences' for the given identifier (which
+-- should already exist in the signature).
+setArgOccurrences :: MonadTCState m => QName -> [Occurrence] -> m ()
+setArgOccurrences d os = modifyArgOccurrences d $ const os
+
+modifyArgOccurrences :: MonadTCState m => QName -> ([Occurrence] -> [Occurrence]) -> m ()
+modifyArgOccurrences d f =
+  modifySignature $ updateDefinition d $ updateDefArgOccurrences f
+
+setTreeless :: QName -> TTerm -> TCM ()
+setTreeless q t =
+  modifyGlobalDefinition q $ updateTheDef $ \case
+    fun@Function{} -> fun{ funTreeless = Just $ Compiled t Nothing }
+    _ -> __IMPOSSIBLE__
+
+setCompiledArgUse :: QName -> [ArgUsage] -> TCM ()
+setCompiledArgUse q use =
+  modifyGlobalDefinition q $ updateTheDef $ \case
+    fun@Function{} ->
+      fun{ funTreeless = funTreeless fun <&> \ c -> c { cArgUsage = Just use } }
+    _ -> __IMPOSSIBLE__
+
+getCompiled :: HasConstInfo m => QName -> m (Maybe Compiled)
+getCompiled q = do
+  (theDef <$> getConstInfo q) <&> \case
+    Function{ funTreeless = t } -> t
+    _                           -> Nothing
+
+-- | Returns a list of length 'conArity'.
+--   If no erasure analysis has been performed yet, this will be a list of 'False's.
+getErasedConArgs :: HasConstInfo m => QName -> m [Bool]
+getErasedConArgs q = do
+  def <- getConstInfo q
+  case theDef def of
+    Constructor{ conArity, conErased } -> return $
+      fromMaybe (replicate conArity False) conErased
+    _ -> __IMPOSSIBLE__
+
+setErasedConArgs :: QName -> [Bool] -> TCM ()
+setErasedConArgs q args = modifyGlobalDefinition q $ updateTheDef $ \case
+    def@Constructor{ conArity }
+      | length args == conArity -> def{ conErased = Just args }
+      | otherwise               -> __IMPOSSIBLE__
+    def -> def   -- no-op for non-constructors
+
+getTreeless :: HasConstInfo m => QName -> m (Maybe TTerm)
+getTreeless q = fmap cTreeless <$> getCompiled q
+
+getCompiledArgUse :: HasConstInfo m => QName -> m (Maybe [ArgUsage])
+getCompiledArgUse q = (cArgUsage =<<) <$> getCompiled q
+
+-- | add data constructors to a datatype
+addDataCons :: QName -> [QName] -> TCM ()
+addDataCons d cs = modifySignature $ updateDefinition d $ updateTheDef $ \ def ->
+  let !cs' = cs ++ dataCons def in
+  case def of
+    Datatype{} -> def {dataCons = cs' }
+    _          -> __IMPOSSIBLE__
+
+-- | Get the mutually recursive identifiers of a symbol from the signature.
+getMutual :: QName -> TCM (Maybe [QName])
+getMutual d = getMutual_ . theDef <$> getConstInfo d
+
+-- | Get the mutually recursive identifiers from a `Definition`.
+getMutual_ :: Defn -> Maybe [QName]
+getMutual_ = \case
+    Function {  funMutual = m } -> m
+    Datatype { dataMutual = m } -> m
+    Record   {  recMutual = m } -> m
+    _ -> Nothing
+
+-- | Set the mutually recursive identifiers.
+setMutual :: QName -> [QName] -> TCM ()
+setMutual d m = modifySignature $ updateDefinition d $ updateTheDef $ \ def ->
+  case def of
+    Function{} -> def { funMutual = Just m }
+    Datatype{} -> def {dataMutual = Just m }
+    Record{}   -> def { recMutual = Just m }
+    _          -> if null m then def else __IMPOSSIBLE__ -- nothing to do
+
+-- | Check whether two definitions are mutually recursive.
+mutuallyRecursive :: QName -> QName -> TCM Bool
+mutuallyRecursive d d1 = (d `elem`) . fromMaybe __IMPOSSIBLE__ <$> getMutual d1
+
+-- | A function/data/record definition is nonRecursive if it is not even mutually
+--   recursive with itself.
+definitelyNonRecursive_ :: Defn -> Bool
+definitelyNonRecursive_ = maybe False null . getMutual_
+
+-- | Get the number of parameters to the current module.
+getCurrentModuleFreeVars :: TCM Nat
+getCurrentModuleFreeVars = size <$> (lookupSection =<< currentModule)
+
+--   For annoying reasons the qnameModule of a pattern lambda is not correct
+--   (#2883), so make sure to grab the right module for those.
+getDefModule :: HasConstInfo m => QName -> m (Either SigError ModuleName)
+getDefModule f = mapRight modName <$> getConstInfo' f
+  where
+    modName def = case theDef def of
+      Function{ funExtLam = Just (ExtLamInfo m _ _) } -> m
+      _                                               -> qnameModule f
+
+-- | Compute the number of free variables of a defined name. This is the sum of
+--   number of parameters shared with the current module and the number of
+--   anonymous variables (if the name comes from a let-bound module).
+getDefFreeVars :: (Functor m, Applicative m, ReadTCState m, MonadTCEnv m) => QName -> m Nat
+getDefFreeVars = getModuleFreeVars . qnameModule
+
+freeVarsToApply :: (Functor m, HasConstInfo m, HasOptions m,
+                    ReadTCState m, MonadTCEnv m, MonadDebug m)
+                => QName -> m Args
+freeVarsToApply q = do
+  vs <- moduleParamsToApply $ qnameModule q
+  -- Andreas, 2021-07-14, issue #5470
+  -- getConstInfo will fail if q is not in scope,
+  -- but in this case there are no free vars to apply, since
+  -- we cannot be in a child module of its defining module.
+  -- So if we short cut the nil-case here, we avoid the internal error of #5470.
+  if null vs then return [] else do
+  t <- defType <$> getConstInfo q
+  let TelV tel _ = telView'UpTo (size vs) t
+  unless (size tel == size vs) __IMPOSSIBLE__
+  return $ zipWith (\ arg dom -> unArg arg <$ argFromDom dom) vs $ telToList tel
+
+{-# SPECIALIZE getModuleFreeVars :: ModuleName -> TCM Nat #-}
+{-# SPECIALIZE getModuleFreeVars :: ModuleName -> ReduceM Nat #-}
+getModuleFreeVars :: (Functor m, Applicative m, MonadTCEnv m, ReadTCState m)
+                  => ModuleName -> m Nat
+getModuleFreeVars m = do
+  m0   <- commonParentModule m <$> currentModule
+  (+) <$> getAnonymousVariables m <*> (size <$> lookupSection m0)
+
+-- | Compute the context variables to apply a definition to.
+--
+--   We have to insert the module telescope of the common prefix
+--   of the current module and the module where the definition comes from.
+--   (Properly raised to the current context.)
+--
+--   Example:
+--   @
+--      module M₁ Γ where
+--        module M₁ Δ where
+--          f = ...
+--        module M₃ Θ where
+--          ... M₁.M₂.f [insert Γ raised by Θ]
+--   @
+moduleParamsToApply :: (Functor m, Applicative m, HasOptions m,
+                        MonadTCEnv m, ReadTCState m, MonadDebug m)
+                    => ModuleName -> m Args
+moduleParamsToApply m = do
+
+  traceSDoc "tc.sig.param" 90 ("computing module parameters of " <+> pretty m) $ do
+
+  -- Jesper, 2020-01-22: If the module parameter substitution for the
+  -- module cannot be found, that likely means we are within a call to
+  -- @inTopContext@. In that case we should provide no arguments for
+  -- the module parameters (see #4383).
+  caseMaybeM (getModuleParameterSub m) (return []) $ \sub -> do
+
+  traceSDoc "tc.sig.param" 60 (do
+    cxt <- getContext
+    nest 2 $ vcat
+      [ "cxt  = " <+> prettyTCM (PrettyContext cxt)
+      , "sub  = " <+> pretty sub
+      ]) $ do
+
+  -- Get the correct number of free variables (correctly raised) of @m@.
+  n   <- getModuleFreeVars m
+  traceSDoc "tc.sig.param" 60 (nest 2 $ "n    = " <+> text (show n)) $ do
+  tel <- take n . telToList <$> lookupSection m
+  traceSDoc "tc.sig.param" 60 (nest 2 $ "tel  = " <+> pretty tel) $ do
+  unless (size tel == n) __IMPOSSIBLE__
+  let args = applySubst sub $ zipWith (\ i a -> var i <$ argFromDom a) (downFrom n) tel
+  traceSDoc "tc.sig.param" 60 (nest 2 $ "args = " <+> prettyList_ (map pretty args)) $ do
+
+  -- Apply the original ArgInfo, as the hiding information in the current
+  -- context might be different from the hiding information expected by @m@.
+
+  getSection m >>= \case
+    Nothing -> do
+      -- We have no section for @m@.
+      -- This should only happen for toplevel definitions, and then there
+      -- are no free vars to apply, or?
+      -- unless (null args) __IMPOSSIBLE__
+      -- No, this invariant is violated by private modules, see Issue1701a.
+      return args
+    Just (Section stel) -> do
+      -- The section telescope of @m@ should be as least
+      -- as long as the number of free vars @m@ is applied to.
+      -- We still check here as in no case, we want @zipWith@ to silently
+      -- drop some @args@.
+      -- And there are also anonymous modules, thus, the invariant is not trivial.
+      when (size stel < size args) __IMPOSSIBLE__
+      return $ zipWith (\ !dom (Arg _ v) -> v <$ argFromDom dom) (telToList stel) args
+
+-- | Unless all variables in the context are module parameters, create a fresh
+--   module to capture the non-module parameters. Used when unquoting to make
+--   sure generated definitions work properly.
+inFreshModuleIfFreeParams :: TCM a -> TCM a
+inFreshModuleIfFreeParams k = do
+  msub <- getModuleParameterSub =<< currentModule
+  if isNothing msub || msub == Just IdS then k else do
+    m  <- currentModule
+    m' <- qualifyM m . mnameFromList1 . singleton <$>
+            freshName_ ("_" :: String)
+    addSection m'
+    withCurrentModule m' k
+
+-- | Instantiate a closed definition with the correct part of the current
+--   context.
+{-# SPECIALIZE instantiateDef :: Definition -> TCM Definition #-}
+instantiateDef
+  :: ( Functor m, HasConstInfo m, HasOptions m
+     , ReadTCState m, MonadTCEnv m, MonadDebug m )
+  => Definition -> m Definition
+instantiateDef d = do
+  vs  <- freeVarsToApply $ defName d
+  verboseS "tc.sig.inst" 30 $ do
+    ctx <- getContext
+    m   <- currentModule
+    reportSDoc "tc.sig.inst" 30 $
+      "instDef in" <+> pretty m <> ":" <+> pretty (defName d) <+>
+      fsep (map pretty $ zipWith (<$) (reverse $ map (fst . unDom) ctx) vs)
+  return $ d `apply` vs
+
+instantiateRewriteRule :: (Functor m, HasConstInfo m, HasOptions m,
+                           ReadTCState m, MonadTCEnv m, MonadDebug m)
+                       => RewriteRule -> m RewriteRule
+instantiateRewriteRule rew = do
+  traceSDoc "rewriting" 95 ("instantiating rewrite rule" <+> pretty (rewName rew) <+> "to the local context.") $ do
+  vs  <- freeVarsToApply $ rewName rew
+  let rew' = rew `apply` vs
+  traceSLn "rewriting" 95 ("instantiated rewrite rule: ") $ do
+  traceSLn "rewriting" 95 (show rew') $ do
+  return rew'
+
+instantiateRewriteRules :: (Functor m, HasConstInfo m, HasOptions m,
+                            ReadTCState m, MonadTCEnv m, MonadDebug m)
+                        => RewriteRules -> m RewriteRules
+instantiateRewriteRules = mapM instantiateRewriteRule
+
+-- | Return the abstract view of a definition, /regardless/ of whether
+-- the definition would be treated abstractly.
+alwaysMakeAbstract :: Definition -> Maybe Definition
+alwaysMakeAbstract d =
+  do
+    def <- makeAbs $ theDef d
+    pure d { defArgOccurrences = [] -- no positivity info for abstract things!
+           , defPolarity       = [] -- no polarity info for abstract things!
+           , theDef = def
+           }
+  where
+    makeAbs d@Axiom{}            = Just d
+    makeAbs d@DataOrRecSig{}     = Just d
+    makeAbs d@GeneralizableVar{} = Just d
+    makeAbs d@Datatype {} = Just $ AbstractDefn d
+    makeAbs d@Function {} = Just $ AbstractDefn d
+    makeAbs Constructor{} = Nothing
+    -- Andreas, 2012-11-18:  Make record constructor and projections abstract.
+    -- Andreas, 2017-08-14:  Projections are actually not abstract (issue #2682).
+    -- Return the Defn under a wrapper to allow e.g. eligibleForProjectionLike
+    -- to see whether the abstract thing is a record type or not.
+    makeAbs d@Record{}    = Just $ AbstractDefn d
+    makeAbs Primitive{}   = __IMPOSSIBLE__
+    makeAbs PrimitiveSort{} = __IMPOSSIBLE__
+    makeAbs AbstractDefn{} = __IMPOSSIBLE__
+
+-- | Enter abstract mode. Abstract definition in the current module are transparent.
+{-# SPECIALIZE inAbstractMode :: TCM a -> TCM a #-}
+inAbstractMode :: MonadTCEnv m => m a -> m a
+inAbstractMode = localTC $ \e -> e { envAbstractMode = AbstractMode }
+
+-- | Not in abstract mode. All abstract definitions are opaque.
+{-# SPECIALIZE inConcreteMode :: TCM a -> TCM a #-}
+inConcreteMode :: MonadTCEnv m => m a -> m a
+inConcreteMode = localTC $ \e -> e { envAbstractMode = ConcreteMode }
+
+-- | Ignore abstract mode. All abstract definitions are transparent.
+ignoreAbstractMode :: MonadTCEnv m => m a -> m a
+ignoreAbstractMode = localTC $ \e -> e { envAbstractMode = IgnoreAbstractMode }
+
+-- | Go under the given opaque block. The unfolding set will turn opaque
+-- definitions transparent.
+{-# SPECIALIZE underOpaqueId :: OpaqueId -> TCM a -> TCM a #-}
+underOpaqueId :: MonadTCEnv m => OpaqueId -> m a -> m a
+underOpaqueId i = localTC $ \e -> e { envCurrentOpaqueId = Just i }
+
+-- | Outside of any opaque blocks.
+{-# SPECIALIZE notUnderOpaque :: TCM a -> TCM a #-}
+notUnderOpaque :: MonadTCEnv m => m a -> m a
+notUnderOpaque = localTC $ \e -> e { envCurrentOpaqueId = Nothing }
+
+-- | Enter the reducibility environment associated with a definition:
+-- The environment will have the same concreteness as the name, and we
+-- will be in the opaque block enclosing the name, if any.
+{-# SPECIALIZE inConcreteOrAbstractMode :: QName -> (Definition -> TCM a) -> TCM a #-}
+inConcreteOrAbstractMode :: (MonadTCEnv m, HasConstInfo m) => QName -> (Definition -> m a) -> m a
+inConcreteOrAbstractMode q cont = do
+  -- Andreas, 2015-07-01: If we do not ignoreAbstractMode here,
+  -- we will get ConcreteDef for abstract things, as they are turned into axioms.
+  def <- ignoreAbstractMode $ getConstInfo q
+  let
+    k1 = case defAbstract def of
+      AbstractDef -> inAbstractMode
+      ConcreteDef -> inConcreteMode
+
+    k2 = case defOpaque def of
+      OpaqueDef i    -> underOpaqueId i
+      TransparentDef -> notUnderOpaque
+  k2 (k1 (cont def))
+
+-- | Get type of a constant, instantiated to the current context.
+{-# SPECIALIZE typeOfConst :: QName -> TCM Type #-}
+typeOfConst :: (HasConstInfo m, ReadTCState m) => QName -> m Type
+typeOfConst q = defType <$> (instantiateDef =<< getConstInfo q)
+
+-- | Get relevance of a constant.
+{-# SPECIALIZE relOfConst :: QName -> TCM Relevance #-}
+relOfConst :: HasConstInfo m => QName -> m Relevance
+relOfConst q = getRelevance <$> getConstInfo q
+
+-- | Get modality of a constant.
+{-# SPECIALIZE modalityOfConst :: QName -> TCM Modality #-}
+modalityOfConst :: HasConstInfo m => QName -> m Modality
+modalityOfConst q = getModality <$> getConstInfo q
+
+-- | The number of dropped parameters for a definition.
+--   0 except for projection(-like) functions and constructors.
+droppedPars :: Definition -> Int
+droppedPars d = case theDef d of
+    Axiom{}                  -> 0
+    DataOrRecSig{}           -> 0
+    GeneralizableVar{}       -> 0
+    def@Function{}           -> projectionArgs d
+    Datatype  {dataPars = _} -> 0  -- not dropped
+    Record     {recPars = _} -> 0  -- not dropped
+    Constructor{conPars = n} -> n
+    Primitive{}              -> 0
+    PrimitiveSort{}          -> 0
+    AbstractDefn{}           -> __IMPOSSIBLE__
+
+-- | Is it the name of a record projection?
+{-# SPECIALIZE isProjection :: QName -> TCM (Maybe Projection) #-}
+isProjection :: HasConstInfo m => QName -> m (Maybe Projection)
+isProjection qn = isProjection_ . theDef <$> getConstInfo qn
+
+isProjection_ :: Defn -> Maybe Projection
+isProjection_ def =
+  case def of
+    Function { funProjection = Right result } -> Just result
+    _                                         -> Nothing
+
+-- | Is it the name of a non-irrelevant record projection?
+{-# SPECIALIZE isProjection :: QName -> TCM (Maybe Projection) #-}
+isRelevantProjection :: HasConstInfo m => QName -> m (Maybe Projection)
+isRelevantProjection qn = isRelevantProjection_ <$> getConstInfo qn
+
+isRelevantProjection_ :: Definition -> Maybe Projection
+isRelevantProjection_ def =
+  if isIrrelevant def then Nothing else isProjection_ $ theDef def
+
+-- | Is it a function marked STATIC?
+isStaticFun :: Defn -> Bool
+isStaticFun = (^. funStatic)
+
+-- | Is it a function marked INLINE?
+isInlineFun :: Defn -> Bool
+isInlineFun = (^. funInline)
+
+-- | Returns @True@ if we are dealing with a proper projection,
+--   i.e., not a projection-like function nor a record field value
+--   (projection applied to argument).
+isProperProjection :: Defn -> Bool
+isProperProjection d = caseMaybe (isProjection_ d) False $ \ isP ->
+  (projIndex isP > 0) && isJust (projProper isP)
+
+-- | Number of dropped initial arguments of a projection(-like) function.
+projectionArgs :: Definition -> Int
+projectionArgs = maybe 0 (max 0 . pred . projIndex) . isRelevantProjection_
+
+-- | Check whether a definition uses copatterns.
+usesCopatterns :: (HasConstInfo m) => QName -> m Bool
+usesCopatterns q = defCopatternLHS <$> getConstInfo q
+
+-- | Apply a function @f@ to its first argument, producing the proper
+--   postfix projection if @f@ is a projection which is not irrelevant.
+applyDef :: (HasConstInfo m)
+         => ProjOrigin -> QName -> Arg Term -> m Term
+applyDef o f a = do
+  let fallback = return $ Def f [Apply a]
+  -- Andreas, 2022-03-07, issue #5809: don't drop parameters of irrelevant projections.
+  caseMaybeM (isRelevantProjection f) fallback $ \ isP -> do
+    if projIndex isP <= 0 then fallback else do
+      -- Get the original projection, if existing.
+      if isNothing (projProper isP) then fallback else do
+        return $ unArg a `applyE` [Proj o $ projOrig isP]
diff --git a/src/full/Agda/TypeChecking/Monad/Signature.hs-boot b/src/full/Agda/TypeChecking/Monad/Signature.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Signature.hs-boot
@@ -0,0 +1,56 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Signature where
+
+import qualified Control.Monad.Fail as Fail
+import Control.Monad.Reader
+import Control.Monad.State
+
+import Agda.Syntax.Abstract.Name (QName)
+import Agda.Syntax.Internal (ModuleName, Telescope)
+
+import Agda.TypeChecking.Monad.Base
+  ( TCM, ReadTCState, HasOptions, MonadTCEnv
+  , Definition, RewriteRules
+  )
+import Agda.TypeChecking.Monad.Debug (MonadDebug)
+
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+data SigError = SigUnknown String | SigAbstract | SigCubicalNotErasure
+
+notSoPrettySigCubicalNotErasure :: QName -> String
+
+class ( Functor m
+      , Applicative m
+      , Fail.MonadFail m
+      , HasOptions m
+      , MonadDebug m
+      , MonadTCEnv m
+      ) => HasConstInfo m where
+  getConstInfo :: QName -> m Definition
+  getConstInfo q = getConstInfo' q >>= \case
+      Right d -> return d
+      Left (SigUnknown err) -> __IMPOSSIBLE_VERBOSE__ err
+      Left SigAbstract      -> __IMPOSSIBLE_VERBOSE__ $
+        "Abstract, thus, not in scope: " ++ prettyShow q
+      Left SigCubicalNotErasure -> __IMPOSSIBLE_VERBOSE__ $
+        notSoPrettySigCubicalNotErasure q
+
+  getConstInfo' :: QName -> m (Either SigError Definition)
+  -- getConstInfo' q = Right <$> getConstInfo q
+  getRewriteRulesFor :: QName -> m RewriteRules
+
+  default getConstInfo' :: (HasConstInfo n, MonadTrans t, m ~ t n) => QName -> m (Either SigError Definition)
+  getConstInfo' = lift . getConstInfo'
+
+  default getRewriteRulesFor :: (HasConstInfo n, MonadTrans t, m ~ t n) => QName -> m RewriteRules
+  getRewriteRulesFor = lift . getRewriteRulesFor
+
+instance HasConstInfo m => HasConstInfo (ReaderT r m)
+instance HasConstInfo m => HasConstInfo (StateT s m)
+
+instance HasConstInfo TCM where
+
+inFreshModuleIfFreeParams :: TCM a -> TCM a
+lookupSection :: (Functor m, ReadTCState m) => ModuleName -> m Telescope
diff --git a/src/full/Agda/TypeChecking/Monad/SizedTypes.hs b/src/full/Agda/TypeChecking/Monad/SizedTypes.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/SizedTypes.hs
@@ -0,0 +1,335 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Stuff for sized types that does not require modules
+--   "Agda.TypeChecking.Reduce" or "Agda.TypeChecking.Constraints"
+--   (which import "Agda.TypeChecking.Monad").
+
+module Agda.TypeChecking.Monad.SizedTypes where
+
+import Control.Monad.Except
+
+import qualified Data.Foldable as Fold
+import qualified Data.Traversable as Trav
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.State
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- * Testing for type 'Size'
+------------------------------------------------------------------------
+
+-- | Result of querying whether size variable @i@ is bounded by another
+--   size.
+data BoundedSize
+  =  BoundedLt Term -- ^ yes @i : Size< t@
+  |  BoundedNo
+     deriving (Eq, Show)
+
+-- | Check if a type is the 'primSize' type. The argument should be 'reduce'd.
+class IsSizeType a where
+  isSizeType :: (HasOptions m, HasBuiltins m) => a -> m (Maybe BoundedSize)
+
+instance IsSizeType a => IsSizeType (Dom a) where
+  isSizeType = isSizeType . unDom
+
+instance IsSizeType a => IsSizeType (b,a) where
+  isSizeType = isSizeType . snd
+
+instance IsSizeType a => IsSizeType (Type' a) where
+  isSizeType = isSizeType . unEl
+
+instance IsSizeType Term where
+  isSizeType v = isSizeTypeTest <*> pure v
+
+instance IsSizeType CompareAs where
+  isSizeType (AsTermsOf a) = isSizeType a
+  isSizeType AsSizes       = return $ Just BoundedNo
+  isSizeType AsTypes       = return Nothing
+
+isSizeTypeTest :: (HasOptions m, HasBuiltins m) => m (Term -> Maybe BoundedSize)
+isSizeTypeTest =
+  flip (ifM sizedTypesOption) (return $ const Nothing) $ do
+    (size, sizelt) <- getBuiltinSize
+    let testType (Def d [])        | Just d == size   = Just BoundedNo
+        testType (Def d [Apply v]) | Just d == sizelt = Just $ BoundedLt $ unArg v
+        testType _                                    = Nothing
+    return testType
+
+getBuiltinDefName :: (HasBuiltins m) => BuiltinId -> m (Maybe QName)
+getBuiltinDefName s = fromDef <$> getBuiltin' s
+  where
+    fromDef (Just (Def d [])) = Just d
+    fromDef _                 = Nothing
+
+getBuiltinSize :: (HasBuiltins m) => m (Maybe QName, Maybe QName)
+getBuiltinSize = do
+  size   <- getBuiltinDefName builtinSize
+  sizelt <- getBuiltinDefName builtinSizeLt
+  return (size, sizelt)
+
+isSizeNameTest :: (HasOptions m, HasBuiltins m) => m (QName -> Bool)
+isSizeNameTest = ifM sizedTypesOption
+  isSizeNameTestRaw
+  (return $ const False)
+
+isSizeNameTestRaw :: (HasOptions m, HasBuiltins m) => m (QName -> Bool)
+isSizeNameTestRaw = do
+  (size, sizelt) <- getBuiltinSize
+  return $ (`elem` [size, sizelt]) . Just
+
+-- | Test whether OPTIONS --sized-types and whether
+--   the size built-ins are defined.
+haveSizedTypes :: TCM Bool
+haveSizedTypes = do
+    Def _ [] <- primSize
+    Def _ [] <- primSizeInf
+    Def _ [] <- primSizeSuc
+    sizedTypesOption
+  `catchError` \_ -> return False
+
+-- | Test whether the SIZELT builtin is defined.
+haveSizeLt :: TCM Bool
+haveSizeLt = isJust <$> getBuiltinDefName builtinSizeLt
+
+-- | Add polarity info to a SIZE builtin.
+builtinSizeHook :: BuiltinId -> QName -> Type -> TCM ()
+builtinSizeHook s q t = do
+  when (s `elem` [builtinSizeLt, builtinSizeSuc]) $ do
+    modifySignature $ updateDefinition q
+      $ updateDefPolarity       (const [Covariant])
+      . updateDefArgOccurrences (const [StrictPos])
+  when (s == builtinSizeMax) $ do
+    modifySignature $ updateDefinition q
+      $ updateDefPolarity       (const [Covariant, Covariant])
+      . updateDefArgOccurrences (const [StrictPos, StrictPos])
+{-
+      . updateDefType           (const tmax)
+  where
+    -- TODO: max : (i j : Size) -> Size< (suc (max i j))
+    tmax =
+-}
+
+------------------------------------------------------------------------
+-- * Constructors
+------------------------------------------------------------------------
+
+-- | The sort of built-in types @SIZE@ and @SIZELT@.
+sizeSort :: Sort
+sizeSort = mkType 0
+
+-- | The type of built-in types @SIZE@ and @SIZELT@.
+sizeUniv :: Type
+sizeUniv = sort $ sizeSort
+
+-- | The built-in type @SIZE@ with user-given name.
+sizeType_ :: QName -> Type
+sizeType_ size = El sizeSort $ Def size []
+
+{-# SPECIALIZE sizeType :: TCM Type #-}
+-- | The built-in type @SIZE@.
+sizeType :: (HasBuiltins m, MonadTCEnv m, ReadTCState m) => m Type
+sizeType = El sizeSort . fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSize
+
+-- | The name of @SIZESUC@.
+sizeSucName :: (HasBuiltins m, HasOptions m) => m (Maybe QName)
+sizeSucName = do
+  ifM (not <$> sizedTypesOption) (return Nothing) $ do
+    getBuiltin' builtinSizeSuc >>= \case
+      Just (Def x []) -> return $ Just x
+      _               -> return Nothing
+
+{-# SPECIALIZE sizeSuc :: Nat -> Term -> TCM Term #-}
+sizeSuc :: HasBuiltins m => Nat -> Term -> m Term
+sizeSuc n v | n < 0     = __IMPOSSIBLE__
+            | n == 0    = return v
+            | otherwise = do
+  Def suc [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSizeSuc
+  return $ fromMaybe __IMPOSSIBLE__ (iterate (sizeSuc_ suc) v !!! n)
+
+sizeSuc_ :: QName -> Term -> Term
+sizeSuc_ suc v = Def suc [Apply $ defaultArg v]
+
+-- | Transform list of terms into a term build from binary maximum.
+sizeMax :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+        => List1 Term -> m Term
+sizeMax vs = case vs of
+  v :| [] -> return v
+  vs  -> do
+    Def max [] <- primSizeMax
+    return $ foldr1 (\ u v -> Def max $ map (Apply . defaultArg) [u,v]) vs
+
+
+------------------------------------------------------------------------
+-- * Viewing and unviewing sizes
+------------------------------------------------------------------------
+
+-- | A useful view on sizes.
+data SizeView = SizeInf | SizeSuc Term | OtherSize Term
+
+-- | Expects argument to be 'reduce'd.
+sizeView :: (HasBuiltins m, MonadTCEnv m, ReadTCState m)
+         => Term -> m SizeView
+sizeView v = do
+  Def inf [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSizeInf
+  Def suc [] <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSizeSuc
+  case v of
+    Def x []        | x == inf -> return SizeInf
+    Def x [Apply u] | x == suc -> return $ SizeSuc (unArg u)
+    _                          -> return $ OtherSize v
+
+-- | A de Bruijn index under some projections.
+
+data ProjectedVar = ProjectedVar
+  { pvIndex :: Int
+  , prProjs :: [(ProjOrigin, QName)]
+  }
+  deriving (Show)
+
+-- | Ignore 'ProjOrigin' in equality test.
+
+instance Eq ProjectedVar where
+  ProjectedVar i prjs == ProjectedVar i' prjs' =
+    i == i' && map snd prjs == map snd prjs'
+
+viewProjectedVar :: Term -> Maybe ProjectedVar
+viewProjectedVar = \case
+  Var i es -> ProjectedVar i <$> mapM isProjElim es
+  _ -> Nothing
+
+unviewProjectedVar :: ProjectedVar -> Term
+unviewProjectedVar (ProjectedVar i prjs) = Var i $ map (uncurry Proj) prjs
+
+type Offset = Nat
+
+-- | A deep view on sizes.
+data DeepSizeView
+  = DSizeInf
+  | DSizeVar ProjectedVar Offset
+  | DSizeMeta MetaId Elims Offset
+  | DOtherSize Term
+  deriving (Show)
+
+instance Pretty DeepSizeView where
+  pretty = \case
+    DSizeInf        -> "∞"
+    DSizeVar pv o    -> pretty (unviewProjectedVar pv) <+> "+" <+> pretty o
+    DSizeMeta x es o -> pretty (MetaV x es) <+> "+" <+> pretty o
+    DOtherSize t     -> pretty t
+
+data SizeViewComparable a
+  = NotComparable
+  | YesAbove DeepSizeView a
+  | YesBelow DeepSizeView a
+  deriving (Functor)
+
+-- | @sizeViewComparable v w@ checks whether @v >= w@ (then @Left@)
+--   or @v <= w@ (then @Right@).  If uncomparable, it returns @NotComparable@.
+sizeViewComparable :: DeepSizeView -> DeepSizeView -> SizeViewComparable ()
+sizeViewComparable v w = case (v,w) of
+  (DSizeInf, _) -> YesAbove w ()
+  (_, DSizeInf) -> YesBelow w ()
+  (DSizeVar x n, DSizeVar y m) | x == y -> if n >= m then YesAbove w () else YesBelow w ()
+  _ -> NotComparable
+
+sizeViewSuc_ :: QName -> DeepSizeView -> DeepSizeView
+sizeViewSuc_ suc = \case
+  DSizeInf         -> DSizeInf
+  DSizeVar i n     -> DSizeVar i (n + 1)
+  DSizeMeta x vs n -> DSizeMeta x vs (n + 1)
+  DOtherSize u     -> DOtherSize $ sizeSuc_ suc u
+
+-- | @sizeViewPred k v@ decrements @v@ by @k@ (must be possible!).
+sizeViewPred :: Nat -> DeepSizeView -> DeepSizeView
+sizeViewPred 0 = id
+sizeViewPred k = \case
+  DSizeInf -> DSizeInf
+  DSizeVar  i    n | n >= k -> DSizeVar  i    (n - k)
+  DSizeMeta x vs n | n >= k -> DSizeMeta x vs (n - k)
+  _ -> __IMPOSSIBLE__
+
+-- | @sizeViewOffset v@ returns the number of successors or Nothing when infty.
+sizeViewOffset :: DeepSizeView -> Maybe Offset
+sizeViewOffset = \case
+  DSizeInf         -> Nothing
+  DSizeVar i n     -> Just n
+  DSizeMeta x vs n -> Just n
+  DOtherSize u     -> Just 0
+
+-- | Remove successors common to both sides.
+removeSucs :: (DeepSizeView, DeepSizeView) -> (DeepSizeView, DeepSizeView)
+removeSucs (v, w) = (sizeViewPred k v, sizeViewPred k w)
+  where k = case (sizeViewOffset v, sizeViewOffset w) of
+              (Just  n, Just  m) -> min n m
+              (Just  n, Nothing) -> n
+              (Nothing, Just  m) -> m
+              (Nothing, Nothing) -> 0
+
+-- | Turn a size view into a term.
+unSizeView :: SizeView -> TCM Term
+unSizeView SizeInf       = primSizeInf
+unSizeView (SizeSuc v)   = sizeSuc 1 v
+unSizeView (OtherSize v) = return v
+
+unDeepSizeView :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+               => DeepSizeView -> m Term
+unDeepSizeView = \case
+  DSizeInf         -> primSizeInf
+  DSizeVar pv    n -> sizeSuc n $ unviewProjectedVar pv
+  DSizeMeta x us n -> sizeSuc n $ MetaV x us
+  DOtherSize u     -> return u
+
+------------------------------------------------------------------------
+-- * View on sizes where maximum is pulled to the top
+------------------------------------------------------------------------
+
+type SizeMaxView = List1 DeepSizeView
+type SizeMaxView' = [DeepSizeView]
+
+maxViewMax :: SizeMaxView -> SizeMaxView -> SizeMaxView
+maxViewMax v w = case (v,w) of
+  (DSizeInf :| _, _) -> singleton DSizeInf
+  (_, DSizeInf :| _) -> singleton DSizeInf
+  _                 -> Fold.foldr maxViewCons w v
+
+-- | @maxViewCons v ws = max v ws@.  It only adds @v@ to @ws@ if it is not
+--   subsumed by an element of @ws@.
+maxViewCons :: DeepSizeView -> SizeMaxView -> SizeMaxView
+maxViewCons _ (DSizeInf :| _) = singleton DSizeInf
+maxViewCons DSizeInf _        = singleton DSizeInf
+maxViewCons v ws = case sizeViewComparableWithMax v ws of
+  NotComparable  -> List1.cons v ws
+  YesAbove _ ws' -> v :| ws'
+  YesBelow{}     -> ws
+
+-- | @sizeViewComparableWithMax v ws@ tries to find @w@ in @ws@ that compares with @v@
+--   and singles this out.
+--   Precondition: @v /= DSizeInv@.
+sizeViewComparableWithMax :: DeepSizeView -> SizeMaxView -> SizeViewComparable SizeMaxView'
+sizeViewComparableWithMax v (w :| ws) =
+  case (ws, sizeViewComparable v w) of
+    (w':ws', NotComparable) -> (w:) <$> sizeViewComparableWithMax v (w' :| ws')
+    (ws    , r)             -> fmap (const ws) r
+
+
+maxViewSuc_ :: QName -> SizeMaxView -> SizeMaxView
+maxViewSuc_ suc = fmap (sizeViewSuc_ suc)
+
+unMaxView :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m)
+          => SizeMaxView -> m Term
+unMaxView vs = sizeMax =<< Trav.mapM unDeepSizeView vs
diff --git a/src/full/Agda/TypeChecking/Monad/State.hs b/src/full/Agda/TypeChecking/Monad/State.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/State.hs
@@ -0,0 +1,558 @@
+-- | Lenses for 'TCState' and more.
+
+module Agda.TypeChecking.Monad.State where
+
+import qualified Control.Exception as E
+
+import Control.Monad       (void, when)
+import Control.Monad.Trans (MonadIO, liftIO)
+
+import Data.Maybe
+
+import qualified Data.Map as Map
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.HashMap.Strict as HMap
+
+import Agda.Benchmarking
+
+import Agda.Interaction.Response
+  (InteractionOutputCallback, Response)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Scope.Base
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Abstract (PatternSynDefn, PatternSynDefns)
+import Agda.Syntax.Abstract.PatternSynonyms
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Warnings
+
+import Agda.TypeChecking.Monad.Debug (reportSDoc, reportSLn, verboseS)
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.CompiledClause
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Lens
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Monad (bracket_)
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+-- | Resets the non-persistent part of the type checking state.
+
+resetState :: TCM ()
+resetState = do
+    pers <- getsTC stPersistentState
+    putTC $ initState { stPersistentState = pers }
+
+-- | Resets all of the type checking state.
+--
+--   Keep only 'Benchmark' and backend information.
+
+resetAllState :: TCM ()
+resetAllState = do
+    b <- getBenchmark
+    backends <- useTC stBackends
+    putTC $ updatePersistentState (\ s -> s { stBenchmark = b }) initState
+    stBackends `setTCLens` backends
+-- resetAllState = putTC initState
+
+-- | Restore 'TCState' after performing subcomputation.
+--
+--   In contrast to 'Agda.Utils.Monad.localState', the 'Benchmark'
+--   info from the subcomputation is saved.
+localTCState :: TCM a -> TCM a
+localTCState = bracket_ getTC (\ s -> do
+   b <- getBenchmark
+   putTC s
+   modifyBenchmark $ const b)
+
+-- | Same as 'localTCState' but also returns the state in which we were just
+--   before reverting it.
+localTCStateSaving :: TCM a -> TCM (a, TCState)
+localTCStateSaving compute = do
+  oldState <- getTC
+  result <- compute
+  newState <- getTC
+  do
+    b <- getBenchmark
+    putTC oldState
+    modifyBenchmark $ const b
+  return (result, newState)
+
+-- | Same as 'localTCState' but keep all warnings.
+localTCStateSavingWarnings :: TCM a -> TCM a
+localTCStateSavingWarnings compute = do
+  (result, newState) <- localTCStateSaving compute
+  modifyTC $ over stTCWarnings $ const $ newState ^. stTCWarnings
+  return result
+
+data SpeculateResult = SpeculateAbort | SpeculateCommit
+
+-- | Allow rolling back the state changes of a TCM computation.
+speculateTCState :: TCM (a, SpeculateResult) -> TCM a
+speculateTCState m = do
+  ((x, res), newState) <- localTCStateSaving m
+  case res of
+    SpeculateAbort  -> return x
+    SpeculateCommit -> x <$ putTC newState
+
+speculateTCState_ :: TCM SpeculateResult -> TCM ()
+speculateTCState_ m = void $ speculateTCState $ ((),) <$> m
+
+-- | A fresh TCM instance.
+--
+-- The computation is run in a fresh state, with the exception that
+-- the persistent state is preserved. If the computation changes the
+-- state, then these changes are ignored, except for changes to the
+-- persistent state. (Changes to the persistent state are also ignored
+-- if errors other than type errors or IO exceptions are encountered.)
+
+freshTCM :: TCM a -> TCM (Either TCErr a)
+freshTCM m = do
+  ps <- useTC lensPersistentState
+  let s = set lensPersistentState ps initState
+  r <- liftIO $ (Right <$> runTCM initEnv s m) `E.catch` (return . Left)
+  case r of
+    Right (a, s) -> do
+      setTCLens lensPersistentState $ s ^. lensPersistentState
+      return $ Right a
+    Left err -> do
+      case err of
+        TypeError { tcErrState = s } ->
+          setTCLens lensPersistentState $ s ^. lensPersistentState
+        IOException s _ _ ->
+          setTCLens lensPersistentState $ s ^. lensPersistentState
+        _ -> return ()
+      return $ Left err
+
+---------------------------------------------------------------------------
+-- * Lens for persistent states and its fields
+---------------------------------------------------------------------------
+
+lensPersistentState :: Lens' TCState PersistentTCState
+lensPersistentState f s =
+  f (stPersistentState s) <&> \ p -> s { stPersistentState = p }
+
+updatePersistentState
+  :: (PersistentTCState -> PersistentTCState) -> (TCState -> TCState)
+updatePersistentState f s = s { stPersistentState = f (stPersistentState s) }
+
+modifyPersistentState :: (PersistentTCState -> PersistentTCState) -> TCM ()
+modifyPersistentState = modifyTC . updatePersistentState
+
+-- | Lens for 'stAccumStatistics'.
+
+lensAccumStatisticsP :: Lens' PersistentTCState Statistics
+lensAccumStatisticsP f s = f (stAccumStatistics s) <&> \ a ->
+  s { stAccumStatistics = a }
+
+lensAccumStatistics :: Lens' TCState Statistics
+lensAccumStatistics =  lensPersistentState . lensAccumStatisticsP
+
+---------------------------------------------------------------------------
+-- * Scope
+---------------------------------------------------------------------------
+
+{-# INLINE getScope #-}
+-- | Get the current scope.
+getScope :: ReadTCState m => m ScopeInfo
+getScope = useR stScope
+
+{-# INLINE setScope #-}
+-- | Set the current scope.
+setScope :: ScopeInfo -> TCM ()
+setScope scope = modifyScope (const scope)
+
+{-# INLINE modifyScope_ #-}
+-- | Modify the current scope without updating the inverse maps.
+modifyScope_ :: MonadTCState m => (ScopeInfo -> ScopeInfo) -> m ()
+modifyScope_ f = stScope `modifyTCLens` f
+
+{-# INLINE modifyScope #-}
+-- | Modify the current scope.
+modifyScope :: MonadTCState m => (ScopeInfo -> ScopeInfo) -> m ()
+modifyScope f = modifyScope_ (recomputeInverseScopeMaps . f)
+
+{-# INLINE useScope #-}
+-- | Get a part of the current scope.
+useScope :: ReadTCState m => Lens' ScopeInfo a -> m a
+useScope l = useR $ stScope . l
+
+{-# INLINE locallyScope #-}
+-- | Run a computation in a modified scope.
+locallyScope :: ReadTCState m => Lens' ScopeInfo a -> (a -> a) -> m b -> m b
+locallyScope l = locallyTCState $ stScope . l
+
+{-# INLINE withScope #-}
+-- | Run a computation in a local scope.
+withScope :: ReadTCState m => ScopeInfo -> m a -> m (a, ScopeInfo)
+withScope s m = locallyTCState stScope (recomputeInverseScopeMaps . const s) $ (,) <$> m <*> getScope
+
+{-# INLINE withScope_ #-}
+-- | Same as 'withScope', but discard the scope from the computation.
+withScope_ :: ReadTCState m => ScopeInfo -> m a -> m a
+withScope_ s m = fst <$> withScope s m
+
+-- | Discard any changes to the scope by a computation.
+localScope :: TCM a -> TCM a
+localScope m = do
+  scope <- getScope
+  x <- m
+  setScope scope
+  return x
+
+-- | Scope error.
+notInScopeError :: C.QName -> TCM a
+notInScopeError x = do
+  printScope "unbound" 5 ""
+  typeError $ NotInScope [x]
+
+notInScopeWarning :: C.QName -> TCM ()
+notInScopeWarning x = do
+  printScope "unbound" 5 ""
+  warning $ NotInScopeW [x]
+
+-- | Debug print the scope.
+printScope :: String -> Int -> String -> TCM ()
+printScope tag v s = verboseS ("scope." ++ tag) v $ do
+  scope <- getScope
+  reportSDoc ("scope." ++ tag) v $ return $ vcat [ text s, pretty scope ]
+
+---------------------------------------------------------------------------
+-- * Signature
+---------------------------------------------------------------------------
+
+-- ** Lens for 'stSignature' and 'stImports'
+
+{-# INLINE modifySignature  #-}
+modifySignature :: MonadTCState m => (Signature -> Signature) -> m ()
+modifySignature f = stSignature `modifyTCLens` f
+
+{-# INLINE modifyImportedSignature #-}
+modifyImportedSignature :: MonadTCState m => (Signature -> Signature) -> m ()
+modifyImportedSignature f = stImports `modifyTCLens` f
+
+{-# INLINE getSignature #-}
+getSignature :: ReadTCState m => m Signature
+getSignature = useR stSignature
+
+{-# SPECIALIZE modifyGlobalDefinition :: QName -> (Definition -> Definition) -> TCM () #-}
+-- | Update a possibly imported definition. Warning: changes made to imported
+--   definitions (during type checking) will not persist outside the current
+--   module. This function is currently used to update the compiled
+--   representation of a function during compilation.
+modifyGlobalDefinition :: MonadTCState m => QName -> (Definition -> Definition) -> m ()
+modifyGlobalDefinition q f = do
+  modifySignature         $ updateDefinition q f
+  modifyImportedSignature $ updateDefinition q f
+
+{-# INLINE setSignature #-}
+setSignature :: MonadTCState m => Signature -> m ()
+setSignature sig = modifySignature $ const sig
+
+{-# SPECIALIZE withSignature :: Signature -> TCM a -> TCM a #-}
+-- | Run some computation in a different signature, restore original signature.
+withSignature :: (ReadTCState m, MonadTCState m) => Signature -> m a -> m a
+withSignature sig m = do
+  sig0 <- getSignature
+  setSignature sig
+  r <- m
+  setSignature sig0
+  return r
+
+-- ** Modifiers for rewrite rules
+addRewriteRulesFor :: QName -> RewriteRules -> [QName] -> Signature -> Signature
+addRewriteRulesFor f rews matchables =
+    over sigRewriteRules (HMap.insertWith mappend f rews)
+  . updateDefinition f (updateTheDef setNotInjective . setCopatternLHS)
+  . (setMatchableSymbols f matchables)
+    where
+      setNotInjective def@Function{} = def { funInv = NotInjective }
+      setNotInjective def            = def
+
+      setCopatternLHS =
+        updateDefCopatternLHS (|| any hasProjectionPattern rews)
+
+      hasProjectionPattern rew = any (isJust . isProjElim) $ rewPats rew
+
+setMatchableSymbols :: QName -> [QName] -> Signature -> Signature
+setMatchableSymbols f matchables =
+  foldr ((.) . (\g -> updateDefinition g setMatchable)) id matchables
+    where
+      setMatchable def = def { defMatchable = Set.insert f $ defMatchable def }
+
+-- ** Modifiers for parts of the signature
+
+lookupDefinition :: QName -> Signature -> Maybe Definition
+lookupDefinition q sig = HMap.lookup q $ sig ^. sigDefinitions
+
+updateDefinitions :: (Definitions -> Definitions) -> Signature -> Signature
+updateDefinitions = over sigDefinitions
+
+updateDefinition :: QName -> (Definition -> Definition) -> Signature -> Signature
+updateDefinition q f = updateDefinitions $ HMap.adjust f q
+
+updateTheDef :: (Defn -> Defn) -> (Definition -> Definition)
+updateTheDef f def = def { theDef = f (theDef def) }
+
+updateDefType :: (Type -> Type) -> (Definition -> Definition)
+updateDefType f def = def { defType = f (defType def) }
+
+updateDefArgOccurrences :: ([Occurrence] -> [Occurrence]) -> (Definition -> Definition)
+updateDefArgOccurrences f def = def { defArgOccurrences = f (defArgOccurrences def) }
+
+updateDefPolarity :: ([Polarity] -> [Polarity]) -> (Definition -> Definition)
+updateDefPolarity f def = def { defPolarity = f (defPolarity def) }
+
+updateDefCompiledRep :: (CompiledRepresentation -> CompiledRepresentation) -> (Definition -> Definition)
+updateDefCompiledRep f def = def { defCompiledRep = f (defCompiledRep def) }
+
+addCompilerPragma :: BackendName -> CompilerPragma -> Definition -> Definition
+addCompilerPragma backend pragma = updateDefCompiledRep $ Map.insertWith (++) backend [pragma]
+
+updateFunClauses :: ([Clause] -> [Clause]) -> (Defn -> Defn)
+updateFunClauses f def@Function{ funClauses = cs} = def { funClauses = f cs }
+updateFunClauses f _                              = __IMPOSSIBLE__
+
+updateCovering :: ([Clause] -> [Clause]) -> (Defn -> Defn)
+updateCovering f def@Function{ funCovering = cs} = def { funCovering = f cs }
+updateCovering f _                               = __IMPOSSIBLE__
+
+updateCompiledClauses :: (Maybe CompiledClauses -> Maybe CompiledClauses) -> (Defn -> Defn)
+updateCompiledClauses f def@Function{ funCompiled = cc} = def { funCompiled = f cc }
+updateCompiledClauses f _                              = __IMPOSSIBLE__
+
+updateDefCopatternLHS :: (Bool -> Bool) -> Definition -> Definition
+updateDefCopatternLHS f def@Defn{ defCopatternLHS = b } = def { defCopatternLHS = f b }
+
+updateDefBlocked :: (Blocked_ -> Blocked_) -> Definition -> Definition
+updateDefBlocked f def@Defn{ defBlocked = b } = def { defBlocked = f b }
+
+---------------------------------------------------------------------------
+-- * Top level module
+---------------------------------------------------------------------------
+
+-- | Tries to convert a raw top-level module name to a top-level
+-- module name.
+
+topLevelModuleName :: RawTopLevelModuleName -> TCM TopLevelModuleName
+topLevelModuleName raw = do
+  hash <- BiMap.lookup raw <$> useR stTopLevelModuleNames
+  case hash of
+    Just hash -> return (unsafeTopLevelModuleName raw hash)
+    Nothing   -> do
+      let hash = hashRawTopLevelModuleName raw
+      when (hash == noModuleNameHash) $ typeError $ GenericError $
+        "The module name " ++ prettyShow raw ++ " has a reserved " ++
+        "hash (you may want to consider renaming the module with " ++
+        "this name)"
+      raw' <- BiMap.invLookup hash <$> useR stTopLevelModuleNames
+      case raw' of
+        Just raw' -> typeError $ GenericError $
+          "Module name hash collision for " ++ prettyShow raw ++
+          " and " ++ prettyShow raw' ++ " (you may want to consider " ++
+          "renaming one of these modules)"
+        Nothing -> do
+          stTopLevelModuleNames `modifyTCLens'`
+            BiMap.insert (killRange raw) hash
+          return (unsafeTopLevelModuleName raw hash)
+
+-- | Set the top-level module. This affects the global module id of freshly
+--   generated names.
+
+setTopLevelModule :: TopLevelModuleName -> TCM ()
+setTopLevelModule top = do
+  let hash = moduleNameId top
+  stFreshNameId `setTCLens'` NameId 0 hash
+  stFreshOpaqueId `setTCLens'` OpaqueId 0 hash
+  stFreshMetaId `setTCLens'`
+    MetaId { metaId     = 0
+           , metaModule = hash
+           }
+
+-- | The name of the current top-level module, if any.
+{-# SPECIALIZE
+    currentTopLevelModule :: TCM (Maybe TopLevelModuleName) #-}
+{-# SPECIALIZE
+    currentTopLevelModule :: ReduceM (Maybe TopLevelModuleName) #-}
+currentTopLevelModule ::
+  (MonadTCEnv m, ReadTCState m) => m (Maybe TopLevelModuleName)
+currentTopLevelModule = do
+  m <- useR stCurrentModule
+  case m of
+    Just (_, top) -> return (Just top)
+    Nothing       -> do
+      p <- asksTC envImportPath
+      return $ case p of
+        top : _ -> Just top
+        []      -> Nothing
+
+-- | Use a different top-level module for a computation. Used when generating
+--   names for imported modules.
+withTopLevelModule :: TopLevelModuleName -> TCM a -> TCM a
+withTopLevelModule x m = do
+  nextN <- useTC stFreshNameId
+  nextM <- useTC stFreshMetaId
+  nextO <- useTC stFreshOpaqueId
+  setTopLevelModule x
+  y <- m
+  stFreshMetaId `setTCLens` nextM
+  stFreshNameId `setTCLens` nextN
+  stFreshOpaqueId `setTCLens` nextO
+  return y
+
+{-# SPECIALIZE currentModuleNameHash :: TCM ModuleNameHash #-}
+currentModuleNameHash :: ReadTCState m => m ModuleNameHash
+currentModuleNameHash = do
+  NameId _ h <- useTC stFreshNameId
+  return h
+
+---------------------------------------------------------------------------
+-- * Foreign code
+---------------------------------------------------------------------------
+
+addForeignCode :: BackendName -> String -> TCM ()
+addForeignCode backend code = do
+  r <- asksTC envRange  -- can't use TypeChecking.Monad.Trace.getCurrentRange without cycle
+  modifyTCLens (stForeignCode . key backend) $
+    Just . ForeignCodeStack . (ForeignCode r code :) . maybe [] getForeignCodeStack
+
+---------------------------------------------------------------------------
+-- * Interaction output callback
+---------------------------------------------------------------------------
+
+getInteractionOutputCallback :: ReadTCState m => m InteractionOutputCallback
+getInteractionOutputCallback
+  = getsTC $ stInteractionOutputCallback . stPersistentState
+
+appInteractionOutputCallback :: Response -> TCM ()
+appInteractionOutputCallback r
+  = getInteractionOutputCallback >>= \ cb -> cb r
+
+setInteractionOutputCallback :: InteractionOutputCallback -> TCM ()
+setInteractionOutputCallback cb
+  = modifyPersistentState $ \ s -> s { stInteractionOutputCallback = cb }
+
+---------------------------------------------------------------------------
+-- * Pattern synonyms
+---------------------------------------------------------------------------
+
+getPatternSyns :: ReadTCState m => m PatternSynDefns
+getPatternSyns = useR stPatternSyns
+
+setPatternSyns :: PatternSynDefns -> TCM ()
+setPatternSyns m = modifyPatternSyns (const m)
+
+-- | Lens for 'stPatternSyns'.
+modifyPatternSyns :: (PatternSynDefns -> PatternSynDefns) -> TCM ()
+modifyPatternSyns f = stPatternSyns `modifyTCLens` f
+
+getPatternSynImports :: ReadTCState m => m PatternSynDefns
+getPatternSynImports = useR stPatternSynImports
+
+-- | Get both local and imported pattern synonyms
+getAllPatternSyns :: ReadTCState m => m PatternSynDefns
+getAllPatternSyns = Map.union <$> getPatternSyns <*> getPatternSynImports
+
+lookupPatternSyn :: AmbiguousQName -> TCM PatternSynDefn
+lookupPatternSyn (AmbQ xs) = do
+  defs <- traverse lookupSinglePatternSyn xs
+  case mergePatternSynDefs defs of
+    Just def   -> return def
+    Nothing    -> typeError $ CannotResolveAmbiguousPatternSynonym $ List1.zip xs defs
+
+lookupSinglePatternSyn :: QName -> TCM PatternSynDefn
+lookupSinglePatternSyn x = do
+    s <- getPatternSyns
+    case Map.lookup x s of
+        Just d  -> return d
+        Nothing -> do
+            si <- getPatternSynImports
+            case Map.lookup x si of
+                Just d  -> return d
+                Nothing -> notInScopeError $ qnameToConcrete x
+
+---------------------------------------------------------------------------
+-- * Benchmark
+---------------------------------------------------------------------------
+
+-- | Lens getter for 'Benchmark' from 'TCState'.
+theBenchmark :: TCState -> Benchmark
+theBenchmark = stBenchmark . stPersistentState
+
+{-# INLINE updateBenchmark #-}
+-- | Lens map for 'Benchmark'.
+updateBenchmark :: (Benchmark -> Benchmark) -> TCState -> TCState
+updateBenchmark f = updatePersistentState $ \ s -> s { stBenchmark = f (stBenchmark s) }
+
+-- | Lens getter for 'Benchmark' from 'TCM'.
+getBenchmark :: TCM Benchmark
+getBenchmark = getsTC $ theBenchmark
+
+{-# INLINE modifyBenchmark #-}
+-- | Lens modify for 'Benchmark'.
+modifyBenchmark :: (Benchmark -> Benchmark) -> TCM ()
+modifyBenchmark = modifyTC' . updateBenchmark
+
+---------------------------------------------------------------------------
+-- * Instance definitions
+---------------------------------------------------------------------------
+
+-- | Look through the signature and reconstruct the instance table.
+addImportedInstances :: Signature -> TCM ()
+addImportedInstances sig = do
+  let itable = Map.fromListWith Set.union
+               [ (c, Set.singleton i)
+               | (i, Defn{ defInstance = Just c }) <- HMap.toList $ sig ^. sigDefinitions ]
+  stImportedInstanceDefs `modifyTCLens` Map.unionWith Set.union itable
+
+-- | Lens for 'stInstanceDefs'.
+updateInstanceDefs :: (TempInstanceTable -> TempInstanceTable) -> (TCState -> TCState)
+updateInstanceDefs = over stInstanceDefs
+
+modifyInstanceDefs :: (TempInstanceTable -> TempInstanceTable) -> TCM ()
+modifyInstanceDefs = modifyTC . updateInstanceDefs
+
+getAllInstanceDefs :: TCM TempInstanceTable
+getAllInstanceDefs = do
+  (table,xs) <- useTC stInstanceDefs
+  itable <- useTC stImportedInstanceDefs
+  let !table' = Map.unionWith Set.union itable table
+  return (table', xs)
+
+getAnonInstanceDefs :: TCM (Set QName)
+getAnonInstanceDefs = snd <$> getAllInstanceDefs
+
+-- | Remove all instances whose type is still unresolved.
+clearAnonInstanceDefs :: TCM ()
+clearAnonInstanceDefs = modifyInstanceDefs $ mapSnd $ const Set.empty
+
+-- | Add an instance whose type is still unresolved.
+addUnknownInstance :: QName -> TCM ()
+addUnknownInstance x = do
+  reportSLn "tc.decl.instance" 10 $
+    "adding definition " ++ prettyShow x ++
+    " to the instance table (the type is not yet known)"
+  modifyInstanceDefs $ mapSnd $ Set.insert x
+
+-- | Add instance to some ``class''.
+addNamedInstance
+  :: QName  -- ^ Name of the instance.
+  -> QName  -- ^ Name of the class.
+  -> TCM ()
+addNamedInstance x n = do
+  reportSLn "tc.decl.instance" 10 $
+    "adding definition " ++ prettyShow x ++ " to instance table for " ++ prettyShow n
+  -- Mark x as instance for n.
+  modifySignature $ updateDefinition x $ \ d -> d { defInstance = Just n }
+  -- Add x to n's instances.
+  modifyInstanceDefs $ mapFst $ Map.insertWith Set.union n $ Set.singleton x
diff --git a/src/full/Agda/TypeChecking/Monad/Statistics.hs b/src/full/Agda/TypeChecking/Monad/Statistics.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Statistics.hs
@@ -0,0 +1,94 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Collect statistics.
+
+module Agda.TypeChecking.Monad.Statistics
+    ( MonadStatistics(..), tick, tickN, tickMax, getStatistics, modifyStatistics, printStatistics
+    ) where
+
+import Control.DeepSeq
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Writer
+import Control.Monad.Trans.Maybe
+
+import qualified Data.Map as Map
+import qualified Text.PrettyPrint.Boxes as Boxes
+
+import Agda.Syntax.TopLevelModuleName (TopLevelModuleName)
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug
+
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.String
+
+class ReadTCState m => MonadStatistics m where
+  modifyCounter :: String -> (Integer -> Integer) -> m ()
+
+  default modifyCounter
+    :: (MonadStatistics n, MonadTrans t, t n ~ m)
+    =>  String -> (Integer -> Integer) -> m ()
+  modifyCounter x = lift . modifyCounter x
+
+instance MonadStatistics m => MonadStatistics (ExceptT e m)
+instance MonadStatistics m => MonadStatistics (MaybeT m)
+instance MonadStatistics m => MonadStatistics (ReaderT r m)
+instance MonadStatistics m => MonadStatistics (StateT  s m)
+instance (MonadStatistics m, Monoid w) => MonadStatistics (WriterT w m)
+
+instance MonadStatistics TCM where
+  modifyCounter x f = modifyStatistics $ force . update
+    where
+      -- We need to be strict in the map.
+      -- Andreas, 2014-03-22:  Could we take Data.Map.Strict instead of this hack?
+      -- Or force the map by looking up the very element we inserted?
+      -- force m = Map.lookup x m `seq` m
+      -- Or use insertLookupWithKey?
+      -- update m = old `seq` m' where
+      --   (old, m') = Map.insertLookupWithKey (\ _ new old -> f old) x dummy m
+      -- Ulf, 2018-04-10: Neither of these approaches are strict enough in the
+      -- map (nor are they less hacky). It's not enough to be strict in the
+      -- values stored in the map, we also need to be strict in the *structure*
+      -- of the map. A less hacky solution is to deepseq the map.
+      force m = rnf m `seq` m
+      update  = Map.insertWith (\ new old -> f old) x dummy
+      dummy   = f 0
+
+-- | Get the statistics.
+getStatistics :: ReadTCState m => m Statistics
+getStatistics = useR stStatistics
+
+-- | Modify the statistics via given function.
+modifyStatistics :: (Statistics -> Statistics) -> TCM ()
+modifyStatistics f = stStatistics `modifyTCLens` f
+
+-- | Increase specified counter by @1@.
+tick :: MonadStatistics m => String -> m ()
+tick x = tickN x 1
+
+-- | Increase specified counter by @n@.
+tickN :: MonadStatistics m => String -> Integer -> m ()
+tickN s n = modifyCounter s (n +)
+
+-- | Set the specified counter to the maximum of its current value and @n@.
+tickMax :: MonadStatistics m => String -> Integer -> m ()
+tickMax s n = modifyCounter s (max n)
+
+-- | Print the given statistics.
+printStatistics
+  :: (MonadDebug m, MonadTCEnv m, HasOptions m)
+  => Maybe TopLevelModuleName -> Statistics -> m ()
+printStatistics mmname stats = do
+  unlessNull (Map.toList stats) $ \ stats -> do
+    let -- First column (left aligned) is accounts.
+        col1 = Boxes.vcat Boxes.left  $ map (Boxes.text . fst) stats
+        -- Second column (right aligned) is numbers.
+        col2 = Boxes.vcat Boxes.right $ map (Boxes.text . showThousandSep . snd) stats
+        table = Boxes.hsep 1 Boxes.left [col1, col2]
+    alwaysReportSLn "" 1 $ caseMaybe mmname "Accumulated statistics" $ \ mname ->
+      "Statistics for " ++ prettyShow mname
+    alwaysReportSLn "" 1 $ Boxes.render table
diff --git a/src/full/Agda/TypeChecking/Monad/Trace.hs b/src/full/Agda/TypeChecking/Monad/Trace.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Monad/Trace.hs
@@ -0,0 +1,273 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Monad.Trace where
+
+import Prelude hiding (null)
+
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.Trans.Identity
+import Control.Monad.Writer
+
+import qualified Data.Set as Set
+
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Position as P
+
+import Agda.Interaction.Response
+import Agda.Interaction.Highlighting.Precise
+import Agda.Interaction.Highlighting.Range (rToR, minus)
+
+import Agda.TypeChecking.Monad.Base
+  hiding (ModuleInfo, MetaInfo, Primitive, Constructor, Record, Function, Datatype)
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.State
+
+import Agda.Utils.Function
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+---------------------------------------------------------------------------
+-- * Trace
+---------------------------------------------------------------------------
+
+interestingCall :: Call -> Bool
+interestingCall = \case
+    InferVar{}              -> False
+    InferDef{}              -> False
+    CheckArguments _ [] _ _ -> False
+    SetRange{}              -> False
+    NoHighlighting{}        -> False
+    -- Andreas, 2019-08-07, expanded catch-all pattern.
+    -- The previous presence of a catch-all raises the following question:
+    -- are all of the following really interesting?
+    CheckClause{}             -> True
+    CheckLHS{}                -> True
+    CheckPattern{}            -> True
+    CheckPatternLinearityType{}  -> True
+    CheckPatternLinearityValue{} -> True
+    CheckLetBinding{}         -> True
+    InferExpr{}               -> True
+    CheckExprCall{}           -> True
+    CheckDotPattern{}         -> True
+    IsTypeCall{}              -> True
+    IsType_{}                 -> True
+    CheckArguments{}          -> True
+    CheckMetaSolution{}       -> True
+    CheckTargetType{}         -> True
+    CheckDataDef{}            -> True
+    CheckRecDef{}             -> True
+    CheckConstructor{}        -> True
+    CheckIApplyConfluence{}   -> True
+    CheckConArgFitsIn{}       -> True
+    CheckFunDefCall{}         -> True
+    CheckPragma{}             -> True
+    CheckPrimitive{}          -> True
+    CheckIsEmpty{}            -> True
+    CheckConfluence{}         -> True
+    CheckModuleParameters{}   -> True
+    CheckWithFunctionType{}   -> True
+    CheckSectionApplication{} -> True
+    CheckNamedWhere{}         -> True
+    ScopeCheckExpr{}          -> True
+    ScopeCheckDeclaration{}   -> True
+    ScopeCheckLHS{}           -> True
+    CheckProjection{}         -> True
+    ModuleContents{}          -> True
+
+class (MonadTCEnv m, ReadTCState m) => MonadTrace m where
+
+  -- | Record a function call in the trace.
+  traceCall :: Call -> m a -> m a
+  traceCall call m = do
+    cl <- buildClosure call
+    traceClosureCall cl m
+
+  traceCallM :: m Call -> m a -> m a
+  traceCallM call m = flip traceCall m =<< call
+
+  -- | Like 'traceCall', but resets 'envCall' and the current ranges to the
+  --   previous values in the continuation.
+  --
+  traceCallCPS :: Call -> ((a -> m b) -> m b) -> ((a -> m b) -> m b)
+  traceCallCPS call k ret = do
+
+    -- Save current call and ranges.
+    TCEnv{ envCall = mcall, envRange = r, envHighlightingRange = hr } <- askTC
+
+    -- Run given computation under given call.
+    traceCall call $ k $ \ a -> do
+
+      -- Restore previous call and ranges for the continuation.
+      localTC (\ e -> e{ envCall = mcall, envRange = r, envHighlightingRange = hr }) $
+        ret a
+
+  traceClosureCall :: Closure Call -> m a -> m a
+
+  -- | Lispify and print the given highlighting information.
+  printHighlightingInfo :: RemoveTokenBasedHighlighting -> HighlightingInfo -> m ()
+
+  default printHighlightingInfo
+    :: (MonadTrans t, MonadTrace n, t n ~ m)
+    => RemoveTokenBasedHighlighting -> HighlightingInfo -> m ()
+  printHighlightingInfo r i = lift $ printHighlightingInfo r i
+
+instance MonadTrace m => MonadTrace (IdentityT m) where
+  traceClosureCall c f = IdentityT $ traceClosureCall c $ runIdentityT f
+
+instance MonadTrace m => MonadTrace (ReaderT r m) where
+  traceClosureCall c f = ReaderT $ \r -> traceClosureCall c $ runReaderT f r
+
+instance MonadTrace m => MonadTrace (StateT s m) where
+  traceClosureCall c f = StateT (traceClosureCall c . runStateT f)
+
+instance (MonadTrace m, Monoid w) => MonadTrace (WriterT w m) where
+  traceClosureCall c f = WriterT $ traceClosureCall c $ runWriterT f
+
+instance MonadTrace m => MonadTrace (ExceptT e m) where
+  traceClosureCall c f = ExceptT $ traceClosureCall c $ runExceptT f
+
+instance MonadTrace TCM where
+  traceClosureCall cl m = do
+    -- Andreas, 2016-09-13 issue #2177
+    -- Since the fix of #2092 we may report an error outside the current file.
+    -- (For instance, if we import a module which then happens to have the
+    -- wrong name.)
+    -- Thus, we no longer crash, but just report the alien range.
+    -- -- Andreas, 2015-02-09 Make sure we do not set a range
+    -- -- outside the current file
+    verboseS "check.ranges" 90 $
+      Strict.whenJust (rangeFile callRange) $ \f -> do
+        currentFile <- asksTC envCurrentPath
+        when (currentFile /= Just (rangeFilePath f)) $ do
+          reportSLn "check.ranges" 90 $
+            prettyShow call ++
+            " is setting the current range to " ++ show callRange ++
+            " which is outside of the current file " ++ show currentFile
+
+    -- Compute update to 'Range' and 'Call' components of 'TCEnv'.
+    let withCall = localTC $ foldr (.) id $ concat $
+          [ [ \e -> e { envCall = Just cl } | interestingCall call ]
+          , [ \e -> e { envHighlightingRange = callRange }
+            | callHasRange && highlightCall
+              || isNoHighlighting
+            ]
+          , [ \e -> e { envRange = callRange } | callHasRange ]
+          ]
+
+    -- For interactive highlighting, also wrap computation @m@ in 'highlightAsTypeChecked':
+    ifNotM (pure highlightCall `and2M` do (Interactive ==) . envHighlightingLevel <$> askTC)
+      {-then-} (withCall m)
+      {-else-} $ do
+        oldRange <- envHighlightingRange <$> askTC
+        highlightAsTypeChecked oldRange callRange $
+          withCall m
+    where
+    call = clValue cl
+    callRange = getRange call
+    callHasRange = not $ null callRange
+
+    -- Should the given call trigger interactive highlighting?
+    highlightCall = case call of
+      CheckClause{}             -> True
+      CheckLHS{}                -> True
+      CheckPattern{}            -> True
+      CheckPatternLinearityType{}  -> False
+      CheckPatternLinearityValue{} -> False
+      CheckLetBinding{}         -> True
+      InferExpr{}               -> True
+      CheckExprCall{}           -> True
+      CheckDotPattern{}         -> True
+      IsTypeCall{}              -> True
+      IsType_{}                 -> True
+      InferVar{}                -> True
+      InferDef{}                -> True
+      CheckArguments{}          -> True
+      CheckMetaSolution{}       -> False
+      CheckTargetType{}         -> False
+      CheckDataDef{}            -> True
+      CheckRecDef{}             -> True
+      CheckConstructor{}        -> True
+      CheckConArgFitsIn{}       -> False
+      CheckFunDefCall _ _ _ h   -> h
+      CheckPragma{}             -> True
+      CheckPrimitive{}          -> True
+      CheckIsEmpty{}            -> True
+      CheckConfluence{}         -> False
+      CheckIApplyConfluence{}   -> False
+      CheckModuleParameters{}   -> False
+      CheckWithFunctionType{}   -> True
+      CheckSectionApplication{} -> True
+      CheckNamedWhere{}         -> False
+      ScopeCheckExpr{}          -> False
+      ScopeCheckDeclaration{}   -> False
+      ScopeCheckLHS{}           -> False
+      NoHighlighting{}          -> True
+      CheckProjection{}         -> False
+      SetRange{}                -> False
+      ModuleContents{}          -> False
+
+    isNoHighlighting = case call of
+      NoHighlighting{} -> True
+      _ -> False
+
+  printHighlightingInfo remove info = do
+    modToSrc <- useTC stModuleToSource
+    method   <- viewTC eHighlightingMethod
+    reportS "highlighting" 50
+      [ "Printing highlighting info:"
+      , show info
+      , "  modToSrc = " ++ show modToSrc
+      ]
+    unless (null info) $ do
+      appInteractionOutputCallback $
+          Resp_HighlightingInfo info remove method modToSrc
+
+
+getCurrentRange :: MonadTCEnv m => m Range
+getCurrentRange = asksTC envRange
+
+-- | Sets the current range (for error messages etc.) to the range
+--   of the given object, if it has a range (i.e., its range is not 'noRange').
+setCurrentRange :: (MonadTrace m, HasRange x) => x -> m a -> m a
+setCurrentRange x = applyUnless (null r) $ traceCall $ SetRange r
+  where r = getRange x
+
+-- | @highlightAsTypeChecked rPre r m@ runs @m@ and returns its
+--   result. Additionally, some code may be highlighted:
+--
+-- * If @r@ is non-empty and not a sub-range of @rPre@ (after
+--   'P.continuousPerLine' has been applied to both): @r@ is
+--   highlighted as being type-checked while @m@ is running (this
+--   highlighting is removed if @m@ completes /successfully/).
+--
+-- * Otherwise: Highlighting is removed for @rPre - r@ before @m@
+--   runs, and if @m@ completes successfully, then @rPre - r@ is
+--   highlighted as being type-checked.
+
+highlightAsTypeChecked
+  :: (MonadTrace m)
+  => Range   -- ^ @rPre@
+  -> Range   -- ^ @r@
+  -> m a
+  -> m a
+highlightAsTypeChecked rPre r m
+  | r /= noRange && delta == rPre' = wrap r'    highlight clear
+  | otherwise                      = wrap delta clear     highlight
+  where
+  rPre'     = rToR (P.continuousPerLine rPre)
+  r'        = rToR (P.continuousPerLine r)
+  delta     = rPre' `minus` r'
+  clear     = mempty
+  highlight = parserBased { otherAspects = Set.singleton TypeChecks }
+
+  wrap rs x y = do
+    p rs x
+    v <- m
+    p rs y
+    return v
+    where
+    p rs x = printHighlightingInfo KeepHighlighting (singleton rs x)
diff --git a/src/full/Agda/TypeChecking/Names.hs b/src/full/Agda/TypeChecking/Names.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Names.hs
@@ -0,0 +1,251 @@
+
+{-| EDSL to construct terms without touching De Bruijn indices.
+
+e.g. given t, u :: Term, Γ ⊢ t, u : A, we can build "λ f. f t u" like this:
+
+runNames [] $ do
+  -- @open@ binds @t@ and @u@ to computations that know how to weaken themselves in
+  -- an extended context
+
+  [t,u] <- mapM open [t,u]
+
+  -- @lam@ gives the illusion of HOAS by providing f as a computation.
+  -- It also extends the internal context with the name "f", so that
+  -- @t@ and @u@ will get weakened in the body.
+  -- We apply f with the (<@>) combinator from Agda.TypeChecking.Primitive.
+
+  lam "f" $ \ f -> f <@> t <@> u
+
+-}
+module Agda.TypeChecking.Names where
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import Control.Monad          ( liftM2, unless )
+import Control.Monad.Except   ( MonadError )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Reader   ( MonadReader(..), ReaderT, runReaderT )
+import Control.Monad.State    ( MonadState )
+import Control.Monad.Trans    ( MonadTrans, lift )
+
+import Data.List              ( isSuffixOf )
+
+import Agda.Syntax.Common hiding (Nat)
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad hiding (getConstInfo, typeOfConst)
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Pretty ()  -- instances only
+
+import Agda.Utils.Fail (Fail, runFail_)
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import Agda.Utils.Impossible
+
+instance HasBuiltins m => HasBuiltins (NamesT m) where
+  getBuiltinThing b = lift $ getBuiltinThing b
+
+newtype NamesT m a = NamesT { unName :: ReaderT Names m a }
+  deriving ( Functor
+           , Applicative
+           , Monad
+           , MonadFail
+           , MonadTrans
+           , MonadState s
+           , MonadIO
+           , HasOptions
+           , MonadDebug
+           , MonadTCEnv
+           , MonadTCState
+           , MonadTCM
+           , ReadTCState
+           , MonadReduce
+           , MonadError e
+           , MonadAddContext
+           , HasConstInfo
+           , PureTCM
+           )
+
+
+-- | A list of variable names from a context.
+type Names = [String]
+
+runNamesT :: Names -> NamesT m a -> m a
+runNamesT n m = runReaderT (unName m) n
+
+runNames :: Names -> NamesT Fail a -> a
+runNames n m = runFail_ (runNamesT n m)
+
+currentCxt :: Monad m => NamesT m Names
+currentCxt = NamesT ask
+
+{-# INLINABLE cxtSubst #-}
+-- | @cxtSubst Γ@ returns the substitution needed to go
+--   from Γ to the current context.
+--
+--   Fails if @Γ@ is not a subcontext of the current one.
+cxtSubst :: MonadFail m => Names -> NamesT m (Substitution' a)
+cxtSubst ctx = do
+  ctx' <- currentCxt
+  if (ctx `isSuffixOf` ctx')
+     then return $ raiseS (length ctx' - length ctx)
+     else fail $ "out of context (" ++ show ctx ++ " is not a sub context of " ++ show ctx' ++ ")"
+
+{-# INLINABLE inCxt #-}
+-- | @inCxt Γ t@ takes a @t@ in context @Γ@ and produce an action that
+--   will return @t@ weakened to the current context.
+--
+--   Fails whenever @cxtSubst Γ@ would.
+inCxt :: (MonadFail m, Subst a) => Names -> a -> NamesT m a
+inCxt ctx a = do
+  sigma <- cxtSubst ctx
+  return $ applySubst sigma a
+
+-- | Closed terms
+cl' :: Applicative m => a -> NamesT m a
+cl' = pure
+
+cl :: Monad m => m a -> NamesT m a
+cl = lift
+
+{-# INLINABLE open #-}
+-- | Open terms in the current context.
+open :: (MonadFail m, Subst a) => a -> NamesT m (NamesT m a)
+open a = do
+  ctx <- NamesT ask
+  pure $ inCxt ctx a
+
+-- | Monadic actions standing for variables.
+--
+--   @b@ is quantified over so the same variable can be used e.g. both
+--   as a pattern and as an expression.
+type Var m = forall b. (Subst b, DeBruijn b) => NamesT m b
+
+
+{-# INLINE bind #-}
+-- | @bind n f@ provides @f@ with a fresh variable, which can be used in any extended context.
+--
+--   Returns an @Abs@ which binds the extra variable.
+bind :: MonadFail m => ArgName -> ((forall b. (Subst b, DeBruijn b) => NamesT m b) -> NamesT m a) -> NamesT m (Abs a)
+bind n f = Abs n <$> bind' n f
+
+{-# INLINABLE bind' #-}
+-- | Like @bind@ but returns a bare term.
+bind' :: MonadFail m => ArgName -> ((forall b. (Subst b, DeBruijn b) => NamesT m b) -> NamesT m a) -> NamesT m a
+bind' n f = do
+  cxt <- NamesT ask
+  (NamesT . local (n:) . unName $ f (inCxt (n:cxt) (deBruijnVar 0)))
+
+
+-- * Helpers to build lambda abstractions.
+
+glam :: MonadFail m
+     => ArgInfo -> ArgName -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
+glam info n f = Lam info <$> bind n (\ x -> f x)
+
+lam :: MonadFail m
+    => ArgName -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
+lam n f = glam defaultArgInfo n f
+
+ilam :: MonadFail m
+    => ArgName -> (NamesT m Term -> NamesT m Term) -> NamesT m Term
+ilam n f = glam (setRelevance Irrelevant defaultArgInfo) n f
+
+
+-- * Combinators for n-ary binders.
+
+data AbsN a = AbsN { absNName :: [ArgName], unAbsN :: a } deriving (Functor,Foldable,Traversable)
+
+instance Subst a => Subst (AbsN a) where
+  type SubstArg (AbsN a) = SubstArg a
+  applySubst rho (AbsN xs a) = AbsN xs (applySubst (liftS (length xs) rho) a)
+
+-- | Will crash on @NoAbs@
+toAbsN :: Abs (AbsN a) -> AbsN a
+toAbsN (Abs n x') = AbsN (n : absNName x') (unAbsN x')
+toAbsN NoAbs{}    = __IMPOSSIBLE__
+
+{-# INLINABLE absAppN #-}
+absAppN :: Subst a => AbsN a -> [SubstArg a] -> a
+absAppN f xs = (parallelS $ reverse xs) `applySubst` unAbsN f
+
+type ArgVars m = (forall b. (Subst b, DeBruijn b) => [NamesT m (Arg b)])
+
+type Vars m = (forall b. (Subst b, DeBruijn b) => [NamesT m b])
+
+{-# INLINABLE bindN #-}
+bindN :: ( MonadFail m
+        ) =>
+        [ArgName] -> (Vars m -> NamesT m a) -> NamesT m (AbsN a)
+bindN [] f = AbsN [] <$> f []
+bindN (x:xs) f = toAbsN <$> bind x (\ x -> bindN xs (\ xs -> f (x:xs)))
+
+{-# INLINABLE bindNArg #-}
+bindNArg :: ( MonadFail m
+        ) =>
+        [Arg ArgName] -> (ArgVars m -> NamesT m a) -> NamesT m (AbsN a)
+bindNArg [] f = AbsN [] <$> f []
+bindNArg (Arg i x:xs) f = toAbsN <$> bind x (\ x -> bindNArg xs (\ xs -> f ((Arg i <$> x):xs)))
+
+
+type Vars1 m = (forall b. (Subst b, DeBruijn b) => List1 (NamesT m b))
+
+bindN1 :: MonadFail m
+  => List1 ArgName -> (Vars1 m -> NamesT m a) -> NamesT m (AbsN a)
+bindN1 (x :| xs) f = toAbsN <$> bind x (\ x -> bindN xs (\ xs -> f (x :| xs)))
+
+glamN :: (Functor m, MonadFail m) =>
+         [Arg ArgName] -> (NamesT m Args -> NamesT m Term) -> NamesT m Term
+glamN [] f = f $ pure []
+glamN (Arg i n:ns) f = glam i n $ \ x -> glamN ns (\ xs -> f ((:) <$> (Arg i <$> x) <*> xs))
+
+
+applyN :: ( Monad m
+        , Subst a
+        ) =>
+        NamesT m (AbsN a) -> [NamesT m (SubstArg a)] -> NamesT m a
+applyN f xs = do
+  f <- f
+  xs <- sequence xs
+  unless (length xs == length (absNName f)) $ __IMPOSSIBLE__
+  return $ absAppN f xs
+
+{-# INLINABLE applyN' #-}
+applyN' :: ( Monad m
+        , Subst a
+        ) =>
+        NamesT m (AbsN a) -> NamesT m [SubstArg a] -> NamesT m a
+applyN' f xs = do
+  f <- f
+  xs <- xs
+  unless (length xs == length (absNName f)) $ __IMPOSSIBLE__
+  return $ absAppN f xs
+
+{-# INLINABLE abstractN #-}
+abstractN :: ( MonadFail m
+             , Abstract a
+             ) =>
+             NamesT m Telescope -> (Vars m -> NamesT m a) -> NamesT m a
+abstractN tel f = do
+  tel <- tel
+  u <- bindN (teleNames tel) f
+  return $ abstract tel $ unAbsN u
+
+{-# INLINABLE abstractT #-}
+abstractT :: ( MonadFail m
+             , Abstract a
+             ) =>
+             String -> NamesT m Type -> (Var m -> NamesT m a) -> NamesT m a
+abstractT n ty f = do
+  u <- bind n f
+  ty <- ty
+  let tel = ExtendTel (defaultDom ty) $ Abs n EmptyTel
+  return $ abstract tel $ unAbs u
+
+
+lamTel :: Monad m => NamesT m (Abs [Term]) -> NamesT m ([Term])
+lamTel t = map (Lam defaultArgInfo) . sequenceA <$> t
+
+appTel :: Monad m => NamesT m [Term] -> NamesT m Term -> NamesT m [Term]
+appTel = liftM2 (\ fs x -> map (`apply` [Arg defaultArgInfo x]) fs)
diff --git a/src/full/Agda/TypeChecking/Opacity.hs b/src/full/Agda/TypeChecking/Opacity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Opacity.hs
@@ -0,0 +1,215 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+module Agda.TypeChecking.Opacity
+  ( saturateOpaqueBlocks
+
+  , isAccessibleDef
+  , hasAccessibleDef
+  )
+  where
+
+import Control.Monad.State
+import Control.Exception
+import Control.DeepSeq
+import Control.Monad
+
+import qualified Data.HashMap.Strict as HashMap
+import qualified Data.Map.Strict as Map
+import qualified Data.HashSet as HashSet
+import qualified Data.List as List
+import Data.HashMap.Strict (HashMap)
+import Data.HashSet (HashSet)
+import Data.Map.Strict (Map)
+import Data.Foldable
+import Data.Maybe
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+
+import Agda.TypeChecking.Warnings
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.Impossible
+import Agda.Utils.Monad
+import Agda.Utils.Lens
+
+-- | Ensure that opaque blocks defined in the current module have
+-- saturated unfolding sets.
+saturateOpaqueBlocks
+  :: forall m. (MonadTCState m, ReadTCState m, MonadFresh OpaqueId m, MonadDebug m, MonadTrace m, MonadWarning m, MonadIO m)
+  => [A.Declaration]
+  -> m ()
+saturateOpaqueBlocks moddecs = entry where
+  entry = do
+    known   <- useTC stOpaqueBlocks
+    inverse <- useTC stOpaqueIds
+    OpaqueId _ ourmod <- fresh
+
+    canonical <- useTC stCopiedNames
+    backcopies <- useTC stNameCopies
+
+    reportSDoc "tc.opaque.copy" 45 $ "Canonical names of copied definitions:" $+$ pretty (HashMap.toList canonical)
+    reportSDoc "tc.opaque.copy" 45 $ "Backcopies:" $+$ pretty (HashMap.toList (toList <$> backcopies))
+
+    let
+      isOurs (OpaqueId _ mod, _) = mod == ourmod
+      canonise name = fromMaybe name (HashMap.lookup name canonical)
+      ours = snd <$> filter isOurs (Map.toAscList known)
+
+    () <- liftIO $ evaluate (rnf (canonical, backcopies))
+
+    reportSDoc "tc.opaque" 30 $ vcat $
+      text "Opaque blocks defined in this module:":map pretty ours
+
+    -- Only compute transitive closure for opaque blocks declared in
+    -- the current top-level module. Deserialised blocks are always
+    -- closed, so this work would be redundant.
+    (blocks, names) <- computeClosure canonise known inverse ours
+
+    -- Associate copies with the opaque blocks of their originals. Since
+    -- modules importing this one won't know how to canonicalise names
+    -- we have defined, we make the work easier for them by associating
+    -- copies with their original's opaque blocks.
+    let names' = foldr addBackcopy names (HashMap.toList backcopies)
+
+    reportSDoc "tc.opaque.sat" 30 $ vcat $
+      text "Saturated local opaque blocks":[ pretty block | b@(_,block) <- Map.toList blocks, isOurs b ]
+
+    reportSDoc "tc.opaque.sat.full" 50 $ text "Saturated opaque blocks:" $+$ pretty blocks
+
+    modifyTC' $ \st -> st { stPostScopeState = (stPostScopeState st)
+      { stPostOpaqueBlocks = blocks
+      , stPostOpaqueIds    = names'
+      } }
+
+  -- Actually compute the closure.
+  computeClosure
+    :: (QName -> QName)
+    -> Map OpaqueId OpaqueBlock
+      -- Accumulates the satured opaque blocks; also contains the
+      -- opaque blocks of imported modules.
+    -> Map QName OpaqueId
+      -- Accumulates a mapping from names to opaque blocks; also
+      -- contains imported opaque names.
+    -> [OpaqueBlock]
+      -- List of our opaque blocks, in dependency order.
+    -> m ( Map OpaqueId OpaqueBlock
+         , Map QName OpaqueId
+         )
+  computeClosure canonise !blocks !names [] = pure (blocks, names)
+  computeClosure canonise blocks names (block:xs) = setCurrentRange (opaqueRange block) $ do
+    let
+      yell nm accum = setCurrentRange (getRange nm) $ do
+        warning (UnfoldTransparentName nm)
+        pure accum
+
+      -- Add the unfolding-set of the given name to the accumulator
+      -- value.
+      transitive prenom accum = fromMaybe (yell prenom accum) $ do
+        -- NB: If the name is a local copy, we won't yet have added the
+        -- copy name to an opaque block, but we will have added the
+        -- reduced name (provided it is opaque)
+        let nm = canonise prenom
+        id    <- Map.lookup nm names
+        block <- Map.lookup id blocks
+        pure . pure $ HashSet.union (opaqueUnfolding block) accum
+
+    reportSDoc "tc.opaque.copy" 45 $
+      vcat [ "Stated unfolding clause:  " <+> pretty (HashSet.toList (opaqueUnfolding block))
+           , "with (sub)canonical names:" <+> pretty (canonise <$> HashSet.toList (opaqueUnfolding block))
+           ]
+
+    -- Compute the transitive closure: bring in names
+    --
+    --   ... that are defined as immediate children of the opaque block
+    --   ... that are unfolded by the parent opaque block
+    --   ... that are implied by each name in the unfolding clause.
+    closed <- foldrM transitive
+      (  opaqueDecls block
+      <> foldMap opaqueUnfolding (opaqueParent block >>= flip Map.lookup blocks)
+      )
+      (opaqueUnfolding block)
+
+    let
+      block' = block { opaqueUnfolding = closed }
+
+      -- Update the mapping from names to blocks, so that future
+      -- references to names defined in our opaque block will know the
+      -- right unfolding set.
+      names' = HashSet.foldr (\name -> Map.insert name (opaqueId block)) names
+        (opaqueDecls block)
+
+    computeClosure canonise (Map.insert (opaqueId block) block' blocks) names' xs
+
+  addBackcopy :: (QName, HashSet QName) -> Map QName OpaqueId -> Map QName OpaqueId
+  addBackcopy (from, prop) map
+    | Just id <- Map.lookup from map = foldr (flip Map.insert id) map prop
+    | otherwise = map
+
+-- | Decide whether or not a definition is reducible. Returns 'True' if
+-- the definition /can/ step.
+isAccessibleDef :: TCEnv -> TCState -> Definition -> Bool
+
+-- IgnoreAbstractMode ignores both abstract and opaque. It is used for
+-- getting the original definition (for inConcreteOrAbstractMode), and
+-- for "normalise ignoring abstract" interactively.
+isAccessibleDef env state defn
+  | envAbstractMode env == IgnoreAbstractMode = True
+
+-- Otherwise, actually apply the reducibility rules..
+isAccessibleDef env state defn =
+  let
+    -- Reducibility rules for abstract definitions:
+    concretise def = case envAbstractMode env of
+      -- Being outside an abstract block has no effect on concreteness
+      ConcreteMode       -> def
+
+      -- This clause is redundant with the preceding guard but GHC can't
+      -- figure it out:
+      IgnoreAbstractMode -> ConcreteDef
+
+      AbstractMode
+        -- Symbols from enclosing modules will be made concrete:
+        | current `isLeChildModuleOf` m -> ConcreteDef
+
+        -- Symbols from child modules, or unrelated modules, will keep
+        -- the same concreteness:
+        | otherwise                     -> def
+      where
+        current = dropAnon $ envCurrentModule env
+        m       = dropAnon $ qnameModule (defName defn)
+        dropAnon (MName ms) = MName $ List.dropWhileEnd isNoName ms
+
+    -- Reducibility rule for opaque definitions: If we are operating
+    -- under an unfolding block,
+    clarify def = case envCurrentOpaqueId env of
+      Just oid ->
+        let
+          block = fromMaybe __IMPOSSIBLE__ $ Map.lookup oid (view stOpaqueBlocks state)
+
+          -- Then any name which is a member of the unfolding-set
+          -- associated to that block will be unfolded.
+          okay = defName defn `HashSet.member` opaqueUnfolding block
+        in if okay then TransparentDef else def
+      Nothing -> def
+
+    -- Short-circuit the map lookup for vanilla definitions
+    plainDef = defAbstract defn == ConcreteDef
+            && defOpaque   defn == TransparentDef
+
+  in plainDef
+  || ( concretise (defAbstract defn) == ConcreteDef
+    && clarify    (defOpaque defn)   == TransparentDef)
+
+-- | Will the given 'QName' have a proper definition, or will it be
+-- wrapped in an 'AbstractDefn'?
+hasAccessibleDef
+  :: (ReadTCState m, MonadTCEnv m, HasConstInfo m) => QName -> m Bool
+hasAccessibleDef qn = do
+  env <- askTC
+  st <- getTCState
+  ignoreAbstractMode $ do
+    def <- getConstInfo qn
+    pure $ isAccessibleDef env st def
diff --git a/src/full/Agda/TypeChecking/Opacity.hs-boot b/src/full/Agda/TypeChecking/Opacity.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Opacity.hs-boot
@@ -0,0 +1,13 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Opacity where
+
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Signature (HasConstInfo)
+import Agda.TypeChecking.Monad.Base
+
+import Agda.Syntax.Abstract.Name
+
+isAccessibleDef :: TCEnv -> TCState -> Definition -> Bool
+
+hasAccessibleDef
+  :: (ReadTCState m, MonadTCEnv m, HasConstInfo m) => QName -> m Bool
diff --git a/src/full/Agda/TypeChecking/Patterns/Abstract.hs b/src/full/Agda/TypeChecking/Patterns/Abstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Patterns/Abstract.hs
@@ -0,0 +1,114 @@
+
+-- | Tools to manipulate patterns in abstract syntax
+--   in the TCM (type checking monad).
+
+module Agda.TypeChecking.Patterns.Abstract where
+
+import Control.Monad.Except
+
+import qualified Data.List as List
+import Data.Void
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pattern
+import Agda.Syntax.Concrete (FieldAssignment')
+import Agda.Syntax.Common
+import Agda.Syntax.Info as A
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Warnings (raiseWarningsOnUsage)
+
+import Agda.Utils.Impossible
+
+-- | Expand literal integer pattern into suc/zero constructor patterns.
+--
+expandLitPattern
+  :: (MonadError TCErr m, MonadTCEnv m, ReadTCState m, HasBuiltins m)
+  => A.Pattern -> m A.Pattern
+expandLitPattern = \case
+  A.LitP info (LitNat n)
+    | n < 0     -> negLit -- Andreas, issue #2365, negative literals not yet supported.
+    | n > 20    -> tooBig
+    | otherwise -> do
+      Con z _ _ <- primZero
+      Con s _ _ <- primSuc
+      let r     = getRange info
+      let zero  = A.ConP cinfo (unambiguous $ setRange r $ conName z) []
+          suc p = A.ConP cinfo (unambiguous $ setRange r $ conName s) [defaultNamedArg p]
+          cinfo = A.ConPatInfo ConOCon info ConPatEager
+      return $ foldr ($) zero $ List.genericReplicate n suc
+  p -> return p
+
+  where
+    tooBig = typeError $ GenericError $
+      "Matching on natural number literals is done by expanding " ++
+      "the literal to the corresponding constructor pattern, so " ++
+      "you probably don't want to do it this way."
+    negLit = typeError $ GenericError $
+      "Negative literals are not supported in patterns"
+
+
+-- | Expand away (deeply) all pattern synonyms in a pattern.
+
+-- Unfortunately, the more general type signature
+--
+--   expandPatternSynonyms :: forall a p . APatternLike a p => p -> TCM p
+--
+-- is rejected by GHC 7.10
+--
+--   Could not deduce (APatternLike A.Expr p)
+--     arising from a use of ‘postTraverseAPatternM’
+--
+-- I am mystified (Andreas, 2017-07-27)
+
+-- expandPatternSynonyms :: forall a p . APatternLike a p => p -> TCM p
+
+-- As a workaround, we define this function only for a = A.Exp, p = A.Pattern'
+-- and keep the type class ExpandPatternSynonyms (which would otherwise be superfluous).
+
+expandPatternSynonyms' :: forall e. A.Pattern' e -> TCM (A.Pattern' e)
+expandPatternSynonyms' = postTraverseAPatternM $ \case
+
+  A.PatternSynP i x as -> setCurrentRange i $ do
+    (ns, p) <- killRange <$> lookupPatternSyn x
+
+    -- Andreas, 2020-02-11, issue #3734
+    -- If lookup of ambiguous pattern synonym was successful,
+    -- we are justified to complain if one of the definitions
+    -- involved in the resolution is tagged with a warning.
+    -- This is less than optimal, since we do not rule out
+    -- the invalid alternatives by typing, but we cannot do
+    -- better here.
+    mapM_ raiseWarningsOnUsage $ A.unAmbQ x
+
+    -- Must expand arguments before instantiating otherwise pattern
+    -- synonyms could get into dot patterns (which is __IMPOSSIBLE__).
+    p <- expandPatternSynonyms' (vacuous p :: A.Pattern' e)
+
+    case A.insertImplicitPatSynArgs (A.WildP . PatRange) (getRange x) ns as of
+      Nothing       -> typeError $ BadArgumentsToPatternSynonym x
+      Just (_, _:_) -> typeError $ TooFewArgumentsToPatternSynonym x
+      Just (s, [])  -> do
+        let subE _ = __IMPOSSIBLE__   -- No dot patterns in p
+        return $ setRange (getRange i) $ substPattern' subE s p
+
+  p -> return p
+
+class ExpandPatternSynonyms a where
+  expandPatternSynonyms :: a -> TCM a
+
+  default expandPatternSynonyms
+    :: (Traversable f, ExpandPatternSynonyms b, f b ~ a) => a -> TCM a
+  expandPatternSynonyms = traverse expandPatternSynonyms
+
+instance ExpandPatternSynonyms a => ExpandPatternSynonyms (Maybe a)
+instance ExpandPatternSynonyms a => ExpandPatternSynonyms [a]
+instance ExpandPatternSynonyms a => ExpandPatternSynonyms (Arg a)
+instance ExpandPatternSynonyms a => ExpandPatternSynonyms (Named n a)
+instance ExpandPatternSynonyms a => ExpandPatternSynonyms (FieldAssignment' a)
+
+instance ExpandPatternSynonyms (A.Pattern' e) where
+  expandPatternSynonyms = expandPatternSynonyms'
diff --git a/src/full/Agda/TypeChecking/Patterns/Internal.hs b/src/full/Agda/TypeChecking/Patterns/Internal.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Patterns/Internal.hs
@@ -0,0 +1,51 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs #-}
+
+-- | Tools to manipulate patterns in internal syntax
+--   in the TCM (type checking monad).
+
+module Agda.TypeChecking.Patterns.Internal where
+
+import Control.Monad
+
+import Data.Maybe
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce (reduce)
+import Agda.TypeChecking.Substitute.DeBruijn
+
+import Agda.Utils.Impossible
+
+-- | Convert a term (from a dot pattern) to a DeBruijn pattern.
+
+class TermToPattern a b where
+  termToPattern :: a -> TCM b
+
+  default termToPattern :: (TermToPattern a' b', Traversable f, a ~ f a', b ~ f b') => a -> TCM b
+  termToPattern = traverse termToPattern
+
+instance TermToPattern a b => TermToPattern [a] [b] where
+instance TermToPattern a b => TermToPattern (Arg a) (Arg b) where
+instance TermToPattern a b => TermToPattern (Named c a) (Named c b) where
+
+instance (DeBruijn (Pattern' a)) => TermToPattern Term (Pattern' a) where
+  termToPattern t = (reduce >=> constructorForm) t >>= \case
+    -- Constructors.
+    Con c _ args -> ConP c noConPatternInfo . map (fmap unnamed) <$> termToPattern (fromMaybe __IMPOSSIBLE__ $ allApplyElims args)
+    Var i []    -> return $ deBruijnVar i
+    Lit l       -> return $ litP l
+    t           -> return $ dotP t
+
+dotPatternsToPatterns :: forall a. (DeBruijn (Pattern' a))
+                      => Pattern' a -> TCM (Pattern' a)
+dotPatternsToPatterns = postTraversePatternM dotToPat
+  where
+    dotToPat :: Pattern' a -> TCM (Pattern' a)
+    dotToPat = \case
+      DotP o t -> termToPattern t
+      p        -> return p
diff --git a/src/full/Agda/TypeChecking/Patterns/Match.hs b/src/full/Agda/TypeChecking/Patterns/Match.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Patterns/Match.hs
@@ -0,0 +1,363 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+-- | Pattern matcher used in the reducer for clauses that
+--   have not been compiled to case trees yet.
+
+module Agda.TypeChecking.Patterns.Match where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Reduce.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Monad hiding (constructorForm)
+import Agda.TypeChecking.Monad.Builtin (getName',builtinHComp, builtinConId)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+
+import Agda.Utils.Empty
+import Agda.Utils.Functor (for, ($>), (<&>))
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+-- | If matching is inconclusive (@DontKnow@) we want to know whether
+--   it is due to a particular meta variable.
+data Match a = Yes Simplification (IntMap (Arg a))
+             | No
+             | DontKnow (Blocked ())
+  deriving Functor
+
+instance Null (Match a) where
+  empty = Yes empty empty
+  null (Yes simpl as) = null simpl && null as
+  null _              = False
+
+matchedArgs :: Empty -> Int -> IntMap (Arg a) -> [Arg a]
+matchedArgs err n vs = map (fromMaybe (absurd err)) $ matchedArgs' n vs
+
+matchedArgs' :: Int -> IntMap (Arg a) -> [Maybe (Arg a)]
+matchedArgs' n vs = map get [0 .. n - 1]
+  where
+    get k = IntMap.lookup k vs
+
+-- | Builds a proper substitution from an IntMap produced by match(Co)patterns
+buildSubstitution :: (DeBruijn a)
+                  => Impossible -> Int -> IntMap (Arg a) -> Substitution' a
+buildSubstitution err n vs = foldr cons idS $ matchedArgs' n vs
+  where cons Nothing  = strengthenS' err 1
+        cons (Just v) = consS (unArg v)
+
+
+instance Semigroup (Match a) where
+    -- @NotBlocked (StuckOn e)@ means blocked by a variable.
+    -- In this case, no instantiation of meta-variables will make progress.
+    DontKnow b <> DontKnow b'      = DontKnow $ b <> b'
+    DontKnow m <> _                = DontKnow m
+    _          <> DontKnow m       = DontKnow m
+    -- One could imagine DontKnow _ <> No = No, but would break the
+    -- equivalence to case-trees (Issue 2964).
+    No         <> _                = No
+    _          <> No               = No
+    Yes s us   <> Yes s' vs        = Yes (s <> s') (us <> vs)
+
+instance Monoid (Match a) where
+    mempty = empty
+    mappend = (<>)
+
+-- | Instead of 'zipWithM', we need to use this lazy version
+--   of combining pattern matching computations.
+
+-- Andreas, 2014-05-08, see Issue 1124:
+--
+-- Due to a bug in TypeChecking.Patterns.Match
+-- a failed match of (C n b) against (C O unit)
+-- turned into (C n unit).
+-- This was because all patterns were matched in
+-- parallel, and evaluations of successfull matches
+-- (and a record constructor like unit can always
+-- be successfully matched) were returned, leading
+-- to a reassembly of (C n b) as (C n unit) which is
+-- illtyped.
+
+-- Now patterns are matched left to right and
+-- upon failure, no further matching is performed.
+
+foldMatch
+  :: forall m p v . (IsProjP p, MonadMatch m)
+  => (p -> v -> m (Match Term, v))
+  -> [p] -> [v] -> m (Match Term, [v])
+foldMatch match = loop where
+  loop :: [p] -> [v] -> m (Match Term, [v])
+  loop ps0 vs0 = do
+    case (ps0, vs0) of
+      ([], []) -> return (empty, [])
+      (p : ps, v : vs) -> do
+        (r, v') <- match p v
+        case r of
+          No | Just{} <- isProjP p -> return (No, v' : vs)
+          No -> do
+            -- Issue 2964: Even when the first pattern doesn't match we should
+            -- continue to the next patterns (and potentially block on them)
+            -- because the splitting order in the case tree may not be
+            -- left-to-right.
+            (r', _vs') <- loop ps vs
+            -- Issue 2968: do not use vs' here, because it might
+            -- contain ill-typed terms due to eta-expansion at wrong
+            -- type.
+            return (r <> r', v' : vs)
+          DontKnow m -> return (DontKnow m, v' : vs)
+          Yes{} -> do
+            (r', vs') <- loop ps vs
+            return (r <> r', v' : vs')
+      _ -> __IMPOSSIBLE__
+
+
+-- TODO refactor matchPattern* to work with Elim instead.
+mergeElim :: Elim -> Arg Term -> Elim
+mergeElim Apply{} arg = Apply arg
+mergeElim (IApply x y _) arg = IApply x y (unArg arg)
+mergeElim Proj{} _ = __IMPOSSIBLE__
+
+mergeElims :: [Elim] -> [Arg Term] -> [Elim]
+mergeElims = zipWith mergeElim
+
+type MonadMatch m = PureTCM m
+
+-- | @matchCopatterns ps es@ matches spine @es@ against copattern spine @ps@.
+--
+--   Returns 'Yes' and a substitution for the pattern variables
+--   (in form of IntMap Term) if matching was successful.
+--
+--   Returns 'No' if there was a constructor or projection mismatch.
+--
+--   Returns 'DontKnow' if an argument could not be evaluated to
+--   constructor form because of a blocking meta variable.
+--
+--   In any case, also returns spine @es@ in reduced form
+--   (with all the weak head reductions performed that were necessary
+--   to come to a decision).
+matchCopatterns :: MonadMatch m
+                => [NamedArg DeBruijnPattern]
+                -> [Elim]
+                -> m (Match Term, [Elim])
+matchCopatterns ps vs = do
+  traceSDoc "tc.match" 50
+    (vcat [ "matchCopatterns"
+          , nest 2 $ "ps =" <+> fsep (punctuate comma $ map (prettyTCM . namedArg) ps)
+          , nest 2 $ "vs =" <+> fsep (punctuate comma $ map prettyTCM vs)
+          ]) $ do
+  -- Buggy, see issue 1124:
+  -- mapFst mconcat . unzip <$> zipWithM' (matchCopattern . namedArg) ps vs
+  foldMatch (matchCopattern . namedArg) ps vs
+
+-- | Match a single copattern.
+matchCopattern :: MonadMatch m
+               => DeBruijnPattern
+               -> Elim
+               -> m (Match Term, Elim)
+matchCopattern pat@ProjP{} elim@(Proj _ q) = do
+  p <- normaliseProjP pat <&> \case
+         ProjP _ p -> p
+         _         -> __IMPOSSIBLE__
+  q       <- getOriginalProjection q
+  return $ if p == q then (Yes YesSimplification empty, elim)
+                     else (No,                          elim)
+-- The following two cases are not impossible, see #2964
+matchCopattern ProjP{} elim@Apply{}   = return (No , elim)
+matchCopattern _       elim@Proj{}    = return (No , elim)
+matchCopattern p       (Apply v) = mapSnd Apply <$> matchPattern p v
+matchCopattern p       e@(IApply x y r) = mapSnd (mergeElim e) <$> matchPattern p (defaultArg r)
+
+{-# SPECIALIZE matchPatterns :: [NamedArg DeBruijnPattern] -> [Arg Term] -> TCM (Match Term, [Arg Term]) #-}
+matchPatterns :: MonadMatch m
+              => [NamedArg DeBruijnPattern]
+              -> [Arg Term]
+              -> m (Match Term, [Arg Term])
+matchPatterns ps vs = do
+  reportSDoc "tc.match" 20 $
+     vcat [ "matchPatterns"
+          , nest 2 $ "ps =" <+> prettyTCMPatternList ps
+          , nest 2 $ "vs =" <+> fsep (punctuate comma $ map prettyTCM vs)
+          ]
+
+  traceSDoc "tc.match" 50
+    (vcat [ "matchPatterns"
+          , nest 2 $ "ps =" <+> fsep (punctuate comma $ map (text . show) ps)
+          , nest 2 $ "vs =" <+> fsep (punctuate comma $ map prettyTCM vs)
+          ]) $ do
+  -- Buggy, see issue 1124:
+  -- (ms,vs) <- unzip <$> zipWithM' (matchPattern . namedArg) ps vs
+  -- return (mconcat ms, vs)
+  foldMatch (matchPattern . namedArg) ps vs
+
+-- | Match a single pattern.
+matchPattern :: MonadMatch m
+             => DeBruijnPattern
+             -> Arg Term
+             -> m (Match Term, Arg Term)
+matchPattern p u = case (p, u) of
+  (ProjP{}, _            ) -> __IMPOSSIBLE__
+  (IApplyP _ _ _ x , arg ) -> return (Yes NoSimplification entry, arg)
+    where entry = singleton (dbPatVarIndex x, arg)
+  (VarP _ x , arg          ) -> return (Yes NoSimplification entry, arg)
+    where entry = singleton (dbPatVarIndex x, arg)
+  (DotP _ _ , arg@(Arg _ v)) -> return (Yes NoSimplification empty, arg)
+  (LitP _ l , arg@(Arg _ v)) -> do
+    w <- reduceB v
+    let arg' = arg $> ignoreBlocking w
+    case w of
+      NotBlocked _ (Lit l')
+          | l == l'            -> return (Yes YesSimplification empty , arg')
+          | otherwise          -> return (No                          , arg')
+      Blocked b _              -> return (DontKnow $ Blocked b ()     , arg')
+      NotBlocked r t           -> return (DontKnow $ NotBlocked r' () , arg')
+        where r' = stuckOn (Apply arg') r
+
+  -- Case constructor pattern.
+  (ConP c cpi ps, Arg info v) -> do
+    if not (conPRecord cpi) then fallback c ps (Arg info v) else do
+    isEtaRecordCon (conName c) >>= \case
+      Nothing -> fallback c ps (Arg info v)
+      Just fs -> do
+        -- Case: Eta record constructor.
+        -- This case is necessary if we want to use the clauses before
+        -- record pattern translation (e.g., in type-checking definitions by copatterns).
+        unless (size fs == size ps) __IMPOSSIBLE__
+        mapSnd (Arg info . Con c (fromConPatternInfo cpi) . map Apply) <$> do
+          matchPatterns ps $ for fs $ \ (Arg ai f) -> Arg ai $ v `applyE` [Proj ProjSystem f]
+    where
+    isEtaRecordCon :: HasConstInfo m => QName -> m (Maybe [Arg QName])
+    isEtaRecordCon c = do
+      (theDef <$> getConstInfo c) >>= \case
+        Constructor{ conData = d } -> do
+          (theDef <$> getConstInfo d) >>= \case
+            r@Record{ recFields = fs } | YesEta <- recEtaEquality r -> return $ Just $ map argFromDom fs
+            _ -> return Nothing
+        _ -> __IMPOSSIBLE__
+  (DefP o q ps, v) -> do
+    let f (Def q' vs) | q == q' = Just (Def q, vs)
+        f _                     = Nothing
+    fallback' f ps v
+ where
+    -- Default: not an eta record constructor.
+  fallback :: MonadMatch m
+           => ConHead -> [NamedArg DeBruijnPattern] -> Arg Term -> m (Match Term, Arg Term)
+  fallback c ps v = do
+    let f (Con c' ci' vs) | c == c' = Just (Con c' ci',vs)
+        f _                         = Nothing
+    fallback' f ps v
+
+  -- Regardless of blocking, constructors and a properly applied @hcomp@
+  -- can be matched on.
+  isMatchable' :: HasBuiltins m => m (Blocked Term -> Maybe Term)
+  isMatchable' = do
+    [mhcomp,mconid] <- mapM getName' [builtinHComp, builtinConId]
+    return $ \ r ->
+      case ignoreBlocking r of
+        t@Con{} -> Just t
+        t@(Def q [l,a,phi,u,u0]) | Just q == mhcomp
+                -> Just t
+        t@(Def q [l,a,x,y,phi,p]) | Just q == mconid
+                -> Just t
+        -- TODO this covers the transpIx functions, but it's a hack.
+        t@(Def q _) | NotBlocked{blockingStatus = MissingClauses _} <- r -> Just t
+        _       -> Nothing
+
+  -- DefP hcomp and ConP matching.
+  fallback' :: MonadMatch m
+            => (Term -> Maybe (Elims -> Term , Elims))
+            -> [NamedArg DeBruijnPattern]
+            -> Arg Term
+            -> m (Match Term, Arg Term)
+  fallback' mtc ps (Arg info v) = do
+        isMatchable <- isMatchable'
+
+        w <- reduceB v
+        -- Unfold delayed (corecursive) definitions one step. This is
+        -- only necessary if c is a coinductive constructor, but
+        -- it does not hurt to do it all the time.
+{-
+        w <- case w of
+               NotBlocked r (Def f es) ->   -- Andreas, 2014-06-12 TODO: r == ReallyNotBlocked sufficient?
+                 unfoldDefinitionE True reduceB' (Def f []) f es
+                   -- reduceB is used here because some constructors
+                   -- are actually definitions which need to be
+                   -- unfolded (due to open public).
+               _ -> return w
+-}
+        -- Jesper, 23-06-2016: Note that unfoldCorecursion may destroy
+        -- constructor forms, so we only call constructorForm after.
+        w <- traverse constructorForm =<< case w of
+               NotBlocked r u -> liftReduce $ unfoldCorecursion u  -- Andreas, 2014-06-12 TODO: r == ReallyNotBlocked sufficient?
+               _ -> return w
+        let v = ignoreBlocking w
+            arg = Arg info v  -- the reduced argument
+
+        case w of
+          b | Just t <- isMatchable b ->
+            case mtc t of
+              Just (bld, vs) -> do
+                (m, vs1) <- matchPatterns ps (fromMaybe __IMPOSSIBLE__ $ allApplyElims vs)
+                return (yesSimplification m, Arg info $ bld (mergeElims vs vs1))
+              Nothing
+                                    -> return (No                          , arg)
+          Blocked b _               -> return (DontKnow $ Blocked b ()     , arg)
+          NotBlocked r _            -> return (DontKnow $ NotBlocked r' () , arg)
+            where r' = stuckOn (Apply arg) r
+
+yesSimplification :: Match a -> Match a
+yesSimplification = \case
+  Yes _ vs -> Yes YesSimplification vs
+  m -> m
+
+-- Matching patterns against patterns -------------------------------------
+
+-- | Match a single pattern.
+matchPatternP :: MonadMatch m
+              => DeBruijnPattern
+              -> Arg DeBruijnPattern
+              -> m (Match DeBruijnPattern)
+matchPatternP p (Arg info (DotP _ v)) = do
+  (m, arg) <- matchPattern p (Arg info v)
+  return $ fmap (DotP defaultPatternInfo) m
+matchPatternP p arg@(Arg info q) = do
+  let varMatch x = return $ Yes NoSimplification $ singleton (dbPatVarIndex x, arg)
+      termMatch  = do
+        (m, arg) <- matchPattern p (fmap patternToTerm arg)
+        return $ fmap (DotP defaultPatternInfo) m
+  case p of
+    ProjP{}         -> __IMPOSSIBLE__
+    IApplyP _ _ _ x -> varMatch x
+    VarP _ x        -> varMatch x
+    DotP _ _        -> return $ Yes NoSimplification empty
+    LitP{}          -> termMatch -- Literal patterns bind no variables so we can fall back to the Term version.
+    DefP{}          -> termMatch
+
+    ConP c cpi ps ->
+      case q of
+        ConP c' _ qs | c == c'   -> matchPatternsP ps ((map . fmap) namedThing qs)
+                     | otherwise -> return No
+        LitP{} -> fmap toLitP <$> termMatch
+          where toLitP (DotP _ (Lit l)) = litP l   -- All bindings should be to literals
+                toLitP _                = __IMPOSSIBLE__
+        _      -> termMatch
+
+matchPatternsP :: MonadMatch m
+               => [NamedArg DeBruijnPattern]
+               -> [Arg DeBruijnPattern]
+               -> m (Match DeBruijnPattern)
+matchPatternsP ps qs = do
+  mconcat <$> zipWithM matchPatternP (map namedArg ps) qs
diff --git a/src/full/Agda/TypeChecking/Patterns/Match.hs-boot b/src/full/Agda/TypeChecking/Patterns/Match.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Patterns/Match.hs-boot
@@ -0,0 +1,21 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Patterns.Match where
+
+import Data.IntMap (IntMap)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute (DeBruijn)
+
+import Agda.Utils.Impossible
+
+data Match a = Yes Simplification (IntMap (Arg a)) | No | DontKnow (Blocked ())
+
+buildSubstitution :: (DeBruijn a) => Impossible -> Int -> IntMap (Arg a) -> Substitution' a
+
+type MonadMatch m = PureTCM m
+
+matchPatterns   :: MonadMatch m => [NamedArg DeBruijnPattern] -> Args -> m (Match Term, Args)
+matchCopatterns :: MonadMatch m => [NamedArg DeBruijnPattern] -> Elims -> m (Match Term, Elims)
diff --git a/src/full/Agda/TypeChecking/Polarity.hs b/src/full/Agda/TypeChecking/Polarity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Polarity.hs
@@ -0,0 +1,426 @@
+-- | Computing the polarity (variance) of function arguments,
+--   for the sake of subtyping.
+
+module Agda.TypeChecking.Polarity
+  ( -- * Polarity computation
+    computePolarity
+    -- * Auxiliary functions
+  , composePol
+  , nextPolarity
+  , purgeNonvariant
+  , polFromOcc
+  ) where
+
+import Control.Monad  ( forM_, zipWithM )
+
+import Data.Maybe
+import Data.Semigroup ( Semigroup(..) )
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Datatypes (getNumberOfParameters)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.SizedTypes
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Positivity.Occurrence
+
+import Agda.Utils.List
+import Agda.Utils.Maybe ( whenNothingM )
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- * Polarity lattice.
+------------------------------------------------------------------------
+
+-- | Infimum on the information lattice.
+--   'Invariant' is bottom (dominant for inf),
+--   'Nonvariant' is top (neutral for inf).
+(/\) :: Polarity -> Polarity -> Polarity
+Nonvariant /\ b = b
+a /\ Nonvariant = a
+a /\ b | a == b    = a
+       | otherwise = Invariant
+
+-- | 'Polarity' negation, swapping monotone and antitone.
+neg :: Polarity -> Polarity
+neg Covariant     = Contravariant
+neg Contravariant = Covariant
+neg Invariant     = Invariant
+neg Nonvariant    = Nonvariant
+
+-- | What is the polarity of a function composition?
+composePol :: Polarity -> Polarity -> Polarity
+composePol Nonvariant _    = Nonvariant
+composePol _ Nonvariant    = Nonvariant
+composePol Invariant _     = Invariant
+composePol Covariant x     = x
+composePol Contravariant x = neg x
+
+polFromOcc :: Occurrence -> Polarity
+polFromOcc = \case
+  GuardPos  -> Covariant
+  StrictPos -> Covariant
+  JustPos   -> Covariant
+  JustNeg   -> Contravariant
+  Mixed     -> Invariant
+  Unused    -> Nonvariant
+
+------------------------------------------------------------------------
+-- * Auxiliary functions
+------------------------------------------------------------------------
+
+-- | Get the next polarity from a list, 'Invariant' if empty.
+nextPolarity :: [Polarity] -> (Polarity, [Polarity])
+nextPolarity []       = (Invariant, [])
+nextPolarity (p : ps) = (p, ps)
+
+-- | Replace 'Nonvariant' by 'Covariant'.
+--   (Arbitrary bias, but better than 'Invariant', see issue 1596).
+purgeNonvariant :: [Polarity] -> [Polarity]
+purgeNonvariant = map (\ p -> if p == Nonvariant then Covariant else p)
+
+
+-- | A quick transliterations of occurrences to polarities.
+polarityFromPositivity
+  :: (HasConstInfo m, MonadTCEnv m, MonadTCState m, MonadDebug m)
+  => QName -> m ()
+polarityFromPositivity x = inConcreteOrAbstractMode x $ \ def -> do
+
+  -- Get basic polarity from positivity analysis.
+  let npars = droppedPars def
+  let pol0 = replicate npars Nonvariant ++ map polFromOcc (defArgOccurrences def)
+  reportSLn "tc.polarity.set" 15 $
+    "Polarity of " ++ prettyShow x ++ " from positivity: " ++ prettyShow pol0
+
+  -- set the polarity in the signature (not the final polarity, though)
+  setPolarity x $ drop npars pol0
+
+------------------------------------------------------------------------
+-- * Computing the polarity of a symbol.
+------------------------------------------------------------------------
+
+-- | Main function of this module.
+computePolarity
+  :: ( HasOptions m, HasConstInfo m, HasBuiltins m
+     , MonadTCEnv m, MonadTCState m, MonadReduce m, MonadAddContext m, MonadTCError m
+     , MonadDebug m, MonadPretty m )
+  => [QName] -> m ()
+computePolarity xs = do
+
+ -- Andreas, 2017-04-26, issue #2554
+ -- First, for mutual definitions, obtain a crude polarity from positivity.
+ when (length xs >= 2) $ mapM_ polarityFromPositivity xs
+
+ -- Then, refine it.
+ forM_ xs $ \ x -> inConcreteOrAbstractMode x $ \ def -> do
+  reportSLn "tc.polarity.set" 25 $ "Refining polarity of " ++ prettyShow x
+
+  -- Again: get basic polarity from positivity analysis.
+  let npars = droppedPars def
+  let pol0 = replicate npars Nonvariant ++ map polFromOcc (defArgOccurrences def)
+  reportSLn "tc.polarity.set" 15 $
+    "Polarity of " ++ prettyShow x ++ " from positivity: " ++ prettyShow pol0
+
+{-
+  -- get basic polarity from shape of def (arguments matched on or not?)
+  def      <- getConstInfo x
+  let usagePol = usagePolarity $ theDef def
+  reportSLn "tc.polarity.set" 15 $ "Polarity of " ++ prettyShow x ++ " from definition form: " ++ prettyShow usagePol
+  let n = genericLength usagePol  -- n <- getArity x
+  reportSLn "tc.polarity.set" 20 $ "  arity = " ++ show n
+
+  -- refine polarity by positivity information
+  pol0 <- zipWith (/\) usagePol <$> mapM getPol [0..n - 1]
+  reportSLn "tc.polarity.set" 15 $ "Polarity of " ++ prettyShow x ++ " from positivity: " ++ prettyShow pol0
+-}
+
+  -- compute polarity of sized types
+  pol1 <- sizePolarity x pol0
+
+  -- refine polarity again by using type information
+  let t = defType def
+  -- Instantiation takes place in Rules.Decl.instantiateDefinitionType
+  -- t <- instantiateFull t -- Andreas, 2014-04-11 Issue 1099: needed for
+  --                        -- variable occurrence test in  dependentPolarity.
+  reportSDoc "tc.polarity.set" 15 $
+    "Refining polarity with type " <+> prettyTCM t
+  reportSDoc "tc.polarity.set" 60 $
+    "Refining polarity with type (raw): " <+> (text .show) t
+
+  pol <- dependentPolarity t (enablePhantomTypes (theDef def) pol1) pol1
+  reportSLn "tc.polarity.set" 10 $ "Polarity of " ++ prettyShow x ++ ": " ++ prettyShow pol
+
+  -- set the polarity in the signature
+  setPolarity x $ drop npars pol -- purgeNonvariant pol -- temporarily disable non-variance
+
+-- | Data and record parameters are used as phantom arguments all over
+--   the test suite (and possibly in user developments).
+--   @enablePhantomTypes@ turns 'Nonvariant' parameters to 'Covariant'
+--   to enable phantoms.
+enablePhantomTypes :: Defn -> [Polarity] -> [Polarity]
+enablePhantomTypes def pol = case def of
+  Datatype{ dataPars = np } -> enable np
+  Record  { recPars  = np } -> enable np
+  _                         -> pol
+  where enable np = let (pars, rest) = splitAt np pol
+                    in  purgeNonvariant pars ++ rest
+
+{- UNUSED
+-- | Extract a basic approximate polarity info from the shape of definition.
+--   Arguments that are matched against get 'Invariant', others 'Nonvariant'.
+--   For data types, parameters get 'Nonvariant', indices 'Invariant'.
+usagePolarity :: Defn -> [Polarity]
+usagePolarity def = case def of
+    Axiom{}                                 -> []
+    Function{ funClauses = [] }             -> []
+    Function{ funClauses = cs }             -> usage $ map namedClausePats cs
+    Datatype{ dataPars = np, dataIxs = ni } -> genericReplicate np Nonvariant
+    Record{ recPars = n }                   -> genericReplicate n Nonvariant
+    Constructor{}                           -> []
+    Primitive{}                             -> []
+  where
+    usage = foldr1 (zipWith (/\)) . map (map (usagePat . namedArg))
+    usagePat VarP{} = Nonvariant
+    usagePat DotP{} = Nonvariant
+    usagePat ConP{} = Invariant
+    usagePat LitP{} = Invariant
+-}
+
+-- | Make arguments 'Invariant' if the type of a not-'Nonvariant'
+--   later argument depends on it.
+--   Also, enable phantom types by turning 'Nonvariant' into something
+--   else if it is a data/record parameter but not a size argument. [See issue 1596]
+--
+--   Precondition: the "phantom" polarity list has the same length as the polarity list.
+dependentPolarity
+  :: (HasOptions m, HasBuiltins m, MonadReduce m, MonadAddContext m, MonadDebug m)
+  => Type -> [Polarity] -> [Polarity] -> m [Polarity]
+dependentPolarity t _      []          = return []  -- all remaining are 'Invariant'
+dependentPolarity t []     (_ : _)     = __IMPOSSIBLE__
+dependentPolarity t (q:qs) pols@(p:ps) = do
+  t <- reduce $ unEl t
+  reportSDoc "tc.polarity.dep" 20 $ "dependentPolarity t = " <+> prettyTCM t
+  reportSDoc "tc.polarity.dep" 70 $ "dependentPolarity t = " <+> (text . show) t
+  case t of
+    Pi dom b -> do
+      ps <- underAbstraction dom b $ \ c -> dependentPolarity c qs ps
+      let fallback = ifM (isJust <$> isSizeType (unDom dom)) (return p) (return q)
+      p <- case b of
+        Abs{} | p /= Invariant  ->
+          -- Andreas, 2014-04-11 see Issue 1099
+          -- Free variable analysis is not in the monad,
+          -- hence metas must have been instantiated before!
+          ifM (relevantInIgnoringNonvariant 0 (absBody b) ps)
+            {- then -} (return Invariant)
+            {- else -} fallback
+        _ -> fallback
+      return $ p : ps
+    _ -> return pols
+
+-- | Check whether a variable is relevant in a type expression,
+--   ignoring domains of non-variant arguments.
+relevantInIgnoringNonvariant :: MonadReduce m => Nat -> Type -> [Polarity] -> m Bool
+relevantInIgnoringNonvariant i t []     = return $ i `relevantInIgnoringSortAnn` t
+relevantInIgnoringNonvariant i t (p:ps) =
+  ifNotPiType t
+    {-then-} (\ t -> return $ i `relevantInIgnoringSortAnn` t) $
+    {-else-} \ a b ->
+      if p /= Nonvariant && i `relevantInIgnoringSortAnn` a
+        then return True
+        else relevantInIgnoringNonvariant (i + 1) (absBody b) ps
+
+------------------------------------------------------------------------
+-- * Sized types
+------------------------------------------------------------------------
+
+-- | Hack for polarity of size indices.
+--   As a side effect, this sets the positivity of the size index.
+--   See test/succeed/PolaritySizeSucData.agda for a case where this is needed.
+sizePolarity
+  :: forall m .
+     ( HasOptions m, HasConstInfo m, HasBuiltins m, ReadTCState m
+     , MonadTCEnv m, MonadTCState m, MonadReduce m, MonadAddContext m, MonadTCError m
+     , MonadDebug m, MonadPretty m )
+  => QName -> [Polarity] -> m [Polarity]
+sizePolarity d pol0 = do
+  let exit = return pol0
+  ifNotM sizedTypesOption exit $ {- else -} do
+    def <- getConstInfo d
+    case theDef def of
+      Datatype{ dataPars = np, dataCons = cons } -> do
+        let TelV tel _      = telView' $ defType def
+            (parTel, ixTel) = splitAt np $ telToList tel
+        case ixTel of
+          []                 -> exit  -- No size index
+          Dom{unDom = (_,a)} : _ -> ifM ((/= Just BoundedNo) <$> isSizeType a) exit $ do
+            -- we assume the size index to be 'Covariant' ...
+            let pol   = take np pol0
+                polCo = pol ++ [Covariant]
+                polIn = pol ++ [Invariant]
+            setPolarity d $ polCo
+            -- and seek confirm it by looking at the constructor types
+            let check :: QName -> m Bool
+                check c = do
+                  t <- defType <$> getConstInfo c
+                  addContext (telFromList parTel) $ do
+                    let pars = map (defaultArg . var) $ downFrom np
+                    TelV conTel target <- telView =<< (t `piApplyM` pars)
+                    loop target conTel
+                  where
+                  loop :: Type -> Telescope -> m Bool
+                  -- no suitable size argument
+                  loop _ EmptyTel = do
+                    reportSDoc "tc.polarity.size" 15 $
+                      "constructor" <+> prettyTCM c <+> "fails size polarity check"
+                    return False
+
+                  -- try argument @dom@
+                  loop target (ExtendTel dom tel) = do
+                    isSz <- isSizeType dom
+                    underAbstraction dom tel $ \ tel -> do
+                      let continue = loop target tel
+
+                      -- check that dom == Size
+                      if isSz /= Just BoundedNo then continue else do
+
+                        -- check that the size argument appears in the
+                        -- right spot in the target type
+                        let sizeArg = size tel
+                        isLin <- addContext tel $ checkSizeIndex d sizeArg target
+                        if not isLin then continue else do
+
+                          -- check that only positive occurences in tel
+                          pols <- zipWithM polarity [0..] $ map (snd . unDom) $ telToList tel
+                          reportSDoc "tc.polarity.size" 25 $
+                            text $ "to pass size polarity check, the following polarities need all to be covariant: " ++ prettyShow pols
+                          if any (`notElem` [Nonvariant, Covariant]) pols then continue else do
+                            reportSDoc "tc.polarity.size" 15 $
+                              "constructor" <+> prettyTCM c <+> "passes size polarity check"
+                            return True
+
+            ifNotM (andM $ map check cons)
+                (return polIn) -- no, does not conform to the rules of sized types
+              $ do  -- yes, we have a sized type here
+                -- Andreas, 2015-07-01
+                -- As a side effect, mark the size also covariant for subsequent
+                -- positivity checking (which feeds back into polarity analysis).
+                modifyArgOccurrences d $ \ occ -> take np occ ++ [JustPos]
+                return polCo
+      _ -> exit
+
+-- | @checkSizeIndex d i a@ checks that constructor target type @a@
+--   has form @d ps (↑ⁿ i) idxs@ where @|ps| = np(d)@.
+--
+--   Precondition: @a@ is reduced and of form @d ps idxs0@.
+checkSizeIndex
+  :: (HasConstInfo m, ReadTCState m, MonadDebug m, MonadPretty m, MonadTCError m)
+  => QName -> Nat -> Type -> m Bool
+checkSizeIndex d i a = do
+  reportSDoc "tc.polarity.size" 15 $ withShowAllArguments $ vcat
+    [ "checking that constructor target type " <+> prettyTCM a
+    , "  is data type " <+> prettyTCM d
+    , "  and has size index (successor(s) of) " <+> prettyTCM (var i)
+    ]
+  case unEl a of
+    Def d0 es -> do
+      whenNothingM (sameDef d d0) __IMPOSSIBLE__
+      np <- fromMaybe __IMPOSSIBLE__ <$> getNumberOfParameters d0
+      let (pars, Apply ix : ixs) = splitAt np es
+      s <- deepSizeView $ unArg ix
+      case s of
+        DSizeVar (ProjectedVar j []) _ | i == j
+          -> return $ not $ freeIn i (pars ++ ixs)
+        _ -> return False
+    _ -> __IMPOSSIBLE__
+
+-- | @polarity i a@ computes the least polarity of de Bruijn index @i@
+--   in syntactic entity @a@.
+polarity
+  :: (HasPolarity a, HasConstInfo m, MonadReduce m)
+  => Nat -> a -> m Polarity
+polarity i x = getLeastPolarity $ polarity' i Covariant x
+
+-- | A monoid for lazily computing the infimum of the polarities of a variable in some object.
+-- Allows short-cutting.
+
+newtype LeastPolarity m = LeastPolarity { getLeastPolarity :: m Polarity}
+
+instance Monad m => Singleton Polarity (LeastPolarity m) where
+  singleton = LeastPolarity . return
+
+instance Monad m => Semigroup (LeastPolarity m) where
+  LeastPolarity mp <> LeastPolarity mq = LeastPolarity $ do
+    mp >>= \case
+      Invariant  -> return Invariant  -- Shortcut for the absorbing element.
+      Nonvariant -> mq                -- The neutral element.
+      p          -> (p /\) <$> mq
+
+instance Monad m => Monoid (LeastPolarity m) where
+  mempty  = singleton Nonvariant
+  mappend = (<>)
+
+-- | Bind for 'LeastPolarity'.
+(>>==) :: Monad m => m a -> (a -> LeastPolarity m) -> LeastPolarity m
+m >>== k = LeastPolarity $ m >>= getLeastPolarity . k
+
+-- | @polarity' i p a@ computes the least polarity of de Bruijn index @i@
+--   in syntactic entity @a@, where root occurrences count as @p@.
+--
+--   Ignores occurrences in sorts.
+class HasPolarity a where
+  polarity'
+    :: (HasConstInfo m, MonadReduce m)
+    => Nat -> Polarity -> a -> LeastPolarity m
+
+  default polarity'
+    :: (HasConstInfo m, MonadReduce m, HasPolarity b, Foldable t, t b ~ a)
+    => Nat -> Polarity -> a -> LeastPolarity m
+  polarity' i = foldMap . polarity' i
+
+instance HasPolarity a => HasPolarity [a]
+instance HasPolarity a => HasPolarity (Arg a)
+instance HasPolarity a => HasPolarity (Dom a)
+instance HasPolarity a => HasPolarity (Elim' a)
+instance HasPolarity a => HasPolarity (Level' a)
+instance HasPolarity a => HasPolarity (PlusLevel' a)
+
+-- | Does not look into sort.
+instance HasPolarity a => HasPolarity (Type'' t a)
+
+instance (HasPolarity a, HasPolarity b) => HasPolarity (a, b) where
+  polarity' i p (x, y) = polarity' i p x <> polarity' i p y
+
+instance HasPolarity a => HasPolarity (Abs a) where
+  polarity' i p (Abs   _ b) = polarity' (i + 1) p b
+  polarity' i p (NoAbs _ v) = polarity' i p v
+
+instance HasPolarity Term where
+  polarity' i p v = instantiate v >>== \case
+    -- Andreas, 2012-09-06: taking the polarity' of the arguments
+    -- without taking the variance of the function into account seems wrong.
+    Var n ts
+      | n == i    -> singleton p <> polarity' i Invariant ts
+      | otherwise -> polarity' i Invariant ts
+    Lam _ t       -> polarity' i p t
+    Lit _         -> mempty
+    Level l       -> polarity' i p l
+    Def x ts      -> getPolarity x >>== \ pols ->
+                       let ps = map (composePol p) pols ++ repeat Invariant
+                       in  mconcat $ zipWith (polarity' i) ps ts
+    Con _ _ ts    -> polarity' i p ts   -- Constructors can be seen as monotone in all args.
+    Pi a b        -> polarity' i (neg p) a <> polarity' i p b
+    Sort s        -> mempty -- polarity' i p s -- mempty
+    MetaV _ ts    -> polarity' i Invariant ts
+    DontCare t    -> polarity' i p t -- mempty
+    Dummy{}       -> mempty
diff --git a/src/full/Agda/TypeChecking/Polarity.hs-boot b/src/full/Agda/TypeChecking/Polarity.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Polarity.hs-boot
@@ -0,0 +1,19 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Polarity where
+
+import Agda.Syntax.Abstract.Name                        (QName)
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin                  (HasBuiltins)
+import Agda.TypeChecking.Monad.Context                  (MonadAddContext)
+import Agda.TypeChecking.Monad.Debug                    (MonadDebug)
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Signature (HasConstInfo)
+import {-# SOURCE #-} Agda.TypeChecking.Pretty          (MonadPretty)
+
+computePolarity
+  :: ( HasOptions m, HasConstInfo m, HasBuiltins m
+     , MonadTCEnv m, MonadTCState m, MonadReduce m, MonadAddContext m, MonadTCError m
+     , MonadDebug m, MonadPretty m )
+  => [QName] -> m ()
+
+composePol      :: Polarity -> Polarity -> Polarity
diff --git a/src/full/Agda/TypeChecking/Positivity.hs b/src/full/Agda/TypeChecking/Positivity.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Positivity.hs
@@ -0,0 +1,871 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+-- | Check that a datatype is strictly positive.
+module Agda.TypeChecking.Positivity where
+
+import Prelude hiding ( null )
+
+import Control.Applicative hiding (empty)
+import Control.DeepSeq
+import Control.Monad        ( forM_, guard, liftM2 )
+import Control.Monad.Reader ( MonadReader(..), asks, Reader, runReader )
+
+import Data.Either
+import qualified Data.Foldable as Fold
+import Data.Function (on)
+import Data.Graph (SCC(..))
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Sequence (Seq)
+import qualified Data.Sequence as DS
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Debug.Trace
+
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Position (HasRange(..), noRange)
+import Agda.TypeChecking.Datatypes ( isDataOrRecordType )
+import Agda.TypeChecking.Functions
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+import Agda.Utils.Function (applyUnless)
+import Agda.Utils.Functor
+import Agda.Utils.List
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Syntax.Common.Pretty (Pretty, prettyShow)
+import Agda.Utils.SemiRing
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+type Graph n e = Graph.Graph n e
+
+-- | Check that the datatypes in the mutual block containing the given
+--   declarations are strictly positive.
+--
+--   Also add information about positivity and recursivity of records
+--   to the signature.
+checkStrictlyPositive :: Info.MutualInfo -> Set QName -> TCM ()
+checkStrictlyPositive mi qset = do
+  -- compute the occurrence graph for qs
+  let qs = Set.toList qset
+  reportSDoc "tc.pos.tick" 100 $ "positivity of" <+> prettyTCM qs
+  g <- buildOccurrenceGraph qset
+  let (gstar, sccs) =
+        Graph.gaussJordanFloydWarshallMcNaughtonYamada $ fmap occ g
+  reportSDoc "tc.pos.tick" 100 $ "constructed graph"
+  reportSLn "tc.pos.graph" 5 $ "Positivity graph: N=" ++ show (size $ Graph.nodes g) ++
+                               " E=" ++ show (length $ Graph.edges g)
+  reportSDoc "tc.pos.graph" 10 $ vcat
+    [ "positivity graph for" <+> fsep (map prettyTCM qs)
+    , nest 2 $ prettyTCM g
+    ]
+  reportSLn "tc.pos.graph" 5 $
+    "Positivity graph (completed): E=" ++ show (length $ Graph.edges gstar)
+  reportSDoc "tc.pos.graph" 50 $ vcat
+    [ "transitive closure of positivity graph for" <+>
+      prettyTCM qs
+    , nest 2 $ prettyTCM gstar
+    ]
+
+  -- remember argument occurrences for qs in the signature
+  setArgOccs qset qs gstar
+  reportSDoc "tc.pos.tick" 100 $ "set args"
+
+  -- check positivity for all strongly connected components of the graph for qs
+  reportSDoc "tc.pos.graph.sccs" 10 $ do
+    let (triv, others) = partitionEithers $ for sccs $ \case
+          AcyclicSCC v -> Left v
+          CyclicSCC vs -> Right vs
+    sep [ text $ show (length triv) ++ " trivial sccs"
+        , text $ show (length others) ++ " non-trivial sccs with lengths " ++
+            show (map length others)
+        ]
+  reportSLn "tc.pos.graph.sccs" 15 $
+    "  sccs = " ++ prettyShow [ scc | CyclicSCC scc <- sccs ]
+  forM_ sccs $ \case
+    -- If the mutuality information has never been set, we set it to []
+    AcyclicSCC (DefNode q) -> whenM (isNothing <$> getMutual q) $ do
+      reportSLn "tc.pos.mutual" 10 $ "setting " ++ prettyShow q ++ " to non-recursive"
+      -- Andreas, 2017-04-26, issue #2555
+      -- We should not have @DefNode@s pointing outside our formal mutual block.
+      unless (Set.member q qset) __IMPOSSIBLE__
+      setMutual q []
+    AcyclicSCC (ArgNode{}) -> return ()
+    CyclicSCC scc          -> setMut [ q | DefNode q <- scc ]
+  mapM_ (checkPos g gstar) qs
+  reportSDoc "tc.pos.tick" 100 $ "checked positivity"
+
+  where
+    checkPos :: Graph Node (Edge OccursWhere) ->
+                Graph Node Occurrence ->
+                QName -> TCM ()
+    checkPos g gstar q = inConcreteOrAbstractMode q $ \ _def -> do
+      -- we check positivity only for data or record definitions
+      whenJustM (isDatatype q) $ \ dr -> do
+        reportSDoc "tc.pos.check" 10 $ "Checking positivity of" <+> prettyTCM q
+
+        let loop :: Maybe Occurrence
+            loop = Graph.lookup (DefNode q) (DefNode q) gstar
+
+            g' :: Graph Node (Edge (Seq OccursWhere))
+            g' = fmap (fmap DS.singleton) g
+
+            -- Note the property
+            -- Internal.Utils.Graph.AdjacencyMap.Unidirectional.prop_productOfEdgesInBoundedWalk,
+            -- which relates productOfEdgesInBoundedWalk to
+            -- gaussJordanFloydWarshallMcNaughtonYamada.
+
+            reason bound =
+              case productOfEdgesInBoundedWalk
+                     occ g' (DefNode q) (DefNode q) bound of
+                Just (Edge _ how) -> how
+                Nothing           -> __IMPOSSIBLE__
+
+            how :: String -> Occurrence -> TCM Doc
+            how msg bound = fsep $
+                  [prettyTCM q] ++ pwords "is" ++
+                  pwords (msg ++ ", because it occurs") ++
+                  [prettyTCM (reason bound)]
+
+        -- if we have a negative loop, raise error
+
+        -- ASR (23 December 2015). We don't raise a strictly positive
+        -- error if the NO_POSITIVITY_CHECK pragma was set on in the
+        -- mutual block. See Issue 1614.
+        when (Info.mutualPositivityCheck mi == YesPositivityCheck) $
+          whenM positivityCheckEnabled $
+            case loop of
+            Just o | o <= JustPos ->
+              warning $ NotStrictlyPositive q (reason JustPos)
+            _ -> return ()
+
+        -- if we find an unguarded record, mark it as such
+        case dr of
+          IsData -> return ()
+          IsRecord pat -> case loop of
+            Just o | o <= StrictPos -> do
+              reportSDoc "tc.pos.record" 5 $ how "not guarded" StrictPos
+              unguardedRecord q pat
+              checkInduction q
+            -- otherwise, if the record is recursive, mark it as well
+            Just o | o <= GuardPos -> do
+              reportSDoc "tc.pos.record" 5 $ how "recursive" GuardPos
+              recursiveRecord q
+              checkInduction q
+            -- If the record is not recursive, switch on eta
+            -- unless it is coinductive or a no-eta-equality record.
+            Nothing -> do
+              reportSDoc "tc.pos.record" 10 $
+                "record type " <+> prettyTCM q <+>
+                "is not recursive"
+              nonRecursiveRecord q
+            _ -> return ()
+
+    checkInduction :: QName -> TCM ()
+    checkInduction q =
+      -- ASR (01 January 2016). We don't raise this error if the
+      -- NO_POSITIVITY_CHECK pragma was set on in the record. See
+      -- Issue 1760.
+      when (Info.mutualPositivityCheck mi == YesPositivityCheck) $
+        whenM positivityCheckEnabled $ do
+        -- Check whether the recursive record has been declared as
+        -- 'Inductive' or 'Coinductive'.  Otherwise, error.
+        unlessM (isJust . recInduction . theDef <$> getConstInfo q) $
+          setCurrentRange (nameBindingSite $ qnameName q) $
+            typeError . GenericDocError =<<
+              "Recursive record" <+> prettyTCM q <+>
+              "needs to be declared as either inductive or coinductive"
+
+    occ (Edge o _) = o
+
+    isDatatype :: QName -> TCM (Maybe DataOrRecord)
+    isDatatype q = do
+      def <- theDef <$> getConstInfo q
+      return $ case def of
+        Datatype{dataClause = Nothing} -> Just IsData
+        Record  {recClause  = Nothing, recPatternMatching } -> Just $ IsRecord recPatternMatching
+        _ -> Nothing
+
+    -- Set the mutually recursive identifiers for a SCC.
+    setMut :: [QName] -> TCM ()
+    setMut [] = return ()  -- nothing to do
+    setMut qs = forM_ qs $ \ q -> do
+      reportSLn "tc.pos.mutual" 10 $ "setting " ++ prettyShow q ++ " to (mutually) recursive"
+      setMutual q qs
+      -- TODO: The previous line produces data of quadratic size
+      -- (which has to be processed upon serialization).  Presumably qs is
+      -- usually short, but in some cases (for instance for generated
+      -- code) it may be long. Wouldn't it be better to assign a
+      -- unique identifier to each SCC, and avoid storing lists?
+
+    -- Set the polarity of the arguments to a couple of definitions
+    setArgOccs :: Set QName -> [QName] -> Graph Node Occurrence -> TCM ()
+    setArgOccs qset qs g = do
+      -- Andreas, 2018-05-11, issue #3049: we need to be pessimistic about
+      -- argument polarity beyond the formal arity of the function.
+      --
+      -- -- Compute a map from each name in q to the maximal argument index
+      -- let maxs = Map.fromListWith max
+      --      [ (q, i) | ArgNode q i <- Set.toList $ Graph.nodes g, q `Set.member` qset ]
+      forM_ qs $ \ q -> inConcreteOrAbstractMode q $ \ def -> when (hasDefinition $ theDef def) $ do
+        reportSDoc "tc.pos.args" 10 $ "checking args of" <+> prettyTCM q
+        n <- getDefArity def
+        -- If there is no outgoing edge @ArgNode q i@, all @n@ arguments are @Unused@.
+        -- Otherwise, we obtain the occurrences from the Graph.
+        let findOcc i = fromMaybe Unused $ Graph.lookup (ArgNode q i) (DefNode q) g
+            args = -- caseMaybe (Map.lookup q maxs) (replicate n Unused) $ \ m ->
+              map findOcc [0 .. n-1]  -- [0 .. max m (n - 1)] -- triggers issue #3049
+        reportSDoc "tc.pos.args" 10 $ sep
+          [ "args of" <+> prettyTCM q <+> "="
+          , nest 2 $ prettyList $ map prettyTCM args
+          ]
+        -- The list args can take a long time to compute, but contains
+        -- small elements, and is stored in the interface (right?), so
+        -- it is computed deep-strictly.
+        setArgOccurrences q $!! args
+      where
+      -- Andreas, 2018-11-23, issue #3404
+      -- Only assign argument occurrences to things which have a definition.
+      -- Things without a definition would be judged "constant" in all arguments,
+      -- since no occurrence could possibly be found, naturally.
+      hasDefinition :: Defn -> Bool
+      hasDefinition = \case
+        Axiom{}            -> False
+        DataOrRecSig{}     -> False
+        GeneralizableVar{} -> False
+        AbstractDefn{}     -> False
+        Primitive{}        -> False
+        PrimitiveSort{}    -> False
+        Constructor{}      -> False
+        Function{}         -> True
+        Datatype{}         -> True
+        Record{}           -> True
+
+getDefArity :: Definition -> TCM Int
+getDefArity def = do
+  subtract (projectionArgs def) <$> arity' (defType def)
+  where
+  -- A variant of "\t -> arity <$> instantiateFull t".
+  arity' :: Type -> TCM Int
+  arity' t = do
+    t <- instantiate t
+    case unEl t of
+      Pi _ t -> succ <$> arity' (unAbs t)
+      _      -> return 0
+
+-- Computing occurrences --------------------------------------------------
+
+data Item = AnArg Nat
+          | ADef QName
+  deriving (Eq, Ord, Show)
+
+instance HasRange Item where
+  getRange (AnArg _) = noRange
+  getRange (ADef qn)   = getRange qn
+
+instance Pretty Item where
+  prettyPrec p (AnArg i) = P.mparens (p > 9) $ "AnArg" P.<+> P.pretty i
+  prettyPrec p (ADef qn) = P.mparens (p > 9) $ "ADef"  P.<+> P.pretty qn
+
+type Occurrences = Map Item [OccursWhere]
+
+-- | Used to build 'Occurrences' and occurrence graphs.
+data OccurrencesBuilder
+  = Concat [OccurrencesBuilder]
+  | OccursAs Where OccurrencesBuilder
+  | OccursHere Item
+  | OnlyVarsUpTo Nat OccurrencesBuilder
+    -- ^ @OnlyVarsUpTo n occs@ discards occurrences of de Bruijn index
+    -- @>= n@.
+
+-- | Used to build 'Occurrences' and occurrence graphs.
+data OccurrencesBuilder'
+  = Concat' [OccurrencesBuilder']
+  | OccursAs' Where OccurrencesBuilder'
+  | OccursHere' Item
+
+-- | The semigroup laws only hold up to flattening of 'Concat'.
+instance Semigroup OccurrencesBuilder where
+  occs1 <> occs2 = Concat [occs1, occs2]
+
+-- | The monoid laws only hold up to flattening of 'Concat'.
+instance Monoid OccurrencesBuilder where
+  mempty  = Concat []
+  mappend = (<>)
+  mconcat = Concat
+
+-- | Removes 'OnlyVarsUpTo' entries.
+preprocess :: OccurrencesBuilder -> OccurrencesBuilder'
+preprocess ob = case pp Nothing ob of
+  Nothing -> Concat' []
+  Just ob -> ob
+  where
+  pp :: Maybe Nat  -- Variables larger than or equal to this number, if any,
+                   -- are not retained.
+     -> OccurrencesBuilder
+     -> Maybe OccurrencesBuilder'
+  pp !m = \case
+    Concat obs -> case mapMaybe (pp m) obs of
+      []  -> Nothing
+      obs -> return (Concat' obs)
+
+    OccursAs w ob -> OccursAs' w <$> pp m ob
+
+    OnlyVarsUpTo n ob -> pp (Just $! maybe n (min n) m) ob
+
+    OccursHere i -> do
+      guard keep
+      return (OccursHere' i)
+      where
+      keep = case (m, i) of
+        (Nothing, _)      -> True
+        (_, ADef _)       -> True
+        (Just m, AnArg i) -> i < m
+
+-- | An interpreter for 'OccurrencesBuilder'.
+--
+-- WARNING: There can be lots of sharing between the generated
+-- 'OccursWhere' entries. Traversing all of these entries could be
+-- expensive. (See 'computeEdges' for an example.)
+flatten :: OccurrencesBuilder -> Map Item Integer
+flatten =
+  Map.fromListWith (+) .
+  flip flatten' [] .
+  preprocess
+  where
+  flatten'
+    :: OccurrencesBuilder'
+    -> [(Item, Integer)]
+    -> [(Item, Integer)]
+  flatten' (Concat' obs)    = foldr (\occs f -> flatten' occs . f) id obs
+  flatten' (OccursAs' _ ob) = flatten' ob
+  flatten' (OccursHere' i)  = ((i, 1) :)
+
+-- | Context for computing occurrences.
+data OccEnv = OccEnv
+  { vars :: [Maybe Item]
+    -- ^ Items corresponding to the free variables.
+    --
+    --   Potential invariant: It seems as if the list has the form
+    --   @'genericReplicate' n 'Nothing' ++ 'map' ('Just' . 'AnArg') is@,
+    --   for some @n@ and @is@, where @is@ is decreasing
+    --   (non-strictly).
+  , inf  :: Maybe QName
+    -- ^ Name for ∞ builtin.
+  }
+
+-- | Monad for computing occurrences.
+type OccM = Reader OccEnv
+
+instance (Semigroup a, Monoid a) => Monoid (OccM a) where
+  mempty  = return mempty
+  mappend = (<>)
+  mconcat = mconcat <.> sequence
+
+withExtendedOccEnv :: Maybe Item -> OccM a -> OccM a
+withExtendedOccEnv i = withExtendedOccEnv' [i]
+
+withExtendedOccEnv' :: [Maybe Item] -> OccM a -> OccM a
+withExtendedOccEnv' is = local $ \ e -> e { vars = is ++ vars e }
+
+-- | Running the monad
+getOccurrences
+  :: (Show a, PrettyTCM a, ComputeOccurrences a)
+  => [Maybe Item]  -- ^ Extension of the 'OccEnv', usually a local variable context.
+  -> a
+  -> TCM OccurrencesBuilder
+getOccurrences vars a = do
+  reportSDoc "tc.pos.occ" 70 $ "computing occurrences in " <+> text (show a)
+  reportSDoc "tc.pos.occ" 20 $ "computing occurrences in " <+> prettyTCM a
+  runReader (occurrences a) . OccEnv vars . fmap nameOfInf <$> coinductionKit
+
+class ComputeOccurrences a where
+  occurrences :: a -> OccM OccurrencesBuilder
+
+  default occurrences :: (Foldable t, ComputeOccurrences b, t b ~ a) => a -> OccM OccurrencesBuilder
+  occurrences = foldMap occurrences
+
+instance ComputeOccurrences Clause where
+  occurrences cl = do
+    let ps    = namedClausePats cl
+        items = IntMap.elems $ patItems ps -- sorted from low to high DBI
+    -- TODO #3733: handle hcomp/transp clauses properly
+    if hasDefP ps then return mempty else do
+    (Concat (mapMaybe matching (zip [0..] ps)) <>) <$> do
+      withExtendedOccEnv' items $
+        occurrences $ clauseBody cl
+    where
+      matching (i, p)
+        | properlyMatching (namedThing $ unArg p) =
+            Just $ OccursAs Matched $ OccursHere $ AnArg i
+        | otherwise                  = Nothing
+
+      -- @patItems ps@ creates a map from the pattern variables of @ps@
+      -- to the index of the argument they are bound in.
+      patItems ps = mconcat $ zipWith patItem [0..] ps
+
+      -- @patItem i p@ assigns index @i@ to each pattern variable in @p@
+      patItem :: Int -> NamedArg DeBruijnPattern -> IntMap (Maybe Item)
+      patItem i p = Fold.foldMap makeEntry ixs
+        where
+          ixs = map dbPatVarIndex $ lefts $ map unArg $ patternVars $ namedThing <$> p
+
+          makeEntry x = singleton (x, Just $ AnArg i)
+
+instance ComputeOccurrences Term where
+  occurrences v = case unSpine v of
+    Var i args -> (asks (occI . vars)) <> (OccursAs VarArg <$> occurrences args)
+      where
+      occI vars = maybe mempty OccursHere $ indexWithDefault unbound vars i
+      unbound = flip trace __IMPOSSIBLE__ $
+              "impossible: occurrence of de Bruijn index " ++ show i ++
+              " in vars " ++ show vars ++ " is unbound"
+
+    Def d args   -> do
+      inf <- asks inf
+      let occsAs = if Just d /= inf then OccursAs . DefArg d else \ n ->
+            -- the principal argument of builtin INF (∞) is the second (n==1)
+            -- the first is a level argument (n==0, counting from 0!)
+            if n == 1 then OccursAs UnderInf else OccursAs (DefArg d n)
+      occs <- mapM occurrences args
+      return . Concat $ OccursHere (ADef d) : zipWith occsAs [0..] occs
+
+    Con _ _ args -> occurrences args
+    MetaV _ args -> OccursAs MetaArg <$> occurrences args
+    Pi a b       -> (OccursAs LeftOfArrow <$> occurrences a) <> occurrences b
+    Lam _ b      -> occurrences b
+    Level l      -> occurrences l
+    Lit{}        -> mempty
+    Sort{}       -> mempty
+    -- Jesper, 2020-01-12: this information is also used for the
+    -- occurs check, so we need to look under DontCare (see #4371)
+    DontCare v   -> occurrences v
+    Dummy{}      -> mempty
+
+instance ComputeOccurrences Level where
+  occurrences (Max _ as) = occurrences as
+
+instance ComputeOccurrences PlusLevel where
+  occurrences (Plus _ l) = occurrences l
+
+instance ComputeOccurrences Type where
+  occurrences (El _ v) = occurrences v
+
+instance ComputeOccurrences a => ComputeOccurrences (Tele a) where
+  occurrences EmptyTel        = mempty
+  occurrences (ExtendTel a b) = occurrences (a, b)
+
+instance ComputeOccurrences a => ComputeOccurrences (Abs a) where
+  occurrences (Abs   _ b) = withExtendedOccEnv Nothing $ occurrences b
+  occurrences (NoAbs _ b) = occurrences b
+
+instance ComputeOccurrences a => ComputeOccurrences (Elim' a) where
+  occurrences Proj{}         = __IMPOSSIBLE__  -- unSpine
+  occurrences (Apply a)      = occurrences a
+  occurrences (IApply x y a) = occurrences (x,(y,a)) -- TODO Andrea: conservative
+
+instance ComputeOccurrences a => ComputeOccurrences (Arg a)   where
+instance ComputeOccurrences a => ComputeOccurrences (Dom a)   where
+instance ComputeOccurrences a => ComputeOccurrences [a]       where
+instance ComputeOccurrences a => ComputeOccurrences (Maybe a) where
+
+instance (ComputeOccurrences a, ComputeOccurrences b) => ComputeOccurrences (a, b) where
+  occurrences (x, y) = occurrences x <> occurrences y
+
+-- | Computes the number of occurrences of different 'Item's in the
+-- given definition.
+--
+-- WARNING: There can be lots of sharing between the 'OccursWhere'
+-- entries. Traversing all of these entries could be expensive. (See
+-- 'computeEdges' for an example.)
+computeOccurrences :: QName -> TCM (Map Item Integer)
+computeOccurrences q = flatten <$> computeOccurrences' q
+
+-- | Computes the occurrences in the given definition.
+computeOccurrences' :: QName -> TCM OccurrencesBuilder
+computeOccurrences' q = inConcreteOrAbstractMode q $ \ def -> do
+  reportSDoc "tc.pos" 25 $ do
+    let a = defAbstract def
+    m <- asksTC envAbstractMode
+    cur <- asksTC envCurrentModule
+    o <- asksTC envCurrentOpaqueId
+    "computeOccurrences" <+> prettyTCM q <+> text (show a) <+> text (show o) <+> text (show m)
+      <+> prettyTCM cur
+  OccursAs (InDefOf q) <$> case theDef def of
+
+    Function{funClauses = cs} -> do
+      cs <- mapM etaExpandClause =<< instantiateFull cs
+      Concat . zipWith (OccursAs . InClause) [0..] <$>
+        mapM (getOccurrences []) cs
+
+    Datatype{dataClause = Just c} -> getOccurrences [] =<< instantiateFull c
+    Datatype{dataPars = np0, dataCons = cs}       -> do
+      -- Andreas, 2013-02-27 (later edited by someone else): First,
+      -- include each index of an inductive family.
+      TelV tel _ <- telView $ defType def
+      -- Andreas, 2017-04-26, issue #2554: count first index as parameter if it has type Size.
+      -- We compute sizeIndex=1 if first first index has type Size, otherwise sizeIndex==0
+      sizeIndex <- caseList (drop np0 $ telToList tel) (return 0) $ \ dom _ -> do
+        caseMaybeM (isSizeType dom) (return 0) $ \ _ -> return 1
+      let np = np0 + sizeIndex
+      let xs = [np .. size tel - 1] -- argument positions corresponding to indices
+      let ioccs = Concat $ map (OccursHere . AnArg) [np0 .. np - 1]
+                        ++ map (OccursAs IsIndex . OccursHere . AnArg) xs
+      -- Then, we compute the occurrences in the constructor types.
+      let conOcc c = do
+            -- Andreas, 2020-02-15, issue #4447:
+            -- Allow UnconfimedReductions here to make sure we get the constructor type
+            -- in same way as it was obtained when the data types was checked.
+            (TelV tel t, bnd) <- putAllowedReductions allReductions $
+              telViewUpToPathBoundary' (-1) . defType =<< getConstInfo c
+            let (tel0,tel1) = splitTelescopeAt np tel
+            -- Do not collect occurrences in the data parameters.
+            -- Normalization needed e.g. for test/succeed/Bush.agda.
+            -- (Actually, for Bush.agda, reducing the parameters should be sufficient.)
+            tel1' <- addContext tel0 $ normalise $ tel1
+            let vars    = map (Just . AnArg) . downFrom
+                varsTel = vars (size tel)
+            -- Occurrences in the types of the constructor arguments.
+            mappend (mappend
+                       (OccursAs (ConArgType c) <$>
+                        getOccurrences (vars np) tel1')
+                       (OccursAs (ConEndpoint c) <$>
+                        getOccurrences varsTel bnd)) $ do
+              -- Occurrences in the indices of the data type the constructor targets.
+              -- Andreas, 2020-02-15, issue #4447:
+              -- WAS: @t@ is not necessarily a data type, but it could be something
+              -- that reduces to a data type once UnconfirmedReductions are confirmed
+              -- as safe by the termination checker.
+              -- In any case, if @t@ is not showing itself as the data type, we need to
+              -- do something conservative.  We will just collect *all* occurrences
+              -- and flip their sign (variance) using 'LeftOfArrow'.
+              case unEl t of
+                Def q' vs
+                  | q == q' -> do
+                      let indices = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ drop np vs
+                      OccursAs (IndArgType c) . OnlyVarsUpTo np <$> getOccurrences varsTel indices
+                  | otherwise -> __IMPOSSIBLE__  -- this ought to be impossible now (but hasn't been before, see #4447)
+                Pi{}       -> __IMPOSSIBLE__  -- eliminated  by telView
+                MetaV{}    -> __IMPOSSIBLE__  -- not a constructor target; should have been solved by now
+                Var{}      -> __IMPOSSIBLE__  -- not a constructor target
+                Sort{}     -> __IMPOSSIBLE__  -- not a constructor target
+                Lam{}      -> __IMPOSSIBLE__  -- not a type
+                Lit{}      -> __IMPOSSIBLE__  -- not a type
+                Con{}      -> __IMPOSSIBLE__  -- not a type
+                Level{}    -> __IMPOSSIBLE__  -- not a type
+                DontCare{} -> __IMPOSSIBLE__  -- not a type
+                Dummy{}    -> __IMPOSSIBLE__
+      mconcat $ pure ioccs : map conOcc cs
+
+    Record{recClause = Just c} -> getOccurrences [] =<< instantiateFull c
+    Record{recPars = np, recTel = tel} -> do
+      let (tel0,tel1) = splitTelescopeAt np tel
+          vars = map (Just . AnArg) $ downFrom np
+      getOccurrences vars =<< addContext tel0 (normalise tel1) -- Andreas, 2017-01-01, issue #1899, treat like data types
+
+    -- Arguments to other kinds of definitions are hard-wired.
+    Constructor{}      -> mempty
+    Axiom{}            -> mempty
+    DataOrRecSig{}     -> mempty
+    Primitive{}        -> mempty
+    PrimitiveSort{}    -> mempty
+    GeneralizableVar{} -> mempty
+    AbstractDefn{}     -> __IMPOSSIBLE__
+
+-- Building the occurrence graph ------------------------------------------
+
+data Node = DefNode !QName
+          | ArgNode !QName !Nat
+  deriving (Eq, Ord)
+
+-- | Edge labels for the positivity graph.
+data Edge a = Edge !Occurrence a
+  deriving (Eq, Ord, Show, Functor)
+
+-- | Merges two edges between the same source and target.
+
+mergeEdges :: Edge a -> Edge a -> Edge a
+mergeEdges _                    e@(Edge Mixed _)     = e -- dominant
+mergeEdges e@(Edge Mixed _)     _                    = e
+mergeEdges (Edge Unused _)      e                    = e -- neutral
+mergeEdges e                    (Edge Unused _)      = e
+mergeEdges (Edge JustNeg _)     e@(Edge JustNeg _)   = e
+mergeEdges _                    e@(Edge JustNeg w)   = Edge Mixed w
+mergeEdges e@(Edge JustNeg w)   _                    = Edge Mixed w
+mergeEdges _                    e@(Edge JustPos _)   = e -- dominates strict pos.
+mergeEdges e@(Edge JustPos _)   _                    = e
+mergeEdges _                    e@(Edge StrictPos _) = e -- dominates 'GuardPos'
+mergeEdges e@(Edge StrictPos _) _                    = e
+mergeEdges (Edge GuardPos _)    e@(Edge GuardPos _)  = e
+
+-- | These operations form a semiring if we quotient by the relation
+-- \"the 'Occurrence' components are equal\".
+
+instance SemiRing (Edge (Seq OccursWhere)) where
+  ozero = Edge ozero DS.empty
+  oone  = Edge oone  DS.empty
+
+  oplus = mergeEdges
+
+  otimes (Edge o1 w1) (Edge o2 w2) = Edge (otimes o1 o2) (w1 DS.>< w2)
+
+-- | WARNING: There can be lots of sharing between the 'OccursWhere'
+-- entries in the edges. Traversing all of these entries could be
+-- expensive. (See 'computeEdges' for an example.)
+buildOccurrenceGraph :: Set QName -> TCM (Graph Node (Edge OccursWhere))
+buildOccurrenceGraph qs =
+  Graph.fromEdgesWith mergeEdges . concat <$>
+    mapM defGraph (Set.toList qs)
+  where
+    defGraph :: QName -> TCM [Graph.Edge Node (Edge OccursWhere)]
+    defGraph q = inConcreteOrAbstractMode q $ \ _def -> do
+      occs <- computeOccurrences' q
+
+      reportSDoc "tc.pos.occs" 40 $
+        (("Occurrences in" <+> prettyTCM q) <> ":")
+          $+$
+        nest 2 (vcat $
+           map (\(i, n) ->
+                   (pretty i <> ":") <+> text (show n) <+>
+                   "occurrences") $
+           List.sortBy (compare `on` snd) $
+           Map.toList (flatten occs))
+
+      -- Placing this line before the reportSDoc lines above creates a
+      -- space leak: occs is retained for too long.
+      es <- computeEdges qs q occs
+
+      reportSDoc "tc.pos.occs.edges" 60 $
+        "Edges:"
+          $+$
+        nest 2 (vcat $
+           map (\e ->
+                   let Edge o w = Graph.label e in
+                   prettyTCM (Graph.source e) <+>
+                   "-[" <+> (return (P.pretty o) <> ",") <+>
+                                 return (P.pretty w) <+> "]->" <+>
+                   prettyTCM (Graph.target e))
+               es)
+
+      return es
+
+-- | Computes all non-'ozero' occurrence graph edges represented by
+-- the given 'OccurrencesBuilder'.
+--
+-- WARNING: There can be lots of sharing between the 'OccursWhere'
+-- entries in the edges. Traversing all of these entries could be
+-- expensive. For instance, for the function @F@ in
+-- @benchmark/misc/SlowOccurrences.agda@ a large number of edges from
+-- the argument @X@ to the function @F@ are computed. These edges have
+-- polarity 'StrictPos', 'JustNeg' or 'JustPos', and contain the
+-- following 'OccursWhere' elements:
+--
+-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0])@,
+--
+-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow'])@,
+--
+-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow', 'LeftOfArrow'])@,
+--
+-- * @'OccursWhere' _ 'DS.empty' ('DS.fromList' ['InDefOf' "F", 'InClause' 0, 'LeftOfArrow', 'LeftOfArrow', 'LeftOfArrow'])@,
+--
+-- * and so on.
+computeEdges
+  :: Set QName
+     -- ^ The names in the current mutual block.
+  -> QName
+     -- ^ The current name.
+  -> OccurrencesBuilder
+  -> TCM [Graph.Edge Node (Edge OccursWhere)]
+computeEdges muts q ob =
+  ($ []) <$> mkEdge StrictPos (preprocess ob)
+                    __IMPOSSIBLE__ DS.empty DS.empty
+  where
+  mkEdge
+     :: Occurrence
+     -> OccurrencesBuilder'
+     -> Node          -- The current target node.
+     -> DS.Seq Where  -- 'Where' information encountered before the current target
+                      -- node was (re)selected.
+     -> DS.Seq Where  -- 'Where' information encountered after the current target
+                      -- node was (re)selected.
+     -> TCM ([Graph.Edge Node (Edge OccursWhere)] ->
+             [Graph.Edge Node (Edge OccursWhere)])
+  mkEdge !pol ob to cs os = case ob of
+    Concat' obs ->
+      foldr (liftM2 (.)) (return id)
+            [ mkEdge pol ob to cs os | ob <- obs ]
+
+    OccursAs' w ob -> do
+      (to', pol) <- mkEdge' to pol w
+      let mk = mkEdge pol ob
+      case to' of
+        Nothing -> mk to cs            (os DS.|> w)
+        Just to -> mk to (cs DS.>< os) (DS.singleton w)
+
+    OccursHere' i ->
+      let o = OccursWhere (getRange i) cs os in
+      case i of
+        AnArg i ->
+          return $ applyUnless (null pol) (Graph.Edge
+            { Graph.source = ArgNode q i
+            , Graph.target = to
+            , Graph.label  = Edge pol o
+            } :)
+        ADef q' ->
+          -- Andreas, 2017-04-26, issue #2555
+          -- Skip nodes pointing outside the mutual block.
+          return $ applyUnless (null pol || Set.notMember q' muts)
+            (Graph.Edge
+               { Graph.source = DefNode q'
+               , Graph.target = to
+               , Graph.label  = Edge pol o
+               } :)
+
+  -- This function might return a new target node.
+  mkEdge'
+    :: Node  -- The current target node.
+    -> Occurrence
+    -> Where
+    -> TCM (Maybe Node, Occurrence)
+  mkEdge' to !pol = \case
+    VarArg         -> mixed
+    MetaArg        -> mixed
+    LeftOfArrow    -> negative
+    DefArg d i     -> do
+      pol' <- isGuarding d
+      if Set.member d muts
+        then return (Just (ArgNode d i), pol')
+        else addPol =<< otimes pol' <$> getArgOccurrence d i
+    UnderInf       -> addPol GuardPos -- Andreas, 2012-06-09: ∞ is guarding
+    ConArgType _   -> keepGoing
+    IndArgType _   -> mixed
+    ConEndpoint _  -> keepGoing
+    InClause _     -> keepGoing
+    Matched        -> mixed -- consider arguments matched against as used
+    IsIndex        -> mixed -- And similarly for indices.
+    InDefOf d      -> do
+      pol' <- isGuarding d
+      return (Just (DefNode d), pol')
+    where
+    keepGoing   = return (Nothing, pol)
+    mixed       = return (Nothing, Mixed)
+    negative    = return (Nothing, otimes pol JustNeg)
+    addPol pol' = return (Nothing, otimes pol pol')
+
+  isGuarding d = do
+    isDataOrRecordType d <&> \case
+      Just IsData -> GuardPos  -- a datatype is guarding
+      _           -> StrictPos
+
+-- Pretty-printing -----------------------------------------------------
+
+instance Pretty Node where
+  pretty = \case
+    DefNode q   -> P.pretty q
+    ArgNode q i -> P.pretty q <> P.text ("." ++ show i)
+
+instance PrettyTCM Node where
+  prettyTCM = return . P.pretty
+
+instance PrettyTCMWithNode (Edge OccursWhere) where
+  prettyTCMWithNode (WithNode n (Edge o w)) = vcat
+    [ prettyTCM o <+> prettyTCM n
+    , nest 2 $ return $ P.pretty w
+    ]
+
+instance PrettyTCM (Seq OccursWhere) where
+  prettyTCM =
+    fmap snd . prettyOWs . map adjustLeftOfArrow . uniq . Fold.toList
+    where
+      nth 0 = pwords "first"
+      nth 1 = pwords "second"
+      nth 2 = pwords "third"
+      nth n = pwords $ show (n + 1) ++ "th"
+
+      -- Removes consecutive duplicates.
+      uniq :: [OccursWhere] -> [OccursWhere]
+      uniq = map List1.head . List1.groupBy ((==) `on` snd')
+        where
+        snd' (OccursWhere _ _ ws) = ws
+
+      prettyOWs :: MonadPretty m => [OccursWhere] -> m (String, Doc)
+      prettyOWs []  = __IMPOSSIBLE__
+      prettyOWs [o] = do
+        (s, d) <- prettyOW o
+        return (s, d <> ".")
+      prettyOWs (o:os) = do
+        (s1, d1) <- prettyOW  o
+        (s2, d2) <- prettyOWs os
+        return (s1, d1 <> ("," P.<+> "which" P.<+> P.text s2 P.$$ d2))
+
+      prettyOW :: MonadPretty m => OccursWhere -> m (String, Doc)
+      prettyOW (OccursWhere _ cs ws)
+        | null cs   = prettyWs ws
+        | otherwise = do
+            (s, d1) <- prettyWs ws
+            (_, d2) <- prettyWs cs
+            return (s, d1 P.$$ "(" <> d2 <> ")")
+
+      prettyWs :: MonadPretty m => Seq Where -> m (String, Doc)
+      prettyWs ws = case Fold.toList ws of
+        [InDefOf d, IsIndex] ->
+          (,) "is" <$> fsep (pwords "an index of" ++ [prettyTCM d])
+        _ ->
+          (,) "occurs" <$>
+            Fold.foldrM (\w d -> return d $$ fsep (prettyW w)) empty ws
+
+      prettyW :: MonadPretty m => Where -> [m Doc]
+      prettyW = \case
+        LeftOfArrow  -> pwords "to the left of an arrow"
+        DefArg q i   -> pwords "in the" ++ nth i ++ pwords "argument of" ++
+                          [prettyTCM q]
+        UnderInf     -> pwords "under" ++
+                        [do -- this cannot fail if an 'UnderInf' has been generated
+                            Def inf _ <- fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinInf
+                            prettyTCM inf]
+        VarArg       -> pwords "in an argument of a bound variable"
+        MetaArg      -> pwords "in an argument of a metavariable"
+        ConArgType c -> pwords "in the type of the constructor" ++ [prettyTCM c]
+        IndArgType c -> pwords "in an index of the target type of the constructor" ++ [prettyTCM c]
+        ConEndpoint c
+                     -> pwords "in an endpoint of the target of the" ++
+                        pwords "higher constructor" ++ [prettyTCM c]
+        InClause i   -> pwords "in the" ++ nth i ++ pwords "clause"
+        Matched      -> pwords "as matched against"
+        IsIndex      -> pwords "as an index"
+        InDefOf d    -> pwords "in the definition of" ++ [prettyTCM d]
+
+      adjustLeftOfArrow :: OccursWhere -> OccursWhere
+      adjustLeftOfArrow (OccursWhere r cs os) =
+        OccursWhere r (DS.filter (not . isArrow) cs) $
+          noArrows
+            DS.><
+          case DS.viewl startsWithArrow of
+            DS.EmptyL  -> DS.empty
+            w DS.:< ws -> w DS.<| DS.filter (not . isArrow) ws
+        where
+        (noArrows, startsWithArrow) = DS.breakl isArrow os
+
+        isArrow LeftOfArrow{} = True
+        isArrow _             = False
diff --git a/src/full/Agda/TypeChecking/Positivity/Occurrence.hs b/src/full/Agda/TypeChecking/Positivity/Occurrence.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Positivity/Occurrence.hs
@@ -0,0 +1,231 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Occurrences.
+
+module Agda.TypeChecking.Positivity.Occurrence
+  ( Occurrence(..)
+  , OccursWhere(..)
+  , Where(..)
+  , boundToEverySome
+  , productOfEdgesInBoundedWalk
+  ) where
+
+import Control.DeepSeq
+import Control.Monad
+
+import Data.Foldable (toList)
+
+import Data.Map.Strict (Map)
+import qualified Data.Map.Strict as Map
+import Data.Sequence (Seq)
+
+import GHC.Generics (Generic)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Position
+
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional (Graph)
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.SemiRing
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- Specification of occurrences -------------------------------------------
+
+-- Operations and instances in Agda.TypeChecking.Positivity.
+
+-- | Description of an occurrence.
+data OccursWhere
+  = OccursWhere Range (Seq Where) (Seq Where)
+    -- ^ The elements of the sequences, read from left to right,
+    -- explain how to get to the occurrence. The second sequence
+    -- includes the main information, and if the first sequence is
+    -- non-empty, then it includes information about the context of
+    -- the second sequence.
+  deriving (Show, Eq, Ord, Generic)
+
+instance NFData OccursWhere
+
+-- | One part of the description of an occurrence.
+data Where
+  = LeftOfArrow
+  | DefArg QName Nat -- ^ in the nth argument of a define constant
+  | UnderInf         -- ^ in the principal argument of built-in ∞
+  | VarArg           -- ^ as an argument to a bound variable
+  | MetaArg          -- ^ as an argument of a metavariable
+  | ConArgType QName -- ^ in the type of a constructor
+  | IndArgType QName -- ^ in a datatype index of a constructor
+  | ConEndpoint QName
+                     -- ^ in an endpoint of a higher constructor
+  | InClause Nat     -- ^ in the nth clause of a defined function
+  | Matched          -- ^ matched against in a clause of a defined function
+  | IsIndex          -- ^ is an index of an inductive family
+  | InDefOf QName    -- ^ in the definition of a constant
+  deriving (Show, Eq, Ord, Generic)
+
+instance NFData Where
+
+-- | Subterm occurrences for positivity checking.
+--   The constructors are listed in increasing information they provide:
+--   @Mixed <= JustPos <= StrictPos <= GuardPos <= Unused@
+--   @Mixed <= JustNeg <= Unused@.
+data Occurrence
+  = Mixed     -- ^ Arbitrary occurrence (positive and negative).
+  | JustNeg   -- ^ Negative occurrence.
+  | JustPos   -- ^ Positive occurrence, but not strictly positive.
+  | StrictPos -- ^ Strictly positive occurrence.
+  | GuardPos  -- ^ Guarded strictly positive occurrence (i.e., under ∞).  For checking recursive records.
+  | Unused    --  ^ No occurrence.
+  deriving (Show, Eq, Ord, Enum, Bounded)
+
+-- Pretty instances.
+
+instance Pretty Occurrence where
+  pretty = text . \case
+    Unused    -> "_"
+    Mixed     -> "*"
+    JustNeg   -> "-"
+    JustPos   -> "+"
+    StrictPos -> "++"
+    GuardPos  -> "g+"
+
+instance Pretty Where where
+  pretty = \case
+    LeftOfArrow  -> "LeftOfArrow"
+    DefArg q i   -> "DefArg"     <+> pretty q <+> pretty i
+    UnderInf     -> "UnderInf"
+    VarArg       -> "VarArg"
+    MetaArg      -> "MetaArg"
+    ConArgType q -> "ConArgType" <+> pretty q
+    IndArgType q -> "IndArgType" <+> pretty q
+    ConEndpoint q
+                 -> "ConEndpoint" <+> pretty q
+    InClause i   -> "InClause"   <+> pretty i
+    Matched      -> "Matched"
+    IsIndex      -> "IsIndex"
+    InDefOf q    -> "InDefOf"    <+> pretty q
+
+instance Pretty OccursWhere where
+  pretty = \case
+    OccursWhere _r ws1 ws2 ->
+      "OccursWhere _" <+> pretty (toList ws1) <+> pretty (toList ws2)
+
+-- Other instances for 'Occurrence'.
+
+instance NFData Occurrence where rnf x = seq x ()
+
+instance KillRange Occurrence where
+  killRange = id
+
+-- | 'Occurrence' is a complete lattice with least element 'Mixed'
+--   and greatest element 'Unused'.
+--
+--   It forms a commutative semiring where 'oplus' is meet (glb)
+--   and 'otimes' is composition. Both operations are idempotent.
+--
+--   For 'oplus', 'Unused' is neutral (zero) and 'Mixed' is dominant.
+--   For 'otimes', 'StrictPos' is neutral (one) and 'Unused' is dominant.
+
+instance SemiRing Occurrence where
+  ozero = Unused
+  oone  = StrictPos
+
+  oplus Mixed _           = Mixed     -- dominant
+  oplus _ Mixed           = Mixed
+  oplus Unused o          = o         -- neutral
+  oplus o Unused          = o
+  oplus JustNeg  JustNeg  = JustNeg
+  oplus JustNeg  o        = Mixed     -- negative and any form of positve
+  oplus o        JustNeg  = Mixed
+  oplus GuardPos o        = o         -- second-rank neutral
+  oplus o GuardPos        = o
+  oplus StrictPos o       = o         -- third-rank neutral
+  oplus o StrictPos       = o
+  oplus JustPos JustPos   = JustPos
+
+  otimes Unused _            = Unused     -- dominant
+  otimes _ Unused            = Unused
+  otimes Mixed _             = Mixed      -- second-rank dominance
+  otimes _ Mixed             = Mixed
+  otimes JustNeg JustNeg     = JustPos
+  otimes JustNeg _           = JustNeg    -- third-rank dominance
+  otimes _ JustNeg           = JustNeg
+  otimes JustPos _           = JustPos    -- fourth-rank dominance
+  otimes _ JustPos           = JustPos
+  otimes GuardPos _          = GuardPos   -- _ `elem` [StrictPos, GuardPos]
+  otimes _ GuardPos          = GuardPos
+  otimes StrictPos StrictPos = StrictPos  -- neutral
+
+instance StarSemiRing Occurrence where
+  ostar Mixed     = Mixed
+  ostar JustNeg   = Mixed
+  ostar JustPos   = JustPos
+  ostar StrictPos = StrictPos
+  ostar GuardPos  = StrictPos
+  ostar Unused    = StrictPos
+
+instance Null Occurrence where
+  empty = Unused
+
+-- Other instances for 'OccursWhere'.
+
+-- There is an orphan PrettyTCM instance for Seq OccursWhere in
+-- Agda.TypeChecking.Positivity.
+
+instance Sized OccursWhere where
+  size    (OccursWhere _ cs os) = 1 + size cs + size os
+  natSize (OccursWhere _ cs os) = 1 + natSize cs + natSize os
+
+-- | The map contains bindings of the form @bound |-> ess@, satisfying
+-- the following property: for every non-empty list @w@,
+-- @'foldr1' 'otimes' w '<=' bound@ iff
+-- @'or' [ 'all' every w '&&' 'any' some w | (every, some) <- ess ]@.
+
+boundToEverySome ::
+  Map Occurrence [(Occurrence -> Bool, Occurrence -> Bool)]
+boundToEverySome = Map.fromListWith __IMPOSSIBLE__
+  [ ( JustPos
+    , [((/= Unused), (`elem` [Mixed, JustNeg, JustPos]))]
+    )
+  , ( StrictPos
+    , [ ((/= Unused), (`elem` [Mixed, JustNeg, JustPos]))
+      , ((not . (`elem` [Unused, GuardPos])), const True)
+      ]
+    )
+  , ( GuardPos
+    , [((/= Unused), const True)]
+    )
+  ]
+
+-- | @productOfEdgesInBoundedWalk occ g u v bound@ returns a value
+-- distinct from 'Nothing' iff there is a walk @c@ (a list of edges)
+-- in @g@, from @u@ to @v@, for which the product @'foldr1' 'otimes'
+-- ('map' occ c) '<=' bound@. In this case the returned value is
+-- @'Just' ('foldr1' 'otimes' c)@ for one such walk @c@.
+--
+-- Preconditions: @u@ and @v@ must belong to @g@, and @bound@ must
+-- belong to the domain of @boundToEverySome@.
+
+-- There is a property for this function in
+-- Internal.Utils.Graph.AdjacencyMap.Unidirectional.
+
+productOfEdgesInBoundedWalk ::
+  (SemiRing e, Ord n) =>
+  (e -> Occurrence) -> Graph n e -> n -> n -> Occurrence -> Maybe e
+productOfEdgesInBoundedWalk occ g u v bound =
+  case Map.lookup bound boundToEverySome of
+    Nothing  -> __IMPOSSIBLE__
+    Just ess ->
+      case msum [ Graph.walkSatisfying
+                    (every . occ . Graph.label)
+                    (some . occ . Graph.label)
+                    g u v
+                | (every, some) <- ess
+                ] of
+        Just es@(_ : _) -> Just (foldr1 otimes (map Graph.label es))
+        Just []         -> __IMPOSSIBLE__
+        Nothing         -> Nothing
diff --git a/src/full/Agda/TypeChecking/Pretty.hs b/src/full/Agda/TypeChecking/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty.hs
@@ -0,0 +1,574 @@
+
+module Agda.TypeChecking.Pretty
+    ( module Agda.TypeChecking.Pretty
+    , module Data.Semigroup -- This re-export can be removed once <GHC-8.4 is dropped.
+    , module Reexport
+    ) where
+
+import Prelude hiding ( null )
+
+import Control.Applicative  (liftA2)
+import Control.Monad
+import Control.Monad.Except
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.Maybe
+import Data.String    ()
+import Data.Semigroup (Semigroup((<>)))
+import qualified Data.Foldable as Fold
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Fixity
+import Agda.Syntax.Internal
+import Agda.Syntax.Literal
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Translation.ReflectedToAbstract
+import Agda.Syntax.Translation.AbstractToConcrete
+import qualified Agda.Syntax.Translation.AbstractToConcrete as Reexport (MonadAbsToCon)
+import qualified Agda.Syntax.Translation.ReflectedToAbstract as R
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Abstract.Pretty as AP
+import Agda.Syntax.Concrete.Pretty (bracesAndSemicolons)
+import qualified Agda.Syntax.Concrete.Pretty as CP
+import qualified Agda.Syntax.Info as A
+import Agda.Syntax.Scope.Base  (AbstractName(..))
+import Agda.Syntax.Scope.Monad (withContextPrecedence)
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Substitute
+
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional (Graph)
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.Permutation ( Permutation )
+import Agda.Syntax.Common.Pretty      ( Pretty, prettyShow )
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size        ( natSize )
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Wrappers for pretty printing combinators
+---------------------------------------------------------------------------
+
+type Doc = P.Doc
+
+comma, colon, equals :: Applicative m => m Doc
+comma  = pure P.comma
+colon  = pure P.colon
+equals = pure P.equals
+
+{-# INLINE pretty #-}
+pretty :: (Applicative m, P.Pretty a) => a -> m Doc
+pretty x = pure $ P.pretty x
+
+{-# INLINE prettyA #-}
+prettyA :: (ToConcrete a, P.Pretty (ConOfAbs a), MonadAbsToCon m) => a -> m Doc
+prettyA x = AP.prettyA x
+
+{-# INLINE prettyAs #-}
+prettyAs :: (ToConcrete a, ConOfAbs a ~ [ce], P.Pretty ce, MonadAbsToCon m) => a -> m Doc
+prettyAs x = AP.prettyAs x
+
+{-# INLINE text #-}
+text :: Applicative m => String -> m Doc
+text s = pure $ P.text s
+
+multiLineText :: Applicative m => String -> m Doc
+multiLineText s = pure $ P.multiLineText s
+
+pwords :: Applicative m => String -> [m Doc]
+pwords s = map pure $ P.pwords s
+
+fwords :: Applicative m => String -> m Doc
+fwords s = pure $ P.fwords s
+
+sep, fsep, hsep, hcat, vcat :: (Applicative m, Foldable t) => t (m Doc) -> m Doc
+sep ds  = P.sep  <$> sequenceA (Fold.toList ds)
+fsep ds = P.fsep <$> sequenceA (Fold.toList ds)
+hsep ds = P.hsep <$> sequenceA (Fold.toList ds)
+hcat ds = P.hcat <$> sequenceA (Fold.toList ds)
+vcat ds = P.vcat <$> sequenceA (Fold.toList ds)
+
+hang :: Applicative m => m Doc -> Int -> m Doc -> m Doc
+hang p n q = P.hang <$> p <*> pure n <*> q
+
+infixl 6 <+>, <?>
+infixl 5 $$, $+$
+
+($$), ($+$), (<+>), (<?>) :: Applicative m => m Doc -> m Doc -> m Doc
+d1 $$ d2  = (P.$$) <$> d1 <*> d2
+d1 $+$ d2 = (P.$+$) <$> d1 <*> d2
+d1 <+> d2 = (P.<+>) <$> d1 <*> d2
+d1 <?> d2 = (P.<?>) <$> d1 <*> d2
+
+nest :: Functor m => Int -> m Doc -> m Doc
+nest n d   = P.nest n <$> d
+
+braces, dbraces, brackets, parens, parensNonEmpty
+  , doubleQuotes, quotes :: Functor m => m Doc -> m Doc
+braces d   = P.braces <$> d
+dbraces d  = CP.dbraces <$> d
+brackets d = P.brackets <$> d
+parens d   = P.parens <$> d
+parensNonEmpty d = P.parensNonEmpty <$> d
+doubleQuotes   d = P.doubleQuotes   <$> d
+quotes         d = P.quotes         <$> d
+
+pshow :: (Applicative m, Show a) => a -> m Doc
+pshow = pure . P.pshow
+
+-- | Comma-separated list in brackets.
+prettyList :: (Applicative m, Semigroup (m Doc), Foldable t) => t (m Doc) -> m Doc
+prettyList ds = P.pretty <$> sequenceA (Fold.toList ds)
+
+-- | 'prettyList' without the brackets.
+prettyList_ :: (Applicative m, Semigroup (m Doc), Foldable t) => t (m Doc) -> m Doc
+prettyList_ ds = fsep $ punctuate comma ds
+
+{-# INLINABLE punctuate #-}
+punctuate :: (Applicative m, Semigroup (m Doc), Foldable t) => m Doc -> t (m Doc) -> [m Doc]
+punctuate d ts
+  | null ds   = []
+  | otherwise = zipWith (<>) ds (replicate n d ++ [pure empty])
+  where
+    ds = Fold.toList ts
+    n  = length ds - 1
+
+---------------------------------------------------------------------------
+-- * The PrettyTCM class
+---------------------------------------------------------------------------
+
+type MonadPretty m = MonadAbsToCon m
+
+-- This instance is to satify the constraints of superclass MonadPretty:
+-- | This instance is more specific than a generic instance
+-- @Semigroup a => Semigroup (TCM a)@.
+instance {-# OVERLAPPING #-} Semigroup (TCM Doc)         where (<>) = liftA2 (<>)
+
+
+class PrettyTCM a where
+  prettyTCM :: MonadPretty m => a -> m Doc
+
+-- | Pretty print with a given context precedence
+prettyTCMCtx :: (PrettyTCM a, MonadPretty m) => Precedence -> a -> m Doc
+prettyTCMCtx p = withContextPrecedence p . prettyTCM
+
+instance {-# OVERLAPPING #-} PrettyTCM String where prettyTCM = text
+instance PrettyTCM Bool                       where prettyTCM = pretty
+instance PrettyTCM C.Name                     where prettyTCM = pretty
+instance PrettyTCM C.QName                    where prettyTCM = pretty
+instance PrettyTCM TopLevelModuleName         where prettyTCM = pretty
+instance PrettyTCM Comparison                 where prettyTCM = pretty
+instance PrettyTCM Literal                    where prettyTCM = pretty
+instance PrettyTCM Nat                        where prettyTCM = pretty
+instance PrettyTCM ProblemId                  where prettyTCM = pretty
+instance PrettyTCM Range                      where prettyTCM = pretty
+instance PrettyTCM CheckpointId               where prettyTCM = pretty
+-- instance PrettyTCM Interval where prettyTCM = pretty
+-- instance PrettyTCM Position where prettyTCM = pretty
+
+{-# SPECIALIZE prettyTCM :: String             -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Bool               -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: C.Name             -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: C.QName            -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: TopLevelModuleName -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Comparison         -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Literal            -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Nat                -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: ProblemId          -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Range              -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: CheckpointId       -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (Closure a) where
+  prettyTCM cl = enterClosure cl prettyTCM
+
+instance {-# OVERLAPPABLE #-} PrettyTCM a => PrettyTCM [a] where
+  prettyTCM = prettyList . map prettyTCM
+
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => [a] -> TCM Doc #-}
+
+instance {-# OVERLAPPABLE #-} PrettyTCM a => PrettyTCM (Maybe a) where
+  prettyTCM = maybe empty prettyTCM
+
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => Maybe a -> TCM Doc #-}
+
+instance (PrettyTCM a, PrettyTCM b) => PrettyTCM (a,b) where
+  prettyTCM (a, b) = parens $ prettyTCM a <> comma <> prettyTCM b
+
+{-# SPECIALIZE prettyTCM :: (PrettyTCM a, PrettyTCM b) => (a, b) -> TCM Doc #-}
+
+instance (PrettyTCM a, PrettyTCM b, PrettyTCM c) => PrettyTCM (a,b,c) where
+  prettyTCM (a, b, c) = parens $
+    prettyTCM a <> comma <> prettyTCM b <> comma <> prettyTCM c
+
+{-# SPECIALIZE prettyTCM :: (PrettyTCM a, PrettyTCM b, PrettyTCM c) => (a, b, c) -> TCM Doc #-}
+
+instance PrettyTCM Term               where prettyTCM = prettyA <=< reify
+instance PrettyTCM Type               where prettyTCM = prettyA <=< reify
+instance PrettyTCM Sort               where prettyTCM = prettyA <=< reify
+instance PrettyTCM DisplayTerm        where prettyTCM = prettyA <=< reify
+instance PrettyTCM NamedClause        where prettyTCM = prettyA <=< reify
+instance PrettyTCM (QNamed Clause)    where prettyTCM = prettyA <=< reify
+instance PrettyTCM Level              where prettyTCM = prettyA <=< reify . Level
+instance PrettyTCM (Named_ Term)      where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Arg Term)         where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Arg Type)         where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Arg Bool)         where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Arg String)       where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Arg A.Expr)       where prettyTCM = prettyA <=< reify
+instance PrettyTCM (NamedArg A.Expr)  where prettyTCM = prettyA <=< reify
+instance PrettyTCM (NamedArg Term)    where prettyTCM = prettyA <=< reify
+instance PrettyTCM (Dom Type)         where prettyTCM = prettyA <=< reify
+instance PrettyTCM ContextEntry       where prettyTCM = prettyA <=< reify
+instance PrettyTCM Permutation        where prettyTCM = text . show
+instance PrettyTCM Polarity           where prettyTCM = text . show
+instance PrettyTCM IsForced           where prettyTCM = text . show
+
+{-# SPECIALIZE prettyTCM :: Term              -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Type              -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Sort              -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: DisplayTerm       -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: NamedClause       -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (QNamed Clause)   -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Level             -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Named_ Term)     -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Arg Term)        -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Arg Type)        -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Arg Bool)        -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Arg A.Expr)      -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (NamedArg A.Expr) -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (NamedArg Term)   -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: (Dom Type)        -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: ContextEntry      -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Permutation       -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: Polarity          -> TCM Doc #-}
+{-# SPECIALIZE prettyTCM :: IsForced          -> TCM Doc #-}
+
+prettyR
+  :: (R.ToAbstract r, PrettyTCM (R.AbsOfRef r), MonadPretty m, MonadError TCErr m)
+  => r -> m Doc
+prettyR = prettyTCM <=< toAbstractWithoutImplicit
+
+instance (Pretty a, PrettyTCM a, EndoSubst a) => PrettyTCM (Substitution' a) where
+  prettyTCM IdS        = "idS"
+  prettyTCM (Wk m IdS) = "wkS" <+> pretty m
+  prettyTCM (EmptyS _) = "emptyS"
+  prettyTCM rho = prettyTCM u <+> comma <+> prettyTCM rho1
+    where
+      (rho1, rho2) = splitS 1 rho
+      u            = lookupS rho2 0
+
+instance PrettyTCM Clause where
+  prettyTCM cl = do
+    x <- qualify_ <$> freshName_ ("<unnamedclause>" :: String)
+    prettyTCM (QNamed x cl)
+{-# SPECIALIZE prettyTCM :: Clause -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (Judgement a) where
+  prettyTCM (HasType a cmp t) = prettyTCM a <+> ":" <+> prettyTCM t
+  prettyTCM (IsSort  a t) = "Sort" <+> prettyTCM a <+> ":" <+> prettyTCM t
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => Judgement a -> TCM Doc #-}
+
+instance PrettyTCM MetaId where
+  prettyTCM x = do
+    mn <- getMetaNameSuggestion x
+    prettyTCM $ NamedMeta mn x
+{-# SPECIALIZE prettyTCM :: MetaId -> TCM Doc #-}
+
+instance PrettyTCM NamedMeta where
+  prettyTCM (NamedMeta s m) = do
+    current <- currentModuleNameHash
+    prefix  <-
+      if metaModule m == current
+      then return empty
+      else do
+        modName <- BiMap.invLookup (metaModule m) <$>
+                   useR stTopLevelModuleNames
+        return $ case modName of
+          Nothing      -> __IMPOSSIBLE__
+          Just modName -> pretty modName <> text "."
+    let inBetween = case s of
+          ""  -> text "_"
+          "_" -> text "_"
+          s   -> text $ "_" ++ s ++ "_"
+    prefix <> inBetween <> text (show (metaId m))
+{-# SPECIALIZE prettyTCM :: NamedMeta -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (Blocked a) where
+  prettyTCM (Blocked x a) = ("[" <+> prettyTCM a <+> "]") <> text (P.prettyShow x)
+  prettyTCM (NotBlocked _ x) = prettyTCM x
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => Blocked a -> TCM Doc #-}
+
+instance (PrettyTCM k, PrettyTCM v) => PrettyTCM (Map k v) where
+  prettyTCM m = "Map" <> braces (sep $ punctuate comma
+    [ hang (prettyTCM k <+> "=") 2 (prettyTCM v) | (k, v) <- Map.toList m ])
+{-# SPECIALIZE prettyTCM :: (PrettyTCM k, PrettyTCM v) => Map k v -> TCM Doc  #-}
+
+-- instance {-# OVERLAPPING #-} PrettyTCM ArgName where
+--   prettyTCM = text . P.prettyShow
+
+-- instance (Reify a e, ToConcrete e c, P.Pretty c, PrettyTCM a) => PrettyTCM (Elim' a) where
+instance PrettyTCM Elim where
+  prettyTCM (IApply x y v) = "I$" <+> prettyTCM v
+  prettyTCM (Apply v) = "$" <+> prettyTCM v
+  prettyTCM (Proj _ f)= "." <> prettyTCM f
+{-# SPECIALIZE prettyTCM :: Elim -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (MaybeReduced a) where
+  prettyTCM = prettyTCM . ignoreReduced
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => MaybeReduced a -> TCM Doc #-}
+
+instance PrettyTCM EqualityView where
+  prettyTCM v = prettyTCM $ equalityUnview v
+{-# SPECIALIZE prettyTCM :: EqualityView -> TCM Doc #-}
+
+instance PrettyTCM A.Expr where
+  prettyTCM = prettyA; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM A.TypedBinding where
+  prettyTCM = prettyA; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM A.Pattern where
+  prettyTCM = prettyA; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM Relevance where
+  prettyTCM = pretty; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM Quantity where
+  prettyTCM = pretty; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM Erased where
+  prettyTCM = pretty; {-# INLINE prettyTCM #-}
+
+instance PrettyTCM Modality where
+  prettyTCM mod = hsep
+    [ prettyTCM (getQuantity mod)
+    , prettyTCM (getRelevance mod)
+    ]
+{-# SPECIALIZE prettyTCM :: Modality -> TCM Doc #-}
+
+instance PrettyTCM Blocker where
+  prettyTCM (UnblockOnAll us) = "all" <> parens (fsep $ punctuate "," $ map prettyTCM $ Set.toList us)
+  prettyTCM (UnblockOnAny us) = "any" <> parens (fsep $ punctuate "," $ map prettyTCM $ Set.toList us)
+  prettyTCM (UnblockOnMeta m) = prettyTCM m
+  prettyTCM (UnblockOnProblem p) = "problem" <+> pretty p
+  prettyTCM (UnblockOnDef q) = "definition" <+> pretty q
+{-# SPECIALIZE prettyTCM :: Blocker -> TCM Doc #-}
+
+instance PrettyTCM CompareAs where
+  prettyTCM (AsTermsOf a) = ":" <+> prettyTCMCtx TopCtx a
+  prettyTCM AsSizes       = ":" <+> do prettyTCM =<< sizeType
+  prettyTCM AsTypes       = empty
+{-# SPECIALIZE prettyTCM :: CompareAs -> TCM Doc #-}
+
+instance PrettyTCM TypeCheckingProblem where
+  prettyTCM (CheckExpr cmp e a) =
+    sep [ prettyA e <+> ":?", prettyTCM a ]
+  prettyTCM (CheckArgs _ _ _ es t0 t1 _) =
+    sep [ parens $ "_ :" <+> prettyTCM t0
+        , nest 2 $ prettyList $ map prettyA es
+        , nest 2 $ ":?" <+> prettyTCM t1 ]
+  prettyTCM (CheckProjAppToKnownPrincipalArg cmp e _ _ _ t _ _ _ _) = prettyTCM (CheckExpr cmp e t)
+  prettyTCM (CheckLambda cmp (Arg ai (xs, mt)) e t) =
+    sep [ pure CP.lambda <+>
+          (CP.prettyRelevance ai .
+           CP.prettyHiding ai (if isNothing mt && natSize xs == 1 then id
+                               else P.parens) <$> do
+            fsep $
+              map prettyTCM (List1.toList xs) ++
+              caseMaybe mt [] (\ a -> [":", prettyTCM a])) <+>
+          pure CP.arrow <+>
+          prettyTCM e <+>
+          ":?"
+        , prettyTCM t
+        ]
+  prettyTCM (DoQuoteTerm _ v _) = do
+    e <- reify v
+    prettyTCM (A.App A.defaultAppInfo_ (A.QuoteTerm A.exprNoRange) (defaultNamedArg e))
+{-# SPECIALIZE prettyTCM :: TypeCheckingProblem -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (WithHiding a) where
+  prettyTCM (WithHiding h a) = CP.prettyHiding h id <$> prettyTCM a
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => WithHiding a -> TCM Doc #-}
+
+instance PrettyTCM Name where
+  prettyTCM x = P.pretty <$> abstractToConcrete_ x
+{-# SPECIALIZE prettyTCM :: Name -> TCM Doc #-}
+
+instance PrettyTCM QName where
+  prettyTCM x = P.pretty <$> abstractToConcrete_ x
+{-# SPECIALIZE prettyTCM :: Name -> TCM Doc #-}
+
+instance PrettyTCM ModuleName where
+  prettyTCM x = P.pretty <$> abstractToConcrete_ x
+{-# SPECIALIZE prettyTCM :: ModuleName -> TCM Doc #-}
+
+instance PrettyTCM AbstractName where
+  prettyTCM = prettyTCM . anameName
+{-# SPECIALIZE prettyTCM :: AbstractName -> TCM Doc #-}
+
+instance PrettyTCM ConHead where
+  prettyTCM = prettyTCM . conName
+{-# SPECIALIZE prettyTCM :: ConHead -> TCM Doc #-}
+
+instance PrettyTCM Telescope where
+  prettyTCM tel = P.fsep . map P.pretty <$> do
+      tel <- reify tel
+      runAbsToCon $ bindToConcrete tel return
+{-# SPECIALIZE prettyTCM :: Telescope -> TCM Doc #-}
+
+newtype PrettyContext = PrettyContext Context
+
+instance PrettyTCM PrettyContext where
+  prettyTCM (PrettyContext ctx) = prettyTCM $ telFromList' nameToArgName $ reverse ctx
+{-# SPECIALIZE prettyTCM :: PrettyContext -> TCM Doc #-}
+
+instance PrettyTCM DBPatVar where
+  prettyTCM = prettyTCM . var . dbPatVarIndex
+{-# SPECIALIZE prettyTCM :: DBPatVar -> TCM Doc #-}
+
+instance PrettyTCM a => PrettyTCM (Pattern' a) where
+  prettyTCM :: forall m. MonadPretty m => Pattern' a -> m Doc
+  prettyTCM (IApplyP _ _ _ x)    = prettyTCM x
+  prettyTCM (VarP _ x)    = prettyTCM x
+  prettyTCM (DotP _ t)    = ".(" <> prettyTCM t <> ")"
+  prettyTCM (DefP o q ps) = parens $
+        prettyTCM q <+> fsep (map (prettyTCM . namedArg) ps)
+  prettyTCM (ConP c i ps) = -- (if b then braces else parens) $ prTy $
+        parens $
+        prettyTCM c <+> fsep (map (prettyTCM . namedArg) ps)
+      where
+        -- NONE OF THESE BINDINGS IS USED AT THE MOMENT:
+        b = conPRecord i && patOrigin (conPInfo i) /= PatOCon
+        showRec :: m Doc -- Defined, but currently not used
+        showRec = sep
+          [ "record"
+          , bracesAndSemicolons <$> zipWithM showField (conFields c) ps
+          ]
+        showField :: Arg QName -> NamedArg (Pattern' a) -> m Doc -- NB:: Defined but not used
+        showField (Arg ai x) p =
+          sep [ prettyTCM (A.qnameName x) <+> "=" , nest 2 $ prettyTCM $ namedArg p ]
+        showCon :: m Doc -- NB:: Defined but not used
+        showCon = parens $ prTy $ prettyTCM c <+> fsep (map (prettyTCM . namedArg) ps)
+        prTy d = caseMaybe (conPType i) d $ \ t -> d  <+> ":" <+> prettyTCM t
+  prettyTCM (LitP _ l)    = text (P.prettyShow l)
+  prettyTCM (ProjP _ q)   = text ("." ++ P.prettyShow q)
+{-# SPECIALIZE prettyTCM :: PrettyTCM a => Pattern' a -> TCM Doc #-}
+
+{-# SPECIALIZE prettyTCMPatterns :: [NamedArg DeBruijnPattern] -> TCM [Doc] #-}
+-- | Proper pretty printing of patterns:
+prettyTCMPatterns :: MonadPretty m => [NamedArg DeBruijnPattern] -> m [Doc]
+prettyTCMPatterns = mapM prettyA <=< reifyPatterns
+
+{-# SPECIALIZE prettyTCMPatternList :: [NamedArg DeBruijnPattern] -> TCM Doc #-}
+prettyTCMPatternList :: MonadPretty m => [NamedArg DeBruijnPattern] -> m Doc
+prettyTCMPatternList = prettyList . map prettyA <=< reifyPatterns
+
+instance PrettyTCM (Elim' DisplayTerm) where
+  prettyTCM (IApply x y v) = "$" <+> prettyTCM v
+  prettyTCM (Apply v) = "$" <+> prettyTCM (unArg v)
+  prettyTCM (Proj _ f)= "." <> prettyTCM f
+{-# SPECIALIZE prettyTCM :: Elim' DisplayTerm -> TCM Doc #-}
+
+instance PrettyTCM NLPat where
+  prettyTCM (PVar x bvs) = prettyTCM (Var x (map (Apply . fmap var) bvs))
+  prettyTCM (PDef f es) = parens $
+    prettyTCM f <+> fsep (map prettyTCM es)
+  prettyTCM (PLam i u)  = parens $
+    text ("λ " ++ absName u ++ " →") <+>
+    addContext (absName u) (prettyTCM $ absBody u)
+  prettyTCM (PPi a b)   = parens $
+    text ("(" ++ absName b ++ " :") <+> (prettyTCM (unDom a) <> ") →") <+>
+    addContext (absName b) (prettyTCM $ unAbs b)
+  prettyTCM (PSort s)        = prettyTCM s
+  prettyTCM (PBoundVar i []) = prettyTCM (var i)
+  prettyTCM (PBoundVar i es) = parens $ prettyTCM (var i) <+> fsep (map prettyTCM es)
+  prettyTCM (PTerm t)   = "." <> parens (prettyTCM t)
+{-# SPECIALIZE prettyTCM :: NLPat -> TCM Doc #-}
+
+instance PrettyTCM NLPType where
+  prettyTCM (NLPType s a) = prettyTCM a
+{-# SPECIALIZE prettyTCM :: NLPType -> TCM Doc #-}
+
+instance PrettyTCM NLPSort where
+  prettyTCM = \case
+    PUniv u l -> parens $ text (showUniv u) <+> prettyTCM l
+      -- Andreas, 2023-05-11, preserving Jesper's printing hack for now...
+    PInf u n  -> prettyTCM (Inf u n :: Sort)
+    PSizeUniv -> prettyTCM (SizeUniv :: Sort)
+    PLockUniv -> prettyTCM (LockUniv :: Sort)
+    PLevelUniv -> prettyTCM (LevelUniv :: Sort)
+    PIntervalUniv -> prettyTCM (IntervalUniv :: Sort)
+{-# SPECIALIZE prettyTCM :: NLPSort -> TCM Doc #-}
+
+instance PrettyTCM (Elim' NLPat) where
+  prettyTCM (IApply x y v) = prettyTCM v
+  prettyTCM (Apply v) = prettyTCM (unArg v)
+  prettyTCM (Proj _ f)= "." <> prettyTCM f
+{-# SPECIALIZE prettyTCM :: Elim' NLPat -> TCM Doc #-}
+
+instance PrettyTCM (Type' NLPat) where
+  prettyTCM = prettyTCM . unEl
+{-# SPECIALIZE prettyTCM :: Type' NLPat -> TCM Doc #-}
+
+instance PrettyTCM RewriteRule where
+  prettyTCM (RewriteRule q gamma f ps rhs b c) = fsep
+    [ prettyTCM q
+    , prettyTCM gamma <+> " |- "
+    , addContext gamma $ sep
+      [ prettyTCM (PDef f ps)
+      , " --> "
+      , prettyTCM rhs
+      , " : "
+      , prettyTCM b
+      ]
+    ]
+{-# SPECIALIZE prettyTCM :: RewriteRule -> TCM Doc #-}
+
+instance PrettyTCM Occurrence where
+  prettyTCM occ  = text $ "-[" ++ prettyShow occ ++ "]->"
+{-# SPECIALIZE prettyTCM :: Occurrence -> TCM Doc #-}
+
+-- | Pairing something with a node (for printing only).
+data WithNode n a = WithNode n a
+
+-- | Pretty-print something paired with a (printable) node.
+-- | This intermediate typeclass exists to avoid UndecidableInstances.
+class PrettyTCMWithNode a where
+  prettyTCMWithNode :: (PrettyTCM n, MonadPretty m) => WithNode n a -> m Doc
+
+instance PrettyTCMWithNode Occurrence where
+  prettyTCMWithNode (WithNode n o) = prettyTCM o <+> prettyTCM n
+
+instance (PrettyTCM n, PrettyTCMWithNode e) => PrettyTCM (Graph n e) where
+  prettyTCM g = vcat $ map pr $ Map.assocs $ Graph.graph g
+    where
+      pr (n, es) = sep
+        [ prettyTCM n
+        , nest 2 $ vcat $ map (prettyTCMWithNode . uncurry WithNode) $ Map.assocs es
+        ]
+{-# SPECIALIZE prettyTCM :: (PrettyTCM n, PrettyTCMWithNode e) => (Graph n e) -> TCM Doc #-}
+
+instance PrettyTCM SplitTag where
+  prettyTCM (SplitCon c)  = prettyTCM c
+  prettyTCM (SplitLit l)  = prettyTCM l
+  prettyTCM SplitCatchall = return underscore
+{-# SPECIALIZE prettyTCM :: SplitTag -> TCM Doc #-}
+
+instance PrettyTCM Candidate where
+  prettyTCM c = case candidateKind c of
+    (GlobalCandidate q) -> prettyTCM q
+    LocalCandidate      -> prettyTCM $ candidateTerm c
+{-# SPECIALIZE prettyTCM :: Candidate -> TCM Doc #-}
diff --git a/src/full/Agda/TypeChecking/Pretty.hs-boot b/src/full/Agda/TypeChecking/Pretty.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty.hs-boot
@@ -0,0 +1,63 @@
+module Agda.TypeChecking.Pretty where
+
+import Data.String (IsString)
+import Data.Semigroup (Semigroup)
+
+import Agda.Syntax.Common (NameId)
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import {-# SOURCE #-} Agda.TypeChecking.Monad.MetaVars (MonadInteractionPoints)
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Pure (PureTCM)
+
+import Agda.Utils.Null (Null)
+import Agda.Syntax.Common.Pretty (Doc)
+import qualified Agda.Syntax.Common.Pretty as P
+
+
+text                  :: Applicative m => String -> m Doc
+sep, fsep, hsep, vcat :: (Applicative m, Foldable t) => t (m Doc) -> m Doc
+hang                  :: Applicative m => m Doc -> Int -> m Doc -> m Doc
+($$), (<+>), (<?>)    :: Applicative m => m Doc -> m Doc -> m Doc
+nest                  :: Functor m => Int -> m Doc -> m Doc
+pretty                :: (Applicative m, P.Pretty a) => a -> m Doc
+prettyList_           :: (Applicative m, Semigroup (m Doc), Foldable t) => t (m Doc) -> m Doc
+pwords                :: Applicative m => String -> [m Doc]
+
+-- The definition of MonadAbsToCon is inlined so that the module
+-- Agda.Syntax.Translation.AbstractToConcrete does not need to be
+-- imported.
+type MonadPretty m =
+  ( MonadFresh NameId m
+  , MonadInteractionPoints m
+  , MonadStConcreteNames m
+  , HasOptions m
+  , PureTCM m
+  , IsString (m Doc)
+  , Null (m Doc)
+  , Semigroup (m Doc)
+  )
+
+-- This instance is to satify the constraints of superclass MonadPretty:
+-- This instance is more specific than a generic instance
+-- @Semigroup a => Semigroup (TCM a)@.
+instance {-# OVERLAPPING #-} Semigroup (TCM Doc)
+
+class PrettyTCM a where
+  prettyTCM :: MonadPretty m => a -> m Doc
+
+newtype PrettyContext = PrettyContext Context
+
+instance PrettyTCM a => PrettyTCM (Closure a)
+instance PrettyTCM a => PrettyTCM [a]
+
+instance PrettyTCM Name
+instance PrettyTCM QName
+instance PrettyTCM NamedMeta
+instance PrettyTCM Term
+instance PrettyTCM Elim
+instance PrettyTCM Type
+instance PrettyTCM Sort
+instance PrettyTCM DisplayTerm
+instance PrettyTCM DBPatVar
+instance PrettyTCM PrettyContext
diff --git a/src/full/Agda/TypeChecking/Pretty/Call.hs b/src/full/Agda/TypeChecking/Pretty/Call.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Call.hs
@@ -0,0 +1,242 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Pretty.Call where
+
+import Prelude hiding ( null )
+
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views
+import Agda.Syntax.Common
+import Agda.Syntax.Fixity
+import qualified Agda.Syntax.Concrete.Definitions as D
+import qualified Agda.Syntax.Info as A
+import Agda.Syntax.Position
+import Agda.Syntax.Internal
+import Agda.Syntax.Scope.Monad
+import Agda.Syntax.Translation.AbstractToConcrete
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Pretty
+
+import Agda.Utils.Function
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Pretty as P
+
+import Agda.Utils.Impossible
+
+import Agda.Version (docsUrl)
+
+sayWhere :: MonadPretty m => HasRange a => a -> m Doc -> m Doc
+sayWhere x d = applyUnless (null r) (prettyTCM r $$) d
+  where r = getRange x
+
+sayWhen :: MonadPretty m => Range -> Maybe (Closure Call) -> m Doc -> m Doc
+sayWhen r Nothing   m = sayWhere r m
+sayWhen r (Just cl) m = sayWhere r (m $$ prettyTCM cl)
+
+instance PrettyTCM CallInfo where
+  prettyTCM (CallInfo callInfoTarget callInfoCall) = do
+    let call = prettyTCM callInfoCall
+        r    = getRange callInfoTarget
+    if null $ P.pretty r
+      then call
+      else call $$ nest 2 ("(at" <+> prettyTCM r) <> ")"
+  {-# SPECIALIZE prettyTCM :: CallInfo -> TCM Doc #-}
+
+instance PrettyTCM Call where
+  prettyTCM = withContextPrecedence TopCtx . \case
+
+    CheckClause t cl -> do
+
+      verboseS  "error.checkclause" 40 $ do
+        reportSLn "error.checkclause" 60 $ "prettyTCM CheckClause: cl = " ++ show (deepUnscope cl)
+        clc <- abstractToConcrete_ cl
+        reportSLn "error.checkclause" 40 $ "cl (Concrete) = " ++ show clc
+
+      fsep $
+        pwords "when checking that the clause"
+        ++ [prettyA cl] ++ pwords "has type" ++ [prettyTCM t]
+
+    CheckLHS lhs -> vcat $
+      [ fsep $ pwords "when checking the clause left hand side"
+      , prettyA $ lhs { A.spLhsInfo = (A.spLhsInfo lhs) { A.lhsEllipsis = NoEllipsis } }
+      ]
+
+    CheckPattern p tel t -> addContext tel $ fsep $
+      pwords "when checking that the pattern"
+      ++ [prettyA p] ++ pwords "has type" ++ [prettyTCM t]
+
+    CheckPatternLinearityType x -> fsep $
+      pwords "when checking that all occurrences of pattern variable"
+      ++ [pretty x] ++ pwords "have the same type"
+
+    CheckPatternLinearityValue x -> fsep $
+      pwords "when checking that all occurrences of pattern variable"
+      ++ [pretty x] ++ pwords "have the same value"
+
+    CheckLetBinding b -> fsep $
+      pwords "when checking the let binding" ++ [prettyA b]
+
+    InferExpr e -> fsep $ pwords "when inferring the type of" ++ [prettyA e]
+
+    CheckExprCall cmp e t -> fsep $
+      pwords "when checking that the expression"
+      ++ [prettyA e] ++ pwords "has type" ++ [prettyTCM t]
+
+    IsTypeCall cmp e s -> fsep $
+      pwords "when checking that the expression"
+      ++ [prettyA e] ++ pwords "is a type of sort" ++ [prettyTCM s]
+
+    IsType_ e -> fsep $
+      pwords "when checking that the expression"
+      ++ [prettyA e] ++ pwords "is a type"
+
+    CheckProjection _ x t -> fsep $
+      pwords "when checking the projection" ++
+      [ sep [ prettyTCM x <+> ":"
+            , nest 2 $ prettyTCM t ] ]
+
+    CheckArguments r es t0 t1 -> do
+      TelV tel cod <- telView t0
+      let
+        prefix =
+          pwords "when checking that" ++
+          map hPretty es ++
+          pwords (P.singPlural es "is a valid argument" "are valid arguments")
+      case unEl cod of
+        Dummy{} -> fsep $
+          prefix ++
+          pwords "to a function accepting arguments of type" ++
+          [prettyTCM tel]
+        _ -> fsep $
+          prefix ++
+          pwords "to a function of type" ++
+          [prettyTCM t0]
+
+    CheckMetaSolution r m a v -> fsep $
+      pwords "when checking that the solution" ++ [prettyTCM v] ++
+      pwords "of metavariable" ++ [prettyTCM m] ++
+      pwords "has the expected type" ++ [prettyTCM a]
+
+    CheckTargetType r infTy expTy -> sep
+      [ "when checking that the inferred type of an application"
+      , nest 2 $ prettyTCM infTy
+      , "matches the expected type"
+      , nest 2 $ prettyTCM expTy ]
+
+    CheckRecDef _ x ps cs ->
+      fsep $ pwords "when checking the definition of" ++ [prettyTCM x]
+
+    CheckDataDef _ x ps cs ->
+      fsep $ pwords "when checking the definition of" ++ [prettyTCM x]
+
+    CheckConstructor d _ _ (A.Axiom _ _ _ _ c _) -> fsep $
+      pwords "when checking the constructor" ++ [prettyTCM c] ++
+      pwords "in the declaration of" ++ [prettyTCM d]
+
+    CheckConstructor{} -> __IMPOSSIBLE__
+
+    CheckConArgFitsIn c f t s -> do
+      woK <- withoutKOption
+      let
+        hint = fsep (pwords "Note: this argument is forced by the indices of" ++ [prettyTCM c <> comma] ++ pwords "so this definition would be allowed under --large-indices.")
+        -- Only add hint about large-indices when --with-K
+        addh d
+          | f && not woK = d $$ empty $$ hint
+          | otherwise    = d
+
+      addh $ fsep $
+        pwords "when checking that the type" ++ [prettyTCM t] ++
+        pwords "of an argument to the constructor" ++ [prettyTCM c] ++
+        pwords "fits in the sort" ++ [prettyTCM s] ++
+        pwords "of the datatype."
+
+    CheckFunDefCall _ f _ _ ->
+      fsep $ pwords "when checking the definition of" ++ [prettyTCM f]
+
+    CheckPragma _ p ->
+      fsep $ pwords "when checking the pragma"
+             ++ [prettyA $ RangeAndPragma noRange p]
+
+    CheckPrimitive _ x e -> fsep $
+      pwords "when checking that the type of the primitive function" ++
+      [prettyTCM x] ++ pwords "is" ++ [prettyA e]
+
+    CheckModuleParameters m _tel -> fsep $
+      pwords "when checking the parameters of module" ++ [prettyA m]
+
+    CheckWithFunctionType a -> fsep $
+      pwords "when checking that the type" ++
+      [prettyTCM a] ++ pwords "of the generated with function is well-formed" ++
+      [parens $ text $ docsUrl "language/with-abstraction.html#ill-typed-with-abstractions"]
+
+    CheckDotPattern e v -> fsep $
+      pwords "when checking that the given dot pattern" ++ [prettyA e] ++
+      pwords "matches the inferred value" ++ [prettyTCM v]
+
+    CheckNamedWhere m -> fsep $
+      pwords "when checking the named where block" ++ [prettyA m]
+
+    InferVar x ->
+      fsep $ pwords "when inferring the type of" ++ [prettyTCM x]
+
+    InferDef x ->
+      fsep $ pwords "when inferring the type of" ++ [prettyTCM x]
+
+    CheckIsEmpty r t ->
+      fsep $ pwords "when checking that" ++ [prettyTCM t] ++
+             pwords "has no constructors"
+
+    CheckConfluence r1 r2 ->
+      fsep $ pwords "when checking confluence of the rewrite rule" ++
+             [prettyTCM r1] ++ pwords "with" ++
+             if r1 == r2 then pwords "itself" else [prettyTCM r2]
+
+    ScopeCheckExpr e -> fsep $ pwords "when scope checking" ++ [pretty e]
+
+    ScopeCheckDeclaration d ->
+      fwords ("when scope checking the declaration" ++ suffix) $$
+      nest 2 (vcat $ map pretty ds)
+      where
+      ds     = D.notSoNiceDeclarations d
+      suffix = case ds of
+        [_] -> ""
+        _   -> "s"
+
+    ScopeCheckLHS x p ->
+      fsep $ pwords "when scope checking the left-hand side" ++ [pretty p] ++
+             pwords "in the definition of" ++ [pretty x]
+
+    NoHighlighting -> empty
+
+    SetRange r -> fsep (pwords "when doing something at") <+> prettyTCM r
+
+    CheckSectionApplication _ erased m1 modapp -> fsep $
+      pwords "when checking the module application" ++
+      [prettyA $ A.Apply info erased m1 modapp initCopyInfo empty]
+      where
+      info = A.ModuleInfo noRange noRange Nothing Nothing Nothing
+
+    ModuleContents -> fsep $ pwords "when retrieving the contents of a module"
+
+    CheckIApplyConfluence _ qn fn l r t -> do
+      vcat
+        [ fsep (pwords "when checking that a clause of" ++ [prettyTCM qn] ++ pwords "has the correct boundary.")
+        , ""
+        , "Specifically, the terms"
+        , nest 2 (prettyTCM l)
+        , "and"
+        , nest 2 (prettyTCM r)
+        , fsep (pwords "must be equal, since" ++ [prettyTCM fn] ++ pwords "could reduce to either.")
+        ]
+
+    where
+    hPretty :: MonadPretty m => Arg (Named_ Expr) -> m Doc
+    hPretty a = do
+      withContextPrecedence (ArgumentCtx PreferParen) $
+        pretty =<< abstractToConcreteHiding a a
+  {-# SPECIALIZE prettyTCM :: Call -> TCM Doc #-}
diff --git a/src/full/Agda/TypeChecking/Pretty/Call.hs-boot b/src/full/Agda/TypeChecking/Pretty/Call.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Call.hs-boot
@@ -0,0 +1,13 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Pretty.Call where
+
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad.Base
+
+import {-# SOURCE #-} Agda.TypeChecking.Pretty (MonadPretty)
+
+import Agda.Syntax.Common.Pretty
+
+sayWhen :: MonadPretty m => Range -> Maybe (Closure Call) -> m Doc -> m Doc
diff --git a/src/full/Agda/TypeChecking/Pretty/Constraint.hs b/src/full/Agda/TypeChecking/Pretty/Constraint.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Constraint.hs
@@ -0,0 +1,169 @@
+
+module Agda.TypeChecking.Pretty.Constraint where
+
+import Prelude hiding (null)
+
+import qualified Data.Set as Set
+import Data.Foldable (Foldable)
+import qualified Data.Foldable as Foldable
+import qualified Data.List as List
+import Data.Function (on)
+
+import Control.Monad
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Info     as A
+import Agda.Syntax.Fixity
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Errors
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Impossible
+
+prettyConstraint :: MonadPretty m => ProblemConstraint -> m Doc
+prettyConstraint c = f (locallyTCState stInstantiateBlocking (const True) $ prettyTCM c)
+  where
+    r   = getRange c
+    f :: MonadPretty m => m Doc -> m Doc
+    f d = if null $ P.pretty r
+          then d
+          else d $$ nest 4 ("[ at" <+> prettyTCM r <+> "]")
+{-# SPECIALIZE prettyConstraint :: ProblemConstraint -> TCM Doc #-}
+
+interestingConstraint :: ProblemConstraint -> Bool
+interestingConstraint pc = go $ clValue (theConstraint pc) where
+  go (UnBlock mi) = False
+  go _            = True
+
+prettyInterestingConstraints :: MonadPretty m => [ProblemConstraint] -> m [Doc]
+prettyInterestingConstraints cs = mapM (prettyConstraint . stripPids) $ List.sortBy (compare `on` isBlocked) cs'
+  where
+    isBlocked = not . null . allBlockingProblems . constraintUnblocker
+    cs' = filter interestingConstraint cs
+    interestingPids = Set.unions $ map (allBlockingProblems . constraintUnblocker) cs'
+    stripPids (PConstr pids unblock c) = PConstr (Set.intersection pids interestingPids) unblock c
+{-# SPECIALIZE prettyInterestingConstraints :: [ProblemConstraint] -> TCM [Doc] #-}
+
+prettyRangeConstraint ::
+  (MonadPretty m, Foldable f, Null (f ProblemId)) => Range -> f ProblemId -> Blocker -> Doc -> m Doc
+prettyRangeConstraint r pids unblock c =
+  return c <?>
+  sep [ prange r
+      , parensNonEmpty $ sep
+          [ blockedOn unblock
+          , prPids (Foldable.toList pids)
+          ]
+      ]
+  where
+  prPids []    = empty
+  prPids [pid] = "belongs to problem" <+> prettyTCM pid
+  prPids pids  = "belongs to problems" <+> fsep (punctuate "," $ map prettyTCM pids)
+
+  comma | null pids = empty
+        | otherwise = ","
+
+  blockedOn (UnblockOnAll bs) | Set.null bs = empty
+  blockedOn (UnblockOnAny bs) | Set.null bs = "stuck" <> comma
+  blockedOn u = "blocked on" <+> (prettyTCM u <> comma)
+
+  prange r | null s    = pure empty
+           | otherwise = text $ " [ at " ++ s ++ " ]"
+    where s = P.prettyShow r
+
+instance PrettyTCM ProblemConstraint where
+  prettyTCM (PConstr pids unblock c) =
+    prettyRangeConstraint noRange pids unblock =<< prettyTCM c
+
+instance PrettyTCM Constraint where
+    prettyTCM = \case
+        ValueCmp cmp ty s t -> prettyCmp (prettyTCM cmp) s t <?> prettyTCM ty
+        ValueCmpOnFace cmp p ty s t ->
+            sep [ prettyTCM p <+> "|"
+                , prettyCmp (prettyTCM cmp) s t ]
+            <?> (":" <+> prettyTCMCtx TopCtx ty)
+        ElimCmp cmps fs t v us vs -> prettyCmp "~~" us vs   <?> (":" <+> prettyTCMCtx TopCtx t)
+        LevelCmp cmp a b         -> prettyCmp (prettyTCM cmp) a b
+        SortCmp cmp s1 s2        -> prettyCmp (prettyTCM cmp) s1 s2
+        UnBlock m   -> do
+            -- BlockedConst t <- mvInstantiation <$> lookupMeta m
+            mi <- lookupMetaInstantiation m
+            case mi of
+              BlockedConst t -> prettyCmp ":=" m t
+              PostponedTypeCheckingProblem cl -> enterClosure cl $ \p ->
+                prettyCmp ":=" m p
+              Open{}  -> __IMPOSSIBLE__
+              OpenInstance{} -> __IMPOSSIBLE__
+              InstV{} -> empty
+              -- Andreas, 2017-01-11, issue #2637:
+              -- The size solver instantiates some metas with infinity
+              -- without cleaning up the UnBlock constraints.
+              -- Thus, this case is not IMPOSSIBLE.
+              --
+              -- InstV args t -> do
+              --   reportS "impossible" 10
+              --     [ "UnBlock meta " ++ show m ++ " surprisingly has InstV instantiation:"
+              --     , show m ++ show args ++ " := " ++ show t
+              --     ]
+              --   __IMPOSSIBLE__
+        FindInstance m mcands -> do
+            t <- getMetaTypeInContext m
+            TelV tel _ <- telViewUpTo' (-1) notVisible t
+            sep [ "Resolve instance argument" <?> prettyCmp ":" m t
+                  -- #4071: Non-visible arguments to the meta are in scope of the candidates add
+                  --        those here to not get out of scope deBruijn indices when printing
+                  --        unsolved constraints.
+                , addContext tel cands
+                ]
+          where
+            cands =
+              case mcands of
+                Nothing -> "No candidates yet"
+                Just cnds ->
+                  hang "Candidates" 2 $ vcat
+                    [ hang (overlap c <+> prettyTCM c <+> ":") 2 $
+                            prettyTCM (candidateType c) | c <- cnds ]
+              where overlap c | candidateOverlappable c = "overlap"
+                              | otherwise               = empty
+        IsEmpty r t ->
+            "Is empty:" <?> prettyTCMCtx TopCtx t
+        CheckSizeLtSat t ->
+            "Is not empty type of sizes:" <?> prettyTCMCtx TopCtx t
+        CheckFunDef i q cs err -> do
+            t <- defType <$> getConstInfo q
+            vcat [ "Check definition of" <+> prettyTCM q <+> ":" <+> prettyTCM t
+                 , nest 2 $ "stuck because" <?> prettyTCM err ]
+        HasBiggerSort a -> "Has bigger sort:" <+> prettyTCM a
+        HasPTSRule a b -> "Has PTS rule:" <+> case b of
+          NoAbs _ b -> prettyTCM (a,b)
+          Abs x b   -> "(" <> (prettyTCM a <+> "," <+> addContext x (prettyTCM b)) <> ")"
+        UnquoteTactic v _ _ -> do
+          e <- reify v
+          prettyTCM (A.App A.defaultAppInfo_ (A.Unquote A.exprNoRange) (defaultNamedArg e))
+        CheckDataSort q s -> do
+          hsep [ "Sort", prettyTCM s, "of", prettyTCM q, "admits data/record definitions." ]
+        CheckMetaInst x -> do
+          m <- lookupLocalMeta x
+          case mvJudgement m of
+            HasType{ jMetaType = t } -> prettyTCM x <+> ":" <+> prettyTCM t
+            IsSort{} -> prettyTCM x <+> "is a sort"
+        CheckType t ->
+          prettyTCM t <+> "is a well-formed type"
+        CheckLockedVars t ty lk lk_ty -> do
+          "Lock" <+> prettyTCM lk <+> "|-" <+> prettyTCMCtx TopCtx t <+> ":" <+> prettyTCM ty
+        UsableAtModality _ ms mod t -> "Is usable at" <+> text (verbalize mod) <+> "modality:" <+> prettyTCM t
+          -- TODO: print @ms : Maybe Sort@ as well?
+
+      where
+        prettyCmp
+          :: (PrettyTCM a, PrettyTCM b, MonadPretty m)
+          => m Doc -> a -> b -> m Doc
+        prettyCmp cmp x y = prettyTCMCtx TopCtx x <?> (cmp <+> prettyTCMCtx TopCtx y)
diff --git a/src/full/Agda/TypeChecking/Pretty/Constraint.hs-boot b/src/full/Agda/TypeChecking/Pretty/Constraint.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Constraint.hs-boot
@@ -0,0 +1,12 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Pretty.Constraint where
+
+import Agda.Syntax.Common.Pretty (Doc)
+import Agda.TypeChecking.Pretty (MonadPretty, PrettyTCM)
+import Agda.TypeChecking.Monad.Base (ProblemConstraint)
+
+prettyInterestingConstraints :: MonadPretty m => [ProblemConstraint] -> m [Doc]
+interestingConstraint        :: ProblemConstraint -> Bool
+
+instance PrettyTCM ProblemConstraint
diff --git a/src/full/Agda/TypeChecking/Pretty/Warning.hs b/src/full/Agda/TypeChecking/Pretty/Warning.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Warning.hs
@@ -0,0 +1,581 @@
+
+module Agda.TypeChecking.Pretty.Warning where
+
+import Prelude hiding ( null )
+
+import Control.Monad ( guard, filterM, (<=<) )
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail ( MonadFail )
+
+import Data.Char ( toLower )
+import Data.Function (on)
+import Data.Maybe
+
+import qualified Data.Set as Set
+import Data.Set (Set)
+
+import qualified Data.List as List
+import qualified Data.Text as T
+
+import Agda.TypeChecking.Monad.Base
+import qualified Agda.TypeChecking.Monad.Base.Warning as W
+import Agda.TypeChecking.Monad.Builtin
+import {-# SOURCE #-} Agda.TypeChecking.Errors
+import Agda.TypeChecking.Monad.MetaVars
+import Agda.TypeChecking.Monad.Options
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Constraints
+import Agda.TypeChecking.Monad.State ( getScope )
+import Agda.TypeChecking.Monad ( localTCState, enterClosure )
+import Agda.TypeChecking.Positivity () --instance only
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Pretty.Call () -- instance PrettyTCM CallInfo
+import {-# SOURCE #-} Agda.TypeChecking.Pretty.Constraint (prettyInterestingConstraints, interestingConstraint)
+import Agda.TypeChecking.Warnings (MonadWarning, isUnsolvedWarning, onlyShowIfUnsolved, classifyWarning, WhichWarnings(..), warning_)
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars
+
+import Agda.Syntax.Common ( getHiding, ImportedName'(..), fromImportedName, partitionImportedNames )
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Concrete as C
+import Agda.Syntax.Scope.Base ( concreteNamesInScope, NameOrModule(..) )
+import Agda.Syntax.Internal
+import Agda.Syntax.Translation.InternalToAbstract
+
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Warnings
+
+import Agda.Utils.FileName (filePath)
+import Agda.Utils.Lens
+import Agda.Utils.List ( editDistance )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( Pretty, prettyShow, singPlural )
+import qualified Agda.Syntax.Common.Pretty as P
+
+instance PrettyTCM TCWarning where
+  prettyTCM w@(TCWarning loc _ _ _ _) = do
+    reportSLn "warning" 2 $ "Warning raised at " ++ prettyShow loc
+    pure $ tcWarningPrintedWarning w
+
+{-# SPECIALIZE prettyWarningName :: WarningName -> TCM Doc #-}
+-- | Prefix for a warning text showing name of the warning.
+--   E.g. @warning: -W[no]<warning_name>@
+prettyWarningName :: MonadPretty m => WarningName -> m Doc
+prettyWarningName w = hcat
+  [ "warning: -W[no]"
+  , text $ warningName2String w
+  ]
+
+{-# SPECIALIZE prettyWarning :: Warning -> TCM Doc #-}
+prettyWarning :: MonadPretty m => Warning -> m Doc
+prettyWarning = \case
+
+    UnsolvedMetaVariables ms  ->
+      fsep ( pwords "Unsolved metas at the following locations:" )
+      $$ nest 2 (vcat $ map prettyTCM ms)
+
+    UnsolvedInteractionMetas is ->
+      fsep ( pwords "Unsolved interaction metas at the following locations:" )
+      $$ nest 2 (vcat $ map prettyTCM is)
+
+    InteractionMetaBoundaries is ->
+      fsep ( pwords "Interaction meta(s) at the following location(s) have unsolved boundary constraints:" )
+      $$ nest 2 (vcat $ map prettyTCM (Set.toList (Set.fromList is)))
+
+    UnsolvedConstraints cs -> do
+      pcs <- prettyInterestingConstraints cs
+      if null pcs
+        then fsep $ pwords "Unsolved constraints"  -- #4065: keep minimal warning text
+        else vcat
+          [ fsep $ pwords "Failed to solve the following constraints:"
+          , nest 2 $ return $ P.vcat $ List.nub pcs
+          ]
+
+    TerminationIssue because -> do
+      dropTopLevel <- topLevelModuleDropper
+      fwords "Termination checking failed for the following functions:"
+        $$ nest 2 (fsep $ punctuate comma $
+             map (pretty . dropTopLevel) $
+               concatMap termErrFunctions because)
+        $$ fwords "Problematic calls:"
+        $$ nest 2 (fmap (P.vcat . List.nub) $
+              mapM prettyTCM $ List.sortOn getRange $
+              concatMap termErrCalls because)
+
+    UnreachableClauses f pss -> fsep $
+      pwords "Unreachable" ++ pwords (plural (length pss) "clause")
+        where
+          plural 1 thing = thing
+          plural n thing = thing ++ "s"
+
+    CoverageIssue f pss -> fsep (
+      pwords "Incomplete pattern matching for" ++ [prettyTCM f <> "."] ++
+      pwords "Missing cases:") $$ nest 2 (vcat $ map display pss)
+        where
+        display (tel, ps) = prettyTCM $ NamedClause f True $
+          empty { clauseTel = tel, namedClausePats = ps }
+
+    CoverageNoExactSplit f cs -> vcat $
+      fsep (pwords "Exact splitting is enabled, but the following" ++ pwords (P.singPlural cs "clause" "clauses") ++
+            pwords "could not be preserved as definitional equalities in the translation to a case tree:"
+           ) :
+      map (nest 2 . prettyTCM . NamedClause f True) cs
+
+    InlineNoExactSplit f c -> vcat $
+      [ fsep $
+          pwords "Exact splitting is enabled, but the following clause" ++
+          pwords "is no longer a definitional equality because it was translated to a copattern match:"
+      , nest 2 . prettyTCM . NamedClause f True $ c
+      ]
+
+    NotStrictlyPositive d ocs -> fsep $
+      [prettyTCM d] ++ pwords "is not strictly positive, because it occurs"
+      ++ [prettyTCM ocs]
+
+    UnsupportedIndexedMatch doc -> vcat
+      [ fsep (pwords "This clause uses pattern-matching features that are not yet supported by Cubical Agda,"
+           ++ pwords "the function to which it belongs will not compute when applied to transports."
+             )
+      , ""
+      , "Reason:" <+> pure doc
+      , ""
+      ]
+
+    CantGeneralizeOverSorts ms -> vcat
+            [ text "Cannot generalize over unsolved sort metas:"
+            , nest 2 $ vcat [ prettyTCM x <+> text "at" <+> (pretty =<< getMetaRange x) | x <- ms ]
+            , fsep $ pwords "Suggestion: add a `variable Any : Set _` and replace unsolved metas by Any"
+            ]
+
+    AbsurdPatternRequiresNoRHS ps -> fwords $
+      "The right-hand side must be omitted if there " ++
+      "is an absurd pattern, () or {}, in the left-hand side."
+
+    OldBuiltin old new -> fwords $
+      "Builtin " ++ getBuiltinId old ++ " no longer exists. " ++
+      "It is now bound by BUILTIN " ++ getBuiltinId new
+
+    EmptyRewritePragma -> fsep . pwords $ "Empty REWRITE pragma"
+
+    EmptyWhere         -> fsep . pwords $ "Empty `where' block (ignored)"
+
+    IllformedAsClause s -> fsep . pwords $
+      "`as' must be followed by an identifier" ++ s
+
+    ClashesViaRenaming nm xs -> fsep $ concat $
+      [ [ case nm of NameNotModule -> "Name"; ModuleNotName -> "Module" ]
+      , pwords "clashes introduced by `renaming':"
+      , map prettyTCM xs
+      ]
+
+    UselessPatternDeclarationForRecord s -> fwords $ unwords
+      [ "`pattern' attribute ignored for", s, "record" ]
+      -- the @s@ is a qualifier like "eta" or "coinductive"
+
+    UselessPublic -> fwords $ "Keyword `public' is ignored here"
+
+    UselessHiding xs -> fsep $ concat
+      [ pwords "Ignoring names in `hiding' directive:"
+      , punctuate "," $ map pretty xs
+      ]
+
+    UselessInline q -> fsep $
+      pwords "It is pointless for INLINE'd function" ++ [prettyTCM q] ++
+      pwords "to have a separate Haskell definition"
+
+    WrongInstanceDeclaration -> fwords $
+      "Instances should be of type {Γ} → C, where C evaluates to a postulated name or the name of " ++
+      "a data or record type, so `instance' is ignored here."
+
+    InstanceWithExplicitArg q -> fsep $
+      pwords "Instance declarations with explicit arguments are never considered by instance search," ++
+      pwords "so making" ++ [prettyTCM q] ++ pwords "into an instance has no effect."
+
+    InstanceNoOutputTypeName b -> fsep $
+      pwords "Instance arguments whose type is not {Γ} → C, where C evaluates to a postulated type, " ++
+      pwords "a parameter type or the name of a data or record type, are never considered by instance search," ++
+      pwords "so having an instance argument" ++ [return b] ++ pwords "has no effect."
+
+    InstanceArgWithExplicitArg b -> fsep $
+      pwords "Instance arguments with explicit arguments are never considered by instance search," ++
+      pwords "so having an instance argument" ++ [return b] ++ pwords "has no effect."
+
+    InversionDepthReached f -> do
+      maxDepth <- maxInversionDepth
+      fsep $ pwords "Refusing to invert pattern matching of" ++ [prettyTCM f] ++
+             pwords ("because the maximum depth (" ++ show maxDepth ++ ") has been reached.") ++
+             pwords "Most likely this means you have an unsatisfiable constraint, but it could" ++
+             pwords "also mean that you need to increase the maximum depth using the flag" ++
+             pwords "--inversion-max-depth=N"
+
+    NoGuardednessFlag q ->
+      fsep $ [ prettyTCM q ] ++ pwords "is declared coinductive, but option" ++
+             pwords "--guardedness is not enabled. Coinductive functions on" ++
+             pwords "this type will likely be rejected by the termination" ++
+             pwords "checker unless this flag is enabled."
+
+    GenericWarning d -> return d
+
+    InvalidCharacterLiteral c -> fsep $
+      pwords "Invalid character literal" ++ [text $ show c] ++
+      pwords "(surrogate code points are not supported)"
+
+    UselessPragma _r d -> return d
+
+    SafeFlagPostulate e -> fsep $
+      pwords "Cannot postulate" ++ [pretty e] ++ pwords "with safe flag"
+
+    SafeFlagPragma xs -> fsep $ concat
+      [ [ fwords $ singPlural (words =<< xs) id (++ "s") "Cannot set OPTIONS pragma" ]
+      , map text xs
+      , [ fwords "with safe flag." ]
+      ]
+
+    SafeFlagWithoutKFlagPrimEraseEquality -> fsep (pwords "Cannot use primEraseEquality with safe and without-K flags.")
+
+    WithoutKFlagPrimEraseEquality -> fsep (pwords "Using primEraseEquality with the without-K flag is inconsistent.")
+
+    OptionWarning ow -> pretty ow
+
+    ParseWarning pw -> pretty pw
+
+    DuplicateInterfaceFiles selected ignored -> vcat
+      [ fwords "There are two interface files:"
+      , nest 4 $ text $ filePath selected
+      , nest 4 $ text $ filePath ignored
+      , nest 2 $ fsep $ pwords "Using" ++ [text $ filePath selected] ++ pwords "for now but please remove at least one of them."
+      ]
+
+    DeprecationWarning old new version -> fsep $
+      [text old] ++ pwords "has been deprecated. Use" ++ [text new] ++ pwords
+      "instead. This will be an error in Agda" ++ [text version <> "."]
+
+    NicifierIssue w -> pretty w
+
+    UserWarning str -> text (T.unpack str)
+
+    ModuleDoesntExport m names modules xs -> vcat
+      [ fsep $ pwords "The module" ++ [pretty m] ++ pwords "doesn't export the following:"
+      , prettyNotInScopeNames False (suggestion names)   ys
+      , prettyNotInScopeNames False (suggestion modules) ms
+      ]
+      where
+      ys, ms :: [C.ImportedName]
+      ys            = map ImportedName   ys0
+      ms            = map ImportedModule ms0
+      (ys0, ms0)    = partitionImportedNames xs
+      suggestion zs = maybe empty parens . didYouMean (map C.QName zs) fromImportedName
+
+    DuplicateUsing xs -> fsep $ pwords "Duplicates in `using` directive:" ++ map pretty (List1.toList xs)
+
+    FixityInRenamingModule _rs -> fsep $ pwords "Modules do not have fixity"
+
+    LibraryWarning lw -> pretty lw
+
+    InfectiveImport msg -> return msg
+
+    CoInfectiveImport msg -> return msg
+
+    RewriteNonConfluent lhs rhs1 rhs2 err -> fsep
+      [ "Local confluence check failed:"
+      , prettyTCM lhs , "reduces to both"
+      , prettyTCM rhs1 , "and" , prettyTCM rhs2
+      , "which are not equal because"
+      , return err
+      ]
+
+    RewriteMaybeNonConfluent lhs1 lhs2 cs -> vcat $ concat
+      [ [ fsep $ concat
+          [ pwords "Couldn't determine overlap between left-hand sides"
+          , [ prettyTCM lhs1 , text "and" , prettyTCM lhs2 ]
+          , pwords "because of unsolved constraints:"
+          ]
+        ]
+      , map (nest 2 . return) cs
+      ]
+
+    RewriteAmbiguousRules lhs rhs1 rhs2 -> vcat
+      [ ( fsep $ concat
+          [ pwords "Global confluence check failed:" , [prettyTCM lhs]
+          , pwords "can be rewritten to either" , [prettyTCM rhs1]
+          , pwords "or" , [prettyTCM rhs2 <> "."]
+          ])
+      , fsep $ concat
+        [ pwords "Possible fix: add a rewrite rule with left-hand side"
+        , [prettyTCM lhs] , pwords "to resolve the ambiguity."
+        ]
+      ]
+
+    RewriteMissingRule u v rhou -> vcat
+      [ fsep $ concat
+        [ pwords "Global confluence check failed:" , [prettyTCM u]
+        , pwords "unfolds to" , [prettyTCM v] , pwords "which should further unfold to"
+        , [prettyTCM rhou] , pwords "but it does not."
+        ]
+      , fsep $ concat
+        [ pwords "Possible fix: add a rule to rewrite"
+        , [ prettyTCM v , "to" , prettyTCM rhou ]
+        ]
+      ]
+
+    PragmaCompileErased bn qn -> fsep $ concat
+      [ pwords "The backend"
+      , [ text bn
+        , "erases"
+        , prettyTCM qn
+        ]
+      , pwords "so the COMPILE pragma will be ignored."
+      ]
+
+    NotInScopeW xs -> vcat
+      [ fsep $ pwords "Not in scope:"
+      , do
+        inscope <- Set.toList . concreteNamesInScope <$> getScope
+        prettyNotInScopeNames True (suggestion inscope) xs
+      ]
+      where
+      suggestion inscope x = nest 2 $ par $ concat
+        [ [ "did you forget space around the ':'?"  | ':' `elem` s ]
+        , [ "did you forget space around the '->'?" | "->" `List.isInfixOf` s ]
+        , maybeToList $ didYouMean inscope C.unqualify x
+        ]
+        where
+        par []  = empty
+        par [d] = parens d
+        par ds  = parens $ vcat ds
+        s = P.prettyShow x
+
+    AsPatternShadowsConstructorOrPatternSynonym patsyn -> fsep $ concat
+      [ pwords "Name bound in @-pattern ignored because it shadows"
+      , if patsyn then pwords "pattern synonym" else [ "constructor" ]
+      ]
+
+    PatternShadowsConstructor x c -> fsep $
+      pwords "The pattern variable" ++ [prettyTCM x] ++
+      pwords "has the same name as the constructor" ++ [prettyTCM c]
+
+    PlentyInHardCompileTimeMode o -> fsep $
+      pwords "Ignored use of" ++ [pretty o] ++
+      pwords "in hard compile-time mode"
+
+    RecordFieldWarning w -> prettyRecordFieldWarning w
+
+    NotAffectedByOpaque -> fwords "Only function definitions can be marked opaque. This definition will be treated as transparent."
+
+    UnfoldTransparentName qn -> fsep $
+      pwords "The name" ++ [prettyTCM qn <> ","] ++ pwords "mentioned by an unfolding clause, does not belong to an opaque block. This has no effect."
+
+    UselessOpaque -> "This `opaque` block has no effect."
+
+    FaceConstraintCannotBeHidden ai -> fsep $
+      pwords "Face constraint patterns cannot be" ++ [ pretty (getHiding ai), "arguments"]
+
+    FaceConstraintCannotBeNamed x -> fsep $
+      pwords "Ignoring name" ++ ["`" <> pretty x <> "`"] ++ pwords "given to face constraint pattern"
+
+{-# SPECIALIZE prettyRecordFieldWarning :: RecordFieldWarning -> TCM Doc #-}
+prettyRecordFieldWarning :: MonadPretty m => RecordFieldWarning -> m Doc
+prettyRecordFieldWarning = \case
+  W.DuplicateFields xrs    -> prettyDuplicateFields $ map fst xrs
+  W.TooManyFields q ys xrs -> prettyTooManyFields q ys $ map fst xrs
+
+prettyDuplicateFields :: MonadPretty m => [C.Name] -> m Doc
+prettyDuplicateFields xs = fsep $ concat
+    [ pwords "Duplicate"
+    , fields xs
+    , punctuate comma (map pretty xs)
+    , pwords "in record"
+    ]
+  where
+  fields ys = P.singPlural ys [text "field"] [text "fields"]
+
+{-# SPECIALIZE prettyTooManyFields :: QName -> [C.Name] -> [C.Name] -> TCM Doc  #-}
+prettyTooManyFields :: MonadPretty m => QName -> [C.Name] -> [C.Name] -> m Doc
+prettyTooManyFields r missing xs = fsep $ concat
+    [ pwords "The record type"
+    , [prettyTCM r]
+    , pwords "does not have the"
+    , fields xs
+    , punctuate comma (map pretty xs)
+    , if null missing then [] else concat
+      [ pwords "but it would have the"
+      , fields missing
+      , punctuate comma (map pretty missing)
+      ]
+    ]
+  where
+  fields ys = P.singPlural ys [text "field"] [text "fields"]
+
+{-# SPECIALIZE prettyNotInScopeNames :: (Pretty a, HasRange a) => Bool -> (a -> TCM Doc) -> [a] -> TCM Doc #-}
+-- | Report a number of names that are not in scope.
+prettyNotInScopeNames
+  :: (MonadPretty m, Pretty a, HasRange a)
+  => Bool          -- ^ Print range?
+  -> (a -> m Doc)  -- ^ Correction suggestion generator.
+  -> [a]           -- ^ Names that are not in scope.
+  -> m Doc
+prettyNotInScopeNames printRange suggestion xs = nest 2 $ vcat $ map name xs
+  where
+  name x = fsep
+    [ pretty x
+    , if printRange then "at" <+> prettyTCM (getRange x) else empty
+    , suggestion x
+    ]
+
+{-# SPECIALIZE didYouMean :: (Pretty a, Pretty b) => [C.QName] -> (a -> b) -> a -> Maybe (TCM Doc) #-}
+-- | Suggest some corrections to a misspelled name.
+didYouMean
+  :: (MonadPretty m, Pretty a, Pretty b)
+  => [C.QName]     -- ^ Names in scope.
+  -> (a -> b)      -- ^ Canonization function for similarity search.
+  -> a             -- ^ A name which is not in scope.
+  -> Maybe (m Doc) -- ^ "did you mean" hint.
+didYouMean inscope canon x
+  | null ys   = Nothing
+  | otherwise = Just $ sep
+      [ "did you mean"
+      , nest 2 (vcat $ punctuate " or" $
+                 map (\ y -> text $ "'" ++ y ++ "'") ys)
+        <> "?"
+      ]
+  where
+  strip :: Pretty b => b -> String
+  strip        = map toLower . filter (/= '_') . prettyShow
+  -- dropModule x = fromMaybe x $ List.stripPrefix "module " x
+  maxDist n    = div n 3
+  close a b    = editDistance a b <= maxDist (length a)
+  ys           = map prettyShow $ filter (close (strip $ canon x) . strip . C.unqualify) inscope
+
+
+prettyTCWarnings :: [TCWarning] -> TCM String
+prettyTCWarnings = fmap (unlines . List.intersperse "" . map P.render) . prettyTCWarnings'
+
+renderTCWarnings' :: [TCWarning] -> TCM [String]
+renderTCWarnings' = fmap (map P.render) . prettyTCWarnings'
+
+prettyTCWarnings' :: [TCWarning] -> TCM [Doc]
+prettyTCWarnings' = traverse prettyTCM . filterTCWarnings
+
+-- | If there are several warnings, remove the unsolved-constraints warning
+-- in case there are no interesting constraints to list.
+filterTCWarnings :: [TCWarning] -> [TCWarning]
+filterTCWarnings = \case
+  -- #4065: Always keep the only warning
+  [w] -> [w]
+  -- Andreas, 2019-09-10, issue #4065:
+  -- If there are several warnings, remove the unsolved-constraints warning
+  -- in case there are no interesting constraints to list.
+  ws  -> (`filter` ws) $ \ w -> case tcWarning w of
+    UnsolvedConstraints cs -> any interestingConstraint cs
+    _ -> True
+
+
+-- | Turns warnings, if any, into errors.
+tcWarningsToError :: [TCWarning] -> TCM ()
+tcWarningsToError mws = case (unsolvedHoles, otherWarnings) of
+   ([], [])                   -> return ()
+   (_unsolvedHoles@(_:_), []) -> typeError SolvedButOpenHoles
+   (_, ws@(_:_))              -> typeError $ NonFatalErrors ws
+   where
+   -- filter out unsolved interaction points for imported module so
+   -- that we get the right error message (see test case Fail/Issue1296)
+   (unsolvedHoles, otherWarnings) = List.partition (isUnsolvedIM . tcWarning) mws
+   isUnsolvedIM UnsolvedInteractionMetas{} = True
+   isUnsolvedIM _                          = False
+
+
+-- | Depending which flags are set, one may happily ignore some
+-- warnings.
+
+applyFlagsToTCWarningsPreserving :: HasOptions m => Set WarningName -> [TCWarning] -> m [TCWarning]
+applyFlagsToTCWarningsPreserving additionalKeptWarnings ws = do
+  -- For some reason some SafeFlagPragma seem to be created multiple times.
+  -- This is a way to collect all of them and remove duplicates.
+  let pragmas w = case tcWarning w of { SafeFlagPragma ps -> ([w], ps); _ -> ([], []) }
+  let sfp = case fmap List.nub (foldMap pragmas ws) of
+              (TCWarning loc r w p b:_, sfp) ->
+                 [TCWarning loc r (SafeFlagPragma sfp) p b]
+              _                        -> []
+
+  pragmaWarnings <- (^. warningSet) . optWarningMode <$> pragmaOptions
+  let warnSet = Set.union pragmaWarnings additionalKeptWarnings
+
+  -- filter out the warnings the flags told us to ignore
+  let cleanUp w = let wName = warningName w in
+        wName /= SafeFlagPragma_
+        && wName `Set.member` warnSet
+        && case w of
+          UnsolvedMetaVariables ums    -> not $ null ums
+          UnsolvedInteractionMetas uis -> not $ null uis
+          UnsolvedConstraints ucs      -> not $ null ucs
+          _                            -> True
+
+  return $ sfp ++ filter (cleanUp . tcWarning) ws
+
+applyFlagsToTCWarnings :: HasOptions m => [TCWarning] -> m [TCWarning]
+applyFlagsToTCWarnings = applyFlagsToTCWarningsPreserving Set.empty
+
+{-# SPECIALIZE isBoundaryConstraint :: ProblemConstraint -> TCM (Maybe Range) #-}
+isBoundaryConstraint :: (ReadTCState m, MonadTCM m) => ProblemConstraint -> m (Maybe Range)
+isBoundaryConstraint c =
+  enterClosure (theConstraint c) $ \case
+    ValueCmp _ _ (MetaV mid xs) y | Just xs <- allApplyElims xs ->
+      fmap g <$> liftTCM (isFaceConstraint mid xs)
+    ValueCmp _ _ y (MetaV mid xs) | Just xs <- allApplyElims xs ->
+      fmap g <$> liftTCM (isFaceConstraint mid xs)
+    _ -> pure Nothing
+  where
+    g (a, _, _, _) = getRange a
+
+{-# SPECIALIZE getAllUnsolvedWarnings :: TCM [TCWarning] #-}
+getAllUnsolvedWarnings :: (MonadFail m, ReadTCState m, MonadWarning m, MonadTCM m) => m [TCWarning]
+getAllUnsolvedWarnings = do
+  unsolvedInteractions <- getUnsolvedInteractionMetas
+
+  allCons <- getAllConstraints
+  unsolvedConstraints  <- filterM (fmap isNothing . isBoundaryConstraint) allCons
+  interactionBoundary  <- catMaybes <$> traverse isBoundaryConstraint allCons
+
+  unsolvedMetas        <- getUnsolvedMetas
+
+  let checkNonEmpty c rs = c rs <$ guard (not $ null rs)
+
+  mapM warning_ $ catMaybes
+                [ checkNonEmpty UnsolvedInteractionMetas  unsolvedInteractions
+                , checkNonEmpty UnsolvedMetaVariables     unsolvedMetas
+                , checkNonEmpty UnsolvedConstraints       unsolvedConstraints
+                , checkNonEmpty InteractionMetaBoundaries interactionBoundary
+                ]
+
+-- | Collect all warnings that have accumulated in the state.
+
+{-# SPECIALIZE getAllWarnings :: WhichWarnings -> TCM [TCWarning] #-}
+getAllWarnings :: (MonadFail m, ReadTCState m, MonadWarning m, MonadTCM m) => WhichWarnings -> m [TCWarning]
+getAllWarnings = getAllWarningsPreserving Set.empty
+
+{-# SPECIALIZE getAllWarningsPreserving :: Set WarningName -> WhichWarnings -> TCM [TCWarning] #-}
+getAllWarningsPreserving ::
+  (MonadFail m, ReadTCState m, MonadWarning m, MonadTCM m) => Set WarningName -> WhichWarnings -> m [TCWarning]
+getAllWarningsPreserving keptWarnings ww = do
+  unsolved            <- getAllUnsolvedWarnings
+  collectedTCWarnings <- useTC stTCWarnings
+
+  let showWarn w = classifyWarning w <= ww &&
+                    not (null unsolved && onlyShowIfUnsolved w)
+
+  fmap (filter (showWarn . tcWarning))
+    $ applyFlagsToTCWarningsPreserving keptWarnings
+    $ reverse $ unsolved ++ collectedTCWarnings
+
+getAllWarningsOfTCErr :: TCErr -> TCM [TCWarning]
+getAllWarningsOfTCErr err = case err of
+  TypeError _ tcst cls -> case clValue cls of
+    NonFatalErrors{} -> return []
+    _ -> localTCState $ do
+      putTC tcst
+      ws <- getAllWarnings AllWarnings
+      -- We filter out the unsolved(Metas/Constraints) to stay
+      -- true to the previous error messages.
+      return $ filter (not . isUnsolvedWarning . tcWarning) ws
+  _ -> return []
diff --git a/src/full/Agda/TypeChecking/Pretty/Warning.hs-boot b/src/full/Agda/TypeChecking/Pretty/Warning.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Pretty/Warning.hs-boot
@@ -0,0 +1,11 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Pretty.Warning where
+
+import Agda.Interaction.Options.Warnings (WarningName)
+import Agda.TypeChecking.Monad.Base
+import {-# SOURCE #-} Agda.TypeChecking.Pretty (MonadPretty)
+import Agda.Syntax.Common.Pretty
+
+prettyWarning :: MonadPretty m => Warning -> m Doc
+prettyWarningName :: MonadPretty m => WarningName -> m Doc
diff --git a/src/full/Agda/TypeChecking/Primitive.hs b/src/full/Agda/TypeChecking/Primitive.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive.hs
@@ -0,0 +1,977 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| Primitive functions, such as addition on builtin integers.
+-}
+
+module Agda.TypeChecking.Primitive
+       ( module Agda.TypeChecking.Primitive.Base
+       , module Agda.TypeChecking.Primitive.Cubical
+       , module Agda.TypeChecking.Primitive
+       ) where
+
+import Data.Char
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Data.Maybe
+import Data.Text (Text)
+import qualified Data.Text as T
+import Data.Word
+
+import qualified Agda.Interaction.Options.Lenses as Lens
+
+import Agda.Syntax.Common hiding (Nat)
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic (TermLike(..))
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Monad hiding (getConstInfo, typeOfConst)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Reduce.Monad as Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Level
+
+import Agda.TypeChecking.Quote (quoteTermWithKit, quoteTypeWithKit, quoteDomWithKit, quotingKit)
+import Agda.TypeChecking.Primitive.Base
+import Agda.TypeChecking.Primitive.Cubical
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.Char
+import Agda.Utils.Float
+import Agda.Utils.List
+import Agda.Utils.Maybe (fromMaybeM)
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- Haskell type to Agda type
+
+newtype Nat = Nat { unNat :: Integer }
+            deriving (Eq, Ord, Num, Enum, Real)
+
+-- In GHC > 7.8 deriving Integral causes an unnecessary toInteger
+-- warning.
+instance Integral Nat where
+  toInteger = unNat
+  quotRem (Nat a) (Nat b) = (Nat q, Nat r)
+    where (q, r) = quotRem a b
+
+instance TermLike Nat where
+  traverseTermM _ = pure
+  foldTerm _      = mempty
+
+instance Pretty Nat where
+  pretty = pretty . toInteger
+
+newtype Lvl = Lvl { unLvl :: Integer }
+  deriving (Eq, Ord)
+
+instance Pretty Lvl where
+  pretty = pretty . unLvl
+
+class PrimType a where
+  primType :: a -> TCM Type
+
+  -- This used to be a catch-all instance `PrimType a => PrimTerm a` which required UndecidableInstances.
+  -- Now we declare the instances separately, but enforce the catch-all-ness with a superclass constraint on PrimTerm.
+  default primType :: PrimTerm a => a -> TCM Type
+  primType _ = el $ primTerm (undefined :: a)
+
+class PrimType a => PrimTerm a where
+  primTerm :: a -> TCM Term
+
+instance (PrimType a, PrimType b) => PrimType (a -> b)
+instance (PrimType a, PrimType b) => PrimTerm (a -> b) where
+  primTerm _ = unEl <$> (primType (undefined :: a) --> primType (undefined :: b))
+
+instance (PrimType a, PrimType b) => PrimType (a, b)
+instance (PrimType a, PrimType b) => PrimTerm (a, b) where
+  primTerm _ = do
+    sigKit <- fromMaybeM (typeError $ NoBindingForBuiltin BuiltinSigma) getSigmaKit
+    let sig = Def (sigmaName sigKit) []
+    a'       <- primType (undefined :: a)
+    b'       <- primType (undefined :: b)
+    Type la  <- pure $ getSort a'
+    Type lb  <- pure $ getSort b'
+    pure sig <#> pure (Level la)
+             <#> pure (Level lb)
+             <@> pure (unEl a')
+             <@> pure (nolam $ unEl b')
+
+instance PrimType Integer
+instance PrimTerm Integer where primTerm _ = primInteger
+
+instance PrimType Word64
+instance PrimTerm Word64  where primTerm _ = primWord64
+
+instance PrimType Bool
+instance PrimTerm Bool    where primTerm _ = primBool
+
+instance PrimType Char
+instance PrimTerm Char    where primTerm _ = primChar
+
+instance PrimType Double
+instance PrimTerm Double  where primTerm _ = primFloat
+
+instance PrimType Text
+instance PrimTerm Text    where primTerm _ = primString
+
+instance PrimType Nat
+instance PrimTerm Nat     where primTerm _ = primNat
+
+instance PrimType Lvl
+instance PrimTerm Lvl     where primTerm _ = primLevel
+
+instance PrimType QName
+instance PrimTerm QName   where primTerm _ = primQName
+
+instance PrimType MetaId
+instance PrimTerm MetaId  where primTerm _ = primAgdaMeta
+
+instance PrimType Type
+instance PrimTerm Type    where primTerm _ = primAgdaTerm
+
+instance PrimType Fixity'
+instance PrimTerm Fixity' where primTerm _ = primFixity
+
+instance PrimTerm a => PrimType [a]
+instance PrimTerm a => PrimTerm [a] where
+  primTerm _ = list (primTerm (undefined :: a))
+
+instance PrimTerm a => PrimType (Maybe a)
+instance PrimTerm a => PrimTerm (Maybe a) where
+  primTerm _ = tMaybe (primTerm (undefined :: a))
+
+instance PrimTerm a => PrimType (IO a)
+instance PrimTerm a => PrimTerm (IO a) where
+  primTerm _ = io (primTerm (undefined :: a))
+
+-- From Agda term to Haskell value
+
+class ToTerm a where
+  toTerm  :: TCM (a -> Term)
+  toTermR :: TCM (a -> ReduceM Term)
+
+  toTermR = (pure .) <$> toTerm
+
+instance ToTerm Nat     where toTerm = return $ Lit . LitNat . toInteger
+instance ToTerm Word64  where toTerm = return $ Lit . LitWord64
+instance ToTerm Lvl     where toTerm = return $ Level . ClosedLevel . unLvl
+instance ToTerm Double  where toTerm = return $ Lit . LitFloat
+instance ToTerm Char    where toTerm = return $ Lit . LitChar
+instance ToTerm Text    where toTerm = return $ Lit . LitString
+instance ToTerm QName   where toTerm = return $ Lit . LitQName
+instance ToTerm MetaId  where
+  toTerm = do
+    top <- fromMaybe __IMPOSSIBLE__ <$> currentTopLevelModule
+    return $ Lit . LitMeta top
+
+instance ToTerm Integer where
+  toTerm = do
+    pos     <- primIntegerPos
+    negsuc  <- primIntegerNegSuc
+    fromNat <- toTerm :: TCM (Nat -> Term)
+    let intToTerm = fromNat . fromIntegral :: Integer -> Term
+    let fromInt n | n >= 0    = apply pos    [defaultArg $ intToTerm n]
+                  | otherwise = apply negsuc [defaultArg $ intToTerm (-n - 1)]
+    return fromInt
+
+instance ToTerm Bool where
+  toTerm = do
+    true  <- primTrue
+    false <- primFalse
+    return $ \b -> if b then true else false
+
+instance ToTerm Term where
+  toTerm  = do kit <- quotingKit; runReduceF (quoteTermWithKit kit)
+  toTermR = do quoteTermWithKit <$> quotingKit;
+
+instance ToTerm (Dom Type) where
+  toTerm  = do kit <- quotingKit; runReduceF (quoteDomWithKit kit)
+  toTermR = do quoteDomWithKit <$> quotingKit
+
+instance ToTerm Type where
+  toTerm  = do kit <- quotingKit; runReduceF (quoteTypeWithKit kit)
+  toTermR = quoteTypeWithKit <$> quotingKit
+
+instance ToTerm ArgInfo where
+  toTerm = do
+    info <- primArgArgInfo
+    vis  <- primVisible
+    hid  <- primHidden
+    ins  <- primInstance
+    rel  <- primRelevant
+    irr  <- primIrrelevant
+    return $ \ i -> info `applys`
+      [ case getHiding i of
+          NotHidden  -> vis
+          Hidden     -> hid
+          Instance{} -> ins
+      , case getRelevance i of
+          Relevant   -> rel
+          Irrelevant -> irr
+          NonStrict  -> rel
+      ]
+
+instance ToTerm Fixity' where
+  toTerm = (. theFixity) <$> toTerm
+
+instance ToTerm Fixity where
+  toTerm = do
+    lToTm  <- toTerm
+    aToTm  <- toTerm
+    fixity <- primFixityFixity
+    return $ \ Fixity{fixityAssoc = a, fixityLevel = l} ->
+      fixity `apply` [defaultArg (aToTm a), defaultArg (lToTm l)]
+
+instance ToTerm Associativity where
+  toTerm = do
+    lassoc <- primAssocLeft
+    rassoc <- primAssocRight
+    nassoc <- primAssocNon
+    return $ \ a ->
+      case a of
+        NonAssoc   -> nassoc
+        LeftAssoc  -> lassoc
+        RightAssoc -> rassoc
+
+instance ToTerm Blocker where
+  toTerm = do
+    all <- primAgdaBlockerAll
+    any <- primAgdaBlockerAny
+    meta <- primAgdaBlockerMeta
+    lists <- buildList
+    metaTm <- toTerm
+    let go (UnblockOnAny xs)    = any `apply` [defaultArg (lists (go <$> Set.toList xs))]
+        go (UnblockOnAll xs)    = all `apply` [defaultArg (lists (go <$> Set.toList xs))]
+        go (UnblockOnMeta m)    = meta `apply` [defaultArg (metaTm m)]
+        go (UnblockOnDef _)     = __IMPOSSIBLE__
+        go (UnblockOnProblem _) = __IMPOSSIBLE__
+    pure go
+
+instance ToTerm FixityLevel where
+  toTerm = do
+    (iToTm :: PrecedenceLevel -> Term) <- toTerm
+    related   <- primPrecRelated
+    unrelated <- primPrecUnrelated
+    return $ \ p ->
+      case p of
+        Unrelated -> unrelated
+        Related n -> related `apply` [defaultArg $ iToTm n]
+
+instance (ToTerm a, ToTerm b) => ToTerm (a, b) where
+  toTerm = do
+    sigKit <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+    let con = Con (sigmaCon sigKit) ConOSystem []
+    fromA <- toTerm
+    fromB <- toTerm
+    pure $ \ (a, b) -> con `apply` map defaultArg [fromA a, fromB b]
+
+-- | @buildList A ts@ builds a list of type @List A@. Assumes that the terms
+--   @ts@ all have type @A@.
+buildList :: TCM ([Term] -> Term)
+buildList = do
+    nil'  <- primNil
+    cons' <- primCons
+    let nil       = nil'
+        cons x xs = cons' `applys` [x, xs]
+    return $ foldr cons nil
+
+instance ToTerm a => ToTerm [a] where
+  toTerm = do
+    mkList <- buildList
+    fromA  <- toTerm
+    return $ mkList . map fromA
+
+instance ToTerm a => ToTerm (Maybe a) where
+  toTerm = do
+    nothing <- primNothing
+    just    <- primJust
+    fromA   <- toTerm
+    return $ maybe nothing (apply1 just . fromA)
+
+-- From Haskell value to Agda term
+
+type FromTermFunction a = Arg Term ->
+                          ReduceM (Reduced (MaybeReduced (Arg Term)) a)
+
+class FromTerm a where
+  fromTerm :: TCM (FromTermFunction a)
+
+instance FromTerm Integer where
+  fromTerm = do
+    Con pos _    [] <- primIntegerPos
+    Con negsuc _ [] <- primIntegerNegSuc
+    toNat         <- fromTerm :: TCM (FromTermFunction Nat)
+    return $ \ v -> do
+      b <- reduceB' v
+      let v'  = ignoreBlocking b
+          arg = (<$ v')
+      case unArg (ignoreBlocking b) of
+        Con c ci [Apply u]
+          | c == pos    ->
+            redBind (toNat u)
+              (\ u' -> notReduced $ arg $ Con c ci [Apply $ ignoreReduced u']) $ \ n ->
+            redReturn $ fromIntegral n
+          | c == negsuc ->
+            redBind (toNat u)
+              (\ u' -> notReduced $ arg $ Con c ci [Apply $ ignoreReduced u']) $ \ n ->
+            redReturn $ fromIntegral $ -n - 1
+        _ -> return $ NoReduction (reduced b)
+
+instance FromTerm Nat where
+  fromTerm = fromLiteral $ \case
+    LitNat n -> Just $ fromInteger n
+    _ -> Nothing
+
+instance FromTerm Word64 where
+  fromTerm = fromLiteral $ \ case
+    LitWord64 n -> Just n
+    _ -> Nothing
+
+instance FromTerm Lvl where
+  fromTerm = fromReducedTerm $ \case
+    Level (ClosedLevel n) -> Just $ Lvl n
+    _ -> Nothing
+
+instance FromTerm Double where
+  fromTerm = fromLiteral $ \case
+    LitFloat x -> Just x
+    _ -> Nothing
+
+instance FromTerm Char where
+  fromTerm = fromLiteral $ \case
+    LitChar c -> Just c
+    _ -> Nothing
+
+instance FromTerm Text where
+  fromTerm = fromLiteral $ \case
+    LitString s -> Just s
+    _ -> Nothing
+
+instance FromTerm QName where
+  fromTerm = fromLiteral $ \case
+    LitQName x -> Just x
+    _ -> Nothing
+
+instance FromTerm MetaId where
+  fromTerm = fromLiteral $ \case
+    LitMeta _ x -> Just x
+    _ -> Nothing
+
+instance FromTerm Bool where
+    fromTerm = do
+        true  <- primTrue
+        false <- primFalse
+        fromReducedTerm $ \case
+            t   | t =?= true  -> Just True
+                | t =?= false -> Just False
+                | otherwise   -> Nothing
+        where
+            a =?= b = a === b
+            Def x [] === Def y []   = x == y
+            Con x _ [] === Con y _ [] = x == y
+            Var n [] === Var m []   = n == m
+            _        === _          = False
+
+instance (ToTerm a, FromTerm a) => FromTerm [a] where
+  fromTerm = do
+    nil   <- isCon <$> primNil
+    cons  <- isCon <$> primCons
+    toA   <- fromTerm
+    mkList nil cons toA <$> toTerm
+    where
+      isCon (Lam _ b)   = isCon $ absBody b
+      isCon (Con c _ _) = c
+      isCon v           = __IMPOSSIBLE__
+
+      mkList nil cons toA fromA t = do
+        b <- reduceB' t
+        let t = ignoreBlocking b
+        let arg = (<$ t)
+        case unArg t of
+          Con c ci []
+            | c == nil  -> return $ YesReduction NoSimplification []
+          Con c ci es
+            | c == cons, Just [x,xs] <- allApplyElims es ->
+              redBind (toA x)
+                  (\x' -> notReduced $ arg $ Con c ci (map Apply [ignoreReduced x',xs])) $ \y ->
+              redBind
+                  (mkList nil cons toA fromA xs)
+                  (fmap $ \xs' -> arg $ Con c ci (map Apply [defaultArg $ fromA y, xs'])) $ \ys ->
+              redReturn (y : ys)
+          _ -> return $ NoReduction (reduced b)
+
+instance FromTerm a => FromTerm (Maybe a) where
+  fromTerm = do
+    nothing <- isCon <$> primNothing
+    just    <- isCon <$> primJust
+    toA     <- fromTerm
+    return $ \ t -> do
+      let arg = (<$ t)
+      b <- reduceB' t
+      let t = ignoreBlocking b
+      case unArg t of
+        Con c ci []
+          | c == nothing -> return $ YesReduction NoSimplification Nothing
+        Con c ci es
+          | c == just, Just [x] <- allApplyElims es ->
+            redBind (toA x)
+              (\ x' -> notReduced $ arg $ Con c ci [Apply (ignoreReduced x')])
+              (redReturn . Just)
+        _ -> return $ NoReduction (reduced b)
+
+    where
+      isCon (Lam _ b)   = isCon $ absBody b
+      isCon (Con c _ _) = c
+      isCon v           = __IMPOSSIBLE__
+
+
+fromReducedTerm :: (Term -> Maybe a) -> TCM (FromTermFunction a)
+fromReducedTerm f = return $ \t -> do
+    b <- reduceB' t
+    case f $ unArg (ignoreBlocking b) of
+        Just x  -> return $ YesReduction NoSimplification x
+        Nothing -> return $ NoReduction (reduced b)
+
+fromLiteral :: (Literal -> Maybe a) -> TCM (FromTermFunction a)
+fromLiteral f = fromReducedTerm $ \case
+    Lit lit -> f lit
+    _       -> Nothing
+
+-- | @mkPrimInjective@ takes two Set0 @a@ and @b@ and a function @f@ of type
+--   @a -> b@ and outputs a primitive internalizing the fact that @f@ is injective.
+mkPrimInjective :: Type -> Type -> QName -> TCM PrimitiveImpl
+mkPrimInjective a b qn = do
+  -- Define the type
+  eqName <- primEqualityName
+  let lvl0     = ClosedLevel 0
+  let eq a t u = El (Type lvl0) <$> pure (Def eqName []) <#> pure (Level lvl0)
+                                <#> pure (unEl a) <@> t <@> u
+  let f    = pure (Def qn [])
+  ty <- nPi "t" (pure a) $ nPi "u" (pure a) $
+              (eq b (f <@> varM 1) (f <@> varM 0))
+          --> (eq a (      varM 1) (      varM 0))
+
+    -- Get the constructor corresponding to BUILTIN REFL
+  refl <- getRefl
+
+  -- Implementation: when the equality argument reduces to refl so does the primitive.
+  -- If the user want the primitive to reduce whenever the two values are equal (no
+  -- matter whether the equality is refl), they can combine it with @eraseEquality@.
+  return $ PrimImpl ty $ primFun __IMPOSSIBLE__ 3 $ \ ts -> do
+    let t  = headWithDefault __IMPOSSIBLE__ ts
+    let eq = unArg $ fromMaybe __IMPOSSIBLE__ $ lastMaybe ts
+    reduce' eq >>= \case
+      Con{} -> redReturn $ refl t
+      _     -> return $ NoReduction $ map notReduced ts
+
+-- | Converts 'MetaId's to natural numbers.
+
+metaToNat :: MetaId -> Nat
+metaToNat m =
+  fromIntegral (moduleNameHash $ metaModule m) * 2 ^ 64 +
+  fromIntegral (metaId m)
+
+primMetaToNatInjective :: TCM PrimitiveImpl
+primMetaToNatInjective = do
+  meta  <- primType (undefined :: MetaId)
+  nat   <- primType (undefined :: Nat)
+  toNat <- primFunName <$> getPrimitive PrimMetaToNat
+  mkPrimInjective meta nat toNat
+
+primCharToNatInjective :: TCM PrimitiveImpl
+primCharToNatInjective = do
+  char  <- primType (undefined :: Char)
+  nat   <- primType (undefined :: Nat)
+  toNat <- primFunName <$> getPrimitive PrimCharToNat
+  mkPrimInjective char nat toNat
+
+primStringToListInjective :: TCM PrimitiveImpl
+primStringToListInjective = do
+  string <- primType (undefined :: Text)
+  chars  <- primType (undefined :: String)
+  toList <- primFunName <$> getPrimitive PrimStringToList
+  mkPrimInjective string chars toList
+
+primStringFromListInjective :: TCM PrimitiveImpl
+primStringFromListInjective = do
+  chars  <- primType (undefined :: String)
+  string <- primType (undefined :: Text)
+  fromList <- primFunName <$> getPrimitive PrimStringFromList
+  mkPrimInjective chars string fromList
+
+primWord64ToNatInjective :: TCM PrimitiveImpl
+primWord64ToNatInjective =  do
+  word  <- primType (undefined :: Word64)
+  nat   <- primType (undefined :: Nat)
+  toNat <- primFunName <$> getPrimitive PrimWord64ToNat
+  mkPrimInjective word nat toNat
+
+primFloatToWord64Injective :: TCM PrimitiveImpl
+primFloatToWord64Injective = do
+  float  <- primType (undefined :: Double)
+  mword  <- primType (undefined :: Maybe Word64)
+  toWord <- primFunName <$> getPrimitive PrimFloatToWord64
+  mkPrimInjective float mword toWord
+
+primQNameToWord64sInjective :: TCM PrimitiveImpl
+primQNameToWord64sInjective = do
+  name    <- primType (undefined :: QName)
+  words   <- primType (undefined :: (Word64, Word64))
+  toWords <- primFunName <$> getPrimitive PrimQNameToWord64s
+  mkPrimInjective name words toWords
+
+getRefl :: TCM (Arg Term -> Term)
+getRefl = do
+  -- BUILTIN REFL maybe a constructor with one (the principal) argument or only parameters.
+  -- Get the ArgInfo of the principal argument of refl.
+  con@(Con rf ci []) <- primRefl
+  minfo <- fmap (setOrigin Inserted) <$> getReflArgInfo rf
+  pure $ case minfo of
+    Just ai -> Con rf ci . (:[]) . Apply . setArgInfo ai
+    Nothing -> const con
+
+-- | @primEraseEquality : {a : Level} {A : Set a} {x y : A} -> x ≡ y -> x ≡ y@
+primEraseEquality :: TCM PrimitiveImpl
+primEraseEquality = do
+  -- primEraseEquality is incompatible with --without-K
+  -- We raise an error warning if --safe is set and a mere warning otherwise
+  whenM withoutKOption $
+    ifM (Lens.getSafeMode <$> commandLineOptions)
+      {- then -} (warning SafeFlagWithoutKFlagPrimEraseEquality)
+      {- else -} (warning WithoutKFlagPrimEraseEquality)
+  -- Get the name and type of BUILTIN EQUALITY
+  eq   <- primEqualityName
+  eqTy <- defType <$> getConstInfo eq
+  -- E.g. @eqTy = eqTel → Set a@ where @eqTel = {a : Level} {A : Set a} (x y : A)@.
+  TelV eqTel eqCore <- telView eqTy
+  let eqSort = case unEl eqCore of
+        Sort s -> s
+        _      -> __IMPOSSIBLE__
+
+  -- Construct the type of primEraseEquality, e.g.
+  -- @{a : Level} {A : Set a} {x y : A} → eq {a} {A} x y -> eq {a} {A} x y@.
+  t <- let xeqy = pure $ El eqSort $ Def eq $ map Apply $ teleArgs eqTel in
+       telePi_ (fmap hide eqTel) <$> (xeqy --> xeqy)
+
+  -- Get the constructor corresponding to BUILTIN REFL
+  refl <- getRefl
+
+  -- The implementation of primEraseEquality:
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ (1 + size eqTel) $ \ ts -> do
+    let (u, v) = fromMaybe __IMPOSSIBLE__ $ last2 =<< initMaybe ts
+    -- Andreas, 2013-07-22.
+    -- Note that we cannot call the conversion checker here,
+    -- because 'reduce' might be called in a context where
+    -- some bound variables do not have a type (just __DUMMY_TYPE__),
+    -- and the conversion checker for eliminations does not
+    -- like this.
+    -- We can only do untyped equality, e.g., by normalisation.
+    (u', v') <- normalise' (u, v)
+    if u' == v' then redReturn $ refl u else
+      return $ NoReduction $ map notReduced ts
+
+-- | Get the 'ArgInfo' of the principal argument of BUILTIN REFL.
+--
+--   Returns @Nothing@ for e.g.
+--   @
+--     data Eq {a} {A : Set a} (x : A) : A → Set a where
+--       refl : Eq x x
+--   @
+--
+--   Returns @Just ...@ for e.g.
+--   @
+--     data Eq {a} {A : Set a} : (x y : A) → Set a where
+--       refl : ∀ x → Eq x x
+--   @
+
+getReflArgInfo :: ConHead -> TCM (Maybe ArgInfo)
+getReflArgInfo rf = do
+  def <- getConInfo rf
+  TelV reflTel _ <- telView $ defType def
+  return $ fmap getArgInfo $ listToMaybe $ drop (conPars $ theDef def) $ telToList reflTel
+
+
+-- | Used for both @primForce@ and @primForceLemma@.
+genPrimForce :: TCM Type -> (Term -> Arg Term -> Term) -> TCM PrimitiveImpl
+genPrimForce b ret = do
+  let varEl s a = El (varSort s) <$> a
+      varT s a  = varEl s (varM a)
+      varS s    = pure $ sort $ varSort s
+  t <- hPi "a" (el primLevel) $
+       hPi "b" (el primLevel) $
+       hPi "A" (varS 1) $
+       hPi "B" (varT 2 0 --> varS 1) b
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 6 $ \ ts ->
+    case ts of
+      [a, b, s, t, u, f] -> do
+        u <- reduceB' u
+        let isWHNF Blocked{} = return False
+            isWHNF (NotBlocked _ u) =
+              case unArg u of
+                Lit{}      -> return True
+                Con{}      -> return True
+                Lam{}      -> return True
+                Pi{}       -> return True
+                Sort{}     -> return True  -- sorts and levels are considered whnf
+                Level{}    -> return True
+                DontCare{} -> return True
+                Def q _    -> do
+                  def <- theDef <$> getConstInfo q
+                  return $ case def of
+                    Datatype{} -> True
+                    Record{}   -> True
+                    _          -> False
+                Var{}      -> return False
+                MetaV{}    -> __IMPOSSIBLE__
+                Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+        ifM (isWHNF u)
+            (redReturn $ ret (unArg f) (ignoreBlocking u))
+            (return $ NoReduction $ map notReduced [a, b, s, t] ++ [reduced u, notReduced f])
+      _ -> __IMPOSSIBLE__
+
+primForce :: TCM PrimitiveImpl
+primForce = do
+  let varEl s a = El (varSort s) <$> a
+      varT s a  = varEl s (varM a)
+  genPrimForce (nPi "x" (varT 3 1) $
+                nPi "y" (varT 4 2) (varEl 4 $ varM 2 <@> varM 0) -->
+                varEl 3 (varM 1 <@> varM 0)) $
+    \ f u -> apply f [u]
+
+primForceLemma :: TCM PrimitiveImpl
+primForceLemma = do
+  let varEl s a = El (varSort s) <$> a
+      varT s a  = varEl s (varM a)
+  refl  <- primRefl
+  force <- primFunName <$> getPrimitive PrimForce
+  genPrimForce (nPi "x" (varT 3 1) $
+                nPi "f" (nPi "y" (varT 4 2) $ varEl 4 $ varM 2 <@> varM 0) $
+                varEl 4 $ primEquality <#> varM 4 <#> (varM 2 <@> varM 1)
+                                       <@> (pure (Def force []) <#> varM 5 <#> varM 4 <#> varM 3 <#> varM 2 <@> varM 1 <@> varM 0)
+                                       <@> (varM 0 <@> varM 1)
+               ) $ \ _ _ -> refl
+
+mkPrimLevelZero :: TCM PrimitiveImpl
+mkPrimLevelZero = do
+  t <- primType (undefined :: Lvl)
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 0 $ \_ -> redReturn $ Level $ ClosedLevel 0
+
+mkPrimLevelSuc :: TCM PrimitiveImpl
+mkPrimLevelSuc = do
+  t <- primType (id :: Lvl -> Lvl)
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 1 $ \ ~[a] -> do
+    l <- levelView' $ unArg a
+    redReturn $ Level $ levelSuc l
+
+mkPrimLevelMax :: TCM PrimitiveImpl
+mkPrimLevelMax = do
+  t <- primType (max :: Op Lvl)
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 2 $ \ ~[a, b] -> do
+    a' <- levelView' $ unArg a
+    b' <- levelView' $ unArg b
+    redReturn $ Level $ levelLub a' b'
+
+primLockUniv' :: TCM PrimitiveImpl
+primLockUniv' = do
+  let t = sort $ Type $ levelSuc $ Max 0 []
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 0 $ \_ -> redReturn $ Sort LockUniv
+
+mkPrimFun1TCM :: (FromTerm a, ToTerm b) =>
+                 TCM Type -> (a -> ReduceM b) -> TCM PrimitiveImpl
+mkPrimFun1TCM mt f = do
+    toA   <- fromTerm
+    fromB <- toTermR
+    t     <- mt
+    return $ PrimImpl t $ primFun __IMPOSSIBLE__ 1 $ \ts ->
+      case ts of
+        [v] ->
+          redBind (toA v) singleton $ \ x -> do
+            b <- fromB =<< f x
+            case allMetas Set.singleton b of
+              ms | Set.null ms -> redReturn b
+                 | otherwise   -> return $ NoReduction [reduced (Blocked (unblockOnAllMetas ms) v)]
+        _ -> __IMPOSSIBLE__
+
+-- Tying the knot
+mkPrimFun1 :: (PrimType a, FromTerm a, PrimType b, ToTerm b) =>
+              (a -> b) -> TCM PrimitiveImpl
+mkPrimFun1 f = do
+    toA   <- fromTerm
+    fromB <- toTerm
+    t     <- primType f
+    return $ PrimImpl t $ primFun __IMPOSSIBLE__ 1 $ \ts ->
+      case ts of
+        [v] ->
+          redBind (toA v) singleton $ \ x ->
+          redReturn $ fromB $ f x
+        _ -> __IMPOSSIBLE__
+
+mkPrimFun2 :: ( PrimType a, FromTerm a, ToTerm a
+              , PrimType b, FromTerm b
+              , PrimType c, ToTerm c ) =>
+              (a -> b -> c) -> TCM PrimitiveImpl
+mkPrimFun2 f = do
+    toA   <- fromTerm
+    fromA <- toTerm
+    toB   <- fromTerm
+    fromC <- toTerm
+    t     <- primType f
+    return $ PrimImpl t $ primFun __IMPOSSIBLE__ 2 $ \ts ->
+      case ts of
+        [v,w] ->
+          redBind (toA v)
+              (\v' -> [v', notReduced w]) $ \x ->
+          redBind (toB w)
+              (\w' -> [ reduced $ notBlocked $ Arg (argInfo v) (fromA x)
+                      , w']) $ \y ->
+          redReturn $ fromC $ f x y
+        _ -> __IMPOSSIBLE__
+
+mkPrimFun3 :: ( PrimType a, FromTerm a, ToTerm a
+              , PrimType b, FromTerm b, ToTerm b
+              , PrimType c, FromTerm c
+              , PrimType d, ToTerm d ) =>
+              (a -> b -> c -> d) -> TCM PrimitiveImpl
+mkPrimFun3 f = do
+    (toA, fromA) <- (,) <$> fromTerm <*> toTerm
+    (toB, fromB) <- (,) <$> fromTerm <*> toTerm
+    toC          <- fromTerm
+    fromD        <- toTerm
+    t <- primType f
+    return $ PrimImpl t $ primFun __IMPOSSIBLE__ 3 $ \ts ->
+      let argFrom fromX a x =
+            reduced $ notBlocked $ Arg (argInfo a) (fromX x)
+      in case ts of
+        [a,b,c] ->
+          redBind (toA a)
+              (\a' -> [a', notReduced b, notReduced c]) $ \x ->
+          redBind (toB b)
+              (\b' -> [argFrom fromA a x, b', notReduced c]) $ \y ->
+          redBind (toC c)
+              (\c' -> [ argFrom fromA a x, argFrom fromB b y, c']) $ \z ->
+          redReturn $ fromD $ f x y z
+        _ -> __IMPOSSIBLE__
+
+mkPrimFun4 :: ( PrimType a, FromTerm a, ToTerm a
+              , PrimType b, FromTerm b, ToTerm b
+              , PrimType c, FromTerm c, ToTerm c
+              , PrimType d, FromTerm d
+              , PrimType e, ToTerm e ) =>
+              (a -> b -> c -> d -> e) -> TCM PrimitiveImpl
+mkPrimFun4 f = do
+    (toA, fromA) <- (,) <$> fromTerm <*> toTerm
+    (toB, fromB) <- (,) <$> fromTerm <*> toTerm
+    (toC, fromC) <- (,) <$> fromTerm <*> toTerm
+    toD          <- fromTerm
+    fromE        <- toTerm
+    t <- primType f
+    return $ PrimImpl t $ primFun __IMPOSSIBLE__ 4 $ \ts ->
+      let argFrom fromX a x =
+            reduced $ notBlocked $ Arg (argInfo a) (fromX x)
+      in case ts of
+        [a,b,c,d] ->
+          redBind (toA a)
+              (\a' -> a' : map notReduced [b,c,d]) $ \x ->
+          redBind (toB b)
+              (\b' -> [argFrom fromA a x, b', notReduced c, notReduced d]) $ \y ->
+          redBind (toC c)
+              (\c' -> [ argFrom fromA a x
+                      , argFrom fromB b y
+                      , c', notReduced d]) $ \z ->
+          redBind (toD d)
+              (\d' -> [ argFrom fromA a x
+                      , argFrom fromB b y
+                      , argFrom fromC c z
+                      , d']) $ \w ->
+
+          redReturn $ fromE $ f x y z w
+        _ -> __IMPOSSIBLE__
+
+
+---------------------------------------------------------------------------
+-- * The actual primitive functions
+---------------------------------------------------------------------------
+
+type Op   a = a -> a -> a
+type Fun  a = a -> a
+type Rel  a = a -> a -> Bool
+type Pred a = a -> Bool
+
+primitiveFunctions :: Map PrimitiveId (TCM PrimitiveImpl)
+primitiveFunctions = localTCStateSavingWarnings <$> Map.fromListWith __IMPOSSIBLE__
+  -- Issue #4375          ^^^^^^^^^^^^^^^^^^^^^^^^^^
+  --   Without this the next fresh checkpoint id gets changed building the primitive functions. This
+  --   is bad for caching since it happens when scope checking import declarations (rebinding
+  --   primitives). During type checking, the caching machinery might then load a cached state with
+  --   out-of-date checkpoint ids. Make sure to preserve warnings though, since they include things
+  --   like using unsafe things primitives with `--safe`.
+
+  -- Ulf, 2015-10-28: Builtin integers now map to a datatype, and since you
+  -- can define these functions (reasonably) efficiently using the primitive
+  -- functions on natural numbers there's no need for them anymore. Keeping the
+  -- show function around for convenience, and as a test case for a primitive
+  -- function taking an integer.
+  -- -- Integer functions
+  -- [ "primIntegerPlus"     |-> mkPrimFun2 ((+)        :: Op Integer)
+  -- , "primIntegerMinus"    |-> mkPrimFun2 ((-)        :: Op Integer)
+  -- , "primIntegerTimes"    |-> mkPrimFun2 ((*)        :: Op Integer)
+  -- , "primIntegerDiv"      |-> mkPrimFun2 (div        :: Op Integer)    -- partial
+  -- , "primIntegerMod"      |-> mkPrimFun2 (mod        :: Op Integer)    -- partial
+  -- , "primIntegerEquality" |-> mkPrimFun2 ((==)       :: Rel Integer)
+  -- , "primIntegerLess"     |-> mkPrimFun2 ((<)        :: Rel Integer)
+  -- , "primIntegerAbs"      |-> mkPrimFun1 (Nat . abs  :: Integer -> Nat)
+  -- , "primNatToInteger"    |-> mkPrimFun1 (toInteger  :: Nat -> Integer)
+  [ PrimShowInteger     |-> mkPrimFun1 (T.pack . prettyShow :: Integer -> Text)
+
+  -- Natural number functions
+  , PrimNatPlus           |-> mkPrimFun2 ((+)                     :: Op Nat)
+  , PrimNatMinus          |-> mkPrimFun2 ((\x y -> max 0 (x - y)) :: Op Nat)
+  , PrimNatTimes          |-> mkPrimFun2 ((*)                     :: Op Nat)
+  , PrimNatDivSucAux      |-> mkPrimFun4 ((\k m n j -> k + div (max 0 $ n + m - j) (m + 1)) :: Nat -> Nat -> Op Nat)
+  , PrimNatModSucAux      |->
+      let aux :: Nat -> Nat -> Op Nat
+          aux k m n j | n > j     = mod (n - j - 1) (m + 1)
+                      | otherwise = k + n
+      in mkPrimFun4 aux
+  , PrimNatEquality       |-> mkPrimFun2 ((==) :: Rel Nat)
+  , PrimNatLess           |-> mkPrimFun2 ((<)  :: Rel Nat)
+  , PrimShowNat           |-> mkPrimFun1 (T.pack . prettyShow :: Nat -> Text)
+
+  -- -- Machine words
+  , PrimWord64ToNat      |-> mkPrimFun1 (fromIntegral :: Word64 -> Nat)
+  , PrimWord64FromNat    |-> mkPrimFun1 (fromIntegral :: Nat -> Word64)
+  , PrimWord64ToNatInjective |-> primWord64ToNatInjective
+
+  -- -- Level functions
+  , PrimLevelZero         |-> mkPrimLevelZero
+  , PrimLevelSuc          |-> mkPrimLevelSuc
+  , PrimLevelMax          |-> mkPrimLevelMax
+
+  -- Floating point functions
+  --
+  -- Wen, 2020-08-26: Primitives which convert from Float into other, more
+  -- well-behaved numeric types should check for unrepresentable values, e.g.,
+  -- NaN and the infinities, and return `nothing` if those are encountered, to
+  -- ensure that the returned numbers are sensible. That means `primFloatRound`,
+  -- `primFloatFloor`, `primFloatCeiling`, and `primFloatDecode`. The conversion
+  -- `primFloatRatio` represents NaN as (0,0), and the infinities as (±1,0).
+  --
+  , PrimFloatEquality            |-> mkPrimFun2 doubleEq
+  , PrimFloatInequality          |-> mkPrimFun2 doubleLe
+  , PrimFloatLess                |-> mkPrimFun2 doubleLt
+  , PrimFloatIsInfinite          |-> mkPrimFun1 (isInfinite :: Double -> Bool)
+  , PrimFloatIsNaN               |-> mkPrimFun1 (isNaN :: Double -> Bool)
+  , PrimFloatIsNegativeZero      |-> mkPrimFun1 (isNegativeZero :: Double -> Bool)
+  , PrimFloatIsSafeInteger       |-> mkPrimFun1 isSafeInteger
+  , PrimFloatToWord64            |-> mkPrimFun1 doubleToWord64
+  , PrimFloatToWord64Injective   |-> primFloatToWord64Injective
+  , PrimNatToFloat               |-> mkPrimFun1 (intToDouble :: Nat -> Double)
+  , PrimIntToFloat               |-> mkPrimFun1 (intToDouble :: Integer -> Double)
+  , PrimFloatRound               |-> mkPrimFun1 doubleRound
+  , PrimFloatFloor               |-> mkPrimFun1 doubleFloor
+  , PrimFloatCeiling             |-> mkPrimFun1 doubleCeiling
+  , PrimFloatToRatio             |-> mkPrimFun1 doubleToRatio
+  , PrimRatioToFloat             |-> mkPrimFun2 ratioToDouble
+  , PrimFloatDecode              |-> mkPrimFun1 doubleDecode
+  , PrimFloatEncode              |-> mkPrimFun2 doubleEncode
+  , PrimShowFloat                |-> mkPrimFun1 (T.pack . show :: Double -> Text)
+  , PrimFloatPlus                |-> mkPrimFun2 doublePlus
+  , PrimFloatMinus               |-> mkPrimFun2 doubleMinus
+  , PrimFloatTimes               |-> mkPrimFun2 doubleTimes
+  , PrimFloatNegate              |-> mkPrimFun1 doubleNegate
+  , PrimFloatDiv                 |-> mkPrimFun2 doubleDiv
+  , PrimFloatPow                 |-> mkPrimFun2 doublePow
+  , PrimFloatSqrt                |-> mkPrimFun1 doubleSqrt
+  , PrimFloatExp                 |-> mkPrimFun1 doubleExp
+  , PrimFloatLog                 |-> mkPrimFun1 doubleLog
+  , PrimFloatSin                 |-> mkPrimFun1 doubleSin
+  , PrimFloatCos                 |-> mkPrimFun1 doubleCos
+  , PrimFloatTan                 |-> mkPrimFun1 doubleTan
+  , PrimFloatASin                |-> mkPrimFun1 doubleASin
+  , PrimFloatACos                |-> mkPrimFun1 doubleACos
+  , PrimFloatATan                |-> mkPrimFun1 doubleATan
+  , PrimFloatATan2               |-> mkPrimFun2 doubleATan2
+  , PrimFloatSinh                |-> mkPrimFun1 doubleSinh
+  , PrimFloatCosh                |-> mkPrimFun1 doubleCosh
+  , PrimFloatTanh                |-> mkPrimFun1 doubleTanh
+  , PrimFloatASinh               |-> mkPrimFun1 doubleASinh
+  , PrimFloatACosh               |-> mkPrimFun1 doubleCosh
+  , PrimFloatATanh               |-> mkPrimFun1 doubleTanh
+
+  -- Character functions
+  , PrimCharEquality         |-> mkPrimFun2 ((==) :: Rel Char)
+  , PrimIsLower              |-> mkPrimFun1 isLower
+  , PrimIsDigit              |-> mkPrimFun1 isDigit
+  , PrimIsAlpha              |-> mkPrimFun1 isAlpha
+  , PrimIsSpace              |-> mkPrimFun1 isSpace
+  , PrimIsAscii              |-> mkPrimFun1 isAscii
+  , PrimIsLatin1             |-> mkPrimFun1 isLatin1
+  , PrimIsPrint              |-> mkPrimFun1 isPrint
+  , PrimIsHexDigit           |-> mkPrimFun1 isHexDigit
+  , PrimToUpper              |-> mkPrimFun1 toUpper
+  , PrimToLower              |-> mkPrimFun1 toLower
+  , PrimCharToNat            |-> mkPrimFun1 (fromIntegral . fromEnum :: Char -> Nat)
+  , PrimCharToNatInjective   |-> primCharToNatInjective
+  , PrimNatToChar            |-> mkPrimFun1 (integerToChar . unNat)
+  , PrimShowChar             |-> mkPrimFun1 (T.pack . prettyShow . LitChar)
+
+  -- String functions
+  , PrimStringToList              |-> mkPrimFun1 T.unpack
+  , PrimStringToListInjective     |-> primStringToListInjective
+  , PrimStringFromList            |-> mkPrimFun1 T.pack
+  , PrimStringFromListInjective   |-> primStringFromListInjective
+  , PrimStringAppend              |-> mkPrimFun2 (T.append :: Text -> Text -> Text)
+  , PrimStringEquality            |-> mkPrimFun2 ((==) :: Rel Text)
+  , PrimShowString                |-> mkPrimFun1 (T.pack . prettyShow . LitString)
+  , PrimStringUncons              |-> mkPrimFun1 T.uncons
+
+  -- Other stuff
+  , PrimEraseEquality     |-> primEraseEquality
+    -- This needs to be force : A → ((x : A) → B x) → B x rather than seq because of call-by-name.
+  , PrimForce             |-> primForce
+  , PrimForceLemma        |-> primForceLemma
+  , PrimQNameEquality     |-> mkPrimFun2 ((==) :: Rel QName)
+  , PrimQNameLess         |-> mkPrimFun2 ((<) :: Rel QName)
+  , PrimShowQName         |-> mkPrimFun1 (T.pack . prettyShow :: QName -> Text)
+  , PrimQNameFixity       |-> mkPrimFun1 (nameFixity . qnameName)
+  , PrimQNameToWord64s    |-> mkPrimFun1 ((\ (NameId x (ModuleNameHash y)) -> (x, y)) . nameId . qnameName
+                                          :: QName -> (Word64, Word64))
+  , PrimQNameToWord64sInjective   |-> primQNameToWord64sInjective
+  , PrimMetaEquality      |-> mkPrimFun2 ((==) :: Rel MetaId)
+  , PrimMetaLess          |-> mkPrimFun2 ((<) :: Rel MetaId)
+  , PrimShowMeta          |-> mkPrimFun1 (T.pack . prettyShow :: MetaId -> Text)
+  , PrimMetaToNat         |-> mkPrimFun1 metaToNat
+  , PrimMetaToNatInjective   |-> primMetaToNatInjective
+
+  , PrimIMin              |-> primIMin'
+  , PrimIMax              |-> primIMax'
+  , PrimINeg              |-> primINeg'
+  , PrimPOr               |-> primPOr
+  , PrimComp              |-> primComp
+  , PrimTrans             |-> primTrans'
+  , PrimHComp             |-> primHComp'
+  , PrimPartial           |-> primPartial'
+  , PrimPartialP          |-> primPartialP'
+  , PrimGlue              |-> primGlue'
+  , Prim_glue             |-> prim_glue'
+  , Prim_unglue           |-> prim_unglue'
+  , PrimFaceForall        |-> primFaceForall'
+  , PrimDepIMin           |-> primDepIMin'
+  , PrimIdFace            |-> primIdFace'
+  , PrimIdPath            |-> primIdPath'
+  , PrimIdElim            |-> primIdElim'
+  , PrimSubOut            |-> primSubOut'
+  , PrimConId             |-> primConId'
+  , Prim_glueU            |-> prim_glueU'
+  , Prim_unglueU          |-> prim_unglueU'
+  , PrimLockUniv          |-> primLockUniv'
+  ]
+  where
+    (|->) = (,)
diff --git a/src/full/Agda/TypeChecking/Primitive.hs-boot b/src/full/Agda/TypeChecking/Primitive.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive.hs-boot
@@ -0,0 +1,9 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Primitive where
+
+import Data.Map (Map)
+import Agda.TypeChecking.Monad.Base
+import Agda.Syntax.Builtin (PrimitiveId)
+
+primitiveFunctions :: Map PrimitiveId (TCM PrimitiveImpl)
diff --git a/src/full/Agda/TypeChecking/Primitive/Base.hs b/src/full/Agda/TypeChecking/Primitive/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Base.hs
@@ -0,0 +1,239 @@
+{-# LANGUAGE ApplicativeDo #-}
+
+module Agda.TypeChecking.Primitive.Base where
+
+import Control.Monad             ( mzero )
+import Control.Monad.Fail        ( MonadFail )
+  -- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Trans.Maybe ( MaybeT(..), runMaybeT )
+
+import qualified Data.Map as Map
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Names
+import {-# SOURCE #-} Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce ( reduce )
+import Agda.TypeChecking.Monad.Signature
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.Maybe
+import Agda.Syntax.Common.Pretty ( prettyShow )
+
+-- Type combinators
+
+infixr 4 -->
+infixr 4 .-->
+infixr 4 ..-->
+
+(-->), (.-->), (..-->) :: Applicative m => m Type -> m Type -> m Type
+a --> b = garr id a b
+a .--> b = garr (const $ Irrelevant) a b
+a ..--> b = garr (const $ NonStrict) a b
+
+garr :: Applicative m => (Relevance -> Relevance) -> m Type -> m Type -> m Type
+garr f a b = do
+  a' <- a
+  b' <- b
+  pure $ El (funSort (getSort a') (getSort b')) $
+    Pi (mapRelevance f $ defaultDom a') (NoAbs "_" b')
+
+gpi :: (MonadAddContext m, MonadDebug m)
+    => ArgInfo -> String -> m Type -> m Type -> m Type
+gpi info name a b = do
+  a <- a
+  let dom :: Dom Type
+      dom = defaultNamedArgDom info name a
+  b <- addContext (name, dom) b
+  let y = stringToArgName name
+  return $ El (mkPiSort dom (Abs y b))
+              (Pi dom (Abs y b))
+
+hPi, nPi :: (MonadAddContext m, MonadDebug m)
+         => String -> m Type -> m Type -> m Type
+hPi = gpi $ setHiding Hidden defaultArgInfo
+nPi = gpi defaultArgInfo
+
+hPi', nPi' :: (MonadFail m, MonadAddContext m, MonadDebug m)
+           => String -> NamesT m Type -> (NamesT m Term -> NamesT m Type) -> NamesT m Type
+hPi' s a b = hPi s a (bind' s (\ x -> b x))
+nPi' s a b = nPi s a (bind' s (\ x -> b x))
+
+{-# INLINABLE pPi' #-}
+pPi' :: (MonadAddContext m, HasBuiltins m, MonadDebug m)
+     => String -> NamesT m Term -> (NamesT m Term -> NamesT m Type) -> NamesT m Type
+pPi' n phi b = toFinitePi <$> nPi' n (elSSet $ cl isOne <@> phi) b
+ where
+   isOne = fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinIsOne
+
+-- | Turn a 'Pi' type into one whose domain is annotated finite, i.e.,
+-- one that represents a @Partial@ element rather than an actual
+-- function.
+toFinitePi :: Type -> Type
+toFinitePi (El s (Pi d b)) = El s $ Pi
+  (setRelevance Irrelevant $ d { domIsFinite = True })
+  b
+toFinitePi _ = __IMPOSSIBLE__
+
+el' :: Applicative m => m Term -> m Term -> m Type
+el' l a = El <$> (tmSort <$> l) <*> a
+
+els :: Applicative m => m Sort -> m Term -> m Type
+els l a = El <$> l <*> a
+
+el's :: Applicative m => m Term -> m Term -> m Type
+el's l a = El <$> (SSet . atomicLevel <$> l) <*> a
+
+elInf :: Functor m => m Term -> m Type
+elInf t = (El (Inf UType 0) <$> t)
+
+elSSet :: Functor m => m Term -> m Type
+elSSet t = (El (SSet $ ClosedLevel 0) <$> t)
+
+nolam :: Term -> Term
+nolam = Lam defaultArgInfo . NoAbs "_"
+
+varM :: Applicative m => Int -> m Term
+varM = pure . var
+
+infixl 9 <@>, <#>
+
+gApply :: Applicative m => Hiding -> m Term -> m Term -> m Term
+gApply h a b = gApply' (setHiding h defaultArgInfo) a b
+
+gApply' :: Applicative m => ArgInfo -> m Term -> m Term -> m Term
+gApply' info a b = do
+    x <- a
+    y <- b
+    pure $ x `apply` [Arg info y]
+
+(<@>),(<#>),(<..>) :: Applicative m => m Term -> m Term -> m Term
+(<@>) = gApply NotHidden
+(<#>) = gApply Hidden
+(<..>) = gApply' (setRelevance Irrelevant defaultArgInfo)
+
+(<@@>) :: Applicative m => m Term -> (m Term,m Term,m Term) -> m Term
+t <@@> (x,y,r) = do
+  t <- t
+  x <- x
+  y <- y
+  r <- r
+  pure $ t `applyE` [IApply x y r]
+
+list :: TCM Term -> TCM Term
+list t = primList <@> t
+
+tMaybe :: TCM Term -> TCM Term
+tMaybe t = primMaybe <@> t
+
+io :: TCM Term -> TCM Term
+io t = primIO <@> t
+
+path :: TCM Term -> TCM Term
+path t = primPath <@> t
+
+el :: Functor m => m Term -> m Type
+el t = El (mkType 0) <$> t
+
+-- | The universe @Set0@ as a type.
+tset :: Applicative m => m Type
+tset = pure $ sort (mkType 0)
+
+-- | @SizeUniv@ as a sort.
+sSizeUniv :: Sort
+sSizeUniv = SizeUniv
+
+-- | @SizeUniv@ as a type.
+tSizeUniv :: Applicative m => m Type
+tSizeUniv = pure $ sort sSizeUniv
+
+tLevelUniv :: Applicative m => m Type
+tLevelUniv = pure $ sort $ LevelUniv
+
+-- | Abbreviation: @argN = 'Arg' 'defaultArgInfo'@.
+argN :: e -> Arg e
+argN = Arg defaultArgInfo
+
+domN :: e -> Dom e
+domN = defaultDom
+
+-- | Abbreviation: @argH = 'hide' 'Arg' 'defaultArgInfo'@.
+argH :: e -> Arg e
+argH = Arg $ setHiding Hidden defaultArgInfo
+
+domH :: e -> Dom e
+domH = setHiding Hidden . defaultDom
+
+---------------------------------------------------------------------------
+-- * Accessing the primitive functions
+---------------------------------------------------------------------------
+
+lookupPrimitiveFunction :: PrimitiveId -> TCM PrimitiveImpl
+lookupPrimitiveFunction x =
+  fromMaybe (do
+                reportSDoc "tc.prim" 20 $ "Lookup of primitive function" <+> pretty x <+> "failed"
+                typeError $ NoSuchPrimitiveFunction (getBuiltinId x))
+            (Map.lookup x primitiveFunctions)
+
+lookupPrimitiveFunctionQ :: QName -> TCM (PrimitiveId, PrimitiveImpl)
+lookupPrimitiveFunctionQ q = do
+  let s = prettyShow (nameCanonical $ qnameName q)
+  case primitiveById s of
+    Nothing -> typeError $ NoSuchPrimitiveFunction s
+    Just s -> do
+      PrimImpl t pf <- lookupPrimitiveFunction s
+      return (s, PrimImpl t $ pf { primFunName = q })
+
+getBuiltinName :: (HasBuiltins m, MonadReduce m) => BuiltinId -> m (Maybe QName)
+getBuiltinName b = runMaybeT $ getQNameFromTerm =<< MaybeT (getBuiltin' b)
+
+-- | Convert a name in 'Term' form back to 'QName'.
+--
+getQNameFromTerm :: MonadReduce m => Term -> MaybeT m QName
+getQNameFromTerm v = do
+    v <- reduce v
+    case unSpine v of
+      Def x _   -> return x
+      Con x _ _ -> return $ conName x
+      Lam _ b   -> getQNameFromTerm $ unAbs b
+      _ -> mzero
+
+isBuiltin :: (HasBuiltins m, MonadReduce m) => QName -> BuiltinId -> m Bool
+isBuiltin q b = (Just q ==) <$> getBuiltinName b
+
+------------------------------------------------------------------------
+-- * Builtin Sigma
+------------------------------------------------------------------------
+
+data SigmaKit = SigmaKit
+  { sigmaName :: QName
+  , sigmaCon  :: ConHead
+  , sigmaFst  :: QName
+  , sigmaSnd  :: QName
+  }
+  deriving (Eq,Show)
+
+getSigmaKit :: (HasBuiltins m, HasConstInfo m) => m (Maybe SigmaKit)
+getSigmaKit = do
+  ms <- getBuiltinName' builtinSigma
+  case ms of
+    Nothing -> return Nothing
+    Just sigma -> do
+      def <- theDef <$> getConstInfo sigma
+      case def of
+        Record { recFields = [fst,snd], recConHead = con } -> do
+          return . Just $ SigmaKit
+            { sigmaName = sigma
+            , sigmaCon  = con
+            , sigmaFst  = unDom fst
+            , sigmaSnd  = unDom snd
+            }
+        _ -> __IMPOSSIBLE__  -- This invariant is ensured in bindBuiltinSigma
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical.hs b/src/full/Agda/TypeChecking/Primitive/Cubical.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical.hs
@@ -0,0 +1,1313 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# LANGUAGE TypeFamilies #-}
+
+module Agda.TypeChecking.Primitive.Cubical
+  ( module Agda.TypeChecking.Primitive.Cubical
+  , module Agda.TypeChecking.Primitive.Cubical.Id
+  , module Agda.TypeChecking.Primitive.Cubical.Base
+  , module Agda.TypeChecking.Primitive.Cubical.Glue
+  , module Agda.TypeChecking.Primitive.Cubical.HCompU
+  )
+  where
+
+import Prelude hiding (null, (!!))
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans ( lift )
+import Control.Exception
+
+import Data.String ()
+
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import qualified Data.List as List
+import Data.Foldable hiding (null)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import qualified Agda.Syntax.Common.Pretty as P
+
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Primitive.Base
+import Agda.TypeChecking.Monad
+
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+
+import Agda.Utils.Impossible
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.Tuple
+import Agda.Utils.Size
+import Agda.Utils.BoolSet (BoolSet)
+import qualified Agda.Utils.BoolSet as BoolSet
+
+import Agda.TypeChecking.Primitive.Cubical.HCompU
+import Agda.TypeChecking.Primitive.Cubical.Glue
+import Agda.TypeChecking.Primitive.Cubical.Base
+import Agda.TypeChecking.Primitive.Cubical.Id
+
+primPOr :: TCM PrimitiveImpl
+primPOr = do
+  requireCubical CErased ""
+  t    <- runNamesT [] $
+          hPi' "a" (els (pure LevelUniv) (cl primLevel))    $ \ a  ->
+          nPi' "i" primIntervalType $ \ i  ->
+          nPi' "j" primIntervalType $ \ j  ->
+          hPi' "A" (pPi' "o" (imax i j) $ \o -> el' (cl primLevelSuc <@> a) (Sort . tmSort <$> a)) $ \ bA ->
+          ((pPi' "i1" i $ \ i1 -> el' a $ bA <..> (cl primIsOne1 <@> i <@> j <@> i1))) -->
+          ((pPi' "j1" j $ \ j1 -> el' a $ bA <..> (cl primIsOne2 <@> i <@> j <@> j1))) -->
+          pPi' "o" (imax i j) (\ o -> el' a $ bA <..> o)
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 6 $ \ ts -> do
+    case ts of
+     [l,i,j,a,u,v] -> do
+       si <- reduceB' i
+       vi <- intervalView $ unArg $ ignoreBlocking si
+       case vi of
+        IOne -> redReturn (unArg u)
+        IZero -> redReturn (unArg v)
+        _ -> do
+          sj <- reduceB' j
+          vj <- intervalView $ unArg $ ignoreBlocking sj
+          case vj of
+            IOne -> redReturn (unArg v)
+            IZero -> redReturn (unArg u)
+            _ -> return $ NoReduction [notReduced l,reduced si,reduced sj,notReduced a,notReduced u,notReduced v]
+
+
+     _ -> __IMPOSSIBLE__
+
+primPartial' :: TCM PrimitiveImpl
+primPartial' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+       hPi' "a" (els (pure LevelUniv) (cl primLevel)) (\ a ->
+        nPi' "φ" primIntervalType $ \ _ ->
+        nPi' "A" (sort . tmSort <$> a) $ \ bA ->
+        (sort . tmSSort <$> a))
+  isOne <- primIsOne
+  v <- runNamesT [] $
+        lam "a" $ \ l ->
+        lam "φ" $ \ phi ->
+        lam "A" $ \ a ->
+        unEl <$> pPi' "p" phi (\_ -> el' l a)
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 0 $ \ _ -> redReturn v
+
+primPartialP' :: TCM PrimitiveImpl
+primPartialP' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+       hPi' "a" (els (pure LevelUniv) (cl primLevel)) (\ a ->
+        nPi' "φ" primIntervalType $ \ phi ->
+        nPi' "A" (pPi' "o" phi $ \ _ -> el' (cl primLevelSuc <@> a) (Sort . tmSort <$> a)) $ \ bA ->
+        (sort . tmSSort <$> a))
+  v <- runNamesT [] $
+        lam "a" $ \ l ->
+        lam "φ" $ \ phi ->
+        lam "A" $ \ a ->
+        unEl <$> pPi' "p" phi (\ p -> el' l (a <@> p))
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 0 $ \ _ -> redReturn v
+
+primSubOut' :: TCM PrimitiveImpl
+primSubOut' = do
+  requireCubical CErased ""
+  t    <- runNamesT [] $
+          hPi' "a" (els (pure LevelUniv) (cl primLevel)) $ \ a ->
+          hPi' "A" (el' (cl primLevelSuc <@> a) (Sort . tmSort <$> a)) $ \ bA ->
+          hPi' "φ" primIntervalType $ \ phi ->
+          hPi' "u" (el's a $ cl primPartial <#> a <@> phi <@> bA) $ \ u ->
+          el's a (cl primSub <#> a <@> bA <@> phi <@> u) --> el' a bA
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 5 $ \ ts -> do
+    case ts of
+      [a,bA,phi,u,x] -> do
+        view <- intervalView'
+        sphi <- reduceB' phi
+        case view $ unArg $ ignoreBlocking sphi of
+          IOne -> redReturn =<< (return (unArg u) <..> getTerm (getBuiltinId PrimSubOut) BuiltinItIsOne)
+          _ -> do
+            sx <- reduceB' x
+            mSubIn <- getBuiltinName' builtinSubIn
+            case unArg $ ignoreBlocking $ sx of
+              Def q [_,_,_, Apply t] | Just q == mSubIn -> redReturn (unArg t)
+              _ -> return $ NoReduction $ map notReduced [a,bA] ++ [reduced sphi, notReduced u, reduced sx]
+      _ -> __IMPOSSIBLE__
+
+primTrans' :: TCM PrimitiveImpl
+primTrans' = do
+  requireCubical CErased ""
+  t    <- runNamesT [] $
+          hPi' "a" (primIntervalType --> els (pure LevelUniv) (cl primLevel)) $ \ a ->
+          nPi' "A" (nPi' "i" primIntervalType $ \ i -> (sort . tmSort <$> (a <@> i))) $ \ bA ->
+          nPi' "φ" primIntervalType $ \ phi ->
+          (el' (a <@> cl primIZero) (bA <@> cl primIZero) --> el' (a <@> cl primIOne) (bA <@> cl primIOne))
+  return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 4 [] $ \ts nelims -> do
+    primTransHComp DoTransp ts nelims
+
+primHComp' :: TCM PrimitiveImpl
+primHComp' = do
+  requireCubical CErased ""
+  t    <- runNamesT [] $
+          hPi' "a" (els (pure LevelUniv) (cl primLevel)) $ \ a ->
+          hPi' "A" (sort . tmSort <$> a) $ \ bA ->
+          hPi' "φ" primIntervalType $ \ phi ->
+          nPi' "i" primIntervalType (\ i -> pPi' "o" phi $ \ _ -> el' a bA) -->
+          (el' a bA --> el' a bA)
+  let occs = [Mixed, StrictPos, Mixed, StrictPos, StrictPos]
+  return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 5 occs $ \ts nelims -> do
+    primTransHComp DoHComp ts nelims
+
+-- | Construct a helper for CCHM composition, with a string indicating
+-- what function uses it.
+mkComp :: forall m. HasBuiltins m
+       => String
+       -> NamesT m (NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term)
+mkComp s = do
+  let getTermLocal :: IsBuiltin a => a -> NamesT m Term
+      getTermLocal = getTerm s
+  tIMax  <- getTermLocal builtinIMax
+  tINeg  <- getTermLocal builtinINeg
+  tHComp <- getTermLocal builtinHComp
+  tTrans <- getTermLocal builtinTrans
+  iz     <- getTermLocal builtinIZero
+  io     <- getTermLocal builtinIOne
+
+  let
+    forward la bA r u = pure tTrans
+      <#> (lam "i" $ \i -> la <@> (i `imax` r))
+      <@> (lam "i" $ \i -> bA <@> (i `imax` r))
+      <@> r
+      <@> u
+
+  pure $ \la bA phi u u0 ->
+    pure tHComp <#> (la <@> pure io) <#> (bA <@> pure io) <#> phi
+                <@> lam "i" (\i -> ilam "o" $ \o ->
+                        forward la bA i (u <@> i <..> o))
+                <@> forward la bA (pure iz) u0
+
+-- | Construct an application of buitlinComp. Use instead of 'mkComp' if
+-- reducing directly to hcomp + transport would be problematic.
+mkCompLazy
+  :: HasBuiltins m
+  => String
+  -> NamesT m (NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term)
+mkCompLazy s = do
+  let getTermLocal = getTerm s
+  tComp <- getTermLocal builtinComp
+  pure $ \la bA phi u u0 -> pure tComp <#> la <#> bA <#> phi <@> u <@> u0
+
+-- | Implementation of Kan operations for Pi types. The implementation
+-- of @transp@ and @hcomp@ for Pi types has many commonalities, so most
+-- of it is shared between the two cases.
+doPiKanOp
+  :: KanOperation -- ^ Are we composing or transporting?
+  -> ArgName      -- ^ Name of the binder
+  -> FamilyOrNot (Dom Type, Abs Type)
+  -- ^ The domain and codomain of the Pi type.
+  -> ReduceM (Maybe Term)
+doPiKanOp cmd t ab = do
+  let getTermLocal :: IsBuiltin a => a -> ReduceM Term
+      getTermLocal = getTerm $ kanOpName cmd ++ " for function types"
+  tTrans <- getTermLocal builtinTrans
+  tHComp <- getTermLocal builtinHComp
+  tINeg <- getTermLocal builtinINeg
+  tIMax <- getTermLocal builtinIMax
+  iz    <- getTermLocal builtinIZero
+
+  -- We must guarantee that the codomain is a fibrant type, i.e. one
+  -- that supports hcomp and transp. Otherwise, what are we even doing!
+  let
+    toLevel' t = do
+      s <- reduce $ getSort t
+      case s of
+        Type l -> return (Just l)
+        _      -> return Nothing
+    -- But this case is actually impossible:
+    toLevel t = fromMaybe __IMPOSSIBLE__ <$> toLevel' t
+
+  caseMaybeM (toLevel' . absBody . snd . famThing $ ab) (return Nothing) $ \ _ -> do
+  runNamesT [] $ do
+
+    -- When doing transport in Pi types, we need to distinguish a couple
+    -- of different cases depending on the sort of the domain, since
+    -- there are a couple of different possibilities for how we end up
+    -- with a fibrant Pi type:
+    trFibrantDomain <- do
+      let
+        (x, f) = case ab of
+          IsFam (a, _) -> (a, \ a -> runNames [] $ lam "i" (const (pure a)))
+          IsNot (a, _) -> (a, id)
+      s <- reduce $ getSort x
+      case s of
+        -- We're looking at a fibrant Pi with fibrant domain: Transport
+        -- backwards along the domain.
+        Type lx -> do
+          [la, bA] <- mapM (open . f) [Level lx, unEl . unDom $ x]
+          pure $ Just $ \iOrNot phi a0 ->
+            pure tTrans <#> lam "j" (\j -> la <@> iOrNot j)
+              <@> lam "j" (\ j -> bA <@> iOrNot j)
+              <@> phi
+              <@> a0
+
+        -- We're looking a fibrant Pi whose domain is a lock: No need to do anything.
+        LockUniv -> return $ Just $ \_ _ a0 -> a0
+
+        -- We're looking at an unmarked path type. Make sure that the
+        -- domain is actually the interval before continuing without an
+        -- adjustment, though!
+        IntervalUniv -> do
+          x' <- reduceB $ unDom x
+          mInterval <- getBuiltinName' builtinInterval
+          case unEl $ ignoreBlocking x' of
+            Def q [] | Just q == mInterval -> return $ Just $ \_ _ a0 -> a0
+            _ -> return Nothing
+
+        _ -> return Nothing
+
+    caseMaybe trFibrantDomain (return Nothing) $ \trA -> Just <$> do
+    [phi, u0] <- mapM (open . unArg) [ignoreBlocking (kanOpCofib cmd), kanOpBase cmd]
+
+    glam (getArgInfo (fst $ famThing ab)) (absName $ snd $ famThing ab) $ \u1 -> do
+      case (cmd, ab) of
+
+        -- hcomp u u0 x = hcomp (λ i o → u i o x) (u0 x). Short and sweet :)
+        (HCompOp _ u _, IsNot (a , b)) -> do
+          bT <- (raise 1 b `absApp`) <$> u1
+          u <- open (raise 1 (unArg u))
+          pure tHComp
+            <#> (Level <$> toLevel bT)
+            <#> pure (unEl bT)
+            <#> phi
+            <@> lam "i" (\ i -> ilam "o" $ \ o -> gApply (getHiding a) (u <@> i <..> o) u1)
+            <@> gApply (getHiding a) u0 u1
+
+        -- transp (λ i → (a : A i) → B i x) φ f u1 =
+        --  transp (λ i → B i (transp (λ j → A (i ∨ ~ j)) (φ ∨ i) x)) φ
+        --    (f (transp (λ j → A (~ j) φ x)))
+        (TranspOp _ _, IsFam (a , b)) -> do
+          -- trA is a function of three arguments which builds the
+          -- transport fillers in the opposite direction, hence its
+          -- first argument is called "iOrNot" where it's relevant.
+          let
+            -- Γ , u1 : A[i1] , i : I
+            v i = trA (imax i . ineg) (imax phi i) u1
+            bB v = consS v (liftS 1 $ raiseS 1) `applySubst`
+              (absBody b {- Γ , i : I , x : A[i] -})
+
+            -- Compute B @0 v, in the right scope
+            tLam = Lam defaultArgInfo
+
+          -- We know how to substitute v into B, but it's open in a
+          -- variable, so we close over it here:
+          bT <- bind "i" $ \ x -> fmap bB . v $ x
+
+          pure tTrans
+            <#> (tLam <$> traverse (fmap Level . toLevel) bT)
+            <@> (pure . tLam $ unEl <$> bT)
+            <@> phi
+            <@> gApply (getHiding a) u0 (v (pure iz))
+
+        (_, _) -> __IMPOSSIBLE_VERBOSE__ "Invalid Kan operation in doPiKanOp"
+
+-- | Compute Kan operations in a type of dependent paths.
+doPathPKanOp
+  :: KanOperation
+  -> FamilyOrNot (Arg Term)
+  -> FamilyOrNot (Arg Term, Arg Term, Arg Term)
+  -> ReduceM (Reduced MaybeReducedArgs Term)
+doPathPKanOp (HCompOp phi u u0) (IsNot l) (IsNot (bA,x,y)) = do
+  let getTermLocal = getTerm "primHComp for path types"
+  tHComp <- getTermLocal builtinHComp
+
+  redReturn <=< runNamesT [] $ do
+    [l, u, u0, phi, bA, x, y] <- mapM (open . unArg) [l, u, u0, ignoreBlocking phi, bA, x, y]
+
+    -- hcomp in path spaces is simply hcomp in the underlying space, but
+    -- fixing the endpoints at (j ∨ ~ j) in the new direction to those
+    -- in the Path type.
+    lam "j" $ \ j ->
+      pure tHComp <#> l <#> (bA <@> j) <#> (phi `imax` (ineg j `imax` j))
+        <@> lam "i'" (\i -> combineSys l (bA <@> i)
+          [ (phi,    ilam "o" (\ o -> u <@> i <..> o <@@> (x, y, j)))
+          , (j,      ilam "o" (const y))
+          , (ineg j, ilam "o" (const x)) ])
+        <@> (u0 <@@> (x, y, j))
+
+doPathPKanOp (TranspOp phi u0) (IsFam l) (IsFam (bA,x,y)) = do
+  let getTermLocal = getTerm "transport for path types"
+  iz <- getTermLocal builtinIZero
+  io <- getTermLocal builtinIOne
+
+  -- Transport in path types becomes /CCHM/ composition in the
+  -- underlying line of spaces. The intuition is that not only do we
+  -- have to fix the endpoints (using composition) but also actually
+  -- transport. CCHM composition conveniently does that for us!
+  --
+  -- Γ ⊢ l : I → Level
+  --     l is already a function "coming in"
+  -- Γ, i ⊢ bA   : Type (l i)
+  -- Γ, i ⊢ x, y : bA
+  -- Γ ⊢ u0 : PathP (A/i0) (x/i0) (y/i0)
+  -- Γ, φ ⊢ bA constant
+  --
+  --   transp {l} (λ i → PathP A x y) φ p = λ j →
+  --      comp {λ i → l j} (λ i → A i j) (φ ∨ j ∨ ~ j) λ i where
+  --        (φ = i1 ∨ i = i0) → p j
+  --        (j = i0)          → x i
+  --        (j = i1)          → y i
+  --   : PathP A/i1 x/i1 y/i1
+
+  redReturn <=< runNamesT [] $ do
+    -- In reality to avoid a round-trip between primComp we use mkComp
+    -- here.
+    comp <- mkComp $ "transport for path types"
+    [l, u0, phi] <- traverse (open . unArg) [l, u0, ignoreBlocking phi]
+    [bA, x, y] <- mapM (\ a -> open . runNames [] $ lam "i" (const (pure $ unArg a))) [bA, x, y]
+    -- Γ ⊢ bA : (i : I) → Type (l i)
+    -- Γ ⊢ x, y : (i : I) → bA i
+
+    lam "j" $ \ j ->
+      comp l (lam "i" $ \ i -> bA <@> i <@> j) (phi `imax` (ineg j `imax` j))
+        (lam "i'" $ \i -> combineSys (l <@> i) (bA <@> i <@> j)
+          [ (phi, ilam "o" (\o -> u0 <@@> (x <@> pure iz, y <@> pure iz, j)))
+          -- Note that here we have lines of endpoints, which we must
+          -- apply to fix the endpoints:
+          , (j,      ilam "_" (const (y <@> i)))
+          , (ineg j, ilam "_" (const (x <@> i)))
+          ])
+        (u0 <@@> (x <@> pure iz, y <@> pure iz, j))
+doPathPKanOp a0 _ _ = __IMPOSSIBLE__
+
+redReturnNoSimpl :: a -> ReduceM (Reduced a' a)
+redReturnNoSimpl = pure . YesReduction NoSimplification
+
+primTransHComp :: Command -> [Arg Term] -> Int -> ReduceM (Reduced MaybeReducedArgs Term)
+primTransHComp cmd ts nelims = do
+  (l,bA,phi,u,u0) <- pure $ case (cmd,ts) of
+    (DoTransp, [l, bA, phi, u0]) -> (IsFam l, IsFam bA, phi, Nothing, u0)
+    (DoHComp, [l, bA, phi, u, u0]) -> (IsNot l, IsNot bA, phi, Just u, u0)
+    _ -> __IMPOSSIBLE__
+  sphi <- reduceB' phi
+  vphi <- intervalView $ unArg $ ignoreBlocking sphi
+  let clP s = getTerm "primTransHComp" s
+
+  -- WORK
+  case vphi of
+    -- When φ = i1, we know what to do! These cases are counted as
+    -- simplifications.
+    IOne -> redReturn =<< case cmd of
+      DoHComp -> runNamesT [] $ do
+        -- If we're composing, then we definitely had a partial element
+        -- to extend. But now it's just a total element, so we can
+        -- just.. return it:
+        u <- open $ unArg $ fromMaybe __IMPOSSIBLE__ u
+        u <@> clP builtinIOne <..> clP builtinItIsOne
+      DoTransp ->
+        -- Otherwise we're in the constant part of the line to transport
+        -- over, so we must return the argument unchanged.
+        pure $ unArg u0
+
+    _ -> do
+    let
+      fallback' sc = do
+        -- Possibly optimise the partial element to reduce the size of
+        -- hcomps:
+        u' <- case cmd of
+          DoHComp -> (:[]) <$> case vphi of
+            -- If φ=i0 then tabulating equality for Partial φ A
+            -- guarantees that u = is constantly isOneEmpty,
+            -- regardless of how big the original term is, and
+            -- isOneEmpty is *tiny*, so let's use that:
+            IZero -> fmap (reduced . notBlocked . argN) . runNamesT [] $ do
+                [l,c] <- mapM (open . unArg) [famThing l, ignoreBlocking sc]
+                lam "i" $ \ i -> clP builtinIsOneEmpty <#> l <#> ilam "o" (\ _ -> c)
+
+            -- Otherwise we have some interesting formula (though
+            -- definitely not IOne!) and we have to keep the partial
+            -- element as-is.
+            _ -> pure $ notReduced $ fromMaybe __IMPOSSIBLE__ u
+          DoTransp -> return []
+
+        pure . NoReduction $ [notReduced (famThing l), reduced sc, reduced sphi] ++ u' ++ [notReduced u0]
+
+    -- Reduce the type whose Kan operations we're composing over:
+    sbA <- reduceB' bA
+    t <- case unArg <$> ignoreBlocking sbA of
+      IsFam (Lam _ t) -> Just . fmap IsFam <$> reduceB' (absBody t)
+      IsFam _         -> pure Nothing
+      IsNot t         -> pure . Just . fmap IsNot $ (t <$ sbA)
+
+    case t of
+      -- If we don't have a grasp of the Kan operations then at least we
+      -- can reuse the work we did for reducing the type later.
+      Nothing -> fallback' (famThing <$> sbA)
+      Just st  -> do
+        -- Similarly, if we're stuck for another reason, we can reuse
+        -- the work for reducing the family.
+        let
+          fallback = fallback' (fmap famThing $ st *> sbA)
+          t = ignoreBlocking st
+          operation = case cmd of
+            DoTransp -> TranspOp { kanOpCofib = sphi, kanOpBase = u0 }
+            DoHComp -> HCompOp
+              { kanOpCofib = sphi, kanOpSides = fromMaybe __IMPOSSIBLE__ u, kanOpBase = u0 }
+
+        mHComp <- getPrimitiveName' builtinHComp
+        mGlue <- getPrimitiveName' builtinGlue
+        mId   <- getBuiltinName' builtinId
+        pathV <- pathView'
+
+        -- By cases on the family, determine what Kan operation we defer
+        -- to:
+        case famThing t of
+          -- Metavariables are stuck
+          MetaV m _ -> fallback' (fmap famThing $ blocked_ m *> sbA)
+
+          -- TODO: absName t instead of "i"
+          Pi a b
+            -- For Π types, we prefer to keep the Kan operations around,
+            -- so only actually reduce if we applied them to a nonzero
+            -- positive of eliminations
+            | nelims > 0 -> maybe fallback redReturn =<< doPiKanOp operation "i" ((a, b) <$ t)
+            | otherwise -> fallback
+
+          -- For Type, we have two possibilities:
+          Sort (Type l)
+            -- transp (λ i → Type _) φ is always the identity function.
+            | DoTransp <- cmd -> redReturn $ unArg u0
+            -- hcomp {Type} is actually a normal form! This is the
+            -- "HCompU" optimisation; We do not use Glue for hcomp in
+            -- the universe.
+            | DoHComp <- cmd -> fallback
+
+          -- Glue types have their own implementation of Kan operations
+          -- which are implemented in a different module:
+          Def q [Apply la, Apply lb, Apply bA, Apply phi', Apply bT, Apply e] | Just q == mGlue -> do
+            maybe fallback redReturn =<< doGlueKanOp
+              operation ((la, lb, bA, phi', bT, e) <$ t) Head
+
+          -- Formal homogeneous compositions in the universe: Our family
+          -- is @hcomp {A = Type l}@, so we defer to the implementation
+          -- of Kan operations for HCompU implemented above.
+          Def q [Apply _, Apply s, Apply phi', Apply bT, Apply bA]
+            | Just q == mHComp, Sort (Type la) <- unArg s  -> do
+            maybe fallback redReturn =<< doHCompUKanOp
+              operation ((Level la <$ s, phi', bT, bA) <$ t) Head
+
+          -- PathP types have the same optimisation as for Pi types:
+          -- Only compute the Kan operation if there's >0 eliminations.
+          d | PathType _ _ _ bA x y <- pathV (El __DUMMY_SORT__ d) -> do
+            if nelims > 0 then doPathPKanOp operation l ((bA, x, y) <$ t) else fallback
+
+          -- Identity types:
+          Def q [Apply _ , Apply bA , Apply x , Apply y] | Just q == mId -> do
+            maybe fallback return =<< doIdKanOp operation l ((bA, x, y) <$ t)
+
+          Def q es -> do
+            info <- getConstInfo q
+            let
+              lam_i = Lam defaultArgInfo . Abs "i"
+
+              -- When should Kan operations on a record value reduce?
+              doR r@Record{recEtaEquality' = eta} = case theEtaEquality eta of
+                -- If it's a no-eta, pattern-matching record, then the
+                -- Kan operations behave as they do for data types; Only
+                -- reduce when the base is a constructor
+                NoEta PatternMatching -> case unArg u0 of
+                  Con{} -> True
+                  _ -> False
+                -- For every other case, we can reduce into a value
+                -- defined by copatterns; However, this would expose the
+                -- internal name of transp/hcomp when printed, so hold
+                -- off until there are projections.
+                _ -> nelims > 0
+              doR _ = False
+
+            -- Record and data types have their own implementations of
+            -- the Kan operations, which get generated as part of their
+            -- definition.
+            case theDef info of
+              r@Record{recComp = kit, recEtaEquality' = eta}
+                | doR r, Just as <- allApplyElims es, DoTransp <- cmd, Just transpR <- nameOfTransp kit ->
+                  -- Optimisation: If the record has no parameters then we can ditch the transport.
+                  if recPars r == 0
+                     then redReturn $ unArg u0
+                     else redReturn $ Def transpR [] `apply` (map (fmap lam_i) as ++ [ignoreBlocking sphi, u0])
+
+                -- Records know how to hcomp themselves:
+                | doR r, Just as <- allApplyElims es, DoHComp <- cmd, Just hCompR <- nameOfHComp kit ->
+                  redReturn $ Def hCompR [] `apply` (as ++ [ignoreBlocking sphi, fromMaybe __IMPOSSIBLE__ u,u0])
+
+                -- If this is a record with no fields, then compData
+                -- will know what to do with it:
+                | Just as <- allApplyElims es, [] <- recFields r -> compData Nothing False (recPars r) cmd l (as <$ t) sbA sphi u u0
+
+              -- For data types, if this data type is indexed and/or a
+              -- higher inductive type, then hcomp is normal; But
+              -- compData knows what to do for the general cases.
+              Datatype{dataPars = pars, dataIxs = ixs, dataPathCons = pcons, dataTransp = mtrD}
+                | and [null pcons && ixs == 0 | DoHComp  <- [cmd]], Just as <- allApplyElims es ->
+                  compData mtrD ((not $ null $ pcons) || ixs > 0) (pars + ixs) cmd l (as <$ t) sbA sphi u u0
+
+              -- Is this an axiom with constrant transport? Then. Well. Transport is constant.
+              Axiom constTransp | constTransp, [] <- es, DoTransp <- cmd -> redReturn $ unArg u0
+
+              _          -> fallback
+
+          _ -> fallback
+  where
+    allComponentsBack unview phi u p = do
+            let
+              boolToI b = if b then unview IOne else unview IZero
+              lamlam t = Lam defaultArgInfo (Abs "i" (Lam (setRelevance Irrelevant defaultArgInfo) (Abs "o" t)))
+            as <- decomposeInterval phi
+            (flags,t_alphas) <- fmap unzip . forM as $ \ (bs,ts) -> do
+                 let u' = listS bs' `applySubst` u
+                     bs' = IntMap.toAscList $ IntMap.map boolToI bs
+                     -- Γ₁, i : I, Γ₂, j : I, Γ₃  ⊢ weaken : Γ₁, Γ₂, Γ₃   for bs' = [(j,_),(i,_)]
+                     -- ordering of "j,i,.." matters.
+                 let weaken = foldr (\ j s -> s `composeS` raiseFromS j 1) idS (map fst bs')
+                 t <- reduce2Lam u'
+                 return $ (p $ ignoreBlocking t, listToMaybe [ (weaken `applySubst` (lamlam <$> t),bs) | null ts ])
+            return $ (flags,t_alphas)
+    compData mtrD False _ cmd@DoHComp (IsNot l) (IsNot ps) fsc sphi (Just u) a0 = do
+      let getTermLocal :: IsBuiltin a => a -> ReduceM Term
+          getTermLocal = getTerm $ "builtinHComp for data types"
+
+      let sc = famThing <$> fsc
+      tEmpty <- getTermLocal builtinIsOneEmpty
+      tPOr   <- getTermLocal builtinPOr
+      iO   <- getTermLocal builtinIOne
+      iZ   <- getTermLocal builtinIZero
+      tMin <- getTermLocal builtinIMin
+      tNeg <- getTermLocal builtinINeg
+      let iNeg t = tNeg `apply` [argN t]
+          iMin t u = tMin `apply` [argN t, argN u]
+          iz = pure iZ
+      constrForm <- do
+        mz <- getTerm' builtinZero
+        ms <- getTerm' builtinSuc
+        return $ \ t -> fromMaybe t (constructorForm' mz ms t)
+      su  <- reduceB' u
+      sa0 <- reduceB' a0
+      view   <- intervalView'
+      unview <- intervalUnview'
+      let f = unArg . ignoreBlocking
+          phi = f sphi
+          a0 = f sa0
+          isLit t@(Lit lt) = Just t
+          isLit _ = Nothing
+          isCon (Con h _ _) = Just h
+          isCon _           = Nothing
+          combine l ty d [] = d
+          combine l ty d [(psi,u)] = u
+          combine l ty d ((psi,u):xs)
+            = pure tPOr <#> l <@> psi <@> foldr (imax . fst) iz xs
+                        <#> ilam "o" (\ _ -> ty) -- the type
+                        <@> u <@> (combine l ty d xs)
+          noRed' su = return $ NoReduction [notReduced l,reduced sc, reduced sphi, reduced su', reduced sa0]
+            where
+              su' = case view phi of
+                     IZero -> notBlocked $ argN $ runNames [] $ do
+                                 [l,c] <- mapM (open . unArg) [l,ignoreBlocking sc]
+                                 lam "i" $ \ i -> pure tEmpty <#> l
+                                                              <#> ilam "o" (\ _ -> c)
+                     _     -> su
+          sameConHeadBack Nothing Nothing su k = noRed' su
+          sameConHeadBack lt h su k = do
+            let u = unArg . ignoreBlocking $ su
+            (b, ts) <- allComponentsBack unview phi u $ \ t ->
+                        (isLit t == lt, isCon (constrForm t) == h)
+            let
+              (lit,hd) = unzip b
+
+            if isJust lt && and lit then redReturn a0 else do
+            su <- caseMaybe (sequence ts) (return su) $ \ ts -> do
+              let (us,bools) = unzip ts
+              fmap ((sequenceA_ us $>) . argN) $ do
+              let
+                phis :: [Term]
+                phis = for bools $ \ m ->
+                            foldr (iMin . (\(i,b) -> applyUnless b iNeg $ var i)) iO (IntMap.toList m)
+              runNamesT [] $ do
+                u <- open u
+                [l,c] <- mapM (open . unArg) [l,ignoreBlocking sc]
+                phis <- mapM open phis
+                us   <- mapM (open . ignoreBlocking) us
+                lam "i" $ \ i -> do
+                  combine l c (u <@> i) $ zip phis (map (\ t -> t <@> i) us)
+
+            if isJust h && and hd then k (fromMaybe __IMPOSSIBLE__ h) su
+                      else noRed' su
+
+      sameConHeadBack (isLit a0) (isCon a0) su $ \ h su -> do
+            let u = unArg . ignoreBlocking $ su
+            Constructor{ conComp = cm } <- theDef <$> getConstInfo (conName h)
+            case nameOfHComp cm of
+              Just hcompD -> redReturn $ Def hcompD [] `apply`
+                                          (ps ++ map argN [phi,u,a0])
+              Nothing        -> noRed' su
+
+    compData mtrD        _     0     DoTransp (IsFam l) (IsFam ps) fsc sphi Nothing a0 = redReturn $ unArg a0
+    compData (Just trD) isHIT _ cmd@DoTransp (IsFam l) (IsFam ps) fsc sphi Nothing a0 = do
+      let sc = famThing <$> fsc
+      let f = unArg . ignoreBlocking
+          phi :: Term
+          phi = f $ sphi
+      let lam_i = Lam defaultArgInfo . Abs "i"
+      redReturn $ Def trD [] `apply` (map (fmap lam_i) ps ++ map argN [phi,unArg a0])
+
+    compData mtrD isHIT _ cmd@DoTransp (IsFam l) (IsFam ps) fsc sphi Nothing a0 = do
+      let getTermLocal :: IsBuiltin a => a -> ReduceM Term
+          getTermLocal = getTerm $ getBuiltinId builtinTrans ++ " for data types"
+      let sc = famThing <$> fsc
+      mhcompName <- getName' builtinHComp
+      constrForm <- do
+        mz <- getTerm' builtinZero
+        ms <- getTerm' builtinSuc
+        return $ \ t -> fromMaybe t (constructorForm' mz ms t)
+      sa0 <- reduceB' a0
+      let f = unArg . ignoreBlocking
+          phi = f sphi
+          a0 = f sa0
+          noRed = return $ NoReduction [notReduced l,reduced sc, reduced sphi, reduced sa0]
+      let lam_i = Lam defaultArgInfo . Abs "i"
+      case constrForm a0 of
+        Con h _ args -> do
+          Constructor{ conComp = cm } <- theDef <$> getConstInfo (conName h)
+          case nameOfTransp cm of
+              Just transpD -> redReturn $ Def transpD [] `apply`
+                                          (map (fmap lam_i) ps ++ map argN [phi,a0])
+              Nothing        -> noRed
+        Def q es | isHIT, Just q == mhcompName, Just [_l0,_c0,psi,u,u0] <- allApplyElims es -> do
+           let bC = ignoreBlocking sc
+           hcomp <- getTermLocal builtinHComp
+           transp <- getTermLocal builtinTrans
+           io <- getTermLocal builtinIOne
+           iz <- getTermLocal builtinIZero
+           redReturn <=< runNamesT [] $ do
+             [l,bC,phi,psi,u,u0] <- mapM (open . unArg) [l,bC,ignoreBlocking sphi,psi,u,u0]
+             -- hcomp (sc 1) [psi |-> transp sc phi u] (transp sc phi u0)
+             pure hcomp <#> (l <@> pure io) <#> (bC <@> pure io) <#> psi
+                   <@> lam "j" (\ j -> ilam "o" $ \ o ->
+                        pure transp <#> l <@> bC <@> phi <@> (u <@> j <..> o))
+                   <@> (pure transp <#> l <@> bC <@> phi <@> u0)
+        _ -> noRed
+    compData mtrX isHITorIx nargs cmd l t sbA sphi u u0 = do
+      () <- reportSDoc "impossible" 10 $ "compData" <+> (nest 2 . vcat)
+       [ "mtrX:       " <+> pretty mtrX
+       , "isHITorIx:  " <+> pretty isHITorIx
+       , "nargs:      " <+> pretty nargs
+       , "cmd:        " <+> text (show cmd)
+       , "l:          " <+> familyOrNot l
+       , "t:          " <+> familyOrNot t <+> pretty (famThing t)
+       , "sbA:          " <+> familyOrNot (ignoreBlocking $ sbA)
+       , "sphi:       " <+> pretty (ignoreBlocking sphi)
+       , "isJust u:   " <+> pretty (isJust u)
+       , "u0:         " <+> pretty u0
+       ]
+      __IMPOSSIBLE__
+
+--    compData _ _ _ _ _ _ _ _ _ _ = __IMPOSSIBLE__
+
+-- | CCHM 'primComp' is implemented in terms of 'hcomp' and 'transport'.
+-- The definition of it comes from 'mkComp'.
+primComp :: TCM PrimitiveImpl
+primComp = do
+  requireCubical CErased ""
+  t    <- runNamesT [] $
+          hPi' "a" (primIntervalType --> els (pure LevelUniv) (cl primLevel)) $ \ a ->
+          nPi' "A" (nPi' "i" primIntervalType $ \ i -> (sort . tmSort <$> (a <@> i))) $ \ bA ->
+          hPi' "φ" primIntervalType $ \ phi ->
+          nPi' "i" primIntervalType (\ i -> pPi' "o" phi $ \ _ -> el' (a <@> i) (bA <@> i)) -->
+          (el' (a <@> cl primIZero) (bA <@> cl primIZero) --> el' (a <@> cl primIOne) (bA <@> cl primIOne))
+  one <- primItIsOne
+  io  <- primIOne
+  return $ PrimImpl t $ PrimFun __IMPOSSIBLE__ 5 [] $ \ts nelims -> do
+    case ts of
+      [l,c,phi,u,a0] -> do
+        sphi <- reduceB' phi
+        vphi <- intervalView $ unArg $ ignoreBlocking sphi
+        case vphi of
+          -- Though we short-circuit evaluation for the rule
+          --    comp A i1 (λ _ .1=1 → u) u ==> u
+          -- rather than going through the motions of hcomp and transp.
+          IOne -> redReturn (unArg u `apply` [argN io, argN one])
+          _    -> do
+            redReturnNoSimpl <=< runNamesT [] $ do
+              comp <- mkComp (getBuiltinId PrimComp)
+              [l,c,phi,u,a0] <- mapM (open . unArg) [l,c,phi,u,a0]
+              comp l c phi u a0
+
+      _ -> __IMPOSSIBLE__
+
+
+-- TODO Andrea: keep reductions that happen under foralls?
+primFaceForall' :: TCM PrimitiveImpl
+primFaceForall' = do
+  requireCubical CErased ""
+  t <- (primIntervalType --> primIntervalType) --> primIntervalType
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 1 $ \case
+    [phi] -> do
+      sphi <- reduceB' phi
+      case unArg $ ignoreBlocking $ sphi of
+        Lam _ t -> do
+          t <- reduce' t
+          case t of
+            NoAbs _ t -> redReturn t
+            Abs _ t ->
+              maybe (return $ NoReduction [reduced sphi]) redReturn
+                =<< toFaceMapsPrim t
+        _ -> return (NoReduction [reduced sphi])
+    _ -> __IMPOSSIBLE__
+  where
+    toFaceMapsPrim t = do
+      view <- intervalView'
+      unview <- intervalUnview'
+      us' <- decomposeInterval t
+      fr <- getTerm (getBuiltinId PrimFaceForall) PrimFaceForall
+      let
+        v = view t
+        -- We decomposed the interval expression, without regard for
+        -- inconsistent mappings, and now we keep only those which are
+        -- stuck (the ts) and those which do not mention the 0th variable.
+        us :: [[Either (Int, Bool) Term]]
+        us = [ map Left (IntMap.toList bsm) ++ map Right ts
+             | (bsm, ts) <- us', 0 `IntMap.notMember` bsm
+             ]
+
+        -- Turn a face mapping back into an interval expression:
+        fm (i, b) = if b then var (i - 1) else unview (INeg (argN (var $ i - 1)))
+        -- Apply ∀ to any indecomposable expressions we have encountered
+        ffr t = fr `apply` [argN $ Lam defaultArgInfo $ Abs "i" t]
+
+        -- Unfold one step of the foldr to avoid generation of the last
+        -- ∧ i1. Marginal savings at best but it's cleaner.
+        conjuncts :: [Either (Int, Bool) Term] -> Term
+        conjuncts [] = unview IOne
+        conjuncts [x] = either fm ffr x
+        conjuncts (x:xs) =
+          foldr (\x r -> unview (IMin (argN (either fm ffr x)) (argN r)))
+            (either fm ffr x)
+            xs
+
+        disjuncts = foldr
+          (\conj rest -> unview (IMax (argN (conjuncts conj)) (argN rest)))
+          (unview IZero)
+          us
+      --   traceSLn "cube.forall" 20 (unlines [show v, show us', show us, show r]) $
+      return $ case us' of
+        [(m, [_])] | null m -> Nothing
+        _ -> Just disjuncts
+
+-- | Tries to @primTransp@ a whole telescope of arguments, following the rule for Σ types.
+--   If a type in the telescope does not support transp, @transpTel@ throws it as an exception.
+transpTel :: Abs Telescope -- Γ ⊢ i.Δ
+          -> Term          -- Γ ⊢ φ : F  -- i.Δ const on φ
+          -> Args          -- Γ ⊢ δ : Δ[0]
+          -> ExceptT (Closure (Abs Type)) TCM Args      -- Γ ⊢ Δ[1]
+transpTel = transpTel' False
+
+
+transpTel' :: (PureTCM m, MonadError TCErr m) =>
+          Bool -> Abs Telescope -- Γ ⊢ i.Δ
+          -> Term          -- Γ ⊢ φ : F  -- i.Δ const on φ
+          -> Args          -- Γ ⊢ δ : Δ[0]
+          -> ExceptT (Closure (Abs Type)) m Args      -- Γ ⊢ Δ[1]
+transpTel' flag delta phi args = transpSysTel' flag delta [] phi args
+
+type LM m a = NamesT (ExceptT (Closure (Abs Type)) m) a
+-- transporting with an extra system/partial element
+-- or composing when some of the system is known to be constant.
+transpSysTel' :: forall m. (PureTCM m, MonadError TCErr m) =>
+          Bool
+          -> Abs Telescope -- Γ ⊢ i.Δ
+          -> [(Term,Abs [Term])] -- [(ψ,i.δ)] with  Γ,ψ ⊢ i.δ : [i : I]. Δ[i]  -- the proof of [ψ] is not in scope.
+          -> Term          -- Γ ⊢ φ : F  -- i.Δ const on φ and all i.δ const on φ ∧ ψ
+          -> Args          -- Γ ⊢ δ : Δ[0]
+          -> ExceptT (Closure (Abs Type)) m Args      -- Γ ⊢ Δ[1]
+transpSysTel' flag delta us phi args = do
+  reportSDoc "cubical.prim.transpTel" 20 $
+      sep [ text "transpSysTel'"
+          , (text "delta  =" <+>) $ nest 2 $ addContext ("i" :: String, __DUMMY_DOM__) $ prettyTCM (unAbs delta)
+--          , (text "us =" <+>) $ nest 2 $ prettyList $ map prettyTCM us
+          , (text "phi    =" <+>) $ nest 2 $ prettyTCM phi
+          , (text "args   =" <+>) $ nest 2 $ prettyList $ map prettyTCM args
+          ]
+  let getTermLocal :: IsBuiltin a => a -> ExceptT e m Term
+      getTermLocal = getTerm "transpSys"
+  tTransp <- lift primTrans
+  tComp <- getTermLocal builtinComp
+  tPOr <- getTermLocal builtinPOr
+  iz <- lift primIZero
+  imin <- lift primIMin
+  imax <- lift primIMax
+  ineg <- lift primINeg
+  let
+    noTranspError t = do
+      reportSDoc "cubical.prim.transpTel" 20 $ nest 2 $ (text "error type =" <+>) $
+        addContext ("i" :: String, __DUMMY_DOM__) $ prettyTCM $ unAbs t
+      lift . throwError =<< buildClosure t
+    bapp :: forall m a. (Applicative m, Subst a) => m (Abs a) -> m (SubstArg a) -> m a
+    bapp t u = lazyAbsApp <$> t <*> u
+    doGTransp l t us phi a | null us = pure tTransp <#> l <@> (Lam defaultArgInfo . fmap unEl <$> t) <@> phi <@> a
+                           | otherwise = pure tComp <#> l <@> (Lam defaultArgInfo . fmap unEl <$> t) <#> face <@> uphi <@> a
+      where
+        -- [phi -> a; us]
+        face = foldr (\ x y -> pure imax <@> x <@> y) (pure iz) (phi : map fst us)
+        uphi = lam "i" $ \ i -> ilam "o" $ \ o -> do
+          let sys' = (phi , a) : map (mapSnd (`bapp` i)) us
+              sys = map (mapSnd $ ilam "o" . const) sys'
+          combine (l <@> i) (unEl <$> bapp t i) __IMPOSSIBLE__ sys <..> o
+    combine l ty d [] = d
+    combine l ty d [(psi,u)] = u
+    combine l ty d ((psi,u):xs)
+            = pure tPOr <#> l <@> psi <@> (foldr (\ x y -> pure imax <@> x <@> y) (pure iz) (map fst xs))
+                        <#> (ilam "o" $ \ _ -> ty) -- the type
+                        <@> u <@> (combine l ty d xs)
+
+    gTransp :: Maybe (LM m Term) -> LM m (Abs Type) -> [(LM m Term,LM m (Abs Term))] -> LM m Term -> LM m Term -> LM m Term
+    gTransp (Just l) t u phi a
+     | flag = do
+      t' <- t
+      us' <- mapM snd u
+      case ( 0 `freeIn` (raise 1 t' `lazyAbsApp` var 0)
+           , 0 `freeIn` map (\ u -> raise 1 u `lazyAbsApp` var 0) us'
+           ) of
+        (False,False) -> a
+        (False,True)  -> doGTransp l t u phi a -- TODO? optimize to "hcomp (l <@> io) (bapp t io) ((phi,NoAbs a):u) a" ?
+        (True,_) -> doGTransp l t u phi a
+     | otherwise = doGTransp l t u phi a
+
+    gTransp Nothing t sys phi a = do
+      let (psis,us) = unzip sys
+      -- Γ ⊢ i.Ξ
+      xi <- (open =<<) $ do
+        bind "i" $ \ i -> do
+          TelV xi _ <- (lift . telView =<<) $ t `bapp` i
+          return xi
+      argnames <- do
+        teleArgNames . unAbs <$> xi
+      glamN argnames $ \ xi_args -> do
+        b' <- bind "i" $ \ i -> do
+          ti <- t `bapp` i
+          xin <- bind "i" $ \ i -> xi `bapp` (pure ineg <@> i)
+          xi_args <- xi_args
+          ni <- pure ineg <@> i
+          phi <- phi
+          lift $ piApplyM ti =<< trFillTel' flag xin phi xi_args ni
+        usxi <- forM us $ \ u -> bind "i" $ \ i -> do
+          ui <- u `bapp` i
+          xin <- bind "i" $ \ i -> xi `bapp` (pure ineg <@> i)
+          xi_args <- xi_args
+          ni <- pure ineg <@> i
+          phi <- phi
+          lift $ apply ui <$> trFillTel' flag xin phi xi_args ni
+        axi <- do
+          a <- a
+          xif <- bind "i" $ \ i -> xi `bapp` (pure ineg <@> i)
+          phi <- phi
+          xi_args <- xi_args
+          lift $ apply a <$> transpTel' flag xif phi xi_args
+        s <- reduce $ getSort (absBody b')
+        reportSDoc "cubical.transp" 20 $ pretty (raise 1 b' `lazyAbsApp` var 0)
+        let noTranspSort = if 0 `freeIn` (raise 1 b' `lazyAbsApp` var 0) || 0 `freeIn` (map (`lazyAbsApp` var 0) (raise 1 usxi))
+              then noTranspError b'
+              else return axi
+
+        case s of
+          Type l -> do
+            l <- open $ lam_i (Level l)
+            b' <- open b'
+            axi <- open axi
+            usxi <- mapM open usxi
+            gTransp (Just l) b' (zip psis usxi) phi axi
+          Inf _ _  -> noTranspSort
+          SSet _  -> noTranspSort
+          SizeUniv -> noTranspSort
+          LockUniv -> noTranspSort
+          IntervalUniv -> noTranspSort
+          Prop{}  -> noTranspSort
+          _ -> noTranspError b'
+    lam_i = Lam defaultArgInfo . Abs "i"
+    go :: Telescope -> [[(Term,Term)]] -> Term -> Args -> ExceptT (Closure (Abs Type)) m Args
+    go EmptyTel            [] _  []       = return []
+    go (ExtendTel t delta) (u:us) phi (a:args) = do
+      -- Γ,i ⊢ t
+      -- Γ,i ⊢ (x : t). delta
+      -- Γ ⊢ a : t[0]
+      s <- reduce $ getSort t
+      -- Γ ⊢ b : t[1]    Γ, i ⊢ bf : t[i]
+      (b,bf) <- runNamesT [] $ do
+        l <- case s of
+               SSet _ -> return Nothing
+               IntervalUniv -> return Nothing
+               SizeUniv     -> return Nothing
+               LockUniv     -> return Nothing
+               Inf _ _ -> return Nothing
+               Type l -> Just <$> open (lam_i (Level l))
+               _ -> noTranspError (Abs "i" (unDom t))
+        t <- open $ Abs "i" (unDom t)
+        u <- forM u $ \ (psi,upsi) -> do
+              (,) <$> open psi <*> open (Abs "i" upsi)
+        [phi,a] <- mapM open [phi, unArg a]
+        b <- gTransp l t u phi a
+        bf <- bind "i" $ \ i -> do
+                            gTransp ((<$> l) $ \ l -> lam "j" $ \ j -> l <@> (pure imin <@> i <@> j))
+                                    (bind "j" $ \ j -> t `bapp` (pure imin <@> i <@> j))
+                                    u
+                                    (pure imax <@> (pure ineg <@> i) <@> phi)
+                                    a
+        return (b, absBody bf)
+      (:) (b <$ a) <$> go (lazyAbsApp delta bf) us phi args
+    go EmptyTel            _ _ _ = __IMPOSSIBLE__
+    go (ExtendTel t delta) _ _ _ = __IMPOSSIBLE__
+  let (psis,uss) = unzip us
+      us' | null us = replicate (length args) []
+          | otherwise = map (zip psis) $ List.transpose (map absBody uss)
+  go (absBody delta) us' phi args
+
+-- | Like @transpTel@ but performing a transpFill.
+trFillTel :: Abs Telescope -- Γ ⊢ i.Δ
+          -> Term
+          -> Args          -- Γ ⊢ δ : Δ[0]
+          -> Term          -- Γ ⊢ r : I
+          -> ExceptT (Closure (Abs Type)) TCM Args      -- Γ ⊢ Δ[r]
+trFillTel = trFillTel' False
+
+trFillTel' :: (PureTCM m, MonadError TCErr m) =>
+          Bool
+          -> Abs Telescope -- Γ ⊢ i.Δ
+          -> Term
+          -> Args          -- Γ ⊢ δ : Δ[0]
+          -> Term          -- Γ ⊢ r : I
+          -> ExceptT (Closure (Abs Type)) m Args      -- Γ ⊢ Δ[r]
+trFillTel' flag delta phi args r = do
+  imin <- lift primIMin
+  imax <- lift primIMax
+  ineg <- lift primINeg
+  transpTel' flag (Abs "j" $ raise 1 delta `lazyAbsApp` (imin `apply` (map argN [var 0, raise 1 r])))
+            (imax `apply` [argN $ ineg `apply` [argN r], argN phi])
+            args
+
+
+
+-- hcompTel' :: Bool -> Telescope -> [(Term,Abs [Term])] -> [Term] -> ExceptT (Closure (Abs Type)) TCM [Term]
+-- hcompTel' b delta sides base = undefined
+
+-- hFillTel' :: Bool -> Telescope -- Γ ⊢ Δ
+--           -> [(Term,Abs [Term])]  -- [(φ,i.δ)] with  Γ,φ ⊢ i.δ : I → Δ
+--           -> [Term]            -- Γ ⊢ δ0 : Δ, matching the [(φ,i.δ)]
+--           -> Term -- Γ ⊢ r : I
+--           -> ExceptT (Closure (Abs Type)) TCM [Term]
+-- hFillTel' b delta sides base = undefined
+
+pathTelescope
+  :: forall m. (PureTCM m, MonadError TCErr m) =>
+  Telescope -- Δ
+  -> [Arg Term] -- lhs : Δ
+  -> [Arg Term] -- rhs : Δ
+  -> m Telescope
+pathTelescope tel lhs rhs = do
+  x <- runExceptT (pathTelescope' tel lhs rhs)
+  case x of
+    Left t -> do
+      enterClosure t $ \ t ->
+                 typeError . GenericDocError =<<
+                    (text "The sort of" <+> pretty t <+> text "should be of the form \"Set l\"")
+    Right tel -> return tel
+
+pathTelescope'
+  :: forall m. (PureTCM m, MonadError (Closure Type) m) =>
+  Telescope -- Δ
+  -> [Arg Term] -- lhs : Δ
+  -> [Arg Term] -- rhs : Δ
+  -> m Telescope
+pathTelescope' tel lhs rhs = do
+  pathp <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPathP
+  go pathp (raise 1 tel) lhs rhs
+ where
+  -- Γ,i ⊢ Δ, Γ ⊢ lhs : Δ[0], Γ ⊢ rhs : Δ[1]
+  go :: Term -> Telescope -> [Arg Term] -> [Arg Term] -> m Telescope
+  go pathp (ExtendTel a tel) (u : lhs) (v : rhs) = do
+    let t = unDom a
+    l <- subst 0 __DUMMY_TERM__ <$> getLevel t
+    let a' = El (Type l) (apply pathp $ [argH $ Level l] ++ map argN [Lam defaultArgInfo (Abs "i" $ unEl t), unArg u, unArg v])
+        -- Γ,eq : u ≡ v, i : I ⊢ m = eq i : t[i]
+        -- m  = runNames [] $ do
+        --        [u,v] <- mapM (open . unArg) [u,v]
+        --        bind "eq" $ \ eq -> bind "i" $ \ i ->
+    (ExtendTel (a' <$ a) <$>) . runNamesT [] $ do
+      let nm = (absName tel)
+      tel <- open $ Abs "i" tel
+      [u,v] <- mapM (open . unArg) [u,v]
+      [lhs,rhs] <- mapM open [lhs,rhs]
+      bind nm $ \ eq -> do
+        lhs <- lhs
+        rhs <- rhs
+        tel' <- bind "i" $ \ i ->
+                  lazyAbsApp <$> (lazyAbsApp <$> tel <*> i) <*> (eq <@@> (u, v, i))
+        lift $ go pathp (absBody tel') lhs rhs
+  go _ EmptyTel [] [] = return EmptyTel
+  go _ _ _ _ = __IMPOSSIBLE__
+  getLevel :: Type -> m Level
+  getLevel t = do
+    s <- reduce $ getSort t
+    case s of
+      Type l -> pure l
+      s      -> throwError =<< buildClosure t
+
+data TranspError = CannotTransp {errorType :: (Closure (Abs Type)) }
+
+instance Exception TranspError
+instance Show TranspError where
+  show _ = "TranspError"
+
+tryTranspError :: TCM a -> TCM (Either (Closure (Abs Type)) a)
+tryTranspError (TCM m) = TCM $ \ s env -> do
+  mapLeft errorType <$> (try (m s env))
+
+transpPathPTel' ::
+             NamesT TCM (Abs (Abs Telescope)) -- ^ j.i.Δ                 const on φ
+             -> [NamesT TCM Term]          -- ^ x : (i : I) → Δ[0,i]  const on φ
+             -> [NamesT TCM Term]          -- ^ y : (i : I) → Δ[1,i]  const on φ
+             -> NamesT TCM Term            -- ^ φ
+             -> [NamesT TCM Term]          -- ^ p : PathP (λ j → Δ[j,0]) (x 0) (y 0)
+             -> NamesT TCM [Arg Term] -- PathP (λ j → Δ[j,0]) (x 1) (y 1) [ φ ↦ q ]
+transpPathPTel' theTel x y phi p = do
+ let neg j = cl primINeg <@> j
+ -- is the open overkill?
+ qs <- (open =<<) $ fmap (fmap (\ (Abs n (Arg i t)) -> Arg i (Lam defaultArgInfo $ Abs n t)) . sequenceA)
+                  $ bind "j" $ \ j -> do
+   theTel <- absApp <$> theTel <*> j
+   faces <- sequence [neg j, j]
+   us <- forM [x,y] $ \ z -> do
+           bind "i" $ \ i -> forM z (<@> i)
+   let sys = zip faces us
+   -- [(neg j, bind "i" $ \ i -> flip map x (<@> i))
+   -- ,(j , bind "i" $ \ i -> flip map y (<@> i))]
+   phi <- phi
+   p0 <- mapM (<@> j) p
+   let toArgs = zipWith (\ a t -> t <$ a) (teleArgNames (unAbs $ theTel))
+   eq <- lift . runExceptT $ transpSysTel' False theTel sys phi (toArgs p0)
+   either (lift . lift . throw . CannotTransp) pure eq
+ qs
+
+transpPathTel' ::
+             NamesT TCM (Abs Telescope) -- ^ i.Δ                 const on φ
+             -> [NamesT TCM Term]          -- ^ x : (i : I) → Δ[i]  const on φ
+             -> [NamesT TCM Term]          -- ^ y : (i : I) → Δ[i]  const on φ
+             -> NamesT TCM Term            -- ^ φ
+             -> [NamesT TCM Term]          -- ^ p : Path (Δ[0]) (x 0) (y 0)
+             -> NamesT TCM [Arg Term] -- Path (Δ[1]) (x 1) (y 1) [ φ ↦ q ]
+transpPathTel' theTel x y phi p = do
+ let neg j = cl primINeg <@> j
+ -- is the open overkill?
+ qs <- (open =<<) $ fmap (fmap (\ (Abs n (Arg i t)) -> Arg i (Lam defaultArgInfo $ Abs n t)) . sequenceA)
+                  $ bind "j" $ \ j -> do
+   theTel <- theTel
+   faces <- sequence $ [neg j, j]
+   us <- forM [x,y] $ \ z -> do
+           bind "i" $ \ i -> forM z (<@> i)
+   let sys = zip faces us
+   -- [(neg j, bind "i" $ \ i -> flip map x (<@> i))
+   -- ,(j , bind "i" $ \ i -> flip map y (<@> i))]
+   phi <- phi
+   p0 <- mapM (<@> j) p
+   let toArgs = zipWith (\ a t -> t <$ a) (teleArgNames (unAbs theTel))
+   eq <- lift . runExceptT $ transpSysTel' False theTel sys phi (toArgs p0)
+   either (lift . lift . throw . CannotTransp) pure eq
+ qs
+
+trFillPathTel' ::
+               NamesT TCM (Abs Telescope) -- ^ i.Δ                 const on φ
+             -> [NamesT TCM Term]          -- ^ x : (i : I) → Δ[i]  const on φ
+             -> [NamesT TCM Term]          -- ^ y : (i : I) → Δ[i]  const on φ
+             -> NamesT TCM Term            -- ^ φ
+             -> [NamesT TCM Term]          -- ^ p : Path (Δ[0]) (x 0) (y 0)
+             -> NamesT TCM Term            -- ^ r
+             -> NamesT TCM [Arg Term] -- Path (Δ[r]) (x r) (y r) [ φ ↦ q; (r = 0) ↦ q ]
+trFillPathTel' tel x y phi p r = do
+  let max i j = cl primIMin <@> i <@> j
+  let min i j = cl primIMin <@> i <@> j
+  let neg i = cl primINeg <@> i
+  x' <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> forM x (<@> (min r i))
+  y' <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> forM y (<@> (min r i))
+  transpPathTel' (bind "i" $ \ i -> absApp <$> tel <*> min r i)
+                 x'
+                 y'
+                 (max phi (neg r))
+                 p
+
+trFillPathPTel' ::
+               NamesT TCM (Abs (Abs Telescope)) -- ^ j.i.Δ                 const on φ
+             -> [NamesT TCM Term]          -- ^ x : (i : I) → Δ[0,i]  const on φ
+             -> [NamesT TCM Term]          -- ^ y : (i : I) → Δ[1,i]  const on φ
+             -> NamesT TCM Term            -- ^ φ
+             -> [NamesT TCM Term]          -- ^ p : Path (\ j -> Δ[j,0]) (x 0) (y 0)
+             -> NamesT TCM Term            -- ^ r
+             -> NamesT TCM [Arg Term] -- Path (\ j → Δ[j,r]) (x r) (y r) [ φ ↦ q; (r = 0) ↦ q ]
+trFillPathPTel' tel x y phi p r = do
+  let max i j = cl primIMin <@> i <@> j
+  let min i j = cl primIMin <@> i <@> j
+  let neg i = cl primINeg <@> i
+  x' <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> forM x (<@> (min r i))
+  y' <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> forM y (<@> (min r i))
+  transpPathPTel' (bind "j" $ \ j -> bind "i" $ \ i -> absApp <$> (absApp <$> tel <*> j) <*> min r i)
+                 x'
+                 y'
+                 (max phi (neg r))
+                 p
+
+
+
+-- given Γ ⊢ I type, and Γ ⊢ Δ telescope, build Δ^I such that
+-- Γ ⊢ (x : A, y : B x, ...)^I = (x : I → A, y : (i : I) → B (x i), ...)
+expTelescope :: Type -> Telescope -> Telescope
+expTelescope int tel = unflattenTel names ys
+  where
+    stel = size tel
+    xs = flattenTel tel
+    names = teleNames tel
+    t = ExtendTel (defaultDom $ raise stel int) (Abs "i" EmptyTel)
+    s = expS stel
+    ys = map (fmap (abstract t) . applySubst s) xs
+
+
+-- | Γ, Δ^I, i : I |- expS |Δ| : Γ, Δ
+expS :: Nat -> Substitution
+expS stel = prependS __IMPOSSIBLE__
+  [ Just (var n `apply` [Arg defaultArgInfo $ var 0]) | n <- [1..stel] ]
+  (raiseS (stel + 1))
+
+
+-- * Special cases of Type
+-----------------------------------------------------------
+
+-- | A @Type@ with sort @Type l@
+--   Such a type supports both hcomp and transp.
+data LType = LEl Level Term deriving (Eq,Show)
+
+fromLType :: LType -> Type
+fromLType (LEl l t) = El (Type l) t
+
+lTypeLevel :: LType -> Level
+lTypeLevel (LEl l t) = l
+
+toLType :: MonadReduce m => Type -> m (Maybe LType)
+toLType ty = do
+  sort <- reduce $ getSort ty
+  case sort of
+    Type l -> return $ Just $ LEl l (unEl ty)
+    _      -> return $ Nothing
+
+instance Subst LType where
+  type SubstArg LType = Term
+  applySubst rho (LEl l t) = LEl (applySubst rho l) (applySubst rho t)
+
+-- | A @Type@ that either has sort @Type l@ or is a closed definition.
+--   Such a type supports some version of transp.
+--   In particular we want to allow the Interval as a @ClosedType@.
+data CType = ClosedType Sort QName | LType LType deriving (Eq,Show)
+
+instance P.Pretty CType where
+  pretty = P.pretty . fromCType
+
+fromCType :: CType -> Type
+fromCType (ClosedType s q) = El s (Def q [])
+fromCType (LType t) = fromLType t
+
+toCType :: MonadReduce m => Type -> m (Maybe CType)
+toCType ty = do
+  sort <- reduce $ getSort ty
+  case sort of
+    Type l -> return $ Just $ LType (LEl l (unEl ty))
+    SSet{} -> do
+      t <- reduce (unEl ty)
+      case t of
+        Def q [] -> return $ Just $ ClosedType sort q
+        _        -> return $ Nothing
+    _      -> return $ Nothing
+
+instance Subst CType where
+  type SubstArg CType = Term
+  applySubst rho (ClosedType s q) = ClosedType (applySubst rho s) q
+  applySubst rho (LType t) = LType $ applySubst rho t
+
+hcomp
+  :: (HasBuiltins m, MonadError TCErr m, MonadReduce m, MonadPretty m)
+  => NamesT m Type
+  -> [(NamesT m Term, NamesT m Term)]
+  -> NamesT m Term
+  -> NamesT m Term
+hcomp ty sys u0 = do
+  iz <- primIZero
+  tHComp <- primHComp
+  let max i j = cl primIMax <@> i <@> j
+  ty <- ty
+  (l, ty) <- toLType ty >>= \case
+    Just (LEl l ty) -> return (l, ty)
+    Nothing -> lift $ do -- TODO: support Setω properly
+      typeError . GenericDocError =<< sep
+        [ text "Cubical Agda: cannot generate hcomp clauses at type", prettyTCM ty ]
+  l <- open $ Level l
+  ty <- open $ ty
+  face <- (foldr max (pure iz) $ map fst $ sys)
+  sys <- lam "i'" $ \ i -> combineSys l ty [(phi, u <@> i) | (phi,u) <- sys]
+  pure tHComp <#> l <#> ty <#> pure face <@> pure sys <@> u0
+
+transpSys :: (HasBuiltins m, MonadError TCErr m, MonadReduce m) =>
+               NamesT m (Abs Type) -- ty
+               -> [(NamesT m Term, NamesT m Term)] -- sys
+               -> NamesT m Term -- φ
+               -> NamesT m Term
+               -> NamesT m Term
+transpSys ty sys phi u = do
+  let max i j = cl primIMax <@> i <@> j
+  iz <- primIZero
+  tTransp <- primTrans
+  tComp <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinComp
+  l_ty <- bind "i" $ \ i -> do
+      ty <- absApp <$> ty <*> i
+      toLType ty >>= \case
+        Just (LEl l ty) -> return (l,ty)
+        Nothing -> return (__DUMMY_LEVEL__, unEl ty) -- TODO: properly support Setω
+  l <- open $ Lam defaultArgInfo . fmap (Level . fst) $ l_ty
+  ty <- open $ Lam defaultArgInfo . fmap snd $ l_ty
+
+  if null sys then pure tTransp <#> l <@> ty <@> phi <@> u else do
+
+  let face = max phi (foldr max (pure iz) $ map fst $ sys)
+  sys <- (open =<<) $ lam "i'" $ \ i -> do
+    let base = (phi, ilam "o" $ \ _ -> u)
+    combineSys l ty $ base : [(phi, u <@> i) | (phi,u) <- sys]
+
+  pure tComp <#> l <@> ty <#> face <@> sys <@> u
+
+debugClause :: String -> Clause -> TCM ()
+debugClause s c = do
+      reportSDoc s 20 $
+        "gamma:" <+> prettyTCM gamma
+      reportSDoc s 20 $ addContext gamma $
+        "ps   :" <+> prettyTCM (patternsToElims ps)
+      reportSDoc s 20 $ addContext gamma $
+        "type :" <+> maybe "nothing" prettyTCM rhsTy
+      reportSDoc s 20 $ addContext gamma $
+        "body :" <+> maybe "nothing" prettyTCM rhs
+
+      reportSDoc s 30 $
+        addContext gamma $ "c:" <+> pretty c
+  where
+    gamma = clauseTel c
+    ps = namedClausePats c
+    rhsTy = clauseType c
+    rhs = clauseBody c
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs b/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs
@@ -0,0 +1,443 @@
+-- | Implementations of the basic primitives of Cubical Agda: The
+-- interval and its operations.
+
+module Agda.TypeChecking.Primitive.Cubical.Base
+  ( requireCubical
+  , primIntervalType
+  , primIMin', primIMax', primDepIMin', primINeg'
+  , imax, imin, ineg
+
+  , Command(..), KanOperation(..), kanOpName, TermPosition(..), headStop
+  , FamilyOrNot(..), familyOrNot
+
+    -- * Helper functions for building terms
+  , combineSys, combineSys'
+  , fiber, hfill
+  , decomposeInterval', decomposeInterval
+  , reduce2Lam
+  , isCubicalSubtype
+  )
+  where
+
+import Control.Monad        ( msum, mzero )
+import Control.Monad.Except ( MonadError )
+
+import qualified Data.IntMap as IntMap
+import Data.IntMap (IntMap)
+import Data.String (IsString (fromString))
+import Data.Bifunctor (second)
+import Data.Either (partitionEithers)
+import Data.Maybe (fromMaybe, maybeToList)
+
+import qualified Agda.Utils.BoolSet as BoolSet
+import Agda.Utils.Impossible (__IMPOSSIBLE__)
+import Agda.Utils.BoolSet (BoolSet)
+import Agda.Utils.Functor
+
+import Agda.TypeChecking.Monad.Signature (HasConstInfo)
+import Agda.TypeChecking.Monad.Debug (__IMPOSSIBLE_VERBOSE__)
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Pure
+import Agda.TypeChecking.Monad.Base
+
+import Agda.TypeChecking.Substitute.Class (absBody, raise, apply)
+
+import Agda.TypeChecking.Reduce (Reduce(..), reduceB', reduce', reduce)
+import Agda.TypeChecking.Names (NamesT, runNamesT, ilam, lam)
+
+import Agda.Interaction.Options.Base (optCubical)
+
+import Agda.Syntax.Common
+  (Cubical(..), Arg(..), Relevance(..), setRelevance, defaultArgInfo, hasQuantity0)
+
+import Agda.TypeChecking.Primitive.Base
+  (SigmaKit(..), (-->), nPi', pPi', (<@>), (<#>), (<..>), argN, getSigmaKit)
+
+import Agda.Syntax.Internal
+
+
+-- | Checks that the correct variant of Cubical Agda is activated.
+-- Note that @--erased-cubical@ \"counts as\" @--cubical@ in erased
+-- contexts.
+requireCubical
+  :: Cubical -- ^ Which variant of Cubical Agda is required?
+  -> String  -- ^ Why, exactly, do we need Cubical to be enabled?
+  -> TCM ()
+requireCubical wanted s = do
+  cubical         <- optCubical <$> pragmaOptions
+  inErasedContext <- hasQuantity0 <$> viewTC eQuantity
+  case cubical of
+    Just CFull -> return ()
+    Just CErased | wanted == CErased || inErasedContext -> return ()
+    _ -> typeError $ GenericError $ "Missing option " ++ opt ++ s
+  where
+  opt = case wanted of
+    CFull   -> "--cubical"
+    CErased -> "--cubical or --erased-cubical"
+
+-- | Our good friend the interval type.
+primIntervalType :: (HasBuiltins m, MonadError TCErr m, MonadTCEnv m, ReadTCState m) => m Type
+primIntervalType = El intervalSort <$> primInterval
+
+-- | Negation on the interval. Negation satisfies De Morgan's laws, and
+-- their implementation is handled here.
+primINeg' :: TCM PrimitiveImpl
+primINeg' = do
+  requireCubical CErased ""
+  t <- primIntervalType --> primIntervalType
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 1 $ \case
+    [x] -> do
+      unview <- intervalUnview'
+      view <- intervalView'
+      sx <- reduceB' x
+      ix <- intervalView (unArg $ ignoreBlocking sx)
+
+      -- Apply De Morgan's laws.
+      let
+        ineg :: Arg Term -> Arg Term
+        ineg = fmap (unview . f . view)
+
+        f ix = case ix of
+          IZero    -> IOne
+          IOne     -> IZero
+          IMin x y -> IMax (ineg x) (ineg y)
+          IMax x y -> IMin (ineg x) (ineg y)
+          INeg x   -> OTerm (unArg x)
+          OTerm t  -> INeg (Arg defaultArgInfo t)
+
+      -- We force the argument in case it happens to be an interval
+      -- expression, but it's quite possible that it's _not_. In those
+      -- cases, negation is stuck.
+      case ix of
+        OTerm t -> return $ NoReduction [reduced sx]
+        _       -> redReturn (unview $ f ix)
+    _ -> __IMPOSSIBLE_VERBOSE__ "implementation of primINeg called with wrong arity"
+
+-- | 'primDepIMin' expresses that cofibrations are closed under @Σ@.
+-- Thus, it serves as a dependent version of 'primIMin' (which, recall,
+-- implements @_∧_@). This is required for the construction of the Kan
+-- operations in @Id@.
+primDepIMin' :: TCM PrimitiveImpl
+primDepIMin' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+       nPi' "φ" primIntervalType $ \ φ ->
+       pPi' "o" φ (\ o -> primIntervalType) --> primIntervalType
+  -- Note that the type here is @(φ : I) → (.(IsOne φ) → I) → I@, since
+  -- @Partial φ I@ is not well-sorted.
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 2 $ \case
+    [x,y] -> do
+      sx <- reduceB' x
+      ix <- intervalView (unArg $ ignoreBlocking sx)
+      itisone <- getTerm "primDepIMin" builtinItIsOne
+      case ix of
+        -- Σ 0 iy is 0, and additionally P is def.eq. to isOneEmpty.
+        IZero -> redReturn =<< intervalUnview IZero
+        -- Σ 1 iy is (iy 1=1).
+        IOne  -> redReturn =<< (pure (unArg y) <@> pure itisone)
+        _     -> do
+          -- Hack: We cross our fingers and really hope that eventually
+          -- ix may turn out to be i1. Regardless we evaluate iy 1=1, to
+          -- short-circuit evaluate a couple of cases:
+          sy <- reduceB' y
+          iy <- intervalView =<< reduce' =<< (pure (unArg $ ignoreBlocking sy) <@> pure itisone)
+          case iy of
+            -- Σ _ (λ _ → 0) is always 0
+            IZero -> redReturn =<< intervalUnview IZero
+            -- Σ ix (λ _ → 1) only depends on ix
+            IOne  -> redReturn (unArg $ ignoreBlocking sx)
+            -- Otherwise we're well and truly blocked.
+            _     -> return $ NoReduction [reduced sx, reduced sy]
+    _ -> __IMPOSSIBLE_VERBOSE__ "implementation of primDepIMin called with wrong arity"
+
+-- | Internal helper for constructing binary operations on the interval,
+-- parameterised by their unit and absorbing elements.
+primIBin :: IntervalView -> IntervalView -> TCM PrimitiveImpl
+primIBin unit absorber = do
+  requireCubical CErased ""
+  t <- primIntervalType --> primIntervalType --> primIntervalType
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 2 $ \case
+    [x,y] -> do
+      -- Evaluation here is short-circuiting: If the LHS is either the
+      -- absorbing or unit element, then the RHS does not matter.
+      sx <- reduceB' x
+      ix <- intervalView (unArg $ ignoreBlocking sx)
+      case ix of
+        ix | ix ==% absorber -> redReturn =<< intervalUnview absorber
+        ix | ix ==% unit     -> return $ YesReduction YesSimplification (unArg y)
+        _ -> do
+          -- And in the case where the LHS is stuck, we can make
+          -- progress by comparing the LHS to the absorbing/unit
+          -- elements.
+          sy <- reduceB' y
+          iy <- intervalView (unArg $ ignoreBlocking sy)
+          case iy of
+            iy | iy ==% absorber -> redReturn =<< intervalUnview absorber
+            iy | iy ==% unit     -> return $ YesReduction YesSimplification (unArg x)
+            _                    -> return $ NoReduction [reduced sx,reduced sy]
+    _ -> __IMPOSSIBLE_VERBOSE__ "binary operation on the interval called with incorrect arity"
+  where
+    (==%) IZero IZero = True
+    (==%) IOne IOne = True
+    (==%) _ _ = False
+{-# INLINE primIBin #-}
+
+-- | Implements both the @min@ connection /and/ conjunction on the
+-- cofibration classifier.
+primIMin' :: TCM PrimitiveImpl
+primIMin' = do
+  requireCubical CErased ""
+  primIBin IOne IZero
+
+-- | Implements both the @max@ connection /and/ disjunction on the
+-- cofibration classifier.
+primIMax' :: TCM PrimitiveImpl
+primIMax' = do
+  requireCubical CErased ""
+  primIBin IZero IOne
+
+-- | A helper for evaluating @max@ on the interval in TCM&co.
+imax :: HasBuiltins m => m Term -> m Term -> m Term
+imax x y = do
+  x' <- x
+  y' <- y
+  intervalUnview (IMax (argN x') (argN y'))
+
+-- | A helper for evaluating @min@ on the interval in TCM&co.
+imin :: HasBuiltins m => m Term -> m Term -> m Term
+imin x y = do
+  x' <- x
+  y' <- y
+  intervalUnview (IMin (argN x') (argN y'))
+
+-- | A helper for evaluating @neg@ on the interval in TCM&co.
+ineg :: HasBuiltins m => m Term -> m Term
+ineg x = do
+  x' <- x
+  intervalUnview (INeg (argN x'))
+
+data Command = DoTransp | DoHComp
+  deriving (Eq, Show)
+
+-- | The built-in name associated with a particular Kan operation.
+kanOpName :: KanOperation -> String
+kanOpName TranspOp{} = getBuiltinId PrimTrans
+kanOpName HCompOp{}  = getBuiltinId PrimHComp
+
+-- | Our Kan operations are @transp@ and @hcomp@. The KanOperation
+-- record stores the data associated with a Kan operation on arbitrary
+-- types: A cofibration and an element of that type.
+data KanOperation
+  -- | A transport problem consists of a cofibration, marking where the
+  -- transport is constant, and a term to move from the fibre over i0 to
+  -- the fibre over i1.
+  = TranspOp
+    { kanOpCofib :: Blocked (Arg Term)
+      -- ^ When this cofibration holds, the transport must
+      -- definitionally be the identity. This is handled generically by
+      -- 'primTransHComp' but specific Kan operations may still need it.
+    , kanOpBase :: Arg Term
+      -- ^ This is the term in @A i0@ which we are transporting.
+    }
+  -- | A composition problem consists of a partial element and a base.
+  -- Semantically, this is justified by the types being Kan fibrations,
+  -- i.e., having the lifting property against trivial cofibrations.
+  -- While the specified cofibration may not be trivial, (φ ∨ ~ r) for r
+  -- ∉ φ is *always* a trivial cofibration.
+  | HCompOp
+    { kanOpCofib :: Blocked (Arg Term)
+      -- ^ Extent of definition of the partial element we are lifting
+      -- against.
+    , kanOpSides :: Arg Term
+      -- ^ The partial element itself
+    , kanOpBase  :: Arg Term
+      -- ^ The base.
+    }
+
+-- | Are we looking at a family of things, or at a single thing?
+data FamilyOrNot a
+  = IsFam { famThing :: a }
+  | IsNot { famThing :: a }
+  deriving (Eq,Show,Functor,Foldable,Traversable)
+
+familyOrNot :: IsString p => FamilyOrNot a -> p
+familyOrNot (IsFam x) = "IsFam"
+familyOrNot (IsNot x) = "IsNot"
+
+instance Reduce a => Reduce (FamilyOrNot a) where
+  reduceB' x = traverse id <$> traverse reduceB' x
+  reduce' x = traverse reduce' x
+
+-- | For the Kan operations in @Glue@ and @hcomp {Type}@, we optimise
+-- evaluation a tiny bit by differentiating the term produced when
+-- evaluating a Kan operation by itself vs evaluating it under @unglue@.
+-- (See @headStop@ below.)
+data TermPosition
+  = Head
+  | Eliminated
+  deriving (Eq,Show)
+
+-- | Kan operations for the "unstable" type formers (@Glue@, @hcomp {Type}@) are
+-- computed "negatively": they never actually produce a @glue φ t a@ term. Instead,
+-- we block the computation unless such a term would reduce further, which happens
+-- in two cases:
+--
+-- * when the formula @φ@ is i1, in which case we reduce to @t@;
+-- * when we're under an @unglue@, i.e. in 'Eliminated' 'TermPosition', in which case
+--   we reduce to @a@.
+headStop :: PureTCM m => TermPosition -> m Term -> m Bool
+headStop tpos phi
+  | Head <- tpos = do
+    phi <- intervalView =<< (reduce =<< phi)
+    return $ not $ isIOne phi
+  | otherwise = return False
+
+-- | Build a partial element. The type of the resulting partial element
+-- can depend on the computed extent, which we denote by @φ@ here. Note
+-- that @φ@ is the n-ary disjunction of all the @ψ@s.
+combineSys
+  :: HasBuiltins m
+  => NamesT m Term -- The level @l : Level@
+  -> NamesT m Term -- The type @A : Partial φ (Type l)@.
+  -> [(NamesT m Term, NamesT m Term)]
+  -- ^ A list of @(ψ, PartialP ψ λ o → A (... o ...))@ mappings. Note
+  -- that by definitional proof-irrelevance of @IsOne@, the actual
+  -- injection can not matter here.
+  -> NamesT m Term
+combineSys l ty xs = snd <$> combineSys' l ty xs
+
+-- | Build a partial element, and compute its extent. See 'combineSys'
+-- for the details.
+combineSys'
+  :: forall m. HasBuiltins m
+  => NamesT m Term -- The level @l@
+  -> NamesT m Term -- The type @A@
+  -> [(NamesT m Term, NamesT m Term)]
+  -> NamesT m (Term,Term)
+combineSys' l ty xs = do
+  tPOr <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPOr
+  tMax <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIMax
+  iz <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIZero
+  tEmpty <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinIsOneEmpty
+
+  let
+    pOr l ty phi psi u0 u1 = pure tPOr
+      <#> l <@> phi <@> psi <#> (ilam "o" $ \ _ -> ty)
+      <@> u0 <@> u1
+
+    -- In one pass, compute the disjunction of all the cofibrations and
+    -- compute the primPOr expression.
+    combine :: [(NamesT m Term, NamesT m Term)] -> NamesT m (Term, Term)
+    combine [] = (iz,) <$> (pure tEmpty <#> l <#> (ilam "o" $ \ _ -> ty))
+    combine [(psi, u)] = (,) <$> psi <*> u
+    combine ((psi, u):xs) = do
+      (phi, c) <- combine xs
+      (,) <$> imax psi (pure phi) <*> pOr l ty psi (pure phi) u (pure c)
+  combine xs
+
+-- | Helper function for constructing the type of fibres of a function
+-- over a given point.
+fiber
+  :: (HasBuiltins m, HasConstInfo m)
+  => NamesT m Term -- @la : Level@
+  -> NamesT m Term -- @lb : Level@
+  -> NamesT m Term -- @A : Type la@
+  -> NamesT m Term -- @B : Type lb@
+  -> NamesT m Term -- @f : A → B@
+  -> NamesT m Term -- @x : B@
+  -> NamesT m Term -- @Σ[ x ∈ A ] (f a ≡ x)@
+fiber la lb bA bB f b = do
+  tPath <- getTerm "fiber" builtinPath
+  kit <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+  pure (Def (sigmaName kit) [])
+    <#> la <#> lb
+    <@> bA
+    <@> lam "a" (\ a -> pure tPath <#> lb <#> bB <@> (f <@> a) <@> b)
+
+-- | Helper function for constructing the filler of a given composition
+-- problem.
+hfill
+  :: (HasBuiltins m, HasConstInfo m)
+  => NamesT m Term -- @la : Level@
+  -> NamesT m Term -- @A : Type la@
+  -> NamesT m Term -- @φ : I@. Cofibration
+  -> NamesT m Term -- @u : Partial φ A@.
+  -> NamesT m Term -- @u0 : A@. Must agree with @u@ on @φ@
+  -> NamesT m Term -- @i : I@. Position along the cube.
+  -> NamesT m Term
+hfill la bA phi u u0 i = do
+  tHComp <- getTerm "hfill" builtinHComp
+  pure tHComp <#> la <#> bA <#> (imax phi (ineg i))
+    <@> lam "j" (\ j -> combineSys la bA
+        [ (phi,    ilam "o" (\o -> u <@> (imin i j) <..> o))
+        , (ineg i, ilam "o" (\_ -> u0))
+        ])
+    <@> u0
+
+{-# SPECIALIZE decomposeInterval :: Term -> TCM [(IntMap Bool, [Term])] #-}
+-- | Decompose an interval expression @i : I@ as in
+-- 'decomposeInterval'', but discard any inconsistent mappings.
+decomposeInterval :: HasBuiltins m => Term -> m [(IntMap Bool, [Term])]
+decomposeInterval t = do
+  decomposeInterval' t <&> \xs ->
+    [ (bm, ts) | (bsm, ts) <- xs, bm <- maybeToList $ traverse BoolSet.toSingleton bsm ]
+
+{-# SPECIALIZE decomposeInterval' :: Term -> TCM [(IntMap BoolSet, [Term])] #-}
+-- | Decompose an interval expression @φ : I@ into a set of possible
+-- assignments for the variables mentioned in @φ@, together any leftover
+-- neutral terms that could not be put into 'IntervalView' form.
+decomposeInterval' :: HasBuiltins m => Term -> m [(IntMap BoolSet, [Term])]
+decomposeInterval' t = do
+  view   <- intervalView'
+  unview <- intervalUnview'
+  let
+    f :: IntervalView -> [[Either (Int,Bool) Term]]
+    -- TODO handle primIMinDep
+    -- TODO? handle forall
+    f IZero = mzero     -- No assignments are possible
+    f IOne  = return [] -- No assignments are necessary
+    -- Take the cartesian product
+    f (IMin x y) = do
+      xs <- (f . view . unArg) x
+      ys <- (f . view . unArg) y
+      return (xs ++ ys)
+    -- Take the union
+    f (IMax x y) = msum $ map (f . view . unArg) [x,y]
+    -- Invert the possible assignments and negate the neutrals
+    f (INeg x) =
+      map (either (\ (x,y) -> Left (x,not y)) (Right . unview . INeg . argN))
+        <$> (f . view . unArg) x
+    f (OTerm (Var i [])) = return [Left (i,True)]
+    f (OTerm t)          = return [Right t]
+
+  return [ (bsm, ts)
+         | xs <- f (view t)
+         , let (bs,ts) = partitionEithers xs
+         , let bsm     = IntMap.fromListWith BoolSet.union $ map (second BoolSet.singleton) bs
+         ]
+
+reduce2Lam :: Term -> ReduceM (Blocked Term)
+reduce2Lam t = do
+  t <- reduce' t
+  case lam2Abs Relevant t of
+    t -> underAbstraction_ t $ \ t -> do
+      t <- reduce' t
+      case lam2Abs Irrelevant t of
+        t -> underAbstraction_ t reduceB'
+  where
+    lam2Abs rel (Lam _ t) = absBody t <$ t
+    lam2Abs rel t         = Abs "y" (raise 1 t `apply` [setRelevance rel $ argN $ var 0])
+
+-- | Are we looking at an application of the 'Sub' type? If so, return:
+-- * The type we're an extension of
+-- * The extent
+-- * The partial element.
+isCubicalSubtype :: PureTCM m => Type -> m (Maybe (Term, Term, Term, Term))
+isCubicalSubtype t = do
+  t <- reduce t
+  msub <- getBuiltinName' builtinSub
+  case unEl t of
+    Def q es | Just q == msub, Just (level:typ:phi:ext:_) <- allApplyElims es -> do
+      pure (pure (unArg level, unArg typ, unArg phi, unArg ext))
+    _ -> pure Nothing
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs-boot b/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical/Base.hs-boot
@@ -0,0 +1,8 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Primitive.Cubical.Base where
+
+import Agda.TypeChecking.Monad.Pure
+import Agda.Syntax.Internal
+
+isCubicalSubtype :: PureTCM m => Type -> m (Maybe (Term, Term, Term, Term))
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical/Glue.hs b/src/full/Agda/TypeChecking/Primitive/Cubical/Glue.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical/Glue.hs
@@ -0,0 +1,399 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Primitive.Cubical.Glue
+  ( mkGComp
+  , doGlueKanOp
+
+  , primGlue'
+  , prim_glue'
+  , prim_unglue'
+  )
+  where
+
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Pure
+
+import Agda.TypeChecking.Names
+  ( NamesT, runNamesT, runNames, cl, lam, open, ilam )
+import Agda.TypeChecking.Primitive.Cubical.Base
+import Agda.TypeChecking.Reduce
+  ( reduceB' )
+import Agda.TypeChecking.Substitute
+  ( absBody, apply, sort, applyE )
+
+import Agda.Syntax.Common
+  ( Cubical(..), Arg(..)
+  , ConOrigin(..), ProjOrigin(..)
+  , Relevance(..)
+  , setRelevance
+  )
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Primitive.Base
+  ( (-->), nPi', pPi', hPi', el, el', (<@>), (<@@>), (<#>), argN, argH, (<..>)
+  , SigmaKit(..), getSigmaKit
+  )
+
+import Agda.Utils.Functor
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible
+  ( __IMPOSSIBLE__ )
+
+-- | Define a "ghcomp" version of gcomp. Normal comp looks like:
+--
+-- comp^i A [ phi -> u ] u0 = hcomp^i A(1/i) [ phi -> forward A i u ] (forward A 0 u0)
+--
+-- So for "gcomp" we compute:
+--
+-- gcomp^i A [ phi -> u ] u0 = hcomp^i A(1/i) [ phi -> forward A i u, ~ phi -> forward A 0 u0 ] (forward A 0 u0)
+--
+-- The point of this is that gcomp does not produce any empty
+-- systems (if phi = 0 it will reduce to "forward A 0 u".
+mkGComp :: forall m. HasBuiltins m
+        => String
+        -> NamesT m (NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term -> NamesT m Term)
+mkGComp s = do
+  let getTermLocal :: IsBuiltin a => a -> NamesT m Term
+      getTermLocal = getTerm s
+  tPOr <- getTermLocal builtinPOr
+  tIMax <- getTermLocal builtinIMax
+  tIMin <- getTermLocal builtinIMin
+  tINeg <- getTermLocal builtinINeg
+  tHComp <- getTermLocal builtinHComp
+  tTrans <- getTermLocal builtinTrans
+  io      <- getTermLocal builtinIOne
+  iz      <- getTermLocal builtinIZero
+  let forward la bA r u = pure tTrans <#> lam "i" (\ i -> la <@> (i `imax` r))
+                                      <@> lam "i" (\ i -> bA <@> (i `imax` r))
+                                      <@> r
+                                      <@> u
+  return $ \ la bA phi u u0 ->
+    pure tHComp <#> (la <@> pure io)
+                <#> (bA <@> pure io)
+                <#> imax phi (ineg phi)
+                <@> lam "i" (\ i -> combineSys (la <@> i) (bA <@> i)
+                                      [ (phi,      ilam "o" $ \o -> forward la bA i (u <@> i <..> o))
+                                      , (ineg phi, ilam "o" $ \o -> forward la bA (pure iz) u0)
+                                      ])
+                <@> forward la bA (pure iz) u0
+
+-- | Perform the Kan operations for a @Glue φ A (T , e)@ type.
+doGlueKanOp
+  :: forall m. PureTCM m
+  => KanOperation -- ^ Are we composing or transporting?
+  -> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term, Arg Term, Arg Term)
+  -- ^ The data of the Glue operation: The levels of @A@ and @T@, @A@
+  -- itself, the extent of @T@, @T@ itself, and the family of
+  -- equivalences.
+  -> TermPosition
+  -- ^ Are we computing a plain hcomp/transp or are we computing under
+  -- @unglue@?
+  -> m (Maybe Term)
+
+doGlueKanOp (HCompOp psi u u0) (IsNot (la, lb, bA, phi, bT, e)) tpos = do
+-- hcomp {psi} u u0 : Glue {la} {lb} bA {φ} (bT, e)
+-- ... |- la, lb : Level
+-- ... |- bA : Type la
+-- ... |- bT : Partial φ (Type lB)
+-- ... |- e : PartialP φ λ o → bT o ≃ bA
+  let getTermLocal :: IsBuiltin a => a -> m Term
+      getTermLocal = getTerm $ getBuiltinId builtinHComp ++ " for " ++ getBuiltinId builtinGlue
+  tHComp   <- getTermLocal builtinHComp
+  tEFun    <- getTermLocal builtinEquivFun
+  tunglue  <- getTermLocal builtin_unglue
+  io       <- getTermLocal builtinIOne
+  tItIsOne <- getTermLocal builtinItIsOne
+  view     <- intervalView'
+
+  runNamesT [] $ do
+    [psi, u, u0] <- mapM (open . unArg) [ignoreBlocking psi, u, u0]
+    [la, lb, bA, phi, bT, e] <- mapM (open . unArg) [la, lb, bA, phi, bT, e]
+
+    ifM (headStop tpos phi) (return Nothing) $ Just <$> do
+    let
+      tf i o   = hfill lb (bT <..> o) psi u u0 i
+      unglue g = pure tunglue <#> la <#> lb <#> bA <#> phi <#> bT <#> e <@> g
+
+      a1 = pure tHComp <#> la <#> bA <#> (imax psi phi)
+        <@> lam "i" (\i -> combineSys la bA
+            [ (psi, ilam "o" (\o -> unglue (u <@> i <..> o)))
+            , (phi, ilam "o" (\o -> pure tEFun <#> lb <#> la <#> (bT <..> o) <#> bA <@> (e <..> o) <@> tf i o))
+            ])
+        <@> unglue u0
+
+      t1 = tf (pure io)
+
+    case tpos of
+      Head       -> t1 (pure tItIsOne)
+      Eliminated -> a1
+
+-- ...    |- psi, u0
+-- ..., i |- la, lb, bA, phi, bT, e
+doGlueKanOp (TranspOp psi u0) (IsFam (la, lb, bA, phi, bT, e)) tpos = do
+-- transp (λ i → Glue {la} {lb} bA {φ} (bT , e)) ψ u0
+  let
+    localUse = getBuiltinId builtinTrans ++ " for " ++ getBuiltinId builtinGlue
+    getTermLocal :: IsBuiltin a => a -> m Term
+    getTermLocal = getTerm localUse
+  tHComp <- getTermLocal builtinHComp
+  tTrans <- getTermLocal builtinTrans
+  tForall <- getTermLocal builtinFaceForall
+  tEFun   <- getTermLocal builtinEquivFun
+  tEProof <- getTermLocal builtinEquivProof
+  toutS   <- getTermLocal builtinSubOut
+  tunglue <- getTermLocal builtin_unglue
+  io      <- getTermLocal builtinIOne
+  iz      <- getTermLocal builtinIZero
+  tLMax   <- getTermLocal builtinLevelMax
+  tTransp <- getTermLocal builtinTranspProof
+  tItIsOne <- getTermLocal builtinItIsOne
+  kit <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+  runNamesT [] $ do
+
+    gcomp <- mkGComp localUse
+
+    -- transpFill: transp (λ j → bA (i ∧ j)) (φ ∨ ~ i) u0
+    -- connects u0 and transp bA i0 u0
+    let transpFill la bA phi u0 i =
+          pure tTrans <#> lam "j" (\ j -> la <@> imin i j)
+                      <@> lam "j" (\ j -> bA <@> imin i j)
+                      <@> (imax phi (ineg i))
+                      <@> u0
+    [psi,u0] <- mapM (open . unArg) [ignoreBlocking psi,u0]
+    [la, lb, bA, phi, bT, e] <- mapM (\ a -> open . runNames [] $ lam "i" (const (pure $ unArg a))) [la, lb, bA, phi, bT, e]
+
+    -- Andreas, 2022-03-24, fixing #5838
+    -- Following the updated note
+    --
+    --   Simon Huber, A Cubical Type Theory for Higher Inductive Types
+    --   https://simhu.github.io/misc/hcomp.pdf (February 2022)
+    --
+    -- See: https://github.com/agda/agda/issues/5755#issuecomment-1043797776
+
+    -- unglue_u0 i = unglue la[i/i] lb[i/i] bA[i/i] phi[i/i] bT[i/i] e[i/e] u0
+    let unglue_u0 i = foldl (<#>) (pure tunglue) (map (<@> i) [la, lb, bA, phi, bT, e]) <@> u0
+
+    view <- intervalView'
+
+    ifM (headStop tpos (phi <@> pure io)) (return Nothing) $ Just <$> do
+    let
+      tf i o = transpFill lb (lam "i" $ \ i -> bT <@> i <..> o) psi u0 i
+      t1 o = tf (pure io) o
+
+      -- compute "forall. phi"
+      forallphi = pure tForall <@> phi
+
+      -- a1 with gcomp
+      -- a1 = gcomp (ψ ∨ (∀ i. φ)) (λ { i (ψ = i1) → unglue_u0 i ; i ((∀ i. φ) = i1) → equivFun ... })
+      --        (unglue_u0 i0)
+      a1 = gcomp la bA (imax psi forallphi)
+        (lam "i" $ \ i -> combineSys (la <@> i) (bA <@> i)
+          [ (psi,       ilam "o" $ \_ -> unglue_u0 i)
+          , (forallphi, ilam "o" $ \o -> w i o <@> (tf i o))
+          ])
+        (unglue_u0 (pure iz))
+
+      max l l' = pure tLMax <@> l <@> l'
+      sigCon x y = pure (Con (sigmaCon kit) ConOSystem []) <@> x <@> y
+
+      -- The underlying function of our partial equivalence at the given
+      -- endpoint of the interval, together with proof (o : IsOne φ).
+      w i o = pure tEFun <#> (lb <@> i)
+                         <#> (la <@> i)
+                         <#> (bT <@> i <..> o)
+                         <#> (bA <@> i)
+                         <@> (e <@> i <..> o)
+
+      -- Type of fibres of the partial equivalence over a1.
+      fiberT o = fiber (lb <@> pure io) (la <@> pure io)
+        (bT <@> (pure io) <..> o) (bA <@> pure io)
+        (w (pure io) o)
+        a1
+
+      -- We don't have to do anything special for "~ forall. phi"
+      -- here (to implement "ghcomp") as it is taken care off by
+      -- tEProof in t1'alpha below
+      pe o = -- o : IsOne φ
+        combineSys (max (la <@> pure io) (lb <@> pure io)) (fiberT o)
+          [ (psi       , ilam "o" $ \_ -> sigCon u0     (lam "_" $ \_ -> a1))
+          , (forallphi , ilam "o" $ \o -> sigCon (t1 o) (lam "_" $ \_ -> a1))
+          ]
+      -- pe is a partial fibre of the equivalence with extent (ψ ∨ ∀ i. φ)
+      -- over a1
+
+      -- "ghcomp" is implemented in the proof of tEProof
+      -- (see src/data/lib/prim/Agda/Builtin/Cubical/Glue.agda)
+      t1'alpha o = -- o : IsOne φ
+         -- Because @e i1 1=1@ is an equivalence, we can extend the
+         -- partial fibre @pe@ to an actual fibre of (e i1 1=1) over a1.
+         pure toutS <#> (max (la <@> pure io) (lb <@> pure io)) <#> fiberT o
+          <#> imax psi forallphi
+          <#> pe o
+          <@> (pure tEProof
+                <#> (lb <@> pure io)        <#> (la <@> pure io)
+                <@> (bT <@> pure io <..> o) <@> (bA <@> pure io)
+                <@> (e <@> pure io <..> o)  <@> a1
+                <@> (imax psi forallphi)
+                <@> pe o)
+
+      -- TODO: optimize?
+      t1' o = t1'alpha o <&> (`applyE` [Proj ProjSystem (sigmaFst kit)])
+      alpha o = t1'alpha o <&> (`applyE` [Proj ProjSystem (sigmaSnd kit)])
+      a1' = pure tHComp <#> (la <@> pure io) <#> (bA <@> pure io)
+        <#> imax (phi <@> pure io) psi
+        <@> lam "j" (\j -> combineSys (la <@> pure io) (bA <@> pure io)
+          [ (phi <@> pure io, ilam "o" $ \o -> alpha o <@@> (w (pure io) o <@> t1' o, a1, j))
+          , (psi,             ilam "o" $ \o -> a1)
+          ])
+        <@> a1
+
+    -- glue1 (ilam "o" t1') a1'
+    case tpos of
+      Head -> t1' (pure tItIsOne)
+      Eliminated -> a1'
+doGlueKanOp _ _ _ = __IMPOSSIBLE__
+
+-- The implementation of 'primGlue'. Handles reduction where the partial
+-- element is defined.
+primGlue' :: TCM PrimitiveImpl
+primGlue' = do
+  requireCubical CFull ""
+  -- primGlue
+  --   : {la lb : Level} (A : Type la) {φ : I}
+  --   → (T : Partial φ (Type lb)
+  --   → (e : PartialP φ λ o → A ≃ T o)
+  --   → Type lb
+  t <- runNamesT [] $
+       hPi' "la" (el $ cl primLevel) (\ la ->
+       hPi' "lb" (el $ cl primLevel) $ \ lb ->
+       nPi' "A" (sort . tmSort <$> la) $ \ a ->
+       hPi' "φ" primIntervalType $ \ φ ->
+       nPi' "T" (pPi' "o" φ $ \ o -> el' (cl primLevelSuc <@> lb) (Sort . tmSort <$> lb)) $ \ t ->
+       pPi' "o" φ (\ o -> el' (cl primLevelMax <@> la <@> lb) $ cl primEquiv <#> lb <#> la <@> (t <@> o) <@> a)
+       --> (sort . tmSort <$> lb))
+  view <- intervalView'
+  one <- primItIsOne
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 6 $ \ts ->
+    case ts of
+     [la,lb,a,phi,t,e] -> do
+       sphi <- reduceB' phi
+       -- If @φ = i1@ then we reduce to @T 1=1@, since @Glue@ is also a Kan operation.
+       case view $ unArg $ ignoreBlocking $ sphi of
+         IOne -> redReturn $ unArg t `apply` [argN one]
+         -- Otherwise we're a regular ol' type.
+         _    -> return (NoReduction $ map notReduced [la,lb,a] ++ [reduced sphi] ++ map notReduced [t,e])
+     _ -> __IMPOSSIBLE__
+
+-- | The implementation of 'prim_glue', the introduction form for @Glue@
+-- types.
+prim_glue' :: TCM PrimitiveImpl
+prim_glue' = do
+  requireCubical CFull ""
+  t <- runNamesT [] $
+       hPi' "la" (el $ cl primLevel) (\ la ->
+       hPi' "lb" (el $ cl primLevel) $ \ lb ->
+       hPi' "A" (sort . tmSort <$> la) $ \ a ->
+       hPi' "φ" primIntervalType $ \ φ ->
+       hPi' "T" (pPi' "o" φ $ \ o ->  el' (cl primLevelSuc <@> lb) (Sort . tmSort <$> lb)) $ \ t ->
+       hPi' "e" (pPi' "o" φ $ \ o -> el' (cl primLevelMax <@> la <@> lb) $ cl primEquiv <#> lb <#> la <@> (t <@> o) <@> a) $ \ e ->
+       pPi' "o" φ (\ o -> el' lb (t <@> o)) --> (el' la a --> el' lb (cl primGlue <#> la <#> lb <@> a <#> φ <@> t <@> e)))
+
+  -- Takes a partial element of @t : T@ and an element of the base type @A@
+  -- which extends @e t@, and makes it into a Glue.
+  view <- intervalView'
+  one <- primItIsOne
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 8 $ \case
+    [la, lb, bA, phi, bT, e, t, a] -> do
+      sphi <- reduceB' phi
+      -- When @φ = 1@ then @t : T@ is totally defined.
+      case view $ unArg $ ignoreBlocking $ sphi of
+        IOne -> redReturn $ unArg t `apply` [argN one]
+        -- Otherwise we'll just wait to get unglued.
+        _    -> return (NoReduction $ map notReduced [la,lb,bA] ++ [reduced sphi] ++ map notReduced [bT,e,t,a])
+    _ -> __IMPOSSIBLE__
+
+-- | The implementation of 'prim_unglue', the elimination form for
+-- @Glue@ types.
+prim_unglue' :: TCM PrimitiveImpl
+prim_unglue' = do
+  requireCubical CFull ""
+  t <- runNamesT [] $
+       hPi' "la" (el $ cl primLevel) (\ la ->
+       hPi' "lb" (el $ cl primLevel) $ \ lb ->
+       hPi' "A" (sort . tmSort <$> la) $ \ a ->
+       hPi' "φ" primIntervalType $ \ φ ->
+       hPi' "T" (pPi' "o" φ $ \ o ->  el' (cl primLevelSuc <@> lb) (Sort . tmSort <$> lb)) $ \ t ->
+       hPi' "e" (pPi' "o" φ $ \ o -> el' (cl primLevelMax <@> la <@> lb) $ cl primEquiv <#> lb <#> la <@> (t <@> o) <@> a) $ \ e ->
+       (el' lb (cl primGlue <#> la <#> lb <@> a <#> φ <@> t <@> e)) --> el' la a)
+
+  -- Takes an element @b : Glue φ A (T, e)@ to an element of @A@ which,
+  -- under @φ@, agrees with @e b@. Recall that @φ ⊢ e : A → T@ and @φ ⊢
+  -- Glue φ A (T, e) = T@ so this is well-typed.
+  view <- intervalView'
+  one <- primItIsOne
+  mGlue <- getPrimitiveName' builtinGlue
+  mglue <- getPrimitiveName' builtin_glue
+  mtransp <- getPrimitiveName' builtinTrans
+  mhcomp <- getPrimitiveName' builtinHComp
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 7 $ \case
+    [la, lb, bA, phi, bT, e, b] -> do
+      sphi <- reduceB' phi
+      case view $ unArg $ ignoreBlocking $ sphi of
+        -- When @φ = i1@ we have @Glue i1 A (T , e) = T@ so @b : T@,
+        -- and we must produce @unglue b : A [ i1 → e b ]@. But that's
+        -- just @e b@!
+        IOne -> do
+          let argOne = setRelevance Irrelevant $ argN one
+          tEFun <- getTerm (getBuiltinId builtin_unglue) builtinEquivFun
+          redReturn $ tEFun `apply` [lb,la,argH $ unArg bT `apply` [argOne],bA, argN $ unArg e `apply` [argOne],b]
+
+        -- Otherwise we're dealing with a proper glued thing.
+        -- Definitely a sticky situation!
+        _    -> do
+          sb <- reduceB' b
+          let fallback sbA = return (NoReduction $ map notReduced [la,lb] ++ map reduced [sbA, sphi] ++ map notReduced [bT,e] ++ [reduced sb])
+          case unArg $ ignoreBlocking $ sb of
+            -- Case 1: unglue (glue a) = a. This agrees with the @φ =
+            -- i1@ reduction because under @φ@, the argument to
+            -- @glue@ must be in the image of the equivalence.
+            Def q es
+              | Just [_, _, _, _, _, _, _, a] <- allApplyElims es
+              , Just q == mglue -> redReturn $ unArg a
+
+            -- Case 2: unglue (transp (λ i → Glue ...) r u0).
+            -- Defer to the implementation of @doGlueKanOp DoTransp ... Eliminated@: It knows how to unglue itself.
+            Def q [Apply l, Apply bA, Apply r, Apply u0] | Just q == mtransp -> do
+              sbA <- reduceB' bA
+              -- Require that bA be a lambda abstraction...
+              case unArg $ ignoreBlocking sbA of
+                Lam _ t -> do
+                  -- And that its body reduces to a Glue type.
+                  st <- reduceB' (absBody t)
+                  case ignoreBlocking st of
+                    -- In this case, we use the Glue data extracted from
+                    -- the family we're transporting over.
+                    Def g es | Just [la', lb', bA', phi', bT', e'] <- allApplyElims es, Just g == mGlue -> do
+                        redReturn . fromMaybe __IMPOSSIBLE__ =<<
+                          doGlueKanOp (TranspOp (notBlocked r) u0) (IsFam (la',lb',bA',phi',bT',e')) Eliminated
+                    _ -> fallback (st *> sbA)
+                _ -> fallback sbA
+
+            -- Case 3: unglue (hcomp u u0).
+            -- Defer to the implementation of @doGlueKanOp DoHComp ... Eliminated@: It knows how to unglue itself.
+            Def q [Apply l,Apply bA,Apply r,Apply u,Apply u0] | Just q == mhcomp -> do
+              sbA <- reduceB' bA
+              case unArg $ ignoreBlocking sbA of
+                -- Idem: use the Glue data from the type we're doing
+                -- hcomp in.
+                Def g es | Just [la', lb', bA', phi', bT', e'] <- allApplyElims es, Just g == mGlue -> do
+                  redReturn . fromMaybe __IMPOSSIBLE__ =<<
+                    doGlueKanOp (HCompOp (notBlocked r) u u0) (IsNot (la',lb',bA',phi',bT',e')) Eliminated
+                _ -> fallback sbA
+
+            _ -> return (NoReduction $ map notReduced [la,lb,bA] ++ [reduced sphi] ++ map notReduced [bT,e] ++ [reduced sb])
+    _ -> __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical/HCompU.hs b/src/full/Agda/TypeChecking/Primitive/Cubical/HCompU.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical/HCompU.hs
@@ -0,0 +1,292 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Primitive.Cubical.HCompU
+  ( doHCompUKanOp
+  , prim_glueU'
+  , prim_unglueU'
+  )
+  where
+
+import Control.Monad
+
+import Agda.Syntax.Common
+  ( Cubical(..), Arg(..)
+  , ProjOrigin(..)
+  )
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Pure
+
+import Agda.TypeChecking.Names
+  ( runNamesT, runNames, cl, lam, open, ilam )
+import Agda.TypeChecking.Primitive.Base
+  ( (-->), nPi', pPi', hPi', el, el', el's, (<@>), (<@@>), (<#>), argN, (<..>)
+  , SigmaKit(..), getSigmaKit
+  )
+import Agda.TypeChecking.Primitive.Cubical.Glue
+import Agda.TypeChecking.Primitive.Cubical.Base
+import Agda.TypeChecking.Reduce
+  ( reduceB', reduceB )
+import Agda.TypeChecking.Substitute
+  ( absBody, apply, sort, applyE )
+
+import Agda.Utils.Functor
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible (__IMPOSSIBLE__)
+
+-- | Perform the Kan operations for an @hcomp {A = Type} {φ} u u0@ type.
+doHCompUKanOp
+  :: forall m. PureTCM m
+  => KanOperation
+  -> FamilyOrNot (Arg Term, Arg Term, Arg Term, Arg Term)
+  -> TermPosition
+  -> m (Maybe Term)
+
+-- TODO (Amy, 2022-08-17): This is literally the same algorithm as
+-- doGlueKanOp, but specialised for using transport as the equivalence.
+-- Can we deduplicate them?
+doHCompUKanOp (HCompOp psi u u0) (IsNot (la, phi, bT, bA)) tpos = do
+  let getTermLocal :: IsBuiltin a => a -> m Term
+      getTermLocal = getTerm $ getBuiltinId builtinHComp ++ " for " ++ getBuiltinId builtinHComp ++ " of Set"
+  io       <- getTermLocal builtinIOne
+  iz       <- getTermLocal builtinIZero
+  tHComp   <- getTermLocal builtinHComp
+  tTransp  <- getTermLocal builtinTrans
+  tunglue  <- getTermLocal builtin_unglueU
+  tLSuc    <- getTermLocal builtinLevelSuc
+  tSubIn   <- getTermLocal builtinSubIn
+  tItIsOne <- getTermLocal builtinItIsOne
+  runNamesT [] $ do
+    [psi, u, u0] <- mapM (open . unArg) [ignoreBlocking psi, u, u0]
+    [la, phi, bT, bA] <- mapM (open . unArg) [la, phi, bT, bA]
+
+    ifM (headStop tpos phi) (return Nothing) $ Just <$> do
+
+    let
+      transp la bA a0 = pure tTransp <#> lam "i" (const la) <@> lam "i" bA <@> pure iz <@> a0
+      tf i o = hfill la (bT <@> pure io <..> o) psi u u0 i
+
+      bAS = pure tSubIn <#> (pure tLSuc <@> la) <#> (Sort . tmSort <$> la) <#> phi <@> bA
+      unglue g = pure tunglue <#> la <#> phi <#> bT <#> bAS <@> g
+
+      a1 = pure tHComp <#> la <#> bA <#> (imax psi phi)
+        <@> lam "i" (\i -> combineSys la bA
+            [ (psi, ilam "o" (\o -> unglue (u <@> i <..> o)))
+            , (phi, ilam "o" (\ o -> transp la (\i -> bT <@> (ineg i) <..> o) (tf i o)))
+            ])
+        <@> unglue u0
+
+      t1 = tf (pure io)
+
+    -- pure tglue <#> la <#> phi <#> bT <#> bAS <@> (ilam "o" $ \ o -> t1 o) <@> a1
+    case tpos of
+      Eliminated -> a1
+      Head       -> t1 (pure tItIsOne)
+
+
+doHCompUKanOp (TranspOp psi u0) (IsFam (la, phi, bT, bA)) tpos = do
+  let
+    localUse = getBuiltinId builtinTrans ++ " for " ++ getBuiltinId builtinHComp ++ " of Set"
+    getTermLocal :: IsBuiltin a => a -> m Term
+    getTermLocal = getTerm localUse
+  tPOr <- getTermLocal builtinPOr
+  tIMax <- getTermLocal builtinIMax
+  tIMin <- getTermLocal builtinIMin
+  tINeg <- getTermLocal builtinINeg
+  tHComp <- getTermLocal builtinHComp
+  tTrans <- getTermLocal builtinTrans
+  tTranspProof <- getTermLocal builtinTranspProof
+  tSubIn <- getTermLocal builtinSubIn
+  tForall  <- getTermLocal builtinFaceForall
+  io      <- getTermLocal builtinIOne
+  iz      <- getTermLocal builtinIZero
+  tLSuc   <- getTermLocal builtinLevelSuc
+  tPath   <- getTermLocal builtinPath
+  tItIsOne   <- getTermLocal builtinItIsOne
+  kit <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+  runNamesT [] $ do
+    -- Helper definitions we'll use:
+    gcomp <- mkGComp localUse
+
+    let
+      transp la bA a0 = pure tTrans <#> lam "i" (const la) <@> lam "i" bA <@> pure iz <@> a0
+      transpFill la bA phi u0 i = pure tTrans
+        <#> ilam "j" (\ j -> la <@> imin i j)
+        <@> ilam "j" (\ j -> bA <@> imin i j)
+        <@> (imax phi (ineg i))
+        <@> u0
+
+    [psi, u0] <- mapM (open . unArg) [ignoreBlocking psi, u0]
+
+    [la, phi, bT, bA] <- mapM (\a -> open . runNames [] $ lam "i" (const (pure $ unArg a))) [la, phi, bT, bA]
+
+    -- Andreas, 2022-03-25, issue #5838.
+    -- Port the fix of @unglueTranspGlue@ and @doGlueKanOp DoTransp@
+    -- also to @doHCompUKanOp DoTransp@, as suggested by Tom Jack and Anders Mörtberg.
+    -- We define @unglue_u0 i@ that is first used with @i@ and then with @i0@.
+    -- The original code used it only with @i0@.
+    tunglue <- cl $ getTermLocal builtin_unglueU
+    let
+      bAS i = pure tSubIn
+        <#> (pure tLSuc <@> (la <@> i)) <#> (Sort . tmSort <$> (la <@> i)) <#> (phi <@> i)
+        <@> (bA <@> i)
+      unglue_u0 i = pure tunglue
+        <#> (la <@> i) <#> (phi <@> i) <#> (bT <@> i)
+        <#> bAS i <@> u0
+
+    ifM (headStop tpos (phi <@> pure io)) (return Nothing) $ Just <$> do
+
+    let
+      tf i o = transpFill la (lam "i" $ \ i -> bT <@> i <@> pure io <..> o) psi u0 i
+      t1 o   = tf (pure io) o
+
+      -- compute "forall. phi"
+      forallphi = pure tForall <@> phi
+
+      -- a1 with gcomp
+      a1 = gcomp la bA (imax psi forallphi)
+        (lam "i" $ \ i -> combineSys (la <@> i) (bA <@> i)
+          [ (psi,       ilam "o" $ \_ -> unglue_u0 i)
+          , (forallphi, ilam "o" (\o -> transp (la <@> i) (\j -> bT <@> i <@> ineg j <..> o) (tf i o)))
+          ])
+          (unglue_u0 (pure iz))
+
+      w i o = lam "x" $ transp (la <@> i) (\j -> bT <@> i <@> ineg j <..> o)
+
+      pt o = -- o : [ φ 1 ]
+        combineSys (la <@> pure io) (bT <@> pure io <@> pure io <..> o)
+          [ (psi       , ilam "o" $ \_ -> u0)
+          , (forallphi , ilam "o" $ \o -> t1 o)
+          ]
+
+      -- "ghcomp" is implemented in the proof of tTranspProof
+      -- (see src/data/lib/prim/Agda/Builtin/Cubical/HCompU.agda)
+      t1'alpha o = -- o : [ φ 1 ]
+         pure tTranspProof
+          <#> (la <@> pure io) <@> lam "i" (\i -> bT <@> pure io <@> ineg i <..> o)
+          <@> imax psi forallphi
+          <@> pt o
+          <@> (pure tSubIn <#> (la <@> pure io) <#> (bA <@> pure io) <#> imax psi forallphi
+                <@> a1)
+
+      -- TODO: optimize?
+      t1' o   = t1'alpha o <&> (`applyE` [Proj ProjSystem (sigmaFst kit)])
+      alpha o = t1'alpha o <&> (`applyE` [Proj ProjSystem (sigmaSnd kit)])
+      a1' = pure tHComp <#> (la <@> pure io) <#> (bA <@> pure io)
+        <#> imax (phi <@> pure io) psi
+        <@> lam "j" (\j -> combineSys (la <@> pure io) (bA <@> pure io)
+          [ (phi <@> pure io, ilam "o" $ \o -> alpha o <@@> (w (pure io) o <@> t1' o, a1, j))
+          , (psi,             ilam "o" $ \o -> a1)
+          ])
+        <@> a1
+
+    -- glue1 (ilam "o" t1') a1'
+    case tpos of
+      Eliminated -> a1'
+      Head       -> t1' (pure tItIsOne)
+doHCompUKanOp _ _ _ = __IMPOSSIBLE__
+
+-- | The implementation of 'prim_glueU', the introduction form for
+-- @hcomp@ types.
+prim_glueU' :: TCM PrimitiveImpl
+prim_glueU' = do
+-- TODO (Amy, 2022-08-17): Same thing about duplicated code with Glue
+-- applies here.
+  requireCubical CErased ""
+  t <- runNamesT [] $
+       hPi' "la" (el $ cl primLevel) (\ la ->
+       hPi' "φ" primIntervalType $ \ φ ->
+       hPi' "T" (nPi' "i" primIntervalType $ \ _ -> pPi' "o" φ $ \ o -> sort . tmSort <$> la) $ \ t ->
+       hPi' "A" (el's (cl primLevelSuc <@> la) $ cl primSub <#> (cl primLevelSuc <@> la) <@> (Sort . tmSort <$> la) <@> φ <@> (t <@> primIZero)) $ \ a -> do
+       let bA = (cl primSubOut <#> (cl primLevelSuc <@> la) <#> (Sort . tmSort <$> la) <#> φ <#> (t <@> primIZero) <@> a)
+       pPi' "o" φ (\ o -> el' la (t <@> cl primIOne <..> o))
+         --> (el' la bA)
+         --> el' la (cl primHComp <#> (cl primLevelSuc <@> la) <#> (Sort . tmSort <$> la) <#> φ <@> t <@> bA))
+  view <- intervalView'
+  one <- primItIsOne
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 6 $ \ts ->
+    case ts of
+      [la,phi,bT,bA,t,a] -> do
+       sphi <- reduceB' phi
+       case view $ unArg $ ignoreBlocking $ sphi of
+         IOne -> redReturn $ unArg t `apply` [argN one]
+         _    -> return (NoReduction $ map notReduced [la] ++ [reduced sphi] ++ map notReduced [bT,bA,t,a])
+      _ -> __IMPOSSIBLE__
+
+-- | The implementation of 'prim_unglueU', the elimination form for
+-- @hcomp@ types.
+prim_unglueU' :: TCM PrimitiveImpl
+prim_unglueU' = do
+-- TODO (Amy, 2022-08-17): Same thing about duplicated code with Glue
+-- applies here.
+  requireCubical CErased ""
+  t <- runNamesT [] $
+       hPi' "la" (el $ cl primLevel) (\ la ->
+       hPi' "φ" primIntervalType $ \ φ ->
+       hPi' "T" (nPi' "i" primIntervalType $ \ _ -> pPi' "o" φ $ \ o -> sort . tmSort <$> la) $ \ t ->
+       hPi' "A" (el's (cl primLevelSuc <@> la) $ cl primSub <#> (cl primLevelSuc <@> la) <@> (Sort . tmSort <$> la) <@> φ <@> (t <@> primIZero)) $ \ a -> do
+       let bA = (cl primSubOut <#> (cl primLevelSuc <@> la) <#> (Sort . tmSort <$> la) <#> φ <#> (t <@> primIZero) <@> a)
+       el' la (cl primHComp <#> (cl primLevelSuc <@> la) <#> (Sort . tmSort <$> la) <#> φ <@> t <@> bA)
+         --> el' la bA)
+
+  view <- intervalView'
+  one <- primItIsOne
+  mglueU <- getPrimitiveName' builtin_glueU
+  mtransp <- getPrimitiveName' builtinTrans
+  mHCompU <- getPrimitiveName' builtinHComp
+  let mhcomp = mHCompU
+
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 5 $ \case
+    [la,phi,bT,bA,b] -> do
+      sphi <- reduceB' phi
+      case view $ unArg $ ignoreBlocking $ sphi of
+        -- Case where the hcomp has reduced away: Transport backwards
+        -- along the partial element we've glued.
+        IOne -> do
+          tTransp <- getTerm (getBuiltinId builtin_unglueU) builtinTrans
+          iNeg    <- getTerm (getBuiltinId builtin_unglueU) builtinINeg
+          iZ      <- getTerm (getBuiltinId builtin_unglueU) builtinIZero
+          redReturn <=< runNamesT [] $ do
+            [la,bT,b] <- mapM (open . unArg) [la,bT,b]
+            pure tTransp <#> lam "i" (\ _ -> la) <@> lam "i" (\ i -> bT <@> ineg i <..> pure one)
+              <@> pure iZ <@> b
+
+        -- Otherwise, we're dealing with a proper glu- didn't I already
+        -- make this joke? Oh, yeah, in prim_unglue, right.
+        _ -> do
+          sb <- reduceB' b
+          let fallback sbA = return (NoReduction $ map notReduced [la] ++ [reduced sphi] ++ map notReduced [bT,bA] ++ [reduced sb])
+          case unArg $ ignoreBlocking $ sb of
+            -- Project:
+            Def q es | Just [_,_,_,_,_, a] <- allApplyElims es, Just q == mglueU -> redReturn $ unArg a
+
+            -- Transport:
+            Def q [Apply l, Apply bA, Apply r, Apply u0] | Just q == mtransp -> do
+              sbA <- reduceB bA
+              case unArg $ ignoreBlocking sbA of
+                Lam _ t -> do
+                  st <- reduceB' (absBody t)
+                  case ignoreBlocking st of
+                    Def h es | Just [la,_,phi,bT,bA] <- allApplyElims es, Just h == mHCompU -> do
+                      redReturn . fromMaybe __IMPOSSIBLE__ =<<
+                        doHCompUKanOp (TranspOp (notBlocked r) u0) (IsFam (la,phi,bT,bA)) Eliminated
+                    _ -> fallback (st *> sbA)
+                _  -> fallback sbA
+
+            -- Compose:
+            Def q [Apply l,Apply bA,Apply r,Apply u,Apply u0] | Just q == mhcomp -> do
+              sbA <- reduceB bA
+              case unArg $ ignoreBlocking sbA of
+                Def h es | Just [la,_,phi,bT,bA] <- allApplyElims es, Just h == mHCompU -> do
+                  redReturn . fromMaybe __IMPOSSIBLE__ =<<
+                    doHCompUKanOp (HCompOp (notBlocked r) u u0) (IsNot (la,phi,bT,bA)) Eliminated
+                _ -> fallback sbA
+            _ -> return (NoReduction $ map notReduced [la] ++ [reduced sphi] ++ map notReduced [bT,bA] ++ [reduced sb])
+
+    _ -> __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/Primitive/Cubical/Id.hs b/src/full/Agda/TypeChecking/Primitive/Cubical/Id.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Primitive/Cubical/Id.hs
@@ -0,0 +1,292 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Implementation of the primitives relating to Cubical identity types.
+
+module Agda.TypeChecking.Primitive.Cubical.Id
+  ( -- * General elimination form
+    primIdElim'
+  -- * Introduction form
+  , primConId'
+  -- * Projection maps (primarily used internally)
+  , primIdFace'
+  , primIdPath'
+  -- * Kan operations
+  , doIdKanOp
+  )
+  where
+
+import qualified Data.IntMap as IntMap
+import Data.Traversable
+import Data.Maybe
+
+import Agda.Syntax.Common
+  ( Cubical(..), Arg(..), defaultArgInfo, defaultArg )
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug (__IMPOSSIBLE_VERBOSE__)
+
+import Agda.TypeChecking.Names
+  ( runNamesT, runNames, cl, lam, ilam, open )
+import Agda.TypeChecking.Primitive.Base
+  ( (-->), nPi', hPi', el, el', el's, (<@>), (<#>), (<..>), argN )
+import Agda.TypeChecking.Primitive.Cubical.Base
+import Agda.TypeChecking.Reduce
+  ( reduceB' )
+import Agda.TypeChecking.Substitute
+  ( apply, sort, listS, applySubst )
+
+import Agda.Utils.Impossible (__IMPOSSIBLE__)
+
+-- | Primitive elimination rule for the cubical identity types. Unlike
+-- J, @idElim@ makes explicit the structure of Swan's identity types as
+-- being pairs of a cofibration and a path. Moreover, it records that
+-- the path is definitionally @refl@ under that cofibration.
+primIdElim' :: TCM PrimitiveImpl
+primIdElim' = do
+  -- The implementation here looks terrible but most of it is actually
+  -- the type.
+  requireCubical CErased ""
+  t <- runNamesT [] $
+    hPi' "a" (el $ cl primLevel) $ \ a ->
+    hPi' "c" (el $ cl primLevel) $ \ c ->
+    hPi' "A" (sort . tmSort <$> a) $ \ bA ->
+    hPi' "x" (el' a bA) $ \ x ->
+    nPi' "C" (nPi' "y" (el' a bA) $ \ y ->
+              el' a (cl primId <#> a <#> bA <@> x <@> y) --> (sort . tmSort <$> c)) $ \ bC ->
+    -- To construct (C : (y : A) → Id A x y → Type c), it suffices to:
+
+    -- For all cofibrations φ,
+    nPi' "φ" primIntervalType (\ phi ->
+      -- For all y : A [ φ → (λ _ → x) ]
+      nPi' "y" (el's a $ cl primSub <#> a <@> bA <@> phi <@> lam "o" (const x)) $ \ y ->
+      let pathxy = cl primPath <#> a <@> bA <@> x <@> outSy
+          outSy  = cl primSubOut <#> a <#> bA <#> phi <#> lam "o" (const x) <@> y
+          reflx  = lam "o" $ \ _ -> lam "i" $ \ _ -> x -- TODO Andrea, should block on o
+      -- For all w : (Path A x (outS y)) [ φ (λ _ → refl {x = outS y} ]
+      in nPi' "w" (el's a $ cl primSub <#> a <@> pathxy <@> phi <@> reflx) $ \ w ->
+      let outSw = (cl primSubOut <#> a <#> pathxy <#> phi <#> reflx <@> w)
+      in el' c $ bC <@> outSy <@> (cl primConId <#> a <#> bA <#> x <#> outSy <@> phi <@> outSw))
+      -- Construct an inhabitant of (C (outS y) (conid φ (outS w)))
+    -->
+    hPi' "y" (el' a bA) (\ y ->
+      nPi' "p" (el' a $ cl primId <#> a <#> bA <@> x <@> y) $ \ p ->
+      el' c $ bC <@> y <@> p)
+
+  -- Implementation starts here:
+  conid <- primConId
+  sin <- primSubIn
+  path <- primPath
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 8 $ \case
+    [a,c,bA,x,bC,f,y,p] -> do
+      sp <- reduceB' p
+      cview <- conidView'
+      case cview (unArg x) $ unArg $ ignoreBlocking sp of
+        -- Record that the right endpoint and the path definitionally
+        -- agree with x φ holds. This is guaranteed internally by the
+        -- typing rule for @conId@ but can't be recovered from
+        -- @primIdPath@ and @primIdFace@ (see #2598)
+        Just (phi, w) -> do
+          let y' = sin `apply` [a, bA, phi, argN (unArg y)]
+          let w' = sin `apply` [a, argN (path `apply` [a, bA, x, y]), phi, argN (unArg w)]
+          redReturn $ unArg f `apply` [phi, defaultArg y', defaultArg w']
+        _ -> return $ NoReduction $ map notReduced [a,c,bA,x,bC,f,y] ++ [reduced sp]
+    _ -> __IMPOSSIBLE_VERBOSE__ "implementation of primIdElim called with wrong arity"
+
+-- | Introduction form for the cubical identity types.
+primConId' :: TCM PrimitiveImpl
+primConId' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+    hPi' "a" (el $ cl primLevel) $ \ a ->
+    hPi' "A" (sort . tmSort <$> a) $ \ bA ->
+    hPi' "x" (el' a bA) $ \ x ->
+    hPi' "y" (el' a bA) $ \ y ->
+    primIntervalType -- Cofibration
+    --> (el' a $ cl primPath <#> a <#> bA <@> x <@> y)
+    --> (el' a $ cl primId <#> a <#> bA <@> x <@> y)
+
+  -- Implementation note: conId, as the name implies, is a constructor.
+  -- It's not represented as a constructor because users can't match on
+  -- it (but we, internally, can: see createMissingConIdClause).
+
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 6 $ \case
+    [l,bA,x,y,phi,p] -> do
+      sphi <- reduceB' phi
+      view <- intervalView'
+      case view $ unArg $ ignoreBlocking sphi of
+        -- But even though it's a constructor, it does reduce, in some
+        -- cases: If the cofibration is definitely true, then we return
+        -- reflId.  TODO: Handle this in the conversion checker instead?
+        IOne -> do
+          reflId <- getTerm (getBuiltinId builtinConId) builtinReflId
+          redReturn $ reflId
+        _ -> return $ NoReduction $ map notReduced [l,bA,x,y] ++ [reduced sphi, notReduced p]
+    _ -> __IMPOSSIBLE_VERBOSE__ "implementation of primConId called with wrong arity"
+
+-- | Extract the underlying cofibration from an inhabitant of the
+-- cubical identity types.
+--
+-- TODO (Amy, 2022-08-17): Projecting a cofibration from a Kan type
+-- violates the cubical phase distinction.
+primIdFace' :: TCM PrimitiveImpl
+primIdFace' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+    hPi' "a" (el $ cl primLevel) $ \ a ->
+    hPi' "A" (sort . tmSort <$> a) $ \ bA ->
+    hPi' "x" (el' a bA) $ \ x ->
+    hPi' "y" (el' a bA) $ \ y ->
+    el' a (cl primId <#> a <#> bA <@> x <@> y)
+    --> primIntervalType
+
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 5 $ \case
+    [l,bA,x,y,t] -> do
+      st <- reduceB' t
+      mConId <- getName' builtinConId
+      cview <- conidView'
+      case cview (unArg x) $ unArg (ignoreBlocking st) of
+        Just (phi, _) -> redReturn (unArg phi)
+        _ -> return $ NoReduction $ map notReduced [l,bA,x,y] ++ [reduced st]
+    _ -> __IMPOSSIBLE__
+
+-- | Extract the underlying path from an inhabitant of the
+-- cubical identity types.
+primIdPath' :: TCM PrimitiveImpl
+primIdPath' = do
+  requireCubical CErased ""
+  t <- runNamesT [] $
+    hPi' "a" (el $ cl primLevel) $ \ a ->
+    hPi' "A" (sort . tmSort <$> a) $ \ bA ->
+    hPi' "x" (el' a bA) $ \ x ->
+    hPi' "y" (el' a bA) $ \ y ->
+    el' a (cl primId <#> a <#> bA <@> x <@> y)
+    --> el' a (cl primPath <#> a <#> bA <@> x <@> y)
+
+  return $ PrimImpl t $ primFun __IMPOSSIBLE__ 5 $ \case
+    [l,bA,x,y,t] -> do
+      st <- reduceB' t
+      mConId <- getName' builtinConId
+      cview <- conidView'
+      case cview (unArg x) $ unArg (ignoreBlocking st) of
+        Just (_, w) -> redReturn (unArg w)
+        _ -> return $ NoReduction $ map notReduced [l,bA,x,y] ++ [reduced st]
+    _ -> __IMPOSSIBLE__
+
+-- | Check that a term matches a given predicate on every consistent
+-- substitution of interval variables which makes the given cofibration
+-- hold.
+onEveryFace
+  :: Term -- ^ The cofibration @φ@
+  -> Term -- ^ The term to test
+  -> (Term -> Bool)
+  -- ^ The predicate to test with.
+  -> ReduceM Bool
+onEveryFace phi u p = do
+  unview <- intervalUnview'
+  let boolToI b = if b then unview IOne else unview IZero
+  as <- decomposeInterval phi
+  bools <- for as $ \ (bs,ts) -> do
+    let u' = listS (IntMap.toAscList $ IntMap.map boolToI bs) `applySubst` u
+    t <- reduce2Lam u'
+    return $! p $ ignoreBlocking t
+  pure (and bools)
+
+doIdKanOp
+  :: KanOperation           -- ^ Are we composing or transporting?
+  -> FamilyOrNot (Arg Term) -- ^ Level argument
+  -> FamilyOrNot (Arg Term, Arg Term, Arg Term)
+    -- ^ Domain, left and right endpoints of the identity type
+  -> ReduceM (Maybe (Reduced t Term))
+doIdKanOp kanOp l bA_x_y = do
+  let getTermLocal :: IsBuiltin a => a -> ReduceM Term
+      getTermLocal = getTerm $ kanOpName kanOp ++ " for " ++ getBuiltinId builtinId
+
+  unview <- intervalUnview'
+  mConId <- getName' builtinConId
+  cview <- conidView'
+  let isConId t = isJust $ cview __DUMMY_TERM__ t
+
+  sa0 <- reduceB' (kanOpBase kanOp)
+  -- TODO: wasteful to compute b even when cheaper checks might fail
+  --
+  -- Should we go forward with the Kan operation? This is the case when
+  -- doing transport always, and when every face fo the partial element
+  -- has reduced to @conid@ otherwise. Note that @conidView@ treats
+  -- @reflId@ as though it were @conid i1 refl@.
+  b <- case kanOp of
+    TranspOp{}    -> return True
+    HCompOp _ u _ ->
+      onEveryFace (unArg . ignoreBlocking . kanOpCofib $ kanOp) (unArg u) isConId
+
+  case mConId of
+    Just conid | isConId (unArg . ignoreBlocking $ sa0), b -> (Just <$>) . (redReturn =<<) $ do
+      tHComp    <- getTermLocal builtinHComp
+      tTrans    <- getTermLocal builtinTrans
+      tIMin     <- getTermLocal builtinDepIMin
+      idFace    <- getTermLocal builtinIdFace
+      idPath    <- getTermLocal builtinIdPath
+      tPathType <- getTermLocal builtinPath
+      tConId    <- getTermLocal builtinConId
+
+      runNamesT [] $ do
+        let
+          io = pure $ unview IOne
+          iz = pure $ unview IZero
+          conId = pure tConId
+
+          eval TranspOp{} l bA phi _ u0 =
+            pure tTrans <#> l <@> bA <@> phi <@> u0
+          eval HCompOp{} l bA phi u u0 =
+            pure tHComp <#> (l <@> io) <#> (bA <@> io) <#> phi <@> u <@> u0
+
+        -- Compute a line of levels. So we can invoke 'eval' uniformly.
+        l <- case l of
+          IsFam l -> open . unArg $ l
+          IsNot l -> open (Lam defaultArgInfo $ NoAbs "_" $ unArg l)
+
+        p0 <- open . unArg $ kanOpBase kanOp
+
+        -- p is the partial element we are extending against. This is
+        -- used to compute the resulting cofibration, so we fake a
+        -- partial element when doing transport.
+        p <- case kanOp of
+          HCompOp _ u _ -> do
+            u <- open . unArg $ u
+            pure $ \i o -> u <@> i <..> o
+          TranspOp{} -> do
+            pure $ \i o -> p0
+
+        phi <- open . unArg . ignoreBlocking $ kanOpCofib kanOp
+
+        -- Similarly to the fake line of levels above, fake lines of
+        -- everything even when we're doing composition, for uniformity
+        -- of eval.
+        [bA, x, y] <- case bA_x_y of
+          IsFam (bA, x, y) -> for [bA, x, y] $ \a ->
+            open $ runNames [] $ lam "i" (const (pure $ unArg a))
+          IsNot (bA, x, y) -> for [bA, x, y] $ \a ->
+            open (Lam defaultArgInfo $ NoAbs "_" $ unArg a)
+
+        -- The resulting path is constant when when
+        --    @Σ φ λ o → -- primIdFace p i1 o@
+        -- holds. That's why cofibrations have to be closed under Σ,
+        -- c.f. primDepIMin.
+        cof <- pure tIMin
+          <@> phi
+          <@> ilam "o" (\o ->
+            pure idFace <#> (l <@> io) <#> (bA <@> io) <#> (x <@> io) <#> (y <@> io) <@> (p io o))
+
+        -- Do the Kan operation for our faces in the Path type.
+        path <- eval kanOp l
+          (lam "i" $ \i -> pure tPathType <#> (l <@> i) <#> (bA <@> i) <@> (x <@> i) <@> (y <@> i))
+          phi
+          (lam "i" $ \i -> ilam "o" $ \o ->
+            pure idPath <#> (l <@> i) <#> (bA <@> i) <#> (x <@> i) <#> (y <@> i) <@> (p i o))
+          (pure idPath <#> (l <@> iz) <#> (bA <@> iz) <#> (x <@> iz) <#> (y <@> iz) <@> p0)
+
+        conId <#> (l <@> io) <#> (bA <@> io) <#> (x <@> io) <#> (y <@> io)
+          <@> pure cof
+          <@> pure path
+    _ -> return $ Nothing
diff --git a/src/full/Agda/TypeChecking/ProjectionLike.hs b/src/full/Agda/TypeChecking/ProjectionLike.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/ProjectionLike.hs
@@ -0,0 +1,500 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Dropping initial arguments (``parameters'') from a function which can be
+--   easily reconstructed from its principal argument.
+--
+--   A function which has such parameters is called ``projection-like''.
+--
+--   The motivation for this optimization comes from the use of nested records.
+--
+--   First, let us look why proper projections need not store the parameters:
+--   The type of a projection @f@ is of the form
+--   @
+--      f : Γ → R Γ → C
+--   @
+--   where @R@ is the record type and @C@ is the type of the field @f@.
+--   Given a projection application
+--   @
+--      p pars u
+--   @
+--   we know that the type of the principal argument @u@ is
+--   @
+--      u : R pars
+--   @
+--   thus, the parameters @pars@ are redundant in the projection application
+--   if we can always infer the type of @u@.
+--   For projections, this is case, because the principal argument @u@ must be
+--   neutral; otherwise, if it was a record value, we would have a redex,
+--   yet Agda maintains a β-normal form.
+--
+--   The situation for projections can be generalized to ``projection-like''
+--   functions @f@.  Conditions:
+--
+--     1. The type of @f@ is of the form @f : Γ → D Γ → ...@ for some
+--        type constructor @D@ which can never reduce.
+--
+--     2. For every reduced welltyped application @f pars u ...@,
+--        the type of @u@ is inferable.
+--
+--   This then allows @pars@ to be dropped always.
+--
+--   Condition 2 is approximated by a bunch of criteria, for details see function
+--   'makeProjection'.
+--
+--   Typical projection-like functions are compositions of projections
+--   which arise from nested records.
+--
+--   Notes:
+--
+--     1. This analysis could be dualized to ``constructor-like'' functions
+--        whose parameters are reconstructable from the target type.
+--        But such functions would need to be fully applied.
+--
+--     2. A more general analysis of which arguments are reconstructible
+--        can be found in
+--
+--          Jason C. Reed, Redundancy elimination for LF
+--          LFTMP 2004.
+
+module Agda.TypeChecking.ProjectionLike where
+
+import Control.Monad
+
+import qualified Data.Map as Map
+import Data.Monoid (Any(..), getAny)
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Free (runFree, IgnoreSorts(..))
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Positivity
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce (reduce, abortIfBlocked)
+import Agda.TypeChecking.Telescope
+
+import Agda.TypeChecking.DropArgs
+
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- | View for a @Def f (Apply a : es)@ where @isRelevantProjection f@.
+--   Used for projection-like @f@s.
+data ProjectionView
+  = ProjectionView
+    { projViewProj  :: QName
+    , projViewSelf  :: Arg Term
+    , projViewSpine :: Elims
+    }
+    -- ^ A projection or projection-like function, applied to its
+    --   principal argument
+  | LoneProjectionLike QName ArgInfo
+    -- ^ Just a lone projection-like function, missing its principal
+    --   argument (from which we could infer the parameters).
+  | NoProjection Term
+    -- ^ Not a projection or projection-like thing.
+
+-- | Semantics of 'ProjectionView'.
+unProjView :: ProjectionView -> Term
+unProjView pv =
+  case pv of
+    ProjectionView f a es   -> Def f (Apply a : es)
+    LoneProjectionLike f ai -> Def f []
+    NoProjection v          -> v
+
+-- | Top-level 'ProjectionView' (no reduction).
+{-# SPECIALIZE projView :: Term -> TCM ProjectionView #-}
+projView :: HasConstInfo m => Term -> m ProjectionView
+projView v = do
+  let fallback = return $ NoProjection v
+  case v of
+    Def f es -> caseMaybeM (isRelevantProjection f) fallback $ \ isP -> do
+      if projIndex isP <= 0 then fallback else do
+        case es of
+          []           -> return $ LoneProjectionLike f $ projArgInfo isP
+          Apply a : es -> return $ ProjectionView f a es
+          -- Since a projection is a function, it cannot be projected itself.
+          Proj{}  : _  -> __IMPOSSIBLE__
+          -- The principal argument of a projection-like cannot be the interval?
+          IApply{} : _ -> __IMPOSSIBLE__
+
+    _ -> fallback
+
+{-# SPECIALIZE reduceProjectionLike :: Term -> TCM Term #-}
+-- | Reduce away top-level projection like functions.
+--   (Also reduces projections, but they should not be there,
+--   since Internal is in lambda- and projection-beta-normal form.)
+--
+reduceProjectionLike :: PureTCM m => Term -> m Term
+reduceProjectionLike v = do
+  -- Andreas, 2013-11-01 make sure we do not reduce a constructor
+  -- because that could be folded back into a literal by reduce.
+  pv <- projView v
+  case pv of
+    ProjectionView{} -> onlyReduceProjections $ reduce v
+                            -- ordinary reduce, only different for Def's
+    _                -> return v
+
+data ProjEliminator = EvenLone | ButLone | NoPostfix
+  deriving Eq
+
+{-# SPECIALIZE elimView :: ProjEliminator -> Term -> TCM Term #-}
+-- | Turn prefix projection-like function application into postfix ones.
+--   This does just one layer, such that the top spine contains
+--   the projection-like functions as projections.
+--   Used in 'compareElims' in @TypeChecking.Conversion@
+--   and in "Agda.TypeChecking.CheckInternal".
+--
+--   If the 'Bool' is 'True', a lone projection like function will be
+--   turned into a lambda-abstraction, expecting the principal argument.
+--   If the 'Bool' is 'False', it will be returned unaltered.
+--
+--   No precondition.
+--   Preserves constructorForm, since it really does only something
+--   on (applications of) projection-like functions.
+elimView :: PureTCM m => ProjEliminator -> Term -> m Term
+elimView pe v = do
+  reportSDoc "tc.conv.elim" 60 $ "elimView of " <+> prettyTCM v
+  v <- reduceProjectionLike v
+  reportSDoc "tc.conv.elim" 65 $
+    "elimView (projections reduced) of " <+> prettyTCM v
+  case pe of
+    NoPostfix -> return v
+    _         -> do
+      pv <- projView v
+      case pv of
+        NoProjection{}        -> return v
+        LoneProjectionLike f ai
+          | pe == EvenLone  -> return $ Lam ai $ Abs "r" $ Var 0 [Proj ProjPrefix f]
+          | otherwise     -> return v
+        ProjectionView f a es -> (`applyE` (Proj ProjPrefix f : es)) <$> elimView pe (unArg a)
+
+{-# SPECIALIZE eligibleForProjectionLike :: QName -> TCM Bool #-}
+-- | Which @Def@types are eligible for the principle argument
+--   of a projection-like function?
+eligibleForProjectionLike :: (HasConstInfo m) => QName -> m Bool
+eligibleForProjectionLike d = eligible . theDef <$> getConstInfo d
+  where
+  eligible = \case
+    Datatype{} -> True
+    Record{}   -> True
+    Axiom{}    -> True
+    DataOrRecSig{}     -> True
+    GeneralizableVar{} -> False
+    Function{}    -> False
+    Primitive{}   -> False
+    PrimitiveSort{} -> False
+    Constructor{} -> __IMPOSSIBLE__
+    AbstractDefn d -> eligible d
+      -- Andreas, 2017-08-14, issue #2682:
+      -- Abstract records still export the projections.
+      -- Andreas, 2016-10-11 AIM XXIV
+      -- Projection-like at abstract types violates the parameter reconstructibility property.
+      -- See test/Fail/AbstractTypeProjectionLike.
+
+-- | Turn a definition into a projection if it looks like a projection.
+--
+-- Conditions for projection-likeness of @f@:
+--
+--   1. The type of @f@ must be of the shape @Γ → D Γ → C@ for @D@
+--      a name (@Def@) which is 'eligibleForProjectionLike':
+--      @data@ / @record@ / @postulate@.
+--
+--   2. The application of f should only get stuck if the principal argument
+--      is inferable (neutral).  Thus:
+--
+--      a. @f@ cannot have absurd clauses (which are stuck even if the principal
+--         argument is a constructor).
+--
+--      b. @f@ cannot be abstract as it does not reduce outside abstract blocks
+--         (always stuck).
+--
+--      c. @f@ cannot match on other arguments than the principal argument.
+--
+--      d. @f@ cannot match deeply.
+--
+--      e. @f@s body may not mention the parameters.
+--
+--      f. A rhs of @f@ cannot be a record expression, since this will be
+--         translated to copatterns by recordExpressionsToCopatterns.
+--         Thus, an application of @f@ waiting for a projection
+--         can be stuck even when the principal argument is a constructor.
+--
+--      g. @f@ cannot be an irrelevant definition (Andreas, 2022-03-07, #5809),
+--         as those are not reduced.
+--
+-- For internal reasons:
+--
+--   3. @f@ cannot be constructor headed
+--
+--   4. @f@ cannot be recursive, since we have not implemented a function
+--      which goes through the bodies of the @f@ and the mutually recursive
+--      functions and drops the parameters from all applications of @f@.
+--
+-- Examples for these reasons: see test/Succeed/NotProjectionLike.agda
+
+makeProjection :: QName -> TCM ()
+makeProjection x = whenM (optProjectionLike <$> pragmaOptions) $ do
+ inTopContext $ do
+  reportSLn "tc.proj.like" 70 $ "Considering " ++ prettyShow x ++ " for projection likeness"
+  defn <- getConstInfo x
+  let t = defType defn
+  reportSDoc "tc.proj.like" 20 $ sep
+    [ "Checking for projection likeness "
+    , prettyTCM x <+> " : " <+> prettyTCM t
+    ]
+  if isIrrelevant defn then
+    reportSDoc "tc.proj.like" 30 $ "  projection-like functions cannot be irrelevant"
+  else case theDef defn of
+    Function{funClauses = cls}
+      | any (isNothing . clauseBody) cls ->
+        reportSLn "tc.proj.like" 30 $ "  projection-like functions cannot have absurd clauses"
+      | any (maybe __IMPOSSIBLE__ isRecordExpression . clauseBody) cls ->
+        reportSLn "tc.proj.like" 30 $ "  projection-like functions cannot have record rhss"
+    -- Constructor-headed functions can't be projection-like (at the moment). The reason
+    -- for this is that invoking constructor-headedness will circumvent the inference of
+    -- the dropped arguments.
+    -- Nor can abstract definitions be projection-like since they won't reduce
+    -- outside the abstract block.
+    def@Function{funProjection = Left MaybeProjection, funClauses = cls,
+                 funSplitTree = st0, funCompiled = cc0, funInv = NotInjective,
+                 funMutual = Just [], -- Andreas, 2012-09-28: only consider non-mutual funs
+                 funAbstr = ConcreteDef, funOpaque = TransparentDef} -> do
+      ps0 <- filterM validProj $ candidateArgs [] t
+      reportSLn "tc.proj.like" 30 $ if null ps0 then "  no candidates found"
+                                                else "  candidates: " ++ prettyShow ps0
+      unless (null ps0) $ do
+        -- Andreas 2012-09-26: only consider non-recursive functions for proj.like.
+        -- Issue 700: problems with recursive funs. in term.checker and reduction
+        ifM recursive (reportSLn "tc.proj.like" 30 $ "  recursive functions are not considered for projection-likeness") $ do
+          {- else -}
+          case lastMaybe (filter (checkOccurs cls . snd) ps0) of
+            Nothing -> reportSDoc "tc.proj.like" 50 $ nest 2 $ vcat
+              [ "occurs check failed"
+              , nest 2 $ "clauses =" <?> vcat (map pretty cls) ]
+            Just (d, n) -> do
+              -- Yes, we are projection-like!
+              reportSDoc "tc.proj.like" 10 $ vcat
+                [ prettyTCM x <+> " : " <+> prettyTCM t
+                , nest 2 $ sep
+                  [ "is projection like in argument",  prettyTCM n, "for type", prettyTCM (unArg d) ]
+                ]
+              __CRASH_WHEN__ "tc.proj.like.crash" 1000
+
+              let cls' = map (dropArgs n) cls
+                  cc   = dropArgs n cc0
+                  st   = dropArgs n st0
+              reportSLn "tc.proj.like" 60 $ unlines
+                [ "  rewrote clauses to"
+                , "    " ++ show cc
+                ]
+
+              -- Andreas, 2013-10-20 build parameter dropping function
+              let pIndex = n + 1
+                  tel = take pIndex $ telToList $ theTel $ telView' t
+              unless (length tel == pIndex) __IMPOSSIBLE__
+              let projection = Projection
+                    { projProper   = Nothing
+                    , projOrig     = x
+                    , projFromType = d
+                    , projIndex    = pIndex
+                    , projLams     = ProjLams $ map (argFromDom . fmap fst) tel
+                    }
+              let newDef = def
+                           { funProjection     = Right projection
+                           , funClauses        = cls'
+                           , funSplitTree      = st
+                           , funCompiled       = cc
+                           , funInv            = dropArgs n $ funInv def
+                           }
+              addConstant x $ defn { defPolarity       = drop n $ defPolarity defn
+                                   , defArgOccurrences = drop n $ defArgOccurrences defn
+                                   , defDisplay        = []
+                                   , theDef            = newDef
+                                   }
+    Function{funInv = Inverse{}} ->
+      reportSLn "tc.proj.like" 30 $ "  injective functions can't be projections"
+    Function{funAbstr = AbstractDef} ->
+      reportSLn "tc.proj.like" 30 $ "  abstract functions can't be projections"
+    Function{funOpaque = OpaqueDef _} ->
+      reportSLn "tc.proj.like" 30 $ "  opaque functions can't be projections"
+    Function{funProjection = Right{}} ->
+      reportSLn "tc.proj.like" 30 $ "  already projection like"
+    Function{funProjection = Left NeverProjection} ->
+      reportSLn "tc.proj.like" 30 $ "  the user has asked for it not to be projection-like"
+    Function{funMutual = Just (_:_)} ->
+      reportSLn "tc.proj.like" 30 $ "  mutual functions can't be projections"
+    Function{funMutual = Nothing} ->
+      reportSLn "tc.proj.like" 30 $ "  mutuality check has not run yet"
+    Axiom{}        -> reportSLn "tc.proj.like" 30 $ "  not a function, but Axiom"
+    DataOrRecSig{} -> reportSLn "tc.proj.like" 30 $ "  not a function, but DataOrRecSig"
+    GeneralizableVar{} -> reportSLn "tc.proj.like" 30 $ "  not a function, but GeneralizableVar"
+    AbstractDefn{} -> reportSLn "tc.proj.like" 30 $ "  not a function, but AbstractDefn"
+    Constructor{}  -> reportSLn "tc.proj.like" 30 $ "  not a function, but Constructor"
+    Datatype{}     -> reportSLn "tc.proj.like" 30 $ "  not a function, but Datatype"
+    Primitive{}    -> reportSLn "tc.proj.like" 30 $ "  not a function, but Primitive"
+    PrimitiveSort{} -> reportSLn "tc.proj.like" 30 $ "  not a function, but PrimitiveSort"
+    Record{}       -> reportSLn "tc.proj.like" 30 $ "  not a function, but Record"
+  where
+    -- If the user wrote a record expression as rhs,
+    -- the recordExpressionsToCopatterns translation will turn this into copatterns,
+    -- violating the conditions of projection-likeness.
+    -- Andreas, 2019-07-11, issue #3843.
+    isRecordExpression :: Term -> Bool
+    isRecordExpression = \case
+      Con _ ConORec _ -> True
+      _ -> False
+    -- @validProj (d,n)@ checks whether the head @d@ of the type of the
+    -- @n@th argument is injective in all args (i.d. being name of data/record/axiom).
+    validProj :: (Arg QName, Int) -> TCM Bool
+    validProj (_, 0) = return False
+    validProj (d, _) = eligibleForProjectionLike (unArg d)
+
+    -- NOTE: If the following definition turns out to be slow, then
+    -- one could perhaps reuse information computed by the termination
+    -- and/or positivity checkers.
+    recursive = do
+      occs <- computeOccurrences x
+      case Map.lookup (ADef x) occs of
+        Just n | n >= 1 -> return True -- recursive occurrence
+        _               -> return False
+
+    checkOccurs cls n = all (nonOccur n) cls
+
+    nonOccur n cl =
+        (take n p == [0..n - 1]) &&
+        onlyMatch n ps &&  -- projection-like functions are only allowed to match on the eliminatee
+                          -- otherwise we may end up projecting from constructor applications, in
+                          -- which case we can't reconstruct the dropped parameters
+        checkBody m n b
+      where
+        Perm _ p = fromMaybe __IMPOSSIBLE__ $ clausePerm cl
+        ps       = namedClausePats cl
+        b        = compiledClauseBody cl  -- Renumbers variables to match order in patterns
+                                          -- and includes dot patterns as variables.
+        m        = size $ concatMap patternVars ps  -- This also counts dot patterns!
+
+
+    onlyMatch n ps = all (shallowMatch . namedArg) (take 1 ps1) &&
+                     noMatches (ps0 ++ drop 1 ps1)
+      where
+        (ps0, ps1) = splitAt n ps
+        shallowMatch (ConP _ _ ps) = noMatches ps
+        shallowMatch _             = True
+        noMatches = all (noMatch . namedArg)
+        noMatch ConP{} = False
+        noMatch DefP{} = False
+        noMatch LitP{} = False
+        noMatch ProjP{}= False
+        noMatch VarP{} = True
+        noMatch DotP{} = True
+        noMatch IApplyP{} = True
+
+    -- Make sure non of the parameters occurs in the body of the function.
+    checkBody m n b = not . getAny $ runFree badVar IgnoreNot b
+      where badVar x = Any $ m - n <= x && x < m
+
+    -- @candidateArgs [var 0,...,var(n-1)] t@ adds @(n,d)@ to the output,
+    -- if @t@ is a function-type with domain @t 0 .. (n-1)@
+    -- (the domain of @t@ is the type of the arg @n@).
+    --
+    -- This means that from the type of arg @n@ all previous arguments
+    -- can be computed by a simple matching.
+    -- (Provided the @d@ is data/record/postulate, checked in @validProj@).
+    --
+    -- E.g. f : {x : _}(y : _){z : _} -> D x y z -> ...
+    -- will return (D,3) as a candidate (amongst maybe others).
+    --
+    candidateArgs :: [Term] -> Type -> [(Arg QName, Int)]
+    candidateArgs vs t =
+      case unEl t of
+        Pi a b
+          | Def d es <- unEl $ unDom a,
+            Just us  <- allApplyElims es,
+            vs == map unArg us -> (d <$ argFromDom a, length vs) : candidateRec b
+          | otherwise          -> candidateRec b
+        _                      -> []
+      where
+        candidateRec NoAbs{}   = []
+        candidateRec (Abs x t) = candidateArgs (var (size vs) : vs) t
+
+{-# SPECIALIZE inferNeutral :: Term -> TCM Type #-}
+-- | Infer type of a neutral term.
+--   See also @infer@ in @Agda.TypeChecking.CheckInternal@, which has a very similar
+--   logic but also type checks all arguments.
+inferNeutral :: (PureTCM m, MonadBlock m) => Term -> m Type
+inferNeutral u = do
+  reportSDoc "tc.infer" 20 $ "inferNeutral" <+> prettyTCM u
+  case u of
+    Var i es -> do
+      a <- typeOfBV i
+      loop a (Var i) es
+    Def f es -> do
+      whenJustM (isRelevantProjection f) $ \_ -> nonInferable
+      a <- defType <$> getConstInfo f
+      loop a (Def f) es
+    MetaV x es -> do -- we assume meta instantiations to be well-typed
+      a <- metaType x
+      loop a (MetaV x) es
+    _ -> nonInferable
+  where
+    nonInferable :: MonadDebug m => m a
+    nonInferable = __IMPOSSIBLE_VERBOSE__ $ unlines
+      [ "inferNeutral: non-inferable term:"
+      , "  " ++ prettyShow u
+      ]
+    loop :: (PureTCM m, MonadBlock m) => Type -> (Elims -> Term) -> Elims -> m Type
+    loop t hd [] = return t
+    loop t hd (e:es) = do
+      t' <- case e of
+        Apply (Arg ai v) ->
+          ifPiType t (\_ b -> return $ b `absApp` v) __IMPOSSIBLE__
+        IApply x y r ->
+          ifPath t (\_ b -> return $ b `absApp` r) __IMPOSSIBLE__
+        Proj o f -> do
+          -- @projectTyped@ expects the type to be reduced.
+          t <- reduce t
+          ifJustM (projectTyped (hd []) t o f) (\(_,_,t') -> return t') __IMPOSSIBLE__
+      loop t' (hd . (e:)) es
+
+{-# SPECIALIZE computeDefType :: QName -> Elims -> TCM Type #-}
+-- | Compute the head type of a Def application. For projection-like functions
+--   this requires inferring the type of the principal argument.
+computeDefType :: (PureTCM m, MonadBlock m) => QName -> Elims -> m Type
+computeDefType f es = do
+  def <- getConstInfo f
+  -- To compute the type @a@ of a projection-like @f@,
+  -- we have to infer the type of its first argument.
+  let defaultResult = return $ defType def
+  -- Find a first argument to @f@.
+  case es of
+    _ | projectionArgs def <= 0 -> defaultResult
+    (Apply arg : _) -> do
+      -- Infer its type.
+      reportSDoc "tc.infer" 30 $
+        "inferring type of internal arg: " <+> prettyTCM arg
+      -- Jesper, 2023-02-06: infer crashes on non-inferable terms,
+      -- e.g. applications of projection-like functions. Hence we bring them
+      -- into postfix form.
+      targ <- inferNeutral =<< elimView EvenLone (unArg arg)
+      reportSDoc "tc.infer" 30 $
+        "inferred type: " <+> prettyTCM targ
+      -- getDefType wants the argument type reduced.
+      -- Andreas, 2016-02-09, Issue 1825: The type of arg might be
+      -- a meta-variable, e.g. in interactive development.
+      -- In this case, we postpone.
+      targ <- abortIfBlocked targ
+      fromMaybeM __IMPOSSIBLE__ $ getDefType f targ
+    _ -> defaultResult
diff --git a/src/full/Agda/TypeChecking/ProjectionLike.hs-boot b/src/full/Agda/TypeChecking/ProjectionLike.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/ProjectionLike.hs-boot
@@ -0,0 +1,10 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.ProjectionLike where
+
+import Agda.Syntax.Abstract.Name (QName)
+import Agda.TypeChecking.Monad.Base
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Signature (HasConstInfo)
+
+makeProjection :: QName -> TCM ()
+eligibleForProjectionLike :: (HasConstInfo m) => QName -> m Bool
diff --git a/src/full/Agda/TypeChecking/Quote.hs b/src/full/Agda/TypeChecking/Quote.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Quote.hs
@@ -0,0 +1,387 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Quote where
+
+import Control.Monad
+
+import Data.Maybe (fromMaybe)
+import qualified Data.Text as T
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern ( hasDefP )
+import Agda.Syntax.Literal
+import Agda.Syntax.TopLevelModuleName
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive.Base
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Impossible
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Size
+
+-- | Parse @quote@.
+quotedName :: (MonadTCError m, MonadAbsToCon m) => A.Expr -> m QName
+quotedName = \case
+  A.Var x          -> genericError $ "Cannot quote a variable " ++ prettyShow x
+  A.Def x          -> return x
+  A.Macro x        -> return x
+  A.Proj _o p      -> unambiguous p
+  A.Con c          -> unambiguous c
+  A.ScopedExpr _ e -> quotedName e
+  e -> genericDocError =<< do
+    text "Can only quote defined names, but encountered" <+> prettyA e
+  where
+  unambiguous xs
+    | Just x <- getUnambiguous xs = return x
+    | otherwise =
+        genericError $ "quote: Ambiguous name: " ++ prettyShow (unAmbQ xs)
+
+
+data QuotingKit = QuotingKit
+  { quoteTermWithKit   :: Term       -> ReduceM Term
+  , quoteTypeWithKit   :: Type       -> ReduceM Term
+  , quoteDomWithKit    :: Dom Type   -> ReduceM Term
+  , quoteDefnWithKit   :: Definition -> ReduceM Term
+  , quoteListWithKit   :: forall a. (a -> ReduceM Term) -> [a] -> ReduceM Term
+  }
+
+quotingKit :: TCM QuotingKit
+quotingKit = do
+  currentModule   <- fromMaybe __IMPOSSIBLE__ <$> currentTopLevelModule
+  hidden          <- primHidden
+  instanceH       <- primInstance
+  visible         <- primVisible
+  relevant        <- primRelevant
+  irrelevant      <- primIrrelevant
+  quantity0       <- primQuantity0
+  quantityω       <- primQuantityω
+  modality        <- primModalityConstructor
+  nil             <- primNil
+  cons            <- primCons
+  abs             <- primAbsAbs
+  arg             <- primArgArg
+  arginfo         <- primArgArgInfo
+  var             <- primAgdaTermVar
+  lam             <- primAgdaTermLam
+  extlam          <- primAgdaTermExtLam
+  def             <- primAgdaTermDef
+  con             <- primAgdaTermCon
+  pi              <- primAgdaTermPi
+  sort            <- primAgdaTermSort
+  meta            <- primAgdaTermMeta
+  lit             <- primAgdaTermLit
+  litNat          <- primAgdaLitNat
+  litWord64       <- primAgdaLitNat
+  litFloat        <- primAgdaLitFloat
+  litChar         <- primAgdaLitChar
+  litString       <- primAgdaLitString
+  litQName        <- primAgdaLitQName
+  litMeta         <- primAgdaLitMeta
+  normalClause    <- primAgdaClauseClause
+  absurdClause    <- primAgdaClauseAbsurd
+  varP            <- primAgdaPatVar
+  conP            <- primAgdaPatCon
+  dotP            <- primAgdaPatDot
+  litP            <- primAgdaPatLit
+  projP           <- primAgdaPatProj
+  absurdP         <- primAgdaPatAbsurd
+  set             <- primAgdaSortSet
+  setLit          <- primAgdaSortLit
+  prop            <- primAgdaSortProp
+  propLit         <- primAgdaSortPropLit
+  inf             <- primAgdaSortInf
+  unsupportedSort <- primAgdaSortUnsupported
+  sucLevel        <- primLevelSuc
+  lub             <- primLevelMax
+  lkit            <- requireLevels
+  Con z _ _       <- primZero
+  Con s _ _       <- primSuc
+  unsupported     <- primAgdaTermUnsupported
+
+  agdaDefinitionFunDef          <- primAgdaDefinitionFunDef
+  agdaDefinitionDataDef         <- primAgdaDefinitionDataDef
+  agdaDefinitionRecordDef       <- primAgdaDefinitionRecordDef
+  agdaDefinitionPostulate       <- primAgdaDefinitionPostulate
+  agdaDefinitionPrimitive       <- primAgdaDefinitionPrimitive
+  agdaDefinitionDataConstructor <- primAgdaDefinitionDataConstructor
+
+  let (@@) :: Apply a => ReduceM a -> ReduceM Term -> ReduceM a
+      t @@ u = apply <$> t <*> ((:[]) . defaultArg <$> u)
+
+      (!@) :: Apply a => a -> ReduceM Term -> ReduceM a
+      t !@ u = pure t @@ u
+
+      (!@!) :: Apply a => a -> Term -> ReduceM a
+      t !@! u = pure t @@ pure u
+
+      quoteHiding :: Hiding -> ReduceM Term
+      quoteHiding Hidden     = pure hidden
+      quoteHiding Instance{} = pure instanceH
+      quoteHiding NotHidden  = pure visible
+
+      quoteRelevance :: Relevance -> ReduceM Term
+      quoteRelevance Relevant   = pure relevant
+      quoteRelevance Irrelevant = pure irrelevant
+      quoteRelevance NonStrict  = pure relevant
+
+      quoteQuantity :: Quantity -> ReduceM Term
+      quoteQuantity (Quantity0 _) = pure quantity0
+      quoteQuantity (Quantity1 _) = __IMPOSSIBLE__
+      quoteQuantity (Quantityω _) = pure quantityω
+
+      -- TODO: quote Annotation
+      quoteModality :: Modality -> ReduceM Term
+      quoteModality m =
+        modality !@ quoteRelevance (getRelevance m)
+                 @@ quoteQuantity  (getQuantity  m)
+
+      quoteArgInfo :: ArgInfo -> ReduceM Term
+      quoteArgInfo (ArgInfo h m _ _ _) =
+        arginfo !@ quoteHiding h
+                @@ quoteModality m
+
+      quoteLit :: Literal -> ReduceM Term
+      quoteLit l@LitNat{}    = litNat    !@! Lit l
+      quoteLit l@LitWord64{} = litWord64 !@! Lit l
+      quoteLit l@LitFloat{}  = litFloat  !@! Lit l
+      quoteLit l@LitChar{}   = litChar   !@! Lit l
+      quoteLit l@LitString{} = litString !@! Lit l
+      quoteLit l@LitQName{}  = litQName  !@! Lit l
+      quoteLit l@LitMeta {}  = litMeta   !@! Lit l
+
+      -- We keep no ranges in the quoted term, so the equality on terms
+      -- is only on the structure.
+      quoteSortLevelTerm :: Term -> Term -> Level -> ReduceM Term
+      quoteSortLevelTerm fromLit fromLevel (ClosedLevel n) = fromLit !@! Lit (LitNat n)
+      quoteSortLevelTerm fromLit fromLevel l               = fromLevel !@ quoteTerm (unlevelWithKit lkit l)
+
+      quoteSort :: Sort -> ReduceM Term
+      quoteSort (Type t) = quoteSortLevelTerm setLit set t
+      quoteSort (Prop t) = quoteSortLevelTerm propLit prop t
+      quoteSort (Inf u n) = case u of
+        UType -> inf !@! Lit (LitNat n)
+        UProp -> pure unsupportedSort
+        USSet -> pure unsupportedSort
+      quoteSort SSet{}   = pure unsupportedSort
+      quoteSort SizeUniv = pure unsupportedSort
+      quoteSort LockUniv = pure unsupportedSort
+      quoteSort LevelUniv = pure unsupportedSort
+      quoteSort IntervalUniv = pure unsupportedSort
+      quoteSort PiSort{} = pure unsupportedSort
+      quoteSort FunSort{} = pure unsupportedSort
+      quoteSort UnivSort{}   = pure unsupportedSort
+      quoteSort (MetaS x es) = quoteTerm $ MetaV x es
+      quoteSort (DefS d es)  = quoteTerm $ Def d es
+      quoteSort (DummyS s)   =__IMPOSSIBLE_VERBOSE__ s
+
+      quoteType :: Type -> ReduceM Term
+      quoteType (El _ t) = quoteTerm t
+
+      quoteQName :: QName -> ReduceM Term
+      quoteQName x = pure $ Lit $ LitQName x
+
+      quotePats :: [NamedArg DeBruijnPattern] -> ReduceM Term
+      quotePats ps = list $ map (quoteArg quotePat . fmap namedThing) ps
+
+      quotePat :: DeBruijnPattern -> ReduceM Term
+      quotePat p@(VarP _ x)
+       | patternOrigin p == Just PatOAbsurd = absurdP !@! quoteNat (toInteger $ dbPatVarIndex x)
+      quotePat (VarP o x)        = varP !@! quoteNat (toInteger $ dbPatVarIndex x)
+      quotePat (DotP _ t)        = dotP !@ quoteTerm t
+      quotePat (ConP c _ ps)     = conP !@ quoteQName (conName c) @@ quotePats ps
+      quotePat (LitP _ l)        = litP !@ quoteLit l
+      quotePat (ProjP _ x)       = projP !@ quoteQName x
+      -- #4763: quote IApply co/patterns as though they were variables
+      quotePat (IApplyP _ _ _ x) = varP !@! quoteNat (toInteger $ dbPatVarIndex x)
+      quotePat DefP{}            = pure unsupported
+
+      quoteClause :: Either a Projection -> Clause -> ReduceM Term
+      quoteClause proj cl@Clause{ clauseTel = tel, namedClausePats = ps, clauseBody = body} =
+        case body of
+          Nothing -> absurdClause !@ quoteTelescope tel @@ quotePats ps'
+          Just b  -> normalClause !@ quoteTelescope tel @@ quotePats ps' @@ quoteTerm b
+        where
+          -- #5128: restore dropped parameters if projection-like
+          ps' =
+            case proj of
+              Left _ -> ps
+              Right p  -> pars ++ ps
+                where
+                  n    = projIndex p - 1
+                  pars = map toVar $ take n $ zip (downFrom $ size tel) (telToList tel)
+                  toVar (i, d) = argFromDom d <&> \ (x, _) -> unnamed $ I.varP (DBPatVar x i)
+
+      quoteTelescope :: Telescope -> ReduceM Term
+      quoteTelescope tel = quoteList quoteTelEntry $ telToList tel
+
+      quoteTelEntry :: Dom (ArgName, Type) -> ReduceM Term
+      quoteTelEntry dom@Dom{ unDom = (x , t) } = do
+        SigmaKit{..} <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+        Con sigmaCon ConOSystem [] !@! quoteString x @@ quoteDom quoteType (fmap snd dom)
+
+      list :: [ReduceM Term] -> ReduceM Term
+      list = foldr (\ a as -> cons !@ a @@ as) (pure nil)
+
+      quoteList :: (a -> ReduceM Term) -> [a] -> ReduceM Term
+      quoteList q xs = list (map q xs)
+
+      quoteDom :: (a -> ReduceM Term) -> Dom a -> ReduceM Term
+      quoteDom q Dom{domInfo = info, unDom = t} = arg !@ quoteArgInfo info @@ q t
+
+      quoteAbs :: Subst a => (a -> ReduceM Term) -> Abs a -> ReduceM Term
+      quoteAbs q (Abs s t)   = abs !@! quoteString s @@ q t
+      quoteAbs q (NoAbs s t) = abs !@! quoteString s @@ q (raise 1 t)
+
+      quoteArg :: (a -> ReduceM Term) -> Arg a -> ReduceM Term
+      quoteArg q (Arg info t) = arg !@ quoteArgInfo info @@ q t
+
+      quoteArgs :: Args -> ReduceM Term
+      quoteArgs ts = list (map (quoteArg quoteTerm) ts)
+
+      -- has the clause been generated (in particular by --cubical)?
+      -- TODO: have an explicit clause origin field?
+      generatedClause :: Clause -> Bool
+      generatedClause cl = hasDefP (namedClausePats cl)
+
+      quoteTerm :: Term -> ReduceM Term
+      quoteTerm v = do
+        v <- instantiate' v
+        case unSpine v of
+          Var n es   ->
+             let ts = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+             in  var !@! Lit (LitNat $ fromIntegral n) @@ quoteArgs ts
+          Lam info t -> lam !@ quoteHiding (getHiding info) @@ quoteAbs quoteTerm t
+          Def x es   -> do
+            defn <- getConstInfo x
+            r <- isReconstructed
+            -- #2220: remember to restore dropped parameters
+            let
+              conOrProjPars = defParameters defn r
+              ts = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+              qx Function{ funExtLam = Just (ExtLamInfo m False _), funClauses = cs } = do
+                    -- An extended lambda should not have any extra parameters!
+                    unless (null conOrProjPars) __IMPOSSIBLE__
+                    cs <- return $ filter (not . generatedClause) cs
+                    n <- size <$> lookupSection m
+                    let (pars, args) = splitAt n ts
+                    extlam !@ list (map (quoteClause (Left ()) . (`apply` pars)) cs)
+                           @@ list (map (quoteArg quoteTerm) args)
+              qx df@Function{ funExtLam = Just (ExtLamInfo _ True _), funCompiled = Just Fail{}, funClauses = [cl] } = do
+                    -- See also corresponding code in InternalToAbstract
+                    let n = length (namedClausePats cl) - 1
+                        pars = take n ts
+                    extlam !@ list [quoteClause (Left ()) $ cl `apply` pars ]
+                           @@ list (drop n $ map (quoteArg quoteTerm) ts)
+              qx _ = do
+                n <- getDefFreeVars x
+                def !@! quoteName x
+                     @@ list (drop n $ conOrProjPars ++ map (quoteArg quoteTerm) ts)
+            qx (theDef defn)
+          Con x ci es | Just ts <- allApplyElims es -> do
+            r <- isReconstructed
+            cDef <- getConstInfo (conName x)
+            n    <- getDefFreeVars (conName x)
+            let args = list $ drop n $ defParameters cDef r ++ map (quoteArg quoteTerm) ts
+            con !@! quoteConName x @@ args
+          Con x ci es -> pure unsupported
+          Pi t u     -> pi !@  quoteDom quoteType t
+                            @@ quoteAbs quoteType u
+          Level l    -> quoteTerm (unlevelWithKit lkit l)
+          Lit l      -> lit !@ quoteLit l
+          Sort s     -> sort !@ quoteSort s
+          MetaV x es -> meta !@! quoteMeta currentModule x
+                              @@ quoteArgs vs
+            where vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          DontCare u -> quoteTerm u
+          Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+      defParameters :: Definition -> Bool -> [ReduceM Term]
+      defParameters def True  = []
+      defParameters def False = map par hiding
+        where
+          np = case theDef def of
+                 Constructor{ conPars = np }         -> np
+                 Function{ funProjection = Right p } -> projIndex p - 1
+                 _                                   -> 0
+          TelV tel _ = telView' (defType def)
+          hiding     = take np $ telToList tel
+          par d      = arg !@ quoteArgInfo (domInfo d)
+                           @@ pure unsupported
+
+      quoteDefn :: Definition -> ReduceM Term
+      quoteDefn def =
+        case theDef def of
+          Function{funClauses = cs, funProjection = proj} ->
+           do
+            -- re #3733: maybe these should be quoted but marked as generated?
+            cs <- return $ filter (not . generatedClause) cs
+            agdaDefinitionFunDef !@ quoteList (quoteClause proj) cs
+          Datatype{dataPars = np, dataCons = cs} ->
+            agdaDefinitionDataDef !@! quoteNat (fromIntegral np) @@ quoteList (pure . quoteName) cs
+          Record{recConHead = c, recFields = fs} ->
+            agdaDefinitionRecordDef
+              !@! quoteName (conName c)
+              @@ quoteList (quoteDom (pure . quoteName)) fs
+          Axiom{}       -> pure agdaDefinitionPostulate
+          DataOrRecSig{} -> pure agdaDefinitionPostulate
+          GeneralizableVar{} -> pure agdaDefinitionPostulate  -- TODO: reflect generalizable vars
+          AbstractDefn{}-> pure agdaDefinitionPostulate
+          Primitive{primClauses = cs} | not $ null cs ->
+            agdaDefinitionFunDef !@ quoteList (quoteClause (Left ())) cs
+          Primitive{}   -> pure agdaDefinitionPrimitive
+          PrimitiveSort{} -> pure agdaDefinitionPrimitive
+          Constructor{conData = d} ->
+            agdaDefinitionDataConstructor !@! quoteName d
+
+  return $ QuotingKit quoteTerm quoteType (quoteDom quoteType) quoteDefn quoteList
+
+quoteString :: String -> Term
+quoteString = Lit . LitString . T.pack
+
+quoteName :: QName -> Term
+quoteName x = Lit (LitQName x)
+
+quoteNat :: Integer -> Term
+quoteNat n
+  | n >= 0    = Lit (LitNat n)
+  | otherwise = __IMPOSSIBLE__
+
+quoteConName :: ConHead -> Term
+quoteConName = quoteName . conName
+
+quoteMeta :: TopLevelModuleName -> MetaId -> Term
+quoteMeta m = Lit . LitMeta m
+
+quoteTerm :: Term -> TCM Term
+quoteTerm v = do
+  kit <- quotingKit
+  runReduceM (quoteTermWithKit kit v)
+
+quoteType :: Type -> TCM Term
+quoteType v = do
+  kit <- quotingKit
+  runReduceM (quoteTypeWithKit kit v)
+
+quoteDom :: Dom Type -> TCM Term
+quoteDom v = do
+  kit <- quotingKit
+  runReduceM (quoteDomWithKit kit v)
+
+quoteDefn :: Definition -> TCM Term
+quoteDefn def = do
+  kit <- quotingKit
+  runReduceM (quoteDefnWithKit kit def)
+
+quoteList :: [Term] -> TCM Term
+quoteList xs = do
+  kit <- quotingKit
+  runReduceM (quoteListWithKit kit pure xs)
diff --git a/src/full/Agda/TypeChecking/ReconstructParameters.hs b/src/full/Agda/TypeChecking/ReconstructParameters.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/ReconstructParameters.hs
@@ -0,0 +1,179 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Reconstruct dropped parameters from constructors.  Used by
+--   with-abstraction to avoid ill-typed abstractions (#745). Note that the
+--   term is invalid after parameter reconstruction. Parameters need to be
+--   dropped again before using it.
+
+module Agda.TypeChecking.ReconstructParameters where
+
+import Data.Functor ( ($>) )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Generic
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.CheckInternal
+import Agda.TypeChecking.ProjectionLike
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Datatypes
+
+import Agda.Utils.Size
+import Agda.Utils.Either
+import Agda.Utils.Function (applyWhen)
+
+import Agda.Utils.Impossible
+
+reconstructParametersInType :: Type -> TCM Type
+reconstructParametersInType = reconstructParametersInType' defaultAction
+
+reconstructParametersInType' :: Action TCM -> Type -> TCM Type
+reconstructParametersInType' act a =
+  traverse (reconstructParameters' act (sort $ getSort a)) a
+
+reconstructParametersInTel :: Telescope -> TCM Telescope
+reconstructParametersInTel EmptyTel = return EmptyTel
+reconstructParametersInTel (ExtendTel a tel) = do
+  ar <- reconstructParametersInType (unDom a)
+  addContext (absName tel, a) $
+    ExtendTel (ar <$ a) <$> traverse reconstructParametersInTel tel
+
+reconstructParametersInEqView :: EqualityView -> TCM EqualityView
+reconstructParametersInEqView (EqualityType s eq l a u v) =
+  EqualityType s eq l <$> traverse (reconstructParameters $ sort s) a
+                      <*> traverse (reconstructParameters $ El s $ unArg a) u
+                      <*> traverse (reconstructParameters $ El s $ unArg a) v
+reconstructParametersInEqView (OtherType a) = OtherType <$> reconstructParametersInType a
+reconstructParametersInEqView (IdiomType a) = IdiomType <$> reconstructParametersInType a
+
+reconstructParameters :: Type -> Term -> TCM Term
+reconstructParameters = reconstructParameters' defaultAction
+
+reconstructParameters' :: Action TCM -> Type -> Term -> TCM Term
+reconstructParameters' act a v = do
+  reportSDoc "tc.reconstruct" 30 $
+    sep [ "reconstructing parameters in"
+        , nest 2 $ sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM a ] ]
+  v <- checkInternal' (reconstructAction' act) v CmpLeq a
+
+  reportSDoc "tc.reconstruct" 30 $
+    nest 2 $ "-->" <+> prettyTCM v
+  return v
+
+reconstructAction :: Action TCM
+reconstructAction = reconstructAction' defaultAction
+
+reconstructAction' :: Action TCM -> Action TCM
+reconstructAction' act = act{ postAction = \ty tm -> postAction act ty tm >>= reconstruct ty }
+
+reconstruct :: Type -> Term -> TCM Term
+reconstruct ty v = do
+    reportSDoc "tc.reconstruct" 30 $
+      sep [ "reconstructing in"
+      , nest 2 $ sep [ prettyTCM v <+> ":", nest 2 $ prettyTCM ty ] ]
+    case v of
+      Con h ci vs -> do
+        hh <- fromRight __IMPOSSIBLE__ <$> getConHead (conName h)
+        TelV tel dataTy <- telView ty
+        reportSDoc "tc.reconstruct" 50 $
+          sep [ "reconstructing"
+              , nest 2 $ sep [ prettyTCM v <+> ":"
+                             , nest 2 $ prettyTCM dataTy ] ]
+        pars <- addContext tel $ extractParameters (conName h) dataTy
+        -- If the constructor is underapplied, we need to escape from the telescope.
+        let escape = applySubst $ strengthenS __IMPOSSIBLE__ $ size tel
+        return $ Con hh ci $ map Apply (escape pars) ++ vs
+      Def f es -> projView v >>= \case
+        ProjectionView _f a es -> do
+          recTy <- infer =<< dropParameters (unArg a)
+          pars <- extractParameters f recTy
+          loop ty (Def f . (map Apply pars ++) . (Apply a:)) es
+        LoneProjectionLike _f i -> reduce (unEl ty) >>= \case
+          Pi recTy _ -> do
+            pars <- extractParameters f (unDom recTy)
+            return $ Def f $ map Apply pars
+          _ -> __IMPOSSIBLE__
+        NoProjection{} -> do
+          ty <- defType <$> getConstInfo f
+          loop ty (Def f) es
+      Var i es -> do
+        ty <- typeOfBV i
+        loop ty (Var i) es
+      MetaV m es -> do
+        ty <- getMetaType m
+        loop ty (MetaV m) es
+      _ -> return v
+
+  where
+    -- @loop ty f vs@ where @ty@ is the type of @f []@ and vs are valid
+    -- arguments to something of type @ty@
+    loop :: Type -> (Elims -> Term) -> Elims -> TCM Term
+    loop ty f []           = do
+      reportSDoc "tc.reconstruct" 50 $ "Loop ended" <+> pretty (f [])
+      return $ f []
+    loop ty f (Apply u:es) = do
+      reportSDoc "tc.reconstruct" 50 $ "The type before app is:" <+> pretty ty
+      reportSDoc "tc.reconstruct" 50 $ "The term before app is:" <+> prettyTCM (f [])
+      uu <- dropParameters u
+      reportSDoc "tc.reconstruct" 50 $ "The app is:" <+> pretty uu
+      ty' <- piApplyM ty uu
+      reportSDoc "tc.reconstruct" 50 $ "The type after app is:" <+> pretty ty'
+      loop ty' (f . (Apply u :)) es
+    loop ty f (Proj o p:es) = do
+      reportSDoc "tc.reconstruct" 50 $ "The type is:" <+> pretty ty
+      reportSDoc "tc.reconstruct" 50 $ "The term is:" <+> pretty (f [])
+      reportSDoc "tc.reconstruct" 50 $ "The proj is:" <+> prettyTCM p
+      pars <- extractParameters p ty
+      ~(Just (El _ (Pi _ b))) <- getDefType p =<< reduce ty
+      let fTm = f []
+      fe <- dropParameters fTm
+      loop (absApp b fe) (Def p . (map Apply pars ++) . (Apply (defaultArg fTm) :)) es
+    loop ty _ (IApply {}:vs) = __IMPOSSIBLE__
+
+-- Extract the parameters from the type of a constructor
+-- application or the type of the principal argument of a
+-- projection.
+extractParameters :: QName -> Type -> TCM Args
+extractParameters q ty = reduce (unEl ty) >>= \case
+  Def d prePs -> do
+    dt <- defType <$> getConstInfo d
+    reportSDoc "tc.reconstruct" 50 $ "Start traversing parameters: " <+> pretty prePs
+    postPs <- checkInternal' reconstructAction prePs CmpEq (dt , Def d)
+    reportSDoc "tc.reconstruct" 50 $ "Traversed parameters:" <+> pretty postPs
+    info <- getConstInfo q
+    let mkParam erasure =
+            applyWhen erasure (applyQuantity zeroQuantity)
+          . hideAndRelParams
+          . isApplyElim' __IMPOSSIBLE__
+    if -- Case: data or record constructor
+       | Constructor{ conPars = n, conErasure = e } <- theDef info ->
+           return $ map (mkParam e) $ take n postPs
+       -- Case: regular projection
+       | isProperProjection (theDef info) ->
+         case theDef info of
+           Function{ funErasure = e } ->
+             return $ map (mkParam e) postPs
+           _ -> __IMPOSSIBLE__
+       -- Case: projection-like function
+       | otherwise -> do
+           TelV tel _ <- telViewUpTo (size postPs) $ defType info
+           return $ zipWith ($>) (teleArgs tel :: Args) $ map (unArg . isApplyElim' __IMPOSSIBLE__) postPs
+  _ -> __IMPOSSIBLE__
+
+dropParameters :: TermLike a => a -> TCM a
+dropParameters = traverseTermM $
+    \case
+        Con c ci vs -> do
+          Constructor{ conData = d } <- theDef <$> getConstInfo (conName c)
+          Just n <- defParameters <$> getConstInfo d
+          return $ Con c ci $ drop n vs
+        v@(Def f vs) -> do
+          isRelevantProjection f >>= \case
+            Nothing -> return v
+            Just pr -> return $ applyE (projDropPars pr ProjSystem) vs
+        v -> return v
diff --git a/src/full/Agda/TypeChecking/RecordPatterns.hs b/src/full/Agda/TypeChecking/RecordPatterns.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/RecordPatterns.hs
@@ -0,0 +1,900 @@
+
+-- | Code which replaces pattern matching on record constructors with
+-- uses of projection functions.
+
+module Agda.TypeChecking.RecordPatterns
+  ( translateRecordPatterns
+  , translateCompiledClauses
+  , translateSplitTree
+  , recordPatternToProjections
+  , recordRHSToCopatterns
+  ) where
+
+import Control.Arrow          ( first, second )
+import Control.Monad          ( forM, join, unless, when, zipWithM )
+import Control.Monad.Fix      ( mfix )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Reader   ( MonadReader(..), ReaderT(..), runReaderT )
+import Control.Monad.State    ( MonadState(..), StateT(..), runStateT )
+import Control.Monad.Trans    ( lift )
+
+import qualified Data.List as List
+import Data.Maybe
+import qualified Data.Map as Map
+
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Syntax.Common.Pretty (Pretty(..), prettyShow)
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern as I
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty hiding (pretty)
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Interaction.Options
+
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Monad
+import Agda.Utils.Permutation hiding (dropFrom)
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+import Agda.Utils.Update (MonadChange, tellDirty)
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Record pattern translation for let bindings
+---------------------------------------------------------------------------
+
+-- | Take a record pattern @p@ and yield a list of projections
+--   corresponding to the pattern variables, from left to right.
+--
+--   E.g. for @(x , (y , z))@ we return @[ fst, fst . snd, snd . snd ]@.
+--
+--   If it is not a record pattern, error 'ShouldBeRecordPattern' is raised.
+recordPatternToProjections :: DeBruijnPattern -> TCM [Term -> Term]
+recordPatternToProjections p =
+  case p of
+    VarP{}       -> return [ id ]
+    LitP{}       -> typeError $ ShouldBeRecordPattern p
+    DotP{}       -> typeError $ ShouldBeRecordPattern p
+    ConP c ci ps -> do
+      unless (conPRecord ci) $
+        typeError $ ShouldBeRecordPattern p
+      let t = unArg $ fromMaybe __IMPOSSIBLE__ $ conPType ci
+      reportSDoc "tc.rec" 45 $ vcat
+        [ "recordPatternToProjections: "
+        , nest 2 $ "constructor pattern " <+> prettyTCM p <+> " has type " <+> prettyTCM t
+        ]
+      reportSLn "tc.rec" 70 $ "  type raw: " ++ show t
+      fields <- getRecordTypeFields t
+      concat <$> zipWithM comb (map proj fields) (map namedArg ps)
+    ProjP{}      -> __IMPOSSIBLE__ -- copattern cannot appear here
+    IApplyP{}    -> typeError $ ShouldBeRecordPattern p
+    DefP{}       -> typeError $ ShouldBeRecordPattern p
+  where
+    proj p = (`applyE` [Proj ProjSystem $ unDom p])
+    comb :: (Term -> Term) -> DeBruijnPattern -> TCM [Term -> Term]
+    comb prj p = map (\ f -> f . prj) <$> recordPatternToProjections p
+
+
+---------------------------------------------------------------------------
+-- * Record pattern translation for compiled clauses
+---------------------------------------------------------------------------
+
+-- | Take a matrix of booleans (at least one row!) and summarize the columns
+--   using conjunction.
+conjColumns :: [[Bool]] -> [Bool]
+conjColumns =  foldl1 (zipWith (&&))
+
+-- UNUSED Liang-Ting 2019-07-16
+---- | @insertColumn i a m@ inserts a column before the @i@th column in
+----   matrix @m@ and fills it with value @a@.
+--insertColumn :: Int -> a -> [[a]] -> [[a]]
+--insertColumn i a rows = map ins rows where
+--  ins row = let (init, last) = splitAt i row in init ++ a : last
+
+{- UNUSED
+-- | @cutColumn i m@ removes the @i@th column from matrix @m@.
+cutColumn :: Int -> [[a]] -> [[a]]
+cutColumn i rows = map cut rows where
+  cut row = let (init, _:last) = splitAt i row in init ++ last
+
+-- | @cutColumns i n xss = (yss, xss')@ cuts out a submatrix @yss@
+--   of width @n@ from @xss@, starting at column @i@.
+cutColumns :: Int -> Int -> [[a]] -> ([[a]], [[a]])
+cutColumns i n rows = unzip (map (cutSublist i n) rows)
+-}
+
+-- UNUSED Liang-Ting 2019-07-16
+---- | @cutSublist i n xs = (xs', ys, xs'')@ cuts out a sublist @ys@
+----   of width @n@ from @xs@, starting at column @i@.
+--cutSublist :: Int -> Int -> [a] -> ([a], [a], [a])
+--cutSublist i n row =
+--  let (init, rest) = splitAt i row
+--      (mid , last) = splitAt n rest
+--  in  (init, mid, last)
+
+getEtaAndArity :: SplitTag -> TCM (Bool, Nat)
+getEtaAndArity (SplitCon c) =
+  getConstructorInfo c <&> \case
+    DataCon n           -> (False, n)
+    RecordCon _ eta n _ -> (eta == YesEta, n)
+getEtaAndArity (SplitLit l) = return (False, 0)
+getEtaAndArity SplitCatchall = return (False, 1)
+
+translateCompiledClauses
+  :: forall m. (HasConstInfo m, MonadChange m)
+  => CompiledClauses -> m CompiledClauses
+translateCompiledClauses cc = ignoreAbstractMode $ do
+  reportSDoc "tc.cc.record" 20 $ vcat
+    [ "translate record patterns in compiled clauses"
+    , nest 2 $ return $ pretty cc
+    ]
+  cc <- loop cc
+  reportSDoc "tc.cc.record" 20 $ vcat
+    [ "translated compiled clauses (no eta record patterns):"
+    , nest 2 $ return $ pretty cc
+    ]
+  cc <- recordExpressionsToCopatterns cc
+  reportSDoc "tc.cc.record" 20 $ vcat
+    [ "translated compiled clauses (record expressions to copatterns):"
+    , nest 2 $ return $ pretty cc
+    ]
+  return cc
+  where
+
+    loop :: CompiledClauses -> m (CompiledClauses)
+    loop cc = case cc of
+      Fail{}    -> return cc
+      Done{}    -> return cc
+      Case i cs -> loops i cs
+
+    loops :: Arg Int               -- split variable
+          -> Case CompiledClauses  -- original split tree
+          -> m CompiledClauses
+    loops i cs@Branches{ projPatterns   = comatch
+                       , conBranches    = conMap
+                       , etaBranch      = eta
+                       , litBranches    = litMap
+                       , fallThrough    = fT
+                       , catchAllBranch = catchAll
+                       , lazyMatch      = lazy } = do
+
+      catchAll <- traverse loop catchAll
+      litMap   <- traverse loop litMap
+      (conMap, eta) <- do
+        let noEtaCase = (, Nothing) <$> (traverse . traverse) loop conMap
+            yesEtaCase b ch = (Map.empty,) . Just . (ch,) <$> traverse loop b
+        case Map.toList conMap of
+              -- This is already an eta match. Still need to recurse though.
+              -- This can happen (#2981) when we
+              -- 'revisitRecordPatternTranslation' in Rules.Decl, due to
+              -- inferred eta.
+          _ | Just (ch, b) <- eta -> yesEtaCase b ch
+          [(c, b)] | not comatch -> -- possible eta-match
+            getConstructorInfo' c >>= \ case
+              Just (RecordCon pm YesEta _ar fs) -> yesEtaCase b $
+                ConHead c (IsRecord pm) Inductive (map argFromDom fs)
+              _ -> noEtaCase
+          _ -> noEtaCase
+      return $ Case i cs{ conBranches    = conMap
+                        , etaBranch      = eta
+                        , litBranches    = litMap
+                        , fallThrough    = fT
+                        , catchAllBranch = catchAll
+                        }
+
+{- UNUSED
+instance Monoid CompiledClauses where
+  mempty = __IMPOSSIBLE__
+  mappend (Case n c) (Case n' c') | n == n' = Case n $ mappend c c'
+  mappend _ _ = __IMPOSSIBLE__
+
+mergeCatchAll :: CompiledClauses -> Maybe CompiledClauses -> CompiledClauses
+mergeCatchAll cc ca = maybe cc (mappend cc) ca
+{-
+  case (cc, ca) of
+    (_       , Nothing) -> cc
+    (Case n c, Just (Case n' c')) | n == n' -> Case n $ mappend c c'
+    _                   -> __IMPOSSIBLE__ -- this would mean non-determinism
+-}
+-}
+
+
+-- | Transform definitions returning record values to use copatterns instead.
+--   This allows e.g. termination-checking constructor-style coinduction.
+--
+--   For example:
+--
+--   @
+--     nats : Nat → Stream Nat
+--     nats n = n ∷ nats (1 + n)
+--   @
+--
+--   The clause is translated to:
+--
+--   @
+--     nats n .head = n
+--     nats n .tail = nats (1 + n)
+--   @
+--
+--   A change is signalled if definitional equalities might not hold after the
+--   translation, e.g. if a non-eta constructor was turned to copattern matching.
+recordRHSsToCopatterns ::
+     forall m. (MonadChange m, PureTCM m)
+  => [Clause]
+  -> m [Clause]
+recordRHSsToCopatterns cls = do
+  reportSLn "tc.inline.con" 40 $ "enter recordRHSsToCopatterns with " ++ show (length cls) ++ " clauses"
+  concatMapM recordRHSToCopatterns cls
+
+recordRHSToCopatterns ::
+     forall m. (MonadChange m, PureTCM m)
+  => Clause
+  -> m [Clause]
+recordRHSToCopatterns cl = do
+  reportSLn "tc.inline.con" 40 $ "enter recordRHSToCopatterns"
+
+  case cl of
+
+    -- RHS must be fully applied coinductive constructor/record expression.
+    cl@Clause{ namedClausePats = ps
+             , clauseBody      = Just v0@(Con con@(ConHead c _ _ind fs) _ci es)
+             , clauseType      = mt
+             }
+      | not (null fs)           -- at least one field
+      , length fs == length es  -- fully applied
+      , Just vs <- allApplyElims es
+
+          -- Only expand constructors labelled @{-# INLINE c #-}@.
+      -> inlineConstructor c >>= \case
+        Nothing  -> return [cl]
+        Just eta -> do
+
+          mt <- traverse reduce mt
+
+          -- If it may change definitional equality,
+          -- announce that the translation actually fired.
+          unless eta tellDirty
+
+          -- Iterate the translation for nested constructor rhss.
+          recordRHSsToCopatterns =<< do
+
+            -- Create one clause per projection.
+            forM (zip fs vs) $ \ (f, v) -> do
+
+              -- Get the type of the field.
+              let inst :: Type -> m (Maybe Type)
+                  inst t = fmap thd3 <$> projectTyped v0 t ProjSystem (unArg f)
+
+              let fuse :: Maybe (Arg (Maybe a)) -> Maybe (Arg a)
+                  fuse = join . fmap distributeF
+
+              mt' :: Maybe (Arg Type) <- fuse <$> traverse (traverse inst) mt
+
+              -- Make clause ... .f = v
+              return cl
+                { namedClausePats = ps ++ [ unnamed . ProjP ProjSystem <$> f ]
+                , clauseBody      = Just $ unArg v
+                , clauseType      = mt'
+                }
+
+    -- Otherwise: no change.
+    cl -> return [cl]
+
+  where
+    -- @Nothing@ means do not inline, @Just eta@ means inline.
+    inlineConstructor :: QName -> m (Maybe Bool)
+    inlineConstructor c = getConstInfo c <&> theDef >>= \case
+      Constructor { conData, conInline } -> do
+        reportSLn "tc.inline.con" 80 $
+          ("can" ++) $ applyUnless conInline ("not" ++) $ " inline constructor " ++ prettyShow c
+        if not conInline then return Nothing else Just <$> isEtaRecord conData
+      _ -> return Nothing
+
+-- | Transform definitions returning record expressions to use copatterns
+--   instead. This prevents terms from blowing up when reduced.
+recordExpressionsToCopatterns
+  :: (HasConstInfo m, MonadChange m)
+  => CompiledClauses
+  -> m CompiledClauses
+recordExpressionsToCopatterns = \case
+    Case i bs -> Case i <$> traverse recordExpressionsToCopatterns bs
+    cc@Fail{} -> return cc
+    cc@(Done xs (Con c ConORec es)) -> do  -- don't translate if using the record /constructor/
+      let vs = map unArg $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      irrProj <- optIrrelevantProjections <$> pragmaOptions
+      getConstructorInfo (conName c) >>= \ case
+        RecordCon CopatternMatching YesEta ar fs
+          | ar > 0                                     -- only for eta-records with at least one field
+          , length vs == ar                            -- where the constructor application is saturated
+          , irrProj || not (any isIrrelevant fs) -> do -- and irrelevant projections (if any) are allowed
+              tellDirty
+              Case (defaultArg $ length xs) <$> do
+                -- translate new cases recursively (there might be nested record expressions)
+                traverse recordExpressionsToCopatterns $ Branches
+                  { projPatterns   = True
+                  , conBranches    = Map.fromListWith __IMPOSSIBLE__ $
+                      zipWith (\ f v -> (unDom f, WithArity 0 $ Done xs v)) fs vs
+                  , etaBranch      = Nothing
+                  , litBranches    = Map.empty
+                  , catchAllBranch = Nothing
+                  , fallThrough    = Nothing
+                  , lazyMatch      = False
+                  }
+        _ -> return cc
+    cc@Done{} -> return cc
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+---- | @replaceByProjections i projs cc@ replaces variables @i..i+n-1@
+----   (counted from left) by projections @projs_1 i .. projs_n i@.
+----
+----   If @n==0@, we matched on a zero-field record, which means that
+----   we are actually introduce a new variable, increasing split
+----   positions greater or equal to @i@ by one.
+----   Otherwise, we have to lower
+----
+--replaceByProjections :: Arg Int -> [QName] -> CompiledClauses -> CompiledClauses
+--replaceByProjections (Arg ai i) projs cc =
+--  let n = length projs
+--
+--      loop :: Int -> CompiledClauses -> CompiledClauses
+--      loop i cc = case cc of
+--        Case j cs
+--
+--        -- if j < i, we leave j untouched, but we increase i by the number
+--        -- of variables replacing j in the branches
+--          | unArg j < i -> Case j $ loops i cs
+--
+--        -- if j >= i then we shrink j by (n-1)
+--          | otherwise   -> Case (j <&> \ k -> k - (n-1)) $ fmap (loop i) cs
+--
+--        Done xs v ->
+--        -- we have to delete (n-1) variables from xs
+--        -- and instantiate v suitably with the projections
+--          let (xs0,xs1,xs2)     = cutSublist i n xs
+--              names | null xs1  = ["r"]
+--                    | otherwise = map unArg xs1
+--              x                 = Arg ai $ foldr1 appendArgNames names
+--              xs'               = xs0 ++ x : xs2
+--              us                = map (\ p -> Var 0 [Proj ProjSystem p]) (reverse projs)
+--              -- go from level (i + n - 1) to index (subtract from |xs|-1)
+--              index             = length xs - (i + n)
+--          in  Done xs' $ applySubst (liftS (length xs2) $ us ++# raiseS 1) v
+--          -- The body is NOT guarded by lambdas!
+--          -- WRONG: underLambdas i (flip apply) (map defaultArg us) v
+--
+--        Fail -> Fail
+--
+--      loops :: Int -> Case CompiledClauses -> Case CompiledClauses
+--      loops i bs@Branches{ conBranches    = conMap
+--                         , litBranches    = litMap
+--                         , catchAllBranch = catchAll } =
+--        bs{ conBranches    = fmap (\ (WithArity n c) -> WithArity n $ loop (i + n - 1) c) conMap
+--          , litBranches    = fmap (loop (i - 1)) litMap
+--          , catchAllBranch = fmap (loop i) catchAll
+--          }
+--  in  loop i cc
+
+-- UNUSED Liang-Ting 2019-07-16
+---- | Check if a split is on a record constructor, and return the projections
+----   if yes.
+--isRecordCase :: Case c -> TCM (Maybe ([QName], c))
+--isRecordCase (Branches { conBranches = conMap
+--                       , litBranches = litMap
+--                       , catchAllBranch = Nothing })
+--  | Map.null litMap
+--  , [(con, WithArity _ br)] <- Map.toList conMap = do
+--    isRC <- isRecordConstructor con
+--    case isRC of
+--      Just (r, Record { recFields = fs }) -> return $ Just (map unArg fs, br)
+--      Just (r, _) -> __IMPOSSIBLE__
+--      Nothing -> return Nothing
+--isRecordCase _ = return Nothing
+
+---------------------------------------------------------------------------
+-- * Record pattern translation for split trees
+---------------------------------------------------------------------------
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Split tree annotation.
+--data RecordSplitNode = RecordSplitNode
+--  { _splitTag           :: SplitTag -- ^ Constructor name/literal for this branch.
+--  , _splitArity         :: Int      -- ^ Arity of the constructor.
+--  , _splitRecordPattern :: Bool     -- ^ Should we translate this split away?
+--  }
+
+-- | Split tree annotated for record pattern translation.
+--type RecordSplitTree  = SplitTree' RecordSplitNode
+--type RecordSplitTrees = SplitTrees' RecordSplitNode
+
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Bottom-up procedure to annotate split tree.
+--recordSplitTree :: SplitTree -> TCM RecordSplitTree
+--recordSplitTree = snd <.> loop
+--  where
+--
+--    loop :: SplitTree -> TCM ([Bool], RecordSplitTree)
+--    loop = \case
+--      SplittingDone n -> return (replicate n True, SplittingDone n)
+--      SplitAt i ts    -> do
+--        (xs, ts) <- loops (unArg i) ts
+--        return (xs, SplitAt i ts)
+--
+--    loops :: Int -> SplitTrees -> TCM ([Bool], RecordSplitTrees)
+--    loops i ts = do
+--      (xss, ts) <- unzip <$> do
+--        forM ts $ \ (c, t) -> do
+--          (xs, t) <- loop t
+--          (isRC, n) <- getEtaAndArity c
+--          let (xs0, rest) = splitAt i xs
+--              (xs1, xs2)  = splitAt n rest
+--              x           = isRC && and xs1
+--              xs'         = xs0 ++ x : xs2
+--          return (xs, (RecordSplitNode c n x, t))
+--      return (foldl1 (zipWith (&&)) xss, ts)
+
+-- | Bottom-up procedure to record-pattern-translate split tree.
+translateSplitTree :: SplitTree -> TCM SplitTree
+translateSplitTree = snd <.> loop
+  where
+
+    -- @loop t = return (xs, t')@ returns the translated split tree @t'@
+    -- plus the status @xs@ of the clause variables
+    --   True  = variable will never be split on in @t'@ (virgin variable)
+    --   False = variable will be spilt on in @t'@
+    loop :: SplitTree -> TCM ([Bool], SplitTree)
+    loop = \case
+      SplittingDone n ->
+        -- start with n virgin variables
+        return (replicate n True, SplittingDone n)
+      SplitAt i lz ts    -> do
+        (x, xs, ts) <- loops (unArg i) ts
+        -- if we case on record constructor, drop case
+        let t' = if x then
+                   case ts of
+                     [(c,t)] -> t
+                     _       -> __IMPOSSIBLE__
+                  -- else retain case
+                  else SplitAt i lz ts
+        return (xs, t')
+
+    -- @loops i ts = return (x, xs, ts')@ cf. @loop@
+    -- @x@ says wether at arg @i@ we have a record pattern split
+    -- that can be removed
+    loops :: Int -> SplitTrees -> TCM (Bool, [Bool], SplitTrees)
+    loops i ts = do
+      -- note: ts not empty
+      (rs, xss, ts) <- unzip3 <$> do
+        forM ts $ \ (c, t) -> do
+          (xs, t) <- loop t
+          (isRC, n) <- getEtaAndArity c
+          -- now drop variables from i to i+n-1
+          let (xs0, rest) = splitAt i xs
+              (xs1, xs2)  = splitAt n rest
+              -- if all dropped variables are virgins and we are record cons.
+              -- then new variable x is also virgin
+              -- and we can translate away the split
+              x           = isRC && and xs1
+              -- xs' = updated variables
+              xs'         = xs0 ++ x : xs2
+              -- delete splits from t if record match
+              t'          = if x then dropFrom i (n - 1) t else t
+          return (x, xs', (c, t'))
+      -- x = did we split on a record constructor?
+      let x = and rs
+      -- invariant: if record constructor, then exactly one constructor
+      if x then unless (rs == [True]) __IMPOSSIBLE__
+      -- else no record constructor
+       else when (or rs) __IMPOSSIBLE__
+      return (x, conjColumns xss, ts)
+
+-- | @dropFrom i n@ drops arguments @j@  with @j < i + n@ and @j >= i@.
+--   NOTE: @n@ can be negative, in which case arguments are inserted.
+class DropFrom a where
+  dropFrom :: Int -> Int -> a -> a
+
+instance DropFrom (SplitTree' c) where
+  dropFrom i n = \case
+    SplittingDone m -> SplittingDone (m - n)
+    SplitAt x@(Arg ai j) lz ts
+      | j >= i + n -> SplitAt (Arg ai $ j - n) lz $ dropFrom i n ts
+      | j < i      -> SplitAt x lz $ dropFrom i n ts
+      | otherwise  -> __IMPOSSIBLE__
+
+instance DropFrom (c, SplitTree' c) where
+  dropFrom i n (c, t) = (c, dropFrom i n t)
+
+instance DropFrom a => DropFrom [a] where
+  dropFrom i n ts = map (dropFrom i n) ts
+
+{-
+-- | Check if a split is on a record constructor, and return the projections
+--   if yes.
+isRecordSplit :: SplitTrees -> TCM (Maybe ([QName], c))
+isRecordSplit (Branches { conBranches = conMap
+                       , litBranches = litMap
+                       , catchAllBranch = Nothing })
+  | Map.null litBranches
+  , [(con,br)] <- Map.toList conMap = do
+    isRC <- isRecordConstructor con
+    case isRC of
+      Just (r, Record { recFields = fs }) -> return $ Just (map unArg fs, br)
+      Just (r, _) -> __IMPOSSIBLE__
+      Nothing -> return Nothing
+isRecordSplit _ = return Nothing
+
+-}
+
+
+---------------------------------------------------------------------------
+-- * Record pattern translation for function definitions
+---------------------------------------------------------------------------
+
+-- | Replaces pattern matching on record constructors with uses of
+-- projection functions. Does not remove record constructor patterns
+-- which have sub-patterns containing non-record constructor or
+-- literal patterns.
+
+translateRecordPatterns :: Clause -> TCM Clause
+translateRecordPatterns clause = do
+  -- ps: New patterns, in left-to-right order, in the context of the
+  -- old RHS.
+
+  -- s: Partial substitution taking the old pattern variables
+  -- (including dot patterns; listed from left to right) to terms in
+  -- the context of the new RHS.
+
+  -- cs: List of changes, with types in the context of the old
+  -- telescope.
+
+  (ps, s, cs) <- runRecPatM $ translatePatterns $ unnumberPatVars $ namedClausePats clause
+
+  let -- Number of variables + dot patterns in new clause.
+      noNewPatternVars = size cs
+
+      s'   = reverse s
+      mkSub s = s ++# raiseS noNewPatternVars
+
+      -- Substitution used to convert terms in the old RHS's
+      -- context to terms in the new RHS's context.
+      rhsSubst = mkSub s' -- NB:: Defined but not used
+
+      -- Substitution used to convert terms in the old telescope's
+      -- context to terms in the new RHS's context.
+      perm = fromMaybe __IMPOSSIBLE__ $ clausePerm clause
+      rhsSubst' = mkSub $ permute (reverseP perm) s'
+      -- TODO: Is it OK to replace the definition above with the
+      -- following one?
+      --
+      --   rhsSubst' = mkSub $ permute (clausePerm clause) s
+
+      -- The old telescope, flattened and in textual left-to-right
+      -- order (i.e. the type signature for the variable which occurs
+      -- first in the list of patterns comes first).
+      flattenedOldTel =
+        permute (invertP __IMPOSSIBLE__ $ compactP perm) $
+        zip (teleNames $ clauseTel clause) $
+        flattenTel $
+        clauseTel clause
+
+      -- The new telescope, still flattened, with types in the context
+      -- of the new RHS, in textual left-to-right order, and with
+      -- Nothing in place of dot patterns.
+      substTel = map . fmap . second . applySubst
+      newTel' =
+        substTel rhsSubst' $
+        translateTel cs $
+        flattenedOldTel
+
+      -- Permutation taking the new variable and dot patterns to the
+      -- new telescope.
+      newPerm = adjustForDotPatterns $
+                  reorderTel_ $ map (maybe __DUMMY_DOM__ snd) newTel'
+        -- It is important that __DUMMY_DOM__ does not mention any variable
+        -- (see the definition of reorderTel).
+        where
+        isDotP n = case List.genericIndex cs n of
+                     Left DotP{} -> True
+                     _           -> False
+
+        adjustForDotPatterns (Perm n is) =
+          Perm n (filter (not . isDotP) is)
+
+      -- Substitution used to convert terms in the new RHS's context
+      -- to terms in the new telescope's context.
+      lhsSubst' = renaming impossible (reverseP newPerm)
+
+      -- Substitution used to convert terms in the old telescope's
+      -- context to terms in the new telescope's context.
+      lhsSubst = applySubst lhsSubst' rhsSubst'
+
+      -- The new telescope.
+      newTel =
+        uncurry unflattenTel . unzip $
+        map (fromMaybe __IMPOSSIBLE__) $
+        permute newPerm $
+        substTel lhsSubst' $
+        newTel'
+
+      -- New clause.
+      c = clause
+            { clauseTel       = newTel
+            , namedClausePats = numberPatVars __IMPOSSIBLE__ newPerm $ applySubst lhsSubst ps
+            , clauseBody      = applySubst lhsSubst $ clauseBody clause
+            }
+
+  reportSDoc "tc.lhs.recpat" 20 $ vcat
+      [ "Original clause:"
+      , nest 2 $ inTopContext $ vcat
+        [ "delta =" <+> prettyTCM (clauseTel clause)
+        , "pats  =" <+> text (show $ clausePats clause)
+        ]
+      , "Intermediate results:"
+      , nest 2 $ vcat
+        [ "ps        =" <+> text (show ps)
+        , "s         =" <+> prettyTCM s
+        , "cs        =" <+> prettyTCM cs
+        , "flattenedOldTel =" <+> (text . show) flattenedOldTel
+        , "newTel'   =" <+> (text . show) newTel'
+        , "newPerm   =" <+> prettyTCM newPerm
+        ]
+      ]
+
+  reportSDoc "tc.lhs.recpat" 20 $ vcat
+        [ "lhsSubst' =" <+> (text . show) lhsSubst'
+        , "lhsSubst  =" <+> (text . show) lhsSubst
+        , "newTel  =" <+> prettyTCM newTel
+        ]
+
+  reportSDoc "tc.lhs.recpat" 10 $
+    escapeContext impossible (size $ clauseTel clause) $ vcat
+      [ "Translated clause:"
+      , nest 2 $ vcat
+        [ "delta =" <+> prettyTCM (clauseTel c)
+        , "ps    =" <+> text (show $ clausePats c)
+        , "body  =" <+> text (show $ clauseBody c)
+        , "body  =" <+> addContext (clauseTel c) (maybe "_|_" prettyTCM (clauseBody c))
+        ]
+      ]
+
+  return c
+
+------------------------------------------------------------------------
+-- Record pattern monad
+
+-- | A monad used to translate record patterns.
+--
+-- The state records the number of variables produced so far, the
+-- reader records the total number of variables produced by the entire
+-- computation. Functions using this monad need to be sufficiently
+-- lazy in the reader component.
+
+newtype RecPatM a = RecPatM (TCMT (ReaderT Nat (StateT Nat IO)) a)
+  deriving (Functor, Applicative, Monad,
+            MonadIO, MonadTCM, HasOptions,
+            MonadTCEnv, MonadTCState)
+
+-- | Runs a computation in the 'RecPatM' monad.
+
+runRecPatM :: RecPatM a -> TCM a
+runRecPatM (RecPatM m) =
+  mapTCMT (\m -> do
+             (x, noVars) <- mfix $ \ ~(_, noVars) ->
+                              runStateT (runReaderT m noVars) 0
+             return x)
+          m
+
+-- | Returns the next pattern variable, and the corresponding term.
+
+nextVar :: RecPatM (Pattern, Term)
+nextVar = RecPatM $ do
+  n <- lift get
+  lift $ put $ succ n
+  noVars <- lift ask
+  return (varP "r", var $ noVars - n - 1)
+
+------------------------------------------------------------------------
+-- Types used to record changes to a clause
+
+-- | @VarPat@ stands for variable patterns, and @DotPat@ for dot
+-- patterns.
+
+data Kind = VarPat | DotPat
+  deriving Eq
+
+-- | @'Left' p@ means that a variable (corresponding to the pattern
+-- @p@, a variable or dot pattern) should be kept unchanged. @'Right'
+-- (n, x, t)@ means that @n 'VarPat'@ variables, and @n 'DotPat'@ dot
+-- patterns, should be removed, and a new variable, with the name @x@,
+-- inserted instead. The type of the new variable is @t@.
+
+type Change  = Either Pattern (Kind -> Nat, ArgName, Dom Type)
+type Changes = [Change]
+
+instance Pretty (Kind -> Nat) where
+  pretty f =
+    ("(VarPat:" P.<+> P.text (show $ f VarPat) P.<+>
+    "DotPat:"  P.<+> P.text (show $ f DotPat)) <> ")"
+
+instance PrettyTCM (Kind -> Nat) where
+  prettyTCM = return . pretty
+
+instance PrettyTCM Change where
+  prettyTCM (Left  p) = prettyTCM p
+  prettyTCM (Right (f, x, t)) = "Change" <+> prettyTCM f <+> text x <+> prettyTCM t
+
+-- | Record pattern trees.
+
+data RecordTree
+  = Leaf Pattern
+    -- ^ Corresponds to variable and dot patterns; contains the
+    -- original pattern.
+  | RecCon (Arg Type) [(Term -> Term, RecordTree)]
+    -- ^ @RecCon t args@ stands for a record constructor application:
+    -- @t@ is the type of the application, and the list contains a
+    -- projection function and a tree for every argument.
+
+------------------------------------------------------------------------
+-- Record pattern trees
+
+-- | @projections t@ returns a projection for every non-dot leaf
+-- pattern in @t@. The term is the composition of the projection
+-- functions from the leaf to the root.
+--
+-- Every term is tagged with its origin: a variable pattern or a dot
+-- pattern.
+
+projections :: RecordTree -> [(Term -> Term, Kind)]
+projections (Leaf (DotP{})) = [(id, DotPat)]
+projections (Leaf (VarP{})) = [(id, VarPat)]
+projections (Leaf _)        = __IMPOSSIBLE__
+projections (RecCon _ args) =
+  concatMap (\ (p, t) -> map (first (. p)) $ projections t)
+            args
+
+-- | Converts a record tree to a single pattern along with information
+-- about the deleted pattern variables.
+
+removeTree :: RecordTree -> RecPatM (Pattern, [Term], Changes)
+removeTree tree = do
+  (pat, x) <- nextVar
+  let ps = projections tree
+      s  = map (\(p, _) -> p x) ps
+
+      count k = length $ filter ((== k) . snd) ps
+
+  return $ case tree of
+    Leaf p     -> (p,   s, [Left p])
+    RecCon t _ -> (pat, s, [Right (count, "r", domFromArg t)])
+
+------------------------------------------------------------------------
+-- Translation of patterns
+
+-- | Removes record constructors from patterns.
+--
+-- Returns the following things:
+--
+-- * The new pattern.
+--
+-- * A substitution which maps the /old/ pattern variables (in the
+--   order they occurred in the pattern; not including dot patterns)
+--   to terms (either the new name of the variable, or a projection
+--   applied to a new pattern variable).
+--
+-- * A list explaining the changes to the variables bound in the
+--   pattern.
+--
+-- Record patterns containing non-record constructor patterns are not
+-- translated (though their sub-patterns may be).
+--
+-- Example: The pattern @rec1 (con1 a) (rec2 b c) (rec3 d)@ should
+-- yield the pattern @rec1 (con1 x) y z@, along with a substitution
+-- similar to @[x, proj2-1 y, proj2-2 y, proj3-1 z]@.
+--
+-- This function assumes that literals are never of record type.
+
+translatePattern :: Pattern -> RecPatM (Pattern, [Term], Changes)
+translatePattern p@(ConP c ci ps)
+  -- Andreas, 2015-05-28 only translate implicit record patterns
+  | conPRecord ci , PatOSystem <- patOrigin (conPInfo ci) = do
+      r <- recordTree p
+      case r of
+        Left  r -> r
+        Right t -> removeTree t
+  | otherwise = do
+      (ps, s, cs) <- translatePatterns ps
+      return (ConP c ci ps, s, cs)
+translatePattern p@(DefP o q ps) = do
+      (ps, s, cs) <- translatePatterns ps
+      return (DefP o q ps, s, cs)
+translatePattern p@VarP{} = removeTree (Leaf p)
+translatePattern p@DotP{} = removeTree (Leaf p)
+translatePattern p@LitP{} = return (p, [], [])
+translatePattern p@ProjP{}= return (p, [], [])
+translatePattern p@IApplyP{}= return (p, [], [])
+
+translatePatterns :: [NamedArg Pattern] -> RecPatM ([NamedArg Pattern], [Term], Changes)
+translatePatterns ps = do
+  (ps', ss, cs) <- unzip3 <$> mapM (translatePattern . namedArg) ps
+  return (zipWith (\p -> fmap (p <$)) ps' ps, concat ss, concat cs)
+
+-- | Traverses a pattern and returns one of two things:
+--
+-- * If there is no non-record constructor in the pattern, then
+--   @'Right' ps@ is returned, where @ps@ contains one projection for
+--   every variable in the input pattern (in the order they are
+--   encountered).
+--
+-- * Otherwise the output is a computation returning the same kind of
+--   result as that coming from 'translatePattern'. (Computations are
+--   returned rather than values to ensure that variable numbers are
+--   allocated in the right order.)
+--
+-- Assumes that literals are never of record type.
+
+recordTree ::
+  Pattern ->
+  RecPatM (Either (RecPatM (Pattern, [Term], Changes)) RecordTree)
+-- Andreas, 2015-05-28 only translate implicit record patterns
+recordTree p@(ConP c ci ps) | conPRecord ci , PatOSystem <- patOrigin (conPInfo ci) = do
+  let t = fromMaybe __IMPOSSIBLE__ $ conPType ci
+  rs <- mapM (recordTree . namedArg) ps
+  case allRight rs of
+    Nothing ->
+      return $ Left $ do
+        (ps', ss, cs) <- unzip3 <$> mapM (either id removeTree) rs
+        return (ConP c ci (ps' `withNamedArgsFrom` ps),
+                concat ss, concat cs)
+    Just ts -> liftTCM $ do
+      t <- reduce t
+      reportSDoc "tc.rec" 45 $ vcat
+        [ "recordTree: "
+        , nest 2 $ "constructor pattern " <+> prettyTCM p <+> " has type " <+> prettyTCM t
+        ]
+      -- Andreas, 2018-03-03, see #2989:
+      -- The content of an @Arg@ might not be reduced (if @Arg@ is @Irrelevant@).
+      fields <- getRecordTypeFields =<< reduce (unArg t)
+--      let proj p = \x -> Def (unArg p) [defaultArg x]
+      let proj p = (`applyE` [Proj ProjSystem $ unDom p])
+      return $ Right $ RecCon t $ zip (map proj fields) ts
+recordTree p@(ConP _ ci _) = return $ Left $ translatePattern p
+recordTree p@DefP{} = return $ Left $ translatePattern p
+recordTree p@VarP{} = return (Right (Leaf p))
+recordTree p@DotP{} = return (Right (Leaf p))
+recordTree p@LitP{} = return $ Left $ translatePattern p
+recordTree p@ProjP{}= return $ Left $ translatePattern p
+recordTree p@IApplyP{}= return $ Left $ translatePattern p
+
+------------------------------------------------------------------------
+-- Translation of the clause telescope and body
+
+-- | Translates the telescope.
+
+translateTel
+  :: Changes
+     -- ^ Explanation of how the telescope should be changed. Types
+     -- should be in the context of the old telescope.
+  -> [(ArgName, Dom Type)]
+     -- ^ Old telescope, flattened, in textual left-to-right
+     -- order.
+  -> [Maybe (ArgName, Dom Type)]
+     -- ^ New telescope, flattened, in textual left-to-right order.
+     -- 'Nothing' is used to indicate the locations of dot patterns.
+translateTel (Left (DotP{}) : rest)   tel = Nothing : translateTel rest tel
+translateTel (Right (n, x, t) : rest) tel = Just (x, t) :
+                                              translateTel rest
+                                                (drop (n VarPat) tel)
+translateTel (Left _ : rest) (t : tel)    = Just t : translateTel rest tel
+translateTel []              []           = []
+translateTel (Left _ : _)    []           = __IMPOSSIBLE__
+translateTel []              (_ : _)      = __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/Records.hs b/src/full/Agda/TypeChecking/Records.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Records.hs
@@ -0,0 +1,1037 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Records where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans.Maybe
+import Control.Monad.Writer
+import Control.Applicative
+
+import Data.Bifunctor
+import qualified Data.List as List
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.HashMap.Strict as HMap
+
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Concrete (FieldAssignment'(..))
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Internal.MetaVars (unblockOnAnyMetaIn)
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base (isNameInScope)
+
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Base.Warning as W
+import Agda.TypeChecking.Pretty as TCM
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Reduce.Monad () --instance only
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+import {-# SOURCE #-} Agda.TypeChecking.Primitive.Cubical.Base (isCubicalSubtype)
+import {-# SOURCE #-} Agda.TypeChecking.ProjectionLike (eligibleForProjectionLike)
+
+import Agda.Utils.Empty
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor (for, ($>), (<&>))
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+mkCon :: ConHead -> ConInfo -> Args -> Term
+mkCon h info args = Con h info (map Apply args)
+
+-- | Order the fields of a record construction.
+orderFields
+  :: forall a . HasRange a
+  => QName             -- ^ Name of record type (for error message).
+  -> (Arg C.Name -> a) -- ^ How to fill a missing field.
+  -> [Arg C.Name]      -- ^ Field names of the record type.
+  -> [(C.Name, a)]     -- ^ Provided fields with content in the record expression.
+  -> Writer [RecordFieldWarning] [a]           -- ^ Content arranged in official order.
+orderFields r fill axs fs = do
+  -- reportSDoc "tc.record" 30 $ vcat
+  --   [ "orderFields"
+  --   , "  official fields: " <+> sep (map pretty xs)
+  --   , "  provided fields: " <+> sep (map pretty ys)
+  --   ]
+  unlessNull alien     $ warn $ W.TooManyFields r missing
+  unlessNull duplicate $ warn $ W.DuplicateFields
+  return $ for axs $ \ ax -> fromMaybe (fill ax) $ lookup (unArg ax) uniq
+  where
+    (uniq, duplicate) = nubAndDuplicatesOn fst fs   -- separating duplicate fields
+    xs        = map unArg axs                       -- official fields (accord. record type)
+    missing   = filter (not . hasElem (map fst fs)) xs  -- missing  fields
+    alien     = filter (not . hasElem xs . fst) fs      -- spurious fields
+    warn w    = tell . singleton . w . map (second getRange)
+
+-- | Raise generated 'RecordFieldWarning's as warnings.
+warnOnRecordFieldWarnings :: Writer [RecordFieldWarning] a -> TCM a
+warnOnRecordFieldWarnings comp = do
+  let (res, ws) = runWriter comp
+  mapM_ (warning . RecordFieldWarning) ws
+  return res
+
+-- | Raise generated 'RecordFieldWarning's as errors.
+failOnRecordFieldWarnings :: Writer [RecordFieldWarning] a -> TCM a
+failOnRecordFieldWarnings comp = do
+  let (res, ws) = runWriter comp
+  mapM_ (typeError . recordFieldWarningToError) ws
+    -- This will raise the first warning (if any) as error.
+  return res
+
+-- | Order the fields of a record construction.
+--   Raise generated 'RecordFieldWarning's as warnings.
+orderFieldsWarn
+  :: forall a . HasRange a
+  => QName             -- ^ Name of record type (for error message).
+  -> (Arg C.Name -> a) -- ^ How to fill a missing field.
+  -> [Arg C.Name]      -- ^ Field names of the record type.
+  -> [(C.Name, a)]     -- ^ Provided fields with content in the record expression.
+  -> TCM [a]           -- ^ Content arranged in official order.
+orderFieldsWarn r fill axs fs = warnOnRecordFieldWarnings $ orderFields r fill axs fs
+
+-- | Order the fields of a record construction.
+--   Raise generated 'RecordFieldWarning's as errors.
+orderFieldsFail
+  :: forall a . HasRange a
+  => QName             -- ^ Name of record type (for error message).
+  -> (Arg C.Name -> a) -- ^ How to fill a missing field.
+  -> [Arg C.Name]      -- ^ Field names of the record type.
+  -> [(C.Name, a)]     -- ^ Provided fields with content in the record expression.
+  -> TCM [a]           -- ^ Content arranged in official order.
+orderFieldsFail r fill axs fs = failOnRecordFieldWarnings $ orderFields r fill axs fs
+
+-- | A record field assignment @record{xs = es}@ might not mention all
+--   visible fields.  @insertMissingFields@ inserts placeholders for
+--   the missing visible fields and returns the values in order
+--   of the fields in the record declaration.
+insertMissingFields
+  :: forall a . HasRange a
+  => QName                -- ^ Name of record type (for error reporting).
+  -> (C.Name -> a)        -- ^ Function to generate a placeholder for missing visible field.
+  -> [FieldAssignment' a] -- ^ Given fields.
+  -> [Arg C.Name]         -- ^ All record field names with 'ArgInfo'.
+  -> Writer [RecordFieldWarning] [NamedArg a]
+       -- ^ Given fields enriched by placeholders for missing explicit fields.
+insertMissingFields r placeholder fs axs = do
+  -- Compute the list of given fields, decorated with the ArgInfo from the record def.
+  let arg x e = caseMaybe (List.find ((x ==) . unArg) axs) (defaultNamedArg e) $ \ a ->
+        nameIfHidden a e <$ a
+      givenFields = [ (x, Just $ arg x e) | FieldAssignment x e <- fs ]
+
+  -- Omitted explicit fields are filled in with placeholders.
+  -- Omitted implicit or instance fields
+  -- are still left out and inserted later by checkArguments_.
+  catMaybes <$> orderFields r fill axs givenFields
+  where
+    fill :: Arg C.Name -> Maybe (NamedArg a)
+    fill ax
+      | visible ax = Just $ setOrigin Inserted $ unnamed . placeholder <$> ax
+      | otherwise  = Nothing
+    -- Andreas, 2017-04-13, issue #2494
+    -- We need to put the field names as argument names for hidden arguments.
+    -- Otherwise, insertImplicit does not do the right thing.
+    nameIfHidden :: Arg C.Name -> c -> Named_ c
+    nameIfHidden ax
+      | visible ax = unnamed
+      | otherwise  = named $ WithOrigin Inserted $ Ranged (getRange ax) $ prettyShow $ unArg ax
+
+-- | A record field assignment @record{xs = es}@ might not mention all
+--   visible fields.  @insertMissingFields@ inserts placeholders for
+--   the missing visible fields and returns the values in order
+--   of the fields in the record declaration.
+insertMissingFieldsWarn
+  :: forall a . HasRange a
+  => QName                -- ^ Name of record type (for error reporting).
+  -> (C.Name -> a)        -- ^ Function to generate a placeholder for missing visible field.
+  -> [FieldAssignment' a] -- ^ Given fields.
+  -> [Arg C.Name]         -- ^ All record field names with 'ArgInfo'.
+  -> TCM [NamedArg a]     -- ^ Given fields enriched by placeholders for missing explicit fields.
+insertMissingFieldsWarn r placeholder fs axs =
+  warnOnRecordFieldWarnings $ insertMissingFields r placeholder fs axs
+
+-- | A record field assignment @record{xs = es}@ might not mention all
+--   visible fields.  @insertMissingFields@ inserts placeholders for
+--   the missing visible fields and returns the values in order
+--   of the fields in the record declaration.
+insertMissingFieldsFail
+  :: forall a . HasRange a
+  => QName                -- ^ Name of record type (for error reporting).
+  -> (C.Name -> a)        -- ^ Function to generate a placeholder for missing visible field.
+  -> [FieldAssignment' a] -- ^ Given fields.
+  -> [Arg C.Name]         -- ^ All record field names with 'ArgInfo'.
+  -> TCM [NamedArg a]     -- ^ Given fields enriched by placeholders for missing explicit fields.
+insertMissingFieldsFail r placeholder fs axs =
+  failOnRecordFieldWarnings $ insertMissingFields r placeholder fs axs
+
+-- | Get the definition for a record. Throws an exception if the name
+--   does not refer to a record or the record is abstract.
+getRecordDef :: (HasConstInfo m, ReadTCState m, MonadError TCErr m) => QName -> m Defn
+getRecordDef r = maybe err return =<< isRecord r
+  where err = typeError $ ShouldBeRecordType (El __DUMMY_SORT__ $ Def r [])
+
+-- | Get the record name belonging to a field name.
+getRecordOfField :: QName -> TCM (Maybe QName)
+getRecordOfField d = caseMaybeM (isProjection d) (return Nothing) $
+  \ Projection{ projProper = proper, projFromType = r} ->
+    return $ unArg r <$ proper -- if proper then Just (unArg r) else Nothing
+
+-- | Get the field names of a record.
+getRecordFieldNames :: (HasConstInfo m, ReadTCState m, MonadError TCErr m)
+                    => QName -> m [Dom C.Name]
+getRecordFieldNames r = recordFieldNames <$> getRecordDef r
+
+getRecordFieldNames_ :: (HasConstInfo m, ReadTCState m)
+                     => QName -> m (Maybe [Dom C.Name])
+getRecordFieldNames_ r = fmap recordFieldNames <$> isRecord r
+
+recordFieldNames :: Defn -> [Dom C.Name]
+recordFieldNames = map (fmap (nameConcrete . qnameName)) . recFields
+
+-- | Find all records with at least the given fields.
+findPossibleRecords :: [C.Name] -> TCM [QName]
+findPossibleRecords fields = do
+  defs  <- HMap.elems <$> useTC (stSignature . sigDefinitions)
+  idefs <- HMap.elems <$> useTC (stImports   . sigDefinitions)
+  scope <- getScope
+  return $ filter (`isNameInScope` scope) $ cands defs ++ cands idefs
+  where
+    cands defs = [ defName d | d <- defs, possible d ]
+    possible def =
+      -- Check whether the given fields are contained
+      -- in the fields of record @def@ (if it is a record).
+      case theDef def of
+        Record{ recFields = fs } -> Set.isSubsetOf given $
+          Set.fromList $ map (nameConcrete . qnameName . unDom) fs
+        _ -> False
+    given = Set.fromList fields
+
+-- | Get the field types of a record.
+getRecordFieldTypes :: QName -> TCM Telescope
+getRecordFieldTypes r = recTel <$> getRecordDef r
+
+-- | Get the field names belonging to a record type.
+getRecordTypeFields
+  :: Type  -- ^ Record type.  Need not be reduced.
+  -> TCM [Dom QName]
+getRecordTypeFields t = do
+  t <- reduce t  -- Andreas, 2018-03-03, fix for #2989.
+  case unEl t of
+    Def r _ -> do
+      rDef <- theDef <$> getConstInfo r
+      case rDef of
+        Record { recFields = fields } -> return fields
+        _ -> __IMPOSSIBLE__
+    _ -> __IMPOSSIBLE__
+
+-- | Returns the given record type's constructor name (with an empty
+-- range).
+getRecordConstructor :: (HasConstInfo m, ReadTCState m, MonadError TCErr m) => QName -> m ConHead
+getRecordConstructor r = killRange . recConHead <$> getRecordDef r
+
+-- | Check if a name refers to a record.
+--   If yes, return record definition.
+{-# SPECIALIZE isRecord :: QName -> TCM (Maybe Defn) #-}
+{-# SPECIALIZE isRecord :: QName -> ReduceM (Maybe Defn) #-}
+isRecord :: HasConstInfo m => QName -> m (Maybe Defn)
+isRecord r = do
+  def <- theDef <$> getConstInfo r
+  return $ case def of
+    Record{} -> Just def
+    _        -> Nothing
+
+-- | Reduce a type and check whether it is a record type.
+--   Succeeds only if type is not blocked by a meta var.
+--   If yes, return its name, parameters, and definition.
+isRecordType :: PureTCM m => Type -> m (Maybe (QName, Args, Defn))
+isRecordType t = either (const Nothing) Just <$> tryRecordType t
+
+-- | Reduce a type and check whether it is a record type.
+--   Succeeds only if type is not blocked by a meta var.
+--   If yes, return its name, parameters, and definition.
+--   If no, return the reduced type (unless it is blocked).
+tryRecordType :: PureTCM m => Type -> m (Either (Blocked Type) (QName, Args, Defn))
+tryRecordType t = ifBlocked t (\ m a -> return $ Left $ Blocked m a) $ \ nb t -> do
+  let no = return $ Left $ NotBlocked nb t
+  case unEl t of
+    Def r es -> do
+      let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      caseMaybeM (isRecord r) no $ \ def -> return $ Right (r,vs,def)
+    _ -> no
+
+-- | Get the original projection info for name.
+{-# SPECIALIZE origProjection :: QName -> TCM (QName, Definition, Maybe Projection) #-}
+origProjection ::  HasConstInfo m => QName -> m (QName, Definition, Maybe Projection)
+origProjection f = do
+  def <- getConstInfo f
+  let proj     = isProjection_ $ theDef def
+      fallback = return (f, def, proj)
+  caseMaybe proj fallback $
+    \ p@Projection{ projProper = proper, projOrig = f' } ->
+      if isNothing proper || f == f' then fallback else do
+        def <- getConstInfo f'
+        return (f', def, isProjection_ $ theDef def)
+
+-- | @getDefType f t@ computes the type of (possibly projection-(like))
+--   function @f@ whose first argument has type @t@.
+--   The `parameters' for @f@ are extracted from @t@.
+--   @Nothing@ if @f@ is projection(like) but
+--   @t@ is not a data/record/axiom type.
+--
+--   Precondition: @t@ is reduced.
+--
+--   See also: 'Agda.TypeChecking.Datatypes.getConType'
+getDefType :: PureTCM m => QName -> Type -> m (Maybe Type)
+getDefType f t = do
+  -- Andreas, Issue #1973: we need to take the original projection
+  -- since the parameters from the reduced type t are correct for
+  -- the original projection only.
+  -- Due to module application, the given (non-original) projection f
+  -- may expect less parameters, those corresponding to a unreduced
+  -- version of t (which we cannot obtain here).
+  (f, def, mp) <- origProjection f
+  let a = defType def
+  -- if @f@ is not a projection (like) function, @a@ is the correct type
+      fallback = return $ Just a
+  reportSDoc "tc.deftype" 20 $ vcat
+    [ "definition f =" <+> prettyTCM f <+> text ("  -- raw: " ++ prettyShow f)
+    , "has type   a =" <+> prettyTCM a
+    , "principal  t =" <+> prettyTCM t
+    ]
+  caseMaybe mp fallback $
+    \ (Projection{ projIndex = n }) -> if n <= 0 then fallback else do
+      -- otherwise, we have to instantiate @a@ to the "parameters" of @f@
+      let npars | n == 0    = __IMPOSSIBLE__
+                | otherwise = n - 1
+      reportSLn "tc.deftype" 20 $ "projIndex    = " ++ show n
+      -- we get the parameters from type @t@
+      case unEl t of
+        Def d es -> do
+          -- Andreas, 2013-10-22
+          -- we need to check this @Def@ is fully reduced.
+          -- If it is stuck due to disabled reductions
+          -- (because of failed termination check),
+          -- we will produce garbage parameters.
+          ifNotM (eligibleForProjectionLike d) failNotElig $ {- else -} do
+            -- now we know it is reduced, we can safely take the parameters
+            let pars = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ take npars es
+            reportSDoc "tc.deftype" 20 $ vcat
+              [ text $ "head d     = " ++ prettyShow d
+              , "parameters =" <+> sep (map prettyTCM pars)
+              ]
+            reportSDoc "tc.deftype" 60 $ "parameters = " <+> pretty pars
+            if length pars < npars then failure "does not supply enough parameters"
+            else Just <$> a `piApplyM` pars
+        _ -> failNotDef
+  where
+    failNotElig = failure "is not eligible for projection-likeness"
+    failNotDef  = failure "is not a Def."
+    failure reason = do
+      reportSDoc "tc.deftype" 25 $ sep
+        [ "Def. " <+> prettyTCM f <+> " is projection(like)"
+        , "but the type "
+        , prettyTCM t
+        , text $ "of its argument " ++ reason
+        ]
+      reportSDoc "tc.deftype" 60 $ "raw type: " <+> pretty t
+      return $ case unEl t of
+        Dummy{} -> Just __DUMMY_TYPE__
+        _       -> Nothing
+
+-- | Apply a projection to an expression with a known type, returning
+--   the type of the projected value.
+--   The given type should either be a record type or a type eligible for
+--   the principal argument of a projection-like function.
+shouldBeProjectible :: (PureTCM m, MonadTCError m, MonadBlock m)
+                    => Term -> Type -> ProjOrigin -> QName -> m Type
+-- shouldBeProjectible t f = maybe failure return =<< projectionType t f
+shouldBeProjectible v t o f = do
+  t <- abortIfBlocked t
+  projectTyped v t o f >>= \case
+    Just (_ , _ , ft) -> return ft
+    Nothing -> case t of
+      El _ Dummy{} -> return __DUMMY_TYPE__
+      _ -> typeError $ ShouldBeRecordType t
+    -- TODO: more accurate error that makes sense also for proj.-like funs.
+
+-- | The analogue of 'piApply'.  If @v@ is a value of record type @t@
+--   with field @f@, then @projectTyped v t f@ returns the type of @f v@.
+--   And also the record type (as first result).
+--
+--   Works also for projection-like definitions @f@.
+--   In this case, the first result is not a record type.
+--
+--   Precondition: @t@ is reduced.
+--
+projectTyped
+  :: PureTCM m
+  => Term        -- ^ Head (record value).
+  -> Type        -- ^ Its type.
+  -> ProjOrigin
+  -> QName       -- ^ Projection.
+  -> m (Maybe (Dom Type, Term, Type))
+projectTyped v t o f = caseMaybeM (getDefType f t) (return Nothing) $ \ tf -> do
+  ifNotPiType tf (const $ return Nothing) {- else -} $ \ dom b -> do
+  u <- applyDef o f (argFromDom dom $> v)
+  return $ Just (dom, u, b `absApp` v)
+
+-- | Typing of an elimination.
+
+data ElimType
+  = ArgT (Dom Type)           -- ^ Type of the argument.
+  | ProjT
+    { projTRec   :: Dom Type  -- ^ The type of the record which is eliminated.
+    , projTField :: Type      -- ^ The type of the field.
+    }
+
+instance PrettyTCM ElimType where
+  prettyTCM (ArgT a)    = prettyTCM a
+  prettyTCM (ProjT a b) =
+    "." TCM.<> parens (prettyTCM a <+> "->" <+> prettyTCM b)
+
+-- | Given a head and its type, compute the types of the eliminations.
+
+typeElims :: Type -> Term -> Elims -> TCM [ElimType]
+typeElims a _ [] = return []
+typeElims a self (e : es) = do
+  case e of
+    -- Andrea 02/08/2017: when going from patterns to elims we
+    -- generate an Apply elim even for Path types, because we use VarP
+    -- for both, so we have to allow for a Path type here.
+    Apply v -> ifNotPiOrPathType a __IMPOSSIBLE__ {- else -} $ \ a b -> do
+      (ArgT a :) <$> typeElims (absApp b $ unArg v) (self `applyE` [e]) es
+    Proj o f -> do
+      a <- reduce a
+      (dom, self, a) <- fromMaybe __IMPOSSIBLE__ <$> projectTyped self a o f
+      (ProjT dom a :) <$> typeElims a self es
+    IApply{} -> __IMPOSSIBLE__
+
+-- | Given a term with a given type and a list of eliminations, returning the
+--   type of the term applied to the eliminations.
+eliminateType :: (PureTCM m) => m Empty -> Term -> Type -> Elims -> m Type
+eliminateType err = eliminateType' err . applyE
+
+eliminateType' :: (PureTCM m) => m Empty -> (Elims -> Term) -> Type -> Elims -> m Type
+eliminateType' err hd t [] = return t
+eliminateType' err hd t (e : es) = case e of
+  Apply v -> do
+    t' <- piApplyM' err t v
+    eliminateType' err (hd . (e:)) t' es
+  Proj o f -> reduce t >>= getDefType f >>= \case
+    Just a -> ifNotPiType a (\_ -> absurd <$> err) $ \_ c ->
+      eliminateType' err (hd . (e:)) (c `absApp` (hd [])) es
+    Nothing -> absurd <$> err
+  IApply _ _ r -> do
+    t' <- piApplyM' err t r
+    eliminateType' err (hd . (e:)) t' es
+
+-- | Check if a name refers to an eta expandable record.
+--
+-- The answer is no for a record type with an erased constructor
+-- unless the current quantity is \"erased\".
+{-# SPECIALIZE isEtaRecord :: QName -> TCM Bool #-}
+{-# SPECIALIZE isEtaRecord :: QName -> ReduceM Bool #-}
+isEtaRecord :: HasConstInfo m => QName -> m Bool
+isEtaRecord r = do
+  isRec <- isRecord r
+  case isRec of
+    Nothing -> return False
+    Just r
+      | recEtaEquality r /= YesEta -> return False
+      | otherwise                  -> do
+        constructorQ <- getQuantity <$>
+                          getConstInfo (conName (recConHead r))
+        currentQ     <- viewTC eQuantity
+        return $ constructorQ `moreQuantity` currentQ
+
+{-# SPECIALIZE isEtaCon :: QName -> TCM Bool #-}
+isEtaCon :: HasConstInfo m => QName -> m Bool
+isEtaCon c = getConstInfo' c >>= \case
+  Left (SigUnknown err)     -> __IMPOSSIBLE__
+  Left SigCubicalNotErasure -> __IMPOSSIBLE__
+  Left SigAbstract          -> return False
+  Right def                 -> case theDef def of
+    Constructor {conData = r} -> isEtaRecord r
+    _ -> return False
+
+-- | Going under one of these does not count as a decrease in size for the termination checker.
+isEtaOrCoinductiveRecordConstructor :: HasConstInfo m => QName -> m Bool
+isEtaOrCoinductiveRecordConstructor c =
+  caseMaybeM (isRecordConstructor c) (return False) $ \ (_, def) -> return $
+    recEtaEquality def == YesEta || recInduction def /= Just Inductive
+      -- If in doubt about coinductivity, then yes.
+
+-- | Check if a name refers to a record which is not coinductive.  (Projections are then size-preserving)
+isInductiveRecord :: HasConstInfo m => QName -> m Bool
+isInductiveRecord r = maybe False ((Just CoInductive /=) . recInduction) <$> isRecord r
+
+-- | Check if a type is an eta expandable record and return the record identifier and the parameters.
+isEtaRecordType :: (HasConstInfo m)
+                => Type -> m (Maybe (QName, Args))
+isEtaRecordType a = case unEl a of
+  Def d es -> do
+    let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+    ifM (isEtaRecord d) (return $ Just (d, vs)) (return Nothing)
+  _        -> return Nothing
+
+-- | Check if a name refers to a record constructor.
+--   If yes, return record definition.
+isRecordConstructor :: HasConstInfo m => QName -> m (Maybe (QName, Defn))
+isRecordConstructor c = getConstInfo' c >>= \case
+  Left (SigUnknown err)     -> __IMPOSSIBLE__
+  Left SigCubicalNotErasure -> __IMPOSSIBLE__
+  Left SigAbstract          -> return Nothing
+  Right def                 -> case theDef $ def of
+    Constructor{ conData = r } -> fmap (r,) <$> isRecord r
+    _                          -> return Nothing
+
+-- | Check if a constructor name is the internally generated record constructor.
+--
+--   Works also for abstract constructors.
+isGeneratedRecordConstructor :: (MonadTCEnv m, HasConstInfo m)
+                             => QName -> m Bool
+isGeneratedRecordConstructor c = ignoreAbstractMode $ do
+  caseMaybeM (isRecordConstructor c) (return False) $ \ (_, def) ->
+    case def of
+      Record{ recNamedCon = False } -> return True
+      _ -> return False
+
+
+-- | Turn off eta for unguarded recursive records.
+--   Projections do not preserve guardedness.
+unguardedRecord :: QName -> PatternOrCopattern -> TCM ()
+unguardedRecord q pat = modifySignature $ updateDefinition q $ updateTheDef $ \case
+  r@Record{} -> r { recEtaEquality' = setEtaEquality (recEtaEquality' r) $ NoEta pat }
+  _ -> __IMPOSSIBLE__
+
+-- | Turn on eta for non-recursive and inductive guarded recursive records,
+--   unless user declared otherwise.
+--   Projections do not preserve guardedness.
+updateEtaForRecord :: QName -> TCM ()
+updateEtaForRecord q = whenM etaEnabled $ do
+
+  -- Do we need to switch on eta for record q?
+  switchEta <- getConstInfo q <&> theDef <&> \case
+    Record{ recInduction = ind, recEtaEquality' = eta }
+      | Inferred NoEta{} <- eta, ind /= Just CoInductive -> True
+      | otherwise -> False
+    _ -> __IMPOSSIBLE__
+
+  when switchEta $ do
+    modifySignature $ updateDefinition q $ over (lensTheDef . lensRecord) $ \ d ->
+      d{ _recEtaEquality' = Inferred YesEta }
+
+-- | Turn on eta for inductive guarded recursive records.
+--   Projections do not preserve guardedness.
+recursiveRecord :: QName -> TCM ()
+recursiveRecord = updateEtaForRecord
+
+-- | Turn on eta for non-recursive record, unless user declared otherwise.
+nonRecursiveRecord :: QName -> TCM ()
+nonRecursiveRecord = updateEtaForRecord
+
+-- | Check whether record type is marked as recursive.
+--
+--   Precondition: record type identifier exists in signature.
+isRecursiveRecord :: QName -> TCM Bool
+isRecursiveRecord q = recRecursive . theDef . fromMaybe __IMPOSSIBLE__ . lookupDefinition q <$> getSignature
+
+{- | @etaExpandBoundVar i = (Δ, σ, τ)@
+
+Precondition: The current context is @Γ = Γ₁, x:R pars, Γ₂@ where
+  @|Γ₂| = i@ and @R@ is a eta-expandable record type
+  with constructor @c@ and fields @Γ'@.
+
+Postcondition: @Δ = Γ₁, Γ', Γ₂[c Γ']@ and @Γ ⊢ σ : Δ@ and @Δ ⊢ τ : Γ@.
+-}
+etaExpandBoundVar :: Int -> TCM (Maybe (Telescope, Substitution, Substitution))
+etaExpandBoundVar i = fmap (\ (delta, sigma, tau, _) -> (delta, sigma, tau)) <$> do
+  expandRecordVar i =<< getContextTelescope
+
+-- | @expandRecordVar i Γ = (Δ, σ, τ, Γ')@
+--
+--   Precondition: @Γ = Γ₁, x:R pars, Γ₂@ where
+--     @|Γ₂| = i@ and @R@ is a eta-expandable record type
+--     with constructor @c@ and fields @Γ'@.
+--
+--   Postcondition: @Δ = Γ₁, Γ', Γ₂[c Γ']@ and @Γ ⊢ σ : Δ@ and @Δ ⊢ τ : Γ@.
+
+expandRecordVar :: PureTCM m => Int -> Telescope -> m (Maybe (Telescope, Substitution, Substitution, Telescope))
+expandRecordVar i gamma0 = do
+  -- Get the context with last variable added last in list.
+  let gamma = telToList gamma0
+  -- Convert the de Bruijn index i to a de Bruijn level
+      l     = size gamma - 1 - i
+  -- Extract type of @i@th de Bruijn index.
+  -- Γ = Γ₁, x:a, Γ₂
+  let (gamma1, dom@(Dom{domInfo = ai, unDom = (x, a)}) : gamma2) = splitAt l gamma -- TODO:: Defined but not used dom, ai
+  -- This must be a eta-expandable record type.
+  let failure = do
+        reportSDoc "tc.meta.assign.proj" 25 $
+          "failed to eta-expand variable " <+> pretty x <+>
+          " since its type " <+> prettyTCM a <+>
+          " is not a record type"
+        return Nothing
+  caseMaybeM (isRecordType a) failure $ \ (r, pars, def) -> case recEtaEquality def of
+    NoEta{} -> return Nothing
+    YesEta  -> Just <$> do
+      -- Get the record fields @Γ₁ ⊢ tel@ (@tel = Γ'@).
+      -- TODO: compose argInfo ai with tel.
+      let tel = recTel def `apply` pars
+          m   = size tel
+          fs  = map argFromDom $ recFields def
+      -- Construct the record pattern @Γ₁, Γ' ⊢ u := c ys@.
+          ys  = zipWith (\ f i -> f $> var i) fs $ downFrom m
+          u   = mkCon (recConHead def) ConOSystem ys
+      -- @Γ₁, Γ' ⊢ τ₀ : Γ₁, x:_@
+          tau0 = consS u $ raiseS m
+      -- @Γ₁, Γ', Γ₂ ⊢ τ₀ : Γ₁, x:_, Γ₂@
+          tau  = liftS (size gamma2) tau0
+
+      --  Fields are in order first-first.
+          zs  = for fs $ fmap $ \ f -> Var 0 [Proj ProjSystem f]
+      --  We need to reverse the field sequence to build the substitution.
+      -- @Γ₁, x:_ ⊢ σ₀ : Γ₁, Γ'@
+          sigma0 = reverse (map unArg zs) ++# raiseS 1
+      -- @Γ₁, x:_, Γ₂ ⊢ σ₀ : Γ₁, Γ', Γ₂@
+          sigma  = liftS (size gamma2) sigma0
+
+      -- Construct @Δ@ as telescope.
+      -- Note @Γ₁, x:_ ⊢ Γ₂@, thus, @Γ₁, Γ' ⊢ [τ₀]Γ₂@
+
+          -- Use "f(x)" as variable name for the projection f(x).
+          s     = prettyShow x
+          tel'  = mapAbsNames (\ f -> stringToArgName $ argNameToString f ++ "(" ++ s ++ ")") tel
+          delta = telFromList $ gamma1 ++ telToList tel' ++
+                    telToList (applySubst tau0 $ telFromList gamma2)
+                    -- Andreas, 2017-07-29, issue #2644
+                    -- We cannot substitute directly into a ListTel like gamma2,
+                    -- we have to convert it to a telescope first, otherwise we get garbage.
+
+      return (delta, sigma, tau, tel)
+
+-- | Precondition: variable list is ordered descendingly.  Can be empty.
+expandRecordVarsRecursively :: [Int] -> Telescope -> TCM (Telescope, Substitution, Substitution)
+expandRecordVarsRecursively [] gamma = return (gamma, idS, idS)
+expandRecordVarsRecursively (i : is) gamma = do
+  caseMaybeM (expandRecordVar i gamma) (expandRecordVarsRecursively is gamma)
+  $ \ (gamma1, sigma1, tau1, tel) -> do
+    -- Γ ⊢ σ₁ : Γ₁  and  Γ₁ ⊢ τ₁ : Γ
+    let n = size tel
+        newis = take n $ downFrom $ i + n
+    (gamma2, sigma2, tau2) <- expandRecordVarsRecursively (newis ++ is) gamma1
+    -- Γ₁ ⊢ σ₂ : Γ₂  and  Γ₂ ⊢ τ₂ : Γ₁
+    return (gamma2, applySubst sigma1 sigma2, applySubst tau2 tau1)
+
+-- | @curryAt v (Γ (y : R pars) -> B) n =
+--     ( \ v -> λ Γ ys → v Γ (c ys)            {- curry   -}
+--     , \ v -> λ Γ y → v Γ (p1 y) ... (pm y)  {- uncurry -}
+--     , Γ (ys : As) → B[c ys / y]
+--     )@
+--
+--   where @n = size Γ@.
+curryAt :: Type -> Int -> TCM (Term -> Term, Term -> Term, Type)
+curryAt t n = do
+  -- first, strip the leading n domains (which remain unchanged)
+  TelV gamma core <- telViewUpTo n t
+  case unEl core of
+    -- There should be at least one domain left
+    Pi (dom@Dom{domInfo = ai, unDom = a}) b -> do
+      -- Eta-expand @dom@ along @qs@ into a telescope @tel@, computing a substitution.
+      -- For now, we only eta-expand once.
+      -- This might trigger another call to @etaExpandProjectedVar@ later.
+      -- A more efficient version does all the eta-expansions at once here.
+      (r, pars, def) <- fromMaybe __IMPOSSIBLE__ <$> isRecordType a
+      if | NoEta _ <- recEtaEquality def -> __IMPOSSIBLE__
+         | otherwise -> return ()
+      -- TODO: compose argInfo ai with tel.
+      let tel = recTel def `apply` pars
+          m   = size tel
+          fs  = map argFromDom $ recFields def
+          ys  = zipWith (\ f i -> f $> var i) fs $ downFrom m
+          u   = mkCon (recConHead def) ConOSystem ys
+          b'  = raise m b `absApp` u
+          t'  = gamma `telePi` (tel `telePi` b')
+          gammai = map domInfo $ telToList gamma
+          xs  = reverse $ zipWith (\ ai i -> Arg ai $ var i) gammai [m..]
+          curry v = teleLam gamma $ teleLam tel $
+                      raise (n + m) v `apply` (xs ++ [Arg ai u])
+          zs  = for fs $ fmap $ \ f -> Var 0 [Proj ProjSystem f]
+          atel = sgTel $ (,) (absName b) <$> dom
+          uncurry v = teleLam gamma $ teleLam atel $
+                        raise (n + 1) v `apply` (xs ++ zs)
+      return (curry, uncurry, t')
+    _ -> __IMPOSSIBLE__
+
+{-| @etaExpand r pars u@ computes the eta expansion of record value @u@
+    at record type @r pars@.
+
+    The first argument @r@ should be the name of an eta-expandable record type.
+    Given
+
+      @record R : Set where field x : A; y : B; .z : C@
+
+    and @r : R@,
+
+      @etaExpand R [] r = (tel, [R.x r, R.y r, R.z r])@
+
+    where @tel@ is the record telescope instantiated at the parameters @pars@.
+-}
+etaExpandRecord :: (HasConstInfo m, MonadDebug m, ReadTCState m)
+                => QName -> Args -> Term -> m (Telescope, Args)
+etaExpandRecord = etaExpandRecord' False
+
+-- | Eta expand a record regardless of whether it's an eta-record or not.
+forceEtaExpandRecord :: (HasConstInfo m, MonadDebug m, ReadTCState m, MonadError TCErr m)
+                     => QName -> Args -> Term -> m (Telescope, Args)
+forceEtaExpandRecord = etaExpandRecord' True
+
+etaExpandRecord' :: (HasConstInfo m, MonadDebug m, ReadTCState m)
+                 => Bool -> QName -> Args -> Term -> m (Telescope, Args)
+etaExpandRecord' forceEta r pars u = do
+  def <- fromMaybe __IMPOSSIBLE__ <$> isRecord r
+  (tel, _, _, args) <- etaExpandRecord'_ forceEta r pars def u
+  return (tel, args)
+
+etaExpandRecord_ :: HasConstInfo m
+                 => QName -> Args -> Defn -> Term -> m (Telescope, ConHead, ConInfo, Args)
+etaExpandRecord_ = etaExpandRecord'_ False
+
+etaExpandRecord'_ :: HasConstInfo m
+                  => Bool -> QName -> Args -> Defn -> Term -> m (Telescope, ConHead, ConInfo, Args)
+etaExpandRecord'_ forceEta r pars def u = do
+  let Record{ recConHead     = con
+            , recFields      = xs
+            , recTel         = tel
+            } = def
+      tel' = apply tel pars
+  -- Make sure we do not expand non-eta records (unless forced to):
+  unless (recEtaEquality def == YesEta || forceEta) __IMPOSSIBLE__
+  case u of
+
+    -- Already expanded.
+    Con con_ ci es -> do
+      let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      -- Andreas, 2019-10-21, issue #4148
+      -- @con == con_@ might fail, but their normal forms should be equal.
+      whenNothingM (conName con `sameDef` conName con_) $ do
+        reportSDoc "impossible" 10 $ vcat
+          [ "etaExpandRecord_: the following two constructors should be identical"
+          , nest 2 $ text $ "con  = " ++ prettyShow con
+          , nest 2 $ text $ "con_ = " ++ prettyShow con_
+          ]
+        __IMPOSSIBLE__
+      return (tel', con, ci, args)
+
+    -- Not yet expanded.
+    _ -> do
+      -- Andreas, < 2016-01-18: Note: recFields are always the original projections,
+      -- thus, we can use them in Proj directly.
+      let xs' = for (map argFromDom xs) $ fmap $ \ x -> u `applyE` [Proj ProjSystem x]
+      reportSDoc "tc.record.eta" 20 $ vcat
+        [ "eta expanding" <+> prettyTCM u <+> ":" <+> prettyTCM r
+        , nest 2 $ vcat
+          [ "tel' =" <+> prettyTCM tel'
+          , "args =" <+> prettyTCM xs'
+          ]
+        ]
+      return (tel', con, ConOSystem, xs')
+
+etaExpandAtRecordType :: Type -> Term -> TCM (Telescope, Term)
+etaExpandAtRecordType t u = do
+  (r, pars, def) <- fromMaybe __IMPOSSIBLE__ <$> isRecordType t
+  (tel, con, ci, args) <- etaExpandRecord_ r pars def u
+  return (tel, mkCon con ci args)
+
+-- | The fields should be eta contracted already.
+--
+--   We can eta contract if all fields @f = ...@ are irrelevant
+--   or all fields @f@ are the projection @f v@ of the same value @v@,
+--   but we need at least one relevant field to find the value @v@.
+--
+--   If all fields are erased, we cannot eta-contract.
+
+--   Andreas, 2019-11-06, issue #4168: eta-contraction all-erased record
+--   lead to compilation error.
+
+--   TODO: this can be moved out of TCM.
+--   Andreas, 2018-01-28: attempted just that, but Auto does not
+--   put the conFields there (it does not run in TCM).
+--   If we get rid of Auto, we can do this.  (Tests not involving Auto pass.)
+
+{-# SPECIALIZE etaContractRecord :: QName -> ConHead -> ConInfo -> Args -> TCM Term #-}
+{-# SPECIALIZE etaContractRecord :: QName -> ConHead -> ConInfo -> Args -> ReduceM Term #-}
+etaContractRecord :: HasConstInfo m => QName -> ConHead -> ConInfo -> Args -> m Term
+etaContractRecord r c ci args = if all (not . usableModality) args then fallBack else do
+  Just Record{ recFields = xs } <- isRecord r
+  reportSDoc "tc.record.eta.contract" 20 $ vcat
+    [ "eta contracting record"
+    , nest 2 $ vcat
+      [ "record type r  =" <+> prettyTCM r
+      , "constructor c  =" <+> prettyTCM c
+      , "field names xs =" <+> pretty    xs
+      , "fields    args =" <+> prettyTCM args
+      ]
+    ]
+  case compare (length args) (length xs) of
+    LT -> fallBack       -- Not fully applied
+    GT -> __IMPOSSIBLE__ -- Too many arguments. Impossible.
+    EQ -> do
+      case zipWithM check args xs of
+        Just as -> case catMaybes as of
+          (a:as) ->
+            if all (a ==) as
+              then return a
+              else fallBack
+          _ -> fallBack -- just irrelevant terms
+        _ -> fallBack  -- a Nothing
+  where
+  fallBack = return (mkCon c ci args)
+  check :: Arg Term -> Dom QName -> Maybe (Maybe Term)
+  check a ax = do
+  -- @a@ is the constructor argument, @ax@ the corr. record field name
+    -- skip irrelevant record fields by returning DontCare
+    case (getRelevance a, hasElims $ unArg a) of
+      (Irrelevant, _)   -> Just Nothing
+      -- if @a@ is the record field name applied to a single argument
+      -- then it passes the check
+      (_, Just (_, [])) -> Nothing  -- not a projection
+      (_, Just (h, e0:es0))
+        | (es, Proj _o f) <- initLast1 e0 es0
+        , unDom ax == f -> Just $ Just $ h es
+      _                 -> Nothing
+
+{-# SPECIALIZE isSingletonRecord :: QName -> Args -> TCM Bool #-}
+-- | Is the type a hereditarily singleton record type? May return a
+-- blocking metavariable.
+--
+-- Precondition: The name should refer to a record type, and the
+-- arguments should be the parameters to the type.
+isSingletonRecord :: (PureTCM m, MonadBlock m) => QName -> Args -> m Bool
+isSingletonRecord r ps = isJust <$> isSingletonRecord' False r ps mempty
+
+isSingletonRecordModuloRelevance :: (PureTCM m, MonadBlock m)
+                                 => QName -> Args -> m Bool
+isSingletonRecordModuloRelevance r ps = isJust <$> isSingletonRecord' True r ps mempty
+
+-- | Return the unique (closed) inhabitant if exists.
+--   In case of counting irrelevance in, the returned inhabitant
+--   contains dummy terms.
+isSingletonRecord'
+  :: forall m. (PureTCM m, MonadBlock m)
+  => Bool            -- ^ Should disregard irrelevant fields?
+  -> QName           -- ^ Name of record type to check.
+  -> Args            -- ^ Parameters given to the record type.
+  -> Set QName       -- ^ Non-terminating record types we already encountered.
+                     --   These are considered as non-singletons,
+                     --   otherwise we would construct an infinite inhabitant (in an infinite time...).
+  -> m (Maybe Term)  -- ^ The unique inhabitant, if any.  May contain dummy terms in irrelevant positions.
+isSingletonRecord' regardIrrelevance r ps rs = do
+  reportSDoc "tc.meta.eta" 30 $ vcat
+    [ "Is" <+> prettyTCM (Def r $ map Apply ps) <+> "a singleton record type?"
+    , "  already visited:" <+> hsep (map prettyTCM $ Set.toList rs)
+    ]
+  -- Andreas, 2022-03-10, issue #5823
+  -- We need to make sure we are not infinitely unfolding records, so we only expand each once,
+  -- and keep track of the recursive ones we have already seen.
+  if r `Set.member` rs then no else do
+    caseMaybeM (isRecord r) no $ \ def -> do
+      -- We might not know yet whether a record type is recursive because the positivity checker hasn't run yet.
+      -- In this case, we pessimistically consider the record type to be recursive (@True@).
+      let recursive = maybe True (not . null) $ recMutual def
+      -- Andreas, 2022-03-23, issue #5823
+      -- We may pass through terminating record types as often as we want.
+      -- If the termination checker has not run yet, we pessimistically consider the record type
+      -- to be non-terminating.
+      let nonTerminating = maybe True not $ recTerminates def
+      reportSDoc "tc.meta.eta" 30 $ vcat
+        [ hsep [ prettyTCM r, "is recursive      :", prettyTCM recursive      ]
+        , hsep [ prettyTCM r, "is non-terminating:", prettyTCM nonTerminating ]
+        ]
+      fmap (mkCon (recConHead def) ConOSystem) <$> do
+        check (applyWhen (recursive && nonTerminating) (Set.insert r) rs) $ recTel def `apply` ps
+  where
+  -- Check that all entries of the constructor telescope are singletons.
+  check :: Set QName -> Telescope -> m (Maybe [Arg Term])
+  check rs tel = do
+    reportSDoc "tc.meta.eta" 30 $
+      "isSingletonRecord' checking telescope " <+> prettyTCM tel
+    case tel of
+      EmptyTel -> yes
+      ExtendTel dom tel -> ifM (return regardIrrelevance `and2M` isIrrelevantOrPropM dom)
+        {-then-}
+          (underAbstraction dom tel $ fmap (fmap (Arg (domInfo dom) __DUMMY_TERM__ :)) . check rs)
+        {-else-} $ do
+          caseMaybeM (isSingletonType' regardIrrelevance (unDom dom) rs) no $ \ v -> do
+            underAbstraction dom tel $ fmap (fmap (Arg (domInfo dom) v :)) . check rs
+  no  = return Nothing
+  yes = return $ Just []
+
+-- | Check whether a type has a unique inhabitant and return it.
+--   Can be blocked by a metavar.
+isSingletonType :: (PureTCM m, MonadBlock m) => Type -> m (Maybe Term)
+isSingletonType t = isSingletonType' False t mempty
+
+-- | Check whether a type has a unique inhabitant (irrelevant parts ignored).
+--   Can be blocked by a metavar.
+isSingletonTypeModuloRelevance :: (PureTCM m, MonadBlock m) => Type -> m Bool
+isSingletonTypeModuloRelevance t = isJust <$> isSingletonType' True t mempty
+
+isSingletonType'
+  :: forall m. (PureTCM m, MonadBlock m)
+  => Bool            -- ^ Should disregard irrelevant fields?
+  -> Type            -- ^ Type to check.
+  -> Set QName       -- ^ Non-terminating record typess we already encountered.
+                     --   These are considered as non-singletons,
+                     --   otherwise we would construct an infinite inhabitant (in an infinite time...).
+  -> m (Maybe Term)  -- ^ The unique inhabitant, if any.  May contain dummy terms in irrelevant positions.
+isSingletonType' regardIrrelevance t rs = do
+    TelV tel t <- telView t
+    t <- abortIfBlocked t
+    addContext tel $ do
+      let
+        -- Easy case: η for records.
+        record :: m (Maybe Term)
+        record = runMaybeT $ do
+          (r, ps, def) <- MaybeT $ isRecordType t
+          guard (YesEta == recEtaEquality def)
+          abstract tel <$> MaybeT (isSingletonRecord' regardIrrelevance r ps rs)
+
+        -- Slightly harder case: η for Sub {level} tA phi elt.
+        -- tA : Type level, phi : I, elt : Partial phi tA.
+        subtype :: m (Maybe Term)
+        subtype = runMaybeT $ do
+          (level, tA, phi, elt) <- MaybeT $ isCubicalSubtype t
+          subin <- MaybeT $ getBuiltinName' builtinSubIn
+          itIsOne <- MaybeT $ getBuiltinName' builtinIsOne
+          phiV <- intervalView phi
+          case phiV of
+            -- If phi = i1, then inS (elt 1=1) is the only inhabitant.
+            IOne -> do
+              let
+                argH = Arg $ setHiding Hidden defaultArgInfo
+                it = elt `apply` [defaultArg (Def itIsOne [])]
+              pure (Def subin [] `apply` [argH level, argH tA, argH phi, defaultArg it])
+            -- Otherwise we're blocked
+            OTerm phi' -> patternViolation (unblockOnAnyMetaIn phi')
+            -- This fails the MaybeT: we're not looking at a
+            -- definitional singleton.
+            _ -> fail ""
+
+      (<|>) <$> record <*> subtype
+
+{-# SPECIALIZE isEtaVar :: Term -> Type -> TCM (Maybe Int) #-}
+-- | Checks whether the given term (of the given type) is beta-eta-equivalent
+--   to a variable. Returns just the de Bruijn-index of the variable if it is,
+--   or nothing otherwise.
+isEtaVar :: forall m. PureTCM m => Term -> Type -> m (Maybe Int)
+isEtaVar u a = runMaybeT $ isEtaVarG u a Nothing []
+  where
+    -- Checks whether the term u (of type a) is beta-eta-equivalent to
+    -- `Var i es`, and returns i if it is. If the argument mi is `Just i'`,
+    -- then i and i' are also required to be equal (else Nothing is returned).
+    isEtaVarG :: Term -> Type -> Maybe Int -> [Elim' Int] -> MaybeT m Int
+    isEtaVarG u a mi es = do
+      (u, a) <- reduce (u, a)
+      reportSDoc "tc.lhs" 80 $ "isEtaVarG" <+> nest 2 (vcat
+        [ "u  = " <+> prettyTCM u
+        , "a  = " <+> prettyTCM a
+        , "mi = " <+> text (show mi)
+        , "es = " <+> prettyList_ (map (prettyTCM . fmap var) es)
+        ])
+      case (u, unEl a) of
+        (Var i' es', _) -> do
+          guard $ mi == (i' <$ mi)
+          b <- typeOfBV i'
+          areEtaVarElims (var i') b es' es
+          return i'
+        (_, Def d pars) -> do
+          guard =<< do isEtaRecord d
+          fs <- map unDom . recFields . theDef <$> getConstInfo d
+          is <- forM fs $ \f -> do
+            let o = ProjSystem
+            (_, _, fa) <- MaybeT $ projectTyped u a o f
+            isEtaVarG (u `applyE` [Proj o f]) fa mi (es ++ [Proj o f])
+          case (mi, is) of
+            (Just i, _)     -> return i
+            (Nothing, [])   -> mzero
+            (Nothing, i:is) -> guard (all (== i) is) >> return i
+        (_, Pi dom cod) -> addContext dom $ do
+          let u'  = raise 1 u `apply` [argFromDom dom $> var 0]
+              a'  = absBody cod
+              mi' = fmap (+ 1) mi
+              es' = (fmap . fmap) (+ 1) es ++ [Apply $ argFromDom dom $> 0]
+          (-1 +) <$> isEtaVarG u' a' mi' es'
+        _ -> mzero
+
+    -- `areEtaVarElims u a es es'` checks whether the given elims es (as applied
+    -- to the term u of type a) are beta-eta-equal to either projections or
+    -- variables with de Bruijn indices given by es'.
+    areEtaVarElims :: Term -> Type -> Elims -> [Elim' Int] -> MaybeT m ()
+    areEtaVarElims u a []    []    = return ()
+    areEtaVarElims u a []    (_:_) = mzero
+    areEtaVarElims u a (_:_) []    = mzero
+    areEtaVarElims u a (Proj o f : es) (Proj _ f' : es') = do
+      guard $ f == f'
+      a       <- reduce a
+      (_, _, fa) <- MaybeT $ projectTyped u a o f
+      areEtaVarElims (u `applyE` [Proj o f]) fa es es'
+    -- These two cases can occur only when we're looking at two different
+    -- variables (i.e. one of function type and the other of record type) so
+    -- it's definitely not the variable we're looking for (or someone is playing
+    -- Jedi mind tricks on us)
+    areEtaVarElims u a (Proj{}  : _ ) (Apply _ : _  ) = mzero
+    areEtaVarElims u a (Apply _ : _ ) (Proj{}  : _  ) = mzero
+    areEtaVarElims u a (Proj{} : _ ) (IApply{} : _  ) = mzero
+    areEtaVarElims u a (IApply{} : _ ) (Proj{} : _  ) = mzero
+    areEtaVarElims u a (Apply  _ : _ ) (IApply{} : _  ) = mzero
+    areEtaVarElims u a (IApply{} : _ ) (Apply  _ : _  ) = mzero
+    areEtaVarElims u a (IApply{} : _) (IApply{} : _) = __IMPOSSIBLE__ -- TODO Andrea: not actually impossible, should be done like Apply
+    areEtaVarElims u a (Apply v : es) (Apply i : es') = do
+      ifNotPiType a (const mzero) $ \dom cod -> do
+      _ <- isEtaVarG (unArg v) (unDom dom) (Just $ unArg i) []
+      areEtaVarElims (u `apply` [fmap var i]) (cod `absApp` var (unArg i)) es es'
+
+
+-- | Replace projection patterns by the original projections.
+--
+class NormaliseProjP a where
+  normaliseProjP :: HasConstInfo m => a -> m a
+
+instance NormaliseProjP Clause where
+  normaliseProjP cl = do
+    ps <- normaliseProjP $ namedClausePats cl
+    return $ cl { namedClausePats = ps }
+
+instance NormaliseProjP a => NormaliseProjP [a] where
+  normaliseProjP = traverse normaliseProjP
+
+instance NormaliseProjP a => NormaliseProjP (Arg a) where
+  normaliseProjP = traverse normaliseProjP
+
+instance NormaliseProjP a => NormaliseProjP (Named_ a) where
+  normaliseProjP = traverse normaliseProjP
+
+instance NormaliseProjP (Pattern' x) where
+  normaliseProjP p@VarP{}        = return p
+  normaliseProjP p@DotP{}        = return p
+  normaliseProjP (ConP c cpi ps) = ConP c cpi <$> normaliseProjP ps
+  normaliseProjP (DefP o q ps) = DefP o q <$> normaliseProjP ps
+  normaliseProjP p@LitP{}        = return p
+  normaliseProjP (ProjP o d0)    = ProjP o <$> getOriginalProjection d0
+  normaliseProjP p@IApplyP{}     = return p
diff --git a/src/full/Agda/TypeChecking/Records.hs-boot b/src/full/Agda/TypeChecking/Records.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Records.hs-boot
@@ -0,0 +1,14 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Records where
+
+import Agda.Syntax.Internal
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.TypeChecking.Monad
+
+isRecord :: HasConstInfo m => QName -> m (Maybe Defn)
+isEtaRecord :: HasConstInfo m => QName -> m Bool
+getRecordFieldNames_ :: (HasConstInfo m, ReadTCState m) => QName -> m (Maybe [Dom C.Name])
+etaContractRecord :: HasConstInfo m => QName -> ConHead -> ConInfo -> Args -> m Term
+isGeneratedRecordConstructor :: (MonadTCEnv m, HasConstInfo m) => QName -> m Bool
+isRecordConstructor :: HasConstInfo m => QName -> m (Maybe (QName, Defn))
diff --git a/src/full/Agda/TypeChecking/Reduce.hs b/src/full/Agda/TypeChecking/Reduce.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Reduce.hs
@@ -0,0 +1,1767 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Reduce
+ -- Meta instantiation
+ ( Instantiate, instantiate', instantiate, instantiateWhen
+ -- Recursive meta instantiation
+ , InstantiateFull, instantiateFull', instantiateFull
+ , instantiateFullExceptForDefinitions
+ -- Check for meta (no reduction)
+ , IsMeta, isMeta
+ -- Reduction and blocking
+ , Reduce, reduce', reduceB', reduce, reduceB, reduceWithBlocker, reduceIApply'
+ , reduceDefCopy, reduceDefCopyTCM
+ , reduceHead
+ , slowReduceTerm
+ , unfoldCorecursion, unfoldCorecursionE
+ , unfoldDefinitionE, unfoldDefinitionStep
+ , unfoldInlined
+ , appDef', appDefE'
+ , abortIfBlocked, ifBlocked, isBlocked, fromBlocked, blockOnError
+ -- Simplification
+ , Simplify, simplify, simplifyBlocked'
+ -- Normalization
+ , Normalise, normalise', normalise
+ , slowNormaliseArgs
+ ) where
+
+import Control.Monad ( (>=>), void )
+import Control.Monad.Except
+
+import Data.List ( intercalate )
+import Data.Maybe
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Foldable
+import Data.Traversable
+import Data.HashMap.Strict (HashMap)
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Scope.Base (Scope)
+import Agda.Syntax.Literal
+
+import {-# SOURCE #-} Agda.TypeChecking.Irrelevance (isPropM)
+import Agda.TypeChecking.Monad hiding ( enterClosure, constructorForm )
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.EtaContract
+
+import Agda.TypeChecking.Reduce.Monad
+
+import {-# SOURCE #-} Agda.TypeChecking.CompiledClause.Match
+import {-# SOURCE #-} Agda.TypeChecking.Patterns.Match
+import {-# SOURCE #-} Agda.TypeChecking.Pretty
+import {-# SOURCE #-} Agda.TypeChecking.Rewriting
+import {-# SOURCE #-} Agda.TypeChecking.Reduce.Fast
+import {-# SOURCE #-} Agda.TypeChecking.Opacity
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+
+instantiate :: (Instantiate a, MonadReduce m) => a -> m a
+instantiate = liftReduce . instantiate'
+
+instantiateFull :: (InstantiateFull a, MonadReduce m) => a -> m a
+instantiateFull = liftReduce . instantiateFull'
+
+-- | A variant of 'instantiateFull' that only instantiates those
+-- meta-variables that satisfy the predicate.
+
+instantiateWhen ::
+  (InstantiateFull a, MonadReduce m) =>
+  (MetaId -> ReduceM Bool) ->
+  a -> m a
+instantiateWhen p =
+  liftReduce .
+  localR (\env -> env { redPred = Just p }) .
+  instantiateFull'
+
+{-# INLINE reduce #-}
+reduce :: (Reduce a, MonadReduce m) => a -> m a
+reduce = liftReduce . reduce'
+
+{-# INLINE reduceB #-}
+reduceB :: (Reduce a, MonadReduce m) => a -> m (Blocked a)
+reduceB = liftReduce . reduceB'
+
+-- Reduce a term and also produce a blocker signifying when
+-- this reduction should be retried.
+reduceWithBlocker :: (Reduce a, IsMeta a, MonadReduce m) => a -> m (Blocker, a)
+reduceWithBlocker a = ifBlocked a
+  (\b a' -> return (b, a'))
+  (\_ a' -> return (neverUnblock, a'))
+
+{-# INLINE normalise #-}
+normalise :: (Normalise a, MonadReduce m) => a -> m a
+normalise = liftReduce . normalise'
+
+-- UNUSED
+-- -- | Normalise the given term but also preserve blocking tags
+-- --   TODO: implement a more efficient version of this.
+-- normaliseB :: (MonadReduce m, Reduce t, Normalise t) => t -> m (Blocked t)
+-- normaliseB = normalise >=> reduceB
+
+{-# INLINE simplify #-}
+simplify :: (Simplify a, MonadReduce m) => a -> m a
+simplify = liftReduce . simplify'
+
+-- | Meaning no metas left in the instantiation.
+isFullyInstantiatedMeta :: MetaId -> TCM Bool
+isFullyInstantiatedMeta m = do
+  inst <- lookupMetaInstantiation m
+  case inst of
+    InstV inst -> noMetas <$> instantiateFull (instBody inst)
+    _ -> return False
+
+{-# INLINABLE blockAll #-}
+-- | Blocking on all blockers.
+blockAll :: (Functor f, Foldable f) => f (Blocked a) -> Blocked (f a)
+blockAll bs = blockedOn block $ fmap ignoreBlocking bs
+  where block = unblockOnAll $ foldMap (Set.singleton . blocker) bs
+        blocker NotBlocked{}  = alwaysUnblock
+        blocker (Blocked b _) = b
+
+{-# INLINABLE blockAny #-}
+-- | Blocking on any blockers.
+blockAny :: (Functor f, Foldable f) => f (Blocked a) -> Blocked (f a)
+blockAny bs = blockedOn block $ fmap ignoreBlocking bs
+  where block = case foldMap blocker bs of
+                  [] -> alwaysUnblock -- no blockers
+                  bs -> unblockOnAny $ Set.fromList bs
+        blocker NotBlocked{}  = []
+        blocker (Blocked b _) = [b]
+
+{-# SPECIALIZE blockOnError :: Blocker -> TCM a -> TCM a #-}
+-- | Run the given computation but turn any errors into blocked computations with the given blocker
+blockOnError :: MonadError TCErr m => Blocker -> m a -> m a
+blockOnError blocker f
+  | blocker == neverUnblock = f
+  | otherwise               = f `catchError` \case
+    TypeError{}         -> throwError $ PatternErr blocker
+    PatternErr blocker' -> throwError $ PatternErr $ unblockOnEither blocker blocker'
+    err@Exception{}     -> throwError err
+    err@IOException{}   -> throwError err
+
+-- | Instantiate something.
+--   Results in an open meta variable or a non meta.
+--   Doesn't do any reduction, and preserves blocking tags (when blocking meta
+--   is uninstantiated).
+class Instantiate t where
+  instantiate' :: t -> ReduceM t
+
+  default instantiate' :: (t ~ f a, Traversable f, Instantiate a) => t -> ReduceM t
+  instantiate' = traverse instantiate'
+
+instance Instantiate t => Instantiate [t]
+instance Instantiate t => Instantiate (Map k t)
+instance Instantiate t => Instantiate (Maybe t)
+instance Instantiate t => Instantiate (Strict.Maybe t)
+
+instance Instantiate t => Instantiate (Abs t)
+instance Instantiate t => Instantiate (Arg t)
+instance Instantiate t => Instantiate (Elim' t)
+instance Instantiate t => Instantiate (Tele t)
+instance Instantiate t => Instantiate (IPBoundary' t)
+
+instance Instantiate () where
+    instantiate' () = pure ()
+
+instance (Instantiate a, Instantiate b) => Instantiate (a,b) where
+    instantiate' (x,y) = (,) <$> instantiate' x <*> instantiate' y
+
+instance (Instantiate a, Instantiate b,Instantiate c) => Instantiate (a,b,c) where
+    instantiate' (x,y,z) = (,,) <$> instantiate' x <*> instantiate' y <*> instantiate' z
+
+-- | Run the second computation if the 'redPred' predicate holds for
+-- the given meta-variable (or if the predicate is not defined), and
+-- otherwise the first computation.
+
+ifPredicateDoesNotHoldFor ::
+  MetaId -> ReduceM a -> ReduceM a -> ReduceM a
+ifPredicateDoesNotHoldFor m doesNotHold holds = do
+  pred <- redPred <$> askR
+  case pred of
+    Nothing -> holds
+    Just p  -> ifM (p m) holds doesNotHold
+
+instance Instantiate Term where
+  instantiate' t@(MetaV x es) = ifPredicateDoesNotHoldFor x (return t) $ do
+    blocking <- view stInstantiateBlocking <$> getTCState
+
+    m <- lookupMeta x
+    case m of
+      Just (Left rmv) -> cont (rmvInstantiation rmv)
+
+      Just (Right mv) -> case mvInstantiation mv of
+         InstV inst -> cont inst
+
+         _ | Just m' <- mvTwin mv, blocking ->
+           instantiate' (MetaV m' es)
+
+         Open -> return t
+
+         OpenInstance -> return t
+
+         BlockedConst u
+           | blocking  -> instantiate' . unBrave $
+                          BraveTerm u `applyE` es
+           | otherwise -> return t
+
+         PostponedTypeCheckingProblem _ -> return t
+
+      Nothing -> __IMPOSSIBLE_VERBOSE__
+                   ("Meta-variable not found: " ++ prettyShow x)
+    where
+    cont i = instantiate' inst
+      where
+      -- A slight complication here is that the meta might be underapplied,
+      -- in which case we have to build the lambda abstraction before
+      -- applying the substitution, or overapplied in which case we need to
+      -- fall back to applyE.
+      (es1, es2) = splitAt (length (instTel i)) es
+      vs1 = reverse $ map unArg $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es1
+      rho = vs1 ++# wkS (length vs1) idS
+            -- really should be .. ++# emptyS but using wkS makes it reduce to idS
+            -- when applicable
+      -- specification:
+      -- inst == foldr mkLam (instBody i) (instTel i) `applyE` es
+      inst =
+        applySubst rho
+          (foldr mkLam (instBody i) $ drop (length es1) (instTel i))
+          `applyE` es2
+
+  instantiate' (Level l) = levelTm <$> instantiate' l
+  instantiate' (Sort s) = Sort <$> instantiate' s
+  instantiate' t = return t
+
+instance Instantiate t => Instantiate (Type' t) where
+  instantiate' (El s t) = El <$> instantiate' s <*> instantiate' t
+
+instance Instantiate Level where
+  instantiate' (Max m as) = levelMax m <$> instantiate' as
+
+-- Use Traversable instance
+instance Instantiate t => Instantiate (PlusLevel' t)
+
+instance Instantiate a => Instantiate (Blocked a) where
+  instantiate' v@NotBlocked{} = return v
+  instantiate' v@(Blocked b u) = instantiate' b >>= \ case
+    b | b == alwaysUnblock -> notBlocked <$> instantiate' u
+      | otherwise          -> return $ Blocked b u
+
+instance Instantiate Blocker where
+  instantiate' (UnblockOnAll bs) = unblockOnAll . Set.fromList <$> mapM instantiate' (Set.toList bs)
+  instantiate' (UnblockOnAny bs) = unblockOnAny . Set.fromList <$> mapM instantiate' (Set.toList bs)
+  instantiate' b@(UnblockOnMeta x) =
+    ifM (isInstantiatedMeta x) (return alwaysUnblock) (return b)
+  instantiate' (UnblockOnProblem pi) =
+    ifM (isProblemSolved pi) (return alwaysUnblock) (return $ UnblockOnProblem pi)
+  instantiate' b@UnblockOnDef{} = return b
+
+instance Instantiate Sort where
+  instantiate' = \case
+    MetaS x es -> instantiate' (MetaV x es) >>= \case
+      Sort s'      -> return s'
+      MetaV x' es' -> return $ MetaS x' es'
+      Def d es'    -> return $ DefS d es'
+      _            -> __IMPOSSIBLE__
+    s -> return s
+
+instance (Instantiate t, Instantiate e) => Instantiate (Dom' t e) where
+    instantiate' (Dom i n b tac x) = Dom i n b <$> instantiate' tac <*> instantiate' x
+
+instance Instantiate a => Instantiate (Closure a) where
+    instantiate' cl = do
+        x <- enterClosure cl instantiate'
+        return $ cl { clValue = x }
+
+instance Instantiate Constraint where
+  instantiate' (ValueCmp cmp t u v) = do
+    (t,u,v) <- instantiate' (t,u,v)
+    return $ ValueCmp cmp t u v
+  instantiate' (ValueCmpOnFace cmp p t u v) = do
+    ((p,t),u,v) <- instantiate' ((p,t),u,v)
+    return $ ValueCmpOnFace cmp p t u v
+  instantiate' (ElimCmp cmp fs t v as bs) =
+    ElimCmp cmp fs <$> instantiate' t <*> instantiate' v <*> instantiate' as <*> instantiate' bs
+  instantiate' (LevelCmp cmp u v)   = uncurry (LevelCmp cmp) <$> instantiate' (u,v)
+  instantiate' (SortCmp cmp a b)    = uncurry (SortCmp cmp) <$> instantiate' (a,b)
+  instantiate' (UnBlock m)          = return $ UnBlock m
+  instantiate' (FindInstance m cs)  = FindInstance m <$> mapM instantiate' cs
+  instantiate' (IsEmpty r t)        = IsEmpty r <$> instantiate' t
+  instantiate' (CheckSizeLtSat t)   = CheckSizeLtSat <$> instantiate' t
+  instantiate' c@CheckFunDef{}      = return c
+  instantiate' (HasBiggerSort a)    = HasBiggerSort <$> instantiate' a
+  instantiate' (HasPTSRule a b)     = uncurry HasPTSRule <$> instantiate' (a,b)
+  instantiate' (CheckLockedVars a b c d) =
+    CheckLockedVars <$> instantiate' a <*> instantiate' b <*> instantiate' c <*> instantiate' d
+  instantiate' (UnquoteTactic t h g) = UnquoteTactic <$> instantiate' t <*> instantiate' h <*> instantiate' g
+  instantiate' (CheckDataSort q s)  = CheckDataSort q <$> instantiate' s
+  instantiate' c@CheckMetaInst{}    = return c
+  instantiate' (CheckType t)        = CheckType <$> instantiate' t
+  instantiate' (UsableAtModality cc ms mod t) = flip (UsableAtModality cc) mod <$> instantiate' ms <*> instantiate' t
+
+instance Instantiate CompareAs where
+  instantiate' (AsTermsOf a) = AsTermsOf <$> instantiate' a
+  instantiate' AsSizes       = return AsSizes
+  instantiate' AsTypes       = return AsTypes
+
+instance Instantiate Candidate where
+  instantiate' (Candidate q u t ov) = Candidate q <$> instantiate' u <*> instantiate' t <*> pure ov
+
+instance Instantiate EqualityView where
+  instantiate' (OtherType t)            = OtherType
+    <$> instantiate' t
+  instantiate' (IdiomType t)            = IdiomType
+    <$> instantiate' t
+  instantiate' (EqualityType s eq l t a b) = EqualityType
+    <$> instantiate' s
+    <*> return eq
+    <*> mapM instantiate' l
+    <*> instantiate' t
+    <*> instantiate' a
+    <*> instantiate' b
+
+---------------------------------------------------------------------------
+-- * Reduction to weak head normal form.
+---------------------------------------------------------------------------
+
+-- | Is something (an elimination of) a meta variable?
+--   Does not perform any reductions.
+
+class IsMeta a where
+  isMeta :: a -> Maybe MetaId
+
+instance IsMeta Term where
+  isMeta (MetaV m _) = Just m
+  isMeta _           = Nothing
+
+instance IsMeta a => IsMeta (Sort' a) where
+  isMeta (MetaS m _) = Just m
+  isMeta _           = Nothing
+
+instance IsMeta a => IsMeta (Type'' t a) where
+  isMeta = isMeta . unEl
+
+instance IsMeta a => IsMeta (Elim' a) where
+  isMeta Proj{}    = Nothing
+  isMeta IApply{}  = Nothing
+  isMeta (Apply a) = isMeta a
+
+instance IsMeta a => IsMeta (Arg a) where
+  isMeta = isMeta . unArg
+
+instance IsMeta a => IsMeta (Level' a) where
+  isMeta (Max 0 [l]) = isMeta l
+  isMeta _           = Nothing
+
+instance IsMeta a => IsMeta (PlusLevel' a) where
+  isMeta (Plus 0 l)  = isMeta l
+  isMeta _           = Nothing
+
+instance IsMeta CompareAs where
+  isMeta (AsTermsOf a) = isMeta a
+  isMeta AsSizes       = Nothing
+  isMeta AsTypes       = Nothing
+
+-- | Case on whether a term is blocked on a meta (or is a meta).
+--   That means it can change its shape when the meta is instantiated.
+ifBlocked
+  :: (Reduce t, IsMeta t, MonadReduce m)
+  => t -> (Blocker -> t -> m a) -> (NotBlocked -> t -> m a) -> m a
+ifBlocked t blocked unblocked = do
+  t <- reduceB t
+  case t of
+    Blocked m t     -> blocked m t
+    NotBlocked nb t -> case isMeta t of -- #4899: MetaS counts as NotBlocked at the moment
+      Just m    -> blocked (unblockOnMeta m) t
+      Nothing   -> unblocked nb t
+
+-- | Throw pattern violation if blocked or a meta.
+abortIfBlocked :: (MonadReduce m, MonadBlock m, IsMeta t, Reduce t) => t -> m t
+abortIfBlocked t = ifBlocked t (const . patternViolation) (const return)
+
+isBlocked
+  :: (Reduce t, IsMeta t, MonadReduce m)
+  => t -> m (Maybe Blocker)
+isBlocked t = ifBlocked t (\m _ -> return $ Just m) (\_ _ -> return Nothing)
+
+-- | Throw a pattern violation if the argument is @Blocked@,
+--   otherwise return the value embedded in the @NotBlocked@.
+fromBlocked :: MonadBlock m => Blocked a -> m a
+fromBlocked (Blocked b _) = patternViolation b
+fromBlocked (NotBlocked _ x) = return x
+
+class Reduce t where
+  reduce'  :: t -> ReduceM t
+  reduceB' :: t -> ReduceM (Blocked t)
+
+  reduce'  t = ignoreBlocking <$> reduceB' t
+  reduceB' t = notBlocked <$> reduce' t
+
+instance Reduce Type where
+    reduce'  (El s t) = workOnTypes $ El s <$> reduce' t
+    reduceB' (El s t) = workOnTypes $ fmap (El s) <$> reduceB' t
+
+instance Reduce Sort where
+    reduceB' s = do
+      s <- instantiate' s
+      let done | MetaS x _ <- s = return $ blocked x s
+               | otherwise      = return $ notBlocked s
+      case s of
+        PiSort a s1 s2 -> reduceB' (s1 , s2) >>= \case
+          Blocked b (s1',s2') -> return $ Blocked b $ PiSort a s1' s2'
+          NotBlocked _ (s1',s2') -> do
+            -- Jesper, 2022-10-12: do instantiateFull here because
+            -- `piSort'` does checking of free variables, and if we
+            -- don't instantiate we might end up blocking on a solved
+            -- metavariable.
+            s2' <- instantiateFull s2'
+            case piSort' a s1' s2' of
+              Left b -> return $ Blocked b $ PiSort a s1' s2'
+              Right s -> reduceB' s
+        FunSort s1 s2 -> reduceB' (s1 , s2) >>= \case
+          Blocked b (s1',s2') -> return $ Blocked b $ FunSort s1' s2'
+          NotBlocked _ (s1',s2') -> do
+            case funSort' s1' s2' of
+              Left b -> return $ Blocked b $ FunSort s1' s2'
+              Right s -> reduceB' s
+        UnivSort s1 -> reduceB' s1 >>= \case
+          Blocked b s1' -> return $ Blocked b $ UnivSort s1'
+          NotBlocked _ s1' -> case univSort' s1' of
+            Left b -> return $ Blocked b $ UnivSort s1'
+            Right s -> reduceB' s
+        Univ u l   -> notBlocked . Univ u <$> reduce l
+        Inf _ _    -> done
+        SizeUniv   -> done
+        LockUniv   -> done
+        LevelUniv  -> do
+          levelUniverseEnabled <- isLevelUniverseEnabled
+          if levelUniverseEnabled
+          then done
+          else return $ notBlocked (mkType 0)
+        IntervalUniv -> done
+        MetaS x es -> done
+        DefS d es  -> done -- postulated sorts do not reduce
+        DummyS{}   -> done
+
+instance Reduce Elim where
+  reduce' (Apply v) = Apply <$> reduce' v
+  reduce' (Proj o f)= pure $ Proj o f
+  reduce' (IApply x y v) = IApply <$> reduce' x <*> reduce' y <*> reduce' v
+
+instance Reduce Level where
+  reduce'  (Max m as) = levelMax m <$> mapM reduce' as
+  reduceB' (Max m as) = fmap (levelMax m) . blockAny <$> traverse reduceB' as
+
+instance Reduce PlusLevel where
+  reduceB' (Plus n l) = fmap (Plus n) <$> reduceB' l
+
+instance (Subst a, Reduce a) => Reduce (Abs a) where
+  reduceB' b@(Abs x _) = fmap (Abs x) <$> underAbstraction_ b reduceB'
+  reduceB' (NoAbs x v) = fmap (NoAbs x) <$> reduceB' v
+
+-- Lists are never blocked
+instance Reduce t => Reduce [t] where
+    reduce' = traverse reduce'
+
+-- Maybes are never blocked
+instance Reduce t => Reduce (Maybe t) where
+    reduce' = traverse reduce'
+
+instance Reduce t => Reduce (Arg t) where
+    reduce' a = case getRelevance a of
+      Irrelevant -> return a             -- Don't reduce' irr. args!?
+                                         -- Andreas, 2018-03-03, caused #2989.
+      _          -> traverse reduce' a
+
+    reduceB' t = traverse id <$> traverse reduceB' t
+
+instance Reduce t => Reduce (Dom t) where
+    reduce' = traverse reduce'
+    reduceB' t = traverse id <$> traverse reduceB' t
+
+instance (Reduce a, Reduce b) => Reduce (a,b) where
+    reduce' (x,y)  = (,) <$> reduce' x <*> reduce' y
+    reduceB' (x,y) = do
+      x <- reduceB' x
+      y <- reduceB' y
+      let blk = void x `mappend` void y
+          xy  = (ignoreBlocking x , ignoreBlocking y)
+      return $ blk $> xy
+
+instance (Reduce a, Reduce b,Reduce c) => Reduce (a,b,c) where
+    reduce' (x,y,z) = (,,) <$> reduce' x <*> reduce' y <*> reduce' z
+    reduceB' (x,y,z) = do
+      x <- reduceB' x
+      y <- reduceB' y
+      z <- reduceB' z
+      let blk = void x `mappend` void y `mappend` void z
+          xyz = (ignoreBlocking x , ignoreBlocking y , ignoreBlocking z)
+      return $ blk $> xyz
+
+reduceIApply :: ReduceM (Blocked Term) -> [Elim] -> ReduceM (Blocked Term)
+reduceIApply = reduceIApply' reduceB'
+
+reduceIApply' :: (Term -> ReduceM (Blocked Term)) -> ReduceM (Blocked Term) -> [Elim] -> ReduceM (Blocked Term)
+reduceIApply' red d (IApply x y r : es) = do
+  view <- intervalView'
+  r <- reduceB' r
+  -- We need to propagate the blocking information so that e.g.
+  -- we postpone "someNeutralPath ?0 = a" rather than fail.
+  case view (ignoreBlocking r) of
+   IZero -> red (applyE x es)
+   IOne  -> red (applyE y es)
+   _     -> fmap (<* r) (reduceIApply' red d es)
+reduceIApply' red d (_ : es) = reduceIApply' red d es
+reduceIApply' _   d [] = d
+
+instance Reduce DeBruijnPattern where
+  reduceB' (DotP o v) = fmap (DotP o) <$> reduceB' v
+  reduceB' p          = return $ notBlocked p
+
+instance Reduce Term where
+  reduceB' = {-# SCC "reduce'<Term>" #-} maybeFastReduceTerm
+
+shouldTryFastReduce :: ReduceM Bool
+shouldTryFastReduce = optFastReduce <$> pragmaOptions
+
+maybeFastReduceTerm :: Term -> ReduceM (Blocked Term)
+maybeFastReduceTerm v = do
+  let tryFast = case v of
+                  Def{}   -> True
+                  Con{}   -> True
+                  MetaV{} -> True
+                  _       -> False
+  if not tryFast then slowReduceTerm v
+                 else
+    case v of
+      MetaV x _ -> ifM (isOpen x) (return $ blocked x v) (maybeFast v)
+      _         -> maybeFast v
+  where
+    isOpen x = isOpenMeta <$> lookupMetaInstantiation x
+    maybeFast v = ifM shouldTryFastReduce (fastReduce v) (slowReduceTerm v)
+
+slowReduceTerm :: Term -> ReduceM (Blocked Term)
+slowReduceTerm v = do
+    v <- instantiate' v
+    let done | MetaV x _ <- v = return $ blocked x v
+             | otherwise      = return $ notBlocked v
+        iapp = reduceIApply done
+    case v of
+--    Andreas, 2012-11-05 not reducing meta args does not destroy anything
+--    and seems to save 2% sec on the standard library
+--      MetaV x args -> notBlocked . MetaV x <$> reduce' args
+      MetaV x es -> iapp es
+      Def f es   -> flip reduceIApply es $ unfoldDefinitionE reduceB' (Def f []) f es
+      Con c ci es -> do
+          -- Constructors can reduce' when they come from an
+          -- instantiated module.
+          -- also reduce when they are path constructors
+          v <- flip reduceIApply es
+                 $ unfoldDefinitionE reduceB' (Con c ci []) (conName c) es
+          traverse reduceNat v
+      Sort s   -> done
+      Level l  -> ifM (SmallSet.member LevelReductions <$> asksTC envAllowedReductions)
+                    {- then -} (fmap levelTm <$> reduceB' l)
+                    {- else -} done
+      Pi _ _   -> done
+      Lit _    -> done
+      Var _ es  -> iapp es
+      Lam _ _  -> done
+      DontCare _ -> done
+      Dummy{}    -> done
+    where
+      -- NOTE: reduceNat can traverse the entire term.
+      reduceNat v@(Con c ci []) = do
+        mz  <- getBuiltin' builtinZero
+        case v of
+          _ | Just v == mz  -> return $ Lit $ LitNat 0
+          _                 -> return v
+      reduceNat v@(Con c ci [Apply a]) | visible a && isRelevant a = do
+        ms  <- getBuiltin' builtinSuc
+        case v of
+          _ | Just (Con c ci []) == ms -> inc <$> reduce' (unArg a)
+          _                         -> return v
+          where
+            inc = \case
+              Lit (LitNat n) -> Lit $ LitNat $ n + 1
+              w              -> Con c ci [Apply $ defaultArg w]
+      reduceNat v = return v
+
+-- Andreas, 2013-03-20 recursive invokations of unfoldCorecursion
+-- need also to instantiate metas, see Issue 826.
+unfoldCorecursionE :: Elim -> ReduceM (Blocked Elim)
+unfoldCorecursionE (Proj o p)           = notBlocked . Proj o <$> getOriginalProjection p
+unfoldCorecursionE (Apply (Arg info v)) = fmap (Apply . Arg info) <$>
+  unfoldCorecursion v
+unfoldCorecursionE (IApply x y r) = do -- TODO check if this makes sense
+   [x,y,r] <- mapM unfoldCorecursion [x,y,r]
+   return $ IApply <$> x <*> y <*> r
+
+unfoldCorecursion :: Term -> ReduceM (Blocked Term)
+unfoldCorecursion v = do
+  v <- instantiate' v
+  case v of
+    Def f es -> unfoldDefinitionE unfoldCorecursion (Def f []) f es
+    _ -> slowReduceTerm v
+
+-- | If the first argument is 'True', then a single delayed clause may
+-- be unfolded.
+unfoldDefinition ::
+  (Term -> ReduceM (Blocked Term)) ->
+  Term -> QName -> Args -> ReduceM (Blocked Term)
+unfoldDefinition keepGoing v f args =
+  unfoldDefinitionE keepGoing v f (map Apply args)
+
+unfoldDefinitionE ::
+  (Term -> ReduceM (Blocked Term)) ->
+  Term -> QName -> Elims -> ReduceM (Blocked Term)
+unfoldDefinitionE keepGoing v f es = do
+  r <- unfoldDefinitionStep v f es
+  case r of
+    NoReduction v    -> return v
+    YesReduction _ v -> keepGoing v
+
+unfoldDefinition' ::
+  (Simplification -> Term -> ReduceM (Simplification, Blocked Term)) ->
+  Term -> QName -> Elims -> ReduceM (Simplification, Blocked Term)
+unfoldDefinition' keepGoing v0 f es = do
+  r <- unfoldDefinitionStep v0 f es
+  case r of
+    NoReduction v       -> return (NoSimplification, v)
+    YesReduction simp v -> keepGoing simp v
+
+unfoldDefinitionStep :: Term -> QName -> Elims -> ReduceM (Reduced (Blocked Term) Term)
+unfoldDefinitionStep v0 f es =
+  {-# SCC "reduceDef" #-} do
+  traceSDoc "tc.reduce" 90 ("unfoldDefinitionStep v0" <+> pretty v0) $ do
+  info <- getConstInfo f
+  rewr <- instantiateRewriteRules =<< getRewriteRulesFor f
+  allowed <- asksTC envAllowedReductions
+  prp <- runBlocked $ isPropM $ defType info
+  defOk <- shouldReduceDef f
+  let def = theDef info
+      v   = v0 `applyE` es
+      -- Non-terminating functions
+      -- (i.e., those that failed the termination check)
+      -- and delayed definitions
+      -- are not unfolded unless explicitly permitted.
+      dontUnfold = or
+        [ defNonterminating info && SmallSet.notMember NonTerminatingReductions allowed
+        , defTerminationUnconfirmed info && SmallSet.notMember UnconfirmedReductions allowed
+        , prp == Right True
+        , isIrrelevant info
+        , not defOk
+        ]
+      copatterns = defCopatternLHS info
+  case def of
+    Constructor{conSrcCon = c} -> do
+      let hd = Con (c `withRangeOf` f) ConOSystem
+      rewrite (NotBlocked ReallyNotBlocked ()) hd rewr es
+    Primitive{primAbstr = ConcreteDef, primName = x, primClauses = cls} -> do
+      pf <- fromMaybe __IMPOSSIBLE__ <$> getPrimitive' x
+      if FunctionReductions `SmallSet.member` allowed
+        then reducePrimitive x v0 f es pf dontUnfold
+                             cls (defCompiled info) rewr
+        else noReduction $ notBlocked v
+    PrimitiveSort{ primSortSort = s } -> yesReduction NoSimplification $ Sort s `applyE` es
+
+    _  -> do
+      if or
+          [ RecursiveReductions `SmallSet.member` allowed
+          , isJust (isProjection_ def) && ProjectionReductions `SmallSet.member` allowed
+              -- Includes projection-like and irrelevant projections.
+              -- Note: irrelevant projections lead to @dontUnfold@ and
+              -- so are not actually unfolded.
+          , isInlineFun def && InlineReductions `SmallSet.member` allowed
+          , definitelyNonRecursive_ def && or
+            [ copatterns && CopatternReductions `SmallSet.member` allowed
+            , FunctionReductions `SmallSet.member` allowed
+            ]
+          ]
+        then
+          reduceNormalE v0 f (map notReduced es) dontUnfold
+                       (defClauses info) (defCompiled info) rewr
+        else noReduction $ notBlocked v  -- Andrea(s), 2014-12-05 OK?
+
+  where
+    noReduction    = return . NoReduction
+    yesReduction s = return . YesReduction s
+    reducePrimitive x v0 f es pf dontUnfold cls mcc rewr
+      | length es < ar
+                  = noReduction $ NotBlocked Underapplied $ v0 `applyE` es -- not fully applied
+      | otherwise = {-# SCC "reducePrimitive" #-} do
+          let (es1,es2) = splitAt ar es
+              args1     = fromMaybe __IMPOSSIBLE__ $ mapM isApplyElim es1
+          r <- primFunImplementation pf args1 (length es2)
+          case r of
+            NoReduction args1' -> do
+              let es1' = map (fmap Apply) args1'
+              if null cls && null rewr then do
+                noReduction $ applyE (Def f []) <$> do
+                  blockAll $ map mredToBlocked es1' ++ map notBlocked es2
+               else
+                reduceNormalE v0 f (es1' ++ map notReduced es2) dontUnfold cls mcc rewr
+            YesReduction simpl v -> yesReduction simpl $ v `applyE` es2
+      where
+          ar  = primFunArity pf
+
+          mredToBlocked :: IsMeta t => MaybeReduced t -> Blocked t
+          mredToBlocked (MaybeRed NotReduced  e) = notBlocked e
+          mredToBlocked (MaybeRed (Reduced b) e) = e <$ b
+
+    reduceNormalE :: Term -> QName -> [MaybeReduced Elim] -> Bool -> [Clause] -> Maybe CompiledClauses -> RewriteRules -> ReduceM (Reduced (Blocked Term) Term)
+    reduceNormalE v0 f es dontUnfold def mcc rewr = {-# SCC "reduceNormal" #-} do
+      traceSDoc "tc.reduce" 90 ("reduceNormalE v0 =" <+> pretty v0) $ do
+      case (def,rewr) of
+        _ | dontUnfold -> traceSLn "tc.reduce" 90 "reduceNormalE: don't unfold (non-terminating or delayed)" $
+                          defaultResult -- non-terminating or delayed
+        ([],[])        -> traceSLn "tc.reduce" 90 "reduceNormalE: no clauses or rewrite rules" $ do
+          -- no definition for head
+          (defBlocked <$> getConstInfo f) >>= \case
+            Blocked{}    -> noReduction $ Blocked (UnblockOnDef f) vfull
+            NotBlocked{} -> defaultResult
+        (cls,rewr)     -> do
+          ev <- appDefE_ f v0 cls mcc rewr es
+          debugReduce ev
+          return ev
+      where
+      defaultResult = noReduction $ NotBlocked ReallyNotBlocked vfull
+      vfull         = v0 `applyE` map ignoreReduced es
+      debugReduce ev = verboseS "tc.reduce" 90 $ do
+        case ev of
+          NoReduction v -> do
+            reportSDoc "tc.reduce" 90 $ vcat
+              [ "*** tried to reduce " <+> pretty f
+              , "    es =  " <+> sep (map (pretty . ignoreReduced) es)
+              -- , "*** tried to reduce " <+> pretty vfull
+              , "    stuck on" <+> pretty (ignoreBlocking v)
+              ]
+          YesReduction _simpl v -> do
+            reportSDoc "tc.reduce"  90 $ "*** reduced definition: " <+> pretty f
+            reportSDoc "tc.reduce"  95 $ "    result" <+> pretty v
+
+-- | Specialized version to put in boot file.
+reduceDefCopyTCM :: QName -> Elims -> TCM (Reduced () Term)
+reduceDefCopyTCM = reduceDefCopy
+
+-- | Reduce a non-primitive definition if it is a copy linking to another def.
+reduceDefCopy :: forall m. PureTCM m => QName -> Elims -> m (Reduced () Term)
+reduceDefCopy f es = do
+  info <- getConstInfo f
+  case theDef info of
+    _ | not $ defCopy info     -> return $ NoReduction ()
+    Constructor{conSrcCon = c} -> return $ YesReduction YesSimplification (Con c ConOSystem es)
+    _                          -> reduceDef_ info f es
+  where
+    reduceDef_ :: Definition -> QName -> Elims -> m (Reduced () Term)
+    reduceDef_ info f es = case defClauses info of
+      [cl] -> do  -- proper copies always have a single clause
+        let v0 = Def f [] -- TODO: could be Con
+            ps    = namedClausePats cl
+            nargs = length es
+            -- appDefE_ cannot handle underapplied functions, so we eta-expand here if that's the
+            -- case. We use this function to compute display forms from module applications and in
+            -- that case we don't always have saturated applications.
+            (lam, es') = (unlamView xs, newes)
+              where
+                etaArgs [] _ = []
+                etaArgs (p : ps) []
+                  | VarP _ x <- namedArg p = Arg (getArgInfo p) (dbPatVarName x) : etaArgs ps []
+                  | otherwise              = []
+                etaArgs (_ : ps) (_ : es) = etaArgs ps es
+                xs  = etaArgs ps es
+                n   = length xs
+                newes = raise n es ++ [ Apply $ var i <$ x | (i, x) <- zip (downFrom n) xs ]
+        if defNonterminating info
+         then return $ NoReduction ()
+         else do
+            ev <- liftReduce $ appDefE_ f v0 [cl] Nothing mempty $ map notReduced es'
+            case ev of
+              YesReduction simpl t -> return $ YesReduction simpl (lam t)
+              NoReduction{}        -> return $ NoReduction ()
+      []    -> return $ NoReduction ()  -- copies of generalizable variables have no clauses (and don't need unfolding)
+      _:_:_ -> __IMPOSSIBLE__
+
+-- | Reduce simple (single clause) definitions.
+reduceHead :: PureTCM m => Term -> m (Blocked Term)
+reduceHead v = do -- ignoreAbstractMode $ do
+  -- Andreas, 2013-02-18 ignoreAbstractMode leads to information leakage
+  -- see Issue 796
+
+  -- first, possibly rewrite literal v to constructor form
+  v <- constructorForm v
+  traceSDoc "tc.inj.reduce" 30 (ignoreAbstractMode $ "reduceHead" <+> prettyTCM v) $ do
+  case v of
+    Def f es -> do
+
+      abstractMode <- envAbstractMode <$> askTC
+      isAbstract <- not <$> hasAccessibleDef f
+      traceSLn "tc.inj.reduce" 50 (
+        "reduceHead: we are in " ++ show abstractMode ++ "; " ++ prettyShow f ++
+        " is treated " ++ if isAbstract then "abstractly" else "concretely"
+        ) $ do
+      let v0  = Def f []
+          red = liftReduce $ unfoldDefinitionE reduceHead v0 f es
+      def <- theDef <$> getConstInfo f
+      case def of
+        -- Andreas, 2012-11-06 unfold aliases (single clause terminating functions)
+        -- see test/succeed/Issue747
+        -- We restrict this to terminating functions to not make the
+        -- type checker loop here on non-terminating functions.
+        -- see test/fail/TerminationInfiniteRecord
+        Function{ funClauses = [ _ ], funTerminates = Just True } -> do
+          traceSLn "tc.inj.reduce" 50 ("reduceHead: head " ++ prettyShow f ++ " is Function") $ do
+          red
+        Datatype{ dataClause = Just _ } -> red
+        Record{ recClause = Just _ }    -> red
+        _                               -> return $ notBlocked v
+    _ -> return $ notBlocked v
+
+-- | Unfold a single inlined function.
+unfoldInlined :: PureTCM m => Term -> m Term
+unfoldInlined v = do
+  inTypes <- viewTC eWorkingOnTypes
+  case v of
+    _ | inTypes -> return v -- Don't inline in types (to avoid unfolding of goals)
+    Def f es -> do
+      info <- getConstInfo f
+      let def = theDef info
+          irr = isIrrelevant $ defArgInfo info
+      case def of
+        Function{} ->
+          reportSLn "tc.inline" 90 $
+            intercalate "\n"
+            [ "considering to inline " ++ prettyShow f
+            , "irr         = " ++ prettyShow irr
+            , "funInline   = " ++ prettyShow (def ^. funInline)
+            , "funCompiled = " ++ prettyShow (funCompiled def)
+            ]
+        _ -> pure ()
+      case def of   -- Only for simple definitions with no pattern matching (TODO: maybe copatterns?)
+        Function{ funCompiled = Just Done{} }
+          | def ^. funInline , not irr -> do
+              reportSLn "tc.inline" 70 $ "asking to inline " ++ prettyShow f
+              liftReduce $
+                ignoreBlocking <$> unfoldDefinitionE (return . notBlocked) (Def f []) f es
+        _ -> return v
+    _ -> return v
+
+-- | Apply a definition using the compiled clauses, or fall back to
+--   ordinary clauses if no compiled clauses exist.
+appDef_ :: QName -> Term -> [Clause] -> Maybe CompiledClauses -> RewriteRules -> MaybeReducedArgs -> ReduceM (Reduced (Blocked Term) Term)
+appDef_ f v0 cls mcc rewr args = appDefE_ f v0 cls mcc rewr $ map (fmap Apply) args
+
+appDefE_ :: QName -> Term -> [Clause] -> Maybe CompiledClauses -> RewriteRules -> MaybeReducedElims -> ReduceM (Reduced (Blocked Term) Term)
+appDefE_ f v0 cls mcc rewr args =
+  localTC (\ e -> e { envAppDef = Just f }) $
+  maybe (appDefE'' v0 cls rewr args)
+        (\cc -> appDefE v0 cc rewr args) mcc
+
+
+-- | Apply a defined function to it's arguments, using the compiled clauses.
+--   The original term is the first argument applied to the third.
+appDef :: Term -> CompiledClauses -> RewriteRules -> MaybeReducedArgs -> ReduceM (Reduced (Blocked Term) Term)
+appDef v cc rewr args = appDefE v cc rewr $ map (fmap Apply) args
+
+appDefE :: Term -> CompiledClauses -> RewriteRules -> MaybeReducedElims -> ReduceM (Reduced (Blocked Term) Term)
+appDefE v cc rewr es = do
+  traceSDoc "tc.reduce" 90 ("appDefE v = " <+> pretty v) $ do
+  r <- matchCompiledE cc es
+  case r of
+    YesReduction simpl t -> return $ YesReduction simpl t
+    NoReduction es'      -> rewrite (void es') (applyE v) rewr (ignoreBlocking es')
+
+-- | Apply a defined function to it's arguments, using the original clauses.
+appDef' :: QName -> Term -> [Clause] -> RewriteRules -> MaybeReducedArgs -> ReduceM (Reduced (Blocked Term) Term)
+appDef' f v cls rewr args = appDefE' f v cls rewr $ map (fmap Apply) args
+
+appDefE' :: QName -> Term -> [Clause] -> RewriteRules -> MaybeReducedElims -> ReduceM (Reduced (Blocked Term) Term)
+appDefE' f v cls rewr es =
+  localTC (\ e -> e { envAppDef = Just f }) $
+  appDefE'' v cls rewr es
+
+-- | Expects @'envAppDef' = Just f@ in 'TCEnv' to be able to report @'MissingClauses' f@.
+appDefE'' :: Term -> [Clause] -> RewriteRules -> MaybeReducedElims -> ReduceM (Reduced (Blocked Term) Term)
+appDefE'' v cls rewr es = traceSDoc "tc.reduce" 90 ("appDefE' v = " <+> pretty v) $ do
+  goCls cls $ map ignoreReduced es
+  where
+    goCls :: [Clause] -> [Elim] -> ReduceM (Reduced (Blocked Term) Term)
+    goCls cl es = do
+      case cl of
+        -- Andreas, 2013-10-26  In case of an incomplete match,
+        -- we just do not reduce.  This allows adding single function
+        -- clauses after they have been type-checked, to type-check
+        -- the remaining clauses (see Issue 907).
+        -- Andrea(s), 2014-12-05:  We return 'MissingClauses' here, since this
+        -- is the most conservative reason.
+        [] -> do
+          f <- fromMaybe __IMPOSSIBLE__ <$> asksTC envAppDef
+          rewrite (NotBlocked (MissingClauses f) ()) (applyE v) rewr es
+        cl : cls -> do
+          let pats = namedClausePats cl
+              body = clauseBody cl
+              npats = length pats
+              nvars = size $ clauseTel cl
+          -- if clause is underapplied, skip to next clause
+          if length es < npats then goCls cls es else do
+            let (es0, es1) = splitAt npats es
+            (m, es0) <- matchCopatterns pats es0
+            let es = es0 ++ es1
+            case m of
+              No         -> goCls cls es
+              DontKnow b -> rewrite b (applyE v) rewr es
+              Yes simpl vs -- vs is the subst. for the variables bound in body
+                | Just w <- body -> do -- clause has body?
+                    -- TODO: let matchPatterns also return the reduced forms
+                    -- of the original arguments!
+                    -- Andreas, 2013-05-19 isn't this done now?
+                    let sigma = buildSubstitution impossible nvars vs
+                    return $ YesReduction simpl $ applySubst sigma w `applyE` es1
+                | otherwise     -> rewrite (NotBlocked AbsurdMatch ()) (applyE v) rewr es
+
+instance Reduce a => Reduce (Closure a) where
+    reduce' cl = do
+        x <- enterClosure cl reduce'
+        return $ cl { clValue = x }
+{-# SPECIALIZE reduce' :: Closure Constraint -> ReduceM (Closure Constraint) #-}
+
+instance Reduce Telescope where
+  reduce' EmptyTel          = return EmptyTel
+  reduce' (ExtendTel a tel) = ExtendTel <$> reduce' a <*> reduce' tel
+
+instance Reduce Constraint where
+  reduce' (ValueCmp cmp t u v) = do
+    (t,u,v) <- reduce' (t,u,v)
+    return $ ValueCmp cmp t u v
+  reduce' (ValueCmpOnFace cmp p t u v) = do
+    ((p,t),u,v) <- reduce' ((p,t),u,v)
+    return $ ValueCmpOnFace cmp p t u v
+  reduce' (ElimCmp cmp fs t v as bs) =
+    ElimCmp cmp fs <$> reduce' t <*> reduce' v <*> reduce' as <*> reduce' bs
+  reduce' (LevelCmp cmp u v)    = uncurry (LevelCmp cmp) <$> reduce' (u,v)
+  reduce' (SortCmp cmp a b)     = uncurry (SortCmp cmp) <$> reduce' (a,b)
+  reduce' (UnBlock m)           = return $ UnBlock m
+  reduce' (FindInstance m cs)   = FindInstance m <$> mapM reduce' cs
+  reduce' (IsEmpty r t)         = IsEmpty r <$> reduce' t
+  reduce' (CheckSizeLtSat t)    = CheckSizeLtSat <$> reduce' t
+  reduce' c@CheckFunDef{}       = return c
+  reduce' (HasBiggerSort a)     = HasBiggerSort <$> reduce' a
+  reduce' (HasPTSRule a b)      = uncurry HasPTSRule <$> reduce' (a,b)
+  reduce' (UnquoteTactic t h g) = UnquoteTactic <$> reduce' t <*> reduce' h <*> reduce' g
+  reduce' (CheckLockedVars a b c d) =
+    CheckLockedVars <$> reduce' a <*> reduce' b <*> reduce' c <*> reduce' d
+  reduce' (CheckDataSort q s)   = CheckDataSort q <$> reduce' s
+  reduce' c@CheckMetaInst{}     = return c
+  reduce' (CheckType t)         = CheckType <$> reduce' t
+  reduce' (UsableAtModality cc ms mod t) = flip (UsableAtModality cc) mod <$> reduce' ms <*> reduce' t
+
+instance Reduce CompareAs where
+  reduce' (AsTermsOf a) = AsTermsOf <$> reduce' a
+  reduce' AsSizes       = return AsSizes
+  reduce' AsTypes       = return AsTypes
+
+instance Reduce e => Reduce (Map k e) where
+  reduce' = traverse reduce'
+
+instance Reduce Candidate where
+  reduce' (Candidate q u t ov) = Candidate q <$> reduce' u <*> reduce' t <*> pure ov
+
+instance Reduce EqualityView where
+  reduce' (OtherType t)            = OtherType
+    <$> reduce' t
+  reduce' (IdiomType t)            = IdiomType
+    <$> reduce' t
+  reduce' (EqualityType s eq l t a b) = EqualityType
+    <$> reduce' s
+    <*> return eq
+    <*> mapM reduce' l
+    <*> reduce' t
+    <*> reduce' a
+    <*> reduce' b
+
+instance Reduce t => Reduce (IPBoundary' t) where
+  reduce' = traverse reduce'
+  reduceB' = fmap sequenceA . traverse reduceB'
+
+---------------------------------------------------------------------------
+-- * Simplification
+---------------------------------------------------------------------------
+
+-- | Only unfold definitions if this leads to simplification
+--   which means that a constructor/literal pattern is matched.
+--   We include reduction of IApply patterns, as `p i0` is akin to
+--   matcing on the `i0` constructor of interval.
+class Simplify t where
+  simplify' :: t -> ReduceM t
+
+  default simplify' :: (t ~ f a, Traversable f, Simplify a) => t -> ReduceM t
+  simplify' = traverse simplify'
+
+-- boring instances:
+
+instance Simplify t => Simplify [t]
+instance Simplify t => Simplify (Map k t)
+instance Simplify t => Simplify (Maybe t)
+instance Simplify t => Simplify (Strict.Maybe t)
+
+instance Simplify t => Simplify (Arg t)
+instance Simplify t => Simplify (Elim' t)
+instance Simplify t => Simplify (Named name t)
+instance Simplify t => Simplify (IPBoundary' t)
+
+instance (Simplify a, Simplify b) => Simplify (a,b) where
+    simplify' (x,y) = (,) <$> simplify' x <*> simplify' y
+
+instance (Simplify a, Simplify b, Simplify c) => Simplify (a,b,c) where
+    simplify' (x,y,z) =
+        do  (x,(y,z)) <- simplify' (x,(y,z))
+            return (x,y,z)
+
+instance Simplify Bool where
+  simplify' = return
+
+-- interesting instances:
+
+instance Simplify Term where
+  simplify' v = do
+    v <- instantiate' v
+    let iapp es m = ignoreBlocking <$> reduceIApply' (fmap notBlocked . simplify') (notBlocked <$> m) es
+    case v of
+      Def f vs   -> iapp vs $ do
+        let keepGoing simp v = return (simp, notBlocked v)
+        (simpl, v) <- unfoldDefinition' keepGoing (Def f []) f vs
+        when (simpl == YesSimplification) $
+          reportSDoc "tc.simplify'" 90 $
+            pretty f <+> text ("simplify': unfolding definition returns " ++ show simpl) <+> pretty (ignoreBlocking v)
+        case simpl of
+          YesSimplification -> simplifyBlocked' v -- Dangerous, but if @simpl@ then @v /= Def f vs@
+          NoSimplification  -> Def f <$> simplify' vs
+      MetaV x vs -> iapp vs $ MetaV x  <$> simplify' vs
+      Con c ci vs-> iapp vs $ Con c ci <$> simplify' vs
+      Sort s     -> Sort     <$> simplify' s
+      Level l    -> levelTm  <$> simplify' l
+      Pi a b     -> Pi       <$> simplify' a <*> simplify' b
+      Lit l      -> return v
+      Var i vs   -> iapp vs $ Var i    <$> simplify' vs
+      Lam h v    -> Lam h    <$> simplify' v
+      DontCare v -> dontCare <$> simplify' v
+      Dummy{}    -> return v
+
+simplifyBlocked' :: Simplify t => Blocked t -> ReduceM t
+simplifyBlocked' (Blocked _ t) = return t
+simplifyBlocked' (NotBlocked _ t) = simplify' t  -- Andrea(s), 2014-12-05 OK?
+
+instance Simplify t => Simplify (Type' t) where
+    simplify' (El s t) = El <$> simplify' s <*> simplify' t
+
+instance Simplify Sort where
+    simplify' s = do
+      case s of
+        PiSort a s1 s2 -> piSort <$> simplify' a <*> simplify' s1 <*> simplify' s2
+        FunSort s1 s2 -> funSort <$> simplify' s1 <*> simplify' s2
+        UnivSort s -> univSort <$> simplify' s
+        Univ u s   -> Univ u <$> simplify' s
+        Inf _ _    -> return s
+        SizeUniv   -> return s
+        LockUniv   -> return s
+        LevelUniv  -> return s
+        IntervalUniv -> return s
+        MetaS x es -> MetaS x <$> simplify' es
+        DefS d es  -> DefS d <$> simplify' es
+        DummyS{}   -> return s
+
+instance Simplify Level where
+  simplify' (Max m as) = levelMax m <$> simplify' as
+
+instance Simplify PlusLevel where
+  simplify' (Plus n l) = Plus n <$> simplify' l
+
+instance (Subst a, Simplify a) => Simplify (Abs a) where
+    simplify' a@(Abs x _) = Abs x <$> underAbstraction_ a simplify'
+    simplify' (NoAbs x v) = NoAbs x <$> simplify' v
+
+instance Simplify t => Simplify (Dom t) where
+    simplify' = traverse simplify'
+
+instance Simplify a => Simplify (Closure a) where
+    simplify' cl = do
+        x <- enterClosure cl simplify'
+        return $ cl { clValue = x }
+
+instance (Subst a, Simplify a) => Simplify (Tele a) where
+  simplify' EmptyTel        = return EmptyTel
+  simplify' (ExtendTel a b) = uncurry ExtendTel <$> simplify' (a, b)
+
+instance Simplify ProblemConstraint where
+  simplify' (PConstr pid unblock c) = PConstr pid unblock <$> simplify' c
+
+instance Simplify Constraint where
+  simplify' (ValueCmp cmp t u v) = do
+    (t,u,v) <- simplify' (t,u,v)
+    return $ ValueCmp cmp t u v
+  simplify' (ValueCmpOnFace cmp p t u v) = do
+    ((p,t),u,v) <- simplify' ((p,t),u,v)
+    return $ ValueCmp cmp (AsTermsOf t) u v
+  simplify' (ElimCmp cmp fs t v as bs) =
+    ElimCmp cmp fs <$> simplify' t <*> simplify' v <*> simplify' as <*> simplify' bs
+  simplify' (LevelCmp cmp u v)    = uncurry (LevelCmp cmp) <$> simplify' (u,v)
+  simplify' (SortCmp cmp a b)     = uncurry (SortCmp cmp) <$> simplify' (a,b)
+  simplify' (UnBlock m)           = return $ UnBlock m
+  simplify' (FindInstance m cs)   = FindInstance m <$> mapM simplify' cs
+  simplify' (IsEmpty r t)         = IsEmpty r <$> simplify' t
+  simplify' (CheckSizeLtSat t)    = CheckSizeLtSat <$> simplify' t
+  simplify' c@CheckFunDef{}       = return c
+  simplify' (HasBiggerSort a)     = HasBiggerSort <$> simplify' a
+  simplify' (HasPTSRule a b)      = uncurry HasPTSRule <$> simplify' (a,b)
+  simplify' (UnquoteTactic t h g) = UnquoteTactic <$> simplify' t <*> simplify' h <*> simplify' g
+  simplify' (CheckLockedVars a b c d) =
+    CheckLockedVars <$> simplify' a <*> simplify' b <*> simplify' c <*> simplify' d
+  simplify' (CheckDataSort q s)   = CheckDataSort q <$> simplify' s
+  simplify' c@CheckMetaInst{}     = return c
+  simplify' (CheckType t)         = CheckType <$> simplify' t
+  simplify' (UsableAtModality cc ms mod t) = flip (UsableAtModality cc) mod <$> simplify' ms <*> simplify' t
+
+instance Simplify CompareAs where
+  simplify' (AsTermsOf a) = AsTermsOf <$> simplify' a
+  simplify' AsSizes       = return AsSizes
+  simplify' AsTypes       = return AsTypes
+
+-- UNUSED
+-- instance Simplify ConPatternInfo where
+--   simplify' (ConPatternInfo mr mt) = ConPatternInfo mr <$> simplify' mt
+
+-- UNUSED
+-- instance Simplify Pattern where
+--   simplify' p = case p of
+--     VarP _       -> return p
+--     LitP _       -> return p
+--     ConP c ci ps -> ConP c <$> simplify' ci <*> simplify' ps
+--     DotP v       -> DotP <$> simplify' v
+--     ProjP _      -> return p
+
+instance Simplify DisplayForm where
+  simplify' (Display n ps v) = Display n <$> simplify' ps <*> return v
+
+instance Simplify Candidate where
+  simplify' (Candidate q u t ov) = Candidate q <$> simplify' u <*> simplify' t <*> pure ov
+
+instance Simplify EqualityView where
+  simplify' (OtherType t)            = OtherType
+    <$> simplify' t
+  simplify' (IdiomType t)            = IdiomType
+    <$> simplify' t
+  simplify' (EqualityType s eq l t a b) = EqualityType
+    <$> simplify' s
+    <*> return eq
+    <*> mapM simplify' l
+    <*> simplify' t
+    <*> simplify' a
+    <*> simplify' b
+
+---------------------------------------------------------------------------
+-- * Normalisation
+---------------------------------------------------------------------------
+
+class Normalise t where
+  normalise' :: t -> ReduceM t
+
+  default normalise' :: (t ~ f a, Traversable f, Normalise a) => t -> ReduceM t
+  normalise' = traverse normalise'
+
+-- boring instances:
+
+instance Normalise t => Normalise [t]
+instance Normalise t => Normalise (Map k t)
+instance Normalise t => Normalise (Maybe t)
+instance Normalise t => Normalise (Strict.Maybe t)
+
+-- Arg not included since we do not normalize irrelevant subterms
+-- Elim' not included since it contains Arg
+instance Normalise t => Normalise (Named name t)
+instance Normalise t => Normalise (IPBoundary' t)
+instance Normalise t => Normalise (WithHiding t)
+
+instance (Normalise a, Normalise b) => Normalise (a,b) where
+    normalise' (x,y) = (,) <$> normalise' x <*> normalise' y
+
+instance (Normalise a, Normalise b, Normalise c) => Normalise (a,b,c) where
+    normalise' (x,y,z) =
+        do  (x,(y,z)) <- normalise' (x,(y,z))
+            return (x,y,z)
+
+instance Normalise Bool where
+  normalise' = return
+
+instance Normalise Char where
+  normalise' = return
+
+instance Normalise Int where
+  normalise' = return
+
+instance Normalise DBPatVar where
+  normalise' = return
+
+-- interesting instances:
+
+instance Normalise Sort where
+    normalise' s = do
+      s <- reduce' s
+      case s of
+        PiSort a s1 s2 -> piSort <$> normalise' a <*> normalise' s1 <*> normalise' s2
+        FunSort s1 s2 -> funSort <$> normalise' s1 <*> normalise' s2
+        UnivSort s -> univSort <$> normalise' s
+        Univ u s   -> Univ u <$> normalise' s
+        Inf _ _    -> return s
+        SizeUniv   -> return SizeUniv
+        LockUniv   -> return LockUniv
+        LevelUniv  -> return LevelUniv
+        IntervalUniv -> return IntervalUniv
+        MetaS x es -> return s
+        DefS d es  -> return s
+        DummyS{}   -> return s
+
+instance Normalise t => Normalise (Type' t) where
+    normalise' (El s t) = El <$> normalise' s <*> normalise' t
+
+instance Normalise Term where
+    normalise' v = ifM shouldTryFastReduce (fastNormalise v) (slowNormaliseArgs =<< reduce' v)
+
+slowNormaliseArgs :: Term -> ReduceM Term
+slowNormaliseArgs = \case
+  Var n vs    -> Var n      <$> normalise' vs
+  Con c ci vs -> Con c ci   <$> normalise' vs
+  Def f vs    -> Def f      <$> normalise' vs
+  MetaV x vs  -> MetaV x    <$> normalise' vs
+  v@(Lit _)   -> return v
+  Level l     -> levelTm    <$> normalise' l
+  Lam h b     -> Lam h      <$> normalise' b
+  Sort s      -> Sort       <$> normalise' s
+  Pi a b      -> uncurry Pi <$> normalise' (a, b)
+  v@DontCare{}-> return v
+  v@Dummy{}   -> return v
+
+-- Note: not the default instance for Elim' since we do something special for Arg.
+instance Normalise t => Normalise (Elim' t) where
+  normalise' (Apply v) = Apply <$> normalise' v  -- invokes Normalise Arg here
+  normalise' (Proj o f)= pure $ Proj o f
+  normalise' (IApply x y v) = IApply <$> normalise' x <*> normalise' y <*> normalise' v
+
+instance Normalise Level where
+  normalise' (Max m as) = levelMax m <$> normalise' as
+
+instance Normalise PlusLevel where
+  normalise' (Plus n l) = Plus n <$> normalise' l
+
+instance (Subst a, Normalise a) => Normalise (Abs a) where
+    normalise' a@(Abs x _) = Abs x <$> underAbstraction_ a normalise'
+    normalise' (NoAbs x v) = NoAbs x <$> normalise' v
+
+instance Normalise t => Normalise (Arg t) where
+    normalise' a
+      | isIrrelevant a = return a -- Andreas, 2012-04-02: Do not normalize irrelevant terms!?
+      | otherwise      = traverse normalise' a
+
+instance Normalise t => Normalise (Dom t) where
+    normalise' = traverse normalise'
+
+instance Normalise a => Normalise (Closure a) where
+    normalise' cl = do
+        x <- enterClosure cl normalise'
+        return $ cl { clValue = x }
+
+instance (Subst a, Normalise a) => Normalise (Tele a) where
+  normalise' EmptyTel        = return EmptyTel
+  normalise' (ExtendTel a b) = uncurry ExtendTel <$> normalise' (a, b)
+
+instance Normalise ProblemConstraint where
+  normalise' (PConstr pid unblock c) = PConstr pid unblock <$> normalise' c
+
+instance Normalise Constraint where
+  normalise' (ValueCmp cmp t u v) = do
+    (t,u,v) <- normalise' (t,u,v)
+    return $ ValueCmp cmp t u v
+  normalise' (ValueCmpOnFace cmp p t u v) = do
+    ((p,t),u,v) <- normalise' ((p,t),u,v)
+    return $ ValueCmpOnFace cmp p t u v
+  normalise' (ElimCmp cmp fs t v as bs) =
+    ElimCmp cmp fs <$> normalise' t <*> normalise' v <*> normalise' as <*> normalise' bs
+  normalise' (LevelCmp cmp u v)    = uncurry (LevelCmp cmp) <$> normalise' (u,v)
+  normalise' (SortCmp cmp a b)     = uncurry (SortCmp cmp) <$> normalise' (a,b)
+  normalise' (UnBlock m)           = return $ UnBlock m
+  normalise' (FindInstance m cs)   = FindInstance m <$> mapM normalise' cs
+  normalise' (IsEmpty r t)         = IsEmpty r <$> normalise' t
+  normalise' (CheckSizeLtSat t)    = CheckSizeLtSat <$> normalise' t
+  normalise' c@CheckFunDef{}       = return c
+  normalise' (HasBiggerSort a)     = HasBiggerSort <$> normalise' a
+  normalise' (HasPTSRule a b)      = uncurry HasPTSRule <$> normalise' (a,b)
+  normalise' (UnquoteTactic t h g) = UnquoteTactic <$> normalise' t <*> normalise' h <*> normalise' g
+  normalise' (CheckLockedVars a b c d) =
+    CheckLockedVars <$> normalise' a <*> normalise' b <*> normalise' c <*> normalise' d
+  normalise' (CheckDataSort q s)   = CheckDataSort q <$> normalise' s
+  normalise' c@CheckMetaInst{}     = return c
+  normalise' (CheckType t)         = CheckType <$> normalise' t
+  normalise' (UsableAtModality cc ms mod t) = flip (UsableAtModality cc) mod <$> normalise' ms <*> normalise' t
+
+instance Normalise CompareAs where
+  normalise' (AsTermsOf a) = AsTermsOf <$> normalise' a
+  normalise' AsSizes       = return AsSizes
+  normalise' AsTypes       = return AsTypes
+
+instance Normalise ConPatternInfo where
+  normalise' i = normalise' (conPType i) <&> \ t -> i { conPType = t }
+
+instance Normalise a => Normalise (Pattern' a) where
+  normalise' p = case p of
+    VarP o x     -> VarP o <$> normalise' x
+    LitP{}       -> return p
+    ConP c mt ps -> ConP c <$> normalise' mt <*> normalise' ps
+    DefP o q ps  -> DefP o q <$> normalise' ps
+    DotP o v     -> DotP o <$> normalise' v
+    ProjP{}      -> return p
+    IApplyP o t u x -> IApplyP o <$> normalise' t <*> normalise' u <*> normalise' x
+
+instance Normalise DisplayForm where
+  normalise' (Display n ps v) = Display n <$> normalise' ps <*> return v
+
+instance Normalise Candidate where
+  normalise' (Candidate q u t ov) = Candidate q <$> normalise' u <*> normalise' t <*> pure ov
+
+instance Normalise EqualityView where
+  normalise' (OtherType t)            = OtherType
+    <$> normalise' t
+  normalise' (IdiomType t)            = IdiomType
+    <$> normalise' t
+  normalise' (EqualityType s eq l t a b) = EqualityType
+    <$> normalise' s
+    <*> return eq
+    <*> mapM normalise' l
+    <*> normalise' t
+    <*> normalise' a
+    <*> normalise' b
+
+---------------------------------------------------------------------------
+-- * Full instantiation
+---------------------------------------------------------------------------
+
+-- | @instantiateFull'@ 'instantiate's metas everywhere (and recursively)
+--   but does not 'reduce'.
+class InstantiateFull t where
+  instantiateFull' :: t -> ReduceM t
+
+  default instantiateFull' :: (t ~ f a, Traversable f, InstantiateFull a) => t -> ReduceM t
+  instantiateFull' = traverse instantiateFull'
+
+-- Traversables (doesn't include binders like Abs, Tele):
+
+instance InstantiateFull t => InstantiateFull [t]
+instance InstantiateFull t => InstantiateFull (HashMap k t)
+instance InstantiateFull t => InstantiateFull (Map k t)
+instance InstantiateFull t => InstantiateFull (Maybe t)
+instance InstantiateFull t => InstantiateFull (Strict.Maybe t)
+
+instance InstantiateFull t => InstantiateFull (Arg t)
+instance InstantiateFull t => InstantiateFull (Elim' t)
+instance InstantiateFull t => InstantiateFull (Named name t)
+instance InstantiateFull t => InstantiateFull (WithArity t)
+instance InstantiateFull t => InstantiateFull (IPBoundary' t)
+
+-- Tuples:
+
+instance (InstantiateFull a, InstantiateFull b) => InstantiateFull (a,b) where
+    instantiateFull' (x,y) = (,) <$> instantiateFull' x <*> instantiateFull' y
+
+instance (InstantiateFull a, InstantiateFull b, InstantiateFull c) => InstantiateFull (a,b,c) where
+    instantiateFull' (x,y,z) =
+        do  (x,(y,z)) <- instantiateFull' (x,(y,z))
+            return (x,y,z)
+
+instance (InstantiateFull a, InstantiateFull b, InstantiateFull c, InstantiateFull d) => InstantiateFull (a,b,c,d) where
+    instantiateFull' (x,y,z,w) =
+        do  (x,(y,z,w)) <- instantiateFull' (x,(y,z,w))
+            return (x,y,z,w)
+
+-- Base types:
+
+instance InstantiateFull Bool where
+    instantiateFull' = return
+
+instance InstantiateFull Char where
+    instantiateFull' = return
+
+instance InstantiateFull Int where
+    instantiateFull' = return
+
+instance InstantiateFull ModuleName where
+    instantiateFull' = return
+
+instance InstantiateFull Name where
+    instantiateFull' = return
+
+instance InstantiateFull QName where
+  instantiateFull' = return
+
+instance InstantiateFull Scope where
+    instantiateFull' = return
+
+instance InstantiateFull ConHead where
+  instantiateFull' = return
+
+instance InstantiateFull DBPatVar where
+    instantiateFull' = return
+
+instance InstantiateFull PrimitiveId where
+  instantiateFull' = return
+
+-- Rest:
+
+instance InstantiateFull Sort where
+    instantiateFull' s = do
+        s <- instantiate' s
+        case s of
+            Univ u n   -> Univ u <$> instantiateFull' n
+            PiSort a s1 s2 -> piSort <$> instantiateFull' a <*> instantiateFull' s1 <*> instantiateFull' s2
+            FunSort s1 s2 -> funSort <$> instantiateFull' s1 <*> instantiateFull' s2
+            UnivSort s -> univSort <$> instantiateFull' s
+            Inf _ _    -> return s
+            SizeUniv   -> return s
+            LockUniv   -> return s
+            LevelUniv  -> return s
+            IntervalUniv -> return s
+            MetaS x es -> MetaS x <$> instantiateFull' es
+            DefS d es  -> DefS d <$> instantiateFull' es
+            DummyS{}   -> return s
+
+instance InstantiateFull t => InstantiateFull (Type' t) where
+    instantiateFull' (El s t) =
+      El <$> instantiateFull' s <*> instantiateFull' t
+
+instance InstantiateFull Term where
+    instantiateFull' = instantiate' >=> recurse >=> etaOnce
+      -- Andreas, 2010-11-12 DONT ETA!? eta-reduction breaks subject reduction
+      -- but removing etaOnce now breaks everything
+      where
+        recurse = \case
+          Var n vs    -> Var n <$> instantiateFull' vs
+          Con c ci vs -> Con c ci <$> instantiateFull' vs
+          Def f vs    -> Def f <$> instantiateFull' vs
+          MetaV x vs  -> MetaV x <$> instantiateFull' vs
+          v@Lit{}     -> return v
+          Level l     -> levelTm <$> instantiateFull' l
+          Lam h b     -> Lam h <$> instantiateFull' b
+          Sort s      -> Sort <$> instantiateFull' s
+          Pi a b      -> uncurry Pi <$> instantiateFull' (a,b)
+          DontCare v  -> dontCare <$> instantiateFull' v
+          v@Dummy{}   -> return v
+
+instance InstantiateFull Level where
+  instantiateFull' (Max m as) = levelMax m <$> instantiateFull' as
+
+instance InstantiateFull PlusLevel where
+  instantiateFull' (Plus n l) = Plus n <$> instantiateFull' l
+
+instance InstantiateFull Substitution where
+  instantiateFull' sigma =
+    case sigma of
+      IdS                    -> return IdS
+      EmptyS err             -> return $ EmptyS err
+      Wk   n sigma           -> Wk   n           <$> instantiateFull' sigma
+      Lift n sigma           -> Lift n           <$> instantiateFull' sigma
+      Strengthen bot n sigma -> Strengthen bot n <$> instantiateFull' sigma
+      t :# sigma             -> consS <$> instantiateFull' t
+                                      <*> instantiateFull' sigma
+
+instance InstantiateFull ConPatternInfo where
+    instantiateFull' i = instantiateFull' (conPType i) <&> \ t -> i { conPType = t }
+
+instance InstantiateFull a => InstantiateFull (Pattern' a) where
+    instantiateFull' (VarP o x)     = VarP o <$> instantiateFull' x
+    instantiateFull' (DotP o t)     = DotP o <$> instantiateFull' t
+    instantiateFull' (ConP n mt ps) = ConP n <$> instantiateFull' mt <*> instantiateFull' ps
+    instantiateFull' (DefP o q ps) = DefP o q <$> instantiateFull' ps
+    instantiateFull' l@LitP{}       = return l
+    instantiateFull' p@ProjP{}      = return p
+    instantiateFull' (IApplyP o t u x) = IApplyP o <$> instantiateFull' t <*> instantiateFull' u <*> instantiateFull' x
+
+instance (Subst a, InstantiateFull a) => InstantiateFull (Abs a) where
+    instantiateFull' a@(Abs x _) = Abs x <$> underAbstraction_ a instantiateFull'
+    instantiateFull' (NoAbs x a) = NoAbs x <$> instantiateFull' a
+
+instance (InstantiateFull t, InstantiateFull e) => InstantiateFull (Dom' t e) where
+    instantiateFull' (Dom i n b tac x) = Dom i n b <$> instantiateFull' tac <*> instantiateFull' x
+
+instance InstantiateFull LetBinding where
+  instantiateFull' (LetBinding o v t) = LetBinding o <$> instantiateFull' v <*> instantiateFull' t
+
+-- Andreas, 2021-09-13, issue #5544, need to traverse @checkpoints@ map
+instance InstantiateFull t => InstantiateFull (Open t) where
+  instantiateFull' (OpenThing checkpoint checkpoints modl t) =
+    OpenThing checkpoint
+    <$> (instantiateFull' =<< prune checkpoints)
+    <*> pure modl
+    <*> instantiateFull' t
+    where
+      -- Ulf, 2021-11-17, #5544
+      --  Remove checkpoints that are no longer in scope, since they can
+      --  mention functions that deadcode elimination will get rid of.
+      prune cps = do
+        inscope <- viewTC eCheckpoints
+        return $ cps `Map.intersection` inscope
+
+instance InstantiateFull a => InstantiateFull (Closure a) where
+    instantiateFull' cl = do
+        x <- enterClosure cl instantiateFull'
+        return $ cl { clValue = x }
+
+instance InstantiateFull ProblemConstraint where
+  instantiateFull' (PConstr p u c) = PConstr p u <$> instantiateFull' c
+
+instance InstantiateFull Constraint where
+  instantiateFull' = \case
+    ValueCmp cmp t u v -> do
+      (t,u,v) <- instantiateFull' (t,u,v)
+      return $ ValueCmp cmp t u v
+    ValueCmpOnFace cmp p t u v -> do
+      ((p,t),u,v) <- instantiateFull' ((p,t),u,v)
+      return $ ValueCmpOnFace cmp p t u v
+    ElimCmp cmp fs t v as bs ->
+      ElimCmp cmp fs <$> instantiateFull' t <*> instantiateFull' v <*> instantiateFull' as <*> instantiateFull' bs
+    LevelCmp cmp u v    -> uncurry (LevelCmp cmp) <$> instantiateFull' (u,v)
+    SortCmp cmp a b     -> uncurry (SortCmp cmp) <$> instantiateFull' (a,b)
+    UnBlock m           -> return $ UnBlock m
+    FindInstance m cs   -> FindInstance m <$> mapM instantiateFull' cs
+    IsEmpty r t         -> IsEmpty r <$> instantiateFull' t
+    CheckSizeLtSat t    -> CheckSizeLtSat <$> instantiateFull' t
+    c@CheckFunDef{}     -> return c
+    HasBiggerSort a     -> HasBiggerSort <$> instantiateFull' a
+    HasPTSRule a b      -> uncurry HasPTSRule <$> instantiateFull' (a,b)
+    UnquoteTactic t g h -> UnquoteTactic <$> instantiateFull' t <*> instantiateFull' g <*> instantiateFull' h
+    CheckLockedVars a b c d ->
+      CheckLockedVars <$> instantiateFull' a <*> instantiateFull' b <*> instantiateFull' c <*> instantiateFull' d
+    CheckDataSort q s   -> CheckDataSort q <$> instantiateFull' s
+    c@CheckMetaInst{}   -> return c
+    CheckType t         -> CheckType <$> instantiateFull' t
+    UsableAtModality cc ms mod t -> flip (UsableAtModality cc) mod <$> instantiateFull' ms <*> instantiateFull' t
+
+instance InstantiateFull CompareAs where
+  instantiateFull' (AsTermsOf a) = AsTermsOf <$> instantiateFull' a
+  instantiateFull' AsSizes       = return AsSizes
+  instantiateFull' AsTypes       = return AsTypes
+
+instance InstantiateFull Signature where
+  instantiateFull' (Sig a b c) = uncurry3 Sig <$> instantiateFull' (a, b, c)
+
+instance InstantiateFull Section where
+  instantiateFull' (Section tel) = Section <$> instantiateFull' tel
+
+instance (Subst a, InstantiateFull a) => InstantiateFull (Tele a) where
+  instantiateFull' EmptyTel = return EmptyTel
+  instantiateFull' (ExtendTel a b) = uncurry ExtendTel <$> instantiateFull' (a, b)
+
+instance InstantiateFull Definition where
+    instantiateFull' def@Defn{ defType = t ,defDisplay = df, theDef = d } = do
+      (t, df, d) <- instantiateFull' (t, df, d)
+      return $ def{ defType = t, defDisplay = df, theDef = d }
+
+instance InstantiateFull NLPat where
+  instantiateFull' (PVar x y) = return $ PVar x y
+  instantiateFull' (PDef x y) = PDef <$> instantiateFull' x <*> instantiateFull' y
+  instantiateFull' (PLam x y) = PLam x <$> instantiateFull' y
+  instantiateFull' (PPi x y)  = PPi <$> instantiateFull' x <*> instantiateFull' y
+  instantiateFull' (PSort x)  = PSort <$> instantiateFull' x
+  instantiateFull' (PBoundVar x y) = PBoundVar x <$> instantiateFull' y
+  instantiateFull' (PTerm x)  = PTerm <$> instantiateFull' x
+
+instance InstantiateFull NLPType where
+  instantiateFull' (NLPType s a) = NLPType
+    <$> instantiateFull' s
+    <*> instantiateFull' a
+
+instance InstantiateFull NLPSort where
+  instantiateFull' (PUniv u x) = PUniv u <$> instantiateFull' x
+  instantiateFull' (PInf f n) = return $ PInf f n
+  instantiateFull' PSizeUniv = return PSizeUniv
+  instantiateFull' PLockUniv = return PLockUniv
+  instantiateFull' PLevelUniv = return PLevelUniv
+  instantiateFull' PIntervalUniv = return PIntervalUniv
+
+instance InstantiateFull RewriteRule where
+  instantiateFull' (RewriteRule q gamma f ps rhs t c) =
+    RewriteRule q
+      <$> instantiateFull' gamma
+      <*> pure f
+      <*> instantiateFull' ps
+      <*> instantiateFull' rhs
+      <*> instantiateFull' t
+      <*> pure c
+
+instance InstantiateFull DisplayForm where
+  instantiateFull' (Display n ps v) = uncurry (Display n) <$> instantiateFull' (ps, v)
+
+instance InstantiateFull DisplayTerm where
+  instantiateFull' (DTerm' v es)   = DTerm' <$> instantiateFull' v <*> instantiateFull' es
+  instantiateFull' (DDot' v es)    = DDot'  <$> instantiateFull' v <*> instantiateFull' es
+  instantiateFull' (DCon c ci vs)  = DCon c ci <$> instantiateFull' vs
+  instantiateFull' (DDef c es)     = DDef c <$> instantiateFull' es
+  instantiateFull' (DWithApp v vs ws) = uncurry3 DWithApp <$> instantiateFull' (v, vs, ws)
+
+instance InstantiateFull Defn where
+    instantiateFull' d = case d of
+      Axiom{} -> return d
+      DataOrRecSig{} -> return d
+      GeneralizableVar{} -> return d
+      AbstractDefn d -> AbstractDefn <$> instantiateFull' d
+      Function{ funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv, funExtLam = extLam } -> do
+        (cs, cc, cov, inv) <- instantiateFull' (cs, cc, cov, inv)
+        extLam <- instantiateFull' extLam
+        return $ d { funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv, funExtLam = extLam }
+      Datatype{ dataSort = s, dataClause = cl } -> do
+        s  <- instantiateFull' s
+        cl <- instantiateFull' cl
+        return $ d { dataSort = s, dataClause = cl }
+      Record{ recClause = cl, recTel = tel } -> do
+        cl  <- instantiateFull' cl
+        tel <- instantiateFull' tel
+        return $ d { recClause = cl, recTel = tel }
+      Constructor{} -> return d
+      Primitive{ primClauses = cs } -> do
+        cs <- instantiateFull' cs
+        return $ d { primClauses = cs }
+      PrimitiveSort{} -> return d
+
+instance InstantiateFull ExtLamInfo where
+  instantiateFull' e@(ExtLamInfo { extLamSys = sys}) = do
+    sys <- instantiateFull' sys
+    return $ e { extLamSys = sys}
+
+instance InstantiateFull System where
+  instantiateFull' (System tel sys) = System <$> instantiateFull' tel <*> instantiateFull' sys
+
+instance InstantiateFull FunctionInverse where
+  instantiateFull' NotInjective = return NotInjective
+  instantiateFull' (Inverse inv) = Inverse <$> instantiateFull' inv
+
+instance InstantiateFull a => InstantiateFull (Case a) where
+  instantiateFull' (Branches cop cs eta ls m b lz) =
+    Branches cop
+      <$> instantiateFull' cs
+      <*> instantiateFull' eta
+      <*> instantiateFull' ls
+      <*> instantiateFull' m
+      <*> pure b
+      <*> pure lz
+
+instance InstantiateFull CompiledClauses where
+  instantiateFull' (Fail xs)   = return $ Fail xs
+  instantiateFull' (Done m t)  = Done m <$> instantiateFull' t
+  instantiateFull' (Case n bs) = Case n <$> instantiateFull' bs
+
+instance InstantiateFull Clause where
+    instantiateFull' (Clause rl rf tel ps b t catchall exact recursive unreachable ell wm) =
+       Clause rl rf <$> instantiateFull' tel
+       <*> instantiateFull' ps
+       <*> instantiateFull' b
+       <*> instantiateFull' t
+       <*> return catchall
+       <*> return exact
+       <*> return recursive
+       <*> return unreachable
+       <*> return ell
+       <*> return wm
+
+instance InstantiateFull Instantiation where
+  instantiateFull' (Instantiation a b) =
+    Instantiation a <$> instantiateFull' b
+
+instance InstantiateFull (Judgement MetaId) where
+  instantiateFull' (HasType a b c) =
+    HasType a b <$> instantiateFull' c
+  instantiateFull' (IsSort a b) =
+    IsSort a <$> instantiateFull' b
+
+instance InstantiateFull RemoteMetaVariable where
+  instantiateFull' (RemoteMetaVariable a b c) = RemoteMetaVariable
+    <$> instantiateFull' a
+    <*> return b
+    <*> instantiateFull' c
+
+instance InstantiateFull Interface where
+  instantiateFull' i = do
+    defs <- instantiateFull' (i ^. intSignature . sigDefinitions)
+    instantiateFullExceptForDefinitions'
+      (set (intSignature . sigDefinitions) defs i)
+
+-- | Instantiates everything except for definitions in the signature.
+
+instantiateFullExceptForDefinitions' :: Interface -> ReduceM Interface
+instantiateFullExceptForDefinitions'
+  (Interface h s ft ms mod tlmod scope inside sig metas display userwarn
+     importwarn b foreignCode highlighting libPragmas filePragmas
+     usedOpts patsyns warnings partialdefs oblocks onames) =
+  Interface h s ft ms mod tlmod scope inside
+    <$> ((\s r -> Sig { _sigSections     = s
+                      , _sigDefinitions  = sig ^. sigDefinitions
+                      , _sigRewriteRules = r
+                      })
+         <$> instantiateFull' (sig ^. sigSections)
+         <*> instantiateFull' (sig ^. sigRewriteRules))
+    <*> instantiateFull' metas
+    <*> instantiateFull' display
+    <*> return userwarn
+    <*> return importwarn
+    <*> instantiateFull' b
+    <*> return foreignCode
+    <*> return highlighting
+    <*> return libPragmas
+    <*> return filePragmas
+    <*> return usedOpts
+    <*> return patsyns
+    <*> return warnings
+    <*> return partialdefs
+    <*> return oblocks
+    <*> return onames
+
+-- | Instantiates everything except for definitions in the signature.
+
+instantiateFullExceptForDefinitions ::
+  MonadReduce m => Interface -> m Interface
+instantiateFullExceptForDefinitions =
+  liftReduce . instantiateFullExceptForDefinitions'
+
+instance InstantiateFull a => InstantiateFull (Builtin a) where
+    instantiateFull' (Builtin t) = Builtin <$> instantiateFull' t
+    instantiateFull' (Prim x)   = Prim <$> instantiateFull' x
+    instantiateFull' b@(BuiltinRewriteRelations xs) = pure b
+
+instance InstantiateFull Candidate where
+  instantiateFull' (Candidate q u t ov) =
+    Candidate q <$> instantiateFull' u <*> instantiateFull' t <*> pure ov
+
+instance InstantiateFull EqualityView where
+  instantiateFull' (OtherType t)            = OtherType
+    <$> instantiateFull' t
+  instantiateFull' (IdiomType t)            = IdiomType
+    <$> instantiateFull' t
+  instantiateFull' (EqualityType s eq l t a b) = EqualityType
+    <$> instantiateFull' s
+    <*> return eq
+    <*> mapM instantiateFull' l
+    <*> instantiateFull' t
+    <*> instantiateFull' a
+    <*> instantiateFull' b
diff --git a/src/full/Agda/TypeChecking/Reduce.hs-boot b/src/full/Agda/TypeChecking/Reduce.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Reduce.hs-boot
@@ -0,0 +1,8 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Reduce where
+
+import Agda.Syntax.Internal (Term, Elims, QName)
+import Agda.TypeChecking.Monad.Base (TCM, Reduced)
+
+reduceDefCopyTCM :: QName -> Elims -> TCM (Reduced () Term)
diff --git a/src/full/Agda/TypeChecking/Reduce/Fast.hs b/src/full/Agda/TypeChecking/Reduce/Fast.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Reduce/Fast.hs
@@ -0,0 +1,1479 @@
+{-# LANGUAGE PatternGuards #-}
+
+{-|
+
+This module implements the Agda Abstract Machine used for compile-time reduction. It's a
+call-by-need environment machine with an implicit heap maintained using 'STRef's. See the 'AM' type
+below for a description of the machine.
+
+Some other tricks that improves performance:
+
+- Memoise getConstInfo.
+
+  A big chunk of the time during reduction is spent looking up definitions in the signature. Any
+  long-running reduction will use only a handful definitions though, so memoising getConstInfo is a
+  big win.
+
+- Optimised case trees.
+
+  Since we memoise getConstInfo we can do some preprocessing of the definitions, returning a
+  'CompactDef' instead of a 'Definition'. In particular we streamline the case trees used for
+  matching in a few ways:
+
+    - Drop constructor arity information.
+    - Use NameId instead of QName as map keys.
+    - Special branch for natural number successor.
+
+  None of these changes would make sense to incorporate into the actual case trees. The first two
+  loses information that we need in other places and the third would complicate a lot of code
+  working with case trees.
+
+  'CompactDef' also has a special representation for built-in/primitive
+  functions that can be implemented as pure functions from 'Literal's.
+
+-}
+module Agda.TypeChecking.Reduce.Fast
+  ( fastReduce, fastNormalise ) where
+
+import Prelude hiding ((!!))
+
+import Control.Applicative hiding (empty)
+import Control.Monad.ST
+import Control.Monad.ST.Unsafe (unsafeSTToIO, unsafeInterleaveST)
+
+import qualified Data.HashMap.Strict as HMap
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Map.Strict as MapS
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Semigroup ((<>))
+import Data.Text (Text)
+import qualified Data.Text as T
+
+import System.IO.Unsafe (unsafePerformIO)
+import Data.IORef
+import Data.STRef
+import Data.Char
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Monad hiding (Closure(..))
+import Agda.TypeChecking.Reduce as R
+import Agda.TypeChecking.Rewriting (rewrite)
+import Agda.TypeChecking.Substitute
+
+import Agda.Interaction.Options
+
+import Agda.Utils.CallStack ( withCurrentCallStack )
+import Agda.Utils.Char
+import Agda.Utils.Float
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null (empty)
+import Agda.Utils.Functor
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+import Agda.Utils.Zipper
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+
+import Debug.Trace
+
+-- * Compact definitions
+
+-- This is what the memoised getConstInfo returns. We essentially pick out only the
+-- information needed for fast reduction from the definition.
+
+data CompactDef =
+  CompactDef { cdefNonterminating :: Bool
+             , cdefUnconfirmed    :: Bool
+             , cdefDef            :: CompactDefn
+             , cdefRewriteRules   :: RewriteRules
+             }
+
+data CompactDefn
+  = CFun  { cfunCompiled  :: FastCompiledClauses, cfunProjection :: Maybe QName }
+  | CCon  { cconSrcCon :: ConHead, cconArity :: Int }
+  | CForce   -- ^ primForce
+  | CErase   -- ^ primErase
+  | CTyCon   -- ^ Datatype or record type. Need to know this for primForce.
+  | CAxiom   -- ^ Axiom or abstract defn
+  | CPrimOp Int ([Literal] -> Term) (Maybe FastCompiledClauses)
+            -- ^ Literals in reverse argument order
+  | COther  -- ^ In this case we fall back to slow reduction
+
+data BuiltinEnv = BuiltinEnv
+  { bZero, bSuc, bTrue, bFalse, bRefl :: Maybe ConHead
+  , bPrimForce, bPrimErase  :: Maybe QName }
+
+-- | Compute a 'CompactDef' from a regular definition.
+compactDef :: BuiltinEnv -> Definition -> RewriteRules -> ReduceM CompactDef
+compactDef bEnv def rewr = do
+
+  -- WARNING: don't use isPropM here because it relies on reduction,
+  -- which causes an infinite loop.
+  let isPrp = case getSort (defType def) of
+        Prop{} -> True
+        _      -> False
+
+  shouldReduce <- shouldReduceDef (defName def)
+  allowed <- asksTC envAllowedReductions
+
+  let isConOrProj = case theDef def of
+        Constructor{} -> True
+        Function { funProjection = Right{} } -> True
+        _ -> False
+  let allowReduce = and
+        [ shouldReduce
+        , or
+          [ RecursiveReductions `SmallSet.member` allowed
+          , isConOrProj && ProjectionReductions `SmallSet.member` allowed
+          , isInlineFun (theDef def) && InlineReductions `SmallSet.member` allowed
+          , definitelyNonRecursive_ (theDef def) && or
+            [ defCopatternLHS def && CopatternReductions `SmallSet.member` allowed
+            , FunctionReductions `SmallSet.member` allowed
+            ]
+          ]
+        , not (defNonterminating def) || SmallSet.member NonTerminatingReductions allowed
+        , not (defTerminationUnconfirmed def) || SmallSet.member UnconfirmedReductions allowed
+        , not isPrp
+        , not (isIrrelevant def)
+        ]
+
+  cdefn <-
+    case theDef def of
+      _ | not allowReduce -> pure CAxiom
+      _ | Just (defName def) == bPrimForce bEnv   -> pure CForce
+      _ | Just (defName def) == bPrimErase bEnv ->
+          case telView' (defType def) of
+            TelV tel _ | natSize tel == 5 -> pure CErase
+                       | otherwise        -> pure COther
+                          -- Non-standard equality. Fall back to slow reduce.
+      _ | defBlocked def /= notBlocked_ -> pure COther -- Blocked definition
+      Constructor{conSrcCon = c, conArity = n} -> pure CCon{cconSrcCon = c, cconArity = n}
+      Function{funCompiled = Just cc, funClauses = _:_, funProjection = proj} ->
+        pure CFun{ cfunCompiled   = fastCompiledClauses bEnv cc
+                 , cfunProjection = projOrig <$> either (const Nothing) Just proj }
+      Function{funClauses = []}      -> pure CAxiom
+      Function{}                     -> pure COther -- Incomplete definition
+      Datatype{dataClause = Nothing} -> pure CTyCon
+      Record{recClause = Nothing}    -> pure CTyCon
+      Datatype{}                     -> pure COther -- TODO
+      Record{}                       -> pure COther -- TODO
+      Axiom{}                        -> pure CAxiom
+      DataOrRecSig{}                 -> pure CAxiom
+      AbstractDefn{}                 -> pure CAxiom
+      GeneralizableVar{}             -> __IMPOSSIBLE__
+      PrimitiveSort{}                -> pure COther -- TODO
+      Primitive{}
+        | not (FunctionReductions `SmallSet.member` allowed)
+        -> pure CAxiom
+      Primitive{ primName = name, primCompiled = cc } ->
+        case name of
+          -- "primShowInteger"            -- integers are not literals
+
+          -- Natural numbers
+          PrimNatPlus                  -> mkPrim 2 $ natOp (+)
+          PrimNatMinus                 -> mkPrim 2 $ natOp (\ x y -> max 0 (x - y))
+          PrimNatTimes                 -> mkPrim 2 $ natOp (*)
+          PrimNatDivSucAux             -> mkPrim 4 $ natOp4 divAux
+          PrimNatModSucAux             -> mkPrim 4 $ natOp4 modAux
+          PrimNatLess                  -> mkPrim 2 $ natRel (<)
+          PrimNatEquality              -> mkPrim 2 $ natRel (==)
+
+          -- Word64
+          PrimWord64ToNat              -> mkPrim 1 $ \ [LitWord64 a] -> nat (fromIntegral a)
+          PrimWord64FromNat            -> mkPrim 1 $ \ [LitNat a]    -> word (fromIntegral a)
+
+          -- Levels
+          -- "primLevelZero"              -- levels are not literals
+          -- "primLevelSuc"               -- levels are not literals
+          -- "primLevelMax"               -- levels are not literals
+
+          -- Floats
+          PrimFloatInequality          -> mkPrim 2 $ floatRel (<=)
+          PrimFloatEquality            -> mkPrim 2 $ floatRel (==)
+          PrimFloatLess                -> mkPrim 2 $ floatRel (<)
+          PrimFloatIsInfinite          -> mkPrim 1 $ floatPred isInfinite
+          PrimFloatIsNaN               -> mkPrim 1 $ floatPred isNaN
+          PrimFloatIsNegativeZero      -> mkPrim 1 $ floatPred isNegativeZero
+          PrimFloatIsSafeInteger       -> mkPrim 1 $ floatPred isSafeInteger
+          -- "primFloatToWord64"          -- returns a maybe
+          -- "primFloatToWord64Injective" -- identities are not literals
+          PrimNatToFloat               -> mkPrim 1 $ \ [LitNat a] -> float (fromIntegral a)
+          -- "primIntToFloat"             -- integers are not literals
+          -- "primFloatRound"             -- integers and maybe are not literals
+          -- "primFloatFloor"             -- integers and maybe are not literals
+          -- "primFloatCeiling"           -- integers and maybe are not literals
+          -- "primFloatToRatio"           -- integers and sigma are not literals
+          -- "primRatioToFloat"           -- integers are not literals
+          -- "primFloatDecode"            -- integers and sigma are not literals
+          -- "primFloatEncode"            -- integers are not literals
+          PrimFloatPlus                -> mkPrim 2 $ floatOp (+)
+          PrimFloatMinus               -> mkPrim 2 $ floatOp (-)
+          PrimFloatTimes               -> mkPrim 2 $ floatOp (*)
+          PrimFloatNegate              -> mkPrim 1 $ floatFun negate
+          PrimFloatDiv                 -> mkPrim 2 $ floatOp (/)
+          PrimFloatSqrt                -> mkPrim 1 $ floatFun sqrt
+          PrimFloatExp                 -> mkPrim 1 $ floatFun exp
+          PrimFloatLog                 -> mkPrim 1 $ floatFun log
+          PrimFloatSin                 -> mkPrim 1 $ floatFun sin
+          PrimFloatCos                 -> mkPrim 1 $ floatFun cos
+          PrimFloatTan                 -> mkPrim 1 $ floatFun tan
+          PrimFloatASin                -> mkPrim 1 $ floatFun asin
+          PrimFloatACos                -> mkPrim 1 $ floatFun acos
+          PrimFloatATan                -> mkPrim 1 $ floatFun atan
+          PrimFloatATan2               -> mkPrim 2 $ floatOp atan2
+          PrimFloatSinh                -> mkPrim 1 $ floatFun sinh
+          PrimFloatCosh                -> mkPrim 1 $ floatFun cosh
+          PrimFloatTanh                -> mkPrim 1 $ floatFun tanh
+          PrimFloatASinh               -> mkPrim 1 $ floatFun asinh
+          PrimFloatACosh               -> mkPrim 1 $ floatFun acosh
+          PrimFloatATanh               -> mkPrim 1 $ floatFun atanh
+          PrimFloatPow                 -> mkPrim 2 $ floatOp (**)
+          PrimShowFloat                -> mkPrim 1 $ \ [LitFloat a] -> string (show a)
+
+          -- Characters
+          PrimCharEquality             -> mkPrim 2 $ charRel (==)
+          PrimIsLower                  -> mkPrim 1 $ charPred isLower
+          PrimIsDigit                  -> mkPrim 1 $ charPred isDigit
+          PrimIsAlpha                  -> mkPrim 1 $ charPred isAlpha
+          PrimIsSpace                  -> mkPrim 1 $ charPred isSpace
+          PrimIsAscii                  -> mkPrim 1 $ charPred isAscii
+          PrimIsLatin1                 -> mkPrim 1 $ charPred isLatin1
+          PrimIsPrint                  -> mkPrim 1 $ charPred isPrint
+          PrimIsHexDigit               -> mkPrim 1 $ charPred isHexDigit
+          PrimToUpper                  -> mkPrim 1 $ charFun toUpper
+          PrimToLower                  -> mkPrim 1 $ charFun toLower
+          PrimCharToNat                -> mkPrim 1 $ \ [LitChar a] -> nat (fromIntegral (fromEnum a))
+          PrimNatToChar                -> mkPrim 1 $ \ [LitNat a] -> char (integerToChar a)
+          PrimShowChar                 -> mkPrim 1 $ \ [a] -> string (prettyShow a)
+
+          -- Strings
+          -- "primStringToList"           -- lists are not literals (TODO)
+          -- "primStringFromList"         -- lists are not literals (TODO)
+          PrimStringAppend             -> mkPrim 2 $ \ [LitString a, LitString b] -> text (b <> a)
+          PrimStringEquality           -> mkPrim 2 $ \ [LitString a, LitString b] -> bool (b == a)
+          PrimShowString               -> mkPrim 1 $ \ [a] -> string (prettyShow a)
+
+          -- "primErase"
+          -- "primForce"
+          -- "primForceLemma"
+          PrimQNameEquality            -> mkPrim 2 $ \ [LitQName a, LitQName b] -> bool (b == a)
+          PrimQNameLess                -> mkPrim 2 $ \ [LitQName a, LitQName b] -> bool (b < a)
+          PrimShowQName                -> mkPrim 1 $ \ [LitQName a] -> string (prettyShow a)
+          -- "primQNameFixity"            -- fixities are not literals (TODO)
+          PrimMetaEquality             -> mkPrim 2 $ \ [LitMeta _ a, LitMeta _ b] -> bool (b == a)
+          PrimMetaLess                 -> mkPrim 2 $ \ [LitMeta _ a, LitMeta _ b] -> bool (b < a)
+          PrimShowMeta                 -> mkPrim 1 $ \ [LitMeta _ a] -> string (prettyShow a)
+
+          _                            -> pure COther
+        where
+          fcc = fastCompiledClauses bEnv <$> cc
+          mkPrim n op = pure $ CPrimOp n op fcc
+
+          divAux k m n j = k + div (max 0 $ n + m - j) (m + 1)
+          modAux k m n j | n > j     = mod (n - j - 1) (m + 1)
+                         | otherwise = k + n
+
+          ~(Just true)  = bTrue  bEnv <&> \ c -> Con c ConOSystem []
+          ~(Just false) = bFalse bEnv <&> \ c -> Con c ConOSystem []
+
+          bool   a = if a then true else false
+          nat    a = Lit . LitNat    $! a
+          word   a = Lit . LitWord64 $! a
+          float  a = Lit . LitFloat  $! a
+          text   a = Lit . LitString $! a
+          string a = text (T.pack a)
+          char   a = Lit . LitChar   $! a
+
+          -- Remember reverse order!
+          natOp f [LitNat a, LitNat b] = nat (f b a)
+          natOp _ _ = __IMPOSSIBLE__
+
+          natOp4 f [LitNat a, LitNat b, LitNat c, LitNat d] = nat (f d c b a)
+          natOp4 _ _ = __IMPOSSIBLE__
+
+          natRel f [LitNat a, LitNat b] = bool (f b a)
+          natRel _ _ = __IMPOSSIBLE__
+
+          floatFun f [LitFloat a] = float (f a)
+          floatFun _ _ = __IMPOSSIBLE__
+
+          floatOp f [LitFloat a, LitFloat b] = float (f b a)
+          floatOp _ _ = __IMPOSSIBLE__
+
+          floatPred f [LitFloat a] = bool (f a)
+          floatPred _ _ = __IMPOSSIBLE__
+
+          floatRel f [LitFloat a, LitFloat b] = bool (f b a)
+          floatRel _ _ = __IMPOSSIBLE__
+
+          charFun f [LitChar a] = char (f a)
+          charFun _ _ = __IMPOSSIBLE__
+
+          charPred f [LitChar a] = bool (f a)
+          charPred _ _ = __IMPOSSIBLE__
+
+          charRel f [LitChar a, LitChar b] = bool (f b a)
+          charRel _ _ = __IMPOSSIBLE__
+
+  return $
+    CompactDef { cdefNonterminating = defNonterminating def
+               , cdefUnconfirmed    = defTerminationUnconfirmed def
+               , cdefDef            = cdefn
+               , cdefRewriteRules   = if allowReduce then rewr else []
+               }
+
+-- Faster case trees ------------------------------------------------------
+
+data FastCase c = FBranches
+  { fprojPatterns   :: Bool
+    -- ^ We are constructing a record here (copatterns).
+    --   'conBranches' lists projections.
+  , fconBranches    :: Map NameId c
+    -- ^ Map from constructor (or projection) names to their arity
+    --   and the case subtree.  (Projections have arity 0.)
+  , fsucBranch      :: Maybe c
+  , flitBranches    :: Map Literal c
+    -- ^ Map from literal to case subtree.
+  , fcatchAllBranch :: Maybe c
+    -- ^ (Possibly additional) catch-all clause.
+  , ffallThrough    :: Bool
+    -- ^ (if True) In case of non-canonical argument use catchAllBranch.
+  }
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--noBranches :: FastCase a
+--noBranches = FBranches{ fprojPatterns   = False
+--                      , fconBranches    = Map.empty
+--                      , fsucBranch      = Nothing
+--                      , flitBranches    = Map.empty
+--                      , fcatchAllBranch = Nothing
+--                      , ffallThrough    = False }
+
+-- | Case tree with bodies.
+
+data FastCompiledClauses
+  = FCase Int (FastCase FastCompiledClauses)
+    -- ^ @Case n bs@ stands for a match on the @n@-th argument
+    -- (counting from zero) with @bs@ as the case branches.
+    -- If the @n@-th argument is a projection, we have only 'conBranches'
+    -- with arity 0.
+  | FEta Int [Arg QName] FastCompiledClauses (Maybe FastCompiledClauses)
+    -- ^ Match on record constructor. Can still have a catch-all though. Just
+    --   contains the fields, not the actual constructor.
+  | FDone [Arg ArgName] Term
+    -- ^ @Done xs b@ stands for the body @b@ where the @xs@ contains hiding
+    --   and name suggestions for the free variables. This is needed to build
+    --   lambdas on the right hand side for partial applications which can
+    --   still reduce.
+  | FFail
+    -- ^ Absurd case.
+
+fastCompiledClauses :: BuiltinEnv -> CompiledClauses -> FastCompiledClauses
+fastCompiledClauses bEnv cc =
+  case cc of
+    Fail{}            -> FFail
+    Done xs b         -> FDone xs b
+    Case (Arg _ n) Branches{ etaBranch = Just (c, cc), catchAllBranch = ca } ->
+      FEta n (conFields c) (fastCompiledClauses bEnv $ content cc) (fastCompiledClauses bEnv <$> ca)
+    Case (Arg _ n) bs -> FCase n (fastCase bEnv bs)
+
+fastCase :: BuiltinEnv -> Case CompiledClauses -> FastCase FastCompiledClauses
+fastCase env (Branches proj con _ lit wild fT _) =
+  FBranches
+    { fprojPatterns   = proj
+    , fconBranches    = Map.mapKeysMonotonic (nameId . qnameName) $ fmap (fastCompiledClauses env . content) (stripSuc con)
+    , fsucBranch      = fmap (fastCompiledClauses env . content) $ flip Map.lookup con . conName =<< bSuc env
+    , flitBranches    = fmap (fastCompiledClauses env) lit
+    , ffallThrough    = (Just True ==) fT
+    , fcatchAllBranch = fmap (fastCompiledClauses env) wild }
+  where
+    stripSuc | Just c <- bSuc env = Map.delete (conName c)
+             | otherwise          = id
+
+
+{-# INLINE lookupCon #-}
+lookupCon :: QName -> FastCase c -> Maybe c
+lookupCon c (FBranches _ cons _ _ _ _) = Map.lookup (nameId $ qnameName c) cons
+
+-- QName memo -------------------------------------------------------------
+
+{-# NOINLINE memoQName #-}
+memoQName :: (QName -> a) -> (QName -> a)
+memoQName f = unsafePerformIO $ do
+  tbl <- newIORef Map.empty
+  return (unsafePerformIO . f' tbl)
+  where
+    f' tbl x = do
+      let i = nameId (qnameName x)
+      m <- readIORef tbl
+      case Map.lookup i m of
+        Just y  -> return y
+        Nothing -> do
+          let y = f x
+          writeIORef tbl (Map.insert i y m)
+          return y
+
+-- * Fast reduction
+
+data Normalisation = WHNF | NF
+  deriving (Eq)
+
+-- | The entry point to the reduction machine.
+fastReduce :: Term -> ReduceM (Blocked Term)
+fastReduce = fastReduce' WHNF
+
+fastNormalise :: Term -> ReduceM Term
+fastNormalise v = ignoreBlocking <$> fastReduce' NF v
+
+fastReduce' :: Normalisation -> Term -> ReduceM (Blocked Term)
+fastReduce' norm v = do
+  tcState <- getTCState
+  let name (Con c _ _) = c
+      name _         = __IMPOSSIBLE__
+
+      -- Gather builtins using 'BuiltinAccess' rather than with the default
+      -- 'HasBuiltins ReduceM' instance. This increases laziness, allowing us to
+      -- avoid costly builtin lookups unless needed.
+      builtinName   = fmap name . runBuiltinAccess tcState . getBuiltin'
+      primitiveName = fmap primFunName . runBuiltinAccess tcState . getPrimitive'
+
+      zero  = builtinName builtinZero
+      suc   = builtinName builtinSuc
+      true  = builtinName builtinTrue
+      false = builtinName builtinFalse
+      refl  = builtinName builtinRefl
+
+      force = primitiveName PrimForce
+      erase = primitiveName PrimErase
+
+      bEnv = BuiltinEnv { bZero = zero, bSuc = suc, bTrue = true, bFalse = false, bRefl = refl,
+                          bPrimForce = force, bPrimErase = erase }
+  allowedReductions <- asksTC envAllowedReductions
+  rwr <- optRewriting <$> pragmaOptions
+  constInfo <- unKleisli $ \f -> do
+    info <- getConstInfo f
+    rewr <- if rwr then instantiateRewriteRules =<< getRewriteRulesFor f
+                   else return []
+    compactDef bEnv info rewr
+  ReduceM $ \ redEnv -> reduceTm redEnv bEnv (memoQName constInfo) norm v
+
+unKleisli :: (a -> ReduceM b) -> ReduceM (a -> b)
+unKleisli f = ReduceM $ \ env x -> unReduceM (f x) env
+
+-- * Closures
+
+-- | The abstract machine represents terms as closures containing a 'Term', an environment, and a
+--   spine of eliminations. Note that the environment doesn't necessarily bind all variables in the
+--   term. The variables in the context in which the abstract machine is started are free in
+--   closures. The 'IsValue' argument tracks whether the closure is in weak-head normal form.
+data Closure s = Closure IsValue Term (Env s) (Spine s)
+                 -- ^ The environment applies to the 'Term' argument. The spine contains closures
+                 --   with their own environments.
+
+-- | Used to track if a closure is @Unevaluated@ or a @Value@ (in weak-head normal form), and if so
+--   why it cannot reduce further.
+data IsValue = Value Blocked_ | Unevaled
+
+-- | The spine is a list of eliminations. Application eliminations contain pointers.
+type Spine s = [Elim' (Pointer s)]
+
+isValue :: Closure s -> IsValue
+isValue (Closure isV _ _ _) = isV
+
+setIsValue :: IsValue -> Closure s -> Closure s
+setIsValue isV (Closure _ t env spine) = Closure isV t env spine
+
+-- | Apply a closure to a spine of eliminations. Note that this does not preserve the 'IsValue'
+--   field.
+clApply :: Closure s -> Spine s -> Closure s
+clApply c [] = c
+clApply (Closure _ t env es) es' = Closure Unevaled t env (es <> es')
+
+-- | Apply a closure to a spine, preserving the 'IsValue' field. Use with care, since usually
+--   eliminations do not preserve the value status.
+clApply_ :: Closure s -> Spine s -> Closure s
+clApply_ c [] = c
+clApply_ (Closure b t env es) es' = Closure b t env (es <> es')
+
+-- * Pointers and thunks
+
+-- | Spines and environments contain pointers to closures to enable call-by-need evaluation.
+data Pointer s = Pure (Closure s)
+                 -- ^ Not a pointer. Used for closures that do not need to be shared to avoid
+                 --   unnecessary updates.
+               | Pointer {-# UNPACK #-} !(STPointer s)
+                 -- ^ An actual pointer is an 'STRef' to a 'Thunk'. The thunk is set to 'BlackHole'
+                 --   during the evaluation of its contents to make debugging loops easier.
+
+type STPointer s = STRef s (Thunk (Closure s))
+
+-- | A thunk is either a black hole or contains a value.
+data Thunk a = BlackHole | Thunk a
+  deriving (Functor)
+
+derefPointer :: Pointer s -> ST s (Thunk (Closure s))
+derefPointer (Pure x)      = return (Thunk x)
+derefPointer (Pointer ptr) = readSTRef ptr
+
+-- | In most cases pointers that we dereference do not contain black holes.
+derefPointer_ :: Pointer s -> ST s (Closure s)
+derefPointer_ ptr =
+  derefPointer ptr <&> \case
+    Thunk cl  -> cl
+    BlackHole -> __IMPOSSIBLE__
+
+
+-- | Only use for debug printing!
+unsafeDerefPointer :: Pointer s -> Thunk (Closure s)
+unsafeDerefPointer (Pure x)    = Thunk x
+unsafeDerefPointer (Pointer p) = unsafePerformIO (unsafeSTToIO (readSTRef p))
+
+readPointer :: STPointer s -> ST s (Thunk (Closure s))
+readPointer = readSTRef
+
+storePointer :: STPointer s -> Closure s -> ST s ()
+storePointer ptr !cl = writeSTRef ptr (Thunk cl)
+    -- Note the strict match. To prevent leaking memory in case of unnecessary updates.
+
+blackHole :: STPointer s -> ST s ()
+blackHole ptr = writeSTRef ptr BlackHole
+
+-- | Create a thunk. If the closure is a naked variable we can reuse the pointer from the
+--   environment to avoid creating long pointer chains.
+createThunk :: Closure s -> ST s (Pointer s)
+createThunk (Closure _ (Var x []) env spine)
+  | null spine, Just p <- lookupEnv x env = return p
+createThunk cl = Pointer <$> newSTRef (Thunk cl)
+
+-- | Create a thunk that is not shared or updated.
+pureThunk :: Closure s -> Pointer s
+pureThunk = Pure
+
+-- * Environments
+
+-- | The environment of a closure binds pointers to deBruijn indicies.
+newtype Env s = Env [Pointer s]
+
+emptyEnv :: Env s
+emptyEnv = Env []
+--UNUSED Liang-Ting Chen 2019-07-16
+--isEmptyEnv :: Env s -> Bool
+--isEmptyEnv (Env xs) = null xs
+
+envSize :: Env s -> Int
+envSize (Env xs) = length xs
+
+envToList :: Env s -> [Pointer s]
+envToList (Env xs) = xs
+
+extendEnv :: Pointer s -> Env s -> Env s
+extendEnv p (Env xs) = Env (p : xs)
+
+-- | Unsafe.
+lookupEnv_ :: Int -> Env s -> Pointer s
+lookupEnv_ i (Env e) = indexWithDefault __IMPOSSIBLE__ e i
+
+-- Andreas, 2018-11-12, which isn't this just Agda.Utils.List.!!! ?
+lookupEnv :: Int -> Env s -> Maybe (Pointer s)
+lookupEnv i e | i < n     = Just (lookupEnv_ i e)
+              | otherwise = Nothing
+  where n = envSize e
+
+-- * The Agda Abstract Machine
+
+-- | The abstract machine state has two states 'Eval' and 'Match' that determine what the machine is
+--   currently working on: evaluating a closure in the Eval state and matching a spine against a
+--   case tree in the Match state. Both states contain a 'ControlStack' of continuations for what to
+--   do next. The heap is maintained implicitly using 'STRef's, hence the @s@ parameter.
+data AM s = Eval (Closure s) !(ControlStack s)
+            -- ^ Evaluate the given closure (the focus) to weak-head normal form. If the 'IsValue'
+            --   field of the closure is 'Value' we look at the control stack for what to do. Being
+            --   strict in the control stack is important! We can spend a lot of steps with
+            --   unevaluated closures (where we update, but don't look at the control stack). For
+            --   instance, long chains of 'suc' constructors.
+          | Match QName FastCompiledClauses (Spine s) (MatchStack s) (ControlStack s)
+            -- ^ @Match f cc spine stack ctrl@ Match the arguments @spine@ against the case tree
+            --   @cc@. The match stack contains a (possibly empty) list of 'CatchAll' frames and a
+            --   closure to return in case of a stuck match.
+
+-- | The control stack contains a list of continuations, i.e. what to do with
+--   the result of the current focus.
+type ControlStack s = [ControlFrame s]
+
+-- | The control stack for matching. Contains a list of CatchAllFrame's and the closure to return in
+--   case of a stuck match.
+data MatchStack s = [CatchAllFrame s] :> Closure s
+infixr 2 :>, >:
+
+(>:) :: CatchAllFrame s -> MatchStack s -> MatchStack s
+(>:) c (cs :> cl) = c : cs :> cl
+-- Previously written as:
+--   c >: cs :> cl = c : cs :> cl
+--
+-- However, some versions/tools fail to parse infix data constructors properly.
+-- For example, stylish-haskell@0.9.2.1 fails with the following error:
+--   Language.Haskell.Stylish.Parse.parseModule: could not parse
+--   src/full/Agda/TypeChecking/Reduce/Fast.hs: ParseFailed (SrcLoc
+--   "<unknown>.hs" 625 1) "Parse error in pattern: "
+--
+-- See https://ghc.haskell.org/trac/ghc/ticket/10018 which may be related.
+
+data CatchAllFrame s = CatchAll FastCompiledClauses (Spine s)
+                        -- ^ @CatchAll cc spine@. Case trees are not fully expanded, that is,
+                        --   inner matches can be partial and covered by a catch-all at a higher
+                        --   level. This catch-all is represented on the match stack as a
+                        --   @CatchAll@. @cc@ is the case tree in the catch-all case and @spine@ is
+                        --   the value of the pattern variables at the point of the catch-all.
+
+-- An Elim' with a hole.
+data ElimZipper a = ApplyCxt ArgInfo
+                  | IApplyType a a | IApplyFst a a | IApplySnd a a
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+instance Zipper (ElimZipper a) where
+  type Carrier (ElimZipper a) = Elim' a
+  type Element (ElimZipper a) = a
+
+  firstHole (Apply arg)    = Just (unArg arg, ApplyCxt (argInfo arg))
+  firstHole (IApply a x y) = Just (a, IApplyType x y)
+  firstHole Proj{}         = Nothing
+
+  plugHole x (ApplyCxt i)     = Apply (Arg i x)
+  plugHole a (IApplyType x y) = IApply a x y
+  plugHole x (IApplyFst a y)  = IApply a x y
+  plugHole y (IApplySnd a x)  = IApply a x y
+
+  nextHole a (IApplyType x y) = Right (x, IApplyFst a y)
+  nextHole x (IApplyFst a y)  = Right (y, IApplySnd a x)
+  nextHole y (IApplySnd a x)  = Left (IApply a x y)
+  nextHole x c@ApplyCxt{}     = Left (plugHole x c)
+
+-- | A spine with a single hole for a pointer.
+type SpineContext s = ComposeZipper (ListZipper (Elim' (Pointer s)))
+                                    (ElimZipper (Pointer s))
+
+-- | Control frames are continuations that act on value closures.
+data ControlFrame s = CaseK QName ArgInfo (FastCase FastCompiledClauses) (Spine s) (Spine s) (MatchStack s)
+                        -- ^ @CaseK f i bs spine0 spine1 stack@. Pattern match on the focus (with
+                        --   arg info @i@) using the @bs@ case tree. @f@ is the name of the function
+                        --   doing the matching, and @spine0@ and @spine1@ are the values bound to
+                        --   the pattern variables to the left and right (respectively) of the
+                        --   focus. The match stack contains catch-all cases we need to consider if
+                        --   this match fails.
+                    | ArgK (Closure s) (SpineContext s)
+                        -- ^ @ArgK cl cxt@. Used when computing full normal forms. The closure is
+                        --   the head and the context is the spine with the current focus removed.
+                    | NormaliseK
+                        -- ^ Indicates that the focus should be evaluated to full normal form.
+                    | ForceK QName (Spine s) (Spine s)
+                        -- ^ @ForceK f spine0 spine1@. Evaluating @primForce@ of the focus. @f@ is
+                        --   the name of @primForce@ and is used to build the result if evaluation
+                        --   gets stuck. @spine0@ are the level and type arguments and @spine1@
+                        --   contains (if not empty) the continuation and any additional
+                        --   eliminations.
+                    | EraseK QName (Spine s) (Spine s) (Spine s) (Spine s)
+                        -- ^ @EraseK f spine0 spine1 spine2 spine3@. Evaluating @primErase@. The
+                        --   first contains the level and type arguments. @spine1@ and @spine2@
+                        --   contain at most one argument between them. If in @spine1@ it's the
+                        --   value closure of the first argument to be compared and if in @spine2@
+                        --   it's the unevaluated closure of the second argument.
+                        --   @spine3@ contains the proof of equality we are erasing. It is passed
+                        --   around but never actually inspected.
+                    | NatSucK Integer
+                        -- ^ @NatSucK n@. Add @n@ to the focus. If the focus computes to a natural
+                        --   number literal this returns a new literal, otherwise it constructs @n@
+                        --   calls to @suc@.
+                    | PrimOpK QName ([Literal] -> Term) [Literal] [Pointer s] (Maybe FastCompiledClauses)
+                        -- ^ @PrimOpK f op lits es cc@. Evaluate the primitive function @f@ using
+                        --   the Haskell function @op@. @op@ gets a list of literal values in
+                        --   reverse order for the arguments of @f@ and computes the result as a
+                        --   term. The already computed arguments (in reverse order) are @lits@ and
+                        --   @es@ are the arguments that should be computed after the current focus.
+                        --   In case of built-in functions with corresponding Agda implementations,
+                        --   @cc@ contains the case tree.
+                    | UpdateThunk [STPointer s]
+                        -- ^ @UpdateThunk ps@. Update the pointers @ps@ with the value of the
+                        --   current focus.
+                    | ApplyK (Spine s)
+                        -- ^ @ApplyK spine@. Apply the current focus to the eliminations in @spine@.
+                        --   This is used when a thunk needs to be updated with a partial
+                        --   application of a function.
+
+-- * Compilation and decoding
+
+-- | The initial abstract machine state. Wrap the term to be evaluated in an empty closure. Note
+--   that free variables of the term are treated as constants by the abstract machine. If computing
+--   full normal form we start off the control stack with a 'NormaliseK' continuation.
+compile :: Normalisation -> Term -> AM s
+compile nf t = Eval (Closure Unevaled t emptyEnv []) [NormaliseK | nf == NF]
+
+decodePointer :: Pointer s -> ST s Term
+decodePointer p = decodeClosure_ =<< derefPointer_ p
+
+-- | Note: it's important to be lazy in the spine and environment when decoding. Hence the
+--   'unsafeInterleaveST' here and in 'decodeEnv', and the special version of 'parallelS' in
+--   'decodeClosure'.
+decodeSpine :: Spine s -> ST s Elims
+decodeSpine spine = unsafeInterleaveST $ (traverse . traverse) decodePointer spine
+
+decodeEnv :: Env s -> ST s [Term]
+decodeEnv env = unsafeInterleaveST $ traverse decodePointer (envToList env)
+
+decodeClosure_ :: Closure s -> ST s Term
+decodeClosure_ = ignoreBlocking <.> decodeClosure
+
+-- | Turning an abstract machine closure back into a term. This happens in three cases:
+--    * when reduction is finished and we return the weak-head normal term to the outside world.
+--    * when the abstract machine encounters something it cannot handle and falls back to the slow
+--      reduction engine
+--    * when there are rewrite rules to apply
+decodeClosure :: Closure s -> ST s (Blocked Term)
+decodeClosure (Closure isV t env spine) = do
+    vs <- decodeEnv env
+    es <- decodeSpine spine
+    return $ applyE (applySubst (parS vs) t) es <$ b
+  where
+    parS = foldr (:#) IdS  -- parallelS is too strict
+    b    = case isV of
+             Value b  -> b
+             Unevaled -> notBlocked ()  -- only when falling back to slow reduce in which case the
+                                        -- blocking tag is immediately discarded
+
+-- | Turn a list of internal syntax eliminations into a spine. This builds closures and allocates
+--   thunks for all the 'Apply' elims.
+elimsToSpine :: Env s -> Elims -> ST s (Spine s)
+elimsToSpine env es = do
+    spine <- mapM thunk es
+    forceSpine spine `seq` return spine
+  where
+    -- Need to be strict in mkClosure to avoid memory leak
+    forceSpine = foldl (\ () -> forceEl) ()
+    forceEl (Apply (Arg _ (Pure Closure{}))) = ()
+    forceEl (Apply (Arg _ (Pointer{})))      = ()
+    forceEl _                                = ()
+
+    -- We don't preserve free variables of closures (in the sense of their
+    -- decoding), since we freely add things to the spines.
+    unknownFVs = setFreeVariables unknownFreeVariables
+
+    thunk (Apply (Arg i t)) = Apply . Arg (unknownFVs i) <$> createThunk (closure (getFreeVariables i) t)
+    thunk (Proj o f)        = return (Proj o f)
+    thunk (IApply a x y)    = IApply <$> mkThunk a <*> mkThunk x <*> mkThunk y
+      where mkThunk = createThunk . closure UnknownFVs
+
+    -- Going straight for a value for literals is mostly to make debug traces
+    -- less verbose and doesn't really buy anything performance-wise.
+    closure _ t@Lit{} = Closure (Value $ notBlocked ()) t emptyEnv []
+    closure fv t      = env' `seq` Closure Unevaled t env' []
+      where env' = trimEnvironment fv env
+
+-- | Trim unused entries from an environment. Currently only trims closed terms for performance
+--   reasons.
+trimEnvironment :: FreeVariables -> Env s -> Env s
+trimEnvironment UnknownFVs env = env
+trimEnvironment (KnownFVs fvs) env
+  | IntSet.null fvs = emptyEnv
+    -- Environment trimming is too expensive (costs 50% on some benchmarks), and while it does make
+    -- some cases run in constant instead of linear space you need quite contrived examples to
+    -- notice the effect.
+  | otherwise       = env -- Env $ trim 0 $ envToList env
+  where
+    -- Important: strict enough that the trimming actually happens
+    trim _ [] = []
+    trim i (p : ps)
+      | IntSet.member i fvs = (p :)             $! trim (i + 1) ps
+      | otherwise           = (unusedPointer :) $! trim (i + 1) ps
+
+-- | Build an environment for a body with some given free variables from a spine of arguments.
+--   Returns a triple containing
+--    * the left-over variable names (in case of partial application)
+--    * the environment
+--    * the remaining spine (in case of over-application)
+buildEnv :: [Arg String] -> Spine s -> ([Arg String], Env s, Spine s)
+buildEnv xs spine = go xs spine emptyEnv
+  where
+    go [] sp env = ([], env, sp)
+    go xs0@(x : xs) sp env =
+      case sp of
+        []           -> (xs0, env, sp)
+        Apply c : sp -> go xs sp (unArg c `extendEnv` env)
+        IApply x y r : sp -> go xs sp (r `extendEnv` env)
+        _            -> __IMPOSSIBLE__
+
+unusedPointerString :: Text
+unusedPointerString = T.pack (show (withCurrentCallStack Impossible))
+
+unusedPointer :: Pointer s
+unusedPointer = Pure (Closure (Value $ notBlocked ())
+                     (Lit (LitString unusedPointerString)) emptyEnv [])
+
+-- * Running the abstract machine
+
+-- | Evaluating a term in the abstract machine. It gets the type checking state and environment in
+--   the 'ReduceEnv' argument, some precomputed built-in mappings in 'BuiltinEnv', the memoised
+--   'getConstInfo' function, a couple of flags (allow non-terminating function unfolding, and
+--   whether rewriting is enabled), and a term to reduce. The result is the weak-head normal form of
+--   the term with an attached blocking tag.
+reduceTm :: ReduceEnv -> BuiltinEnv -> (QName -> CompactDef) -> Normalisation -> Term -> Blocked Term
+reduceTm rEnv bEnv !constInfo normalisation =
+    compileAndRun . traceDoc "-- fast reduce --"
+  where
+    -- Helpers to get information from the ReduceEnv.
+    localMetas     = redSt rEnv ^. stSolvedMetaStore
+    remoteMetas    = redSt rEnv ^. stImportedMetaStore
+    -- Are we currently instance searching. In that case we don't fail hard on missing clauses. This
+    -- is a (very unsatisfactory) work-around for #3870.
+    speculative    = redSt rEnv ^. stConsideringInstance
+    getMetaInst m  = case MapS.lookup m localMetas of
+                       Just mv -> Just (mvInstantiation mv)
+                       Nothing -> InstV . rmvInstantiation <$>
+                                    HMap.lookup m remoteMetas
+    partialDefs    = runReduce getPartialDefs
+    rewriteRules f = cdefRewriteRules (constInfo f)
+    callByNeed     = envCallByNeed (redEnv rEnv) && not (optCallByName $ redSt rEnv ^. stPragmaOptions)
+    iview          = runReduce intervalView'
+
+    runReduce :: ReduceM a -> a
+    runReduce m = unReduceM m rEnv
+
+    -- Debug output. Taking care that we only look at the verbosity level once.
+    hasVerb tag lvl = unReduceM (hasVerbosity tag lvl) rEnv
+    doDebug = hasVerb "tc.reduce.fast" 110
+    traceDoc :: Doc -> a -> a
+    traceDoc
+      | doDebug   = trace . show
+      | otherwise = const id
+
+    -- Checking for built-in zero and suc
+    BuiltinEnv{ bZero = zero, bSuc = suc, bRefl = refl0 } = bEnv
+    conNameId = nameId . qnameName . conName
+    isZero = case zero of
+               Nothing -> const False
+               Just z  -> (conNameId z ==) . conNameId
+    isSuc  = case suc of
+               Nothing -> const False
+               Just s  -> (conNameId s ==) . conNameId
+
+    -- If there's a non-standard equality (for instance doubly-indexed) we fall back to slow reduce
+    -- for primErase and "unbind" refl.
+    refl = refl0 >>= \ c -> if cconArity (cdefDef $ constInfo $ conName c) == 0
+                            then Just c else Nothing
+
+    -- The entry point of the machine.
+    compileAndRun :: Term -> Blocked Term
+    compileAndRun t = runST (runAM (compile normalisation t))
+
+    -- Run the machine in a given state. Prints the state if the right verbosity level is active.
+    runAM :: AM s -> ST s (Blocked Term)
+    runAM = if doDebug then \ s -> trace (prettyShow s) (runAM' s)
+                       else runAM'
+
+    -- The main function. This is where the stuff happens!
+    runAM' :: AM s -> ST s (Blocked Term)
+
+    -- Base case: The focus is a value closure and the control stack is empty. Decode and return.
+    runAM' (Eval cl@(Closure Value{} _ _ _) []) = decodeClosure cl
+
+    -- Unevaluated closure: inspect the term and take the appropriate action. For instance,
+    --  - Change to the 'Match' state if a definition
+    --  - Look up in the environment if variable
+    --  - Perform a beta step if lambda and application elimination in the spine
+    --  - Perform a record beta step if record constructor and projection elimination in the spine
+    runAM' s@(Eval cl@(Closure Unevaled t env spine) ctrl) = {-# SCC "runAM.Eval" #-}
+      case t of
+
+        -- Case: definition. Enter 'Match' state if defined function or shift to evaluating an
+        -- argument and pushing the appropriate control frame for primitive functions. Fall back to
+        -- slow reduce for unsupported definitions.
+        Def f [] ->
+          evalIApplyAM spine ctrl $
+          let CompactDef{ cdefNonterminating = nonterm
+                        , cdefUnconfirmed    = unconf
+                        , cdefDef            = def } = constInfo f
+          in case def of
+            CFun{ cfunCompiled = cc } -> runAM (Match f cc spine ([] :> cl) ctrl)
+            CAxiom         -> rewriteAM done
+            CTyCon         -> rewriteAM done
+            CCon{}         -> runAM done   -- Only happens for builtinSharp (which is a Def when you bind it)
+            CForce | (spine0, Apply v : spine1) <- splitAt 4 spine ->
+              evalPointerAM (unArg v) [] (ForceK f spine0 spine1 : ctrl)
+            CForce -> runAM done -- partially applied
+            CErase | (spine0, Apply v : spine1 : spine2) <- splitAt 2 spine ->
+              evalPointerAM (unArg v) [] (EraseK f spine0 [] [spine1] spine2 : ctrl)
+            CErase -> runAM done -- partially applied
+            CPrimOp n op cc | length spine == n,                      -- PrimOps can't be over-applied. They don't
+                              Just (v : vs) <- allApplyElims spine -> -- return functions or records.
+              evalPointerAM (unArg v) [] (PrimOpK f op [] (map unArg vs) cc : ctrl)
+            CPrimOp{} -> runAM done  -- partially applied
+            COther    -> fallbackAM s
+
+        -- Case: zero. Return value closure with literal 0.
+        Con c i [] | isZero c ->
+          runAM (evalTrueValue (Lit (LitNat 0)) emptyEnv spine ctrl)
+
+        -- Case: suc. Suc is strict in its argument to make sure we return a literal whenever
+        -- possible. Push a 'NatSucK' frame on the control stack and evaluate the argument.
+        Con c i [] | isSuc c, Apply v : _ <- spine ->
+          evalPointerAM (unArg v) [] (sucCtrl ctrl)
+
+        -- Case: constructor. Perform beta reduction if projected from, otherwise return a value.
+        Con c i []
+          -- Constructors of types in Prop are not representex as
+          -- CCon, so this match might fail!
+          | CCon{cconSrcCon = c', cconArity = ar} <- cdefDef (constInfo (conName c)) ->
+            evalIApplyAM spine ctrl $
+            case splitAt ar spine of
+              (args, Proj _ p : spine')
+                  -> evalPointerAM (unArg arg) spine' ctrl  -- Andreas #2170: fit argToDontCare here?!
+                where
+                  fields    = map unArg $ conFields c
+                  Just n    = List.elemIndex p fields
+                  Apply arg = args !! n
+              _ -> rewriteAM (evalTrueValue (Con c' i []) env spine ctrl)
+          | otherwise -> runAM done
+
+        -- Case: variable. Look up the variable in the environment and evaluate the resulting
+        -- pointer. If the variable is not in the environment it's a free variable and we adjust the
+        -- deBruijn index appropriately.
+        Var x []   ->
+          evalIApplyAM spine ctrl $
+          case lookupEnv x env of
+            Nothing -> runAM (evalValue (notBlocked ()) (Var (x - envSize env) []) emptyEnv spine ctrl)
+            Just p  -> evalPointerAM p spine ctrl
+
+        -- Case: lambda. Perform the beta reduction if applied. Otherwise it's a value.
+        Lam h b ->
+          case spine of
+            [] -> runAM done
+            elim : spine' ->
+              case b of
+                Abs   _ b -> runAM (evalClosure b (getArg elim `extendEnv` env) spine' ctrl)
+                NoAbs _ b -> runAM (evalClosure b env spine' ctrl)
+          where
+            getArg (Apply v)      = unArg v
+            getArg (IApply _ _ v) = v
+            getArg Proj{}         = __IMPOSSIBLE__
+
+        -- Case: values. Literals and function types are already in weak-head normal form.
+        -- We throw away the environment for literals mostly to make debug printing less verbose.
+        -- And we know the spine is empty since literals cannot be applied or projected.
+        Lit{} -> runAM (evalTrueValue t emptyEnv [] ctrl)
+        Pi{}  -> runAM done
+        DontCare{} -> runAM done
+
+        -- Case: non-empty spine. If the focused term has a non-empty spine, we shift the
+        -- eliminations onto the spine.
+        Def f   es -> shiftElims (Def f   []) emptyEnv env es
+        Con c i es -> shiftElims (Con c i []) emptyEnv env es
+        Var x   es -> shiftElims (Var x   []) env      env es
+
+        -- Case: metavariable. If it's instantiated evaluate the value. Meta instantiations are open
+        -- terms with a specified list of free variables. buildEnv constructs the appropriate
+        -- environment for the closure. Avoiding shifting spines for open metas
+        -- save a bit of performance.
+        MetaV m es -> evalIApplyAM spine ctrl $
+          case getMetaInst m of
+            Nothing ->
+              runAM (Eval (mkValue (blocked m ()) cl) ctrl)
+            Just (InstV i) -> do
+              spine' <- elimsToSpine env es
+              let (zs, env, !spine'') = buildEnv (instTel i) (spine' <> spine)
+              runAM (evalClosure (lams zs (instBody i)) env spine'' ctrl)
+            Just Open{}                         -> __IMPOSSIBLE__
+            Just OpenInstance{}                 -> __IMPOSSIBLE__
+            Just BlockedConst{}                 -> __IMPOSSIBLE__
+            Just PostponedTypeCheckingProblem{} -> __IMPOSSIBLE__
+
+        -- Case: unsupported. These terms are not handled by the abstract machine, so we fall back
+        -- to slowReduceTerm for these.
+        Level{}    -> fallbackAM s
+        Sort{}     -> fallbackAM s
+        Dummy{}    -> fallbackAM s
+
+      where done = Eval (mkValue (notBlocked ()) cl) ctrl
+            shiftElims t env0 env es = do
+              spine' <- elimsToSpine env es
+              runAM (evalClosure t env0 (spine' <> spine) ctrl)
+
+    -- If the current focus is a value closure, we look at the control stack.
+
+    -- Case NormaliseK: The focus is a weak-head value that should be fully normalised.
+    runAM' s@(Eval cl@(Closure b t env spine) (NormaliseK : ctrl)) =
+      case t of
+        Def _   [] -> normaliseArgsAM (Closure b t emptyEnv []) spine ctrl
+        Con _ _ [] -> normaliseArgsAM (Closure b t emptyEnv []) spine ctrl
+        Var _   [] -> normaliseArgsAM (Closure b t emptyEnv []) spine ctrl
+        MetaV _ [] -> normaliseArgsAM (Closure b t emptyEnv []) spine ctrl
+
+        Lit{} -> runAM done
+
+        -- We might get these from fallbackAM
+        Def f   es -> shiftElims (Def f   []) emptyEnv env es
+        Con c i es -> shiftElims (Con c i []) emptyEnv env es
+        Var x   es -> shiftElims (Var x   []) env      env es
+        MetaV m es -> shiftElims (MetaV m []) emptyEnv env es
+
+        _ -> fallbackAM s -- fallbackAM knows about NormaliseK
+
+      where done = Eval (mkValue (notBlocked ()) cl) ctrl
+            shiftElims t env0 env es = do
+              spine' <- elimsToSpine env es
+              runAM (Eval (Closure b t env0 (spine' <> spine)) (NormaliseK : ctrl))
+
+    -- Case: ArgK: We successfully normalised an argument. Start on the next argument, or if there
+    -- isn't one we're done.
+    runAM' (Eval cl (ArgK cl0 cxt : ctrl)) =
+      case nextHole (pureThunk cl) cxt of
+        Left spine      -> runAM (Eval (clApply_ cl0 spine) ctrl)
+        Right (p, cxt') -> evalPointerAM p [] (NormaliseK : ArgK cl0 cxt' : ctrl)
+
+    -- Case: NatSucK m
+
+    -- If literal add m to the literal,
+    runAM' (Eval cl@(Closure Value{} (Lit (LitNat n)) _ _) (NatSucK m : ctrl)) =
+      runAM (evalTrueValue (Lit $! LitNat $! m + n) emptyEnv [] ctrl)
+
+    -- otherwise apply 'suc' m times.
+    runAM' (Eval cl (NatSucK m : ctrl)) =
+        runAM (Eval (mkValue (notBlocked ()) $ plus m cl) ctrl)
+      where
+        plus 0 cl = cl
+        plus n cl =
+          trueValue (Con (fromMaybe __IMPOSSIBLE__ suc) ConOSystem []) emptyEnv $
+                     Apply (defaultArg arg) : []
+          where arg = pureThunk (plus (n - 1) cl)
+
+    -- Case: PrimOpK
+
+    -- If literal apply the primitive function if no more arguments, otherwise
+    -- store the literal in the continuation and evaluate the next argument.
+    runAM' (Eval (Closure _ (Lit a) _ _) (PrimOpK f op vs es cc : ctrl)) =
+      case es of
+        []      -> runAM (evalTrueValue (op (a : vs)) emptyEnv [] ctrl)
+        e : es' -> evalPointerAM e [] (PrimOpK f op (a : vs) es' cc : ctrl)
+
+    -- If not a literal we use the case tree if there is one, otherwise we are stuck.
+    runAM' (Eval cl@(Closure (Value blk) _ _ _) (PrimOpK f _ vs es mcc : ctrl)) =
+      case mcc of
+        Nothing -> rewriteAM (Eval stuck ctrl)
+        Just cc -> runAM (Match f cc spine ([] :> notstuck) ctrl)
+      where
+        p         = pureThunk cl
+        lits      = map (pureThunk . litClos) (reverse vs)
+        spine     = fmap (Apply . defaultArg) $ lits <> [p] <> es
+        stuck     = Closure (Value blk) (Def f []) emptyEnv spine
+        notstuck  = Closure Unevaled    (Def f []) emptyEnv spine
+        litClos l = trueValue (Lit l) emptyEnv []
+
+    -- Case: ForceK. Here we need to check if the argument is a canonical form (i.e. not a variable
+    -- or stuck function call) and if so apply the function argument to the value. If it's not
+    -- canonical we are stuck.
+    runAM' (Eval arg@(Closure (Value blk) t _ _) (ForceK pf spine0 spine1 : ctrl))
+      | isCanonical t =
+        case spine1 of
+          Apply k : spine' ->
+            evalPointerAM (unArg k) (elim : spine') ctrl
+          [] -> -- Partial application of primForce to canonical argument, return λ k → k arg.
+            runAM (evalTrueValue (lam (defaultArg "k") $ Var 0 [Apply $ defaultArg $ Var 1 []])
+                                 (argPtr `extendEnv` emptyEnv) [] ctrl)
+          _ -> __IMPOSSIBLE__
+      | otherwise = rewriteAM (Eval stuck ctrl)
+      where
+        argPtr = pureThunk arg
+        elim   = Apply (defaultArg argPtr)
+        spine' = spine0 <> [elim] <> spine1
+        stuck  = Closure (Value blk) (Def pf []) emptyEnv spine'
+
+        isCanonical = \case
+          Lit{}      -> True
+          Con{}      -> True
+          Lam{}      -> True
+          Pi{}       -> True
+          Sort{}     -> True
+          Level{}    -> True
+          DontCare{} -> True
+          Dummy{}    -> False
+          MetaV{}    -> False
+          Var{}      -> False
+          Def q _  -- Type constructors (data/record) are considered canonical for 'primForce'.
+            | CTyCon <- cdefDef (constInfo q) -> True
+            | otherwise                       -> False
+
+    -- Case: EraseK. We evaluate both arguments to values, then do a simple check for the easy
+    -- cases and otherwise fall back to slow reduce.
+    runAM' (Eval cl2@(Closure Value{} arg2 _ _) (EraseK f spine0 [Apply p1] _ spine3 : ctrl)) = do
+      cl1@(Closure _ arg1 _ sp1) <- derefPointer_ (unArg p1)
+      case (arg1, arg2) of
+        (Lit l1, Lit l2) | l1 == l2, isJust refl ->
+          runAM (evalTrueValue (Con (fromJust refl) ConOSystem []) emptyEnv [] ctrl)
+        _ ->
+          let spine = spine0 ++ map (Apply . hide . defaultArg . pureThunk) [cl1, cl2] ++ spine3 in
+          fallbackAM (evalClosure (Def f []) emptyEnv spine ctrl)
+    runAM' (Eval cl1@(Closure Value{} _ _ _) (EraseK f spine0 [] [Apply p2] spine3 : ctrl)) =
+      evalPointerAM (unArg p2) [] (EraseK f spine0 [Apply $ hide $ defaultArg $ pureThunk cl1] [] spine3 : ctrl)
+    runAM' (Eval _ (EraseK{} : _)) =
+      __IMPOSSIBLE__
+
+    -- Case: UpdateThunk. Write the value to the pointers in the UpdateThunk frame.
+    runAM' (Eval cl@(Closure Value{} _ _ _) (UpdateThunk ps : ctrl)) =
+      mapM_ (`storePointer` cl) ps >> runAM (Eval cl ctrl)
+
+    -- Case: ApplyK. Application after thunk update. Add the spine from the control frame to the
+    -- closure.
+    runAM' (Eval cl@(Closure Value{} _ _ _) (ApplyK spine : ctrl)) =
+      runAM (Eval (clApply cl spine) ctrl)
+
+    -- Case: CaseK. Pattern matching against a value. If it's a stuck value the pattern match is
+    -- stuck and we return the closure from the match stack (see stuckMatch). Otherwise we need to
+    -- find a matching branch switch to the Match state. If there is no matching branch we look for
+    -- a CatchAll in the match stack, or fail if there isn't one (see failedMatch). If the current
+    -- branches contain a catch-all case we need to push a CatchAll on the match stack if picking
+    -- one of the other branches.
+    runAM' (Eval cl@(Closure (Value blk) t env spine) ctrl0@(CaseK f i bs spine0 spine1 stack : ctrl)) =
+      {-# SCC "runAM.CaseK" #-}
+      case blk of
+        Blocked{} | null [()|Con{} <- [t]] -> stuck -- we might as well check the blocking tag first
+        _ -> case t of
+          -- Case: suc constructor
+          Con c ci [] | isSuc c -> matchSuc $ matchCatchall $ failedMatch f stack ctrl
+
+          -- Case: constructor
+          Con c ci [] -> matchCon c ci (length spine) $ matchCatchall $ failedMatch f stack ctrl
+
+          -- Case: non-empty elims. We can get here from a fallback (which builds a value without
+          -- shifting arguments onto spine)
+          Con c ci es -> do
+            spine' <- elimsToSpine env es
+            runAM (evalValue blk (Con c ci []) emptyEnv (spine' <> spine) ctrl0)
+          -- Case: natural number literals. Literal natural number patterns are translated to
+          -- suc-matches, so there is no need to try matchLit.
+          Lit (LitNat 0) -> matchLitZero  $ matchCatchall $ failedMatch f stack ctrl
+          Lit (LitNat n) -> matchLitSuc n $ matchCatchall $ failedMatch f stack ctrl
+
+          -- Case: literal
+          Lit l -> matchLit l $ matchCatchall $ failedMatch f stack ctrl
+
+          -- Case: hcomp
+          Def q [] | isJust $ lookupCon q bs -> matchCon' q (length spine) $ matchCatchall $ failedMatch f stack ctrl
+          Def q es | isJust $ lookupCon q bs -> do
+            spine' <- elimsToSpine env es
+            runAM (evalValue blk (Def q []) emptyEnv (spine' <> spine) ctrl0)
+
+          -- Case: not constructor or literal. In this case we are stuck.
+          _ -> stuck
+      where
+        -- If ffallThrough is set we take the catch-all (if any) rather than being stuck. I think
+        -- this happens for partial functions with --cubical (@saizan: is this true?).
+        stuck | ffallThrough bs = matchCatchall reallyStuck
+              | otherwise       = reallyStuck
+
+        reallyStuck = do
+            -- Compute new reason for being stuck. See Agda.Syntax.Internal.stuckOn for the logic.
+            blk' <- case blk of
+                      Blocked{}      -> return blk
+                      NotBlocked r _ -> decodeClosure_ cl <&> \ v -> NotBlocked (stuckOn (Apply $ Arg i v) r) ()
+            stuckMatch blk' stack ctrl
+
+        -- This the spine at this point in the matching. A catch-all match doesn't change the spine.
+        catchallSpine = spine0 <> [Apply $ Arg i p] <> spine1
+          where p = pureThunk cl -- cl is already a value so no need to thunk it.
+
+        -- Push catch-all frame on the match stack if there is a catch-all (and we're not taking it
+        -- right now).
+        catchallStack = case fcatchAllBranch bs of
+          Nothing -> stack
+          Just cc -> CatchAll cc catchallSpine >: stack
+
+        -- The matchX functions below all take an extra argument which is what to do if there is no
+        -- appropriate branch in the case tree. ifJust is maybe with a different argument order
+        -- letting you chain a bunch if maybe matches in if-then-elseif fashion.
+        (m `ifJust` f) z = maybe z f m
+
+        -- Matching constructor: Switch to the Match state, inserting the constructor arguments in
+        -- the spine between spine0 and spine1.
+        matchCon c ci ar = matchCon' (conName c) ar
+        matchCon' q ar = lookupCon q bs `ifJust` \ cc ->
+          runAM (Match f cc (spine0 <> spine <> spine1) catchallStack ctrl)
+
+        -- Catch-all: Don't add a CatchAll to the match stack since this _is_ the catch-all.
+        matchCatchall = fcatchAllBranch bs `ifJust` \ cc ->
+          runAM (Match f cc catchallSpine stack ctrl)
+
+        -- Matching literal: Switch to the Match state. There are no arguments to add to the spine.
+        matchLit l = Map.lookup l (flitBranches bs) `ifJust` \ cc ->
+          runAM (Match f cc (spine0 <> spine1) catchallStack ctrl)
+
+        -- Matching a 'suc' constructor: Insert the argument in the spine.
+        matchSuc = fsucBranch bs `ifJust` \ cc ->
+            runAM (Match f cc (spine0 <> spine <> spine1) catchallStack ctrl)
+
+        -- Matching a non-zero natural number literal: Subtract one from the literal and
+        -- insert it in the spine for the Match state.
+        matchLitSuc n = fsucBranch bs `ifJust` \ cc ->
+            runAM (Match f cc (spine0 <> [Apply $ defaultArg arg] <> spine1) catchallStack ctrl)
+          where n'  = n - 1
+                arg = pureThunk $ trueValue (Lit $ LitNat n') emptyEnv []
+
+        -- Matching a literal 0. Simply calls matchCon with the zero constructor.
+        matchLitZero = matchCon (fromMaybe __IMPOSSIBLE__ zero) ConOSystem 0
+                            -- If we have a nat literal we have builtin zero.
+
+    -- Case: Match state. Here we look at the case tree and take the appropriate action:
+    --   - FFail: stuck
+    --   - FDone: evaluate body
+    --   - FEta: eta expand argument
+    --   - FCase on projection: pick corresponding branch and keep matching
+    --   - FCase on argument: push CaseK frame on control stack and evaluate argument
+    runAM' (Match f cc spine stack ctrl) = {-# SCC "runAM.Match" #-}
+      case cc of
+        -- Absurd match. You can get here for open terms.
+        FFail -> stuckMatch (NotBlocked AbsurdMatch ()) stack ctrl
+
+        -- Matching complete. Compute the environment for the body and switch to the Eval state.
+        FDone xs body -> do
+            -- Don't ask me why, but not being strict in the spine causes a memory leak.
+            let (zs, env, !spine') = buildEnv xs spine
+            runAM (Eval (Closure Unevaled (lams zs body) env spine') ctrl)
+
+        -- A record pattern match. This does not block evaluation (since that would violate eta
+        -- equality), so in this case we replace the argument with its projections in the spine and
+        -- keep matching.
+        FEta n fs cc ca ->
+          case splitAt n spine of                           -- Question: add lambda here? doesn't
+            (_, [])                    -> done Underapplied -- matter for equality, but might for
+            (spine0, Apply e : spine1) -> do                -- rewriting or 'with'.
+              -- Replace e by its projections in the spine. And don't forget a
+              -- CatchAll frame if there's a catch-all.
+              let projClosure (Arg ai f) = Closure Unevaled (Var 0 []) (extendEnv (unArg e) emptyEnv) [Proj ProjSystem f]
+              projs <- mapM (createThunk . projClosure) fs
+              let spine' = spine0 <> map (Apply . defaultArg) projs <> spine1
+                  stack' = caseMaybe ca stack $ \ cc -> CatchAll cc spine >: stack
+              runAM (Match f cc spine' stack' ctrl)
+            _ -> __IMPOSSIBLE__
+
+        -- Split on nth elimination in the spine. Can be either a regular split or a copattern
+        -- split.
+        FCase n bs ->
+          case splitAt n spine of
+            -- If the nth elimination is not given, we're stuck.
+            (_, []) -> done Underapplied
+            -- Apply elim: push the current match on the control stack and evaluate the argument
+            (spine0, Apply e : spine1) ->
+              evalPointerAM (unArg e) [] $ CaseK f (argInfo e) bs spine0 spine1 stack : ctrl
+            -- Projection elim: in this case we must be in a copattern split and find the projection
+            -- in the case tree and keep going. If it's not there it might be because it's not the
+            -- original projection (issue #2265). If so look up the original projection instead.
+            -- That _really_ should be there since copattern splits cannot be partial. Except of
+            -- course, the user might still have written a partial function so we should check
+            -- partialDefs before throwing an impossible (#3012).
+            (spine0, Proj o p : spine1) ->
+              case lookupCon p bs <|> ((`lookupCon` bs) =<< op) of
+                Nothing
+                  | f `elem` partialDefs -> stuckMatch (NotBlocked (MissingClauses f) ()) stack ctrl
+                  | otherwise          -> __IMPOSSIBLE__
+                Just cc -> runAM (Match f cc (spine0 <> spine1) stack ctrl)
+              where CFun{ cfunProjection = op } = cdefDef (constInfo p)
+            (_, IApply{} : _) -> __IMPOSSIBLE__ -- Paths cannot be defined by pattern matching
+      where done why = stuckMatch (NotBlocked why ()) stack ctrl
+
+    -- 'evalPointerAM p spine ctrl'. Evaluate the closure pointed to by 'p' applied to 'spine' with
+    -- the control stack 'ctrl'. If 'p' points to an unevaluated thunk, a 'BlackHole' is written to
+    -- the pointer and an 'UpdateThunk' frame is pushed to the control stack. In this case the
+    -- application to the spine has to be deferred until after the update through an 'ApplyK' frame.
+    evalPointerAM :: Pointer s -> Spine s -> ControlStack s -> ST s (Blocked Term)
+    evalPointerAM (Pure cl)   spine ctrl = runAM (Eval (clApply cl spine) ctrl)
+    evalPointerAM (Pointer p) spine ctrl = readPointer p >>= \ case
+      BlackHole -> __IMPOSSIBLE__
+      Thunk cl@(Closure Unevaled _ _ _) | callByNeed -> do
+        blackHole p
+        runAM (Eval cl $ updateThunkCtrl p $ [ApplyK spine | not (null spine)] ++ ctrl)
+      Thunk cl -> runAM (Eval (clApply cl spine) ctrl)
+
+    -- 'evalIApplyAM spine ctrl fallback' checks if any 'IApply x y r' has a canonical 'r' (i.e. 0 or 1),
+    -- in that case continues evaluating 'x' or 'y' with the rest of 'spine' and same 'ctrl'.
+    -- If no such 'IApply' is found we continue with 'fallback'.
+    evalIApplyAM :: Spine s -> ControlStack s -> ST s (Blocked Term) -> ST s (Blocked Term)
+    evalIApplyAM es ctrl fallback = go es
+      where
+        -- written as a worker/wrapper to possibly trigger some
+        -- specialization wrt fallback
+        go []                  = fallback
+        go (IApply x y r : es) = do
+          br <- evalPointerAM r [] []
+          case iview $ ignoreBlocking br of
+            IZero -> evalPointerAM x es ctrl
+            IOne  -> evalPointerAM y es ctrl
+            _     -> (<* br) <$> go es
+        go (e : es) = go es
+
+    -- Normalise the spine and apply the closure to the result. The closure must be a value closure.
+    normaliseArgsAM :: Closure s -> Spine s -> ControlStack s -> ST s (Blocked Term)
+    normaliseArgsAM cl []    ctrl = runAM (Eval cl ctrl)  -- nothing to do
+    normaliseArgsAM cl spine ctrl =
+      case firstHole spine of -- v Only projections, nothing to do. Note clApply_ and not clApply (or we'd loop)
+        Nothing       -> runAM (Eval (clApply_ cl spine) ctrl)
+        Just (p, cxt) -> evalPointerAM p [] (NormaliseK : ArgK cl cxt : ctrl)
+
+    -- Fall back to slow reduction. This happens if we encounter a definition that's not supported
+    -- by the machine (like a primitive function that does not work on literals), or a term that is
+    -- not supported (Level and Sort at the moment). In this case we decode the current
+    -- focus to a 'Term', call slow reduction and pack up the result in a value closure. If the top
+    -- of the control stack is a 'NormaliseK' and the focus is a value closure (i.e. already in
+    -- weak-head normal form) we call 'slowNormaliseArgs' and pop the 'NormaliseK' frame. Otherwise
+    -- we use 'slowReduceTerm' to compute a weak-head normal form.
+    fallbackAM :: AM s -> ST s (Blocked Term)
+    fallbackAM (Eval c ctrl) = do
+        v <- decodeClosure_ c
+        runAM (mkValue $ runReduce $ slow v)
+      where mkValue b = evalValue (() <$ b) (ignoreBlocking b) emptyEnv [] ctrl'
+            (slow, ctrl') = case ctrl of
+              NormaliseK : ctrl'
+                | Value{} <- isValue c -> (notBlocked <.> slowNormaliseArgs, ctrl')
+              _                        -> (slowReduceTerm, ctrl)
+    fallbackAM _ = __IMPOSSIBLE__
+
+    -- Applying rewrite rules to the current focus. This needs to decode the current focus, call
+    -- rewriting and pack the result back up in a closure. In case some rewrite rules actually fired
+    -- the next state is an unevaluated closure, otherwise it's a value closure.
+    rewriteAM :: AM s -> ST s (Blocked Term)
+    rewriteAM s@(Eval (Closure (Value blk) t env spine) ctrl)
+      | null rewr = runAM s
+      | otherwise = traceDoc ("R" <+> pretty s) $ do
+        v0 <- decodeClosure_ (Closure Unevaled t env [])
+        es <- decodeSpine spine
+        case runReduce (rewrite blk (applyE v0) rewr es) of
+          NoReduction b    -> runAM (evalValue (() <$ b) (ignoreBlocking b) emptyEnv [] ctrl)
+          YesReduction _ v -> runAM (evalClosure v emptyEnv [] ctrl)
+      where rewr = case t of
+                     Def f []   -> rewriteRules f
+                     Con c _ [] -> rewriteRules (conName c)
+                     _          -> __IMPOSSIBLE__
+    rewriteAM _ =
+      __IMPOSSIBLE__
+
+    -- Add a NatSucK frame to the control stack. Pack consecutive suc's into a single frame.
+    sucCtrl :: ControlStack s -> ControlStack s
+    sucCtrl (NatSucK !n : ctrl) = NatSucK (n + 1) : ctrl
+    sucCtrl               ctrl  = NatSucK 1 : ctrl
+
+    -- Add a UpdateThunk frame to the control stack. Pack consecutive updates into a single frame.
+    updateThunkCtrl :: STPointer s -> ControlStack s -> ControlStack s
+    updateThunkCtrl p (UpdateThunk ps : ctrl) = UpdateThunk (p : ps) : ctrl
+    updateThunkCtrl p                   ctrl  = UpdateThunk [p] : ctrl
+
+    -- When matching is stuck we return the closure from the 'MatchStack' with the appropriate
+    -- 'IsValue' set.
+    stuckMatch :: Blocked_ -> MatchStack s -> ControlStack s -> ST s (Blocked Term)
+    stuckMatch blk (_ :> cl) ctrl = rewriteAM (Eval (mkValue blk cl) ctrl)
+
+    -- On a mismatch we find the next 'CatchAll' on the control stack and
+    -- continue matching from there. If there isn't one we get an incomplete
+    -- matching error (or get stuck if the function is marked partial).
+    failedMatch :: QName -> MatchStack s -> ControlStack s -> ST s (Blocked Term)
+    failedMatch f (CatchAll cc spine : stack :> cl) ctrl = runAM (Match f cc spine (stack :> cl) ctrl)
+    failedMatch f ([] :> cl) ctrl
+        -- Bad work-around for #3870: don't fail hard during instance search.
+      | speculative          = rewriteAM (Eval (mkValue (NotBlocked (MissingClauses f) ()) cl) ctrl)
+      | f `elem` partialDefs = rewriteAM (Eval (mkValue (NotBlocked (MissingClauses f) ()) cl) ctrl)
+      | otherwise            = rewriteAM (Eval (mkValue (NotBlocked ReallyNotBlocked ()) cl) ctrl)  -- See #5396
+
+    -- Some helper functions to build machine states and closures.
+    evalClosure t env spine = Eval (Closure Unevaled t env spine)
+    evalValue b t env spine = Eval (Closure (Value b) t env spine)
+    evalTrueValue           = evalValue $ notBlocked ()
+    trueValue t env spine   = Closure (Value $ notBlocked ()) t env spine
+    mkValue b               = setIsValue (Value b)
+
+    -- Building lambdas
+    lams :: [Arg String] -> Term -> Term
+    lams xs t = foldr lam t xs
+
+    lam :: Arg String -> Term -> Term
+    lam x t = Lam (argInfo x) (Abs (unArg x) t)
+
+-- Pretty printing --------------------------------------------------------
+
+instance Pretty a => Pretty (FastCase a) where
+  prettyPrec p (FBranches _cop cs suc ls m _) =
+    mparens (p > 0) $ vcat (prettyMap_ cs ++ prettyMap_ ls ++ prSuc suc ++ prC m)
+    where
+      prC Nothing = []
+      prC (Just x) = ["_ ->" <?> pretty x]
+
+      prSuc Nothing  = []
+      prSuc (Just x) = ["suc ->" <?> pretty x]
+
+instance Pretty FastCompiledClauses where
+  pretty (FDone xs t) = ("done" <+> prettyList xs) <?> prettyPrec 10 t
+  pretty FFail        = "fail"
+  pretty (FEta n _ cc ca) =
+    text ("eta " ++ show n ++ " of") <?>
+      vcat ("{} ->" <?> pretty cc :
+            [ "_ ->" <?> pretty cc | Just cc <- [ca] ])
+  pretty (FCase n bs) | fprojPatterns bs =
+    sep [ text $ "project " ++ show n
+        , nest 2 $ pretty bs
+        ]
+  pretty (FCase n bs) =
+    text ("case " ++ show n ++ " of") <?> pretty bs
+
+instance Pretty a => Pretty (Thunk a) where
+  prettyPrec _ BlackHole  = "<BLACKHOLE>"
+  prettyPrec p (Thunk cl) = prettyPrec p cl
+
+instance Pretty (Pointer s) where
+  prettyPrec p = prettyPrec p . unsafeDerefPointer
+
+instance Pretty (Closure s) where
+  prettyPrec _ (Closure Value{} (Lit (LitString unused)) _ _)
+    | unused == unusedPointerString = "_"
+  prettyPrec p (Closure isV t env spine) =
+    mparens (p > 9) $ fsep [ text tag
+                           , nest 2 $ prettyPrec 10 t
+                           , nest 2 $ prettyList $ zipWith envEntry [0..] (envToList env)
+                           , nest 2 $ prettyList spine ]
+      where envEntry i c = text ("@" ++ show i ++ " =") <+> pretty c
+            tag = case isV of Value{} -> "V"; Unevaled -> "E"
+
+instance Pretty (AM s) where
+  prettyPrec p (Eval cl ctrl)  = prettyPrec p cl <?> prettyList ctrl
+  prettyPrec p (Match f cc sp stack ctrl) =
+    mparens (p > 9) $ sep [ "M" <+> pretty f
+                          , nest 2 $ prettyList sp
+                          , nest 2 $ prettyPrec 10 cc
+                          , nest 2 $ pretty stack
+                          , nest 2 $ prettyList ctrl ]
+
+instance Pretty (CatchAllFrame s) where
+  pretty CatchAll{} = "CatchAll"
+
+instance Pretty (MatchStack s) where
+  pretty ([] :> _) = empty
+  pretty (ca :> _) = prettyList ca
+
+instance Pretty (ControlFrame s) where
+  prettyPrec p (CaseK f _ _ _ _ mc)       = mparens (p > 9) $ ("CaseK" <+> pretty (qnameName f)) <?> pretty mc
+  prettyPrec p (ForceK _ spine0 spine1)   = mparens (p > 9) $ "ForceK" <?> prettyList (spine0 <> spine1)
+  prettyPrec p (EraseK _ sp0 sp1 sp2 sp3) = mparens (p > 9) $ sep [ "EraseK"
+                                                                  , nest 2 $ prettyList sp0
+                                                                  , nest 2 $ prettyList sp1
+                                                                  , nest 2 $ prettyList sp2
+                                                                  , nest 2 $ prettyList sp3 ]
+  prettyPrec _ (NatSucK n)              = text ("+" ++ show n)
+  prettyPrec p (PrimOpK f _ vs cls _)   = mparens (p > 9) $ sep [ "PrimOpK" <+> pretty f
+                                                                , nest 2 $ prettyList vs
+                                                                , nest 2 $ prettyList cls ]
+  prettyPrec p (UpdateThunk ps)         = mparens (p > 9) $ "UpdateThunk" <+> text (show (length ps))
+  prettyPrec p (ApplyK spine)           = mparens (p > 9) $ "ApplyK" <?> prettyList spine
+  prettyPrec p NormaliseK               = "NormaliseK"
+  prettyPrec p (ArgK cl _)              = mparens (p > 9) $ sep [ "ArgK" <+> prettyPrec 10 cl ]
diff --git a/src/full/Agda/TypeChecking/Reduce/Fast.hs-boot b/src/full/Agda/TypeChecking/Reduce/Fast.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Reduce/Fast.hs-boot
@@ -0,0 +1,10 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Reduce.Fast where
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+
+fastReduce    :: Term -> ReduceM (Blocked Term)
+fastNormalise :: Term -> ReduceM Term
+
diff --git a/src/full/Agda/TypeChecking/Reduce/Monad.hs b/src/full/Agda/TypeChecking/Reduce/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Reduce/Monad.hs
@@ -0,0 +1,110 @@
+{-# LANGUAGE CPP #-}
+{-# OPTIONS_GHC -Wunused-imports #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.TypeChecking.Reduce.Monad
+  ( constructorForm
+  , enterClosure
+  , getConstInfo
+  , askR, applyWhenVerboseS
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad         ( liftM2 )
+
+import qualified Data.Map as Map
+import Data.Maybe
+
+import System.IO.Unsafe
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad hiding (enterClosure, constructorForm)
+import Agda.TypeChecking.Substitute
+
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+#ifdef DEBUG
+import Agda.Utils.Monad
+#endif
+import Agda.Syntax.Common.Pretty () --instance only
+
+
+instance HasBuiltins ReduceM where
+  getBuiltinThing b =
+    liftM2 (unionMaybeWith unionBuiltin)
+      (Map.lookup b <$> useR stLocalBuiltins)
+      (Map.lookup b <$> useR stImportedBuiltins)
+
+constructorForm :: HasBuiltins m => Term -> m Term
+constructorForm v = do
+  mz <- getBuiltin' builtinZero
+  ms <- getBuiltin' builtinSuc
+  return $ fromMaybe v $ constructorForm' mz ms v
+
+enterClosure :: LensClosure c a => c -> (a -> ReduceM b) -> ReduceM b
+enterClosure c | Closure _sig env scope cps x <- c ^. lensClosure = \case
+  -- The \case is a hack to correctly associate the where block to the rhs
+  -- rather than to the expression in the pattern guard.
+  f -> localR (mapRedEnvSt inEnv inState) (f x)
+    where
+    inEnv   e = env
+    inState s =
+      -- TODO: use the signature here? would that fix parts of issue 118?
+      set stScope scope $ set stModuleCheckpoints cps s
+
+withFreshR :: (ReadTCState m, HasFresh i) => (i -> m a) -> m a
+withFreshR f = do
+  s <- getTCState
+  let (i, s') = nextFresh s
+  withTCState (const s') (f i)
+
+instance MonadAddContext ReduceM where
+  withFreshName r s k = withFreshR $ \i -> k (mkName r i s)
+
+  addCtx = defaultAddCtx
+
+  addLetBinding' = defaultAddLetBinding'
+
+  updateContext rho f ret = withFreshR $ \ chkpt ->
+    localTC (\e -> e { envContext = f $ envContext e
+                     , envCurrentCheckpoint = chkpt
+                     , envCheckpoints = Map.insert chkpt IdS $
+                                          fmap (applySubst rho) (envCheckpoints e)
+                     }) ret
+        -- let-bindings keep track of own their context
+
+instance MonadDebug ReduceM where
+
+  traceDebugMessage k n s cont = do
+    ReduceEnv env st _ <- askR
+    unsafePerformIO $ do
+      _ <- runTCM env st $ displayDebugMessage k n s
+      return $ cont
+
+  formatDebugMessage k n d = do
+    ReduceEnv env st _ <- askR
+    unsafePerformIO $ do
+      (s , _) <- runTCM env st $ formatDebugMessage k n d
+      return $ return s
+
+#ifdef DEBUG
+  verboseBracket k n s = applyWhenVerboseS k n $
+    bracket_ (openVerboseBracket k n s) (const $ closeVerboseBracket k n)
+#else
+  verboseBracket k n s ma = ma
+  {-# INLINE verboseBracket #-}
+#endif
+
+  getVerbosity      = defaultGetVerbosity
+  getProfileOptions = defaultGetProfileOptions
+  isDebugPrinting   = defaultIsDebugPrinting
+  nowDebugPrinting  = defaultNowDebugPrinting
+
+instance HasConstInfo ReduceM where
+  getRewriteRulesFor = defaultGetRewriteRulesFor
+  getConstInfo' q = do
+    ReduceEnv env st _ <- askR
+    defaultGetConstInfo st env q
+
+instance PureTCM ReduceM where
diff --git a/src/full/Agda/TypeChecking/Rewriting.hs b/src/full/Agda/TypeChecking/Rewriting.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting.hs
@@ -0,0 +1,451 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+{-# LANGUAGE GADTs #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-- | Rewriting with arbitrary rules.
+--
+--   The user specifies a relation symbol by the pragma
+--   @
+--       {-\# BUILTIN REWRITE rel \#-}
+--   @
+--   where @rel@ should be of type @Δ → (lhs rhs : A) → Set i@.
+--
+--   Then the user can add rewrite rules by the pragma
+--   @
+--       {-\# REWRITE q \#-}
+--   @
+--   where @q@ should be a closed term of type @Γ → rel us lhs rhs@.
+--
+--   We then intend to add a rewrite rule
+--   @
+--       Γ ⊢ lhs ↦ rhs : B
+--   @
+--   to the signature where @B = A[us/Δ]@.
+--
+--   To this end, we normalize @lhs@, which should be of the form
+--   @
+--       f ts
+--   @
+--   for a @'Def'@-symbol f (postulate, function, data, record, constructor).
+--   Further, @FV(ts) = dom(Γ)@.
+--   The rule @q :: Γ ⊢ f ts ↦ rhs : B@ is added to the signature
+--   to the definition of @f@.
+--
+--   When reducing a term @Ψ ⊢ f vs@ is stuck, we try the rewrites for @f@,
+--   by trying to unify @vs@ with @ts@.
+--   This is for now done by substituting fresh metas Xs for the bound
+--   variables in @ts@ and checking equality with @vs@
+--   @
+--       Ψ ⊢ (f ts)[Xs/Γ] = f vs : B[Xs/Γ]
+--   @
+--   If successful (no open metas/constraints), we replace @f vs@ by
+--   @rhs[Xs/Γ]@ and continue reducing.
+
+module Agda.TypeChecking.Rewriting where
+
+import Prelude hiding (null)
+
+import Control.Monad
+
+import Data.Foldable (toList)
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Abstract.Name
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Conversion
+import qualified Agda.TypeChecking.Positivity.Occurrence as Pos
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Rewriting.Confluence
+import Agda.TypeChecking.Rewriting.NonLinMatch
+import Agda.TypeChecking.Rewriting.NonLinPattern
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Size
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+import Agda.Utils.Either
+
+requireOptionRewriting :: TCM ()
+requireOptionRewriting =
+  unlessM (optRewriting <$> pragmaOptions) $ typeError NeedOptionRewriting
+
+-- | Check that the name given to the BUILTIN REWRITE is actually
+--   a relation symbol.
+--   I.e., its type should be of the form @Δ → (lhs : A) (rhs : B) → Set ℓ@.
+--   Note: we do not care about hiding/non-hiding of lhs and rhs.
+verifyBuiltinRewrite :: Term -> Type -> TCM ()
+verifyBuiltinRewrite v t = do
+  requireOptionRewriting
+  caseMaybeM (relView t)
+    (typeError $ IncorrectTypeForRewriteRelation v ShouldAcceptAtLeastTwoArguments) $
+    \ (RelView tel delta a b core) -> do
+    unless (visible a && visible b) $ typeError $ IncorrectTypeForRewriteRelation v FinalTwoArgumentsNotVisible
+    case unEl core of
+      Sort{}   -> return ()
+      Con{}    -> __IMPOSSIBLE__
+      Level{}  -> __IMPOSSIBLE__
+      Lam{}    -> __IMPOSSIBLE__
+      Pi{}     -> __IMPOSSIBLE__
+      _ -> typeError $ IncorrectTypeForRewriteRelation v (TypeDoesNotEndInSort core tel)
+
+-- | Deconstructing a type into @Δ → t → t' → core@.
+data RelView = RelView
+  { relViewTel   :: Telescope  -- ^ The whole telescope @Δ, t, t'@.
+  , relViewDelta :: ListTel    -- ^ @Δ@.
+  , relViewType  :: Dom Type   -- ^ @t@.
+  , relViewType' :: Dom Type   -- ^ @t'@.
+  , relViewCore  :: Type       -- ^ @core@.
+  }
+
+-- | Deconstructing a type into @Δ → t → t' → core@.
+--   Returns @Nothing@ if not enough argument types.
+relView :: Type -> TCM (Maybe RelView)
+relView t = do
+  TelV tel core <- telView t
+  let n                = size tel
+      (delta, lastTwo) = splitAt (n - 2) $ telToList tel
+  if size lastTwo < 2 then return Nothing else do
+    let [a, b] = fmap snd <$> lastTwo
+    return $ Just $ RelView tel delta a b core
+
+-- | Check the given rewrite rules and add them to the signature.
+addRewriteRules :: [QName] -> TCM ()
+addRewriteRules qs = do
+
+  -- Check the rewrite rules
+  rews <- mapM checkRewriteRule qs
+
+  -- Add rewrite rules to the signature
+  forM_ rews $ \rew -> do
+    let f = rewHead rew
+        matchables = getMatchables rew
+    reportSDoc "rewriting" 10 $
+      "adding rule" <+> prettyTCM (rewName rew) <+>
+      "to the definition of" <+> prettyTCM f
+    reportSDoc "rewriting" 30 $ "matchable symbols: " <+> prettyTCM matchables
+    modifySignature $ addRewriteRulesFor f [rew] matchables
+
+  -- Run confluence check for the new rules
+  -- (should be done after adding all rules, see #3795)
+  whenJustM (optConfluenceCheck <$> pragmaOptions) $ \confChk -> do
+    -- Warn if --cubical is enabled
+    whenJustM (optCubical <$> pragmaOptions) $ \_ -> genericWarning
+      "Confluence checking for --cubical is not yet supported, confluence checking might be incomplete"
+    -- Global confluence checker requires rules to be sorted
+    -- according to the generality of their lhs
+    when (confChk == GlobalConfluenceCheck) $
+      forM_ (nubOn id $ map rewHead rews) sortRulesOfSymbol
+    checkConfluenceOfRules confChk rews
+    reportSDoc "rewriting" 10 $
+      "done checking confluence of rules" <+> prettyList_ (map (prettyTCM . rewName) rews)
+
+-- Auxiliary function for checkRewriteRule.
+-- | Get domain of rewrite relation.
+rewriteRelationDom :: QName -> TCM (ListTel, Dom Type)
+rewriteRelationDom rel = do
+  -- We know that the type of rel is that of a relation.
+  relV <- relView =<< do defType <$> getConstInfo rel
+  let RelView _tel delta a _a' _core = fromMaybe __IMPOSSIBLE__ relV
+  reportSDoc "rewriting" 30 $ do
+    "rewrite relation at type " <+> do
+      inTopContext $ prettyTCM (telFromList delta) <+> " |- " <+> do
+        addContext delta $ prettyTCM a
+  return (delta, a)
+
+-- | Check the validity of @q : Γ → rel us lhs rhs@ as rewrite rule
+--   @
+--       Γ ⊢ lhs ↦ rhs : B
+--   @
+--   where @B = A[us/Δ]@.
+--   Remember that @rel : Δ → A → A → Set i@, so
+--   @rel us : (lhs rhs : A[us/Δ]) → Set i@.
+--   Returns the checked rewrite rule to be added to the signature.
+checkRewriteRule :: QName -> TCM RewriteRule
+checkRewriteRule q = do
+  requireOptionRewriting
+  let failNoBuiltin = typeError $ GenericError $
+        "Cannot add rewrite rule without prior BUILTIN REWRITE"
+  rels <- fromMaybeM failNoBuiltin getBuiltinRewriteRelations
+  reportSDoc "rewriting.relations" 40 $ vcat
+    [ "Rewrite relations:"
+    , prettyList $ map prettyTCM $ toList rels
+    ]
+  def <- instantiateDef =<< getConstInfo q
+  -- Issue 1651: Check that we are not adding a rewrite rule
+  -- for a type signature whose body has not been type-checked yet.
+  when (isEmptyFunction $ theDef def) $
+    typeError $ IllegalRewriteRule q BeforeFunctionDefinition
+  -- Get rewrite rule (type of q).
+  TelV gamma1 core <- telView $ defType def
+  reportSDoc "rewriting" 30 $ vcat
+    [ "attempting to add rewrite rule of type "
+    , prettyTCM gamma1
+    , " |- " <+> do addContext gamma1 $ prettyTCM core
+    ]
+  let failureBlocked :: Blocker -> TCM a
+      failureBlocked b
+        | not (null ms) = typeError $ IllegalRewriteRule q (ContainsUnsolvedMetaVariables ms)
+        | not (null ps) = typeError $ IllegalRewriteRule q (BlockedOnProblems ps)
+        | not (null qs) = typeError $ IllegalRewriteRule q (RequiresDefinitions qs)
+        | otherwise = __IMPOSSIBLE__
+        where
+          ms = allBlockingMetas b
+          ps = allBlockingProblems b
+          qs = allBlockingDefs b
+  let failureFreeVars :: IntSet -> TCM a
+      failureFreeVars xs = typeError $ IllegalRewriteRule q (VariablesNotBoundByLHS xs)
+  let failureNonLinearPars :: IntSet -> TCM a
+      failureNonLinearPars xs = typeError $ IllegalRewriteRule q (VariablesBoundMoreThanOnce xs)
+  let failureIllegalRule :: TCM a -- TODO:: Defined but not used
+      failureIllegalRule = typeError $ IllegalRewriteRule q EmptyReason
+
+  -- Check that type of q targets rel.
+  case unEl core of
+    Def rel es@(_:_:_) | rel `elem` rels -> do
+      (delta, a) <- rewriteRelationDom rel
+      -- Because of the type of rel (Γ → sort), all es are applications.
+      let vs = map unArg $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      -- The last two arguments are lhs and rhs.
+          n  = size vs
+          (us, [lhs, rhs]) = splitAt (n - 2) vs
+      unless (size delta == size us) __IMPOSSIBLE__
+      lhs <- instantiateFull lhs
+      rhs <- instantiateFull rhs
+      b   <- instantiateFull $ applySubst (parallelS $ reverse us) a
+
+      gamma0 <- getContextTelescope
+      gamma1 <- instantiateFull gamma1
+      let gamma = gamma0 `abstract` gamma1
+
+      -- 2017-06-18, Jesper: Unfold inlined definitions on the LHS.
+      -- This is necessary to replace copies created by imports by their
+      -- original definition.
+      lhs <- modifyAllowedReductions (const $ SmallSet.singleton InlineReductions) $ reduce lhs
+
+      -- Find head symbol f of the lhs, its type, its parameters (in case of a constructor), and its arguments.
+      (f , hd , t , pars , es) <- case lhs of
+        Def f es -> do
+          def <- getConstInfo f
+          checkAxFunOrCon f def
+          return (f , Def f , defType def , [] , es)
+        Con c ci vs -> do
+          let hd = Con c ci
+          ~(Just ((_ , _ , pars) , t)) <- getFullyAppliedConType c $ unDom b
+          pars <- addContext gamma1 $ checkParametersAreGeneral c pars
+          return (conName c , hd , t , pars , vs)
+        _        -> typeError $ IllegalRewriteRule q LHSNotDefOrConstr
+
+      ifNotAlreadyAdded f $ do
+
+      addContext gamma1 $ do
+
+        checkNoLhsReduction f hd es
+
+        ps <- catchPatternErr failureBlocked $
+          patternFrom Relevant 0 (t , Def f) es
+
+        reportSDoc "rewriting" 30 $
+          "Pattern generated from lhs: " <+> prettyTCM (PDef f ps)
+
+        -- We need to check two properties on the variables used in the rewrite rule
+        -- 1. For actually being able to apply the rewrite rule, we need
+        --    that all variables that occur in the rule (on the left or the right)
+        --    are bound in a pattern position on the left.
+        -- 2. To preserve soundness, we need that all the variables that are used
+        --    in the *proof* of the rewrite rule are bound in the lhs.
+        --    For rewrite rules on constructors, we consider parameters to be bound
+        --    even though they don't appear in the lhs, since they can be reconstructed.
+        --    For postulated or abstract rewrite rules, we consider all arguments
+        --    as 'used' (see #5238).
+        let boundVars = nlPatVars ps
+            freeVars  = allFreeVars (ps,rhs)
+            allVars   = IntSet.fromList $ downFrom $ size gamma
+            usedVars  = case theDef def of
+              Function{}     -> usedArgs def
+              Axiom{}        -> allVars
+              AbstractDefn{} -> allVars
+              _              -> __IMPOSSIBLE__
+        reportSDoc "rewriting" 70 $
+          "variables bound by the pattern: " <+> text (show boundVars)
+        reportSDoc "rewriting" 70 $
+          "variables free in the rewrite rule: " <+> text (show freeVars)
+        reportSDoc "rewriting" 70 $
+          "variables used by the rewrite rule: " <+> text (show usedVars)
+        unlessNull (freeVars IntSet.\\ boundVars) failureFreeVars
+        unlessNull (usedVars IntSet.\\ (boundVars `IntSet.union` IntSet.fromList pars)) failureFreeVars
+
+        reportSDoc "rewriting" 70 $
+          "variables bound in (erased) parameter position: " <+> text (show pars)
+        unlessNull (boundVars `IntSet.intersection` IntSet.fromList pars) failureNonLinearPars
+
+        let rew = RewriteRule q gamma f ps rhs (unDom b) False
+
+        reportSDoc "rewriting" 10 $ vcat
+          [ "checked rewrite rule" , prettyTCM rew ]
+        reportSDoc "rewriting" 90 $ vcat
+          [ "checked rewrite rule" , text (show rew) ]
+
+        return rew
+
+    _ -> typeError $ IllegalRewriteRule q DoesNotTargetRewriteRelation
+
+  where
+    checkNoLhsReduction :: QName -> (Elims -> Term)  -> Elims -> TCM ()
+    checkNoLhsReduction f hd es = do
+      -- Skip this check when global confluence check is enabled, as
+      -- redundant rewrite rules may be required to prove confluence.
+      unlessM ((== Just GlobalConfluenceCheck) . optConfluenceCheck <$> pragmaOptions) $ do
+      let v = hd es
+      v' <- reduce v
+      let fail :: TCM a
+          fail = do
+            reportSDoc "rewriting" 20 $ "v  = " <+> text (show v)
+            reportSDoc "rewriting" 20 $ "v' = " <+> text (show v')
+            typeError $ IllegalRewriteRule q (LHSReducesTo v v')
+      es' <- case v' of
+        Def f' es'   | f == f'         -> return es'
+        Con c' _ es' | f == conName c' -> return es'
+        _                              -> fail
+      unless (null es && null es') $ do
+        a   <- computeElimHeadType f es es'
+        pol <- getPolarity' CmpEq f
+        ok  <- dontAssignMetas $ tryConversion $
+                 compareElims pol [] a (Def f []) es es'
+        unless ok fail
+
+    checkAxFunOrCon :: QName -> Definition -> TCM ()
+    checkAxFunOrCon f def = case theDef def of
+      Axiom{}        -> return ()
+      def@Function{} -> do
+        whenJust (maybeRight (funProjection def)) $ \proj -> case projProper proj of
+          Just{} -> typeError $ IllegalRewriteRule q (HeadSymbolIsProjection f)
+          Nothing -> typeError $ IllegalRewriteRule q (HeadSymbolIsProjectionLikeFunction f)
+        whenM (isJust . optConfluenceCheck <$> pragmaOptions) $ do
+          let simpleClause cl = (patternsToElims (namedClausePats cl) , clauseBody cl)
+          cls <- instantiateFull $ map simpleClause $ funClauses def
+          unless (noMetas cls) $ typeError $ IllegalRewriteRule q (HeadSymbolDefContainsMetas f)
+
+      Constructor{}  -> return ()
+      AbstractDefn{} -> return ()
+      Primitive{}    -> return () -- TODO: is this fine?
+      _              -> typeError $ IllegalRewriteRule q (HeadSymbolNotPostulateFunctionConstructor f)
+
+    ifNotAlreadyAdded :: QName -> TCM RewriteRule -> TCM RewriteRule
+    ifNotAlreadyAdded f cont = do
+      rews <- getRewriteRulesFor f
+      -- check if q is already an added rewrite rule
+      case List.find ((q ==) . rewName) rews of
+        Just rew -> do
+          genericWarning =<< do
+            "Rewrite rule " <+> prettyTCM q <+> " has already been added"
+          return rew
+        Nothing -> cont
+
+    usedArgs :: Definition -> IntSet
+    usedArgs def = IntSet.fromList $ map snd $ usedIxs
+      where
+        occs = defArgOccurrences def
+        allIxs = zip occs $ downFrom $ size occs
+        usedIxs = filter (used . fst) allIxs
+        used Pos.Unused = False
+        used _          = True
+
+    checkParametersAreGeneral :: ConHead -> Args -> TCM [Int]
+    checkParametersAreGeneral c vs = do
+        is <- loop vs
+        unless (fastDistinct is) $ errorNotGeneral
+        return is
+      where
+        loop []       = return []
+        loop (v : vs) = case unArg v of
+          Var i [] -> (i :) <$> loop vs
+          _        -> errorNotGeneral
+
+        errorNotGeneral :: TCM a
+        errorNotGeneral = typeError $ IllegalRewriteRule q (ConstructorParamsNotGeneral c vs)
+
+-- | @rewriteWith t f es rew@ where @f : t@
+--   tries to rewrite @f es@ with @rew@, returning the reduct if successful.
+rewriteWith :: Type
+            -> (Elims -> Term)
+            -> RewriteRule
+            -> Elims
+            -> ReduceM (Either (Blocked Term) Term)
+rewriteWith t hd rew@(RewriteRule q gamma _ ps rhs b isClause) es
+ | isClause = return $ Left $ NotBlocked ReallyNotBlocked $ hd es
+ | otherwise = do
+  traceSDoc "rewriting.rewrite" 50 (sep
+    [ "{ attempting to rewrite term " <+> prettyTCM (hd es)
+    , " having head " <+> prettyTCM (hd []) <+> " of type " <+> prettyTCM t
+    , " with rule " <+> prettyTCM rew
+    ]) $ do
+  traceSDoc "rewriting.rewrite" 90 (sep
+    [ "raw: attempting to rewrite term " <+> (text . show) (hd es)
+    , " having head " <+> (text . show) (hd []) <+> " of type " <+> (text . show) t
+    , " with rule " <+> (text . show) rew
+    ]) $ do
+  result <- nonLinMatch gamma (t,hd) ps es
+  case result of
+    Left block -> traceSDoc "rewriting.rewrite" 50 "}" $
+      return $ Left $ block $> hd es -- TODO: remember reductions
+    Right sub  -> do
+      let v' = applySubst sub rhs
+      traceSDoc "rewriting.rewrite" 50 (sep
+        [ "rewrote " <+> prettyTCM (hd es)
+        , " to " <+> prettyTCM v' <+> "}"
+        ]) $ do
+      return $ Right v'
+
+-- | @rewrite b v rules es@ tries to rewrite @v@ applied to @es@ with the
+--   rewrite rules @rules@. @b@ is the default blocking tag.
+rewrite :: Blocked_ -> (Elims -> Term) -> RewriteRules -> Elims -> ReduceM (Reduced (Blocked Term) Term)
+rewrite block hd rules es = do
+  rewritingAllowed <- optRewriting <$> pragmaOptions
+  if (rewritingAllowed && not (null rules)) then do
+    (_ , t) <- fromMaybe __IMPOSSIBLE__ <$> getTypedHead (hd [])
+    loop block t rules =<< instantiateFull' es -- TODO: remove instantiateFull?
+  else
+    return $ NoReduction (block $> hd es)
+  where
+    loop :: Blocked_ -> Type -> RewriteRules -> Elims -> ReduceM (Reduced (Blocked Term) Term)
+    loop block t [] es =
+      traceSDoc "rewriting.rewrite" 20 (sep
+        [ "failed to rewrite " <+> prettyTCM (hd es)
+        , "blocking tag" <+> text (show block)
+        ]) $ do
+      return $ NoReduction $ block $> hd es
+    loop block t (rew:rews) es
+     | let n = rewArity rew, length es >= n = do
+          let (es1, es2) = List.genericSplitAt n es
+          result <- rewriteWith t hd rew es1
+          case result of
+            Left (Blocked m u)    -> loop (block `mappend` Blocked m ()) t rews es
+            Left (NotBlocked _ _) -> loop block t rews es
+            Right w               -> return $ YesReduction YesSimplification $ w `applyE` es2
+     | otherwise = loop (block `mappend` NotBlocked Underapplied ()) t rews es
+
+    rewArity :: RewriteRule -> Int
+    rewArity = length . rewPats
diff --git a/src/full/Agda/TypeChecking/Rewriting.hs-boot b/src/full/Agda/TypeChecking/Rewriting.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting.hs-boot
@@ -0,0 +1,9 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rewriting where
+
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+
+verifyBuiltinRewrite :: Term -> Type -> TCM ()
+rewrite :: Blocked_ -> (Elims -> Term) -> RewriteRules -> Elims -> ReduceM (Reduced (Blocked Term) Term)
diff --git a/src/full/Agda/TypeChecking/Rewriting/Clause.hs b/src/full/Agda/TypeChecking/Rewriting/Clause.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting/Clause.hs
@@ -0,0 +1,84 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rewriting.Clause where
+
+import Data.Maybe
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty
+
+------------------------------------------------------------------------
+-- * Converting clauses to rewrite rules
+------------------------------------------------------------------------
+
+{-# INLINABLE getClausesAsRewriteRules #-}
+-- | Get all the clauses of a definition and convert them to rewrite
+--   rules.
+getClausesAsRewriteRules :: (HasConstInfo m, MonadFresh NameId m) => QName -> m [RewriteRule]
+getClausesAsRewriteRules f = do
+  cls <- defClauses <$> getConstInfo f
+  forMaybeM (zip [1..] cls) $ \(i,cl) -> do
+    clname <- clauseQName f i
+    return $ clauseToRewriteRule f clname cl
+
+{-# INLINABLE clauseQName #-}
+-- | Generate a sensible name for the given clause
+clauseQName :: (HasConstInfo m, MonadFresh NameId m) => QName -> Int -> m QName
+clauseQName f i = QName (qnameModule f) <$> clauseName (qnameName f) i
+  where
+    clauseName n i = freshName noRange (prettyShow n ++ "-clause" ++ show i)
+
+{-# INLINABLE clauseToRewriteRule #-}
+-- | @clauseToRewriteRule f q cl@ converts the clause @cl@ of the
+--   function @f@ to a rewrite rule with name @q@. Returns @Nothing@
+--   if @clauseBody cl@ is @Nothing@. Precondition: @clauseType cl@ is
+--   not @Nothing@.
+clauseToRewriteRule :: QName -> QName -> Clause -> Maybe RewriteRule
+clauseToRewriteRule f q cl | hasDefP (namedClausePats cl) = Nothing
+clauseToRewriteRule f q cl = clauseBody cl <&> \rhs -> RewriteRule
+  { rewName    = q
+  , rewContext = clauseTel cl
+  , rewHead    = f
+  , rewPats    = toNLPat $ namedClausePats cl
+  , rewRHS     = rhs
+  , rewType    = unArg $ fromMaybe __IMPOSSIBLE__  $ clauseType cl
+  , rewFromClause = True
+  }
+
+class ToNLPat a b where
+  toNLPat :: a -> b
+
+  default toNLPat
+    :: ( ToNLPat a' b', Functor f, a ~ f a', b ~ f b')
+    => a -> b
+  toNLPat = fmap toNLPat
+
+instance ToNLPat a b => ToNLPat [a] [b] where
+instance ToNLPat a b => ToNLPat (Dom a) (Dom b) where
+instance ToNLPat a b => ToNLPat (Elim' a) (Elim' b) where
+instance ToNLPat a b => ToNLPat (Abs a) (Abs b) where
+
+instance ToNLPat (Arg DeBruijnPattern) (Elim' NLPat) where
+  toNLPat (Arg ai p) = case p of
+    VarP _ x        -> app $ PVar (dbPatVarIndex x) []
+    DotP _ u        -> app $ PTerm u
+    ConP c _ ps     -> app $ PDef (conName c) $ toNLPat ps
+    LitP o l        -> app $ PTerm $ Lit l
+    ProjP o f       -> Proj o f
+    IApplyP _ u v x -> IApply (PTerm u) (PTerm v) $ PVar (dbPatVarIndex x) []
+    DefP _ f ps     -> app $ PDef f $ toNLPat ps
+
+    where
+      app = Apply . Arg ai
+
+instance ToNLPat (NamedArg DeBruijnPattern) (Elim' NLPat) where
+  toNLPat = toNLPat . fmap namedThing
diff --git a/src/full/Agda/TypeChecking/Rewriting/Confluence.hs b/src/full/Agda/TypeChecking/Rewriting/Confluence.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting/Confluence.hs
@@ -0,0 +1,938 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE NondecreasingIndentation #-}
+
+-- | Checking local or global confluence of rewrite rules.
+--
+-- For checking LOCAL CONFLUENCE of a given rewrite rule @f ps ↦ v@,
+-- we construct critical pairs involving this as the main rule by
+-- searching for:
+--
+-- 1. *Different* rules @f ps' ↦ v'@ where @ps@ and @ps'@ can be
+--    unified@.
+--
+-- 2. Subpatterns @g qs@ of @ps@ and rewrite rules @g qs' ↦ w@ where
+--    @qs@ and @qs'@ can be unified.
+--
+-- Each of these leads to a *critical pair* @v₁ <-- u --> v₂@, which
+-- should satisfy @v₁ = v₂@.
+--
+-- For checking GLOBAL CONFLUENCE, we check the following two
+-- properties:
+--
+-- 1. For any two left-hand sides of the rewrite rules that overlap
+--    (either at the root position or at a subterm), the most general
+--    unifier of the two left-hand sides is again a left-hand side of
+--    a rewrite rule. For example, if there are two rules @suc m + n =
+--    suc (m + n)@ and @m + suc n = suc (m + n)@, then there should
+--    also be a rule @suc m + suc n = suc (suc (m + n))@.
+--
+-- 2. Each rewrite rule should satisfy the *triangle property*: For
+--    any rewrite rule @u = w@ and any single-step parallel unfolding
+--    @u => v@, we should have another single-step parallel unfolding
+--    @v => w@.
+
+
+module Agda.TypeChecking.Rewriting.Confluence
+  ( checkConfluenceOfRules
+  , checkConfluenceOfClauses
+  , sortRulesOfSymbol
+  ) where
+
+import Control.Applicative
+import Control.Arrow ((***))
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Reader
+
+import Data.Either
+import Data.Function ( on )
+import Data.Functor ( ($>) )
+import qualified Data.HashMap.Strict as HMap
+import Data.List ( elemIndex , tails )
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options ( ConfluenceCheck(..) )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Conversion.Pure
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Irrelevance ( isIrrelevantOrPropM )
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Pretty.Warning    ()
+import Agda.TypeChecking.Pretty.Constraint
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Rewriting.Clause
+import Agda.TypeChecking.Rewriting.NonLinMatch
+import Agda.TypeChecking.Rewriting.NonLinPattern
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.ListT
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null (unlessNullM)
+import Agda.Utils.Permutation
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+-- ^ Check confluence of the clauses of the given function wrt rewrite rules of the
+-- constructors they match against
+checkConfluenceOfClauses :: ConfluenceCheck -> QName -> TCM ()
+checkConfluenceOfClauses confChk f = do
+  rews <- getClausesAsRewriteRules f
+  let noMetasInPats rew
+        | noMetas (rewPats rew) = return True
+        | otherwise             = do
+            genericWarning =<< do
+              text "Confluence checking incomplete because the definition of" <+>
+                prettyTCM f <+> text "contains unsolved metavariables."
+            return False
+  rews <- filterM noMetasInPats rews
+  let matchables = map getMatchables rews
+  reportSDoc "rewriting.confluence" 30 $
+    "Function" <+> prettyTCM f <+> "has matchable symbols" <+> prettyList_ (map prettyTCM matchables)
+  modifySignature $ setMatchableSymbols f $ concat matchables
+  let hasRules g = not . null <$> getRewriteRulesFor g
+  forM_ (zip rews matchables) $ \(rew,ms) ->
+    unlessNullM (filterM hasRules ms) $ \_ -> do
+      checkConfluenceOfRules confChk [rew]
+
+-- ^ Check confluence of the given rewrite rules wrt all other rewrite
+--   rules (also amongst themselves).
+checkConfluenceOfRules :: ConfluenceCheck -> [RewriteRule] -> TCM ()
+checkConfluenceOfRules confChk rews = inTopContext $ inAbstractMode $ do
+
+  -- Global confluence: we need to check the triangle property for each rewrite
+  -- rule of each head symbol as well as rules that match on them
+  when (confChk == GlobalConfluenceCheck) $ do
+    let getSymbols rew = let f = rewHead rew in
+         (Set.insert f) . defMatchable <$> getConstInfo f
+    allSymbols <- Set.toList . Set.unions <$> traverse getSymbols rews
+    forM_ allSymbols $ \f -> do
+      rewsf <- getAllRulesFor f
+      forM_ rewsf $ \rew -> do
+        reportSDoc "rewriting.confluence.triangle" 10 $
+          "(re)checking triangle property for rule" <+> prettyTCM (rewName rew)
+        checkTrianglePropertyForRule rew
+
+  forM_ (tails rews) $ listCase (return ()) $ \rew rewsRest -> do
+
+  reportSDoc "rewriting.confluence" 10 $
+    "Checking confluence of rule" <+> prettyTCM (rewName rew)
+  reportSDoc "rewriting.confluence" 30 $
+    "Checking confluence of rule" <+> prettyTCM rew
+
+  let f   = rewHead rew
+      qs  = rewPats rew
+      tel = rewContext rew
+  def <- getConstInfo f
+  (fa , hdf) <- addContext tel $ makeHead def (rewType rew)
+
+  reportSDoc "rewriting.confluence" 30 $ addContext tel $
+    "Head symbol" <+> prettyTCM (hdf []) <+> "of rewrite rule has type" <+> prettyTCM fa
+
+  -- Step 1: check other rewrite rules that overlap at top position
+  forMM_ (getAllRulesFor f) $ \ rew' -> do
+    unless (any (sameRuleName rew') (rew:rewsRest) ||
+            (rewFromClause rew && rewFromClause rew')) $
+      checkConfluenceTop hdf rew rew'
+  reportSDoc "rewriting.confluence" 30 $ "Finished step 1 of confluence check of rule" <+> prettyTCM (rewName rew)
+
+  -- Step 2: check other rewrite rules that overlap with a subpattern
+  -- of this rewrite rule
+  es <- nlPatToTerm qs
+  forMM_ (addContext tel $ allHolesList (fa, hdf) es) $ \ hole -> do
+    let g   = ohHeadName hole
+        hdg = ohHead hole
+    reportSDoc "rewriting.confluence" 40 $
+      "Found hole with head symbol" <+> prettyTCM g
+    rews' <- getAllRulesFor g
+    forM_ rews' $ \rew' -> do
+      unless (any (sameRuleName rew') rewsRest) $
+        checkConfluenceSub hdf hdg rew rew' hole
+  reportSDoc "rewriting.confluence" 30 $ "Finished step 2 of confluence check of rule" <+> prettyTCM (rewName rew)
+
+  -- Step 3: check other rewrite rules that have a subpattern which
+  -- overlaps with this rewrite rule
+  forM_ (defMatchable def) $ \ g -> do
+    reportSDoc "rewriting.confluence" 40 $
+      "Symbol" <+> prettyTCM g <+> "has rules that match on" <+> prettyTCM f
+    forMM_ (getAllRulesFor g) $ \ rew' -> do
+      unless (any (sameRuleName rew') rewsRest) $ do
+        es' <- nlPatToTerm (rewPats rew')
+        let tel' = rewContext rew'
+        def' <- getConstInfo g
+        (ga , hdg) <- addContext tel' $ makeHead def' (rewType rew')
+        forMM_ (addContext tel' $ allHolesList (ga , hdg) es') $ \ hole -> do
+          let f' = ohHeadName hole
+          when (f == f') $ checkConfluenceSub hdg hdf rew' rew hole
+  reportSDoc "rewriting.confluence" 30 $ "Finished step 3 of confluence check of rule" <+> prettyTCM (rewName rew)
+
+  where
+
+    -- Check confluence of two rewrite rules that have the same head symbol,
+    -- e.g. @f ps --> a@ and @f ps' --> b@.
+    checkConfluenceTop :: (Elims -> Term) -> RewriteRule -> RewriteRule -> TCM ()
+    checkConfluenceTop hd rew1 rew2 =
+      traceCall (CheckConfluence (rewName rew1) (rewName rew2)) $
+      localTCStateSavingWarnings $ do
+
+        sub1 <- makeMetaSubst $ rewContext rew1
+        sub2 <- makeMetaSubst $ rewContext rew2
+
+        let f    = rewHead rew1 -- == rewHead rew2
+            a1   = applySubst sub1 $ rewType rew1
+            a2   = applySubst sub2 $ rewType rew2
+
+        es1 <- applySubst sub1 <$> nlPatToTerm (rewPats rew1)
+        es2 <- applySubst sub2 <$> nlPatToTerm (rewPats rew2)
+
+        reportSDoc "rewriting.confluence" 30 $ vcat
+          [ "checkConfluenceTop" <+> prettyTCM (rewName rew1) <+> prettyTCM (rewName rew2)
+          , "  f    = " <+> prettyTCM f
+          , "  ctx1 = " <+> prettyTCM (rewContext rew1)
+          , "  ctx2 = " <+> prettyTCM (rewContext rew2)
+          , "  es1  = " <+> prettyTCM es1
+          , "  es2  = " <+> prettyTCM es2
+          ]
+
+        -- Make sure we are comparing eliminations with the same arity
+        -- (see #3810).
+        let n = min (size es1) (size es2)
+            (es1' , es1r) = splitAt n es1
+            (es2' , es2r) = splitAt n es2
+            esr           = es1r ++ es2r
+
+            lhs1 = hd $ es1' ++ esr
+            lhs2 = hd $ es2' ++ esr
+
+            -- Use type of rewrite rule with the most eliminations
+            a | null es1r = a2
+              | otherwise = a1
+
+        reportSDoc "rewriting.confluence" 20 $ sep
+          [ "Considering potential critical pair at top-level: "
+          , nest 2 $ prettyTCM $ lhs1, " =?= "
+          , nest 2 $ prettyTCM $ lhs2 , " : " , nest 2 $ prettyTCM a
+          ]
+
+        maybeCriticalPair <- tryUnification lhs1 lhs2 $ do
+          -- Unify the left-hand sides of both rewrite rules
+          fa   <- defType <$> getConstInfo f
+          fpol <- getPolarity' CmpEq f
+          onlyReduceTypes $
+            compareElims fpol [] fa (hd []) es1' es2'
+
+          -- Get the rhs of both rewrite rules (after unification). In
+          -- case of different arities, add additional arguments from
+          -- one side to the other side.
+          let rhs1 = applySubst sub1 (rewRHS rew1) `applyE` es2r
+              rhs2 = applySubst sub2 (rewRHS rew2) `applyE` es1r
+
+          return (rhs1 , rhs2)
+
+        whenJust maybeCriticalPair $ uncurry (checkCriticalPair a hd (es1' ++ esr))
+
+    -- Check confluence between two rules that overlap at a subpattern,
+    -- e.g. @f ps[g qs] --> a@ and @g qs' --> b@.
+    checkConfluenceSub :: (Elims -> Term) -> (Elims -> Term) -> RewriteRule -> RewriteRule -> OneHole Elims -> TCM ()
+    checkConfluenceSub hdf hdg rew1 rew2 hole0 = do
+      reportSDoc "rewriting.confluence" 100 $ "foo 2" <+> prettyTCM (rewName rew1) <+> prettyTCM (rewName rew2)
+      traceCall (CheckConfluence (rewName rew1) (rewName rew2)) $ localTCStateSavingWarnings $ do
+
+        reportSDoc "rewriting.confluence" 20 $
+          "Checking confluence of rules" <+> prettyTCM (rewName rew1) <+>
+          "and" <+> prettyTCM (rewName rew2) <+> "at subpattern position"
+
+        sub1 <- makeMetaSubst $ rewContext rew1
+
+        let bvTel0     = ohBoundVars hole0
+            k          = size bvTel0
+            b0         = applySubst (liftS k sub1) $ ohType hole0
+            g          = ohHeadName hole0
+            es0        = applySubst (liftS k sub1) $ ohElims hole0
+            qs2        = rewPats rew2
+
+        -- TODO: support IApply in forceEtaExpansion
+        let isIApply IApply{} = True
+            isIApply _        = False
+        unless (any isIApply $ drop (size es0) qs2) $ do
+
+        -- If the second rewrite rule has more eliminations than the
+        -- subpattern of the first rule, the only chance of overlap is
+        -- by eta-expanding the subpattern of the first rule.
+        hole1 <- addContext bvTel0 $
+          forceEtaExpansion b0 (hdg es0) $ drop (size es0) qs2
+
+        verboseS "rewriting.confluence.eta" 30 $
+          unless (size es0 == size qs2) $
+          addContext bvTel0 $
+          reportSDoc "rewriting.confluence.eta" 30 $ vcat
+            [ "forceEtaExpansion result:"
+            , nest 2 $ "bound vars: " <+> prettyTCM (ohBoundVars hole1)
+            , nest 2 $ "hole contents: " <+> addContext (ohBoundVars hole1) (prettyTCM $ ohContents hole1)
+            ]
+
+        let hole      = hole1 `composeHole` hole0
+            g         = ohHeadName hole -- == rewHead rew2
+            es'       = ohElims hole
+            bvTel     = ohBoundVars hole
+            plug      = ohPlugHole hole
+
+        sub2 <- addContext bvTel $ makeMetaSubst $ rewContext rew2
+
+        let es1 = applySubst (liftS (size bvTel) sub1) es'
+        es2 <- applySubst sub2 <$> nlPatToTerm (rewPats rew2)
+
+        -- Make sure we are comparing eliminations with the same arity
+        -- (see #3810). Because we forced eta-expansion of es1, we
+        -- know that it is at least as long as es2.
+        when (size es1 < size es2) __IMPOSSIBLE__
+        let n = size es2
+            (es1' , es1r) = splitAt n es1
+
+        let lhs1 = applySubst sub1 $ hdf $ plug $ hdg es1
+            lhs2 = applySubst sub1 $ hdf $ plug $ hdg $ es2 ++ es1r
+            a    = applySubst sub1 $ rewType rew1
+
+        reportSDoc "rewriting.confluence" 20 $ sep
+          [ "Considering potential critical pair at subpattern: "
+          , nest 2 $ prettyTCM $ lhs1 , " =?= "
+          , nest 2 $ prettyTCM $ lhs2 , " : " , nest 2 $ prettyTCM a
+          ]
+
+        maybeCriticalPair <- tryUnification lhs1 lhs2 $ do
+          -- Unify the subpattern of the first rewrite rule with the lhs
+          -- of the second one
+          ga   <- defType <$> getConstInfo g
+          gpol <- getPolarity' CmpEq g
+          onlyReduceTypes $ addContext bvTel $
+            compareElims gpol [] ga (hdg []) es1' es2
+
+          -- Right-hand side of first rewrite rule (after unification)
+          let rhs1 = applySubst sub1 $ rewRHS rew1
+
+          -- Left-hand side of first rewrite rule, with subpattern
+          -- rewritten by the second rewrite rule
+          let w = applySubst sub2 (rewRHS rew2) `applyE` es1r
+          reportSDoc "rewriting.confluence" 30 $ sep
+            [ "Plugging hole with w = "
+            , nest 2 $ addContext bvTel $ prettyTCM w
+            ]
+          let rhs2 = applySubst sub1 $ hdf $ plug w
+
+          return (rhs1 , rhs2)
+
+        whenJust maybeCriticalPair $ uncurry (checkCriticalPair a hdf (applySubst sub1 $ plug $ hdg es1))
+
+    checkCriticalPair
+      :: Type     -- Type of the critical pair
+      -> (Elims -> Term)  -- Head of lhs
+      -> Elims            -- Eliminations of lhs
+      -> Term     -- First reduct
+      -> Term     -- Second reduct
+      -> TCM ()
+    checkCriticalPair a hd es rhs1 rhs2 = do
+
+      (a,es,rhs1,rhs2) <- instantiateFull (a,es,rhs1,rhs2)
+
+      let ms = Set.toList $ allMetas singleton $ (a,es,rhs1,rhs2)
+
+      reportSDoc "rewriting.confluence" 30 $ sep
+        [ "Abstracting over metas: "
+        , prettyList_ (map (text . show) ms)
+        ]
+      (gamma , (a,es,rhs1,rhs2)) <- fromMaybe __IMPOSSIBLE__ <$>
+        abstractOverMetas ms (a,es,rhs1,rhs2)
+
+      addContext gamma $ reportSDoc "rewriting.confluence" 10 $ sep
+        [ "Found critical pair: "
+        , nest 2 $ prettyTCM (hd es)
+        , " ---> " , nest 2 $ prettyTCM rhs1
+        , " =?= " , nest 2 $ prettyTCM rhs2
+        , " : " , nest 2 $ prettyTCM a ]
+      reportSDoc "rewriting.confluence" 30 $ do
+        gamma <- instantiateFull gamma
+        sep [ "Context of critical pair: "
+            , nest 2 $ prettyTCM gamma ]
+
+      addContext gamma $ case confChk of
+
+        -- Local confluence check: check that critical pair has a
+        -- common reduct.
+        LocalConfluenceCheck -> do
+            dontAssignMetas $ noConstraints $ equalTerm a rhs1 rhs2
+          `catchError` \case
+            TypeError _ s err -> do
+              prettyErr <- withTCState (const s) $ prettyTCM err
+              warning $ RewriteNonConfluent (hd es) rhs1 rhs2 prettyErr
+            err           -> throwError err
+
+        -- Global confluence check: enforce that MGU is again the LHS
+        -- of a rewrite rule (actual global confluence then follows
+        -- from the triangle property which was checked before).
+        GlobalConfluenceCheck -> do
+          (f, t) <- fromMaybe __IMPOSSIBLE__ <$> getTypedHead (hd [])
+
+          let checkEqualLHS :: RewriteRule -> TCM Bool
+              checkEqualLHS (RewriteRule q delta _ ps _ _ _) = do
+                onlyReduceTypes (nonLinMatch delta (t , hd) ps es) >>= \case
+                  Left _    -> return False
+                  Right sub -> do
+                    let us = applySubst sub $ map var $ downFrom $ size delta
+                        as = applySubst sub $ flattenTel delta
+                    reportSDoc "rewriting.confluence.global" 35 $
+                      prettyTCM (hd es) <+> "is an instance of the LHS of rule" <+> prettyTCM q <+> "with instantiation" <+> prettyList_ (map prettyTCM us)
+                    ok <- allDistinctVars $ zip us as
+                    when ok $ reportSDoc "rewriting.confluence.global" 30 $
+                      "It is equal to the LHS of rewrite rule" <+> prettyTCM q
+                    return ok
+              allDistinctVars :: [(Term,Dom Type)] -> TCM Bool
+              allDistinctVars us = do
+                us' <- filterM (not <.> isIrrelevantOrPropM . snd) us
+                mis <- traverse (\(u,a) -> isEtaVar u (unDom a)) $ us'
+                case sequence mis of
+                  Just is -> return $ fastDistinct is
+                  Nothing -> return False
+
+          rews <- getAllRulesFor f
+          let sameRHS = onlyReduceTypes $ pureEqualTerm a rhs1 rhs2
+          unlessM (sameRHS `or2M` anyM rews checkEqualLHS) $ addContext gamma $
+            warning $ RewriteAmbiguousRules (hd es) rhs1 rhs2
+
+    checkTrianglePropertyForRule :: RewriteRule -> TCM ()
+    checkTrianglePropertyForRule (RewriteRule q gamma f ps rhs b c) = addContext gamma $ do
+      u  <- nlPatToTerm $ PDef f ps
+      -- First element in the list is the "best reduct" @ρ(u)@
+      (rhou,vs) <- fromMaybe __IMPOSSIBLE__ . uncons <$> allParallelReductions u
+      reportSDoc "rewriting.confluence" 40 $ ("rho(" <> prettyTCM u <> ") =") <+> prettyTCM rhou
+      reportSDoc "rewriting.confluence" 40 $ ("S(" <> prettyTCM u <> ") =") <+> prettyList_ (map prettyTCM vs)
+      -- If present, last element is always equal to u
+      caseMaybe (initLast vs) (return ()) $ \(vs',u') -> do
+        unless (u == u') __IMPOSSIBLE__
+        forM_ vs' $ \v -> unlessM (checkParallelReductionStep b v rhou) $
+          warning $ RewriteMissingRule u v rhou
+
+    checkParallelReductionStep :: Type -> Term -> Term -> TCM Bool
+    checkParallelReductionStep a u w = do
+      reportSDoc "rewriting.confluence.global" 30 $ fsep
+        [ "Global confluence: checking if" , prettyTCM u
+        , "reduces to" , prettyTCM w , "in one parallel step." ]
+      anyListT (parReduce u) $ \v -> do
+        reportSDoc "rewriting.confluence.global" 30 $ fsep
+          [ prettyTCM u , " reduces to " , prettyTCM v
+          ]
+        eq <- onlyReduceTypes $ pureEqualTerm a v w
+        when eq $ reportSDoc "rewriting.confluence.global" 30 $ fsep
+          [ "  which is equal to" , prettyTCM w
+          ]
+        return eq
+
+
+sortRulesOfSymbol :: QName -> TCM ()
+sortRulesOfSymbol f = do
+    rules <- sortRules =<< getRewriteRulesFor f
+    modifySignature $ over sigRewriteRules $ HMap.insert f rules
+  where
+    sortRules :: PureTCM m => [RewriteRule] -> m [RewriteRule]
+    sortRules rs = do
+      ordPairs <- deleteLoops . Set.fromList . map (rewName *** rewName) <$>
+        filterM (uncurry $ flip moreGeneralLHS) [(r1,r2) | r1 <- rs, r2 <- rs]
+      let perm = fromMaybe __IMPOSSIBLE__ $
+                   topoSort (\r1 r2 -> (rewName r1,rewName r2) `Set.member` ordPairs) rs
+      reportSDoc "rewriting.confluence.sort" 50 $ "sorted rules: " <+>
+        prettyList_ (map (prettyTCM . rewName) $ permute perm rs)
+      return $ permute perm rs
+
+    moreGeneralLHS :: PureTCM m => RewriteRule -> RewriteRule -> m Bool
+    moreGeneralLHS r1 r2
+      | sameRuleName r1 r2       = return False
+      | rewHead r1 /= rewHead r2 = return False
+      | otherwise                = addContext (rewContext r2) $ do
+          def <- getConstInfo $ rewHead r1
+          (t, hd) <- makeHead def (rewType r2)
+          (vs :: Elims) <- nlPatToTerm $ rewPats r2
+          res <- isRight <$> onlyReduceTypes (nonLinMatch (rewContext r1) (t, hd) (rewPats r1) vs)
+          when res $ reportSDoc "rewriting.confluence.sort" 55 $
+            "the lhs of " <+> prettyTCM (rewName r1) <+>
+            "is more general than the lhs of" <+> prettyTCM (rewName r2)
+          return res
+
+    deleteLoops :: Ord a => Set (a,a) -> Set (a,a)
+    deleteLoops xs = Set.filter (\(x,y) -> not $ (y,x) `Set.member` xs) xs
+
+makeHead :: PureTCM m => Definition -> Type -> m (Type , Elims -> Term)
+makeHead def a = case theDef def of
+  Constructor{ conSrcCon = ch } -> do
+    ca <- snd . fromMaybe __IMPOSSIBLE__ <$> getFullyAppliedConType ch a
+    return (ca , Con ch ConOSystem)
+  -- For record projections @f : R Δ → A@, we rely on the invariant
+  -- that any clause is fully general in the parameters, i.e. it
+  -- is quantified over the parameter telescope @Δ@
+  Function { funProjection = Right proj } -> do
+    let f          = projOrig proj
+        r          = unArg $ projFromType proj
+    rtype <- defType <$> getConstInfo r
+    TelV ptel _ <- telView rtype
+    n <- getContextSize
+    let pars :: Args
+        pars = raise (n - size ptel) $ teleArgs ptel
+    ftype <- defType def `piApplyM` pars
+    return (ftype , Def f)
+  _ -> return (defType def , Def $ defName def)
+
+sameRuleName :: RewriteRule -> RewriteRule -> Bool
+sameRuleName = (==) `on` rewName
+
+-- | Get both clauses and rewrite rules for the given symbol
+getAllRulesFor :: (HasConstInfo m, MonadFresh NameId m) => QName -> m [RewriteRule]
+getAllRulesFor f = (++) <$> getRewriteRulesFor f <*> getClausesAsRewriteRules f
+
+-- | Build a substitution that replaces all variables in the given
+--   telescope by fresh metavariables.
+makeMetaSubst :: (MonadMetaSolver m) => Telescope -> m Substitution
+makeMetaSubst gamma = parallelS . reverse . map unArg <$> newTelMeta gamma
+
+computingOverlap :: (MonadTCEnv m) => m a -> m a
+computingOverlap = locallyTC eConflComputingOverlap $ const True
+
+-- | Try to run the TCM action, return @Just x@ if it succeeds with
+--   result @x@ or @Nothing@ if it throws a type error. Abort if there
+--   are any constraints.
+tryUnification :: Term -> Term -> TCM a -> TCM (Maybe a)
+tryUnification lhs1 lhs2 f = computingOverlap (Just <$> f)
+  `catchError` \case
+    err@TypeError{} -> do
+      reportSDoc "rewriting.confluence" 20 $ vcat
+        [ "Unification failed with error: "
+        , nest 2 $ prettyTCM err
+        ]
+      return Nothing
+    err -> throwError err
+  `ifNoConstraints` return $ \pid _ -> do
+    cs <- getConstraintsForProblem pid
+    prettyCs <- prettyInterestingConstraints cs
+    warning $ RewriteMaybeNonConfluent lhs1 lhs2 prettyCs
+    return Nothing
+
+
+type MonadParallelReduce m =
+  ( PureTCM m
+  , MonadFresh NameId m
+  )
+
+-- | List all possible single-step parallel reductions of the given term.
+allParallelReductions :: (MonadParallelReduce m, ParallelReduce a) => a -> m [a]
+allParallelReductions = sequenceListT . parReduce
+
+-- | Single-step parallel reduction of a given term.
+--   The monad 'm' can be instantiated in multiple ways:
+--   * Use 'MaybeT TCM' to get the "optimal reduct" obtained by
+--     applying rewrite rules eagerly.
+--   * Use 'ListT TCM' to obtain all possible one-step parallel
+--     reductions.
+class ParallelReduce a where
+  parReduce :: (MonadParallelReduce m, MonadPlus m) => a -> m a
+
+  default parReduce
+    :: ( MonadParallelReduce m, MonadPlus m
+       , Traversable f, a ~ f b, ParallelReduce b)
+    => a -> m a
+  parReduce = traverse parReduce
+
+-- | Compute possible one-step reductions by applying a rewrite rule
+--   at the top-level and reducing all subterms in the position of a
+--   variable of the rewrite rule in parallel.
+topLevelReductions :: (MonadParallelReduce m, MonadPlus m) => (Elims -> Term) -> Elims -> m Term
+topLevelReductions hd es = do
+  reportSDoc "rewriting.parreduce" 30 $ "topLevelReductions" <+> prettyTCM (hd es)
+  -- Get type of head symbol
+  (f , t) <- fromMaybe __IMPOSSIBLE__ <$> getTypedHead (hd [])
+  reportSDoc "rewriting.parreduce" 60 $ "topLevelReductions: head symbol" <+> prettyTCM (hd []) <+> ":" <+> prettyTCM t
+  RewriteRule q gamma _ ps rhs b c <- scatterMP (getAllRulesFor f)
+  reportSDoc "rewriting.parreduce" 60 $ "topLevelReductions: trying rule" <+> prettyTCM q
+  -- Don't reduce if underapplied
+  guard $ length es >= length ps
+  let (es0 , es1) = splitAt (length ps) es
+  onlyReduceTypes (nonLinMatch gamma (t,hd) ps es0) >>= \case
+    -- Matching failed: no reduction
+    Left block -> empty
+    -- Matching succeeded
+    Right sub -> do
+      let vs = map (lookupS sub) $ [0..(size gamma-1)]
+      sub' <- parallelS <$> parReduce vs
+      es1' <- parReduce es1
+      let w = (applySubst sub' rhs) `applyE` es1'
+      reportSDoc "rewriting.parreduce" 50 $ "topLevelReductions: rewrote" <+> prettyTCM (hd es) <+> "to" <+> prettyTCM w
+      return w
+
+instance ParallelReduce Term where
+  parReduce = \case
+    -- Interesting cases
+    (Def f es) -> (topLevelReductions (Def f) es) <|> (Def f <$> parReduce es)
+    (Con c ci es) -> (topLevelReductions (Con c ci) es) <|> (Con c ci <$> parReduce es)
+
+    -- Congruence cases
+    Lam i u  -> Lam i <$> parReduce u
+    Var x es -> Var x <$> parReduce es
+    Pi a b   -> Pi    <$> parReduce a <*> parReduce b
+    Sort s   -> Sort  <$> parReduce s
+
+    -- Base cases
+    u@Lit{}      -> return u
+    u@Level{}    -> return u -- TODO: is this fine?
+    u@DontCare{} -> return u
+    u@Dummy{}    -> return u -- not __IMPOSSIBLE__ because of presence of Dummy
+                             -- parameters for rewrite rules on constructors.
+
+    -- Impossible cases
+    MetaV{}    -> __IMPOSSIBLE__
+
+instance ParallelReduce Sort where
+  parReduce = pure -- TODO: is this fine?
+
+instance ParallelReduce a => ParallelReduce (Arg a) where
+instance ParallelReduce a => ParallelReduce (Dom a) where
+instance ParallelReduce a => ParallelReduce (Type' a) where
+instance ParallelReduce a => ParallelReduce [a] where
+
+instance ParallelReduce a => ParallelReduce (Elim' a) where
+  parReduce (Apply u)  = Apply <$> parReduce u
+  parReduce e@Proj{}   = pure e
+  parReduce e@IApply{} = pure e -- TODO
+
+instance (Free a, Subst a, ParallelReduce a) => ParallelReduce (Abs a) where
+  parReduce = mapAbstraction __DUMMY_DOM__ parReduce
+
+
+-- | Given metavariables ms and some x, construct a telescope Γ and
+--   replace all occurrences of the given metavariables in @x@ by
+--   normal variables from Γ. Returns @Nothing@ if metas have cyclic
+--   dependencies.
+abstractOverMetas :: (MetasToVars a) => [MetaId] -> a -> TCM (Maybe (Telescope, a))
+abstractOverMetas ms x = do
+
+  -- Sort metas in dependency order
+  forMM (dependencySortMetas ms) $ \ms' -> do
+
+    -- Get types and suggested names of metas
+    as <- forM ms' getMetaType
+    ns <- forM ms' getMetaNameSuggestion
+
+    -- Construct telescope (still containing the metas)
+    let n     = size ms'
+        gamma = unflattenTel' n ns $ map defaultDom as
+
+    -- Replace metas by variables
+    let metaIndex x = (n-1-) <$> elemIndex x ms'
+    runReaderT (metasToVars (gamma, x)) metaIndex
+
+-- ^ A @OneHole p@ is a @p@ with a subpattern @f ps@ singled out.
+data OneHole a = OneHole
+  { ohBoundVars :: Telescope     -- Telescope of bound variables at the hole
+  , ohType      :: Type          -- Type of the term in the hole
+  , ohPlugHole  :: Term -> a     -- Plug the hole with some term
+  , ohHead      :: Elims -> Term -- The head symbol of the term in the hole
+  , ohElims     :: Elims         -- The eliminations of the term in the hole
+  } deriving (Functor)
+
+ohHeadName :: OneHole a -> QName
+ohHeadName oh = case ohHead oh [] of
+  Def f _   -> f
+  Con c _ _ -> conName c
+  _         -> __IMPOSSIBLE__
+
+ohContents :: OneHole a -> Term
+ohContents oh = ohHead oh $ ohElims oh
+
+-- | The trivial hole
+idHole :: Type -> Term -> OneHole Term
+idHole a = \case
+  Def f es    -> OneHole EmptyTel a id (Def f) es
+  Con c ci es -> OneHole EmptyTel a id (Con c ci) es
+  _           -> __IMPOSSIBLE__
+
+-- | Plug a hole with another hole
+composeHole :: OneHole Term -> OneHole a -> OneHole a
+composeHole inner outer = OneHole
+  { ohBoundVars = ohBoundVars outer `abstract` ohBoundVars inner
+  , ohType      = ohType inner
+  , ohPlugHole  = ohPlugHole outer . ohPlugHole inner
+  , ohHead      = ohHead inner
+  , ohElims     = ohElims inner
+  }
+
+ohAddBV :: ArgName -> Dom Type -> OneHole a -> OneHole a
+ohAddBV x a oh = oh { ohBoundVars = ExtendTel a $ Abs x $ ohBoundVars oh }
+
+-- ^ Given a @p : a@, @allHoles p@ lists all the possible
+--   decompositions @p = p'[(f ps)/x]@.
+class (TermSubst p, Free p) => AllHoles p where
+  allHoles :: (Alternative m, PureTCM m) => TypeOf p -> p -> m (OneHole p)
+
+allHoles_
+  :: ( Alternative m , PureTCM m , AllHoles p , TypeOf p ~ () )
+  => p -> m (OneHole p)
+allHoles_ = allHoles ()
+
+allHolesList
+  :: ( PureTCM m , AllHoles p)
+  => TypeOf p -> p -> m [OneHole p]
+allHolesList a = sequenceListT . allHoles a
+
+-- | Given a term @v : a@ and eliminations @es@, force eta-expansion
+--   of @v@ to match the structure (Apply/Proj) of the eliminations.
+--
+--   Examples:
+--
+--   1. @v : _A@ and @es = [$ w]@: this will instantiate
+--      @_A := (x : _A1) → _A2@ and return the @OneHole Term@
+--      @λ x → [v x]@.
+--
+--   2. @v : _A@ and @es = [.fst]@: this will instantiate
+--      @_A := _A1 × _A2@ and return the @OneHole Term@
+--      @([v .fst]) , (v .snd)@.
+forceEtaExpansion :: Type -> Term -> [Elim' a] -> TCM (OneHole Term)
+forceEtaExpansion a v [] = return $ idHole a v
+forceEtaExpansion a v (e:es) = case e of
+
+  Apply (Arg i w) -> do
+
+    -- Force a to be a pi type
+    reportSDoc "rewriting.confluence.eta" 40 $ fsep
+      [ "Forcing" , prettyTCM v , ":" , prettyTCM a , "to take one more argument" ]
+    dom <- defaultArgDom i <$> newTypeMeta_
+    cod <- addContext dom $ newTypeMeta_
+    equalType a $ mkPi (("x",) <$> dom) cod
+
+    -- Construct body of eta-expansion
+    let body = raise 1 v `apply` [Arg i $ var 0]
+
+    -- Continue with remaining eliminations
+    addContext dom $ ohAddBV "x" dom . fmap (Lam i . mkAbs "x") <$>
+      forceEtaExpansion cod body es
+
+  Proj o f -> do
+
+    -- Force a to be the right record type for projection by f
+    reportSDoc "rewriting.confluence.eta" 40 $ fsep
+      [ "Forcing" , prettyTCM v , ":" , prettyTCM a , "to be projectible by" , prettyTCM f ]
+    r <- fromMaybe __IMPOSSIBLE__ <$> getRecordOfField f
+    rdef <- getConstInfo r
+    let ra = defType rdef
+    pars <- newArgsMeta ra
+    s <- ra `piApplyM` pars >>= \s -> ifIsSort s return __IMPOSSIBLE__
+    equalType a $ El s (Def r $ map Apply pars)
+
+    -- Eta-expand v at record type r, and get field corresponding to f
+    (_ , c , ci , fields) <- etaExpandRecord_ r pars (theDef rdef) v
+    let fs        = map argFromDom $ recFields $ theDef rdef
+        i         = fromMaybe __IMPOSSIBLE__ $ elemIndex f $ map unArg fs
+        fContent  = unArg $ fromMaybe __IMPOSSIBLE__ $ fields !!! i
+        fUpdate w = Con c ci $ map Apply $ updateAt i (w <$) fields
+
+    -- Get type of field corresponding to f
+    ~(Just (El _ (Pi b c))) <- getDefType f =<< reduce a
+    let fa = c `absApp` v
+
+    -- Continue with remaining eliminations
+    fmap fUpdate <$> forceEtaExpansion fa fContent es
+
+  IApply{} -> __IMPOSSIBLE__ -- Not yet implemented
+
+-- ^ Instances for @AllHoles@
+
+instance AllHoles p => AllHoles (Arg p) where
+  allHoles a x = fmap (x $>) <$> allHoles (unDom a) (unArg x)
+
+instance AllHoles p => AllHoles (Dom p) where
+  allHoles a x = fmap (x $>) <$> allHoles a (unDom x)
+
+instance AllHoles (Abs Term) where
+  allHoles (dom , a) x = addContext (absName x , dom) $
+    ohAddBV (absName a) dom . fmap (mkAbs $ absName x) <$>
+      allHoles (absBody a) (absBody x)
+
+instance AllHoles (Abs Type) where
+  allHoles dom a = addContext (absName a , dom) $
+    ohAddBV (absName a) dom . fmap (mkAbs $ absName a) <$>
+      allHoles_ (absBody a)
+
+instance AllHoles Elims where
+  allHoles (a,hd) [] = empty
+  allHoles (a,hd) (e:es) = do
+    reportSDoc "rewriting.confluence.hole" 65 $ fsep
+      [ "Head symbol" , prettyTCM (hd []) , ":" , prettyTCM a
+      , "is eliminated by" , prettyTCM e
+      ]
+    case e of
+      Apply x -> do
+        ~(Pi b c) <- unEl <$> reduce a
+        let a'  = c `absApp` unArg x
+            hd' = hd . (e:)
+        (fmap ((:es) . Apply) <$> allHoles b x)
+         <|> (fmap (e:) <$> allHoles (a' , hd') es)
+      Proj o f -> do
+        ~(Just (El _ (Pi b c))) <- getDefType f =<< reduce a
+        let a' = c `absApp` hd []
+        hd' <- applyE <$> applyDef o f (argFromDom b $> hd [])
+        fmap (e:) <$> allHoles (a' , hd') es
+      IApply x y u -> empty -- TODO: support --confluence-check + --cubical
+
+instance AllHoles Type where
+  allHoles _ (El s a) = workOnTypes $
+    fmap (El s) <$> allHoles (sort s) a
+
+instance AllHoles Term where
+  allHoles a u = do
+    reportSDoc "rewriting.confluence.hole" 60 $ fsep
+      [ "Getting holes of term" , prettyTCM u , ":" , prettyTCM a ]
+    case u of
+      Var i es       -> do
+        ai <- typeOfBV i
+        fmap (Var i) <$> allHoles (ai , Var i) es
+      Lam i u        -> do
+        ~(Pi b c) <- unEl <$> reduce a
+        fmap (Lam i) <$> allHoles (b,c) u
+      Lit l          -> empty
+      v@(Def f es)   -> do
+        fa <- defType <$> getConstInfo f
+        pure (idHole a v)
+         <|> (fmap (Def f) <$> allHoles (fa , Def f) es)
+      v@(Con c ci es) -> do
+        ca <- snd . fromMaybe __IMPOSSIBLE__ <$> do
+          getFullyAppliedConType c =<< reduce a
+        pure (idHole a v)
+         <|> (fmap (Con c ci) <$> allHoles (ca , Con c ci) es)
+      Pi a b         ->
+        (fmap (\a -> Pi a b) <$> allHoles_ a) <|>
+        (fmap (\b -> Pi a b) <$> allHoles a b)
+      Sort s         -> fmap Sort <$> allHoles_ s
+      Level l        -> fmap Level <$> allHoles_ l
+      MetaV{}        -> __IMPOSSIBLE__
+      DontCare{}     -> empty
+      Dummy{}        -> empty
+
+instance AllHoles Sort where
+  allHoles _ = \case
+    Univ u l     -> fmap (Univ u) <$> allHoles_ l
+    Inf _ _      -> empty
+    SizeUniv     -> empty
+    LockUniv     -> empty
+    LevelUniv    -> empty
+    IntervalUniv -> empty
+    PiSort{}     -> __IMPOSSIBLE__
+    FunSort{}    -> __IMPOSSIBLE__
+    UnivSort{}   -> __IMPOSSIBLE__
+    MetaS{}      -> __IMPOSSIBLE__
+    DefS f es    -> do
+      fa <- defType <$> getConstInfo f
+      fmap (DefS f) <$> allHoles (fa , Def f) es
+    DummyS{}     -> empty
+
+instance AllHoles Level where
+  allHoles _ (Max n ls) = fmap (Max n) <$> allHoles_ ls
+
+instance AllHoles [PlusLevel] where
+  allHoles _ []     = empty
+  allHoles _ (l:ls) =
+    (fmap (:ls) <$> allHoles_ l)
+    <|> (fmap (l:) <$> allHoles_ ls)
+
+instance AllHoles PlusLevel where
+  allHoles _ (Plus n l) = do
+    la <- levelType'
+    fmap (Plus n) <$> allHoles la l
+
+
+-- | Convert metavariables to normal variables. Warning: doesn't
+--   convert sort metas.
+class MetasToVars a where
+  metasToVars
+    :: (MonadReader (MetaId -> Maybe Nat) m , HasBuiltins m)
+    => a -> m a
+
+  default metasToVars
+    :: ( MetasToVars a', Traversable f, a ~ f a'
+       , MonadReader (MetaId -> Maybe Nat) m , HasBuiltins m)
+    => a -> m a
+  metasToVars = traverse metasToVars
+
+instance MetasToVars a => MetasToVars [a] where
+instance MetasToVars a => MetasToVars (Arg a) where
+instance MetasToVars a => MetasToVars (Dom a) where
+instance MetasToVars a => MetasToVars (Elim' a) where
+
+instance MetasToVars a => MetasToVars (Abs a) where
+  metasToVars (Abs   i x) = Abs i   <$> local (fmap succ .) (metasToVars x)
+  metasToVars (NoAbs i x) = NoAbs i <$> metasToVars x
+
+instance MetasToVars Term where
+  metasToVars = \case
+    Var i es   -> Var i    <$> metasToVars es
+    Lam i u    -> Lam i    <$> metasToVars u
+    Lit l      -> pure (Lit l)
+    Def f es   -> Def f    <$> metasToVars es
+    Con c i es -> Con c i  <$> metasToVars es
+    Pi a b     -> Pi       <$> metasToVars a <*> metasToVars b
+    Sort s     -> Sort     <$> metasToVars s
+    Level l    -> Level    <$> metasToVars l
+    MetaV x es -> asks ($ x) >>= \case
+      Just i   -> Var i    <$> metasToVars es
+      Nothing  -> MetaV x  <$> metasToVars es
+    DontCare u -> DontCare <$> metasToVars u
+    Dummy s es -> Dummy s  <$> metasToVars es
+
+instance MetasToVars Type where
+  metasToVars (El s t) = El <$> metasToVars s <*> metasToVars t
+
+instance MetasToVars Sort where
+  metasToVars = \case
+    Univ u l   -> Univ u <$> metasToVars l
+    Inf u n    -> pure $ Inf u n
+    SizeUniv   -> pure SizeUniv
+    LockUniv   -> pure LockUniv
+    LevelUniv  -> pure LevelUniv
+    IntervalUniv -> pure IntervalUniv
+    PiSort s t u -> PiSort   <$> metasToVars s <*> metasToVars t <*> metasToVars u
+    FunSort s t -> FunSort <$> metasToVars s <*> metasToVars t
+    UnivSort s -> UnivSort <$> metasToVars s
+    MetaS x es -> MetaS x  <$> metasToVars es
+    DefS f es  -> DefS f   <$> metasToVars es
+    DummyS s   -> pure $ DummyS s
+
+instance MetasToVars Level where
+  metasToVars (Max n ls) = Max n <$> metasToVars ls
+
+instance MetasToVars PlusLevel where
+  metasToVars (Plus n x) = Plus n <$> metasToVars x
+
+instance MetasToVars a => MetasToVars (Tele a) where
+  metasToVars EmptyTel = pure EmptyTel
+  metasToVars (ExtendTel a tel) = ExtendTel <$> metasToVars a <*> metasToVars tel
+
+instance (MetasToVars a, MetasToVars b) => MetasToVars (a,b) where
+  metasToVars (x,y) = (,) <$> metasToVars x <*> metasToVars y
+
+instance (MetasToVars a, MetasToVars b, MetasToVars c) => MetasToVars (a,b,c) where
+  metasToVars (x,y,z) = (,,) <$> metasToVars x <*> metasToVars y <*> metasToVars z
+
+instance (MetasToVars a, MetasToVars b, MetasToVars c, MetasToVars d) => MetasToVars (a,b,c,d) where
+  metasToVars (x,y,z,w) = (,,,) <$> metasToVars x <*> metasToVars y <*> metasToVars z <*> metasToVars w
diff --git a/src/full/Agda/TypeChecking/Rewriting/NonLinMatch.hs b/src/full/Agda/TypeChecking/Rewriting/NonLinMatch.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting/NonLinMatch.hs
@@ -0,0 +1,460 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+{- |  Non-linear matching of the lhs of a rewrite rule against a
+      neutral term.
+
+Given a lhs
+
+  Δ ⊢ lhs : B
+
+and a candidate term
+
+  Γ ⊢ t : A
+
+we seek a substitution Γ ⊢ σ : Δ such that
+
+  Γ ⊢ B[σ] = A   and
+  Γ ⊢ lhs[σ] = t : A
+
+-}
+
+module Agda.TypeChecking.Rewriting.NonLinMatch where
+
+import Prelude hiding (null, sequence)
+
+import Control.Applicative  ( Alternative )
+import Control.Monad        ( void )
+import Control.Monad.Except ( MonadError(..), ExceptT, runExceptT )
+import Control.Monad.State  ( MonadState, StateT, runStateT )
+
+import qualified Control.Monad.Fail as Fail
+
+import Data.Maybe
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Conversion.Pure
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Free.Reduce
+import Agda.TypeChecking.Irrelevance (isPropM)
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Monad hiding (constructorForm)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Reduce.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Primitive.Cubical.Base
+
+import Agda.Utils.Either
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+
+-- | Monad for non-linear matching.
+newtype NLM a = NLM { unNLM :: ExceptT Blocked_ (StateT NLMState ReduceM) a }
+  deriving ( Functor, Applicative, Monad, Fail.MonadFail
+           , Alternative, MonadPlus
+           , MonadError Blocked_, MonadState NLMState
+           , HasBuiltins, HasConstInfo, HasOptions, ReadTCState
+           , MonadTCEnv, MonadReduce, MonadAddContext, MonadDebug
+           , PureTCM
+           )
+
+instance MonadBlock NLM where
+  patternViolation b = throwError $ Blocked b ()
+  catchPatternErr h f = catchError f $ \case
+    Blocked b _      -> h b
+    err@NotBlocked{} -> throwError err
+
+data NLMState = NLMState
+  { _nlmSub   :: Sub
+  , _nlmEqs   :: PostponedEquations
+  }
+
+instance Null NLMState where
+  empty  = NLMState { _nlmSub = empty , _nlmEqs = empty }
+  null s = null (s ^. nlmSub) && null (s ^. nlmEqs)
+
+nlmSub :: Lens' NLMState Sub
+nlmSub f s = f (_nlmSub s) <&> \x -> s {_nlmSub = x}
+
+nlmEqs :: Lens' NLMState PostponedEquations
+nlmEqs f s = f (_nlmEqs s) <&> \x -> s {_nlmEqs = x}
+
+runNLM :: (MonadReduce m) => NLM () -> m (Either Blocked_ NLMState)
+runNLM nlm = do
+  (ok,out) <- liftReduce $ runStateT (runExceptT $ unNLM nlm) empty
+  case ok of
+    Left block -> return $ Left block
+    Right _    -> return $ Right out
+
+matchingBlocked :: Blocked_ -> NLM ()
+matchingBlocked = throwError
+
+-- | Add substitution @i |-> v : a@ to result of matching.
+tellSub :: Relevance -> Int -> Type -> Term -> NLM ()
+tellSub r i a v = do
+  old <- IntMap.lookup i <$> use nlmSub
+  case old of
+    Nothing -> nlmSub %= IntMap.insert i (r,v)
+    Just (r',v')
+      | isIrrelevant r  -> return ()
+      | isIrrelevant r' -> nlmSub %= IntMap.insert i (r,v)
+      | otherwise       -> whenJustM (equal a v v') matchingBlocked
+
+tellEq :: Telescope -> Telescope -> Type -> Term -> Term -> NLM ()
+tellEq gamma k a u v = do
+  traceSDoc "rewriting.match" 30 (sep
+               [ "adding equality between" <+> addContext (gamma `abstract` k) (prettyTCM u)
+               , " and " <+> addContext k (prettyTCM v) ]) $ do
+  nlmEqs %= (PostponedEquation k a u v:)
+
+type Sub = IntMap (Relevance, Term)
+
+-- | Matching against a term produces a constraint
+--   which we have to verify after applying
+--   the substitution computed by matching.
+data PostponedEquation = PostponedEquation
+  { eqFreeVars :: Telescope -- ^ Telescope of free variables in the equation
+  , eqType :: Type    -- ^ Type of the equation, living in same context as the rhs.
+  , eqLhs :: Term     -- ^ Term from pattern, living in pattern context.
+  , eqRhs :: Term     -- ^ Term from scrutinee, living in context where matching was invoked.
+  }
+type PostponedEquations = [PostponedEquation]
+
+-- | Match a non-linear pattern against a neutral term,
+--   returning a substitution.
+
+class Match a b where
+  match :: Relevance  -- ^ Are we currently matching in an irrelevant context?
+        -> Telescope  -- ^ The telescope of pattern variables
+        -> Telescope  -- ^ The telescope of lambda-bound variables
+        -> TypeOf b   -- ^ The type of the pattern
+        -> a          -- ^ The pattern to match
+        -> b          -- ^ The term to be matched against the pattern
+        -> NLM ()
+
+instance Match a b => Match (Arg a) (Arg b) where
+  match r gamma k t p v = let r' = r `composeRelevance` getRelevance p
+                          in  match r' gamma k (unDom t) (unArg p) (unArg v)
+
+instance Match [Elim' NLPat] Elims where
+  match r gamma k (t, hd) [] [] = return ()
+  match r gamma k (t, hd) [] _  = matchingBlocked $ NotBlocked ReallyNotBlocked ()
+  match r gamma k (t, hd) _  [] = matchingBlocked $ NotBlocked ReallyNotBlocked ()
+  match r gamma k (t, hd) (p:ps) (v:vs) =
+   traceSDoc "rewriting.match" 50 (sep
+     [ "matching elimination " <+> addContext (gamma `abstract` k) (prettyTCM p)
+     , "  with               " <+> addContext k (prettyTCM v)
+     , "  eliminating head   " <+> addContext k (prettyTCM $ hd []) <+> ":" <+> addContext k (prettyTCM t)]) $ do
+
+   let no  = matchingBlocked $ NotBlocked ReallyNotBlocked ()
+   case (p,v) of
+    (Apply p, Apply v) -> (addContext k $ unEl <$> reduce t) >>= \case
+      Pi a b -> do
+        match r gamma k a p v
+        let t'  = absApp b (unArg v)
+            hd' = hd . (Apply v:)
+        match r gamma k (t',hd') ps vs
+      t -> traceSDoc "rewriting.match" 20
+        ("application at non-pi type (possible non-confluence?) " <+> prettyTCM t) mzero
+
+    (IApply x y p , IApply u v i) -> (addContext k $ pathView =<< reduce t) >>= \case
+      PathType s q l b _u _v -> do
+        Right interval <- runExceptT primIntervalType
+        match r gamma k interval p i
+        let t' = El s $ unArg b `apply` [ defaultArg i ]
+        let hd' = hd . (IApply u v i:)
+        match r gamma k (t',hd') ps vs
+      t -> traceSDoc "rewriting.match" 20
+        ("interval application at non-pi type (possible non-confluence?) " <+> prettyTCM (pathUnview t)) mzero
+
+    (Proj o f, Proj o' f') | f == f' -> do
+      addContext k (getDefType f =<< reduce t) >>= \case
+        Just (El _ (Pi a b)) -> do
+          let u = hd []
+              t' = b `absApp` u
+          hd' <- addContext k $ applyE <$> applyDef o f (argFromDom a $> u)
+          match r gamma k (t',hd') ps vs
+        _ -> no
+
+    (Proj _ f, Proj _ f') | otherwise -> do
+      traceSDoc "rewriting.match" 20 (sep
+        [ "mismatch between projections " <+> prettyTCM f
+        , " and " <+> prettyTCM f' ]) mzero
+
+    (Apply{}, Proj{} ) -> no
+    (Proj{} , Apply{}) -> no
+
+    (IApply{} , _    ) -> __IMPOSSIBLE__ -- TODO
+    (_ , IApply{}    ) -> __IMPOSSIBLE__ -- TODO
+
+instance Match a b => Match (Dom a) (Dom b) where
+  match r gamma k t p v = match r gamma k t (unDom p) (unDom v)
+
+instance Match NLPType Type where
+  match r gamma k _ (NLPType sp p) (El s a) = workOnTypes $ do
+    match r gamma k () sp s
+    match r gamma k (sort s) p a
+
+instance Match NLPSort Sort where
+  match r gamma k _ p s = do
+    bs <- addContext k $ reduceB s
+    let b = void bs
+        s = ignoreBlocking bs
+        yes = return ()
+        no  = matchingBlocked $ NotBlocked ReallyNotBlocked ()
+    traceSDoc "rewriting.match" 30 (sep
+      [ "matching pattern " <+> addContext (gamma `abstract` k) (prettyTCM p)
+      , "  with sort      " <+> addContext k (prettyTCM s) ]) $ do
+    case (p , s) of
+      (PUniv u lp    , Univ u' l) | u == u'          -> match r gamma k () lp l
+      (PInf up np    , Inf u n)   | up == u, np == n -> yes
+      (PSizeUniv     , SizeUniv)                     -> yes
+      (PLockUniv     , LockUniv)                     -> yes
+      (PLevelUniv    , LevelUniv)                    -> yes
+      (PIntervalUniv , IntervalUniv)                 -> yes
+
+      -- blocked cases
+      (_ , UnivSort{}) -> matchingBlocked b
+      (_ , PiSort{}  ) -> matchingBlocked b
+      (_ , FunSort{} ) -> matchingBlocked b
+      (_ , MetaS m _ ) -> matchingBlocked $ blocked_ m
+
+      -- all other cases do not match
+      (_ , _) -> no
+
+instance Match NLPat Level where
+  match r gamma k _ p l = do
+    t <- El (mkType 0) . fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinLevel
+    v <- reallyUnLevelView l
+    match r gamma k t p v
+
+instance Match NLPat Term where
+  match r0 gamma k t p v = do
+    vbt <- addContext k $ reduceB (v,t)
+    let n = size k
+        b = void vbt
+        (v,t) = ignoreBlocking vbt
+        prettyPat  = withShowAllArguments $ addContext (gamma `abstract` k) (prettyTCM p)
+        prettyTerm = withShowAllArguments $ addContext k $ prettyTCM v
+        prettyType = withShowAllArguments $ addContext k $ prettyTCM t
+    etaRecord <- addContext k $ isEtaRecordType t
+    pview <- pathViewAsPi'whnf
+    prop <- fromRight __IMPOSSIBLE__ <.> runBlocked . addContext k $ isPropM t
+    let r = if prop then Irrelevant else r0
+    traceSDoc "rewriting.match" 30 (sep
+      [ "matching pattern " <+> prettyPat
+      , "  with term      " <+> prettyTerm
+      , "  of type        " <+> prettyType ]) $ do
+    traceSDoc "rewriting.match" 80 (vcat
+      [ "  raw pattern:  " <+> text (show p)
+      , "  raw term:     " <+> text (show v)
+      , "  raw type:     " <+> text (show t) ]) $ do
+    traceSDoc "rewriting.match" 70 (vcat
+      [ "pattern vars:   " <+> prettyTCM gamma
+      , "bound vars:     " <+> prettyTCM k ]) $ do
+    let yes = return ()
+        no msg = if r == Irrelevant then yes else do
+          traceSDoc "rewriting.match" 10 (sep
+            [ "mismatch between" <+> prettyPat
+            , " and " <+> prettyTerm
+            , " of type " <+> prettyType
+            , msg ]) $ do
+          traceSDoc "rewriting.match" 30 (sep
+            [ "blocking tag from reduction: " <+> text (show b) ]) $ do
+          matchingBlocked b
+        block b' = if r == Irrelevant then yes else do
+          traceSDoc "rewriting.match" 10 (sep
+            [ "matching blocked on meta"
+            , text (show b') ]) $ do
+          traceSDoc "rewriting.match" 30 (sep
+            [ "blocking tag from reduction: " <+> text (show b') ]) $ do
+          matchingBlocked (b `mappend` b')
+        maybeBlock = \case
+          MetaV m es -> matchingBlocked $ blocked_ m
+          _          -> no ""
+    case p of
+      PVar i bvs -> traceSDoc "rewriting.match" 60 ("matching a PVar: " <+> text (show i)) $ do
+        let allowedVars :: IntSet
+            allowedVars = IntSet.fromList (map unArg bvs)
+            badVars :: IntSet
+            badVars = IntSet.difference (IntSet.fromList (downFrom n)) allowedVars
+            perm :: Permutation
+            perm = Perm n $ reverse $ map unArg $ bvs
+            tel :: Telescope
+            tel = permuteTel perm k
+        ok <- addContext k $ reallyFree badVars v
+        case ok of
+          Left b         -> block b
+          Right Nothing  -> no ""
+          Right (Just v) ->
+            let t' = telePi  tel $ renameP impossible perm t
+                v' = teleLam tel $ renameP impossible perm v
+            in tellSub r (i-n) t' v'
+
+      PDef f ps -> traceSDoc "rewriting.match" 60 ("matching a PDef: " <+> prettyTCM f) $ do
+        v <- addContext k $ constructorForm =<< unLevel v
+        case v of
+          Def f' es
+            | f == f'   -> do
+                ft <- addContext k $ defType <$> getConstInfo f
+                match r gamma k (ft , Def f) ps es
+          Con c ci vs
+            | f == conName c -> do
+                addContext k (getFullyAppliedConType c t) >>= \case
+                  Just (_ , ct) -> match r gamma k (ct , Con c ci) ps vs
+                  Nothing -> no ""
+          _ | Pi a b <- unEl t -> do
+            let ai    = domInfo a
+                pbody = PDef f $ raise 1 ps ++ [ Apply $ Arg ai $ PTerm $ var 0 ]
+                body  = raise 1 v `apply` [ Arg (domInfo a) $ var 0 ]
+                k'    = ExtendTel a (Abs (absName b) k)
+            match r gamma k' (absBody b) pbody body
+          _ | Just (d, pars) <- etaRecord -> do
+          -- If v is not of record constructor form but we are matching at record
+          -- type, e.g., we eta-expand both v to (c vs) and
+          -- the pattern (p = PDef f ps) to @c (p .f1) ... (p .fn)@.
+            def <- addContext k $ theDef <$> getConstInfo d
+            (tel, c, ci, vs) <- addContext k $ etaExpandRecord_ d pars def v
+            addContext k (getFullyAppliedConType c t) >>= \case
+              Just (_ , ct) -> do
+                let flds = map argFromDom $ recFields def
+                    mkField fld = PDef f (ps ++ [Proj ProjSystem fld])
+                    -- Issue #3335: when matching against the record constructor,
+                    -- don't add projections but take record field directly.
+                    ps'
+                      | conName c == f = ps
+                      | otherwise      = map (Apply . fmap mkField) flds
+                match r gamma k (ct, Con c ci) ps' (map Apply vs)
+              Nothing -> no ""
+          v -> maybeBlock v
+      PLam i p' -> case unEl t of
+        Pi a b -> do
+          let body = raise 1 v `apply` [Arg i (var 0)]
+              k'   = ExtendTel a (Abs (absName b) k)
+          match r gamma k' (absBody b) (absBody p') body
+        _ | Left ((a,b),(x,y)) <- pview t -> do
+          let body = raise 1 v `applyE` [ IApply (raise 1 x) (raise 1 y) $ var 0 ]
+              k'   = ExtendTel a (Abs "i" k)
+          match r gamma k' (absBody b) (absBody p') body
+        v -> maybeBlock v
+      PPi pa pb -> case v of
+        Pi a b -> do
+          match r gamma k () pa a
+          let k' = ExtendTel a (Abs (absName b) k)
+          match r gamma k' () (absBody pb) (absBody b)
+        v -> maybeBlock v
+      PSort ps -> case v of
+        Sort s -> match r gamma k () ps s
+        v -> maybeBlock v
+      PBoundVar i ps -> case v of
+        Var i' es | i == i' -> do
+          let ti = unDom $ indexWithDefault __IMPOSSIBLE__ (flattenTel k) i
+          match r gamma k (ti , Var i) ps es
+        _ | Pi a b <- unEl t -> do
+          let ai    = domInfo a
+              pbody = PBoundVar (1 + i) $ raise 1 ps ++ [ Apply $ Arg ai $ PTerm $ var 0 ]
+              body  = raise 1 v `apply` [ Arg ai $ var 0 ]
+              k'    = ExtendTel a (Abs (absName b) k)
+          match r gamma k' (absBody b) pbody body
+        _ | Just (d, pars) <- etaRecord -> do
+          def <- addContext k $ theDef <$> getConstInfo d
+          (tel, c, ci, vs) <- addContext k $ etaExpandRecord_ d pars def v
+          addContext k (getFullyAppliedConType c t) >>= \case
+            Just (_ , ct) -> do
+              let flds = map argFromDom $ recFields def
+                  ps'  = map (fmap $ \fld -> PBoundVar i (ps ++ [Proj ProjSystem fld])) flds
+              match r gamma k (ct, Con c ci) (map Apply ps') (map Apply vs)
+            Nothing -> no ""
+        v -> maybeBlock v
+      PTerm u -> traceSDoc "rewriting.match" 60 ("matching a PTerm" <+> addContext (gamma `abstract` k) (prettyTCM u)) $
+        tellEq gamma k t u v
+
+makeSubstitution :: Telescope -> Sub -> Maybe Substitution
+makeSubstitution gamma sub =
+  parallelS <$> traverse val [0 .. size gamma-1]
+    where
+      val i = case IntMap.lookup i sub of
+                Just (Irrelevant, v) -> Just $ dontCare v
+                Just (_         , v) -> Just v
+                Nothing              -> Nothing
+
+{-# SPECIALIZE checkPostponedEquations :: Substitution -> PostponedEquations -> TCM (Maybe Blocked_) #-}
+checkPostponedEquations :: PureTCM m
+                        => Substitution -> PostponedEquations -> m (Maybe Blocked_)
+checkPostponedEquations sub eqs = forM' eqs $
+  \ (PostponedEquation k a lhs rhs) -> do
+      let lhs' = applySubst (liftS (size k) sub) lhs
+      traceSDoc "rewriting.match" 30 (sep
+        [ "checking postponed equality between" , addContext k (prettyTCM lhs')
+        , " and " , addContext k (prettyTCM rhs) ]) $ do
+      addContext k $ equal a lhs' rhs
+
+-- main function
+nonLinMatch :: (PureTCM m, Match a b)
+            => Telescope -> TypeOf b -> a -> b -> m (Either Blocked_ Substitution)
+nonLinMatch gamma t p v = do
+  let no msg b = traceSDoc "rewriting.match" 10 (sep
+                   [ "matching failed during" <+> text msg
+                   , "blocking: " <+> text (show b) ]) $ return (Left b)
+  caseEitherM (runNLM $ match Relevant gamma EmptyTel t p v) (no "matching") $ \ s -> do
+    let msub = makeSubstitution gamma $ s ^. nlmSub
+        eqs = s ^. nlmEqs
+    traceSDoc "rewriting.match" 90 (text $ "msub = " ++ show msub) $ case msub of
+      Nothing -> no "checking that all variables are bound" notBlocked_
+      Just sub -> do
+        ok <- checkPostponedEquations sub eqs
+        case ok of
+          Nothing -> return $ Right sub
+          Just b  -> no "checking of postponed equations" b
+
+-- | Typed βη-equality, also handles empty record types.
+--   Returns `Nothing` if the terms are equal, or `Just b` if the terms are not
+--   (where b contains information about possible metas blocking the comparison)
+equal :: PureTCM m => Type -> Term -> Term -> m (Maybe Blocked_)
+equal a u v = runBlocked (pureEqualTerm a u v) >>= \case
+  Left b      -> return $ Just $ Blocked b ()
+  Right True  -> return Nothing
+  Right False -> traceSDoc "rewriting.match" 10 (sep
+      [ "mismatch between " <+> prettyTCM u
+      , " and " <+> prettyTCM v
+      ]) $ do
+    return $ Just $ NotBlocked ReallyNotBlocked ()
+
+-- | Utility function for getting the name and type of a head term (i.e. a
+--   `Def` or `Con` with no arguments)
+getTypedHead :: PureTCM m => Term -> m (Maybe (QName, Type))
+getTypedHead = \case
+  Def f []   -> Just . (f,) . defType <$> getConstInfo f
+  Con (ConHead { conName = c }) _ [] -> do
+    -- Andreas, 2018-09-08, issue #3211:
+    -- discount module parameters for constructor heads
+    vs <- freeVarsToApply c
+    -- Jesper, 2020-06-17, issue #4755: add dummy arguments in
+    -- case we don't have enough parameters
+    getNumberOfParameters c >>= \case
+      Just npars -> do
+        let ws = replicate (npars - size vs) $ defaultArg __DUMMY_TERM__
+        t0 <- defType <$> getConstInfo c
+        t <- t0 `piApplyM` (vs ++ ws)
+        return $ Just (c , t)
+      Nothing -> return Nothing
+  _ -> return Nothing
diff --git a/src/full/Agda/TypeChecking/Rewriting/NonLinPattern.hs b/src/full/Agda/TypeChecking/Rewriting/NonLinPattern.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rewriting/NonLinPattern.hs
@@ -0,0 +1,415 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+{- | Various utility functions dealing with the non-linear, higher-order
+     patterns used for rewrite rules.
+-}
+
+module Agda.TypeChecking.Rewriting.NonLinPattern where
+
+import Prelude hiding ( null )
+
+import Control.Monad        ( (>=>), forM )
+import Control.Monad.Reader ( asks )
+
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Defs
+import Agda.Syntax.Internal.MetaVars ( AllMetas, unblockOnAllMetasIn )
+
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Free.Lazy
+import Agda.TypeChecking.Irrelevance (isPropM)
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Primitive.Cubical.Base
+
+import Agda.Utils.Functor
+import Agda.Utils.Impossible
+import Agda.Utils.List
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+-- | Turn a term into a non-linear pattern, treating the
+--   free variables as pattern variables.
+--   The first argument indicates the relevance we are working under: if this
+--   is Irrelevant, then we construct a pattern that never fails to match.
+--   The second argument is the number of bound variables (from pattern lambdas).
+--   The third argument is the type of the term.
+
+class PatternFrom a b where
+  patternFrom :: Relevance -> Int -> TypeOf a -> a -> TCM b
+
+instance (PatternFrom a b) => PatternFrom (Arg a) (Arg b) where
+  patternFrom r k t u = let r' = r `composeRelevance` getRelevance u
+                        in  traverse (patternFrom r' k $ unDom t) u
+
+instance PatternFrom Elims [Elim' NLPat] where
+  patternFrom r k (t,hd) = \case
+    [] -> return []
+    (Apply u : es) -> do
+      (a, b) <- assertPi t
+      p   <- patternFrom r k a u
+      let t'  = absApp b (unArg u)
+      let hd' = hd . (Apply u:)
+      ps  <- patternFrom r k (t',hd') es
+      return $ Apply p : ps
+    (IApply x y i : es) -> do
+      (s, q, l, b, u, v) <- assertPath t
+      let t' = El s $ unArg b `apply` [ defaultArg i ]
+      let hd' = hd . (IApply x y i:)
+      interval <- primIntervalType
+      p   <- patternFrom r k interval i
+      ps  <- patternFrom r k (t',hd') es
+      return $ IApply (PTerm x) (PTerm y) p : ps
+    (Proj o f : es) -> do
+      (a,b) <- assertProjOf f t
+      let u = hd []
+          t' = b `absApp` u
+      hd' <- applyDef o f (argFromDom a $> u)
+      ps  <- patternFrom r k (t',applyE hd') es
+      return $ Proj o f : ps
+
+instance (PatternFrom a b) => PatternFrom (Dom a) (Dom b) where
+  patternFrom r k t = traverse $ patternFrom r k t
+
+instance PatternFrom Type NLPType where
+  patternFrom r k _ a = workOnTypes $
+    NLPType <$> patternFrom r k () (getSort a)
+            <*> patternFrom r k (sort $ getSort a) (unEl a)
+
+instance PatternFrom Sort NLPSort where
+  patternFrom r k _ s = do
+    s <- abortIfBlocked s
+    case s of
+      Univ u l -> PUniv u <$> patternFrom r k () l
+      Inf u n  -> return $ PInf u n
+      SizeUniv -> return PSizeUniv
+      LockUniv -> return PLockUniv
+      LevelUniv -> return PLevelUniv
+      IntervalUniv -> return PIntervalUniv
+      PiSort _ _ _ -> __IMPOSSIBLE__
+      FunSort _ _ -> __IMPOSSIBLE__
+      UnivSort _ -> __IMPOSSIBLE__
+      MetaS{}  -> __IMPOSSIBLE__
+      DefS{}   -> __IMPOSSIBLE__
+      DummyS s -> do
+        reportS "impossible" 10
+          [ "patternFrom: hit dummy sort with content:"
+          , s
+          ]
+        __IMPOSSIBLE__
+
+instance PatternFrom Level NLPat where
+  patternFrom r k _ l = do
+    t <- levelType
+    v <- reallyUnLevelView l
+    patternFrom r k t v
+
+instance PatternFrom Term NLPat where
+  patternFrom r0 k t v = do
+    t <- abortIfBlocked t
+    etaRecord <- isEtaRecordType t
+    prop <- isPropM t
+    let r = if prop then Irrelevant else r0
+    v <- unLevel =<< abortIfBlocked v
+    reportSDoc "rewriting.build" 60 $ sep
+      [ "building a pattern from term v = " <+> prettyTCM v
+      , " of type " <+> prettyTCM t
+      ]
+    pview <- pathViewAsPi'whnf
+    let done = blockOnMetasIn v >> return (PTerm v)
+    case (unEl t , stripDontCare v) of
+      (Pi a b , _) -> do
+        let body = raise 1 v `apply` [ Arg (domInfo a) $ var 0 ]
+        p <- addContext a (patternFrom r (k + 1) (absBody b) body)
+        return $ PLam (domInfo a) $ Abs (absName b) p
+      _ | Left ((a,b),(x,y)) <- pview t -> do
+        let body = raise 1 v `applyE` [ IApply (raise 1 $ x) (raise 1 $ y) $ var 0 ]
+        p <- addContext a (patternFrom r (k + 1) (absBody b) body)
+        return $ PLam (domInfo a) $ Abs (absName b) p
+      (_ , Var i es)
+       | i < k     -> do
+           t <- typeOfBV i
+           PBoundVar i <$> patternFrom r k (t , Var i) es
+       -- The arguments of `var i` should be distinct bound variables
+       -- in order to build a Miller pattern
+       | Just vs <- allApplyElims es -> do
+           TelV tel rest <- telViewPath =<< typeOfBV i
+           unless (natSize tel >= natSize vs) $ blockOnMetasIn rest >> addContext tel (errNotPi rest)
+           let ts = applySubst (parallelS $ reverse $ map unArg vs) $ map unDom $ flattenTel tel
+           mbvs <- forM (zip ts vs) $ \(t , v) -> do
+             blockOnMetasIn (v,t)
+             isEtaVar (unArg v) t >>= \case
+               Just j | j < k -> return $ Just $ v $> j
+               _              -> return Nothing
+           case sequence mbvs of
+             Just bvs | fastDistinct bvs -> do
+               let allBoundVars = IntSet.fromList (downFrom k)
+                   ok = not (isIrrelevant r) ||
+                        IntSet.fromList (map unArg bvs) == allBoundVars
+               if ok then return (PVar i bvs) else done
+             _ -> done
+       | otherwise -> done
+      (_ , _ ) | Just (d, pars) <- etaRecord -> do
+        def <- theDef <$> getConstInfo d
+        (tel, c, ci, vs) <- etaExpandRecord_ d pars def v
+        ct <- assertConOf c t
+        PDef (conName c) <$> patternFrom r k (ct , Con c ci) (map Apply vs)
+      (_ , Lam{})   -> errNotPi t
+      (_ , Lit{})   -> done
+      (_ , Def f es) | isIrrelevant r -> done
+      (_ , Def f es) -> do
+        Def lsuc [] <- primLevelSuc
+        Def lmax [] <- primLevelMax
+        case es of
+          [x]     | f == lsuc -> done
+          [x , y] | f == lmax -> done
+          _                   -> do
+            ft <- defType <$> getConstInfo f
+            PDef f <$> patternFrom r k (ft , Def f) es
+      (_ , Con c ci vs) | isIrrelevant r -> done
+      (_ , Con c ci vs) -> do
+        ct <- assertConOf c t
+        PDef (conName c) <$> patternFrom r k (ct , Con c ci) vs
+      (_ , Pi a b) | isIrrelevant r -> done
+      (_ , Pi a b) -> do
+        pa <- patternFrom r k () a
+        pb <- addContext a (patternFrom r (k + 1) () $ absBody b)
+        return $ PPi pa (Abs (absName b) pb)
+      (_ , Sort s)     -> PSort <$> patternFrom r k () s
+      (_ , Level l)    -> __IMPOSSIBLE__
+      (_ , DontCare{}) -> __IMPOSSIBLE__
+      (_ , MetaV m _)  -> __IMPOSSIBLE__
+      (_ , Dummy s _)  -> __IMPOSSIBLE_VERBOSE__ s
+
+-- | Convert from a non-linear pattern to a term.
+
+class NLPatToTerm p a where
+  nlPatToTerm :: PureTCM m => p -> m a
+
+  default nlPatToTerm ::
+    ( NLPatToTerm p' a', Traversable f, p ~ f p', a ~ f a'
+    , PureTCM m
+    ) => p -> m a
+  nlPatToTerm = traverse nlPatToTerm
+
+instance NLPatToTerm p a => NLPatToTerm [p] [a] where
+instance NLPatToTerm p a => NLPatToTerm (Arg p) (Arg a) where
+instance NLPatToTerm p a => NLPatToTerm (Dom p) (Dom a) where
+instance NLPatToTerm p a => NLPatToTerm (Elim' p) (Elim' a) where
+instance NLPatToTerm p a => NLPatToTerm (Abs p) (Abs a) where
+
+instance NLPatToTerm Nat Term where
+  nlPatToTerm = return . var
+
+instance NLPatToTerm NLPat Term where
+  nlPatToTerm = \case
+    PVar i xs      -> Var i . map Apply <$> nlPatToTerm xs
+    PTerm u        -> return u
+    PDef f es      -> (theDef <$> getConstInfo f) >>= \case
+      Constructor{ conSrcCon = c } -> Con c ConOSystem <$> nlPatToTerm es
+      _                            -> Def f <$> nlPatToTerm es
+    PLam i u       -> Lam i <$> nlPatToTerm u
+    PPi a b        -> Pi    <$> nlPatToTerm a <*> nlPatToTerm b
+    PSort s        -> Sort  <$> nlPatToTerm s
+    PBoundVar i es -> Var i <$> nlPatToTerm es
+
+instance NLPatToTerm NLPat Level where
+  nlPatToTerm = nlPatToTerm >=> levelView
+
+instance NLPatToTerm NLPType Type where
+  nlPatToTerm (NLPType s a) = El <$> nlPatToTerm s <*> nlPatToTerm a
+
+instance NLPatToTerm NLPSort Sort where
+  nlPatToTerm (PUniv u l) = Univ u <$> nlPatToTerm l
+  nlPatToTerm (PInf u n) = return $ Inf u n
+  nlPatToTerm PSizeUniv = return SizeUniv
+  nlPatToTerm PLockUniv = return LockUniv
+  nlPatToTerm PLevelUniv = return LevelUniv
+  nlPatToTerm PIntervalUniv = return IntervalUniv
+
+-- | Gather the set of pattern variables of a non-linear pattern
+class NLPatVars a where
+  nlPatVarsUnder :: Int -> a -> IntSet
+
+  nlPatVars :: a -> IntSet
+  nlPatVars = nlPatVarsUnder 0
+
+instance {-# OVERLAPPABLE #-} (Foldable f, NLPatVars a) => NLPatVars (f a) where
+  nlPatVarsUnder k = foldMap $ nlPatVarsUnder k
+
+instance NLPatVars NLPType where
+  nlPatVarsUnder k (NLPType l a) = nlPatVarsUnder k (l, a)
+
+instance NLPatVars NLPSort where
+  nlPatVarsUnder k = \case
+    PUniv _ l   -> nlPatVarsUnder k l
+    PInf f n  -> empty
+    PSizeUniv -> empty
+    PLockUniv -> empty
+    PLevelUniv -> empty
+    PIntervalUniv -> empty
+
+instance NLPatVars NLPat where
+  nlPatVarsUnder k = \case
+      PVar i _  -> singleton $ i - k
+      PDef _ es -> nlPatVarsUnder k es
+      PLam _ p  -> nlPatVarsUnder k p
+      PPi a b   -> nlPatVarsUnder k (a, b)
+      PSort s   -> nlPatVarsUnder k s
+      PBoundVar _ es -> nlPatVarsUnder k es
+      PTerm{}   -> empty
+
+instance (NLPatVars a, NLPatVars b) => NLPatVars (a,b) where
+  nlPatVarsUnder k (a,b) = nlPatVarsUnder k a `mappend` nlPatVarsUnder k b
+
+instance NLPatVars a => NLPatVars (Abs a) where
+  nlPatVarsUnder k = \case
+    Abs   _ v -> nlPatVarsUnder (k + 1) v
+    NoAbs _ v -> nlPatVarsUnder k v
+
+-- | Get all symbols that a non-linear pattern matches against
+class GetMatchables a where
+  getMatchables :: a -> [QName]
+
+  default getMatchables :: (Foldable f, GetMatchables a', a ~ f a') => a -> [QName]
+  getMatchables = foldMap getMatchables
+
+instance GetMatchables a => GetMatchables [a] where
+instance GetMatchables a => GetMatchables (Arg a) where
+instance GetMatchables a => GetMatchables (Dom a) where
+instance GetMatchables a => GetMatchables (Elim' a) where
+instance GetMatchables a => GetMatchables (Abs a) where
+
+instance (GetMatchables a, GetMatchables b) => GetMatchables (a,b) where
+  getMatchables (x,y) = getMatchables x ++ getMatchables y
+
+instance GetMatchables NLPat where
+  getMatchables p =
+    case p of
+      PVar _ _       -> empty
+      PDef f es      -> singleton f ++ getMatchables es
+      PLam _ x       -> getMatchables x
+      PPi a b        -> getMatchables (a,b)
+      PSort s        -> getMatchables s
+      PBoundVar i es -> getMatchables es
+      PTerm u        -> getMatchables u
+
+instance GetMatchables NLPType where
+  getMatchables = getMatchables . nlpTypeUnEl
+
+instance GetMatchables NLPSort where
+  getMatchables = \case
+    PUniv _ l -> getMatchables l
+    PInf f n  -> empty
+    PSizeUniv -> empty
+    PLockUniv -> empty
+    PLevelUniv -> empty
+    PIntervalUniv -> empty
+
+instance GetMatchables Term where
+  getMatchables = getDefs' __IMPOSSIBLE__ singleton
+
+instance GetMatchables RewriteRule where
+  getMatchables = getMatchables . rewPats
+
+-- | Only computes free variables that are not bound (see 'nlPatVars'),
+--   i.e., those in a 'PTerm'.
+
+instance Free NLPat where
+  freeVars' = \case
+    PVar _ _       -> mempty
+    PDef _ es      -> freeVars' es
+    PLam _ u       -> freeVars' u
+    PPi a b        -> freeVars' (a,b)
+    PSort s        -> freeVars' s
+    PBoundVar _ es -> freeVars' es
+    PTerm t        -> freeVars' t
+
+instance Free NLPType where
+  freeVars' (NLPType s a) =
+    ifM (asks ((IgnoreNot ==) . feIgnoreSorts))
+      {- then -} (freeVars' (s, a))
+      {- else -} (freeVars' a)
+
+instance Free NLPSort where
+  freeVars' = \case
+    PUniv _ l -> freeVars' l
+    PInf f n  -> mempty
+    PSizeUniv -> mempty
+    PLockUniv -> mempty
+    PLevelUniv -> mempty
+    PIntervalUniv -> mempty
+
+-- Throws a pattern violation if the given term contains any
+-- metavariables.
+blockOnMetasIn :: (MonadBlock m, AllMetas t) => t -> m ()
+blockOnMetasIn t = case unblockOnAllMetasIn t of
+  UnblockOnAll ms | null ms -> return ()
+  b -> patternViolation b
+
+-- Helper functions
+
+
+assertPi :: Type -> TCM (Dom Type, Abs Type)
+assertPi t = abortIfBlocked t >>= \case
+  El _ (Pi a b) -> return (a,b)
+  t             -> errNotPi t
+
+errNotPi :: Type -> TCM a
+errNotPi t = typeError . GenericDocError =<< fsep
+    [ prettyTCM t
+    , "should be a function type, but it isn't."
+    , "Do you have any non-confluent rewrite rules?"
+    ]
+
+assertPath :: Type -> TCM (Sort, QName, Arg Term, Arg Term, Arg Term, Arg Term)
+assertPath t = abortIfBlocked t >>= pathView >>= \case
+  PathType s q l b u v -> return (s,q,l,b,u,v)
+  OType t -> errNotPath t
+
+errNotPath :: Type -> TCM a
+errNotPath t = typeError . GenericDocError =<< fsep
+    [ prettyTCM t
+    , "should be a path type, but it isn't."
+    , "Do you have any non-confluent rewrite rules?"
+    ]
+
+assertProjOf :: QName -> Type -> TCM (Dom Type, Abs Type)
+assertProjOf f t = do
+  t <- abortIfBlocked t
+  getDefType f t >>= \case
+    Just (El _ (Pi a b)) -> return (a,b)
+    _ -> errNotProjOf f t
+
+errNotProjOf :: QName -> Type -> TCM a
+errNotProjOf f t = typeError . GenericDocError =<< fsep
+      [ prettyTCM f , "should be a projection from type"
+      , prettyTCM t , "but it isn't."
+      , "Do you have any non-confluent rewrite rules?"
+      ]
+
+assertConOf :: ConHead -> Type -> TCM Type
+assertConOf c t = getFullyAppliedConType c t >>= \case
+    Just (_ , ct) -> return ct
+    Nothing -> errNotConOf c t
+
+errNotConOf :: ConHead -> Type -> TCM a
+errNotConOf c t = typeError . GenericDocError =<< fsep
+      [ prettyTCM c , "should be a constructor of type"
+      , prettyTCM t , "but it isn't."
+      , "Do you have any non-confluent rewrite rules?"
+      ]
diff --git a/src/full/Agda/TypeChecking/Rules/Application.hs b/src/full/Agda/TypeChecking/Rules/Application.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Application.hs
@@ -0,0 +1,1765 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Application
+  ( checkArguments
+  , checkArguments_
+  , checkApplication
+  , inferApplication
+  , checkProjAppToKnownPrincipalArg
+  , univChecks
+  , suffixToLevel
+  ) where
+
+import Prelude hiding ( null )
+
+import Control.Applicative        ( (<|>) )
+import Control.Monad              ( filterM, forM, forM_, guard, liftM2 )
+import Control.Monad.Except       ( ExceptT, runExceptT, MonadError, catchError, throwError )
+import Control.Monad.Trans
+import Control.Monad.Trans.Maybe
+
+import Data.Bifunctor
+import Data.Maybe
+import Data.Void
+import qualified Data.Foldable as Fold
+import qualified Data.IntSet   as IntSet
+
+import Agda.Interaction.Highlighting.Generate
+  ( storeDisambiguatedConstructor, storeDisambiguatedProjection )
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views as A
+import qualified Agda.Syntax.Info as A
+import Agda.Syntax.Concrete.Pretty () -- only Pretty instances
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Implicit
+import Agda.TypeChecking.Injectivity
+import Agda.TypeChecking.InstanceArguments (postponeInstanceConstraints)
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Modalities
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Rules.Def
+import Agda.TypeChecking.Rules.Term
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Either
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List  ( (!!!), initWithDefault )
+import qualified Agda.Utils.List as List
+import Agda.Utils.List1 ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+-----------------------------------------------------------------------------
+-- * Applications
+-----------------------------------------------------------------------------
+
+-- | Ranges of checked arguments, where present.
+type MaybeRanges = [Maybe Range]
+
+acHeadConstraints :: (Elims -> Term) -> ArgsCheckState a -> [Constraint]
+acHeadConstraints hd ACState{acElims = es, acConstraints = cs} = go hd es cs
+  where
+    go hd [] [] = []
+    go hd (e : es) (c : cs) = maybe id (\ c -> (lazyAbsApp c (hd []) :)) c $ go (hd . (e :)) es cs
+    go _  [] (_:_) = __IMPOSSIBLE__
+    go _  (_:_) [] = __IMPOSSIBLE__
+
+checkHeadConstraints :: (Elims -> Term) -> ArgsCheckState a -> TCM Term
+checkHeadConstraints hd st = do
+  mapM_ solveConstraint_ (acHeadConstraints hd st)
+  return $ hd (acElims st)
+
+
+-- | @checkApplication hd args e t@ checks an application.
+--   Precondition: @Application hs args = appView e@
+--
+--   @checkApplication@ disambiguates constructors
+--   (and continues to 'checkConstructorApplication')
+--   and resolves pattern synonyms.
+checkApplication :: Comparison -> A.Expr -> A.Args -> A.Expr -> Type -> TCM Term
+checkApplication cmp hd args e t =
+  turnOffExpandLastIfExistingMeta hd $
+  postponeInstanceConstraints $ do
+  reportSDoc "tc.check.app" 20 $ vcat
+    [ "checkApplication"
+    , nest 2 $ "hd   = " <+> prettyA hd
+    , nest 2 $ "args = " <+> sep (map prettyA args)
+    , nest 2 $ "e    = " <+> prettyA e
+    , nest 2 $ "t    = " <+> prettyTCM t
+    ]
+  reportSDoc "tc.check.app" 70 $ vcat
+    [ "checkApplication (raw)"
+    , nest 2 $ text $ "hd   = " ++ show hd
+    , nest 2 $ text $ "args = " ++ show (deepUnscope args)
+    , nest 2 $ text $ "e    = " ++ show (deepUnscope e)
+    , nest 2 $ text $ "t    = " ++ show t
+    ]
+  case unScope hd of
+    -- Subcase: unambiguous projection
+    A.Proj o p | Just x <- getUnambiguous p -> do
+      checkUnambiguousProjectionApplication cmp e t x o hd args
+
+    -- Subcase: ambiguous projection
+    A.Proj o p -> do
+      checkProjApp cmp e o (unAmbQ p) args t
+
+    -- Subcase: unambiguous constructor
+    A.Con ambC | Just c <- getUnambiguous ambC -> do
+      -- augment c with record fields, but do not revert to original name
+      con <-
+        fromRightM
+          (sigError (typeError $ AbstractConstructorNotInScope c)) $
+          getOrigConHead c
+      checkConstructorApplication cmp e t con args
+
+    -- Subcase: ambiguous constructor
+    A.Con (AmbQ cs0) -> disambiguateConstructor cs0 args t >>= \ case
+      Left unblock -> postponeTypeCheckingProblem (CheckExpr cmp e t) unblock
+      Right c      -> checkConstructorApplication cmp e t c args
+
+    -- Subcase: pattern synonym
+    A.PatternSyn n -> do
+      (ns, p) <- lookupPatternSyn n
+      p <- return $ setRange (getRange n) $ killRange $ vacuous p   -- Pattern' Void -> Pattern' Expr
+      -- Expand the pattern synonym by substituting for
+      -- the arguments we have got and lambda-lifting
+      -- over the ones we haven't.
+      let meta r = A.Underscore $ A.emptyMetaInfo{ A.metaRange = r }   -- TODO: name suggestion
+      case A.insertImplicitPatSynArgs meta (getRange n) ns args of
+        Nothing      -> typeError $ BadArgumentsToPatternSynonym n
+        Just (s, ns) -> do
+          let p' = A.patternToExpr p
+              e' = A.lambdaLiftExpr (map unArg ns) (A.substExpr s p')
+          checkExpr' cmp e' t
+
+    -- Subcase: macro
+    A.Macro x -> do
+      -- First go: no parameters
+      TelV tel _ <- telView . defType =<< instantiateDef =<< getConstInfo x
+
+      tTerm <- primAgdaTerm
+      tName <- primQName
+
+      -- Andreas, 2021-05-13, can we use @initWithDefault __IMPOSSIBLE__@ here?
+      let argTel   = init $ telToList tel -- last argument is the hole term
+
+          -- inspect macro type to figure out if arguments need to be wrapped in quote/quoteTerm
+          mkArg :: Type -> NamedArg A.Expr -> NamedArg A.Expr
+          mkArg t a | unEl t == tTerm =
+            (fmap . fmap)
+              (A.App (A.defaultAppInfo (getRange a)) (A.QuoteTerm A.exprNoRange) . defaultNamedArg) a
+          mkArg t a | unEl t == tName =
+            (fmap . fmap)
+              (A.App (A.defaultAppInfo (getRange a)) (A.Quote A.exprNoRange) . defaultNamedArg) a
+          mkArg t a | otherwise = a
+
+          makeArgs :: [Dom (String, Type)] -> [NamedArg A.Expr] -> ([NamedArg A.Expr], [NamedArg A.Expr])
+          makeArgs [] args = ([], args)
+          makeArgs _  []   = ([], [])
+          makeArgs tel@(d : tel1) (arg : args) =
+            case insertImplicit arg tel of
+              NoInsertNeeded -> first (mkArg (snd $ unDom d) arg :) $ makeArgs tel1 args
+              ImpInsert is   -> makeArgs (drop (length is) tel) (arg : args)
+              BadImplicits   -> (arg : args, [])  -- fail later in checkHeadApplication
+              NoSuchName{}   -> (arg : args, [])  -- ditto
+
+          (macroArgs, otherArgs) = makeArgs argTel args
+          unq = A.App (A.defaultAppInfo $ fuseRange x args) (A.Unquote A.exprNoRange) . defaultNamedArg
+
+          desugared = A.app (unq $ unAppView $ Application (A.Def x) $ macroArgs) otherArgs
+
+      checkExpr' cmp desugared t
+
+    -- Subcase: unquote
+    A.Unquote _
+      | [arg] <- args -> do
+          (_, hole) <- newValueMeta RunMetaOccursCheck CmpLeq t
+          unquoteM (namedArg arg) hole t
+          return hole
+      | arg : args <- args -> do
+          -- Example: unquote v a b : A
+          --  Create meta H : (x : X) (y : Y x) → Z x y for the hole
+          --  Check a : X, b : Y a
+          --  Unify Z a b == A
+          --  Run the tactic on H
+          tel    <- metaTel args                    -- (x : X) (y : Y x)
+          target <- addContext tel newTypeMeta_      -- Z x y
+          let holeType = telePi_ tel target         -- (x : X) (y : Y x) → Z x y
+          (Just vs, EmptyTel) <- mapFst allApplyElims <$> checkArguments_ CmpLeq ExpandLast (getRange args) args tel
+                                                    -- a b : (x : X) (y : Y x)
+          let rho = reverse (map unArg vs) ++# IdS  -- [x := a, y := b]
+          equalType (applySubst rho target) t       -- Z a b == A
+          (_, hole) <- newValueMeta RunMetaOccursCheck CmpLeq holeType
+          unquoteM (namedArg arg) hole holeType
+          return $ apply hole vs
+      where
+        metaTel :: [Arg a] -> TCM Telescope
+        metaTel []           = pure EmptyTel
+        metaTel (arg : args) = do
+          a <- newTypeMeta_
+          let dom = a <$ domFromArg arg
+          ExtendTel dom . Abs "x" <$>
+            addContext ("x" :: String, dom) (metaTel args)
+
+    -- Subcase: defined symbol or variable.
+    _ -> do
+      v <- checkHeadApplication cmp e t hd args
+      reportSDoc "tc.term.app" 30 $ vcat
+        [ "checkApplication: checkHeadApplication returned"
+        , nest 2 $ "v = " <+> prettyTCM v
+        ]
+      return v
+
+-- | Precondition: @Application hd args = appView e@.
+inferApplication :: ExpandHidden -> A.Expr -> A.Args -> A.Expr -> TCM (Term, Type)
+inferApplication exh hd args e | not (defOrVar hd) = do
+  t <- workOnTypes $ newTypeMeta_
+  v <- checkExpr' CmpEq e t
+  return (v, t)
+inferApplication exh hd args e = postponeInstanceConstraints $ do
+  SortKit{..} <- sortKit
+  case unScope hd of
+    A.Proj o p | isAmbiguous p -> inferProjApp e o (unAmbQ p) args
+    A.Def' x s | Just (sz, u) <- isNameOfUniv x -> inferUniv sz u e x s args
+    _ -> do
+      (f, t0) <- inferHead hd
+      let r = getRange hd
+      res <- runExceptT $ checkArgumentsE CmpEq exh (getRange hd) args t0 Nothing
+      case res of
+        Right st@(ACState{acType = t1}) -> fmap (,t1) $ unfoldInlined =<< checkHeadConstraints f st
+        Left problem -> do
+          t <- workOnTypes $ newTypeMeta_
+          v <- postponeArgs problem CmpEq exh r args t $ \ st -> unfoldInlined =<< checkHeadConstraints f st
+          return (v, t)
+
+-----------------------------------------------------------------------------
+-- * Heads
+-----------------------------------------------------------------------------
+
+inferHeadDef :: ProjOrigin -> QName -> TCM (Elims -> Term, Type)
+inferHeadDef o x = do
+  -- Andreas, 2022-03-07, issue #5809: don't drop parameters of irrelevant projections.
+  proj <- isRelevantProjection x
+  rel  <- getRelevance . defArgInfo <$> getConstInfo x
+  let app =
+        case proj of
+          Nothing -> \ args -> Def x $ map Apply args
+          Just p  -> \ args -> projDropParsApply p o rel args
+  mapFst applyE <$> inferDef app x
+
+-- | Infer the type of a head thing (variable, function symbol, or constructor).
+--   We return a function that applies the head to arguments.
+--   This is because in case of a constructor we want to drop the parameters.
+inferHead :: A.Expr -> TCM (Elims -> Term, Type)
+inferHead e = do
+  case e of
+    A.Var x -> do -- traceCall (InferVar x) $ do
+      (u, a) <- getVarInfo x
+      reportSDoc "tc.term.var" 20 $ hsep
+        [ "variable" , prettyTCM x
+        , "(" , text (show u) , ")"
+        , "has type:" , prettyTCM a
+        ]
+      unless (usableRelevance a) $
+        typeError $ VariableIsIrrelevant x
+      -- Andreas, 2019-06-18, LAIM 2019, issue #3855:
+      -- Conor McBride style quantity judgement:
+      -- The available quantity for variable x must be below
+      -- the required quantity to construct the term x.
+      -- Note: this whole thing does not work for linearity, where we need some actual arithmetics.
+      unlessM ((getQuantity a `moreQuantity`) <$> viewTC eQuantity) $
+        typeError $ VariableIsErased x
+
+      unless (usableCohesion a) $
+        typeError $ VariableIsOfUnusableCohesion x (getCohesion a)
+
+      return (applyE u, unDom a)
+
+    A.Def x  -> inferHeadDef ProjPrefix x
+    A.Def'{} -> __IMPOSSIBLE__ -- handled in checkHeadApplication and inferApplication
+
+    A.Proj o ambP | Just d <- getUnambiguous ambP -> inferHeadDef o d
+    A.Proj{} -> __IMPOSSIBLE__ -- inferHead will only be called on unambiguous projections
+
+    A.Con ambC | Just c <- getUnambiguous ambC -> do
+
+      -- Constructors are polymorphic internally.
+      -- So, when building the constructor term
+      -- we should throw away arguments corresponding to parameters.
+
+      -- First, inferDef will try to apply the constructor
+      -- to the free parameters of the current context. We ignore that.
+      con <-
+        fromRightM
+          (sigError (typeError $ AbstractConstructorNotInScope c)) $
+          getOrigConHead c
+      (u, a) <- inferDef (\ _ -> Con con ConOCon []) c
+
+      -- Next get the number of parameters in the current context.
+      Constructor{conPars = n} <- theDef <$> (instantiateDef =<< getConstInfo c)
+
+      reportSLn "tc.term.con" 7 $ unwords [prettyShow c, "has", show n, "parameters."]
+
+      -- So when applying the constructor throw away the parameters.
+      return (applyE u . drop n, a)
+    A.Con{} -> __IMPOSSIBLE__  -- inferHead will only be called on unambiguous constructors
+    A.QuestionMark i ii -> inferMeta (newQuestionMark ii) i
+    A.Underscore i   -> inferMeta (newValueMeta RunMetaOccursCheck) i
+    e -> do
+      (term, t) <- inferExpr e
+      return (applyE term, t)
+
+inferDef :: (Args -> Term) -> QName -> TCM (Term, Type)
+inferDef mkTerm x =
+  traceCall (InferDef x) $ do
+    -- getConstInfo retrieves the *absolute* (closed) type of x
+    -- instantiateDef relativizes it to the current context
+    d0 <- getConstInfo x
+    d  <- instantiateDef d0
+    reportSDoc "tc.term.def" 10 $ "inferDef" <+> prettyTCM x
+    reportSDoc "tc.term.def" 30 $ "  absolute type:    " <+> inTopContext (prettyTCM $ defType d0)
+    reportSDoc "tc.term.def" 30 $ "  instantiated type:" <+> prettyTCM (defType d)
+    -- Irrelevant defs are only allowed in irrelevant position.
+    -- Erased defs are only allowed in erased position (see #3855).
+    checkModality x d
+    case theDef d of
+      GeneralizableVar{} -> do
+        -- Generalizable variables corresponds to metas created
+        -- at the point where they should be generalized. Module parameters
+        -- have already been applied to the meta, so we don't have to do that
+        -- here.
+        val <- fromMaybe __IMPOSSIBLE__ <$> viewTC (eGeneralizedVars . key x)
+        sub <- checkpointSubstitution (genvalCheckpoint val)
+        let (v, t) = applySubst sub (genvalTerm val, genvalType val)
+        debug [] t v
+        return (v, t)
+      _ -> do
+        -- since x is considered living in the top-level, we have to
+        -- apply it to the current context
+        vs <- freeVarsToApply x
+        reportSDoc "tc.term.def" 30 $ "  free vars:" <+> prettyList_ (map prettyTCM vs)
+        let t = defType d
+            v = mkTerm vs -- applies x to vs, dropping parameters
+
+        -- Andrea 2019-07-16, Check that the supplied arguments
+        -- respect the pure modalities of the current context.
+        -- Pure modalities are based on left-division, so it does not
+        -- rely on "position" like positional modalities.
+        checkModalityArgs d0 vs
+
+        debug vs t v
+        return (v, t)
+  where
+    debug :: Args -> Type -> Term -> TCM ()
+    debug vs t v = do
+      reportSDoc "tc.term.def" 60 $
+        "freeVarsToApply to def " <+> hsep (map (text . show) vs)
+      reportSDoc "tc.term.def" 10 $ vcat
+        [ "inferred def " <+> prettyTCM x <+> hsep (map prettyTCM vs)
+        , nest 2 $ ":" <+> prettyTCM t
+        , nest 2 $ "-->" <+> prettyTCM v ]
+
+-- | @checkHeadApplication e t hd args@ checks that @e@ has type @t@,
+-- assuming that @e@ has the form @hd args@. The corresponding
+-- type-checked term is returned.
+--
+-- If the head term @hd@ is a coinductive constructor, then a
+-- top-level definition @fresh tel = hd args@ (where the clause is
+-- delayed) is added, where @tel@ corresponds to the current
+-- telescope. The returned term is @fresh tel@.
+--
+-- Precondition: The head @hd@ has to be unambiguous, and there should
+-- not be any need to insert hidden lambdas.
+checkHeadApplication :: Comparison -> A.Expr -> Type -> A.Expr -> [NamedArg A.Expr] -> TCM Term
+checkHeadApplication cmp e t hd args = do
+  SortKit{..} <- sortKit
+  sharp <- fmap nameOfSharp <$> coinductionKit
+  conId  <- getNameOfConstrained builtinConId
+  pOr    <- getNameOfConstrained builtinPOr
+  pComp  <- getNameOfConstrained builtinComp
+  pHComp <- getNameOfConstrained builtinHComp
+  pTrans <- getNameOfConstrained builtinTrans
+  mglue  <- getNameOfConstrained builtin_glue
+  mglueU  <- getNameOfConstrained builtin_glueU
+  case hd of
+    A.Def' c s | Just (sz, u) <- isNameOfUniv c -> checkUniv sz u cmp e t c s args
+
+    -- Type checking #. The # that the user can write will be a Def, but the
+    -- sharp we generate in the body of the wrapper is a Con.
+    A.Def c | Just c == sharp -> checkSharpApplication e t c args
+
+    -- Cubical primitives
+    A.Def c | Just c == pComp -> defaultResult' $ Just $ checkPrimComp c
+    A.Def c | Just c == pHComp -> defaultResult' $ Just $ checkPrimHComp c
+    A.Def c | Just c == pTrans -> defaultResult' $ Just $ checkPrimTrans c
+    A.Def c | Just c == conId -> defaultResult' $ Just $ checkConId c
+    A.Def c | Just c == pOr   -> defaultResult' $ Just $ checkPOr c
+    A.Def c | Just c == mglue -> defaultResult' $ Just $ check_glue c
+    A.Def c | Just c == mglueU -> defaultResult' $ Just $ check_glueU c
+
+    _ -> defaultResult
+  where
+  defaultResult :: TCM Term
+  defaultResult = defaultResult' Nothing
+  defaultResult' :: Maybe (MaybeRanges -> Args -> Type -> TCM Args) -> TCM Term
+  defaultResult' mk = do
+    (f, t0) <- inferHead hd
+    expandLast <- asksTC envExpandLast
+    checkArguments cmp expandLast (getRange hd) args t0 t $ \ st@(ACState rs vs _ t1 checkedTarget) -> do
+      let check = do
+           k <- mk
+           as <- allApplyElims vs
+           pure $ k rs as t1
+      vs <- case check of
+              Just ck -> do
+                map Apply <$> ck
+              Nothing -> do
+                return vs
+      v <- unfoldInlined =<< checkHeadConstraints f (st { acElims = vs })
+      coerce' cmp checkedTarget v t1 t
+
+-- Issue #3019 and #4170: Don't insert trailing implicits when checking arguments to existing
+-- metavariables.
+turnOffExpandLastIfExistingMeta :: A.Expr -> TCM a -> TCM a
+turnOffExpandLastIfExistingMeta hd
+  | isExistingMeta = reallyDontExpandLast
+  | otherwise      = id
+  where
+    isExistingMeta = isJust $ A.metaNumber =<< metaInfo hd
+    metaInfo (A.QuestionMark i _) = Just i
+    metaInfo (A.Underscore i)     = Just i
+    metaInfo (A.ScopedExpr _ e)   = metaInfo e
+    metaInfo _                    = Nothing
+
+-----------------------------------------------------------------------------
+-- * Spines
+-----------------------------------------------------------------------------
+
+traceCallE :: Call -> ExceptT e TCM r -> ExceptT e TCM r
+traceCallE call m = do
+  z <- lift $ traceCall call $ runExceptT m
+  case z of
+    Right e  -> return e
+    Left err -> throwError err
+
+-- | If we've already checked the target type we don't have to call coerce.
+coerce' :: Comparison -> CheckedTarget -> Term -> Type -> Type -> TCM Term
+coerce' cmp NotCheckedTarget           v inferred expected = coerce cmp v inferred expected
+coerce' cmp (CheckedTarget Nothing)    v _        _        = return v
+coerce' cmp (CheckedTarget (Just pid)) v _        expected = blockTermOnProblem expected v pid
+
+-- | Check a list of arguments: @checkArgs args t0 t1@ checks that
+--   @t0 = Delta -> t0'@ and @args : Delta@. Inserts hidden arguments to
+--   make this happen.  Returns the evaluated arguments @vs@, the remaining
+--   type @t0'@ (which should be a subtype of @t1@) and any constraints @cs@
+--   that have to be solved for everything to be well-formed.
+
+checkArgumentsE :: Comparison -> ExpandHidden -> Range -> [NamedArg A.Expr] -> Type -> Maybe Type ->
+                   ExceptT (ArgsCheckState [NamedArg A.Expr]) TCM (ArgsCheckState CheckedTarget)
+checkArgumentsE sComp sExpand sRange sArgs sFun sApp = do
+  sPathView <- pathView'
+  checkArgumentsE'
+    S{ sChecked       = NotCheckedTarget
+     , sArgs          = zip sArgs $
+                        List.suffixesSatisfying visible sArgs
+     , sArgsLen       = length sArgs
+     , sSizeLtChecked = False
+     , sSkipCheck     = DontSkip
+     , ..
+     }
+
+-- | State used by 'checkArgumentsE''.
+
+data CheckArgumentsE'State = S
+  { sChecked :: CheckedTarget
+    -- ^ Have we already checked the target?
+  , sComp :: Comparison
+    -- ^ Comparison to use if checking the target type.
+  , sExpand :: ExpandHidden
+    -- ^ Insert trailing hidden arguments?
+  , sRange :: Range
+    -- ^ Range of the function.
+  , sArgs :: [(NamedArg A.Expr, Bool)]
+    -- ^ Arguments, along with information about whether a given
+    -- argument and all remaining arguments are 'visible'.
+  , sArgsLen :: !Nat
+    -- ^ The length of 'sArgs'.
+  , sFun :: Type
+    -- ^ The function's type.
+  , sApp :: Maybe Type
+    -- ^ The type of the application.
+  , sSizeLtChecked :: !Bool
+    -- ^ Have we checked if 'sApp' is 'BoundedLt'?
+  , sSkipCheck :: !SkipCheck
+    -- ^ Should the target type check be skipped?
+  , sPathView :: Type -> PathView
+    -- ^ The function returned by 'pathView''.
+  }
+
+-- | Should the target type check in 'checkArgumentsE'' be skipped?
+
+data SkipCheck
+  = Skip
+  | SkipNext !Nat
+    -- ^ Skip the given number of checks.
+  | DontSkip
+
+checkArgumentsE'
+  :: CheckArgumentsE'State
+  -> ExceptT (ArgsCheckState [NamedArg A.Expr]) TCM (ArgsCheckState CheckedTarget)
+
+-- Case: no arguments, do not insert trailing hidden arguments: We are done.
+checkArgumentsE' S{ sArgs = [], .. }
+  | isDontExpandLast sExpand =
+    return $ ACState
+      { acRanges      = []
+      , acElims       = []
+      , acConstraints = []
+      , acType        = sFun
+      , acData        = sChecked
+      }
+
+-- Case: no arguments, but need to insert trailing hiddens.
+checkArgumentsE' S{ sArgs = [], .. } =
+  traceCallE (CheckArguments sRange [] sFun sApp) $ lift $ do
+    sApp    <- traverse (unEl <.> reduce) sApp
+    (us, t) <- implicitArgs (-1) (expand sApp) sFun
+    return $ ACState
+      { acRanges      = replicate (length us) Nothing
+      , acElims       = map Apply us
+      , acConstraints = replicate (length us) Nothing
+      , acType        = t
+      , acData        = sChecked
+      }
+  where
+  expand (Just (Pi dom _)) Hidden     = not (hidden dom)
+  expand _                 Hidden     = True
+  expand (Just (Pi dom _)) Instance{} = not (isInstance dom)
+  expand _                 Instance{} = True
+  expand _                 NotHidden  = False
+
+-- Case: argument given.
+checkArgumentsE'
+  s@S{ sArgs = sArgs@((arg@(Arg info e), sArgsVisible) : args), .. } =
+
+    traceCallE (CheckArguments sRange (map fst sArgs) sFun sApp) $ do
+      lift $ reportSDoc "tc.term.args" 30 $ sep
+        [ "checkArgumentsE"
+--        , "  sArgs =" <+> prettyA sArgs
+        , nest 2 $ vcat
+          [ "e     =" <+> prettyA e
+          , "sFun  =" <+> prettyTCM sFun
+          , "sApp  =" <+> maybe "Nothing" prettyTCM sApp
+          ]
+        ]
+      -- First, insert implicit arguments, depending on current argument @arg@.
+      let hx = getHiding info  -- hiding of current argument
+          mx :: Maybe ArgName
+          mx = bareNameOf e    -- name of current argument
+          -- do not insert visible arguments
+          expand NotHidden y = False
+          -- insert a hidden argument if arg is not hidden or has different name
+          -- insert an instance argument if arg is not instance  or has different name
+          expand hy        y = not (sameHiding hy hx) || maybe False (y /=) mx
+      reportSDoc "tc.term.args" 30 $ vcat
+        [ "calling implicitNamedArgs"
+        , nest 2 $ "sFun = " <+> prettyTCM sFun
+        , nest 2 $ "hx   = " <+> text (show hx)
+        , nest 2 $ "mx   = " <+> maybe "nothing" prettyTCM mx
+        ]
+      (nargs, sFun) <- lift $ implicitNamedArgs (-1) expand sFun
+      -- Separate names from args.
+      let (mxs, us) = unzip $ map (\ (Arg ai (Named mx u)) -> (mx, Apply $ Arg ai u)) nargs
+          xs        = catMaybes mxs
+
+      -- We need a function type here, but we don't know which kind
+      -- (implicit/explicit). But it might be possible to use injectivity to
+      -- force a pi.
+      sFun <- lift $ forcePiUsingInjectivity sFun
+
+      -- We are done inserting implicit args.  Now, try to check @arg@.
+      ifBlocked sFun
+        (\_ sFun -> throwError $ ACState
+            { acRanges      = replicate (length us) Nothing
+            , acElims       = us
+            , acConstraints = replicate (length us) Nothing
+            , acType        = sFun
+            , acData        = map fst sArgs
+            }) $ \_ sFun -> do
+
+        -- What can go wrong?
+
+        -- 1. We ran out of function types.
+        let shouldBePi
+              -- a) It is an explicit argument, but we ran out of function types.
+              | visible info = lift $ typeError $ ShouldBePi sFun
+              -- b) It is an implicit argument, and we did not insert any implicits.
+              --    Thus, the type was not a function type to start with.
+              | null xs        = lift $ typeError $ ShouldBePi sFun
+              -- c) We did insert implicits, but we ran out of implicit function types.
+              --    Then, we should inform the user that we did not find his one.
+              | otherwise      = lift $ typeError $ WrongNamedArgument arg xs
+
+        -- 2. We have a function type left, but it is the wrong one.
+        --    Our argument must be implicit, case a) is impossible.
+        --    (Otherwise we would have ran out of function types instead.)
+        let wrongPi
+              -- b) We have not inserted any implicits.
+              | null xs   = lift $ typeError $
+                            WrongHidingInApplication sFun
+              -- c) We inserted implicits, but did not find his one.
+              | otherwise = lift $ typeError $ WrongNamedArgument arg xs
+
+        let (skip, next) = case sSkipCheck of
+              Skip       -> (True, Skip)
+              DontSkip   -> (False, DontSkip)
+              SkipNext n -> case compare n 1 of
+                LT -> (False, DontSkip)
+                EQ -> (True,  DontSkip)
+                GT -> (True,  SkipNext (n - 1))
+
+        s <- return s
+          { sRange     = fuseRange sRange e
+          , sArgs      = args
+          , sArgsLen   = sArgsLen - 1
+          , sFun       = sFun
+          , sSkipCheck = next
+          }
+
+        -- Check the target type if we can get away with it.
+        s <- lift $
+          case (sChecked, skip, sApp) of
+            (NotCheckedTarget, False, Just sApp) | sArgsVisible -> do
+              -- How many visible Π's (up to at most sArgsLen) does
+              -- sFun start with?
+              TelV tel tgt <- telViewUpTo' sArgsLen visible sFun
+              let visiblePis = size tel
+
+                  -- The free variables less than visiblePis in tgt.
+                  freeInTgt =
+                    fst $ IntSet.split visiblePis $ freeVars tgt
+
+              rigid <- isRigid s tgt
+              -- The target must be rigid.
+              case rigid of
+                IsNotRigid reason ->
+                      -- Skip the next visiblePis - 1 - k checks.
+                  let skip k   = s{ sSkipCheck =
+                                    SkipNext $ visiblePis - 1 - k
+                                  }
+                      dontSkip = s
+                  in return $ case reason of
+                    Permanent   -> skip 0
+                    Unspecified -> dontSkip
+                    AVar x      ->
+                      if x `IntSet.member` freeInTgt
+                      then skip x
+                      else skip 0
+                IsRigid -> do
+
+                      -- Is any free variable in tgt less than
+                      -- visiblePis?
+                  let dep = not (IntSet.null freeInTgt)
+                  -- The target must be non-dependent.
+                  if dep then return s else do
+
+                  -- Andreas, 2019-03-28, issue #3248:
+                  -- If the target type is SIZELT, we need coerce, leqType is insufficient.
+                  -- For example, we have i : Size <= (Size< ↑ i), but not Size <= (Size< ↑ i).
+                  (isSizeLt, sApp, s) <-
+                    if sSizeLtChecked
+                    then return (False, sApp, s)
+                    else do
+                      sApp     <- reduce sApp
+                      isSizeLt <- isSizeType sApp <&> \case
+                        Just (BoundedLt _) -> True
+                        _                  -> False
+                      return ( isSizeLt
+                             , sApp
+                             , s{ sApp           = Just sApp
+                                , sSizeLtChecked = True
+                                , sSkipCheck     =
+                                    if isSizeLt then Skip else DontSkip
+                                }
+                             )
+                  if isSizeLt then return s else do
+
+                  let tgt1 = applySubst
+                               (strengthenS impossible visiblePis)
+                               tgt
+                  reportSDoc "tc.term.args.target" 30 $ vcat
+                    [ "Checking target types first"
+                    , nest 2 $ "inferred =" <+> prettyTCM tgt1
+                    , nest 2 $ "expected =" <+> prettyTCM sApp ]
+                  chk <-
+                    traceCall
+                      (CheckTargetType
+                         (fuseRange sRange sArgs) tgt1 sApp) $
+                      CheckedTarget <$>
+                        ifNoConstraints_ (compareType sComp tgt1 sApp)
+                          (return Nothing) (return . Just)
+                  return s{ sChecked = chk }
+
+            _ -> return s
+
+        -- sFun <- lift $ forcePi (getHiding info)
+        --                  (maybe "_" rangedThing $ nameOf e) sFun
+        case unEl sFun of
+          Pi (Dom{domInfo = info', domName = dname, unDom = a}) b
+            | let name = bareNameWithDefault "_" dname,
+              sameHiding info info'
+              && (visible info || maybe True (name ==) mx) -> do
+                u <- lift $ applyModalityToContext info' $ do
+                 -- Andreas, 2014-05-30 experiment to check non-dependent arguments
+                 -- after the spine has been processed.  Allows to propagate type info
+                 -- from ascribed type into extended-lambdas.  Would solve issue 1159.
+                 -- However, leaves unsolved type checking problems in the test suite.
+                 -- I do not know what I am doing wrong here.
+                 -- Could be extreme order-sensitivity or my abuse of the postponing
+                 -- mechanism.
+                 -- Andreas, 2016-02-02: Ulf says unless there is actually some meta
+                 -- blocking a postponed type checking problem, we might never retry,
+                 -- since the trigger for retrying constraints is solving a meta.
+                 -- Thus, the following naive use violates some invariant.
+                 -- if not $ isBinderUsed b
+                 -- then postponeTypeCheckingProblem (CheckExpr (namedThing e) a) (return True) else
+                  let e' = e { nameOf = (nameOf e) <|> dname }
+                  checkNamedArg (Arg info' e') a
+
+                let
+                  c = case getLock info' of
+                    IsLock{} -> Just $ Abs "t" $
+                        CheckLockedVars (Var 0 []) (raise 1 sFun)
+                          (raise 1 $ Arg info' u) (raise 1 a)
+                    _ -> Nothing
+                lift $ reportSDoc "tc.term.lock" 40 $ text "lock =" <+> text (show $ getLock info')
+                lift $ reportSDoc "tc.term.lock" 40 $
+                  addContext (defaultDom $ sFun) $
+                  maybe (text "nothing") (prettyTCM . absBody) c
+                -- save relevance info' from domain in argument
+                addCheckedArgs us (getRange e) (Apply $ Arg info' u) c $
+                  checkArgumentsE' s{ sFun = absApp b u }
+            | otherwise -> do
+                reportSDoc "error" 10 $ nest 2 $ vcat
+                  [ text $ "info      = " ++ show info
+                  , text $ "info'     = " ++ show info'
+                  , text $ "absName b = " ++ absName b
+                  , text $ "nameOf e  = " ++ show (nameOf e)
+                  ]
+                wrongPi
+          _
+            | visible info
+            , PathType sort _ _ bA x y <- sPathView sFun -> do
+                lift $ reportSDoc "tc.term.args" 30 $ text $ show bA
+                u <- lift $ checkExpr (namedThing e) =<< primIntervalType
+                addCheckedArgs us (getRange e) (IApply (unArg x) (unArg y) u) Nothing $
+                  checkArgumentsE'
+                    s{ sChecked = NotCheckedTarget
+                     , sFun     = El sort $ unArg bA `apply` [argN u]
+                     }
+          _ -> shouldBePi
+  where
+    -- Andrea: Here one would add constraints too.
+    addCheckedArgs us r u c rec = do
+        st@ACState{acRanges = rs, acElims = vs} <- rec
+        let rs' = replicate (length us) Nothing ++ Just r : rs
+            cs' = replicate (length us) Nothing ++ c : acConstraints st
+        return $ st { acRanges = rs', acElims = us ++ u : vs, acConstraints = cs' }
+      `catchError` \ st@ACState{acRanges = rs, acElims = vs} -> do
+          let rs' = replicate (length us) Nothing ++ Just r : rs
+              cs' = replicate (length us) Nothing ++ c : acConstraints st
+          throwError $ st { acRanges = rs', acElims = us ++ u : vs, acConstraints = cs' }
+
+-- | The result of 'isRigid'.
+
+data IsRigid
+  = IsRigid
+    -- ^ The type is rigid.
+  | IsNotRigid !IsPermanent
+    -- ^ The type is not rigid. If the argument is 'Nothing', then
+    -- this will not change. If the argument is @'Just' reason@, then
+    -- this might change for the given @reason@.
+
+-- | Is the result of 'isRigid' \"permanent\"?
+
+data IsPermanent
+  = Permanent
+    -- ^ Yes.
+  | AVar !Nat
+    -- ^ The result does not change unless the given variable is
+    -- instantiated.
+  | Unspecified
+    -- ^ Maybe, maybe not.
+
+-- | Is the type \"rigid\"?
+
+isRigid :: CheckArgumentsE'State -> Type -> TCM IsRigid
+isRigid s t | PathType{} <- sPathView s t =
+  -- Path is not rigid.
+  return $ IsNotRigid Permanent
+isRigid _ (El _ t) = case t of
+  Var x _    -> return $ IsNotRigid (AVar x)
+  Lam{}      -> return $ IsNotRigid Permanent
+  Lit{}      -> return $ IsNotRigid Permanent
+  Con{}      -> return $ IsNotRigid Permanent
+  Pi dom _   -> return $
+                if visible dom then IsRigid else IsNotRigid Permanent
+  Sort{}     -> return $ IsNotRigid Permanent
+  Level{}    -> return $ IsNotRigid Permanent
+  MetaV{}    -> return $ IsNotRigid Unspecified
+  DontCare{} -> return $ IsNotRigid Permanent
+  Dummy{}    -> return $ IsNotRigid Permanent
+  Def d _    -> getConstInfo d <&> theDef <&> \case
+    Axiom{}                   -> IsRigid
+    DataOrRecSig{}            -> IsRigid
+    AbstractDefn{}            -> IsRigid
+    Function{funClauses = cs} -> if null cs
+                                 then IsRigid
+                                 else IsNotRigid Unspecified
+                                      -- This Reason could perhaps be
+                                      -- more precise (in some cases).
+    Datatype{}                -> IsRigid
+    Record{}                  -> IsRigid
+    Constructor{}             -> __IMPOSSIBLE__
+    GeneralizableVar{}        -> __IMPOSSIBLE__
+    Primitive{}               -> IsNotRigid Unspecified
+    PrimitiveSort{}           -> IsNotRigid Unspecified
+
+-- | Check that a list of arguments fits a telescope.
+--   Inserts hidden arguments as necessary.
+--   Returns the type-checked arguments and the remaining telescope.
+checkArguments_
+  :: Comparison           -- ^ Comparison for target
+  -> ExpandHidden         -- ^ Eagerly insert trailing hidden arguments?
+  -> Range                -- ^ Range of application.
+  -> [NamedArg A.Expr]    -- ^ Arguments to check.
+  -> Telescope            -- ^ Telescope to check arguments against.
+  -> TCM (Elims, Telescope)
+     -- ^ Checked arguments and remaining telescope if successful.
+checkArguments_ cmp exh r args tel = postponeInstanceConstraints $ do
+    z <- runExceptT $
+      checkArgumentsE cmp exh r args (telePi tel __DUMMY_TYPE__) Nothing
+    case z of
+      Right (ACState _ args cs t _) | all isNothing cs -> do
+        let TelV tel' _ = telView' t
+        return (args, tel')
+                                    | otherwise -> do
+        typeError $ GenericError $ "Head constraints are not (yet) supported in this position."
+      Left _ -> __IMPOSSIBLE__  -- type cannot be blocked as it is generated by telePi
+
+-- | @checkArguments cmp exph r args t0 t k@ tries @checkArgumentsE exph args t0 t@.
+-- If it succeeds, it continues @k@ with the returned results.  If it fails,
+-- it registers a postponed typechecking problem and returns the resulting new
+-- meta variable.
+--
+-- Checks @e := ((_ : t0) args) : t@.
+checkArguments ::
+  Comparison -> ExpandHidden -> Range -> [NamedArg A.Expr] -> Type -> Type ->
+  (ArgsCheckState CheckedTarget -> TCM Term) -> TCM Term
+checkArguments cmp exph r args t0 t k = postponeInstanceConstraints $ do
+  z <- runExceptT $ checkArgumentsE cmp exph r args t0 (Just t)
+  case z of
+    Right st -> k st
+      -- vs = evaluated args
+      -- t1 = remaining type (needs to be subtype of t)
+    Left problem -> postponeArgs problem cmp exph r args t k
+      -- if unsuccessful, postpone checking until t0 unblocks
+
+postponeArgs :: (ArgsCheckState [NamedArg A.Expr]) -> Comparison -> ExpandHidden -> Range -> [NamedArg A.Expr] -> Type ->
+                (ArgsCheckState CheckedTarget -> TCM Term) -> TCM Term
+postponeArgs (ACState rs us cs t0 es) cmp exph r args t k = do
+  reportSDoc "tc.term.expr.args" 80 $
+    sep [ "postponed checking arguments"
+        , nest 4 $ prettyList (map (prettyA . namedThing . unArg) args)
+        , nest 2 $ "against"
+        , nest 4 $ prettyTCM t0 ] $$
+    sep [ "progress:"
+        , nest 2 $ "checked" <+> prettyList (map prettyTCM us)
+        , nest 2 $ "remaining" <+> sep [ prettyList (map (prettyA . namedThing . unArg) es)
+                                            , nest 2 $ ":" <+> prettyTCM t0 ] ]
+  postponeTypeCheckingProblem_ (CheckArgs cmp exph r es t0 t $ \ (ACState rs' vs cs' t pid) -> k $ ACState (rs ++ rs') (us ++ vs) (cs ++ cs') t pid)
+
+-----------------------------------------------------------------------------
+-- * Constructors
+-----------------------------------------------------------------------------
+
+-- | Check the type of a constructor application. This is easier than
+--   a general application since the implicit arguments can be inserted
+--   without looking at the arguments to the constructor.
+checkConstructorApplication :: Comparison -> A.Expr -> Type -> ConHead -> [NamedArg A.Expr] -> TCM Term
+checkConstructorApplication cmp org t c args = do
+  reportSDoc "tc.term.con" 50 $ vcat
+    [ "entering checkConstructorApplication"
+    , nest 2 $ vcat
+      [ "org  =" <+> prettyTCM org
+      , "t    =" <+> prettyTCM t
+      , "c    =" <+> prettyTCM c
+      , "args =" <+> prettyTCM args
+    ] ]
+
+  cdef  <- getConInfo c
+
+  checkModality (conName c) cdef
+
+  let paramsGiven = checkForParams args
+  if paramsGiven then fallback else do
+    reportSDoc "tc.term.con" 50 $ "checkConstructorApplication: no parameters explicitly supplied, continuing..."
+
+    let Constructor{conData = d, conPars = npars} = theDef cdef
+    reportSDoc "tc.term.con" 50 $ nest 2 $ "d    =" <+> prettyTCM d
+    -- Issue 661: t maybe an evaluated form of d .., so we evaluate d
+    -- as well and then check wether we deal with the same datatype
+    t0 <- reduce (Def d [])
+    tReduced <- reduce t
+    case (t0, unEl tReduced) of -- Only fully applied constructors get special treatment
+      (Def d0 _, Def d' es) -> do
+        let ~(Just vs) = allApplyElims es
+        reportSDoc "tc.term.con" 50 $ nest 2 $ "d0   =" <+> prettyTCM d0
+        reportSDoc "tc.term.con" 50 $ nest 2 $ "d'   =" <+> prettyTCM d'
+        reportSDoc "tc.term.con" 50 $ nest 2 $ "vs   =" <+> prettyTCM vs
+        if d' /= d0 then fallback else do
+         -- Issue 661: d' may take more parameters than d, in particular
+         -- these additional parameters could be a module parameter telescope.
+         -- Since we get the constructor type ctype from d but the parameters
+         -- from t = Def d' vs, we drop the additional parameters.
+         npars' <- getNumberOfParameters d'
+         caseMaybe (sequenceA $ Pair (Just npars) npars') fallback $ \ (Pair n n') -> do
+           reportSDoc "tc.term.con" 50 $ nest 2 $ text $ "n    = " ++ show n
+           reportSDoc "tc.term.con" 50 $ nest 2 $ text $ "n'   = " ++ show n'
+           when (n > n')  -- preprocessor does not like ', so put on next line
+             __IMPOSSIBLE__
+           let ps    = take n $ drop (n' - n) vs
+               ctype = defType cdef
+           reportSDoc "tc.term.con" 20 $ vcat
+             [ "special checking of constructor application of" <+> prettyTCM c
+             , nest 2 $ vcat [ "ps     =" <+> prettyTCM ps
+                             , "ctype  =" <+> prettyTCM ctype ] ]
+           let ctype' = ctype `piApply` ps
+           reportSDoc "tc.term.con" 20 $ nest 2 $ "ctype' =" <+> prettyTCM ctype'
+           -- get the parameter names
+           let TelV ptel _ = telView'UpTo n ctype
+           let pnames = map (fmap fst) $ telToList ptel
+           -- drop the parameter arguments
+               args' = dropArgs pnames args
+           -- check the non-parameter arguments
+           expandLast <- asksTC envExpandLast
+           checkArguments cmp expandLast (getRange c) args' ctype' t $ \ st@(ACState _ _ _ t' targetCheck) -> do
+             reportSDoc "tc.term.con" 20 $ nest 2 $ vcat
+               [ text "es     =" <+> prettyTCM es
+               , text "t'     =" <+> prettyTCM t' ]
+             v <- checkHeadConstraints (Con c ConOCon) st
+             coerce' cmp targetCheck v t' t
+      _ -> do
+        reportSDoc "tc.term.con" 50 $ nest 2 $ "we are not at a datatype, falling back"
+        fallback
+  where
+    fallback = checkHeadApplication cmp org t (A.Con (unambiguous $ conName c)) args
+
+    -- Check if there are explicitly given hidden arguments,
+    -- in which case we fall back to default type checking.
+    -- We could work harder, but let's not for now.
+    --
+    -- Andreas, 2012-04-18: if all inital args are underscores, ignore them
+    checkForParams args =
+      let (hargs, rest) = break visible args
+          notUnderscore A.Underscore{} = False
+          notUnderscore _              = True
+      in  any (notUnderscore . unScope . namedArg) hargs
+
+    -- Drop the constructor arguments that correspond to parameters.
+    dropArgs [] args                = args
+    dropArgs ps []                  = args
+    dropArgs ps args@(arg : args')
+      | Just p   <- name,
+        Just ps' <- namedPar p ps   = dropArgs ps' args'
+      | Nothing  <- name,
+        Just ps' <- unnamedPar h ps = dropArgs ps' args'
+      | otherwise                   = args
+      where
+        name = bareNameOf arg
+        h    = getHiding arg
+
+        namedPar   x = dropPar ((x ==) . unDom)
+        unnamedPar h = dropPar (sameHiding h)
+
+        dropPar this (p : ps) | this p    = Just ps
+                              | otherwise = dropPar this ps
+        dropPar _ [] = Nothing
+
+-- | Return an unblocking action in case of failure.
+type DisambiguateConstructor = TCM (Either Blocker ConHead)
+
+-- | Returns an unblocking action in case of failure.
+disambiguateConstructor :: List1 QName -> A.Args -> Type -> DisambiguateConstructor
+disambiguateConstructor cs0 args t = do
+  reportSLn "tc.check.term.con" 40 $ "Ambiguous constructor: " ++ prettyShow cs0
+  reportSDoc "tc.check.term.con" 40 $ vcat $ "Arguments:" : map (nest 2 . prettyTCM) args
+
+  -- Get the datatypes of the various constructors
+  let getData Constructor{conData = d} = d
+      getData _                        = __IMPOSSIBLE__
+  reportSLn "tc.check.term.con" 40 $ "  ranges before: " ++ prettyShow (getRange cs0)
+  -- We use the reduced constructor when disambiguating, but
+  -- the original constructor for type checking. This is important
+  -- since they may have different types (different parameters).
+  -- See issue 279.
+  -- Andreas, 2017-08-13, issue #2686: ignore abstract constructors
+  ccons  <- List1.rights <$> do
+     forM cs0 $ \ c -> mapRight (c,) <$> getConForm c
+  reportSLn "tc.check.term.con" 40 $ "  reduced: " ++ prettyShow (map snd ccons)
+  case ccons of
+    []    -> typeError $ AbstractConstructorNotInScope $ List1.head cs0
+    [(c0,con)] -> do
+      let c = setConName c0 con
+      reportSLn "tc.check.term.con" 40 $ "  only one non-abstract constructor: " ++ prettyShow c
+      decideOn c
+    (c0,_):_   -> do
+      dcs :: [(QName, Type, ConHead)] <- forM ccons $ \ (c, con) -> do
+        t   <- defType <$> getConstInfo c
+        def <- getConInfo con
+        pure (getData (theDef def), t, setConName c con)
+      -- Type error
+      let badCon t = typeError $ DoesNotConstructAnElementOf c0 t
+
+      -- Lets look at the target type at this point
+      TelV tel t1 <- telViewPath t
+      addContext tel $ do
+       reportSDoc "tc.check.term.con" 40 $ nest 2 $
+         "target type: " <+> prettyTCM t1
+       -- If we don't have a target type yet, try to look at the argument types.
+       ifBlocked t1 (\ b _ -> disambiguateByArgs dcs $ return $ Left b) $ \ _ t' ->
+         caseMaybeM (isDataOrRecord $ unEl t') (badCon t') $ \ (d, _) -> do
+           let dcs' = filter ((d ==) . fst3) dcs
+           case map thd3 dcs' of
+             [c] -> decideOn c
+             []  -> badCon $ t' $> Def d []
+             -- If the information from the target type did not eliminate ambiguity fully,
+             -- try to further eliminate alternatives by looking at the arguments.
+             c:cs-> disambiguateByArgs dcs' $
+                      typeError $ CantResolveOverloadedConstructorsTargetingSameDatatype d $
+                        fmap conName $ c :| cs
+  where
+  decideOn :: ConHead -> DisambiguateConstructor
+  decideOn c = do
+    reportSLn "tc.check.term.con" 40 $ "  decided on: " ++ prettyShow c
+    storeDisambiguatedConstructor (conInductive c) (conName c)
+    return $ Right c
+
+  -- Look at simple visible arguments (variables (bound and generalizable ones) and defined names).
+  -- From these we can compute an approximate type effortlessly:
+  -- 1. Throw away hidden domains (needed for generalizable variables).
+  -- 2. If the remainder is a defined name that is not blocked on anything, we take this name as
+  --    approximate type of the argument.
+  -- This gives us a skeleton @[Maybe QName]@.  Compute the same from the constructor types
+  -- of the candidates and see if we find any mismatches that allow us to rule out the candidate.
+  disambiguateByArgs :: [(QName, Type, ConHead)] -> DisambiguateConstructor -> DisambiguateConstructor
+  disambiguateByArgs dcs fallback = do
+
+    -- Look for visible arguments that are just variables,
+    -- so that we can get their type directly from the context
+    -- without full-fledged type inference.
+    askel <- visibleVarArgs
+    reportSDoc "tc.check.term.con" 40 $ hsep $
+      "trying disambiguation by arguments" : map prettyTCM askel
+    reportSDoc "tc.check.term.con" 80 $ hsep $
+      "trying disambiguation by arguments" : map pretty askel
+
+    -- Filter out candidates with definitive mismatches.
+    cands <- filterM (\ (_d, t, _c) -> matchSkel askel =<< visibleConDoms t) dcs
+    case cands of
+      [(_d, _t, c)] -> decideOn c
+      _ -> fallback
+    where
+
+    -- @match@ is successful if there no name conflict (q ≠ q')
+    -- and the argument skeleton is not longer thatn the constructor skeleton.
+    match ::
+          [Maybe QName]   -- Specification (argument skeleton).
+       -> [Maybe QName]   -- Candidate (constructor skeleton).
+       -> Bool
+    match = curry $ \case
+      ([], _ ) -> True
+      (_ , []) -> False
+      (Just q : ms, Just q' : ms') -> q == q' && match ms ms'
+      (_ : ms, _ : ms') -> match ms ms'
+
+    -- @match@ with debug printing.
+    matchSkel :: [Maybe QName] -> [Maybe QName] -> TCM Bool
+    matchSkel argsSkel conSkel = do
+      let res = match argsSkel conSkel
+      reportSDoc "tc.check.term.con" 40 $ vcat
+        [ "matchSkel returns" <+> pretty res <+> "on:"
+        , nest 2 $ pretty argsSkel
+        , nest 2 $ pretty conSkel
+        ]
+      return res
+
+    -- Only look at visible arguments that are variables or similar identifiers.
+    -- For variables/symbols @Just getTypeHead@ else @Nothing@.
+    visibleVarArgs :: TCM [Maybe QName]
+    visibleVarArgs = forM (filter visible args) $ \ (arg :: NamedArg A.Expr) -> do
+        let v = unScope $ namedArg arg
+        reportSDoc "tc.check.term.con" 40 $ "is this a variable? :" <+> prettyTCM v
+        reportSDoc "tc.check.term.con" 90 $ "is this a variable? :" <+> (text . show) v
+        case v of
+
+          -- We can readly grab the type of a variable from the context.
+          A.Var x -> do
+            t <- unDom . snd <$> getVarInfo x
+            reportSDoc "tc.check.term.con" 40 $ "type of variable:" <+> prettyTCM t
+            -- Just keep the name @D@ of type @D vs@
+            getTypeHead t
+
+          -- We can also grab the type of defined symbols if we find them in the signature.
+          A.Def x -> do
+            getConstInfo' x >>= \case
+              Right def -> getTypeHead $ defType def
+              Left{} -> return Nothing
+          _ -> return Nothing
+
+    -- List of visible arguments of the constructor candidate.
+    -- E.g. vcons : {A : Set} {n : Nat} (x : A) (xs : Vec A n) → Vec A (suc n)
+    -- becomes vcons : ? → Vec → .
+    visibleConDoms :: Type -> TCM [Maybe QName]
+    visibleConDoms t = do
+      TelV tel _ <- telViewPath t
+      mapM (getTypeHead . snd . unDom) $ filter visible $ telToList tel
+
+-- | If type is of the form @F vs@ and not blocked in any way, return @F@.
+getTypeHead :: Type -> TCM (Maybe QName)
+getTypeHead t = do
+  res <- ifBlocked t (\ _ _ -> return Nothing) $ \ nb t -> do
+    case nb of
+      ReallyNotBlocked -> do
+        -- Drop initial hidden domains (only needed for generalizable variables).
+        TelV _ core <- telViewUpTo' (0-1) (not . visible) t
+        case unEl core of
+          Def q _ -> return $ Just q
+          _ -> return Nothing
+      -- In the other cases, we do not get the data name.
+      _ -> return Nothing
+  reportSDoc "tc.check.term.con" 80 $ hcat $ "getTypeHead(" : prettyTCM t : ") = " : pretty res : []
+  return res
+
+
+---------------------------------------------------------------------------
+-- * Projections
+---------------------------------------------------------------------------
+
+checkUnambiguousProjectionApplication :: Comparison -> A.Expr -> Type -> QName -> ProjOrigin -> A.Expr -> [NamedArg A.Expr] -> TCM Term
+checkUnambiguousProjectionApplication cmp e t x o hd args = do
+  let fallback = checkHeadApplication cmp e t hd args
+  -- Andreas, 2021-02-19, issue #3289
+  -- If a postfix projection was moved to the head by appView,
+  -- we have to patch the first argument with the correct hiding info.
+  case (o, args) of
+    (ProjPostfix, arg : rest) -> do
+      -- Andreas, 2021-11-19, issue #5657:
+      -- If @x@ has been brought into scope by e.g. @open R r@, it is no longer
+      -- a projection even though the scope checker labels it so.
+      -- Thus, @isProjection@ may fail.
+      caseMaybeM (isProjection x) fallback $ \ pr -> do
+        checkHeadApplication cmp e t hd (setArgInfo (projArgInfo pr) arg : rest)
+    _ -> fallback
+
+-- | Inferring the type of an overloaded projection application.
+--   See 'inferOrCheckProjApp'.
+
+inferProjApp :: A.Expr -> ProjOrigin -> List1 QName -> A.Args -> TCM (Term, Type)
+inferProjApp e o ds args0 = do
+  (v, t, _) <- inferOrCheckProjApp e o ds args0 Nothing
+  return (v, t)
+
+-- | Checking the type of an overloaded projection application.
+--   See 'inferOrCheckProjApp'.
+
+checkProjApp  :: Comparison -> A.Expr -> ProjOrigin -> List1 QName -> A.Args -> Type -> TCM Term
+checkProjApp cmp e o ds args0 t = do
+  (v, ti, targetCheck) <- inferOrCheckProjApp e o ds args0 (Just (cmp, t))
+  coerce' cmp targetCheck v ti t
+
+-- | Checking the type of an overloaded projection application.
+--   See 'inferOrCheckProjAppToKnownPrincipalArg'.
+
+checkProjAppToKnownPrincipalArg  :: Comparison -> A.Expr -> ProjOrigin -> List1 QName -> A.Args -> Type -> Int -> Term -> Type -> PrincipalArgTypeMetas -> TCM Term
+checkProjAppToKnownPrincipalArg cmp e o ds args0 t k v0 pt patm = do
+  (v, ti, targetCheck) <- inferOrCheckProjAppToKnownPrincipalArg e o ds args0 (Just (cmp, t)) k v0 pt (Just patm)
+  coerce' cmp targetCheck v ti t
+
+-- | Inferring or Checking an overloaded projection application.
+--
+--   The overloaded projection is disambiguated by inferring the type of its
+--   principal argument, which is the first visible argument.
+
+inferOrCheckProjApp
+  :: A.Expr
+     -- ^ The whole expression which constitutes the application.
+  -> ProjOrigin
+     -- ^ The origin of the projection involved in this projection application.
+  -> List1 QName
+     -- ^ The projection name (potentially ambiguous).
+  -> A.Args
+     -- ^ The arguments to the projection.
+  -> Maybe (Comparison, Type)
+     -- ^ The expected type of the expression (if 'Nothing', infer it).
+  -> TCM (Term, Type, CheckedTarget)
+     -- ^ The type-checked expression and its type (if successful).
+inferOrCheckProjApp e o ds args mt = do
+  reportSDoc "tc.proj.amb" 20 $ vcat
+    [ "checking ambiguous projection"
+    , text $ "  ds   = " ++ prettyShow ds
+    , text   "  args = " <+> sep (map prettyTCM args)
+    , text   "  t    = " <+> caseMaybe mt "Nothing" prettyTCM
+    ]
+
+  let cmp = caseMaybe mt CmpEq fst
+
+      -- Postpone the whole type checking problem
+      -- if type of principal argument (or the type where we get it from)
+      -- is blocked by meta m.
+      postpone b = do
+        tc <- caseMaybe mt newTypeMeta_ (return . snd)
+        v <- postponeTypeCheckingProblem (CheckExpr cmp e tc) b
+        return (v, tc, NotCheckedTarget)
+
+  -- The following cases need to be considered:
+  -- 1. No arguments to the projection.
+  -- 2. Arguments (parameters), but not the principal argument.
+  -- 3. Argument(s) including the principal argument.
+
+  -- For now, we only allow ambiguous projections if the first visible
+  -- argument is the record value.
+
+  case filter (visible . snd) $ zip [0..] args of
+
+    -- Case: we have no visible argument to the projection.
+    -- In inference mode, we really need the visible argument, postponing does not help
+    [] -> caseMaybe mt (refuseProjNotApplied ds) $ \ (cmp , t) -> do
+      -- If we have the type, we can try to get the type of the principal argument.
+      -- It is the first visible argument.
+      TelV _ptel core <- telViewUpTo' (-1) (not . visible) t
+      ifBlocked core (\ m _ -> postpone m) $ {-else-} \ _ core -> do
+      ifNotPiType core (\ _ -> refuseProjNotApplied ds) $ {-else-} \ dom _b -> do
+      ifBlocked (unDom dom) (\ m _ -> postpone m) $ {-else-} \ _ ta -> do
+      caseMaybeM (isRecordType ta) (refuseProjNotRecordType ds Nothing ta) $ \ (_q, _pars, defn) -> do
+      case defn of
+        Record { recFields = fs } -> do
+          case forMaybe fs $ \ f -> Fold.find (unDom f ==) ds of
+            [] -> refuseProjNoMatching ds
+            [d] -> do
+              storeDisambiguatedProjection d
+              -- checkHeadApplication will check the target type
+              (, t, CheckedTarget Nothing) <$>
+                checkHeadApplication cmp e t (A.Proj o $ unambiguous d) args
+            _ -> __IMPOSSIBLE__
+        _ -> __IMPOSSIBLE__
+
+    -- Case: we have a visible argument
+    ((k, arg) : _) -> do
+      (v0, ta) <- inferExpr $ namedArg arg
+      reportSDoc "tc.proj.amb" 25 $ vcat
+        [ "  principal arg " <+> prettyTCM arg
+        , "  has type "      <+> prettyTCM ta
+        ]
+      inferOrCheckProjAppToKnownPrincipalArg e o ds args mt k v0 ta Nothing
+
+-- | Same arguments 'inferOrCheckProjApp' above but also gets the position,
+--   value and type of the principal argument.
+inferOrCheckProjAppToKnownPrincipalArg
+  :: A.Expr
+     -- ^ The whole expression which constitutes the application.
+  -> ProjOrigin
+     -- ^ The origin of the projection involved in this projection application.
+  -> List1 QName
+     -- ^ The projection name (potentially ambiguous).
+  -> A.Args
+     -- ^ The arguments to the projection.
+  -> Maybe (Comparison, Type)
+     -- ^ The expected type of the expression (if 'Nothing', infer it).
+  -> Int
+     -- ^ The position of the principal argument.
+  -> Term
+     -- ^ The value of the principal argument.
+  -> Type
+     -- ^ The type of the principal argument.
+  -> Maybe PrincipalArgTypeMetas
+     -- ^ The metas previously created for the principal argument's type, when
+     --   picking up a postponed problem. 'Nothing', otherwise.
+  -> TCM (Term, Type, CheckedTarget)
+     -- ^ The type-checked expression and its type (if successful).
+inferOrCheckProjAppToKnownPrincipalArg e o ds args mt k v0 ta mpatm = do
+  let cmp = caseMaybe mt CmpEq fst
+      postpone b patm = do
+        tc <- caseMaybe mt newTypeMeta_ (return . snd)
+        v <- postponeTypeCheckingProblem (CheckProjAppToKnownPrincipalArg cmp e o ds args tc k v0 ta patm) b
+        return (v, tc, NotCheckedTarget)
+  -- ta should be a record type (after introducing the hidden args in v0)
+  patm@(PrincipalArgTypeMetas vargs ta) <- case mpatm of
+    -- keep using the previously created metas, when picking up a postponed
+    -- problem - see #4924
+    Just patm -> return patm
+    -- create fresh metas
+    Nothing -> uncurry PrincipalArgTypeMetas <$> implicitArgs (-1) (not . visible) ta
+  let v = v0 `apply` vargs
+  ifBlocked ta (\ m _ -> postpone m patm) {-else-} $ \ _ ta -> do
+  caseMaybeM (isRecordType ta) (refuseProjNotRecordType ds (Just v0) ta) $ \ (q, _pars0, _) -> do
+
+      -- try to project it with all of the possible projections
+      let try d = do
+            reportSDoc "tc.proj.amb" 30 $ vcat
+              [ text $ "trying projection " ++ prettyShow d
+              , "  td  = " <+> caseMaybeM (getDefType d ta) "Nothing" prettyTCM
+              ]
+
+            -- get the original projection name
+            def <- lift $ getConstInfo d
+            let isP = isProjection_ $ theDef def
+            reportSDoc "tc.proj.amb" 40 $ vcat $
+              text ( "  isProjection = " ++ caseMaybe isP "no" (const "yes")
+                   ) : caseMaybe isP [] (\ Projection{ projProper = proper, projOrig = orig } ->
+              [ text $ "  proper       = " ++ show proper
+              , text $ "  orig         = " ++ prettyShow orig
+              ])
+
+            -- Andreas, 2017-01-21, issue #2422
+            -- The scope checker considers inherited projections (from nested records)
+            -- as projections and allows overloading.  However, since they are defined
+            -- as *composition* of projections, the type checker does *not* recognize them,
+            -- and @isP@ will be @Nothing@.
+            -- However, we can ignore this, as we only need the @orig@inal projection name
+            -- for removing false ambiguity.  Thus, we skip these checks:
+
+            -- Projection{ projProper = proper, projOrig = orig } <- MaybeT $ return isP
+            -- guard $ isJust proper
+            let orig = caseMaybe isP d projOrig
+
+            -- try to eliminate
+            (dom, u, tb) <- MaybeT (projectTyped v ta o d `catchError` \ _ -> return Nothing)
+            reportSDoc "tc.proj.amb" 30 $ vcat
+              [ "  dom = " <+> prettyTCM dom
+              , "  u   = " <+> prettyTCM u
+              , "  tb  = " <+> prettyTCM tb
+              ]
+            (q', pars, _) <- MaybeT $ isRecordType $ unDom dom
+            reportSDoc "tc.proj.amb" 30 $ vcat
+              [ "  q   = " <+> prettyTCM q
+              , "  q'  = " <+> prettyTCM q'
+              ]
+            guard (q == q')
+            -- Get the type of the projection and check
+            -- that the first visible argument is the record value.
+            let tfull = defType def
+            TelV tel _ <- lift $ telViewUpTo' (-1) (not . visible) tfull
+            reportSDoc "tc.proj.amb" 30 $ vcat
+              [ text $ "  size tel  = " ++ show (size tel)
+              , text $ "  size pars = " ++ show (size pars)
+              ]
+            -- See issue 1960 for when the following assertion fails for
+            -- the correct disambiguation.
+            -- guard (natSize tel == natSize pars)
+
+            guard =<< do isNothing <$> do lift $ checkModality' d def
+            return (orig, (d, (pars, (dom, u, tb))))
+
+      cands <- List1.groupOn fst . List1.catMaybes <$> mapM (runMaybeT . try) ds
+      case cands of
+        [] -> refuseProjNoMatching ds
+        (_:_:_) -> refuseProj ds $ fwords "several matching candidates can be applied."
+        -- case: just one matching projection d
+        -- the term u = d v
+        -- the type tb is the type of this application
+        [ (_orig, (d, (pars, (_dom,u,tb)))) :| _ ] -> do
+          storeDisambiguatedProjection d
+
+          -- Check parameters
+          tfull <- typeOfConst d
+          (_,_) <- checkKnownArguments (take k args) pars tfull
+
+          -- Check remaining arguments
+          let r     = getRange e
+              args' = drop (k + 1) args
+          z <- runExceptT $ checkArgumentsE cmp ExpandLast r args' tb (snd <$> mt)
+          case z of
+            Right st@(ACState _ _ _ trest targetCheck) -> do
+              v <- checkHeadConstraints (u `applyE`) st
+              return (v, trest, targetCheck)
+            Left problem -> do
+              -- In the inference case:
+              -- To create a postponed type checking problem,
+              -- we do not use typeDontCare, but create a meta.
+              tc <- caseMaybe mt newTypeMeta_ (return . snd)
+              v  <- postponeArgs problem cmp ExpandLast r args' tc $ \ st@(ACState _ _ _ trest targetCheck) -> do
+                      v <- checkHeadConstraints (u `applyE`) st
+                      coerce' cmp targetCheck v trest tc
+
+              return (v, tc, NotCheckedTarget)
+
+-- | Throw 'AmbiguousOverloadedProjection' with additional explanation.
+refuseProj :: List1 QName -> TCM Doc -> TCM a
+refuseProj ds reason = typeError . AmbiguousOverloadedProjection ds =<< reason
+
+refuseProjNotApplied, refuseProjNoMatching :: List1 QName -> TCM a
+refuseProjNotApplied    ds = refuseProj ds $ fwords "it is not applied to a visible argument"
+refuseProjNoMatching    ds = refuseProj ds $ fwords "no matching candidate found"
+refuseProjNotRecordType :: List1 QName -> Maybe Term -> Type -> TCM a
+refuseProjNotRecordType ds pValue pType = do
+  let dType = prettyTCM pType
+  let dValue = caseMaybe pValue (return empty) prettyTCM
+  refuseProj ds $ fsep $
+    ["principal argument", dValue, "has type", dType, "while it should be of record type"]
+
+-----------------------------------------------------------------------------
+-- * Sorts
+-----------------------------------------------------------------------------
+
+checkUniv
+  :: UnivSize -> Univ -> Comparison -> A.Expr -> Type
+  -> QName -> Suffix -> [NamedArg A.Expr] -> TCM Term
+checkUniv sz u cmp e t q suffix args = do
+  (v, t0) <- inferUniv sz u e q suffix args
+  coerce cmp v t0 t
+
+inferUniv :: UnivSize -> Univ -> A.Expr -> QName -> Suffix -> [NamedArg A.Expr] -> TCM (Term, Type)
+inferUniv sz u e q s args = do
+  univChecks u
+  case sz of
+    USmall -> inferLeveledSort u q s args
+    ULarge -> inferUnivOmega u q s args
+
+univChecks :: Univ -> TCM ()
+univChecks = \case
+  UProp -> unlessM isPropEnabled $ typeError NeedOptionProp
+  UType -> pure ()
+  USSet -> unlessM isTwoLevelEnabled $ typeError NeedOptionTwoLevel
+
+suffixToLevel :: Suffix -> Integer
+suffixToLevel = \case
+  NoSuffix -> 0
+  Suffix n -> n
+
+inferLeveledSort ::
+     Univ                -- ^ The universe type.
+  -> QName               -- ^ Name of the universe, for error reporting.
+  -> Suffix              -- ^ Level of the universe given via suffix (optional).
+  -> [NamedArg A.Expr]   -- ^ Level of the universe given via argument (absent if suffix).
+  -> TCM (Term, Type)    -- ^ Universe and its sort.
+inferLeveledSort u q suffix = \case
+  [] -> do
+    let n = suffixToLevel suffix
+    return (Sort (Univ u $ ClosedLevel n) , sort (Univ (univUniv u) $ ClosedLevel $ n + 1))
+  [arg] -> do
+    unless (visible arg) $ typeError $ WrongHidingInApplication $ sort $ Univ u $ ClosedLevel 0
+    unlessM hasUniversePolymorphism $ genericError
+      "Use --universe-polymorphism to enable level arguments to Set"
+    l <- applyRelevanceToContext NonStrict $ checkLevel arg
+    return (Sort $ Univ u l , sort (Univ (univUniv u) $ levelSuc l))
+  arg : _ -> typeError $ TooManyArgumentsToLeveledSort q
+
+inferUnivOmega ::
+     Univ                -- ^ The universe type.
+  -> QName               -- ^ Name of the universe, for error reporting.
+  -> Suffix              -- ^ Level of the universe given via suffix (optional).
+  -> [NamedArg A.Expr]   -- ^ Level of the universe given via argument (should be absent).
+  -> TCM (Term, Type)    -- ^ Universe and its sort.
+inferUnivOmega u q suffix = \case
+  [] -> do
+    let n = suffixToLevel suffix
+    return (Sort (Inf u n) , sort (Inf (univUniv u) $ 1 + n))
+  arg : _ -> typeError $ TooManyArgumentsToUnivOmega q
+
+-----------------------------------------------------------------------------
+-- * Coinduction
+-----------------------------------------------------------------------------
+
+checkSharpApplication :: A.Expr -> Type -> QName -> [NamedArg A.Expr] -> TCM Term
+checkSharpApplication e t c args = do
+  arg <- case args of
+           [a] | visible a -> return $ namedArg a
+           _ -> typeError $ GenericError $ prettyShow c ++ " must be applied to exactly one argument."
+
+  -- The name of the fresh function.
+  i <- fresh :: TCM Int
+  let name = filter (/= '_') (prettyShow $ A.nameConcrete $ A.qnameName c) ++ "-" ++ show i
+
+  kit <- coinductionKit'
+  let flat = nameOfFlat kit
+      inf  = nameOfInf  kit
+
+  -- Add the type signature of the fresh function to the
+  -- signature.
+  -- To make sure we can type check the generated function we have to make
+  -- sure that its type is \inf. The reason for this is that we don't yet
+  -- postpone checking of patterns when we don't know their types (Issue480).
+  forcedType <- do
+    lvl <- levelType
+    (_, l) <- newValueMeta RunMetaOccursCheck CmpLeq lvl
+    lv  <- levelView l
+    (_, a) <- newValueMeta RunMetaOccursCheck CmpEq (sort $ Type lv)
+    return $ El (Type lv) $ Def inf [Apply $ setHiding Hidden $ defaultArg l, Apply $ defaultArg a]
+
+  wrapper <- inFreshModuleIfFreeParams $
+             setRunTimeModeUnlessInHardCompileTimeMode $ do
+    -- Andreas, 2019-10-12: create helper functions in non-erased mode.
+    -- Otherwise, they are not usable in meta-solutions in the term world.
+    -- #4743: Except if hard compile-time mode is enabled.
+    c' <- setRange (getRange c) <$>
+            liftM2 qualify (killRange <$> currentModule)
+                           (freshName_ name)
+
+    -- Define and type check the fresh function.
+    mod <- currentModality
+    abs <- asksTC (^. lensIsAbstract)
+    let info   = A.mkDefInfo (A.nameConcrete $ A.qnameName c') noFixity'
+                             PublicAccess abs noRange
+        core   = A.LHSProj { A.lhsDestructor = unambiguous flat
+                           , A.lhsFocus      = defaultNamedArg $ A.LHSHead c' []
+                           , A.lhsPats       = [] }
+        clause = A.Clause (A.LHS empty core) []
+                          (A.RHS arg Nothing)
+                          A.noWhereDecls False
+
+    i <- currentOrFreshMutualBlock
+
+    -- If we are in irrelevant position, add definition irrelevantly.
+    -- If we are in erased position, add definition as erased.
+    -- TODO: is this sufficient?
+    addConstant c' =<< do
+      let ai = setModality mod defaultArgInfo
+      lang <- getLanguage
+      fun  <- emptyFunction
+      useTerPragma $
+        (defaultDefn ai c' forcedType lang fun)
+        { defMutual = i }
+
+    checkFunDef info c' [clause]
+
+    reportSDoc "tc.term.expr.coind" 15 $ do
+      def <- theDef <$> getConstInfo c'
+      vcat $
+        [ "The coinductive wrapper"
+        , nest 2 $ prettyTCM mod <> (prettyTCM c' <+> ":")
+        , nest 4 $ prettyTCM t
+        , nest 2 $ prettyA clause
+        ]
+    return c'
+
+  -- The application of the fresh function to the relevant
+  -- arguments.
+  e' <- Def wrapper . map Apply <$> getContextArgs
+
+  reportSDoc "tc.term.expr.coind" 15 $ vcat $
+      [ "The coinductive constructor application"
+      , nest 2 $ prettyTCM e
+      , "was translated into the application"
+      , nest 2 $ prettyTCM e'
+      ]
+
+  blockTerm t $ e' <$ workOnTypes (leqType forcedType t)
+
+-----------------------------------------------------------------------------
+-- * Cubical
+-----------------------------------------------------------------------------
+
+-- | "pathAbs (PathView s _ l a x y) t" builds "(\ t) : pv"
+--   Preconditions: PathView is PathType, and t[i0] = x, t[i1] = y
+pathAbs :: PathView -> Abs Term -> TCM Term
+pathAbs (OType _) t = __IMPOSSIBLE__
+pathAbs (PathType s path l a x y) t = do
+  return $ Lam defaultArgInfo t
+
+-- | @primComp : ∀ {ℓ} (A : (i : I) → Set (ℓ i)) (φ : I) (u : ∀ i → Partial φ (A i)) (a : A i0) → A i1@
+--
+--   Check:  @u i0 = (λ _ → a) : Partial φ (A i0)@.
+--
+checkPrimComp :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+checkPrimComp c rs vs _ = do
+  case vs of
+    -- WAS: [l, a, phi, u, a0] -> do
+    l : a : phi : u : a0 : rest -> do
+      iz <- Arg defaultArgInfo <$> intervalUnview IZero
+      let lz = unArg l `apply` [iz]
+          az = unArg a `apply` [iz]
+      ty <- el's (pure (unArg l `apply` [iz])) $ primPartial <#> pure (unArg l `apply` [iz]) <@> pure (unArg phi) <@> pure (unArg a `apply` [iz])
+      bAz <- el' (pure $ lz) (pure $ az)
+      a0 <- blockArg bAz (rs !!! 4) a0 $ do
+        equalTerm ty -- (El (getSort t1) (apply (unArg a) [iz]))
+          (Lam defaultArgInfo $ NoAbs "_" $ unArg a0)
+          (apply (unArg u) [iz])
+      return $ l : a : phi : u : a0 : rest
+    _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+-- | @primHComp : ∀ {ℓ} {A : Set ℓ} {φ : I} (u : ∀ i → Partial φ A) (a : A) → A@
+--
+--   Check:  @u i0 = (λ _ → a) : Partial φ A@.
+--
+checkPrimHComp :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+checkPrimHComp c rs vs _ = do
+  case vs of
+    -- WAS: [l, a, phi, u, a0] -> do
+    l : a : phi : u : a0 : rest -> do
+      -- iz = i0
+      iz <- Arg defaultArgInfo <$> intervalUnview IZero
+      -- ty = Partial φ A
+      ty <- el's (pure (unArg l)) $ primPartial <#> pure (unArg l) <@> pure (unArg phi) <@> pure (unArg a)
+      -- (λ _ → a) = u i0 : ty
+      bA <- el' (pure $ unArg l) (pure $ unArg a)
+      a0 <- blockArg bA (rs !!! 4) a0 $ do
+        equalTerm ty -- (El (getSort t1) (apply (unArg a) [iz]))
+            (Lam defaultArgInfo $ NoAbs "_" $ unArg a0)
+            (apply (unArg u) [iz])
+      return $ l : a : phi : u : a0 : rest
+    _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+-- | @transp : ∀{ℓ} (A : (i : I) → Set (ℓ i)) (φ : I) (a0 : A i0) → A i1@
+--
+--   Check:  If φ, then @A i = A i0 : Set (ℓ i)@ must hold for all @i : I@.
+--
+checkPrimTrans :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+checkPrimTrans c rs vs _ = do
+  case vs of
+    -- Andreas, 2019-03-02, issue #3601, why exactly 4 arguments?
+    -- Only 3 are needed to check the side condition.
+    -- WAS:
+    -- [l, a, phi, a0] -> do
+    l : a : phi : rest -> do
+      iz <- Arg defaultArgInfo <$> intervalUnview IZero
+      -- ty = (i : I) -> Set (l i)
+      ty <- runNamesT [] $ do
+        l <- open $ unArg l
+        nPi' "i" primIntervalType $ \ i -> (sort . tmSort <$> (l <@> i))
+      a <- blockArg ty (rs !!! 1) a $ do
+        equalTermOnFace (unArg phi) ty
+          (unArg a)
+          (Lam defaultArgInfo $ NoAbs "_" $ apply (unArg a) [iz])
+      return $ l : a : phi : rest
+    _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+blockArg :: HasRange r => Type -> r -> Arg Term -> TCM () -> TCM (Arg Term)
+blockArg t r a m =
+  setCurrentRange (getRange $ r) $ fmap (a $>) $ blockTerm t $ m >> return (unArg a)
+
+checkConId :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+checkConId c rs vs t1 = do
+  case vs of
+   args@[_, _, _, _, phi, p] -> do
+      iv@(PathType s _ l a x y) <- idViewAsPath t1
+      let ty = pathUnview iv
+      -- the following duplicates reduction of phi
+      const_x <- blockTerm ty $ do
+          equalTermOnFace (unArg phi) (El s (unArg a)) (unArg x) (unArg y)
+          pathAbs iv (NoAbs (stringToArgName "_") (unArg x))
+      p <- blockArg ty (rs !!! 5) p $ do
+        equalTermOnFace (unArg phi) ty (unArg p) const_x   -- G, phi |- p = \ i . x
+      return $ initWithDefault __IMPOSSIBLE__ args ++ [p]
+      -- phi <- reduce phi
+      -- forallFaceMaps (unArg phi) $ \ alpha -> do
+      --   iv@(PathType s _ l a x y) <- idViewAsPath (applySubst alpha t1)
+      --   let ty = pathUnview iv
+      --   equalTerm (El s (unArg a)) (unArg x) (unArg y) -- precondition for cx being well-typed at ty
+      --   cx <- pathAbs iv (NoAbs (stringToArgName "_") (applySubst alpha (unArg x)))
+      --   equalTerm ty (applySubst alpha (unArg p)) cx   -- G, phi |- p = \ i . x
+   _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+
+-- The following comment contains silly ' escapes to calm CPP about ∨ (\vee).
+-- May not be haddock-parseable.
+
+-- ' @primPOr : ∀ {ℓ} (φ₁ φ₂ : I) {A : Partial (φ₁ ∨ φ₂) (Set ℓ)}
+-- '         → (u : PartialP φ₁ (λ (o : IsOne φ₁) → A (IsOne1 φ₁ φ₂ o)))
+-- '         → (v : PartialP φ₂ (λ (o : IsOne φ₂) → A (IsOne2 φ₁ φ₂ o)))
+-- '         → PartialP (φ₁ ∨ φ₂) A@
+-- '
+-- ' Checks: @u = v : PartialP (φ₁ ∨ φ₂) A@ whenever @IsOne (φ₁ ∧ φ₂)@.
+checkPOr :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+checkPOr c rs vs _ = do
+  case vs of
+   l : phi1 : phi2 : a : u : v : rest -> do
+      phi <- intervalUnview (IMin phi1 phi2)
+      reportSDoc "tc.term.por" 10 $ text (show phi)
+      t1 <- runNamesT [] $ do
+             [l,a] <- mapM (open . unArg) [l,a]
+             psi <- open =<< intervalUnview (IMax phi1 phi2)
+             pPi' "o" psi $ \ o -> el' l (a <..> o)
+      tv <- runNamesT [] $ do
+             [l,a,phi1,phi2] <- mapM (open . unArg) [l,a,phi1,phi2]
+             pPi' "o" phi2 $ \ o -> el' l (a <..> (cl primIsOne2 <@> phi1 <@> phi2 <@> o))
+      v <- blockArg tv (rs !!! 5) v $ do
+        -- ' φ₁ ∧ φ₂  ⊢ u , v : PartialP (φ₁ ∨ φ₂) \ o → a o
+        equalTermOnFace phi t1 (unArg u) (unArg v)
+      return $ l : phi1 : phi2 : a : u : v : rest
+   _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+-- | @prim^glue : ∀ {ℓ ℓ'} {A : Set ℓ} {φ : I}
+--              → {T : Partial φ (Set ℓ')} → {e : PartialP φ (λ o → T o ≃ A)}
+--              → (t : PartialP φ T) → (a : A) → primGlue A T e@
+--
+--   Check   @φ ⊢ a = e 1=1 (t 1=1)@  or actually the equivalent:  @(\ _ → a) = (\ o -> e o (t o)) : PartialP φ A@
+check_glue :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+check_glue c rs vs _ = do
+  case vs of
+   -- WAS: [la, lb, bA, phi, bT, e, t, a] -> do
+   la : lb : bA : phi : bT : e : t : a : rest -> do
+      let iinfo = setRelevance Irrelevant defaultArgInfo
+      v <- runNamesT [] $ do
+            [lb, la, bA, phi, bT, e, t] <- mapM (open . unArg) [lb, la, bA, phi, bT, e, t]
+            let f o = cl primEquivFun <#> lb <#> la <#> (bT <..> o) <#> bA <@> (e <..> o)
+            glam iinfo "o" $ \ o -> f o <@> (t <..> o)
+      ty <- runNamesT [] $ do
+            [lb, phi, bA] <- mapM (open . unArg) [lb, phi, bA]
+            el's lb $ cl primPartialP <#> lb <@> phi <@> glam iinfo "o" (\ _ -> bA)
+      let a' = Lam iinfo (NoAbs "o" $ unArg a)
+      ta <- el' (pure $ unArg la) (pure $ unArg bA)
+      a <- blockArg ta (rs !!! 7) a $ equalTerm ty a' v
+      return $ la : lb : bA : phi : bT : e : t : a : rest
+   _ -> typeError $ CubicalPrimitiveNotFullyApplied c
+
+
+-- | @prim^glueU : ∀ {ℓ} {φ : I}
+--              → {T : I → Partial φ (Set ℓ)} → {A : Set ℓ [ φ ↦ T i0 ]}
+--              → (t : PartialP φ (T i1)) → (a : outS A) → hcomp T (outS A)@
+--
+--   Check   @φ ⊢ a = transp (\ i -> T 1=1 (~ i)) i0 (t 1=1)@  or actually the equivalent:
+--           @(\ _ → a) = (\o -> transp (\ i -> T o (~ i)) i0 (t o)) : PartialP φ (T i0)@
+check_glueU :: QName -> MaybeRanges -> Args -> Type -> TCM Args
+check_glueU c rs vs _ = do
+  case vs of
+   -- WAS: [la, lb, bA, phi, bT, e, t, a] -> do
+   la : phi : bT : bA : t : a : rest -> do
+      let iinfo = setRelevance Irrelevant defaultArgInfo
+      v <- runNamesT [] $ do
+            [la, phi, bT, bA, t] <- mapM (open . unArg) [la, phi, bT, bA, t]
+            let f o = cl primTrans <#> lam "i" (const la) <@> lam "i" (\ i -> bT <@> (cl primINeg <@> i) <..> o) <@> cl primIZero
+            glam iinfo "o" $ \ o -> f o <@> (t <..> o)
+      ty <- runNamesT [] $ do
+            [la, phi, bT] <- mapM (open . unArg) [la, phi, bT]
+            pPi' "o" phi $ \ o -> el' la (bT <@> cl primIZero <..> o)
+      let a' = Lam iinfo (NoAbs "o" $ unArg a)
+      ta <- runNamesT [] $ do
+            [la, phi, bT, bA] <- mapM (open . unArg) [la, phi, bT, bA]
+            el' la (cl primSubOut <#> (cl primLevelSuc <@> la) <#> (Sort . tmSort <$> la) <#> phi <#> (bT <@> cl primIZero) <@> bA)
+      a <- blockArg ta (rs !!! 5) a $ equalTerm ty a' v
+      return $ la : phi : bT : bA : t : a : rest
+   _ -> typeError $ CubicalPrimitiveNotFullyApplied c
diff --git a/src/full/Agda/TypeChecking/Rules/Application.hs-boot b/src/full/Agda/TypeChecking/Rules/Application.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Application.hs-boot
@@ -0,0 +1,27 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Application where
+
+import Data.List.NonEmpty (NonEmpty)
+
+import Agda.Syntax.Common (NamedArg, ProjOrigin)
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.TypeChecking.Monad.Base
+
+checkArguments :: Comparison -> ExpandHidden -> Range -> [NamedArg A.Expr] -> Type -> Type ->
+                  (ArgsCheckState CheckedTarget -> TCM Term) -> TCM Term
+
+checkArguments_ :: Comparison -> ExpandHidden -> Range -> [NamedArg A.Expr] -> Telescope ->
+                   TCM (Elims, Telescope)
+
+checkApplication :: Comparison -> A.Expr -> A.Args -> A.Expr -> Type -> TCM Term
+
+inferApplication :: ExpandHidden -> A.Expr -> A.Args -> A.Expr -> TCM (Term, Type)
+
+checkProjAppToKnownPrincipalArg  :: Comparison -> A.Expr -> ProjOrigin -> NonEmpty QName -> A.Args -> Type -> Int -> Term -> Type -> PrincipalArgTypeMetas -> TCM Term
+
+univChecks :: Univ -> TCM ()
+
+suffixToLevel :: Suffix -> Integer
diff --git a/src/full/Agda/TypeChecking/Rules/Builtin.hs b/src/full/Agda/TypeChecking/Rules/Builtin.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Builtin.hs
@@ -0,0 +1,1084 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Builtin
+  ( bindBuiltin
+  , bindBuiltinNoDef
+  , builtinKindOfName
+  , bindPostulatedName
+  , isUntypedBuiltin
+  , bindUntypedBuiltin
+  ) where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans.Maybe
+
+import Data.List (find, sortBy)
+import Data.Function (on)
+
+import Agda.Interaction.Options.Base
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+
+import Agda.TypeChecking.Monad
+
+import qualified Agda.TypeChecking.CompiledClause as CC
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Constraints ( noConstraints )
+import Agda.TypeChecking.Functions
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Rules.Term ( checkExpr , inferExpr )
+import Agda.TypeChecking.Warnings
+
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Builtin.Coinduction
+import {-# SOURCE #-} Agda.TypeChecking.Rewriting
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.List1 (pattern (:|))
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Checking builtin pragmas
+---------------------------------------------------------------------------
+
+builtinPostulate :: TCM Type -> BuiltinDescriptor
+builtinPostulate = BuiltinPostulate Relevant
+
+builtinPostulateC :: Cubical -> TCM Type -> BuiltinDescriptor
+builtinPostulateC c m =
+  BuiltinPostulate Relevant $ requireCubical c "" >> m
+
+findBuiltinInfo :: BuiltinId -> Maybe BuiltinInfo
+findBuiltinInfo b = find ((b ==) . builtinName) coreBuiltins
+
+coreBuiltins :: [BuiltinInfo]
+coreBuiltins =
+  [ (builtinList                             |-> BuiltinData (tset --> tset) [builtinNil, builtinCons])
+  , (builtinArg                              |-> BuiltinData (tset --> tset) [builtinArgArg])
+  , (builtinAbs                              |-> BuiltinData (tset --> tset) [builtinAbsAbs])
+  , (builtinArgInfo                          |-> BuiltinData tset [builtinArgArgInfo])
+  , (builtinBool                             |-> BuiltinData tset [builtinTrue, builtinFalse])
+  , (builtinNat                              |-> BuiltinData tset [builtinZero, builtinSuc])
+  , (builtinMaybe                            |-> BuiltinData (tset --> tset) [builtinNothing, builtinJust])
+  , (builtinSigma                            |-> BuiltinData (runNamesT [] $
+                                                              hPi' "la" (el $ cl primLevel) $ \ a ->
+                                                              hPi' "lb" (el $ cl primLevel) $ \ b ->
+                                                              nPi' "A" (sort . tmSort <$> a) $ \bA ->
+                                                              nPi' "B" (el' a bA --> (sort . tmSort <$> b)) $ \bB ->
+                                                              ((sort . tmSort) <$> (cl primLevelMax <@> a <@> b))
+                                                              )
+                                                             [BuiltinSigmaCon])
+  , (builtinUnit                             |-> BuiltinData tset [builtinUnitUnit])  -- actually record, but they are treated the same
+  , (builtinAgdaLiteral                      |-> BuiltinData tset [builtinAgdaLitNat, builtinAgdaLitWord64, builtinAgdaLitFloat,
+                                                                   builtinAgdaLitChar, builtinAgdaLitString,
+                                                                   builtinAgdaLitQName, builtinAgdaLitMeta])
+  , (builtinAgdaPattern                      |-> BuiltinData tset [builtinAgdaPatVar, builtinAgdaPatCon, builtinAgdaPatDot,
+                                                                   builtinAgdaPatLit, builtinAgdaPatProj, builtinAgdaPatAbsurd])
+  , (builtinAgdaPatVar                       |-> BuiltinDataCons (tnat --> tpat))
+  , (builtinAgdaPatCon                       |-> BuiltinDataCons (tqname --> tlist (targ tpat) --> tpat))
+  , (builtinAgdaPatDot                       |-> BuiltinDataCons (tterm --> tpat))
+  , (builtinAgdaPatLit                       |-> BuiltinDataCons (tliteral --> tpat))
+  , (builtinAgdaPatProj                      |-> BuiltinDataCons (tqname --> tpat))
+  , (builtinAgdaPatAbsurd                    |-> BuiltinDataCons (tnat --> tpat))
+  , (builtinLevel                            |-> builtinPostulate tLevelUniv)
+  , (builtinWord64                           |-> builtinPostulate tset)
+  , (builtinInteger                          |-> BuiltinData tset [builtinIntegerPos, builtinIntegerNegSuc])
+  , (builtinIntegerPos                       |-> BuiltinDataCons (tnat --> tinteger))
+  , (builtinIntegerNegSuc                    |-> BuiltinDataCons (tnat --> tinteger))
+  , (builtinFloat                            |-> builtinPostulate tset)
+  , (builtinChar                             |-> builtinPostulate tset)
+  , (builtinString                           |-> builtinPostulate tset)
+  , (builtinQName                            |-> builtinPostulate tset)
+  , (builtinAgdaMeta                         |-> builtinPostulate tset)
+  , (builtinIO                               |-> builtinPostulate (tset --> tset))
+  , (builtinPath                             |-> BuiltinUnknown
+                                                             (Just $ requireCubical CErased "" >>
+                                                             hPi "a" (el primLevel) (
+                                                              hPi "A" (return $ sort $ varSort 0) $
+                                                              (El (varSort 1) <$> varM 0) -->
+                                                              (El (varSort 1) <$> varM 0) -->
+                                                              return (sort $ varSort 1)))
+                                                             verifyPath)
+  , (builtinPathP                            |-> builtinPostulateC CErased (hPi "a" (el primLevel) $
+                                                              nPi "A" (tinterval --> return (sort $ varSort 0)) $
+                                                              (El (varSort 1) <$> varM 0 <@> primIZero) -->
+                                                              (El (varSort 1) <$> varM 0 <@> primIOne) -->
+                                                              return (sort $ varSort 1)))
+  , (builtinIntervalUniv                     |-> BuiltinSort SortIntervalUniv)
+  , (builtinInterval                         |-> BuiltinData (requireCubical CErased "" >>
+                                                              (return $ sort IntervalUniv)) [builtinIZero,builtinIOne])
+  , (builtinSub                              |-> builtinPostulateC CErased (runNamesT [] $ hPi' "a" (el $ cl primLevel) $ \ a ->
+                                                                   nPi' "A" (el' (cl primLevelSuc <@> a) (Sort . tmSort <$> a)) $ \ bA ->
+                                                                   nPi' "φ" (cl tinterval) $ \ phi ->
+                                                                   el's a (cl primPartial <#> a <@> phi <@> bA) --> (ssort . atomicLevel <$> a)
+                                                                  ))
+  , (builtinSubIn                            |-> builtinPostulateC CErased (runNamesT [] $
+                                                                   hPi' "a" (el $ cl primLevel) $ \ a ->
+                                                                   hPi' "A" (el' (cl primLevelSuc <@> a) (Sort . tmSort <$> a)) $ \ bA ->
+                                                                   hPi' "φ" (cl tinterval) $ \ phi ->
+                                                                   nPi' "x" (el' a bA) $ \ x ->
+                                                                   el's a $ cl primSub <#> a <@> bA <@> phi <@> lam "o" (\ _ -> x)))
+  , (builtinIZero                            |-> BuiltinDataCons tinterval)
+  , (builtinIOne                             |-> BuiltinDataCons tinterval)
+  , (builtinPartial                          |-> BuiltinPrim PrimPartial (const $ return ()))
+  , (builtinPartialP                         |-> BuiltinPrim PrimPartialP (const $ return ()))
+  , (builtinIsOne                            |-> builtinPostulateC CErased (tinterval --> return (ssort $ ClosedLevel 0)))
+  , (builtinItIsOne                          |-> builtinPostulateC CErased (elSSet $ primIsOne <@> primIOne))
+  , (builtinIsOne1                           |-> builtinPostulateC CErased (runNamesT [] $
+                                                                   nPi' "i" (cl tinterval) $ \ i ->
+                                                                   nPi' "j" (cl tinterval) $ \ j ->
+                                                                   nPi' "i1" (elSSet $ cl primIsOne <@> i) $ \ i1 ->
+                                                                   (elSSet $ cl primIsOne <@> (cl primIMax <@> i <@> j))))
+  , (builtinIsOne2                           |-> builtinPostulateC CErased (runNamesT [] $
+                                                                   nPi' "i" (cl tinterval) $ \ i ->
+                                                                   nPi' "j" (cl tinterval) $ \ j ->
+                                                                   nPi' "j1" (elSSet $ cl primIsOne <@> j) $ \ j1 ->
+                                                                   (elSSet $ cl primIsOne <@> (cl primIMax <@> i <@> j))))
+  , (builtinIsOneEmpty                       |-> builtinPostulateC CErased (runNamesT [] $
+                                                                   hPi' "l" (el $ cl primLevel) $ \ l ->
+                                                                   hPi' "A" (pPi' "o" (cl primIZero) $ \ _ ->
+                                                                                  el' (cl primLevelSuc <@> l) (Sort . tmSort <$> l)) $ \ bA ->
+                                                                   pPi' "o" (cl primIZero) (\ o ->
+                                                                        el' l $ gApply' (setRelevance Irrelevant defaultArgInfo) bA o)))
+
+  , (builtinId                               |-> BuiltinData ((>>) (requireCubical CErased "") $ hPi "a" (el primLevel) $
+                                                              hPi "A" (return $ sort $ varSort 0) $
+                                                              (El (varSort 1) <$> varM 0) -->
+                                                              (El (varSort 1) <$> varM 0) -->
+                                                             return (sort $ varSort 1)) [builtinReflId])
+  , (builtinReflId                           |-> BuiltinDataCons ((>>) (requireCubical CErased "") $ runNamesT [] $
+                                                              hPi' "a" (el primLevel) $ \ l ->
+                                                              hPi' "A" (sort . tmSort <$> l) $ \ bA ->
+                                                              hPi' "x" (el' l bA) $ \ x ->
+                                                              el' l (primId <#> l <#> bA <@> x <@> x)))
+  , (builtinEquiv                            |-> BuiltinUnknown (Just $ requireCubical CErased "" >> runNamesT [] (
+                                                                    hPi' "l" (el $ cl primLevel) $ \ a ->
+                                                                    hPi' "l'" (el $ cl primLevel) $ \ b ->
+                                                                    nPi' "A" (sort . tmSort <$> a) $ \bA ->
+                                                                    nPi' "B" (sort . tmSort <$> b) $ \bB ->
+                                                                    ((sort . tmSort) <$> (cl primLevelMax <@> a <@> b))
+                                                                  ))
+                                                                   (const $ const $ return ()))
+  , (builtinEquivFun                         |-> BuiltinUnknown (Just $ requireCubical CErased "" >> runNamesT [] (
+                                                                 hPi' "l" (el $ cl primLevel) $ \ a ->
+                                                                 hPi' "l'" (el $ cl primLevel) $ \ b ->
+                                                                 hPi' "A" (sort . tmSort <$> a) $ \bA ->
+                                                                 hPi' "B" (sort . tmSort <$> b) $ \bB ->
+                                                                 el' (cl primLevelMax <@> a <@> b) (cl primEquiv <#> a <#> b <@> bA <@> bB) -->
+                                                                 (el' a bA --> el' b bB)
+                                                               ))
+                                                                (const $ const $ return ()))
+  , (builtinEquivProof                       |-> BuiltinUnknown (Just $ requireCubical CErased "" >> runNamesT [] (
+                                                               hPi' "l" (el $ cl primLevel) $ \ la ->
+                                                               hPi' "l'" (el $ cl primLevel) $ \ lb ->
+                                                               nPi' "A" (sort . tmSort <$> la) $ \ bA ->
+                                                               nPi' "B" (sort . tmSort <$> lb) $ \ bB ->
+                                                               nPi' "e" (el' (cl primLevelMax <@> la <@> lb)
+                                                                             (cl primEquiv <#> la <#> lb <@> bA <@> bB)) $ \ e -> do
+                                                               nPi' "b" (el' lb bB) $ \ b -> do
+                                                                let f = cl primEquivFun <#> la <#> lb <#> bA <#> bB <@> e
+                                                                    lub = cl primLevelMax <@> la <@> lb
+                                                                    fiber = el' lub
+                                                                                (cl primSigma <#> la <#> lb
+                                                                                  <@> bA
+                                                                                  <@> lam "a" (\ a ->
+                                                                                         cl primPath <#> lb <#> bB <@> (f <@> a) <@> b))
+                                                                nPi' "φ" (cl tinterval) $ \ phi ->
+                                                                  nPi' "f" (pPi' "o" phi (\ o -> fiber)) $ \ pfib ->
+                                                                    el' lub (cl primSub <#> lub <#> fmap unEl fiber <@> phi <@> pfib)
+                                                             ))
+                                                              (const $ const $ return ()))
+  , (builtinTranspProof                       |-> BuiltinUnknown (Just $ requireCubical CErased "" >> runNamesT [] (
+                                                               hPi' "l" (el $ cl primLevel) $ \ la -> do
+                                                               nPi' "e" (cl tinterval --> (sort . tmSort <$> la)) $ \ e -> do
+                                                               let lb = la; bA = e <@> cl primIZero; bB = e <@> cl primIOne
+                                                               nPi' "φ" (cl tinterval) $ \ phi -> do
+                                                               nPi' "a" (pPi' "o" phi (\ _ -> el' la bA)) $ \ a -> do
+                                                               let f = cl primTrans <#> lam "i" (\ _ -> la) <@> e <@> cl primIZero
+                                                                   z = ilam "o" $ \ o -> f <@> (a <@> o)
+                                                               nPi' "b" (el's lb (cl primSub <#> lb <@> bB <@> phi <@> z)) $ \ b' -> do
+                                                               let b = cl primSubOut <#> lb <#> bB <#> phi <#> z <@> b'
+                                                                   fiber = el' la
+                                                                               (cl primSigma <#> la <#> lb
+                                                                                  <@> bA
+                                                                                  <@> lam "a" (\ a ->
+                                                                                         cl primPath <#> lb <#> bB <@> (f <@> a) <@> b))
+                                                               fiber
+                                                             ))
+                                                              (const $ const $ return ()))
+  , (builtinAgdaSort                         |-> BuiltinData tset
+                                                   [ builtinAgdaSortSet, builtinAgdaSortLit
+                                                   , builtinAgdaSortProp, builtinAgdaSortPropLit
+                                                   , builtinAgdaSortInf, builtinAgdaSortUnsupported])
+  , (builtinAgdaTerm                         |-> BuiltinData tset
+                                                   [ builtinAgdaTermVar, builtinAgdaTermLam, builtinAgdaTermExtLam
+                                                   , builtinAgdaTermDef, builtinAgdaTermCon
+                                                   , builtinAgdaTermPi, builtinAgdaTermSort
+                                                   , builtinAgdaTermLit, builtinAgdaTermMeta
+                                                   , builtinAgdaTermUnsupported])
+  , builtinAgdaErrorPart                     |-> BuiltinData tset [ builtinAgdaErrorPartString, builtinAgdaErrorPartTerm, builtinAgdaErrorPartPatt, builtinAgdaErrorPartName ]
+  , builtinAgdaErrorPartString               |-> BuiltinDataCons (tstring --> terrorpart)
+  , builtinAgdaErrorPartTerm                 |-> BuiltinDataCons (tterm --> terrorpart)
+  , builtinAgdaErrorPartPatt                 |-> BuiltinDataCons (tpat --> terrorpart)
+  , builtinAgdaErrorPartName                 |-> BuiltinDataCons (tqname --> terrorpart)
+  , builtinAgdaBlocker                       |-> BuiltinData tset [ builtinAgdaBlockerAll, builtinAgdaBlockerAny, builtinAgdaBlockerMeta ]
+  , builtinAgdaBlockerAny                    |-> BuiltinDataCons (tlist tblocker --> tblocker)
+  , builtinAgdaBlockerAll                    |-> BuiltinDataCons (tlist tblocker --> tblocker)
+  , builtinAgdaBlockerMeta                   |-> BuiltinDataCons (tmeta --> tblocker)
+  -- Andreas, 2017-01-12, issue #2386: special handling of builtinEquality
+  -- , (builtinEquality                         |-> BuiltinData (hPi "a" (el primLevel) $
+  --                                                             hPi "A" (return $ sort $ varSort 0) $
+  --                                                             (El (varSort 1) <$> varM 0) -->
+  --                                                             (El (varSort 1) <$> varM 0) -->
+  --                                                             return (sort $ varSort 1))
+  --                                                            [builtinRefl])
+  , (builtinHiding                           |-> BuiltinData tset [builtinHidden, builtinInstance, builtinVisible])
+    -- Relevance
+  , (builtinRelevance                        |-> BuiltinData tset [builtinRelevant, builtinIrrelevant])
+  , (builtinRelevant                         |-> BuiltinDataCons trelevance)
+  , (builtinIrrelevant                       |-> BuiltinDataCons trelevance)
+    -- Quantity
+  , (builtinQuantity                         |-> BuiltinData tset [builtinQuantity0, builtinQuantityω])
+  , (builtinQuantity0                        |-> BuiltinDataCons tquantity)
+  , (builtinQuantityω                        |-> BuiltinDataCons tquantity)
+    -- Modality
+  , (builtinModality                         |-> BuiltinData tset [builtinModalityConstructor])
+  , (builtinModalityConstructor              |-> BuiltinDataCons (trelevance --> tquantity --> tmodality))
+    -- Associativity
+  , builtinAssoc                             |-> BuiltinData tset [builtinAssocLeft, builtinAssocRight, builtinAssocNon]
+  , builtinAssocLeft                         |-> BuiltinDataCons tassoc
+  , builtinAssocRight                        |-> BuiltinDataCons tassoc
+  , builtinAssocNon                          |-> BuiltinDataCons tassoc
+    -- Precedence
+  , builtinPrecedence                        |-> BuiltinData tset [builtinPrecRelated, builtinPrecUnrelated]
+  , builtinPrecRelated                       |-> BuiltinDataCons (tfloat --> tprec)
+  , builtinPrecUnrelated                     |-> BuiltinDataCons tprec
+    -- Fixity
+  , builtinFixity                            |-> BuiltinData tset [builtinFixityFixity]
+  , builtinFixityFixity                      |-> BuiltinDataCons (tassoc --> tprec --> tfixity)
+  -- Andreas, 2017-01-12, issue #2386: special handling of builtinEquality
+  -- , (builtinRefl                             |-> BuiltinDataCons (hPi "a" (el primLevel) $
+  --                                                                 hPi "A" (return $ sort $ varSort 0) $
+  --                                                                 hPi "x" (El (varSort 1) <$> varM 0) $
+  --                                                                 El (varSort 2) <$> primEquality <#> varM 2 <#> varM 1 <@> varM 0 <@> varM 0))
+  , (builtinRewrite                          |-> BuiltinUnknown Nothing verifyBuiltinRewrite)
+  , (builtinNil                              |-> BuiltinDataCons (hPi "A" tset (el (list v0))))
+  , (builtinCons                             |-> BuiltinDataCons (hPi "A" tset (tv0 --> el (list v0) --> el (list v0))))
+  , (builtinNothing                          |-> BuiltinDataCons (hPi "A" tset (el (tMaybe v0))))
+  , (builtinJust                             |-> BuiltinDataCons (hPi "A" tset (tv0 --> el (tMaybe v0))))
+  , (builtinZero                             |-> BuiltinDataCons tnat)
+  , (builtinSuc                              |-> BuiltinDataCons (tnat --> tnat))
+  , (builtinTrue                             |-> BuiltinDataCons tbool)
+  , (builtinFalse                            |-> BuiltinDataCons tbool)
+  , (builtinArgArg                           |-> BuiltinDataCons (hPi "A" tset (targinfo --> tv0 --> targ tv0)))
+  , (builtinAbsAbs                           |-> BuiltinDataCons (hPi "A" tset (tstring  --> tv0 --> tabs tv0)))
+  , (builtinArgArgInfo                       |-> BuiltinDataCons (thiding --> tmodality --> targinfo))
+  , (builtinAgdaTermVar                      |-> BuiltinDataCons (tnat --> targs --> tterm))
+  , (builtinAgdaTermLam                      |-> BuiltinDataCons (thiding --> tabs tterm --> tterm))
+  , (builtinAgdaTermExtLam                   |-> BuiltinDataCons (tlist tclause --> targs --> tterm))
+  , (builtinAgdaTermDef                      |-> BuiltinDataCons (tqname --> targs --> tterm))
+  , (builtinAgdaTermCon                      |-> BuiltinDataCons (tqname --> targs --> tterm))
+  , (builtinAgdaTermPi                       |-> BuiltinDataCons (targ ttype --> tabs ttype --> tterm))
+  , (builtinAgdaTermSort                     |-> BuiltinDataCons (tsort --> tterm))
+  , (builtinAgdaTermLit                      |-> BuiltinDataCons (tliteral --> tterm))
+  , (builtinAgdaTermMeta                     |-> BuiltinDataCons (tmeta --> targs --> tterm))
+  , (builtinAgdaTermUnsupported              |-> BuiltinDataCons tterm)
+  , (builtinAgdaLitNat                       |-> BuiltinDataCons (tnat --> tliteral))
+  , (builtinAgdaLitWord64                    |-> BuiltinDataCons (tword64 --> tliteral))
+  , (builtinAgdaLitFloat                     |-> BuiltinDataCons (tfloat --> tliteral))
+  , (builtinAgdaLitChar                      |-> BuiltinDataCons (tchar --> tliteral))
+  , (builtinAgdaLitString                    |-> BuiltinDataCons (tstring --> tliteral))
+  , (builtinAgdaLitQName                     |-> BuiltinDataCons (tqname --> tliteral))
+  , (builtinAgdaLitMeta                      |-> BuiltinDataCons (tmeta --> tliteral))
+  , (builtinHidden                           |-> BuiltinDataCons thiding)
+  , (builtinInstance                         |-> BuiltinDataCons thiding)
+  , (builtinVisible                          |-> BuiltinDataCons thiding)
+  , (builtinSizeUniv                         |-> builtinPostulate tsetOmega) -- SizeUniv : Setω
+  , (builtinSize                             |-> builtinPostulate tSizeUniv)
+  , (builtinSizeLt                           |-> builtinPostulate (tsize ..--> tSizeUniv))
+  , (builtinSizeSuc                          |-> builtinPostulate (tsize --> tsize))
+  , (builtinSizeInf                          |-> builtinPostulate tsize)
+  -- postulate max : {i : Size} -> Size< i -> Size< i -> Size< i
+  , (builtinSizeMax                          |-> builtinPostulate (tsize --> tsize --> tsize))
+     -- (hPi "i" tsize $ let a = el $ primSizeLt <@> v0 in (a --> a --> a)))
+  , (builtinAgdaSortSet                      |-> BuiltinDataCons (tterm --> tsort))
+  , (builtinAgdaSortLit                      |-> BuiltinDataCons (tnat --> tsort))
+  , (builtinAgdaSortProp                     |-> BuiltinDataCons (tterm --> tsort))
+  , (builtinAgdaSortPropLit                  |-> BuiltinDataCons (tnat --> tsort))
+  , (builtinAgdaSortInf                      |-> BuiltinDataCons (tnat --> tsort))
+  , (builtinAgdaSortUnsupported              |-> BuiltinDataCons tsort)
+  , (builtinNatPlus                          |-> BuiltinPrim PrimNatPlus verifyPlus)
+  , (builtinNatMinus                         |-> BuiltinPrim PrimNatMinus verifyMinus)
+  , (builtinNatTimes                         |-> BuiltinPrim PrimNatTimes verifyTimes)
+  , (builtinNatDivSucAux                     |-> BuiltinPrim PrimNatDivSucAux verifyDivSucAux)
+  , (builtinNatModSucAux                     |-> BuiltinPrim PrimNatModSucAux verifyModSucAux)
+  , (builtinNatEquals                        |-> BuiltinPrim PrimNatEquality verifyEquals)
+  , (builtinNatLess                          |-> BuiltinPrim PrimNatLess verifyLess)
+  , (builtinLevelUniv                        |-> BuiltinSort SortLevelUniv)
+  , (builtinLevelZero                        |-> BuiltinPrim PrimLevelZero (const $ return ()))
+  , (builtinLevelSuc                         |-> BuiltinPrim PrimLevelSuc (const $ return ()))
+  , (builtinLevelMax                         |-> BuiltinPrim PrimLevelMax verifyMax)
+  , (builtinProp                             |-> BuiltinSort SortProp)
+  , (builtinSet                              |-> BuiltinSort SortSet)
+  , (builtinStrictSet                        |-> BuiltinSort SortStrictSet)
+  , (builtinPropOmega                        |-> BuiltinSort SortPropOmega)
+  , (builtinSetOmega                         |-> BuiltinSort SortSetOmega)
+  , (builtinSSetOmega                        |-> BuiltinSort SortStrictSetOmega)
+  , (builtinAgdaClause                       |-> BuiltinData tset [builtinAgdaClauseClause, builtinAgdaClauseAbsurd])
+  , (builtinAgdaClauseClause                 |-> BuiltinDataCons (ttelescope --> tlist (targ tpat) --> tterm --> tclause))
+  , (builtinAgdaClauseAbsurd                 |-> BuiltinDataCons (ttelescope --> tlist (targ tpat) --> tclause))
+  , (builtinAgdaDefinition                   |-> BuiltinData tset [builtinAgdaDefinitionFunDef
+                                                                  ,builtinAgdaDefinitionDataDef
+                                                                  ,builtinAgdaDefinitionDataConstructor
+                                                                  ,builtinAgdaDefinitionRecordDef
+                                                                  ,builtinAgdaDefinitionPostulate
+                                                                  ,builtinAgdaDefinitionPrimitive])
+  , (builtinAgdaDefinitionFunDef             |-> BuiltinDataCons (tlist tclause --> tdefn))
+  , (builtinAgdaDefinitionDataDef            |-> BuiltinDataCons (tnat --> tlist tqname --> tdefn))
+  , (builtinAgdaDefinitionDataConstructor    |-> BuiltinDataCons (tqname --> tdefn))
+  , (builtinAgdaDefinitionRecordDef          |-> BuiltinDataCons (tqname --> tlist (targ tqname) --> tdefn))
+  , (builtinAgdaDefinitionPostulate          |-> BuiltinDataCons tdefn)
+  , (builtinAgdaDefinitionPrimitive          |-> BuiltinDataCons tdefn)
+  , builtinAgdaTCM                           |-> builtinPostulate (hPi "a" tlevel $ tsetL 0 --> tsetL 0)
+  , builtinAgdaTCMReturn                     |-> builtinPostulate (hPi "a" tlevel  $
+                                                                   hPi "A" (tsetL 0) $
+                                                                   elV 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMBind                       |-> builtinPostulate (hPi "a" tlevel  $ hPi "b" tlevel $
+                                                                   hPi "A" (tsetL 1) $ hPi "B" (tsetL 1) $
+                                                                   tTCM 3 (varM 1) --> (elV 3 (varM 1) --> tTCM 2 (varM 0)) --> tTCM 2 (varM 0))
+  , builtinAgdaTCMUnify                      |-> builtinPostulate (tterm --> tterm --> tTCM_ primUnit)
+  , builtinAgdaTCMTypeError                  |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tlist terrorpart --> tTCM 1 (varM 0))
+  , builtinAgdaTCMInferType                  |-> builtinPostulate (tterm --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMCheckType                  |-> builtinPostulate (tterm --> ttype --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMNormalise                  |-> builtinPostulate (tterm --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMReduce                     |-> builtinPostulate (tterm --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMCatchError                 |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $
+                                                                   tTCM 1 (varM 0) --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMGetContext                 |-> builtinPostulate (tTCM_ (unEl <$> ttelescope))
+  , builtinAgdaTCMExtendContext              |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $
+                                                                   tstring --> targ ttype --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMInContext                  |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $
+                                                                   ttelescope --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMFreshName                  |-> builtinPostulate (tstring --> tTCM_ primQName)
+  , builtinAgdaTCMDeclareDef                 |-> builtinPostulate (targ tqname --> ttype --> tTCM_ primUnit)
+  , builtinAgdaTCMDeclarePostulate           |-> builtinPostulate (targ tqname --> ttype --> tTCM_ primUnit)
+  , builtinAgdaTCMDeclareData                |-> builtinPostulate (tqname --> tnat --> ttype --> tTCM_ primUnit)
+  , builtinAgdaTCMDefineData                 |-> builtinPostulate (tqname --> tlist (tpair primLevelZero primLevelZero tqname ttype) --> tTCM_ primUnit)
+  , builtinAgdaTCMDefineFun                  |-> builtinPostulate (tqname --> tlist tclause --> tTCM_ primUnit)
+  , builtinAgdaTCMGetType                    |-> builtinPostulate (tqname --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMGetDefinition              |-> builtinPostulate (tqname --> tTCM_ primAgdaDefinition)
+  , builtinAgdaTCMQuoteTerm                  |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ elV 1 (varM 0) --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMUnquoteTerm                |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tterm --> tTCM 1 (varM 0))
+  , builtinAgdaTCMQuoteOmegaTerm             |-> builtinPostulate (hPi "A" tsetOmega $ (elInf $ varM 0) --> tTCM_ primAgdaTerm)
+  , builtinAgdaTCMBlock                      |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tblocker --> tTCM 1 (varM 0))
+  , builtinAgdaTCMCommit                     |-> builtinPostulate (tTCM_ primUnit)
+  , builtinAgdaTCMIsMacro                    |-> builtinPostulate (tqname --> tTCM_ primBool)
+  , builtinAgdaTCMWithNormalisation          |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tbool --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMWithReconstructed          |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tbool --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMWithExpandLast             |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tbool --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMWithReduceDefs             |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ (tpair primLevelZero primLevelZero tbool (tlist tqname)) --> tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMAskNormalisation           |-> builtinPostulate (tTCM_ (unEl <$> tbool))
+  , builtinAgdaTCMAskReconstructed           |-> builtinPostulate (tTCM_ (unEl <$> tbool))
+  , builtinAgdaTCMAskExpandLast              |-> builtinPostulate (tTCM_ (unEl <$> tbool))
+  , builtinAgdaTCMAskReduceDefs              |-> builtinPostulate (tTCM_ (unEl <$> (tpair primLevelZero primLevelZero tbool (tlist tqname))))
+  , builtinAgdaTCMFormatErrorParts           |-> builtinPostulate (tlist terrorpart --> tTCM_ primString)
+  , builtinAgdaTCMDebugPrint                 |-> builtinPostulate (tstring --> tnat --> tlist terrorpart --> tTCM_ primUnit)
+
+  , builtinAgdaTCMNoConstraints              |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $ tTCM 1 (varM 0) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMRunSpeculative             |-> builtinPostulate (hPi "a" tlevel $ hPi "A" (tsetL 0) $
+                                                                   tTCM 1 (primSigma <#> varM 1 <#> primLevelZero <@> varM 0 <@> (Lam defaultArgInfo . Abs "_" <$> primBool)) --> tTCM 1 (varM 0))
+  , builtinAgdaTCMExec                       |-> builtinPostulate (tstring --> tlist tstring --> tstring -->
+                                                                   tTCM_ (primSigma <#> primLevelZero <#> primLevelZero <@> primNat <@>
+                                                                          (Lam defaultArgInfo . Abs "_" <$> (primSigma <#> primLevelZero <#> primLevelZero <@> primString <@>
+                                                                           (Lam defaultArgInfo . Abs "_" <$> primString)))))
+  , builtinAgdaTCMGetInstances               |-> builtinPostulate (tmeta --> tTCM_ (list primAgdaTerm))
+  , builtinAgdaTCMPragmaForeign              |-> builtinPostulate (tstring --> tstring --> tTCM_ primUnit)
+  , builtinAgdaTCMPragmaCompile              |-> builtinPostulate (tstring --> tqname --> tstring --> tTCM_ primUnit)
+  ]
+  where
+        (|->) = BuiltinInfo
+
+        v0 :: TCM Term
+        v0 = varM 0
+
+        tv0 :: TCM Type
+        tv0 = el v0
+
+        arg :: TCM Term -> TCM Term
+        arg t = primArg <@> t
+
+        elV x a = El (varSort x) <$> a
+
+        tsetL l    = return $ sort (varSort l)
+        tsetOmega  = return $ sort $ Inf UType 0
+        tlevel     = el primLevel
+        tlist x    = el $ list (fmap unEl x)
+        tmaybe x   = el $ tMaybe (fmap unEl x)
+        tpair lx ly x y = el $ primSigma
+                            <#> lx
+                            <#> ly
+                            <@> fmap unEl x
+                            <@> (Lam defaultArgInfo . NoAbs "_" <$> fmap unEl y)
+        targ x     = el (arg (fmap unEl x))
+        tabs x     = el (primAbs <@> fmap unEl x)
+        targs      = el (list (arg primAgdaTerm))
+        tterm      = el primAgdaTerm
+        terrorpart = el primAgdaErrorPart
+        tnat       = el primNat
+        tword64    = el primWord64
+        tinteger   = el primInteger
+        tfloat     = el primFloat
+        tchar      = el primChar
+        tstring    = el primString
+        tqname     = el primQName
+        tmeta      = el primAgdaMeta
+        tblocker   = el primAgdaBlocker
+        tsize      = El sSizeUniv <$> primSize
+        tbool      = el primBool
+        thiding    = el primHiding
+        trelevance = el primRelevance
+        tquantity  = el primQuantity
+        tmodality  = el primModality
+        tassoc     = el primAssoc
+        tprec      = el primPrecedence
+        tfixity    = el primFixity
+--        tcolors    = el (list primAgdaTerm) -- TODO guilhem
+        targinfo   = el primArgInfo
+        ttype      = el primAgdaTerm
+        tsort      = el primAgdaSort
+        tdefn      = el primAgdaDefinition
+        tliteral   = el primAgdaLiteral
+        tpat       = el primAgdaPattern
+        tclause    = el primAgdaClause
+        ttelescope = tlist (tpair primLevelZero primLevelZero tstring (targ ttype))
+        tTCM l a   = elV l (primAgdaTCM <#> varM l <@> a)
+        tTCM_ a    = el (primAgdaTCM <#> primLevelZero <@> a)
+        tinterval  = El IntervalUniv <$> primInterval
+
+        verifyPlus plus =
+            verify ["n","m"] $ \(@@) zero suc (==) (===) choice -> do
+                let m = var 0
+                    n = var 1
+                    x + y = plus @@ x @@ y
+
+                -- We allow recursion on any argument
+                choice
+                    [ do n + zero  == n
+                         n + suc m == suc (n + m)
+                    , do suc n + m == suc (n + m)
+                         zero  + m == m
+                    ]
+
+        verifyMinus minus =
+            verify ["n","m"] $ \(@@) zero suc (==) (===) choice -> do
+                let m = var 0
+                    n = var 1
+                    x - y = minus @@ x @@ y
+
+                -- We allow recursion on any argument
+                zero  - zero  == zero
+                zero  - suc m == zero
+                suc n - zero  == suc n
+                suc n - suc m == (n - m)
+
+        verifyTimes times = do
+            plus <- primNatPlus
+            verify ["n","m"] $ \(@@) zero suc (==) (===) choice -> do
+                let m = var 0
+                    n = var 1
+                    x + y = plus  @@ x @@ y
+                    x * y = times @@ x @@ y
+
+                choice
+                    [ do n * zero == zero
+                         choice [ (n * suc m) == (n + (n * m))
+                                , (n * suc m) == ((n * m) + n)
+                                ]
+                    , do zero * n == zero
+                         choice [ (suc n * m) == (m + (n * m))
+                                , (suc n * m) == ((n * m) + m)
+                                ]
+                    ]
+
+        verifyDivSucAux dsAux =
+            verify ["k","m","n","j"] $ \(@@) zero suc (==) (===) choice -> do
+                let aux k m n j = dsAux @@ k @@ m @@ n @@ j
+                    k           = var 0
+                    m           = var 1
+                    n           = var 2
+                    j           = var 3
+
+                aux k m zero    j       == k
+                aux k m (suc n) zero    == aux (suc k) m n m
+                aux k m (suc n) (suc j) == aux k m n j
+
+        verifyModSucAux dsAux =
+            verify ["k","m","n","j"] $ \(@@) zero suc (==) (===) choice -> do
+                let aux k m n j = dsAux @@ k @@ m @@ n @@ j
+                    k           = var 0
+                    m           = var 1
+                    n           = var 2
+                    j           = var 3
+
+                aux k m zero    j       == k
+                aux k m (suc n) zero    == aux zero m n m
+                aux k m (suc n) (suc j) == aux (suc k) m n j
+
+        verifyEquals eq =
+            verify ["n","m"] $ \(@@) zero suc (==) (===) choice -> do
+            true  <- primTrue
+            false <- primFalse
+            let x == y = eq @@ x @@ y
+                m      = var 0
+                n      = var 1
+            (zero  == zero ) === true
+            (suc n == suc m) === (n == m)
+            (suc n == zero ) === false
+            (zero  == suc n) === false
+
+        verifyLess leq =
+            verify ["n","m"] $ \(@@) zero suc (==) (===) choice -> do
+            true  <- primTrue
+            false <- primFalse
+            let x < y = leq @@ x @@ y
+                m     = var 0
+                n     = var 1
+            (n     < zero)  === false
+            (suc n < suc m) === (n < m)
+            (zero  < suc m) === true
+
+        verifyMax maxV = return ()  -- TODO: make max a postulate
+
+        verify xs = verify' primNat primZero primSuc xs
+
+        verify' ::  TCM Term -> TCM Term -> TCM Term ->
+                    [String] -> ( (Term -> Term -> Term) -> Term -> (Term -> Term) ->
+                                (Term -> Term -> TCM ()) ->
+                                (Term -> Term -> TCM ()) ->
+                                ([TCM ()] -> TCM ()) -> TCM a) -> TCM a
+        verify' pNat pZero pSuc xs f = do
+            nat  <- El (mkType 0) <$> pNat
+            zero <- pZero
+            s    <- pSuc
+            let x == y  = noConstraints $ equalTerm nat x y
+                -- Andreas: 2013-10-21 I put primBool here on the inside
+                -- since some Nat-builtins do not require Bool-builtins
+                x === y = do bool <- El (mkType 0) <$> primBool
+                             noConstraints $ equalTerm bool x y
+                suc n  = s `apply1` n
+                choice = foldr1 (\x y -> x `catchError` \_ -> y)
+            xs <- mapM freshName_ xs
+            addContext (xs, domFromArg $ defaultArg nat) $ f apply1 zero suc (==) (===) choice
+
+        verifyPath :: Term -> Type -> TCM ()
+        verifyPath path t = do
+          let hlam n t = glam (setHiding Hidden defaultArgInfo) n t
+          noConstraints $ equalTerm t path =<< runNamesT [] (
+            hlam "l" $ \ l -> hlam "A" $ \ bA -> cl primPathP <#> l <@> lam "i" (\ _ -> bA))
+
+-- | Checks that builtin with name @b : String@ of type @t : Term@
+--   is a data type or inductive record with @n : Int@ constructors.
+--   Returns the name of the data/record type.
+inductiveCheck :: BuiltinId -> Int -> Term -> TCM (QName, Definition)
+inductiveCheck b n t = do
+  caseMaybeM (headSymbol t) no $ \q -> do
+      def <- getConstInfo q
+      let yes = return (q, def)
+      case theDef def of
+        Datatype { dataCons = cs }
+          | length cs == n -> yes
+          | otherwise      -> no
+        Record { recInduction = ind } | n == 1 && ind /= Just CoInductive -> yes
+        _ -> no
+  where
+  headSymbol :: Term -> TCM (Maybe QName)
+  headSymbol t = reduce t >>= \case
+    Def q _ -> return $ Just q
+    Lam _ b -> headSymbol $ lazyAbsApp b __DUMMY_TERM__
+    _       -> return Nothing
+
+  no
+    | n == 1 = typeError $ GenericError $ unwords
+        [ "The builtin", getBuiltinId b
+        , "must be a datatype with a single constructor"
+        , "or an (inductive) record type"
+        ]
+    | otherwise = typeError $ GenericError $ unwords
+        [ "The builtin", getBuiltinId b
+        , "must be a datatype with", show n
+        , "constructors"
+        ]
+
+-- | @bindPostulatedName builtin q m@ checks that @q@ is a postulated
+-- name, and binds the builtin @builtin@ to the term @m q def@,
+-- where @def@ is the current 'Definition' of @q@.
+
+bindPostulatedName ::
+  BuiltinId -> ResolvedName -> (QName -> Definition -> TCM Term) -> TCM ()
+bindPostulatedName builtin x m = do
+  q   <- getName x
+  def <- getConstInfo q
+  case theDef def of
+    Axiom {} -> bindBuiltinName builtin =<< m q def
+    _        -> err
+  where
+  err :: forall m a. MonadTCError m => m a
+  err = typeError $ GenericError $
+          "The argument to BUILTIN " ++ getBuiltinId builtin ++
+          " must be a postulated name"
+  getName = \case
+    DefinedName _ d NoSuffix -> return $ anameName d
+    _ -> err
+
+addHaskellPragma :: QName -> String -> TCM ()
+addHaskellPragma = addPragma ghcBackendName
+
+bindAndSetHaskellCode :: BuiltinId -> String -> Term -> TCM ()
+bindAndSetHaskellCode b hs t = do
+  d <- fromMaybe __IMPOSSIBLE__ <$> getDef t
+  bindBuiltinName b t
+  addHaskellPragma d hs
+
+bindBuiltinBool :: Term -> TCM ()
+bindBuiltinBool = bindAndSetHaskellCode builtinBool "= type Bool"
+
+-- | Check that we're not trying to bind true and false to the same
+-- constructor.
+checkBuiltinBool :: TCM ()
+checkBuiltinBool = do
+  true  <- getBuiltin' builtinTrue
+  false <- getBuiltin' builtinFalse
+  when (true == false) $
+    genericError "Cannot bind TRUE and FALSE to the same constructor"
+
+bindBuiltinInt :: Term -> TCM ()
+bindBuiltinInt = bindAndSetHaskellCode builtinInteger "= type Integer"
+
+bindBuiltinNat :: Term -> TCM ()
+bindBuiltinNat t = do
+  bindBuiltinData builtinNat t
+  name <- fromMaybe __IMPOSSIBLE__ <$> getDef t
+  addHaskellPragma name "= type Integer"
+
+-- | Only use for datatypes with distinct arities of constructors.
+--   Binds the constructors together with the datatype.
+bindBuiltinData :: BuiltinId -> Term -> TCM ()
+bindBuiltinData s t = do
+  bindBuiltinName s t
+  name <- fromMaybe __IMPOSSIBLE__ <$> getDef t
+  Datatype{ dataCons = cs } <- theDef <$> getConstInfo name
+  let getArity c = do
+        Constructor{ conArity = a } <- theDef <$> getConstInfo c
+        return a
+      getBuiltinArity (BuiltinDataCons t) = arity <$> t
+      getBuiltinArity _ = __IMPOSSIBLE__
+      sortByM f xs = map fst . sortBy (compare `on` snd) . zip xs <$> mapM f xs
+  -- Order constructurs by arity
+  cs <- sortByM getArity cs
+  -- Do the same for the builtins
+  let bcis = fromMaybe __IMPOSSIBLE__ $ do
+        BuiltinData _ bcs <- builtinDesc <$> findBuiltinInfo s
+        mapM findBuiltinInfo bcs
+  bcis <- sortByM (getBuiltinArity . builtinDesc) bcis
+  unless (length cs == length bcis) __IMPOSSIBLE__  -- we already checked this
+  zipWithM_ (\ c bci -> bindBuiltinInfo bci (A.Con $ unambiguous $ setRange (getRange name) c)) cs bcis
+
+bindBuiltinUnit :: Term -> TCM ()
+bindBuiltinUnit t = do
+  unit <- fromMaybe __IMPOSSIBLE__ <$> getDef t
+  def <- theDef <$> getConstInfo unit
+  case def of
+    Record { recFields = [], recConHead = con } -> do
+      bindBuiltinName builtinUnit t
+      bindBuiltinName builtinUnitUnit (Con con ConOSystem [])
+    _ -> genericError "Builtin UNIT must be a singleton record type"
+
+bindBuiltinSigma :: Term -> TCM ()
+bindBuiltinSigma t = do
+  sigma <- fromMaybe __IMPOSSIBLE__ <$> getDef t
+  def <- theDef <$> getConstInfo sigma
+  case def of
+    Record { recFields = [fst,snd], recConHead = con } -> do
+      bindBuiltinName builtinSigma t
+    _ -> genericError "Builtin SIGMA must be a record type with two fields"
+
+-- | Bind BUILTIN EQUALITY and BUILTIN REFL.
+bindBuiltinEquality :: ResolvedName -> TCM ()
+bindBuiltinEquality x = do
+  (v, _t) <- inferExpr (A.nameToExpr x)
+
+  -- Equality needs to be a data type with 1 constructor
+  (eq, def) <- inductiveCheck builtinEquality 1 v
+
+  -- Check that the type is the type of a polymorphic relation, i.e.,
+  -- Γ → (A : Set _) → A → A → Set _
+  TelV eqTel eqCore <- telView $ defType def
+  let no = genericError "The type of BUILTIN EQUALITY must be a polymorphic relation"
+
+  -- The target is a sort since eq is a data type.
+  unless (isJust $ isSort $ unEl eqCore) __IMPOSSIBLE__
+
+  -- The types of the last two arguments must be the third-last argument
+  unless (natSize eqTel >= 3) no
+  let (a, b) = fromMaybe __IMPOSSIBLE__ $ last2 $ telToList eqTel
+  [a,b] <- reduce $ map (unEl . snd . unDom) [a,b]
+  unless (deBruijnView a == Just 0) no
+  unless (deBruijnView b == Just 1) no
+
+  -- Get the single constructor.
+  case theDef def of
+    Datatype { dataCons = [c] } -> do
+      bindBuiltinName builtinEquality v
+
+      -- Check type of REFL.  It has to be of the form
+      -- pars → (x : A) → Eq ... x x
+
+      -- Check the arguments
+      cdef <- getConstInfo c
+      TelV conTel conCore <- telView $ defType cdef
+      ts <- reduce $ map (unEl . snd . unDom) $ drop (conPars $ theDef cdef) $ telToList conTel
+      -- After dropping the parameters, there should be maximally one argument.
+      unless (length ts <= 1) wrongRefl
+      unless (all ((Just 0 ==) . deBruijnView) ts) wrongRefl
+
+      -- Check the target
+      case unEl conCore of
+        Def _ es -> do
+          let vs = map unArg $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          (a,b) <- reduce $ fromMaybe __IMPOSSIBLE__ $ last2 vs
+          unless (deBruijnView a == Just 0) wrongRefl
+          unless (deBruijnView b == Just 0) wrongRefl
+          bindBuiltinName builtinRefl (Con (ConHead c IsData Inductive []) ConOSystem [])
+        _ -> __IMPOSSIBLE__
+    _ -> genericError "Builtin EQUALITY must be a data type with a single constructor"
+  where
+  wrongRefl = genericError "Wrong type of constructor of BUILTIN EQUALITY"
+
+bindBuiltinInfo :: BuiltinInfo -> A.Expr -> TCM ()
+bindBuiltinInfo (BuiltinInfo s d) e = do
+    case d of
+      BuiltinData t cs -> do
+        v <- checkExpr e =<< t
+        unless (s == builtinUnit) $ do
+          void $ inductiveCheck s (length cs) v
+        if | s == builtinEquality -> __IMPOSSIBLE__ -- bindBuiltinEquality v
+           | s == builtinBool     -> bindBuiltinBool     v
+           | s == builtinNat      -> bindBuiltinNat      v
+           | s == builtinInteger  -> bindBuiltinInt      v
+           | s == builtinUnit     -> bindBuiltinUnit     v
+           | s == builtinSigma    -> bindBuiltinSigma    v
+           | s == builtinList     -> bindBuiltinData s   v
+           | s == builtinMaybe    -> bindBuiltinData s   v
+           | otherwise            -> bindBuiltinName s   v
+
+      BuiltinDataCons t -> do
+
+        let name (Lam h b)  = name (absBody b)
+            name (Con c ci _) = Con c ci []
+            name _          = __IMPOSSIBLE__
+
+        v0 <- checkExpr e =<< t
+
+        case e of
+          A.Con{} -> return ()
+          _       -> typeError $ BuiltinMustBeConstructor s e
+
+        let v@(Con h _ []) = name v0
+
+        bindBuiltinName s v
+
+        when (s `elem` [builtinFalse, builtinTrue]) checkBuiltinBool
+
+      BuiltinPrim pfname axioms -> do
+        case e of
+          A.Def qx -> do
+
+            PrimImpl t pf <- lookupPrimitiveFunction pfname
+            v <- checkExpr e t
+
+            axioms v
+
+            info <- getConstInfo qx
+            let cls = defClauses info
+                a   = defAbstract info
+                o   = defOpaque info
+                mcc = defCompiled info
+                inv = defInverse info
+            -- What happens if defArgOccurrences info does not match
+            -- primFunArgOccurrences pf? Let's require the latter to
+            -- be the empty list.
+            unless (primFunArgOccurrences pf == []) __IMPOSSIBLE__
+            bindPrimitive pfname $ pf { primFunName = qx }
+            addConstant qx $ info { theDef = Primitive { primAbstr    = a
+                                                       , primName     = pfname
+                                                       , primClauses  = cls
+                                                       , primInv      = inv
+                                                       , primCompiled = mcc
+                                                       , primOpaque   = o
+                                                       } }
+
+            -- needed? yes, for checking equations for mul
+            bindBuiltinName s v
+
+          _ -> typeError $ GenericError $ "Builtin " ++ getBuiltinId s ++ " must be bound to a function"
+
+      BuiltinSort{} -> __IMPOSSIBLE__ -- always a "BuiltinNoDef"
+
+      BuiltinPostulate rel t -> do
+        t' <- t
+        v <- applyRelevanceToContext rel $ checkExpr e t'
+        let err = typeError $ GenericError $
+                    "The argument to BUILTIN " ++ getBuiltinId s ++ " must be a postulated name"
+        case e of
+          A.Def q -> do
+            def <- getConstInfo q
+            case theDef def of
+              Axiom {} -> do
+                builtinSizeHook s q t'
+                -- And compilation pragmas for base types
+                when (s == builtinLevel)  $ setConstTranspAxiom q >> addHaskellPragma q "= type ()"
+                when (s == builtinChar)   $ setConstTranspAxiom q >> addHaskellPragma q "= type Char"
+                when (s == builtinString) $ setConstTranspAxiom q >> addHaskellPragma q "= type Data.Text.Text"
+                when (s == builtinFloat)  $ setConstTranspAxiom q >> addHaskellPragma q "= type Double"
+                when (s == builtinWord64) $ setConstTranspAxiom q >> addHaskellPragma q "= type MAlonzo.RTE.Word64"
+                when (s == builtinPathP)  $ builtinPathPHook q
+                bindBuiltinName s v
+              _        -> err
+          _ -> err
+
+      BuiltinUnknown mt f -> do
+        (v, t) <- caseMaybe mt (inferExpr e) $ \ tcmt -> do
+          t <- tcmt
+          (,t) <$> checkExpr e t
+        f v t
+        if | s == builtinRewrite -> runMaybeT (getQNameFromTerm v) >>= \case
+              Nothing -> genericError "Invalid rewrite relation"
+              Just q  -> bindBuiltinRewriteRelation q
+           | otherwise           -> bindBuiltinName s v
+
+setConstTranspAxiom :: QName -> TCM ()
+setConstTranspAxiom q =
+  modifySignature $ updateDefinition q $ updateTheDef (const $ constTranspAxiom)
+
+builtinPathPHook :: QName -> TCM ()
+builtinPathPHook q =
+      modifySignature $ updateDefinition q
+      $ updateDefPolarity       id
+      . updateDefArgOccurrences (const [Unused,StrictPos,Mixed,Mixed])
+
+builtinIdHook :: QName -> TCM ()
+builtinIdHook q = do
+      modifySignature $ updateDefinition q
+        $ updateDefPolarity       id
+        . updateDefArgOccurrences (const [Unused,StrictPos,Mixed,Mixed])
+      modifySignature $ updateDefinition q
+        $ updateTheDef (\ def@Datatype{} -> def { dataPars = 3, dataIxs = 1})
+
+builtinReflIdHook :: QName -> TCM ()
+builtinReflIdHook q = do
+      modifySignature $ updateDefinition q
+        $ updateTheDef (\ def@Constructor{} -> def { conPars = 3, conArity = 0})
+
+-- | Bind a builtin thing to an expression.
+bindBuiltin :: BuiltinId -> ResolvedName -> TCM ()
+bindBuiltin b x = do
+  unlessM ((0 ==) <$> getContextSize) $ do
+    -- Andreas, 2017-11-01, issue #2824
+    -- Only raise an error if the name for the builtin is defined in a parametrized module.
+    let
+      failure :: forall m a. MonadTCError m => m a
+      failure = typeError $ BuiltinInParameterisedModule b
+    -- Get the non-empty list of AbstractName for x
+    xs <- case x of
+      VarName{}            -> failure
+      DefinedName _ x NoSuffix -> return $ x :| []
+      DefinedName _ x Suffix{} -> failure
+      FieldName xs         -> return xs
+      ConstructorName _ xs -> return xs
+      PatternSynResName xs -> failure
+      UnknownName          -> failure
+    -- For ambiguous names, we check all of their definitions:
+    unlessM (allM xs $ null <.> lookupSection . qnameModule . anameName) $
+      failure
+  -- Since the name was define in a parameter-free context, we can switch to the empty context.
+  -- (And we should!)
+  inTopContext $ do
+  if | b == builtinRefl  -> warning $ OldBuiltin b builtinEquality
+     | b == builtinZero  -> now builtinNat b
+     | b == builtinSuc   -> now builtinNat b
+     | b == builtinNil   -> now builtinList b
+     | b == builtinCons  -> now builtinList b
+     | b == builtinInf   -> bindBuiltinInf x
+     | b == builtinSharp -> bindBuiltinSharp x
+     | b == builtinFlat  -> bindBuiltinFlat x
+     | b == builtinEquality -> bindBuiltinEquality x
+     | Just i <- findBuiltinInfo b -> bindBuiltinInfo i (A.nameToExpr x)
+     | otherwise -> typeError $ NoSuchBuiltinName (getBuiltinId b)
+  where
+    now new b = warning $ OldBuiltin b new
+
+isUntypedBuiltin :: BuiltinId -> Bool
+isUntypedBuiltin = hasElem [ builtinFromNat, builtinFromNeg, builtinFromString ]
+
+bindUntypedBuiltin :: BuiltinId -> ResolvedName -> TCM ()
+bindUntypedBuiltin b = \case
+  DefinedName _ x NoSuffix -> bind x
+  DefinedName _ x Suffix{} -> wrong
+  FieldName (x :| [])  -> bind x
+  FieldName (x :| _)   -> amb x
+  VarName _x _bnd      -> wrong
+  UnknownName          -> wrong
+  ConstructorName _ xs -> err xs
+  PatternSynResName xs -> err xs
+  where
+  bind x = bindBuiltinName b (Def (anameName x) [])
+  wrong  = genericError $ "The argument to BUILTIN " ++ getBuiltinId b ++ " must be a defined name"
+  amb x  = genericDocError =<< do text "Name " <+> prettyTCM x <+> text " is ambiguous"
+  err (x :| xs1)
+    | null xs1  = wrong
+    | otherwise = amb x
+
+-- | Bind a builtin thing to a new name.
+--
+-- Since their type is closed, it does not matter whether we are in a
+-- parameterized module when we declare them.
+-- We simply ignore the parameters.
+bindBuiltinNoDef :: BuiltinId -> A.QName -> TCM ()
+bindBuiltinNoDef b q = inTopContext $ do
+  when (b `elem` sizeBuiltins) $ unlessM sizedTypesOption $
+    genericError $ "Cannot declare size BUILTIN " ++ getBuiltinId b ++ " with option --no-sized-types"
+  case builtinDesc <$> findBuiltinInfo b of
+
+    Just (BuiltinPostulate rel mt) -> do
+      -- We start by adding the corresponding postulate
+      t   <- mt
+      fun <- emptyFunctionData
+      addConstant' q (setRelevance rel defaultArgInfo) q t (def fun)
+      -- And we then *modify* the definition based on our needs:
+      -- We add polarity information for SIZE-related definitions
+      builtinSizeHook b q t
+      -- Finally, bind the BUILTIN in the environment.
+      bindBuiltinName b $ Def q []
+      where
+        -- Andreas, 2015-02-14
+        -- Special treatment of SizeUniv, should maybe be a primitive.
+        def fun
+            | b == builtinSizeUniv = FunctionDefn $ fun
+                { _funClauses    = [ (empty :: Clause) { clauseBody = Just $ Sort sSizeUniv } ]
+                , _funCompiled   = Just (CC.Done [] $ Sort sSizeUniv)
+                , _funMutual     = Just []
+                , _funTerminates = Just True
+                }
+            | otherwise = defaultAxiom
+
+    Just (BuiltinPrim name axioms) -> do
+      PrimImpl t pf <- lookupPrimitiveFunction name
+      bindPrimitive name $ pf { primFunName = q }
+      let v   = Def q []
+          def = Primitive { primAbstr    = ConcreteDef
+                          , primName     = name
+                          , primClauses  = []
+                          , primInv      = NotInjective
+                          , primCompiled = Just (CC.Done [] $ Def q [])
+                          , primOpaque   = TransparentDef
+                          }
+      lang <- getLanguage
+      addConstant q $
+        (defaultDefn defaultArgInfo q t lang def)
+          { defArgOccurrences = primFunArgOccurrences pf }
+      axioms v
+      bindBuiltinName b v
+
+    Just (BuiltinDataCons mt) -> do
+      t       <- mt
+      d       <- return $! getPrimName $ unEl t
+      erasure <- optErasure <$> pragmaOptions
+      let
+        ch = ConHead q IsData Inductive []
+        def = Constructor
+              { conPars   = 0   -- Andrea TODO: fix zeros
+              , conArity  = 0
+              , conSrcCon = ch
+              , conData   = d
+              , conAbstr  = ConcreteDef
+              , conComp   = emptyCompKit
+              , conProj   = Nothing
+              , conForced = []
+              , conErased = Nothing
+              , conErasure = erasure
+              , conInline  = False
+              }
+      addConstant' q defaultArgInfo q t def
+      addDataCons d [q]
+
+      when (b == builtinReflId)     $ builtinReflIdHook q
+
+      bindBuiltinName b $ Con ch ConOSystem []
+
+    Just (BuiltinData mt cs) -> do
+      t <- mt
+      addConstant' q defaultArgInfo q t (def t)
+      when (b == builtinId)     $ builtinIdHook q
+      bindBuiltinName b $ Def q []
+      where
+        def t = Datatype
+              { dataPars       = 0
+              , dataIxs        = 0
+              , dataClause     = Nothing
+              , dataCons       = []     -- Constructors are added later
+              , dataSort       = getSort t
+              , dataAbstr      = ConcreteDef
+              , dataMutual     = Nothing
+              , dataPathCons   = []
+              , dataTranspIx   = Nothing -- Id has custom transp def.
+              , dataTransp     = Nothing
+              }
+
+    Just (BuiltinSort builtinSort) -> do
+      let s = case builtinSort of
+                SortUniv u       -> Univ u $ ClosedLevel 0
+                SortOmega u      -> Inf u 0
+                SortIntervalUniv -> IntervalUniv
+                SortLevelUniv    -> LevelUniv
+          def = PrimitiveSort builtinSort s
+      -- Check for the cubical flag if the sort requries it
+      case builtinSort of
+        SortIntervalUniv -> requireCubical CErased ""
+        _ -> return ()
+      addConstant' q defaultArgInfo q (sort $ univSort s) def
+      bindBuiltinName b $ Def q []
+
+    Just{}  -> __IMPOSSIBLE__
+    Nothing -> __IMPOSSIBLE__ -- typeError $ NoSuchBuiltinName b
+
+
+builtinKindOfName :: BuiltinId -> Maybe KindOfName
+builtinKindOfName = distinguish <.> findBuiltinInfo
+  where
+  distinguish d = case builtinDesc d of
+    BuiltinDataCons{}  -> ConName
+    BuiltinData{}      -> DataName       -- Andreas, 2020-04-13: Crude.  Could be @RecName@.
+    BuiltinPrim{}      -> PrimName
+    BuiltinPostulate{} -> AxiomName
+    BuiltinSort{}      -> PrimName
+    BuiltinUnknown{}   -> OtherDefName
diff --git a/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs b/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs
@@ -0,0 +1,181 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | Handling of the INFINITY, SHARP and FLAT builtins.
+------------------------------------------------------------------------
+
+module Agda.TypeChecking.Rules.Builtin.Coinduction where
+
+import Agda.Interaction.Options.Base
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import Agda.Syntax.Scope.Base
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Rules.Builtin
+import Agda.TypeChecking.Rules.Term
+
+import Agda.Utils.Lens
+
+-- | The type of @∞@.
+
+typeOfInf :: TCM Type
+typeOfInf = hPi "a" (el primLevel) $
+            (return . sort $ varSort 0) --> (return . sort $ varSort 0)
+
+-- | The type of @♯_@.
+
+typeOfSharp :: TCM Type
+typeOfSharp = hPi "a" (el primLevel) $
+              hPi "A" (return . sort $ varSort 0) $
+              (El (varSort 1) <$> varM 0) -->
+              (El (varSort 1) <$> primInf <#> varM 1 <@> varM 0)
+
+-- | The type of @♭@.
+
+typeOfFlat :: TCM Type
+typeOfFlat = hPi "a" (el primLevel) $
+             hPi "A" (return . sort $ varSort 0) $
+             (El (varSort 1) <$> primInf <#> varM 1 <@> varM 0) -->
+             (El (varSort 1) <$> varM 0)
+
+-- | Binds the INFINITY builtin, but does not change the type's
+-- definition.
+
+bindBuiltinInf :: ResolvedName -> TCM ()
+bindBuiltinInf x = bindPostulatedName builtinInf x $ \inf _ -> do
+  _ <- checkExpr (A.Def inf) =<< typeOfInf
+  return $ Def inf []
+
+-- | Binds the SHARP builtin, and changes the definitions of INFINITY
+-- and SHARP.
+
+-- The following (no longer supported) definition is used:
+--
+-- codata ∞ {a} (A : Set a) : Set a where
+--   ♯_ : (x : A) → ∞ A
+
+bindBuiltinSharp :: ResolvedName -> TCM ()
+bindBuiltinSharp x =
+  bindPostulatedName builtinSharp x $ \sharp sharpDefn -> do
+    sharpType <- typeOfSharp
+    TelV fieldTel _ <- telView sharpType
+    _ <- checkExpr (A.Def sharp) sharpType
+    Def inf _ <- primInf
+    infDefn   <- getConstInfo inf
+    erasure   <- optErasure <$> pragmaOptions
+    addConstant (defName infDefn) $
+      infDefn { defPolarity       = [] -- not monotone
+              , defArgOccurrences = [Unused, StrictPos]
+              , theDef = Record
+                  { recPars           = 2
+                  , recInduction      = Just CoInductive
+                  , recClause         = Nothing
+                  , recConHead        = ConHead sharp (IsRecord CopatternMatching) CoInductive []  -- flat is added later
+                  , recNamedCon       = True
+                  , recFields         = []  -- flat is added later
+                  , recTel            = fieldTel
+                  , recEtaEquality'   = Inferred $ NoEta CopatternMatching
+                  , recPatternMatching= CopatternMatching
+                  , recMutual         = Just []
+                  , recTerminates     = Just True  -- not recursive
+                  , recAbstr          = ConcreteDef
+                  , recComp           = emptyCompKit
+                  }
+              }
+    addConstant sharp $
+      sharpDefn { theDef = Constructor
+                    { conPars   = 2
+                    , conArity  = 1
+                    , conSrcCon = ConHead sharp (IsRecord CopatternMatching) CoInductive [] -- flat is added as field later
+                    , conData   = defName infDefn
+                    , conAbstr  = ConcreteDef
+                    , conComp   = emptyCompKit
+                    , conProj   = Nothing
+                    , conForced = []
+                    , conErased = Nothing
+                    , conErasure = erasure
+                    , conInline  = True  -- This might make the sharp-translation superfluous.
+                    }
+                }
+    return $ Def sharp []
+
+-- | Binds the FLAT builtin, and changes its definition.
+
+-- The following (no longer supported) definition is used:
+--
+--   ♭ : ∀ {a} {A : Set a} → ∞ A → A
+--   ♭ (♯ x) = x
+
+bindBuiltinFlat :: ResolvedName -> TCM ()
+bindBuiltinFlat x =
+  bindPostulatedName builtinFlat x $ \ flat flatDefn -> do
+    _ <- checkExpr (A.Def flat) =<< typeOfFlat
+    Def sharp _ <- primSharp
+    kit         <- requireLevels
+    Def inf _   <- primInf
+    let sharpCon = ConHead sharp (IsRecord CopatternMatching) CoInductive [defaultArg flat]
+        level    = El (mkType 0) $ Def (typeName kit) []
+        tel     :: Telescope
+        tel      = ExtendTel (domH $ level)                  $ Abs "a" $
+                   ExtendTel (domH $ sort $ varSort 0)       $ Abs "A" $
+                   ExtendTel (domN $ El (varSort 1) $ var 0) $ Abs "x" $
+                   EmptyTel
+        infA     = El (varSort 2) $ Def inf [ Apply $ defaultArg $ var 1 ]
+        cpi      = noConPatternInfo { conPType = Just $ defaultArg infA
+                                    , conPLazy = True }
+    let clause   = Clause
+          { clauseLHSRange  = noRange
+          , clauseFullRange = noRange
+          , clauseTel       = tel
+          , namedClausePats = [ argN $ Named Nothing $
+              ConP sharpCon cpi [ argN $ Named Nothing $ debruijnNamedVar "x" 0 ] ]
+          , clauseBody      = Just $ var 0
+          , clauseType      = Just $ defaultArg $ El (varSort 2) $ var 1
+          , clauseCatchall    = False
+          , clauseExact       = Just True
+          , clauseRecursive   = Just False
+          , clauseUnreachable = Just False
+          , clauseEllipsis    = NoEllipsis
+          , clauseWhereModule = Nothing
+          }
+        cc = Case (defaultArg 0) $ conCase sharp False $ WithArity 1 $ Done [defaultArg "x"] $ var 0
+        projection = Projection
+          { projProper   = Just inf
+          , projOrig     = flat
+          , projFromType = defaultArg inf
+          , projIndex    = 3
+          , projLams     = ProjLams $ [ argH "a" , argH "A" , argN "x" ]
+          }
+    fun <- emptyFunctionData
+    addConstant flat $
+      flatDefn { defPolarity       = []
+               , defArgOccurrences = [StrictPos]  -- changing that to [Mixed] destroys monotonicity of 'Rec' in test/succeed/GuardednessPreservingTypeConstructors
+               , defCopatternLHS = hasProjectionPatterns cc
+               , theDef = FunctionDefn fun
+                   { _funClauses      = [clause]
+                   , _funCompiled     = Just $ cc
+                   , _funProjection   = Right projection
+                   , _funMutual       = Just []
+                   , _funTerminates   = Just True
+                   }
+                }
+
+    -- register flat as record field for constructor sharp
+    modifySignature $ updateDefinition sharp $ updateTheDef $ over lensConstructor $ \ def ->
+      def { _conSrcCon = sharpCon }
+    modifySignature $ updateDefinition inf $ updateTheDef $ over lensRecord $ \ def ->
+      def { _recConHead = sharpCon, _recFields = [defaultDom flat] }
+    return $ Def flat []
+
+-- The coinductive primitives.
+-- moved to TypeChecking.Monad.Builtin
diff --git a/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs-boot b/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Builtin/Coinduction.hs-boot
@@ -0,0 +1,16 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Builtin.Coinduction where
+
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Internal (Type)
+import Agda.TypeChecking.Monad
+
+typeOfInf   :: TCM Type
+typeOfSharp :: TCM Type
+typeOfFlat  :: TCM Type
+
+bindBuiltinInf   :: ResolvedName -> TCM ()
+bindBuiltinSharp :: ResolvedName -> TCM ()
+bindBuiltinFlat  :: ResolvedName -> TCM ()
+
diff --git a/src/full/Agda/TypeChecking/Rules/Data.hs b/src/full/Agda/TypeChecking/Rules/Data.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Data.hs
@@ -0,0 +1,1876 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Data where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Trans
+import Control.Monad.Trans.Maybe
+import Control.Exception as E
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options.Base
+
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Abstract.Views (deepUnscope)
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Scope.Monad
+
+import {-# SOURCE #-} Agda.TypeChecking.CompiledClause.Compile
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Generalize
+import Agda.TypeChecking.Implicit
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Positivity.Occurrence (Occurrence(StrictPos))
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Forcing
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Telescope
+
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Term ( isType_ )
+
+import Agda.Utils.Either
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Datatypes
+---------------------------------------------------------------------------
+
+-- | Type check a datatype definition. Assumes that the type has already been
+--   checked.
+checkDataDef :: A.DefInfo -> QName -> UniverseCheck -> A.DataDefParams -> [A.Constructor] -> TCM ()
+checkDataDef i name uc (A.DataDefParams gpars ps) cs =
+    traceCall (CheckDataDef (getRange name) name ps cs) $ do
+
+        -- Add the datatype module
+        addSection (qnameToMName name)
+
+        -- Look up the type of the datatype.
+        def <- instantiateDef =<< getConstInfo name
+        t   <- instantiateFull $ defType def
+        let npars =
+              case theDef def of
+                DataOrRecSig n -> n
+                _              -> __IMPOSSIBLE__
+
+        -- If the data type is erased, then hard compile-time mode is
+        -- entered.
+        setHardCompileTimeModeIfErased' def $ do
+
+        -- Make sure the shape of the type is visible
+        let unTelV (TelV tel a) = telePi tel a
+        t <- unTelV <$> telView t
+
+        parNames <- getGeneralizedParameters gpars name
+
+        -- Top level free vars
+        freeVars <- getContextSize
+
+        -- The parameters are in scope when checking the constructors.
+        dataDef <- bindGeneralizedParameters parNames t $ \ gtel t0 ->
+                   bindParameters (npars - length parNames) ps t0 $ \ ptel t0 -> do
+
+            -- The type we get from bindParameters is Θ -> s where Θ is the type of
+            -- the indices. We count the number of indices and return s.
+            -- We check that s is a sort.
+            let TelV ixTel s0 = telView' t0
+                nofIxs = size ixTel
+
+            s <- workOnTypes $ do
+              -- Andreas, 2016-11-02 issue #2290
+              -- Trying to unify the sort with a fresh sort meta which is
+              -- defined outside the index telescope is the most robust way
+              -- to check independence of the indices.
+              -- However, it might give the dreaded "Cannot instantiate meta..."
+              -- error which we replace by a more understandable error
+              -- in case of a suspected dependency.
+              s <- newSortMetaBelowInf
+              catchError_ (addContext ixTel $ equalType s0 $ raise nofIxs $ sort s) $ \ err ->
+                  if any (`freeIn` s0) [0..nofIxs - 1] then typeError $ SortCannotDependOnItsIndex name t0
+                  else throwError err
+              reduce s
+
+            withK   <- not . optWithoutK <$>
+                       pragmaOptions
+            erasure <- optErasure <$> pragmaOptions
+            -- Parameters are always hidden in constructors. If
+            -- --erasure is used, then the parameters are erased for
+            -- non-indexed data types, and if --with-K is active this
+            -- applies also to indexed data types.
+            let tel  = abstract gtel ptel
+                tel' = applyWhen (erasure && (withK || nofIxs == 0)) (applyQuantity zeroQuantity) .
+                       hideAndRelParams <$>
+                       tel
+
+            reportSDoc "tc.data.sort" 20 $ vcat
+              [ "checking datatype" <+> prettyTCM name
+              , nest 2 $ vcat
+                [ "type (parameters instantiated):   " <+> prettyTCM t0
+                , "type (full):   " <+> prettyTCM t
+                , "sort:   " <+> prettyTCM s
+                , "indices:" <+> text (show nofIxs)
+                , "gparams:" <+> text (show parNames)
+                , "params: " <+> text (show $ deepUnscope ps)
+                ]
+              ]
+            let npars = size tel
+
+            -- Change the datatype from an axiom to a datatype with no constructors.
+            let dataDef = DatatypeData
+                  { _dataPars       = npars
+                  , _dataIxs        = nofIxs
+                  , _dataClause     = Nothing
+                  , _dataCons       = []     -- Constructors are added later
+                  , _dataSort       = s
+                  , _dataAbstr      = Info.defAbstract i
+                  , _dataMutual     = Nothing
+                  , _dataPathCons   = []     -- Path constructors are added later
+                  , _dataTranspIx   = Nothing -- Generated later if nofIxs > 0.
+                  , _dataTransp     = Nothing -- Added later
+                  }
+
+            escapeContext impossible npars $ do
+              addConstant' name defaultArgInfo name t $ DatatypeDefn dataDef
+                -- polarity and argOcc.s determined by the positivity checker
+
+            -- Check the types of the constructors
+            pathCons <- forM cs $ \ c -> do
+              isPathCons <- checkConstructor name uc tel' nofIxs s c
+              return $ if isPathCons == PathCons then Just (A.axiomName c) else Nothing
+
+
+            -- cubical: the interval universe does not contain datatypes
+            -- similar: SizeUniv, ...
+            checkDataSort name s
+
+            -- when `--without-K`, all the indices should fit in the
+            -- sort of the datatype (see #3420).
+            -- Andreas, 2019-07-16, issue #3916:
+            -- NoUniverseCheck should also disable the index sort check!
+            unless (uc == NoUniverseCheck) $
+              whenM withoutKOption $ do
+                let s' = case s of
+                      Prop l -> Type l
+                      _      -> s
+                checkIndexSorts s' ixTel
+
+            -- Return the data definition
+            return dataDef{ _dataPathCons = catMaybes pathCons
+                          }
+
+        let cons   = map A.axiomName cs  -- get constructor names
+
+        (mtranspix, transpFun) <-
+          ifM (optCubicalCompatible <$> pragmaOptions)
+            (do mtranspix <- inTopContext $ defineTranspIx name
+                transpFun <- inTopContext $
+                               defineTranspFun name mtranspix cons
+                                 (_dataPathCons dataDef)
+                return (mtranspix, transpFun))
+            (return (Nothing, Nothing))
+
+        -- Add the datatype to the signature with its constructors.
+        -- It was previously added without them.
+        addConstant' name defaultArgInfo name t $ DatatypeDefn
+            dataDef{ _dataCons = cons
+                   , _dataTranspIx = mtranspix
+                   , _dataTransp   = transpFun
+                   }
+
+-- | Make sure that the target universe admits data type definitions.
+--   E.g. @IUniv@, @SizeUniv@ etc. do not accept new constructions.
+checkDataSort :: QName -> Sort -> TCM ()
+checkDataSort name s = setCurrentRange name $ do
+  ifBlocked s postpone {-else-} $ \ _ (s :: Sort) -> do
+    let
+      yes :: TCM ()
+      yes = return ()
+      no  :: TCM ()
+      no  = typeError $ SortDoesNotAdmitDataDefinitions name s
+    case s of
+      -- Sorts that admit data definitions.
+      Univ _ _     -> yes
+      Inf _ _      -> yes
+      DefS _ _     -> yes
+      -- Sorts that do not admit data definitions.
+      SizeUniv     -> no
+      LockUniv     -> no
+      LevelUniv    -> no
+      IntervalUniv -> no
+      -- Blocked sorts.
+      PiSort _ _ _ -> __IMPOSSIBLE__
+      FunSort _ _  -> __IMPOSSIBLE__
+      UnivSort _   -> __IMPOSSIBLE__
+      MetaS _ _    -> __IMPOSSIBLE__
+      DummyS _     -> __IMPOSSIBLE__
+  where
+    postpone :: Blocker -> Sort -> TCM ()
+    postpone b s = addConstraint b $ CheckDataSort name s
+
+-- | Ensure that the type is a sort.
+--   If it is not directly a sort, compare it to a 'newSortMetaBelowInf'.
+forceSort :: Type -> TCM Sort
+forceSort t = reduce (unEl t) >>= \case
+  Sort s -> return s
+  _      -> do
+    s <- newSortMetaBelowInf
+    equalType t (sort s)
+    return s
+
+
+-- | Type check a constructor declaration. Checks that the constructor targets
+--   the datatype and that it fits inside the declared sort.
+--   Returns the non-linear parameters.
+checkConstructor
+  :: QName         -- ^ Name of data type.
+  -> UniverseCheck -- ^ Check universes?
+  -> Telescope     -- ^ Parameter telescope.
+  -> Nat           -- ^ Number of indices of the data type.
+  -> Sort          -- ^ Sort of the data type.
+  -> A.Constructor -- ^ Constructor declaration (type signature).
+  -> TCM IsPathCons
+checkConstructor d uc tel nofIxs s (A.ScopedDecl scope [con]) = do
+  setScope scope
+  checkConstructor d uc tel nofIxs s con
+checkConstructor d uc tel nofIxs s con@(A.Axiom _ i ai Nothing c e) =
+    traceCall (CheckConstructor d tel s con) $ do
+{- WRONG
+      -- Andreas, 2011-04-26: the following happens to the right of ':'
+      -- we may use irrelevant arguments in a non-strict way in types
+      t' <- workOnTypes $ do
+-}
+        debugEnter c e
+        -- check that we are relevant
+        case getRelevance ai of
+          Relevant   -> return ()
+          Irrelevant -> typeError $ GenericError $ "Irrelevant constructors are not supported"
+          NonStrict  -> typeError $ GenericError $ "Shape-irrelevant constructors are not supported"
+        case getQuantity ai of
+          Quantityω{} -> return ()
+          Quantity0{} -> return ()
+          Quantity1{} -> typeError $ GenericError $ "Quantity-restricted constructors are not supported"
+
+        -- If the constructor is erased, then hard compile-time mode
+        -- is entered.
+        setHardCompileTimeModeIfErased' ai $ do
+
+        -- check that the type of the constructor is well-formed
+        (t, isPathCons) <- checkConstructorType e d
+
+        -- compute which constructor arguments are forced (only point constructors)
+        forcedArgs <- if isPathCons == PointCons
+                      then computeForcingAnnotations c t
+                      else return []
+        -- check that the sort (universe level) of the constructor type
+        -- is contained in the sort of the data type
+        -- (to avoid impredicative existential types)
+        debugFitsIn s
+        -- To allow propositional squash, we turn @Prop ℓ@ into @Set ℓ@
+        -- for the purpose of checking the type of the constructors.
+        let s' = case s of
+              Prop l -> Type l
+              _      -> s
+        arity <- applyQuantityToJudgement ai $
+          fitsIn c uc forcedArgs t s'
+        -- this may have instantiated some metas in s, so we reduce
+        s <- reduce s
+        debugAdd c t
+
+        (TelV fields _, boundary) <- telViewUpToPathBoundaryP (-1) t
+
+        -- We assume that the current context matches the parameters
+        -- of the datatype in an empty context (c.f. getContextSize above).
+        params <- getContextTelescope
+
+        (con, comp, projNames) <- do
+            -- Name for projection of ith field of constructor c is just c-i
+            names <- forM [0 .. size fields - 1] $ \ i ->
+              freshAbstractQName'_ $ P.prettyShow (A.qnameName c) ++ "-" ++ show i
+
+            -- nofIxs == 0 means the data type can be reconstructed
+            -- by appling the QName d to the parameters.
+            let dataT = El s $ Def d $ map Apply $ teleArgs params
+
+            reportSDoc "tc.data.con.comp" 5 $ inTopContext $ vcat $
+              [ "params =" <+> pretty params
+              , "dataT  =" <+> pretty dataT
+              , "fields =" <+> pretty fields
+              , "names  =" <+> pretty names
+              ]
+
+            let con = ConHead c IsData Inductive $ zipWith (<$) names $ map argFromDom $ telToList fields
+
+            defineProjections d con params names fields dataT
+            -- Andreas, 2024-01-05 issue #7048:
+            -- Only define hcomp when --cubical-compatible.
+            cubicalCompatible <- optCubicalCompatible <$> pragmaOptions
+            -- Cannot compose indexed inductive types yet.
+            comp <- if cubicalCompatible && nofIxs == 0 && Info.defAbstract i == ConcreteDef
+                    then inTopContext $ defineCompData d con params names fields dataT boundary
+                    else return emptyCompKit
+            return (con, comp, Just names)
+
+        -- add parameters to constructor type and put into signature
+        escapeContext impossible (size tel) $ do
+          erasure <- optErasure <$> pragmaOptions
+          addConstant' c ai c (telePi tel t) $ Constructor
+              { conPars   = size tel
+              , conArity  = arity
+              , conSrcCon = con
+              , conData   = d
+              , conAbstr  = Info.defAbstract i
+              , conComp   = comp
+              , conProj   = projNames
+              , conForced = forcedArgs
+              , conErased = Nothing  -- computed during compilation to treeless
+              , conErasure = erasure
+              , conInline  = False
+              }
+
+        -- Add the constructor to the instance table, if needed
+        case Info.defInstance i of
+          InstanceDef _r -> setCurrentRange c $ do
+            -- Including the range of the @instance@ keyword, like
+            -- @(getRange (r,c))@, does not produce good results.
+            -- Andreas, 2020-01-28, issue #4360:
+            -- Use addTypedInstance instead of addNamedInstance
+            -- to detect unusable instances.
+            addTypedInstance c t
+            -- addNamedInstance c d
+          NotInstanceDef -> pure ()
+
+        return isPathCons
+
+  where
+    -- Issue 3362: we need to do the `constructs` call inside the
+    -- generalization, so unpack the A.Generalize
+    checkConstructorType (A.ScopedExpr s e) d = withScope_ s $ checkConstructorType e d
+    checkConstructorType e d = do
+      let check k e = do
+            t <- workOnTypes $ isType_ e
+            -- check that the type of the constructor ends in the data type
+            n <- getContextSize
+            debugEndsIn t d (n - k)
+            isPathCons <- constructs (n - k) k t d
+            return (t, isPathCons)
+
+      case e of
+        A.Generalized s e -> do
+          (_, t, isPathCons) <- generalizeType' s (check 1 e)
+          return (t, isPathCons)
+        _ -> check 0 e
+
+    debugEnter c e =
+      reportSDoc "tc.data.con" 5 $ vcat
+        [ "checking constructor" <+> prettyTCM c <+> ":" <+> prettyTCM e
+        ]
+    debugEndsIn t d n =
+      reportSDoc "tc.data.con" 15 $ vcat
+        [ sep [ "checking that"
+              , nest 2 $ prettyTCM t
+              , "ends in" <+> prettyTCM d
+              ]
+        , nest 2 $ "nofPars =" <+> text (show n)
+        ]
+    debugFitsIn s =
+      reportSDoc "tc.data.con" 15 $ sep
+        [ "checking that the type fits in"
+        , nest 2 $ prettyTCM s
+        ]
+    debugAdd c t =
+      reportSDoc "tc.data.con" 5 $ vcat
+        [ "adding constructor" <+> prettyTCM c <+> ":" <+> prettyTCM t
+        ]
+checkConstructor _ _ _ _ _ _ = __IMPOSSIBLE__ -- constructors are axioms
+
+defineCompData :: QName      -- datatype name
+               -> ConHead
+               -> Telescope  -- Γ parameters
+               -> [QName]    -- projection names
+               -> Telescope  -- Γ ⊢ Φ field types
+               -> Type       -- Γ ⊢ T target type
+               -> Boundary   -- [(i,t_i,b_i)],  Γ.Φ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : B_i
+               -> TCM CompKit
+defineCompData d con params names fsT t boundary = do
+  required <- mapM getTerm'
+    [ someBuiltin builtinInterval
+    , someBuiltin builtinIZero
+    , someBuiltin builtinIOne
+    , someBuiltin builtinIMin
+    , someBuiltin builtinIMax
+    , someBuiltin builtinINeg
+    , someBuiltin builtinPOr
+    , someBuiltin builtinItIsOne
+    ]
+  if not (all isJust required) then return $ emptyCompKit else do
+    hcomp  <- whenDefined (null boundary) [builtinHComp,builtinTrans]
+      (defineKanOperationD DoHComp  d con params names fsT t boundary)
+    transp <- whenDefined True            [builtinTrans]
+      (defineKanOperationD DoTransp d con params names fsT t boundary)
+    return $ CompKit
+      { nameOfTransp = transp
+      , nameOfHComp  = hcomp
+      }
+  where
+    -- Δ^I, i : I |- sub Δ : Δ
+    sub tel = [ var n `apply` [Arg defaultArgInfo $ var 0] | n <- [1..size tel] ] ++# EmptyS __IMPOSSIBLE__
+    withArgInfo tel = zipWith Arg (map domInfo . telToList $ tel)
+
+    defineKanOperationD cmd d con params names fsT t boundary = do
+      let project = (\ t p -> apply (Def p []) [argN t])
+      stuff <- defineKanOperationForFields cmd
+                 (guard (not $ null boundary) >> Just (Con con ConOSystem $ teleElims fsT boundary))
+                 project d params fsT (map argN names) t
+      caseMaybe stuff (return Nothing) $ \ ((theName, gamma , ty, _cl_types , bodies), theSub) -> do
+
+      iz <- primIZero
+      body <- do
+        case cmd of
+          DoHComp -> return $ Con con ConOSystem (map Apply $ withArgInfo fsT bodies)
+          DoTransp | null boundary {- && null ixs -} -> return $ Con con ConOSystem (map Apply $ withArgInfo fsT bodies)
+                   | otherwise -> do
+            io <- primIOne
+            tIMax <- primIMax
+            tIMin <- primIMin
+            tINeg <- primINeg
+            tPOr  <- fromMaybe __IMPOSSIBLE__ <$> getTerm' builtinPOr
+            tHComp <- primHComp
+            -- Δ = params
+            -- Δ ⊢ Φ = fsT
+            -- (δ : Δ) ⊢ T = R δ
+            -- (δ : Δ) ⊢ con : Φ → R δ  -- no indexing
+            -- boundary = [(i,t_i,u_i)]
+            -- Δ.Φ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : B_i
+            -- Δ.Φ | PiPath Φ boundary (R δ) |- teleElims fsT boundary : R δ
+            -- Γ = ((δ : Δ^I), φ, us : Φ[δ 0]) = gamma
+            -- Γ ⊢ ty = R (δ i1)
+            -- (γ : Γ) ⊢ cl_types = (flatten Φ)[n ↦ f_n (transpR γ)]
+            -- Γ ⊢ bodies : Φ[δ i1]
+            -- Γ ⊢ t : ty
+            -- Γ, i : I ⊢ theSub : Δ.Φ
+            let
+
+              -- Δ.Φ ⊢ u = Con con ConOSystem $ teleElims fsT boundary : R δ
+              u = Con con ConOSystem $ teleElims fsT boundary
+              -- Γ ⊢ u
+              the_u = liftS (size fsT) d0 `applySubst` u
+                where
+                  -- δ : Δ^I, φ : F ⊢ [δ 0] : Δ
+                  d0 :: Substitution
+                  d0 = wkS 1 -- Δ^I, φ : F ⊢ Δ
+                             (consS iz IdS `composeS` sub params) -- Δ^I ⊢ Δ
+                                       -- Δ^I , i:I ⊢ sub params : Δ
+              the_phi = raise (size fsT) $ var 0
+              -- Γ ⊢ sigma : Δ.Φ
+              -- sigma = [δ i1,bodies]
+              -- sigma = theSub[i1]
+              sigma = reverse bodies ++# d1
+               where
+                -- δ i1
+                d1 :: Substitution
+                d1 = wkS (size gamma - size params) -- Γ ⊢ Δ
+                       (consS io IdS `composeS` sub params) -- Δ^I ⊢ Δ
+                                 -- Δ^I , i:I ⊢ sub params : Δ
+
+              -- Δ.Φ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : R δ
+              bs = fullBoundary fsT boundary
+              -- ψ = sigma `applySubst` map (\ i → i ∨ ~ i) . map fst $ boundary
+              -- Γ ⊢ t : R (δ i1)
+              w1' = Con con ConOSystem $ sigma `applySubst` teleElims fsT boundary
+              -- (δ, φ, u0) : Γ ⊢
+              -- w1 = hcomp (\ i → R (δ i1))
+              --            (\ i → [ ψ ↦ α (~ i), φ ↦ u0])
+              --            w1'
+              imax x y = pure tIMax <@> x <@> y
+              ineg r = pure tINeg <@> r
+              lvlOfType = (\ (Type l) -> Level l) . getSort
+              pOr la i j u0 u1 = pure tPOr <#> (lvlOfType <$> la) <@> i <@> j
+                                           <#> ilam "o" (\ _ -> unEl <$> la) <@> u0 <@> u1
+              absAp x y = liftM2 absApp x y
+
+              mkFace (r,(u1,u2)) = runNamesT [] $ do
+                -- Γ
+                phi <- open the_phi  -- (δ , φ , us) ⊢ φ
+                -- Γ ⊢ ty = Abs i. R (δ i)
+                ty <- open (Abs "i" $ (liftS 1 (raiseS (size gamma - size params)) `composeS` sub params) `applySubst` t)
+
+                bind "i" $ \ i -> do
+                  -- Γ, i
+                  [r,u1,u2] <- mapM (open . applySubst theSub) [r,u1,u2]
+                  psi <- imax r (ineg r)
+                  let
+                    -- Γ, i ⊢ squeeze u = primTrans (\ j -> ty [i := i ∨ j]) (φ ∨ i) u
+                    squeeze u = cl primTrans
+                                          <#> lam "j" (\ j -> lvlOfType <$> ty `absAp` (imax i j))
+                                          <@> lam "j" (\ j -> unEl <$> ty `absAp` (imax i j))
+                                          <@> (phi `imax` i)
+                                          <@> u
+                  alpha <- pOr (ty `absAp` i)
+                              (ineg r)
+                              r
+                           (ilam "o" $ \ _ -> squeeze u1) (ilam "o" $ \ _ -> squeeze u2)
+                  return $ (psi, alpha)
+
+            -- Γ ⊢ Abs i. [(ψ_n,α_n : [ψ] → R (δ i))]
+            faces <- mapM mkFace bs
+
+            runNamesT [] $ do
+                -- Γ
+                w1' <- open w1'
+                phi <- open the_phi
+                u   <- open the_u
+                -- R (δ i1)
+                ty <- open ty
+                faces <- mapM (\ x -> liftM2 (,) (open . noabsApp __IMPOSSIBLE__ $ fmap fst x) (open $ fmap snd x)) faces
+                let
+                  thePsi = foldl1 imax (map fst faces)
+                  hcomp ty phi sys a0 = pure tHComp <#> (lvlOfType <$> ty)
+                                                    <#> (unEl <$> ty)
+                                                    <#> phi
+                                                    <@> sys
+                                                    <@> a0
+                let
+                 sys = lam "i" $ \ i -> do
+                  let
+                    recurse [(psi,alpha)] = alpha `absAp` (ineg i)
+                    recurse ((psi,alpha):xs) = pOr ty
+                                                   psi  theOr
+                                                   (alpha `absAp` (ineg i)) (recurse xs)
+                      where
+                        theOr = foldl1 imax (map fst xs)
+                    recurse [] = __IMPOSSIBLE__
+                    sys_alpha = recurse faces
+                  pOr ty
+                                                   thePsi    phi
+                                                   sys_alpha (ilam "o" $ \ _ -> u)
+                hcomp ty (thePsi `imax` phi) sys w1'
+
+
+      let
+
+        -- δ : Δ^I, φ : F ⊢ [δ 0] : Δ
+        d0 :: Substitution
+        d0 = wkS 1 -- Δ^I, φ : F ⊢ Δ
+                       (consS iz IdS `composeS` sub params) -- Δ^I ⊢ Δ
+                                 -- Δ^I , i:I ⊢ sub params : Δ
+
+        -- Δ.Φ ⊢ u = Con con ConOSystem $ teleElims fsT boundary : R δ
+--        u = Con con ConOSystem $ teleElims fsT boundary
+        up = ConP con (ConPatternInfo defaultPatternInfo False False Nothing False) $
+               telePatterns (d0 `applySubst` fsT) (liftS (size fsT) d0 `applySubst` boundary)
+--        gamma' = telFromList $ take (size gamma - 1) $ telToList gamma
+
+        -- (δ , φ , fs : Φ[d0]) ⊢ u[liftS Φ d0]
+        -- (δ , φ, u) : Γ ⊢ body
+        -- Δ ⊢ Φ = fsT
+        -- (δ , φ , fs : Φ[d0]) ⊢ u[liftS Φ d0] `consS` raiseS Φ : Γ
+--        (tel',theta) = (abstract gamma' (d0 `applySubst` fsT), (liftS (size fsT) d0 `applySubst` u) `consS` raiseS (size fsT))
+
+      let
+        pats | null boundary = teleNamedArgs gamma
+             | otherwise     = take (size gamma - size fsT) (teleNamedArgs gamma) ++ [argN $ unnamed $ up]
+        clause = Clause
+          { clauseTel         = gamma
+          , clauseType        = Just . argN $ ty
+          , namedClausePats   = pats
+          , clauseFullRange   = noRange
+          , clauseLHSRange    = noRange
+          , clauseCatchall    = False
+          , clauseBody        = Just $ body
+          , clauseExact       = Just True
+          , clauseRecursive   = Nothing
+              -- Andreas 2020-02-06 TODO
+              -- Or: Just False;  is it known to be non-recursive?
+          , clauseUnreachable = Just False
+          , clauseEllipsis    = NoEllipsis
+          , clauseWhereModule = Nothing
+          }
+        cs = [clause]
+      addClauses theName cs
+      (mst, _, cc) <- inTopContext (compileClauses Nothing cs)
+      whenJust mst $ setSplitTree theName
+      setCompiledClauses theName cc
+      setTerminates theName True
+      return $ Just theName
+
+    whenDefined False _ _ = return Nothing
+    whenDefined True xs m = do
+      xs <- mapM getTerm' xs
+      if all isJust xs then m else return Nothing
+
+-- Andrea: TODO handle Irrelevant fields somehow.
+-- | Define projections for non-indexed data types (families don't work yet).
+--   Of course, these projections are partial functions in general.
+--
+--   Precondition: we are in the context Γ of the data type parameters.
+defineProjections :: QName      -- datatype name
+                  -> ConHead
+                  -> Telescope  -- Γ parameters
+                  -> [QName]    -- projection names
+                  -> Telescope  -- Γ ⊢ Φ field types
+                  -> Type       -- Γ ⊢ T target type
+                  -> TCM ()
+defineProjections dataName con params names fsT t = do
+  let
+    -- Γ , (d : T) ⊢ Φ[n ↦ proj n d]
+    fieldTypes = ([ Def f [] `apply` [argN $ var 0] | f <- reverse names ] ++# raiseS 1) `applySubst`
+                    flattenTel fsT  -- Γ , Φ ⊢ Φ
+    -- ⊢ Γ , (d : T)
+    projTel    = abstract params (ExtendTel (defaultDom t) (Abs "d" EmptyTel))
+    np         = size params
+
+  forM_ (zip3 (downFrom (size fieldTypes)) names fieldTypes) $ \ (i,projName,ty) -> do
+    let
+      projType = abstract projTel <$> ty
+      cpi    = ConPatternInfo defaultPatternInfo False False (Just $ argN $ raise (size fsT) t) False
+      conp   = defaultNamedArg $ ConP con cpi $ teleNamedArgs fsT
+      sigma  = Con con ConOSystem (map Apply $ teleArgs fsT) `consS` raiseS (size fsT)
+      clause = empty
+          { clauseTel         = abstract params fsT
+          , namedClausePats   = [ conp ]
+          , clauseBody        = Just $ var i
+          , clauseType        = Just $ argN $ applySubst sigma $ unDom ty
+          , clauseRecursive   = Just False  -- non-recursive
+          , clauseUnreachable = Just False
+          }
+
+    reportSDoc "tc.data.proj" 20 $ inTopContext $ sep
+      [ "proj" <+> prettyTCM (i,ty)
+      , nest 2 $ sep [ prettyTCM projName, ":", prettyTCM projType ]
+      ]
+
+    -- Andreas, 2020-02-14, issue #4437
+    -- Define data projections as projection-like from the start.
+    noMutualBlock $ do
+      let cs = [ clause ]
+      (mst, _, cc) <- compileClauses Nothing cs
+      fun          <- emptyFunctionData <&> \fun -> fun
+                { _funClauses    = cs
+                , _funCompiled   = Just cc
+                , _funSplitTree  = mst
+                , _funProjection = Right Projection
+                    { projProper   = Nothing
+                    , projOrig     = projName
+                    , projFromType = Arg (getArgInfo ty) dataName
+                    , projIndex    = np + 1
+                    , projLams     = ProjLams $ map (argFromDom . fmap fst) $ telToList projTel
+                    }
+                , _funMutual     = Just []
+                , _funTerminates = Just True
+                }
+      lang <- getLanguage
+      inTopContext $ addConstant projName $
+        (defaultDefn defaultArgInfo projName (unDom projType) lang $ FunctionDefn fun)
+          { defNoCompilation  = True
+          , defArgOccurrences = [StrictPos]
+          }
+
+      reportSDoc "tc.data.proj.fun" 60 $ inTopContext $ vcat
+        [ "proj" <+> prettyTCM i
+        , nest 2 $ pretty fun
+        ]
+
+
+freshAbstractQName'_ :: String -> TCM QName
+freshAbstractQName'_ = freshAbstractQName noFixity' . C.simpleName
+
+
+-- | Defines and returns the name of the `transpIx` function.
+defineTranspIx :: QName  -- ^ datatype name
+               -> TCM (Maybe QName)
+defineTranspIx d = do
+  def <- getConstInfo d
+  case theDef def of
+    Datatype { dataPars = npars
+             , dataIxs = nixs
+             , dataSort = s}
+     -> do
+      let t = defType def
+      reportSDoc "tc.data.ixs" 20 $ vcat
+        [ "name :" <+> prettyTCM d
+        , "type :" <+> prettyTCM t
+        , "npars:" <+> pretty npars
+        , "nixs :" <+> pretty nixs
+        ]
+      if nixs == 0 then return Nothing else do
+      trIx <- freshAbstractQName'_ $ "transpX-" ++ P.prettyShow (A.qnameName d)
+      TelV params t' <- telViewUpTo npars t
+      TelV ixs    dT <- telViewUpTo nixs t'
+      -- params     ⊢ s
+      -- params     ⊢ ixs
+      -- params.ixs ⊢ dT
+      reportSDoc "tc.data.ixs" 20 $ vcat
+        [ "params :" <+> prettyTCM params
+        , "ixs    :" <+> (addContext params $ prettyTCM ixs)
+        , "dT     :" <+> (addContext params $ addContext ixs $ prettyTCM dT)
+        ]
+      -- theType <- abstract params <$> undefined
+      interval <- primIntervalType
+      let deltaI = expTelescope interval ixs
+      iz <- primIZero
+      io@(Con c _ _) <- primIOne
+      imin <- getPrimitiveTerm builtinIMin
+      imax <- getPrimitiveTerm builtinIMax
+      ineg <- getPrimitiveTerm builtinINeg
+      transp <- getPrimitiveTerm builtinTrans
+      por <- getPrimitiveTerm builtinPOr
+      one <- primItIsOne
+      -- reportSDoc "trans.rec" 20 $ text $ show params
+      -- reportSDoc "trans.rec" 20 $ text $ show deltaI
+      -- reportSDoc "trans.rec" 10 $ text $ show fsT
+
+      -- let thePrefix = "transp-"
+      -- theName <- freshAbstractQName'_ $ thePrefix ++ P.prettyShow (A.qnameName name)
+
+      -- reportSLn "trans.rec" 5 $ ("Generated name: " ++ show theName ++ " " ++ showQNameId theName)
+
+      -- record type in 'exponentiated' context
+      -- (params : Γ)(ixs : Δ^I), i : I |- T[params, ixs i]
+      let rect' = sub ixs `applySubst` El (raise (size ixs) s) (Def d (teleElims (abstract params ixs) []))
+      addContext params $ reportSDoc "tc.data.ixs" 20 $ "deltaI:" <+> prettyTCM deltaI
+      addContext params $ addContext deltaI $ addContext ("i"::String, defaultDom interval) $ do
+        reportSDoc "tc.data.ixs" 20 $ "rect':" <+> pretty (sub ixs)
+        reportSDoc "tc.data.ixs" 20 $ "rect':" <+> pretty rect'
+
+      theType <- (abstract (setHiding Hidden <$> params) <$>) . (abstract deltaI <$>) $ runNamesT [] $ do
+                  rect' <- open (runNames [] $ bind "i" $ \ x -> let _ = x `asTypeOf` pure (undefined :: Term) in
+                                                                 pure rect')
+                  nPi' "phi" (primIntervalType) $ \ phi ->
+                   (absApp <$> rect' <*> pure iz) --> (absApp <$> rect' <*> pure io)
+
+      reportSDoc "tc.data.ixs" 20 $ "transpIx:" <+> prettyTCM theType
+      let
+        ctel = abstract params $ abstract deltaI $ ExtendTel (defaultDom $ subst 0 iz rect') (Abs "t" EmptyTel)
+        ps = telePatterns ctel []
+        cpi = noConPatternInfo { conPType = Just (defaultArg interval) }
+        pat :: NamedArg (Pattern' DBPatVar)
+        pat = defaultNamedArg $ ConP c cpi []
+        clause = empty
+          { clauseTel         = ctel
+          , namedClausePats   = init ps ++ [pat, last ps]
+
+          , clauseBody        = Just $ var 0
+          , clauseType        = Just $ defaultArg $ raise 1 $ subst 0 io rect'
+          , clauseRecursive   = Just False  -- non-recursive
+          , clauseUnreachable = Just False
+          }
+
+      noMutualBlock $ do
+        let cs = [ clause ]
+--        we do not compile clauses as that leads to throwing missing clauses errors.
+--        (mst, _, cc) <- compileClauses Nothing cs
+        fun <- emptyFunctionData <&> \fun -> fun
+                  { _funClauses    = cs
+               --   , _funCompiled   = Just cc
+               --   , _funSplitTree  = mst
+                  , _funProjection = Left MaybeProjection
+                  , _funMutual     = Just []
+                  , _funTerminates = Just True
+                  , _funIsKanOp    = Just d
+                  }
+        inTopContext $ do
+         reportSDoc "tc.transpx.type" 15 $ vcat
+           [ "type of" <+> prettyTCM trIx <+> ":"
+           , nest 2 $ prettyTCM theType
+           ]
+
+         addConstant trIx $
+          (defaultDefn defaultArgInfo trIx theType (Cubical CErased) $ FunctionDefn fun)
+            { defNoCompilation  = True
+            }
+
+        -- reportSDoc "tc.data.proj.fun" 60 $ inTopContext $ vcat
+        --   [ "proj" <+> prettyTCM i
+        --   , nest 2 $ pretty fun
+        --   ]
+      -- addContext ctel $ do
+      --   let es = teleElims ctel []
+      --   r <- reduce $ Def trIx es
+      --   reportSDoc "tc.data.ixs" 20 $ "reducedx:" <+> prettyTCM r
+      --   r <- reduce $ Def trIx (init es ++ [Apply $ argN io, last es])
+      --   reportSDoc "tc.data.ixs" 20 $ "reduced1:" <+> prettyTCM r
+      return $ Just trIx
+    _ -> __IMPOSSIBLE__
+  where
+
+    -- Γ, Δ^I, i : I |- sub (Γ ⊢ Δ) : Γ, Δ
+    sub tel = expS $ size tel
+
+
+defineTranspFun :: QName -- ^ datatype
+                -> Maybe QName -- ^ transpX "constructor"
+                -> [QName]     -- ^ constructor names
+                -> [QName]     -- ^ path cons
+                -> TCM (Maybe QName) -- transp function for the datatype.
+defineTranspFun d mtrX cons pathCons = do
+  def <- getConstInfo d
+  case theDef def of
+    Datatype { dataPars = npars
+             , dataIxs = nixs
+             , dataSort = s@(Type _)
+--             , dataCons = cons -- not there yet
+             }
+     -> do
+      let t = defType def
+      reportSDoc "tc.data.transp" 20 $ vcat
+        [ "name :" <+> prettyTCM d
+        , "type :" <+> prettyTCM t
+        , "npars:" <+> pretty npars
+        , "nixs :" <+> pretty nixs
+        ]
+      trD <- freshAbstractQName'_ $ "transp" ++ P.prettyShow (A.qnameName d)
+      TelV params t' <- telViewUpTo npars t
+      TelV ixs    dT <- telViewUpTo nixs t'
+
+      let tel = abstract params ixs
+      mixs <- runMaybeT $ traverse (traverse (MaybeT . toLType)) ixs
+      caseMaybe mixs (return Nothing) $ \ _ -> do
+
+      io@(Con io_c _ []) <- primIOne
+      iz <- primIZero
+
+      interval <- primIntervalType
+      let telI = expTelescope interval tel
+          sigma = sub tel
+          dTs = (sigma `applySubst` El s (Def d $ map Apply $ teleArgs tel))
+
+      theType <- (abstract telI <$>) $ runNamesT [] $ do
+                  dT <- open $ Abs "i" $ dTs
+                  nPi' "phi" primIntervalType $ \ phi ->
+                   (absApp <$> dT <*> pure iz) --> (absApp <$> dT <*> pure io)
+
+
+      reportSDoc "tc.data.transp" 20 $ "transpD:" <+> prettyTCM theType
+
+
+      noMutualBlock $ do
+        fun <- emptyFunction
+        inTopContext $ addConstant trD $
+          (defaultDefn defaultArgInfo trD theType (Cubical CErased) fun)
+        let
+          ctel = abstract telI $ ExtendTel (defaultDom $ subst 0 iz dTs) (Abs "t" EmptyTel)
+          ps = telePatterns ctel []
+          cpi = noConPatternInfo { conPType = Just (defaultArg interval)
+                                 , conPFallThrough = True
+                                 }
+          pat :: NamedArg (Pattern' DBPatVar)
+          pat = defaultNamedArg $ ConP io_c cpi []
+          clause = empty
+            { clauseTel         = ctel
+            , namedClausePats   = init ps ++ [pat, last ps]
+
+            , clauseBody        = Just $ var 0
+            , clauseType        = Just $ defaultArg $ raise 1 $ subst 0 io dTs
+            , clauseRecursive   = Just False  -- non-recursive
+            , clauseUnreachable = Just False
+            }
+        let debugNoTransp cl = enterClosure cl $ \ t -> do
+              reportSDoc "tc.data.transp" 20 $ addContext ("i" :: String, __DUMMY_DOM__) $
+                "could not transp" <+> prettyTCM (absBody t)
+        -- TODO: if no params nor indexes trD phi u0 = u0.
+        ecs <- tryTranspError $ (clause:) <$> defineConClause trD (not $ null pathCons) mtrX npars nixs ixs telI sigma dTs cons
+        caseEitherM (pure ecs) (\ cl -> debugNoTransp cl >> return Nothing) $ \ cs -> do
+        (mst, _, cc) <- compileClauses Nothing cs
+        fun <- emptyFunctionData <&> \fun -> fun
+                  { _funClauses    = cs
+                  , _funCompiled   = Just cc
+                  , _funSplitTree  = mst
+                  , _funProjection = Left MaybeProjection
+                  , _funMutual     = Just []
+                  , _funTerminates = Just True
+                  , _funIsKanOp    = Just d
+                  }
+        inTopContext $ addConstant trD $
+          (defaultDefn defaultArgInfo trD theType (Cubical CErased) $ FunctionDefn fun)
+            { defNoCompilation  = True
+            }
+        reportSDoc "tc.data.transp" 20 $ sep
+          [ "transp: compiled clauses of " <+> prettyTCM trD
+          , nest 2 $ return $ P.pretty cc
+          ]
+
+        return $ Just trD
+
+
+    Datatype {} -> return Nothing
+    _           -> __IMPOSSIBLE__
+  where
+    -- Γ, Δ^I, i : I |- sub (Γ ⊢ Δ) : Γ, Δ
+    sub tel = expS (size tel)
+
+defineConClause :: QName -- ^ trD
+                -> Bool  -- ^ HIT
+                -> Maybe QName -- ^ trX
+                -> Nat  -- ^ npars = size Δ
+                -> Nat  -- ^ nixs = size X
+                -> Telescope -- ^ Δ ⊢ X
+                -> Telescope -- ^ (Δ.X)^I
+                -> Substitution -- ^ (Δ.X)^I, i : I ⊢ σ : Δ.X
+                -> Type       -- ^ (Δ.X)^I, i : I ⊢ D[δ i,x i] -- datatype
+                -> [QName]      -- ^ Constructors
+                -> TCM [Clause]
+defineConClause trD' isHIT mtrX npars nixs xTel' telI sigma dT' cnames = do
+
+  unless (isNothing mtrX == (nixs == 0)) $ __IMPOSSIBLE__
+
+  io <- primIOne
+  iz <- primIZero
+  tHComp <- primHComp
+  tINeg <- primINeg
+  let max i j = cl primIMax <@> i <@> j
+  let min i j = cl primIMin <@> i <@> j
+  let neg i = cl primINeg <@> i
+  let hcomp ty sys u0 = do
+          ty <- ty
+          Just (LEl l ty) <- toLType ty
+          l <- open $ Level l
+          ty <- open $ ty
+          face <- (foldr max (pure iz) $ map fst $ sys)
+          sys <- lam "i'" $ \ i -> combineSys l ty [(phi, u <@> i) | (phi,u) <- sys]
+          pure tHComp <#> l <#> ty <#> pure face <@> pure sys <@> u0
+  interval <- primIntervalType
+  let intervalTel nm = ExtendTel (defaultDom interval) (Abs nm EmptyTel)
+
+  let (parI,ixsI) = splitTelescopeAt npars telI
+  let
+    abstract_trD :: MonadFail m => (Vars m -> Vars m -> Vars m -> NamesT m Telescope) -> NamesT m Telescope
+    abstract_trD k = do
+               ixsI <- open $ AbsN (teleNames parI) ixsI
+               parI <- open parI
+               abstractN parI $ \ delta -> do
+               abstractN (ixsI `applyN` delta) $ \ x -> do
+               abstractN (pure $ intervalTel "phi") $ \ phi -> do
+               k delta x phi
+    bind_trD :: MonadFail m => (ArgVars m -> ArgVars m -> ArgVars m -> NamesT m b) ->
+                NamesT m (AbsN (AbsN (AbsN b)))
+    bind_trD k = do
+      bindNArg (teleArgNames parI) $ \ delta_ps -> do
+      bindNArg (teleArgNames ixsI) $ \ x_ps -> do
+      bindNArg (teleArgNames $ intervalTel "phi") $ \ phi_ps -> do
+      k delta_ps x_ps phi_ps
+  let trD = bindNArg (teleArgNames parI) $ \ delta ->
+            bindNArg (teleArgNames ixsI) $ \ x ->
+            bindN ["phi","u0"]           $ \ [phi,u0] ->
+              ((Def trD' [] `apply`) <$> sequence (delta ++ x)) <@> phi <@> u0
+  -- [Δ] ⊢ X
+  let xTel = pure $ AbsN (teleNames parI) xTel'
+  -- [δ : Δ^I, x : X^I, i : I] ⊢ D (δ i) (x i)
+  let dT = pure $ AbsN (teleNames parI ++ teleNames ixsI ++ ["i"]) dT'
+
+  let hcompComputes = not $ isHIT || nixs > 0
+  c_HComp <- if hcompComputes then return [] else do
+      reportSDoc "tc.data.transp.con" 20 $ "======================="
+      reportSDoc "tc.data.transp.con" 20 $ "hcomp"
+      qHComp <- fromMaybe __IMPOSSIBLE__ <$> getPrimitiveName' builtinHComp
+      hcomp_ty <- defType <$> getConstInfo qHComp
+      gamma <- runNamesT [] $ do
+               ixsI <- open $ AbsN (teleNames parI) ixsI
+               parI <- open parI
+               abstract_trD $ \ delta x _ -> do
+               Just (LEl l ty) <- toLType =<< (dT `applyN` (delta ++ x ++ [pure iz]))
+               -- (φ : I), (I → Partial φ (D (δ i0) (x i0))), D (δ i0) (x i0)
+               TelV args _ <- lift $ telView =<< piApplyM hcomp_ty [Level l,ty]
+               unless (size args == 3) __IMPOSSIBLE__
+               pure args
+      res <- runNamesT [] $ do
+        let hcompArgs = map argN ["phi","u","u0"]
+        bind_trD $ \ delta_ps x_ps phi_ps -> do
+        let x = map (fmap unArg) x_ps
+        let delta = map (fmap unArg) delta_ps
+        let [phi] = map (fmap unArg) phi_ps
+        bindNArg hcompArgs $ \ as0 -> do -- as0 : aTel[delta 0]
+        let
+          origPHComp = do
+            Just (LEl l t) <- toLType =<< (dT `applyN` (delta ++ x ++ [pure iz]))
+            let ds = map (argH . unnamed . dotP) [Level l, t]
+            ps0@[_hphi,_u,_u0] <- sequence $ as0
+            pure $ DefP defaultPatternInfo qHComp $ ds ++ ps0
+          psHComp = sequence $ delta_ps ++ x_ps ++ phi_ps ++ [argN . unnamed <$> origPHComp]
+        let
+          rhsTy = dT `applyN` (delta ++ x ++ [pure io])
+        -- trD δ x φ (hcomp [hφ ↦ u] u0) ↦ rhsHComp
+        let rhsHComp = do
+              let [hphi,u,u0] = map (fmap unArg) as0
+              -- TODO: should trD be transp for the datatype?
+              let baseHComp = trD `applyN` delta `applyN` x `applyN` [phi,u0]
+              let sideHComp = lam "i" $ \ i -> ilam "o" $ \ o -> do
+                     trD `applyN` delta `applyN` x `applyN` [phi,u <@> i <..> o]
+              hcomp rhsTy [(hphi, sideHComp)] baseHComp
+        (,,) <$> psHComp <*> rhsTy <*> rhsHComp
+      let (ps,rhsTy,rhs) = unAbsN $ unAbsN $ unAbsN $ unAbsN $ res
+      (:[]) <$> mkClause gamma ps rhsTy rhs
+
+
+  c_trX   <- caseMaybe mtrX (pure []) $ \ trX -> do
+        reportSDoc "tc.data.transp.con" 20 $ "======================="
+        reportSDoc "tc.data.transp.con" 20 $ prettyTCM trX
+        gamma <- runNamesT [] $ do
+                     ixsI <- open $ AbsN (teleNames parI) ixsI
+                     parI <- open parI
+                     abstract_trD $ \ delta _ _ -> do
+                     let delta0_refl = for delta $ \ p -> lam "i" $ \ _ -> p <@> pure iz
+                     abstractN (ixsI `applyN` delta0_refl) $ \ x' -> do
+                     abstractN (pure $ intervalTel "phi'") $ \ _ -> do
+                     ty <- dT `applyN` (delta0_refl ++ x' ++ [pure iz])
+                     pure $ ExtendTel (defaultDom ty) $ Abs "t" EmptyTel
+        res <- runNamesT [] $
+          bind_trD $ \ delta_ps x_ps phi_ps -> do
+          let x = map (fmap unArg) x_ps
+          let delta = map (fmap unArg) delta_ps
+          let [phi] = map (fmap unArg) phi_ps
+          --- pattern matching args below
+          bindNArg (map (fmap (++ "'")) (teleArgNames ixsI)) $ \ x'_ps -> do
+          let x' = map (fmap unArg) x'_ps :: [NamesT TCM Term]
+          let phi'name = teleArgNames $ intervalTel "phi'"
+          bindNArg phi'name $ \ phi'_ps -> do
+          let phi's = map (fmap unArg) phi'_ps
+          bindNArg [argN "t"] $ \ as0 -> do
+          let deltaArg i = do
+                i <- i
+                xs <- sequence delta_ps
+                pure $ map (fmap (`apply` [argN i])) xs
+
+          let
+            origPTrX = do
+              x'_ps <- sequence x'_ps
+              phi'_ps <- sequence phi'_ps
+              ds <- map (setHiding Hidden . fmap (unnamed . dotP)) <$> deltaArg (pure iz)
+              ps0@[_t] <- sequence as0
+              pure $ DefP defaultPatternInfo trX $ ds ++ x'_ps ++ phi'_ps ++ ps0
+            psTrX = sequence $ delta_ps ++ x_ps ++ phi_ps ++ [argN . unnamed <$> origPTrX]
+
+            rhsTy = dT `applyN` (delta ++ x ++ [pure io])
+
+          -- trD δ x φ (trX x' φ' t) ↦ rhsTrx
+          let rhsTrX = do
+                let [t] = map (fmap unArg) as0
+                let [phi'] = phi's
+                let telXdeltai = bind "i" $ \ i -> applyN xTel (map (<@> i) delta)
+                let reflx1 = for x $ \ q -> lam "i" $ \ _ -> q <@> pure io
+                let symx' = for x' $ \ q' -> lam "i" $ \ i -> q' <@> neg i
+                x_tr <- mapM (open . unArg) =<< transpPathTel' telXdeltai symx' reflx1 phi' x
+                let baseTrX = trD `applyN` delta `applyN` x_tr `applyN` [phi `min` phi',t]
+                let sideTrX = lam "j" $ \ j -> ilam "o" $ \ _ -> do
+                      let trD_f = trD `applyN` (for delta $ \ p -> lam "i" $ \ i -> p <@> (i `min` neg j))
+                                      `applyN` (for x_tr  $ \ p -> lam "i" $ \ i -> p <@> (i `min` neg j))
+                                      `applyN` [(phi `min` phi') `max` j,t]
+                      let x_tr_f = fmap (fmap (\ (Abs n (Arg i t)) -> Arg i $ Lam defaultArgInfo (Abs n t)) . sequence) $
+                           bind "i" $ \ i -> do
+                            j <- j
+                            map (fmap (`apply` [argN j])) <$> trFillPathTel' telXdeltai symx' reflx1 phi' x (neg i)
+                      let args = liftM2 (++) (map (setHiding Hidden) <$> deltaArg (pure io)) x_tr_f
+                      (apply (Def trX []) <$> args) <@> (phi' `max` neg j) <@> trD_f
+                hcomp rhsTy [(phi,sideTrX),(phi',lam "i" $ \ _ -> ilam "o" $ \ _ -> baseTrX)]
+                            baseTrX
+
+          (,,) <$> psTrX <*> rhsTy <*> rhsTrX
+
+
+        let (ps,rhsTy,rhs) = unAbsN $ unAbsN $ unAbsN $ unAbsN $ unAbsN $ unAbsN $ res
+        (:[]) <$> mkClause gamma ps rhsTy rhs
+
+  fmap ((c_HComp ++ c_trX) ++) $ forM cnames $ \ cname -> do
+    def <- getConstInfo cname
+    let
+      Constructor
+       { conPars = npars'
+       , conArity = nargs
+       , conSrcCon = chead
+       } = theDef def
+    do
+        let tcon = defType def
+
+        reportSDoc "tc.data.transp.con" 20 $ "======================="
+        reportSDoc "tc.data.transp.con" 20 $ "tcon:" <+> prettyTCM (conName chead) <+> prettyTCM tcon
+
+        unless (conName chead == cname && npars' == npars) $ __IMPOSSIBLE__
+
+
+        TelV prm tcon' <- telViewUpTo npars' tcon
+        -- Δ ⊢ aTel
+        -- Δ.aTel ⊢ ty
+        -- Δ.aTel ⊢ [(φ,(l,r))] = boundary : ty
+        (TelV aTel ty, boundary) <- telViewUpToPathBoundary nargs tcon'
+
+        Def _ es <- unEl <$> reduce ty
+        -- Δ.aTel ⊢ con_ixs : X
+        let con_ixs = fromMaybe __IMPOSSIBLE__ $ allApplyElims $ drop npars es
+
+        reportSDoc "tc.data.transp.con" 20 $
+          addContext prm $ "aTel:" <+> prettyTCM aTel
+        reportSDoc "tc.data.transp.con" 20 $
+          addContext prm $ addContext aTel $ "ty:" <+> prettyTCM ty
+        reportSDoc "tc.data.transp.con" 20 $
+          addContext prm $ addContext aTel $ "boundary:" <+> prettyTCM boundary
+
+        gamma <- runNamesT [] $ do
+                     ixsI <- open $ AbsN (teleNames parI) ixsI
+                     aTel <- open $ AbsN (teleNames prm) aTel
+                     parI <- open parI
+                     abstract_trD $ \ delta _ _ -> do
+                     let args = aTel `applyN` map (<@> pure iz) delta
+                     args
+        res <- runNamesT [] $ do
+          let aTelNames = teleNames aTel
+              aTelArgs = teleArgNames aTel
+          con_ixs <- open $ AbsN (teleNames prm ++ teleNames aTel) $ map unArg con_ixs
+          bndry <- open $ AbsN (teleNames prm ++ teleNames aTel) $ boundary
+          u    <- open $ AbsN (teleNames prm ++ aTelNames) $ Con chead ConOSystem (teleElims aTel boundary)
+          aTel <- open $ AbsN (teleNames prm) aTel
+          -- bsys : Abs Δ.Args ([phi] → ty)
+          (bsysFace,bsys) <- do
+            p <- bindN (teleNames prm ++ aTelNames) $ \ ts -> do
+              Just (LEl l ty) <- toLType ty
+              l <- open (Level l)
+              ty <- open ty
+              bs <- bndry `applyN` ts
+              xs <- mapM (\(phi,u) -> (,) <$> open phi <*> open u) $ do
+                (i,(l,r)) <- bs
+                let pElem t = Lam (setRelevance Irrelevant defaultArgInfo) $ NoAbs "o" t
+                [(tINeg `apply` [argN i],pElem l),(i,pElem r)]
+              combineSys' l ty xs
+            (,) <$> open (fst <$> p) <*> open (snd <$> p)
+          bind_trD $ \ delta_ps x_ps phi_ps -> do
+          let x = map (fmap unArg) x_ps
+          let delta = map (fmap unArg) delta_ps
+          let [phi] = map (fmap unArg) phi_ps
+          --- pattern matching args below
+          bindNArg aTelArgs $ \ as0 -> do -- as0 : aTel[delta 0]
+
+          let aTel0 = aTel `applyN` map (<@> pure iz) delta
+
+          -- telePatterns is not context invariant, so we need an open here where the context ends in aTel0.
+          ps0 <- (open =<<) $ (telePatterns <$> aTel0 <*> (applyN bndry $ map (<@> pure iz) delta ++ map (fmap unArg) as0))
+
+          let deltaArg i = do
+                i <- i
+                xs <- sequence delta_ps
+                pure $ map (fmap (`apply` [argN i])) xs
+
+          let
+            origP = ConP chead noConPatternInfo <$> ps0
+            ps = sequence $ delta_ps ++ x_ps ++ phi_ps ++ [argN . unnamed <$> origP]
+          let
+            orig = patternToTerm <$> origP
+            rhsTy = dT `applyN` (delta ++ x ++ [pure io])
+
+          (,,) <$> ps <*> rhsTy <*> do
+
+          -- Declared Constructors.
+          let aTelI = bind "i" $ \ i -> aTel `applyN` map (<@> i) delta
+
+          eas1 <- (=<<) (lift . runExceptT) $ transpTel <$> aTelI <*> phi <*> sequence as0
+
+          caseEitherM (pure eas1) (lift . lift . E.throw . CannotTransp) $ \ as1 -> do
+
+          as1 <- mapM (open . unArg) as1
+
+          as01 <- (open =<<) $ bind "i" $ \ i -> do
+            eas01 <- (=<<) (lift . runExceptT) $ trFillTel <$> aTelI <*> phi <*> sequence as0 <*> i
+            caseEitherM (pure eas01) (lift . lift . E.throw . CannotTransp) pure
+
+          let argApp a t = liftM2 (\ a t -> fmap (`apply` [argN t]) a) a t
+          let
+            argLam :: MonadFail m => String -> (Var m -> NamesT m (Arg Term)) -> NamesT m (Arg Term)
+            argLam n f = (\ (Abs n (Arg i t)) -> Arg i $ Lam defaultArgInfo $ Abs n t) <$> bind "n" f
+          let cas1 = applyN u $ map (<@> pure io) delta ++ as1
+
+          let base | Nothing <- mtrX = cas1
+                   | Just trX <- mtrX = do
+                       let theTel = bind "j" $ \ j -> bind "i" $ \ i -> applyN xTel (map (<@> max i j) delta)
+                       let theLeft = lamTel $ bind "i" $ \ i -> do
+                             as01 <- mapM (open . unArg) =<< (absApp <$> as01 <*> i)
+                             con_ixs `applyN` (map (<@> i) delta ++ as01)
+                       theLeft <- mapM open =<< theLeft
+                       theRight <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> do
+                         con_ixs `applyN` (map (<@> pure io) delta ++ as1)
+
+                       trx' <- transpPathPTel' theTel x theRight phi theLeft
+                       let args = liftM2 (++) (map (setHiding Hidden) <$> deltaArg (pure io)) (forM trx' $ \ q' -> do
+                                                                       q' <- open q'
+                                                                       argLam "i" $ \ i -> q' `argApp` neg i)
+                       (apply (Def trX []) <$> args) <@> phi <@> cas1
+
+
+          if null boundary then base else do
+
+          -- We have to correct the boundary for path constructors.
+
+          -- bline : Abs I ([phi] → ty)
+          let blineFace = applyN bsysFace $ map (<@> pure io) delta ++ as1
+          let bline = do
+                let theTel = bind "j" $ \ j -> bind "i" $ \ i -> applyN xTel (map (<@> max i j) delta)
+                let theLeft = lamTel $ bind "i" $ \ i -> do
+                      as01 <- mapM (open . unArg) =<< (absApp <$> as01 <*> i)
+                      con_ixs `applyN` (map (<@> i) delta ++ as01)
+                theLeft <- mapM open =<< theLeft
+                theRight <- (mapM open =<<) $ lamTel $ bind "i" $ \ i -> do
+                  con_ixs `applyN` (map (<@> pure io) delta ++ as1)
+                let q2_f = bind "i" $ \ i -> map unArg <$> trFillPathPTel' theTel x theRight phi theLeft i
+
+                lam "i" $ \ i -> do
+                let v0 = do
+                     as01 <- mapM (open . unArg) =<< (absApp <$> as01 <*> i)
+                     applyN bsys $ map (<@> i) delta ++ as01
+                let squeezedv0 = ilam "o" $ \ o -> do
+                      let
+                        delta_f :: [NamesT TCM Term]
+                        delta_f = for delta $ \ p -> lam "j" $ \ j -> p <@> (j `max` i)
+                      x_f <- (mapM open =<<) $ lamTel $ bind "j" $ \ j ->
+                                 (absApp <$> q2_f <*> j) `appTel` i
+                      trD `applyN` delta_f `applyN` x_f `applyN` [phi `max` i, v0 <..> o]
+
+                caseMaybe mtrX squeezedv0 $ \ trX -> ilam "o" $ \ o -> do
+                  q2 <- transpPathPTel' theTel x theRight phi theLeft
+                  let args = liftM2 (++) (map (setHiding Hidden) <$> deltaArg (pure io))
+                                         (forM q2 $ \ q' -> do
+                                            q' <- open q'
+                                            argLam "j" $ \ j -> q' `argApp` (neg j `min` i))
+
+                  (apply (Def trX []) <$> args) <@> (neg i `max` phi) <@> (squeezedv0 <..> o)
+          hcomp
+             rhsTy
+             [(blineFace,lam "i" $ \ i -> bline <@> (neg i))
+             ,(phi      ,lam "i" $ \ _ -> ilam "o" $ \ _ -> orig)
+             ]
+             base
+
+        let
+          (ps,rhsTy,rhs) = unAbsN $ unAbsN $ unAbsN $ unAbsN $ res
+        mkClause gamma ps rhsTy rhs
+  where
+    mkClause gamma ps rhsTy rhs = do
+      let
+        c = Clause
+            { clauseTel         = gamma
+            , clauseType        = Just . argN $ rhsTy
+            , namedClausePats   = ps
+            , clauseFullRange   = noRange
+            , clauseLHSRange    = noRange
+            , clauseCatchall    = False
+            , clauseBody        = Just $ rhs
+            , clauseRecursive   = Nothing
+            -- it is indirectly recursive through transp, does it count?
+            , clauseUnreachable = Just False
+            , clauseEllipsis    = NoEllipsis
+            , clauseExact       = Nothing
+            , clauseWhereModule = Nothing
+            }
+      reportSDoc "tc.data.transp.con" 20 $
+        "gamma:" <+> prettyTCM gamma
+      reportSDoc "tc.data.transp.con" 20 $ addContext gamma $
+        "ps   :" <+> prettyTCM (patternsToElims ps)
+      reportSDoc "tc.data.transp.con" 20 $ addContext gamma $
+        "type :" <+> prettyTCM rhsTy
+      reportSDoc "tc.data.transp.con" 20 $ addContext gamma $
+        "body :" <+> prettyTCM rhs
+
+      reportSDoc "tc.data.transp.con" 30 $
+        addContext gamma $ "c:" <+> pretty c
+      return c
+
+
+defineKanOperationForFields
+  :: Command
+  -> (Maybe Term)            -- ^ PathCons, Δ.Φ ⊢ u : R δ
+  -> (Term -> QName -> Term) -- ^ how to apply a "projection" to a term
+  -> QName       -- ^ some name, e.g. record name
+  -> Telescope   -- ^ param types Δ
+  -> Telescope   -- ^ fields' types Δ ⊢ Φ
+  -> [Arg QName] -- ^ fields' names
+  -> Type        -- ^ record type Δ ⊢ T
+  -> TCM (Maybe ((QName, Telescope, Type, [Dom Type], [Term]), Substitution))
+defineKanOperationForFields cmd pathCons project name params fsT fns rect =
+   case cmd of
+       DoTransp -> runMaybeT $ do
+         fsT' <- traverse (traverse (MaybeT . toCType)) fsT
+         lift $ defineTranspForFields pathCons project name params fsT' fns rect
+       DoHComp -> runMaybeT $ do
+         fsT' <- traverse (traverse (MaybeT . toLType)) fsT
+         rect' <- MaybeT $ toLType rect
+         lift $ defineHCompForFields project name params fsT' fns rect'
+
+
+-- invariant: resulting tel Γ is such that Γ = ... , (φ : I), (a0 : ...)
+--            where a0 has type matching the arguments of primTrans.
+defineTranspForFields
+  :: (Maybe Term)            -- ^ PathCons, Δ.Φ ⊢ u : R δ
+  -> (Term -> QName -> Term) -- ^ how to apply a "projection" to a term
+  -> QName       -- ^ some name, e.g. record name
+  -> Telescope   -- ^ param types Δ
+  -> Tele (Dom CType)   -- ^ fields' types Δ ⊢ Φ
+  -> [Arg QName] -- ^ fields' names
+  -> Type        -- ^ record type Δ ⊢ T
+  -> TCM ((QName, Telescope, Type, [Dom Type], [Term]), Substitution)
+     -- ^ @((name, tel, rtype, clause_types, bodies), sigma)@
+     --   name: name of transport function for this constructor/record. clauses still missing.
+     --   tel: Ξ telescope for the RHS, Ξ ⊃ (Δ^I, φ : I), also Ξ ⊢ us0 : Φ[δ 0]
+     --   rtype: Ξ ⊢ T' := T[δ 1]
+     --   clause_types: Ξ ⊢ Φ' := Φ[δ 1]
+     --   bodies: Ξ ⊢ us1 : Φ'
+     --   sigma:  Ξ, i : I ⊢ σ : Δ.Φ -- line [δ 0,us0] ≡ [δ 0,us1]
+defineTranspForFields pathCons applyProj name params fsT fns rect = do
+  interval <- primIntervalType
+  let deltaI = expTelescope interval params
+  iz <- primIZero
+  io <- primIOne
+  imin <- getPrimitiveTerm builtinIMin
+  imax <- getPrimitiveTerm builtinIMax
+  ineg <- getPrimitiveTerm builtinINeg
+  transp <- getPrimitiveTerm builtinTrans
+  -- por <- getPrimitiveTerm "primPOr"
+  -- one <- primItIsOne
+  reportSDoc "trans.rec" 20 $ pretty params
+  reportSDoc "trans.rec" 20 $ pretty deltaI
+  reportSDoc "trans.rec" 10 $ pretty fsT
+
+  let thePrefix = "transp-"
+  theName <- freshAbstractQName'_ $ thePrefix ++ P.prettyShow (A.qnameName name)
+
+  reportSLn "trans.rec" 5 $ ("Generated name: " ++ show theName ++ " " ++ showQNameId theName)
+
+  theType <- (abstract deltaI <$>) $ runNamesT [] $ do
+              rect' <- open (runNames [] $ bind "i" $ \ x -> let _ = x `asTypeOf` pure (undefined :: Term) in
+                                                             pure rect')
+              nPi' "phi" primIntervalType $ \ phi ->
+               (absApp <$> rect' <*> pure iz) --> (absApp <$> rect' <*> pure io)
+
+  reportSDoc "trans.rec" 20 $ prettyTCM theType
+  reportSDoc "trans.rec" 60 $ text $ "sort = " ++ show (getSort rect')
+
+  lang <- getLanguage
+  fun  <- emptyFunctionData
+  noMutualBlock $ addConstant theName $
+    (defaultDefn defaultArgInfo theName theType lang
+       (FunctionDefn fun{ _funTerminates = Just True
+                        , _funIsKanOp    = Just name
+                        }))
+      { defNoCompilation = True }
+  -- ⊢ Γ = gamma = (δ : Δ^I) (φ : I) (u0 : R (δ i0))
+  -- Γ ⊢     rtype = R (δ i1)
+  TelV gamma rtype <- telView theType
+
+
+  let
+      -- (γ : Γ) ⊢ transpR γ : rtype
+      theTerm = Def theName [] `apply` teleArgs gamma
+
+      -- (γ : Γ) ⊢ (flatten Φ[δ i1])[n ↦ f_n (transpR γ)]
+      clause_types = parallelS [theTerm `applyProj` (unArg fn)
+                               | fn <- reverse fns] `applySubst`
+                       flattenTel (singletonS 0 io `applySubst` fsT') -- Γ, Φ[δ i1] ⊢ flatten Φ[δ i1]
+
+      -- Γ, i : I ⊢ [δ i] : Δ
+      delta_i = (liftS 1 (raiseS (size gamma - size deltaI)) `composeS` sub params) -- Defined but not used
+
+      -- Γ, i : I ⊢ Φ[δ i]
+      fsT' = (liftS 1 (raiseS (size gamma - size deltaI)) `composeS` sub params)  `applySubst`
+               fsT -- Δ ⊢ Φ
+      lam_i = Lam defaultArgInfo . Abs "i"
+
+
+
+      -- (δ , φ , u0) : Γ ⊢ φ : I
+      -- the_phi = var 1
+      -- -- (δ , φ , u0) : Γ ⊢ u0 : R (δ i0)
+      -- the_u0  = var 0
+
+      -- Γ' = (δ : Δ^I, φ : I)
+      gamma' = telFromList $ take (size gamma - 1) $ telToList gamma
+
+      -- δ : Δ^I, φ : F ⊢ [δ 0] : Δ
+      d0 :: Substitution
+      d0 = wkS 1 -- Δ^I, φ : F ⊢ Δ
+                       (consS iz IdS `composeS` sub params) -- Δ^I ⊢ Δ
+                                 -- Δ^I , i:I ⊢ sub params : Δ
+
+      -- Ξ , Ξ ⊢ θ : Γ, Ξ ⊢ φ, Ξ ⊢ u : R (δ i0), Ξ ⊢ us : Φ[δ i0]
+      (tel,theta,the_phi,the_u0, the_fields) =
+        case pathCons of
+          -- (δ : Δ).Φ ⊢ u : R δ
+          Just u -> (abstract gamma' (d0 `applySubst` fmap (fmap fromCType) fsT) -- Ξ = δ : Δ^I, φ : F, _ : Φ[δ i0]
+                    , (liftS (size fsT) d0 `applySubst` u) `consS` raiseS (size fsT)
+                    , raise (size fsT) (var 0)
+                    , (liftS (size fsT) d0 `applySubst` u)
+                    , drop (size gamma') $ map unArg $ teleArgs tel)
+          Nothing -> (gamma, IdS, var 1, var 0, map (\ fname -> var 0 `applyProj` unArg fname) fns )
+
+      fsT_tel = (liftS 1 (raiseS (size tel - size deltaI)) `composeS` sub params) `applySubst` fsT
+
+      iMin x y = imin `apply` [argN x, argN y]
+      iMax x y = imax `apply` [argN x, argN y]
+      iNeg x = ineg `apply` [argN x]
+
+      -- .. ⊢ field : filled_ty' i0
+      mkBody (field, filled_ty') = do
+        let
+          filled_ty = lam_i $ (unEl . fromCType . unDom) filled_ty'
+          -- Γ ⊢ l : I -> Level of filled_ty
+        -- sort <- reduce $ getSort $ unDom filled_ty'
+        case unDom filled_ty' of
+          LType (LEl l _) -> do
+            let lvl = lam_i $ Level l
+            return $ runNames [] $ do
+             lvl <- open lvl
+             [phi,field] <- mapM open [the_phi,field]
+             pure transp <#> lvl <@> pure filled_ty
+                                 <@> phi
+                                 <@> field
+          -- interval arg
+          ClosedType{}  ->
+            return $ runNames [] $ do
+            [field] <- mapM open [field]
+            field
+
+  let
+        -- ' Ξ , i : I ⊢ τ = [(\ j → δ (i ∧ j)), φ ∨ ~ i, u] : Ξ
+        tau = parallelS $ us ++ (phi `iMax` iNeg (var 0))
+                        : map (\ d -> Lam defaultArgInfo $ Abs "i" $ raise 1 d `apply` [argN $ (iMin (var 0) (var 1))]) ds
+         where
+          -- Ξ, i : I
+          (us, phi:ds) = splitAt (size tel - size gamma') $ reverse (raise 1 (map unArg (teleArgs tel)))
+
+  let
+    go acc [] = return []
+    go acc ((fname,field_ty) : ps) = do
+      -- Ξ, i : I, Φ[δ i]|_f ⊢ Φ_f = field_ty
+      -- Ξ ⊢ b : field_ty [i := i1][acc]
+      -- Ξ ⊢ parallesS acc : Φ[δ i1]|_f
+      -- Ξ , i : I ⊢ τ = [(\ j → δ (i ∨ j), φ ∨ ~ i, us] : Ξ
+      -- Ξ , i : I ⊢ parallesS (acc[τ]) : Φ[δ i1]|_f
+      -- Ξ, i : I ⊢ field_ty [parallesS (acc[τ])]
+      let
+        filled_ty = parallelS (tau `applySubst` acc) `applySubst` field_ty
+      b <- mkBody (fname,filled_ty)
+      bs <- go (b : acc) ps
+      return $ b : bs
+
+  bodys <- go [] (zip the_fields (map (fmap snd) $ telToList fsT_tel)) -- ∀ f.  Ξ, i : I, Φ[δ i]|_f ⊢ Φ[δ i]_f
+  let
+    -- Ξ, i : I ⊢ ... : Δ.Φ
+    theSubst = reverse (tau `applySubst` bodys) ++# (liftS 1 (raiseS (size tel - size deltaI)) `composeS` sub params)
+  return $ ((theName, tel, theta `applySubst` rtype, map (fmap fromCType) clause_types, bodys), theSubst)
+  where
+    -- record type in 'exponentiated' context
+    -- (params : Δ^I), i : I |- T[params i]
+    rect' = sub params `applySubst` rect
+    -- Δ^I, i : I |- sub Δ : Δ
+    sub tel = expS $ size tel
+
+-- invariant: resulting tel Γ is such that Γ = (δ : Δ), (φ : I), (u : ...), (a0 : R δ))
+--            where u and a0 have types matching the arguments of primHComp.
+defineHCompForFields
+  :: (Term -> QName -> Term) -- ^ how to apply a "projection" to a term
+  -> QName       -- ^ some name, e.g. record name
+  -> Telescope   -- ^ param types Δ
+  -> Tele (Dom LType)   -- ^ fields' types Δ ⊢ Φ
+  -> [Arg QName] -- ^ fields' names
+  -> LType        -- ^ record type (δ : Δ) ⊢ R[δ]
+  -> TCM ((QName, Telescope, Type, [Dom Type], [Term]),Substitution)
+defineHCompForFields applyProj name params fsT fns rect = do
+  interval <- primIntervalType
+  let delta = params
+  iz <- primIZero
+  io <- primIOne
+  imin <- getPrimitiveTerm builtinIMin
+  imax <- getPrimitiveTerm builtinIMax
+  tIMax <- getPrimitiveTerm builtinIMax
+  ineg <- getPrimitiveTerm builtinINeg
+  hcomp <- getPrimitiveTerm builtinHComp
+  transp <- getPrimitiveTerm builtinTrans
+  por <- getPrimitiveTerm builtinPOr
+  one <- primItIsOne
+  reportSDoc "comp.rec" 20 $ text $ show params
+  reportSDoc "comp.rec" 20 $ text $ show delta
+  reportSDoc "comp.rec" 10 $ text $ show fsT
+
+  let thePrefix = "hcomp-"
+  theName <- freshAbstractQName'_ $ thePrefix ++ P.prettyShow (A.qnameName name)
+
+  reportSLn "hcomp.rec" 5 $ ("Generated name: " ++ show theName ++ " " ++ showQNameId theName)
+
+  theType <- (abstract delta <$>) $ runNamesT [] $ do
+              rect <- open $ fromLType rect
+              nPi' "phi" primIntervalType $ \ phi ->
+               nPi' "i" primIntervalType (\ i ->
+                pPi' "o" phi $ \ _ -> rect) -->
+               rect --> rect
+
+  reportSDoc "hcomp.rec" 20 $ prettyTCM theType
+  reportSDoc "hcomp.rec" 60 $ text $ "sort = " ++ show (lTypeLevel rect)
+
+  lang <- getLanguage
+  fun  <- emptyFunctionData
+  noMutualBlock $ addConstant theName $
+    (defaultDefn defaultArgInfo theName theType lang
+       (FunctionDefn fun{ _funTerminates = Just True
+                        , _funIsKanOp    = Just name
+                        }))
+      { defNoCompilation = True }
+  --   ⊢ Γ = gamma = (δ : Δ) (φ : I) (_ : (i : I) -> Partial φ (R δ)) (_ : R δ)
+  -- Γ ⊢     rtype = R δ
+  TelV gamma rtype <- telView theType
+
+  let -- Γ ⊢ R δ
+      drect_gamma = raiseS (size gamma - size delta) `applySubst` rect
+
+  reportSDoc "hcomp.rec" 60 $ text $ "sort = " ++ show (lTypeLevel drect_gamma)
+
+  let
+
+      -- (γ : Γ) ⊢ hcompR γ : rtype
+      compTerm = Def theName [] `apply` teleArgs gamma
+
+      -- (δ, φ, u, u0) : Γ ⊢ φ : I
+      the_phi = var 2
+      -- (δ, φ, u, u0) : Γ ⊢ u : (i : I) → [φ] → R (δ i)
+      the_u   = var 1
+      -- (δ, φ, u, u0) : Γ ⊢ u0 : R (δ i0)
+      the_u0  = var 0
+
+      -- ' (δ, φ, u, u0) : Γ ⊢ fillR Γ : (i : I) → rtype[ δ ↦ (\ j → δ (i ∧ j))]
+      fillTerm = runNames [] $ do
+        rect <- open . unEl  . fromLType  $ drect_gamma
+        lvl  <- open . Level . lTypeLevel $ drect_gamma
+        params     <- mapM open $ take (size delta) $ teleArgs gamma
+        [phi,w,w0] <- mapM open [the_phi,the_u,the_u0]
+        -- (δ : Δ, φ : I, w : .., w0 : R δ) ⊢
+        -- ' fillR Γ = λ i → hcompR δ (φ ∨ ~ i) (\ j → [ φ ↦ w (i ∧ j) , ~ i ↦ w0 ]) w0
+        --           = hfillR δ φ w w0
+        lam "i" $ \ i -> do
+          args <- sequence params
+          psi  <- pure imax <@> phi <@> (pure ineg <@> i)
+          u <- lam "j" (\ j -> pure por <#> lvl
+                                        <@> phi
+                                        <@> (pure ineg <@> i)
+                                        <#> lam "_" (\ o -> rect)
+                                        <@> (w <@> (pure imin <@> i <@> j))
+                                        <@> lam "_" (\ o -> w0) -- TODO wait for i = 0
+                       )
+          u0 <- w0
+          pure $ Def theName [] `apply` (args ++ [argN psi, argN u, argN u0])
+
+      -- (γ : Γ) ⊢ (flatten Φ)[n ↦ f_n (compR γ)]
+      clause_types = parallelS [compTerm `applyProj` (unArg fn)
+                               | fn <- reverse fns] `applySubst`
+                       flattenTel (raiseS (size gamma - size delta) `applySubst` fsT) -- Γ, Φ ⊢ flatten Φ
+      -- Δ ⊢ Φ = fsT
+      -- Γ, i : I ⊢ Φ'
+      fsT' = raiseS ((size gamma - size delta) + 1) `applySubst` fsT
+
+      -- Γ, i : I ⊢ (flatten Φ')[n ↦ f_n (fillR Γ i)]
+      filled_types = parallelS [raise 1 fillTerm `apply` [argN $ var 0] `applyProj` (unArg fn)
+                               | fn <- reverse fns] `applySubst`
+                       flattenTel fsT' -- Γ, i : I, Φ' ⊢ flatten Φ'
+
+
+  comp <- do
+        let
+          imax i j = pure tIMax <@> i <@> j
+        let forward la bA r u = pure transp <#> lam "i" (\ i -> la <@> (i `imax` r))
+                                            <@> lam "i" (\ i -> bA <@> (i `imax` r))
+                                            <@> r
+                                            <@> u
+        return $ \ la bA phi u u0 ->
+          pure hcomp <#> (la <@> pure io) <#> (bA <@> pure io) <#> phi
+                      <@> lam "i" (\ i -> ilam "o" $ \ o ->
+                              forward la bA i (u <@> i <..> o))
+                      <@> forward la bA (pure iz) u0
+  let
+      mkBody (fname, filled_ty') = do
+        let
+          proj t = (`applyProj` unArg fname) <$> t
+          filled_ty = Lam defaultArgInfo (Abs "i" $ (unEl . fromLType . unDom) filled_ty')
+          -- Γ ⊢ l : I -> Level of filled_ty
+        l <- reduce $ lTypeLevel $ unDom filled_ty'
+        let lvl = Lam defaultArgInfo (Abs "i" $ Level l)
+        return $ runNames [] $ do
+             lvl <- open lvl
+             [phi,w,w0] <- mapM open [the_phi,the_u,the_u0]
+             filled_ty <- open filled_ty
+
+             comp lvl
+                  filled_ty
+                  phi
+                  (lam "i" $ \ i -> ilam "o" $ \ o -> proj $ w <@> i <..> o) -- TODO wait for phi = 1
+                  (proj w0)
+
+  reportSDoc "hcomp.rec" 60 $ text $ "filled_types sorts:" ++ show (map (getSort . fromLType . unDom) filled_types)
+
+  bodys <- mapM mkBody (zip fns filled_types)
+  return $ ((theName, gamma, rtype, map (fmap fromLType) clause_types, bodys),IdS)
+
+
+getGeneralizedParameters :: Set Name -> QName -> TCM [Maybe Name]
+getGeneralizedParameters gpars name | Set.null gpars = return []
+getGeneralizedParameters gpars name = do
+  -- Drop the named parameters that shouldn't be in scope (if the user
+  -- wrote a split data type)
+  let inscope x = x <$ guard (Set.member x gpars)
+  map (>>= inscope) . defGeneralizedParams <$> (instantiateDef =<< getConstInfo name)
+
+-- | Bind the named generalized parameters.
+bindGeneralizedParameters :: [Maybe Name] -> Type -> (Telescope -> Type -> TCM a) -> TCM a
+bindGeneralizedParameters [] t ret = ret EmptyTel t
+bindGeneralizedParameters (name : names) t ret =
+  case unEl t of
+    Pi a b -> ext $ bindGeneralizedParameters names (unAbs b) $ \ tel t -> ret (ExtendTel a (tel <$ b)) t
+      where
+        ext | Just x <- name = addContext (x, a)
+            | otherwise      = addContext (absName b, a)
+    _      -> __IMPOSSIBLE__
+
+-- | Bind the parameters of a datatype.
+--
+--   We allow omission of hidden parameters at the definition site.
+--   Example:
+--   @
+--     data D {a} (A : Set a) : Set a
+--     data D A where
+--       c : A -> D A
+--   @
+
+bindParameters
+  :: Int            -- ^ Number of parameters
+  -> [A.LamBinding] -- ^ Bindings from definition site.
+  -> Type           -- ^ Pi-type of bindings coming from signature site.
+  -> (Telescope -> Type -> TCM a)
+     -- ^ Continuation, accepting parameter telescope and rest of type.
+     --   The parameters are part of the context when the continutation is invoked.
+  -> TCM a
+
+bindParameters 0 [] a ret = ret EmptyTel a
+
+bindParameters 0 (par : _) _ _ = setCurrentRange par $
+  typeError $ UnexpectedParameter par
+
+bindParameters npars [] t ret =
+  case unEl t of
+    Pi a b | not (visible a) -> do
+              x <- freshName_ (absName b)
+              bindParameter npars [] x a b ret
+           | otherwise ->
+              typeError $ ExpectedBindingForParameter a b
+    _ -> __IMPOSSIBLE__
+
+bindParameters npars par@(A.DomainFull (A.TBind _ _ xs e) : bs) a ret =
+  setCurrentRange par $
+  typeError $ UnexpectedTypeSignatureForParameter xs
+
+bindParameters _ (A.DomainFull A.TLet{} : _) _ _ = __IMPOSSIBLE__
+
+bindParameters _ (par@(A.DomainFree _ arg) : ps) _ _
+  | getModality arg /= defaultModality = setCurrentRange par $
+      typeError $ UnexpectedModalityAnnotationInParameter par
+
+bindParameters npars ps0@(par@(A.DomainFree _ arg) : ps) t ret = do
+  let x          = namedArg arg
+      TelV tel _ = telView' t
+  case insertImplicit arg $ telToList tel of
+    NoInsertNeeded -> continue ps $ A.unBind $ A.binderName x
+    ImpInsert _    -> continue ps0 =<< freshName_ (absName b)
+    BadImplicits   -> setCurrentRange par $
+      typeError $ UnexpectedParameter par
+    NoSuchName x   -> setCurrentRange par $
+      typeError $ NoParameterOfName x
+  where
+    Pi dom@(Dom{domInfo = info', unDom = a}) b = unEl t -- TODO:: Defined but not used: info', a
+    continue ps x = bindParameter npars ps x dom b ret
+
+bindParameter :: Int -> [A.LamBinding] -> Name -> Dom Type -> Abs Type -> (Telescope -> Type -> TCM a) -> TCM a
+bindParameter npars ps x a b ret =
+  addContext (x, a) $
+    bindParameters (npars - 1) ps (absBody b) $ \ tel s ->
+      ret (ExtendTel a $ Abs (nameToArgName x) tel) s
+
+-- | Check that the arguments to a constructor fits inside the sort of the datatype.
+--   The third argument is the type of the constructor.
+--
+--   When @--without-K@ is active and the type is fibrant the
+--   procedure also checks that the type is usable at the current
+--   modality. See #4784 and #5434.
+--
+--   As a side effect, return the arity of the constructor.
+
+fitsIn :: QName -> UniverseCheck -> [IsForced] -> Type -> Sort -> TCM Int
+fitsIn con uc forceds conT s = do
+  reportSDoc "tc.data.fits" 10 $
+    sep [ "does" <+> prettyTCM conT
+        , "of sort" <+> prettyTCM (getSort conT)
+        , "fit in" <+> prettyTCM s <+> "?"
+        ]
+  -- The code below would be simpler, but doesn't allow datatypes
+  -- to be indexed by the universe level.
+  -- s' <- instantiateFull (getSort t)
+  -- noConstraints $ s' `leqSort` s
+
+  withoutK <- withoutKOption
+  when withoutK $ do
+    q <- viewTC eQuantity
+    usableAtModality' (Just s) ConstructorType (setQuantity q unitModality) (unEl conT)
+
+  li <- optLargeIndices <$> pragmaOptions
+  fitsIn' li forceds conT s
+  where
+  fitsIn' li forceds t s = do
+    vt <- do
+      t <- pathViewAsPi t
+      return $ case t of
+                    Left (a,b)     -> Just (True ,a,b)
+                    Right (El _ t) | Pi a b <- t
+                                   -> Just (False,a,b)
+                    _              -> Nothing
+    case vt of
+      Just (isPath, dom, b) -> do
+        let
+          (forced, forceds') = nextIsForced forceds
+          isf = isForced forced
+
+        unless (isf && li) $ do
+          sa <- reduce $ getSort dom
+          unless (isPath || uc == NoUniverseCheck || sa == SizeUniv) $
+            traceCall (CheckConArgFitsIn con isf (unDom dom) s) $
+            sa `leqSort` s
+
+        addContext (absName b, dom) $ do
+          succ <$> fitsIn' li forceds' (absBody b) (raise 1 s)
+      _ -> do
+        getSort t `leqSort` s
+        return 0
+
+-- | When --without-K is enabled, we should check that the sorts of
+--   the index types fit into the sort of the datatype.
+checkIndexSorts :: Sort -> Telescope -> TCM ()
+checkIndexSorts s = \case
+  EmptyTel -> return ()
+  ExtendTel a tel' -> do
+    let sa = getSort a
+    -- Andreas, 2020-10-19, allow Size indices
+    unless (sa == SizeUniv) $ sa `leqSort` s
+    underAbstraction a tel' $ checkIndexSorts (raise 1 s)
+
+-- | Return the parameters that share variables with the indices
+-- nonLinearParameters :: Int -> Type -> TCM [Int]
+-- nonLinearParameters nPars t =
+
+data IsPathCons = PathCons | PointCons
+  deriving (Eq,Show)
+
+-- | Check that a type constructs something of the given datatype. The first
+--   argument is the number of parameters to the datatype and the second the
+--   number of additional non-parameters in the context (1 when generalizing, 0
+--   otherwise).
+--
+constructs :: Int -> Int -> Type -> QName -> TCM IsPathCons
+constructs nofPars nofExtraVars t q = constrT nofExtraVars t
+    where
+        -- The number n counts the proper (non-parameter) constructor arguments.
+        constrT :: Nat -> Type -> TCM IsPathCons
+        constrT n t = do
+            t <- reduce t
+            pathV <- pathViewAsPi'whnf
+            case unEl t of
+                Pi _ (NoAbs _ b)  -> constrT n b
+                Pi a b            -> underAbstraction a b $ constrT (n + 1)
+                  -- OR: addCxtString (absName b) a $ constrT (n + 1) (absBody b)
+                _ | Left ((a,b),_) <- pathV t -> do
+                      _ <- case b of
+                             NoAbs _ b -> constrT n b
+                             b         -> underAbstraction a b $ constrT (n + 1)
+                      return PathCons
+                Def d es | d == q -> do
+                  let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+                  let (pars, ixs) = splitAt nofPars vs
+                  -- check that the constructor parameters are the data parameters
+                  checkParams n pars
+                  return PointCons
+                MetaV{} -> do
+                  def <- getConstInfo q
+                  -- Analyse the type of q (name of the data type)
+                  let td = defType def
+                  TelV tel core <- telView td
+                  -- Construct the parameter arguments
+                  -- The parameters are @n + nofPars - 1 .. n@
+                  let us = zipWith (\ arg x -> var x <$ arg ) (telToArgs tel) $
+                             take nofPars $ downFrom (nofPars + n)
+                  -- The indices are fresh metas
+                  xs <- newArgsMeta =<< piApplyM td us
+                  let t' = El (raise n $ dataSort $ theDef def) $ Def q $ map Apply $ us ++ xs
+                  -- Andreas, 2017-11-07, issue #2840
+                  -- We should not postpone here, otherwise we might upset the positivity checker.
+                  ifM (tryConversion $ equalType t t')
+                      (constrT n t')
+                      (typeError $ ShouldEndInApplicationOfTheDatatype t)
+                _ -> typeError $ ShouldEndInApplicationOfTheDatatype t
+
+        checkParams n vs = zipWithM_ sameVar vs ps
+            where
+                nvs = length vs
+                ps  = reverse $ take nvs [n..]
+
+                sameVar arg i
+                  -- skip irrelevant parameters
+                  | isIrrelevant arg = return ()
+                  | otherwise = do
+                    t <- typeOfBV i
+                    equalTerm t (unArg arg) (var i)
+
+
+-- | Is the type coinductive? Returns 'Nothing' if the answer cannot
+-- be determined.
+
+isCoinductive :: Type -> TCM (Maybe Bool)
+isCoinductive t = do
+  El s t <- reduce t
+  case t of
+    Def q _ -> do
+      def <- getConstInfo q
+      case theDef def of
+        Axiom       {} -> return (Just False)
+        DataOrRecSig{} -> return Nothing
+        Function    {} -> return Nothing
+        Datatype    {} -> return (Just False)
+        Record      {  recInduction = Just CoInductive } -> return (Just True)
+        Record      {  recInduction = _                } -> return (Just False)
+        GeneralizableVar{} -> __IMPOSSIBLE__
+        Constructor {} -> __IMPOSSIBLE__
+        Primitive   {} -> __IMPOSSIBLE__
+        PrimitiveSort{} -> __IMPOSSIBLE__
+        AbstractDefn{} -> __IMPOSSIBLE__
+    Var   {} -> return Nothing
+    Lam   {} -> __IMPOSSIBLE__
+    Lit   {} -> __IMPOSSIBLE__
+    Level {} -> __IMPOSSIBLE__
+    Con   {} -> __IMPOSSIBLE__
+    Pi    {} -> return (Just False)
+    Sort  {} -> return (Just False)
+    MetaV {} -> return Nothing
+    DontCare{} -> __IMPOSSIBLE__
+    Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
diff --git a/src/full/Agda/TypeChecking/Rules/Data.hs-boot b/src/full/Agda/TypeChecking/Rules/Data.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Data.hs-boot
@@ -0,0 +1,8 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Data where
+
+import Agda.Syntax.Internal         ( QName, Sort )
+import Agda.TypeChecking.Monad.Base ( TCM )
+
+checkDataSort :: QName -> Sort -> TCM ()
diff --git a/src/full/Agda/TypeChecking/Rules/Decl.hs b/src/full/Agda/TypeChecking/Rules/Decl.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Decl.hs
@@ -0,0 +1,1123 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Decl where
+
+import Prelude hiding ( null )
+
+import Control.Monad
+import Control.Monad.Writer (tell)
+
+import Data.Either (partitionEithers)
+import qualified Data.Foldable as Fold
+import qualified Data.Map.Strict as MapS
+import Data.Maybe
+import qualified Data.Set as Set
+import Data.Set (Set)
+
+import Agda.Interaction.Highlighting.Generate
+import Agda.Interaction.Options
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views (deepUnscopeDecl, deepUnscopeDecls)
+import Agda.Syntax.Internal
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Position
+import Agda.Syntax.Common
+import Agda.Syntax.Literal
+import Agda.Syntax.Scope.Base ( KindOfName(..) )
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Monad.Benchmark (MonadBench, Phase)
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.IApplyConfluence
+import Agda.TypeChecking.Generalize
+import Agda.TypeChecking.Injectivity
+import Agda.TypeChecking.Level.Solve
+import Agda.TypeChecking.Positivity
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Polarity
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.ProjectionLike
+import Agda.TypeChecking.Unquote
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.RecordPatterns
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Rewriting
+import Agda.TypeChecking.SizedTypes.Solve
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Warnings
+
+import Agda.TypeChecking.Rules.Application
+import Agda.TypeChecking.Rules.Term
+import Agda.TypeChecking.Rules.Data    ( checkDataDef )
+import Agda.TypeChecking.Rules.Record  ( checkRecDef )
+import Agda.TypeChecking.Rules.Def     ( checkFunDef, newSection, useTerPragma )
+import Agda.TypeChecking.Rules.Builtin
+import Agda.TypeChecking.Rules.Display ( checkDisplayPragma )
+
+import Agda.Termination.TermCheck
+
+import Agda.Utils.Function ( applyUnless )
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Size
+import Agda.Utils.Update
+import qualified Agda.Utils.SmallSet as SmallSet
+
+import Agda.Utils.Impossible
+
+-- | Cached checkDecl
+checkDeclCached :: A.Declaration -> TCM ()
+checkDeclCached d@A.ScopedDecl{} = checkDecl d
+checkDeclCached
+  d@(A.Section _ erased mname (A.GeneralizeTel _ tbinds) _) = do
+  e <- readFromCachedLog  -- Can ignore the set of generalizable vars (they occur in the telescope)
+  reportSLn "cache.decl" 10 $ "checkDeclCached: " ++ show (isJust e)
+  case e of
+    Just (EnterSection erased' mname' tbinds', _)
+      | erased == erased' && mname == mname' && tbinds == tbinds' ->
+        return ()
+    _ -> cleanCachedLog
+  writeToCurrentLog $ EnterSection erased mname tbinds
+  checkDecl d
+  readFromCachedLog >>= \case
+    Just (LeaveSection mname', _) | mname == mname' -> return ()
+    _ -> cleanCachedLog
+  writeToCurrentLog $ LeaveSection mname
+
+checkDeclCached d = do
+    e <- readFromCachedLog
+
+    reportSLn "cache.decl" 10 $ "checkDeclCached: " ++ show (isJust e)
+
+    case e of
+      (Just (Decl d',s)) | compareDecl d d' -> do
+        restorePostScopeState s
+        reportSLn "cache.decl" 50 $ "range: " ++ prettyShow (getRange d)
+        printSyntaxInfo (getRange d)
+      _ -> do
+        cleanCachedLog
+        checkDeclWrap d
+    writeToCurrentLog $ Decl d
+ where
+   compareDecl A.Section{} A.Section{} = __IMPOSSIBLE__
+   compareDecl A.ScopedDecl{} A.ScopedDecl{} = __IMPOSSIBLE__
+   compareDecl x y = x == y
+   -- changes to CS inside a RecDef or Mutual ought not happen,
+   -- but they do happen, so we discard them.
+   ignoreChanges m = localCache $ do
+     cleanCachedLog
+     m
+   checkDeclWrap d@A.RecDef{} = ignoreChanges $ checkDecl d
+   checkDeclWrap d@A.Mutual{} = ignoreChanges $ checkDecl d
+   checkDeclWrap d            = checkDecl d
+
+-- | Type check a sequence of declarations.
+checkDecls :: [A.Declaration] -> TCM ()
+checkDecls ds = do
+  reportSLn "tc.decl" 45 $ "Checking " ++ show (length ds) ++ " declarations..."
+  mapM_ checkDecl ds
+
+-- | Type check a single declaration.
+
+checkDecl :: A.Declaration -> TCM ()
+checkDecl d = setCurrentRange d $ do
+    reportSDoc "tc.decl" 10 $ "checking declaration"
+    debugPrintDecl d
+    reportSDoc "tc.decl" 90 $ (text . show) (deepUnscopeDecl d)
+    reportSDoc "tc.decl" 10 $ prettyA d  -- Might loop, see e.g. Issue 1597
+
+    let -- What kind of final checks/computations should be performed
+        -- if we're not inside a mutual block?
+        none        m = m $>  Nothing           -- skip all checks
+        meta        m = m $>  Just (return ())  -- do the usual checks
+        mutual i ds m = m <&> Just . uncurry (mutualChecks i d ds)
+        impossible  m = m $>  __IMPOSSIBLE__
+                        -- We're definitely inside a mutual block.
+
+    (finalChecks, metas) <- metasCreatedBy $ case d of
+      A.Axiom{}                -> meta $ checkTypeSignature d
+      A.Generalize s i info x e -> meta $ inConcreteMode $ checkGeneralize s i info x e
+      A.Field{}                -> typeError FieldOutsideRecord
+      A.Primitive i x e        -> meta $ checkPrimitive i x e
+      A.Mutual i ds            -> mutual i ds $ checkMutual i ds
+      A.Section _r er x tel ds -> meta $ checkSection er x tel ds
+      A.Apply i er x mapp ci d -> meta $ checkSectionApplication i er x mapp ci d
+      A.Import _ _ dir         -> none $ checkImportDirective dir
+      A.Pragma i p             -> none $ checkPragma i p
+      A.ScopedDecl scope ds    -> none $ setScope scope >> mapM_ checkDeclCached ds
+      A.FunDef i x cs          -> impossible $ check x i $ checkFunDef i x cs
+      A.DataDef i x uc ps cs   -> impossible $ check x i $ checkDataDef i x uc ps cs
+      A.RecDef i x uc dir ps tel cs -> impossible $ check x i $ do
+                                    checkRecDef i x uc dir ps tel cs
+                                    blockId <- mutualBlockOf x
+
+                                    -- Andreas, 2016-10-01 testing whether
+                                    -- envMutualBlock is set correctly.
+                                    -- Apparently not.
+                                    verboseS "tc.decl.mutual" 70 $ do
+                                      current <- asksTC envMutualBlock
+                                      unless (Just blockId == current) $ do
+                                        reportS "" 0
+                                          [ "mutual block id discrepancy for " ++ prettyShow x
+                                          , "  current    mut. bl. = " ++ show current
+                                          , "  calculated mut. bl. = " ++ show blockId
+                                          ]
+
+                                    return (blockId, Set.singleton x)
+      A.DataSig i er x ps t    -> impossible $ checkSig DataName i er x ps t
+      A.RecSig i er x ps t     -> none $ checkSig RecName i er x ps t
+                                  -- A record signature is always followed by a
+                                  -- record definition. Metas should not be
+                                  -- frozen until after the definition has been
+                                  -- checked. NOTE: Metas are not frozen
+                                  -- immediately after the last field. Perhaps
+                                  -- they should be (unless we're in a mutual
+                                  -- block).
+      A.Open _ _ dir           -> none $ checkImportDirective dir
+      A.UnfoldingDecl{}        -> none $ return ()
+      A.PatternSynDef{}        -> none $ return ()
+                                  -- Open and PatternSynDef are just artifacts
+                                  -- from the concrete syntax, retained for
+                                  -- highlighting purposes.
+      -- Andreas, 2019-08-19, issue #4010, observe @abstract@ also for unquoting.
+      -- TODO: is it possible that some of the unquoted declarations/definitions
+      -- are abstract and some are not?  Then allowing all to look into abstract things,
+      -- as we do here, will leak information about the implementation of abstract things.
+      -- TODO: Benchmarking for unquote.
+      A.UnquoteDecl mi is xs e -> checkMaybeAbstractly is $ checkUnquoteDecl mi is xs e
+      A.UnquoteDef is xs e     -> impossible $ checkMaybeAbstractly is $ checkUnquoteDef is xs e
+      A.UnquoteData is x uc js cs e -> checkMaybeAbstractly (is ++ js) $ do
+        reportSDoc "tc.unquote.data" 20 $ "Checking unquoteDecl data" <+> prettyTCM x
+        Nothing <$ unquoteTop (x:cs) e
+
+    whenNothingM (asksTC envMutualBlock) $ do
+
+      -- Syntax highlighting.
+      highlight_ DontHightlightModuleContents d
+
+      -- Defaulting of levels (only when --cumulativity)
+      whenM (optCumulativity <$> pragmaOptions) $
+        defaultLevelsToZero (openMetas metas)
+
+      -- Post-typing checks.
+      whenJust finalChecks $ \ theMutualChecks -> do
+        reportSLn "tc.decl" 20 $ "Attempting to solve constraints before freezing."
+        wakeupConstraints_   -- solve emptiness and instance constraints
+        checkingWhere <- asksTC envCheckingWhere
+        solveSizeConstraints $ if checkingWhere then DontDefaultToInfty else DefaultToInfty
+        wakeupConstraints_   -- Size solver might have unblocked some constraints
+        case d of
+            A.Generalize{} -> pure ()
+            _ -> do
+              reportSLn "tc.decl" 20 $ "Freezing all open metas."
+              void $ freezeMetas (openMetas metas)
+
+        theMutualChecks
+
+    where
+
+    -- Switch maybe to abstract mode, benchmark, and debug print bracket.
+    check :: forall m i a
+          . ( MonadTCEnv m, MonadPretty m, MonadDebug m
+            , MonadBench m, Bench.BenchPhase m ~ Phase
+            , AnyIsAbstract i
+            , AllAreOpaque i
+            )
+          => QName -> i -> m a -> m a
+    check x i m = Bench.billTo [Bench.Definition x] $ do
+      reportSDoc "tc.decl" 5 $ ("Checking" <+> prettyTCM x) <> "."
+      reportSLn "tc.decl.abstract" 25 $ show $ anyIsAbstract i
+      r <- checkMaybeAbstractly i m
+      reportSDoc "tc.decl" 5 $ ("Checked" <+> prettyTCM x) <> "."
+      return r
+
+    -- Switch to AbstractMode if any of the i is AbstractDef.
+    checkMaybeAbstractly :: forall m i a . ( MonadTCEnv m, AnyIsAbstract i, AllAreOpaque i )
+                         => i -> m a -> m a
+    checkMaybeAbstractly abs cont = do
+      let
+        k1 = localTC (set lensIsAbstract (anyIsAbstract abs))
+      k2 <- case jointOpacity abs of
+        UniqueOpaque i     -> pure $ localTC $ \env -> env { envCurrentOpaqueId = Just i }
+        NoOpaque           -> pure id
+        DifferentOpaque hs -> __IMPOSSIBLE__
+      k1 (k2 cont)
+
+-- Some checks that should be run at the end of a mutual block. The
+-- set names contains the names defined in the mutual block.
+mutualChecks :: Info.MutualInfo -> A.Declaration -> [A.Declaration] -> MutualId -> Set QName -> TCM ()
+mutualChecks mi d ds mid names = do
+  -- Andreas, 2014-04-11: instantiate metas in definition types
+  let nameList = Set.toList names
+  mapM_ instantiateDefinitionType nameList
+  -- Andreas, 2017-03-23: check positivity before termination.
+  -- This allows us to reuse the information about SCCs
+  -- to skip termination of non-recursive functions.
+  modifyAllowedReductions (SmallSet.delete UnconfirmedReductions) $
+    checkPositivity_ mi names
+  -- Andreas, 2013-02-27: check termination before injectivity,
+  -- to avoid making the injectivity checker loop.
+  localTC (\ e -> e { envMutualBlock = Just mid }) $
+    checkTermination_ d
+  revisitRecordPatternTranslation nameList -- Andreas, 2016-11-19 issue #2308
+
+  mapM_ checkIApplyConfluence_ nameList
+
+  -- Andreas, 2015-03-26 Issue 1470:
+  -- Restricting coinduction to recursive does not solve the
+  -- actual problem, and prevents interesting sound applications
+  -- of sized types.
+  -- checkCoinductiveRecords  ds
+
+  -- Andreas, 2019-07-11: The following remarks about injectivity
+  -- and polarity seem outdated, since the UnusedArg Relevance has
+  -- been removed.
+  -- -- Andreas, 2012-09-11:  Injectivity check stores clauses
+  -- -- whose 'Relevance' is affected by polarity computation,
+  -- -- so do it here (again).
+  -- -- Andreas, 2015-07-01:  In particular, 'UnusedArg's of local functions
+  -- -- are only recognized after the polarity computation.
+  -- -- See Issue 1366 for an example where injectivity of a local function
+  -- -- is used to solve metas.  It fails if we do injectivity analysis
+  -- -- before polarity only.
+  -- However, we need to repeat injectivity checking after termination checking,
+  -- since more reductions are available after termination checking, thus,
+  -- more instances of injectivity can be recognized.
+  checkInjectivity_        names
+  checkProjectionLikeness_ names
+
+-- | Check if there is a inferred eta record type in the mutual block.
+--   If yes, repeat the record pattern translation for all function definitions
+--   in the block.
+--   This is necessary since the original record pattern translation will
+--   have skipped record patterns of the new record types (as eta was off for them).
+--   See issue #2308 (and #2197).
+revisitRecordPatternTranslation :: [QName] -> TCM ()
+revisitRecordPatternTranslation qs = do
+  -- rs: inferred eta record types of this mutual block
+  -- qccs: compiled clauses of definitions
+  (rs, qccs) <- partitionEithers . catMaybes <$> mapM classify qs
+  unless (null rs) $ forM_ qccs $ \(q,cc) -> do
+    (cc, recordExpressionBecameCopatternLHS) <- runChangeT $ translateCompiledClauses cc
+    modifySignature $ updateDefinition q
+      $ updateTheDef (updateCompiledClauses $ const $ Just cc)
+      . updateDefCopatternLHS (|| recordExpressionBecameCopatternLHS)
+  where
+  -- Walk through the definitions and return the set of inferred eta record types
+  -- and the set of function definitions in the mutual block
+  classify q = inConcreteOrAbstractMode q $ \ def -> do
+    case theDef def of
+      Record{ recEtaEquality' = Inferred YesEta } -> return $ Just $ Left q
+      Function
+        { funProjection = Left MaybeProjection
+            -- Andreas, 2017-08-10, issue #2664:
+            -- Do not record pattern translate record projection definitions!
+        , funCompiled   = Just cc
+        } -> return $ Just $ Right (q, cc)
+      _ -> return Nothing
+
+type FinalChecks = Maybe (TCM ())
+
+checkUnquoteDecl :: Info.MutualInfo -> [A.DefInfo] -> [QName] -> A.Expr -> TCM FinalChecks
+checkUnquoteDecl mi is xs e = do
+  reportSDoc "tc.unquote.decl" 20 $ "Checking unquoteDecl" <+> sep (map prettyTCM xs)
+  Nothing <$ unquoteTop xs e
+
+checkUnquoteDef :: [A.DefInfo] -> [QName] -> A.Expr -> TCM ()
+checkUnquoteDef _ xs e = do
+  reportSDoc "tc.unquote.decl" 20 $ "Checking unquoteDef" <+> sep (map prettyTCM xs)
+  () <$ unquoteTop xs e
+
+-- | Run a reflected TCM computatation expected to define a given list of
+--   names.
+unquoteTop :: [QName] -> A.Expr -> TCM [QName]
+unquoteTop xs e = do
+  tcm   <- primAgdaTCM
+  unit  <- primUnit
+  lzero <- primLevelZero
+  let vArg = defaultArg
+      hArg = setHiding Hidden . vArg
+  m    <- applyQuantityToJudgement zeroQuantity $
+            checkExpr e $ El (mkType 0) $ apply tcm [hArg lzero, vArg unit]
+  res  <- runUnquoteM $ tell xs >> evalTCM m
+  case res of
+    Left err      -> typeError $ UnquoteFailed err
+    Right (_, xs) -> return xs
+
+-- | Instantiate all metas in 'Definition' associated to 'QName'.
+--   Makes sense after freezing metas. Some checks, like free variable
+--   analysis, are not in 'TCM', so they will be more precise (see issue 1099)
+--   after meta instantiation.
+--   Precondition: name has been added to signature already.
+instantiateDefinitionType :: QName -> TCM ()
+instantiateDefinitionType q = do
+  reportSLn "tc.decl.inst" 20 $ "instantiating type of " ++ prettyShow q
+  t  <- defType . fromMaybe __IMPOSSIBLE__ . lookupDefinition q <$> getSignature
+  t' <- instantiateFull t
+  modifySignature $ updateDefinition q $ updateDefType $ const t'
+  reportSDoc "tc.decl.inst" 30 $ vcat
+    [ "  t  = " <+> prettyTCM t
+    , "  t' = " <+> prettyTCM t'
+    ]
+
+-- Andreas, 2014-04-11
+-- UNUSED, costs a couple of sec on the std-lib
+-- -- | Instantiate all metas in 'Definition' associated to 'QName'.
+-- --   Makes sense after freezing metas.
+-- --   Some checks, like free variable analysis, are not in 'TCM',
+-- --   so they will be more precise (see issue 1099) after meta instantiation.
+-- --
+-- --   Precondition: name has been added to signature already.
+-- instantiateDefinition :: QName -> TCM ()
+-- instantiateDefinition q = do
+--   reportSLn "tc.decl.inst" 20 $ "instantiating " ++ prettyShow q
+--   sig <- getSignature
+--   let def = fromMaybe __IMPOSSIBLE__ $ lookupDefinition q sig
+--   def <- instantiateFull def
+--   modifySignature $ updateDefinition q $ const def
+
+data HighlightModuleContents = DontHightlightModuleContents | DoHighlightModuleContents
+  deriving (Eq)
+
+-- | Highlight a declaration. Called after checking a mutual block (to ensure
+--   we have the right definitions for all names). For modules inside mutual
+--   blocks we haven't highlighted their contents, but for modules not in a
+--   mutual block we have. Hence the flag.
+highlight_ :: HighlightModuleContents -> A.Declaration -> TCM ()
+highlight_ hlmod d = do
+  reportSDoc "tc.decl" 45 $
+    text "Highlighting a declaration with the following spine:"
+      $$
+    text (show $ A.declarationSpine d)
+  let highlight d = generateAndPrintSyntaxInfo d Full True
+  Bench.billTo [Bench.Highlighting] $ case d of
+    A.Axiom{}                -> highlight d
+    A.Field{}                -> __IMPOSSIBLE__
+    A.Primitive{}            -> highlight d
+    A.Mutual i ds            -> mapM_ (highlight_ DoHighlightModuleContents) $ deepUnscopeDecls ds
+    A.Apply{}                -> highlight d
+    A.Import{}               -> highlight d
+    A.Pragma{}               -> highlight d
+    A.ScopedDecl{}           -> return ()
+    A.FunDef{}               -> highlight d
+    A.DataDef{}              -> highlight d
+    A.DataSig{}              -> highlight d
+    A.Open{}                 -> highlight d
+    A.PatternSynDef{}        -> highlight d
+    A.UnfoldingDecl{}        -> highlight d
+    A.Generalize{}           -> highlight d
+    A.UnquoteDecl{}          -> highlight d
+    A.UnquoteDef{}           -> highlight d
+    A.UnquoteData{}          -> highlight d
+    A.Section i er x tel ds  -> do
+      highlight (A.Section i er x tel [])
+      when (hlmod == DoHighlightModuleContents) $ mapM_ (highlight_ hlmod) (deepUnscopeDecls ds)
+    A.RecSig{}               -> highlight d
+    A.RecDef i x uc dir ps tel cs ->
+      highlight (A.RecDef i x uc dir ps dummy cs)
+      -- The telescope has already been highlighted.
+      where
+      -- Andreas, 2016-01-22, issue 1790
+      -- The expression denoting the record constructor type
+      -- is replace by a dummy expression in order to /not/
+      -- generate highlighting from it.
+      -- Simply because all the highlighting info is wrong
+      -- in the record constructor type:
+      -- i) fields become bound variables,
+      -- ii) declarations become let-bound variables.
+      -- We do not need that crap.
+      dummy = A.Lit empty $ LitString $
+        "do not highlight construct(ed/or) type"
+
+-- | Termination check a declaration.
+checkTermination_ :: A.Declaration -> TCM ()
+checkTermination_ d = Bench.billTo [Bench.Termination] $ do
+  reportSLn "tc.decl" 20 $ "checkDecl: checking termination..."
+  -- If there are some termination errors, we throw a warning.
+  -- The termination checker already marked non-terminating functions as such.
+  unlessNullM (termDecl d) $ \ termErrs -> do
+    warning $ TerminationIssue termErrs
+
+-- | Check a set of mutual names for positivity.
+checkPositivity_ :: Info.MutualInfo -> Set QName -> TCM ()
+checkPositivity_ mi names = Bench.billTo [Bench.Positivity] $ do
+  -- Positivity checking.
+  reportSLn "tc.decl" 20 $ "checkDecl: checking positivity..."
+  checkStrictlyPositive mi names
+
+  -- Andreas, 2012-02-13: Polarity computation uses information from the
+  -- positivity check, so it needs happen after the positivity check.
+  computePolarity $ Set.toList names
+
+-- | Check that all coinductive records are actually recursive.
+--   (Otherwise, one can implement invalid recursion schemes just like
+--   for the old coinduction.)
+checkCoinductiveRecords :: [A.Declaration] -> TCM ()
+checkCoinductiveRecords ds = forM_ ds $ \case
+  A.RecDef _ q _ dir _ _ _
+    | Just (Ranged r CoInductive) <- recInductive dir -> setCurrentRange r $ do
+    unlessM (isRecursiveRecord q) $ typeError $ GenericError $
+      "Only recursive records can be coinductive"
+  _ -> return ()
+
+-- | Check a set of mutual names for constructor-headedness.
+checkInjectivity_ :: Set QName -> TCM ()
+checkInjectivity_ names = Bench.billTo [Bench.Injectivity] $ do
+  reportSLn "tc.decl" 20 $ "checkDecl: checking injectivity..."
+  -- Andreas, 2015-07-01, see Issue1366b:
+  -- Injectivity check needs also to be run for abstract definitions.
+  -- Fold.forM_ names $ \ q -> ignoreAbstractMode $ do -- NOT NECESSARY after all
+  Fold.forM_ names $ \ q -> inConcreteOrAbstractMode q $ \ def -> do
+    -- For abstract q, we should be inAbstractMode,
+    -- otherwise getConstInfo returns Axiom.
+    --
+    -- Andreas, 2015-07-01:
+    -- Quite surprisingly, inAbstractMode does not allow us to look
+    -- at a local definition (@where@ block) of an abstract definition.
+    -- This is because the local definition is defined in a strict submodule.
+    -- We can only see through abstract definitions in the current module
+    -- or super modules inAbstractMode.
+    -- I changed that in Monad.Signature.treatAbstractly', so we can see
+    -- our own local definitions.
+    case theDef def of
+      d@Function{ funClauses = cs, funTerminates = term, funProjection = mproj }
+        | term /= Just True -> do
+            -- Not terminating, thus, running the injectivity check could get us into a loop.
+            reportSLn "tc.inj.check" 35 $
+              prettyShow q ++ " is not verified as terminating, thus, not considered for injectivity"
+        | isProperProjection d -> do
+            reportSLn "tc.inj.check" 40 $
+              prettyShow q ++ " is a projection, thus, not considered for injectivity"
+        | otherwise -> do
+
+            inv <- checkInjectivity q cs
+            modifySignature $ updateDefinition q $ updateTheDef $ const $
+              d { funInv = inv }
+
+      _ -> do
+        abstr <- asksTC envAbstractMode
+        reportSLn "tc.inj.check" 40 $
+          "we are in " ++ show abstr ++ " and " ++
+             prettyShow q ++ " is abstract or not a function, thus, not considered for injectivity"
+
+-- | Check a set of mutual names for projection likeness.
+--
+--   Only a single, non-abstract function can be projection-like.
+--   Making an abstract function projection-like would break the
+--   invariant that the type of the principle argument of a projection-like
+--   function is always inferable.
+
+checkProjectionLikeness_ :: Set QName -> TCM ()
+checkProjectionLikeness_ names = Bench.billTo [Bench.ProjectionLikeness] $ do
+      -- Non-mutual definitions can be considered for
+      -- projection likeness
+      let ds = Set.toList names
+      reportSLn "tc.proj.like" 20 $ "checkDecl: checking projection-likeness of " ++ prettyShow ds
+      case ds of
+        [d] -> do
+          def <- getConstInfo d
+          -- For abstract identifiers, getConstInfo returns Axiom.
+          -- Thus, abstract definitions are not considered for projection-likeness.
+          case theDef def of
+            Function{} -> makeProjection (defName def)
+            _          -> reportSLn "tc.proj.like" 25 $
+              prettyShow d ++ " is abstract or not a function, thus, not considered for projection-likeness"
+        _ -> reportSLn "tc.proj.like" 25 $
+               "mutual definitions are not considered for projection-likeness"
+
+-- | Freeze metas created by given computation if in abstract mode.
+whenAbstractFreezeMetasAfter :: A.DefInfo -> TCM a -> TCM a
+whenAbstractFreezeMetasAfter Info.DefInfo{defAccess, defAbstract, defOpaque} m = do
+  if (defAbstract == ConcreteDef && defOpaque == TransparentDef) then m else do
+    (a, ms) <- metasCreatedBy m
+    reportSLn "tc.decl" 20 $ "Attempting to solve constraints before freezing."
+    wakeupConstraints_   -- solve emptiness and instance constraints
+    xs <- freezeMetas (openMetas ms)
+    reportSDoc "tc.decl.ax" 20 $ vcat
+      [ "Abstract type signature produced new open metas: " <+>
+        sep (map prettyTCM $ MapS.keys (openMetas ms))
+      , "We froze the following ones of these:            " <+>
+        sep (map prettyTCM $ Set.toList xs)
+      ]
+    return a
+
+checkGeneralize :: Set QName -> A.DefInfo -> ArgInfo -> QName -> A.Expr -> TCM ()
+checkGeneralize s i info x e = do
+
+    reportSDoc "tc.decl.gen" 20 $ sep
+      [ "checking type signature of generalizable variable" <+> prettyTCM x <+> ":"
+      , nest 2 $ prettyTCM e
+      ]
+
+    -- Check the signature and collect the created metas.
+    (telNames, tGen) <-
+      generalizeType s $ locallyTC eGeneralizeMetas (const YesGeneralizeMeta) $
+        workOnTypes $ isType_ e
+    let n = length telNames
+
+    reportSDoc "tc.decl.gen" 10 $ sep
+      [ "checked type signature of generalizable variable" <+> prettyTCM x <+> ":"
+      , nest 2 $ prettyTCM tGen
+      ]
+
+    lang <- getLanguage
+    addConstant x $ (defaultDefn info x tGen lang GeneralizableVar)
+                    { defArgGeneralizable = SomeGeneralizableArgs n }
+
+
+-- | Type check an axiom.
+checkAxiom :: KindOfName -> A.DefInfo -> ArgInfo ->
+              Maybe [Occurrence] -> QName -> A.Expr -> TCM ()
+checkAxiom = checkAxiom' Nothing
+
+-- | Data and record type signatures need to remember the generalized
+--   parameters for when checking the corresponding definition, so for these we
+--   pass in the parameter telescope separately.
+checkAxiom' :: Maybe A.GeneralizeTelescope -> KindOfName -> A.DefInfo -> ArgInfo ->
+               Maybe [Occurrence] -> QName -> A.Expr -> TCM ()
+checkAxiom' gentel kind i info0 mp x e = whenAbstractFreezeMetasAfter i $ defaultOpenLevelsToZero $ do
+  -- Andreas, 2016-07-19 issues #418 #2102:
+  -- We freeze metas in type signatures of abstract definitions, to prevent
+  -- leakage of implementation details.
+
+  -- If the axiom is erased, then hard compile-time mode is entered.
+  setHardCompileTimeModeIfErased' info0 $ do
+
+  -- Andreas, 2012-04-18  if we are in irrelevant context, axioms are irrelevant
+  -- even if not declared as such (Issue 610).
+  rel <- max (getRelevance info0) <$> viewTC eRelevance
+
+  -- Andrea, 2019-07-16 Cohesion is purely based on left-division, it
+  -- does not take envModality into account.
+  let c = getCohesion info0
+  let mod  = Modality rel (getQuantity info0) c
+  let info = setModality mod info0
+  applyCohesionToContext c $ do
+
+  reportSDoc "tc.decl.ax" 20 $ sep
+    [ text $ "checking type signature"
+    , nest 2 $ (prettyTCM mod <> prettyTCM x) <+> ":" <+> prettyTCM e
+    , nest 2 $ caseMaybe gentel "(no gentel)" $ \ _ -> "(has gentel)"
+    ]
+
+  (genParams, npars, t) <- workOnTypes $ case gentel of
+        Nothing     -> ([], 0,) <$> isType_ e
+        Just gentel ->
+          checkGeneralizeTelescope Nothing gentel $ \ genParams ptel -> do
+            t <- workOnTypes $ isType_ e
+            return (genParams, size ptel, abstract ptel t)
+
+  reportSDoc "tc.decl.ax" 10 $ sep
+    [ text $ "checked type signature"
+    , nest 2 $ (prettyTCM mod <> prettyTCM x) <+> ":" <+> prettyTCM t
+    , nest 2 $ "of sort " <+> prettyTCM (getSort t)
+    ]
+
+  unless (null genParams) $
+    reportSLn "tc.decl.ax" 40 $ "  generalized params: " ++ show genParams
+
+  -- Jesper, 2018-06-05: should be done AFTER generalizing
+  --whenM (optDoubleCheck <$> pragmaOptions) $ workOnTypes $ do
+  --  checkInternal (unEl t) (sort $ getSort t)
+
+  -- Andreas, 2015-03-17 Issue 1428: Do not postulate sizes in parametrized
+  -- modules!
+  when (kind == AxiomName) $ do
+    whenM ((== SizeUniv) <$> do reduce $ getSort t) $ do
+      whenM ((> 0) <$> getContextSize) $ do
+        typeError $ GenericError $ "We don't like postulated sizes in parametrized modules."
+
+  -- Ensure that polarity pragmas do not contain too many occurrences.
+  (occs, pols) <- case mp of
+    Nothing   -> return ([], [])
+    Just occs -> do
+      TelV tel _ <- telView t
+      let n = length (telToList tel)
+      when (n < length occs) $
+        typeError $ TooManyPolarities x n
+      let pols = map polFromOcc occs
+      reportSLn "tc.polarity.pragma" 10 $
+        "Setting occurrences and polarity for " ++ prettyShow x ++ ":\n  " ++
+        prettyShow occs ++ "\n  " ++ prettyShow pols
+      return (occs, pols)
+
+
+  -- Set blocking tag to MissingClauses if we still expect clauses
+  let blk = case kind of
+        FunName   -> NotBlocked (MissingClauses x) ()
+        MacroName -> NotBlocked (MissingClauses x) ()
+        _         -> NotBlocked ReallyNotBlocked ()
+
+  -- Not safe. See Issue 330
+  -- t <- addForcingAnnotations t
+
+  lang <- getLanguage
+  funD <- emptyFunctionData
+
+  let defn = defaultDefn info x t lang $
+        case kind of   -- #4833: set abstract already here so it can be inherited by with functions
+          FunName   -> fun
+          MacroName -> set funMacro True fun
+          DataName  -> DataOrRecSig npars
+          RecName   -> DataOrRecSig npars
+          AxiomName -> defaultAxiom     -- Old comment: NB: used also for data and record type sigs
+          _         -> __IMPOSSIBLE__
+        where fun = FunctionDefn funD{ _funAbstr = Info.defAbstract i, _funOpaque = Info.defOpaque i }
+
+  addConstant x =<< do
+    useTerPragma $ defn
+        { defArgOccurrences    = occs
+        , defPolarity          = pols
+        , defGeneralizedParams = genParams
+        , defBlocked           = blk
+        }
+
+  -- Add the definition to the instance table, if needed
+  case Info.defInstance i of
+    InstanceDef _r -> setCurrentRange x $ addTypedInstance x t
+      -- Put highlighting on name only; including the instance keyword,
+      -- like @(getRange (r,x))@, does not produce good results.
+    NotInstanceDef -> pure ()
+
+  traceCall (IsType_ e) $ do -- need Range for error message
+    -- Andreas, 2016-06-21, issue #2054
+    -- Do not default size metas to ∞ in local type signatures
+    checkingWhere <- asksTC envCheckingWhere
+    solveSizeConstraints $ if checkingWhere then DontDefaultToInfty else DefaultToInfty
+
+-- | Type check a primitive function declaration.
+checkPrimitive :: A.DefInfo -> QName -> Arg A.Expr -> TCM ()
+checkPrimitive i x (Arg info e) =
+    traceCall (CheckPrimitive (getRange i) x e) $ do
+    (name, PrimImpl t' pf) <- lookupPrimitiveFunctionQ x
+    -- Certain "primitive" functions are BUILTIN rather than
+    -- primitive.
+    let builtinPrimitives =
+          [ PrimNatPlus
+          , PrimNatMinus
+          , PrimNatTimes
+          , PrimNatDivSucAux
+          , PrimNatModSucAux
+          , PrimNatEquality
+          , PrimNatLess
+          , PrimLevelZero
+          , PrimLevelSuc
+          , PrimLevelMax
+          ]
+    when (name `elem` builtinPrimitives) $ do
+      reportSDoc "tc.prim" 20 $ pretty name <+> "is a BUILTIN, not a primitive!"
+      typeError $ NoSuchPrimitiveFunction (getBuiltinId name)
+    t <- isType_ e
+    noConstraints $ equalType t t'
+    let s  = prettyShow $ qnameName x
+    -- Checking the ArgInfo. Currently all primitive definitions require default
+    -- ArgInfos, and likely very few will have different ArgInfos in the
+    -- future. Thus, rather than, the arguably nicer solution of adding an
+    -- ArgInfo to PrimImpl we simply check the few special primitives here.
+    let expectedInfo =
+          case name of
+            -- Currently no special primitives
+            _ -> defaultArgInfo
+    unless (info == expectedInfo) $
+      typeError $ WrongArgInfoForPrimitive name info expectedInfo
+    bindPrimitive name pf
+    lang <- getLanguage
+    addConstant x
+      (defaultDefn info x t lang Primitive
+        { primAbstr    = Info.defAbstract i
+        , primOpaque   = TransparentDef
+        , primName     = name
+        , primClauses  = []
+        , primInv      = NotInjective
+        , primCompiled = Nothing })
+      { defArgOccurrences = primFunArgOccurrences pf }
+
+-- | Check a pragma.
+checkPragma :: Range -> A.Pragma -> TCM ()
+checkPragma r p =
+    traceCall (CheckPragma r p) $ case p of
+        A.BuiltinPragma rb x
+          | any isUntypedBuiltin b -> return ()
+          | Just b' <- b -> bindBuiltin b' x
+          | otherwise -> typeError $ NoSuchBuiltinName ident
+          where
+            ident = rangedThing rb
+            b = builtinById ident
+        A.BuiltinNoDefPragma rb _kind x
+          | Just b' <- builtinById b -> bindBuiltinNoDef b' x
+          | otherwise -> typeError $ NoSuchBuiltinName b
+          where b = rangedThing rb
+        A.RewritePragma _ qs -> addRewriteRules qs
+        A.CompilePragma b x s -> do
+          -- Check that x resides in the same module (or a child) as the pragma.
+          x' <- defName <$> getConstInfo x  -- Get the canonical name of x.
+          unlessM ((x' `isInModule`) <$> currentModule) $
+            typeError $ GenericError $
+              "COMPILE pragmas must appear in the same module as their corresponding definitions,"
+          addPragma (rangedThing b) x s
+        A.StaticPragma x -> do
+          def <- getConstInfo x
+          case theDef def of
+            Function{} -> markStatic x
+            _          -> typeError $ GenericError "STATIC directive only works on functions"
+        A.InjectivePragma x -> markInjective x
+        A.NotProjectionLikePragma qn -> do
+          def <- getConstInfo qn
+          case theDef def of
+            it@Function{} ->
+              modifyGlobalDefinition qn $ \def -> def { theDef = it { funProjection = Left NeverProjection } }
+            _ -> typeError $ GenericError "NOT_PROJECTION_LIKE directive only applies to functions"
+        A.InlinePragma b x -> do
+          def <- getConstInfo x
+          case theDef def of
+            Function{} -> markInline b x
+            d@Constructor{ conSrcCon } | copatternMatchingAllowed conSrcCon
+              -> modifyGlobalDefinition x $ set lensTheDef d{ conInline = b }
+            _ -> typeError $ GenericError $ applyUnless b ("NO" ++) "INLINE directive only works on functions or constructors of records that allow copattern matching"
+        A.OptionsPragma{} -> typeError $ GenericError $ "OPTIONS pragma only allowed at beginning of file, before top module declaration"
+        A.DisplayPragma f ps e -> checkDisplayPragma f ps e
+        A.EtaPragma r -> do
+          let noRecord = typeError $ GenericError $
+                "ETA pragma is only applicable to coinductive records"
+          caseMaybeM (isRecord r) noRecord $ \case
+            Record{ recInduction = ind, recEtaEquality' = eta } -> do
+              unless (ind == Just CoInductive) $ noRecord
+              if | Specified NoEta{} <- eta -> typeError $ GenericError $
+                     "ETA pragma conflicts with no-eta-equality declaration"
+                 | otherwise -> return ()
+            _ -> __IMPOSSIBLE__
+          modifySignature $ updateDefinition r $ updateTheDef $ \case
+            def@Record{} -> def { recEtaEquality' = Specified YesEta }
+            _ -> __IMPOSSIBLE__
+
+-- | Type check a bunch of mutual inductive recursive definitions.
+--
+-- All definitions which have so far been assigned to the given mutual
+-- block are returned.
+checkMutual :: Info.MutualInfo -> [A.Declaration] -> TCM (MutualId, Set QName)
+checkMutual i ds = inMutualBlock $ \ blockId -> defaultOpenLevelsToZero $ do
+
+  reportSDoc "tc.decl.mutual" 20 $ vcat $
+      (("Checking mutual block" <+> text (show blockId)) <> ":") :
+      map (nest 2 . prettyA) ds
+
+  insertMutualBlockInfo blockId i
+  localTC ( set eTerminationCheck (() <$ Info.mutualTerminationCheck i)
+          . set eCoverageCheck (Info.mutualCoverageCheck i)) $
+    mapM_ checkDecl ds
+
+  (blockId, ) . mutualNames <$> lookupMutualBlock blockId
+
+    -- check record or data type signature
+checkSig ::
+  KindOfName -> A.DefInfo -> Erased -> QName -> A.GeneralizeTelescope ->
+  A.Expr -> TCM ()
+checkSig kind i erased x gtel t =
+  checkTypeSignature' (Just gtel) $
+  A.Axiom kind i (setQuantity (asQuantity erased) defaultArgInfo)
+    Nothing x t
+
+-- | Type check the type signature of an inductive or recursive definition.
+checkTypeSignature :: A.TypeSignature -> TCM ()
+checkTypeSignature = checkTypeSignature' Nothing
+
+checkTypeSignature' :: Maybe A.GeneralizeTelescope -> A.TypeSignature -> TCM ()
+checkTypeSignature' gtel (A.ScopedDecl scope ds) = do
+  setScope scope
+  mapM_ (checkTypeSignature' gtel) ds
+checkTypeSignature' gtel (A.Axiom funSig i info mp x e) =
+  Bench.billTo [Bench.Definition x] $
+  Bench.billTo [Bench.Typing, Bench.TypeSig] $
+    let abstr = case Info.defAccess i of
+          PrivateAccess{}
+            | Info.defAbstract i == AbstractDef -> inConcreteMode
+              -- Issue #2321, only go to AbstractMode for abstract definitions
+              -- Issue #418, #3744, in fact don't go to AbstractMode at all
+            | otherwise -> inConcreteMode
+          PublicAccess  -> inConcreteMode
+    in abstr $ checkAxiom' gtel funSig i info mp x e
+checkTypeSignature' _ _ =
+  __IMPOSSIBLE__   -- type signatures are always axioms
+
+
+-- | Type check a module.
+
+checkSection ::
+  Erased -> ModuleName -> A.GeneralizeTelescope -> [A.Declaration] ->
+  TCM ()
+checkSection e x tel ds =
+  newSection e x tel $ mapM_ checkDeclCached ds
+
+
+-- | Helper for 'checkSectionApplication'.
+--
+--   Matches the arguments of the module application with the
+--   module parameters.
+--
+--   Returns the remaining module parameters as an open telescope.
+--   Warning: the returned telescope is /not/ the final result,
+--   an actual instantiation of the parameters does not occur.
+checkModuleArity
+  :: ModuleName           -- ^ Name of applied module.
+  -> Telescope            -- ^ The module parameters.
+  -> [NamedArg A.Expr]  -- ^ The arguments this module is applied to.
+  -> TCM Telescope        -- ^ The remaining module parameters (has free de Bruijn indices!).
+checkModuleArity m tel args = check tel args
+  where
+    bad = typeError $ ModuleArityMismatch m tel args
+
+    check :: Telescope -> [NamedArg A.Expr] -> TCM Telescope
+    check tel []             = return tel
+    check EmptyTel (_:_)     = bad
+    check (ExtendTel dom@Dom{domInfo = info} btel) args0@(Arg info' arg : args) =
+      let name = bareNameOf arg
+          my   = bareNameOf dom
+          tel  = absBody btel in
+      case (argInfoHiding info, argInfoHiding info', name) of
+        (Instance{}, NotHidden, _)        -> check tel args0
+        (Instance{}, Hidden, _)           -> check tel args0
+        (Instance{}, Instance{}, Nothing) -> check tel args
+        (Instance{}, Instance{}, Just x)
+          | Just x == my                  -> check tel args
+          | otherwise                     -> check tel args0
+        (Hidden, NotHidden, _)            -> check tel args0
+        (Hidden, Instance{}, _)           -> check tel args0
+        (Hidden, Hidden, Nothing)         -> check tel args
+        (Hidden, Hidden, Just x)
+          | Just x == my                  -> check tel args
+          | otherwise                     -> check tel args0
+        (NotHidden, NotHidden, _)         -> check tel args
+        (NotHidden, Hidden, _)            -> bad
+        (NotHidden, Instance{}, _)        -> bad
+
+-- | Check an application of a section.
+checkSectionApplication
+  :: Info.ModuleInfo
+  -> Erased              -- ^ Should \"everything\" be treated as
+                         --   erased?
+  -> ModuleName          -- ^ Name @m1@ of module defined by the module macro.
+  -> A.ModuleApplication -- ^ The module macro @λ tel → m2 args@.
+  -> A.ScopeCopyInfo     -- ^ Imported names and modules
+  -> A.ImportDirective
+  -> TCM ()
+checkSectionApplication i er m1 modapp copyInfo dir =
+  traceCall (CheckSectionApplication (getRange i) er m1 modapp) $ do
+  checkImportDirective dir
+  -- A (non-erased) section application is type-checked in a
+  -- non-erased context (#5410), except if hard compile-time mode is
+  -- enabled (#4743).
+  setRunTimeModeUnlessInHardCompileTimeMode $
+    checkSectionApplication' i er m1 modapp copyInfo
+
+-- | Check an application of a section. (Do not invoke this procedure
+-- directly, use 'checkSectionApplication'.)
+checkSectionApplication'
+  :: Info.ModuleInfo
+  -> Erased
+  -> ModuleName          -- ^ Name @m1@ of module defined by the module macro.
+  -> A.ModuleApplication -- ^ The module macro @λ tel → m2 args@.
+  -> A.ScopeCopyInfo     -- ^ Imported names and modules
+  -> TCM ()
+checkSectionApplication'
+  i er m1 (A.SectionApp ptel m2 args) copyInfo = do
+  -- If the section application is erased, then hard compile-time mode
+  -- is entered.
+  warnForPlentyInHardCompileTimeMode er
+  setHardCompileTimeModeIfErased er $ do
+  -- Module applications can appear in lets, in which case we treat
+  -- lambda-bound variables as additional parameters to the module.
+  extraParams <- do
+    mfv <- getCurrentModuleFreeVars
+    fv  <- getContextSize
+    return (fv - mfv)
+  when (extraParams > 0) $ reportSLn "tc.mod.apply" 30 $ "Extra parameters to " ++ prettyShow m1 ++ ": " ++ show extraParams
+  -- Type-check the LHS (ptel) of the module macro.
+  checkTelescope ptel $ \ ptel -> do
+    -- We are now in the context @ptel@.
+    -- Get the correct parameter telescope of @m2@. This is the fully lifted
+    -- telescope obtained by `lookupSection` instantiated with the module
+    -- parameters of `m2` currently in scope. For instance
+    -- ```
+    --  module _ (A : Set) where
+    --    module M (B : Set) where ...
+    --    module M' = M B
+    -- ```
+    -- In the application `M' = M B`, `tel = (A B : Set)` and
+    -- `moduleParamsToApply M = [A]`, so the resulting parameter telescope is
+    -- `tel' = (B : Set)`.
+    tel <- lookupSection m2
+    vs  <- moduleParamsToApply m2
+    let tel'  = apply tel vs
+    -- Compute the remaining parameter telescope after stripping of
+    -- the initial parameters that are determined by the @args@.
+    -- Warning: @etaTel@ is not well-formed in @ptel@, since
+    -- the actual application has not happened.
+    etaTel <- checkModuleArity m2 tel' args
+    -- Take the module parameters that will be instantiated by @args@.
+    let tel'' = telFromList $ take (size tel' - size etaTel) $ telToList tel'
+    reportSDoc "tc.mod.apply" 15 $
+        "applying section" <+> prettyTCM m2
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "args =" <+> sep (map prettyA args)
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "ptel =" <+> escapeContext impossible (size ptel) (prettyTCM ptel)
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "tel  =" <+> prettyTCM tel
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "tel' =" <+> prettyTCM tel'
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "tel''=" <+> prettyTCM tel''
+    reportSDoc "tc.mod.apply" 15 $
+        nest 2 $ "eta  =" <+> escapeContext impossible (size ptel) (addContext tel'' $ prettyTCM etaTel)
+
+    -- Now, type check arguments.
+    ts <- noConstraints (checkArguments_ CmpEq DontExpandLast (getRange i) args tel') >>= \case
+      (ts', etaTel') | (size etaTel == size etaTel')
+                     , Just ts <- allApplyElims ts' -> return ts
+      _ -> __IMPOSSIBLE__
+    -- Perform the application of the module parameters.
+    let aTel = tel' `apply` ts
+    reportSDoc "tc.mod.apply" 15 $ vcat
+      [ nest 2 $ "aTel =" <+> prettyTCM aTel
+      ]
+    -- Andreas, 2014-04-06, Issue 1094:
+    -- Add the section with well-formed telescope.
+    addContext (KeepNames aTel) $ do
+      reportSDoc "tc.mod.apply" 80 $
+        "addSection" <+> prettyTCM m1 <+> (getContextTelescope >>= \ tel -> inTopContext (prettyTCM tel))
+      addSection m1
+
+    reportSDoc "tc.mod.apply" 20 $ vcat
+      [ sep [ "applySection", prettyTCM m1, "=", prettyTCM m2, fsep $ map prettyTCM (vs ++ ts) ]
+      , nest 2 $ pretty copyInfo
+      ]
+    args <- instantiateFull $ vs ++ ts
+    let n = size aTel
+    etaArgs <- inTopContext $ addContext aTel getContextArgs
+    addContext (KeepNames aTel) $
+      applySection m1 (ptel `abstract` aTel) m2 (raise n args ++ etaArgs) copyInfo
+
+checkSectionApplication' _ Erased{} _ A.RecordModuleInstance{} _ =
+  __IMPOSSIBLE__
+checkSectionApplication'
+  i NotErased{} m1 (A.RecordModuleInstance x) copyInfo = do
+  let name = mnameToQName x
+  tel' <- lookupSection x
+  vs   <- moduleParamsToApply x
+  let tel = tel' `apply` vs
+      args = teleArgs tel
+
+      telInst :: Telescope
+      telInst = instFinal tel
+
+      -- Locate last (rightmost) parameter and make it @Instance@.
+      -- Issue #3463: also name it so it can be given by name.
+      instFinal :: Telescope -> Telescope
+      -- Telescopes do not have @NoAbs@.
+      instFinal (ExtendTel _ NoAbs{}) = __IMPOSSIBLE__
+      -- Found last parameter: switch it to @Instance@.
+      instFinal (ExtendTel dom (Abs n EmptyTel)) =
+                 ExtendTel do' (Abs n EmptyTel)
+        where do' = makeInstance dom { domName = Just $ WithOrigin Inserted $ unranged "r" }
+      -- Otherwise, keep searchinf for last parameter:
+      instFinal (ExtendTel arg (Abs n tel)) =
+                 ExtendTel arg (Abs n (instFinal tel))
+      -- Before instFinal is invoked, we have checked that the @tel@ is not empty.
+      instFinal EmptyTel = __IMPOSSIBLE__
+
+  reportSDoc "tc.mod.apply" 20 $ vcat
+    [ sep [ "applySection", prettyTCM name, "{{...}}" ]
+    , nest 2 $ "x       =" <+> prettyTCM x
+    , nest 2 $ "name    =" <+> prettyTCM name
+    , nest 2 $ "tel     =" <+> prettyTCM tel
+    , nest 2 $ "telInst =" <+> prettyTCM telInst
+    , nest 2 $ "vs      =" <+> sep (map prettyTCM vs)
+    -- , nest 2 $ "args    =" <+> sep (map prettyTCM args)
+    ]
+  reportSDoc "tc.mod.apply" 60 $ vcat
+    [ nest 2 $ "vs      =" <+> text (show vs)
+    -- , nest 2 $ "args    =" <+> text (show args)
+    ]
+  when (tel == EmptyTel) $
+    typeError $ GenericError $ prettyShow (qnameToConcrete name) ++ " is not a parameterised section"
+
+  addContext telInst $ do
+    vs <- moduleParamsToApply x
+    reportSDoc "tc.mod.apply" 20 $ vcat
+      [ nest 2 $ "vs      =" <+> sep (map prettyTCM vs)
+      , nest 2 $ "args    =" <+> sep (map (parens . prettyTCM) args)
+      ]
+    reportSDoc "tc.mod.apply" 60 $ vcat
+      [ nest 2 $ "vs      =" <+> text (show vs)
+      , nest 2 $ "args    =" <+> text (show args)
+      ]
+    addSection m1
+    applySection m1 telInst x (vs ++ args) copyInfo
+
+-- | Checks that @open public@ is not used in hard compile-time mode.
+checkImportDirective :: A.ImportDirective -> TCM ()
+checkImportDirective dir = do
+  hard <- viewTC eHardCompileTimeMode
+  when (hard && isJust (publicOpen dir)) $ typeError $ NotSupported $
+    "open public in hard compile-time mode " ++
+    "(for instance in erased modules)"
+
+------------------------------------------------------------------------
+-- * Debugging
+------------------------------------------------------------------------
+
+class ShowHead a where
+  showHead :: a -> String
+
+instance ShowHead A.Declaration where
+  showHead d =
+    case d of
+      A.Axiom        {} -> "Axiom"
+      A.Field        {} -> "Field"
+      A.Primitive    {} -> "Primitive"
+      A.Mutual       {} -> "Mutual"
+      A.Section      {} -> "Section"
+      A.Apply        {} -> "Apply"
+      A.Import       {} -> "Import"
+      A.Pragma       {} -> "Pragma"
+      A.Open         {} -> "Open"
+      A.FunDef       {} -> "FunDef"
+      A.DataSig      {} -> "DataSig"
+      A.DataDef      {} -> "DataDef"
+      A.RecSig       {} -> "RecSig"
+      A.RecDef       {} -> "RecDef"
+      A.PatternSynDef{} -> "PatternSynDef"
+      A.Generalize   {} -> "Generalize"
+      A.UnquoteDecl  {} -> "UnquoteDecl"
+      A.ScopedDecl   {} -> "ScopedDecl"
+      A.UnquoteDef   {} -> "UnquoteDef"
+      A.UnquoteData  {} -> "UnquoteDecl data"
+      A.UnfoldingDecl{} -> "UnfoldingDecl"
+
+debugPrintDecl :: A.Declaration -> TCM ()
+debugPrintDecl d = do
+    verboseS "tc.decl" 45 $ do
+      reportSLn "tc.decl" 45 $ "checking a " ++ showHead d
+      case d of
+        A.Section info erased mname tel ds -> do
+          reportSLn "tc.decl" 45 $
+            "section " ++ prettyShow mname ++ " has "
+              ++ show (length $ A.generalizeTel tel) ++ " parameters and "
+              ++ show (length ds) ++ " declarations"
+          reportSDoc "tc.decl" 45 $
+            prettyA $ A.Section info erased mname tel []
+          forM_ ds $ \ d -> do
+            reportSDoc "tc.decl" 45 $ prettyA d
+        _ -> return ()
diff --git a/src/full/Agda/TypeChecking/Rules/Decl.hs-boot b/src/full/Agda/TypeChecking/Rules/Decl.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Decl.hs-boot
@@ -0,0 +1,17 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Decl where
+
+import Agda.Syntax.Info (ModuleInfo)
+import Agda.Syntax.Abstract
+import Agda.Syntax.Common
+import Agda.Syntax.Scope.Base
+import Agda.TypeChecking.Monad.Base (TCM)
+
+checkDecls :: [Declaration] -> TCM ()
+checkDecl  :: Declaration -> TCM ()
+checkSig   :: KindOfName -> DefInfo -> Erased -> QName ->
+              GeneralizeTelescope -> Expr -> TCM ()
+checkSectionApplication ::
+  ModuleInfo -> Erased -> ModuleName -> ModuleApplication ->
+  ScopeCopyInfo -> ImportDirective -> TCM ()
diff --git a/src/full/Agda/TypeChecking/Rules/Def.hs b/src/full/Agda/TypeChecking/Rules/Def.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Def.hs
@@ -0,0 +1,1294 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Def where
+
+import Prelude hiding ( null )
+
+import Control.Monad        ( forM, forM_ )
+import Control.Monad.Except ( MonadError(..) )
+
+import Data.Bifunctor
+import Data.Function (on)
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Maybe
+import Data.Semigroup (Semigroup((<>)))
+
+import Agda.Interaction.Options
+
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Concrete.Pretty as C
+import Agda.Syntax.Position
+import Agda.Syntax.Abstract.Pattern as A
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Abstract.Views as A
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern as I
+import Agda.Syntax.Internal.MetaVars (allMetasList)
+import qualified Agda.Syntax.Info as Info
+import Agda.Syntax.Info hiding (defAbstract)
+
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Warnings ( warning, genericWarning )
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Inlining
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Patterns.Abstract (expandPatternSynonyms)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.CheckInternal
+import Agda.TypeChecking.With
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Telescope.Path
+import Agda.TypeChecking.Injectivity
+import Agda.TypeChecking.SizedTypes.Solve
+import Agda.TypeChecking.Rewriting.Confluence
+import Agda.TypeChecking.CompiledClause (CompiledClauses'(..), hasProjectionPatterns)
+import Agda.TypeChecking.CompiledClause.Compile
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.RecordPatterns ( recordRHSToCopatterns )
+import Agda.TypeChecking.Sort
+
+import Agda.TypeChecking.Rules.Term
+import Agda.TypeChecking.Rules.LHS                 ( checkLeftHandSide, LHSResult(..), bindAsPatterns )
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Decl ( checkDecls )
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import qualified Agda.Utils.SmallSet as SmallSet
+import Agda.Utils.Update
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Definitions by pattern matching
+---------------------------------------------------------------------------
+
+checkFunDef :: A.DefInfo -> QName -> [A.Clause] -> TCM ()
+checkFunDef i name cs = do
+        -- Reset blocking tag (in case a previous attempt was blocked)
+        modifySignature $ updateDefinition name $ updateDefBlocked $ const $
+          NotBlocked (MissingClauses name) ()
+        -- Get the type and relevance of the function
+        def <- instantiateDef =<< getConstInfo name
+        let t    = defType def
+        let info = getArgInfo def
+
+        -- If the function is erased, then hard compile-time mode is
+        -- entered.
+        setHardCompileTimeModeIfErased' info $ do
+
+        case isAlias cs t of  -- #418: Don't use checkAlias for abstract definitions, since the type
+                              -- of an abstract function must not be informed by its definition.
+          Just (e, mc, x)
+            | Info.defAbstract i == ConcreteDef, Info.defOpaque i == TransparentDef ->
+              traceCall (CheckFunDefCall (getRange i) name cs True) $ do
+                -- Andreas, 2012-11-22: if the alias is in an abstract block
+                -- it has been frozen.  We unfreeze it to enable type inference.
+                -- See issue 729.
+                -- Ulf, 2021-02-09: also unfreeze metas in the sort of this type
+                whenM (isFrozen x) $ do
+                  xs <- allMetasList . jMetaType . mvJudgement <$> lookupLocalMeta x
+                  mapM_ unfreezeMeta (x : xs)
+                checkAlias t info i name e mc
+            | otherwise -> do -- Warn about abstract alias (will never work!)
+              -- Ulf, 2021-11-18, #5620: Don't warn if the meta is solved. A more intuitive solution
+              -- would be to not treat definitions with solved meta types as aliases, but in mutual
+              -- blocks you might actually have solved the type of an alias by the time you get to
+              -- the definition. See test/Succeed/SizeInfinity.agda for an example where this
+              -- happens.
+              let
+                what
+                  | Info.defOpaque i == TransparentDef = "abstract"
+                  | otherwise                          = "opaque"
+              whenM (isOpenMeta <$> lookupMetaInstantiation x) $
+                setCurrentRange i $ genericWarning =<<
+                  "Missing type signature for" <+> text what <+> "definition" <+> (prettyTCM name <> ".") $$
+                  fsep (pwords ("Types of " ++ what ++ " definitions are never inferred since this would leak") ++
+                        pwords ("information that should be " ++ what ++ "."))
+              checkFunDef' t info Nothing Nothing i name cs
+          _ -> checkFunDef' t info Nothing Nothing i name cs
+
+        -- If it's a macro check that it ends in Term → TC ⊤
+        let ismacro = isMacro . theDef $ def
+        when (ismacro || Info.defMacro i == MacroDef) $ checkMacroType t
+    `catchIlltypedPatternBlockedOnMeta` \ (err, blocker) -> do
+        reportSDoc "tc.def" 20 $ vcat $
+          [ "checking function definition got stuck on: " <+> pretty blocker ]
+        modifySignature $ updateDefinition name $ updateDefBlocked $ const $ Blocked blocker ()
+        addConstraint blocker $ CheckFunDef i name cs err
+
+checkMacroType :: Type -> TCM ()
+checkMacroType t = do
+  TelV tel tr <- telView t
+
+  let telList = telToList tel
+      resType = abstract (telFromList (drop (length telList - 1) telList)) tr
+  expectedType <- el primAgdaTerm --> el (primAgdaTCM <#> primLevelZero <@> primUnit)
+  equalType resType expectedType
+    `catchError` \ _ -> typeError $ MacroResultTypeMismatch expectedType
+
+-- | A single clause without arguments and without type signature is an alias.
+isAlias :: [A.Clause] -> Type -> Maybe (A.Expr, Maybe C.Expr, MetaId)
+isAlias cs t =
+        case trivialClause cs of
+          -- if we have just one clause without pattern matching and
+          -- without a type signature, then infer, to allow
+          -- "aliases" for things starting with hidden abstractions
+          Just (e, mc) | Just x <- isMeta (unEl t) -> Just (e, mc, x)
+          _ -> Nothing
+  where
+    isMeta (MetaV x _) = Just x
+    isMeta _           = Nothing
+    trivialClause [A.Clause (A.LHS i (A.LHSHead f [])) _ (A.RHS e mc) wh _]
+      | null wh     = Just (e, mc)
+    trivialClause _ = Nothing
+
+-- | Check a trivial definition of the form @f = e@
+checkAlias :: Type -> ArgInfo -> A.DefInfo -> QName -> A.Expr -> Maybe C.Expr -> TCM ()
+checkAlias t ai i name e mc =
+  let clause = A.Clause { clauseLHS          = A.SpineLHS (LHSInfo (getRange i) NoEllipsis) name []
+                        , clauseStrippedPats = []
+                        , clauseRHS          = A.RHS e mc
+                        , clauseWhereDecls   = A.noWhereDecls
+                        , clauseCatchall     = False } in
+  atClause name 0 t Nothing clause $ do
+  reportSDoc "tc.def.alias" 10 $ "checkAlias" <+> vcat
+    [ text (prettyShow name) <+> colon  <+> prettyTCM t
+    , text (prettyShow name) <+> equals <+> prettyTCM e
+    ]
+
+  -- Infer the type of the rhs.
+  -- Andreas, 2018-06-09, issue #2170.
+  -- The context will only be resurrected if we have --irrelevant-projections.
+  v <- applyModalityToContextFunBody ai $ checkDontExpandLast CmpLeq e t
+
+  reportSDoc "tc.def.alias" 20 $ "checkAlias: finished checking"
+
+  solveSizeConstraints DontDefaultToInfty
+
+  v <- instantiateFull v  -- if we omit this, we loop (stdlib: Relation.Binary.Sum)
+    -- or the termination checker might stumble over levels in sorts
+    -- that cannot be converted to expressions without the level built-ins
+    -- (test/succeed/Issue655.agda)
+
+  -- compute body modification for irrelevant definitions, see issue 610
+  let bodyMod = case getRelevance ai of
+        Irrelevant -> dontCare
+        _          -> id
+
+  -- Add the definition
+  fun <- emptyFunctionData
+  addConstant' name ai name t $ set funMacro (Info.defMacro i == MacroDef) $
+      FunctionDefn fun
+          { _funClauses   = [ Clause  -- trivial clause @name = v@
+              { clauseLHSRange    = getRange i
+              , clauseFullRange   = getRange i
+              , clauseTel         = EmptyTel
+              , namedClausePats   = []
+              , clauseBody        = Just $ bodyMod v
+              , clauseType        = Just $ Arg ai t
+              , clauseCatchall    = False
+              , clauseExact       = Just True
+              , clauseRecursive   = Nothing   -- we don't know yet
+              , clauseUnreachable = Just False
+              , clauseEllipsis    = NoEllipsis
+              , clauseWhereModule = Nothing
+              } ]
+          , _funCompiled  = Just $ Done [] $ bodyMod v
+          , _funSplitTree = Just $ SplittingDone 0
+          , _funAbstr     = Info.defAbstract i
+          , _funOpaque    = Info.defOpaque i
+          }
+
+  -- Andreas, 2017-01-01, issue #2372:
+  -- Add the definition to the instance table, if needed, to update its type.
+  case Info.defInstance i of
+    InstanceDef _r -> setCurrentRange name $ addTypedInstance name t
+      -- Put highlighting on the name only;
+      -- @(getRange (r, name))@ does not give good results.
+    NotInstanceDef -> pure ()
+
+  reportSDoc "tc.def.alias" 20 $ "checkAlias: leaving"
+
+
+-- | Type check a definition by pattern matching.
+checkFunDef' :: Type             -- ^ the type we expect the function to have
+             -> ArgInfo          -- ^ is it irrelevant (for instance)
+             -> Maybe ExtLamInfo -- ^ does the definition come from an extended lambda
+                                 --   (if so, we need to know some stuff about lambda-lifted args)
+             -> Maybe QName      -- ^ is it a with function (if so, what's the name of the parent function)
+             -> A.DefInfo        -- ^ range info
+             -> QName            -- ^ the name of the function
+             -> [A.Clause]       -- ^ the clauses to check
+             -> TCM ()
+checkFunDef' t ai extlam with i name cs =
+  checkFunDefS t ai extlam with i name Nothing cs
+
+-- | Type check a definition by pattern matching.
+checkFunDefS :: Type             -- ^ the type we expect the function to have
+             -> ArgInfo          -- ^ is it irrelevant (for instance)
+             -> Maybe ExtLamInfo -- ^ does the definition come from an extended lambda
+                                 --   (if so, we need to know some stuff about lambda-lifted args)
+             -> Maybe QName      -- ^ is it a with function (if so, what's the name of the parent function)
+             -> A.DefInfo        -- ^ range info
+             -> QName            -- ^ the name of the function
+             -> Maybe Substitution -- ^ substitution (from with abstraction) that needs to be applied to module parameters
+             -> [A.Clause]       -- ^ the clauses to check
+             -> TCM ()
+checkFunDefS t ai extlam with i name withSub cs = do
+
+    traceCall (CheckFunDefCall (getRange i) name cs True) $ do
+        reportSDoc "tc.def.fun" 10 $
+          sep [ "checking body of" <+> prettyTCM name
+              , nest 2 $ ":" <+> prettyTCM t
+              , nest 2 $ "full type:" <+> (prettyTCM . defType =<< getConstInfo name)
+              ]
+
+        reportSDoc "tc.def.fun" 70 $
+          sep $ "clauses:" : map (nest 2 . text . show . A.deepUnscope) cs
+
+        cs <- return $ map A.lhsToSpine cs
+
+        reportSDoc "tc.def.fun" 70 $
+          sep $ "spine clauses:" : map (nest 2 . text . show . A.deepUnscope) cs
+
+        -- Ensure that all clauses have the same number of trailing hidden patterns
+        -- This is necessary since trailing implicits are no longer eagerly inserted.
+        -- Andreas, 2013-10-13
+        -- Since we have flexible function arity, it is no longer necessary
+        -- to patch clauses to same arity
+        -- cs <- trailingImplicits t cs
+
+        -- Check the clauses
+        cs <- traceCall NoHighlighting $ do -- To avoid flicker.
+          forM (zip cs [0..]) $ \ (c, clauseNo) -> do
+            atClause name clauseNo t withSub c $ do
+              (c,b) <- applyModalityToContextFunBody ai $ do
+                checkClause t withSub c
+              -- Andreas, 2013-11-23 do not solve size constraints here yet
+              -- in case we are checking the body of an extended lambda.
+              -- 2014-04-24: The size solver requires each clause to be
+              -- checked individually, since otherwise we get constraints
+              -- in typing contexts which are not prefixes of each other.
+              whenNothing extlam $ solveSizeConstraints DontDefaultToInfty
+              -- Andreas, 2013-10-27 add clause as soon it is type-checked
+              -- TODO: instantiateFull?
+              inTopContext $ addClauses name [c]
+              return (c,b)
+
+        (cs, CPC isOneIxs) <- return $ (second mconcat . unzip) cs
+
+        let isSystem = not . null $ isOneIxs
+
+        canBeSystem <- do
+          -- allow VarP and ConP i0/i1 fallThrough = yes, DotP
+          let pss = map namedClausePats cs
+              allowed = \case
+                VarP{} -> True
+                -- pattern inserted by splitPartial
+                ConP _ cpi [] | conPFallThrough cpi -> True
+                DotP{} -> True
+                _      -> False
+          return $! all (allowed . namedArg) (concat pss)
+        when isSystem $ unless canBeSystem $
+          typeError $ GenericError "no pattern matching or path copatterns in systems!"
+
+
+        reportSDoc "tc.def.fun" 70 $ inTopContext $ do
+          sep $ "checked clauses:" : map (nest 2 . text . show) cs
+
+        -- After checking, remove the clauses again.
+        -- (Otherwise, @checkInjectivity@ loops for issue 801).
+        modifyFunClauses name (const [])
+
+        reportSDoc "tc.cc" 25 $ inTopContext $ do
+          sep [ "clauses before injectivity test"
+              , nest 2 $ prettyTCM $ map (QNamed name) cs  -- broken, reify (QNamed n cl) expect cl to live at top level
+              ]
+        reportSDoc "tc.cc" 60 $ inTopContext $ do
+          sep [ "raw clauses: "
+              , nest 2 $ sep $ map (text . show . QNamed name) cs
+              ]
+
+        -- Needed to calculate the proper fullType below.
+        applyCohesionToContext ai $ do
+
+        -- Systems have their own coverage and "coherence" check, we
+        -- also add an absurd clause for the cases not needed.
+        (cs,sys) <- if not isSystem then return (cs, empty) else do
+                 fullType <- flip abstract t <$> getContextTelescope
+                 sys <- inTopContext $ checkSystemCoverage name (IntSet.toList isOneIxs) fullType cs
+                 tel <- getContextTelescope
+                 let c = Clause
+                       { clauseFullRange = noRange
+                       , clauseLHSRange  = noRange
+                       , clauseTel       = tel
+                       , namedClausePats = teleNamedArgs tel
+                       , clauseBody      = Nothing
+                       , clauseType      = Just (defaultArg t)
+                       , clauseCatchall    = False
+                       , clauseExact       = Just True
+                       , clauseRecursive   = Just False
+                       , clauseUnreachable = Just False
+                       , clauseEllipsis    = NoEllipsis
+                       , clauseWhereModule = Nothing
+                       }
+                 return (cs ++ [c], pure sys)
+
+        -- Annotate the clauses with which arguments are actually used.
+        cs <- instantiateFull {- =<< mapM rebindClause -} cs
+        -- Andreas, 2010-11-12
+        -- rebindClause is the identity, and instantiateFull eta-contracts
+        -- removing this eta-contraction fixes issue 361
+        -- however, Data.Star.Decoration.gmapAll no longer type-checks
+        -- possibly due to missing eta-contraction!?
+
+        -- Inline copattern record constructors on demand.
+        cs <- concat <$> do
+          forM cs $ \ cl -> do
+            (cls, nonExactSplit) <- runChangeT $ recordRHSToCopatterns cl
+            when nonExactSplit do
+              -- If we inlined a non-eta constructor,
+              -- issue a warning that the clause does not hold as definitional equality.
+              warning $ InlineNoExactSplit name cl
+            return cls
+
+        -- Check if the function is injective.
+        -- Andreas, 2015-07-01 we do it here in order to resolve metas
+        -- in mutual definitions, e.g. the U/El definition in succeed/Issue439.agda
+        -- We do it again for the mutual block after termination checking, see Rules.Decl.
+        reportSLn "tc.inj.def" 20 $ "checkFunDef': checking injectivity..."
+        inv <- Bench.billTo [Bench.Injectivity] $
+          checkInjectivity name cs
+
+        reportSDoc "tc.cc" 15 $ inTopContext $ do
+          sep [ "clauses before compilation"
+              , nest 2 $ sep $ map (prettyTCM . QNamed name) cs
+              ]
+
+        reportSDoc "tc.cc.raw" 65 $ do
+          sep [ "clauses before compilation"
+              , nest 2 $ sep $ map (text . show) cs
+              ]
+
+        -- add clauses for the coverage (& confluence) checker (needs to reduce)
+        inTopContext $ addClauses name cs
+
+        reportSDoc "tc.cc.type" 60 $ "  type   : " <+> (text . prettyShow) t
+        reportSDoc "tc.cc.type" 60 $ "  context: " <+> (text . prettyShow =<< getContextTelescope)
+
+        fullType <- flip telePi t <$> getContextTelescope
+
+        reportSLn  "tc.cc.type" 80 $ show fullType
+
+        -- Coverage check and compile the clauses
+        (mst, _recordExpressionBecameCopatternLHS, cc) <- Bench.billTo [Bench.Coverage] $
+          unsafeInTopContext $ compileClauses (if isSystem then Nothing else (Just (name, fullType)))
+                                        cs
+        -- Andreas, 2019-10-21 (see also issue #4142):
+        -- We ignore whether the clause compilation turned some
+        -- record expressions into copatterns
+        -- (_recordExpressionsBecameCopatternLHS),
+        -- since the defCopatternLHS flag is anyway set by traversing
+        -- the compiled clauses looking for a copattern match
+        -- (hasProjectionPatterns).
+
+        -- Clause compilation runs the coverage checker, which might add
+        -- some extra clauses.
+        cs <- defClauses <$> getConstInfo name
+
+        reportSDoc "tc.cc" 60 $ inTopContext $ do
+          sep [ "compiled clauses of" <+> prettyTCM name
+              , nest 2 $ pretty cc
+              ]
+
+        -- The macro tag might be on the type signature
+        ismacro <- isMacro . theDef <$> getConstInfo name
+
+        covering <- funCovering . theDef <$> getConstInfo name
+
+        -- Add the definition
+        inTopContext $ addConstant name =<< do
+
+          reportSDoc "tc.def.fun.clauses" 15 $ inTopContext $ do
+            vcat [ "final clauses for" <+> prettyTCM name <+>  ":"
+                 , nest 2 $ vcat $ map (prettyTCM . QNamed name) cs
+                 ]
+
+          -- If there was a pragma for this definition, we can set the
+          -- funTerminates field directly.
+          fun  <- emptyFunctionData
+          defn <- autoInline $
+             set funMacro (ismacro || Info.defMacro i == MacroDef) $
+             FunctionDefn fun
+             { _funClauses        = cs
+             , _funCompiled       = Just cc
+             , _funSplitTree      = mst
+             , _funInv            = inv
+             , _funAbstr          = Info.defAbstract i
+             , _funOpaque         = Info.defOpaque i
+             , _funExtLam         = (\ e -> e { extLamSys = sys }) <$> extlam
+             , _funWith           = with
+             , _funCovering       = covering
+             }
+          lang <- getLanguage
+          useTerPragma $
+            updateDefCopatternLHS (const $ hasProjectionPatterns cc) $
+            (defaultDefn ai name fullType lang defn)
+
+        reportSDoc "tc.def.fun" 10 $ do
+          sep [ "added " <+> prettyTCM name <+> ":"
+              , nest 2 $ prettyTCM . defType =<< getConstInfo name
+              ]
+
+        -- Jesper, 2019-05-30: if the constructors used in the
+        -- lhs of a clause have rewrite rules, we need to check
+        -- confluence here
+        whenJustM (optConfluenceCheck <$> pragmaOptions) $ \confChk -> inTopContext $
+          checkConfluenceOfClauses confChk name
+
+-- | Set 'funTerminates' according to termination info in 'TCEnv',
+--   which comes from a possible termination pragma.
+useTerPragma :: Definition -> TCM Definition
+useTerPragma def@Defn{ defName = name, theDef = fun@Function{}} = do
+  tc <- viewTC eTerminationCheck
+  let terminates = case tc of
+        NonTerminating -> Just False
+        Terminating    -> Just True
+        _              -> Nothing
+  reportS "tc.fundef" 30 $
+    [ "funTerminates of " ++ prettyShow name ++ " set to " ++ show terminates
+    , "  tc = " ++ show tc
+    ]
+  return $ def { theDef = fun { funTerminates = terminates }}
+useTerPragma def = return def
+
+-- | Modify all the LHSCore of the given RHS.
+-- (Used to insert patterns for @rewrite@ or the inspect idiom)
+mapLHSCores :: (A.LHSCore -> A.LHSCore) -> (A.RHS -> A.RHS)
+mapLHSCores f = \case
+  A.WithRHS aux es cs -> A.WithRHS aux es $ for cs $
+    \ (A.Clause (A.LHS info core)     spats rhs                 ds catchall) ->
+       A.Clause (A.LHS info (f core)) spats (mapLHSCores f rhs) ds catchall
+  A.RewriteRHS qes spats rhs wh -> A.RewriteRHS qes spats (mapLHSCores f rhs) wh
+  rhs@A.AbsurdRHS -> rhs
+  rhs@A.RHS{}     -> rhs
+
+-- | Insert some names into the with-clauses LHS of the given RHS.
+-- (Used for the inspect idiom)
+insertNames :: [Arg (Maybe A.BindName)] -> A.RHS -> A.RHS
+insertNames = mapLHSCores . insertInspects
+
+insertInspects :: [Arg (Maybe A.BindName)] -> A.LHSCore -> A.LHSCore
+insertInspects ps = \case
+  A.LHSWith core wps [] ->
+    let ps' = map (fmap $ fmap patOfName) ps in
+    A.LHSWith core (insertIn ps' wps) []
+  -- Andreas, AIM XXXV, 2022-05-09, issue #5728:
+  -- Cases other than LHSWith actually do not make sense, but let them
+  -- through to get a proper error later.
+  lhs -> lhs
+
+  where
+
+    patOfName :: A.BindName -> Arg A.Pattern
+    patOfName = defaultArg . A.VarP
+
+    insertIn :: [Arg (Maybe (Arg a))]
+             -> [Arg a] -> [Arg a]
+    insertIn []                 wps  = wps
+    insertIn (Arg info nm : ps) (w : wps) | visible info =
+      w : (maybe [] pure nm) ++ insertIn ps wps
+    insertIn (Arg info nm : ps) wps       | notVisible info =
+          (maybe [] pure nm) ++ insertIn ps wps
+    insertIn _ _ = __IMPOSSIBLE__
+
+
+-- | Insert some with-patterns into the with-clauses LHS of the given RHS.
+-- (Used for @rewrite@)
+insertPatterns :: [Arg A.Pattern] -> A.RHS -> A.RHS
+insertPatterns pats = mapLHSCores (insertPatternsLHSCore pats)
+
+-- | Insert with-patterns before the trailing with patterns.
+-- If there are none, append the with-patterns.
+insertPatternsLHSCore :: [Arg A.Pattern] -> A.LHSCore -> A.LHSCore
+insertPatternsLHSCore pats = \case
+  A.LHSWith core wps [] -> A.LHSWith core (pats ++ wps) []
+  core                  -> A.LHSWith core pats []
+
+-- | Parameters for creating a @with@-function.
+data WithFunctionProblem
+  = NoWithFunction
+  | WithFunction
+    { wfParentName :: QName                             -- ^ Parent function name.
+    , wfName       :: QName                             -- ^ With function name.
+    , wfParentType :: Type                              -- ^ Type of the parent function.
+    , wfParentTel  :: Telescope                         -- ^ Context of the parent patterns.
+    , wfBeforeTel  :: Telescope                         -- ^ Types of arguments to the with function before the with expressions (needed vars).
+    , wfAfterTel   :: Telescope                         -- ^ Types of arguments to the with function after the with expressions (unneeded vars).
+    , wfExprs      :: [Arg (Term, EqualityView)]        -- ^ With and rewrite expressions and their types.
+    , wfRHSType    :: Type                              -- ^ Type of the right hand side.
+    , wfParentPats :: [NamedArg DeBruijnPattern]        -- ^ Parent patterns.
+    , wfParentParams :: Nat                             -- ^ Number of module parameters in parent patterns
+    , wfPermSplit  :: Permutation                       -- ^ Permutation resulting from splitting the telescope into needed and unneeded vars.
+    , wfPermParent :: Permutation                       -- ^ Permutation reordering the variables in the parent pattern.
+    , wfPermFinal  :: Permutation                       -- ^ Final permutation (including permutation for the parent clause).
+    , wfClauses    :: List1 A.Clause                    -- ^ The given clauses for the with function
+    , wfCallSubst :: Substitution                       -- ^ Subtsitution to generate call for the parent.
+    }
+
+checkSystemCoverage
+  :: QName
+  -> [Int]
+  -> Type
+  -> [Clause]
+  -> TCM System
+checkSystemCoverage f [n] t cs = do
+  reportSDoc "tc.sys.cover" 10 $ text (show (n , length cs)) <+> prettyTCM t
+  TelV gamma t <- telViewUpTo n t
+  addContext gamma $ do
+  TelV (ExtendTel a _) _ <- telViewUpTo 1 t
+  a <- reduce $ unEl $ unDom a
+
+  case a of
+    Def q [Apply phi] -> do
+      [iz,io] <- mapM getBuiltinName' [builtinIZero, builtinIOne]
+      ineg <- primINeg
+      imin <- primIMin
+      imax <- primIMax
+      i0 <- primIZero
+      i1 <- primIOne
+      let
+        isDir (ConP q _ []) | Just (conName q) == iz = Just False
+        isDir (ConP q _ []) | Just (conName q) == io = Just True
+        isDir _ = Nothing
+
+        collectDirs :: [Int] -> [DeBruijnPattern] -> [(Int,Bool)]
+        collectDirs [] [] = []
+        collectDirs (i : is) (p : ps) | Just d <- isDir p = (i,d) : collectDirs is ps
+                                      | otherwise         = collectDirs is ps
+        collectDirs _ _ = __IMPOSSIBLE__
+
+        dir :: (Int,Bool) -> Term
+        dir (i,False) = ineg `apply` [argN $ var i]
+        dir (i,True) = var i
+
+        -- andI and orI have cases for singletons to improve error messages.
+        andI, orI :: [Term] -> Term
+        andI [] = i1
+        andI [t] = t
+        andI (t:ts) = (\ x -> imin `apply` [argN t, argN x]) $ andI ts
+
+        orI [] = i0
+        orI [t] = t
+        orI (t:ts) = imax `apply` [argN t, argN (orI ts)]
+
+      let
+        pats = map (take n . map (namedThing . unArg) . namedClausePats) cs
+        alphas :: [[(Int,Bool)]] -- the face maps corresponding to each clause
+        alphas = map (collectDirs (downFrom n)) pats
+        phis :: [Term] -- the φ terms for each clause (i.e. the alphas as terms)
+        phis = map (andI . (map dir)) alphas
+        psi = orI $ phis
+        pcs = zip phis cs
+
+      reportSDoc "tc.sys.cover" 20 $ fsep $ map prettyTCM pats
+      interval <- primIntervalType
+      reportSDoc "tc.sys.cover" 10 $ "equalTerm " <+> prettyTCM (unArg phi) <+> prettyTCM psi
+      equalTerm interval (unArg phi) psi
+
+      forM_ (initWithDefault __IMPOSSIBLE__ $
+             initWithDefault __IMPOSSIBLE__ $ List.tails pcs) $ \ ((phi1,cl1):pcs') -> do
+        forM_ pcs' $ \ (phi2,cl2) -> do
+          phi12 <- reduce (imin `apply` [argN phi1, argN phi2])
+          forallFaceMaps phi12 (\ _ _ -> __IMPOSSIBLE__) $ \_ sigma -> do
+            let args = sigma `applySubst` teleArgs gamma
+                t' = sigma `applySubst` t
+                fromReduced (YesReduction _ x) = x
+                fromReduced (NoReduction x) = ignoreBlocking x
+                body cl = do
+                  let extra = length (drop n $ namedClausePats cl)
+                  TelV delta _ <- telViewUpTo extra t'
+                  fmap (abstract delta) $ addContext delta $ do
+                    fmap fromReduced $ runReduceM $
+                      appDef' f (Def f []) [cl] [] (map notReduced $ raise (size delta) args ++ teleArgs delta)
+            v1 <- body cl1
+            v2 <- body cl2
+            equalTerm t' v1 v2
+
+      sys <- forM (zip alphas cs) $ \ (alpha,cl) -> do
+
+            let
+                -- Δ = Γ_α , Δ'α
+                delta = clauseTel cl
+                -- Δ ⊢ b
+                Just b = clauseBody cl
+                -- Δ ⊢ ps : Γ , o : [φ] , Δ'
+                -- we assume that there's no pattern matching other
+                -- than from the system
+                ps = namedClausePats cl
+                extra = length (drop (size gamma + 1) ps)
+                -- size Δ'α = size Δ' = extra
+                -- Γ , α ⊢ u
+                takeLast n xs = drop (length xs - n) xs
+                weak [] = idS
+                weak (i:is) = weak is `composeS` liftS i (raiseS 1)
+                tel = telFromList (takeLast extra (telToList delta))
+                u = abstract tel (liftS extra (weak $ List.sort $ map fst alpha) `applySubst` b)
+            return (map (first var) alpha,u)
+
+      reportSDoc "tc.sys.cover.sys" 20 $ fsep $ prettyTCM gamma : map prettyTCM sys
+      reportSDoc "tc.sys.cover.sys" 40 $ fsep $ (text . show) gamma : map (text . show) sys
+      return (System gamma sys) -- gamma uses names from the type, not the patterns, could we do better?
+    _ -> __IMPOSSIBLE__
+checkSystemCoverage _ _ t cs = __IMPOSSIBLE__
+
+
+-- * Info that is needed after all clauses have been processed.
+
+data ClausesPostChecks = CPC
+    { cpcPartialSplits :: IntSet
+      -- ^ Which argument indexes have a partial split.
+    }
+
+instance Semigroup ClausesPostChecks where
+  CPC xs <> CPC xs' = CPC (IntSet.union xs xs')
+
+instance Monoid ClausesPostChecks where
+  mempty  = CPC empty
+  mappend = (<>)
+
+-- | The LHS part of checkClause.
+checkClauseLHS :: Type -> Maybe Substitution -> A.SpineClause -> (LHSResult -> TCM a) -> TCM a
+checkClauseLHS t withSub c@(A.Clause lhs@(A.SpineLHS i x aps) strippedPats rhs0 wh catchall) ret = do
+    reportSDoc "tc.lhs.top" 30 $ "Checking clause" $$ prettyA c
+    unlessNull (trailingWithPatterns aps) $ \ withPats -> do
+      typeError $ UnexpectedWithPatterns $ map namedArg withPats
+    traceCall (CheckClause t c) $ do
+      aps <- expandPatternSynonyms aps
+      unless (null strippedPats) $ reportSDoc "tc.lhs.top" 50 $
+        "strippedPats:" <+> vcat [ prettyA p <+> "=" <+> prettyTCM v <+> ":" <+> prettyTCM a | A.ProblemEq p v a <- strippedPats ]
+      closed_t <- flip abstract t <$> getContextTelescope
+      checkLeftHandSide (CheckLHS lhs) (Just x) aps t withSub strippedPats ret
+
+-- | Type check a function clause.
+
+checkClause
+  :: Type          -- ^ Type of function defined by this clause.
+  -> Maybe Substitution  -- ^ Module parameter substitution arising from with-abstraction.
+  -> A.SpineClause -- ^ Clause.
+  -> TCM (Clause,ClausesPostChecks)  -- ^ Type-checked clause
+
+checkClause t withSub c@(A.Clause lhs@(A.SpineLHS i x aps) strippedPats rhs0 wh catchall) = do
+  cxtNames <- reverse . map (fst . unDom) <$> getContext
+  checkClauseLHS t withSub c $ \ lhsResult@(LHSResult npars delta ps absurdPat trhs patSubst asb psplit ixsplit) -> do
+        -- Note that we might now be in irrelevant context,
+        -- in case checkLeftHandSide walked over an irrelevant projection pattern.
+
+        -- Subtle: checkRHS expects the function type to be the lambda lifted
+        -- type. If we're checking a with-function that's already the case,
+        -- otherwise we need to abstract over the module telescope.
+        t' <- case withSub of
+                Just{}  -> return t
+                Nothing -> do
+                  theta <- lookupSection (qnameModule x)
+                  return $ abstract theta t
+
+        -- At this point we should update the named dots potential with-clauses
+        -- in the right-hand side. When checking a clause we expect the named
+        -- dots to live in the context of the closest parent lhs, but the named
+        -- dots added by buildWithFunction live in the context of the
+        -- with-function arguments before pattern matching. That's what we need
+        -- patSubst for.
+        let rhs = updateRHS rhs0
+            updateRHS rhs@A.RHS{}               = rhs
+            updateRHS rhs@A.AbsurdRHS{}         = rhs
+            updateRHS (A.WithRHS q es cs)       = A.WithRHS q es $ fmap updateClause cs
+            updateRHS (A.RewriteRHS qes spats rhs wh) =
+              A.RewriteRHS qes (applySubst patSubst spats) (updateRHS rhs) wh
+
+            updateClause (A.Clause f spats rhs wh ca) =
+              A.Clause f (applySubst patSubst spats) (updateRHS rhs) wh ca
+
+        (body, with) <- bindAsPatterns asb $ checkWhere wh $ checkRHS i x aps t' lhsResult rhs
+
+        -- Note that the with function doesn't necessarily share any part of
+        -- the context with the parent (but withSub will take you from parent
+        -- to child).
+
+        wbody <- unsafeInTopContext $ Bench.billTo [Bench.Typing, Bench.With] $ checkWithFunction cxtNames with
+
+        body <- return $ body `mplus` wbody
+
+        whenM (optDoubleCheck <$> pragmaOptions) $ case body of
+          Just v  -> do
+            reportSDoc "tc.lhs.top" 30 $ vcat
+              [ "double checking rhs"
+              , nest 2 (prettyTCM v <+> " : " <+> prettyTCM (unArg trhs))
+              ]
+            noConstraints $ withFrozenMetas $ checkInternal v CmpLeq $ unArg trhs
+          Nothing -> return ()
+
+        reportSDoc "tc.lhs.top" 10 $ vcat
+          [ "Clause before translation:"
+          , nest 2 $ vcat
+            [ "delta =" <+> do escapeContext impossible (size delta) $ prettyTCM delta
+            , "ps    =" <+> do P.fsep <$> prettyTCMPatterns ps
+            , "body  =" <+> maybe "_|_" prettyTCM body
+            , "type  =" <+> prettyTCM t
+            ]
+          ]
+
+        reportSDoc "tc.lhs.top" 60 $ escapeContext impossible (size delta) $ vcat
+          [ "Clause before translation (raw):"
+          , nest 2 $ vcat
+            [ "ps    =" <+> text (show ps)
+            , "body  =" <+> text (show body)
+            , "type  =" <+> text (show t)
+            ]
+          ]
+
+        -- compute body modification for irrelevant definitions, see issue 610
+        rel <- viewTC eRelevance
+        let bodyMod body = case rel of
+              Irrelevant -> dontCare <$> body
+              _          -> body
+
+        -- absurd clauses don't define computational behaviour, so it's fine to
+        -- treat them as catchalls.
+        let catchall' = catchall || isNothing body
+
+        -- absurd clauses are not exact
+        let exact = if isNothing body then Just False else Nothing -- we don't know yet
+
+        return $ (, CPC psplit)
+          Clause { clauseLHSRange  = getRange i
+                 , clauseFullRange = getRange c
+                 , clauseTel       = killRange delta
+                 , namedClausePats = ps
+                 , clauseBody      = bodyMod body
+                 , clauseType      = Just trhs
+                 , clauseCatchall  = catchall'
+                 , clauseExact       = exact
+                 , clauseRecursive   = Nothing -- we don't know yet
+                 , clauseUnreachable = Nothing -- we don't know yet
+                 , clauseEllipsis    = lhsEllipsis i
+                 , clauseWhereModule = A.whereModule wh
+                 }
+
+
+
+-- | Generate the abstract pattern corresponding to Refl
+getReflPattern :: TCM A.Pattern
+getReflPattern = do
+  -- Get the name of builtin REFL.
+  Con reflCon _ [] <- primRefl
+
+  reflInfo <- fmap (setOrigin Inserted) <$> getReflArgInfo reflCon
+  let patInfo = ConPatInfo ConOCon patNoRange ConPatEager
+  -- The REFL constructor might have an argument
+  let reflArg = maybeToList $ fmap (\ ai -> Arg ai $ unnamed $ A.WildP patNoRange) reflInfo
+
+  pure $ A.ConP patInfo (unambiguous $ conName reflCon) reflArg
+
+-- | Type check the @with@ and @rewrite@ lhss and/or the rhs.
+checkRHS
+  :: LHSInfo                 -- ^ Range of lhs.
+  -> QName                   -- ^ Name of function.
+  -> [NamedArg A.Pattern]    -- ^ Patterns in lhs.
+  -> Type                    -- ^ Top-level type of function.
+  -> LHSResult               -- ^ Result of type-checking patterns
+  -> A.RHS                   -- ^ Rhs to check.
+  -> TCM (Maybe Term, WithFunctionProblem)
+                                              -- Note: the as-bindings are already bound (in checkClause)
+checkRHS i x aps t lhsResult@(LHSResult _ delta ps absurdPat trhs _ _asb _ _) rhs0 =
+  handleRHS rhs0 where
+
+  handleRHS :: A.RHS -> TCM (Maybe Term, WithFunctionProblem)
+  handleRHS rhs = case rhs of
+    A.RHS e _                  -> ordinaryRHS e
+    A.AbsurdRHS                -> noRHS
+    A.RewriteRHS eqs ps rhs wh -> rewriteEqnsRHS eqs ps rhs wh
+    A.WithRHS aux es cs        -> withRHS aux es cs
+
+  -- Ordinary case: f xs = e
+  ordinaryRHS :: A.Expr -> TCM (Maybe Term, WithFunctionProblem)
+  ordinaryRHS e = Bench.billTo [Bench.Typing, Bench.CheckRHS] $ do
+    -- If there is an absurd pattern, we do not need a RHS. If we have
+    -- one we complain, ignore it and return the same @(Nothing, NoWithFunction)@
+    -- as the case dealing with @A.AbsurdRHS@.
+    mv <- if absurdPat
+          then do
+            ps <- instantiateFull ps
+            Nothing <$ setCurrentRange e (warning $ AbsurdPatternRequiresNoRHS ps)
+          else Just <$> checkExpr e (unArg trhs)
+    return (mv, NoWithFunction)
+
+  -- Absurd case: no right hand side
+  noRHS :: TCM (Maybe Term, WithFunctionProblem)
+  noRHS = do
+    unless absurdPat $ typeError $ NoRHSRequiresAbsurdPattern aps
+    return (Nothing, NoWithFunction)
+
+  -- With case: @f xs with {a} in eqa | b in eqb | {{c}} | ...; ... | ps1 = rhs1; ... | ps2 = rhs2; ...@
+  -- We need to modify the patterns `ps1, ps2, ...` in the user-provided clauses
+  -- to insert the {eqb} names so that the equality proofs are available on the various RHS.
+  withRHS ::
+       QName             -- name of the with-function
+    -> [A.WithExpr]      -- @[{a} in eqa, b in eqb, {{c}}, ...]@
+    -> List1 A.Clause    -- @[(ps1 = rhs1), (ps2 = rhs), ...]@
+    -> TCM (Maybe Term, WithFunctionProblem)
+  withRHS aux es cs = do
+
+    reportSDoc "tc.with.top" 15 $ vcat
+      [ "TC.Rules.Def.checkclause reached A.WithRHS"
+      , sep $ prettyA aux : map (parens . prettyA . namedThing) es
+      ]
+    reportSDoc "tc.with.top" 20 $ do
+      nfv <- getCurrentModuleFreeVars
+      m   <- currentModule
+      sep [ "with function module:" <+>
+             prettyList (map prettyTCM $ mnameToList m)
+          ,  text $ "free variables: " ++ show nfv
+          ]
+
+    -- Infer the types of the with expressions
+
+    vtys <- forM es $ \ (Named nm we) -> do
+              (e, ty) <- inferExprForWith we
+              pure $ (<$ we) . (e,) $ case nm of
+                Nothing -> OtherType ty
+                Just{}  -> IdiomType ty
+
+    let names = map (\ (Named nm e) -> nm <$ e) es
+    cs <- forM cs $ \ c@(A.Clause (A.LHS i core) eqs rhs wh b) -> do
+      let rhs'  = insertNames    names rhs
+      let core' = insertInspects names core
+      pure $ A.Clause (A.LHS i core') eqs rhs' wh b
+
+    -- Andreas, 2016-01-23, Issue #1796
+    -- Run the size constraint solver to improve with-abstraction
+    -- in case the with-expression contains size metas.
+    solveSizeConstraints DefaultToInfty
+
+    checkWithRHS x aux t lhsResult vtys cs
+
+  -- Rewrite case: f xs (rewrite / invert) a | b | c | ...
+  rewriteEqnsRHS
+    :: [A.RewriteEqn]
+    -> [A.ProblemEq]
+    -> A.RHS
+    -> A.WhereDeclarations
+    -> TCM (Maybe Term, WithFunctionProblem)
+
+  rewriteEqnsRHS [] strippedPats rhs wh = checkWhere wh $ handleRHS rhs
+      -- Case: @rewrite@
+      -- Andreas, 2014-01-17, Issue 1402:
+      -- If the rewrites are discarded since lhs=rhs, then
+      -- we can actually have where clauses.
+  rewriteEqnsRHS (r:rs) strippedPats rhs wh = case r of
+    Rewrite ((qname, eq) :| qes) ->
+      rewriteEqnRHS qname eq $
+        List1.ifNull qes {-then-} rs {-else-} $ \ qes -> Rewrite qes : rs
+    Invert qname pes -> invertEqnRHS qname (List1.toList pes) rs
+
+    where
+
+    -- @invert@ clauses
+    invertEqnRHS :: QName -> [Named A.BindName (A.Pattern,A.Expr)] -> [A.RewriteEqn] -> TCM (Maybe Term, WithFunctionProblem)
+    invertEqnRHS qname pes rs = do
+
+      let (npats, es) = unzipWith (\ (Named nm (p , e)) -> (Named nm p, Named nm e)) pes
+      -- Infer the types of the with expressions
+      vtys <- forM es $ \ (Named nm we) -> do
+        (e, ty) <- inferExprForWith (defaultArg we)
+        pure $ defaultArg . (e,) $ case nm of
+          Nothing -> OtherType ty
+          Just{}  -> IdiomType ty
+
+      let pats = concatMap (map defaultArg) $
+            for npats $ \ (Named nm p) -> case nm of
+              Nothing -> [p]
+              Just n  -> [p, A.VarP n]
+
+      -- Andreas, 2016-04-14, see also Issue #1796
+      -- Run the size constraint solver to improve with-abstraction
+      -- in case the with-expression contains size metas.
+      solveSizeConstraints DefaultToInfty
+
+      let rhs' = insertPatterns pats rhs
+          (rhs'', outerWhere) -- the where clauses should go on the inner-most with
+            | null rs  = (rhs', wh)
+            | otherwise = (A.RewriteRHS rs strippedPats rhs' wh, A.noWhereDecls)
+          -- Andreas, 2014-03-05 kill range of copied patterns
+          -- since they really do not have a source location.
+          cl = A.Clause (A.LHS i $ insertPatternsLHSCore pats $ A.LHSHead x $ killRange aps)
+                 strippedPats rhs'' outerWhere False
+
+      reportSDoc "tc.invert" 60 $ vcat
+        [ text "invert"
+        , "  rhs' = " <> (text . show) rhs'
+        ]
+      checkWithRHS x qname t lhsResult vtys $ singleton cl
+
+    -- @rewrite@ clauses
+    rewriteEqnRHS
+      :: QName
+      -> A.Expr
+      -> [A.RewriteEqn]
+      -> TCM (Maybe Term, WithFunctionProblem)
+    rewriteEqnRHS qname eq rs = do
+
+      -- Action for skipping this rewrite.
+      -- We do not want to create unsolved metas in case of
+      -- a futile rewrite with a reflexive equation.
+      -- Thus, we restore the state in this case,
+      -- unless the rewrite expression contains questionmarks.
+      st <- getTC
+      -- TODO:: recurse defined but not used
+      let recurse = do
+           st' <- getTC
+           -- Comparing the whole stInteractionPoints maps is a bit
+           -- wasteful, but we assume
+           -- 1. rewriting with a reflexive equality to happen rarely,
+           -- 2. especially with ?-holes in the rewrite expression
+           -- 3. and a large overall number of ?s.
+           let sameIP = (==) `on` (^. stInteractionPoints)
+           when (sameIP st st') $ putTC st
+           handleRHS $ A.RewriteRHS rs strippedPats rhs wh
+
+      -- Get value and type of rewrite-expression.
+
+      (proof, eqt) <- inferExpr eq
+
+      -- Andreas, 2016-04-14, see also Issue #1796
+      -- Run the size constraint solver to improve with-abstraction
+      -- in case the with-expression contains size metas.
+      solveSizeConstraints DefaultToInfty
+
+      -- Check that the type is actually an equality (lhs ≡ rhs)
+      -- and extract lhs, rhs, and their type.
+
+      t' <- reduce =<< instantiateFull eqt
+      (eqt,rewriteType,rewriteFrom,rewriteTo) <- equalityView t' >>= \case
+        eqt@(EqualityType _s _eq _params (Arg _ dom) a b) -> do
+          s <- sortOf dom
+          return (eqt, El s dom, unArg a, unArg b)
+          -- Note: the sort _s of the equality need not be the sort of the type @dom@!
+        OtherType{} -> typeError $ CannotRewriteByNonEquation t'
+        IdiomType{} -> typeError $ CannotRewriteByNonEquation t'
+
+      reflPat <- getReflPattern
+
+      -- Andreas, 2015-12-25  Issue #1740:
+      -- After the fix of #520, rewriting with a reflexive equation
+      -- has to be desugared as matching against refl.
+      let isReflexive = tryConversion $ dontAssignMetas $
+           equalTerm rewriteType rewriteFrom rewriteTo
+
+      (pats', withExpr, withType) <- do
+        ifM isReflexive
+          {-then-} (return ([ reflPat ]                    , proof, OtherType t'))
+          {-else-} (return ([ A.WildP patNoRange, reflPat ], proof, eqt))
+      let pats = defaultArg <$> pats'
+
+      let rhs' = insertPatterns pats rhs
+          (rhs'', outerWhere) -- the where clauses should go on the inner-most with
+            | null rs  = (rhs', wh)
+            | otherwise = (A.RewriteRHS rs strippedPats rhs' wh, A.noWhereDecls)
+          -- Andreas, 2014-03-05 kill range of copied patterns
+          -- since they really do not have a source location.
+          cl = A.Clause (A.LHS i $ insertPatternsLHSCore pats $ A.LHSHead x $ killRange aps)
+                 strippedPats rhs'' outerWhere False
+
+      reportSDoc "tc.rewrite" 60 $ vcat
+        [ text "rewrite"
+        , "  rhs' = " <> (text . show) rhs'
+        ]
+      checkWithRHS x qname t lhsResult [defaultArg (withExpr, withType)] $ singleton cl
+
+checkWithRHS
+  :: QName                             -- ^ Name of function.
+  -> QName                             -- ^ Name of the with-function.
+  -> Type                              -- ^ Type of function.
+  -> LHSResult                         -- ^ Result of type-checking patterns
+  -> [Arg (Term, EqualityView)]        -- ^ Expressions and types of with-expressions.
+  -> List1 A.Clause                    -- ^ With-clauses to check.
+  -> TCM (Maybe Term, WithFunctionProblem)
+                                -- Note: as-bindings already bound (in checkClause)
+checkWithRHS x aux t (LHSResult npars delta ps _absurdPat trhs _ _asb _ _) vtys0 cs =
+  verboseBracket "tc.with.top" 25 "checkWithRHS" $ do
+    Bench.billTo [Bench.Typing, Bench.With] $ do
+        withArgs <- withArguments vtys0
+        let perm = fromMaybe __IMPOSSIBLE__ $ dbPatPerm ps
+
+        reportSDoc "tc.with.top" 30 $ vcat $
+          -- declared locally because we do not want to use the unzip'd thing!
+          let (vs, as) = unzipWith unArg vtys0 in
+          [ "vs (before normalization) =" <+> prettyTCM vs
+          , "as (before normalization) =" <+> prettyTCM as
+          ]
+        reportSDoc "tc.with.top" 45 $ vcat $
+          -- declared locally because we do not want to use the unzip'd thing!
+          let (vs, as) = unzipWith unArg vtys0 in
+          [ "vs (before norm., raw) =" <+> pretty vs
+          ]
+        vtys0 <- normalise vtys0
+
+        -- Andreas, 2012-09-17: for printing delta,
+        -- we should remove it from the context first
+        reportSDoc "tc.with.top" 25 $ escapeContext impossible (size delta) $ vcat
+          [ "delta  =" <+> prettyTCM delta
+          ]
+        reportSDoc "tc.with.top" 25 $ vcat $
+          -- declared locally because we do not want to use the unzip'd thing!
+          let (vs, as) = unzipWith unArg vtys0 in
+          [ "vs     =" <+> prettyTCM vs
+          , "as     =" <+> prettyTCM as
+          , "perm   =" <+> text (show perm)
+          ]
+
+        -- Split the telescope into the part needed to type the with arguments
+        -- and all the other stuff
+        let (delta1, delta2, perm', t', vtys) = splitTelForWith delta (unArg trhs) vtys0
+        let finalPerm = composeP perm' perm
+
+        reportSLn "tc.with.top" 75 $ "delta  = " ++ show delta
+
+        -- Andreas, 2012-09-17: for printing delta,
+        -- we should remove it from the context first
+        reportSDoc "tc.with.top" 25 $ escapeContext impossible (size delta) $ vcat
+          [ "delta1 =" <+> prettyTCM delta1
+          , "delta2 =" <+> addContext delta1 (prettyTCM delta2)
+          ]
+        reportSDoc "tc.with.top" 25 $ vcat
+          [ "perm'  =" <+> text (show perm')
+          , "fPerm  =" <+> text (show finalPerm)
+          ]
+
+        -- Create the body of the original function
+
+        -- All the context variables
+        us <- getContextTerms
+        let n = size us
+            m = size delta
+            -- First the variables bound outside this definition
+            (us0, us1') = splitAt (n - m) us
+            -- Then permute the rest and grab those needed to for the with arguments
+            (us1, us2)  = splitAt (size delta1) $ permute perm' us1'
+            -- Now stuff the with arguments in between and finish with the remaining variables
+            argsS = parallelS $ reverse $ us0 ++ us1 ++ map unArg withArgs ++ us2
+            v         = Nothing -- generated by checkWithFunction
+        -- Andreas, 2013-02-26 add with-name to signature for printing purposes
+        addConstant aux =<< do
+          lang <- getLanguage
+          useTerPragma =<<
+            defaultDefn defaultArgInfo aux __DUMMY_TYPE__ lang <$>
+              emptyFunction
+
+        reportSDoc "tc.with.top" 20 $ vcat $
+          let (vs, as) = unzipWith unArg vtys in
+          [ "    with arguments" <+> do escapeContext impossible (size delta) $ addContext delta1 $ prettyList (map prettyTCM vs)
+          , "             types" <+> do escapeContext impossible (size delta) $ addContext delta1 $ prettyList (map prettyTCM as)
+          , "           context" <+> (prettyTCM =<< getContextTelescope)
+          , "             delta" <+> do escapeContext impossible (size delta) $ prettyTCM delta
+          , "            delta1" <+> do escapeContext impossible (size delta) $ prettyTCM delta1
+          , "            delta2" <+> do escapeContext impossible (size delta) $ addContext delta1 $ prettyTCM delta2
+          ]
+
+        return (v, WithFunction x aux t delta delta1 delta2 vtys t' ps npars perm' perm finalPerm cs argsS)
+
+-- | Invoked in empty context.
+checkWithFunction :: [Name] -> WithFunctionProblem -> TCM (Maybe Term)
+checkWithFunction _ NoWithFunction = return Nothing
+checkWithFunction cxtNames (WithFunction f aux t delta delta1 delta2 vtys b qs npars perm' perm finalPerm cs argsS) = do
+
+  let -- Δ₁ ws Δ₂ ⊢ withSub : Δ′    (where Δ′ is the context of the parent lhs)
+      withSub :: Substitution
+      withSub = let as = map (snd . unArg) vtys in
+                liftS (size delta2) (wkS (countWithArgs as) idS)
+                `composeS` renaming impossible (reverseP perm')
+
+  reportSDoc "tc.with.top" 10 $ vcat
+    [ "checkWithFunction"
+    , nest 2 $ vcat $
+      let (vs, as) = unzipWith unArg vtys in
+      [ "delta1 =" <+> prettyTCM delta1
+      , "delta2 =" <+> addContext delta1 (prettyTCM delta2)
+      , "t      =" <+> prettyTCM t
+      , "as     =" <+> addContext delta1 (prettyTCM as)
+      , "vs     =" <+> do addContext delta1 $ prettyTCM vs
+      , "b      =" <+> do addContext delta1 $ addContext delta2 $ prettyTCM b
+      , "qs     =" <+> do addContext delta $ prettyTCMPatternList qs
+      , "perm'  =" <+> text (show perm')
+      , "perm   =" <+> text (show perm)
+      , "fperm  =" <+> text (show finalPerm)
+      , "withSub=" <+> text (show withSub)
+      ]
+    ]
+
+  -- Add the type of the auxiliary function to the signature
+
+  -- Jesper, 2020-04-05: Currently variable generalization inserts
+  -- dummy terms, we have to reduce projections to get rid of them.
+  -- (see also #1332).
+  let reds = SmallSet.fromList [ProjectionReductions]
+  delta1 <- modifyAllowedReductions (const reds) $ normalise delta1
+
+  -- Generate the type of the with function
+  (withFunType, n) <- do
+    let ps = renaming impossible (reverseP perm') `applySubst` qs
+    reportSDoc "tc.with.bndry" 40 $ addContext delta1 $ addContext delta2
+                                  $ text "ps =" <+> pretty ps
+    let vs = iApplyVars ps
+    bndry <- if null vs then return [] else do
+      iz <- primIZero
+      io <- primIOne
+      let tm = Def f (patternsToElims ps)
+      return [(i,(inplaceS i iz `applySubst` tm, inplaceS i io `applySubst` tm)) | i <- vs]
+    reportSDoc "tc.with.bndry" 40 $ addContext delta1 $ addContext delta2
+                                  $ text "bndry =" <+> pretty bndry
+    withFunctionType delta1 vtys delta2 b bndry
+  reportSDoc "tc.with.type" 10 $ sep [ "with-function type:", nest 2 $ prettyTCM withFunType ]
+  reportSDoc "tc.with.type" 50 $ sep [ "with-function type:", nest 2 $ pretty withFunType ]
+
+  call_in_parent <- do
+    (TelV tel _,bs) <- telViewUpToPathBoundaryP (n + size delta) withFunType
+    return $ argsS `applySubst` Def aux (teleElims tel bs)
+
+  reportSDoc "tc.with.top" 20 $ addContext delta $ "with function call" <+> prettyTCM call_in_parent
+
+  -- Andreas, 2013-10-21
+  -- Check generated type directly in internal syntax.
+  setCurrentRange cs $
+    traceCall NoHighlighting $   -- To avoid flicker.
+    traceCall (CheckWithFunctionType withFunType) $
+    checkType withFunType
+
+  -- With display forms are closed
+  df <- inTopContext $ makeOpen =<< withDisplayForm f aux delta1 delta2 n qs perm' perm
+
+  reportSLn "tc.with.top" 20 "created with display form"
+
+  case dget df of
+    Display n ts dt ->
+      reportSDoc "tc.with.top" 20 $ "Display" <+> fsep
+        [ text (show n)
+        , prettyList $ map prettyTCM ts
+        , prettyTCM dt
+        ]
+  addConstant aux =<< do
+    lang <- getLanguage
+    fun  <- emptyFunction
+    useTerPragma $
+      (defaultDefn defaultArgInfo aux withFunType lang fun)
+        { defDisplay = [df] }
+  -- solveSizeConstraints -- Andreas, 2012-10-16 does not seem necessary
+
+  reportSDoc "tc.with.top" 10 $ sep
+    [ "added with function" <+> (prettyTCM aux) <+> "of type"
+    , nest 2 $ prettyTCM withFunType
+    , nest 2 $ "-|" <+> (prettyTCM =<< getContextTelescope)
+    ]
+  reportSDoc "tc.with.top" 70 $ vcat
+    [ nest 2 $ text $ "raw with func. type = " ++ show withFunType
+    ]
+
+
+  -- Construct the body for the with function
+  cs <- return $ fmap (A.lhsToSpine) cs
+  cs <- buildWithFunction cxtNames f aux t delta qs npars withSub finalPerm (size delta1) n cs
+  cs <- return $ fmap (A.spineToLhs) cs
+
+  -- #4833: inherit abstract mode from parent
+  abstr <- defAbstract <$> ignoreAbstractMode (getConstInfo f)
+
+  -- Check the with function
+  let info = Info.mkDefInfo (nameConcrete $ qnameName aux) noFixity' PublicAccess abstr (getRange cs)
+  ai <- defArgInfo <$> getConstInfo f
+  checkFunDefS withFunType ai Nothing (Just f) info aux (Just withSub) $ List1.toList cs
+  return $ Just $ call_in_parent
+
+-- | Type check a where clause.
+checkWhere
+  :: A.WhereDeclarations -- ^ Where-declarations to check.
+  -> TCM a               -- ^ Continuation.
+  -> TCM a
+checkWhere wh@(A.WhereDecls whmod whNamed ds) ret = do
+  when (not whNamed) $ ensureNoNamedWhereInRefinedContext whmod
+  loop ds
+  where
+    loop = \case
+      Nothing -> ret
+      -- [A.ScopedDecl scope ds] -> withScope_ scope $ loop ds  -- IMPOSSIBLE
+      Just (A.Section _ e m tel ds) -> newSection e m tel $ do
+          localTC (\ e -> e { envCheckingWhere = True }) $ do
+            checkDecls ds
+            ret
+      _ -> __IMPOSSIBLE__
+
+    -- #2897: We can't handle named where-modules in refined contexts.
+    ensureNoNamedWhereInRefinedContext Nothing = return ()
+    ensureNoNamedWhereInRefinedContext (Just m) = traceCall (CheckNamedWhere m) $ do
+      args <- map unArg <$> (moduleParamsToApply =<< currentModule)
+      unless (isWeakening args) $ do -- weakened contexts are fine
+        names <- map (argNameToString . fst . unDom) . telToList <$>
+                (lookupSection =<< currentModule)
+        typeError $ NamedWhereModuleInRefinedContext args names
+      where
+        isWeakening [] = True
+        isWeakening (Var i [] : args) = isWk (i - 1) args
+          where
+            isWk i []                = True
+            isWk i (Var j [] : args) = i == j && isWk (i - 1) args
+            isWk _ _ = False
+        isWeakening _ = False
+
+
+-- | Enter a new section during type-checking.
+
+newSection ::
+  Erased -> ModuleName -> A.GeneralizeTelescope -> TCM a -> TCM a
+newSection e m gtel@(A.GeneralizeTel _ tel) cont = do
+  -- If the section is erased, then hard compile-time mode is entered.
+  warnForPlentyInHardCompileTimeMode e
+  setHardCompileTimeModeIfErased e $ do
+  reportSDoc "tc.section" 10 $
+    "checking section" <+> (C.prettyErased e <$> prettyTCM m) <+>
+    fsep (map prettyA tel)
+
+  checkGeneralizeTelescope (Just m) gtel $ \ _ tel' -> do
+    reportSDoc "tc.section" 10 $
+      "adding section:" <+> prettyTCM m <+> text (show (size tel'))
+
+    addSection m
+
+    reportSDoc "tc.section" 10 $ inTopContext $
+      nest 4 $ "actual tele:" <+> do prettyTCM =<< lookupSection m
+
+    withCurrentModule m cont
+
+-- | Set the current clause number.
+
+atClause :: QName -> Int -> Type -> Maybe Substitution -> A.SpineClause -> TCM a -> TCM a
+atClause name i t sub cl ret = do
+  clo <- buildClosure ()
+  localTC (\ e -> e { envClause = IPClause name i t sub cl clo }) ret
diff --git a/src/full/Agda/TypeChecking/Rules/Def.hs-boot b/src/full/Agda/TypeChecking/Rules/Def.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Def.hs-boot
@@ -0,0 +1,17 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Def where
+
+import Agda.Syntax.Abstract as A
+import Agda.Syntax.Common
+import Agda.TypeChecking.Monad
+import qualified Agda.Syntax.Internal as I
+
+checkFunDef :: DefInfo -> QName -> [Clause] -> TCM ()
+
+checkFunDef' :: I.Type -> ArgInfo -> Maybe ExtLamInfo -> Maybe QName -> DefInfo -> QName -> [Clause] -> TCM ()
+
+newSection ::
+   Erased -> ModuleName -> A.GeneralizeTelescope -> TCM a -> TCM a
+
+useTerPragma :: Definition -> TCM Definition
diff --git a/src/full/Agda/TypeChecking/Rules/Display.hs b/src/full/Agda/TypeChecking/Rules/Display.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Display.hs
@@ -0,0 +1,133 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Display (checkDisplayPragma) where
+
+import Control.Monad.State
+import Data.Maybe
+
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Common
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Pretty
+
+import Agda.Syntax.Common.Pretty (prettyShow)
+
+import Agda.Utils.Impossible
+
+checkDisplayPragma :: QName -> [NamedArg A.Pattern] -> A.Expr -> TCM ()
+checkDisplayPragma f ps e = do
+  df <- inTopContext $ do
+          pappToTerm f id ps $ \ n args -> do
+            -- pappToTerm puts Var 0 for every variable. We get to know how many there were (n) so
+            -- now we can renumber them with decreasing deBruijn indices.
+            let lhs = renumberElims (n - 1) $ map I.Apply args
+            v <- exprToTerm e
+            return $ Display n lhs (DTerm v)
+  reportSLn "tc.display.pragma" 20 $ "Adding display form for " ++ prettyShow f ++ "\n  " ++ show df
+  addDisplayForm f df
+
+type ToTm = StateT Nat TCM
+
+patternsToTerms :: Telescope -> [NamedArg A.Pattern] -> (Int -> Args -> TCM a) -> TCM a
+patternsToTerms _ [] ret = ret 0 []
+patternsToTerms EmptyTel (p : ps) ret =
+  patternToTerm (namedArg p) $ \n v ->
+  patternsToTerms EmptyTel ps     $ \m vs -> ret (n + m) (inheritHiding p v : vs)
+patternsToTerms (ExtendTel a tel) (p : ps) ret
+  | fromMaybe __IMPOSSIBLE__ $ fittingNamedArg p a =
+      patternToTerm (namedArg p) $ \n v ->
+      patternsToTerms (unAbs tel) ps  $ \m vs -> ret (n + m) (inheritHiding p v : vs)
+  | otherwise =
+      bindWild $ patternsToTerms (unAbs tel) (p : ps) $ \n vs ->
+      ret (1 + n) (inheritHiding a (Var 0 []) : vs)
+
+inheritHiding :: LensHiding a => a -> b -> Arg b
+inheritHiding a b = setHiding (getHiding a) (defaultArg b)
+
+pappToTerm :: QName -> (Args -> b) -> [NamedArg A.Pattern] -> (Int -> b -> TCM a) -> TCM a
+pappToTerm x f ps ret = do
+  def <- getConstInfo x
+  TelV tel _ <- telView $ defType def
+  let dropTel n = telFromList . drop n . telToList
+      pars =
+        case theDef def of
+          Constructor { conPars = p } -> p
+          Function { funProjection = Right Projection{projIndex = i} }
+            | i > 0 -> i - 1
+          _ -> 0
+
+  patternsToTerms (dropTel pars tel) ps $ \ n vs -> ret n (f vs)
+
+patternToTerm :: A.Pattern -> (Nat -> Term -> TCM a) -> TCM a
+patternToTerm p ret =
+  case p of
+    A.VarP A.BindName{unBind = x}   -> bindVar x $ ret 1 (Var 0 [])
+    A.ConP _ cs ps
+      | Just c <- getUnambiguous cs -> pappToTerm c (Con (ConHead c IsData Inductive []) ConOCon . map Apply) ps ret
+      | otherwise                   -> ambigErr "constructor" cs
+    A.ProjP _ _ ds
+      | Just d <- getUnambiguous ds -> ret 0 (Def d [])
+      | otherwise                   -> ambigErr "projection" ds
+    A.DefP _ fs ps
+      | Just f <- getUnambiguous fs -> pappToTerm f (Def f . map Apply) ps ret
+      | otherwise                   -> ambigErr "DefP" fs
+    A.LitP _ l                      -> ret 0 $ Lit l
+    A.WildP _                       -> bindWild $ ret 1 (Var 0 [])
+    _ -> genericDocError =<< vcat [ "Pattern not allowed in DISPLAY pragma:", prettyA p ]
+  where
+    ambigErr thing (AmbQ xs) =
+      genericDocError =<< do
+        text ("Ambiguous " ++ thing ++ ":") <?>
+          fsep (punctuate comma (fmap pretty xs))
+
+bindWild :: TCM a -> TCM a
+bindWild ret = do
+  x <- freshNoName_
+  bindVar x ret
+
+bindVar :: Name -> TCM a -> TCM a
+bindVar x ret = addContext x ret
+
+exprToTerm :: A.Expr -> TCM Term
+exprToTerm e =
+  case unScope e of
+    A.Var x  -> fst <$> getVarInfo x
+    A.Def f  -> pure $ Def f []
+    A.Con c  -> pure $ Con (ConHead (headAmbQ c) IsData Inductive []) ConOCon [] -- Don't care too much about ambiguity here
+    A.Lit _ l  -> pure $ Lit l
+    A.App _ e arg  -> apply <$> exprToTerm e <*> ((:[]) . inheritHiding arg <$> exprToTerm (namedArg arg))
+
+    A.Proj _ f -> pure $ Def (headAmbQ f) []   -- only for printing so we don't have to worry too much here
+    A.PatternSyn f -> pure $ Def (headAmbQ f) []
+    A.Macro f      -> pure $ Def f []
+
+    A.WithApp{}      -> notAllowed "with application"
+    A.QuestionMark{} -> notAllowed "holes"
+    A.Underscore{}   -> notAllowed "metavariables"
+    A.Lam{}          -> notAllowed "lambdas"
+    A.AbsurdLam{}    -> notAllowed "lambdas"
+    A.ExtendedLam{}  -> notAllowed "lambdas"
+    _                -> typeError $ GenericError $ "TODO: exprToTerm " ++ show e
+  where
+    notAllowed s = typeError $ GenericError $ "Not allowed in DISPLAY pragma right-hand side: " ++ s
+
+renumberElims :: Nat -> Elims -> Elims
+renumberElims n es = evalState (renumbers es) n
+  where
+    next :: State Nat Nat
+    next = do i <- get; i <$ put (i - 1)
+
+    renumbers :: Elims -> State Nat Elims
+    renumbers = (traverse . traverse) renumber
+
+    renumber :: Term -> State Nat Term
+    renumber (Var 0 [])   = var <$> next
+    renumber (Def f es)   = Def f <$> renumbers es
+    renumber (Con c h es) = Con c h <$> renumbers es
+    renumber (Lit l)      = pure $ Lit l
+    renumber _            = __IMPOSSIBLE__ -- We need only handle the result of patternToTerm here
diff --git a/src/full/Agda/TypeChecking/Rules/LHS.hs b/src/full/Agda/TypeChecking/Rules/LHS.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS.hs
@@ -0,0 +1,2090 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.LHS
+  ( checkLeftHandSide
+  , LHSResult(..)
+  , bindAsPatterns
+  , IsFlexiblePattern(..)
+  , DataOrRecord
+  , checkSortOfSplitVar
+  ) where
+
+import Prelude hiding ( null )
+
+import Data.Function (on)
+import Data.Maybe
+
+import Control.Arrow (left)
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.Writer       ( MonadWriter(..), runWriterT )
+import Control.Monad.Trans.Maybe
+
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import Data.List (findIndex)
+import qualified Data.List as List
+import Data.Semigroup ( Semigroup )
+import qualified Data.Semigroup as Semigroup
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.Interaction.Highlighting.Generate
+  ( storeDisambiguatedConstructor, storeDisambiguatedProjection, disambiguateRecordFields)
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Lenses
+
+import Agda.Syntax.Internal as I hiding (DataOrRecord)
+import Agda.Syntax.Internal.Pattern
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views (asView, deepUnscope)
+import Agda.Syntax.Concrete (FieldAssignment'(..),LensInScope(..))
+import Agda.Syntax.Common as Common
+import Agda.Syntax.Info as A
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad
+
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.CheckInternal (checkInternal)
+import Agda.TypeChecking.Datatypes hiding (isDataOrRecordType)
+import Agda.TypeChecking.Errors (dropTopLevelModule)
+import Agda.TypeChecking.Irrelevance
+-- Prevent "Ambiguous occurrence ‘DontKnow’" when loading with ghci.
+-- (DontKnow is one of the constructors of ErrorNonEmpty *and* UnifactionResult').
+-- We can't explicitly hide just the constructor here because it isn't in the
+-- hs-boot file.
+import {-# SOURCE #-} Agda.TypeChecking.Empty (ensureEmptyType)
+import Agda.TypeChecking.Patterns.Abstract
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records hiding (getRecordConstructor)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Telescope.Path
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Warnings (warning)
+
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Term (checkExpr, isType_)
+import Agda.TypeChecking.Rules.LHS.Problem
+import Agda.TypeChecking.Rules.LHS.ProblemRest
+import Agda.TypeChecking.Rules.LHS.Unify
+import Agda.TypeChecking.Rules.LHS.Implicit
+
+import Agda.Utils.CallStack ( HasCallStack, withCallerCallStack )
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (prettyShow)
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+import Agda.TypeChecking.Free (freeIn)
+
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Compute the set of flexible patterns in a list of patterns. The result is
+----   the deBruijn indices of the flexible patterns.
+--flexiblePatterns :: [NamedArg A.Pattern] -> TCM FlexibleVars
+--flexiblePatterns nps = do
+--  forMaybeM (zip (downFrom $ length nps) nps) $ \ (i, Arg ai p) -> do
+--    runMaybeT $ (\ f -> FlexibleVar (getHiding ai) (getOrigin ai) f (Just i) i) <$> maybeFlexiblePattern p
+
+-- | A pattern is flexible if it is dotted or implicit, or a record pattern
+--   with only flexible subpatterns.
+class IsFlexiblePattern a where
+  maybeFlexiblePattern :: (HasConstInfo m, MonadDebug m) => a -> MaybeT m FlexibleVarKind
+
+  isFlexiblePattern :: (HasConstInfo m, MonadDebug m) => a -> m Bool
+  isFlexiblePattern p =
+    maybe False notOtherFlex <$> runMaybeT (maybeFlexiblePattern p)
+    where
+    notOtherFlex = \case
+      RecordFlex fls -> all notOtherFlex fls
+      ImplicitFlex   -> True
+      DotFlex        -> True
+      OtherFlex      -> False
+
+instance IsFlexiblePattern A.Pattern where
+  maybeFlexiblePattern p = do
+    reportSDoc "tc.lhs.flex" 30 $ "maybeFlexiblePattern" <+> prettyA p
+    reportSDoc "tc.lhs.flex" 60 $ "maybeFlexiblePattern (raw) " <+> (text . show . deepUnscope) p
+    case p of
+      A.DotP{}  -> return DotFlex
+      A.VarP{}  -> return ImplicitFlex
+      A.WildP{} -> return ImplicitFlex
+      A.AsP _ _ p -> maybeFlexiblePattern p
+      A.ConP _ cs qs | Just c <- getUnambiguous cs ->
+        ifM (isNothing <$> isRecordConstructor c) (return OtherFlex) {-else-}
+            (maybeFlexiblePattern qs)
+      A.LitP{}  -> return OtherFlex
+      A.AnnP _ _ p -> maybeFlexiblePattern p
+      _ -> mzero
+
+instance IsFlexiblePattern (I.Pattern' a) where
+  maybeFlexiblePattern p =
+    case p of
+      I.DotP{}  -> return DotFlex
+      I.ConP _ i ps
+        | conPRecord i , PatOSystem <- patOrigin (conPInfo i) -> return ImplicitFlex  -- expanded from ImplicitP
+        | conPRecord i -> maybeFlexiblePattern ps
+        | otherwise -> mzero
+      I.VarP{}  -> mzero
+      I.LitP{}  -> mzero
+      I.ProjP{} -> mzero
+      I.IApplyP{} -> mzero
+      I.DefP{} -> mzero -- TODO Andrea check semantics
+
+-- | Lists of flexible patterns are 'RecordFlex'.
+instance IsFlexiblePattern a => IsFlexiblePattern [a] where
+  maybeFlexiblePattern ps = RecordFlex <$> mapM maybeFlexiblePattern ps
+
+instance IsFlexiblePattern a => IsFlexiblePattern (Arg a) where
+  maybeFlexiblePattern = maybeFlexiblePattern . unArg
+
+instance IsFlexiblePattern a => IsFlexiblePattern (Common.Named name a) where
+  maybeFlexiblePattern = maybeFlexiblePattern . namedThing
+
+-- | Update the given LHS state:
+--   1. simplify problem equations
+--   2. rename telescope variables
+--   3. introduce trailing patterns
+updateLHSState :: LHSState a -> TCM (LHSState a)
+updateLHSState st = do
+  let tel     = st ^. lhsTel
+      problem = st ^. lhsProblem
+  eqs' <- addContext tel $ updateProblemEqs $ problem ^. problemEqs
+  tel' <- useNamesFromProblemEqs eqs' tel
+  updateProblemRest $ set lhsTel tel' $ set (lhsProblem . problemEqs) eqs' st
+
+-- | Update the user patterns in the given problem, simplifying equations
+--   between constructors where possible.
+updateProblemEqs
+ :: [ProblemEq] -> TCM [ProblemEq]
+updateProblemEqs eqs = do
+  reportSDoc "tc.lhs.top" 20 $ vcat
+    [ "updateProblem: equations to update"
+    , nest 2 $ if null eqs then "(none)" else vcat $ map prettyTCM eqs
+    ]
+
+  eqs' <- updates eqs
+
+  reportSDoc "tc.lhs.top" 20 $ vcat
+    [ "updateProblem: new equations"
+    , nest 2 $ if null eqs' then "(none)" else vcat $ map prettyTCM eqs'
+    ]
+
+  return eqs'
+
+  where
+
+    updates :: [ProblemEq] -> TCM [ProblemEq]
+    updates = concat <.> traverse update
+
+    update :: ProblemEq -> TCM [ProblemEq]
+    update eq@(ProblemEq A.WildP{} _ _) = return []
+    update eq@(ProblemEq p@A.ProjP{} _ _) = typeError $ IllformedProjectionPatternAbstract p
+    update eq@(ProblemEq p@(A.AsP info x p') v a) =
+      (ProblemEq (A.VarP x) v a :) <$> update (ProblemEq p' v a)
+
+    update eq@(ProblemEq p@(A.AnnP _ _ A.WildP{}) v a) = return [eq]
+    update eq@(ProblemEq p@(A.AnnP info ty p') v a) =
+      (ProblemEq (A.AnnP info ty (A.WildP patNoRange)) v a :) <$> update (ProblemEq p' v a)
+
+    update eq@(ProblemEq p v a) = reduce v >>= constructorForm >>= \case
+      Con c ci es -> do
+        let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+        -- we should only simplify equations between fully applied constructors
+        contype <- getFullyAppliedConType c =<< reduce (unDom a)
+        caseMaybe contype (return [eq]) $ \((d,_,pars),b) -> do
+        TelV ctel _ <- telViewPath b
+
+        -- Andrea 15/10/2020: propagate modality to constructor arguments
+        let updMod = composeModality (getModality a)
+        ctel <- return $ mapModality updMod <$> ctel
+
+        let bs = instTel ctel (map unArg vs)
+
+        p <- expandLitPattern p
+        case p of
+          A.AsP{} -> __IMPOSSIBLE__
+          A.AnnP{} -> __IMPOSSIBLE__
+          A.ConP cpi ambC ps -> do
+            (c',_) <- disambiguateConstructor ambC d pars
+
+            -- Issue #3014: If the constructor is forced but the user wrote a
+            -- different constructor,that's an error. We simply keep the
+            -- problem equation, this will result in a proper error message later.
+            if conName c /= conName c' then return [eq] else do
+
+            -- Insert implicit patterns
+            ps <- insertImplicitPatterns ExpandLast ps ctel
+            reportSDoc "tc.lhs.imp" 20 $
+              "insertImplicitPatternsT returned" <+> fsep (map prettyA ps)
+
+            -- Check argument count and hiding (not just count: #3074)
+            let checkArgs [] [] _ _ = return ()
+                checkArgs (p : ps) (v : vs) nExpected nActual
+                  | getHiding p == getHiding v = checkArgs ps vs (nExpected + 1) (nActual + 1)
+                  | otherwise                  = setCurrentRange p $ typeError WrongHidingInLHS
+                checkArgs [] vs nExpected nActual = typeError $
+                  WrongNumberOfConstructorArguments (conName c) (nExpected + length vs) nActual
+                checkArgs (p : ps) [] nExpected nActual = setCurrentRange p $ typeError $
+                  WrongNumberOfConstructorArguments (conName c) nExpected (nActual + 1 + (length ps))
+
+            checkArgs ps vs 0 0
+
+            updates $ zipWith3 ProblemEq (map namedArg ps) (map unArg vs) bs
+
+          A.RecP pi fs -> do
+            axs <- map argFromDom . recFields . theDef <$> getConstInfo d
+
+            -- Andreas, 2018-09-06, issue #3122.
+            -- Associate the concrete record field names used in the record pattern
+            -- to their counterpart in the record type definition.
+            disambiguateRecordFields (map _nameFieldA fs) (map unArg axs)
+
+            let cxs = map (fmap (nameConcrete . qnameName)) axs
+
+            -- In fs omitted explicit fields are replaced by underscores,
+            -- and the fields are put in the correct order.
+            ps <- insertMissingFieldsFail d (const $ A.WildP patNoRange) fs cxs
+
+            -- We also need to insert missing implicit or instance fields.
+            ps <- insertImplicitPatterns ExpandLast ps ctel
+
+            let eqs = zipWith3 ProblemEq (map namedArg ps) (map unArg vs) bs
+            updates eqs
+
+          _ -> return [eq]
+
+      Lit l | A.LitP _ l' <- p , l == l' -> return []
+
+      _ | A.EqualP{} <- p -> do
+        itisone <- liftTCM primItIsOne
+        ifM (tryConversion $ equalTerm (unDom a) v itisone) (return []) (return [eq])
+
+      _ -> return [eq]
+
+    instTel :: Telescope -> [Term] -> [Dom Type]
+    instTel EmptyTel _                   = []
+    instTel (ExtendTel arg tel) (u : us) = arg : instTel (absApp tel u) us
+    instTel ExtendTel{} []               = __IMPOSSIBLE__
+
+
+-- | Check if a problem is solved.
+--   That is, if the patterns are all variables,
+--   and there is no 'problemRest'.
+isSolvedProblem :: Problem a -> Bool
+isSolvedProblem problem = null (problem ^. problemRestPats) &&
+  problemAllVariables problem
+
+-- | Check if a problem consists only of variable patterns.
+--   (Includes the 'problemRest').
+problemAllVariables :: Problem a -> Bool
+problemAllVariables problem =
+    all isSolved $
+      map namedArg (problem ^. problemRestPats) ++ problemInPats problem
+  where
+    -- need further splitting:
+    isSolved A.ConP{}        = False
+    isSolved A.LitP{}        = False
+    isSolved A.RecP{}        = False  -- record pattern
+    -- solved:
+    isSolved A.VarP{}        = True
+    isSolved A.WildP{}       = True
+    isSolved A.DotP{}        = True
+    isSolved A.AbsurdP{}     = True
+    -- recursive cases
+    isSolved (A.AsP _ _ p)   = isSolved p
+    isSolved (A.AnnP _ _ p)  = isSolved p
+    -- impossible:
+    isSolved A.ProjP{}       = __IMPOSSIBLE__
+    isSolved A.DefP{}        = __IMPOSSIBLE__
+    isSolved A.PatternSynP{} = __IMPOSSIBLE__  -- expanded before
+    isSolved A.EqualP{}      = False -- __IMPOSSIBLE__
+    isSolved A.WithP{}       = __IMPOSSIBLE__
+
+-- | For each user-defined pattern variable in the 'Problem', check
+-- that the corresponding data type (if any) does not contain a
+-- constructor of the same name (which is not in scope); this
+-- \"shadowing\" could indicate an error, and is not allowed.
+--
+-- Precondition: The problem has to be solved.
+
+noShadowingOfConstructors :: ProblemEq -> TCM ()
+noShadowingOfConstructors problem@(ProblemEq p _ (Dom{domInfo = info, unDom = El _ a})) =
+  case p of
+   A.WildP       {} -> return ()
+   A.AbsurdP     {} -> return ()
+   A.DotP        {} -> return ()
+   A.EqualP      {} -> return ()
+   A.AsP _ _ p      -> noShadowingOfConstructors $ problem { problemInPat = p }
+   A.AnnP _ _ p     -> noShadowingOfConstructors $ problem { problemInPat = p }
+   A.ConP        {} -> __IMPOSSIBLE__
+   A.RecP        {} -> __IMPOSSIBLE__
+   A.ProjP       {} -> __IMPOSSIBLE__
+   A.DefP        {} -> __IMPOSSIBLE__
+   A.LitP        {} -> __IMPOSSIBLE__
+   A.PatternSynP {} -> __IMPOSSIBLE__
+   A.WithP       {} -> __IMPOSSIBLE__
+   -- Andreas, 2017-12-01, issue #2859.
+   -- Due to parameter refinement, there can be (invisible) variable patterns from module
+   -- parameters that shadow constructors.
+   -- Thus, only complain about user written variable that shadow constructors.
+   A.VarP A.BindName{unBind = x} -> when (getOrigin info == UserWritten) $ do
+    reportSDoc "tc.lhs.shadow" 30 $ vcat
+      [ text $ "checking whether pattern variable " ++ prettyShow x ++ " shadows a constructor"
+      , nest 2 $ "type of variable =" <+> prettyTCM a
+      , nest 2 $ "position of variable =" <+> (text . show) (getRange x)
+      ]
+    reportSDoc "tc.lhs.shadow" 70 $ nest 2 $ "a =" <+> pretty a
+
+    -- Get a conflicting data or record constructor, if any.
+    mc <- runMaybeT do
+
+      -- Is the type of the pattern variable a data or pattern record type?
+      a  <- lift $ reduce a
+      (d, dr) <- MaybeT $ isDataOrRecord a
+      guard $ patternMatchingAllowed dr
+
+      -- Look for a constructor with the same name as the pattern variable.
+      cs <- lift $ getConstructors d
+      MaybeT $ pure $ List.find ((A.nameConcrete x ==) . A.nameConcrete . A.qnameName) cs
+
+    -- Alert if there is a constructor of the same name.
+    whenJust mc \ c -> setCurrentRange x $
+      warning $ PatternShadowsConstructor (nameConcrete x) c
+    --
+    -- Andreas, 2023-09-08, issue #6829:
+    -- I rewrote the code originally dating from 2009, commit:
+    -- https://github.com/agda/agda/commit/5d5095ba080b04f16867d4ed5af4ba7091f1a773
+    -- The code survived for almost 15 years, but it slept through the advent
+    -- of matchable record constructors in 2010 (Agda 2.2.8):
+    -- https://github.com/agda/agda/blob/283730b392d7c21c54b53b0f486802ec143e4af7/doc/release-notes/2.2.8.md#L7-L9
+    -- Here are comments on the last version of the code I'd like to preserve,
+    -- as they reflect some considerations and design decisions:
+    --
+            -- Abstract constructors cannot be brought into scope,
+            -- even by a bigger import list.
+            -- Thus, they cannot be confused with variables.
+            -- Alternatively, we could do getConstInfo in ignoreAbstractMode,
+            -- then Agda would complain if a variable shadowed an abstract constructor.
+          -- TODO: in the future some stuck primitives might allow constructors
+      -- TODO: If the type is a meta-variable, should the test be
+      -- postponed? If there is a problem, then it will be caught when
+      -- the completed module is type checked, so it is safe to skip
+      -- the test here. However, users may be annoyed if they get an
+      -- error in code which has already passed the type checker.
+
+-- | Check that a dot pattern matches it's instantiation.
+checkDotPattern :: DotPattern -> TCM ()
+checkDotPattern (Dot e v (Dom{domInfo = info, unDom = a})) =
+  traceCall (CheckDotPattern e v) $ do
+  reportSDoc "tc.lhs.dot" 15 $
+    sep [ "checking dot pattern"
+        , nest 2 $ prettyA e
+        , nest 2 $ "=" <+> prettyTCM v
+        , nest 2 $ ":" <+> prettyTCM a
+        ]
+  applyModalityToContext info $ do
+    u <- checkExpr e a
+    reportSDoc "tc.lhs.dot" 50 $
+      sep [ "equalTerm"
+          , nest 2 $ pretty a
+          , nest 2 $ pretty u
+          , nest 2 $ pretty v
+          ]
+    equalTerm a u v
+
+checkAbsurdPattern :: AbsurdPattern -> TCM ()
+checkAbsurdPattern (Absurd r a) = ensureEmptyType r a
+
+checkAnnotationPattern :: AnnotationPattern -> TCM ()
+checkAnnotationPattern (Ann t a) = do
+  reportSDoc "tc.lhs.ann" 15 $
+    sep [ "checking type annotation in pattern"
+        , nest 2 $ prettyA t
+        , nest 2 $ "=" <+> prettyTCM a
+        ]
+  b <- isType_ t
+  equalType a b
+
+-- | After splitting is complete, we transfer the origins
+--   We also transfer the locations of absurd patterns, since these haven't
+--   been introduced yet in the internal pattern.
+transferOrigins :: [NamedArg A.Pattern]
+                -> [NamedArg DeBruijnPattern]
+                -> TCM [NamedArg DeBruijnPattern]
+transferOrigins ps qs = do
+  reportSDoc "tc.lhs.origin" 40 $ vcat
+    [ "transferOrigins"
+    , nest 2 $ vcat
+      [ "ps  =   " <+> prettyA ps
+      , "qs  =   " <+> pretty qs
+      ]
+    ]
+  transfers ps qs
+
+  where
+    transfers :: [NamedArg A.Pattern]
+              -> [NamedArg DeBruijnPattern]
+              -> TCM [NamedArg DeBruijnPattern]
+    transfers [] qs
+      | all notVisible qs = return $ map (setOrigin Inserted) qs
+      | otherwise         = __IMPOSSIBLE__
+    transfers (p : ps) [] = __IMPOSSIBLE__
+    transfers (p : ps) (q : qs)
+      | matchingArgs p q = do
+          q' <- mapNameOf (maybe id (const . Just) $ getNameOf p) -- take NamedName from p if present
+              . setOrigin (getOrigin p)
+            <$> (traverse $ traverse $ transfer $ namedArg p) q
+          (q' :) <$> transfers ps qs
+      | otherwise = (setOrigin Inserted q :) <$> transfers (p : ps) qs
+
+    transfer :: A.Pattern -> DeBruijnPattern -> TCM DeBruijnPattern
+    transfer p q = case (asView p , q) of
+
+      ((asB , anns , A.ConP pi _ ps) , ConP c (ConPatternInfo i r ft mb l) qs) -> do
+        let cpi = ConPatternInfo (PatternInfo PatOCon asB) r ft mb l
+        ConP c cpi <$> transfers ps qs
+
+      ((asB , anns , A.RecP pi fs) , ConP c (ConPatternInfo i r ft mb l) qs) -> do
+        let Def d _  = unEl $ unArg $ fromMaybe __IMPOSSIBLE__ mb
+            axs = map (nameConcrete . qnameName . unArg) (conFields c) `withArgsFrom` qs
+            cpi = ConPatternInfo (PatternInfo PatORec asB) r ft mb l
+        ps <- insertMissingFieldsFail d (const $ A.WildP patNoRange) fs axs
+        ConP c cpi <$> transfers ps qs
+
+      ((asB , anns , p) , ConP c (ConPatternInfo i r ft mb l) qs) -> do
+        let cpi = ConPatternInfo (PatternInfo (patOrig p) asB) r ft mb l
+        return $ ConP c cpi qs
+
+      ((asB , anns , p) , VarP _ x) -> return $ VarP (PatternInfo (patOrig p) asB) x
+
+      ((asB , anns , p) , DotP _ u) -> return $ DotP (PatternInfo (patOrig p) asB) u
+
+      ((asB , anns , p) , LitP _ l) -> return $ LitP (PatternInfo (patOrig p) asB) l
+
+      _ -> return q
+
+    patOrig :: A.Pattern -> PatOrigin
+    patOrig (A.VarP x)      = PatOVar (A.unBind x)
+    patOrig A.DotP{}        = PatODot
+    patOrig A.ConP{}        = PatOCon
+    patOrig A.RecP{}        = PatORec
+    patOrig A.WildP{}       = PatOWild
+    patOrig A.AbsurdP{}     = PatOAbsurd
+    patOrig A.LitP{}        = PatOLit
+    patOrig A.EqualP{}      = PatOCon --TODO: origin for EqualP
+    patOrig A.AsP{}         = __IMPOSSIBLE__
+    patOrig A.ProjP{}       = __IMPOSSIBLE__
+    patOrig A.DefP{}        = __IMPOSSIBLE__
+    patOrig A.PatternSynP{} = __IMPOSSIBLE__
+    patOrig A.WithP{}       = __IMPOSSIBLE__
+    patOrig A.AnnP{}        = __IMPOSSIBLE__
+
+    matchingArgs :: NamedArg A.Pattern -> NamedArg DeBruijnPattern -> Bool
+    matchingArgs p q
+      -- The arguments match if
+      -- 1. they are both projections,
+      | isJust (A.isProjP p) = isJust (isProjP q)
+      -- 2. or they are both visible,
+      | visible p && visible q = True
+      -- 3. or they have the same hiding and the argument is not named,
+      | sameHiding p q && isNothing (getNameOf p) = True
+      -- 4. or they have the same hiding and the same name.
+      | sameHiding p q && namedSame p q = True
+      -- Otherwise this argument was inserted by the typechecker.
+      | otherwise = False
+
+
+-- | If a user-written variable occurs more than once, it should be bound
+--   to the same internal variable (or term) in all positions.
+--   Returns the list of patterns with the duplicate user patterns removed.
+checkPatternLinearity :: [ProblemEq] -> TCM [ProblemEq]
+checkPatternLinearity eqs = do
+  reportSDoc "tc.lhs.linear" 30 $ "Checking linearity of pattern variables"
+  check Map.empty eqs
+  where
+    check :: Map A.BindName (Term, Type) -> [ProblemEq] -> TCM [ProblemEq]
+    check _ [] = return []
+    check vars (eq@(ProblemEq p u a) : eqs) = do
+      reportSDoc "tc.lhs.linear" 40 $ sep
+        [ "linearity: checking pattern "
+        , prettyA p
+        , " equal to term "
+        , prettyTCM u
+        , " of type "
+        , prettyTCM a
+        ]
+      case p of
+        A.VarP x -> do
+          let y = A.unBind x
+          reportSLn "tc.lhs.linear" 60 $
+            "pattern variable " ++ prettyShow (A.nameConcrete y) ++ " with id " ++ show (A.nameId y)
+          case Map.lookup x vars of
+            Just (v , b) -> do
+              traceCall (CheckPatternLinearityType $ A.nameConcrete y) $
+                noConstraints $ equalType (unDom a) b
+              traceCall (CheckPatternLinearityValue $ A.nameConcrete y) $
+                noConstraints $ equalTerm (unDom a) u v
+              check vars eqs
+            Nothing -> (eq:) <$> do
+              check (Map.insert x (u,unDom a) vars) eqs
+        A.AsP _ x p ->
+          check vars $ [ProblemEq (A.VarP x) u a, ProblemEq p u a] ++ eqs
+        A.AnnP _ _ A.WildP{} -> continue
+        A.AnnP r t p -> (ProblemEq (A.AnnP r t (A.WildP patNoRange)) u a:) <$>
+          check vars (ProblemEq p u a : eqs)
+        A.WildP{}       -> continue
+        A.DotP{}        -> continue
+        A.AbsurdP{}     -> continue
+        A.ConP{}        -> __IMPOSSIBLE__
+        A.ProjP{}       -> __IMPOSSIBLE__
+        A.DefP{}        -> __IMPOSSIBLE__
+        A.LitP{}        -> __IMPOSSIBLE__
+        A.PatternSynP{} -> __IMPOSSIBLE__
+        A.RecP{}        -> __IMPOSSIBLE__
+        A.EqualP{}      -> __IMPOSSIBLE__
+        A.WithP{}       -> __IMPOSSIBLE__
+
+      where continue = (eq:) <$> check vars eqs
+
+-- | Construct the context for a left hand side, making up out-of-scope names
+--   for unnamed variables.
+computeLHSContext :: [Maybe A.Name] -> Telescope -> TCM Context
+computeLHSContext = go [] []
+  where
+    go cxt _ []        tel@ExtendTel{} = do
+      reportSDoc "impossible" 10 $
+        "computeLHSContext: no patterns left, but tel =" <+> prettyTCM tel
+      __IMPOSSIBLE__
+    go cxt _ (_ : _)   EmptyTel = __IMPOSSIBLE__
+    go cxt _ []        EmptyTel = return cxt
+    go cxt taken (x : xs) tel0@(ExtendTel a tel) = do
+        name <- maybe (dummyName taken $ absName tel) return x
+        let e = (name,) <$> a
+        go (e : cxt) (name : taken) xs (absBody tel)
+
+    dummyName taken s =
+      if isUnderscore s then freshNoName_
+      else setNotInScope <$> freshName_ (argNameToString s)
+
+-- | Bind as patterns
+bindAsPatterns :: [AsBinding] -> TCM a -> TCM a
+bindAsPatterns []                ret = ret
+bindAsPatterns (AsB x v a m : asb) ret = do
+  reportSDoc "tc.lhs.as" 10 $ "as pattern" <+> prettyTCM x <+>
+    sep [ ":" <+> prettyTCM a
+        , "=" <+> prettyTCM v
+        ]
+  addLetBinding (setModality m defaultArgInfo) Inserted x v a $ bindAsPatterns asb ret
+
+-- | Since with-abstraction can change the type of a variable, we have to
+--   recheck the stripped with patterns when checking a with function.
+recheckStrippedWithPattern :: ProblemEq -> TCM ()
+recheckStrippedWithPattern (ProblemEq p v a) = checkInternal v CmpLeq (unDom a)
+  `catchError` \_ -> typeError $ IllTypedPatternAfterWithAbstraction p
+
+-- | Result of checking the LHS of a clause.
+data LHSResult = LHSResult
+  { lhsParameters   :: Nat
+    -- ^ The number of original module parameters. These are present in the
+    -- the patterns.
+  , lhsVarTele      :: Telescope
+    -- ^ Δ : The types of the pattern variables, in internal dependency order.
+    -- Corresponds to 'clauseTel'.
+  , lhsPatterns     :: [NamedArg DeBruijnPattern]
+    -- ^ The patterns in internal syntax.
+  , lhsHasAbsurd    :: Bool
+    -- ^ Whether the LHS has at least one absurd pattern.
+  , lhsBodyType     :: Arg Type
+    -- ^ The type of the body. Is @bσ@ if @Γ@ is defined.
+    -- 'Irrelevant' to indicate the rhs must be checked in irrelevant mode.
+  , lhsPatSubst     :: Substitution
+    -- ^ Substitution version of @lhsPatterns@, only up to the first projection
+    -- pattern. @Δ |- lhsPatSubst : Γ@. Where @Γ@ is the argument telescope of
+    -- the function. This is used to update inherited dot patterns in
+    -- with-function clauses.
+  , lhsAsBindings   :: [AsBinding]
+    -- ^ As-bindings from the left-hand side. Return instead of bound since we
+    -- want them in where's and right-hand sides, but not in with-clauses
+    -- (Issue 2303).
+  , lhsPartialSplit :: IntSet
+    -- ^ have we done a partial split?
+  , lhsIndexedSplit :: Bool
+    -- ^ have we split on an indexed type?
+  }
+
+instance InstantiateFull LHSResult where
+  instantiateFull' (LHSResult n tel ps abs t sub as psplit ixsplit) = LHSResult n
+    <$> instantiateFull' tel
+    <*> instantiateFull' ps
+    <*> instantiateFull' abs
+    <*> instantiateFull' t
+    <*> instantiateFull' sub
+    <*> instantiateFull' as
+    <*> pure psplit
+    <*> pure ixsplit
+
+-- | Check a LHS. Main function.
+--
+--   @checkLeftHandSide a ps a ret@ checks that user patterns @ps@ eliminate
+--   the type @a@ of the defined function, and calls continuation @ret@
+--   if successful.
+
+checkLeftHandSide :: forall a.
+     Call
+     -- ^ Trace, e.g. 'CheckLHS' or 'CheckPattern'.
+  -> Maybe QName
+     -- ^ The name of the definition we are checking.
+  -> [NamedArg A.Pattern]
+     -- ^ The patterns.
+  -> Type
+     -- ^ The expected type @a = Γ → b@.
+  -> Maybe Substitution
+     -- ^ Module parameter substitution from with-abstraction.
+  -> [ProblemEq]
+     -- ^ Patterns that have been stripped away by with-desugaring.
+     -- ^ These should not contain any proper matches.
+  -> (LHSResult -> TCM a)
+     -- ^ Continuation.
+  -> TCM a
+checkLeftHandSide call f ps a withSub' strippedPats =
+ Bench.billToCPS [Bench.Typing, Bench.CheckLHS] $
+ traceCallCPS call $ \ ret -> do
+
+  -- To allow module parameters to be refined by matching, we're adding the
+  -- context arguments as wildcard patterns and extending the type with the
+  -- context telescope.
+  cxt <- map (setOrigin Inserted) . reverse <$> getContext
+  let tel = telFromList' prettyShow cxt
+      cps = [ unnamed . A.VarP . A.mkBindName . fst <$> argFromDom d
+            | d <- cxt ]
+      eqs0 = zipWith3 ProblemEq (map namedArg cps) (map var $ downFrom $ size tel) (flattenTel tel)
+
+  let finalChecks :: LHSState a -> TCM a
+      finalChecks (LHSState delta qs0 (Problem eqs rps _) b psplit ixsplit) = do
+
+        reportSDoc "tc.lhs.top" 20 $ vcat
+          [ "lhs: final checks with remaining equations"
+          , nest 2 $ if null eqs then "(none)" else addContext delta $ vcat $ map prettyTCM eqs
+          , "qs0 =" <+> addContext delta (prettyTCMPatternList qs0)
+          ]
+
+        unless (null rps) __IMPOSSIBLE__
+
+        addContext delta $ do
+          mapM_ noShadowingOfConstructors eqs
+
+          -- When working --without-K or --cubical-compatible, we have
+          -- to check that the target type can be used at the “ambient”
+          -- modality. For --cubical-compatible, this just improves an
+          -- error message (printing the type rather than the generated
+          -- RHS). For --without-K, it implements the same check without
+          -- necessarily generating --cubical code.
+          -- The reason for this check is that a clause
+          --    foo : x ≡ y → ... → T y
+          --    foo refl ... = ...
+          -- in Cubical mode, gets elaborated to an extra clause of the
+          -- form
+          --    foo (transp p φ x) ... = transp (λ i → T (p i)) φ (foo x ...)
+          -- (approximately), where T is the target type. That is: to
+          -- implement the substitution T[y/x], we use an actual
+          -- transport. See #5448.
+
+        arity_a <- arityPiPath a
+        -- Compute substitution from the out patterns @qs0@
+        let notProj ProjP{} = False
+            notProj _       = True
+            numPats  = length $ takeWhile (notProj . namedArg) qs0
+
+            -- We have two slightly different cases here: normal function and
+            -- with-function. In both cases the goal is to build a substitution
+            -- from the context Γ of the previous checkpoint to the current lhs
+            -- context Δ:
+            --
+            --    Δ ⊢ paramSub : Γ
+            --
+            --  * Normal function, f
+            --
+            --    Γ = cxt = module parameter telescope of f
+            --    Ψ = non-parameter arguments of f (we have f : Γ Ψ → A)
+            --    Δ   ⊢ patSub  : Γ Ψ
+            --    Γ Ψ ⊢ weakSub : Γ
+            --    paramSub = patSub ∘ weakSub
+            --
+            --  * With-function
+            --
+            --    Γ = lhs context of the parent clause (cxt = [])
+            --    Ψ = argument telescope of with-function
+            --    Θ = inserted implicit patterns not in Ψ (#2827)
+            --        (this happens if the goal computes to an implicit
+            --         function type after some matching in the with-clause)
+            --
+            --    Ψ   ⊢ withSub : Γ
+            --    Δ   ⊢ patSub  : Ψ Θ
+            --    Ψ Θ ⊢ weakSub : Ψ
+            --    paramSub = patSub ∘ weakSub ∘ withSub
+            --
+            --    To compute Θ we can look at the arity of the with-function
+            --    and compare it to numPats. This works since the with-function
+            --    type is fully reduced.
+
+            weakSub :: Substitution
+            weakSub | isJust withSub' = wkS (max 0 $ numPats - arity_a) idS -- if numPats < arity, Θ is empty
+                    | otherwise       = wkS (numPats - length cxt) idS
+            withSub  = fromMaybe idS withSub'
+            patSub   = map (patternToTerm . namedArg) (reverse $ take numPats qs0) ++# EmptyS impossible
+            paramSub = patSub `composeS` weakSub `composeS` withSub
+
+        eqs <- addContext delta $ checkPatternLinearity eqs
+
+        leftovers@(LeftoverPatterns patVars asb0 dots absurds annps otherPats)
+          <- addContext delta $ getLeftoverPatterns eqs
+
+        reportSDoc "tc.lhs.leftover" 30 $ vcat
+          [ "leftover patterns: " , nest 2 (addContext delta $ prettyTCM leftovers) ]
+
+        unless (null otherPats) __IMPOSSIBLE__
+
+        -- Get the user-written names for the pattern variables
+        let (vars, asb1) = getUserVariableNames delta patVars
+            asb          = asb0 ++ asb1
+
+        -- Rename internal patterns with these names
+        let makeVar     = maybe deBruijnVar $ debruijnNamedVar . nameToArgName
+            ren         = parallelS $ zipWith makeVar (reverse vars) [0..]
+
+        qs <- transferOrigins (cps ++ ps) $ applySubst ren qs0
+
+        let hasAbsurd = not . null $ absurds
+
+        let lhsResult = LHSResult (length cxt) delta qs hasAbsurd b patSub asb (IntSet.fromList $ catMaybes psplit) ixsplit
+
+        -- Debug output
+        reportSDoc "tc.lhs.top" 10 $
+          vcat [ "checked lhs:"
+               , nest 2 $ vcat
+                 [ "delta   = " <+> prettyTCM delta
+                 , "dots    = " <+> addContext delta (brackets $ fsep $ punctuate comma $ map prettyTCM dots)
+                 , "asb     = " <+> addContext delta (brackets $ fsep $ punctuate comma $ map prettyTCM asb)
+                 , "absurds = " <+> addContext delta (brackets $ fsep $ punctuate comma $ map prettyTCM absurds)
+                 , "qs      = " <+> addContext delta (prettyList $ map pretty qs)
+                 , "b       = " <+> addContext delta (prettyTCM b)
+                 ]
+               ]
+        reportSDoc "tc.lhs.top" 30 $
+          nest 2 $ vcat
+                 [ "vars   = " <+> pretty vars
+                 , "b      = " <+> pretty b
+                 ]
+        reportSDoc "tc.lhs.top" 20 $ nest 2 $ "withSub  = " <+> pretty withSub
+        reportSDoc "tc.lhs.top" 20 $ nest 2 $ "weakSub  = " <+> pretty weakSub
+        reportSDoc "tc.lhs.top" 20 $ nest 2 $ "patSub   = " <+> pretty patSub
+        reportSDoc "tc.lhs.top" 20 $ nest 2 $ "paramSub = " <+> pretty paramSub
+
+        newCxt <- computeLHSContext vars delta
+
+        updateContext paramSub (const newCxt) $ do
+
+          reportSDoc "tc.lhs.top" 10 $ "bound pattern variables"
+          reportSDoc "tc.lhs.top" 60 $ nest 2 $ "context = " <+> (pretty =<< getContextTelescope)
+          reportSDoc "tc.lhs.top" 10 $ nest 2 $ "type  = " <+> prettyTCM b
+          reportSDoc "tc.lhs.top" 60 $ nest 2 $ "type  = " <+> pretty b
+
+          bindAsPatterns asb $ do
+
+            -- Check dot patterns
+            mapM_ checkDotPattern dots
+            mapM_ checkAbsurdPattern absurds
+            mapM_ checkAnnotationPattern annps
+
+          -- Issue2303: don't bind asb' for the continuation (return in lhsResult instead)
+          ret lhsResult
+
+  st0 <- initLHSState tel eqs0 ps a finalChecks
+
+  -- after we have introduced variables, we can add the patterns stripped by
+  -- with-desugaring to the state.
+  let withSub = fromMaybe __IMPOSSIBLE__ withSub'
+  withEqs <- updateProblemEqs $ applySubst withSub strippedPats
+  -- Jesper, 2017-05-13: re-check the stripped patterns here!
+  inTopContext $ addContext (st0 ^. lhsTel) $
+    forM_ withEqs recheckStrippedWithPattern
+
+  let st = over (lhsProblem . problemEqs) (++ withEqs) st0
+
+  -- doing the splits:
+  (result, block) <- unsafeInTopContext $ runWriterT $ (`runReaderT` (size cxt)) $ checkLHS f st
+  return result
+
+-- | Check that this split will generate a modality-correct internal
+-- clause when --cubical-compatible is used. This means that the type of
+-- anything which might be transported must be modality-correct. This is
+-- necessarily an approximate check. We assume that any argument which
+-- (a) comes after and (b) mentions a dotted argument will be
+-- transported, which is probably an overestimate.
+conSplitModalityCheck
+  :: Modality
+  -- ^ Modality to check at
+  -> PatternSubstitution
+  -- ^ Substitution resulting from index unification. @Γ ⊢ ρ : Δ'@,
+  -- where @Δ'@ is the context we're in, and @Γ@ is the clause telescope
+  -- before unification.
+  -> Int       -- ^ Variable x at which we split
+  -> Telescope -- ^ The telescope @Γ@ itself
+  -> Type      -- ^ Target type of the clause.
+  -> TCM ()
+conSplitModalityCheck mod rho blocking gamma target = when (any ((/= defaultModality) . getModality) gamma) $ do
+  reportSDoc "tc.lhs.top" 30 $ vcat
+    [ "LHS modality check for modality: " <+> prettyTCM mod
+    , "rho:    " <+> inTopContext (prettyTCM rho)
+    , "gamma:  " <+> inTopContext (prettyTCM gamma)
+    , "target: " <+> prettyTCM target <+> parens (pretty target)
+    , "Δ'target: " <+> prettyTCM (applyPatSubst rho target)
+    , "blocking:" <+> prettyTCM blocking
+    ]
+  case firstForced rho (length gamma) of
+    Just ix -> do
+      -- We've found a forced argument. This means that the unifier has
+      -- decided to kill a unification variable, and any of its
+      -- occurrences in the generated term will be replaced by an
+      -- occurrence of a path, and any terms whose types mention that
+      -- variable will be transported.
+      let
+        (gamma0, delta) = splitTelescopeAt (length gamma - ix) gamma
+        name = inTopContext . addContext gamma . nameOfBV
+        delta'target = applyPatSubst rho target
+      reportSDoc "tc.lhs.top" 30 $ vcat
+        [ "found forced argument!"
+        , "forced: " <+> prettyTCM ix
+        , "before: " <+> inTopContext (prettyTCM gamma0)
+        , "after:  " <+> inTopContext (addContext gamma0 (prettyTCM delta))
+        ]
+      forced <- name ix
+      forM_ (zip [ix - 1, ix - 2 ..] (telToList delta)) $ \(arg, d) -> do
+        -- Example: The first argument after the first forced variable. So
+        -- we have e.g.:
+        --   Γ = Γ₀.x.Δ
+        --   Δ' ⊢ ρ : Γ₀.x.Δ
+        --   Γ₀ ⊢ x : Type
+        -- but we need
+        --   Δ' ⊢ x : Type,
+        -- since Δ' is the context we are in. Then we have
+        --   Γ ⊢ x[wkS |Δ|] : Type
+        -- and consequently
+        --   Δ' ⊢ x[wkS |Δ|][ρ] : Type
+        let
+          rho' = composeS rho (wkS (arg + 1) idS)
+        ty' <- reduce (applyPatSubst rho' (unEl (snd (unDom d))))
+        let
+          -- It's actually rather tricky to know when, exactly, a
+          -- transport will be needed in a position that forces an
+          -- usable-at-modality check. Our current heuristic is:
+          --
+          -- The variable we're looking at has a fibrant type, with the
+          -- first forced variable free.
+          -- The variable appears free in the result type.
+          docheck = and
+            [ ix `freeIn` applySubst (wkS (arg + 1) idS) (unEl (snd (unDom d)))
+            , arg /= blocking
+            , arg `freeIn` target
+            ]
+        reportSDoc "tc.lhs.top" 30 $ vcat
+          [ "arg:        " <+> pretty arg
+          , "arg type:   " <+> prettyTCM (applySubst (wkS (arg + 1) idS) (unEl (snd (unDom d))))
+          , "check       " <+> pretty docheck
+          ]
+        argn <- name arg
+        when docheck $
+          usableAtModality (IndexedClauseArg forced argn) mod ty'
+    Nothing -> pure ()
+
+  -- ALways check the target clause type. Specifically, we check it both
+  -- in Δ' and in Γ. The check in Δ' will sometimes let slip by a
+  -- quantity violation which is masked by an indexed match (recall that
+  -- the unifier likes to replace @0-variables for @ω-variables). A
+  -- concrete case where this happens is #5468. Check in Δ' first since
+  -- that will have the forced variable names.
+  usableAtModality IndexedClause mod (unEl (applyPatSubst rho target))
+  inTopContext $ addContext gamma $ usableAtModality IndexedClause mod (unEl target)
+  where
+    -- Find the first dotted pattern in the substitution. "First" =
+    -- "earliest bound", so counts down from the length of the
+    -- telescope.
+    firstForced :: PatternSubstitution -> Int -> Maybe Int
+    firstForced pat level
+      | level >= 0 = case lookupS pat level of
+        DotP{} -> Just level
+        _ -> firstForced pat (level - 1)
+      | otherwise = Nothing
+
+-- | Determine which splits should be tried.
+splitStrategy :: [ProblemEq] -> [ProblemEq]
+splitStrategy = filter shouldSplit
+  where
+    shouldSplit :: ProblemEq -> Bool
+    shouldSplit problem@(ProblemEq p v a) = case p of
+      A.LitP{}    -> True
+      A.RecP{}    -> True
+      A.ConP{}    -> True
+      A.EqualP{}  -> True
+
+      A.VarP{}    -> False
+      A.WildP{}   -> False
+      A.DotP{}    -> False
+      A.AbsurdP{} -> False
+
+      A.AsP _ _ p  -> shouldSplit $ problem { problemInPat = p }
+      A.AnnP _ _ p -> shouldSplit $ problem { problemInPat = p }
+
+      A.ProjP{}       -> __IMPOSSIBLE__
+      A.DefP{}        -> __IMPOSSIBLE__
+      A.PatternSynP{} -> __IMPOSSIBLE__
+      A.WithP{}       -> __IMPOSSIBLE__
+
+
+-- | The loop (tail-recursive): split at a variable in the problem until problem is solved
+checkLHS
+  :: forall tcm a. (MonadTCM tcm, PureTCM tcm, MonadWriter Blocked_ tcm, MonadError TCErr tcm, MonadTrace tcm, MonadReader Nat tcm)
+  => Maybe QName      -- ^ The name of the definition we are checking.
+  -> LHSState a       -- ^ The current state.
+  -> tcm a
+checkLHS mf = updateModality checkLHS_ where
+    -- If the target type is irrelevant or in Prop,
+    -- we need to check the lhs in irr. cxt. (see Issue 939).
+ updateModality cont st@(LHSState tel ip problem target psplit _) = do
+      let m = getModality target
+      applyModalityToContext m $ do
+        cont $ over (lhsTel . listTel)
+                 (map $ inverseApplyModalityButNotQuantity m) st
+        -- Andreas, 2018-10-23, issue #3309
+        -- the modalities in the clause telescope also need updating.
+
+ checkLHS_ st@(LHSState tel ip problem target psplit ixsplit) = do
+  reportSDoc "tc.lhs" 40 $ "tel is" <+> prettyTCM tel
+  reportSDoc "tc.lhs" 40 $ "ip is" <+> pretty ip
+  reportSDoc "tc.lhs" 40 $ "target is" <+> addContext tel (prettyTCM target)
+  if isSolvedProblem problem then
+    liftTCM $ (problem ^. problemCont) st
+  else do
+
+    reportSDoc "tc.lhs.top" 30 $ vcat
+      [ "LHS state: " , nest 2 (prettyTCM st) ]
+
+    unlessM (optPatternMatching <$> getsTC getPragmaOptions) $
+      unless (problemAllVariables problem) $
+        typeError $ GenericError $ "Pattern matching is disabled"
+
+    let splitsToTry = splitStrategy $ problem ^. problemEqs
+
+    foldr trySplit trySplitRest splitsToTry >>= \case
+      Right st' -> checkLHS mf st'
+      -- If no split works, give error from first split.
+      -- This is conservative, but might not be the best behavior.
+      -- It might be better to print all the errors instead.
+      Left (err:_) -> throwError err
+      Left []      -> __IMPOSSIBLE__
+
+  where
+
+    trySplit :: ProblemEq
+             -> tcm (Either [TCErr] (LHSState a))
+             -> tcm (Either [TCErr] (LHSState a))
+    trySplit eq tryNextSplit = runExceptT (splitArg eq) >>= \case
+      Right st' -> return $ Right st'
+      Left err  -> left (err:) <$> tryNextSplit
+
+    -- If there are any remaining user patterns, try to split on them
+    trySplitRest :: tcm (Either [TCErr] (LHSState a))
+    trySplitRest = case problem ^. problemRestPats of
+      []    -> return $ Left []
+      (p:_) -> left singleton <$> runExceptT (splitRest p)
+
+    splitArg :: ProblemEq -> ExceptT TCErr tcm (LHSState a)
+    -- Split on constructor/literal pattern
+    splitArg (ProblemEq p v Dom{unDom = a}) = traceCall (CheckPattern p tel a) $ do
+
+      reportSDoc "tc.lhs.split" 30 $ sep
+        [ "split looking at pattern"
+        , nest 2 $ "p =" <+> prettyA p
+        ]
+
+      -- in order to split, v must be a variable.
+      i <- liftTCM $ addContext tel $ ifJustM (isEtaVar v a) return $
+             softTypeError $ SplitOnNonVariable v a
+
+      let pos = size tel - (i + 1)
+          (delta1, tel'@(ExtendTel dom adelta2)) = splitTelescopeAt pos tel -- TODO:: tel' defined but not used
+
+      p <- liftTCM $ expandLitPattern p
+      let splitOnPat = \case
+            (A.LitP _ l)      -> splitLit delta1 dom adelta2 l
+            p@A.RecP{}        -> splitCon delta1 dom adelta2 p Nothing
+            p@(A.ConP _ c ps) -> splitCon delta1 dom adelta2 p $ Just c
+            p@(A.EqualP _ ts) -> splitPartial delta1 dom adelta2 ts
+            A.AsP _ _ p       -> splitOnPat p
+            A.AnnP _ _ p      -> splitOnPat p
+
+            A.VarP{}        -> __IMPOSSIBLE__
+            A.WildP{}       -> __IMPOSSIBLE__
+            A.DotP{}        -> __IMPOSSIBLE__
+            A.AbsurdP{}     -> __IMPOSSIBLE__
+            A.ProjP{}       -> __IMPOSSIBLE__
+            A.DefP{}        -> __IMPOSSIBLE__
+            A.PatternSynP{} -> __IMPOSSIBLE__
+            A.WithP{}       -> __IMPOSSIBLE__
+      splitOnPat p
+
+
+    splitRest :: NamedArg A.Pattern -> ExceptT TCErr tcm (LHSState a)
+    splitRest p = setCurrentRange p $ do
+      reportSDoc "tc.lhs.split" 20 $ sep
+        [ "splitting problem rest"
+        , nest 2 $ "projection pattern =" <+> prettyA p
+        , nest 2 $ "eliminates type    =" <+> prettyTCM target
+        ]
+      reportSDoc "tc.lhs.split" 80 $ sep
+        [ nest 2 $ text $ "projection pattern (raw) = " ++ show p
+        ]
+
+      -- @p@ should be a projection pattern projection from @target@
+      (orig, ambProjName) <- ifJust (A.isProjP p) return $ addContext tel $ do
+        block <- isBlocked target
+        softTypeError $ CannotEliminateWithPattern block p (unArg target)
+
+      (projName, comatchingAllowed, recName, projType, ai) <- suspendErrors $ do
+        -- Andreas, 2018-10-18, issue #3289: postfix projections do not have hiding
+        -- information for their principal argument; we do not parse @{r}.p@ and the like.
+        let h = if orig == ProjPostfix then Nothing else Just $ getHiding p
+        addContext tel $ disambiguateProjection h ambProjName target
+
+      unless comatchingAllowed $ do
+        hardTypeError $ ComatchingDisabledForRecord recName
+
+      -- Compute the new rest type by applying the projection type to 'self'.
+      -- Note: we cannot be in a let binding.
+      f <- ifJust mf return $ hardTypeError $
+             GenericError "Cannot use copatterns in a let binding"
+      let self = Def f $ patternsToElims ip
+      target' <- traverse (`piApplyM` self) projType
+
+      -- Compute the new state
+      let projP    = applyWhen (orig == ProjPostfix) (setHiding NotHidden) $
+                       Arg ai $ Named Nothing (ProjP orig projName)
+          ip'      = ip ++ [projP]
+          -- drop the projection pattern (already splitted)
+          problem' = over problemRestPats (drop 1) problem
+      liftTCM $ updateLHSState (LHSState tel ip' problem' target' psplit ixsplit)
+
+
+    -- Split a Partial.
+    --
+    -- Example for splitPartial:
+    -- @
+    --   g : ∀ i j → Partial (i ∨ j) A
+    --   g i j (i = 1) = a i j
+    --   g i j (j = 1) = b i j
+    -- @
+    -- leads to, in the first clause:
+    -- @
+    --   dom   = IsOne (i ∨ j)
+    --   ts    = [(i, 1)]
+    --   phi   = i
+    --   sigma = [1/i]
+    -- @
+    -- Final clauses:
+    -- @
+    --   g : ∀ i j → Partial (i ∨ j) A
+    --   g 1? j  .itIsOne = a 1 j
+    --   g i  1? .itIsOne = b i 1
+    -- @
+    -- Herein, ? indicates a 'conPFallThrough' pattern.
+    --
+    -- Example for splitPartial:
+    -- @
+    --   h : ∀ i j → Partial (i & ¬ j) A
+    --   h i j (i = 1) (j = 0)
+    --   -- ALT: h i j (i & ¬ j = 1)
+    -- @
+    -- gives
+    -- @
+    --   dom = IsOne (i & ¬ j)
+    --   ts  = [(i,1), (j,0)]  -- ALT: [(i & ¬ j, 1)]
+    --   phi = i & ¬ j
+    --   sigma = [1/i,0/j]
+    -- @
+    --
+    -- Example for splitPartial:
+    -- @
+    --   g : ∀ i j → Partial (i ∨ j) A
+    --   g i j (i ∨ j = 1) = a i j
+    -- @
+    -- leads to, in the first clause:
+    -- @
+    --   dom   = IsOne (i ∨ j)
+    --   ts    = [(i ∨ j, 1)]
+    --   phi   = i ∨ j
+    --   sigma = fails because several substitutions [[1/i],[1/j]] correspond to phi
+    -- @
+
+    splitPartial :: Telescope     -- The types of arguments before the one we split on
+                 -> Dom Type      -- The type of the argument we split on
+                 -> Abs Telescope -- The types of arguments after the one we split on
+                 -> [(A.Expr, A.Expr)] -- [(φ₁ = b1),..,(φn = bn)]
+                 -> ExceptT TCErr tcm (LHSState a)
+    splitPartial delta1 dom adelta2 ts = do
+
+      unless (domIsFinite dom) $ liftTCM $ addContext delta1 $
+        softTypeError $ SplitOnPartial dom
+
+      tInterval <- liftTCM $ primIntervalType
+
+      names <- liftTCM $ addContext tel $ do
+        LeftoverPatterns{patternVariables = vars} <- getLeftoverPatterns $ problem ^. problemEqs
+        return $ take (size delta1) $ fst $ getUserVariableNames tel vars
+
+      -- Problem: The context does not match the checkpoints in checkLHS,
+      --          however we still need a proper checkpoint substitution
+      --          for checkExpr below.
+      --
+      -- Solution: partial splits are not allowed when there are
+      --           constructor patterns (checked in checkDef), so
+      --           newContext is an extension of the definition
+      --           context.
+      --
+      -- i.e.: Given
+      --
+      --             Γ = context where def is checked, also last checkpoint.
+      --
+      --       Then
+      --
+      --             newContext = Γ Ξ
+      --             cpSub = raiseS |Ξ|
+      --
+      lhsCxtSize <- ask -- size of the context before checkLHS call.
+      reportSDoc "tc.lhs.split.partial" 10 $ "lhsCxtSize =" <+> prettyTCM lhsCxtSize
+
+      newContext <- liftTCM $ computeLHSContext names delta1
+      reportSDoc "tc.lhs.split.partial" 10 $ "newContext =" <+> prettyTCM newContext
+
+      let cpSub = raiseS $ size newContext - lhsCxtSize
+
+      (gamma,sigma) <- liftTCM $ updateContext cpSub (const newContext) $ do
+         ts <- forM ts $ \ (t,u) -> do
+                 reportSDoc "tc.lhs.split.partial" 10 $ "currentCxt =" <+> (prettyTCM =<< getContext)
+                 reportSDoc "tc.lhs.split.partial" 10 $ text "t, u (Expr) =" <+> prettyTCM (t,u)
+                 t <- checkExpr t tInterval
+                 u <- checkExpr u tInterval
+                 reportSDoc "tc.lhs.split.partial" 10 $ text "t, u        =" <+> pretty (t, u)
+                 u <- intervalView =<< reduce u
+                 case u of
+                   IZero -> primINeg <@> pure t
+                   IOne  -> return t
+                   _     -> typeError $ GenericError $ "Only 0 or 1 allowed on the rhs of face"
+         -- Example: ts = (i=0) (j=1) will result in phi = ¬ i & j
+         phi <- case ts of
+                   [] -> do
+                     a <- reduce (unEl $ unDom dom)
+                     -- builtinIsOne is defined, since this is a precondition for having Partial
+                     isone <- fromMaybe __IMPOSSIBLE__ <$>  -- newline because of CPP
+                       getBuiltinName' builtinIsOne
+                     case a of
+                       Def q [Apply phi] | q == isone -> return (unArg phi)
+                       _           -> typeError $ BuiltinMustBeIsOne a
+
+                   _  -> foldl (\ x y -> primIMin <@> x <@> y) primIOne (map pure ts)
+         reportSDoc "tc.lhs.split.partial" 10 $ text "phi           =" <+> prettyTCM phi
+         reportSDoc "tc.lhs.split.partial" 30 $ text "phi           =" <+> pretty phi
+         phi <- reduce phi
+         reportSDoc "tc.lhs.split.partial" 10 $ text "phi (reduced) =" <+> prettyTCM phi
+         refined <- forallFaceMaps phi (\ bs m t -> typeError $ GenericError $ "face blocked on meta")
+                            (\_ sigma -> (,sigma) <$> getContextTelescope)
+         case refined of
+           [(gamma,sigma)] -> return (gamma,sigma)
+           []              -> typeError $ GenericError $ "The face constraint is unsatisfiable."
+           _               -> typeError $ GenericError $ "Cannot have disjunctions in a face constraint."
+      itisone <- liftTCM primItIsOne
+      -- substitute the literal in p1 and dpi
+      reportSDoc "tc.lhs.faces" 60 $ text $ show sigma
+
+      let oix = size adelta2 -- de brujin index of IsOne
+          o_n = fromMaybe __IMPOSSIBLE__ $
+            findIndex (\ x -> case namedThing (unArg x) of
+                                   VarP _ x -> dbPatVarIndex x == oix
+                                   _        -> False) ip
+          delta2' = absApp adelta2 itisone
+          delta2 = applySubst sigma delta2'
+          mkConP (Con c _ [])
+             = ConP c (noConPatternInfo { conPType = Just (Arg defaultArgInfo tInterval)
+                                              , conPFallThrough = True })
+                          []
+          mkConP (Var i []) = VarP defaultPatternInfo (DBPatVar "x" i)
+          mkConP _          = __IMPOSSIBLE__
+          rho0 = fmap mkConP sigma
+
+          rho    = liftS (size delta2) $ consS (DotP defaultPatternInfo itisone) rho0
+
+          delta'   = abstract gamma delta2
+          eqs'     = applyPatSubst rho $ problem ^. problemEqs
+          ip'      = applySubst rho ip
+          target'  = applyPatSubst rho target
+
+      -- Compute the new state
+      let problem' = set problemEqs eqs' problem
+      reportSDoc "tc.lhs.split.partial" 60 $ text (show problem')
+      liftTCM $ updateLHSState (LHSState delta' ip' problem' target' (psplit ++ [Just o_n]) ixsplit)
+
+
+    splitLit :: Telescope      -- The types of arguments before the one we split on
+             -> Dom Type       -- The type of the literal we split on
+             -> Abs Telescope  -- The types of arguments after the one we split on
+             -> Literal        -- The literal written by the user
+             -> ExceptT TCErr tcm (LHSState a)
+    splitLit delta1 dom@Dom{domInfo = info, unDom = a} adelta2 lit = do
+      let delta2 = absApp adelta2 (Lit lit)
+          delta' = abstract delta1 delta2
+          rho    = singletonS (size delta2) (litP lit)
+          -- Andreas, 2015-06-13 Literals are closed, so no need to raise them!
+          -- rho    = liftS (size delta2) $ singletonS 0 (Lit lit)
+          -- rho    = [ var i | i <- [0..size delta2 - 1] ]
+          --       ++ [ raise (size delta2) $ Lit lit ]
+          --       ++ [ var i | i <- [size delta2 ..] ]
+          eqs'     = applyPatSubst rho $ problem ^. problemEqs
+          ip'      = applySubst rho ip
+          target'  = applyPatSubst rho target
+
+      -- Andreas, 2010-09-07 cannot split on irrelevant args
+      unless (usableRelevance info) $
+        addContext delta1 $ softTypeError $ SplitOnIrrelevant dom
+
+      -- Andreas, 2018-10-17, we can however split on erased things
+      -- if there is a single constructor (checked in Coverage).
+      --
+      -- Thus, no checking of (usableQuantity info) here.
+
+      unlessM (splittableCohesion info) $
+        addContext delta1 $ softTypeError $ SplitOnUnusableCohesion dom
+
+      -- check that a is indeed the type of lit (otherwise fail softly)
+      -- if not, fail softly since it could be instantiated by a later split.
+      suspendErrors $ equalType a =<< litType lit
+
+      -- Compute the new state
+      let problem' = set problemEqs eqs' problem
+      liftTCM $ updateLHSState (LHSState delta' ip' problem' target' psplit ixsplit)
+
+
+    splitCon :: Telescope      -- The types of arguments before the one we split on
+             -> Dom Type       -- The type of the constructor we split on
+             -> Abs Telescope  -- The types of arguments after the one we split on
+             -> A.Pattern      -- The pattern written by the user
+             -> Maybe AmbiguousQName  -- @Just c@ for a (possibly ambiguous) constructor @c@, or
+                                      -- @Nothing@ for a record pattern
+             -> ExceptT TCErr tcm (LHSState a)
+    splitCon delta1 dom@Dom{domInfo = info, unDom = a} adelta2 focusPat ambC = do
+      let delta2 = absBody adelta2
+
+      reportSDoc "tc.lhs.split" 10 $ vcat
+        [ "checking lhs"
+        , nest 2 $ "tel =" <+> prettyTCM tel
+        , nest 2 $ "rel =" <+> text (show $ getRelevance info)
+        , nest 2 $ "mod =" <+> text (show $ getModality  info)
+        ]
+
+      reportSDoc "tc.lhs.split" 15 $ vcat
+        [ "split problem"
+        , nest 2 $ vcat
+          [ "delta1 = " <+> prettyTCM delta1
+          , "a      = " <+> addContext delta1 (prettyTCM a)
+          , "delta2 = " <+> addContext delta1
+                              (addContext ("x" :: String, dom) (prettyTCM delta2))
+          ]
+        ]
+
+      -- We cannot split on (shape-)irrelevant arguments.
+      reportSLn "tc.lhs.split" 30 $ "split ConP: relevance is " ++ show (getRelevance info)
+      unless (usableRelevance info) $ addContext delta1 $
+        softTypeError $ SplitOnIrrelevant dom
+
+      -- Andreas, 2018-10-17, we can however split on erased things
+      -- if there is a single constructor (checked in Coverage).
+      --
+      -- Thus, no checking of (usableQuantity info) here.
+
+      unlessM (splittableCohesion info) $
+        addContext delta1 $ softTypeError $ SplitOnUnusableCohesion dom
+
+      -- Should we attempt to compute a left inverse for this clause? When
+      -- --cubical-compatible --flat-split is given, we don't generate a
+      -- left inverse (at all). This means that, when the coverage checker
+      -- gets to the clause this was in, it won't generate a (malformed!)
+      -- transpX clause for @♭ matching.
+      -- TODO(Amy): properly support transpX when @♭ stuff is in the
+      -- context.
+      let genTrx = boolToMaybe ((getCohesion info == Flat)) SplitOnFlat
+
+      -- We should be at a data/record type
+      (dr, d, pars, ixs) <- addContext delta1 $ isDataOrRecordType a
+      let isRec = case dr of
+            IsData{}   -> False
+            IsRecord{} -> True
+
+      checkMatchingAllowed d dr  -- No splitting on coinductive constructors.
+      addContext delta1 $ checkSortOfSplitVar dr a delta2 (Just target)
+
+      -- Jesper, 2019-09-13: if the data type we split on is a strict
+      -- set, we locally enable --with-K during unification.
+      withKIfStrict <- reduce (getSort a) <&> \ dsort ->
+        applyWhen (isStrictDataSort dsort) $ locallyTC eSplitOnStrict $ const True
+
+      -- The constructor should construct an element of this datatype
+      (c :: ConHead, b :: Type) <- liftTCM $ addContext delta1 $ case ambC of
+        Just ambC -> disambiguateConstructor ambC d pars
+        Nothing   -> getRecordConstructor d pars a
+
+      -- Don't split on lazy (non-eta) constructor
+      case focusPat of
+        A.ConP cpi _ _ | conPatLazy cpi == ConPatLazy ->
+          unlessM (isEtaRecord d) $ softTypeError $ ForcedConstructorNotInstantiated focusPat
+        _ -> return ()
+
+      -- The type of the constructor will end in an application of the datatype
+      (TelV gamma (El _ ctarget), boundary) <- liftTCM $ telViewPathBoundaryP b
+      let Def d' es' = ctarget
+          cixs = drop (size pars) $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es'
+
+      -- Δ₁Γ ⊢ boundary
+      reportSDoc "tc.lhs.split.con" 50 $ text "  boundary = " <+> prettyTCM boundary
+
+      unless (d == d') {-'-} __IMPOSSIBLE__
+
+      -- Get names for the constructor arguments from the user patterns
+      gamma <- liftTCM $ case focusPat of
+        A.ConP _ _ ps -> do
+          ps <- insertImplicitPatterns ExpandLast ps gamma
+          return $ useNamesFromPattern ps gamma
+        A.RecP _ fs -> do
+          axs <- map argFromDom . recordFieldNames . theDef <$> getConstInfo d
+          ps <- insertMissingFieldsFail d (const $ A.WildP patNoRange) fs axs
+          ps <- insertImplicitPatterns ExpandLast ps gamma
+          return $ useNamesFromPattern ps gamma
+        _ -> __IMPOSSIBLE__
+
+      -- Andreas 2010-09-07  propagate relevance info to new vars
+      -- Andreas 2018-10-17  propagate modality
+      let updMod = composeModality (getModality info)
+      gamma <- return $ mapModality updMod <$> gamma
+
+      -- Get the type of the datatype.
+      da <- (`piApply` pars) . defType <$> getConstInfo d
+      reportSDoc "tc.lhs.split" 30 $ "  da = " <+> prettyTCM da
+
+      reportSDoc "tc.lhs.top" 15 $ addContext delta1 $
+        sep [ "preparing to unify"
+            , nest 2 $ vcat
+              [ "c      =" <+> prettyTCM c <+> ":" <+> prettyTCM b
+              , "d      =" <+> prettyTCM (Def d (map Apply pars)) <+> ":" <+> prettyTCM da
+              , "isRec  =" <+> (text . show) isRec
+              , "gamma  =" <+> prettyTCM gamma
+              , "pars   =" <+> brackets (fsep $ punctuate comma $ map prettyTCM pars)
+              , "ixs    =" <+> brackets (fsep $ punctuate comma $ map prettyTCM ixs)
+              , "cixs   =" <+> addContext gamma (brackets (fsep $ punctuate comma $ map prettyTCM cixs))
+              ]
+            ]
+                 -- We ignore forcing for make-case
+      cforced <- ifM (viewTC eMakeCase) (return []) $
+                 {-else-} defForced <$> getConstInfo (conName c)
+
+      let delta1Gamma = delta1 `abstract` gamma
+          da'  = raise (size gamma) da
+          ixs' = raise (size gamma) ixs
+          -- Variables in Δ₁ are not forced, since the unifier takes care to not introduce forced
+          -- variables.
+          forced = replicate (size delta1) NotForced ++ cforced
+
+      -- All variables are flexible.
+      let flex = allFlexVars forced $ delta1Gamma
+
+      -- Unify constructor target and given type (in Δ₁Γ)
+      -- Given: Δ₁  ⊢ D pars : Φ → Setᵢ
+      --        Δ₁  ⊢ c      : Γ → D pars cixs
+      --        Δ₁  ⊢ ixs    : Φ
+      --        Δ₁Γ ⊢ cixs   : Φ
+      -- unification of ixs and cixs in context Δ₁Γ gives us a telescope Δ₁'
+      -- and a substitution ρ₀ such that
+      --        Δ₁' ⊢ ρ₀ : Δ₁Γ
+      --        Δ₁' ⊢ (ixs)ρ₀ ≡ (cixs)ρ₀ : Φρ₀
+      -- We can split ρ₀ into two parts ρ₁ and ρ₂, giving
+      --        Δ₁' ⊢ ρ₁ : Δ₁
+      --        Δ₁' ⊢ ρ₂ : Γρ₁
+      -- Application of the constructor c gives
+      --        Δ₁' ⊢ (c Γ)(ρ₀) : (D pars cixs)(ρ₁;ρ₂)
+      -- We have
+      --        cixs(ρ₁;ρ₂)
+      --         ≡ cixs(ρ₀)   (since ρ₀=ρ₁;ρ₂)
+      --         ≡ ixs(ρ₀)    (by unification)
+      --         ≡ ixs(ρ₁)    (since ixs doesn't actually depend on Γ)
+      -- so     Δ₁' ⊢ (c Γ)(ρ₀) : (D pars ixs)ρ₁
+      -- Putting this together with ρ₁ gives ρ₃ = ρ₁;c ρ₂
+      --        Δ₁' ⊢ ρ₁;(c Γ)(ρ₀) : Δ₁(x : D vs ws)
+      -- and lifting over Δ₂ gives the final substitution ρ = ρ₃;Δ₂
+      -- from Δ' = Δ₁';Δ₂ρ₃
+      --        Δ' ⊢ ρ : Δ₁(x : D vs ws)Δ₂
+
+      -- Andrea 2019-07-17 propagate the Cohesion to the equation telescope
+      -- TODO: should we propagate the modality in general?
+      -- See also Coverage checking.
+      da' <- addContext delta1Gamma $ do
+             let updCoh = composeCohesion (getCohesion info)
+             TelV tel dt <- telView da'
+             return $ abstract (mapCohesion updCoh <$> tel) a
+
+      let stuck b errs = softTypeError $ SplitError $
+            UnificationStuck b (conName c) (delta1 `abstract` gamma) cixs ixs' errs
+
+      liftTCM (withKIfStrict $ unifyIndices genTrx delta1Gamma flex da' cixs ixs') >>= \case
+
+        -- Mismatch.  Report and abort.
+        NoUnify neg -> hardTypeError $ ImpossibleConstructor (conName c) neg
+
+        UnifyBlocked block -> stuck (Just block) []
+
+        -- Unclear situation.  Try next split.
+        UnifyStuck errs -> stuck Nothing errs
+
+        -- Success.
+        Unifies (delta1',rho0,es) -> do
+
+          reportSDoc "tc.lhs.top" 15 $ "unification successful"
+          reportSDoc "tc.lhs.top" 20 $ nest 2 $ vcat
+            [ "delta1' =" <+> prettyTCM delta1'
+            , "rho0    =" <+> addContext delta1' (prettyTCM rho0)
+            , "es      =" <+> addContext delta1' (prettyTCM $ (fmap . fmap . fmap) patternToTerm es)
+            ]
+
+          -- split substitution into part for Δ₁ and part for Γ
+          let (rho1,rho2) = splitS (size gamma) rho0
+
+          reportSDoc "tc.lhs.top" 20 $ addContext delta1' $ nest 2 $ vcat
+            [ "rho1    =" <+> prettyTCM rho1
+            , "rho2    =" <+> prettyTCM rho2
+            ]
+
+          -- Andreas, 2010-09-09, save the type.
+          -- It is relative to Δ₁, but it should be relative to Δ₁'
+          let a' = applyPatSubst rho1 a
+
+          -- Also remember if we are a record pattern.
+          let cpi = ConPatternInfo { conPInfo   = PatternInfo PatOCon []
+                                   , conPRecord = isRec
+                                   , conPFallThrough = False
+                                   , conPType   = Just $ Arg info a'
+                                   , conPLazy   = False } -- Don't mark eta-record matches as lazy (#4254)
+
+          -- compute final context and substitution
+          let crho    = ConP c cpi $ applySubst rho0 $ (telePatterns gamma boundary)
+              rho3    = consS crho rho1
+              delta2' = applyPatSubst rho3 delta2
+              delta'  = delta1' `abstract` delta2'
+              rho     = liftS (size delta2) rho3
+
+          reportSDoc "tc.lhs.top" 20 $ addContext delta1' $ nest 2 $ vcat
+            [ "crho    =" <+> prettyTCM crho
+            , "rho3    =" <+> prettyTCM rho3
+            , "delta2' =" <+> prettyTCM delta2'
+            ]
+          reportSDoc "tc.lhs.top" 70 $ addContext delta1' $ nest 2 $ vcat
+            [ "crho    =" <+> pretty crho
+            , "rho3    =" <+> pretty rho3
+            , "delta2' =" <+> pretty delta2'
+            ]
+
+          reportSDoc "tc.lhs.top" 15 $ nest 2 $ vcat
+            [ "delta'  =" <+> prettyTCM delta'
+            , "rho     =" <+> addContext delta' (prettyTCM rho)
+            ]
+
+          -- Compute the new out patterns and target type.
+          let ip'      = applySubst rho ip
+              target'  = applyPatSubst rho target
+
+          -- Update the problem equations
+          let eqs' = applyPatSubst rho $ problem ^. problemEqs
+              problem' = set problemEqs eqs' problem
+
+          -- The result type's quantity is set to 0 for erased
+          -- constructors, but not if the match is made in an erased
+          -- position, or if the original constructor definition is
+          -- not erased.
+          cq <- getQuantity <$> getOriginalConstInfo (conName c)
+          let target'' = mapQuantity updResMod target'
+                where
+                  erased = case getQuantity info of
+                    Quantity0{} -> True
+                    Quantity1{} -> __IMPOSSIBLE__
+                    Quantityω{} -> False
+                  -- either sets to Quantity0 or is the identity.
+                  updResMod q =
+                    case cq of
+                     _ | erased  -> q
+                     Quantity0{} -> composeQuantity cq q
+                                 -- zero-out, preserves origin
+                     Quantity1{} -> __IMPOSSIBLE__
+                     Quantityω{} -> q
+
+          liftTCM $ addContext delta' $ do
+            withoutK <- optWithoutK <$> pragmaOptions
+            cubical <- optCubicalCompatible <$> pragmaOptions
+            mod <- currentModality
+            when ((withoutK || cubical) && not (null ixs)) $
+              conSplitModalityCheck mod rho (length delta2) tel (unArg target)
+
+          -- if rest type reduces,
+          -- extend the split problem by previously not considered patterns
+          st' <- liftTCM $ updateLHSState $ LHSState delta' ip' problem' target'' psplit (ixsplit || not (null ixs))
+
+          reportSDoc "tc.lhs.top" 12 $ sep
+            [ "new problem from rest"
+            , nest 2 $ vcat
+              [ "delta'  =" <+> prettyTCM (st' ^. lhsTel)
+              , "eqs'    =" <+> addContext (st' ^. lhsTel) (prettyTCM $ st' ^. (lhsProblem . problemEqs))
+              , "ip'     =" <+> addContext (st' ^. lhsTel) (pretty $ st' ^. lhsOutPat)
+              ]
+            ]
+          return st'
+
+
+-- | Ensures that we are not performing pattern matching on coinductive constructors.
+
+checkMatchingAllowed :: (MonadTCError m)
+  => QName         -- ^ The name of the data or record type the constructor belongs to.
+  -> DataOrRecord  -- ^ Information about data or (co)inductive (no-)eta-equality record.
+  -> m ()
+checkMatchingAllowed d = \case
+  IsRecord InductionAndEta { recordInduction=ind, recordEtaEquality=eta }
+    | Just CoInductive <- ind -> typeError $
+        GenericError "Pattern matching on coinductive types is not allowed"
+    | not $ patternMatchingAllowed eta -> typeError $ SplitOnNonEtaRecord d
+    | otherwise -> return ()
+  IsData -> return ()
+
+-- | When working with a monad @m@ implementing @MonadTCM@ and @MonadError TCErr@,
+--   @suspendErrors f@ performs the TCM action @f@ but catches any errors and throws
+--   them in the monad @m@ instead.
+suspendErrors :: (MonadTCM m, MonadError TCErr m) => TCM a -> m a
+suspendErrors f = do
+  ok <- liftTCM $ (Right <$> f) `catchError` (return . Left)
+  either throwError return ok
+
+-- | A more direct implementation of the specification
+--   @softTypeError err == suspendErrors (typeError err)@
+softTypeError :: (HasCallStack, ReadTCState m, MonadError TCErr m, MonadTCEnv m) => TypeError -> m a
+softTypeError err = withCallerCallStack $ \loc ->
+  throwError =<< typeError' loc err
+
+-- | A convenient alias for @liftTCM . typeError@. Throws the error directly
+--   in the TCM even if there is a surrounding monad also implementing
+--   @MonadError TCErr@.
+hardTypeError :: (HasCallStack, MonadTCM m) => TypeError -> m a
+hardTypeError = withCallerCallStack $ \loc -> liftTCM . typeError' loc
+
+type DataOrRecord = DataOrRecord' InductionAndEta
+
+-- | Check if the type is a data or record type and return its name,
+--   definition, parameters, and indices. Fails softly if the type could become
+--   a data/record type by instantiating a variable/metavariable, or fail hard
+--   otherwise.
+isDataOrRecordType
+  :: (MonadTCM m, PureTCM m)
+  => Type
+  -> ExceptT TCErr m (DataOrRecord, QName, Args, Args)
+       -- ^ The 'Args' are parameters and indices.
+
+isDataOrRecordType a0 = ifBlocked a0 blocked $ \case
+  ReallyNotBlocked -> \ a -> case unEl a of
+
+    -- Subcase: split type is a Def.
+    Def d es -> liftTCM (theDef <$> getConstInfo d) >>= \case
+
+      Datatype{dataPars = np} -> do
+
+        whenM (isInterval a) $ hardTypeError =<< notData
+
+        let (pars, ixs) = splitAt np $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+        return (IsData, d, pars, ixs)
+
+      Record{ recInduction, recEtaEquality' } -> do
+        let pars = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+        return (IsRecord InductionAndEta {recordInduction=recInduction, recordEtaEquality=recEtaEquality' }, d, pars, [])
+
+      -- Issue #2253: the data type could be abstract.
+      AbstractDefn{} -> hardTypeError $ SplitOnAbstract d
+
+      -- the type could be an axiom
+      Axiom{} -> hardTypeError =<< notData
+
+      -- Can't match before we have the definition
+      DataOrRecSig{} -> hardTypeError $ SplitOnUnchecked d
+
+      -- Issue #2997: the type could be a Def that does not reduce for some reason
+      -- (abstract, failed termination checking, NON_TERMINATING, ...)
+      Function{}    -> hardTypeError =<< notData
+
+      Constructor{} -> __IMPOSSIBLE__
+
+      -- Issue #3620: Some primitives are types too.
+      -- Not data though, at least currently 11/03/2018.
+      Primitive{}   -> hardTypeError =<< notData
+
+      PrimitiveSort{} -> hardTypeError =<< notData
+
+      GeneralizableVar{} -> __IMPOSSIBLE__
+
+    -- variable: fail softly
+    Var{}      -> softTypeError =<< notData
+    MetaV{}    -> __IMPOSSIBLE__  -- That is handled in @blocked@.
+
+    -- pi or sort: fail hard
+    Pi{}       -> hardTypeError =<< notData
+    Sort{}     -> hardTypeError =<< notData
+
+    Lam{}      -> __IMPOSSIBLE__
+    Lit{}      -> __IMPOSSIBLE__
+    Con{}      -> __IMPOSSIBLE__
+    Level{}    -> __IMPOSSIBLE__
+    DontCare{} -> __IMPOSSIBLE__
+    Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+  -- neutral type: fail softly
+  StuckOn{}     -> \ _a -> softTypeError =<< notData
+  AbsurdMatch{} -> \ _a -> softTypeError =<< notData
+
+  -- missing clauses: fail hard
+  -- TODO: postpone checking of the whole clause until later?
+  MissingClauses{} -> \ _a -> hardTypeError =<< notData
+
+  -- underapplied type: should not happen
+  Underapplied{} -> __IMPOSSIBLE__
+
+  where
+  notData      = liftTCM $ SplitError . NotADatatype <$> buildClosure a0
+  blocked b _a = softTypeError =<< do liftTCM $ SplitError . BlockedType b <$> buildClosure a0
+
+-- | Get the constructor of the given record type together with its type.
+--   Throws an error if the type is not a record type.
+getRecordConstructor
+  :: QName  -- ^ Name @d@ of the record type
+  -> Args   -- ^ Parameters @pars@ of the record type
+  -> Type   -- ^ The record type @Def d pars@ (for error reporting)
+  -> TCM (ConHead, Type)
+getRecordConstructor d pars a = do
+  con <- (theDef <$> getConstInfo d) >>= \case
+    Record{recConHead = con} -> return $ killRange con
+    _ -> typeError $ ShouldBeRecordType a
+  b <- (`piApply` pars) . defType <$> getConstInfo (conName con)
+  return (con, b)
+
+
+-- | Disambiguate a projection based on the record type it is supposed to be
+--   projecting from. Returns the unambiguous projection name and its type.
+--   Throws an error if the type is not a record type.
+disambiguateProjection
+  :: Maybe Hiding   -- ^ Hiding info of the projection's principal argument.
+                    --   @Nothing@ if 'Postfix' projection.
+  -> AmbiguousQName -- ^ Name of the projection to be disambiguated.
+  -> Arg Type       -- ^ Record type we are projecting from.
+  -> TCM (QName, Bool, QName, Arg Type, ArgInfo)
+       -- ^ @Bool@ signifies whether copattern matching is allowed at
+       --   the inferred record type.
+disambiguateProjection h ambD@(AmbQ ds) b = do
+  -- If the target is not a record type, that's an error.
+  -- It could be a meta, but since we cannot postpone lhs checking, we crash here.
+  caseMaybeM (liftTCM $ isRecordType $ unArg b) notRecord $ \(r, vs, def) -> case def of
+    Record{ recFields = fs, recInduction, recEtaEquality' = eta } -> do
+      reportSDoc "tc.lhs.split" 20 $ sep
+        [ text $ "we are of record type r  = " ++ prettyShow r
+        , text   "applied to parameters vs = " <+> prettyTCM vs
+        , text $ "and have fields       fs = " ++ prettyShow (map argFromDom fs)
+        ]
+      let comatching = recInduction == Just CoInductive
+                    || copatternMatchingAllowed eta
+      -- Try the projection candidates.
+      -- First, we try to find a disambiguation that doesn't produce
+      -- any new constraints.
+      tryDisambiguate False fs r vs comatching $ \ _ ->
+          -- If this fails, we try again with constraints, but we require
+          -- the solution to be unique.
+          tryDisambiguate True fs r vs comatching $ \case
+            ([]   , []      ) -> __IMPOSSIBLE__
+            (err:_, []      ) -> throwError err
+            (_    , disambs@((d,a):_)) -> typeError $ AmbiguousProjection d (map fst disambs)
+    _ -> __IMPOSSIBLE__
+
+  where
+    tryDisambiguate constraintsOk fs r vs comatching failure = do
+      -- Note that tryProj wraps TCM in an ExceptT, collecting errors
+      -- instead of throwing them to the user immediately.
+      disambiguations <- mapM (runExceptT . tryProj constraintsOk fs r vs) ds
+      case List1.partitionEithers disambiguations of
+        (_ , (d, (a, ai, mst)) : disambs) | constraintsOk <= null disambs -> do
+          mapM_ putTC mst -- Activate state changes
+          -- From here, we have the correctly disambiguated projection.
+          -- For highlighting, we remember which name we disambiguated to.
+          -- This is safe here (fingers crossed) as we won't decide on a
+          -- different projection even if we backtrack and come here again.
+          liftTCM $ storeDisambiguatedProjection d
+          return (d, comatching, r, a, ai)
+        other -> failure other
+
+    notRecord = wrongProj $ List1.head ds
+
+    wrongProj :: (MonadTCM m, MonadError TCErr m, ReadTCState m) => QName -> m a
+    wrongProj d = softTypeError =<< do
+      liftTCM $ if isAmbiguous ambD then CannotEliminateWithProjection b True <$> dropTopLevelModule d
+                else pure $ CannotEliminateWithProjection b False d
+
+    tryProj
+      :: Bool                 -- Are we allowed to create new constraints?
+      -> [Dom QName]          -- Fields of record type under consideration.
+      -> QName                -- Name of record type we are eliminating.
+      -> Args                 -- Parameters of record type we are eliminating.
+      -> QName                -- Candidate projection.
+      -> ExceptT TCErr TCM (QName, (Arg Type, ArgInfo, Maybe TCState))
+           -- TCState contains possibly new constraints/meta solutions.
+    tryProj constraintsOk fs r vs d0 = isProjection d0 >>= \case
+      -- Not a projection
+      Nothing -> wrongProj d0
+      Just proj -> do
+        let d = projOrig proj
+
+        -- Andreas, 2015-05-06 issue 1413 projProper=Nothing is not impossible
+        qr <- maybe (wrongProj d) return $ projProper proj
+
+        -- If projIndex==0, then the projection is already applied
+        -- to the record value (like in @open R r@), and then it
+        -- is no longer a projection but a record field.
+        when (null $ projLams proj) $ wrongProj d
+        reportSLn "tc.lhs.split" 90 "we are a projection pattern"
+        -- If the target is not a record type, that's an error.
+        -- It could be a meta, but since we cannot postpone lhs checking, we crash here.
+        reportSDoc "tc.lhs.split" 20 $ sep
+          [ text $ "proj                  d0 = " ++ prettyShow d0
+          , text $ "original proj         d  = " ++ prettyShow d
+          ]
+        -- Get the field decoration.
+        -- If the projection pattern name @d@ is not a field name,
+        -- we have to try the next projection name.
+        -- If this was not an ambiguous projection, that's an error.
+        argd <- maybe (wrongProj d) return $ List.find ((d ==) . unDom) fs
+
+        -- Issue4998: This used to use the hiding from the principal argument, but this is not
+        -- relevant for the ArgInfo of the clause rhs. We return that separately so we can set the
+        -- correct hiding for the projection pattern in splitRest above.
+        let ai = getArgInfo argd
+
+        reportSDoc "tc.lhs.split" 20 $ vcat
+          [ text $ "original proj relevance  = " ++ show (getRelevance argd)
+          , text $ "original proj quantity   = " ++ show (getQuantity  argd)
+          ]
+        -- Andreas, 2016-12-31, issue #2374:
+        -- We can also disambiguate by hiding info.
+        -- Andreas, 2018-10-18, issue #3289: postfix projections have no hiding info.
+        unless (caseMaybe h True $ sameHiding $ projArgInfo proj) $
+          softTypeError $ WrongHidingInProjection d
+
+        -- Andreas, 2016-12-31, issue #1976: Check parameters.
+        let chk = checkParameters qr r vs
+        mst <- suspendErrors $
+          if constraintsOk then Just . snd <$> localTCStateSaving chk
+          else Nothing <$ nonConstraining chk
+
+        -- Get the type of projection d applied to "self"
+        dType <- liftTCM $ defType <$> getConstInfo d  -- full type!
+        reportSDoc "tc.lhs.split" 20 $ sep
+          [ "we are being projected by dType = " <+> prettyTCM dType
+          ]
+        projType <- liftTCM $ dType `piApplyM` vs
+        return (d0, (Arg ai projType, projArgInfo proj, mst))
+
+-- | Disambiguate a constructor based on the data type it is supposed to be
+--   constructing. Returns the unambiguous constructor name and its type.
+--   Precondition: type should be a data/record type.
+disambiguateConstructor
+  :: AmbiguousQName    -- ^ The name of the constructor to be disambiguated.
+  -> QName             -- ^ Name of the datatype.
+  -> Args              -- ^ Parameters of the datatype
+  -> TCM (ConHead, Type)
+disambiguateConstructor ambC@(AmbQ cs) d pars = do
+  d <- canonicalName d
+  cons <- theDef <$> getConstInfo d >>= \case
+    def@Datatype{} -> return $ dataCons def
+    def@Record{}   -> return $ [conName $ recConHead def]
+    _              -> __IMPOSSIBLE__
+
+  -- First, try do disambiguate with nonConstraining,
+  -- if that fails, try again allowing constraint/solution generation.
+  tryDisambiguate False d cons $ \ _ ->
+    tryDisambiguate True d cons $ \case
+        ([]   , [] ) -> __IMPOSSIBLE__
+        (err:_, [] ) -> throwError err
+        -- If all disambiguations point to the same original constructor
+        -- meaning that only the parameters may differ,
+        -- then throw more specific error.
+        (_    , [_]) -> typeError $ CantResolveOverloadedConstructorsTargetingSameDatatype d cs
+        (_    , disambs@(((c,_,_) :| _) : _)) -> typeError $
+          AmbiguousConstructor c (map (conName . snd3) $ List1.concat disambs)
+
+  where
+    tryDisambiguate
+      :: Bool     -- May we constrain/solve metas to arrive at unique disambiguation?
+      -> QName    -- Data/record type.
+      -> [QName]  -- Its constructor(s).
+      -> ( ( [TCErr]
+           , [List1 (QName, ConHead, (Type, Maybe TCState))]
+           )
+           -> TCM (ConHead, Type) )  -- Failure continuation, taking
+                                     -- possible disambiguations
+                                     -- grouped by the original
+                                     -- constructor name in 'ConHead'.
+      -> TCM (ConHead, Type)  -- Unique disambiguation and its type.
+    tryDisambiguate constraintsOk d cons failure = do
+      reportSDoc "tc.lhs.disamb" 30 $ sep $ List.concat $
+        [ [ "tryDisambiguate" ]
+        , if constraintsOk then [ "(allowing new constraints)" ] else empty
+        , map (nest 2 . pretty) $ List1.toList cs
+        , [ "against" ]
+        , map (nest 2 . pretty) cons
+        ]
+      disambiguations <- mapM (runExceptT . tryCon constraintsOk cons d pars) cs
+      -- Q: can we be more lazy, like using the ListT monad?
+      -- Andreas, 2020-06-17: Not really, since we need to make sure
+      -- that only a single candidate remains, and if not,
+      -- report all alternatives in the error message.
+      let (errs, fits0) = List1.partitionEithers disambiguations
+      reportSDoc "tc.lhs.disamb" 40 $ vcat $ do
+        let hideSt (c0,c,(a,mst)) = (c0, c, (a, ("(state change)" :: String) <$ mst))
+        "remaining candidates: " : map (nest 2 . prettyTCM . hideSt) fits0
+      dedupCons fits0 >>= \case
+
+        -- Single candidate remains.
+        [ (c0,c,(a,mst)) :| [] ] -> do
+          reportSDoc "tc.lhs.disamb" 30 $ sep $
+            [ "tryDisambiguate suceeds with"
+            , pretty c0
+            , ":"
+            , prettyTCM a
+            ]
+          -- Andreas, 2020-06-16, issue #4135
+          -- If disambiguation succeeded with new constraints/solutions,
+          -- put them into action.
+          whenJust mst putTC
+          -- If there are multiple candidates for the constructor pattern, exactly one of
+          -- which type checks, remember our choice for highlighting info.
+          when (isAmbiguous ambC) $ liftTCM $
+            storeDisambiguatedConstructor (conInductive c) c0
+          return (c,a)
+
+        -- Either no candidate constructor in 'cs' type checks, or multiple candidates
+        -- type check.
+        groups -> failure (errs, groups)
+
+    abstractConstructor c = softTypeError $
+      AbstractConstructorNotInScope c
+
+    wrongDatatype c d = softTypeError $
+      ConstructorPatternInWrongDatatype c d
+
+    tryCon
+      :: Bool        -- Are we allowed to constrain metas?
+      -> [QName]     -- Constructors of data type under consideration.
+      -> QName       -- Name of data/record type we are eliminating.
+      -> Args        -- Parameters of data/record type we are eliminating.
+      -> QName       -- Candidate constructor.
+      -> ExceptT TCErr TCM (QName, ConHead, (Type, Maybe TCState))
+           -- If this candidate succeeds, return its disambiguation
+           -- its type, and maybe the state obtained after checking it
+           -- (which may contain new constraints/solutions).
+    tryCon constraintsOk cons d pars c = getConstInfo' c >>= \case
+      Left (SigUnknown err)     -> __IMPOSSIBLE__
+      Left SigCubicalNotErasure -> __IMPOSSIBLE__
+      Left SigAbstract          -> abstractConstructor c
+      Right def                 -> do
+        let con = conSrcCon (theDef def) `withRangeOf` c
+        unless (conName con `elem` cons) $ wrongDatatype c d
+
+        -- Andreas, 2013-03-22 fixing issue 279
+        -- To resolve ambiguous constructors, Agda always looks up
+        -- their original definition and reconstructs the parameters
+        -- from the type @Def d vs@ we check against.
+        -- However, the constructor could come from a module instantiation
+        -- with some of the parameters already fixed.
+        -- Agda did not make sure the two parameter lists coincide,
+        -- so we add a check here.
+        -- I guess this issue could be solved more systematically,
+        -- but the extra check here is non-invasive to the existing code.
+        -- Andreas, 2016-12-31 fixing issue #1975
+        -- Do this also for constructors which were originally ambiguous.
+        let chk = checkConstructorParameters c d pars
+        mst <- suspendErrors $
+          if constraintsOk then Just . snd <$> localTCStateSaving chk
+          else Nothing <$ nonConstraining chk
+
+        -- Get the type from the original constructor.
+        -- Andreas, 2020-06-17 TODO:
+        -- Couldn't we return this type from checkConstructorParameters?
+        cType <- (`piApply` pars) . defType <$> getConInfo con
+
+        return (c, con, (cType, mst))
+
+    -- This deduplication identifies different names of the same
+    -- constructor, ensuring that the "ambiguous constructor" error
+    -- does not fire for the case described in #4130.
+    --
+    -- Andreas, 2020-06-17, issue #4135:
+    -- However, we need to distinguish different occurrences
+    -- of the same original constructor if it is used
+    -- with different data parameters, as recorded in the @Type@.
+    dedupCons ::
+      forall a.       [ (a, ConHead, (Type, Maybe TCState)) ]
+         -> TCM [ List1 (a, ConHead, (Type, Maybe TCState)) ]
+    dedupCons cands = do
+      -- Group candidates by original constructor name.
+      let groups = List1.groupWith (conName . snd3) cands
+      -- Eliminate duplicates (same type) from groups.
+      mapM (List1.nubM (cmpM `on` thd3)) groups
+      where
+      -- The types come possibly with their own state.
+      cmpM (a1, mst1) (a2, mst2) = do
+        let cmpTypes = tryConversion $ equalType a1 a2
+        case (mst1, mst2) of
+          (Nothing, Nothing) -> cmpTypes
+          (Just st, Nothing) -> inState st cmpTypes
+          (Nothing, Just st) -> inState st cmpTypes
+          -- Andreas, 2020-06-17, issue #4135.
+          -- If the state has diverged into two states we give up.
+          -- For instance, one state may say `?0 := true`
+          -- and the other `?0 := false`.
+          -- The types may be both `D ?0`, which is the same
+          -- but diverges in the different states.
+          -- We do not check states for equality.
+          --
+          -- Of course, this is conservative and not maximally extensional.
+          -- We might throw an ambiguity error too eagerly,
+          -- but this can always be worked around.
+          (Just{},  Just{})  -> return False
+      inState st m = localTCState $ do putTC st; m
+
+-- | @checkConstructorParameters c d pars@ checks that the data/record type
+--   behind @c@ is has initial parameters (coming e.g. from a module instantiation)
+--   that coincide with an prefix of @pars@.
+checkConstructorParameters :: MonadTCM tcm => QName -> QName -> Args -> tcm ()
+checkConstructorParameters c d pars = do
+  dc <- liftTCM $ getConstructorData c
+  checkParameters dc d pars
+
+-- | Check that given parameters match the parameters of the inferred
+--   constructor/projection.
+checkParameters
+  :: MonadTCM tcm
+  => QName  -- ^ The record/data type name of the chosen constructor/projection.
+  -> QName  -- ^ The record/data type name as supplied by the type signature.
+  -> Args   -- ^ The parameters.
+  -> tcm ()
+checkParameters dc d pars = liftTCM $ do
+  a  <- reduce (Def dc [])
+  case a of
+    Def d0 es -> do -- compare parameters
+      let vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      reportSDoc "tc.lhs.split" 40 $ vcat $
+        [ "checkParameters"
+        , nest 2 $ "d                   =" <+> (text . prettyShow) d
+        , nest 2 $ "d0 (should be == d) =" <+> (text . prettyShow) d0
+        , nest 2 $ "dc                  =" <+> (text . prettyShow) dc
+        , nest 2 $ "vs                  =" <+> prettyTCM vs
+        , nest 2 $ "pars                =" <+> prettyTCM pars
+        ]
+      -- when (d0 /= d) __IMPOSSIBLE__ -- d could have extra qualification
+      t <- typeOfConst d
+      compareArgs [] [] t (Def d []) vs (take (length vs) pars)
+    _ -> __IMPOSSIBLE__
+
+checkSortOfSplitVar :: (MonadTCM m, PureTCM m, MonadError TCErr m,
+                        LensSort a, PrettyTCM a, LensSort ty, PrettyTCM ty)
+                    => DataOrRecord -> a -> Telescope -> Maybe ty -> m ()
+checkSortOfSplitVar dr a tel mtarget = do
+  liftTCM (reduce $ getSort a) >>= \case
+    Type{} -> whenM isTwoLevelEnabled checkFibrantSplit
+    Prop{} -> checkPropSplit
+    SSet{} -> return ()
+    Inf u _ -> when (univFibrancy u == IsFibrant) $ whenM isTwoLevelEnabled checkFibrantSplit
+    sa      -> softTypeError =<< do
+      liftTCM $ SortOfSplitVarError <$> isBlocked sa <*> sep
+        [ "Cannot split on datatype in sort" , prettyTCM (getSort a) ]
+
+  where
+    checkPropSplit
+      | IsRecord InductionAndEta { recordInduction=Nothing } <- dr = return ()
+      | Just target <- mtarget = do
+        reportSDoc "tc.sort.check" 20 $ "target prop:" <+> prettyTCM target
+        checkIsProp target
+      | otherwise              = do
+          reportSDoc "tc.sort.check" 20 $ "no target prop"
+          splitOnPropError dr
+
+    checkIsProp t = runBlocked (isPropM t) >>= \case
+      Left b      -> splitOnPropError dr -- TODO
+      Right False -> splitOnPropError dr
+      Right True  -> return ()
+
+    checkFibrantSplit
+      | IsRecord _ <- dr       = return ()
+      | Just target <- mtarget = do
+          reportSDoc "tc.sort.check" 20 $ "target:" <+> prettyTCM target
+          checkIsFibrant target
+          forM_ (telToList tel) $ \ d -> do
+            let ty = snd $ unDom d
+            checkIsCoFibrant ty
+      | otherwise              = do
+          reportSDoc "tc.sort.check" 20 $ "no target"
+          splitOnFibrantError Nothing
+
+    -- Cofibrant types are those that could be the domain of a fibrant
+    -- pi type. (Notion by C. Sattler).
+    checkIsCoFibrant t = runBlocked (isCoFibrantSort t) >>= \case
+      Left b      -> splitOnFibrantError' t $ Just b
+      Right False -> unlessM (isInterval t) $
+                       splitOnFibrantError' t $ Nothing
+      Right True  -> return ()
+
+    checkIsFibrant t = runBlocked (isFibrant t) >>= \case
+      Left b      -> splitOnFibrantError $ Just b
+      Right False -> splitOnFibrantError Nothing
+      Right True  -> return ()
+
+    splitOnPropError dr = softTypeError $ SplitInProp dr
+
+    splitOnFibrantError' t mb = softTypeError =<< do
+      liftTCM $ SortOfSplitVarError mb <$> fsep
+        [ "Cannot eliminate fibrant type" , prettyTCM a
+        , "unless context type", prettyTCM t, "is also fibrant."
+        ]
+
+    splitOnFibrantError mb = softTypeError =<< do
+      liftTCM $ SortOfSplitVarError mb <$> fsep
+        [ "Cannot eliminate fibrant type" , prettyTCM a
+        , "unless target type is also fibrant"
+        ]
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/Implicit.hs b/src/full/Agda/TypeChecking/Rules/LHS/Implicit.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/Implicit.hs
@@ -0,0 +1,106 @@
+
+module Agda.TypeChecking.Rules.LHS.Implicit where
+
+import Prelude hiding (null)
+
+import Control.Monad.Except
+import Control.Monad.IO.Class
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Info
+import Agda.Syntax.Internal as I
+import qualified Agda.Syntax.Abstract as A
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Implicit
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible
+
+implicitP :: ArgInfo -> NamedArg A.Pattern
+implicitP info = Arg (setOrigin Inserted info) $ unnamed $ A.WildP $ PatRange $ noRange
+
+-- | Insert implicit patterns in a list of patterns.
+--   Even if 'DontExpandLast', trailing SIZELT patterns are inserted.
+insertImplicitPatterns
+  :: (PureTCM m, MonadError TCErr m, MonadFresh NameId m, MonadTrace m)
+  => ExpandHidden -> [NamedArg A.Pattern]
+  -> Telescope -> m [NamedArg A.Pattern]
+insertImplicitPatterns exh ps tel =
+  insertImplicitPatternsT exh ps (telePi tel __DUMMY_TYPE__)
+
+-- | Insert trailing SizeLt patterns, if any.
+insertImplicitSizeLtPatterns :: PureTCM m => Type -> m [NamedArg A.Pattern]
+insertImplicitSizeLtPatterns t = do
+  -- Testing for SizeLt.  In case of blocked type, we return no.
+  -- We assume that on the LHS, we know the type.  (TODO: Sufficient?)
+  isSize <- isSizeTypeTest
+  let isBounded BoundedNo   = False
+      isBounded BoundedLt{} = True
+      isSizeLt t = maybe False isBounded . isSize . unEl <$> reduce t
+
+  -- Search for the last SizeLt type among the hidden arguments.
+  TelV tel _ <- telView t
+  let ts = takeWhile (not . visible) $ telToList tel
+  keep <- dropWhileEndM (not <.> isSizeLt . snd . unDom) ts
+  -- Insert implicit patterns upto (including) the last SizeLt type.
+  return $ map (implicitP . domInfo) keep
+
+-- | Insert implicit patterns in a list of patterns.
+--   Even if 'DontExpandLast', trailing SIZELT patterns are inserted.
+insertImplicitPatternsT
+  :: (PureTCM m, MonadError TCErr m, MonadFresh NameId m, MonadTrace m)
+  => ExpandHidden -> [NamedArg A.Pattern] -> Type
+  -> m [NamedArg A.Pattern]
+insertImplicitPatternsT DontExpandLast [] a = insertImplicitSizeLtPatterns a
+insertImplicitPatternsT exh            ps a = do
+  TelV tel b <- telViewUpTo' (-1) (not . visible) a
+  reportSDoc "tc.lhs.imp" 20 $
+    vcat [ "insertImplicitPatternsT"
+         , nest 2 $ "ps  = " <+> do
+             brackets $ fsep $ punctuate comma $ map prettyA ps
+         , nest 2 $ "tel = " <+> prettyTCM tel
+         , nest 2 $ "b   = " <+> addContext tel (prettyTCM b)
+         ]
+  reportSDoc "tc.lhs.imp" 70 $
+    vcat [ "insertImplicitPatternsT"
+         , nest 2 $ "ps  = " <+> (text . show) ps
+         , nest 2 $ "tel = " <+> (text . show) tel
+         , nest 2 $ "b   = " <+> (text . show) b
+         ]
+  case ps of
+    [] -> insImp dummy tel
+    p : _ -> setCurrentRange p $ do
+      -- Andreas, 2015-05-11.
+      -- If p is a projection pattern, make it visible for the purpose of
+      -- calling insImp / insertImplicit, to get correct behavior.
+      let p' = applyWhen (isJust $ A.isProjP p) (setHiding NotHidden) p
+      hs <- insImp p' tel
+      -- Continue with implicit patterns inserted before @p@.
+      -- The list @hs ++ ps@ cannot be empty.
+      let ps0@(~(p1 : ps1)) = hs ++ ps
+      reduce a >>= piOrPath >>= \case
+        -- If @a@ is a function (or path) type, continue inserting after @p1@.
+        Left (dom, cod) -> underAbstraction dom cod $ \b ->
+          (p1 :) <$> insertImplicitPatternsT exh ps1 b
+        -- Otherwise, we are done.
+        Right{}     -> return ps0
+  where
+    dummy = defaultNamedArg (A.VarP __IMPOSSIBLE__)
+
+    insImp p EmptyTel = return []
+    insImp p tel = case insertImplicit p $ telToList tel of
+      BadImplicits   -> typeError WrongHidingInLHS
+      NoSuchName x   -> typeError WrongHidingInLHS
+      ImpInsert n    -> return $ map implicitArg n
+
+    implicitArg d = implicitP $ getArgInfo d
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/Problem.hs b/src/full/Agda/TypeChecking/Rules/LHS/Problem.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/Problem.hs
@@ -0,0 +1,416 @@
+
+module Agda.TypeChecking.Rules.LHS.Problem
+       ( FlexibleVars , FlexibleVarKind(..) , FlexibleVar(..) , allFlexVars
+       , FlexChoice(..) , ChooseFlex(..)
+       , ProblemEq(..) , Problem(..) , problemEqs
+       , problemRestPats, problemCont, problemInPats
+       , AsBinding(..) , DotPattern(..) , AbsurdPattern(..), AnnotationPattern(..)
+       , LHSState(..) , lhsTel , lhsOutPat , lhsProblem , lhsTarget
+       , LeftoverPatterns(..), getLeftoverPatterns, getUserVariableNames
+       ) where
+
+import Prelude hiding (null)
+
+import Control.Arrow        ( (***) )
+import Control.Monad        ( zipWithM )
+import Control.Monad.Writer ( MonadWriter(..), Writer, runWriter )
+
+import Data.Functor (($>))
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.List ( partition )
+import Data.Semigroup ( Semigroup, (<>) )
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Internal
+import Agda.Syntax.Abstract (ProblemEq(..))
+import qualified Agda.Syntax.Abstract as A
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty
+
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Null
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import qualified Agda.Syntax.Common.Pretty as PP
+
+type FlexibleVars   = [FlexibleVar Nat]
+
+-- | When we encounter a flexible variable in the unifier, where did it come from?
+--   The alternatives are ordered such that we will assign the higher one first,
+--   i.e., first we try to assign a @DotFlex@, then...
+data FlexibleVarKind
+  = RecordFlex [FlexibleVarKind]
+      -- ^ From a record pattern ('ConP').
+      --   Saves the 'FlexibleVarKind' of its subpatterns.
+  | ImplicitFlex -- ^ From a hidden formal argument or underscore ('WildP').
+  | DotFlex      -- ^ From a dot pattern ('DotP').
+  | OtherFlex    -- ^ From a non-record constructor or literal ('ConP' or 'LitP').
+  deriving (Eq, Show)
+
+-- | Flexible variables are equipped with information where they come from,
+--   in order to make a choice which one to assign when two flexibles are unified.
+data FlexibleVar a = FlexibleVar
+  { flexArgInfo :: ArgInfo
+  , flexForced  :: IsForced
+  , flexKind    :: FlexibleVarKind
+  , flexPos     :: Maybe Int
+  , flexVar     :: a
+  } deriving (Eq, Show, Functor, Foldable, Traversable)
+
+instance LensArgInfo (FlexibleVar a) where
+  getArgInfo = flexArgInfo
+  setArgInfo ai fl = fl { flexArgInfo = ai }
+  mapArgInfo f  fl = fl { flexArgInfo = f (flexArgInfo fl) }
+
+instance LensHiding (FlexibleVar a)
+instance LensOrigin (FlexibleVar a)
+instance LensModality (FlexibleVar a)
+
+-- UNUSED
+-- defaultFlexibleVar :: a -> FlexibleVar a
+-- defaultFlexibleVar a = FlexibleVar Hidden Inserted ImplicitFlex Nothing a
+
+-- UNUSED
+-- flexibleVarFromHiding :: Hiding -> a -> FlexibleVar a
+-- flexibleVarFromHiding h a = FlexibleVar h ImplicitFlex Nothing a
+
+allFlexVars :: [IsForced] -> Telescope -> FlexibleVars
+allFlexVars forced tel = zipWith3 makeFlex (downFrom n) (telToList tel) fs
+  where
+    n  = size tel
+    fs = forced ++ repeat NotForced
+    makeFlex i d f = FlexibleVar (getArgInfo d) f ImplicitFlex (Just i) i
+
+data FlexChoice = ChooseLeft | ChooseRight | ChooseEither | ExpandBoth
+  deriving (Eq, Show)
+
+instance Semigroup FlexChoice where
+  ExpandBoth   <> _            = ExpandBoth
+  _            <> ExpandBoth   = ExpandBoth
+  ChooseEither <> y            = y
+  x            <> ChooseEither = x
+  ChooseLeft   <> ChooseRight  = ExpandBoth -- If there's dot patterns on both sides,
+  ChooseRight  <> ChooseLeft   = ExpandBoth -- we need to eta-expand
+  ChooseLeft   <> ChooseLeft   = ChooseLeft
+  ChooseRight  <> ChooseRight  = ChooseRight
+
+instance Monoid FlexChoice where
+  mempty  = ChooseEither
+  mappend = (<>)
+
+class ChooseFlex a where
+  chooseFlex :: a -> a -> FlexChoice
+
+instance ChooseFlex FlexibleVarKind where
+  chooseFlex DotFlex         DotFlex         = ChooseEither
+  chooseFlex DotFlex         _               = ChooseLeft
+  chooseFlex _               DotFlex         = ChooseRight
+  chooseFlex (RecordFlex xs) (RecordFlex ys) = chooseFlex xs ys
+  chooseFlex (RecordFlex xs) y               = chooseFlex xs (repeat y)
+  chooseFlex x               (RecordFlex ys) = chooseFlex (repeat x) ys
+  chooseFlex ImplicitFlex    ImplicitFlex    = ChooseEither
+  chooseFlex ImplicitFlex    _               = ChooseLeft
+  chooseFlex _               ImplicitFlex    = ChooseRight
+  chooseFlex OtherFlex       OtherFlex       = ChooseEither
+
+instance ChooseFlex a => ChooseFlex [a] where
+  chooseFlex xs ys = mconcat $ zipWith chooseFlex xs ys
+
+instance ChooseFlex a => ChooseFlex (Maybe a) where
+  chooseFlex Nothing Nothing = ChooseEither
+  chooseFlex Nothing (Just y) = ChooseLeft
+  chooseFlex (Just x) Nothing = ChooseRight
+  chooseFlex (Just x) (Just y) = chooseFlex x y
+
+instance ChooseFlex ArgInfo where
+  chooseFlex ai1 ai2 = firstChoice [ chooseFlex (getOrigin ai1) (getOrigin ai2)
+                                   , chooseFlex (getHiding ai1) (getHiding ai2) ]
+
+instance ChooseFlex IsForced where
+  chooseFlex NotForced NotForced = ChooseEither
+  chooseFlex NotForced Forced    = ChooseRight
+  chooseFlex Forced    NotForced = ChooseLeft
+  chooseFlex Forced    Forced    = ChooseEither
+
+instance ChooseFlex Hiding where
+  chooseFlex Hidden     Hidden     = ChooseEither
+  chooseFlex Hidden     _          = ChooseLeft
+  chooseFlex _          Hidden     = ChooseRight
+  chooseFlex Instance{} Instance{} = ChooseEither
+  chooseFlex Instance{} _          = ChooseLeft
+  chooseFlex _          Instance{} = ChooseRight
+  chooseFlex _          _          = ChooseEither
+
+instance ChooseFlex Origin where
+  chooseFlex Inserted  Inserted  = ChooseEither
+  chooseFlex Inserted  _         = ChooseLeft
+  chooseFlex _         Inserted  = ChooseRight
+  chooseFlex Reflected Reflected = ChooseEither
+  chooseFlex Reflected _         = ChooseLeft
+  chooseFlex _         Reflected = ChooseRight
+  chooseFlex _         _         = ChooseEither
+
+instance ChooseFlex Int where
+  chooseFlex x y = case compare x y of
+    LT -> ChooseLeft
+    EQ -> ChooseEither
+    GT -> ChooseRight
+
+instance (ChooseFlex a) => ChooseFlex (FlexibleVar a) where
+  chooseFlex (FlexibleVar ai1 fc1 f1 p1 i1) (FlexibleVar ai2 fc2 f2 p2 i2) =
+    firstChoice [ chooseFlex f1 f2, chooseFlex fc1 fc2, chooseFlex ai1 ai2
+                , chooseFlex p1 p2, chooseFlex i1 i2]
+
+firstChoice :: [FlexChoice] -> FlexChoice
+firstChoice []                  = ChooseEither
+firstChoice (ChooseEither : xs) = firstChoice xs
+firstChoice (x            : _ ) = x
+
+-- | The user patterns we still have to split on.
+data Problem a = Problem
+  { _problemEqs      :: [ProblemEq]
+    -- ^ User patterns which are typed
+    --   (including the ones generated from implicit arguments).
+  , _problemRestPats :: [NamedArg A.Pattern]
+    -- ^ List of user patterns which could not yet be typed.
+    --   Example:
+    --   @
+    --      f : (b : Bool) -> if b then Nat else Nat -> Nat
+    --      f true          = zero
+    --      f false zero    = zero
+    --      f false (suc n) = n
+    --   @
+    --   In this sitation, for clause 2, we construct an initial problem
+    --   @
+    --      problemEqs      = [false = b]
+    --      problemRestPats = [zero]
+    --   @
+    --   As we instantiate @b@ to @false@, the 'targetType' reduces to
+    --   @Nat -> Nat@ and we can move pattern @zero@ over to @problemEqs@.
+  , _problemCont     :: LHSState a -> TCM a
+    -- ^ The code that checks the RHS.
+  }
+  deriving Show
+
+problemEqs :: Lens' (Problem a) [ProblemEq]
+problemEqs f p = f (_problemEqs p) <&> \x -> p {_problemEqs = x}
+
+problemRestPats :: Lens' (Problem a) [NamedArg A.Pattern]
+problemRestPats f p = f (_problemRestPats p) <&> \x -> p {_problemRestPats = x}
+
+problemCont :: Lens' (Problem a) (LHSState a -> TCM a)
+problemCont f p = f (_problemCont p) <&> \x -> p {_problemCont = x}
+
+problemInPats :: Problem a -> [A.Pattern]
+problemInPats = map problemInPat . (^. problemEqs)
+
+data AsBinding = AsB Name Term Type Modality
+data DotPattern = Dot A.Expr Term (Dom Type)
+data AbsurdPattern = Absurd Range Type
+data AnnotationPattern = Ann A.Expr Type
+
+-- | State worked on during the main loop of checking a lhs.
+--   [Ulf Norell's PhD, page. 35]
+data LHSState a = LHSState
+  { _lhsTel     :: Telescope
+    -- ^ The types of the pattern variables.
+  , _lhsOutPat  :: [NamedArg DeBruijnPattern]
+    -- ^ Patterns after splitting.
+    --   The de Bruijn indices refer to positions in the list of abstract syntax
+    --   patterns in the problem, counted from the back (right-to-left).
+  , _lhsProblem :: Problem a
+    -- ^ User patterns of supposed type @delta@.
+  , _lhsTarget  :: Arg Type
+    -- ^ Type eliminated by 'problemRestPats' in the problem.
+    --   Can be 'Irrelevant' to indicate that we came by
+    --   an irrelevant projection and, hence, the rhs must
+    --   be type-checked in irrelevant mode.
+  , _lhsPartialSplit :: ![Maybe Int]
+    -- ^ have we splitted with a PartialFocus?
+  , _lhsIndexedSplit :: !Bool
+    -- ^ Have we split on any indexed inductive types?
+  }
+
+lhsTel :: Lens' (LHSState a) Telescope
+lhsTel f p = f (_lhsTel p) <&> \x -> p {_lhsTel = x}
+
+lhsOutPat :: Lens' (LHSState a) [NamedArg DeBruijnPattern]
+lhsOutPat f p = f (_lhsOutPat p) <&> \x -> p {_lhsOutPat = x}
+
+lhsProblem :: Lens' (LHSState a) (Problem a)
+lhsProblem f p = f (_lhsProblem p) <&> \x -> p {_lhsProblem = x}
+
+lhsTarget :: Lens' (LHSState a) (Arg Type)
+lhsTarget f p = f (_lhsTarget p) <&> \x -> p {_lhsTarget = x}
+
+data PatVarPosition = PVLocal | PVParam
+  deriving (Show, Eq)
+
+data LeftoverPatterns = LeftoverPatterns
+  { patternVariables :: IntMap [(A.Name,PatVarPosition)]
+  , asPatterns       :: [AsBinding]
+  , dotPatterns      :: [DotPattern]
+  , absurdPatterns   :: [AbsurdPattern]
+  , typeAnnotations  :: [AnnotationPattern]
+  , otherPatterns    :: [A.Pattern]
+  }
+
+instance Semigroup LeftoverPatterns where
+  x <> y = LeftoverPatterns
+    { patternVariables = IntMap.unionWith (++) (patternVariables x) (patternVariables y)
+    , asPatterns       = asPatterns x ++ asPatterns y
+    , dotPatterns      = dotPatterns x ++ dotPatterns y
+    , absurdPatterns   = absurdPatterns x ++ absurdPatterns y
+    , typeAnnotations  = typeAnnotations x ++ typeAnnotations y
+    , otherPatterns    = otherPatterns x ++ otherPatterns y
+    }
+
+instance Null LeftoverPatterns where
+  empty = LeftoverPatterns empty [] [] [] [] []
+  null (LeftoverPatterns as bs cs ds es fs) = null as && null bs && null cs && null ds && null es && null fs
+
+
+instance Monoid LeftoverPatterns where
+  mempty  = empty
+  mappend = (<>)
+
+instance PP.Pretty PatVarPosition where
+  pretty = PP.text . show
+
+instance PrettyTCM LeftoverPatterns where
+  prettyTCM (LeftoverPatterns varp asb dotp absurdp annp otherp) = vcat
+    [ "pattern variables: " <+> pretty (IntMap.toList varp)
+    , "as bindings:       " <+> prettyList_ (map prettyTCM asb)
+    , "dot patterns:      " <+> prettyList_ (map prettyTCM dotp)
+    , "absurd patterns:   " <+> prettyList_ (map prettyTCM absurdp)
+    , "type annotations:  " <+> prettyList_ (map prettyTCM annp)
+    , "other patterns:    " <+> prettyList_ (map prettyA otherp)
+    ]
+
+-- | Classify remaining patterns after splitting is complete into pattern
+--   variables, as patterns, dot patterns, and absurd patterns.
+--   Precondition: there are no more constructor patterns.
+getLeftoverPatterns
+  :: forall m. PureTCM m
+  => [ProblemEq] -> m LeftoverPatterns
+getLeftoverPatterns eqs = do
+  reportSDoc "tc.lhs.top" 30 $ "classifying leftover patterns"
+  params <- Set.fromList . teleNames <$> (lookupSection =<< currentModule)
+  let isParamName = (`Set.member` params) . nameToArgName
+  mconcat <$> mapM (getLeftoverPattern isParamName) eqs
+  where
+    patternVariable x i  = empty { patternVariables = singleton (i,[(x,PVLocal)]) }
+    moduleParameter x i  = empty { patternVariables = singleton (i,[(x,PVParam)]) }
+    asPattern x v a      = empty { asPatterns       = singleton (AsB x v (unDom a) (getModality a)) }
+    dotPattern e v a     = empty { dotPatterns      = singleton (Dot e v a) }
+    absurdPattern info a = empty { absurdPatterns   = singleton (Absurd info a) }
+    annPattern t a       = empty { typeAnnotations  = singleton (Ann t a) }
+    otherPattern p       = empty { otherPatterns    = singleton p }
+
+    getLeftoverPattern :: (A.Name -> Bool) -> ProblemEq -> m LeftoverPatterns
+    getLeftoverPattern isParamName (ProblemEq p v a) = case p of
+      (A.VarP A.BindName{unBind = x}) -> isEtaVar v (unDom a) >>= \case
+        Just i  | isParamName x -> return $ moduleParameter x i
+                | otherwise     -> return $ patternVariable x i
+        Nothing -> return $ asPattern x v a
+      (A.WildP _)       -> return mempty
+      (A.AsP info A.BindName{unBind = x} p)  -> (asPattern x v a `mappend`) <$> do
+        getLeftoverPattern isParamName $ ProblemEq p v a
+      (A.DotP info e)   -> return $ dotPattern e v a
+      (A.AbsurdP info)  -> return $ absurdPattern (getRange info) (unDom a)
+      (A.AnnP info t p) -> (annPattern t (unDom a) `mappend`) <$> do
+        getLeftoverPattern isParamName $ ProblemEq p v a
+      _                 -> return $ otherPattern p
+
+-- | Build a renaming for the internal patterns using variable names from
+--   the user patterns. If there are multiple user names for the same internal
+--   variable, the unused ones are returned as as-bindings.
+--   Names that are not also module parameters are preferred over
+--   those that are.
+getUserVariableNames
+  :: Telescope                         -- ^ The telescope of pattern variables
+  -> IntMap [(A.Name,PatVarPosition)]  -- ^ The list of user names for each pattern variable
+  -> ([Maybe A.Name], [AsBinding])
+getUserVariableNames tel names = runWriter $
+  zipWithM makeVar (flattenTel tel) (downFrom $ size tel)
+
+  where
+    makeVar :: Dom Type -> Int -> Writer [AsBinding] (Maybe A.Name)
+    makeVar a i = case partitionIsParam (IntMap.findWithDefault [] i names) of
+      ([]     , [])   -> return Nothing
+      ((x:xs) , [])   -> tellAsBindings xs $> (Just x)
+      (xs     , y:ys) -> tellAsBindings (xs ++ ys) $> (Just y)
+      where
+        tellAsBindings = tell . map (\y -> AsB y (var i) (unDom a) (getModality a))
+
+    partitionIsParam :: [(A.Name,PatVarPosition)] -> ([A.Name],[A.Name])
+    partitionIsParam = (map fst *** map fst) . partition ((== PVParam) . snd)
+
+
+instance Subst (Problem a) where
+  type SubstArg (Problem a) = Term
+  applySubst rho (Problem eqs rps cont) = Problem (applySubst rho eqs) rps cont
+
+instance Subst AsBinding where
+  type SubstArg AsBinding = Term
+  applySubst rho (AsB x v a m) = (\(v,a) -> AsB x v a m) $ applySubst rho (v, a)
+
+instance Subst DotPattern where
+  type SubstArg DotPattern = Term
+  applySubst rho (Dot e v a) = uncurry (Dot e) $ applySubst rho (v, a)
+
+instance Subst AbsurdPattern where
+  type SubstArg AbsurdPattern = Term
+  applySubst rho (Absurd r a) = Absurd r $ applySubst rho a
+
+instance PrettyTCM ProblemEq where
+  prettyTCM (ProblemEq p v a) = sep
+    [ prettyA p <+> "="
+    , nest 2 $ prettyTCM v <+> ":"
+    , nest 2 $ prettyTCM a
+    ]
+
+instance PrettyTCM AsBinding where
+  prettyTCM (AsB x v a m) =
+    sep [ prettyTCM x <> "@" <> parens (prettyTCM v)
+        , nest 2 $ ":" <+> prettyTCM a
+        ]
+
+instance PrettyTCM DotPattern where
+  prettyTCM (Dot e v a) = sep
+    [ prettyA e <+> "="
+    , nest 2 $ prettyTCM v <+> ":"
+    , nest 2 $ prettyTCM a
+    ]
+
+instance PrettyTCM AbsurdPattern where
+  prettyTCM (Absurd r a) = "() :" <+> prettyTCM a
+
+instance PrettyTCM AnnotationPattern where
+  prettyTCM (Ann a p) = prettyTCM p <+> ":" <+> prettyA a
+
+instance PP.Pretty AsBinding where
+  pretty (AsB x v a m) =
+    PP.pretty x PP.<+> "=" PP.<+>
+      PP.hang (PP.pretty v PP.<+> ":") 2 (PP.pretty a)
+
+instance InstantiateFull AsBinding where
+  instantiateFull' (AsB x v a m) = AsB x <$> instantiateFull' v <*> instantiateFull' a <*> pure m
+
+instance PrettyTCM (LHSState a) where
+  prettyTCM (LHSState tel outPat (Problem eqs rps _) target _ _) = vcat
+    [ "tel             = " <+> prettyTCM tel
+    , "outPat          = " <+> addContext tel (prettyTCMPatternList outPat)
+    , "problemEqs      = " <+> addContext tel (prettyList_ $ map prettyTCM eqs)
+    , "problemRestPats = " <+> prettyList_ (map prettyA rps)
+    , "target          = " <+> addContext tel (prettyTCM target)
+    ]
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/ProblemRest.hs b/src/full/Agda/TypeChecking/Rules/LHS/ProblemRest.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/ProblemRest.hs
@@ -0,0 +1,167 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.LHS.ProblemRest where
+
+import Control.Monad
+import Control.Monad.Except
+
+import Data.Maybe
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import qualified Agda.Syntax.Abstract as A
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Substitute
+
+import Agda.TypeChecking.Rules.LHS.Problem
+import Agda.TypeChecking.Rules.LHS.Implicit
+
+import Agda.Utils.Functor
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- | Rename the variables in a telescope using the names from a given pattern.
+--
+--   If there are not at least as many patterns as entries as in the telescope,
+--   the names of the remaining entries in the telescope are unchanged.
+--   If there are too many patterns, there should be a type error later.
+--
+useNamesFromPattern :: [NamedArg A.Pattern] -> Telescope -> Telescope
+useNamesFromPattern ps tel = telFromList (zipWith ren ps telList ++ telRemaining)
+  where
+    telList = telToList tel
+    telRemaining = drop (length ps) telList -- telescope entries beyond patterns
+    ren (Arg ai (Named nm p)) dom@Dom{ unDom = (y, a) } =
+      case p of
+        -- Andreas, 2017-10-12, issue #2803, also preserve user-written hidden names.
+        -- However, not if the argument is named, because then the name in the telescope
+        -- is significant for implicit insertion.
+        A.VarP A.BindName{unBind = x}
+          | not (isNoName x)
+          , visible dom || (getOrigin ai == UserWritten && isNothing nm) ->
+          dom{ unDom = (nameToArgName x, a) }
+        A.AbsurdP{} | visible dom -> dom{ unDom = (stringToArgName "()", a) }
+        A.PatternSynP{} -> __IMPOSSIBLE__  -- ensure there are no syns left
+        -- Andreas, 2016-05-10, issue 1848: if context variable has no name, call it "x"
+        _ | visible dom && isNoName y -> dom{ unDom = (stringToArgName "x", a) }
+          | otherwise                  -> dom
+
+useNamesFromProblemEqs
+  :: forall m. PureTCM m
+  => [ProblemEq] -> Telescope -> m Telescope
+useNamesFromProblemEqs eqs tel = addContext tel $ do
+  names <- fst . getUserVariableNames tel . patternVariables <$> getLeftoverPatterns eqs
+  let argNames = map (fmap nameToArgName) names
+  return $ renameTel argNames tel
+
+useOriginFrom :: (LensOrigin a, LensOrigin b) => [a] -> [b] -> [a]
+useOriginFrom = zipWith $ \x y -> setOrigin (getOrigin y) x
+
+-- | Are there any untyped user patterns left?
+noProblemRest :: Problem a -> Bool
+noProblemRest (Problem _ rp _) = null rp
+
+-- | Construct an initial 'LHSState' from user patterns.
+--   Example:
+--   @
+--
+--      Case : {A : Set} → Maybe A → Set → Set → Set
+--      Case nothing  B C = B
+--      Case (just _) B C = C
+--
+--      sample : {A : Set} (m : Maybe A) → Case m Bool (Maybe A → Bool)
+--      sample (just a) (just b) = true
+--      sample (just a) nothing  = false
+--      sample nothing           = true
+--   @
+--   The problem generated for the first clause of @sample@
+--   with patterns @just a, just b@ would be:
+--   @
+--      lhsTel        = [A : Set, m : Maybe A]
+--      lhsOutPat     = ["A", "m"]
+--      lhsProblem    = Problem ["A" = _, "just a" = "a"]
+--                              ["_", "just a"]
+--                              ["just b"] []
+--      lhsTarget     = "Case m Bool (Maybe A -> Bool)"
+--   @
+initLHSState
+  :: Telescope             -- ^ The initial telescope @delta@ of parameters.
+  -> [ProblemEq]           -- ^ The problem equations inherited from the parent clause (living in @delta@).
+  -> [NamedArg A.Pattern]  -- ^ The user patterns.
+  -> Type                  -- ^ The type the user patterns eliminate (living in @delta@).
+  -> (LHSState a -> TCM a) -- ^ Continuation for when checking the patterns is complete.
+  -> TCM (LHSState a)      -- ^ The initial LHS state constructed from the user patterns.
+initLHSState delta eqs ps a ret = do
+  reportSDoc "tc.lhs.init" 40 $ vcat
+    [ "initLHSState"
+    , nest 2 $ "delta = " <+> prettyTCM delta
+    , nest 2 $ "a     = " <+> addContext delta (prettyTCM a)
+    ]
+  let problem = Problem eqs ps ret
+      qs0     = teleNamedArgs delta
+
+  updateProblemRest $ LHSState delta qs0 problem (Arg (defaultArgInfo { argInfoModality = unitModality }) a) [] False
+
+-- | Try to move patterns from the problem rest into the problem.
+--   Possible if type of problem rest has been updated to a function type.
+updateProblemRest
+  :: forall m a. (PureTCM m, MonadError TCErr m, MonadTrace m, MonadFresh NameId m)
+  => LHSState a -> m (LHSState a)
+updateProblemRest st@(LHSState tel0 qs0 p@(Problem oldEqs ps ret) a psplit ixsplit) = addContext tel0 $ do
+  ps <- insertImplicitPatternsT ExpandLast ps $ unArg a
+  reportSDoc "tc.lhs.imp" 20 $
+    "insertImplicitPatternsT returned" <+> fsep (map prettyA ps)
+  -- (Issue 734: Do only the necessary telView to preserve clause types as much as possible.)
+  let m = length $ takeWhile (isNothing . A.isProjP) ps
+  (TelV gamma b, boundary) <- telViewUpToPathBoundaryP m $ unArg a
+  forM_ (zip ps (telToList gamma)) $ \(p, a) ->
+    unless (sameHiding p a) $ setCurrentRange p $ typeError WrongHidingInLHS
+  let tel1      = useNamesFromPattern ps gamma
+      n         = size tel1
+      (ps1,ps2) = splitAt n ps
+      tel       = telFromList $ telToList tel0 ++ telToList tel1
+      qs1       = telePatterns tel1 boundary
+      newEqs    = zipWith3 ProblemEq
+                    (map namedArg ps1)
+                    (map (patternToTerm . namedArg) qs1)
+                    (flattenTel tel1 `useOriginFrom` ps1)
+      tau       = raiseS n
+  reportSDoc "tc.lhs.problem" 10 $ addContext tel0 $ vcat
+    [ "checking lhs -- updated split problem:"
+    , nest 2 $ vcat
+      [ "ps    =" <+> fsep (map prettyA ps)
+      , "a     =" <+> prettyTCM a
+      , "tel1  =" <+> prettyTCM tel1
+      , "ps1   =" <+> fsep (map prettyA ps1)
+      , "ps2   =" <+> fsep (map prettyA ps2)
+      , "b     =" <+> addContext tel1 (prettyTCM b)
+      ]
+    ]
+  reportSDoc "tc.lhs.problem" 60 $ addContext tel0 $ vcat
+    [ nest 2 $ vcat
+      [ "ps    =" <+> (text . show) ps
+      , "a     =" <+> (text . show) a
+      , "tel1  =" <+> (text . show) tel1
+      , "ps1   =" <+> (text . show) ps1
+      , "ps2   =" <+> (text . show) ps2
+      , "b     =" <+> (text . show) b
+      , "qs1   =" <+> fsep (map pretty qs1)
+      ]
+    ]
+  return $ LHSState
+    { _lhsTel     = tel
+    , _lhsOutPat  = applySubst tau qs0 ++ qs1
+    , _lhsProblem = Problem
+                   { _problemEqs      = applyPatSubst tau oldEqs ++ newEqs
+                   , _problemRestPats = ps2
+                   , _problemCont     = ret
+                   }
+    , _lhsTarget  = a $> b
+    , _lhsPartialSplit = psplit
+    , _lhsIndexedSplit = ixsplit
+    }
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/Unify.hs b/src/full/Agda/TypeChecking/Rules/LHS/Unify.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/Unify.hs
@@ -0,0 +1,997 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+-- | Unification algorithm for specializing datatype indices, as described in
+--     \"Unifiers as Equivalences: Proof-Relevant Unification of Dependently
+--     Typed Data\" by Jesper Cockx, Dominique Devriese, and Frank Piessens
+--     (ICFP 2016).
+--
+--   This is the unification algorithm used for checking the left-hand side
+--   of clauses (see @Agda.TypeChecking.Rules.LHS@), coverage checking (see
+--   @Agda.TypeChecking.Coverage@) and indirectly also for interactive case
+--   splitting (see @Agda.Interaction.MakeCase@).
+--
+--   A unification problem (of type @UnifyState@) consists of:
+--
+--   1. A telescope @varTel@ of free variables, some or all of which are
+--      flexible (as indicated by @flexVars@).
+--
+--   2. A telescope @eqTel@ containing the types of the equations.
+--
+--   3. Left- and right-hand sides for each equation:
+--      @varTel ⊢ eqLHS : eqTel@ and @varTel ⊢ eqRHS : eqTel@.
+--
+--   The unification algorithm can end in three different ways:
+--   (type @UnificationResult@):
+--
+--   - A *positive success* @Unifies (tel, sigma, ps)@ with @tel ⊢ sigma : varTel@,
+--     @tel ⊢ eqLHS [ varTel ↦ sigma ] ≡ eqRHS [ varTel ↦ sigma ] : eqTel@,
+--     and @tel ⊢ ps : eqTel@. In this case, @sigma;ps@ is an *equivalence*
+--     between the telescopes @tel@ and @varTel(eqLHS ≡ eqRHS)@.
+--
+--   - A *negative success* @NoUnify err@ means that a conflicting equation
+--     was found (e.g an equation between two distinct constructors or a cycle).
+--
+--   - A *failure* @UnifyStuck err@ means that the unifier got stuck.
+--
+--   The unification algorithm itself consists of two parts:
+--
+--   1. A *unification strategy* takes a unification problem and produces a
+--      list of suggested unification rules (of type @UnifyStep@). Strategies
+--      can be constructed by composing simpler strategies (see for example the
+--      definition of @completeStrategyAt@).
+--
+--   2. The *unification engine* @unifyStep@ takes a unification rule and tries
+--      to apply it to the given state, writing the result to the UnifyOutput
+--      on a success.
+--
+--   The unification steps (of type @UnifyStep@) are the following:
+--
+--   - *Deletion* removes a reflexive equation @u =?= v : a@ if the left- and
+--     right-hand side @u@ and @v@ are (definitionally) equal. This rule results
+--     in a failure if --without-K is enabled (see \"Pattern Matching Without K\"
+--     by Jesper Cockx, Dominique Devriese, and Frank Piessens (ICFP 2014).
+--
+--   - *Solution* solves an equation if one side is (eta-equivalent to) a
+--     flexible variable. In case both sides are flexible variables, the
+--     unification strategy makes a choice according to the @chooseFlex@
+--     function in @Agda.TypeChecking.Rules.LHS.Problem@.
+--
+--   - *Injectivity* decomposes an equation of the form
+--     @c us =?= c vs : D pars is@ where @c : Δc → D pars js@ is a constructor
+--     of the inductive datatype @D@ into a sequence of equations
+--     @us =?= vs : delta@. In case @D@ is an indexed datatype,
+--     *higher-dimensional unification* is applied (see below).
+--
+--   - *Conflict* detects absurd equations of the form
+--     @c₁ us =?= c₂ vs : D pars is@ where @c₁@ and @c₂@ are two distinct
+--     constructors of the datatype @D@.
+--
+--   - *Cycle* detects absurd equations of the form @x =?= v : D pars is@ where
+--     @x@ is a variable of the datatype @D@ that occurs strongly rigid in @v@.
+--
+--   - *EtaExpandVar* eta-expands a single flexible variable @x : R@ where @R@
+--     is a (eta-expandable) record type, replacing it by one variable for each
+--     field of @R@.
+--
+--   - *EtaExpandEquation* eta-expands an equation @u =?= v : R@ where @R@ is a
+--     (eta-expandable) record type, replacing it by one equation for each field
+--     of @R@. The left- and right-hand sides of these equations are the
+--     projections of @u@ and @v@.
+--
+--   - *LitConflict* detects absurd equations of the form @l₁ =?= l₂ : A@ where
+--     @l₁@ and @l₂@ are distinct literal terms.
+--
+--   - *StripSizeSuc* simplifies an equation of the form
+--     @sizeSuc x =?= sizeSuc y : Size@ to @x =?= y : Size@.
+--
+--   - *SkipIrrelevantEquation@ removes an equation between irrelevant terms.
+--
+--   - *TypeConInjectivity* decomposes an equation of the form
+--     @D us =?= D vs : Set i@ where @D@ is a datatype. This rule is only used
+--     if --injective-type-constructors is enabled.
+--
+--   Higher-dimensional unification (new, does not yet appear in any paper):
+--   If an equation of the form @c us =?= c vs : D pars is@ is encountered where
+--   @c : Δc → D pars js@ is a constructor of an indexed datatype
+--   @D pars : Φ → Set ℓ@, it is in general unsound to just simplify this
+--   equation to @us =?= vs : Δc@. For this reason, the injectivity rule in the
+--   paper restricts the indices @is@ to be distinct variables that are bound in
+--   the telescope @eqTel@. But we can be more general by introducing new
+--   variables @ks@ to the telescope @eqTel@ and equating these to @is@:
+--   @
+--       Δ₁(x : D pars is)Δ₂
+--        ≃
+--       Δ₁(ks : Φ)(x : D pars ks)(ps : is ≡Φ ks)Δ₂
+--   @
+--   Since @ks@ are distinct variables, it's now possible to apply injectivity
+--   to the equation @x@, resulting in the following new equation telescope:
+--   @
+--     Δ₁(ys : Δc)(ps : is ≡Φ js[Δc ↦ ys])Δ₂
+--   @
+--   Now we can solve the equations @ps@ by recursively calling the unification
+--   algorithm with flexible variables @Δ₁(ys : Δc)@. This is called
+--   *higher-dimensional unification* since we are unifying equality proofs
+--   rather than terms. If the higher-dimensional unification succeeds, the
+--   resulting telescope serves as the new equation telescope for the original
+--   unification problem.
+
+module Agda.TypeChecking.Rules.LHS.Unify
+  ( UnificationResult
+  , UnificationResult'(..)
+  , NoLeftInv(..)
+  , unifyIndices'
+  , unifyIndices ) where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.State
+import Control.Monad.Writer (WriterT(..), MonadWriter(..))
+import Control.Monad.Except
+
+import Data.Semigroup hiding (Arg)
+import qualified Data.List as List
+import qualified Data.IntSet as IntSet
+import qualified Data.IntMap as IntMap
+import Data.IntMap (IntMap)
+
+import qualified Agda.Benchmarking as Bench
+
+import Agda.Interaction.Options (optInjectiveTypeConstructors)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+import Agda.TypeChecking.Conversion.Pure
+import Agda.TypeChecking.Constraints ()
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.Reduce
+import qualified Agda.TypeChecking.Patterns.Match as Match
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Free.Precompute
+import Agda.TypeChecking.Free.Reduce
+import Agda.TypeChecking.Records
+
+import Agda.TypeChecking.Rules.LHS.Problem
+import Agda.TypeChecking.Rules.LHS.Unify.Types
+import Agda.TypeChecking.Rules.LHS.Unify.LeftInverse
+
+import Agda.Utils.Benchmark
+import Agda.Utils.Either
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.ListT
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.PartialOrd
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+
+-- | Result of 'unifyIndices'.
+type UnificationResult = UnificationResult'
+  ( Telescope                  -- @tel@
+  , PatternSubstitution        -- @sigma@ s.t. @tel ⊢ sigma : varTel@
+  , [NamedArg DeBruijnPattern] -- @ps@    s.t. @tel ⊢ ps    : eqTel @
+  )
+
+type FullUnificationResult = UnificationResult'
+  ( Telescope                  -- @tel@
+  , PatternSubstitution        -- @sigma@ s.t. @tel ⊢ sigma : varTel@
+  , [NamedArg DeBruijnPattern] -- @ps@    s.t. @tel ⊢ ps    : eqTel @
+  , Either NoLeftInv (Substitution, Substitution) -- (τ,leftInv)
+  )
+
+data UnificationResult' a
+  = Unifies  a                        -- ^ Unification succeeded.
+  | NoUnify  NegativeUnification      -- ^ Terms are not unifiable.
+  | UnifyBlocked Blocker              -- ^ Unification got blocked on a metavariable
+  | UnifyStuck   [UnificationFailure] -- ^ Some other error happened, unification got stuck.
+  deriving (Show, Functor, Foldable, Traversable)
+
+-- | Unify indices.
+--
+--   In @unifyIndices gamma flex a us vs@,
+--
+--   * @us@ and @vs@ are the argument lists to unify, eliminating type @a@.
+--
+--   * @gamma@ is the telescope of free variables in @us@ and @vs@.
+--
+--   * @flex@ is the set of flexible (instantiable) variabes in @us@ and @vs@.
+--
+--   The result is the most general unifier of @us@ and @vs@.
+unifyIndices
+  :: (PureTCM m, MonadBench m, BenchPhase m ~ Bench.Phase, MonadError TCErr m)
+  => Maybe NoLeftInv -- ^ Do we have a reason for not computing a left inverse?
+  -> Telescope       -- ^ @gamma@
+  -> FlexibleVars    -- ^ @flex@
+  -> Type            -- ^ @a@
+  -> Args            -- ^ @us@
+  -> Args            -- ^ @vs@
+  -> m UnificationResult
+unifyIndices linv tel flex a us vs =
+  Bench.billTo [Bench.Typing, Bench.CheckLHS, Bench.UnifyIndices] $
+    fmap (\(a,b,c,_) -> (a,b,c)) <$> unifyIndices' linv tel flex a us vs
+
+unifyIndices'
+  :: (PureTCM m, MonadError TCErr m)
+  => Maybe NoLeftInv -- ^ Do we have a reason for not computing a left inverse?
+  -> Telescope     -- ^ @gamma@
+  -> FlexibleVars  -- ^ @flex@
+  -> Type          -- ^ @a@
+  -> Args          -- ^ @us@
+  -> Args          -- ^ @vs@
+  -> m FullUnificationResult
+unifyIndices' linv tel flex a [] [] = return $ Unifies (tel, idS, [], Right (idS, raiseS 1))
+unifyIndices' linv tel flex a us vs = do
+    reportSDoc "tc.lhs.unify" 10 $
+      sep [ "unifyIndices"
+          , ("tel  =" <+>) $ nest 2 $ prettyTCM tel
+          , ("flex =" <+>) $ nest 2 $ addContext tel $ text $ show $ map flexVar flex
+          , ("a    =" <+>) $ nest 2 $ addContext tel $ parens (prettyTCM a)
+          , ("us   =" <+>) $ nest 2 $ addContext tel $ prettyList $ map prettyTCM us
+          , ("vs   =" <+>) $ nest 2 $ addContext tel $ prettyList $ map prettyTCM vs
+          ]
+    initialState    <- initUnifyState tel flex a us vs
+    reportSDoc "tc.lhs.unify" 20 $ "initial unifyState:" <+> prettyTCM initialState
+    (result,log) <- runUnifyLogT $ unify initialState rightToLeftStrategy
+    forM result $ \ s -> do -- Unifies case
+        let output = mconcat [output | (UnificationStep _ _ output,_) <- log ]
+        let ps = applySubst (unifyProof output) $ teleNamedArgs (eqTel initialState)
+        tauInv <- do
+          strict     <- asksTC envSplitOnStrict
+          cubicalCompatible <- cubicalCompatibleOption
+          withoutK <- withoutKOption
+          case linv of
+            Just reason -> pure (Left reason)
+            Nothing
+              | strict            -> pure (Left SplitOnStrict)
+              | cubicalCompatible -> buildLeftInverse initialState log
+              | withoutK          -> pure (Left NoCubical)
+              | otherwise         -> pure (Left WithKEnabled)
+        reportSDoc "tc.lhs.unify" 20 $ "ps:" <+> pretty ps
+        return $ (varTel s, unifySubst output, ps, tauInv)
+
+
+
+type UnifyStrategy = forall m. (PureTCM m, MonadPlus m) => UnifyState -> m UnifyStep
+
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--leftToRightStrategy :: UnifyStrategy
+--leftToRightStrategy s =
+--    msum (for [0..n-1] $ \k -> completeStrategyAt k s)
+--  where n = size $ eqTel s
+
+rightToLeftStrategy :: UnifyStrategy
+rightToLeftStrategy s =
+    msum (for (downFrom n) $ \k -> completeStrategyAt k s)
+  where n = size $ eqTel s
+
+completeStrategyAt :: Int -> UnifyStrategy
+completeStrategyAt k s = msum $ map (\strat -> strat k s) $
+-- ASR (2021-02-07). The below eta-expansions are required by GHC >=
+-- 9.0.1 (see Issue #4955).
+    [ (\n -> skipIrrelevantStrategy n)
+    , (\n -> basicUnifyStrategy n)
+    , (\n -> literalStrategy n)
+    , (\n -> dataStrategy n)
+    , (\n -> etaExpandVarStrategy  n)
+    , (\n -> etaExpandEquationStrategy n)
+    , (\n -> injectiveTypeConStrategy n)
+    , (\n -> injectivePragmaStrategy n)
+    , (\n -> simplifySizesStrategy n)
+    , (\n -> checkEqualityStrategy n)
+    ]
+
+-- | @isHom n x@ returns x lowered by n if the variables 0..n-1 don't occur in x.
+--
+-- This is naturally sensitive to normalization.
+isHom :: (Free a, Subst a) => Int -> a -> Maybe a
+isHom n x = do
+  guard $ getAll $ runFree (All . (>= n)) IgnoreNot x
+  return $ raise (-n) x
+
+findFlexible :: Int -> FlexibleVars -> Maybe (FlexibleVar Nat)
+findFlexible i flex = List.find ((i ==) . flexVar) flex
+
+basicUnifyStrategy :: Int -> UnifyStrategy
+basicUnifyStrategy k s = do
+  Equal dom@Dom{unDom = a} u v <- eqUnLevel (getEquality k s)
+    -- Andreas, 2019-02-23: reduce equality for the sake of isHom?
+  ha <- fromMaybeMP $ isHom n a
+  (mi, mj) <- addContext (varTel s) $ (,) <$> isEtaVar u ha <*> isEtaVar v ha
+  reportSDoc "tc.lhs.unify" 30 $ "isEtaVar results: " <+> text (show [mi,mj])
+  case (mi, mj) of
+    (Just i, Just j)
+     | i == j -> mzero -- Taken care of by checkEqualityStrategy
+    (Just i, Just j)
+     | Just fi <- findFlexible i flex
+     , Just fj <- findFlexible j flex -> do
+       let choice = chooseFlex fi fj
+           firstTryLeft  = msum [ return (Solution k dom{unDom = ha} fi v left)
+                                , return (Solution k dom{unDom = ha} fj u right)]
+           firstTryRight = msum [ return (Solution k dom{unDom = ha} fj u right)
+                                , return (Solution k dom{unDom = ha} fi v left)]
+       reportSDoc "tc.lhs.unify" 40 $ "fi = " <+> text (show fi)
+       reportSDoc "tc.lhs.unify" 40 $ "fj = " <+> text (show fj)
+       reportSDoc "tc.lhs.unify" 40 $ "chooseFlex: " <+> text (show choice)
+       case choice of
+         ChooseLeft   -> firstTryLeft
+         ChooseRight  -> firstTryRight
+         ExpandBoth   -> mzero -- This should be taken care of by etaExpandEquationStrategy
+         ChooseEither -> firstTryRight
+    (Just i, _)
+     | Just fi <- findFlexible i flex -> return $ Solution k dom{unDom = ha} fi v left
+    (_, Just j)
+     | Just fj <- findFlexible j flex -> return $ Solution k dom{unDom = ha} fj u right
+    _ -> mzero
+  where
+    flex = flexVars s
+    n = eqCount s
+    left = Left (); right = Right ()
+
+dataStrategy :: Int -> UnifyStrategy
+dataStrategy k s = do
+  Equal Dom{unDom = a} u v <- eqConstructorForm =<< eqUnLevel =<< getReducedEqualityUnraised k s
+  sortOk <- reduce (getSort a) <&> \case
+    Type{} -> True
+    Inf{}  -> True
+    SSet{} -> True
+    _      -> False
+  case unEl a of
+    Def d es | sortOk -> do
+      npars <- catMaybesMP $ getNumberOfParameters d
+      let (pars,ixs) = splitAt npars $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+      reportSDoc "tc.lhs.unify" 40 $ addContext (varTel s `abstract` eqTel s) $
+        "Found equation at datatype " <+> prettyTCM d
+         <+> " with parameters " <+> prettyTCM (raise (size (eqTel s) - k) pars)
+      case (u, v) of
+        (Con c _ _   , Con c' _ _  ) | c == c' -> return $ Injectivity k a d pars ixs c
+        (Con c _ _   , Con c' _ _  ) -> return $ Conflict k a d pars u v
+        (Var i []  , v         ) -> ifOccursStronglyRigid i v $ return $ Cycle k a d pars i v
+        (u         , Var j []  ) -> ifOccursStronglyRigid j u $ return $ Cycle k a d pars j u
+        _ -> mzero
+    _ -> mzero
+  where
+    ifOccursStronglyRigid i u ret = do
+        -- Call forceNotFree to reduce u as far as possible
+        -- around any occurrences of i
+        (_ , u) <- forceNotFree (singleton i) u
+        case flexRigOccurrenceIn i u of
+          Just StronglyRigid -> ret
+          _ -> mzero
+
+checkEqualityStrategy :: Int -> UnifyStrategy
+checkEqualityStrategy k s = do
+  let Equal Dom{unDom = a} u v = getEquality k s
+      n = eqCount s
+  ha <- fromMaybeMP $ isHom n a
+  return $ Deletion k ha u v
+
+literalStrategy :: Int -> UnifyStrategy
+literalStrategy k s = do
+  let n = eqCount s
+  Equal Dom{unDom = a} u v <- eqUnLevel $ getEquality k s
+  ha <- fromMaybeMP $ isHom n a
+  (u, v) <- reduce (u, v)
+  case (u , v) of
+    (Lit l1 , Lit l2)
+     | l1 == l2  -> return $ Deletion k ha u v
+     | otherwise -> return $ LitConflict k ha l1 l2
+    _ -> mzero
+
+etaExpandVarStrategy :: Int -> UnifyStrategy
+etaExpandVarStrategy k s = do
+  Equal Dom{unDom = a} u v <- eqUnLevel =<< getReducedEquality k s
+  shouldEtaExpand u v a s `mplus` shouldEtaExpand v u a s
+  where
+    -- TODO: use IsEtaVar to check if the term is a variable
+    shouldEtaExpand :: Term -> Term -> Type -> UnifyStrategy
+    shouldEtaExpand (Var i es) v a s = do
+      fi       <- fromMaybeMP $ findFlexible i (flexVars s)
+      reportSDoc "tc.lhs.unify" 50 $
+        "Found flexible variable " <+> text (show i)
+      -- Issue 2888: Do this if there are only projections or if it's a singleton
+      -- record or if it's unified against a record constructor term. Basically
+      -- we need to avoid EtaExpandEquation if EtaExpandVar is possible, or the
+      -- forcing translation is unhappy.
+      let k  = varCount s - 1 - i -- position of var i in telescope
+          b0 = unDom $ getVarTypeUnraised k s
+      b         <- addContext (telFromList $ take k $ telToList $ varTel s) $ reduce b0
+      (d, pars) <- catMaybesMP $ isEtaRecordType b
+      ps        <- fromMaybeMP $ allProjElims es
+      guard =<< orM
+        [ pure $ not $ null ps
+        , isRecCon v  -- is the other term a record constructor?
+        , (Right True ==) <$> runBlocked (isSingletonRecord d pars)
+        ]
+      reportSDoc "tc.lhs.unify" 50 $
+        "with projections " <+> prettyTCM (map snd ps)
+      reportSDoc "tc.lhs.unify" 50 $
+        "at record type " <+> prettyTCM d
+      return $ EtaExpandVar fi d pars
+    shouldEtaExpand _ _ _ _ = mzero
+
+    isRecCon (Con c _ _) = isJust <$> isRecordConstructor (conName c)
+    isRecCon _           = return False
+
+etaExpandEquationStrategy :: Int -> UnifyStrategy
+etaExpandEquationStrategy k s = do
+  -- Andreas, 2019-02-23, re #3578, is the following reduce redundant?
+  Equal Dom{unDom = a} u v <- getReducedEqualityUnraised k s
+  (d, pars) <- catMaybesMP $ addContext tel $ isEtaRecordType a
+  guard =<< orM
+    [ (Right True ==) <$> runBlocked (isSingletonRecord d pars)
+    , shouldProject u
+    , shouldProject v
+    ]
+  return $ EtaExpandEquation k d pars
+  where
+    shouldProject :: PureTCM m => Term -> m Bool
+    shouldProject = \case
+      Def f es   -> usesCopatterns f
+      Con c _ _  -> isJust <$> isRecordConstructor (conName c)
+
+      Var _ _    -> return False
+      Lam _ _    -> __IMPOSSIBLE__
+      Lit _      -> __IMPOSSIBLE__
+      Pi _ _     -> __IMPOSSIBLE__
+      Sort _     -> __IMPOSSIBLE__
+      Level _    -> __IMPOSSIBLE__
+      MetaV _ _  -> return False
+      DontCare _ -> return False
+      Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+    tel = varTel s `abstract` telFromList (take k $ telToList $ eqTel s)
+
+simplifySizesStrategy :: Int -> UnifyStrategy
+simplifySizesStrategy k s = do
+  isSizeName <- isSizeNameTest
+  Equal Dom{unDom = a} u v <- getReducedEquality k s
+  case unEl a of
+    Def d _ -> do
+      guard $ isSizeName d
+      su <- sizeView u
+      sv <- sizeView v
+      case (su, sv) of
+        (SizeSuc u, SizeSuc v) -> return $ StripSizeSuc k u v
+        (SizeSuc u, SizeInf  ) -> return $ StripSizeSuc k u v
+        (SizeInf  , SizeSuc v) -> return $ StripSizeSuc k u v
+        _ -> mzero
+    _ -> mzero
+
+injectiveTypeConStrategy :: Int -> UnifyStrategy
+injectiveTypeConStrategy k s = do
+  injTyCon <- optInjectiveTypeConstructors <$> pragmaOptions
+  guard injTyCon
+  eq <- eqUnLevel =<< getReducedEquality k s
+  case eq of
+    Equal a u@(Def d es) v@(Def d' es') | d == d' -> do
+      -- d must be a data, record or axiom
+      def <- getConstInfo d
+      guard $ case theDef def of
+                Datatype{} -> True
+                Record{}   -> True
+                Axiom{}    -> True
+                DataOrRecSig{} -> True
+                AbstractDefn{} -> False -- True triggers issue #2250
+                Function{}   -> False
+                Primitive{}  -> False
+                PrimitiveSort{} -> __IMPOSSIBLE__
+                GeneralizableVar{} -> __IMPOSSIBLE__
+                Constructor{} -> __IMPOSSIBLE__  -- Never a type!
+      let us = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es'
+      return $ TypeConInjectivity k d us vs
+    _ -> mzero
+
+injectivePragmaStrategy :: Int -> UnifyStrategy
+injectivePragmaStrategy k s = do
+  eq <- eqUnLevel =<< getReducedEquality k s
+  case eq of
+    Equal a u@(Def d es) v@(Def d' es') | d == d' -> do
+      -- d must have an injective pragma
+      def <- getConstInfo d
+      guard $ defInjective def
+      let us = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+          vs = fromMaybe __IMPOSSIBLE__ $ allApplyElims es'
+      return $ TypeConInjectivity k d us vs
+    _ -> mzero
+
+skipIrrelevantStrategy :: Int -> UnifyStrategy
+skipIrrelevantStrategy k s = do
+  let Equal a _ _ = getEquality k s                                 -- reduce not necessary
+  addContext (varTel s `abstract` eqTel s) $
+    guard . (== Right True) =<< runBlocked (isIrrelevantOrPropM a)  -- reduction takes place here
+  -- TODO: do something in case the above is blocked (i.e. `Left b`)
+  return $ SkipIrrelevantEquation k
+
+
+----------------------------------------------------
+-- Actually doing the unification
+----------------------------------------------------
+
+unifyStep
+  :: (PureTCM m, MonadWriter UnifyOutput m, MonadError TCErr m)
+  => UnifyState -> UnifyStep -> m (UnificationResult' UnifyState)
+unifyStep s Deletion{ deleteAt = k , deleteType = a , deleteLeft = u , deleteRight = v } = do
+    -- Check definitional equality of u and v
+    isReflexive <- addContext (varTel s) $ runBlocked $ pureEqualTerm a u v
+    withoutK <- withoutKOption
+    splitOnStrict <- asksTC envSplitOnStrict
+    case isReflexive of
+      Left block   -> return $ UnifyBlocked block
+      Right False  -> return $ UnifyStuck []
+      Right True | withoutK && not splitOnStrict
+                   -> return $ UnifyStuck [UnifyReflexiveEq (varTel s) a u]
+      Right True   -> do
+        let (s', sigma) = solveEq k u s
+        tellUnifyProof sigma
+        Unifies <$> lensEqTel reduce s'
+
+unifyStep s step@Solution{} = solutionStep RetryNormalised s step
+
+unifyStep s (Injectivity k a d pars ixs c) = do
+  ifM (consOfHIT $ conName c) (return $ UnifyStuck []) $ do
+  withoutK <- withoutKOption
+
+  -- Split equation telescope into parts before and after current equation
+  let (eqListTel1, _ : eqListTel2) = splitAt k $ telToList $ eqTel s
+      (eqTel1, eqTel2) = (telFromList eqListTel1, telFromList eqListTel2)
+
+  -- Get constructor telescope and target indices
+  cdef  <- getConInfo c
+  let ctype  = defType cdef `piApply` pars
+  addContext (varTel s `abstract` eqTel1) $ reportSDoc "tc.lhs.unify" 40 $
+    "Constructor type: " <+> prettyTCM ctype
+  TelV ctel ctarget <- addContext (varTel s `abstract` eqTel1) $ telView ctype
+  let cixs = case unEl ctarget of
+               Def d' es | d == d' ->
+                 let args = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+                 in  drop (length pars) args
+               _ -> __IMPOSSIBLE__
+
+  -- Get index telescope of the datatype
+  dtype    <- (`piApply` pars) . defType <$> getConstInfo d
+  addContext (varTel s `abstract` eqTel1) $ reportSDoc "tc.lhs.unify" 40 $
+    "Datatype type: " <+> prettyTCM dtype
+
+  -- This is where the magic of higher-dimensional unification happens
+  -- We need to generalize the indices `ixs` to the target indices of the
+  -- constructor `cixs`. This is done by calling the unification algorithm
+  -- recursively (this doesn't get stuck in a loop because a type should
+  -- never be indexed over itself). Note the similarity with the
+  -- computeNeighbourhood function in Agda.TypeChecking.Coverage.
+  let hduTel = eqTel1 `abstract` ctel
+      notforced = replicate (size hduTel) NotForced
+
+  -- The left inverse computed here is not actually used when computing
+  -- a left inverse for the overall match, so as a slight optimisation
+  -- we just don't bother computing it. __IMPOSSIBLE__ because that
+  -- field in the result is never evaluated.
+  res <- addContext (varTel s) $ unifyIndices' (Just __IMPOSSIBLE__)
+           hduTel
+           (allFlexVars notforced hduTel)
+           (raise (size ctel) dtype)
+           (raise (size ctel) ixs)
+           cixs
+  case res of
+    -- Higher-dimensional unification can never end in a conflict,
+    -- because `cong c1 ...` and `cong c2 ...` don't even have the
+    -- same type for distinct constructors c1 and c2.
+    NoUnify _ -> __IMPOSSIBLE__
+
+    -- Higher-dimensional unification is blocked: propagate
+    UnifyBlocked block -> return $ UnifyBlocked block
+
+    -- Higher-dimensional unification has failed. If not --without-K,
+    -- we can simply ignore the higher-dimensional equations and
+    -- simplify the equation as in the non-indexed case.
+    UnifyStuck _ | not withoutK -> do
+      -- using the same variable names as in the case where hdu succeeds.
+      let eqTel1' = eqTel1 `abstract` ctel
+          rho1    = raiseS (size ctel)
+          ceq     = ConP c noConPatternInfo $ teleNamedArgs ctel
+          rho3    = consS ceq rho1
+          eqTel2' = applyPatSubst rho3 eqTel2
+          eqTel'  = eqTel1' `abstract` eqTel2'
+          rho     = liftS (size eqTel2) rho3
+
+      tellUnifyProof rho
+
+      eqTel' <- addContext (varTel s) $ reduce eqTel'
+
+      -- Compute new lhs and rhs by matching the old ones against rho
+      (lhs', rhs') <- addContext (varTel s) $ do
+        let ps = applySubst rho $ teleNamedArgs $ eqTel s
+        (lhsMatch, _) <- Match.matchPatterns ps $ eqLHS s
+        (rhsMatch, _) <- Match.matchPatterns ps $ eqRHS s
+        case (lhsMatch, rhsMatch) of
+          (Match.Yes _ lhs', Match.Yes _ rhs') -> return
+            (reverse $ Match.matchedArgs __IMPOSSIBLE__ (size eqTel') lhs',
+             reverse $ Match.matchedArgs __IMPOSSIBLE__ (size eqTel') rhs')
+          _ -> __IMPOSSIBLE__
+
+      return $ Unifies $ s { eqTel = eqTel' , eqLHS = lhs' , eqRHS = rhs' }
+
+
+    UnifyStuck _ -> let n           = eqCount s
+                        Equal Dom{unDom = a} u v = getEquality k s
+                    in return $ UnifyStuck [UnifyIndicesNotVars
+                         (varTel s `abstract` eqTel s) a
+                         (raise n u) (raise n v) (raise (n-k) ixs)]
+
+    Unifies (eqTel1', rho0, _, _) -> do
+      -- Split ps0 into parts for eqTel1 and ctel
+      let (rho1, rho2) = splitS (size ctel) rho0
+
+      -- Compute new equation telescope context and substitution
+      let ceq     = ConP c noConPatternInfo $ applySubst rho2 $ teleNamedArgs ctel
+          rho3    = consS ceq rho1
+          eqTel2' = applyPatSubst rho3 eqTel2
+          eqTel'  = eqTel1' `abstract` eqTel2'
+          rho     = liftS (size eqTel2) rho3
+
+      tellUnifyProof rho
+
+      eqTel' <- addContext (varTel s) $ reduce eqTel'
+
+      -- Compute new lhs and rhs by matching the old ones against rho
+      (lhs', rhs') <- addContext (varTel s) $ do
+        let ps = applySubst rho $ teleNamedArgs $ eqTel s
+        (lhsMatch, _) <- Match.matchPatterns ps $ eqLHS s
+        (rhsMatch, _) <- Match.matchPatterns ps $ eqRHS s
+        case (lhsMatch, rhsMatch) of
+          (Match.Yes _ lhs', Match.Yes _ rhs') -> return
+            (reverse $ Match.matchedArgs __IMPOSSIBLE__ (size eqTel') lhs',
+             reverse $ Match.matchedArgs __IMPOSSIBLE__ (size eqTel') rhs')
+          _ -> __IMPOSSIBLE__
+
+      return $ Unifies $ s { eqTel = eqTel' , eqLHS = lhs' , eqRHS = rhs' }
+
+unifyStep s Conflict
+  { conflictLeft  = u
+  , conflictRight = v
+  } =
+  case u of
+    Con h _ _ -> do
+      ifM (consOfHIT $ conName h) (return $ UnifyStuck []) $ do
+        return $ NoUnify $ UnifyConflict (varTel s) u v
+    _ -> __IMPOSSIBLE__
+unifyStep s Cycle
+  { cycleVar        = i
+  , cycleOccursIn   = u
+  } =
+  case u of
+    Con h _ _ -> do
+      ifM (consOfHIT $ conName h) (return $ UnifyStuck []) $ do
+        return $ NoUnify $ UnifyCycle (varTel s) i u
+    _ -> __IMPOSSIBLE__
+
+unifyStep s EtaExpandVar{ expandVar = fi, expandVarRecordType = d , expandVarParameters = pars } = do
+  recd <- fromMaybe __IMPOSSIBLE__ <$> isRecord d
+  let delta = recTel recd `apply` pars
+      c     = recConHead recd
+  let nfields         = size delta
+      (varTel', rho)  = expandTelescopeVar (varTel s) (m-1-i) delta c
+      projectFlexible = [ FlexibleVar (getArgInfo fi) (flexForced fi) (projFlexKind j) (flexPos fi) (i + j) | j <- [0 .. nfields - 1] ]
+  tellUnifySubst $ rho
+  return $ Unifies $ UState
+    { varTel   = varTel'
+    , flexVars = projectFlexible ++ liftFlexibles nfields (flexVars s)
+    , eqTel    = applyPatSubst rho $ eqTel s
+    , eqLHS    = applyPatSubst rho $ eqLHS s
+    , eqRHS    = applyPatSubst rho $ eqRHS s
+    }
+  where
+    i = flexVar fi
+    m = varCount s
+
+    projFlexKind :: Int -> FlexibleVarKind
+    projFlexKind j = case flexKind fi of
+      RecordFlex ks -> indexWithDefault ImplicitFlex ks j
+      ImplicitFlex  -> ImplicitFlex
+      DotFlex       -> DotFlex
+      OtherFlex     -> OtherFlex
+
+    liftFlexible :: Int -> Int -> Maybe Int
+    liftFlexible n j = if j == i then Nothing else Just (if j > i then j + (n-1) else j)
+
+    liftFlexibles :: Int -> FlexibleVars -> FlexibleVars
+    liftFlexibles n fs = mapMaybe (traverse $ liftFlexible n) fs
+
+unifyStep s EtaExpandEquation{ expandAt = k, expandRecordType = d, expandParameters = pars } = do
+  recd  <- fromMaybe __IMPOSSIBLE__ <$> isRecord d
+  let delta = recTel recd `apply` pars
+      c     = recConHead recd
+  lhs   <- expandKth $ eqLHS s
+  rhs   <- expandKth $ eqRHS s
+  let (tel, sigma) = expandTelescopeVar (eqTel s) k delta c
+  tellUnifyProof sigma
+  Unifies <$> do
+   lensEqTel reduce $ s
+    { eqTel    = tel
+    , eqLHS    = lhs
+    , eqRHS    = rhs
+    }
+  where
+    expandKth us = do
+      let (us1,v:us2) = fromMaybe __IMPOSSIBLE__ $ splitExactlyAt k us
+      vs <- snd <$> etaExpandRecord d pars (unArg v)
+      vs <- reduce vs
+      return $ us1 ++ vs ++ us2
+
+unifyStep s LitConflict
+  { litType          = a
+  , litConflictLeft  = l
+  , litConflictRight = l'
+  } = return $ NoUnify $ UnifyConflict (varTel s) (Lit l) (Lit l')
+
+unifyStep s (StripSizeSuc k u v) = do
+  sizeTy <- sizeType
+  sizeSu <- sizeSuc 1 (var 0)
+  let n          = eqCount s
+      sub        = liftS (n-k-1) $ consS sizeSu $ raiseS 1
+      eqFlatTel  = flattenTel $ eqTel s
+      eqFlatTel' = applySubst sub $ updateAt k (fmap $ const sizeTy) $ eqFlatTel
+      eqTel'     = unflattenTel (teleNames $ eqTel s) eqFlatTel'
+  -- TODO: tellUnifyProof sub
+  -- but sizeSu is not a constructor, so sub is not a PatternSubstitution!
+  return $ Unifies $ s
+    { eqTel = eqTel'
+    , eqLHS = updateAt k (const $ defaultArg u) $ eqLHS s
+    , eqRHS = updateAt k (const $ defaultArg v) $ eqRHS s
+    }
+
+unifyStep s (SkipIrrelevantEquation k) = do
+  let lhs = eqLHS s
+      (s', sigma) = solveEq k (DontCare $ unArg $ indexWithDefault __IMPOSSIBLE__ lhs k) s
+  tellUnifyProof sigma
+  return $ Unifies s'
+
+unifyStep s (TypeConInjectivity k d us vs) = do
+  dtype <- defType <$> getConstInfo d
+  TelV dtel _ <- telView dtype
+  let deq = Def d $ map Apply $ teleArgs dtel
+  -- TODO: tellUnifyProof ???
+  -- but d is not a constructor...
+  Unifies <$> do
+   lensEqTel reduce $ s
+    { eqTel = dtel `abstract` applyUnder k (eqTel s) (raise k deq)
+    , eqLHS = us ++ dropAt k (eqLHS s)
+    , eqRHS = vs ++ dropAt k (eqRHS s)
+    }
+
+data RetryNormalised = RetryNormalised | DontRetryNormalised
+  deriving (Eq, Show)
+
+solutionStep
+  :: (PureTCM m, MonadWriter UnifyOutput m)
+  => RetryNormalised
+  -> UnifyState
+  -> UnifyStep
+  -> m (UnificationResult' UnifyState)
+solutionStep retry s
+  step@Solution{ solutionAt   = k
+               , solutionType = dom@Dom{ unDom = a }
+               , solutionVar  = fi@FlexibleVar{ flexVar = i }
+               , solutionTerm = u } = do
+  let m = varCount s
+
+  -- Now we have to be careful about forced variables in `u`. If they appear
+  -- in pattern positions we need to bind them there rather in their forced positions. We can safely
+  -- ignore non-pattern positions and forced pattern positions, because in that case there will be
+  -- other equations where the variable can be bound.
+  -- NOTE: If we're doing make-case we ignore forced variables. This is safe since we take the
+  -- result of unification and build user clauses that will be checked again with forcing turned on.
+  inMakeCase <- viewTC eMakeCase
+  let forcedVars | inMakeCase = IntMap.empty
+                 | otherwise  = IntMap.fromList [ (flexVar fi, getModality fi) | fi <- flexVars s,
+                                                                                 flexForced fi == Forced ]
+  (p, bound) <- patternBindingForcedVars forcedVars u
+
+  -- To maintain the invariant that each variable in varTel is bound exactly once in the pattern
+  -- substitution we need to turn the bound variables in `p` into dot patterns in the rest of the
+  -- substitution.
+  let dotSub = foldr composeS idS [ inplaceS i (dotP (Var i [])) | i <- IntMap.keys bound ]
+
+  -- We moved the binding site of some forced variables, so we need to update their modalities in
+  -- the telescope. The new modality is the combination of the modality of the variable we are
+  -- instantiating and the modality of the binding site in the pattern (returned by
+  -- patternBindingForcedVars).
+  let updModality md vars tel
+        | IntMap.null vars = tel
+        | otherwise        = telFromList $ zipWith upd (downFrom $ size tel) (telToList tel)
+        where
+          upd i a | Just md' <- IntMap.lookup i vars = setModality (composeModality md md') a
+                  | otherwise                        = a
+  s <- return $ s { varTel = updModality (getModality fi) bound (varTel s) }
+
+  reportSDoc "tc.lhs.unify.force" 45 $ vcat
+    [ "forcedVars =" <+> pretty (IntMap.keys forcedVars)
+    , "u          =" <+> prettyTCM u
+    , "p          =" <+> prettyTCM p
+    , "bound      =" <+> pretty (IntMap.keys bound)
+    , "dotSub     =" <+> pretty dotSub ]
+
+  -- Check that the type of the variable is equal to the type of the equation
+  -- (not just a subtype), otherwise we cannot instantiate (see Issue 2407).
+  let dom'@Dom{ unDom = a' } = getVarType (m-1-i) s
+  equalTypes <- addContext (varTel s) $ runBlocked $ do
+    reportSDoc "tc.lhs.unify" 45 $ "Equation type: " <+> prettyTCM a
+    reportSDoc "tc.lhs.unify" 45 $ "Variable type: " <+> prettyTCM a'
+    pureEqualType a a'
+
+  -- The conditions on the relevances are as follows (see #2640):
+  -- - If the type of the equation is relevant, then the solution must be
+  --   usable in a relevant position.
+  -- - If the type of the equation is (shape-)irrelevant, then the solution
+  --   must be usable in a μ-relevant position where μ is the relevance
+  --   of the variable being solved.
+  --
+  -- Jesper, Andreas, 2018-10-17: the quantity of the equation is morally
+  -- always @Quantity0@, since the indices of the data type are runtime erased.
+  -- Thus, we need not change the quantity of the solution.
+  envmod <- currentModality
+  let eqrel  = getRelevance dom
+      eqmod  = getModality dom
+      varmod = getModality dom'
+      mod    = applyUnless (NonStrict `moreRelevant` eqrel) (setRelevance eqrel)
+             $ applyUnless (usableQuantity envmod) (setQuantity zeroQuantity)
+             $ varmod
+  reportSDoc "tc.lhs.unify" 65 $ text $ "Equation modality: " ++ show (getModality dom)
+  reportSDoc "tc.lhs.unify" 65 $ text $ "Variable modality: " ++ show varmod
+  reportSDoc "tc.lhs.unify" 65 $ text $ "Solution must be usable in a " ++ show mod ++ " position."
+  -- Andreas, 2018-10-18
+  -- Currently, the modality check has problems with meta-variables created in the type signature,
+  -- and thus, in quantity 0, that get into terms using the unifier, and there are checked to be
+  -- non-erased, i.e., have quantity ω.
+  -- Ulf, 2019-12-13. We still do it though.
+  -- Andrea, 2020-10-15: It looks at meta instantiations now.
+  eusable <- addContext (varTel s) $ runExceptT $ usableMod mod u
+  caseEitherM (return eusable) (return . UnifyBlocked) $ \ usable -> do
+
+  reportSDoc "tc.lhs.unify" 45 $ "Modality ok: " <+> prettyTCM usable
+  unless usable $ reportSDoc "tc.lhs.unify" 65 $ "Rejected solution: " <+> prettyTCM u
+
+  -- We need a Flat equality to solve a Flat variable.
+  -- This also ought to take care of the need for a usableCohesion check.
+  if not (getCohesion eqmod `moreCohesion` getCohesion varmod) then return $ UnifyStuck [] else do
+
+  case equalTypes of
+    Left block  -> return $ UnifyBlocked block
+    Right False -> return $ UnifyStuck []
+    Right True | usable ->
+      case solveVar (m - 1 - i) p s of
+        Nothing | retry == RetryNormalised -> do
+          u <- normalise u
+          s <- lensVarTel normalise s
+          solutionStep DontRetryNormalised s step{ solutionTerm = u }
+        Nothing ->
+          return $ UnifyStuck [UnifyRecursiveEq (varTel s) a i u]
+        Just (s', sub) -> do
+          let rho = sub `composeS` dotSub
+          tellUnifySubst rho
+          let (s'', sigma) = solveEq k (applyPatSubst rho u) s'
+          tellUnifyProof sigma
+          return $ Unifies s''
+          -- Andreas, 2019-02-23, issue #3578: do not eagerly reduce
+          -- Unifies <$> liftTCM (reduce s'')
+    Right True -> return $ UnifyStuck [UnifyUnusableModality (varTel s) a i u mod]
+solutionStep _ _ _ = __IMPOSSIBLE__
+
+unify
+  :: (PureTCM m, MonadWriter UnifyLog' m, MonadError TCErr m)
+  => UnifyState -> UnifyStrategy -> m (UnificationResult' UnifyState)
+unify s strategy = if isUnifyStateSolved s
+                   then return $ Unifies s
+                   else tryUnifyStepsAndContinue (strategy s)
+  where
+    tryUnifyStepsAndContinue
+      :: (PureTCM m, MonadWriter UnifyLog' m, MonadError TCErr m)
+      => ListT m UnifyStep -> m (UnificationResult' UnifyState)
+    tryUnifyStepsAndContinue steps = do
+      x <- foldListT tryUnifyStep failure steps
+      case x of
+        Unifies s'     -> unify s' strategy
+        NoUnify err    -> return $ NoUnify err
+        UnifyBlocked b -> return $ UnifyBlocked b
+        UnifyStuck err -> return $ UnifyStuck err
+
+    tryUnifyStep :: (PureTCM m, MonadWriter UnifyLog' m, MonadError TCErr m)
+                 => UnifyStep
+                 -> m (UnificationResult' UnifyState)
+                 -> m (UnificationResult' UnifyState)
+    tryUnifyStep step fallback = do
+      addContext (varTel s) $
+        reportSDoc "tc.lhs.unify" 20 $ "trying unifyStep" <+> prettyTCM step
+      (x, output) <- runWriterT $ unifyStep s step
+      case x of
+        Unifies s'   -> do
+          reportSDoc "tc.lhs.unify" 20 $ "unifyStep successful."
+          reportSDoc "tc.lhs.unify" 20 $ "new unifyState:" <+> prettyTCM s'
+          -- tell output
+          writeUnifyLog $ (UnificationStep s step output,s')
+          return x
+        NoUnify{}       -> return x
+        UnifyBlocked b1 -> do
+          y <- fallback
+          case y of
+            UnifyStuck _    -> return $ UnifyBlocked b1
+            UnifyBlocked b2 -> return $ UnifyBlocked $ unblockOnEither b1 b2
+            _               -> return y
+        UnifyStuck err1 -> do
+          y <- fallback
+          case y of
+            UnifyStuck err2 -> return $ UnifyStuck $ err1 ++ err2
+            _               -> return y
+
+    failure :: Monad m => m (UnificationResult' a)
+    failure = return $ UnifyStuck []
+
+-- | Turn a term into a pattern while binding as many of the given forced variables as possible (in
+--   non-forced positions).
+patternBindingForcedVars :: PureTCM m => IntMap Modality -> Term -> m (DeBruijnPattern, IntMap Modality)
+patternBindingForcedVars forced v = do
+  let v' = precomputeFreeVars_ v
+  runWriterT (evalStateT (go unitModality v') forced)
+  where
+    noForced v = gets $ IntSet.disjoint (precomputedFreeVars v) . IntMap.keysSet
+
+    bind md i = do
+      gets (IntMap.lookup i) >>= \case
+        Just md' | related md POLE md' -> do
+          -- The new binding site must be more relevant (more relevant = smaller).
+          -- "The forcing analysis guarantees that there exists such a position."
+          -- Really? Andreas, 2021-08-18, issue #5506
+          tell   $ IntMap.singleton i md
+          modify $ IntMap.delete i
+          return $ varP (deBruijnVar i)
+        _ -> return $ dotP (Var i [])
+
+    go md v = ifM (noForced v) (return $ dotP v) $ do
+      v' <- lift $ lift $ reduce v
+      case v' of
+        Var i [] -> bind md i  -- we know i is forced
+        Con c ci es
+          | Just vs <- allApplyElims es -> do
+            fs <- defForced <$> getConstInfo (conName c)
+            let goArg Forced    v = return $ fmap (unnamed . dotP) v
+                goArg NotForced v = fmap unnamed <$> traverse (go $ composeModality md $ getModality v) v
+            (ps, bound) <- listen $ zipWithM goArg (fs ++ repeat NotForced) vs
+            if IntMap.null bound
+              then return $ dotP v  -- bound nothing
+              else do
+                let cpi = (toConPatternInfo ci) { conPLazy   = True } -- Not setting conPType. Is this a problem?
+                return $ ConP c cpi $ map (setOrigin Inserted) ps
+          | otherwise -> return $ dotP v   -- Higher constructor (es has IApply)
+
+        -- Non-pattern positions
+        Var _ (_:_) -> return $ dotP v
+        Lam{}       -> return $ dotP v
+        Pi{}        -> return $ dotP v
+        Def{}       -> return $ dotP v
+        MetaV{}     -> return $ dotP v
+        Sort{}      -> return $ dotP v
+        Level{}     -> return $ dotP v
+        DontCare{}  -> return $ dotP v
+        Dummy{}     -> return $ dotP v
+        Lit{}       -> return $ dotP v
+          -- Andreas, 2023-08-20, issue #6767
+          -- The last case is not __IMPOSSIBLE__ (regresssion in 2.6.2).
+          -- It would be if we had reduced to `constructorForm`,
+          -- however, turning a `LitNat` into constructors would only result in churn,
+          -- since literals have no variables that could be bound.
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/Unify/LeftInverse.hs b/src/full/Agda/TypeChecking/Rules/LHS/Unify/LeftInverse.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/Unify/LeftInverse.hs
@@ -0,0 +1,447 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.LHS.Unify.LeftInverse where
+
+import Prelude hiding ((!!), null)
+
+import Control.Monad
+import Control.Monad.State
+import Control.Monad.Except
+
+
+import Agda.Interaction.Options (optCubical)
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive hiding (Nat)
+import Agda.TypeChecking.Names
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Records
+
+import Agda.TypeChecking.Rules.LHS.Problem
+import Agda.TypeChecking.Rules.LHS.Unify.Types
+
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+instance PrettyTCM NoLeftInv where
+  prettyTCM (UnsupportedYet s) = fsep $ pwords "It relies on" ++ [explainStep s <> ","] ++ pwords "which is not yet supported"
+  prettyTCM UnsupportedCxt     = fwords "it relies on higher-dimensional unification, which is not yet supported"
+  prettyTCM (Illegal s)        = fsep $ pwords "It relies on" ++ [explainStep s <> ","] ++ pwords "which is incompatible with" ++ [text "Cubical Agda"]
+  prettyTCM NoCubical          = fwords "Cubical Agda is disabled"
+  prettyTCM WithKEnabled       = fwords "The K rule is enabled"
+  prettyTCM SplitOnStrict      = fwords "It splits on a type in SSet"
+  prettyTCM SplitOnFlat        = fwords "It splits on a @♭ argument"
+
+data NoLeftInv
+  = UnsupportedYet {badStep :: UnifyStep}
+  | Illegal        {badStep :: UnifyStep}
+  | NoCubical
+  | WithKEnabled
+  | SplitOnStrict  -- ^ splitting on a Strict Set.
+  | SplitOnFlat    -- ^ splitting on a @♭ argument
+  | UnsupportedCxt
+  deriving Show
+
+buildLeftInverse :: (PureTCM tcm, MonadError TCErr tcm) => UnifyState -> UnifyLog -> tcm (Either NoLeftInv (Substitution, Substitution))
+buildLeftInverse s0 log = do
+  reportSDoc "tc.lhs.unify.inv.badstep" 20 $ do
+    cubical <- optCubical <$> pragmaOptions
+    "cubical:" <+> text (show cubical)
+  reportSDoc "tc.lhs.unify.inv.badstep" 20 $ do
+    pathp <- getTerm' builtinPathP
+    "pathp:" <+> text (show $ isJust pathp)
+  let cond = andM
+       -- TODO: handle open contexts: they happen during "higher dimensional" unification,
+       --       in injectivity cases.
+       [
+         null <$> getContext
+       ]
+  ifNotM cond (return $ Left UnsupportedCxt) $ do
+  equivs <- forM log $ uncurry buildEquiv
+  case sequence equivs of
+    Left no -> do
+      reportSDoc "tc.lhs.unify.inv.badstep" 20 $ "No Left Inverse:" <+> prettyTCM (badStep no)
+      return (Left no)
+    Right xs -> do
+    -- Γ,φ,us =_Δ vs ⊢ τ0 : Γ', φ
+    -- Γ,φ,us =_Δ vs, i : I ⊢ leftInv0 : Γ,φ,us =_Δ vs
+    -- leftInv0 : [wkS |φ,us =_Δ vs| ρ,φ,refls][τ0] = IdS : Γ,φ,us =_Δ vs
+    (tau0,leftInv0) <- case xs of
+      [] -> return (idS,raiseS 1)
+      xs -> do
+        let
+            loop [] = __IMPOSSIBLE__
+            loop [x] = return $ fst x
+            loop (x:xs) = do
+              r <- loop xs
+              uncurry composeRetract x r
+        (_,_,tau,leftInv) <- loop xs
+        return (tau,leftInv)
+    -- Γ,φ,us =_Δ vs ⊢ τ0 : Γ', φ
+    -- leftInv0 : [wkS |φ,us =_Δ vs| ρ,1,refls][τ] = idS : Γ,φ,us =_Δ vs
+    let tau = tau0 `composeS` raiseS 1
+    unview <- intervalUnview'
+    let replaceAt n x xs = xs0 ++ x:xs1
+                where (xs0,_:xs1) = splitAt n xs
+    let max r s = unview $ IMax (argN r) (argN s)
+        neg r = unview $ INeg (argN r)
+    let phieq = neg (var 0) `max` var (size (eqTel s0) + 1)
+                       -- I + us =_Δ vs -- inplaceS
+    let leftInv = termsS __IMPOSSIBLE__ $ replaceAt (size (varTel s0)) phieq $ map (lookupS leftInv0) $ downFrom (size (varTel s0) + 1 + size (eqTel s0))
+    let working_tel = abstract (varTel s0) (ExtendTel __DUMMY_DOM__ $ Abs "phi0" $ (eqTel s0))
+    reportSDoc "tc.lhs.unify.inv" 20 $ "=== before mod"
+    do
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau0    :" <+> prettyTCM tau0
+        addContext working_tel $ addContext ("r" :: String, __DUMMY_DOM__)
+                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv0:  " <+> prettyTCM leftInv0
+
+    reportSDoc "tc.lhs.unify.inv" 20 $ "=== after mod"
+    do
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM tau
+        addContext working_tel $ addContext ("r" :: String, __DUMMY_DOM__)
+                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv:   " <+> prettyTCM leftInv
+
+    return $ Right (tau,leftInv)
+
+type Retract = (Telescope, Substitution, Substitution, Substitution)
+     -- Γ (the problem, including equalities),
+     -- Δ ⊢ ρ : Γ
+     -- Γ ⊢ τ : Δ
+     -- Γ, i : I ⊢ leftInv : Γ, such that (λi. leftInv) : ρ[τ] = id_Γ
+
+--- Γ ⊢ us : Δ   Γ ⊢ termsS e us : Δ
+termsS ::  DeBruijn a => Impossible -> [a] -> Substitution' a
+termsS e xs = reverse xs ++# EmptyS e
+
+composeRetract :: (PureTCM tcm, MonadError TCErr tcm, MonadDebug tcm,HasBuiltins tcm, MonadAddContext tcm) => Retract -> Term -> Retract -> tcm Retract
+composeRetract (prob0,rho0,tau0,leftInv0) phi0 (prob1,rho1,tau1,leftInv1) = do
+  reportSDoc "tc.lhs.unify.inv" 20 $ "=== composing"
+  reportSDoc "tc.lhs.unify.inv" 20 $ "Γ0   :" <+> prettyTCM prob0
+  addContext prob0 $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau0  :" <+> prettyTCM tau0
+  reportSDoc "tc.lhs.unify.inv" 20 $ "Γ1   :" <+> prettyTCM prob1
+  addContext prob1 $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau1  :" <+> prettyTCM tau1
+
+
+  {-
+  Γ0 = prob0
+  S0 ⊢ ρ0 : Γ0
+  Γ0 ⊢ τ0 : S0
+  Γ0 ⊢ leftInv0 : ρ0[τ0] = idΓ0
+  Γ0 ⊢ φ0
+  Γ0,φ0 ⊢ leftInv0 = refl
+
+  Γ1 = prob1
+  S1 ⊢ ρ1 : Γ1
+  Γ1 ⊢ τ1 : S1
+  Γ1 ⊢ leftInv1 : ρ1[τ1] = idΓ1
+  Γ1 ⊢ φ1 = φ0[τ0] (**)
+  Γ1,φ1 ⊢ leftInv1 = refl
+  S0 = Γ1
+
+  (**) implies?
+  Γ0,φ0 ⊢ leftInv1[τ0] = refl  (*)
+
+
+  S1 ⊢ ρ := ρ0[ρ1] : Γ0
+  Γ0 ⊢ τ := τ1[τ0] : S1
+  -}
+
+  let prob = prob0
+  let rho = rho1 `composeS` rho0
+  let tau = tau0 `composeS` tau1
+
+  addContext prob0 $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau  :" <+> prettyTCM tau
+
+  {-
+  Γ0 ⊢ leftInv : ρ[τ] = idΓ0
+  Γ0 ⊢ leftInv : ρ0[ρ1[τ1]][τ0] = idΓ0
+  Γ0 ⊢ step0 := ρ0[leftInv1[τ0]] : ρ0[ρ1[τ1]][τ0] = ρ0[τ0]
+
+  Γ0,φ0 ⊢ step0 = refl     by (*)
+
+
+  Γ0 ⊢ leftInv := step0 · leftInv0 : ρ0[ρ1[τ1]][τ0] = idΓ0
+
+  Γ0 ⊢ leftInv := tr (\ i → ρ0[ρ1[τ1]][τ0] = leftInv0[i]) φ0 step0
+  Γ0,φ0 ⊢ leftInv = refl  -- because it will become step0, which is refl when φ0
+
+  Γ0, i : I ⊢ hcomp {Γ0} (\ j → \ { (i = 0) -> ρ0[ρ1[τ1]][τ0]
+                                  ; (i = 1) -> leftInv0[j]
+                                  ; (φ0 = 1) -> γ0
+                                  })
+                         (step0[i])
+
+
+
+
+  -}
+  let step0 = liftS 1 tau0 `composeS` leftInv1 `composeS` rho0
+
+  addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv0  :" <+> prettyTCM leftInv0
+  addContext prob1 $ reportSDoc "tc.lhs.unify.inv" 20 $ "rho0  :" <+> prettyTCM rho0
+  addContext prob0 $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau0  :" <+> prettyTCM tau0
+  addContext prob0 $ reportSDoc "tc.lhs.unify.inv" 20 $ "rhos0[tau0]  :" <+> prettyTCM (tau0 `composeS` rho0)
+
+  addContext prob1 $ addContext ("r" :: String, __DUMMY_DOM__) $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv1  :" <+> prettyTCM leftInv1
+  addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) $ reportSDoc "tc.lhs.unify.inv" 20 $ "step0  :" <+> prettyTCM step0
+
+  interval <- primIntervalType
+  max <- primIMax
+  neg <- primINeg
+  Right leftInv <- fmap sequenceA $ addContext prob0 $ runNamesT (teleNames prob0) $ do
+             phi <- open phi0
+             g0 <- open $ raise (size prob0) prob0
+             step0 <- open $ Abs "i" $ step0 `applySubst` teleArgs prob0
+             leftInv0 <- open $ Abs "i" $ map unArg $ leftInv0 `applySubst` teleArgs prob0
+             bind "i" $ \ i -> addContext ("i" :: String, defaultDom interval) $ do
+              tel <- bind "_" $ \ (_ :: NamesT tcm Term) -> g0
+              step0i <- lazyAbsApp <$> step0 <*> i
+              face <- pure max <@> (pure neg <@> i) <@> phi
+              leftInv0 <- leftInv0
+              i <- i
+              -- this composition could be optimized further whenever step0i is actually constant in i.
+              lift $ (runExceptT $ map unArg <$> transpSysTel' True tel [(i, leftInv0)] face step0i)
+  addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) $
+    reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv  :" <+> prettyTCM (absBody leftInv)
+  addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) $
+    reportSDoc "tc.lhs.unify.inv" 40 $ "leftInv  :" <+> pretty (absBody leftInv)
+  addContext prob0 $ addContext ("r" :: String, __DUMMY_DOM__) $
+    reportSDoc "tc.lhs.unify.inv" 40 $ "leftInvSub  :" <+> pretty (termsS __IMPOSSIBLE__ $ absBody $ leftInv)
+  return (prob, rho, tau , termsS __IMPOSSIBLE__ $ absBody $ leftInv)
+
+buildEquiv :: forall tcm. (PureTCM tcm, MonadError TCErr tcm) => UnifyLogEntry -> UnifyState -> tcm (Either NoLeftInv (Retract,Term))
+buildEquiv (UnificationStep st step@(Solution k ty fx tm side) output) next = runExceptT $ do
+        let
+          errorToUnsupported :: ExceptT a tcm b -> ExceptT NoLeftInv tcm b
+          errorToUnsupported m = withExceptT (\ _ -> UnsupportedYet step) m
+        reportSDoc "tc.lhs.unify.inv" 20 $ "step unifyState:" <+> prettyTCM st
+        reportSDoc "tc.lhs.unify.inv" 20 $ "step step:" <+> addContext (varTel st) (prettyTCM step)
+        unview <- intervalUnview'
+        cxt <- getContextTelescope
+        reportSDoc "tc.lhs.unify.inv" 20 $ "context:" <+> prettyTCM cxt
+        let
+          -- k counds in eqs from the left
+          m = varCount st
+          gamma = varTel st
+          eqs = eqTel st
+          u = eqLHS st !! k
+          v = eqRHS st !! k
+          x = flexVar fx
+          neqs = size eqs
+          phis = 1 -- neqs
+        interval <- lift $ primIntervalType
+         -- Γ, φs : I^phis
+        let gamma_phis = abstract gamma $ telFromList $
+              map (defaultDom . (,interval) . ("phi" ++) . show) [0 .. phis - 1]
+        working_tel <- abstract gamma_phis <$>
+          errorToUnsupported (pathTelescope' (raise phis $ eqTel st) (raise phis $ eqLHS st) (raise phis $ eqRHS st))
+        reportSDoc "tc.lhs.unify.inv" 20 $ vcat
+          [ "working tel:" <+> prettyTCM (working_tel :: Telescope)
+          , addContext working_tel $ "working tel args:" <+> prettyTCM (teleArgs working_tel :: [Arg Term])
+          ]
+        (tau,leftInv,phi) <- addContext working_tel $ runNamesT [] $ do
+          let raiseFrom tel x = raise (size working_tel - size tel) x
+
+          [u,v] <- mapM (open . raiseFrom gamma . unArg) [u,v]
+          -- φ
+          let phi = raiseFrom gamma_phis $ var 0
+          -- working_tel ⊢ γ₁,x,γ₂,φ,eqs
+          let all_args = teleArgs working_tel
+          -- Γ₁,x : A,Γ₂
+--          gamma <- open $ raiseFrom EmptyTel gamma
+          -- -- γ₁,x,γ₂,φ,eqs : W
+          -- working_tel <- open $ raiseFrom EmptyTel working_tel
+
+          -- eq_tel <- open $ raiseFrom gamma (eqTel st)
+
+          -- [lhs,rhs] <- mapM (open . raiseFrom gamma) [eqLHS st,eqRHS st]
+          let bindSplit (tel1,tel2) = (tel1,AbsN (teleNames tel1) tel2)
+          -- . ⊢ Γ₁  ,  γ₁. (x : A),Γ₂,φ : I,[lhs ≡ rhs]
+          let (gamma1, xxi) = bindSplit $ splitTelescopeAt (size gamma - x - 1) working_tel
+          let (gamma1_args,xxi_args) = splitAt (size gamma1) all_args
+              (_x_arg:xi_args) = xxi_args
+              (x_arg:xi0,k_arg:xi1) = splitAt ((size gamma - size gamma1) + phis + k) xxi_args
+              -- W ⊢ (x : A),Γ₂,φ : I,[lhs ≡ rhs]
+          let
+            xxi_here :: Telescope
+            xxi_here = absAppN xxi $ map unArg gamma1_args
+          --                                                      x:A,Γ₂                φ
+          let (xpre,krest) = bindSplit $ splitTelescopeAt ((size gamma - size gamma1) + phis + k) xxi_here
+          k_arg <- open $ unArg k_arg
+          xpre <- open xpre
+          krest <- open krest
+          delta <- bindN ["x","eq"] $ \ [x,eq] -> do
+                     let pre = apply1 <$> xpre <*> x
+                     abstractN pre $ \ args ->
+                       apply1 <$> applyN krest (x:args) <*> eq
+--          let delta_zero = absAppN delta $ map unArg [x_arg,k_arg]
+          let d_zero_args = xi0 ++ xi1
+          reportSDoc "tc.lhs.unify.inv" 20 $ "size delta:" <+> text (show $ size $ unAbsN delta)
+          reportSDoc "tc.lhs.unify.inv" 20 $ "size d0args:" <+> text (show $ size d_zero_args)
+          let appSide = case side of
+                          Left{} -> id
+                          Right{} -> unview . INeg . argN
+          let
+                  -- csingl :: NamesT tcm Term -> NamesT tcm [Arg Term]
+                  csingl i = mapM (fmap defaultArg) $ csingl' i
+                  -- csingl' :: NamesT tcm Term -> [NamesT tcm Term]
+                  csingl' i = [ k_arg <@@> (u, v, appSide <$> i)
+                              , lam "j" $ \ j ->
+                                  let r i j = case side of
+                                            Left{} -> unview (IMax (argN j) (argN i))
+                                            Right{} -> unview (IMin (argN j) (argN . unview $ INeg $ argN i))
+                                  in k_arg <@@> (u, v, r <$> i <*> j)
+                              ]
+          let replaceAt n x xs = xs0 ++ x:xs1
+                where (xs0,_:xs1) = splitAt n xs
+              dropAt n xs = xs0 ++ xs1
+                where (xs0,_:xs1) = splitAt n xs
+          delta <- open delta
+          d <- bind "i" $ \ i -> applyN delta (csingl' i)
+
+          -- Andrea 06/06/2018
+          -- We do not actually add a transp/fill if the family is
+          -- constant (TODO: postpone for metas) This is so variables
+          -- whose types do not depend on "x" are left alone, in
+          -- particular those the solution "t" depends on.
+          --
+          -- We might want to instead use the info discovered by the
+          -- solver when checking if "t" depends on "x" to decide what
+          -- to transp and what not to.
+          let flag = True
+                 {-   φ -}
+          tau <- {-dropAt (size gamma - 1 + k) .-} (gamma1_args ++) <$>
+                                                   lift (errorToUnsupported (transpTel' flag d phi d_zero_args))
+          reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM (map (setHiding NotHidden) tau)
+          leftInv <- do
+            gamma1_args <- open gamma1_args
+            phi <- open phi
+            -- xxi_here <- open xxi_here
+            -- (xi_here_f :: Abs Telescope) <- bind "i" $ \ i -> apply <$> xxi_here <*> (take 1 `fmap` csingl i)
+            -- xi_here_f <- open xi_here_f
+            -- xi_args <- open xi_args
+            -- xif <- bind "i" $ \ i -> do
+            --                      m <- (runExceptT <$> (trFillTel' flag <$> xi_here_f <*> phi <*> xi_args <*> i))
+            --                      either __IMPOSSIBLE__ id <$> lift m
+            -- xif <- open xif
+
+            xi0 <- open xi0
+            xi1 <- open xi1
+            delta0 <- bind "i" $ \ i -> apply <$> xpre <*> (take 1 `fmap` csingl i)
+            delta0 <- open delta0
+            xi0f <- bind "i" $ \ i -> do
+                                 m <- trFillTel' flag <$> delta0 <*> phi <*> xi0 <*> i
+                                 lift (errorToUnsupported m)
+            xi0f <- open xi0f
+
+            delta1 <- bind "i" $ \ i -> do
+
+                   args <- mapM (open . unArg) =<< (lazyAbsApp <$> xi0f <*> i)
+                   apply <$> applyN krest ((take 1 $ csingl' i) ++ args) <*> (drop 1 `fmap` csingl i)
+            delta1 <- open delta1
+            xi1f <- bind "i" $ \ i -> do
+                                 m <- trFillTel' flag <$> delta1 <*> phi <*> xi1 <*> i
+                                 lift (errorToUnsupported m)
+            xi1f <- open xi1f
+            fmap absBody $ bind "i" $ \ i' -> do
+              let (+++) m = liftM2 (++) m
+                  i = cl (lift primINeg) <@> i'
+--              replaceAt (size gamma + k) <$> (fmap defaultArg $ cl primIMax <@> phi <@> i) <*> do
+              do
+                gamma1_args +++ (take 1 `fmap` csingl i +++ ((lazyAbsApp <$> xi0f <*> i) +++ (drop 1 `fmap` csingl i +++ (lazyAbsApp <$> xi1f <*> i))))
+          return (tau,leftInv,phi)
+        iz <- lift $ primIZero
+        io <- lift $ primIOne
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tau    :" <+> prettyTCM (map (setHiding NotHidden) tau)
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "tauS   :" <+> prettyTCM (termsS __IMPOSSIBLE__ $ map unArg tau)
+        addContext working_tel $ addContext ("r" :: String, defaultDom interval)
+                               $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv:   " <+> prettyTCM (map (setHiding NotHidden) leftInv)
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv[0]:" <+> (prettyTCM =<< reduce (subst 0 iz $ map (setHiding NotHidden) leftInv))
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "leftInv[1]:" <+> (prettyTCM =<< reduce  (subst 0 io $ map (setHiding NotHidden) leftInv))
+        addContext working_tel $ reportSDoc "tc.lhs.unify.inv" 20 $ "[rho]tau :" <+>
+                                                                                  -- k   φ
+          prettyTCM (applySubst (termsS __IMPOSSIBLE__ $ map unArg tau) $ fromPatternSubstitution
+                                                                      $ raise (size (eqTel st) - 1{-k-} + phis {-neqs{-φs-} - 1{-φ0-}-})
+                                                                      $ unifySubst output)
+        reportSDoc "tc.lhs.unify.inv" 20 $ "."
+        let rho0 = fromPatternSubstitution $ unifySubst output
+        addContext (varTel next) $ addContext (eqTel next) $ reportSDoc "tc.lhs.unify.inv" 20 $
+          "prf :" <+> prettyTCM (fromPatternSubstitution $ unifyProof output)
+        let c0 = Lam defaultArgInfo $ Abs "i" $ raise 1 $ lookupS (fromPatternSubstitution $ unifyProof output) (neqs - k - 1)
+        let c = liftS (size $ eqTel next) (raiseS 1) `applySubst` c0
+        addContext (varTel next) $ addContext ("φ" :: String, __DUMMY_DOM__) $ addContext (raise 1 $ eqTel next) $
+          reportSDoc "tc.lhs.unify.inv" 20 $ "c :" <+> prettyTCM c
+--        let rho = liftS (neqs - k - 1) $ consS (raise (1 + k) c) $ liftS (1 + k) rho0
+        let rho = singletonS (neqs - k - 1) c  `composeS` liftS (1 + neqs) rho0
+        reportSDoc "tc.lhs.unify.inv" 20 $ text "old_sizes: " <+> pretty (size $ varTel st, size $ eqTel st)
+        reportSDoc "tc.lhs.unify.inv" 20 $ text "new_sizes: " <+> pretty (size $ varTel next, size $ eqTel next)
+--        addContext (abstract (varTel next) $ ExtendTel __DUMMY_DOM__ (Abs "φ" $ raise 1 $ eqTel next)) $
+        addContext (varTel next) $ addContext ("φ" :: String, __DUMMY_DOM__) $ addContext (raise 1 $ eqTel next) $
+          reportSDoc "tc.lhs.unify.inv" 20 $ "rho   :" <+> prettyTCM rho
+        return $ ((working_tel
+                 , rho
+                 , termsS __IMPOSSIBLE__ $ map unArg tau
+                 , termsS __IMPOSSIBLE__ $ map unArg leftInv)
+                 , phi)
+buildEquiv (UnificationStep st step@(EtaExpandVar fv _d _args) output) next = fmap Right $ do
+        reportSDoc "tc.lhs.unify.inv" 20 "buildEquiv EtaExpandVar"
+        let
+          gamma = varTel st
+          eqs = eqTel st
+          x = flexVar fv
+          neqs = size eqs
+          phis = 1
+        interval <- primIntervalType
+         -- Γ, φs : I^phis
+        let gamma_phis = abstract gamma $ telFromList $
+              map (defaultDom . (,interval) . ("phi" ++) . show) [0 .. phis - 1]
+        working_tel <- abstract gamma_phis <$>
+          pathTelescope (raise phis $ eqTel st) (raise phis $ eqLHS st) (raise phis $ eqRHS st)
+        let raiseFrom tel x = (size working_tel - size tel) + x
+        let phi = var $ raiseFrom gamma_phis 0
+
+        caseMaybeM (expandRecordVar (raiseFrom gamma x) working_tel) __IMPOSSIBLE__ $ \ (_,tau,rho,_) -> do
+          reportSDoc "tc.lhs.unify.inv" 20 $ addContext working_tel $ "tau    :" <+> prettyTCM tau
+          return $ ((working_tel,rho,tau,raiseS 1),phi)
+
+buildEquiv (UnificationStep st step output) _ = do
+  reportSDoc "tc.lhs.unify.inv" 20 $ "steps"
+  let illegal     = return $ Left $ Illegal step
+      unsupported = return $ Left $ UnsupportedYet step
+  case step of
+    Deletion{}           -> illegal
+    TypeConInjectivity{} -> illegal
+    -- These should end up in a NoUnify
+    Conflict{}    -> __IMPOSSIBLE__
+    LitConflict{} -> __IMPOSSIBLE__
+    Cycle{}       -> __IMPOSSIBLE__
+    _ -> unsupported
+
+{-# SPECIALIZE explainStep :: UnifyStep -> TCM Doc #-}
+explainStep :: MonadPretty m => UnifyStep -> m Doc
+explainStep Injectivity{injectConstructor = ch} =
+  "injectivity of the data constructor" <+> prettyTCM (conName ch)
+explainStep TypeConInjectivity{} = "injectivity of type constructors"
+explainStep Deletion{}           = "the K rule"
+explainStep Solution{}           = "substitution in Setω"
+-- Note: this is the actual reason that a Solution step can fail, rather
+-- than the explanation for the actual step
+explainStep Conflict{}          = "the disjointness of data constructors"
+explainStep LitConflict{}       = "the disjointness of literal values"
+explainStep Cycle{}             = "the impossibility of cyclic values"
+explainStep EtaExpandVar{}      = "eta-expansion of variables"
+explainStep EtaExpandEquation{} = "eta-expansion of equations"
+explainStep StripSizeSuc{}      = "the injectivity of size successors"
+explainStep SkipIrrelevantEquation{} = "ignoring irrelevant equations"
diff --git a/src/full/Agda/TypeChecking/Rules/LHS/Unify/Types.hs b/src/full/Agda/TypeChecking/Rules/LHS/Unify/Types.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/LHS/Unify/Types.hs
@@ -0,0 +1,480 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.LHS.Unify.Types where
+
+import Prelude hiding (null)
+
+import Control.Monad
+import Control.Monad.Writer (WriterT(..), MonadWriter(..))
+
+import Data.Foldable (toList)
+import Data.DList (DList)
+import qualified Data.List as List
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Literal
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Level (reallyUnLevelView)
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.TypeChecking.Rules.LHS.Problem
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+----------------------------------------------------
+-- Equalities
+----------------------------------------------------
+
+data Equality = Equal
+  { _eqType  :: Dom Type
+  , _eqLeft  :: Term
+  , _eqRight :: Term
+  }
+
+-- Jesper, 2020-01-19: The type type lives in the context of the
+-- variables+equations, while the lhs/rhs only depend on the
+-- variables, so there is no way to give a correct Reduce instance.
+-- WRONG:
+-- instance Reduce Equality where
+--   reduce' (Equal a u v) = Equal <$> reduce' a <*> reduce' u <*> reduce' v
+
+eqConstructorForm :: HasBuiltins m => Equality -> m Equality
+eqConstructorForm (Equal a u v) = Equal a <$> constructorForm u <*> constructorForm v
+
+eqUnLevel :: (HasBuiltins m, HasOptions m) => Equality -> m Equality
+eqUnLevel (Equal a u v) = Equal a <$> unLevel u <*> unLevel v
+  where
+    unLevel (Level l) = reallyUnLevelView l
+    unLevel u         = return u
+
+----------------------------------------------------
+-- Unify state
+----------------------------------------------------
+
+data UnifyState = UState
+  { varTel   :: Telescope     -- ^ Don't reduce!
+  , flexVars :: FlexibleVars
+  , eqTel    :: Telescope     -- ^ Can be reduced eagerly.
+  , eqLHS    :: [Arg Term]    -- ^ Ends up in dot patterns (should not be reduced eagerly).
+  , eqRHS    :: [Arg Term]    -- ^ Ends up in dot patterns (should not be reduced eagerly).
+  } deriving (Show)
+-- Issues #3578 and #4125: avoid unnecessary reduction in unifier.
+
+lensVarTel   :: Lens' UnifyState Telescope
+lensVarTel   f s = f (varTel s) <&> \ tel -> s { varTel = tel }
+{-# INLINE lensVarTel #-}
+--UNUSED Liang-Ting Chen 2019-07-16
+--lensFlexVars :: Lens' UnifyState FlexibleVars
+--lensFlexVars f s = f (flexVars s) <&> \ flex -> s { flexVars = flex }
+
+lensEqTel    :: Lens' UnifyState Telescope
+lensEqTel    f s = f (eqTel s) <&> \ x -> s { eqTel = x }
+{-# INLINE lensEqTel #-}
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--lensEqLHS    :: Lens' UnifyState Args
+--lensEqLHS    f s = f (eqLHS s) <&> \ x -> s { eqLHS = x }
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--lensEqRHS    :: Lens' UnifyState Args
+--lensEqRHS    f s = f (eqRHS s) <&> \ x -> s { eqRHS = x }
+
+-- UNUSED Andreas, 2019-10-14
+-- instance Reduce UnifyState where
+--   reduce' (UState var flex eq lhs rhs) =
+--     UState <$> reduce' var
+--            <*> pure flex
+--            <*> reduce' eq
+--            <*> reduce' lhs
+--            <*> reduce' rhs
+
+-- Andreas, 2019-10-14, issues #3578 and #4125:
+-- | Don't ever reduce the whole 'varTel', as it will destroy
+-- readability of the context in interactive editing!
+-- To make sure this insight is not lost, the following
+-- dummy instance should prevent a proper 'Reduce' instance for 'UnifyState'.
+instance Reduce UnifyState where
+  reduce' = __IMPOSSIBLE__
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--reduceEqTel :: UnifyState -> TCM UnifyState
+--reduceEqTel = lensEqTel reduce
+
+-- UNUSED Andreas, 2019-10-14
+-- instance Normalise UnifyState where
+--   normalise' (UState var flex eq lhs rhs) =
+--     UState <$> normalise' var
+--            <*> pure flex
+--            <*> normalise' eq
+--            <*> normalise' lhs
+--            <*> normalise' rhs
+
+instance PrettyTCM UnifyState where
+  prettyTCM state = "UnifyState" $$ nest 2 (vcat $
+    [ "variable tel:  " <+> prettyTCM gamma
+    , "flexible vars: " <+> pshow (map flexVarF $ flexVars state)
+    , "equation tel:  " <+> addContext gamma (prettyTCM delta)
+    , "equations:     " <+> addContext gamma (prettyList_ (zipWith prettyEquality (eqLHS state) (eqRHS state)))
+    ])
+    where
+      flexVarF fi = (flexVar fi, flexForced fi)
+      gamma = varTel state
+      delta = eqTel state
+      prettyEquality x y = prettyTCM x <+> "=?=" <+> prettyTCM y
+
+initUnifyState
+  :: PureTCM m
+  => Telescope -> FlexibleVars -> Type -> Args -> Args -> m UnifyState
+initUnifyState tel flex a lhs rhs = do
+  (tel, a, lhs, rhs) <- instantiateFull (tel, a, lhs, rhs)
+  let n = size lhs
+  unless (n == size rhs) __IMPOSSIBLE__
+  TelV eqTel _ <- telView a
+  unless (n == size eqTel) __IMPOSSIBLE__
+  return $ UState tel flex eqTel lhs rhs
+  -- Andreas, 2019-02-23, issue #3578: do not eagerly reduce
+  -- reduce $ UState tel flex eqTel lhs rhs
+
+isUnifyStateSolved :: UnifyState -> Bool
+isUnifyStateSolved = null . eqTel
+
+varCount :: UnifyState -> Int
+varCount = size . varTel
+
+-- | Get the type of the i'th variable in the given state
+getVarType :: Int -> UnifyState -> Dom Type
+getVarType i s = indexWithDefault __IMPOSSIBLE__ (flattenTel $ varTel s) i
+
+getVarTypeUnraised :: Int -> UnifyState -> Dom Type
+getVarTypeUnraised i s = snd <$> indexWithDefault __IMPOSSIBLE__ (telToList $ varTel s) i
+
+eqCount :: UnifyState -> Int
+eqCount = size . eqTel
+
+-- | Get the k'th equality in the given state. The left- and right-hand sides
+--   of the equality live in the varTel telescope, and the type of the equality
+--   lives in the varTel++eqTel telescope
+getEquality :: Int -> UnifyState -> Equality
+getEquality k UState { eqTel = eqs, eqLHS = lhs, eqRHS = rhs } =
+    Equal (indexWithDefault __IMPOSSIBLE__ (flattenTel eqs) k)
+          (unArg $ indexWithDefault __IMPOSSIBLE__ lhs k)
+          (unArg $ indexWithDefault __IMPOSSIBLE__ rhs k)
+
+getReducedEquality
+  :: (MonadReduce m, MonadAddContext m)
+  => Int -> UnifyState -> m Equality
+getReducedEquality k s = do
+  let Equal a u v = getEquality k s
+  addContext (varTel s) $ Equal
+    <$> addContext (eqTel s) (reduce a)
+    <*> reduce u
+    <*> reduce v
+
+-- | As getEquality, but with the unraised type
+getEqualityUnraised :: Int -> UnifyState -> Equality
+getEqualityUnraised k UState { eqTel = eqs, eqLHS = lhs, eqRHS = rhs } =
+    Equal (snd <$> indexWithDefault __IMPOSSIBLE__ (telToList eqs) k)
+          (unArg $ indexWithDefault __IMPOSSIBLE__ lhs k)
+          (unArg $ indexWithDefault __IMPOSSIBLE__ rhs k)
+
+getReducedEqualityUnraised
+  :: (MonadReduce m, MonadAddContext m)
+  => Int -> UnifyState -> m Equality
+getReducedEqualityUnraised k s = do
+  let Equal a u v = getEqualityUnraised k s
+  addContext (varTel s) $ Equal
+    <$> addContext (telFromList $ take k $ telToList $ eqTel s) (reduce a)
+    <*> reduce u
+    <*> reduce v
+
+--UNUSED Liang-Ting Chen 2019-07-16
+--getEqInfo :: Int -> UnifyState -> ArgInfo
+--getEqInfo k UState { eqTel = eqs } =
+--  domInfo $ indexWithDefault __IMPOSSIBLE__ (telToList eqs) k
+--
+---- | Add a list of equations to the front of the equation telescope
+--addEqs :: Telescope -> [Arg Term] -> [Arg Term] -> UnifyState -> UnifyState
+--addEqs tel us vs s =
+--  s { eqTel = tel `abstract` eqTel s
+--    , eqLHS = us ++ eqLHS s
+--    , eqRHS = vs ++ eqRHS s
+--    }
+--  where k = size tel
+--
+--addEq :: Type -> Arg Term -> Arg Term -> UnifyState -> UnifyState
+--addEq a u v = addEqs (ExtendTel (defaultDom a) (Abs underscore EmptyTel)) [u] [v]
+
+
+
+-- | Instantiate the k'th variable with the given value.
+--   Returns Nothing if there is a cycle.
+solveVar :: Int             -- ^ Index @k@
+         -> DeBruijnPattern -- ^ Solution @u@
+         -> UnifyState -> Maybe (UnifyState, PatternSubstitution)
+solveVar k u s = case instantiateTelescope (varTel s) k u of
+  Nothing -> Nothing
+  Just (tel' , sigma , rho) -> Just $ (,sigma) $ UState
+      { varTel   = tel'
+      , flexVars = permuteFlex (reverseP rho) $ flexVars s
+      , eqTel    = applyPatSubst sigma $ eqTel s
+      , eqLHS    = applyPatSubst sigma $ eqLHS s
+      , eqRHS    = applyPatSubst sigma $ eqRHS s
+      }
+  where
+    permuteFlex :: Permutation -> FlexibleVars -> FlexibleVars
+    permuteFlex perm =
+      mapMaybe $ \(FlexibleVar ai fc k p x) ->
+        FlexibleVar ai fc k p <$> List.elemIndex x (permPicks perm)
+
+applyUnder :: Int -> Telescope -> Term -> Telescope
+applyUnder k tel u
+ | k < 0     = __IMPOSSIBLE__
+ | k == 0    = tel `apply1` u
+ | otherwise = case tel of
+    EmptyTel         -> __IMPOSSIBLE__
+    ExtendTel a tel' -> ExtendTel a $
+      Abs (absName tel') $ applyUnder (k-1) (absBody tel') u
+
+dropAt :: Int -> [a] -> [a]
+dropAt _ [] = __IMPOSSIBLE__
+dropAt k (x:xs)
+ | k < 0     = __IMPOSSIBLE__
+ | k == 0    = xs
+ | otherwise = x : dropAt (k-1) xs
+
+-- | Solve the k'th equation with the given value, which can depend on
+--   regular variables but not on other equation variables.
+solveEq :: Int -> Term -> UnifyState -> (UnifyState, PatternSubstitution)
+solveEq k u s = (,sigma) $ s
+    { eqTel    = applyUnder k (eqTel s) u'
+    , eqLHS    = dropAt k $ eqLHS s
+    , eqRHS    = dropAt k $ eqRHS s
+    }
+  where
+    u'    = raise k u
+    n     = eqCount s
+    sigma = liftS (n-k-1) $ consS (dotP u') idS
+
+--UNUSED Liang-Ting Chen 2019-07-16
+---- | Simplify the k'th equation with the given value (which can depend on other
+----   equation variables). Returns Nothing if there is a cycle.
+--simplifyEq :: Int -> Term -> UnifyState -> Maybe (UnifyState, PatternSubstitution)
+--simplifyEq k u s = case instantiateTelescope (eqTel s) k u of
+--  Nothing -> Nothing
+--  Just (tel' , sigma , rho) -> Just $ (,sigma) $ UState
+--    { varTel   = varTel s
+--    , flexVars = flexVars s
+--    , eqTel    = tel'
+--    , eqLHS    = permute rho $ eqLHS s
+--    , eqRHS    = permute rho $ eqRHS s
+--    }
+--
+----------------------------------------------------
+-- Unification strategies
+----------------------------------------------------
+
+data UnifyStep
+  = Deletion
+    { deleteAt           :: Int
+    , deleteType         :: Type
+    , deleteLeft         :: Term
+    , deleteRight        :: Term
+    }
+  | Solution
+    { solutionAt         :: Int
+    , solutionType       :: Dom Type
+    , solutionVar        :: FlexibleVar Int
+    , solutionTerm       :: Term
+    , solutionSide       :: Either () ()
+      -- ^ side of the equation where the variable is.
+    }
+  | Injectivity
+    { injectAt           :: Int
+    , injectType         :: Type
+    , injectDatatype     :: QName
+    , injectParameters   :: Args
+    , injectIndices      :: Args
+    , injectConstructor  :: ConHead
+    }
+  | Conflict
+    { conflictAt         :: Int
+    , conflictType       :: Type
+    , conflictDatatype   :: QName
+    , conflictParameters :: Args
+    , conflictLeft       :: Term
+    , conflictRight      :: Term
+    }
+  | Cycle
+    { cycleAt            :: Int
+    , cycleType          :: Type
+    , cycleDatatype      :: QName
+    , cycleParameters    :: Args
+    , cycleVar           :: Int
+    , cycleOccursIn      :: Term
+    }
+  | EtaExpandVar
+    { expandVar           :: FlexibleVar Int
+    , expandVarRecordType :: QName
+    , expandVarParameters :: Args
+    }
+  | EtaExpandEquation
+    { expandAt           :: Int
+    , expandRecordType   :: QName
+    , expandParameters   :: Args
+    }
+  | LitConflict
+    { litConflictAt      :: Int
+    , litType            :: Type
+    , litConflictLeft    :: Literal
+    , litConflictRight   :: Literal
+    }
+  | StripSizeSuc
+    { stripAt            :: Int
+    , stripArgLeft       :: Term
+    , stripArgRight      :: Term
+    }
+  | SkipIrrelevantEquation
+    { skipIrrelevantAt   :: Int
+    }
+  | TypeConInjectivity
+    { typeConInjectAt    :: Int
+    , typeConstructor    :: QName
+    , typeConArgsLeft    :: Args
+    , typeConArgsRight   :: Args
+    } deriving (Show)
+
+instance PrettyTCM UnifyStep where
+  prettyTCM step = case step of
+    Deletion k a u v -> "Deletion" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "lhs:        " <+> prettyTCM u
+      , "rhs:        " <+> prettyTCM v
+      ])
+    Solution k a i u s -> "Solution" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "variable:   " <+> text (show (flexVar i, flexPos i, flexForced i, flexKind i))
+      , "term:       " <+> prettyTCM u
+      , "side:       " <+> text (show s)
+      ])
+    Injectivity k a d pars ixs c -> "Injectivity" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "datatype:   " <+> prettyTCM d
+      , "parameters: " <+> prettyList_ (map prettyTCM pars)
+      , "indices:    " <+> prettyList_ (map prettyTCM ixs)
+      , "constructor:" <+> prettyTCM c
+      ])
+    Conflict k a d pars u v -> "Conflict" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "datatype:   " <+> prettyTCM d
+      , "parameters: " <+> prettyList_ (map prettyTCM pars)
+      , "lhs:        " <+> prettyTCM u
+      , "rhs:        " <+> prettyTCM v
+      ])
+    Cycle k a d pars i u -> "Cycle" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "datatype:   " <+> prettyTCM d
+      , "parameters: " <+> prettyList_ (map prettyTCM pars)
+      , "variable:   " <+> text (show i)
+      , "term:       " <+> prettyTCM u
+      ])
+    EtaExpandVar fi r pars -> "EtaExpandVar" $$ nest 2 (vcat $
+      [ "variable:   " <+> text (show fi)
+      , "record type:" <+> prettyTCM r
+      , "parameters: " <+> prettyTCM pars
+      ])
+    EtaExpandEquation k r pars -> "EtaExpandEquation" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "record type:" <+> prettyTCM r
+      , "parameters: " <+> prettyTCM pars
+      ])
+    LitConflict k a u v -> "LitConflict" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "type:       " <+> prettyTCM a
+      , "lhs:        " <+> prettyTCM u
+      , "rhs:        " <+> prettyTCM v
+      ])
+    StripSizeSuc k u v -> "StripSizeSuc" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "lhs:        " <+> prettyTCM u
+      , "rhs:        " <+> prettyTCM v
+      ])
+    SkipIrrelevantEquation k -> "SkipIrrelevantEquation" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      ])
+    TypeConInjectivity k d us vs -> "TypeConInjectivity" $$ nest 2 (vcat $
+      [ "position:   " <+> text (show k)
+      , "datatype:   " <+> prettyTCM d
+      , "lhs:        " <+> prettyList_ (map prettyTCM us)
+      , "rhs:        " <+> prettyList_ (map prettyTCM vs)
+      ])
+
+
+----------------------------------------------------
+-- Unify Log and monad
+----------------------------------------------------
+
+data UnifyLogEntry
+ -- = UnificationDone  UnifyState
+  = UnificationStep UnifyState UnifyStep UnifyOutput
+
+type UnifyLog = [(UnifyLogEntry,UnifyState)]
+
+-- | This variant of 'UnifyLog' is used to ensure that 'tell' is not
+-- expensive.
+type UnifyLog' = DList (UnifyLogEntry, UnifyState)
+
+-- Given varΓ ⊢ eqΓ, varΓ ⊢ us, vs : eqΓ
+data UnifyOutput = UnifyOutput
+  { unifySubst :: PatternSubstitution -- varΓ' ⊢ σ : varΓ
+  , unifyProof :: PatternSubstitution -- varΓ',eqΓ' ⊢ ps : eqΓ[σ]
+                                      -- varΓ', us' =_eqΓ' vs' ⊢ ap(ps) : us[σ] =_{eqΓ[σ]} vs[σ]
+--  , unifyLog   :: UnifyLog
+  }
+
+instance Semigroup UnifyOutput where
+  x <> y = UnifyOutput
+    { unifySubst = unifySubst y `composeS` unifySubst x
+    , unifyProof = unifyProof y `composeS` unifyProof x
+--    , unifyLog   = unifyLog x ++ unifyLog y
+    }
+
+instance Monoid UnifyOutput where
+  mempty  = UnifyOutput IdS IdS -- []
+  mappend = (<>)
+
+type UnifyLogT m a = WriterT UnifyLog' m a
+
+type UnifyStepT m a = WriterT UnifyOutput m a
+
+tellUnifySubst :: MonadWriter UnifyOutput m => PatternSubstitution -> m ()
+tellUnifySubst sub = tell $ UnifyOutput sub IdS
+
+tellUnifyProof :: MonadWriter UnifyOutput m => PatternSubstitution -> m ()
+tellUnifyProof sub = tell $ UnifyOutput IdS sub
+
+writeUnifyLog ::
+  MonadWriter UnifyLog' m => (UnifyLogEntry, UnifyState) -> m ()
+writeUnifyLog x = tell (singleton x) -- UnifyOutput IdS IdS [x]
+
+runUnifyLogT :: Functor m => UnifyLogT m a -> m (a, UnifyLog)
+runUnifyLogT m = mapSnd toList <$> runWriterT m
diff --git a/src/full/Agda/TypeChecking/Rules/Record.hs b/src/full/Agda/TypeChecking/Rules/Record.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Record.hs
@@ -0,0 +1,803 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation   #-}
+
+module Agda.TypeChecking.Rules.Record where
+
+import Prelude hiding (null, not, (&&), (||))
+
+import Control.Monad
+import Data.Maybe
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options
+
+import qualified Agda.Syntax.Abstract as A
+import qualified Agda.Syntax.Abstract.Views as A
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Position
+import qualified Agda.Syntax.Info as Info
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Polarity
+import Agda.TypeChecking.Warnings
+import Agda.TypeChecking.CompiledClause (hasProjectionPatterns)
+import Agda.TypeChecking.CompiledClause.Compile
+
+import Agda.TypeChecking.Rules.Data
+  ( getGeneralizedParameters, bindGeneralizedParameters, bindParameters
+  , checkDataSort, fitsIn, forceSort
+  , defineCompData, defineKanOperationForFields
+  )
+import Agda.TypeChecking.Rules.Term ( isType_ )
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Decl (checkDecl)
+
+import Agda.Utils.Boolean
+import Agda.Utils.Function ( applyWhen )
+import Agda.Utils.List (headWithDefault)
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Utils.POMonoid
+import Agda.Syntax.Common.Pretty (render)
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Records
+---------------------------------------------------------------------------
+
+-- | @checkRecDef i name con ps contel fields@
+--
+--     [@name@]    Record type identifier.
+--
+--     [@con@]     Maybe constructor name and info.
+--
+--     [@ps@]      Record parameters.
+--
+--     [@contel@]  Approximate type of constructor (@fields@ -> dummy).
+--                 Does not include record parameters.
+--
+--     [@fields@]  List of field signatures.
+--
+checkRecDef
+  :: A.DefInfo                 -- ^ Position and other info.
+  -> QName                     -- ^ Record type identifier.
+  -> UniverseCheck             -- ^ Check universes?
+  -> A.RecordDirectives        -- ^ (Co)Inductive, (No)Eta, (Co)Pattern, Constructor?
+  -> A.DataDefParams           -- ^ Record parameters.
+  -> A.Expr                    -- ^ Approximate type of constructor (@fields@ -> dummy).
+                               --   Does not include record parameters.
+  -> [A.Field]                 -- ^ Field signatures.
+  -> TCM ()
+checkRecDef i name uc (RecordDirectives ind eta0 pat con) (A.DataDefParams gpars ps) contel0 fields = do
+
+  -- Andreas, 2022-10-06, issue #6165:
+  -- The target type of the constructor is a meaningless dummy expression which does not type-check.
+  -- We replace it by Set/Type (builtinSet) which is still incorrect but type-checks.
+  -- It will be fixed after type-checking.
+  aType <- A.Def . fromMaybe __IMPOSSIBLE__ <$> getBuiltinName' builtinSet
+  let contel = A.unPiView . (\ (A.PiView tels _) -> A.PiView tels aType) . A.piView $ contel0
+
+  traceCall (CheckRecDef (getRange name) name ps fields) $ do
+    reportSDoc "tc.rec" 10 $ vcat
+      [ "checking record def" <+> prettyTCM name
+      , nest 2 $ "ps ="     <+> prettyList (map prettyA ps)
+      , nest 2 $ "contel =" <+> prettyA contel
+      , nest 2 $ "fields =" <+> prettyA (map Constr fields)
+      ]
+    -- get type of record
+    def <- instantiateDef =<< getConstInfo name
+    t   <- instantiateFull $ defType def
+    let npars =
+          case theDef def of
+            DataOrRecSig n -> n
+            _              -> __IMPOSSIBLE__
+
+    -- If the record type is erased, then hard compile-time mode is
+    -- entered.
+    setHardCompileTimeModeIfErased' def $ do
+
+    parNames <- getGeneralizedParameters gpars name
+
+    bindGeneralizedParameters parNames t $ \ gtel t0 ->
+     bindParameters (npars - length parNames) ps t0 $ \ ptel t0 -> do
+
+      let tel = abstract gtel ptel
+
+      -- Generate type of constructor from field telescope @contel@,
+      -- which is the approximate constructor type (target missing).
+
+      -- Check and evaluate field types.
+      reportSDoc "tc.rec" 15 $ "checking fields"
+      contype <- workOnTypes $ instantiateFull =<< isType_ contel
+      reportSDoc "tc.rec" 20 $ vcat
+        [ "contype = " <+> prettyTCM contype ]
+
+      -- compute the field telescope (does not include record parameters)
+      let TelV ftel _ = telView' contype
+
+      -- Compute correct type of constructor
+
+      -- t = tel -> t0 where t0 must be a sort s
+      TelV idxTel s <- telView t0
+      unless (null idxTel) $ typeError $ ShouldBeASort t0
+      s <- forceSort s
+
+      -- needed for impredicative Prop (not implemented yet)
+      -- ftel <- return $
+      --   if s == Prop
+      --   then telFromList $ map (setRelevance Irrelevant) $ telToList ftel
+      --   else ftel
+
+      reportSDoc "tc.rec" 20 $ do
+        gamma <- getContextTelescope  -- the record params (incl. module params)
+        "gamma = " <+> inTopContext (prettyTCM gamma)
+
+      -- record type (name applied to parameters)
+      rect <- El s . Def name . map Apply <$> getContextArgs
+
+      -- Put in @rect@ as correct target of constructor type.
+      -- Andreas, 2011-05-10 use telePi_ instead of telePi to preserve
+      -- even names of non-dependent fields in constructor type (Issue 322).
+      let contype = telePi_ ftel (raise (size ftel) rect)
+        -- NB: contype does not contain the parameter telescope
+
+      -- Obtain name of constructor (if present).
+      (hasNamedCon, conName) <- case con of
+        Just c  -> return (True, c)
+        Nothing -> do
+          m <- killRange <$> currentModule
+          -- Andreas, 2020-06-01, AIM XXXII
+          -- Using prettyTCM here jinxes the printer, see PR #4699.
+          -- r <- prettyTCM name
+          let r = P.pretty $ qnameName name
+          c <- qualify m <$> freshName_ (render r ++ ".constructor")
+          return (False, c)
+
+      -- Add record type to signature.
+      reportSDoc "tc.rec" 15 $ "adding record type to signature"
+
+      etaenabled <- etaEnabled
+
+      let getName :: A.Declaration -> [Dom QName]
+          getName (A.Field _ x arg)    = [x <$ domFromArg arg]
+          getName (A.ScopedDecl _ [f]) = getName f
+          getName _                    = []
+
+          setTactic dom f = f { domTactic = domTactic dom }
+
+          fs = zipWith setTactic (telToList ftel) $ concatMap getName fields
+
+          -- indCo is what the user wrote: inductive/coinductive/Nothing.
+          -- We drop the Range.
+          indCo = rangedThing <$> ind
+          -- A constructor is inductive unless declared coinductive.
+          conInduction = fromMaybe Inductive indCo
+          -- Andreas, 2016-09-20, issue #2197.
+          -- Eta is inferred by the positivity checker.
+          -- We should turn it off until it is proven to be safe.
+          haveEta      = maybe (Inferred $ NoEta patCopat) Specified eta
+          -- haveEta      = maybe (Inferred $ conInduction == Inductive && etaenabled) Specified eta
+          con = ConHead conName (IsRecord patCopat) conInduction $ map argFromDom fs
+
+          -- A record is irrelevant if all of its fields are.
+          -- In this case, the associated module parameter will be irrelevant.
+          -- See issue 392.
+          -- Unless it's been declared coinductive or no-eta-equality (#2607).
+          recordRelevance
+            | Just NoEta{} <- eta         = Relevant
+            | CoInductive <- conInduction = Relevant
+            | otherwise                   = minimum $ Irrelevant : map getRelevance (telToList ftel)
+
+      -- Andreas, 2017-01-26, issue #2436
+      -- Disallow coinductive records with eta-equality
+      when (conInduction == CoInductive && theEtaEquality haveEta == YesEta) $ do
+        typeError . GenericDocError =<< do
+          sep [ "Agda doesn't like coinductive records with eta-equality."
+              , "If you must, use pragma"
+              , "{-# ETA" <+> prettyTCM name <+> "#-}"
+              ]
+      reportSDoc "tc.rec" 30 $ "record constructor is " <+> prettyTCM con
+
+      -- Jesper, 2021-05-26: Warn when declaring coinductive record
+      -- but neither --guardedness nor --sized-types is enabled.
+      when (conInduction == CoInductive) $ do
+        unlessM ((optGuardedness || optSizedTypes) <$> pragmaOptions) $
+          warning $ NoGuardednessFlag name
+
+      -- Add the record definition.
+
+      -- Andreas, 2016-06-17, Issue #2018:
+      -- Do not rely on @addConstant@ to put in the record parameters,
+      -- as they might be renamed in the context.
+      -- By putting them ourselves (e.g. by using the original type @t@)
+      -- we make sure we get the original names!
+      let npars = size tel
+          telh  = fmap hideAndRelParams tel
+      escapeContext impossible npars $ do
+        addConstant' name defaultArgInfo name t $
+            Record
+              { recPars           = npars
+              , recClause         = Nothing
+              , recConHead        = con
+              , recNamedCon       = hasNamedCon
+              , recFields         = fs
+              , recTel            = telh `abstract` ftel
+              , recAbstr          = Info.defAbstract i
+              , recEtaEquality'   = haveEta
+              , recPatternMatching= patCopat
+              , recInduction      = indCo
+                  -- We retain the original user declaration [(co)inductive]
+                  -- in case the record turns out to be recursive.
+              -- Determined by positivity checker:
+              , recMutual         = Nothing
+              -- Determined by the termination checker:
+              , recTerminates     = Nothing
+              , recComp           = emptyCompKit -- filled in later
+              }
+
+        erasure <- optErasure <$> pragmaOptions
+        -- Add record constructor to signature
+        addConstant' conName defaultArgInfo conName
+             -- If --erasure is used, then the parameters are erased
+             -- in the constructor's type.
+            (applyWhen erasure (fmap $ applyQuantity zeroQuantity) telh
+             `abstract` contype) $
+            Constructor
+              { conPars   = npars
+              , conArity  = size fs
+              , conSrcCon = con
+              , conData   = name
+              , conAbstr  = Info.defAbstract i
+              , conComp   = emptyCompKit  -- filled in later
+              , conProj   = Nothing       -- filled in later
+              , conForced = []
+              , conErased = Nothing
+              , conErasure = erasure
+              , conInline  = False
+              }
+
+      -- Declare the constructor as eligible for instance search
+      case Info.defInstance i of
+        InstanceDef r -> setCurrentRange r $ do
+          -- Andreas, 2020-01-28, issue #4360:
+          -- Use addTypedInstance instead of addNamedInstance
+          -- to detect unusable instances.
+          addTypedInstance conName contype
+          -- addNamedInstance conName name
+        NotInstanceDef -> pure ()
+
+      -- Check that the fields fit inside the sort
+      _ <- fitsIn conName uc [] contype s
+
+      -- Check that the sort admits record declarations.
+      checkDataSort name s
+
+
+      {- Andreas, 2011-04-27 WRONG because field types are checked again
+         and then non-stricts should not yet be irrelevant
+
+      -- make record parameters hidden and non-stricts irrelevant
+      -- ctx <- (reverse . map hideAndRelParams . take (size tel)) <$> getContext
+      -}
+
+{- Andreas, 2013-09-13 DEBUGGING the debug printout
+      reportSDoc "tc.rec" 80 $ sep
+        [ "current module record telescope"
+        , nest 2 $ (prettyTCM =<< getContextTelescope)
+        ]
+      reportSDoc "tc.rec" 80 $ sep
+        [ "current module record telescope"
+        , nest 2 $ (text . show =<< getContextTelescope)
+        ]
+      reportSDoc "tc.rec" 80 $ sep
+        [ "current module record telescope"
+        , nest 2 $ (inTopContext . prettyTCM =<< getContextTelescope)
+        ]
+      reportSDoc "tc.rec" 80 $ sep
+        [ "current module record telescope"
+        , nest 2 $ do
+           tel <- getContextTelescope
+           text (show tel) $+$ do
+           inTopContext $ do
+             prettyTCM tel $+$ do
+               telA <- reify tel
+               text (show telA) $+$ do
+               ctx <- getContextTelescope
+               "should be empty:" <+> prettyTCM ctx
+        ]
+-}
+
+      let info = setRelevance recordRelevance defaultArgInfo
+          addRecordVar =
+            addRecordNameContext (setArgInfo info $ defaultDom rect)
+
+      let m = qnameToMName name  -- Name of record module.
+
+      eraseRecordParameters <- optEraseRecordParameters <$> pragmaOptions
+      let maybeErase :: forall a. LensQuantity a => a -> a
+          maybeErase | eraseRecordParameters = setQuantity zeroQuantity
+                     | otherwise             = id
+
+      -- Andreas, 2016-02-09 setting all parameters hidden in the record
+      -- section telescope changes the semantics, see e.g.
+      -- test/Succeed/RecordInParModule.
+      -- Ulf, 2016-03-02 but it's the right thing to do (#1759)
+      modifyContextInfo (hideOrKeepInstance . maybeErase) $ addRecordVar $ do
+
+        -- Add the record section.
+
+        reportSDoc "tc.rec.def" 10 $ sep
+          [ "record section:"
+          , nest 2 $ sep
+            [ prettyTCM m <+> (inTopContext . prettyTCM =<< getContextTelescope)
+            , fsep $ punctuate comma $ map (return . P.pretty . map argFromDom . getName) fields
+            ]
+          ]
+        reportSDoc "tc.rec.def" 15 $ nest 2 $ vcat
+          [ "field tel =" <+> escapeContext impossible 1 (prettyTCM ftel)
+          ]
+        addSection m
+
+      -- Andreas, 2016-02-09, Issue 1815 (see also issue 1759).
+      -- For checking the record declarations, hide the record parameters
+      -- and the parameters of the parent modules.
+      modifyContextInfo (hideOrKeepInstance . maybeErase) $ do
+        -- If --erasure is used, then the parameters are erased in the
+        -- types of the projections.
+        erasure <- optErasure <$> pragmaOptions
+        params  <- applyWhen erasure (fmap $ applyQuantity zeroQuantity) <$> getContext
+
+        -- Check the types of the fields and the other record declarations.
+        addRecordVar $ withCurrentModule m $ do
+
+          -- Andreas, 2013-09-13, 2016-01-06.
+          -- Argument telescope for the projections: all parameters are hidden.
+          -- This means parameters of the parent modules and of the current
+          -- record type.
+          -- See test/Succeed/ProjectionsTakeModuleTelAsParameters.agda.
+          tel' <- do
+            r <- headWithDefault __IMPOSSIBLE__ <$> getContext
+            return $ telFromList' nameToArgName $ reverse $ r : params
+          setModuleCheckpoint m
+          checkRecordProjections m name hasNamedCon con tel' ftel fields
+
+
+      -- we define composition here so that the projections are already in the signature.
+      whenM (optCubicalCompatible <$> pragmaOptions) do
+        escapeContext impossible npars do
+          addCompositionForRecord name haveEta con tel (map argFromDom fs) ftel rect
+
+      -- The confluence checker needs to know what symbols match against
+      -- the constructor.
+      modifySignature $ updateDefinition conName $ \def ->
+        def { defMatchable = Set.fromList $ map unDom fs }
+
+  where
+  -- Andreas, 2020-04-19, issue #4560
+  -- If the user declared the record constructor as @pattern@,
+  -- then switch on pattern matching for no-eta-equality.
+  -- Default is no pattern matching, but definition by copatterns instead.
+  patCopat = maybe CopatternMatching (const PatternMatching) pat
+  eta      = (patCopat <$) <$> eta0
+
+
+addCompositionForRecord
+  :: QName       -- ^ Datatype name.
+  -> EtaEquality
+  -> ConHead
+  -> Telescope   -- ^ @Γ@ parameters.
+  -> [Arg QName] -- ^ Projection names.
+  -> Telescope   -- ^ @Γ ⊢ Φ@ field types.
+  -> Type        -- ^ @Γ ⊢ T@ target type.
+  -> TCM ()
+addCompositionForRecord name eta con tel fs ftel rect = do
+  cxt <- getContextTelescope
+  inTopContext $ do
+
+    -- Record has no fields: attach composition data to record constructor
+    if null fs then do
+      kit <- defineCompData name con (abstract cxt tel) [] ftel rect []
+      modifySignature $ updateDefinition (conName con) $ updateTheDef $ \case
+        r@Constructor{} -> r { conComp = kit, conProj = Just [] }  -- no projections
+        _ -> __IMPOSSIBLE__
+
+    -- No-eta record with pattern matching (i.e., withOUT copattern
+    -- matching): define composition as for a data type, attach it to
+    -- the record.
+    else if theEtaEquality eta == NoEta PatternMatching then do
+      kit <- defineCompData name con (abstract cxt tel) (unArg <$> fs) ftel rect []
+      modifySignature $ updateDefinition name $ updateTheDef $ \case
+        r@Record{} -> r { recComp = kit }
+        _ -> __IMPOSSIBLE__
+
+    -- Record has fields: attach composition data to record type
+    else do
+      -- If record has irrelevant fields but irrelevant projections are disabled,
+      -- we cannot generate composition data.
+      kit <- ifM (return (any isIrrelevant fs)
+                  `and2M` do not . optIrrelevantProjections <$> pragmaOptions)
+        {-then-} (return emptyCompKit)
+        {-else-} (defineCompKitR name (abstract cxt tel) ftel fs rect)
+      modifySignature $ updateDefinition name $ updateTheDef $ \case
+        r@Record{} -> r { recComp = kit }
+        _          -> __IMPOSSIBLE__
+
+defineCompKitR ::
+    QName          -- ^ some name, e.g. record name
+  -> Telescope   -- ^ param types Δ
+  -> Telescope   -- ^ fields' types Δ ⊢ Φ
+  -> [Arg QName] -- ^ fields' names
+  -> Type        -- ^ record type Δ ⊢ T
+  -> TCM CompKit
+defineCompKitR name params fsT fns rect = do
+  required <- mapM getTerm'
+        [ someBuiltin builtinInterval
+        , someBuiltin builtinIZero
+        , someBuiltin builtinIOne
+        , someBuiltin builtinIMin
+        , someBuiltin builtinIMax
+        , someBuiltin builtinINeg
+        , someBuiltin builtinPOr
+        , someBuiltin builtinItIsOne
+        ]
+  reportSDoc "tc.rec.cxt" 30 $ prettyTCM params
+  reportSDoc "tc.rec.cxt" 30 $ prettyTCM fsT
+  reportSDoc "tc.rec.cxt" 30 $ pretty rect
+  if not $ all isJust required then return $ emptyCompKit else do
+    transp <- whenDefined [builtinTrans]              (defineKanOperationR DoTransp name params fsT fns rect)
+    hcomp  <- whenDefined [builtinTrans,builtinHComp] (defineKanOperationR DoHComp name params fsT fns rect)
+    return $ CompKit
+      { nameOfTransp = transp
+      , nameOfHComp  = hcomp
+      }
+  where
+    whenDefined xs m = do
+      xs <- mapM getTerm' xs
+      if all isJust xs then m else return Nothing
+
+
+defineKanOperationR
+  :: Command
+  -> QName       -- ^ some name, e.g. record name
+  -> Telescope   -- ^ param types Δ
+  -> Telescope   -- ^ fields' types Δ ⊢ Φ
+  -> [Arg QName] -- ^ fields' names
+  -> Type        -- ^ record type Δ ⊢ T
+  -> TCM (Maybe QName)
+defineKanOperationR cmd name params fsT fns rect = do
+  let project = (\ t fn -> t `applyE` [Proj ProjSystem fn])
+  stuff <- fmap fst <$> defineKanOperationForFields cmd Nothing project name params fsT fns rect
+
+  caseMaybe stuff (return Nothing) $ \ (theName, gamma, rtype, clause_types, bodies) -> do
+  -- phi = 1 clause
+  c' <- do
+           io <- primIOne
+           Just io_name <- getBuiltinName' builtinIOne
+           one <- primItIsOne
+           tInterval <- primIntervalType
+           let
+              (ix,rhs) =
+                case cmd of
+                  -- TranspRArgs = phi : I, a0 : ..
+                  -- Γ = Δ^I , CompRArgs
+                  -- pats = ... | phi = i1
+                  -- body = a0
+                  DoTransp -> (1,Var 0 [])
+                  -- HCompRArgs = phi : I, u : .., a0 : ..
+                  -- Γ = Δ, CompRArgs
+                  -- pats = ... | phi = i1
+                  -- body = u i1 itIsOne
+                  DoHComp  -> (2,Var 1 [] `apply` [argN io, setRelevance Irrelevant $ argN one])
+
+              p = ConP (ConHead io_name IsData Inductive [])
+                       (noConPatternInfo { conPType = Just (Arg defaultArgInfo tInterval)
+                                         , conPFallThrough = True })
+                         []
+
+              -- gamma, rtype
+
+              s = singletonS ix p
+
+              pats :: [NamedArg DeBruijnPattern]
+              pats = s `applySubst` teleNamedArgs gamma
+
+              t :: Type
+              t = s `applyPatSubst` rtype
+
+              gamma' :: Telescope
+              gamma' = unflattenTel (ns0 ++ ns1) $ s `applyPatSubst` (g0 ++ g1)
+               where
+                (g0,_:g1) = splitAt (size gamma - 1 - ix) $ flattenTel gamma
+                (ns0,_:ns1) = splitAt (size gamma - 1 - ix) $ teleNames gamma
+
+              c = Clause { clauseFullRange = noRange
+                         , clauseLHSRange  = noRange
+                         , clauseTel       = gamma'
+                         , namedClausePats = pats
+                         , clauseBody      = Just $ rhs
+                         , clauseType      = Just $ argN t
+                         , clauseCatchall    = False
+                         , clauseExact       = Just True
+                         , clauseRecursive   = Just False  -- definitely non-recursive!
+                         , clauseUnreachable = Just False
+                         , clauseEllipsis    = NoEllipsis
+                         , clauseWhereModule = Nothing
+                         }
+           reportSDoc "trans.rec.face" 17 $ text $ show c
+           return c
+  cs <- forM (zip3 fns clause_types bodies) $ \ (fname, clause_ty, body) -> do
+          let
+              pats = teleNamedArgs gamma ++ [defaultNamedArg $ ProjP ProjSystem $ unArg fname]
+              c = Clause { clauseFullRange = noRange
+                         , clauseLHSRange  = noRange
+                         , clauseTel       = gamma
+                         , namedClausePats = pats
+                         , clauseBody      = Just body
+                         , clauseType      = Just $ argN (unDom clause_ty)
+                         , clauseCatchall    = False
+                         , clauseExact       = Just True
+                         , clauseRecursive   = Nothing
+                             -- Andreas 2020-02-06 TODO
+                             -- Or: Just False;  is it known to be non-recursive?
+                         , clauseUnreachable = Just False
+                         , clauseEllipsis    = NoEllipsis
+                         , clauseWhereModule = Nothing
+                         }
+          reportSDoc "trans.rec" 17 $ text $ show c
+          reportSDoc "trans.rec" 16 $ text "type =" <+> text (show (clauseType c))
+          reportSDoc "trans.rec" 15 $ prettyTCM $ abstract gamma (unDom clause_ty)
+          reportSDoc "trans.rec" 10 $ text "body =" <+> prettyTCM (abstract gamma body)
+          return c
+  addClauses theName $ c' : cs
+  reportSDoc "trans.rec" 15 $ text $ "compiling clauses for " ++ show theName
+  (mst, _, cc) <- inTopContext (compileClauses Nothing cs)
+  whenJust mst $ setSplitTree theName
+  setCompiledClauses theName cc
+  reportSDoc "trans.rec" 15 $ text $ "compiled"
+  return $ Just theName
+
+
+{-| @checkRecordProjections m r q tel ftel fs@.
+
+    [@m@    ]  name of the generated module
+
+    [@r@    ]  name of the record type
+
+    [@con@  ]  name of the record constructor
+
+    [@tel@  ]  parameters (perhaps erased) and record variable r ("self")
+
+    [@ftel@ ]  telescope of fields
+
+    [@fs@   ]  the fields to be checked
+-}
+checkRecordProjections ::
+  ModuleName -> QName -> Bool -> ConHead -> Telescope -> Telescope ->
+  [A.Declaration] -> TCM ()
+checkRecordProjections m r hasNamedCon con tel ftel fs = do
+    checkProjs EmptyTel ftel [] fs
+  where
+
+    checkProjs :: Telescope -> Telescope -> [Term] -> [A.Declaration] -> TCM ()
+
+    checkProjs _ _ _ [] = return ()
+
+    checkProjs ftel1 ftel2 vs (A.ScopedDecl scope fs' : fs) =
+      setScope scope >> checkProjs ftel1 ftel2 vs (fs' ++ fs)
+
+    -- Case: projection.
+    checkProjs ftel1 (ExtendTel (dom@Dom{domInfo = ai,unDom = t}) ftel2) vs (A.Field info x _ : fs) =
+      traceCall (CheckProjection (getRange info) x t) $ do
+      -- Andreas, 2012-06-07:
+      -- Issue 387: It is wrong to just type check field types again
+      -- because then meta variables are created again.
+      -- Instead, we take the field type t from the field telescope.
+      reportSDoc "tc.rec.proj" 5 $ sep
+        [ "checking projection" <+> prettyTCM x
+        , nest 2 $ vcat
+          [ "top   =" <+> (inTopContext . prettyTCM =<< getContextTelescope)
+          , "tel   =" <+> (inTopContext . prettyTCM $ tel)
+          ]
+        ]
+      -- Andreas, 2021-05-11, issue #5378
+      -- The impossible is sometimes possible, so splitting out this part...
+      reportSDoc "tc.rec.proj" 5 $ nest 2 $ vcat
+          [ "ftel1 =" <+> escapeContext impossible 1 (prettyTCM ftel1)
+          , "t     =" <+> escapeContext impossible 1 (addContext ftel1 $ prettyTCM t)
+          , "ftel2 =" <+> escapeContext impossible 1 (addContext ftel1 $ underAbstraction dom ftel2 prettyTCM)
+          ]
+      reportSDoc "tc.rec.proj" 55 $ nest 2 $ vcat
+          [ "ftel1 (raw) =" <+> pretty ftel1
+          , "t     (raw) =" <+> pretty t
+          , "ftel2 (raw) =" <+> pretty ftel2
+          ]
+      reportSDoc "tc.rec.proj" 5 $ nest 2 $ vcat
+          [ "vs    =" <+> prettyList_ (map prettyTCM vs)
+          , "abstr =" <+> (text . show) (Info.defAbstract info)
+          , "quant =" <+> (text . show) (getQuantity ai)
+          , "coh   =" <+> (text . show) (getCohesion ai)
+          ]
+
+      -- Cohesion check:
+      -- For a field `@c π : A` we would create a projection `π : .., (@(c^-1) r : R as) -> A`
+      -- So we want to check that `@.., (c^-1 . c) x : A |- x : A` is allowed by the modalities.
+      --
+      -- Alternatively we could create a projection `.. |- π r :c A`
+      -- but that would require support for a `t :c A` judgment.
+      if hasLeftAdjoint (UnderComposition (getCohesion ai))
+        then unless (getCohesion ai == Continuous)
+                    -- Andrea TODO: properly update the context/type of the projection when we add Sharp
+                    __IMPOSSIBLE__
+        else genericError $ "Cannot have record fields with modality " ++ show (getCohesion ai)
+
+      -- The telescope tel includes the variable of record type as last one
+      -- e.g. for cartesion product it is
+      --
+      --   tel = {A' : Set} {B' : Set} (r : Prod A' B')
+
+      -- create the projection functions (instantiate the type with the values
+      -- of the previous fields)
+
+      -- The type of the projection function should be
+      --  {Δ} -> (r : R Δ) -> t
+      -- where Δ are the parameters of R
+
+      {- what are the contexts?
+
+          Δ , ftel₁              ⊢ t
+          Δ , (r : R Δ)          ⊢ parallelS vs : ftel₁
+          Δ , (r : R Δ) , ftel₁  ⊢ t' = raiseFrom (size ftel₁) 1 t
+          Δ , (r : R Δ)          ⊢ t'' = applySubst (parallelS vs) t'
+                                 ⊢ finalt = telePi tel t''
+      -}
+      let t'       = raiseFrom (size ftel1) 1 t
+          t''      = applySubst (parallelS vs) t'
+          finalt   = telePi (replaceEmptyName "r" tel) t''
+          projname = qualify m $ qnameName x
+          projcall o = Var 0 [Proj o projname]
+          rel      = getRelevance ai
+          -- the recursive call
+          recurse  = checkProjs (abstract ftel1 $ ExtendTel dom
+                                 $ Abs (nameToArgName $ qnameName projname) EmptyTel)
+                                (absBody ftel2) (projcall ProjSystem : vs) fs
+
+      reportSDoc "tc.rec.proj" 25 $ nest 2 $ "finalt=" <+> do
+        inTopContext $ prettyTCM finalt
+
+      -- -- Andreas, 2012-02-20 do not add irrelevant projections if
+      -- -- disabled by --no-irrelevant-projections
+      -- ifM (return (rel == Irrelevant) `and2M` do not . optIrrelevantProjections <$> pragmaOptions) recurse $ do
+      -- Andreas, 2018-06-09 issue #2170
+      -- Always create irrelevant projections (because the scope checker accepts irrelevant fields).
+      -- If --no-irrelevant-projections, then their use should be disallowed by the type checker for expressions.
+      do
+        reportSDoc "tc.rec.proj" 10 $ sep
+          [ "adding projection"
+          , nest 2 $ prettyTCM projname <+> ":" <+> inTopContext (prettyTCM finalt)
+          ]
+
+        -- The body should be
+        --  P.xi {tel} (r _ .. x .. _) = x
+        -- Ulf, 2011-08-22: actually we're dropping the parameters from the
+        -- projection functions so the body is now
+        --  P.xi (r _ .. x .. _) = x
+        -- Andreas, 2012-01-12: irrelevant projections get translated to
+        --  P.xi (r _ .. x .. _) = irrAxiom {level of t} {t} x
+        -- PROBLEM: because of dropped parameters, cannot refer to t
+        -- 2012-04-02: DontCare instead of irrAxiom
+
+        -- compute body modification for irrelevant projections
+        let bodyMod = case rel of
+              Relevant   -> id
+              NonStrict  -> id
+              Irrelevant -> dontCare
+
+        let -- Andreas, 2010-09-09: comment for existing code
+            -- split the telescope into parameters (ptel) and the type or the record
+            -- (rt) which should be  R ptel
+            telList = telToList tel
+            (ptelList,[rt]) = splitAt (size tel - 1) telList
+            ptel   = telFromList ptelList
+            cpo    = if hasNamedCon then PatOCon else PatORec
+            cpi    = ConPatternInfo { conPInfo   = PatternInfo cpo []
+                                    , conPRecord = True
+                                    , conPFallThrough = False
+                                    , conPType   = Just $ argFromDom $ fmap snd rt
+                                    , conPLazy   = True }
+            conp   = defaultNamedArg $ ConP con cpi $ teleNamedArgs ftel
+            body   = Just $ bodyMod $ var (size ftel2)
+            cltel  = ptel `abstract` ftel
+            cltype = Just $ Arg ai $ raise (1 + size ftel2) t
+            clause = Clause { clauseLHSRange  = getRange info
+                            , clauseFullRange = getRange info
+                            , clauseTel       = killRange cltel
+                            , namedClausePats = [conp]
+                            , clauseBody      = body
+                            , clauseType      = cltype
+                            , clauseCatchall  = False
+                            , clauseExact       = Just True
+                            , clauseRecursive   = Just False
+                            , clauseUnreachable = Just False
+                            , clauseEllipsis    = NoEllipsis
+                            , clauseWhereModule = Nothing
+                            }
+
+        let projection = Projection
+              { projProper   = Just r
+              , projOrig     = projname
+              -- name of the record type:
+              , projFromType = defaultArg r
+              -- index of the record argument (in the type),
+              -- start counting with 1:
+              , projIndex    = size tel -- which is @size ptel + 1@
+              , projLams     = ProjLams $ map (argFromDom . fmap fst) telList
+              }
+
+        reportSDoc "tc.rec.proj" 70 $ sep
+          [ "adding projection"
+          , nest 2 $ prettyTCM projname <+> pretty clause
+          ]
+        reportSDoc "tc.rec.proj" 10 $ sep
+          [ "adding projection"
+          , nest 2 $ prettyTCM (QNamed projname clause)
+          ]
+
+              -- Record patterns should /not/ be translated when the
+              -- projection functions are defined. Record pattern
+              -- translation is defined in terms of projection
+              -- functions.
+        (mst, _, cc) <- compileClauses Nothing [clause]
+
+        reportSDoc "tc.cc" 60 $ do
+          sep [ "compiled clauses of " <+> prettyTCM projname
+              , nest 2 $ text (show cc)
+              ]
+
+        escapeContext impossible (size tel) $ do
+          lang <- getLanguage
+          fun  <- emptyFunctionData
+          let -- It should be fine to mark a field with @ω in an
+              -- erased record type: the field will be non-erased, but
+              -- the projection will be erased. The following code
+              -- ensures that the use of addConstant does not trigger
+              -- a PlentyInHardCompileTimeMode warning.
+              ai' = flip mapQuantity ai $ \case
+                      Quantityω _ -> Quantityω QωInferred
+                      q           -> q
+          addConstant projname $
+            (defaultDefn ai' projname (killRange finalt) lang $ FunctionDefn
+              fun
+                { _funClauses        = [clause]
+                , _funCompiled       = Just cc
+                , _funSplitTree      = mst
+                , _funProjection     = Right projection
+                , _funMutual         = Just []  -- Projections are not mutually recursive with anything
+                , _funTerminates     = Just True
+                })
+              { defArgOccurrences = [StrictPos]
+              , defCopatternLHS   = hasProjectionPatterns cc
+              }
+          computePolarity [projname]
+
+        case Info.defInstance info of
+          -- fields do not have an @instance@ keyword!?
+          InstanceDef _r -> addTypedInstance projname t
+          NotInstanceDef -> pure ()
+
+        recurse
+
+    -- Case: definition.
+    checkProjs ftel1 ftel2 vs (d : fs) = do
+      checkDecl d
+      checkProjs ftel1 ftel2 vs fs
diff --git a/src/full/Agda/TypeChecking/Rules/Term.hs b/src/full/Agda/TypeChecking/Rules/Term.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Term.hs
@@ -0,0 +1,1699 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.Rules.Term where
+
+import Prelude hiding ( null )
+
+import Control.Monad         ( (<=<), forM )
+import Control.Monad.Except
+
+import Data.Maybe
+import Data.Either (partitionEithers, lefts)
+import qualified Data.List as List
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+
+import Agda.Interaction.Options
+import Agda.Interaction.Highlighting.Generate (disambiguateRecordFields)
+
+import Agda.Syntax.Abstract (Binder, TypedBindingInfo (tbTacticAttr))
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views as A
+import qualified Agda.Syntax.Info as A
+import Agda.Syntax.Concrete.Pretty () -- only Pretty instances
+import Agda.Syntax.Concrete (FieldAssignment'(..), nameFieldA)
+import qualified Agda.Syntax.Concrete.Name as C
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Position
+import Agda.Syntax.Literal
+import Agda.Syntax.Scope.Base ( ThingsInScope, AbstractName
+                              , emptyScopeInfo
+                              , exportedNamesInScope)
+import Agda.Syntax.Scope.Monad (getNamedScope)
+
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.Coverage.SplitTree
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.EtaContract
+import Agda.TypeChecking.Generalize
+import Agda.TypeChecking.Implicit
+import Agda.TypeChecking.InstanceArguments (solveAwakeInstanceConstraints)
+import Agda.TypeChecking.Irrelevance
+import Agda.TypeChecking.IApplyConfluence
+import Agda.TypeChecking.Level
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Patterns.Abstract
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.Quote
+import Agda.TypeChecking.RecordPatterns
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Rules.LHS
+import Agda.TypeChecking.SizedTypes
+import Agda.TypeChecking.SizedTypes.Solve
+import Agda.TypeChecking.Sort
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Unquote
+import Agda.TypeChecking.Warnings
+
+import {-# SOURCE #-} Agda.TypeChecking.Empty ( ensureEmptyType )
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Def (checkFunDef', useTerPragma)
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Decl (checkSectionApplication)
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Application
+
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List1  ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty ( prettyShow )
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Types
+---------------------------------------------------------------------------
+
+-- | Check that an expression is a type.
+isType :: A.Expr -> Sort -> TCM Type
+isType = isType' CmpLeq
+
+-- | Check that an expression is a type.
+--   * If @c == CmpEq@, the given sort must be the minimal sort.
+--   * If @c == CmpLeq@, the given sort may be any bigger sort.
+isType' :: Comparison -> A.Expr -> Sort -> TCM Type
+isType' c e s =
+    traceCall (IsTypeCall c e s) $ do
+    v <- checkExpr' c e (sort s)
+    return $ El s v
+
+-- | Check that an expression is a type and infer its (minimal) sort.
+isType_ :: A.Expr -> TCM Type
+isType_ e = traceCall (IsType_ e) $ do
+  reportResult "tc.term.istype" 15 (\a -> vcat
+    [ "isType_" <?> prettyTCM e
+    , nest 2 $ "returns" <?> prettyTCM a
+    ]) $ do
+  let fallback = isType' CmpEq e =<< do workOnTypes $ newSortMeta
+  SortKit{..} <- sortKit
+  case unScope e of
+    A.Fun i (Arg info t) b -> do
+      a <- setArgInfo info . defaultDom <$> checkPiDomain (info :| []) t
+      b <- isType_ b
+      s <- inferFunSort a (getSort b)
+      let t' = El s $ Pi a $ NoAbs underscore b
+      checkTelePiSort t'
+      --noFunctionsIntoSize t'
+      return t'
+    A.Pi _ tel e -> do
+      (t0, t') <- checkPiTelescope (List1.toList tel) $ \ tel -> do
+        t0  <- instantiateFull =<< isType_ e
+        tel <- instantiateFull tel
+        return (t0, telePi tel t0)
+      checkTelePiSort t'
+      --noFunctionsIntoSize t'
+      return t'
+
+    A.Generalized s e -> do
+      (_, t') <- generalizeType s $ isType_ e
+      --noFunctionsIntoSize t'
+      return t'
+
+    -- Prop/(S)Set(ω)ᵢ
+    A.Def' x suffix
+      | Just (sz, u) <- isNameOfUniv x
+      , let n = suffixToLevel suffix
+      -> do
+        univChecks u
+        return . sort $ case sz of
+          USmall -> Univ u $ ClosedLevel n
+          ULarge -> Inf u n
+
+    -- Prop/(S)et ℓ
+    A.App i s arg
+      | visible arg,
+        A.Def x <- unScope s,
+        Just (USmall, u) <- isNameOfUniv x -> do
+      univChecks u
+      unlessM hasUniversePolymorphism $ genericError $
+        "Use --universe-polymorphism to enable level arguments to " ++ showUniv u
+      -- allow NonStrict variables when checking level
+      --   Set : (NonStrict) Level -> Set\omega
+      applyRelevanceToContext NonStrict $
+        sort . Univ u <$> checkLevel arg
+
+    -- Issue #707: Check an existing interaction point
+    A.QuestionMark minfo ii -> caseMaybeM (lookupInteractionMeta ii) fallback $ \ x -> do
+      -- -- | Just x <- A.metaNumber minfo -> do
+      reportSDoc "tc.ip" 20 $ fsep
+        [ "Rechecking meta "
+        , prettyTCM x
+        , text $ " for interaction point " ++ show ii
+        ]
+      mv <- lookupLocalMeta x
+      let s0 = jMetaType . mvJudgement $ mv
+      -- Andreas, 2016-10-14, issue #2257
+      -- The meta was created in a context of length @n@.
+      let n  = length . envContext . clEnv . miClosRange . mvInfo $ mv
+      (vs, rest) <- splitAt n <$> getContextArgs
+      reportSDoc "tc.ip" 20 $ vcat
+        [ "  s0   = " <+> prettyTCM s0
+        , "  vs   = " <+> prettyTCM vs
+        , "  rest = " <+> prettyTCM rest
+        ]
+      -- We assume the meta variable use here is in an extension of the original context.
+      -- If not we revert to the old buggy behavior of #707 (see test/Succeed/Issue2257b).
+      if (length vs /= n) then fallback else do
+      s1  <- reduce =<< piApplyM s0 vs
+      reportSDoc "tc.ip" 20 $ vcat
+        [ "  s1   = " <+> prettyTCM s1
+        ]
+      reportSDoc "tc.ip" 70 $ vcat
+        [ "  s1   = " <+> text (show s1)
+        ]
+      case unEl s1 of
+        Sort s -> return $ El s $ MetaV x $ map Apply vs
+        _ -> __IMPOSSIBLE__
+
+    _ -> fallback
+
+checkLevel :: NamedArg A.Expr -> TCM Level
+checkLevel arg = do
+  lvl <- levelType
+  levelView =<< checkNamedArg arg lvl
+
+-- | Ensure that a (freshly created) function type does not inhabit 'SizeUniv'.
+--   Precondition:  When @noFunctionsIntoSize t tBlame@ is called,
+--   we are in the context of @tBlame@ in order to print it correctly.
+--   Not being in context of @t@ should not matter, as we are only
+--   checking whether its sort reduces to 'SizeUniv'.
+--
+--   Currently UNUSED since SizeUniv is turned off (as of 2016).
+{-
+noFunctionsIntoSize :: Type -> Type -> TCM ()
+noFunctionsIntoSize t tBlame = do
+  reportSDoc "tc.fun" 20 $ do
+    let El s (Pi dom b) = tBlame
+    sep [ "created function type " <+> prettyTCM tBlame
+        , "with pts rule (" <+> prettyTCM (getSort dom) <+>
+                        "," <+> underAbstraction_ b (prettyTCM . getSort) <+>
+                        "," <+> prettyTCM s <+> ")"
+        ]
+  s <- reduce $ getSort t
+  when (s == SizeUniv) $ do
+    -- Andreas, 2015-02-14
+    -- We have constructed a function type in SizeUniv
+    -- which is illegal to prevent issue 1428.
+    typeError $ FunctionTypeInSizeUniv $ unEl tBlame
+-}
+
+-- | Check that an expression is a type which is equal to a given type.
+isTypeEqualTo :: A.Expr -> Type -> TCM Type
+isTypeEqualTo e0 t = scopedExpr e0 >>= \case
+  A.ScopedExpr{} -> __IMPOSSIBLE__
+  A.Underscore i | isNothing (A.metaNumber i) -> return t
+  e -> workOnTypes $ do
+    t' <- isType e (getSort t)
+    t' <$ leqType t t'
+
+leqType_ :: Type -> Type -> TCM ()
+leqType_ t t' = workOnTypes $ leqType t t'
+
+---------------------------------------------------------------------------
+-- * Telescopes
+---------------------------------------------------------------------------
+
+checkGeneralizeTelescope ::
+     Maybe ModuleName
+       -- ^ The module the telescope belongs to (if any).
+  -> A.GeneralizeTelescope
+       -- ^ Telescope to check and add to the context for the continuation.
+  -> ([Maybe Name] -> Telescope -> TCM a)
+       -- ^ Continuation living in the extended context.
+  -> TCM a
+checkGeneralizeTelescope mm (A.GeneralizeTel vars tel) =
+    tr (generalizeTelescope vars (checkTelescope tel) . curry) . uncurry
+  where
+    tr = applyUnless (null tel) $ applyWhenJust mm $ \ m ->
+      traceCallCPS $ CheckModuleParameters m tel
+
+-- | Type check a (module) telescope.
+--   Binds the variables defined by the telescope.
+checkTelescope :: A.Telescope -> (Telescope -> TCM a) -> TCM a
+checkTelescope = checkTelescope' LamNotPi
+
+-- | Type check the telescope of a dependent function type.
+--   Binds the resurrected variables defined by the telescope.
+--   The returned telescope is unmodified (not resurrected).
+checkPiTelescope :: A.Telescope -> (Telescope -> TCM a) -> TCM a
+checkPiTelescope = checkTelescope' PiNotLam
+
+-- | Flag to control resurrection on domains.
+data LamOrPi
+  = LamNotPi -- ^ We are checking a module telescope.
+             --   We pass into the type world to check the domain type.
+             --   This resurrects the whole context.
+  | PiNotLam -- ^ We are checking a telescope in a Pi-type.
+             --   We stay in the term world, but add resurrected
+             --   domains to the context to check the remaining
+             --   domains and codomain of the Pi-type.
+  deriving (Eq, Show)
+
+-- | Type check a telescope. Binds the variables defined by the telescope.
+checkTelescope' :: LamOrPi -> A.Telescope -> (Telescope -> TCM a) -> TCM a
+checkTelescope' lamOrPi []        ret = ret EmptyTel
+checkTelescope' lamOrPi (b : tel) ret =
+    checkTypedBindings lamOrPi b $ \tel1 ->
+    checkTelescope' lamOrPi tel  $ \tel2 ->
+        ret $ abstract tel1 tel2
+
+-- | Check the domain of a function type.
+--   Used in @checkTypedBindings@ and to typecheck @A.Fun@ cases.
+checkDomain :: (LensLock a, LensModality a) => LamOrPi -> List1 a -> A.Expr -> TCM Type
+checkDomain lamOrPi xs e = do
+    -- Get cohesion and quantity of arguments, which should all be equal because
+    -- they come from the same annotated Π-type.
+    let (c :| cs) = fmap (getCohesion . getModality) xs
+    unless (all (c ==) cs) $ __IMPOSSIBLE__
+
+    let (q :| qs) = fmap (getQuantity . getModality) xs
+    unless (all (q ==) qs) $ __IMPOSSIBLE__
+
+    t <- applyQuantityToJudgement q $
+         applyCohesionToContext c $
+         modEnv lamOrPi $ isType_ e
+    -- Andrea TODO: also make sure that LockUniv implies IsLock
+    when (any (\x -> case getLock x of { IsLock{} -> True ; _ -> False }) xs) $ do
+         -- Solves issue #5033
+        unlessM (isJust <$> getName' builtinLockUniv) $ do
+          typeError $ NoBindingForPrimitive builtinLockUniv
+
+        equalSort (getSort t) LockUniv
+
+    return t
+  where
+        -- if we are checking a typed lambda, we resurrect before we check the
+        -- types, but do not modify the new context entries
+        -- otherwise, if we are checking a pi, we do not resurrect, but
+        -- modify the new context entries
+        modEnv LamNotPi = workOnTypes
+        modEnv _        = id
+
+checkPiDomain :: (LensLock a, LensModality a) => List1 a -> A.Expr -> TCM Type
+checkPiDomain = checkDomain PiNotLam
+
+-- | Check a typed binding and extends the context with the bound variables.
+--   The telescope passed to the continuation is valid in the original context.
+--
+--   Parametrized by a flag whether we check a typed lambda or a Pi. This flag
+--   is needed for irrelevance.
+
+checkTypedBindings :: LamOrPi -> A.TypedBinding -> (Telescope -> TCM a) -> TCM a
+checkTypedBindings lamOrPi (A.TBind r tac xps e) ret = do
+    let xs = fmap (updateNamedArg $ A.unBind . A.binderName) xps
+    tac <- traverse (checkTacticAttribute lamOrPi) (tbTacticAttr tac)
+    whenJust tac $ \ t -> reportSDoc "tc.term.tactic" 30 $ "Checked tactic attribute:" <?> prettyTCM t
+    -- Andreas, 2011-04-26 irrelevant function arguments may appear
+    -- non-strictly in the codomain type
+    -- 2011-10-04 if flag --experimental-irrelevance is set
+    experimental <- optExperimentalIrrelevance <$> pragmaOptions
+
+    t <- checkDomain lamOrPi xps e
+
+    -- Jesper, 2019-02-12, Issue #3534: warn if the type of an
+    -- instance argument does not have the right shape
+    List1.unlessNull (List1.filter isInstance xps) $ \ ixs -> do
+      (tel, target) <- getOutputTypeName t
+      case target of
+        OutputTypeName{} -> return ()
+        OutputTypeVar{}  -> return ()
+        OutputTypeVisiblePi{} -> warning . InstanceArgWithExplicitArg =<< prettyTCM (A.mkTBind r ixs e)
+        OutputTypeNameNotYetKnown{} -> return ()
+        NoOutputTypeName -> warning . InstanceNoOutputTypeName =<< prettyTCM (A.mkTBind r ixs e)
+
+    let setTac tac EmptyTel            = EmptyTel
+        setTac tac (ExtendTel dom tel) = ExtendTel dom{ domTactic = tac } $ setTac (raise 1 tac) <$> tel
+        xs' = fmap (modMod lamOrPi experimental) xs
+    let tel = setTac tac $ namedBindsToTel1 xs t
+
+    addContext (xs', t) $ addTypedPatterns xps (ret tel)
+
+    where
+        -- if we are checking a typed lambda, we resurrect before we check the
+        -- types, but do not modify the new context entries
+        -- otherwise, if we are checking a pi, we do not resurrect, but
+        -- modify the new context entries
+        modEnv LamNotPi = workOnTypes
+        modEnv _        = id
+        modMod PiNotLam xp = applyWhen xp $ mapRelevance irrToNonStrict
+        modMod _        _  = id
+
+checkTypedBindings lamOrPi (A.TLet _ lbs) ret = do
+    checkLetBindings lbs (ret EmptyTel)
+
+-- | After a typed binding has been checked, add the patterns it binds
+addTypedPatterns :: List1 (NamedArg A.Binder) -> TCM a -> TCM a
+addTypedPatterns xps ret = do
+  let ps  = List1.mapMaybe (A.extractPattern . namedArg) xps
+  let lbs = map letBinding ps
+  checkLetBindings lbs ret
+  where
+    letBinding :: (A.Pattern, A.BindName) -> A.LetBinding
+    letBinding (p, n) = A.LetPatBind (A.LetRange r) p (A.Var $ A.unBind n)
+      where r = fuseRange p n
+
+-- | Check a tactic attribute. Should have type Term → TC ⊤.
+checkTacticAttribute :: LamOrPi -> Ranged A.Expr -> TCM Term
+checkTacticAttribute LamNotPi (Ranged r e) = setCurrentRange r $
+  typeError $ TacticAttributeNotAllowed
+checkTacticAttribute PiNotLam (Ranged r e) = do
+  expectedType <- el primAgdaTerm --> el (primAgdaTCM <#> primLevelZero <@> primUnit)
+  checkExpr e expectedType
+
+checkPath :: A.TypedBinding -> A.Expr -> Type -> TCM Term
+checkPath b@(A.TBind _r _tac (xp :| []) typ) body ty = do
+ reportSDoc "tc.term.lambda" 30 $ hsep [ "checking path lambda", prettyA xp ]
+ case (A.extractPattern $ namedArg xp) of
+  Just{}  -> setCurrentRange xp $ genericError $ "Patterns are not allowed in Path-lambdas"
+  Nothing -> do
+    let x    = updateNamedArg (A.unBind . A.binderName) xp
+        info = getArgInfo x
+    PathType s path level typ lhs rhs <- pathView ty
+    interval <- primIntervalType
+    v <- addContext ([x], interval) $
+           checkExpr body (El (raise 1 s) (raise 1 (unArg typ) `apply` [argN $ var 0]))
+    iZero <- primIZero
+    iOne  <- primIOne
+    let lhs' = subst 0 iZero v
+        rhs' = subst 0 iOne  v
+    let t = Lam info $ Abs (namedArgName x) v
+    let btyp i = El s (unArg typ `apply` [argN i])
+    locallyTC eRange (const noRange) $ blockTerm ty $ setCurrentRange body $ do
+      equalTerm (btyp iZero) lhs' (unArg lhs)
+      equalTerm (btyp iOne) rhs' (unArg rhs)
+      return t
+checkPath b body ty = __IMPOSSIBLE__
+
+---------------------------------------------------------------------------
+-- * Lambda abstractions
+---------------------------------------------------------------------------
+
+-- | Type check a lambda expression.
+--   "checkLambda bs e ty"  means  (\ bs -> e) : ty
+checkLambda :: Comparison -> A.TypedBinding -> A.Expr -> Type -> TCM Term
+checkLambda cmp (A.TLet _ lbs) body target =
+  checkLetBindings lbs (checkExpr body target)
+checkLambda cmp b@(A.TBind r tac xps0 typ) body target = do
+  reportSDoc "tc.term.lambda" 30 $ vcat
+    [ "checkLambda before insertion xs =" <+> prettyA xps0
+    ]
+  -- Andreas, 2020-03-25, issue #4481: since we have named lambdas now,
+  -- we need to insert skipped hidden arguments.
+  xps <- insertImplicitBindersT1 xps0 target
+  checkLambda' cmp (A.TBind r tac xps typ) xps typ body target
+
+checkLambda'
+  :: Comparison          -- ^ @cmp@
+  -> A.TypedBinding      -- ^ @TBind _ _ xps typ@
+  -> List1 (NamedArg Binder)   -- ^ @xps@
+  -> A.Expr              -- ^ @typ@
+  -> A.Expr              -- ^ @body@
+  -> Type                -- ^ @target@
+  -> TCM Term
+checkLambda' cmp b xps typ body target = do
+  reportSDoc "tc.term.lambda" 30 $ vcat
+    [ "checkLambda xs =" <+> prettyA xps
+    , "possiblePath   =" <+> prettyTCM possiblePath
+    , "numbinds       =" <+> prettyTCM numbinds
+    , "typ            =" <+> prettyA   (unScope typ)
+    ]
+  reportSDoc "tc.term.lambda" 60 $ vcat
+    [ "info           =" <+> (text . show) info
+    ]
+  TelV tel btyp <- telViewUpTo numbinds target
+  if numbinds == 1 && not (null tel) then useTargetType tel btyp
+  else if possiblePath then trySeeingIfPath
+  else dontUseTargetType
+
+  where
+
+    xs = fmap (updateNamedArg (A.unBind . A.binderName)) xps
+    numbinds = length xps
+    isUnderscore = \case { A.Underscore{} -> True; _ -> False }
+    possiblePath = numbinds == 1 && isUnderscore (unScope typ)
+                   && isRelevant info && visible info
+    info = getArgInfo $ List1.head xs
+
+    trySeeingIfPath = do
+      cubical <- isJust . optCubical <$> pragmaOptions
+      reportSLn "tc.term.lambda" 60 $ "trySeeingIfPath for " ++ show xps
+      let postpone' = if cubical then postpone else \ _ _ -> dontUseTargetType
+      ifBlocked target postpone' $ \ _ t -> do
+        ifNotM (isPathType <$> pathView t) dontUseTargetType {-else-} $ if cubical
+          then checkPath b body t
+          else genericError $ unwords
+                 [ "Option --cubical/--erased-cubical needed to build"
+                 , "a path with a lambda abstraction"
+                 ]
+
+    postpone blocker tgt = flip postponeTypeCheckingProblem blocker $
+      CheckExpr cmp (A.Lam A.exprNoRange (A.DomainFull b) body) tgt
+
+    dontUseTargetType = do
+      -- Checking λ (xs : argsT) → body : target
+      verboseS "tc.term.lambda" 5 $ tick "lambda-no-target-type"
+
+      -- First check that argsT is a valid type
+      argsT <- workOnTypes $ isType_ typ
+      let tel = namedBindsToTel1 xs argsT
+      reportSDoc "tc.term.lambda" 30 $ "dontUseTargetType tel =" <+> pretty tel
+
+      -- Andreas, 2015-05-28 Issue 1523
+      -- If argsT is a SizeLt, it must be non-empty to avoid non-termination.
+      -- TODO: do we need to block checkExpr?
+      checkSizeLtSat $ unEl argsT
+
+      -- Jesper 2019-12-17, #4261: we need to postpone here if
+      -- checking of the record pattern fails; if we try to catch
+      -- higher up the metas created during checking of @argsT@ are
+      -- not available.
+      let postponeOnBlockedPattern m = m `catchIlltypedPatternBlockedOnMeta` \(err , x) -> do
+            reportSDoc "tc.term" 50 $ vcat $
+              [ "checking record pattern stuck on meta: " <+> text (show x) ]
+            t1 <- addContext (xs, argsT) $ workOnTypes newTypeMeta_
+            let e    = A.Lam A.exprNoRange (A.DomainFull b) body
+                tgt' = telePi tel t1
+            w <- postponeTypeCheckingProblem (CheckExpr cmp e tgt') x
+            return (tgt' , w)
+
+      -- Now check body : ?t₁
+      -- DONT USE tel for addContext, as it loses NameIds.
+      -- WRONG: v <- addContext tel $ checkExpr body t1
+      (target0 , w) <- postponeOnBlockedPattern $
+         addContext (xs, argsT) $ addTypedPatterns xps $ do
+           t1 <- workOnTypes newTypeMeta_
+           v  <- checkExpr' cmp body t1
+           return (telePi tel t1 , teleLam tel v)
+
+      -- Do not coerce hidden lambdas
+      if notVisible info || any notVisible xs then do
+        pid <- newProblem_ $ leqType target0 target
+        blockTermOnProblem target w pid
+      else do
+        coerce cmp w target0 target
+
+
+    useTargetType tel@(ExtendTel dom (Abs y EmptyTel)) btyp = do
+        verboseS "tc.term.lambda" 5 $ tick "lambda-with-target-type"
+        reportSLn "tc.term.lambda" 30 $ "useTargetType y  = " ++ y
+
+        let (x :| []) = xs
+        unless (sameHiding dom info) $ typeError $ WrongHidingInLambda target
+        when (isJust $ getNameOf x) $
+          -- Andreas, 2020-03-25, issue #4481: check for correct name
+          unless (namedSame dom x) $
+            setCurrentRange x $ typeError $ WrongHidingInLHS
+        -- Andreas, 2011-10-01 ignore relevance in lambda if not explicitly given
+        info <- lambdaModalityCheck dom info
+        -- Andreas, 2015-05-28 Issue 1523
+        -- Ensure we are not stepping under a possibly non-existing size.
+        -- TODO: do we need to block checkExpr?
+        let a = unDom dom
+        checkSizeLtSat $ unEl a
+        -- We only need to block the final term on the argument type
+        -- comparison. The body will be blocked if necessary. We still want to
+        -- compare the argument types first, so we spawn a new problem for that
+        -- check.
+        (pid, argT) <- newProblem $ isTypeEqualTo typ a
+        -- Andreas, Issue 630: take name from function type if lambda name is "_"
+        v <- lambdaAddContext (namedArg x) y (defaultArgDom info argT) $
+               addTypedPatterns xps $ checkExpr' cmp body btyp
+        blockTermOnProblem target (Lam info $ Abs (namedArgName x) v) pid
+
+    useTargetType _ _ = __IMPOSSIBLE__
+
+-- | Check that modality info in lambda is compatible with modality
+--   coming from the function type.
+--   If lambda has no user-given modality, copy that of function type.
+lambdaModalityCheck :: (LensAnnotation dom, LensModality dom) => dom -> ArgInfo -> TCM ArgInfo
+lambdaModalityCheck dom = lambdaAnnotationCheck (getAnnotation dom) <=< lambdaCohesionCheck m <=< lambdaQuantityCheck m <=< lambdaIrrelevanceCheck m
+  where m = getModality dom
+
+-- | Check that irrelevance info in lambda is compatible with irrelevance
+--   coming from the function type.
+--   If lambda has no user-given relevance, copy that of function type.
+lambdaIrrelevanceCheck :: LensRelevance dom => dom -> ArgInfo -> TCM ArgInfo
+lambdaIrrelevanceCheck dom info
+    -- Case: no specific user annotation: use relevance of function type
+  | getRelevance info == defaultRelevance = return $ setRelevance (getRelevance dom) info
+    -- Case: explicit user annotation is taken seriously
+  | otherwise = do
+      let rPi  = getRelevance dom  -- relevance of function type
+      let rLam = getRelevance info -- relevance of lambda
+      unless (sameRelevance rPi rLam) $
+        typeError WrongIrrelevanceInLambda
+      return info
+
+-- | Check that quantity info in lambda is compatible with quantity
+--   coming from the function type.
+--   If lambda has no user-given quantity, copy that of function type.
+lambdaQuantityCheck :: LensQuantity dom => dom -> ArgInfo -> TCM ArgInfo
+lambdaQuantityCheck dom info
+    -- Case: no specific user annotation: use quantity of function type
+  | noUserQuantity info = return $ setQuantity (getQuantity dom) info
+    -- Case: explicit user annotation is taken seriously
+  | otherwise = do
+      let qPi  = getQuantity dom  -- quantity of function type
+      let qLam = getQuantity info -- quantity of lambda
+      unless (qPi `sameQuantity` qLam) $ do
+        typeError WrongQuantityInLambda
+      return info
+
+lambdaAnnotationCheck :: LensAnnotation dom => dom -> ArgInfo -> TCM ArgInfo
+lambdaAnnotationCheck dom info
+    -- Case: no specific user annotation: use annotation of function type
+  | getAnnotation info == defaultAnnotation = return $ setAnnotation (getAnnotation dom) info
+    -- Case: explicit user annotation is taken seriously
+  | otherwise = do
+      let aPi  = getAnnotation dom  -- annotation of function type
+      let aLam = getAnnotation info -- annotation of lambda
+      unless (aPi == aLam) $ do
+        typeError $ GenericError $ "Wrong annotation in lambda"
+      return info
+
+-- | Check that cohesion info in lambda is compatible with cohesion
+--   coming from the function type.
+--   If lambda has no user-given cohesion, copy that of function type.
+lambdaCohesionCheck :: LensCohesion dom => dom -> ArgInfo -> TCM ArgInfo
+lambdaCohesionCheck dom info
+    -- Case: no specific user annotation: use cohesion of function type
+  | getCohesion info == defaultCohesion = return $ setCohesion (getCohesion dom) info
+    -- Case: explicit user annotation is taken seriously
+  | otherwise = do
+      let cPi  = getCohesion dom  -- cohesion of function type
+      let cLam = getCohesion info -- cohesion of lambda
+      unless (cPi `sameCohesion` cLam) $ do
+        -- if there is a cohesion annotation then
+        -- it better match the domain.
+        typeError WrongCohesionInLambda
+      return info
+
+-- Andreas, issue #630: take name from function type if lambda name is "_".
+lambdaAddContext :: Name -> ArgName -> Dom Type -> TCM a -> TCM a
+lambdaAddContext x y dom
+  | isNoName x = addContext (y, dom)                 -- Note: String instance
+  | otherwise  = addContext (x, dom)                 -- Name instance of addContext
+
+-- | Checking a lambda whose domain type has already been checked.
+checkPostponedLambda :: Comparison -> Arg (List1 (WithHiding Name), Maybe Type) -> A.Expr -> Type -> TCM Term
+-- checkPostponedLambda cmp args@(Arg _    ([]    , _ )) body target = do
+--   checkExpr' cmp body target
+checkPostponedLambda cmp args@(Arg info (WithHiding h x :| xs, mt)) body target = do
+  let postpone _ t = postponeTypeCheckingProblem_ $ CheckLambda cmp args body t
+      lamHiding = mappend h $ getHiding info
+  insertHiddenLambdas lamHiding target postpone $ \ t@(El _ (Pi dom b)) -> do
+    -- Andreas, 2011-10-01 ignore relevance in lambda if not explicitly given
+    info' <- setHiding lamHiding <$> lambdaModalityCheck dom info
+    -- We only need to block the final term on the argument type
+    -- comparison. The body will be blocked if necessary. We still want to
+    -- compare the argument types first, so we spawn a new problem for that
+    -- check.
+    mpid <- caseMaybe mt (return Nothing) $ \ ascribedType -> Just <$> do
+      newProblem_ $ leqType (unDom dom) ascribedType
+    -- We type-check the body with the ascribedType given by the user
+    -- to get better error messages.
+    -- Using the type dom from the usage context would be more precise,
+    -- though.
+    -- TODO: quantity
+    let dom' = setRelevance (getRelevance info') . setHiding lamHiding $
+          maybe dom (dom $>) mt
+    v <- lambdaAddContext x (absName b) dom'  $
+      checkPostponedLambda0 cmp (Arg info (xs, mt)) body $ absBody b
+    let v' = Lam info' $ Abs (nameToArgName x) v
+    maybe (return v') (blockTermOnProblem t v') mpid
+
+checkPostponedLambda0 :: Comparison -> Arg ([WithHiding Name], Maybe Type) -> A.Expr -> Type -> TCM Term
+checkPostponedLambda0 cmp (Arg _    ([]    , _ )) body target =
+  checkExpr' cmp body target
+checkPostponedLambda0 cmp (Arg info (x : xs, mt)) body target =
+  checkPostponedLambda cmp (Arg info (x :| xs, mt)) body target
+
+
+-- | Insert hidden lambda until the hiding info of the domain type
+--   matches the expected hiding info.
+--   Throws 'WrongHidingInLambda'
+insertHiddenLambdas
+  :: Hiding                       -- ^ Expected hiding.
+  -> Type                         -- ^ Expected to be a function type.
+  -> (Blocker -> Type -> TCM Term) -- ^ Continuation on blocked type.
+  -> (Type -> TCM Term)           -- ^ Continuation when expected hiding found.
+                                  --   The continuation may assume that the @Type@
+                                  --   is of the form @(El _ (Pi _ _))@.
+  -> TCM Term                     -- ^ Term with hidden lambda inserted.
+insertHiddenLambdas h target postpone ret = do
+  -- If the target type is blocked, we postpone,
+  -- because we do not know if a hidden lambda needs to be inserted.
+  ifBlocked target postpone $ \ _ t -> do
+    case unEl t of
+
+      Pi dom b -> do
+        let h' = getHiding dom
+        -- Found expected hiding: return function type.
+        if sameHiding h h' then ret t else do
+          -- Found a visible argument but expected a hidden one:
+          -- That's an error, as we cannot insert a visible lambda.
+          if visible h' then typeError $ WrongHidingInLambda target else do
+            -- Otherwise, we found a hidden argument that we can insert.
+            let x    = absName b
+            Lam (setOrigin Inserted $ domInfo dom) . Abs x <$> do
+              addContext (x, dom) $ insertHiddenLambdas h (absBody b) postpone ret
+
+      _ -> typeError $ ShouldBePi target
+
+-- | @checkAbsurdLambda i h e t@ checks absurd lambda against type @t@.
+--   Precondition: @e = AbsurdLam i h@
+checkAbsurdLambda :: Comparison -> A.ExprInfo -> Hiding -> A.Expr -> Type -> TCM Term
+checkAbsurdLambda cmp i h e t =
+  setRunTimeModeUnlessInHardCompileTimeMode $ do
+      -- Andreas, 2019-10-01: check absurd lambdas in non-erased mode.
+      -- Otherwise, they are not usable in meta-solutions in the term world.
+      -- See test/Succeed/Issue3176.agda for an absurd lambda
+      -- created in types.
+      -- #4743: Except if hard compile-time mode is enabled.
+  t <- instantiateFull t
+  ifBlocked t (\ blocker t' -> postponeTypeCheckingProblem (CheckExpr cmp e t') blocker) $ \ _ t' -> do
+    case unEl t' of
+      Pi dom@(Dom{domInfo = info', unDom = a}) b
+        | not (sameHiding h info') -> typeError $ WrongHidingInLambda t'
+        | otherwise -> blockTerm t' $ do
+          ensureEmptyType (getRange i) a
+          -- Add helper function
+          top <- currentModule
+          aux <- qualify top <$> freshName_ (getRange i, absurdLambdaName)
+          -- if we are in irrelevant / erased position, the helper function
+          -- is added as irrelevant / erased
+          mod <- currentModality
+          reportSDoc "tc.term.absurd" 10 $ vcat
+            [ ("Adding absurd function" <+> prettyTCM mod) <> prettyTCM aux
+            , nest 2 $ "of type" <+> prettyTCM t'
+            ]
+          lang <- getLanguage
+          fun  <- emptyFunctionData
+          addConstant aux $
+            (\ d -> (defaultDefn (setModality mod info') aux t' lang d)
+                    { defPolarity       = [Nonvariant]
+                    , defArgOccurrences = [Unused] })
+            $ FunctionDefn fun
+              { _funClauses        =
+                  [ Clause
+                    { clauseLHSRange  = getRange e
+                    , clauseFullRange = getRange e
+                    , clauseTel       = telFromList [fmap (absurdPatternName,) dom]
+                    , namedClausePats = [Arg info' $ Named (Just $ WithOrigin Inserted $ unranged $ absName b) $ absurdP 0]
+                    , clauseBody      = Nothing
+                    , clauseType      = Just $ setModality mod $ defaultArg $ absBody b
+                    , clauseCatchall    = True      -- absurd clauses are safe as catch-alls
+                    , clauseExact       = Just False
+                    , clauseRecursive   = Just False
+                    , clauseUnreachable = Just True -- absurd clauses are unreachable
+                    , clauseEllipsis    = NoEllipsis
+                    , clauseWhereModule = Nothing
+                    }
+                  ]
+              , _funCompiled       = Just $ Fail [Arg info' "()"]
+              , _funSplitTree      = Just $ SplittingDone 0
+              , _funMutual         = Just []
+              , _funTerminates     = Just True
+              , _funExtLam         = Just $ ExtLamInfo top True empty
+              }
+          -- Andreas 2012-01-30: since aux is lifted to toplevel
+          -- it needs to be applied to the current telescope (issue 557)
+          Def aux . map Apply . teleArgs <$> getContextTelescope
+      _ -> typeError $ ShouldBePi t'
+
+-- | @checkExtendedLambda i di erased qname cs e t@ check pattern matching lambda.
+-- Precondition: @e = ExtendedLam i di erased qname cs@
+checkExtendedLambda ::
+  Comparison -> A.ExprInfo -> A.DefInfo -> Erased -> QName ->
+  List1 A.Clause -> A.Expr -> Type -> TCM Term
+checkExtendedLambda cmp i di erased qname cs e t = do
+  mod <- currentModality
+  if isErased erased && not (hasQuantity0 mod) then
+    genericError $ unwords
+      [ "Erased pattern-matching lambdas may only be used in erased"
+      , "contexts"
+      ]
+   else setModeUnlessInHardCompileTimeMode erased $ do
+        -- Erased pattern-matching lambdas are checked in hard
+        -- compile-time mode. For non-erased pattern-matching lambdas
+        -- run-time mode is used, unless the current mode is hard
+        -- compile-time mode.
+   -- Andreas, 2016-06-16 issue #2045
+   -- Try to get rid of unsolved size metas before we
+   -- fix the type of the extended lambda auxiliary function
+   solveSizeConstraints DontDefaultToInfty
+   lamMod <- inFreshModuleIfFreeParams currentModule  -- #2883: need a fresh module if refined params
+   t <- instantiateFull t
+   ifBlocked t (\ m t' -> postponeTypeCheckingProblem_ $ CheckExpr cmp e t') $ \ _ t -> do
+     j   <- currentOrFreshMutualBlock
+     mod <- currentModality
+     let info = setModality mod defaultArgInfo
+
+     reportSDoc "tc.term.exlam" 20 $ vcat
+       [ hsep
+         [ text $ show $ A.defAbstract di
+         , "extended lambda's implementation"
+         , doubleQuotes $ prettyTCM qname
+         , "has type:"
+         ]
+       , prettyTCM t -- <+> " where clauses: " <+> text (show cs)
+       ]
+     args     <- getContextArgs
+
+     -- Andreas, Ulf, 2016-02-02: We want to postpone type checking an extended lambda
+     -- in case the lhs checker failed due to insufficient type info for the patterns.
+     -- Issues 480, 1159, 1811.
+     abstract (A.defAbstract di) $ do
+       -- Andreas, 2013-12-28: add extendedlambda as @Function@, not as @Axiom@;
+       -- otherwise, @addClause@ in @checkFunDef'@ fails (see issue 1009).
+       addConstant qname =<< do
+         lang <- getLanguage
+         fun  <- emptyFunction
+         useTerPragma $
+           (defaultDefn info qname t lang fun)
+             { defMutual = j }
+       checkFunDef' t info (Just $ ExtLamInfo lamMod False empty) Nothing di qname $
+         List1.toList cs
+       whenNothingM (asksTC envMutualBlock) $
+         -- Andrea 10-03-2018: Should other checks be performed here too? e.g. termination/positivity/..
+         checkIApplyConfluence_ qname
+       return $ Def qname $ map Apply args
+  where
+    -- Concrete definitions cannot use information about abstract things.
+    abstract ConcreteDef = inConcreteMode
+    abstract AbstractDef = inAbstractMode
+
+-- | Run a computation.
+--
+--   * If successful, that's it, we are done.
+--
+--   * If @NotADatatype a@ or @CannotEliminateWithPattern p a@
+--     is thrown and type @a@ is blocked on some meta @x@,
+--     reset any changes to the state and pass (the error and) @x@ to the handler.
+--
+--   * If @SplitError (UnificationStuck c tel us vs _)@ is thrown and the unification
+--     problem @us =?= vs : tel@ is blocked on some meta @x@ pass @x@ to the handler.
+--
+--   * If another error was thrown or the type @a@ is not blocked, reraise the error.
+--
+--   Note that the returned meta might only exists in the state where the error was
+--   thrown, thus, be an invalid 'MetaId' in the current state.
+--
+catchIlltypedPatternBlockedOnMeta :: TCM a -> ((TCErr, Blocker) -> TCM a) -> TCM a
+catchIlltypedPatternBlockedOnMeta m handle = do
+
+  -- Andreas, 2016-07-13, issue 2028.
+  -- Save the state to rollback the changes to the signature.
+  st <- getTC
+
+  m `catchError` \ err -> do
+
+    let reraise :: MonadError TCErr m => m a
+        reraise = throwError err
+
+    -- Get the blocker responsible for the type error.
+    -- If we do not find a blocker or the error should not be handled,
+    -- we reraise the error.
+    blocker <- maybe reraise return $ case err of
+      TypeError _ s cl -> case clValue cl of
+        SortOfSplitVarError b _                       -> b
+        SplitError (UnificationStuck b c tel us vs _) -> b
+        SplitError (BlockedType b aClosure)           -> Just b
+        CannotEliminateWithPattern b p a              -> b
+        -- Andrea: TODO look for blocking meta in tClosure and its Sort.
+        -- SplitError (CannotCreateMissingClause _ _ _ tClosure) ->
+        _                                             -> Nothing
+      _ -> Nothing
+
+    reportSDoc "tc.postpone" 20 $ vcat $
+      [ "checking definition blocked on: " <+> prettyTCM blocker ]
+
+    -- Note that we messed up the state a bit.  We might want to unroll these state changes.
+    -- However, they are mostly harmless:
+    -- 1. We created a new mutual block id.
+    -- 2. We added a constant without definition.
+    -- In fact, they are not so harmless, see issue 2028!
+    -- Thus, reset the state!
+    putTC st
+
+    -- There might be metas in the blocker not known in the reset state, as they could have been
+    -- created somewhere on the way to the type error.
+    blocker <- (`onBlockingMetasM` blocker) $ \ x ->
+                lookupMeta x >>= \ case
+      -- Case: we do not know the meta, so cannot unblock.
+      Nothing -> return neverUnblock
+      -- Case: we know the meta here.
+      -- Just m | InstV{} <- mvInstantiation m -> __IMPOSSIBLE__  -- It cannot be instantiated yet.
+      -- Andreas, 2018-11-23: I do not understand why @InstV@ is necessarily impossible.
+      -- The reasoning is probably that the state @st@ is more advanced that @s@
+      -- in which @x@ was blocking, thus metas in @st@ should be more instantiated than
+      -- in @s@.  But issue #3403 presents a counterexample, so let's play save and reraise.
+      -- Ulf, 2020-08-13: But treat this case as not blocked and reraise on both always and never.
+      -- Ulf, 2020-08-13: Previously we returned neverUnblock for frozen metas here, but this is in
+      -- fact not very helpful. Yes there is no hope of solving the problem, but throwing a hard
+      -- error means we rob the user of the tools needed to figure out why the meta has not been
+      -- solved. Better to leave the constraint.
+      Just Left{} -> return alwaysUnblock
+      Just (Right m)
+        | InstV{} <- mvInstantiation m -> return alwaysUnblock
+        | otherwise                    -> return $ unblockOnMeta x
+
+    -- If it's not blocked or we can't ever unblock reraise the error.
+    if blocker `elem` [neverUnblock, alwaysUnblock] then reraise else handle (err, blocker)
+
+---------------------------------------------------------------------------
+-- * Records
+---------------------------------------------------------------------------
+
+-- | Picks up record field assignments from modules that export a definition
+--   that has the same name as the missing field.
+
+expandModuleAssigns
+  :: [Either A.Assign A.ModuleName]  -- ^ Modules and field assignments.
+  -> [C.Name]                        -- ^ Names of fields of the record type.
+  -> TCM A.Assigns                   -- ^ Completed field assignments from modules.
+expandModuleAssigns mfs xs = do
+  let (fs , ms) = partitionEithers mfs
+
+  -- The fields of the record that have not been given by field assignments @fs@
+  -- are looked up in the given modules @ms@.
+  fs' <- forM (xs List.\\ map (view nameFieldA) fs) $ \ f -> do
+
+    -- Get the possible assignments for field f from the modules.
+    pms <- forM ms $ \ m -> do
+      modScope <- getNamedScope m
+      let names :: ThingsInScope AbstractName
+          names = exportedNamesInScope modScope
+      return $
+        case Map.lookup f names of
+          Just (n :| []) -> Just (m, FieldAssignment f $ killRange $ A.nameToExpr n)
+          _ -> Nothing
+
+    -- If we have several matching assignments, that's an error.
+    case catMaybes pms of
+      []        -> return Nothing
+      [(_, fa)] -> return (Just fa)
+      mfas      -> typeError $ AmbiguousField f (map fst mfas)
+  return (fs ++ catMaybes fs')
+
+-- | @checkRecordExpression fs e t@ checks record construction against type @t@.
+-- Precondition @e = Rec _ fs@.
+checkRecordExpression
+  :: Comparison       -- ^ How do we related the inferred type of the record expression
+                      --   to the expected type?  Subtype or equal type?
+  -> A.RecordAssigns  -- ^ @mfs@: modules and field assignments.
+  -> A.Expr           -- ^ Must be @A.Rec _ mfs@.
+  -> Type             -- ^ Expected type of record expression.
+  -> TCM Term         -- ^ Record value in internal syntax.
+checkRecordExpression cmp mfs e t = do
+  reportSDoc "tc.term.rec" 10 $ sep
+    [ "checking record expression"
+    , prettyA e
+    ]
+  ifBlocked t (\ _ t -> guessRecordType t) {-else-} $ \ _ t -> do
+  case unEl t of
+    -- Case: We know the type of the record already.
+    Def r es  -> do
+      let ~(Just vs) = allApplyElims es
+      reportSDoc "tc.term.rec" 20 $ text $ "  r   = " ++ prettyShow r
+
+      reportSDoc "tc.term.rec" 30 $ "  xs  = " <> do
+        text =<< prettyShow . map unDom <$> getRecordFieldNames r
+      reportSDoc "tc.term.rec" 30 $ "  ftel= " <> do
+        prettyTCM =<< getRecordFieldTypes r
+      reportSDoc "tc.term.rec" 30 $ "  con = " <> do
+        text =<< prettyShow <$> getRecordConstructor r
+
+      def <- getRecordDef r
+      let -- Field names (C.Name) with ArgInfo from record type definition.
+          cxs  = map argFromDom $ recordFieldNames def
+          -- Just field names.
+          xs   = map unArg cxs
+          -- Record constructor.
+          con  = killRange $ recConHead def
+      reportSDoc "tc.term.rec" 20 $ vcat
+        [ "  xs  = " <> return (P.pretty xs)
+        , "  ftel= " <> prettyTCM (recTel def)
+        , "  con = " <> return (P.pretty con)
+        ]
+
+      -- Record expressions corresponding to erased record
+      -- constructors can only be used in compile-time mode.
+      constructorQ <- getQuantity <$> getConstInfo (conName con)
+      currentQ     <- viewTC eQuantity
+      unless (constructorQ `moreQuantity` currentQ) $
+        typeError $ GenericError $
+        "A record expression corresponding to an erased record " ++
+        "constructor must only be used in erased settings"
+
+      -- Andreas, 2018-09-06, issue #3122.
+      -- Associate the concrete record field names used in the record expression
+      -- to their counterpart in the record type definition.
+      disambiguateRecordFields (map _nameFieldA $ lefts mfs) (map unDom $ recFields def)
+
+      -- Compute the list of given fields, decorated with the ArgInfo from the record def.
+      -- Andreas, 2019-03-18, issue #3122, also pick up non-visible fields from the modules.
+      fs <- expandModuleAssigns mfs (map unArg cxs)
+
+      -- Compute a list of metas for the missing visible fields.
+      scope <- getScope
+      let re = getRange e
+          meta x = A.Underscore $ A.MetaInfo re scope Nothing (prettyShow x)
+      -- In @es@ omitted explicit fields are replaced by underscores.
+      -- Omitted implicit or instance fields
+      -- are still left out and inserted later by checkArguments_.
+      es <- insertMissingFieldsWarn r meta fs cxs
+
+      args <- checkArguments_ cmp ExpandLast re es (recTel def `apply` vs) >>= \case
+        (elims, remainingTel) | null remainingTel
+                              , Just args <- allApplyElims elims -> return args
+        _ -> __IMPOSSIBLE__
+      -- Don't need to block here!
+      reportSDoc "tc.term.rec" 20 $ text $ "finished record expression"
+      return $ Con con ConORec (map Apply args)
+    _ -> typeError $ ShouldBeRecordType t
+
+  where
+    -- Case: We don't know the type of the record.
+    guessRecordType t = do
+      let fields = [ x | Left (FieldAssignment x _) <- mfs ]
+      rs <- findPossibleRecords fields
+      reportSDoc "tc.term.rec" 30 $ "Possible records for" <+> prettyTCM t <+> "are" <?> pretty rs
+      case rs of
+          -- If there are no records with the right fields we might as well fail right away.
+        [] -> case fields of
+          []  -> genericError "There are no records in scope"
+          [f] -> genericError $ "There is no known record with the field " ++ prettyShow f
+          _   -> genericError $ "There is no known record with the fields " ++ unwords (map prettyShow fields)
+          -- If there's only one record with the appropriate fields, go with that.
+        [r] -> do
+          -- #5198: Don't generate metas for parameters of the current module. In most cases they
+          -- get solved, but not always.
+          def <- instantiateDef =<< getConstInfo r
+          ps  <- freeVarsToApply r
+          let rt = defType def
+          reportSDoc "tc.term.rec" 30 $ "Type of unique record" <+> prettyTCM rt
+          vs  <- newArgsMeta rt
+          target <- reduce $ piApply rt vs
+          s  <- case unEl target of
+                  Sort s  -> return s
+                  v       -> do
+                    reportSDoc "impossible" 10 $ vcat
+                      [ "The impossible happened when checking record expression against meta"
+                      , "Candidate record type r = " <+> prettyTCM r
+                      , "Type of r               = " <+> prettyTCM rt
+                      , "Ends in (should be sort)= " <+> prettyTCM v
+                      , text $ "  Raw                   =  " ++ show v
+                      ]
+                    __IMPOSSIBLE__
+          let inferred = El s $ Def r $ map Apply (ps ++ vs)
+          v <- checkExpr e inferred
+          coerce cmp v inferred t
+          -- Andreas 2012-04-21: OLD CODE, WRONG DIRECTION, I GUESS:
+          -- blockTerm t $ v <$ leqType_ t inferred
+
+          -- If there are more than one possible record we postpone
+        _:_:_ -> do
+          reportSDoc "tc.term.expr.rec" 10 $ sep
+            [ "Postponing type checking of"
+            , nest 2 $ prettyA e <+> ":" <+> prettyTCM t
+            ]
+          postponeTypeCheckingProblem_ $ CheckExpr cmp e t
+
+-- | @checkRecordUpdate cmp ei recexpr fs e t@
+--
+-- Preconditions: @e = RecUpdate ei recexpr fs@ and @t@ is reduced.
+--
+checkRecordUpdate
+  :: Comparison   -- ^ @cmp@
+  -> A.ExprInfo   -- ^ @ei@
+  -> A.Expr       -- ^ @recexpr@
+  -> A.Assigns    -- ^ @fs@
+  -> A.Expr       -- ^ @e = RecUpdate ei recexpr fs@
+  -> Type         -- ^ Need not be reduced.
+  -> TCM Term
+checkRecordUpdate cmp ei recexpr fs eupd t = do
+  ifBlocked t (\ _ _ -> tryInfer) $ {-else-} \ _ t' -> do
+    caseMaybeM (isRecordType t') should $ \ (r, _pars, defn) -> do
+      -- Bind the record value (before update) to a fresh @name@.
+      v <- checkExpr' cmp recexpr t'
+      name <- freshNoName $ getRange recexpr
+      addLetBinding defaultArgInfo Inserted name v t' $ do
+
+        let projs = map argFromDom $ recFields defn
+
+        -- Andreas, 2018-09-06, issue #3122.
+        -- Associate the concrete record field names used in the record expression
+        -- to their counterpart in the record type definition.
+        disambiguateRecordFields (map _nameFieldA fs) (map unArg projs)
+
+        -- Desugar record update expression into record expression.
+        let fs' = map (\ (FieldAssignment x e) -> (x, Just e)) fs
+        axs <- map argFromDom <$> getRecordFieldNames r
+        es  <- orderFieldsWarn r (const Nothing) axs fs'
+        let es'  = zipWith (replaceFields name ei) projs es
+        let erec = A.Rec ei [ Left (FieldAssignment x e) | (Arg _ x, Just e) <- zip axs es' ]
+        -- Call the type checker on the desugared syntax.
+        checkExpr' cmp erec t
+  where
+    replaceFields :: Name -> A.ExprInfo -> Arg A.QName -> Maybe A.Expr -> Maybe A.Expr
+    replaceFields name ei (Arg ai p) Nothing | visible ai = Just $
+      -- omitted visible fields remain unchanged: @{ ...; p = p name; ...}@
+      -- (hidden fields are supposed to be inferred)
+      A.App
+        (A.defaultAppInfo $ getRange ei)
+        (A.Proj ProjSystem $ unambiguous p)
+        (defaultNamedArg $ A.Var name)
+    replaceFields _ _ _ me = me  -- other fields get the user-written updates
+
+    tryInfer = do
+      (_, trec) <- inferExpr recexpr
+      ifBlocked trec (\ _ _ -> postpone) $ {-else-} \ _ _ -> do
+        v <- checkExpr' cmp eupd trec
+        coerce cmp v trec t
+
+    postpone = postponeTypeCheckingProblem_ $ CheckExpr cmp eupd t
+    should   = typeError $ ShouldBeRecordType t
+
+---------------------------------------------------------------------------
+-- * Literal
+---------------------------------------------------------------------------
+
+checkLiteral :: Literal -> Type -> TCM Term
+checkLiteral lit t = do
+  t' <- litType lit
+  coerce CmpEq (Lit lit) t' t
+
+---------------------------------------------------------------------------
+-- * Terms
+---------------------------------------------------------------------------
+
+-- | Remove top layers of scope info of expression and set the scope accordingly
+--   in the 'TCState'.
+
+scopedExpr :: A.Expr -> TCM A.Expr
+scopedExpr (A.ScopedExpr scope e) = setScope scope >> scopedExpr e
+scopedExpr e                      = return e
+
+-- | Type check an expression.
+checkExpr :: A.Expr -> Type -> TCM Term
+checkExpr = checkExpr' CmpLeq
+
+-- Andreas, 2019-10-13, issue #4125:
+-- For the sake of readable types in interactive program construction,
+-- avoid unnecessary unfoldings via 'reduce' in the type checker!
+checkExpr'
+  :: Comparison
+  -> A.Expr
+  -> Type        -- ^ Unreduced!
+  -> TCM Term
+checkExpr' cmp e t =
+  verboseBracket "tc.term.expr.top" 5 "checkExpr" $
+  reportResult "tc.term.expr.top" 15 (\ v -> vcat
+                                              [ "checkExpr" <?> fsep [ prettyTCM e, ":", prettyTCM t ]
+                                              , "  returns" <?> prettyTCM v ]) $
+  traceCall (CheckExprCall cmp e t) $ localScope $ doExpandLast $ unfoldInlined =<< do
+    reportSDoc "tc.term.expr.top" 15 $
+        "Checking" <+> sep
+          [ fsep [ prettyTCM e, ":", prettyTCM t ]
+          , nest 2 $ "at " <+> (text . prettyShow =<< getCurrentRange)
+          ]
+    reportSDoc "tc.term.expr.top.detailed" 80 $
+      "Checking" <+> fsep [ prettyTCM e, ":", text (show t) ]
+    tReduced <- reduce t
+    reportSDoc "tc.term.expr.top" 15 $
+        "    --> " <+> prettyTCM tReduced
+
+    e <- scopedExpr e
+
+    irrelevantIfProp <- (runBlocked $ isPropM t) >>= \case
+      Right True  -> do
+        let mod = unitModality { modRelevance = Irrelevant }
+        return $ fmap dontCare . applyModalityToContext mod
+      _ -> return id
+
+    irrelevantIfProp $ tryInsertHiddenLambda e tReduced $ case e of
+
+        A.ScopedExpr scope e -> __IMPOSSIBLE__ -- setScope scope >> checkExpr e t
+
+        -- a meta variable without arguments: type check directly for efficiency
+        A.QuestionMark i ii -> checkQuestionMark (newValueMeta' RunMetaOccursCheck) cmp t i ii
+        A.Underscore i -> checkUnderscore cmp t i
+
+        A.WithApp _ e es -> typeError $ NotImplemented "type checking of with application"
+
+        e0@(A.App i q (Arg ai e))
+          | A.Quote _ <- unScope q, visible ai -> do
+          x <- quotedName $ namedThing e
+          ty <- qNameType
+          coerce cmp (quoteName x) ty t
+
+          | A.QuoteTerm _ <- unScope q -> do
+             (et, _) <- inferExpr (namedThing e)
+             doQuoteTerm cmp et t
+
+        A.Quote{}     -> genericError "quote must be applied to a defined name"
+        A.QuoteTerm{} -> genericError "quoteTerm must be applied to a term"
+        A.Unquote{}   -> genericError "unquote must be applied to a term"
+
+        A.AbsurdLam i h -> checkAbsurdLambda cmp i h e t
+
+        A.ExtendedLam i di erased qname cs ->
+          checkExtendedLambda cmp i di erased qname cs e t
+
+        A.Lam i (A.DomainFull b) e -> checkLambda cmp b e t
+
+        A.Lam i (A.DomainFree _ x) e0
+          | isNothing (nameOf $ unArg x) && isNothing (A.binderPattern $ namedArg x) ->
+              checkExpr' cmp (A.Lam i (domainFree (getArgInfo x) $ A.unBind <$> namedArg x) e0) t
+          | otherwise -> typeError $ NotImplemented "named arguments in lambdas"
+
+        A.Lit _ lit  -> checkLiteral lit t
+        A.Let i ds e -> checkLetBindings ds $ checkExpr' cmp e t
+        e@A.Pi{} -> do
+            t' <- isType_ e
+            let s = getSort t'
+                v = unEl t'
+            coerce cmp v (sort s) t
+
+        A.Generalized s e -> do
+            (_, t') <- generalizeType s $ isType_ e
+            --noFunctionsIntoSize t' t'
+            let s = getSort t'
+                v = unEl t'
+            coerce cmp v (sort s) t
+
+        e@A.Fun{} -> do
+            t' <- isType_ e
+            let s = getSort t'
+                v = unEl t'
+            coerce cmp v (sort s) t
+
+        A.Rec _ fs  -> checkRecordExpression cmp fs e t
+
+        A.RecUpdate ei recexpr fs -> checkRecordUpdate cmp ei recexpr fs e t
+
+        A.DontCare e -> -- resurrect vars
+          ifM ((Irrelevant ==) <$> viewTC eRelevance)
+            (dontCare <$> do applyRelevanceToContext Irrelevant $ checkExpr' cmp e t)
+            (internalError "DontCare may only appear in irrelevant contexts")
+
+        A.Dot{} -> genericError "Invalid dotted expression"
+
+        -- Application
+        _   | Application hd args <- appView e -> checkApplication cmp hd args e t
+
+      `catchIlltypedPatternBlockedOnMeta` \ (err, x) -> do
+        -- We could not check the term because the type of some pattern is blocked.
+        -- It has to be blocked on some meta, so we can postpone,
+        -- being sure it will be retried when a meta is solved
+        -- (which might be the blocking meta in which case we actually make progress).
+        reportSDoc "tc.term" 50 $ vcat $
+          [ "checking pattern got stuck on meta: " <+> pretty x ]
+        postponeTypeCheckingProblem (CheckExpr cmp e t) x
+
+  where
+  -- Call checkExpr with an hidden lambda inserted if appropriate,
+  -- else fallback.
+  tryInsertHiddenLambda
+    :: A.Expr
+    -> Type      -- Reduced.
+    -> TCM Term
+    -> TCM Term
+  tryInsertHiddenLambda e tReduced fallback
+    -- Insert hidden lambda if all of the following conditions are met:
+    -- type is a hidden function type, {x : A} -> B or {{x : A}} -> B
+    -- expression is not a lambda with the appropriate hiding yet
+    | Pi (Dom{domInfo = info, unDom = a}) b <- unEl tReduced
+        , let h = getHiding info
+        , notVisible h
+        -- expression is not a matching hidden lambda or question mark
+        , not (hiddenLambdaOrHole h e)
+        = do
+      let proceed = doInsert (setOrigin Inserted info) $ absName b
+      expandHidden <- asksTC envExpandLast
+      -- If we skip the lambda insertion for an introduction,
+      -- we will hit a dead end, so proceed no matter what.
+      if definitelyIntroduction then proceed else
+        -- #3019 and #4170: don't insert implicit lambdas in arguments to existing metas
+        if expandHidden == ReallyDontExpandLast then fallback else do
+        -- Andreas, 2017-01-19, issue #2412:
+        -- We do not want to insert a hidden lambda if A is
+        -- possibly empty type of sizes, as this will produce an error.
+        reduce a >>= isSizeType >>= \case
+          Just (BoundedLt u) -> ifBlocked u (\ _ _ -> fallback) $ \ _ v -> do
+            ifM (checkSizeNeverZero v) proceed fallback
+            `catchError` \_ -> fallback
+          _ -> proceed
+
+    | otherwise = fallback
+
+    where
+    re = getRange e
+    rx = caseMaybe (rStart re) noRange $ \ pos -> posToRange pos pos
+
+    doInsert info y = do
+      x <- C.setNotInScope <$> freshName rx y
+      reportSLn "tc.term.expr.impl" 15 $ "Inserting implicit lambda"
+      checkExpr' cmp (A.Lam (A.ExprRange re) (domainFree info $ A.mkBinder x) e) tReduced
+
+    hiddenLambdaOrHole h = \case
+      A.AbsurdLam _ h'          -> sameHiding h h'
+      A.ExtendedLam _ _ _ _ cls -> any hiddenLHS cls
+      A.Lam _ bind _            -> sameHiding h bind
+      A.QuestionMark{}          -> True
+      _                         -> False
+
+    hiddenLHS (A.Clause (A.LHS _ (A.LHSHead _ (a : _))) _ _ _ _) = notVisible a
+    hiddenLHS _ = False
+
+    -- Things with are definitely introductions,
+    -- thus, cannot be of hidden Pi-type, unless they are hidden lambdas.
+    definitelyIntroduction = case e of
+      A.Lam{}        -> True
+      A.AbsurdLam{}  -> True
+      A.Lit{}        -> True
+      A.Pi{}         -> True
+      A.Fun{}        -> True
+      A.Rec{}        -> True
+      A.RecUpdate{}  -> True
+      A.ScopedExpr{} -> __IMPOSSIBLE__
+      _ -> False
+
+---------------------------------------------------------------------------
+-- * Reflection
+---------------------------------------------------------------------------
+
+doQuoteTerm :: Comparison -> Term -> Type -> TCM Term
+doQuoteTerm cmp et t = do
+  et'       <- etaContract =<< instantiateFull et
+  case allMetasList et' of
+    []  -> do
+      q  <- quoteTerm et'
+      ty <- el primAgdaTerm
+      coerce cmp q ty t
+    metas -> postponeTypeCheckingProblem (DoQuoteTerm cmp et t) $ unblockOnAllMetas $ Set.fromList metas
+
+-- | Unquote a TCM computation in a given hole.
+unquoteM :: A.Expr -> Term -> Type -> TCM ()
+unquoteM tacA hole holeType = do
+  tac <- applyQuantityToJudgement zeroQuantity $
+    checkExpr tacA =<< (el primAgdaTerm --> el (primAgdaTCM <#> primLevelZero <@> primUnit))
+  inFreshModuleIfFreeParams $ unquoteTactic tac hole holeType
+
+-- | Run a tactic `tac : Term → TC ⊤` in a hole (second argument) of the type
+--   given by the third argument. Runs the continuation if successful.
+unquoteTactic :: Term -> Term -> Type -> TCM ()
+unquoteTactic tac hole goal = do
+  reportSDoc "tc.term.tactic" 40 $ sep
+    [ "Running tactic" <+> prettyTCM tac
+    , nest 2 $ "on" <+> prettyTCM hole <+> ":" <+> prettyTCM goal ]
+  ok  <- runUnquoteM $ unquoteTCM tac hole
+  case ok of
+    Left (BlockedOnMeta oldState blocker) -> do
+      putTC oldState
+      let stripFreshMeta x = maybe neverUnblock (const $ unblockOnMeta x) <$> lookupLocalMeta' x
+      blocker' <- onBlockingMetasM stripFreshMeta blocker
+      r <- case Set.toList $ allBlockingMetas blocker' of
+            x : _ -> getRange <$> lookupLocalMeta' x
+            []    -> return noRange
+      setCurrentRange r $
+        addConstraint blocker' (UnquoteTactic tac hole goal)
+    Left err -> typeError $ UnquoteFailed err
+    Right _ -> return ()
+
+---------------------------------------------------------------------------
+-- * Meta variables
+---------------------------------------------------------------------------
+
+-- | Check an interaction point without arguments.
+checkQuestionMark
+  :: (Comparison -> Type -> TCM (MetaId, Term))
+  -> Comparison
+  -> Type            -- ^ Not reduced!
+  -> A.MetaInfo
+  -> InteractionId
+  -> TCM Term
+checkQuestionMark new cmp t0 i ii = do
+  reportSDoc "tc.interaction" 20 $ sep
+    [ "Found interaction point"
+    , text . show =<< asksTC (^. lensIsAbstract)
+    , pretty ii
+    , ":"
+    , prettyTCM t0
+    ]
+  reportSDoc "tc.interaction" 60 $ sep
+    [ "Raw:"
+    , text (show t0)
+    ]
+  checkMeta (newQuestionMark' new ii) cmp t0 i -- Andreas, 2013-05-22 use unreduced type t0!
+
+-- | Check an underscore without arguments.
+checkUnderscore :: Comparison -> Type -> A.MetaInfo -> TCM Term
+checkUnderscore = checkMeta (newValueMeta RunMetaOccursCheck)
+
+-- | Type check a meta variable.
+checkMeta :: (Comparison -> Type -> TCM (MetaId, Term)) -> Comparison -> Type -> A.MetaInfo -> TCM Term
+checkMeta newMeta cmp t i = fst <$> checkOrInferMeta newMeta (Just (cmp , t)) i
+
+-- | Infer the type of a meta variable.
+--   If it is a new one, we create a new meta for its type.
+inferMeta :: (Comparison -> Type -> TCM (MetaId, Term)) -> A.MetaInfo -> TCM (Elims -> Term, Type)
+inferMeta newMeta i = mapFst applyE <$> checkOrInferMeta newMeta Nothing i
+
+-- | Type check a meta variable.
+--   If its type is not given, we return its type, or a fresh one, if it is a new meta.
+--   If its type is given, we check that the meta has this type, and we return the same
+--   type.
+checkOrInferMeta
+  :: (Comparison -> Type -> TCM (MetaId, Term))
+  -> Maybe (Comparison , Type)
+  -> A.MetaInfo
+  -> TCM (Term, Type)
+checkOrInferMeta newMeta mt i = do
+  case A.metaNumber i of
+    Nothing -> do
+      setScope (A.metaScope i)
+      (cmp , t) <- maybe ((CmpEq,) <$> workOnTypes newTypeMeta_) return mt
+      (x, v) <- newMeta cmp t
+      setMetaNameSuggestion x (A.metaNameSuggestion i)
+      return (v, t)
+    -- Rechecking an existing metavariable
+    Just x -> do
+      let v = MetaV x []
+      reportSDoc "tc.meta.check" 20 $
+        "checking existing meta " <+> prettyTCM v
+      t' <- metaType x
+      reportSDoc "tc.meta.check" 20 $
+        nest 2 $ "of type " <+> prettyTCM t'
+      case mt of
+        Nothing -> return (v, t')
+        Just (cmp , t) -> (,t) <$> coerce cmp v t' t
+
+-- | Turn a domain-free binding (e.g. lambda) into a domain-full one,
+--   by inserting an underscore for the missing type.
+domainFree :: ArgInfo -> A.Binder' A.Name -> A.LamBinding
+domainFree info x =
+  A.DomainFull $ A.mkTBind r (singleton $ unnamedArg info $ fmap A.mkBindName x)
+               $ A.Underscore underscoreInfo
+  where
+    r = getRange x
+    underscoreInfo = A.MetaInfo
+      { A.metaRange          = r
+      , A.metaScope          = emptyScopeInfo
+      , A.metaNumber         = Nothing
+      , A.metaNameSuggestion = prettyShow $ A.nameConcrete $ A.binderName x
+      }
+
+
+-- | Check arguments whose value we already know.
+--
+--   This function can be used to check user-supplied parameters
+--   we have already computed by inference.
+--
+--   Precondition: The type @t@ of the head has enough domains.
+
+checkKnownArguments
+  :: [NamedArg A.Expr]  -- ^ User-supplied arguments (hidden ones may be missing).
+  -> Args               -- ^ Inferred arguments (including hidden ones).
+  -> Type               -- ^ Type of the head (must be Pi-type with enough domains).
+  -> TCM (Args, Type)   -- ^ Remaining inferred arguments, remaining type.
+checkKnownArguments []           vs t = return (vs, t)
+checkKnownArguments (arg : args) vs t = do
+  (vs', t') <- setCurrentRange arg $ checkKnownArgument arg vs t
+  checkKnownArguments args vs' t'
+
+-- | Check an argument whose value we already know.
+
+checkKnownArgument
+  :: NamedArg A.Expr    -- ^ User-supplied argument.
+  -> Args               -- ^ Inferred arguments (including hidden ones).
+  -> Type               -- ^ Type of the head (must be Pi-type with enough domains).
+  -> TCM (Args, Type)   -- ^ Remaining inferred arguments, remaining type.
+checkKnownArgument arg [] _ = typeError $ InvalidProjectionParameter arg
+-- Andreas, 2019-07-22, while #3353: we should use domName, not absName !!
+-- WAS:
+-- checkKnownArgument arg@(Arg info e) (Arg _infov v : vs) t = do
+--   (dom@Dom{domInfo = info',unDom = a}, b) <- mustBePi t
+--   -- Skip the arguments from vs that do not correspond to e
+--   if not (sameHiding info info'
+--           && (visible info || maybe True (absName b ==) (bareNameOf e)))
+checkKnownArgument arg (Arg _ v : vs) t = do
+  -- Skip the arguments from vs that do not correspond to e
+  (dom@Dom{ unDom = a }, b) <- mustBePi t
+  if not $ fromMaybe __IMPOSSIBLE__ $ fittingNamedArg arg dom
+    -- Continue with the next one
+    then checkKnownArgument arg vs (b `absApp` v)
+    -- Found the right argument
+    else do
+      u <- checkNamedArg arg a
+      equalTerm a u v
+      return (vs, b `absApp` v)
+
+-- | Check a single argument.
+
+checkNamedArg :: NamedArg A.Expr -> Type -> TCM Term
+checkNamedArg arg@(Arg info e0) t0 = do
+  let e = namedThing e0
+  let x = bareNameWithDefault "" e0
+  traceCall (CheckExprCall CmpLeq e t0) $ do
+    reportSDoc "tc.term.args.named" 15 $ do
+        "Checking named arg" <+> sep
+          [ fsep [ prettyTCM arg, ":", prettyTCM t0 ]
+          ]
+    reportSLn "tc.term.args.named" 75 $ "  arg = " ++ show (deepUnscope arg)
+    -- Ulf, 2017-03-24: (#2172) Always treat explicit _ and ? as implicit
+    -- argument (i.e. solve with unification).
+    let checkU = checkMeta (newMetaArg (setHiding Hidden info) x) CmpLeq t0
+    let checkQ = checkQuestionMark (newInteractionMetaArg (setHiding Hidden info) x) CmpLeq t0
+    if not $ isHole e then checkExpr e t0 else localScope $ do
+      -- Note: we need localScope here,
+      -- as scopedExpr manipulates the scope in the state.
+      -- However, we may not pull localScope over checkExpr!
+      -- This is why we first test for isHole, and only do
+      -- scope manipulations if we actually handle the checking
+      -- of e here (and not pass it to checkExpr).
+      scopedExpr e >>= \case
+        A.Underscore i ->  checkU i
+        A.QuestionMark i ii -> checkQ i ii
+        _ -> __IMPOSSIBLE__
+  where
+  isHole A.Underscore{} = True
+  isHole A.QuestionMark{} = True
+  isHole (A.ScopedExpr _ e) = isHole e
+  isHole _ = False
+
+-- | Infer the type of an expression. Implemented by checking against a meta
+--   variable.  Except for neutrals, for them a polymorphic type is inferred.
+inferExpr :: A.Expr -> TCM (Term, Type)
+-- inferExpr e = inferOrCheck e Nothing
+inferExpr = inferExpr' DontExpandLast
+
+inferExpr' :: ExpandHidden -> A.Expr -> TCM (Term, Type)
+inferExpr' exh e = traceCall (InferExpr e) $ do
+  let Application hd args = appView e
+  reportSDoc "tc.infer" 30 $ vcat
+    [ "inferExpr': appView of " <+> prettyA e
+    , "  hd   = " <+> prettyA hd
+    , "  args = " <+> prettyAs args
+    ]
+  reportSDoc "tc.infer" 60 $ vcat
+    [ text $ "  hd (raw) = " ++ show hd
+    ]
+  inferApplication exh hd args e
+
+defOrVar :: A.Expr -> Bool
+defOrVar A.Var{} = True
+defOrVar A.Def'{} = True
+defOrVar A.Proj{} = True
+defOrVar (A.ScopedExpr _ e) = defOrVar e
+defOrVar _     = False
+
+-- | Used to check aliases @f = e@.
+--   Switches off 'ExpandLast' for the checking of top-level application.
+checkDontExpandLast :: Comparison -> A.Expr -> Type -> TCM Term
+checkDontExpandLast cmp e t = case e of
+  _ | Application hd args <- appView e,  defOrVar hd ->
+    traceCall (CheckExprCall cmp e t) $ localScope $ dontExpandLast $ do
+      checkApplication cmp hd args e t
+  _ -> checkExpr' cmp e t -- note that checkExpr always sets ExpandLast
+
+-- | Check whether a de Bruijn index is bound by a module telescope.
+isModuleFreeVar :: Int -> TCM Bool
+isModuleFreeVar i = do
+  params <- moduleParamsToApply =<< currentModule
+  return $ any ((== Var i []) . unArg) params
+
+-- | Infer the type of an expression, and if it is of the form
+--   @{tel} -> D vs@ for some datatype @D@ then insert the hidden
+--   arguments.  Otherwise, leave the type polymorphic.
+inferExprForWith :: Arg A.Expr -> TCM (Term, Type)
+inferExprForWith (Arg info e) = verboseBracket "tc.with.infer" 20 "inferExprForWith" $
+  applyRelevanceToContext (getRelevance info) $ do
+    reportSDoc "tc.with.infer" 20 $ "inferExprforWith " <+> prettyTCM e
+    reportSLn  "tc.with.infer" 80 $ "inferExprforWith " ++ show (deepUnscope e)
+    traceCall (InferExpr e) $ do
+      (v, t) <- inferExpr e
+      v <- reduce v
+      -- Andreas 2014-11-06, issue 1342.
+      -- Check that we do not `with` on a module parameter!
+      case v of
+        Var i [] -> whenM (isModuleFreeVar i) $ do
+          reportSDoc "tc.with.infer" 80 $ vcat
+            [ text $ "with expression is variable " ++ show i
+            , "current modules = " <+> do text . show =<< currentModule
+            , "current module free vars = " <+> do text . show =<< getCurrentModuleFreeVars
+            , "context size = " <+> do text . show =<< getContextSize
+            , "current context = " <+> do prettyTCM =<< getContextTelescope
+            ]
+          typeError $ WithOnFreeVariable e v
+        _        -> return ()
+      -- Possibly insert hidden arguments.
+      TelV tel t0 <- telViewUpTo' (-1) (not . visible) t
+      (v, t) <- case unEl t0 of
+        Def d vs -> do
+          isDataOrRecordType d >>= \case
+            Nothing -> return (v, t)
+            Just{}  -> do
+              (args, t1) <- implicitArgs (-1) notVisible t
+              return (v `apply` args, t1)
+        _ -> return (v, t)
+      -- #6868, #7113: trigger instance search to resolve instances in with-expression
+      solveAwakeConstraints
+      return (v, t)
+
+---------------------------------------------------------------------------
+-- * Let bindings
+---------------------------------------------------------------------------
+
+checkLetBindings :: Foldable t => t A.LetBinding -> TCM a -> TCM a
+checkLetBindings = foldr ((.) . checkLetBinding) id
+
+checkLetBinding :: A.LetBinding -> TCM a -> TCM a
+
+checkLetBinding b@(A.LetBind i info x t e) ret =
+  traceCall (CheckLetBinding b) $ do
+    -- #4131: Only DontExpandLast if no user written type signature
+    let check | getOrigin info == Inserted = checkDontExpandLast
+              | otherwise                  = checkExpr'
+    t <- workOnTypes $ isType_ t
+    v <- applyModalityToContext info $ check CmpLeq e t
+    addLetBinding info UserWritten (A.unBind x) v t ret
+
+checkLetBinding b@(A.LetPatBind i p e) ret =
+  traceCall (CheckLetBinding b) $ do
+    p <- expandPatternSynonyms p
+    (v, t) <- inferExpr' ExpandLast e
+    let -- construct a type  t -> dummy  for use in checkLeftHandSide
+        t0 = El (getSort t) $ Pi (defaultDom t) (NoAbs underscore __DUMMY_TYPE__)
+        p0 = Arg defaultArgInfo (Named Nothing p)
+    reportSDoc "tc.term.let.pattern" 10 $ vcat
+      [ "let-binding pattern p at type t"
+      , nest 2 $ vcat
+        [ "p (A) =" <+> prettyA p
+        , "t     =" <+> prettyTCM t
+        , "cxtRel=" <+> do pretty =<< viewTC eRelevance
+        , "cxtQnt=" <+> do pretty =<< viewTC eQuantity
+        ]
+      ]
+    fvs <- getContextSize
+    checkLeftHandSide (CheckPattern p EmptyTel t) Nothing [p0] t0 Nothing [] $ \ (LHSResult _ delta0 ps _ _t _ asb _ _) -> bindAsPatterns asb $ do
+          -- After dropping the free variable patterns there should be a single pattern left.
+      let p = case drop fvs ps of [p] -> namedArg p; _ -> __IMPOSSIBLE__
+          -- Also strip the context variables from the telescope
+          delta = telFromList $ drop fvs $ telToList delta0
+      reportSDoc "tc.term.let.pattern" 20 $ nest 2 $ vcat
+        [ "p (I) =" <+> prettyTCM p
+        , "delta =" <+> prettyTCM delta
+        , "cxtRel=" <+> do pretty =<< viewTC eRelevance
+        , "cxtQnt=" <+> do pretty =<< viewTC eQuantity
+        ]
+      reportSDoc "tc.term.let.pattern" 80 $ nest 2 $ vcat
+        [ "p (I) =" <+> (text . show) p
+        ]
+      -- We translate it into a list of projections.
+      fs <- recordPatternToProjections p
+      -- We remove the bindings for the pattern variables from the context.
+      cxt0 <- getContext
+      let (binds, cxt) = splitAt (size delta) cxt0
+          toDrop       = length binds
+
+          -- We create a substitution for the let-bound variables
+          -- (unfortunately, we cannot refer to x in internal syntax
+          -- so we have to copy v).
+          sigma = map ($ v) fs
+          -- We apply the types of the let bound-variables to this substitution.
+          -- The 0th variable in a context is the last one, so we reverse.
+          -- Further, we need to lower all other de Bruijn indices by
+          -- the size of delta, so we append the identity substitution.
+          sub    = parallelS (reverse sigma)
+
+      updateContext sub (drop toDrop) $ do
+        reportSDoc "tc.term.let.pattern" 20 $ nest 2 $ vcat
+          [ "delta =" <+> prettyTCM delta
+          , "binds =" <+> prettyTCM binds
+          ]
+        let fdelta = flattenTel delta
+        reportSDoc "tc.term.let.pattern" 20 $ nest 2 $ vcat
+          [ "fdelta =" <+> addContext delta (prettyTCM fdelta)
+          ]
+        let tsl  = applySubst sub fdelta
+        -- We get a list of types
+        let ts   = map unDom tsl
+        -- and relevances.
+        let infos = map domInfo tsl
+        -- We get list of names of the let-bound vars from the context.
+        let xs   = map (fst . unDom) (reverse binds)
+        -- We add all the bindings to the context.
+        foldr (uncurry4 $ flip addLetBinding UserWritten) ret $ List.zip4 infos xs sigma ts
+
+checkLetBinding (A.LetApply i erased x modapp copyInfo dir) ret = do
+  -- Any variables in the context that doesn't belong to the current
+  -- module should go with the new module.
+  -- Example: @f x y = let open M t in u@.
+  -- There are 2 @new@ variables, @x@ and @y@, going into the anonynous module
+  -- @module _ (x : _) (y : _) = M t@.
+  fv   <- getCurrentModuleFreeVars
+  n    <- getContextSize
+  let new = n - fv
+  reportSDoc "tc.term.let.apply" 10 $ "Applying" <+> pretty x <+> prettyA modapp <?> ("with" <+> pshow new <+> "free variables")
+  reportSDoc "tc.term.let.apply" 20 $ vcat
+    [ "context =" <+> (prettyTCM =<< getContextTelescope)
+    , "module  =" <+> (prettyTCM =<< currentModule)
+    , "fv      =" <+> text (show fv)
+    ]
+  checkSectionApplication i erased x modapp copyInfo
+    -- Some other part of the code ensures that "open public" is
+    -- ignored in let expressions. Thus there is no need for
+    -- checkSectionApplication to throw an error if the import
+    -- directive does contain "open public".
+    dir{ publicOpen = Nothing }
+  withAnonymousModule x new ret
+-- LetOpen and LetDeclaredVariable are only used for highlighting.
+checkLetBinding A.LetOpen{} ret = ret
+checkLetBinding (A.LetDeclaredVariable _) ret = ret
diff --git a/src/full/Agda/TypeChecking/Rules/Term.hs-boot b/src/full/Agda/TypeChecking/Rules/Term.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Rules/Term.hs-boot
@@ -0,0 +1,20 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Rules.Term where
+
+import Agda.Syntax.Common (WithHiding, Arg)
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.Utils.List1 (List1)
+
+isType_ :: A.Expr -> TCM Type
+
+checkExpr :: A.Expr -> Type -> TCM Term
+checkExpr' :: Comparison -> A.Expr -> Type -> TCM Term
+inferExpr :: A.Expr -> TCM (Term, Type)
+
+checkPostponedLambda :: Comparison -> Arg (List1 (WithHiding Name), Maybe Type) -> A.Expr -> Type -> TCM Term
+
+doQuoteTerm :: Comparison -> Term -> Type -> TCM Term
+unquoteTactic :: Term -> Term -> Type -> TCM ()
diff --git a/src/full/Agda/TypeChecking/Serialise.hs b/src/full/Agda/TypeChecking/Serialise.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise.hs
@@ -0,0 +1,296 @@
+{-# LANGUAGE CPP #-}
+
+-- Andreas, Makoto, Francesco 2014-10-15 AIM XX:
+-- -O2 does not have any noticable effect on runtime
+-- but sabotages cabal repl with -Werror
+-- (due to a conflict with --interactive warning)
+-- {-# OPTIONS_GHC -O2                      #-}
+
+-- | Structure-sharing serialisation of Agda interface files.
+
+-- -!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-
+-- NOTE: Every time the interface format is changed the interface
+-- version number should be bumped _in the same patch_.
+--
+-- See 'currentInterfaceVersion' below.
+--
+-- -!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-!-
+
+module Agda.TypeChecking.Serialise
+  ( encode, encodeFile, encodeInterface
+  , decode, decodeFile, decodeInterface, decodeHashes
+  , EmbPrj
+  )
+  where
+
+import Prelude hiding ( null )
+
+import System.Directory ( createDirectoryIfMissing )
+import System.FilePath ( takeDirectory )
+
+import Control.Arrow (second)
+import Control.DeepSeq
+import qualified Control.Exception as E
+import Control.Monad
+import Control.Monad.Except
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Reader
+import Control.Monad.State.Strict
+import Control.Monad.ST.Trans
+
+import Data.Array.IArray
+import Data.Array.IO
+import Data.Word
+import Data.Int (Int32)
+import Data.ByteString.Lazy    ( ByteString )
+import Data.ByteString.Builder ( byteString, toLazyByteString )
+import qualified Data.ByteString.Lazy as L
+import qualified Data.Map as Map
+import qualified Data.Binary as B
+import qualified Data.Binary.Get as B
+import qualified Data.Binary.Put as B
+import qualified Data.List as List
+import Data.Function (on)
+
+import qualified Codec.Compression.GZip as G
+import qualified Codec.Compression.Zlib.Internal as Z
+
+import GHC.Compact as C
+
+import qualified Agda.TypeChecking.Monad.Benchmark as Bench
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances () --instance only
+
+import Agda.TypeChecking.Monad
+
+import Agda.Utils.Hash
+import qualified Agda.Utils.HashTable as H
+import Agda.Utils.IORef
+import Agda.Utils.Null
+import qualified Agda.Utils.ProfileOptions as Profile
+
+import Agda.Utils.Impossible
+
+-- Note that the Binary instance for Int writes 64 bits, but throws
+-- away the 32 high bits when reading (at the time of writing, on
+-- 32-bit machines). Word64 does not have these problems.
+
+currentInterfaceVersion :: Word64
+currentInterfaceVersion = 20240102 * 10 + 1
+
+-- | The result of 'encode' and 'encodeInterface'.
+
+data Encoded = Encoded
+  { uncompressed :: ByteString
+    -- ^ The uncompressed bytestring, without hashes and the interface
+    -- version.
+  , compressed :: ByteString
+    -- ^ The compressed bytestring.
+  }
+
+-- | Encodes something. To ensure relocatability file paths in
+-- positions are replaced with module names.
+
+encode :: EmbPrj a => a -> TCM Encoded
+encode a = do
+    collectStats <- hasProfileOption Profile.Serialize
+    newD@(Dict nD ltD stD bD iD dD _tD
+      _nameD
+      _qnameD
+      nC ltC stC bC iC dC tC
+      nameC
+      qnameC
+      stats _) <- liftIO $ emptyDict collectStats
+    root <- liftIO $ (`runReaderT` newD) $ icode a
+    nL  <- benchSort $ l nD
+    stL <- benchSort $ l stD
+    ltL <- benchSort $ l ltD
+    bL  <- benchSort $ l bD
+    iL  <- benchSort $ l iD
+    dL  <- benchSort $ l dD
+    -- Record reuse statistics.
+    whenProfile Profile.Sharing $ do
+      statistics "pointers" tC
+    whenProfile Profile.Serialize $ do
+      statistics "Integer"     iC
+      statistics "Lazy Text"   ltC
+      statistics "Strict Text" stC
+      statistics "Text"        bC
+      statistics "Double"      dC
+      statistics "Node"        nC
+      statistics "Shared Term" tC
+      statistics "A.QName"     qnameC
+      statistics "A.Name"      nameC
+    when collectStats $ do
+      stats <- Map.fromListWith __IMPOSSIBLE__ . map (second toInteger) <$> do
+        liftIO $ List.sort <$> H.toList stats
+      modifyStatistics $ Map.unionWith (+) stats
+    -- Encode hashmaps and root, and compress.
+    bits1 <- Bench.billTo [ Bench.Serialization, Bench.BinaryEncode ] $
+      return $!! B.encode (root, nL, ltL, stL, bL, iL, dL)
+    let compressParams = G.defaultCompressParams
+          { G.compressLevel    = G.bestSpeed
+          , G.compressStrategy = G.huffmanOnlyStrategy
+          }
+    cbits <- Bench.billTo [ Bench.Serialization, Bench.Compress ] $
+      return $!! G.compressWith compressParams bits1
+    let x = B.encode currentInterfaceVersion <> cbits
+    return (Encoded { uncompressed = bits1, compressed = x })
+  where
+    l h = List.map fst . List.sortBy (compare `on` snd) <$> H.toList h
+    benchSort = Bench.billTo [Bench.Serialization, Bench.Sort] . liftIO
+    statistics :: String -> IORef FreshAndReuse -> TCM ()
+    statistics kind ioref = do
+      FreshAndReuse fresh
+#ifdef DEBUG_SERIALISATION
+                          reused
+#endif
+                                 <- liftIO $ readIORef ioref
+      tickN (kind ++ "  (fresh)") $ fromIntegral fresh
+#ifdef DEBUG_SERIALISATION
+      tickN (kind ++ " (reused)") $ fromIntegral reused
+#endif
+
+-- encode :: EmbPrj a => a -> TCM ByteString
+-- encode a = do
+--     fileMod <- sourceToModule
+--     (x, shared, total) <- liftIO $ do
+--       newD@(Dict nD sD iD dD _ _ _ _ _ stats _) <- emptyDict fileMod
+--       root <- runReaderT (icode a) newD
+--       nL <- l nD; sL <- l sD; iL <- l iD; dL <- l dD
+--       (shared, total) <- readIORef stats
+--       return (B.encode currentInterfaceVersion <>
+--               G.compress (B.encode (root, nL, sL, iL, dL)), shared, total)
+--     whenProfile Profile.Sharing $ do
+--       tickN "pointers (reused)" $ fromIntegral shared
+--       tickN "pointers" $ fromIntegral total
+--     return x
+--   where
+--   l h = List.map fst . List.sortBy (compare `on` snd) <$> H.toList h
+
+newtype ListLike a = ListLike { unListLike :: Array Int32 a }
+
+instance B.Binary a => B.Binary (ListLike a) where
+  put = __IMPOSSIBLE__ -- Will never serialise this
+  get = fmap ListLike $ runSTArray $ do
+    n <- lift (B.get :: B.Get Int)
+    arr <- newArray_ (0, fromIntegral n - 1) :: STT s B.Get (STArray s Int32 a)
+
+    -- We'd like to use 'for_ [0..n-1]' here, but unfortunately GHC doesn't unfold
+    -- the list construction and so performs worse than the hand-written version.
+    let
+      getMany i = if i == n then return () else do
+        x <- lift B.get
+        unsafeWriteSTArray arr i x
+        getMany (i + 1)
+    () <- getMany 0
+
+    return arr
+
+-- | Decodes an uncompressed bytestring (without extra hashes or magic
+-- numbers). The result depends on the include path.
+--
+-- Returns 'Nothing' if a decoding error is encountered.
+
+decode :: EmbPrj a => ByteString -> TCM (Maybe a)
+decode s = do
+  mf   <- useTC stModuleToSource
+  incs <- getIncludeDirs
+
+  -- Note that runGetState can raise errors if the input is malformed.
+  -- The decoder is (intended to be) strict enough to ensure that all
+  -- such errors can be caught by the handler here.
+
+  res <- liftIO $ E.handle (\(E.ErrorCall s) -> pure $ Left s) $ do
+    ((r, nL, ltL, stL, bL, iL, dL), s, _) <- return $ runGetState B.get s 0
+    let ar = unListLike
+    when (not (null s)) $ E.throwIO $ E.ErrorCall "Garbage at end."
+    let nL' = ar nL
+    st <- St nL' (ar ltL) (ar stL) (ar bL) (ar iL) (ar dL)
+            <$> liftIO (newArray (bounds nL') MEEmpty)
+            <*> return mf <*> return incs
+    (r, st) <- runStateT (value r) st
+    let !mf = modFile st
+    return $ Right (mf, r)
+
+  case res of
+    Left s -> do
+      reportSLn "import.iface" 5 $ "Error when decoding interface file: " ++ s
+      pure Nothing
+
+    Right (mf, x) -> do
+      setTCLens stModuleToSource mf
+      -- "Compact" the interfaces (without breaking sharing) to
+      -- reduce the amount of memory that is traversed by the
+      -- garbage collector.
+      Bench.billTo [Bench.Deserialization, Bench.Compaction] $
+        liftIO (Just . C.getCompact <$> C.compactWithSharing x)
+
+
+encodeInterface :: Interface -> TCM Encoded
+encodeInterface i = do
+  r <- encode i
+  return r{ compressed = hashes <> compressed r }
+  where
+    hashes :: ByteString
+    hashes = B.runPut $ B.put (iSourceHash i) >> B.put (iFullHash i)
+
+-- | Encodes an interface. To ensure relocatability file paths in
+-- positions are replaced with module names.
+--
+-- An uncompressed bytestring corresponding to the encoded interface
+-- is returned.
+
+encodeFile :: FilePath -> Interface -> TCM ByteString
+encodeFile f i = do
+  r <- encodeInterface i
+  liftIO $ createDirectoryIfMissing True (takeDirectory f)
+  liftIO $ L.writeFile f (compressed r)
+  return (uncompressed r)
+
+-- | Decodes an interface. The result depends on the include path.
+--
+-- Returns 'Nothing' if the file does not start with the right magic
+-- number or some other decoding error is encountered.
+
+decodeInterface :: ByteString -> TCM (Maybe Interface)
+decodeInterface s = do
+
+  -- Note that runGetState and the decompression code below can raise
+  -- errors if the input is malformed. The decoder is (intended to be)
+  -- strict enough to ensure that all such errors can be caught by the
+  -- handler here or the one in decode.
+
+  s <- liftIO $
+       E.handle (\(E.ErrorCall s) -> return (Left s)) $
+       E.evaluate $
+       let (ver, s', _) = runGetState B.get (L.drop 16 s) 0 in
+       if ver /= currentInterfaceVersion
+       then Left "Wrong interface version."
+       else Right $
+            toLazyByteString $
+            Z.foldDecompressStreamWithInput
+              (\s -> (byteString s <>))
+              (\s -> if null s
+                     then mempty
+                     else error "Garbage at end.")
+              (\err -> error (show err))
+              (Z.decompressST Z.gzipFormat Z.defaultDecompressParams)
+              s'
+
+  case s of
+    Right s  -> decode s
+    Left err -> do
+      reportSLn "import.iface" 5 $
+        "Error when decoding interface file: " ++ err
+      return Nothing
+
+decodeHashes :: ByteString -> Maybe (Hash, Hash)
+decodeHashes s
+  | L.length s < 16 = Nothing
+  | otherwise       = Just $ B.runGet getH $ L.take 16 s
+  where getH = (,) <$> B.get <*> B.get
+
+decodeFile :: FilePath -> TCM (Maybe Interface)
+decodeFile f = decodeInterface =<< liftIO (L.readFile f)
diff --git a/src/full/Agda/TypeChecking/Serialise/Base.hs b/src/full/Agda/TypeChecking/Serialise/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Base.hs
@@ -0,0 +1,561 @@
+{-# LANGUAGE CPP                  #-}
+{-# LANGUAGE TypeOperators        #-}
+{-# LANGUAGE DataKinds            #-}
+{-# LANGUAGE UndecidableInstances #-} -- Due to ICODE vararg typeclass
+{-# LANGUAGE MagicHash            #-}
+{-# LANGUAGE UnboxedTuples        #-}
+
+{-
+András, 2023-10-2:
+
+All code in Agda/TypeChecking/Serialise should be strict, since serialization necessarily
+forces all data, eventually.
+  - (<$!>) should be used instead of lazy fmap.
+  - Any redex that's passed to `return`, a lazy constructor, or a function, should
+    be forced beforehand with strict `let`, strict binding or ($!).
+-}
+
+module Agda.TypeChecking.Serialise.Base where
+
+import qualified Control.Exception as E
+import Control.Monad ((<$!>))
+import Control.Monad.Except
+import Control.Monad.IO.Class     ( MonadIO(..) )
+import Control.Monad.Reader
+import Control.Monad.State.Strict (StateT, gets)
+
+import Data.Proxy
+
+import Data.Array.IArray
+import Data.Array.IO
+import qualified Data.HashMap.Strict as Hm
+import qualified Data.ByteString.Lazy as L
+import Data.Hashable
+import Data.Int (Int32)
+import Data.Maybe
+import qualified Data.Binary as B
+import qualified Data.Binary.Get as B
+import qualified Data.Text      as T
+import qualified Data.Text.Lazy as TL
+import Data.Typeable ( cast, Typeable, TypeRep, typeRep, typeRepFingerprint )
+import GHC.Exts (Word(..), timesWord2#, xor#, Any)
+import GHC.Fingerprint.Type
+import Unsafe.Coerce
+
+import Agda.Syntax.Common (NameId)
+import Agda.Syntax.Internal (Term, QName(..), ModuleName(..), nameId)
+import Agda.TypeChecking.Monad.Base (TypeError(GenericError), ModuleToSource)
+
+import Agda.Utils.FileName
+import Agda.Utils.HashTable (HashTable)
+import qualified Agda.Utils.HashTable as H
+import Agda.Utils.IORef
+import Agda.Utils.Lens
+import Agda.Utils.Monad
+import Agda.Utils.Pointer
+import Agda.Utils.TypeLevel
+
+-- | Constructor tag (maybe omitted) and argument indices.
+data Node = Empty | Cons !Int32 !Node deriving Eq
+
+instance Hashable Node where
+  -- Adapted from https://github.com/tkaitchuck/aHash/wiki/AHash-fallback-algorithm
+  hashWithSalt h n = fromIntegral (go (fromIntegral h) n) where
+    xor (W# x) (W# y) = W# (xor# x y)
+
+    foldedMul :: Word -> Word -> Word
+    foldedMul (W# x) (W# y) = case timesWord2# x y of (# hi, lo #) -> W# (xor# hi lo)
+
+    combine :: Word -> Word -> Word
+    combine x y = foldedMul (xor x y) 11400714819323198549
+
+    go :: Word -> Node -> Word
+    go !h Empty       = h
+    go  h (Cons n ns) = go (combine h (fromIntegral n)) ns
+
+  hash = hashWithSalt 3032525626373534813
+
+instance B.Binary Node where
+
+  get = go =<< B.get where
+
+    go :: Int -> B.Get Node
+    go n | n <= 0 =
+      pure Empty
+    go n = do
+      !x    <- B.get
+      !node <- go (n - 1)
+      pure $ Cons x node
+
+  put n = B.put (len n) <> go n where
+
+    len :: Node -> Int
+    len = go 0 where
+      go !acc Empty     = acc
+      go acc (Cons _ n) = go (acc + 1) n
+
+    go :: Node -> B.Put
+    go Empty       = mempty
+    go (Cons n ns) = B.put n <> go ns
+
+-- | Association lists mapping TypeRep fingerprints to values. In some cases
+--   values with different types have the same serialized representation. This
+--   structure disambiguates them.
+data MemoEntry = MEEmpty | MECons {-# unpack #-} !Fingerprint !Any !MemoEntry
+
+-- 2023-10-2 András: `typeRepFingerprint` usually inlines a 4-way case, which
+-- yields significant code size increase as GHC often inlines the same code into
+-- the branches. This wouldn't matter in "normal" code but the serialization
+-- instances use very heavy inlining. The NOINLINE cuts down on the code size.
+fingerprintNoinline :: TypeRep -> Fingerprint
+fingerprintNoinline rep = typeRepFingerprint rep
+{-# NOINLINE fingerprintNoinline #-}
+
+lookupME :: forall a b. Proxy a -> Fingerprint -> MemoEntry -> (a -> b) -> b -> b
+lookupME proxy fprint me found notfound = go fprint me where
+  go :: Fingerprint -> MemoEntry -> b
+  go fp MEEmpty =
+    notfound
+  go fp (MECons fp' x me)
+    | fp == fp' = found (unsafeCoerce x)
+    | True      = go fp me
+{-# NOINLINE lookupME #-}
+
+-- | Structure providing fresh identifiers for hash map
+--   and counting hash map hits (i.e. when no fresh identifier required).
+#ifdef DEBUG_SERIALISATION
+data FreshAndReuse = FreshAndReuse
+  { farFresh :: !Int32 -- ^ Number of hash map misses.
+  , farReuse :: !Int32 -- ^ Number of hash map hits.
+  }
+#else
+newtype FreshAndReuse = FreshAndReuse
+  { farFresh :: Int32 -- ^ Number of hash map misses.
+  }
+#endif
+
+farEmpty :: FreshAndReuse
+farEmpty = FreshAndReuse 0
+#ifdef DEBUG_SERIALISATION
+                           0
+#endif
+
+lensFresh :: Lens' FreshAndReuse Int32
+lensFresh f r = f (farFresh r) <&> \ i -> r { farFresh = i }
+{-# INLINE lensFresh #-}
+
+#ifdef DEBUG_SERIALISATION
+lensReuse :: Lens' FreshAndReuse Int32
+lensReuse f r = f (farReuse r) <&> \ i -> r { farReuse = i }
+{-# INLINE lensReuse #-}
+#endif
+
+-- | Two 'QName's are equal if their @QNameId@ is equal.
+type QNameId = [NameId]
+
+-- | Computing a qualified names composed ID.
+qnameId :: QName -> QNameId
+qnameId (QName (MName ns) n) = map nameId $ n:ns
+
+-- | State of the the encoder.
+data Dict = Dict
+  -- Dictionaries which are serialized:
+  { nodeD        :: !(HashTable Node    Int32)    -- ^ Written to interface file.
+  , stringD      :: !(HashTable String  Int32)    -- ^ Written to interface file.
+  , lTextD       :: !(HashTable TL.Text Int32)    -- ^ Written to interface file.
+  , sTextD       :: !(HashTable T.Text  Int32)    -- ^ Written to interface file.
+  , integerD     :: !(HashTable Integer Int32)    -- ^ Written to interface file.
+  , doubleD      :: !(HashTable Double  Int32)    -- ^ Written to interface file.
+  -- Dicitionaries which are not serialized, but provide
+  -- short cuts to speed up serialization:
+  , termD        :: !(HashTable (Ptr Term) Int32) -- ^ Not written to interface file.
+  -- Andreas, Makoto, AIM XXI
+  -- Memoizing A.Name does not buy us much if we already memoize A.QName.
+  , nameD        :: !(HashTable NameId  Int32)    -- ^ Not written to interface file.
+  , qnameD       :: !(HashTable QNameId Int32)    -- ^ Not written to interface file.
+  -- Fresh UIDs and reuse statistics:
+  , nodeC        :: !(IORef FreshAndReuse)  -- counters for fresh indexes
+  , stringC      :: !(IORef FreshAndReuse)
+  , lTextC       :: !(IORef FreshAndReuse)
+  , sTextC       :: !(IORef FreshAndReuse)
+  , integerC     :: !(IORef FreshAndReuse)
+  , doubleC      :: !(IORef FreshAndReuse)
+  , termC        :: !(IORef FreshAndReuse)
+  , nameC        :: !(IORef FreshAndReuse)
+  , qnameC       :: !(IORef FreshAndReuse)
+  , stats        :: !(HashTable String Int)
+  , collectStats :: !Bool
+    -- ^ If @True@ collect in @stats@ the quantities of
+    --   calls to @icode@ for each @Typeable a@.
+  }
+
+-- | Creates an empty dictionary.
+emptyDict
+  :: Bool
+     -- ^ Collect statistics for @icode@ calls?
+  -> IO Dict
+emptyDict collectStats = Dict
+  <$> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> H.empty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> newIORef farEmpty
+  <*> H.empty
+  <*> pure collectStats
+
+-- | Univeral memo structure, to introduce sharing during decoding
+type Memo = IOArray Int32 MemoEntry
+
+-- | State of the decoder.
+data St = St
+  { nodeE     :: !(Array Int32 [Int32])  -- ^ Obtained from interface file.
+  , stringE   :: !(Array Int32 String)   -- ^ Obtained from interface file.
+  , lTextE    :: !(Array Int32 TL.Text)  -- ^ Obtained from interface file.
+  , sTextE    :: !(Array Int32 T.Text)   -- ^ Obtained from interface file.
+  , integerE  :: !(Array Int32 Integer)  -- ^ Obtained from interface file.
+  , doubleE   :: !(Array Int32 Double)   -- ^ Obtained from interface file.
+  , nodeMemo  :: !Memo
+    -- ^ Created and modified by decoder.
+    --   Used to introduce sharing while deserializing objects.
+  , modFile   :: !ModuleToSource
+    -- ^ Maps module names to file names. Constructed by the decoder.
+  , includes  :: ![AbsolutePath]
+    -- ^ The include directories.
+  }
+
+-- | Monad used by the encoder.
+
+type S a = ReaderT Dict IO a
+
+-- | Monad used by the decoder.
+--
+-- 'TCM' is not used because the associated overheads would make
+-- decoding slower.
+
+type R = StateT St IO
+
+-- | Throws an error which is suitable when the data stream is
+-- malformed.
+
+malformed :: R a
+malformed = liftIO $ E.throwIO $ E.ErrorCall "Malformed input."
+{-# NOINLINE malformed #-} -- 2023-10-2 András: cold code, so should be out-of-line.
+
+class Typeable a => EmbPrj a where
+  icode :: a -> S Int32  -- ^ Serialization (wrapper).
+  icod_ :: a -> S Int32  -- ^ Serialization (worker).
+  value :: Int32 -> R a  -- ^ Deserialization.
+
+  icode a = do
+    !r <- icod_ a
+    tickICode a
+    pure r
+  {-# INLINE icode #-}
+
+  -- Simple enumeration types can be (de)serialized using (from/to)Enum.
+  default value :: (Enum a, Bounded a) => Int32 -> R a
+  value i =
+    let i' = fromIntegral i in
+    if i' >= fromEnum (minBound :: a) && i' <= fromEnum (maxBound :: a)
+    then pure $! toEnum i'
+    else malformed
+
+  default icod_ :: (Enum a, Bounded a) => a -> S Int32
+  icod_ x = return $! fromIntegral $! fromEnum x
+
+-- | The actual logic of `tickICode` is cold code, so it's out-of-line,
+--   to decrease code size and avoid cache pollution.
+goTickIcode :: forall a. Typeable a => Proxy a -> S ()
+goTickIcode p = do
+  let key = "icode " ++ show (typeRep p)
+  hmap <- asks stats
+  liftIO $ do
+    n <- fromMaybe 0 <$> H.lookup hmap key
+    H.insert hmap key $! n + 1
+{-# NOINLINE goTickIcode #-}
+
+-- | Increase entry for @a@ in 'stats'.
+tickICode :: forall a. Typeable a => a -> S ()
+tickICode _ = whenM (asks collectStats) $ goTickIcode (Proxy :: Proxy a)
+{-# INLINE tickICode #-}
+
+-- | Data.Binary.runGetState is deprecated in favour of runGetIncremental.
+--   Reimplementing it in terms of the new function. The new Decoder type contains
+--   strict byte strings so we need to be careful not to feed the entire lazy byte
+--   string to the decoder at once.
+runGetState :: B.Get a -> L.ByteString -> B.ByteOffset -> (a, L.ByteString, B.ByteOffset)
+runGetState g s n = feed (B.runGetIncremental g) (L.toChunks s)
+  where
+    feed (B.Done s n' x) ss     = (x, L.fromChunks (s : ss), n + n')
+    feed (B.Fail _ _ err) _     = error err
+    feed (B.Partial f) (s : ss) = feed (f $ Just s) ss
+    feed (B.Partial f) []       = feed (f Nothing) []
+
+-- Specializing icodeX leads to Warning like
+-- src/full/Agda/TypeChecking/Serialise.hs:1297:1: Warning:
+--     RULE left-hand side too complicated to desugar
+--       case cobox_aQY5 of _ [Occ=Dead] { ghc-prim:GHC.Types.Eq# cobox ->
+--       icodeX @ String $dEq_aQY3 $dHashable_aQY4
+--       }
+--
+-- type ICodeX k
+--   =  (Dict -> HashTable k Int32)
+--   -> (Dict -> IORef Int32)
+--   -> k -> S Int32
+-- {-# SPECIALIZE icodeX :: ICodeX String  #-}
+-- {-# SPECIALIZE icodeX :: ICodeX Integer #-}
+-- {-# SPECIALIZE icodeX :: ICodeX Double  #-}
+-- {-# SPECIALIZE icodeX :: ICodeX Node    #-}
+
+-- Andreas, 2014-10-16 AIM XX:
+-- Inlining this increases Serialization time by 10%
+-- Makoto's theory: code size increase might lead to
+-- instruction cache misses.
+-- {-# INLINE icodeX #-}
+icodeX :: (Eq k, Hashable k)
+  =>  (Dict -> HashTable k Int32)
+  -> (Dict -> IORef FreshAndReuse)
+  -> k -> S Int32
+icodeX dict counter key = do
+  d <- asks dict
+  c <- asks counter
+  liftIO $ do
+    mi <- H.lookup d key
+    case mi of
+      Just i  -> do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' c $ over lensReuse (+ 1)
+#endif
+        return $! i
+      Nothing -> do
+        !fresh <- (^. lensFresh) <$> do readModifyIORef' c $ over lensFresh (+ 1)
+        H.insert d key fresh
+        return fresh
+
+-- Instead of inlining icodeX, we manually specialize it to
+-- its four uses: Integer, String, Double, Node.
+-- Not a great gain (hardly noticeable), but not harmful.
+
+icodeInteger :: Integer -> S Int32
+icodeInteger key = do
+  d <- asks integerD
+  c <- asks integerC
+  liftIO $ do
+    mi <- H.lookup d key
+    case mi of
+      Just i  -> do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' c $ over lensReuse (+ 1)
+#endif
+        return $! i
+      Nothing -> do
+        !fresh <- (^. lensFresh) <$> do readModifyIORef' c $ over lensFresh (+ 1)
+        H.insert d key fresh
+        return fresh
+
+icodeDouble :: Double -> S Int32
+icodeDouble key = do
+  d <- asks doubleD
+  c <- asks doubleC
+  liftIO $ do
+    mi <- H.lookup d key
+    case mi of
+      Just i  -> do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' c $ over lensReuse (+ 1)
+#endif
+        return $! i
+      Nothing -> do
+        !fresh <- (^. lensFresh) <$> do readModifyIORef' c $ over lensFresh (+ 1)
+        H.insert d key fresh
+        return fresh
+
+icodeString :: String -> S Int32
+icodeString key = do
+  d <- asks stringD
+  c <- asks stringC
+  liftIO $ do
+    mi <- H.lookup d key
+    case mi of
+      Just i  -> do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' c $ over lensReuse (+ 1)
+#endif
+        return i
+      Nothing -> do
+        !fresh <- (^. lensFresh) <$> do readModifyIORef' c $ over lensFresh (+ 1)
+        H.insert d key fresh
+        return fresh
+
+icodeNode :: Node -> S Int32
+icodeNode key = do
+  d <- asks nodeD
+  c <- asks nodeC
+  liftIO $ do
+    mi <- H.lookup d key
+    case mi of
+      Just i  -> do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' c $ over lensReuse (+ 1)
+#endif
+        return $! i
+      Nothing -> do
+        !fresh <- (^. lensFresh) <$> do readModifyIORef' c $ over lensFresh (+ 1)
+        H.insert d key fresh
+        return fresh
+
+-- icodeN :: [Int32] -> S Int32
+-- icodeN = icodeX nodeD nodeC
+
+-- | @icode@ only if thing has not seen before.
+icodeMemo
+  :: (Ord a, Hashable a)
+  => (Dict -> HashTable a Int32)    -- ^ Memo structure for thing of key @a@.
+  -> (Dict -> IORef FreshAndReuse)  -- ^ Statistics.
+  -> a        -- ^ Key to the thing.
+  -> S Int32  -- ^ Fallback computation to encode the thing.
+  -> S Int32  -- ^ Encoded thing.
+icodeMemo getDict getCounter a icodeP = do
+    h  <- asks getDict
+    mi <- liftIO $ H.lookup h a
+    st <- asks getCounter
+    case mi of
+      Just i  -> liftIO $ do
+#ifdef DEBUG_SERIALISATION
+        modifyIORef' st $ over lensReuse (+ 1)
+#endif
+        return $! i
+      Nothing -> do
+        liftIO $ modifyIORef' st $ over lensFresh (+ 1)
+        !i <- icodeP
+        liftIO $ H.insert h a i
+        return i
+
+{-# INLINE vcase #-}
+-- | @vcase value ix@ decodes thing represented by @ix :: Int32@
+--   via the @valu@ function and stores it in 'nodeMemo'.
+--   If @ix@ is present in 'nodeMemo', @valu@ is not used, but
+--   the thing is read from 'nodeMemo' instead.
+vcase :: forall a . EmbPrj a => ([Int32] -> R a) -> Int32 -> R a
+vcase valu = \ix -> do
+    memo <- gets nodeMemo
+    let fp = fingerprintNoinline (typeRep (Proxy :: Proxy a))
+    -- to introduce sharing, see if we have seen a thing
+    -- represented by ix before
+    slot <- liftIO $ readArray memo ix
+    lookupME (Proxy :: Proxy a) fp slot
+      -- use the stored value
+      pure
+      -- read new value and save it
+      do !v <- valu . (! ix) =<< gets nodeE
+         liftIO $ writeArray memo ix $! MECons fp (unsafeCoerce v) slot
+         return v
+
+-- | @icodeArgs proxy (a1, ..., an)@ maps @icode@ over @a1@, ..., @an@
+--   and returns the corresponding list of @Int32@.
+
+class ICODE t b where
+  icodeArgs :: IsBase t ~ b => All EmbPrj (Domains t) =>
+               Proxy t -> StrictProducts (Domains t) -> S Node
+
+instance IsBase t ~ 'True => ICODE t 'True where
+  icodeArgs _ _  = return Empty
+  {-# INLINE icodeArgs #-}
+
+instance ICODE t (IsBase t) => ICODE (a -> t) 'False where
+  icodeArgs _ (Pair a as) = do
+    !hd   <- icode a
+    !node <- icodeArgs (Proxy :: Proxy t) as
+    pure $ Cons hd node
+  {-# INLINE icodeArgs #-}
+
+-- | @icodeN tag t a1 ... an@ serialises the arguments @a1@, ..., @an@ of the
+--   constructor @t@ together with a tag @tag@ picked to disambiguate between
+--   different constructors.
+--   It corresponds to @icodeNode . (tag :) =<< mapM icode [a1, ..., an]@
+
+{-# INLINE icodeN #-}
+icodeN :: forall t. ICODE t (IsBase t) => StrictCurrying (Domains t) (S Int32) =>
+          All EmbPrj (Domains t) =>
+          Int32 -> t -> Arrows (Domains t) (S Int32)
+icodeN tag _ =
+  strictCurrys (Proxy :: Proxy (Domains t)) (Proxy :: Proxy (S Int32)) $ \ !args -> do
+    !node <- icodeArgs (Proxy :: Proxy t) args
+    icodeNode $ Cons tag node
+
+-- | @icodeN'@ is the same as @icodeN@ except that there is no tag
+{-# INLINE icodeN' #-}
+icodeN' :: forall t. ICODE t (IsBase t) => StrictCurrying (Domains t) (S Int32) =>
+           All EmbPrj (Domains t) =>
+           t -> Arrows (Domains t) (S Int32)
+icodeN' _ =
+  strictCurrys (Proxy :: Proxy (Domains t)) (Proxy :: Proxy (S Int32)) $ \ !args -> do
+    !node <- icodeArgs (Proxy :: Proxy t) args
+    icodeNode node
+
+-- Instead of having up to 25 versions of @valu N@, we define
+-- the class VALU which generates them by typeclass resolution.
+-- All of these should get inlined at compile time.
+
+class VALU t b where
+
+  valuN' :: b ~ IsBase t =>
+            All EmbPrj (Domains t) =>
+            t -> StrictProducts (Constant Int32 (Domains t)) -> R (CoDomain t)
+
+  valueArgs :: b ~ IsBase t =>
+               All EmbPrj (CoDomain t ': Domains t) =>
+               Proxy t -> [Int32] -> Maybe (StrictProducts (Constant Int32 (Domains t)))
+
+instance VALU t 'True where
+  {-# INLINE valuN' #-}
+  valuN' c () = return c
+
+  {-# INLINE valueArgs #-}
+  valueArgs _ xs = case xs of
+    [] -> Just ()
+    _  -> Nothing
+
+
+instance VALU t (IsBase t) => VALU (a -> t) 'False where
+  {-# INLINE valuN' #-}
+  valuN' c (Pair a as) = do
+    !v <- value a
+    let !cv = c v
+    valuN' cv as
+
+  {-# INLINE valueArgs #-}
+  valueArgs _ xs = case xs of
+    x : xs' -> Pair x <$!> valueArgs (Proxy :: Proxy t) xs'
+    _       -> Nothing
+
+{-# INLINE valuN #-}
+valuN :: forall t. VALU t (IsBase t) =>
+         StrictCurrying (Constant Int32 (Domains t)) (R (CoDomain t)) =>
+         All EmbPrj (Domains t) =>
+         t -> Arrows (Constant Int32 (Domains t)) (R (CoDomain t))
+valuN f = strictCurrys (Proxy :: Proxy (Constant Int32 (Domains t)))
+                 (Proxy :: Proxy (R (CoDomain t)))
+                 (valuN' f)
+
+{-# INLINE valueN #-}
+valueN :: forall t. VALU t (IsBase t) =>
+          All EmbPrj (CoDomain t ': Domains t) =>
+          t -> Int32 -> R (CoDomain t)
+valueN t = vcase valu where
+  valu int32s = case valueArgs (Proxy :: Proxy t) int32s of
+                  Nothing -> malformed
+                  Just vs -> valuN' t vs
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances.hs b/src/full/Agda/TypeChecking/Serialise/Instances.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances.hs
@@ -0,0 +1,34 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-- Only instances exported
+module Agda.TypeChecking.Serialise.Instances () where
+
+import Agda.Syntax.Position
+import Agda.Syntax.TopLevelModuleName
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Common (SerialisedRange(..))
+import Agda.TypeChecking.Serialise.Instances.Highlighting ()
+import Agda.TypeChecking.Serialise.Instances.Errors ()
+import Agda.Utils.Hash
+
+type RangedImportedModules =
+  [(SerialisedRange, TopLevelModuleName, Hash)]
+
+fromImportedModules ::
+  [(TopLevelModuleName, Hash)] -> RangedImportedModules
+fromImportedModules ms = [(SerialisedRange $ getRange x, x, hash) | (x, hash) <- ms]
+
+toImportedModules ::
+  RangedImportedModules -> [(TopLevelModuleName, Hash)]
+toImportedModules ms = [(setRange (underlyingRange r) x, hash) | (r, x, hash) <- ms]
+
+instance EmbPrj Interface where
+  icod_ (Interface a b c d e f g h i j k l m n o p q r s t u v w x) =
+      icodeN' interface a b c (fromImportedModules d) e f g h i j k l m n o p q r s t u v w x
+    where interface a b c = Interface a b c . toImportedModules
+
+  value = valueN interface
+    where interface a b c = Interface a b c . toImportedModules
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Abstract.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Abstract.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Abstract.hs
@@ -0,0 +1,244 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.TypeChecking.Serialise.Instances.Abstract where
+
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+
+import Agda.Syntax.Common
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Info
+import Agda.Syntax.Scope.Base
+import Agda.Syntax.Fixity
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Common () --instance only
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.Impossible
+
+-- Don't serialize the tactic.
+instance EmbPrj A.BindName where
+  icod_ (A.BindName a) = icodeN' A.BindName a
+  value = valueN A.BindName
+
+instance EmbPrj Scope where
+  icod_ (Scope a b c d e) = icodeN' Scope a b c d e
+
+  value = valueN Scope
+
+instance EmbPrj DataOrRecordModule where
+  icod_ IsDataModule   = pure 0
+  icod_ IsRecordModule = pure 1
+
+  value = \case
+    0 -> pure IsDataModule
+    1 -> pure IsRecordModule
+    _ -> malformed
+
+instance EmbPrj NameSpaceId where
+  icod_ PublicNS        = pure 0
+  icod_ PrivateNS       = pure 1
+  icod_ ImportedNS      = pure 2
+
+  value = \case
+    0 -> pure PublicNS
+    1 -> pure PrivateNS
+    2 -> pure ImportedNS
+    _ -> malformed
+
+instance EmbPrj Access where
+  icod_ (PrivateAccess UserWritten) = pure 0
+  icod_ PrivateAccess{}             = pure 1
+  icod_ PublicAccess                = pure 2
+
+  value = \case
+    0 -> pure $ PrivateAccess UserWritten
+    1 -> pure $ PrivateAccess Inserted
+    2 -> pure PublicAccess
+    _ -> malformed
+
+instance EmbPrj NameSpace where
+  icod_ (NameSpace a b c) = icodeN' NameSpace a b c
+
+  value = valueN NameSpace
+
+instance EmbPrj WhyInScope where
+  icod_ Defined       = icodeN' Defined
+  icod_ (Opened a b)  = icodeN 0 Opened a b
+  icod_ (Applied a b) = icodeN 1 Applied a b
+
+  value = vcase valu where
+    valu []        = valuN Defined
+    valu [0, a, b] = valuN Opened a b
+    valu [1, a, b] = valuN Applied a b
+    valu _         = malformed
+
+-- Issue #1346: QNames are shared on their nameIds, so serializing will lose fixity information for
+-- rebound fixities. We don't care about that in terms, but in the scope it's important to keep the
+-- right fixity. Thus serialize the fixity separately.
+
+data AbsNameWithFixity = AbsNameWithFixity Fixity A.QName KindOfName WhyInScope NameMetadata
+
+toAbsName :: AbsNameWithFixity -> AbstractName
+toAbsName (AbsNameWithFixity fx a b c d) = AbsName (set lensFixity fx a) b c d
+
+fromAbsName :: AbstractName -> AbsNameWithFixity
+fromAbsName (AbsName a b c d) = AbsNameWithFixity (a ^. lensFixity) a b c d
+
+instance EmbPrj AbsNameWithFixity where
+  icod_ (AbsNameWithFixity a b c d e) = icodeN' AbsNameWithFixity a b c d e
+  value = valueN AbsNameWithFixity
+
+instance EmbPrj AbstractName where
+  icod_ a = icod_ (fromAbsName a)
+  value = toAbsName <.> value
+
+instance EmbPrj NameMetadata where
+  icod_ NoMetadata                  = icodeN' NoMetadata
+  icod_ (GeneralizedVarsMetadata a) = icodeN' GeneralizedVarsMetadata a
+
+  value = vcase valu where
+    valu []  = valuN NoMetadata
+    valu [a] = valuN GeneralizedVarsMetadata a
+    valu _   = malformed
+
+instance EmbPrj A.Suffix where
+  icod_ A.NoSuffix   = icodeN' A.NoSuffix
+  icod_ (A.Suffix a) = icodeN' A.Suffix a
+
+  value = vcase valu where
+    valu []  = valuN A.NoSuffix
+    valu [a] = valuN A.Suffix a
+    valu _   = malformed
+
+instance EmbPrj AbstractModule where
+  icod_ (AbsModule a b) = icodeN' AbsModule a b
+
+  value = valueN AbsModule
+
+instance EmbPrj KindOfName where
+  -- -- Enums have a generic EmbPrj
+  --
+  -- icod_ DefName        = icodeN' DefName
+  -- icod_ ConName        = icodeN 1 ConName
+  -- icod_ FldName        = icodeN 2 FldName
+  -- icod_ PatternSynName = icodeN 3 PatternSynName
+  -- icod_ QuotableName   = icodeN 4 QuotableName
+  -- icod_ MacroName      = icodeN 5 MacroName
+  -- icod_ GeneralizeName = icodeN 6 GeneralizeName
+  -- icod_ DisallowedGeneralizeName = icodeN 7 DisallowedGeneralizeName
+
+  -- value = vcase valu where
+  --   valu []  = valuN DefName
+  --   valu [1] = valuN ConName
+  --   valu [2] = valuN FldName
+  --   valu [3] = valuN PatternSynName
+  --   valu [4] = valuN QuotableName
+  --   valu [5] = valuN MacroName
+  --   valu [6] = valuN GeneralizeName
+  --   valu [7] = valuN DisallowedGeneralizeName
+  --   valu _   = malformed
+
+instance EmbPrj BindingSource where
+  icod_ LambdaBound   = pure 0
+  icod_ PatternBound  = pure 1
+  icod_ LetBound      = pure 2
+  icod_ WithBound     = pure 3
+
+  value = \case
+    0 -> pure LambdaBound
+    1 -> pure PatternBound
+    2 -> pure LetBound
+    3 -> pure WithBound
+    _ -> malformed
+
+instance EmbPrj LocalVar where
+  icod_ (LocalVar a b c)  = icodeN' LocalVar a b c
+
+  value = valueN LocalVar
+
+instance EmbPrj ConPatInfo where
+  icod_ (ConPatInfo a _ b) = icodeN' (\a b -> ConPatInfo a patNoRange b) a b
+
+  value = valueN $ \a b -> ConPatInfo a patNoRange b
+
+instance EmbPrj ConPatLazy
+
+-- Only for pattern synonyms (where a is Void)
+instance EmbPrj a => EmbPrj (A.Pattern' a) where
+  icod_ (A.VarP a)            = icodeN 0 A.VarP a
+  icod_ (A.ConP a b c)        = icodeN 1 A.ConP a b c
+  icod_ (A.DefP p a b)        = icodeN 2 (A.DefP p) a b
+  icod_ t@(A.WildP p)         = icodeN 3 t
+  icod_ (A.AsP p a b)         = icodeN 4 (A.AsP p) a b
+  icod_ (A.DotP p a)          = icodeN 5 (A.DotP p) a
+  icod_ t@(A.AbsurdP _)       = icodeN 6 t
+  icod_ (A.LitP i a)          = icodeN 7 (A.LitP i) a
+  icod_ (A.ProjP p a b)       = icodeN 8 (A.ProjP p) a b
+  icod_ (A.PatternSynP p a b) = icodeN 9 (A.PatternSynP p) a b
+  icod_ (A.RecP p a)          = icodeN 10 (A.RecP p) a
+  icod_ (A.EqualP _ a)        = __IMPOSSIBLE__
+  icod_ (A.WithP i a)         = icodeN 11 (A.WithP i) a
+  icod_ (A.AnnP i a p)        = icodeN 12 (A.AnnP i) a p
+
+  value = vcase valu where
+    valu [0, a]       = valuN A.VarP a
+    valu [1, a, b, c] = valuN A.ConP a b c
+    valu [2, a, b]    = valuN (A.DefP i) a b
+    valu [3]          = valuN (A.WildP i)
+    valu [4, a, b]    = valuN (A.AsP i) a b
+    valu [5, a]       = valuN (A.DotP i) a
+    valu [6]          = valuN (A.AbsurdP i)
+    valu [7, a]       = valuN (A.LitP i) a
+    valu [8, a, b]    = valuN (A.ProjP i) a b
+    valu [9, a, b]    = valuN (A.PatternSynP i) a b
+    valu [10, a]      = valuN (A.RecP i) a
+    valu [11, a]      = valuN (A.WithP i) a
+    valu [12, a, b]   = valuN (A.AnnP i) a b
+    valu _            = malformed
+
+    i = patNoRange
+
+instance EmbPrj ParenPreference where
+  icod_ PreferParen     = icodeN' PreferParen
+  icod_ PreferParenless = icodeN 1 PreferParenless
+  value = vcase valu where
+    valu []  = valuN PreferParen
+    valu [1] = valuN PreferParenless
+    valu _   = malformed
+
+instance EmbPrj Precedence where
+  icod_ TopCtx                 = icodeN' TopCtx
+  icod_ FunctionSpaceDomainCtx = icodeN 1 FunctionSpaceDomainCtx
+  icod_ (LeftOperandCtx a)     = icodeN 2 LeftOperandCtx a
+  icod_ (RightOperandCtx a b)  = icodeN 3 RightOperandCtx a b
+  icod_ FunctionCtx            = icodeN 4 FunctionCtx
+  icod_ (ArgumentCtx a)        = icodeN 5 ArgumentCtx a
+  icod_ InsideOperandCtx       = icodeN 6 InsideOperandCtx
+  icod_ WithFunCtx             = icodeN 7 WithFunCtx
+  icod_ WithArgCtx             = icodeN 8 WithArgCtx
+  icod_ DotPatternCtx          = icodeN 9 DotPatternCtx
+
+  value = vcase valu where
+    valu []        = valuN TopCtx
+    valu [1]       = valuN FunctionSpaceDomainCtx
+    valu [2, a]    = valuN LeftOperandCtx a
+    valu [3, a, b] = valuN RightOperandCtx a b
+    valu [4]       = valuN FunctionCtx
+    valu [5, a]    = valuN ArgumentCtx a
+    valu [6]       = valuN InsideOperandCtx
+    valu [7]       = valuN WithFunCtx
+    valu [8]       = valuN WithArgCtx
+    valu [9]       = valuN DotPatternCtx
+    valu _         = malformed
+
+instance EmbPrj ScopeInfo where
+  icod_ (ScopeInfo a b c d e f g h i j) = icodeN' (\ a b c d e -> ScopeInfo a b c d e f g h i j) a b c d e
+
+  value = valueN (\ a b c d e -> ScopeInfo a b c d e Map.empty Map.empty Set.empty Map.empty Map.empty)
+
+instance EmbPrj NameOrModule
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Common.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Common.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Common.hs
@@ -0,0 +1,749 @@
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+{-# LANGUAGE UndecidableInstances #-}
+
+module Agda.TypeChecking.Serialise.Instances.Common (SerialisedRange(..)) where
+
+import qualified Control.Exception as E
+import Control.Monad              ( (<=<), (<$!>) )
+import Control.Monad.IO.Class     ( MonadIO(..) )
+import Control.Monad.Except       ( MonadError(..) )
+import Control.Monad.Reader       ( MonadReader(..), asks )
+import Control.Monad.State.Strict ( gets, modify )
+
+import Data.Array.IArray
+import Data.Word
+import qualified Data.Foldable as Fold
+import Data.Hashable
+import Data.Int (Int32)
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.IntSet as IntSet
+import Data.IntSet (IntSet)
+import qualified Data.Set as Set
+import Data.Sequence (Seq)
+import qualified Data.Sequence as Seq
+import Data.Strict.Tuple (Pair(..))
+import qualified Data.Text      as T
+import qualified Data.Text.Lazy as TL
+import Data.Typeable
+import Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as HMap
+
+import Data.Void
+
+import Agda.Syntax.Common
+import Agda.Syntax.Builtin
+import Agda.Syntax.Concrete.Name as C
+import qualified Agda.Syntax.Concrete as C
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Position as P
+import Agda.Syntax.Literal
+import Agda.Syntax.TopLevelModuleName
+import Agda.Interaction.FindFile
+import Agda.Interaction.Library
+
+import Agda.TypeChecking.Serialise.Base
+
+import Agda.Utils.BiMap (BiMap)
+import qualified Agda.Utils.BiMap as BiMap
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.List2 (List2(List2))
+import qualified Agda.Utils.List2 as List2
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Trie (Trie(..))
+import Agda.Utils.WithDefault
+
+import Agda.Utils.Impossible
+import Agda.Utils.CallStack
+
+instance {-# OVERLAPPING #-} EmbPrj String where
+  icod_   = icodeString
+  value i = (! i) <$!> gets stringE
+
+instance EmbPrj TL.Text where
+  icod_   = icodeX lTextD lTextC
+  value i = (! i) <$!> gets lTextE
+
+instance EmbPrj T.Text where
+  icod_   = icodeX sTextD sTextC
+  value i = (! i) <$!> gets sTextE
+
+instance EmbPrj Integer where
+  icod_   = icodeInteger
+  value i = (! i) <$!> gets integerE
+
+instance EmbPrj Word64 where
+  icod_ i = icodeN' (undefined :: Int32 -> Int32 -> Int32) (int32 q) (int32 r)
+    where (q, r) = quotRem i (2 ^ 32)
+          int32 :: Word64 -> Int32
+          int32 = fromIntegral
+
+  value = vcase valu where
+    valu [a, b] = return $! n * mod (fromIntegral a) n + mod (fromIntegral b) n
+    valu _      = malformed
+    n = 2 ^ 32
+
+instance EmbPrj Int32 where
+  icod_ i = return i
+  value i = return i
+
+instance EmbPrj Int where
+  icod_ i = return $! fromIntegral i
+  value i = return $! fromIntegral i
+
+instance EmbPrj Char where
+  icod_ c = return $! fromIntegral $ fromEnum c
+  value i = return $! toEnum $ fromInteger $ toInteger i
+
+instance EmbPrj Double where
+  icod_   = icodeDouble
+  value i = (! i) <$!> gets doubleE
+
+instance EmbPrj Void where
+  icod_ = absurd
+  value = vcase valu where valu _ = malformed
+
+instance EmbPrj () where
+  icod_ () = pure 0
+
+  value 0 = pure ()
+  value _ = malformed
+
+instance (EmbPrj a, EmbPrj b) => EmbPrj (a, b) where
+  icod_ (a, b) = icodeN' (,) a b
+
+  value = valueN (,)
+
+instance (EmbPrj a, EmbPrj b) => EmbPrj (Pair a b) where
+  icod_ (a :!: b) = icodeN' (:!:) a b
+
+  value = valueN (:!:)
+
+instance (EmbPrj a, EmbPrj b, EmbPrj c) => EmbPrj (a, b, c) where
+  icod_ (a, b, c) = icodeN' (,,) a b c
+
+  value = valueN (,,)
+
+instance (EmbPrj a, EmbPrj b) => EmbPrj (Either a b) where
+  icod_ (Left  x) = icodeN 0 Left x
+  icod_ (Right x) = icodeN 1 Right x
+
+  value = vcase valu where
+    valu [0, x] = valuN Left  x
+    valu [1, x] = valuN Right x
+    valu _   = malformed
+
+instance EmbPrj a => EmbPrj (Maybe a) where
+  icod_ Nothing  = icodeN' Nothing
+  icod_ (Just x) = icodeN' Just x
+
+  value = vcase valu where
+    valu []  = valuN Nothing
+    valu [x] = valuN Just x
+    valu _   = malformed
+
+instance EmbPrj a => EmbPrj (Strict.Maybe a) where
+  icod_ m = icode (Strict.toLazy m)
+  value m = Strict.toStrict <$!> value m
+
+instance EmbPrj Bool where
+  icod_ False = pure 0
+  icod_ True  = pure 1
+
+  value 0 = pure False
+  value 1 = pure True
+  value _ = malformed
+
+instance EmbPrj FileType where
+  icod_ AgdaFileType  = pure 0
+  icod_ MdFileType    = pure 1
+  icod_ RstFileType   = pure 2
+  icod_ TexFileType   = pure 3
+  icod_ OrgFileType   = pure 4
+  icod_ TypstFileType = pure 5
+
+  value = \case
+    0 -> pure AgdaFileType
+    1 -> pure MdFileType
+    2 -> pure RstFileType
+    3 -> pure TexFileType
+    4 -> pure OrgFileType
+    5 -> pure TypstFileType
+    _ -> malformed
+
+instance EmbPrj Cubical where
+  icod_ CErased = icodeN'  CErased
+  icod_ CFull   = icodeN 0 CFull
+
+  value = vcase $ \case
+    []  -> valuN CErased
+    [0] -> valuN CFull
+    _   -> malformed
+
+instance EmbPrj Language where
+  icod_ WithoutK    = icodeN'  WithoutK
+  icod_ WithK       = icodeN 0 WithK
+  icod_ (Cubical a) = icodeN 1 Cubical a
+
+  value = vcase $ \case
+    []     -> valuN WithoutK
+    [0]    -> valuN WithK
+    [1, a] -> valuN Cubical a
+    _      -> malformed
+
+instance EmbPrj a => EmbPrj (Position' a) where
+  icod_ (P.Pn file pos line col) = icodeN' P.Pn file pos line col
+
+  value = valueN P.Pn
+
+instance (EmbPrj a, Typeable b) => EmbPrj (WithDefault' a b) where
+  icod_ = \case
+    Default -> icodeN' Default
+    Value b -> icodeN' Value b
+
+  value = vcase $ \case
+    []  -> valuN Default
+    [a] -> valuN Value a
+    _ -> malformed
+
+instance EmbPrj TopLevelModuleName where
+  icod_ (TopLevelModuleName a b c) = icodeN' TopLevelModuleName a b c
+
+  value = valueN TopLevelModuleName
+
+instance {-# OVERLAPPABLE #-} EmbPrj a => EmbPrj [a] where
+  icod_ xs = icodeNode =<< go xs where
+    go :: [a] -> S Node
+    go []     = pure Empty
+    go (a:as) = do {n <- icode a; ns <- go as; pure $! Cons n ns}
+
+  value = vcase (mapM value)
+
+instance EmbPrj a => EmbPrj (List1 a) where
+  icod_ = icod_ . List1.toList
+  value = maybe malformed return . List1.nonEmpty <=< value
+
+instance EmbPrj a => EmbPrj (List2 a) where
+  icod_ = icod_ . List2.toList
+  value = maybe malformed return . List2.fromListMaybe <=< value
+
+instance (EmbPrj k, EmbPrj v, EmbPrj (BiMap.Tag v)) =>
+         EmbPrj (BiMap k v) where
+  icod_ m = icode (BiMap.toDistinctAscendingLists m)
+  value m = BiMap.fromDistinctAscendingLists <$!> value m
+
+
+-- | Encode a list of key-value pairs as a flat list.
+mapPairsIcode :: (EmbPrj k, EmbPrj v) => [(k, v)] -> S Int32
+mapPairsIcode xs = icodeNode =<< convert Empty xs where
+  -- As we need to call `convert' in the tail position, the resulting list is
+  -- written (and read) in reverse order, with the highest pair first in the
+  -- resulting list.
+  convert !ys [] = return ys
+  convert  ys ((start, entry):xs) = do
+    start <- icode start
+    entry <- icode entry
+    convert (Cons start (Cons entry ys)) xs
+
+mapPairsValue :: (EmbPrj k, EmbPrj v) => [Int32] -> R [(k, v)]
+mapPairsValue = convert [] where
+  convert ys [] = return ys
+  convert ys (start:entry:xs) = do
+    !start <- value start
+    !entry <- value entry
+    convert ((start, entry):ys) xs
+  convert _ _ = malformed
+
+instance (Ord a, EmbPrj a, EmbPrj b) => EmbPrj (Map a b) where
+  icod_ m = mapPairsIcode (Map.toAscList m)
+  value = vcase ((Map.fromDistinctAscList <$!>) . mapPairsValue)
+
+instance (Ord a, EmbPrj a) => EmbPrj (Set a) where
+  icod_ s = icode (Set.toAscList s)
+  value s = Set.fromDistinctAscList <$!> value s
+
+instance EmbPrj IntSet where
+  icod_ s = icode (IntSet.toAscList s)
+  value s = IntSet.fromDistinctAscList <$!> value s
+
+instance (Ord a, EmbPrj a, EmbPrj b) => EmbPrj (Trie a b) where
+  icod_ (Trie a b)= icodeN' Trie a b
+
+  value = valueN Trie
+
+instance EmbPrj a => EmbPrj (Seq a) where
+  icod_ s = icode (Fold.toList s)
+  value s = Seq.fromList <$!> value s
+
+instance EmbPrj a => EmbPrj (P.Interval' a) where
+  icod_ (P.Interval p q) = icodeN' P.Interval p q
+
+  value = valueN P.Interval
+
+instance EmbPrj RangeFile where
+  icod_ (RangeFile _ Nothing)  = __IMPOSSIBLE__
+  icod_ (RangeFile _ (Just a)) = icode a
+
+  value r = do
+    m :: TopLevelModuleName
+            <- value r
+    mf      <- gets modFile
+    incs    <- gets includes
+    (r, mf) <- liftIO $ findFile'' incs m mf
+    modify $ \s -> s { modFile = mf }
+    case r of
+      Left err -> liftIO $ E.throwIO $ E.ErrorCall $ "file not found: " ++ show err
+      Right f  -> let !sfp = srcFilePath f in return $ RangeFile sfp (Just m)
+
+-- | Ranges are always deserialised as 'noRange'.
+
+instance EmbPrj Range where
+  icod_ _ = icodeN' ()
+  value _ = return noRange
+
+-- | Ranges that should be serialised properly.
+
+newtype SerialisedRange = SerialisedRange { underlyingRange :: Range }
+
+instance EmbPrj SerialisedRange where
+  icod_ (SerialisedRange r) = icodeN' P.intervalsToRange (P.rangeFile r) (P.rangeIntervals r)
+
+  value i = SerialisedRange <$!> valueN P.intervalsToRange i
+
+instance EmbPrj C.Name where
+  icod_ (C.NoName a b)     = icodeN 0 C.NoName a b
+  icod_ (C.Name r nis xs)  = icodeN 1 C.Name r nis xs
+
+  value = vcase valu where
+    valu [0, a, b]       = valuN C.NoName a b
+    valu [1, r, nis, xs] = valuN C.Name   r nis xs
+    valu _               = malformed
+
+instance EmbPrj NamePart where
+  icod_ Hole   = icodeN' Hole
+  icod_ (Id a) = icodeN' Id a
+
+  value = vcase valu where
+    valu []  = valuN Hole
+    valu [a] = valuN Id a
+    valu _   = malformed
+
+instance EmbPrj NameInScope where
+  icod_ InScope    = icodeN' InScope
+  icod_ NotInScope = icodeN 0 NotInScope
+
+  value = vcase valu where
+    valu []  = valuN InScope
+    valu [0] = valuN NotInScope
+    valu _   = malformed
+
+instance EmbPrj C.QName where
+  icod_ (Qual    a b) = icodeN' Qual a b
+  icod_ (C.QName a  ) = icodeN' C.QName a
+
+  value = vcase valu where
+    valu [a, b] = valuN Qual    a b
+    valu [a]    = valuN C.QName a
+    valu _      = malformed
+
+instance (EmbPrj a, EmbPrj b) => EmbPrj (ImportedName' a b) where
+  icod_ (ImportedModule a) = icodeN 1 ImportedModule a
+  icod_ (ImportedName a)   = icodeN 2 ImportedName a
+
+  value = vcase valu where
+    valu [1, a] = valuN ImportedModule a
+    valu [2, a] = valuN ImportedName a
+    valu _ = malformed
+
+instance EmbPrj Associativity where
+  icod_ LeftAssoc  = pure 0
+  icod_ RightAssoc = pure 1
+  icod_ NonAssoc   = pure 2
+
+  value = \case
+    0 -> pure LeftAssoc
+    1 -> pure RightAssoc
+    2 -> pure NonAssoc
+    _ -> malformed
+
+instance EmbPrj FixityLevel where
+  icod_ Unrelated   = icodeN' Unrelated
+  icod_ (Related a) = icodeN' Related a
+
+  value = vcase valu where
+    valu []  = valuN Unrelated
+    valu [a] = valuN Related a
+    valu _   = malformed
+
+instance EmbPrj Fixity where
+  icod_ (Fixity a b c) = icodeN' Fixity a b c
+
+  value = valueN Fixity
+
+instance EmbPrj Fixity' where
+  icod_ (Fixity' a b r) = icodeN' (\ a b -> Fixity' a b r) a b  -- discard theNameRange
+
+  value = valueN (\ f n -> Fixity' f n noRange)
+
+instance EmbPrj BoundVariablePosition where
+  icod_ (BoundVariablePosition a b) = icodeN' BoundVariablePosition a b
+
+  value = valueN BoundVariablePosition
+
+instance EmbPrj NotationPart where
+  icod_ (VarPart a b)  = icodeN 0 VarPart a b
+  icod_ (HolePart a b) = icodeN 1 HolePart a b
+  icod_ (WildPart a)   = icodeN 2 WildPart a
+  icod_ (IdPart a)     = icodeN' IdPart a
+
+  value = vcase valu where
+    valu [0, a, b] = valuN VarPart a b
+    valu [1, a, b] = valuN HolePart a b
+    valu [2, a]    = valuN WildPart a
+    valu [a]       = valuN IdPart a
+    valu _         = malformed
+
+instance EmbPrj MetaId where
+  icod_ (MetaId a b) = icode (a, b)
+
+  value m = uncurry MetaId <$!> value m
+
+instance EmbPrj A.QName where
+  icod_ n@(A.QName a b) = icodeMemo qnameD qnameC (qnameId n) $ icodeN' A.QName a b
+
+  value = valueN A.QName
+
+instance EmbPrj A.AmbiguousQName where
+  icod_ (A.AmbQ a) = icode a
+  value n          = A.AmbQ <$!> value n
+
+instance EmbPrj A.ModuleName where
+  icod_ (A.MName a) = icode a
+  value n           = A.MName <$!> value n
+
+instance EmbPrj A.Name where
+  icod_ (A.Name a b c d e f) = icodeMemo nameD nameC a $
+    icodeN' (\ a b c -> A.Name a b c . underlyingRange) a b c (SerialisedRange d) e f
+
+  value = valueN (\a b c d -> A.Name a b c (underlyingRange d))
+
+instance EmbPrj a => EmbPrj (C.FieldAssignment' a) where
+  icod_ (C.FieldAssignment a b) = icodeN' C.FieldAssignment a b
+
+  value = valueN C.FieldAssignment
+
+instance (EmbPrj s, EmbPrj t) => EmbPrj (Named s t) where
+  icod_ (Named a b) = icodeN' Named a b
+
+  value = valueN Named
+
+instance EmbPrj a => EmbPrj (Ranged a) where
+  icod_ (Ranged r x) = icodeN' Ranged r x
+
+  value = valueN Ranged
+
+instance EmbPrj ArgInfo where
+  icod_ (ArgInfo h r o fv ann) = icodeN' ArgInfo h r o fv ann
+
+  value = valueN ArgInfo
+
+instance EmbPrj ModuleNameHash where
+  icod_ (ModuleNameHash a) = icodeN' ModuleNameHash a
+
+  value = valueN ModuleNameHash
+
+instance EmbPrj NameId where
+  icod_ (NameId a b) = icodeN' NameId a b
+
+  value = valueN NameId
+
+instance EmbPrj OpaqueId where
+  icod_ (OpaqueId a b) = icodeN' OpaqueId a b
+
+  value = valueN OpaqueId
+
+instance (Eq k, Hashable k, EmbPrj k, EmbPrj v) => EmbPrj (HashMap k v) where
+  icod_ m = mapPairsIcode (HMap.toList m)
+  value = vcase ((HMap.fromList <$!>) . mapPairsValue)
+
+instance EmbPrj a => EmbPrj (WithHiding a) where
+  icod_ (WithHiding a b) = icodeN' WithHiding a b
+
+  value = valueN WithHiding
+
+instance EmbPrj a => EmbPrj (Arg a) where
+  icod_ (Arg i e) = icodeN' Arg i e
+
+  value = valueN Arg
+
+instance EmbPrj a => EmbPrj (HasEta' a) where
+  icod_ YesEta    = icodeN' YesEta
+  icod_ (NoEta a) = icodeN' NoEta a
+
+  value = vcase valu where
+    valu []  = valuN YesEta
+    valu [a] = valuN NoEta a
+    valu _   = malformed
+
+instance EmbPrj PatternOrCopattern
+
+instance EmbPrj Induction where
+  icod_ Inductive   = icodeN' Inductive
+  icod_ CoInductive = icodeN 1 CoInductive
+
+  value = vcase valu where
+    valu []  = valuN Inductive
+    valu [1] = valuN CoInductive
+    valu _   = malformed
+
+instance EmbPrj Hiding where
+  icod_ Hidden                = return 0
+  icod_ NotHidden             = return 1
+  icod_ (Instance NoOverlap)  = return 2
+  icod_ (Instance YesOverlap) = return 3
+
+  value 0 = return Hidden
+  value 1 = return NotHidden
+  value 2 = return (Instance NoOverlap)
+  value 3 = return (Instance YesOverlap)
+  value _ = malformed
+
+instance EmbPrj Q0Origin where
+  icod_ = \case
+    Q0Inferred -> return 0
+    Q0 _       -> return 1
+    Q0Erased _ -> return 2
+
+  value = \case
+    0 -> return $ Q0Inferred
+    1 -> return $ Q0       noRange
+    2 -> return $ Q0Erased noRange
+    _ -> malformed
+
+instance EmbPrj Q1Origin where
+  icod_ = \case
+    Q1Inferred -> return 0
+    Q1 _       -> return 1
+    Q1Linear _ -> return 2
+
+  value = \case
+    0 -> return $ Q1Inferred
+    1 -> return $ Q1       noRange
+    2 -> return $ Q1Linear noRange
+    _ -> malformed
+
+instance EmbPrj QωOrigin where
+  icod_ = \case
+    QωInferred -> return 0
+    Qω _       -> return 1
+    QωPlenty _ -> return 2
+
+  value = \case
+    0 -> return $ QωInferred
+    1 -> return $ Qω       noRange
+    2 -> return $ QωPlenty noRange
+    _ -> malformed
+
+instance EmbPrj Quantity where
+  icod_ = \case
+    Quantity0 a -> icodeN 0 Quantity0 a
+    Quantity1 a -> icodeN 1 Quantity1 a
+    Quantityω a -> icodeN'  Quantityω a  -- default quantity, shorter code
+
+  value = vcase $ \case
+    [0, a] -> valuN Quantity0 a
+    [1, a] -> valuN Quantity1 a
+    [a]    -> valuN Quantityω a
+    _      -> malformed
+
+-- -- ALT: forget quantity origin when serializing?
+-- instance EmbPrj Quantity where
+--   icod_ Quantity0 = return 0
+--   icod_ Quantity1 = return 1
+--   icod_ Quantityω = return 2
+
+--   value 0 = return Quantity0
+--   value 1 = return Quantity1
+--   value 2 = return Quantityω
+--   value _ = malformed
+
+instance EmbPrj Cohesion where
+  icod_ Flat       = return 0
+  icod_ Continuous = return 1
+  icod_ Squash     = return 2
+
+  value 0 = return Flat
+  value 1 = return Continuous
+  value 2 = return Squash
+  value _ = malformed
+
+instance EmbPrj Modality where
+  icod_ (Modality a b c) = icodeN' Modality a b c
+
+  value = vcase $ \case
+    [a, b, c] -> valuN Modality a b c
+    _ -> malformed
+
+instance EmbPrj Relevance where
+  icod_ Relevant       = return 0
+  icod_ Irrelevant     = return 1
+  icod_ NonStrict      = return 2
+
+  value 0 = return Relevant
+  value 1 = return Irrelevant
+  value 2 = return NonStrict
+  value _ = malformed
+
+instance EmbPrj Annotation where
+  icod_ (Annotation l) = icodeN' Annotation l
+
+  value = valueN Annotation
+
+instance EmbPrj Lock where
+  icod_ IsNotLock          = pure 0
+  icod_ (IsLock LockOTick) = pure 1
+  icod_ (IsLock LockOLock) = pure 2
+
+  value 0 = pure IsNotLock
+  value 1 = pure (IsLock LockOTick)
+  value 2 = pure (IsLock LockOLock)
+  value _ = malformed
+
+instance EmbPrj Origin where
+  icod_ UserWritten = return 0
+  icod_ Inserted    = return 1
+  icod_ Reflected   = return 2
+  icod_ CaseSplit   = return 3
+  icod_ Substitution = return 4
+  icod_ ExpandedPun = return 5
+  icod_ Generalization = return 6
+
+  value 0 = return UserWritten
+  value 1 = return Inserted
+  value 2 = return Reflected
+  value 3 = return CaseSplit
+  value 4 = return Substitution
+  value 5 = return ExpandedPun
+  value 6 = return Generalization
+  value _ = malformed
+
+instance EmbPrj a => EmbPrj (WithOrigin a) where
+  icod_ (WithOrigin a b) = icodeN' WithOrigin a b
+
+  value = valueN WithOrigin
+
+instance EmbPrj FreeVariables where
+  icod_ UnknownFVs   = icodeN' UnknownFVs
+  icod_ (KnownFVs a) = icodeN' KnownFVs a
+
+  value = vcase valu where
+    valu []  = valuN UnknownFVs
+    valu [a] = valuN KnownFVs a
+    valu _   = malformed
+
+instance EmbPrj ConOrigin where
+  icod_ ConOSystem = return 0
+  icod_ ConOCon    = return 1
+  icod_ ConORec    = return 2
+  icod_ ConOSplit  = return 3
+
+  value 0 = return ConOSystem
+  value 1 = return ConOCon
+  value 2 = return ConORec
+  value 3 = return ConOSplit
+  value _ = malformed
+
+instance EmbPrj ProjOrigin where
+  icod_ ProjPrefix  = return 0
+  icod_ ProjPostfix = return 1
+  icod_ ProjSystem  = return 2
+
+  value 0 = return ProjPrefix
+  value 1 = return ProjPostfix
+  value 2 = return ProjSystem
+  value _ = malformed
+
+instance EmbPrj Agda.Syntax.Literal.Literal where
+  icod_ (LitNat    a)   = icodeN' LitNat a
+  icod_ (LitFloat  a)   = icodeN 1 LitFloat a
+  icod_ (LitString a)   = icodeN 2 LitString a
+  icod_ (LitChar   a)   = icodeN 3 LitChar a
+  icod_ (LitQName  a)   = icodeN 5 LitQName a
+  icod_ (LitMeta   a b) = icodeN 6 LitMeta a b
+  icod_ (LitWord64 a)   = icodeN 7 LitWord64 a
+
+  value = vcase valu where
+    valu [a]       = valuN LitNat    a
+    valu [1, a]    = valuN LitFloat  a
+    valu [2, a]    = valuN LitString a
+    valu [3, a]    = valuN LitChar   a
+    valu [5, a]    = valuN LitQName  a
+    valu [6, a, b] = valuN LitMeta   a b
+    valu [7, a]    = valuN LitWord64 a
+    valu _            = malformed
+
+instance EmbPrj IsAbstract where
+  icod_ AbstractDef = icodeN 0 AbstractDef
+  icod_ ConcreteDef = icodeN' ConcreteDef
+
+  value = vcase valu where
+    valu [0] = valuN AbstractDef
+    valu []  = valuN ConcreteDef
+    valu _   = malformed
+
+instance EmbPrj IsOpaque where
+  icod_ (OpaqueDef a)  = icodeN' OpaqueDef a
+  icod_ TransparentDef = icodeN' TransparentDef
+
+  value = vcase valu where
+    valu [a] = valuN OpaqueDef a
+    valu []  = valuN TransparentDef
+    valu _   = malformed
+
+instance EmbPrj SrcLoc where
+  icod_ (SrcLoc p m f sl sc el ec) = icodeN' SrcLoc p m f sl sc el ec
+  value = valueN SrcLoc
+
+instance EmbPrj CallStack where
+  icod_ = icode . getCallStack
+  value = (<$!>) fromCallSiteList . value
+
+instance EmbPrj Impossible where
+  icod_ (Impossible a)              = icodeN 0 Impossible a
+  icod_ (Unreachable a)             = icodeN 1 Unreachable a
+  icod_ (ImpMissingDefinitions a b) = icodeN 2 ImpMissingDefinitions a b
+
+  value = vcase valu where
+    valu [0, a]    = valuN Impossible  a
+    valu [1, a]    = valuN Unreachable a
+    valu [2, a, b] = valuN ImpMissingDefinitions a b
+    valu _         = malformed
+
+instance EmbPrj ExpandedEllipsis where
+  icod_ NoEllipsis = icodeN' NoEllipsis
+  icod_ (ExpandedEllipsis a b) = icodeN 1 ExpandedEllipsis a b
+
+  value = vcase valu where
+    valu []      = valuN NoEllipsis
+    valu [1,a,b] = valuN ExpandedEllipsis a b
+    valu _       = malformed
+
+instance EmbPrj OptionsPragma where
+  icod_ (OptionsPragma a b) = icod_ (a, b)
+
+  value op = uncurry OptionsPragma <$!> value op
+
+instance EmbPrj BuiltinId
+instance EmbPrj PrimitiveId
+
+instance EmbPrj SomeBuiltin where
+  icod_ (BuiltinName x)   = icodeN 0 BuiltinName x
+  icod_ (PrimitiveName x) = icodeN 1 PrimitiveName x
+
+  value = vcase valu where
+    valu [0, x] = valuN BuiltinName x
+    valu [1, x] = valuN PrimitiveName x
+    valu _      = malformed
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Compilers.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Compilers.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Compilers.hs
@@ -0,0 +1,27 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans     #-}
+{-# OPTIONS_GHC -fwarn-unused-imports #-}
+
+module Agda.TypeChecking.Serialise.Instances.Compilers where
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Common
+
+import Agda.TypeChecking.Monad
+
+instance EmbPrj CompilerPragma where
+  icod_ (CompilerPragma a b) =
+    icodeN' (CompilerPragma . underlyingRange) (SerialisedRange a) b
+
+  value = valueN (CompilerPragma . underlyingRange)
+
+instance EmbPrj ForeignCode where
+  icod_ (ForeignCode r a) =
+    icodeN' (ForeignCode . underlyingRange) (SerialisedRange r) a
+
+  value = valueN (ForeignCode . underlyingRange)
+
+instance EmbPrj ForeignCodeStack where
+  icod_ = icod_ . getForeignCodeStack
+  value = fmap ForeignCodeStack . value
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Errors.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Errors.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Errors.hs
@@ -0,0 +1,567 @@
+{-# OPTIONS_GHC -fno-warn-orphans     #-}
+
+module Agda.TypeChecking.Serialise.Instances.Errors where
+
+import Control.Monad
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Internal () --instance only
+import Agda.TypeChecking.Serialise.Instances.Abstract () --instance only
+
+import Agda.Syntax.Concrete.Definitions (DeclarationWarning(..), DeclarationWarning'(..))
+import Agda.Syntax.Parser.Monad
+import Agda.TypeChecking.Monad.Base
+import qualified Agda.TypeChecking.Monad.Base.Warning as W
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Warnings
+import Agda.Interaction.Library.Base
+import Agda.Termination.CutOff
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.ProfileOptions
+
+import Agda.Utils.Impossible
+
+instance EmbPrj TCWarning where
+  icod_ (TCWarning fp a b c d) = icodeN' TCWarning fp a b c d
+  value = valueN TCWarning
+
+-- We don't need to serialise warnings that turn into errors
+instance EmbPrj Warning where
+  icod_ = \case
+    TerminationIssue a                    -> __IMPOSSIBLE__
+    UnreachableClauses a b                -> icodeN 0 UnreachableClauses a b
+    CoverageIssue a b                     -> __IMPOSSIBLE__
+    NotStrictlyPositive a b               -> __IMPOSSIBLE__
+    UnsolvedMetaVariables a               -> __IMPOSSIBLE__
+    UnsolvedInteractionMetas a            -> __IMPOSSIBLE__
+    UnsolvedConstraints a                 -> __IMPOSSIBLE__
+    InteractionMetaBoundaries a           -> __IMPOSSIBLE__
+    OldBuiltin a b                        -> icodeN 1 OldBuiltin a b
+    EmptyRewritePragma                    -> icodeN 2 EmptyRewritePragma
+    UselessPublic                         -> icodeN 3 UselessPublic
+    UselessInline a                       -> icodeN 4 UselessInline a
+    GenericWarning a                      -> icodeN 5 GenericWarning a
+    InvalidCharacterLiteral a             -> __IMPOSSIBLE__
+    SafeFlagPostulate a                   -> __IMPOSSIBLE__
+    SafeFlagPragma a                      -> __IMPOSSIBLE__
+    SafeFlagWithoutKFlagPrimEraseEquality -> __IMPOSSIBLE__
+    DeprecationWarning a b c              -> icodeN 6 DeprecationWarning a b c
+    NicifierIssue a                       -> icodeN 7 NicifierIssue a
+    InversionDepthReached a               -> icodeN 8 InversionDepthReached a
+    UserWarning a                         -> icodeN 9 UserWarning a
+    AbsurdPatternRequiresNoRHS a          -> icodeN 10 AbsurdPatternRequiresNoRHS a
+    ModuleDoesntExport a b c d            -> icodeN 11 ModuleDoesntExport a b c d
+    LibraryWarning a                      -> icodeN 12 LibraryWarning a
+    CoverageNoExactSplit a b              -> icodeN 13 CoverageNoExactSplit a b
+    CantGeneralizeOverSorts a             -> icodeN 14 CantGeneralizeOverSorts a
+    IllformedAsClause a                   -> icodeN 15 IllformedAsClause a
+    WithoutKFlagPrimEraseEquality         -> icodeN 16 WithoutKFlagPrimEraseEquality
+    InstanceWithExplicitArg a             -> icodeN 17 InstanceWithExplicitArg a
+    InfectiveImport a                     -> icodeN 18 InfectiveImport a
+    CoInfectiveImport a                   -> icodeN 19 CoInfectiveImport a
+    InstanceNoOutputTypeName a            -> icodeN 20 InstanceNoOutputTypeName a
+    InstanceArgWithExplicitArg a          -> icodeN 21 InstanceArgWithExplicitArg a
+    WrongInstanceDeclaration              -> icodeN 22 WrongInstanceDeclaration
+    RewriteNonConfluent a b c d           -> icodeN 23 RewriteNonConfluent a b c d
+    RewriteMaybeNonConfluent a b c        -> icodeN 24 RewriteMaybeNonConfluent a b c
+    PragmaCompileErased a b               -> icodeN 25 PragmaCompileErased a b
+    FixityInRenamingModule a              -> icodeN 26 FixityInRenamingModule a
+    NotInScopeW ns                        -> icodeN 27 NotInScopeW ns
+    ClashesViaRenaming a b                -> icodeN 28 ClashesViaRenaming a b
+    RecordFieldWarning a                  -> icodeN 29 RecordFieldWarning a
+    UselessPatternDeclarationForRecord a  -> icodeN 30 UselessPatternDeclarationForRecord a
+    EmptyWhere                            -> icodeN 31 EmptyWhere
+    AsPatternShadowsConstructorOrPatternSynonym a -> icodeN 32 AsPatternShadowsConstructorOrPatternSynonym a
+    DuplicateUsing a                      -> icodeN 33 DuplicateUsing a
+    UselessHiding a                       -> icodeN 34 UselessHiding a
+    UselessPragma a b                     -> icodeN 35 UselessPragma a b
+    RewriteAmbiguousRules a b c           -> icodeN 36 RewriteAmbiguousRules a b c
+    RewriteMissingRule a b c              -> icodeN 37 RewriteMissingRule a b c
+    ParseWarning a                        -> icodeN 38 ParseWarning a
+    NoGuardednessFlag a                   -> icodeN 39 NoGuardednessFlag a
+    UnsupportedIndexedMatch f             -> icodeN 40 UnsupportedIndexedMatch f
+    OptionWarning a                       -> icodeN 41 OptionWarning a
+    PlentyInHardCompileTimeMode a         -> icodeN 42 PlentyInHardCompileTimeMode a
+    NotAffectedByOpaque                   -> icodeN 43 NotAffectedByOpaque
+    UnfoldTransparentName nm              -> icodeN 44 UnfoldTransparentName nm
+    UselessOpaque                         -> icodeN 45 UselessOpaque
+    InlineNoExactSplit a b                -> icodeN 46 InlineNoExactSplit a b
+    FaceConstraintCannotBeHidden a        -> icodeN 47 FaceConstraintCannotBeHidden a
+    FaceConstraintCannotBeNamed a         -> icodeN 48 FaceConstraintCannotBeNamed a
+    PatternShadowsConstructor a b         -> icodeN 49 PatternShadowsConstructor a b
+    -- Not source code related, therefore they should never be serialized
+    DuplicateInterfaceFiles a b           -> __IMPOSSIBLE__
+
+  value = vcase $ \ case
+    [0, a, b]            -> valuN UnreachableClauses a b
+    [1, a, b]            -> valuN OldBuiltin a b
+    [2]                  -> valuN EmptyRewritePragma
+    [3]                  -> valuN UselessPublic
+    [4, a]               -> valuN UselessInline a
+    [5, a]               -> valuN GenericWarning a
+    [6, a, b, c]         -> valuN DeprecationWarning a b c
+    [7, a]               -> valuN NicifierIssue a
+    [8, a]               -> valuN InversionDepthReached a
+    [9, a]               -> valuN UserWarning a
+    [10, a]              -> valuN AbsurdPatternRequiresNoRHS a
+    [11, a, b, c, d]     -> valuN ModuleDoesntExport a b c d
+    [12, a]              -> valuN LibraryWarning a
+    [13, a, b]           -> valuN CoverageNoExactSplit a b
+    [14, a]              -> valuN CantGeneralizeOverSorts a
+    [15, a]              -> valuN IllformedAsClause a
+    [16]                 -> valuN WithoutKFlagPrimEraseEquality
+    [17, a]              -> valuN InstanceWithExplicitArg a
+    [18, a]              -> valuN InfectiveImport a
+    [19, a]              -> valuN CoInfectiveImport a
+    [20, a]              -> valuN InstanceNoOutputTypeName a
+    [21, a]              -> valuN InstanceArgWithExplicitArg a
+    [22]                 -> valuN WrongInstanceDeclaration
+    [23, a, b, c, d]     -> valuN RewriteNonConfluent a b c d
+    [24, a, b, c]        -> valuN RewriteMaybeNonConfluent a b c
+    [25, a, b]           -> valuN PragmaCompileErased a b
+    [26, a]              -> valuN FixityInRenamingModule a
+    [27, ns]             -> valuN NotInScopeW ns
+    [28, a, b]           -> valuN ClashesViaRenaming a b
+    [29, a]              -> valuN RecordFieldWarning a
+    [30, a]              -> valuN UselessPatternDeclarationForRecord a
+    [31]                 -> valuN EmptyWhere
+    [32, a]              -> valuN AsPatternShadowsConstructorOrPatternSynonym a
+    [33, a]              -> valuN DuplicateUsing a
+    [34, a]              -> valuN UselessHiding a
+    [35, a, b]           -> valuN UselessPragma a b
+    [36, a, b, c]        -> valuN RewriteAmbiguousRules a b c
+    [37, a, b, c]        -> valuN RewriteMissingRule a b c
+    [38, a]              -> valuN ParseWarning a
+    [39, a]              -> valuN NoGuardednessFlag a
+    [40, a]              -> valuN UnsupportedIndexedMatch a
+    [41, a]              -> valuN OptionWarning a
+    [42, a]              -> valuN PlentyInHardCompileTimeMode a
+    [43]                 -> valuN NotAffectedByOpaque
+    [44, a]              -> valuN UnfoldTransparentName a
+    [45]                 -> valuN UselessOpaque
+    [46, a, b]           -> valuN InlineNoExactSplit a b
+    [47, a]              -> valuN FaceConstraintCannotBeHidden a
+    [48, a]              -> valuN FaceConstraintCannotBeNamed a
+    [49, a, b]           -> valuN PatternShadowsConstructor a b
+    _ -> malformed
+
+instance EmbPrj OptionWarning where
+  icod_ = \case
+    OptionRenamed a b -> icodeN' OptionRenamed a b
+
+  value = vcase $ \case
+    [a, b] -> valuN OptionRenamed a b
+    _ -> malformed
+
+instance EmbPrj ParseWarning where
+  icod_ = \case
+    OverlappingTokensWarning a -> icodeN 0 OverlappingTokensWarning a
+    UnsupportedAttribute a b   -> icodeN 1 UnsupportedAttribute a b
+    MultipleAttributes a b     -> icodeN 2 MultipleAttributes a b
+
+  value = vcase $ \case
+    [0, a]    -> valuN OverlappingTokensWarning a
+    [1, a, b] -> valuN UnsupportedAttribute a b
+    [2, a, b] -> valuN MultipleAttributes a b
+    _ -> malformed
+
+instance EmbPrj RecordFieldWarning where
+  icod_ = \case
+    W.DuplicateFields a   -> icodeN 0 W.DuplicateFields a
+    W.TooManyFields a b c -> icodeN 1 W.TooManyFields a b c
+
+  value = vcase $ \case
+    [0, a]       -> valuN W.DuplicateFields a
+    [1, a, b, c] -> valuN W.TooManyFields a b c
+    _ -> malformed
+
+instance EmbPrj DeclarationWarning where
+  icod_ (DeclarationWarning a b) = icodeN' DeclarationWarning a b
+  value = vcase $ \case
+    [a, b] -> valuN DeclarationWarning a b
+    _ -> malformed
+
+instance EmbPrj DeclarationWarning' where
+  icod_ = \case
+    UnknownNamesInFixityDecl a        -> icodeN 0 UnknownNamesInFixityDecl a
+    UnknownNamesInPolarityPragmas a   -> icodeN 1 UnknownNamesInPolarityPragmas a
+    PolarityPragmasButNotPostulates a -> icodeN 2 PolarityPragmasButNotPostulates a
+    UselessPrivate a                  -> icodeN 3 UselessPrivate a
+    UselessAbstract a                 -> icodeN 4 UselessAbstract a
+    UselessInstance a                 -> icodeN 5 UselessInstance a
+    EmptyMutual a                     -> icodeN 6 EmptyMutual a
+    EmptyAbstract a                   -> icodeN 7 EmptyAbstract a
+    EmptyPrivate a                    -> icodeN 8 EmptyPrivate a
+    EmptyInstance a                   -> icodeN 9 EmptyInstance a
+    EmptyMacro a                      -> icodeN 10 EmptyMacro a
+    EmptyPostulate a                  -> icodeN 11 EmptyPostulate a
+    InvalidTerminationCheckPragma a   -> icodeN 12 InvalidTerminationCheckPragma a
+    InvalidNoPositivityCheckPragma a  -> icodeN 13 InvalidNoPositivityCheckPragma a
+    InvalidCatchallPragma a           -> icodeN 14 InvalidCatchallPragma a
+    InvalidNoUniverseCheckPragma a    -> icodeN 15 InvalidNoUniverseCheckPragma a
+    UnknownFixityInMixfixDecl a       -> icodeN 16 UnknownFixityInMixfixDecl a
+    MissingDefinitions a              -> icodeN 17 MissingDefinitions a
+    NotAllowedInMutual r a            -> icodeN 18 NotAllowedInMutual r a
+    PragmaNoTerminationCheck r        -> icodeN 19 PragmaNoTerminationCheck r
+    EmptyGeneralize a                 -> icodeN 20 EmptyGeneralize a
+    PragmaCompiled r                  -> icodeN 21 PragmaCompiled r
+    EmptyPrimitive a                  -> icodeN 22 EmptyPrimitive a
+    EmptyField r                      -> icodeN 23 EmptyField r
+    ShadowingInTelescope nrs          -> icodeN 24 ShadowingInTelescope nrs
+    InvalidCoverageCheckPragma r      -> icodeN 25 InvalidCoverageCheckPragma r
+    OpenPublicAbstract r              -> icodeN 26 OpenPublicAbstract r
+    OpenPublicPrivate r               -> icodeN 27 OpenPublicPrivate r
+    EmptyConstructor a                -> icodeN 28 EmptyConstructor a
+    InvalidRecordDirective a          -> icodeN 29 InvalidRecordDirective a
+    InvalidConstructor a              -> icodeN 30 InvalidConstructor a
+    InvalidConstructorBlock a         -> icodeN 31 InvalidConstructorBlock a
+    MissingDeclarations a             -> icodeN 32 MissingDeclarations a
+    HiddenGeneralize r                -> icodeN 33 HiddenGeneralize r
+    SafeFlagEta                    {} -> __IMPOSSIBLE__
+    SafeFlagInjective              {} -> __IMPOSSIBLE__
+    SafeFlagNoCoverageCheck        {} -> __IMPOSSIBLE__
+    SafeFlagNoPositivityCheck      {} -> __IMPOSSIBLE__
+    SafeFlagNoUniverseCheck        {} -> __IMPOSSIBLE__
+    SafeFlagNonTerminating         {} -> __IMPOSSIBLE__
+    SafeFlagPolarity               {} -> __IMPOSSIBLE__
+    SafeFlagTerminating            {} -> __IMPOSSIBLE__
+
+  value = vcase $ \case
+    [0, a]   -> valuN UnknownNamesInFixityDecl a
+    [1, a]   -> valuN UnknownNamesInPolarityPragmas a
+    [2, a]   -> valuN PolarityPragmasButNotPostulates a
+    [3, a]   -> valuN UselessPrivate a
+    [4, a]   -> valuN UselessAbstract a
+    [5, a]   -> valuN UselessInstance a
+    [6, a]   -> valuN EmptyMutual a
+    [7, a]   -> valuN EmptyAbstract a
+    [8, a]   -> valuN EmptyPrivate a
+    [9, a]   -> valuN EmptyInstance a
+    [10,a]   -> valuN EmptyMacro a
+    [11,a]   -> valuN EmptyPostulate a
+    [12,a]   -> valuN InvalidTerminationCheckPragma a
+    [13,a]   -> valuN InvalidNoPositivityCheckPragma a
+    [14,a]   -> valuN InvalidCatchallPragma a
+    [15,a]   -> valuN InvalidNoUniverseCheckPragma a
+    [16,a]   -> valuN UnknownFixityInMixfixDecl a
+    [17,a]   -> valuN MissingDefinitions a
+    [18,r,a] -> valuN NotAllowedInMutual r a
+    [19,r]   -> valuN PragmaNoTerminationCheck r
+    [20,a]   -> valuN EmptyGeneralize a
+    [21,a]   -> valuN PragmaCompiled a
+    [22,a]   -> valuN EmptyPrimitive a
+    [23,r]   -> valuN EmptyField r
+    [24,nrs] -> valuN ShadowingInTelescope nrs
+    [25,r]   -> valuN InvalidCoverageCheckPragma r
+    [26,r]   -> valuN OpenPublicAbstract r
+    [27,r]   -> valuN OpenPublicPrivate r
+    [28,r]   -> valuN EmptyConstructor r
+    [29,r]   -> valuN InvalidRecordDirective r
+    [30,r]   -> valuN InvalidConstructor r
+    [31,r]   -> valuN InvalidConstructorBlock r
+    [32,r]   -> valuN MissingDeclarations r
+    [33,r]   -> valuN HiddenGeneralize r
+    _ -> malformed
+
+instance EmbPrj LibWarning where
+  icod_ = \case
+    LibWarning a b -> icodeN 0 LibWarning a b
+
+  value = vcase $ \case
+    [0, a, b]   -> valuN LibWarning a b
+    _ -> malformed
+
+instance EmbPrj LibWarning' where
+  icod_ = \case
+    UnknownField     a   -> icodeN 0 UnknownField a
+
+  value = vcase $ \case
+    [0, a]    -> valuN UnknownField a
+    _ -> malformed
+
+instance EmbPrj ExecutablesFile where
+  icod_ = \case
+    ExecutablesFile a b -> icodeN 0 ExecutablesFile a b
+
+  value = vcase $ \case
+    [0, a, b] -> valuN ExecutablesFile a b
+    _ -> malformed
+
+instance EmbPrj LibPositionInfo where
+  icod_ = \case
+    LibPositionInfo a b c -> icodeN 0 LibPositionInfo a b c
+
+  value = vcase $ \case
+    [0, a, b, c] -> valuN LibPositionInfo a b c
+    _ -> malformed
+
+instance EmbPrj Doc where
+  icod_ d = icodeN' (undefined :: String -> Doc) (render d)
+
+  value = valueN text
+
+instance EmbPrj InfectiveCoinfective where
+  icod_ Infective   = icodeN' Infective
+  icod_ Coinfective = icodeN 0 Coinfective
+
+  value = vcase valu where
+    valu []  = valuN Infective
+    valu [0] = valuN Coinfective
+    valu _   = malformed
+
+instance EmbPrj PragmaOptions where
+  icod_    (PragmaOptions a b c d e f g h i j k l m n o p q r s t u v w x y z aa bb cc dd ee ff gg hh ii jj kk ll mm nn oo pp qq rr ss tt uu vv ww xx yy zz aaa bbb ccc ddd eee fff ggg hhh iii jjj kkk lll mmm nnn ooo ppp) =
+    icodeN' PragmaOptions a b c d e f g h i j k l m n o p q r s t u v w x y z aa bb cc dd ee ff gg hh ii jj kk ll mm nn oo pp qq rr ss tt uu vv ww xx yy zz aaa bbb ccc ddd eee fff ggg hhh iii jjj kkk lll mmm nnn ooo ppp
+
+  value = valueN PragmaOptions
+
+instance EmbPrj ProfileOptions where
+  icod_ opts = icode (profileOptionsToList opts)
+  value = fmap profileOptionsFromList . value
+
+instance EmbPrj ProfileOption where
+
+instance EmbPrj UnicodeOrAscii
+
+instance EmbPrj ConfluenceCheck where
+  icod_ LocalConfluenceCheck  = icodeN' LocalConfluenceCheck
+  icod_ GlobalConfluenceCheck = icodeN 0 GlobalConfluenceCheck
+
+  value = vcase valu where
+    valu []  = valuN LocalConfluenceCheck
+    valu [0] = valuN GlobalConfluenceCheck
+    valu _   = malformed
+
+instance EmbPrj WarningMode where
+  icod_ (WarningMode a b) = icodeN' WarningMode a b
+
+  value = valueN WarningMode
+
+instance EmbPrj WarningName where
+  icod_ = return . \case
+    OverlappingTokensWarning_                    -> 0
+    UnsupportedAttribute_                        -> 1
+    MultipleAttributes_                          -> 2
+    LibUnknownField_                             -> 3
+    EmptyAbstract_                               -> 4
+    EmptyConstructor_                            -> 5
+    EmptyField_                                  -> 6
+    EmptyGeneralize_                             -> 7
+    EmptyInstance_                               -> 8
+    EmptyMacro_                                  -> 9
+    EmptyMutual_                                 -> 10
+    EmptyPostulate_                              -> 11
+    EmptyPrimitive_                              -> 12
+    EmptyPrivate_                                -> 13
+    EmptyRewritePragma_                          -> 14
+    EmptyWhere_                                  -> 15
+    HiddenGeneralize_                            -> 16
+    InvalidCatchallPragma_                       -> 17
+    InvalidConstructor_                          -> 18
+    InvalidConstructorBlock_                     -> 19
+    InvalidCoverageCheckPragma_                  -> 20
+    InvalidNoPositivityCheckPragma_              -> 21
+    InvalidNoUniverseCheckPragma_                -> 22
+    InvalidRecordDirective_                      -> 23
+    InvalidTerminationCheckPragma_               -> 24
+    MissingDeclarations_                         -> 25
+    MissingDefinitions_                          -> 26
+    NotAllowedInMutual_                          -> 27
+    OpenPublicAbstract_                          -> 28
+    OpenPublicPrivate_                           -> 29
+    PolarityPragmasButNotPostulates_             -> 30
+    PragmaCompiled_                              -> 31
+    PragmaNoTerminationCheck_                    -> 32
+    ShadowingInTelescope_                        -> 33
+    UnknownFixityInMixfixDecl_                   -> 34
+    UnknownNamesInFixityDecl_                    -> 35
+    UnknownNamesInPolarityPragmas_               -> 36
+    UselessAbstract_                             -> 37
+    UselessInstance_                             -> 38
+    UselessPrivate_                              -> 39
+    AbsurdPatternRequiresNoRHS_                  -> 40
+    AsPatternShadowsConstructorOrPatternSynonym_ -> 41
+    CantGeneralizeOverSorts_                     -> 42
+    ClashesViaRenaming_                          -> 43
+    CoverageIssue_                               -> 44
+    CoverageNoExactSplit_                        -> 45
+    DeprecationWarning_                          -> 46
+    DuplicateUsing_                              -> 47
+    FixityInRenamingModule_                      -> 48
+    InvalidCharacterLiteral_                     -> 49
+    UselessPragma_                               -> 50
+    GenericWarning_                              -> 51
+    IllformedAsClause_                           -> 52
+    InstanceArgWithExplicitArg_                  -> 53
+    InstanceWithExplicitArg_                     -> 54
+    InstanceNoOutputTypeName_                    -> 55
+    InversionDepthReached_                       -> 56
+    ModuleDoesntExport_                          -> 57
+    NoGuardednessFlag_                           -> 58
+    NotInScope_                                  -> 59
+    NotStrictlyPositive_                         -> 60
+    UnsupportedIndexedMatch_                     -> 61
+    OldBuiltin_                                  -> 62
+    PragmaCompileErased_                         -> 63
+    RewriteMaybeNonConfluent_                    -> 64
+    RewriteNonConfluent_                         -> 65
+    RewriteAmbiguousRules_                       -> 66
+    RewriteMissingRule_                          -> 67
+    SafeFlagEta_                                 -> 68
+    SafeFlagInjective_                           -> 69
+    SafeFlagNoCoverageCheck_                     -> 70
+    SafeFlagNonTerminating_                      -> 71
+    SafeFlagNoPositivityCheck_                   -> 72
+    SafeFlagNoUniverseCheck_                     -> 73
+    SafeFlagPolarity_                            -> 74
+    SafeFlagPostulate_                           -> 75
+    SafeFlagPragma_                              -> 76
+    SafeFlagTerminating_                         -> 77
+    SafeFlagWithoutKFlagPrimEraseEquality_       -> 78
+    TerminationIssue_                            -> 79
+    UnreachableClauses_                          -> 80
+    UnsolvedConstraints_                         -> 81
+    UnsolvedInteractionMetas_                    -> 82
+    UnsolvedMetaVariables_                       -> 83
+    UselessHiding_                               -> 84
+    UselessInline_                               -> 85
+    UselessPatternDeclarationForRecord_          -> 86
+    UselessPublic_                               -> 87
+    UserWarning_                                 -> 88
+    WithoutKFlagPrimEraseEquality_               -> 89
+    WrongInstanceDeclaration_                    -> 90
+    CoInfectiveImport_                           -> 91
+    InfectiveImport_                             -> 92
+    DuplicateFields_                             -> 93
+    TooManyFields_                               -> 94
+    OptionRenamed_                               -> 95
+    PlentyInHardCompileTimeMode_                 -> 96
+    InteractionMetaBoundaries_                   -> 97
+    NotAffectedByOpaque_                         -> 98
+    UnfoldTransparentName_                       -> 99
+    UselessOpaque_                               -> 100
+    InlineNoExactSplit_                          -> 101
+    FaceConstraintCannotBeHidden_                -> 102
+    FaceConstraintCannotBeNamed_                 -> 103
+    PatternShadowsConstructor_                   -> 104
+    DuplicateInterfaceFiles_                     -> 105
+
+  value = \case
+    0   -> return OverlappingTokensWarning_
+    1   -> return UnsupportedAttribute_
+    2   -> return MultipleAttributes_
+    3   -> return LibUnknownField_
+    4   -> return EmptyAbstract_
+    5   -> return EmptyConstructor_
+    6   -> return EmptyField_
+    7   -> return EmptyGeneralize_
+    8   -> return EmptyInstance_
+    9   -> return EmptyMacro_
+    10  -> return EmptyMutual_
+    11  -> return EmptyPostulate_
+    12  -> return EmptyPrimitive_
+    13  -> return EmptyPrivate_
+    14  -> return EmptyRewritePragma_
+    15  -> return EmptyWhere_
+    16  -> return HiddenGeneralize_
+    17  -> return InvalidCatchallPragma_
+    18  -> return InvalidConstructor_
+    19  -> return InvalidConstructorBlock_
+    20  -> return InvalidCoverageCheckPragma_
+    21  -> return InvalidNoPositivityCheckPragma_
+    22  -> return InvalidNoUniverseCheckPragma_
+    23  -> return InvalidRecordDirective_
+    24  -> return InvalidTerminationCheckPragma_
+    25  -> return MissingDeclarations_
+    26  -> return MissingDefinitions_
+    27  -> return NotAllowedInMutual_
+    28  -> return OpenPublicAbstract_
+    29  -> return OpenPublicPrivate_
+    30  -> return PolarityPragmasButNotPostulates_
+    31  -> return PragmaCompiled_
+    32  -> return PragmaNoTerminationCheck_
+    33  -> return ShadowingInTelescope_
+    34  -> return UnknownFixityInMixfixDecl_
+    35  -> return UnknownNamesInFixityDecl_
+    36  -> return UnknownNamesInPolarityPragmas_
+    37  -> return UselessAbstract_
+    38  -> return UselessInstance_
+    39  -> return UselessPrivate_
+    40  -> return AbsurdPatternRequiresNoRHS_
+    41  -> return AsPatternShadowsConstructorOrPatternSynonym_
+    42  -> return CantGeneralizeOverSorts_
+    43  -> return ClashesViaRenaming_
+    44  -> return CoverageIssue_
+    45  -> return CoverageNoExactSplit_
+    46  -> return DeprecationWarning_
+    47  -> return DuplicateUsing_
+    48  -> return FixityInRenamingModule_
+    49  -> return InvalidCharacterLiteral_
+    50  -> return UselessPragma_
+    51  -> return GenericWarning_
+    52  -> return IllformedAsClause_
+    53  -> return InstanceArgWithExplicitArg_
+    54  -> return InstanceWithExplicitArg_
+    55  -> return InstanceNoOutputTypeName_
+    56  -> return InversionDepthReached_
+    57  -> return ModuleDoesntExport_
+    58  -> return NoGuardednessFlag_
+    59  -> return NotInScope_
+    60  -> return NotStrictlyPositive_
+    61  -> return UnsupportedIndexedMatch_
+    62  -> return OldBuiltin_
+    63  -> return PragmaCompileErased_
+    64  -> return RewriteMaybeNonConfluent_
+    65  -> return RewriteNonConfluent_
+    66  -> return RewriteAmbiguousRules_
+    67  -> return RewriteMissingRule_
+    68  -> return SafeFlagEta_
+    69  -> return SafeFlagInjective_
+    70  -> return SafeFlagNoCoverageCheck_
+    71  -> return SafeFlagNonTerminating_
+    72  -> return SafeFlagNoPositivityCheck_
+    73  -> return SafeFlagNoUniverseCheck_
+    74  -> return SafeFlagPolarity_
+    75  -> return SafeFlagPostulate_
+    76  -> return SafeFlagPragma_
+    77  -> return SafeFlagTerminating_
+    78  -> return SafeFlagWithoutKFlagPrimEraseEquality_
+    79  -> return TerminationIssue_
+    80  -> return UnreachableClauses_
+    81  -> return UnsolvedConstraints_
+    82  -> return UnsolvedInteractionMetas_
+    83  -> return UnsolvedMetaVariables_
+    84  -> return UselessHiding_
+    85  -> return UselessInline_
+    86  -> return UselessPatternDeclarationForRecord_
+    87  -> return UselessPublic_
+    88  -> return UserWarning_
+    89  -> return WithoutKFlagPrimEraseEquality_
+    90  -> return WrongInstanceDeclaration_
+    91  -> return CoInfectiveImport_
+    92  -> return InfectiveImport_
+    93  -> return DuplicateFields_
+    94  -> return TooManyFields_
+    95  -> return OptionRenamed_
+    96  -> return PlentyInHardCompileTimeMode_
+    97  -> return InteractionMetaBoundaries_
+    98  -> return NotAffectedByOpaque_
+    99  -> return UnfoldTransparentName_
+    100 -> return UselessOpaque_
+    101 -> return InlineNoExactSplit_
+    102 -> return FaceConstraintCannotBeHidden_
+    103 -> return FaceConstraintCannotBeNamed_
+    104 -> return PatternShadowsConstructor_
+    105 -> return DuplicateInterfaceFiles_
+    _   -> malformed
+
+
+instance EmbPrj CutOff where
+  icod_ = \case
+    DontCutOff -> icodeN' DontCutOff
+    CutOff a -> icodeN 0 CutOff a
+
+  value = vcase valu where
+    valu [] = valuN DontCutOff
+    valu [0,a] = valuN CutOff a
+    valu _ = malformed
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Highlighting.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Highlighting.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Highlighting.hs
@@ -0,0 +1,154 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.TypeChecking.Serialise.Instances.Highlighting where
+
+import qualified Data.Map.Strict as Map
+import Data.Strict.Tuple (Pair(..))
+import Data.Int (Int32)
+
+import qualified Agda.Interaction.Highlighting.Range   as HR
+import qualified Agda.Interaction.Highlighting.Precise as HP
+import qualified Agda.Utils.RangeMap                   as RM
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Common () --instance only
+
+instance EmbPrj HR.Range where
+  icod_ (HR.Range a b) = icodeN' HR.Range a b
+
+  value = valueN HR.Range
+
+instance EmbPrj HP.NameKind where
+  icod_ HP.Bound           = icodeN' HP.Bound
+  icod_ (HP.Constructor a) = icodeN 1 HP.Constructor a
+  icod_ HP.Datatype        = icodeN 2 ()
+  icod_ HP.Field           = icodeN 3 ()
+  icod_ HP.Function        = icodeN 4 ()
+  icod_ HP.Module          = icodeN 5 ()
+  icod_ HP.Postulate       = icodeN 6 ()
+  icod_ HP.Primitive       = icodeN 7 ()
+  icod_ HP.Record          = icodeN 8 ()
+  icod_ HP.Argument        = icodeN 9 ()
+  icod_ HP.Macro           = icodeN 10 ()
+  icod_ HP.Generalizable   = icodeN 11 ()
+
+  value = vcase valu where
+    valu []      = valuN HP.Bound
+    valu [1 , a] = valuN HP.Constructor a
+    valu [2]     = valuN HP.Datatype
+    valu [3]     = valuN HP.Field
+    valu [4]     = valuN HP.Function
+    valu [5]     = valuN HP.Module
+    valu [6]     = valuN HP.Postulate
+    valu [7]     = valuN HP.Primitive
+    valu [8]     = valuN HP.Record
+    valu [9]     = valuN HP.Argument
+    valu [10]    = valuN HP.Macro
+    valu [11]    = valuN HP.Generalizable
+    valu _       = malformed
+
+instance EmbPrj HP.Aspect where
+  icod_ HP.Comment        = icodeN 0 ()
+  icod_ HP.Keyword       = icodeN 1 ()
+  icod_ HP.String        = icodeN 2 ()
+  icod_ HP.Number        = icodeN 3 ()
+  icod_ HP.Symbol        = icodeN' HP.Symbol
+  icod_ HP.PrimitiveType = icodeN 4 ()
+  icod_ (HP.Name mk b)   = icodeN 5 HP.Name mk b
+  icod_ HP.Pragma        = icodeN 6 ()
+  icod_ HP.Background    = icodeN 7 ()
+  icod_ HP.Markup        = icodeN 8 ()
+  icod_ HP.Hole          = icodeN 9 ()
+
+  value = vcase valu where
+    valu [0]        = valuN HP.Comment
+    valu [1]        = valuN HP.Keyword
+    valu [2]        = valuN HP.String
+    valu [3]        = valuN HP.Number
+    valu []         = valuN HP.Symbol
+    valu [4]        = valuN HP.PrimitiveType
+    valu [5, mk, b] = valuN HP.Name mk b
+    valu [6]        = valuN HP.Pragma
+    valu [7]        = valuN HP.Background
+    valu [8]        = valuN HP.Markup
+    valu [9]        = valuN HP.Hole
+    valu _          = malformed
+
+instance EmbPrj HP.OtherAspect where
+  icod_ HP.Error                = pure 0
+  icod_ HP.ErrorWarning         = pure 1
+  icod_ HP.DottedPattern        = pure 2
+  icod_ HP.UnsolvedMeta         = pure 3
+  icod_ HP.TerminationProblem   = pure 4
+  icod_ HP.IncompletePattern    = pure 5
+  icod_ HP.TypeChecks           = pure 6
+  icod_ HP.UnsolvedConstraint   = pure 7
+  icod_ HP.PositivityProblem    = pure 8
+  icod_ HP.Deadcode             = pure 9
+  icod_ HP.CoverageProblem      = pure 10
+  icod_ HP.CatchallClause       = pure 11
+  icod_ HP.ConfluenceProblem    = pure 12
+  icod_ HP.MissingDefinition    = pure 13
+  icod_ HP.ShadowingInTelescope = pure 14
+
+  value = \case
+    0  -> pure HP.Error
+    1  -> pure HP.ErrorWarning
+    2  -> pure HP.DottedPattern
+    3  -> pure HP.UnsolvedMeta
+    4  -> pure HP.TerminationProblem
+    5  -> pure HP.IncompletePattern
+    6  -> pure HP.TypeChecks
+    7  -> pure HP.UnsolvedConstraint
+    8  -> pure HP.PositivityProblem
+    9  -> pure HP.Deadcode
+    10 -> pure HP.CoverageProblem
+    11 -> pure HP.CatchallClause
+    12 -> pure HP.ConfluenceProblem
+    13 -> pure HP.MissingDefinition
+    14 -> pure HP.ShadowingInTelescope
+    _  -> malformed
+
+instance EmbPrj HP.Aspects where
+  icod_ (HP.Aspects a b c d e) = icodeN' HP.Aspects a b c d e
+
+  value = valueN HP.Aspects
+
+instance EmbPrj HP.DefinitionSite where
+  icod_ (HP.DefinitionSite a b c d) = icodeN' HP.DefinitionSite a b c d
+
+  value = valueN HP.DefinitionSite
+
+instance EmbPrj a => EmbPrj (RM.RangeMap a) where
+  -- Write the RangeMap as flat list rather than a list of (Int, (Int, x)). Much
+  -- like Map, we need to call `convert' in the tail position and so the output
+  -- list is written (and read) in reverse order.
+  icod_ (RM.RangeMap f) = icodeNode =<< convert Empty (Map.toAscList f) where
+    convert :: Node -> [(Int, RM.PairInt a)] -> S Node
+    convert !ys [] = return ys
+    convert  ys ((start, RM.PairInt (end :!: entry)):xs) = do
+      !start <- icode start
+      !end <- icode end
+      !entry <- icode entry
+      convert (Cons start (Cons end (Cons entry ys))) xs
+
+  value = vcase (fmap (RM.RangeMap . Map.fromDistinctAscList) . convert []) where
+    convert :: [(Int, RM.PairInt a)] -> [Int32] -> R [(Int, RM.PairInt a)]
+    convert !ys [] = return ys
+    convert  ys (start:end:entry:xs) = do
+      !start <- value start
+      !end <- value end
+      !entry <- value entry
+      convert ((start, RM.PairInt (end :!: entry)):ys) xs
+    convert _ _ = malformed
+
+instance EmbPrj HP.TokenBased where
+  icod_ HP.TokenBased        = pure 0
+  icod_ HP.NotOnlyTokenBased = pure 1
+
+  value = \case
+    0 -> pure HP.TokenBased
+    1 -> pure HP.NotOnlyTokenBased
+    _ -> malformed
diff --git a/src/full/Agda/TypeChecking/Serialise/Instances/Internal.hs b/src/full/Agda/TypeChecking/Serialise/Instances/Internal.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Serialise/Instances/Internal.hs
@@ -0,0 +1,651 @@
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Agda.TypeChecking.Serialise.Instances.Internal where
+
+import qualified Data.HashSet as HashSet
+import Control.Monad
+import Control.Monad.IO.Class
+
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Position as P
+
+import Agda.TypeChecking.Serialise.Base
+import Agda.TypeChecking.Serialise.Instances.Compilers () --instance only
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Positivity.Occurrence
+import Agda.TypeChecking.Coverage.SplitTree
+
+import Agda.Utils.Functor
+import Agda.Utils.Permutation
+
+import Agda.Utils.Impossible
+
+instance EmbPrj a => EmbPrj (Dom a) where
+  icod_ (Dom a c d e f) = icodeN' Dom a c d e f
+
+  value = valueN Dom
+
+instance EmbPrj Signature where
+  icod_ (Sig a b c) = icodeN' Sig a b c
+
+  value = valueN Sig
+
+instance EmbPrj Section where
+  icod_ (Section a) = icodeN' Section a
+
+  value = valueN Section
+
+instance EmbPrj a => EmbPrj (Tele a) where
+  icod_ EmptyTel        = icodeN' EmptyTel
+  icod_ (ExtendTel a b) = icodeN' ExtendTel a b
+
+  value = vcase valu where
+    valu []     = valuN EmptyTel
+    valu [a, b] = valuN ExtendTel a b
+    valu _      = malformed
+
+instance EmbPrj Permutation where
+  icod_ (Perm a b) = icodeN' Perm a b
+
+  value = valueN Perm
+
+instance EmbPrj a => EmbPrj (Drop a) where
+  icod_ (Drop a b) = icodeN' Drop a b
+
+  value = valueN Drop
+
+instance EmbPrj a => EmbPrj (Elim' a) where
+  icod_ (Apply a)      = icodeN' Apply a
+  icod_ (IApply x y a) = icodeN 0 IApply x y a
+  icod_ (Proj a b)     = icodeN 0 Proj a b
+
+  value = vcase valu where
+    valu [a]       = valuN Apply a
+    valu [0,x,y,a] = valuN IApply x y a
+    valu [0, a, b] = valuN Proj a b
+    valu _         = malformed
+
+instance EmbPrj I.DataOrRecord where
+  icod_ = \case
+    IsData      -> icodeN' IsData
+    IsRecord pm -> icodeN' IsRecord pm
+
+  value = vcase $ \case
+    []   -> valuN IsData
+    [pm] -> valuN IsRecord pm
+    _    -> malformed
+
+instance EmbPrj I.ConHead where
+  icod_ (ConHead a b c d) = icodeN' ConHead a b c d
+
+  value = valueN ConHead
+
+instance (EmbPrj a) => EmbPrj (I.Type' a) where
+  icod_ (El a b) = icodeN' El a b
+
+  value = valueN El
+
+instance EmbPrj a => EmbPrj (I.Abs a) where
+  icod_ (NoAbs a b) = icodeN 0 NoAbs a b
+  icod_ (Abs a b)   = icodeN' Abs a b
+
+  value = vcase valu where
+    valu [a, b]    = valuN Abs a b
+    valu [0, a, b] = valuN NoAbs a b
+    valu _         = malformed
+
+instance EmbPrj I.Term where
+  icod_ (Var     a []) = icodeN' (\ a -> Var a []) a
+  icod_ (Var      a b) = icodeN 0 Var a b
+  icod_ (Lam      a b) = icodeN 1 Lam a b
+  icod_ (Lit      a  ) = icodeN 2 Lit a
+  icod_ (Def      a b) = icodeN 3 Def a b
+  icod_ (Con    a b c) = icodeN 4 Con a b c
+  icod_ (Pi       a b) = icodeN 5 Pi a b
+  icod_ (MetaV    a b) = icodeN 6 MetaV a b
+  icod_ (Sort     a  ) = icodeN 7 Sort a
+  icod_ (DontCare a  ) = icodeN 8 DontCare a
+  icod_ (Level    a  ) = icodeN 9 Level a
+  icod_ (Dummy    a b) = icodeN 10 Dummy a b
+
+  value = vcase valu where
+    valu [a]       = valuN var   a
+    valu [0, a, b] = valuN Var   a b
+    valu [1, a, b] = valuN Lam   a b
+    valu [2, a]    = valuN Lit   a
+    valu [3, a, b] = valuN Def   a b
+    valu [4, a, b, c] = valuN Con a b c
+    valu [5, a, b] = valuN Pi    a b
+    valu [6, a, b] = valuN MetaV a b
+    valu [7, a]    = valuN Sort  a
+    valu [8, a]    = valuN DontCare a
+    valu [9, a]    = valuN Level a
+    valu [10, a, b] = valuN Dummy a b
+    valu _         = malformed
+
+instance EmbPrj Level where
+  icod_ (Max a b) = icodeN' Max a b
+
+  value = valueN Max
+
+instance EmbPrj PlusLevel where
+  icod_ (Plus a b) = icodeN' Plus a b
+
+  value = valueN Plus
+
+instance EmbPrj IsFibrant where
+  icod_ IsFibrant = return 0
+  icod_ IsStrict  = return 1
+
+  value 0 = return IsFibrant
+  value 1 = return IsStrict
+  value _ = malformed
+
+instance EmbPrj Univ where
+
+instance EmbPrj I.Sort where
+  icod_ = \case
+    Univ a b     -> icodeN 0  Univ a b
+    SizeUniv     -> icodeN 2  SizeUniv
+    Inf a b      -> icodeN 3  Inf a b
+    PiSort a b c -> icodeN 4  PiSort a b c
+    FunSort a b  -> icodeN 5  FunSort a b
+    UnivSort a   -> icodeN 6  UnivSort a
+    DefS a b     -> icodeN 7  DefS a b
+    LockUniv     -> icodeN 9  LockUniv
+    IntervalUniv -> icodeN 10 IntervalUniv
+    MetaS a b    -> icodeN 11 MetaS a b
+    DummyS s     -> icodeN 12 DummyS s
+    LevelUniv    -> icodeN 13 LevelUniv
+
+  value = vcase valu where
+    valu [0, a, b] = valuN Univ a b
+    valu [2]       = valuN SizeUniv
+    valu [3, a, b] = valuN Inf a b
+    valu [4, a, b, c] = valuN PiSort a b c
+    valu [5, a, b] = valuN FunSort a b
+    valu [6, a]    = valuN UnivSort a
+    valu [7, a, b] = valuN DefS a b
+    valu [9]       = valuN LockUniv
+    valu [10]      = valuN IntervalUniv
+    valu [11, a, b] = valuN MetaS a b
+    valu [12, s]   = valuN DummyS s
+    valu [13]      = valuN LevelUniv
+    valu _         = malformed
+
+instance EmbPrj DisplayForm where
+  icod_ (Display a b c) = icodeN' Display a b c
+
+  value = valueN Display
+
+instance EmbPrj a => EmbPrj (Open a) where
+  icod_ (OpenThing a b c d) = icodeN' OpenThing a b c d
+
+  value = valueN OpenThing
+
+instance EmbPrj CheckpointId where
+  icod_ (CheckpointId a) = icode a
+  value n                = CheckpointId <$!> value n
+
+instance EmbPrj DisplayTerm where
+  icod_ (DTerm'   a b)   = icodeN' DTerm' a b
+  icod_ (DDot'    a b)   = icodeN 1 DDot' a b
+  icod_ (DCon     a b c) = icodeN 2 DCon a b c
+  icod_ (DDef     a b)   = icodeN 3 DDef a b
+  icod_ (DWithApp a b c) = icodeN 4 DWithApp a b c
+
+  value = vcase valu where
+    valu [a, b]       = valuN DTerm' a b
+    valu [1, a, b]    = valuN DDot' a b
+    valu [2, a, b, c] = valuN DCon a b c
+    valu [3, a, b]    = valuN DDef a b
+    valu [4, a, b, c] = valuN DWithApp a b c
+    valu _            = malformed
+
+instance EmbPrj MutualId where
+  icod_ (MutId a) = icode a
+  value n         = MutId <$!> value n
+
+instance EmbPrj CompKit where
+  icod_ (CompKit a b) = icodeN' CompKit a b
+  value = valueN CompKit
+
+instance EmbPrj Definition where
+  icod_ (Defn a b c d e f g h i j k l m n o p blocked r s) =
+    icodeN' Defn a b (P.killRange c) d e f g h i j k l m n o p (ossify blocked) r s
+    where
+      -- Andreas, 2024-01-02, issue #7044:
+      -- After serialization, a definition can never be unblocked,
+      -- since all metas are ossified.
+      -- Thus, we turn any blocker into 'neverUnblock'.
+      ossify :: Blocked_ -> Blocked_
+      ossify = \case
+        b@NotBlocked{} -> b
+        Blocked b () -> Blocked neverUnblock ()
+  value = valueN Defn
+
+instance EmbPrj NotBlocked where
+  icod_ ReallyNotBlocked = icodeN' ReallyNotBlocked
+  icod_ (StuckOn a)      = icodeN 0 StuckOn a
+  icod_ Underapplied     = icodeN 1 Underapplied
+  icod_ AbsurdMatch      = icodeN 2 AbsurdMatch
+  icod_ (MissingClauses a) = icodeN 3 MissingClauses a
+
+  value = vcase valu where
+    valu []     = valuN ReallyNotBlocked
+    valu [0, a] = valuN StuckOn a
+    valu [1]    = valuN Underapplied
+    valu [2]    = valuN AbsurdMatch
+    valu [3, a] = valuN MissingClauses a
+    valu _      = malformed
+
+-- Andreas, 2024-01-02, issue #7044.
+-- We only serialize 'neverUnblock';
+-- other than that, there should not be any blockers left at serialization time.
+blockedToMaybe :: Blocked_ -> Maybe NotBlocked
+blockedToMaybe = \case
+  NotBlocked a ()       -> Just a
+  Blocked a ()
+    | a == neverUnblock -> Nothing
+    | otherwise         -> __IMPOSSIBLE__
+
+blockedFromMaybe :: Maybe NotBlocked -> Blocked_
+blockedFromMaybe = maybe (Blocked neverUnblock ()) (`NotBlocked` ())
+
+instance EmbPrj Blocked_ where
+  icod_ = icod_ . blockedToMaybe
+  value = blockedFromMaybe <.> value
+
+instance EmbPrj NLPat where
+  icod_ (PVar a b)      = icodeN 0 PVar a b
+  icod_ (PDef a b)      = icodeN 1 PDef a b
+  icod_ (PLam a b)      = icodeN 2 PLam a b
+  icod_ (PPi a b)       = icodeN 3 PPi a b
+  icod_ (PSort a)       = icodeN 4 PSort a
+  icod_ (PBoundVar a b) = icodeN 5 PBoundVar a b
+  icod_ (PTerm a)       = icodeN 6 PTerm a
+
+  value = vcase valu where
+    valu [0, a, b]    = valuN PVar a b
+    valu [1, a, b]    = valuN PDef a b
+    valu [2, a, b]    = valuN PLam a b
+    valu [3, a, b]    = valuN PPi a b
+    valu [4, a]       = valuN PSort a
+    valu [5, a, b]    = valuN PBoundVar a b
+    valu [6, a]       = valuN PTerm a
+    valu _            = malformed
+
+instance EmbPrj NLPType where
+  icod_ (NLPType a b) = icodeN' NLPType a b
+
+  value = valueN NLPType
+
+instance EmbPrj NLPSort where
+  icod_ (PType a)   = icodeN 0 PType a
+  icod_ (PProp a)   = icodeN 1 PProp a
+  icod_ (PInf f a)  = icodeN 2 PInf f a
+  icod_ PSizeUniv   = icodeN 3 PSizeUniv
+  icod_ PLockUniv   = icodeN 4 PLockUniv
+  icod_ PIntervalUniv = icodeN 5 PIntervalUniv
+  icod_ (PSSet a)   = icodeN 6 PSSet a
+  icod_ PLevelUniv = icodeN 7 PLevelUniv
+
+  value = vcase valu where
+    valu [0, a] = valuN PType a
+    valu [1, a] = valuN PProp a
+    valu [2, f, a] = valuN PInf f a
+    valu [3]    = valuN PSizeUniv
+    valu [4]    = valuN PLockUniv
+    valu [5]    = valuN PIntervalUniv
+    valu [6, a] = valuN PSSet a
+    valu [7]    = valuN PLevelUniv
+    valu _      = malformed
+
+instance EmbPrj RewriteRule where
+  icod_ (RewriteRule a b c d e f g) = icodeN' RewriteRule a b c d e f g
+
+  value = valueN RewriteRule
+
+instance EmbPrj Projection where
+  icod_ (Projection a b c d e) = icodeN' Projection a b c d e
+
+  value = valueN Projection
+
+instance EmbPrj ProjLams where
+  icod_ (ProjLams a) = icodeN' ProjLams a
+
+  value = valueN ProjLams
+
+instance EmbPrj System where
+  icod_ (System a b) = icodeN' System a b
+
+  value = valueN System
+
+instance EmbPrj ExtLamInfo where
+  icod_ (ExtLamInfo a b c) = icodeN' ExtLamInfo a b c
+
+  value = valueN ExtLamInfo
+
+instance EmbPrj Polarity where
+  icod_ Covariant     = return 0
+  icod_ Contravariant = return 1
+  icod_ Invariant     = return 2
+  icod_ Nonvariant    = return 3
+
+  value 0 = return Covariant
+  value 1 = return Contravariant
+  value 2 = return Invariant
+  value 3 = return Nonvariant
+  value _ = malformed
+
+instance EmbPrj IsForced where
+  icod_ Forced    = return 0
+  icod_ NotForced = return 1
+
+  value 0 = return Forced
+  value 1 = return NotForced
+  value _ = malformed
+
+instance EmbPrj NumGeneralizableArgs where
+  icod_ NoGeneralizableArgs       = icodeN' NoGeneralizableArgs
+  icod_ (SomeGeneralizableArgs a) = icodeN' SomeGeneralizableArgs a
+
+  value = vcase valu where
+    valu []  = valuN NoGeneralizableArgs
+    valu [a] = valuN SomeGeneralizableArgs a
+    valu _   = malformed
+
+instance EmbPrj DoGeneralize where
+  icod_ YesGeneralizeVar  = return 0
+  icod_ YesGeneralizeMeta = return 1
+  icod_ NoGeneralize      = return 2
+
+  value 0 = return YesGeneralizeVar
+  value 1 = return YesGeneralizeMeta
+  value 2 = return NoGeneralize
+  value _ = malformed
+
+instance EmbPrj Occurrence where
+  icod_ StrictPos = return 0
+  icod_ Mixed     = return 1
+  icod_ Unused    = return 2
+  icod_ GuardPos  = return 3
+  icod_ JustPos   = return 4
+  icod_ JustNeg   = return 5
+
+  value 0 = return StrictPos
+  value 1 = return Mixed
+  value 2 = return Unused
+  value 3 = return GuardPos
+  value 4 = return JustPos
+  value 5 = return JustNeg
+  value _ = malformed
+
+instance EmbPrj EtaEquality where
+  icod_ (Specified a) = icodeN 0 Specified a
+  icod_ (Inferred a)  = icodeN 1 Inferred a
+
+  value = vcase valu where
+    valu [0,a] = valuN Specified a
+    valu [1,a] = valuN Inferred a
+    valu _     = malformed
+
+instance EmbPrj ProjectionLikenessMissing
+
+instance EmbPrj BuiltinSort where
+  icod_ = \case
+    SortUniv  a      -> icodeN 0 SortUniv  a
+    SortOmega a      -> icodeN 1 SortOmega a
+    SortIntervalUniv -> icodeN 2 SortIntervalUniv
+    SortLevelUniv    -> icodeN 3 SortLevelUniv
+
+  value = vcase \case
+    [0, a] -> valuN SortUniv  a
+    [1, a] -> valuN SortOmega a
+    [2]    -> valuN SortIntervalUniv
+    [3]    -> valuN SortLevelUniv
+    _ -> malformed
+
+instance EmbPrj Defn where
+  icod_ (Axiom       a)                                 = icodeN 0 Axiom a
+  icod_ (Function    a b s t u c d e f g h i j k l m)   = icodeN 1 (\ a b s -> Function a b s t) a b s u c d e f g h i j k l m
+  icod_ (Datatype    a b c d e f g h i j)               = icodeN 2 Datatype a b c d e f g h i j
+  icod_ (Record      a b c d e f g h i j k l m)         = icodeN 3 Record a b c d e f g h i j k l m
+  icod_ (Constructor a b c d e f g h i j k)             = icodeN 4 Constructor a b c d e f g h i j k
+  icod_ (Primitive   a b c d e f)                       = icodeN 5 Primitive a b c d e f
+  icod_ (PrimitiveSort a b)                             = icodeN 6 PrimitiveSort a b
+  icod_ AbstractDefn{}                                  = __IMPOSSIBLE__
+  icod_ GeneralizableVar                                = icodeN 7 GeneralizableVar
+  icod_ DataOrRecSig{}                                  = __IMPOSSIBLE__
+
+  value = vcase valu where
+    valu [0, a]                                        = valuN Axiom a
+    valu [1, a, b, s, u, c, d, e, f, g, h, i, j, k, l, m]
+                                                       = valuN (\ a b s -> Function a b s Nothing) a b s u c d e f g h i j k l m
+    valu [2, a, b, c, d, e, f, g, h, i, j]             = valuN Datatype a b c d e f g h i j
+    valu [3, a, b, c, d, e, f, g, h, i, j, k, l, m]    = valuN Record   a b c d e f g h i j k l m
+    valu [4, a, b, c, d, e, f, g, h, i, j, k]          = valuN Constructor a b c d e f g h i j k
+    valu [5, a, b, c, d, e, f]                         = valuN Primitive   a b c d e f
+    valu [6, a, b]                                     = valuN PrimitiveSort a b
+    valu [7]                                           = valuN GeneralizableVar
+    valu _                                             = malformed
+
+instance EmbPrj LazySplit where
+  icod_ StrictSplit = icodeN' StrictSplit
+  icod_ LazySplit   = icodeN 0 LazySplit
+
+  value = vcase valu where
+    valu []  = valuN StrictSplit
+    valu [0] = valuN LazySplit
+    valu _   = malformed
+
+instance EmbPrj SplitTag where
+  icod_ (SplitCon c)  = icodeN 0 SplitCon c
+  icod_ (SplitLit l)  = icodeN 1 SplitLit l
+  icod_ SplitCatchall = icodeN' SplitCatchall
+
+  value = vcase valu where
+    valu []     = valuN SplitCatchall
+    valu [0, c] = valuN SplitCon c
+    valu [1, l] = valuN SplitLit l
+    valu _      = malformed
+
+instance EmbPrj a => EmbPrj (SplitTree' a) where
+  icod_ (SplittingDone a) = icodeN' SplittingDone a
+  icod_ (SplitAt a b c)   = icodeN 0 SplitAt a b c
+
+  value = vcase valu where
+    valu [a]          = valuN SplittingDone a
+    valu [0, a, b, c] = valuN SplitAt a b c
+    valu _            = malformed
+
+instance EmbPrj FunctionFlag where
+  icod_ FunStatic       = pure 0
+  icod_ FunInline       = pure 1
+  icod_ FunMacro        = pure 2
+
+  value = \case
+    0 -> pure FunStatic
+    1 -> pure FunInline
+    2 -> pure FunMacro
+    _ -> malformed
+
+instance EmbPrj a => EmbPrj (WithArity a) where
+  icod_ (WithArity a b) = icodeN' WithArity a b
+
+  value = valueN WithArity
+
+instance EmbPrj a => EmbPrj (Case a) where
+  icod_ (Branches a b c d e f g) = icodeN' Branches a b c d e f g
+
+  value = valueN Branches
+
+-- Opaque blocks are serialised in an abbreviated manner: We only need
+-- the enclosed definitions (3rd argument) and parent (4th argument) to
+-- compute the transitive closure during scope checking, never
+-- afterwards.
+instance EmbPrj OpaqueBlock where
+  icod_ (OpaqueBlock id uf _ _ r) =
+    icodeN' (\id uf ->
+      let !unfolding = HashSet.fromList uf
+      in OpaqueBlock id unfolding mempty Nothing)
+    id (HashSet.toList uf) r
+
+  value = valueN (\id uf -> let !unfolding = HashSet.fromList uf
+                            in OpaqueBlock id unfolding mempty Nothing)
+
+instance EmbPrj CompiledClauses where
+  icod_ (Fail a)   = icodeN' Fail a
+  icod_ (Done a b) = icodeN' Done a (P.killRange b)
+  icod_ (Case a b) = icodeN 2 Case a b
+
+  value = vcase valu where
+    valu [a]       = valuN Fail a
+    valu [a, b]    = valuN Done a b
+    valu [2, a, b] = valuN Case a b
+    valu _         = malformed
+
+instance EmbPrj a => EmbPrj (FunctionInverse' a) where
+  icod_ NotInjective = icodeN' NotInjective
+  icod_ (Inverse a)  = icodeN' Inverse a
+
+  value = vcase valu where
+    valu []  = valuN NotInjective
+    valu [a] = valuN Inverse a
+    valu _   = malformed
+
+instance EmbPrj TermHead where
+  icod_ SortHead     = icodeN' SortHead
+  icod_ PiHead       = icodeN 1 PiHead
+  icod_ (ConsHead a) = icodeN 2 ConsHead a
+  icod_ (VarHead a)  = icodeN 3 VarHead a
+  icod_ UnknownHead  = icodeN 4 UnknownHead
+
+  value = vcase valu where
+    valu []     = valuN SortHead
+    valu [1]    = valuN PiHead
+    valu [2, a] = valuN ConsHead a
+    valu [3, a] = valuN VarHead a
+    valu [4]    = valuN UnknownHead
+    valu _      = malformed
+
+instance EmbPrj I.Clause where
+  icod_ (Clause a b c d e f g h i j k l) = icodeN' Clause a b c d e f g h i j k l
+
+  value = valueN Clause
+
+instance EmbPrj I.ConPatternInfo where
+  icod_ (ConPatternInfo a b c d e) = icodeN' ConPatternInfo a b c d e
+
+  value = valueN ConPatternInfo
+
+instance EmbPrj I.DBPatVar where
+  icod_ (DBPatVar a b) = icodeN' DBPatVar a b
+
+  value = valueN DBPatVar
+
+instance EmbPrj I.PatternInfo where
+  icod_ (PatternInfo a b) = icodeN' PatternInfo a b
+
+  value = valueN PatternInfo
+
+instance EmbPrj I.PatOrigin where
+  icod_ PatOSystem  = icodeN' PatOSystem
+  icod_ PatOSplit   = icodeN 1 PatOSplit
+  icod_ (PatOVar a) = icodeN 2 PatOVar a
+  icod_ PatODot     = icodeN 3 PatODot
+  icod_ PatOWild    = icodeN 4 PatOWild
+  icod_ PatOCon     = icodeN 5 PatOCon
+  icod_ PatORec     = icodeN 6 PatORec
+  icod_ PatOLit     = icodeN 7 PatOLit
+  icod_ PatOAbsurd  = icodeN 8 PatOAbsurd
+
+  value = vcase valu where
+    valu []     = valuN PatOSystem
+    valu [1]    = valuN PatOSplit
+    valu [2, a] = valuN PatOVar a
+    valu [3]    = valuN PatODot
+    valu [4]    = valuN PatOWild
+    valu [5]    = valuN PatOCon
+    valu [6]    = valuN PatORec
+    valu [7]    = valuN PatOLit
+    valu [8]    = valuN PatOAbsurd
+    valu _      = malformed
+
+instance EmbPrj a => EmbPrj (I.Pattern' a) where
+  icod_ (VarP a b  ) = icodeN 0 VarP a b
+  icod_ (ConP a b c) = icodeN 1 ConP a b c
+  icod_ (LitP a b  ) = icodeN 2 LitP a b
+  icod_ (DotP a b  ) = icodeN 3 DotP a b
+  icod_ (ProjP a b ) = icodeN 4 ProjP a b
+  icod_ (IApplyP a b c d) = icodeN 5 IApplyP a b c d
+  icod_ (DefP a b c) = icodeN 6 DefP a b c
+
+  value = vcase valu where
+    valu [0, a, b] = valuN VarP a b
+    valu [1, a, b, c] = valuN ConP a b c
+    valu [2, a, b] = valuN LitP a b
+    valu [3, a, b] = valuN DotP a b
+    valu [4, a, b] = valuN ProjP a b
+    valu [5, a, b, c, d] = valuN IApplyP a b c d
+    valu [6, a, b, c] = valuN DefP a b c
+    valu _         = malformed
+
+instance EmbPrj a => EmbPrj (Builtin a) where
+  icod_ (Prim    a) = icodeN' Prim a
+  icod_ (Builtin a) = icodeN 1 Builtin a
+  icod_ (BuiltinRewriteRelations a) = icodeN 2 BuiltinRewriteRelations a
+
+  value = vcase valu where
+    valu [a]    = valuN Prim    a
+    valu [1, a] = valuN Builtin a
+    valu [2, a] = valuN BuiltinRewriteRelations a
+    valu _      = malformed
+
+instance EmbPrj a => EmbPrj (Substitution' a) where
+  icod_ IdS                = icodeN' IdS
+  icod_ (EmptyS a)         = icodeN' EmptyS a
+  icod_ (a :# b)           = icodeN' (:#) a b
+  icod_ (Strengthen a b c) = icodeN 0 Strengthen a b c
+  icod_ (Wk a b)           = icodeN 1 Wk a b
+  icod_ (Lift a b)         = icodeN 2 Lift a b
+
+  value = vcase valu where
+    valu []           = valuN IdS
+    valu [a]          = valuN EmptyS a
+    valu [a, b]       = valuN (:#) a b
+    valu [0, a, b, c] = valuN Strengthen a b c
+    valu [1, a, b]    = valuN Wk a b
+    valu [2, a, b]    = valuN Lift a b
+    valu _            = malformed
+
+instance EmbPrj Instantiation where
+  icod_ (Instantiation a b) = icodeN' Instantiation a b
+  value = valueN Instantiation
+
+instance EmbPrj Comparison where
+  icod_ CmpEq  = icodeN' CmpEq
+  icod_ CmpLeq = icodeN 0 CmpLeq
+
+  value = vcase valu
+    where
+    valu []  = valuN CmpEq
+    valu [0] = valuN CmpLeq
+    valu _   = malformed
+
+instance EmbPrj a => EmbPrj (Judgement a) where
+  icod_ (HasType a b c) = icodeN' HasType a b c
+  icod_ (IsSort a b)    = icodeN' IsSort a b
+
+  value = vcase valu
+    where
+    valu [a, b, c] = valuN HasType a b c
+    valu [a, b]    = valuN IsSort a b
+    valu _         = malformed
+
+instance EmbPrj RemoteMetaVariable where
+  icod_ (RemoteMetaVariable a b c) = icodeN' RemoteMetaVariable a b c
+  value = valueN RemoteMetaVariable
diff --git a/src/full/Agda/TypeChecking/SizedTypes.hs b/src/full/Agda/TypeChecking/SizedTypes.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SizedTypes.hs
@@ -0,0 +1,632 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.SizedTypes where
+
+import Prelude hiding (null)
+
+import Control.Monad.Except ( MonadError(..) )
+import Control.Monad.Writer ( MonadWriter(..), WriterT(..), runWriterT )
+
+import qualified Data.Foldable as Fold
+import qualified Data.List as List
+import qualified Data.Set as Set
+import Data.Set (Set)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+import Agda.Syntax.Common.Pretty (Pretty)
+import qualified Agda.Syntax.Common.Pretty as P
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Pretty.Constraint () -- instance PrettyTCM Constraint
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import {-# SOURCE #-} Agda.TypeChecking.CheckInternal (MonadCheckInternal, infer)
+import {-# SOURCE #-} Agda.TypeChecking.Constraints () -- instance MonadConstraint TCM
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+
+import Agda.Utils.Functor
+import Agda.Utils.List as List
+import Agda.Utils.List1 (pattern (:|))
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import qualified Agda.Utils.ProfileOptions as Profile
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- * SIZELT stuff
+------------------------------------------------------------------------
+
+-- | Check whether a type is either not a SIZELT or a SIZELT that is non-empty.
+checkSizeLtSat :: Term -> TCM ()
+checkSizeLtSat t = whenM haveSizeLt $ do
+  reportSDoc "tc.size" 10 $ do
+    tel <- getContextTelescope
+    sep
+      [ "checking that " <+> prettyTCM t <+> " is not an empty type of sizes"
+      , if null tel then empty else do
+        "in context " <+> inTopContext (prettyTCM tel)
+      ]
+  reportSLn "tc.size" 60 $ "- raw type = " ++ show t
+  let postpone :: Blocker -> Term -> TCM ()
+      postpone b t = do
+        reportSDoc "tc.size.lt" 20 $ sep
+          [ "- postponing `not empty type of sizes' check for " <+> prettyTCM t ]
+        addConstraint b $ CheckSizeLtSat t
+  let ok :: TCM ()
+      ok = reportSLn "tc.size.lt" 20 $ "- succeeded: not an empty type of sizes"
+  ifBlocked t postpone $ \ _ t -> do
+    reportSLn "tc.size.lt" 20 $ "- type is not blocked"
+    caseMaybeM (isSizeType t) ok $ \ b -> do
+      reportSLn "tc.size.lt" 20 $ " - type is a size type"
+      case b of
+        BoundedNo -> ok
+        BoundedLt b -> do
+          reportSDoc "tc.size.lt" 20 $ " - type is SIZELT" <+> prettyTCM b
+          ifBlocked b (\ x _ -> postpone x t) $ \ _ b -> do
+            reportSLn "tc.size.lt" 20 $ " - size bound is not blocked"
+            catchConstraint (CheckSizeLtSat t) $ do
+              unlessM (checkSizeNeverZero b) $ do
+                typeError . GenericDocError =<< do
+                  "Possibly empty type of sizes " <+> prettyTCM t
+
+-- | Precondition: Term is reduced and not blocked.
+--   Throws a 'patternViolation' if undecided
+checkSizeNeverZero :: Term -> TCM Bool
+checkSizeNeverZero u = do
+  v <- sizeView u
+  case v of
+    SizeInf     -> return True  -- OK, infty is never 0.
+    SizeSuc{}   -> return True  -- OK, a + 1 is never 0.
+    OtherSize u ->
+      case u of
+        Var i [] -> checkSizeVarNeverZero i
+        -- neutral sizes cannot be guaranteed > 0
+        _ -> return False
+
+-- -- | A size variable is never zero if it is the strict upper bound of
+-- --   some other size variable in context.
+-- --   Eg. @i : Size, j : Size< i@ |- i is never zero.
+-- --   Throws a 'patternViolation' if undecided.
+-- checkSizeVarNeverZero :: Int -> TCM Bool
+-- checkSizeVarNeverZero i = do
+--   -- Looking for a variable j : Size< i, we can restrict to the last i
+--   -- entries, as this variable necessarily has been defined later than i.
+--   doms <- take i <$> getContext
+--   -- We raise each type to make sense in the current context.
+--   let ts = zipWith raise [1..] $ map (snd . unDom) doms
+--   reportSDoc "tc.size" 15 $ sep
+--     [ "checking that size " <+> prettyTCM (var i) <+> " is never 0"
+--     , "in context " <+> do sep $ map prettyTCM ts
+--     ]
+--   foldr f (return False) ts
+--   where
+--   f t cont = do
+--     -- If we encounter a blocked type in the context, we cannot
+--     -- definitely say no.
+--     let yes     = return True
+--         no      = cont
+--         perhaps = cont >>= \ res -> if res then return res else patternViolation
+--     ifBlocked t (\ _ _ -> perhaps) $ \ t -> do
+--       caseMaybeM (isSizeType t) no $ \ b -> do
+--         case b of
+--           BoundedNo -> no
+--           BoundedLt u -> ifBlocked u (\ _ _ -> perhaps) $ \ u -> do
+--             case u of
+--                Var i' [] | i == i' -> yes
+--                _ -> no
+
+
+-- | Checks that a size variable is ensured to be @> 0@.
+--   E.g. variable @i@ cannot be zero in context
+--   @(i : Size) (j : Size< ↑ ↑ i) (k : Size< j) (k' : Size< k)@.
+--   Throws a 'patternViolation' if undecided.
+checkSizeVarNeverZero :: Int -> TCM Bool
+checkSizeVarNeverZero i = do
+  reportSDoc "tc.size" 20 $ "checkSizeVarNeverZero" <+> prettyTCM (var i)
+  -- Looking for the minimal value for size variable i,
+  -- we can restrict to the last i
+  -- entries, as only these can contain i in an upper bound.
+  ts <- map (snd . unDom) . take i <$> getContext
+  -- If we encountered a blocking meta in the context, we cannot
+  -- say ``no'' for sure.
+  (n, blockers) <- runWriterT $ minSizeValAux ts $ repeat 0
+  let blocker = unblockOnAll blockers
+  if n > 0 then return True else
+    if blocker == alwaysUnblock
+      then return False
+      else patternViolation blocker
+  where
+  -- Compute the least valuation for size context ts above the
+  -- given valuation and return its last value.
+  minSizeValAux :: [Type] -> [Int] -> WriterT (Set Blocker) TCM Int
+  minSizeValAux _        []      = __IMPOSSIBLE__
+  minSizeValAux []       (n : _) = return n
+  minSizeValAux (t : ts) (n : ns) = do
+    reportSDoc "tc.size" 60 $
+       text ("minSizeVal (n:ns) = " ++ show (take (length ts + 2) $ n:ns) ++
+             " t =") <+> (text . show) t  -- prettyTCM t  -- Wrong context!
+    -- n is the min. value for variable 0 which has type t.
+    let cont = minSizeValAux ts ns
+        perhaps x = tell (Set.singleton x) >> cont
+    -- If we encounter a blocked type in the context, we cannot
+    -- give a definite answer.
+    ifBlocked t (\ x _ -> perhaps x) $ \ _ t -> do
+      caseMaybeM (liftTCM $ isSizeType t) cont $ \ b -> do
+        case b of
+          BoundedNo -> cont
+          BoundedLt u -> ifBlocked u (\ x _ -> perhaps x) $ \ _ u -> do
+            reportSLn "tc.size" 60 $ "minSizeVal upper bound u = " ++ show u
+            v <- liftTCM $ deepSizeView u
+            case v of
+              -- Variable 0 has bound @(< j + m)@
+              -- meaning that @minval(j) > n - m@, i.e., @minval(j) >= n+1-m@.
+              -- Thus, we update the min value for @j@ with function @(max (n+1-m))@.
+              DSizeVar (ProjectedVar j []) m -> do
+                reportSLn "tc.size" 60 $ "minSizeVal upper bound v = " ++ show v
+                let ns' = List.updateAt j (max $ n + 1 - m) ns
+                reportSLn "tc.size" 60 $ "minSizeVal ns' = " ++ show (take (length ts + 1) ns')
+                minSizeValAux ts ns'
+              DSizeMeta x _ _ -> perhaps (unblockOnMeta x)
+              _ -> cont
+
+-- | Check whether a variable in the context is bounded by a size expression.
+--   If @x : Size< a@, then @a@ is returned.
+isBounded :: PureTCM m => Nat -> m BoundedSize
+isBounded i = isBoundedSizeType =<< typeOfBV i
+
+isBoundedProjVar
+  :: (MonadCheckInternal m, PureTCM m)
+  => ProjectedVar -> m BoundedSize
+isBoundedProjVar pv = isBoundedSizeType =<< infer (unviewProjectedVar pv)
+
+isBoundedSizeType :: PureTCM m => Type -> m BoundedSize
+isBoundedSizeType t =
+  reduce (unEl t) >>= \case
+    Def x [Apply u] -> do
+      sizelt <- getBuiltin' builtinSizeLt
+      return $ if (Just (Def x []) == sizelt) then BoundedLt $ unArg u else BoundedNo
+    _ -> return BoundedNo
+
+-- | Whenever we create a bounded size meta, add a constraint
+--   expressing the bound. First argument is the new meta and must be a @MetaV{}@.
+--   In @boundedSizeMetaHook v tel a@, @tel@ includes the current context.
+boundedSizeMetaHook
+  :: ( MonadConstraint m
+     , MonadTCEnv m
+     , ReadTCState m
+     , MonadAddContext m
+     , HasOptions m
+     , HasBuiltins m
+     )
+  => Term -> Telescope -> Type -> m ()
+boundedSizeMetaHook v@(MetaV x _) tel0 a = do
+  res <- isSizeType a
+  case res of
+    Just (BoundedLt u) -> do
+      n <- getContextSize
+      let tel | n > 0     = telFromList $ drop n $ telToList tel0
+              | otherwise = tel0
+      addContext tel $ do
+        v <- sizeSuc 1 $ raise (size tel) v `apply` teleArgs tel
+        -- compareSizes CmpLeq v u
+        addConstraint (unblockOnMeta x) $ ValueCmp CmpLeq AsSizes v u
+    _ -> return ()
+boundedSizeMetaHook _ _ _ = __IMPOSSIBLE__
+
+-- | @trySizeUniv cmp t m n x els1 y els2@
+--   is called as a last resort when conversion checking @m `cmp` n : t@
+--   failed for definitions @m = x els1@ and @n = y els2@,
+--   where the heads @x@ and @y@ are not equal.
+--
+--   @trySizeUniv@ accounts for subtyping between SIZELT and SIZE,
+--   like @Size< i =< Size@.
+--
+--   If it does not succeed it reports failure of conversion check.
+trySizeUniv
+  :: MonadConversion m
+  => Comparison -> CompareAs -> Term -> Term
+  -> QName -> Elims -> QName -> Elims -> m ()
+trySizeUniv cmp t m n x els1 y els2 = do
+  let failure :: forall m a. MonadTCError m => m a
+      failure = typeError $ UnequalTerms cmp m n t
+      forceInfty u = compareSizes CmpEq (unArg u) =<< primSizeInf
+  -- Get the SIZE built-ins.
+  (size, sizelt) <- flip catchError (const failure) $ do
+     Def size   _ <- primSize
+     Def sizelt _ <- primSizeLt
+     return (size, sizelt)
+  case (cmp, els1, els2) of
+     -- Case @Size< _ <= Size@: true.
+     (CmpLeq, [_], [])  | x == sizelt && y == size -> return ()
+     -- Case @Size< u = Size@: forces @u = ∞@.
+     (_, [Apply u], []) | x == sizelt && y == size -> forceInfty u
+     (_, [], [Apply u]) | x == size && y == sizelt -> forceInfty u
+     -- This covers all cases for SIZE and SIZELT.
+     -- The remaining case is for @x@ and @y@ which are not size built-ins.
+     _                                             -> failure
+
+------------------------------------------------------------------------
+-- * Size views that 'reduce'.
+------------------------------------------------------------------------
+
+-- | Compute the deep size view of a term.
+--   Precondition: sized types are enabled.
+deepSizeView :: (PureTCM m, MonadTCError m) => Term -> m DeepSizeView
+deepSizeView v = do
+  Def inf [] <- primSizeInf
+  Def suc [] <- primSizeSuc
+  let loop v =
+        reduce v >>= \case
+          Def x []        | x == inf -> return $ DSizeInf
+          Def x [Apply u] | x == suc -> sizeViewSuc_ suc <$> loop (unArg u)
+
+          Var i es | Just pv <- ProjectedVar i <$> mapM isProjElim es
+                                     -> return $ DSizeVar pv 0
+          MetaV x us                 -> return $ DSizeMeta x us 0
+          v                          -> return $ DOtherSize v
+  loop v
+
+sizeMaxView :: PureTCM m => Term -> m SizeMaxView
+sizeMaxView v = do
+  inf <- getBuiltinDefName builtinSizeInf
+  suc <- getBuiltinDefName builtinSizeSuc
+  max <- getBuiltinDefName builtinSizeMax
+  let loop v = do
+        v <- reduce v
+        case v of
+          Def x []                   | Just x == inf -> return $ singleton $ DSizeInf
+          Def x [Apply u]            | Just x == suc -> maxViewSuc_ (fromJust suc) <$> loop (unArg u)
+          Def x [Apply u1, Apply u2] | Just x == max -> maxViewMax <$> loop (unArg u1) <*> loop (unArg u2)
+          Var i es | Just pv <- ProjectedVar i <$> mapM isProjElim es
+                                        -> return $ singleton $ DSizeVar pv 0
+          MetaV x us                    -> return $ singleton $ DSizeMeta x us 0
+          _                             -> return $ singleton $ DOtherSize v
+  loop v
+
+------------------------------------------------------------------------
+-- * Size comparison that might add constraints.
+------------------------------------------------------------------------
+
+{-# SPECIALIZE compareSizes :: Comparison -> Term -> Term -> TCM () #-}
+-- | Compare two sizes.
+compareSizes :: (MonadConversion m) => Comparison -> Term -> Term -> m ()
+compareSizes cmp u v = verboseBracket "tc.conv.size" 10 "compareSizes" $ do
+  reportSDoc "tc.conv.size" 10 $ vcat
+    [ "Comparing sizes"
+    , nest 2 $ sep [ prettyTCM u <+> prettyTCM cmp
+                   , prettyTCM v
+                   ]
+    ]
+  verboseS "tc.conv.size" 60 $ do
+    u <- reduce u
+    v <- reduce v
+    reportSDoc "tc.conv.size" 60 $
+      nest 2 $ sep [ pretty u <+> prettyTCM cmp
+                   , pretty v
+                   ]
+  whenProfile Profile.Conversion $ tick "compare sizes"
+  us <- sizeMaxView u
+  vs <- sizeMaxView v
+  compareMaxViews cmp us vs
+
+-- | Compare two sizes in max view.
+compareMaxViews :: (MonadConversion m) => Comparison -> SizeMaxView -> SizeMaxView -> m ()
+compareMaxViews cmp us vs = case (cmp, us, vs) of
+  (CmpLeq, _, (DSizeInf :| _)) -> return ()
+  (cmp,    u :| [], v :| []) -> compareSizeViews cmp u v
+  (CmpLeq, us,      v :| []) -> Fold.forM_ us $ \ u -> compareSizeViews cmp u v
+  (CmpLeq, us,      vs)      -> Fold.forM_ us $ \ u -> compareBelowMax u vs
+  (CmpEq,  us,      vs)      -> do
+    compareMaxViews CmpLeq us vs
+    compareMaxViews CmpLeq vs us
+
+-- | @compareBelowMax u vs@ checks @u <= max vs@.  Precondition: @size vs >= 2@
+compareBelowMax :: (MonadConversion m) => DeepSizeView -> SizeMaxView -> m ()
+compareBelowMax u vs = verboseBracket "tc.conv.size" 45 "compareBelowMax" $ do
+  reportSDoc "tc.conv.size" 45 $ sep
+    [ pretty u
+    , pretty CmpLeq
+    , pretty vs
+    ]
+  -- When trying several alternatives, we do not assign metas
+  -- and also do not produce constraints (see 'giveUp' below).
+  -- Andreas, 2019-03-28, issue #3600.
+  alt (dontAssignMetas $ Fold.foldr1 alt $ fmap (compareSizeViews CmpLeq u) vs) $ do
+    reportSDoc "tc.conv.size" 45 $ vcat
+      [ "compareBelowMax: giving up"
+      ]
+    u <- unDeepSizeView u
+    v <- unMaxView vs
+    size <- sizeType
+    giveUp CmpLeq size u v
+  where
+  alt c1 c2 = c1 `catchError` const c2
+
+compareSizeViews :: (MonadConversion m) => Comparison -> DeepSizeView -> DeepSizeView -> m ()
+compareSizeViews cmp s1' s2' = do
+  reportSDoc "tc.conv.size" 45 $ hsep
+    [ "compareSizeViews"
+    , pretty s1'
+    , pretty cmp
+    , pretty s2'
+    ]
+  size <- sizeType
+  let (s1, s2) = removeSucs (s1', s2')
+      withUnView cont = do
+        u <- unDeepSizeView s1
+        v <- unDeepSizeView s2
+        cont u v
+      failure = withUnView $ \ u v -> typeError $ UnequalTerms cmp u v AsSizes
+      continue cmp = withUnView $ compareAtom cmp AsSizes
+  case (cmp, s1, s2) of
+    (CmpLeq, _,            DSizeInf)   -> return ()
+    (CmpEq,  DSizeInf,     DSizeInf)   -> return ()
+    (CmpEq,  DSizeVar{},   DSizeInf)   -> failure
+    (_    ,  DSizeInf,     DSizeVar{}) -> failure
+    (_    ,  DSizeInf,     _         ) -> continue CmpEq
+    (CmpLeq, DSizeVar i n, DSizeVar j m) | i == j -> unless (n <= m) failure
+    (CmpLeq, DSizeVar i n, DSizeVar j m) | i /= j -> do
+       res <- isBoundedProjVar i
+       case res of
+         BoundedNo -> failure
+         BoundedLt u' -> do
+            -- now we have i < u', in the worst case i+1 = u'
+            -- and we want to check i+n <= v
+            v <- unDeepSizeView s2
+            if n > 0 then do
+              u'' <- sizeSuc (n - 1) u'
+              compareSizes cmp u'' v
+             else compareSizes cmp u' =<< sizeSuc 1 v
+    (CmpLeq, s1,        s2)         -> withUnView $ \ u v -> do
+      unlessM (trivial u v) $ giveUp CmpLeq size u v
+    (CmpEq, s1, s2) -> continue cmp
+
+-- | If 'envAssignMetas' then postpone as constraint, otherwise, fail hard.
+--   Failing is required if we speculatively test several alternatives.
+giveUp :: (MonadConversion m) => Comparison -> Type -> Term -> Term -> m ()
+giveUp cmp size u v =
+  ifM (asksTC envAssignMetas)
+    {-then-} (do
+      -- TODO: compute proper blocker
+      unblock <- unblockOnAnyMetaIn <$> instantiateFull [u, v]
+      addConstraint unblock $ ValueCmp CmpLeq AsSizes u v)
+    {-else-} (typeError $ UnequalTerms cmp u v AsSizes)
+
+-- | Checked whether a size constraint is trivial (like @X <= X+1@).
+trivial :: (MonadConversion m) => Term -> Term -> m Bool
+trivial u v = do
+    a@(e , n ) <- oldSizeExpr u
+    b@(e', n') <- oldSizeExpr v
+    let triv = e == e' && n <= n'
+          -- Andreas, 2012-02-24  filtering out more trivial constraints fixes
+          -- test/lib-succeed/SizeInconsistentMeta4.agda
+    reportSDoc "tc.conv.size" 60 $
+      nest 2 $ sep [ if triv then "trivial constraint" else empty
+                   , pretty a <+> "<="
+                   , pretty b
+                   ]
+    return triv
+  `catchError` \_ -> return False
+
+------------------------------------------------------------------------
+-- * Size constraints.
+------------------------------------------------------------------------
+
+-- | Test whether a problem consists only of size constraints.
+isSizeProblem :: (ReadTCState m, HasOptions m, HasBuiltins m) => ProblemId -> m Bool
+isSizeProblem pid = do
+  test <- isSizeTypeTest
+  all (mkIsSizeConstraint test (const True) . theConstraint) <$> getConstraintsForProblem pid
+
+-- | Test whether a constraint speaks about sizes.
+isSizeConstraint :: (HasOptions m, HasBuiltins m) => (Comparison -> Bool) -> Closure Constraint -> m Bool
+isSizeConstraint p c = isSizeTypeTest <&> \ test -> mkIsSizeConstraint test p c
+
+mkIsSizeConstraint :: (Term -> Maybe BoundedSize) -> (Comparison -> Bool) -> Closure Constraint -> Bool
+mkIsSizeConstraint test = isSizeConstraint_ $ isJust . test . unEl
+
+isSizeConstraint_
+  :: (Type -> Bool)       -- ^ Test for being a sized type
+  -> (Comparison -> Bool) -- ^ Restriction to these directions.
+  -> Closure Constraint
+  -> Bool
+isSizeConstraint_ _isSizeType p Closure{ clValue = ValueCmp cmp AsSizes       _ _ } = p cmp
+isSizeConstraint_  isSizeType p Closure{ clValue = ValueCmp cmp (AsTermsOf s) _ _ } = p cmp && isSizeType s
+isSizeConstraint_ _isSizeType _ _ = False
+
+-- | Take out all size constraints of the given direction (DANGER!).
+takeSizeConstraints :: (Comparison -> Bool) -> TCM [ProblemConstraint]
+takeSizeConstraints p = do
+  test <- isSizeTypeTest
+  takeConstraints (mkIsSizeConstraint test p . theConstraint)
+
+-- | Find the size constraints of the matching direction.
+getSizeConstraints :: (Comparison -> Bool) -> TCM [ProblemConstraint]
+getSizeConstraints p = do
+  test <- isSizeTypeTest
+  filter (mkIsSizeConstraint test p . theConstraint) <$> getAllConstraints
+
+-- | Return a list of size metas and their context.
+getSizeMetas :: Bool -> TCM [(MetaId, Type, Telescope)]
+getSizeMetas interactionMetas = do
+  test <- isSizeTypeTest
+  catMaybes <$> do
+    getOpenMetas >>= do
+      mapM $ \ m -> do
+        let no = return Nothing
+        mi <- lookupLocalMeta m
+        case mvJudgement mi of
+          _ | BlockedConst{} <- mvInstantiation mi -> no  -- Blocked terms should not be touched (#2637, #2881)
+          HasType _ cmp a -> do
+            TelV tel b <- telView a
+            -- b is reduced
+            caseMaybe (test $ unEl b) no $ \ _ -> do
+              let yes = return $ Just (m, a, tel)
+              if interactionMetas then yes else do
+                ifM (isJust <$> isInteractionMeta m) no yes
+          _ -> no
+
+{- ROLLED BACK
+getSizeMetas :: TCM ([(MetaId, Int)], [SizeConstraint])
+getSizeMetas = do
+  ms <- getOpenMetas
+  test <- isSizeTypeTest
+  let sizeCon m = do
+        let nothing  = return ([], [])
+        mi <- lookupMeta m
+        case mvJudgement mi of
+          HasType _ a -> do
+            TelV tel b <- telView =<< instantiateFull a
+            let noConstr = return ([(m, size tel)], [])
+            case test b of
+              Nothing            -> nothing
+              Just BoundedNo     -> noConstr
+              Just (BoundedLt u) -> noConstr
+{- WORKS NOT
+              Just (BoundedLt u) -> flip catchError (const $ noConstr) $ do
+                -- we assume the metavariable is used in an
+                -- extension of its creation context
+                ctxIds <- getContextId
+                let a = SizeMeta m $ take (size tel) $ reverse ctxIds
+                (b, n) <- oldSizeExpr u
+                return ([(m, size tel)], [Leq a (n-1) b])
+-}
+          _ -> nothing
+  (mss, css) <- unzip <$> mapM sizeCon ms
+  return (concat mss, concat css)
+-}
+
+------------------------------------------------------------------------
+-- * Size constraint solving.
+------------------------------------------------------------------------
+
+-- | Atomic size expressions.
+data OldSizeExpr
+  = SizeMeta MetaId [Int] -- ^ A size meta applied to de Bruijn indices.
+  | Rigid Int             -- ^ A de Bruijn index.
+  deriving (Eq, Show)
+
+instance Pretty OldSizeExpr where
+  pretty (SizeMeta m _) = P.text "X" <> P.pretty m
+  pretty (Rigid i)      = P.text $ "c" ++ show i
+
+-- | Size constraints we can solve.
+data OldSizeConstraint
+  = Leq OldSizeExpr Int OldSizeExpr
+    -- ^ @Leq a +n b@ represents @a =< b + n@.
+    --   @Leq a -n b@ represents @a + n =< b@.
+  deriving (Show)
+
+instance Pretty OldSizeConstraint where
+  pretty (Leq a n b)
+    | n == 0    = P.pretty a P.<+> "=<" P.<+> P.pretty b
+    | n > 0     = P.pretty a P.<+> "=<" P.<+> P.pretty b P.<+> "+" P.<+> P.text (show n)
+    | otherwise = P.pretty a P.<+> "+" P.<+> P.text (show (-n)) P.<+> "=<" P.<+> P.pretty b
+
+-- | Compute a set of size constraints that all live in the same context
+--   from constraints over terms of type size that may live in different
+--   contexts.
+--
+--   cf. 'Agda.TypeChecking.LevelConstraints.simplifyLevelConstraint'
+oldComputeSizeConstraints :: [ProblemConstraint] -> TCM [OldSizeConstraint]
+oldComputeSizeConstraints [] = return [] -- special case to avoid maximum []
+oldComputeSizeConstraints cs = catMaybes <$> mapM oldComputeSizeConstraint leqs
+  where
+    -- get the constraints plus contexts they are defined in
+    gammas       = map (envContext . clEnv . theConstraint) cs
+    ls           = map (clValue . theConstraint) cs
+    -- compute the longest context (common water level)
+    ns           = map size gammas
+    waterLevel   = maximum ns
+    -- lift all constraints to live in the longest context
+    -- (assuming this context is an extension of the shorter ones)
+    -- by raising the de Bruijn indices
+    leqs = zipWith raise (map (waterLevel -) ns) ls
+
+-- | Turn a constraint over de Bruijn indices into a size constraint.
+oldComputeSizeConstraint :: Constraint -> TCM (Maybe OldSizeConstraint)
+oldComputeSizeConstraint c =
+  case c of
+    ValueCmp CmpLeq _ u v -> do
+        reportSDoc "tc.size.solve" 50 $ sep
+          [ "converting size constraint"
+          , prettyTCM c
+          ]
+        (a, n) <- oldSizeExpr u
+        (b, m) <- oldSizeExpr v
+        return $ Just $ Leq a (m - n) b
+      `catchError` \ err -> case err of
+        PatternErr{} -> return Nothing
+        _            -> throwError err
+    _ -> __IMPOSSIBLE__
+
+-- | Turn a term with de Bruijn indices into a size expression with offset.
+--
+--   Throws a 'patternViolation' if the term isn't a proper size expression.
+oldSizeExpr :: (PureTCM m, MonadBlock m) => Term -> m (OldSizeExpr, Int)
+oldSizeExpr u = do
+  u <- reduce u -- Andreas, 2009-02-09.
+                -- This is necessary to surface the solutions of metavariables.
+  reportSDoc "tc.conv.size" 60 $ "oldSizeExpr:" <+> prettyTCM u
+  s <- sizeView u
+  case s of
+    SizeInf     -> patternViolation neverUnblock
+    SizeSuc u   -> mapSnd (+ 1) <$> oldSizeExpr u
+    OtherSize u -> case u of
+      Var i []  -> return (Rigid i, 0)
+      MetaV m es | Just xs <- mapM isVar es, fastDistinct xs
+                -> return (SizeMeta m xs, 0)
+      _ -> patternViolation neverUnblock
+  where
+    isVar (Proj{})  = Nothing
+    isVar (IApply _ _ v) = isVar (Apply (defaultArg v))
+    isVar (Apply v) = case unArg v of
+      Var i [] -> Just i
+      _        -> Nothing
+
+-- | Compute list of size metavariables with their arguments
+--   appearing in a constraint.
+flexibleVariables :: OldSizeConstraint -> [(MetaId, [Int])]
+flexibleVariables (Leq a _ b) = flex a ++ flex b
+  where
+    flex (Rigid _)       = []
+    flex (SizeMeta m xs) = [(m, xs)]
+
+-- | Convert size constraint into form where each meta is applied
+--   to indices @0,1,..,n-1@ where @n@ is the arity of that meta.
+--
+--   @X[σ] <= t@ becomes @X[id] <= t[σ^-1]@
+--
+--   @X[σ] ≤ Y[τ]@ becomes @X[id] ≤ Y[τ[σ^-1]]@ or @X[σ[τ^1]] ≤ Y[id]@
+--   whichever is defined.  If none is defined, we give up.
+--
+oldCanonicalizeSizeConstraint :: OldSizeConstraint -> Maybe OldSizeConstraint
+oldCanonicalizeSizeConstraint c@(Leq a n b) =
+  case (a,b) of
+    (Rigid{}, Rigid{})       -> return c
+    (SizeMeta m xs, Rigid i) -> do
+      j <- List.elemIndex i xs
+      return $ Leq (SizeMeta m [0..size xs-1]) n (Rigid j)
+    (Rigid i, SizeMeta m xs) -> do
+      j <- List.elemIndex i xs
+      return $ Leq (Rigid j) n (SizeMeta m [0..size xs-1])
+    (SizeMeta m xs, SizeMeta l ys)
+         -- try to invert xs on ys
+       | Just ys' <- mapM (\ y -> List.elemIndex y xs) ys ->
+           return $ Leq (SizeMeta m [0..size xs-1]) n (SizeMeta l ys')
+         -- try to invert ys on xs
+       | Just xs' <- mapM (\ x -> List.elemIndex x ys) xs ->
+           return $ Leq (SizeMeta m xs') n (SizeMeta l [0..size ys-1])
+         -- give up
+       | otherwise -> Nothing
diff --git a/src/full/Agda/TypeChecking/SizedTypes/Solve.hs b/src/full/Agda/TypeChecking/SizedTypes/Solve.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SizedTypes/Solve.hs
@@ -0,0 +1,807 @@
+{-# LANGUAGE NondecreasingIndentation #-}
+
+-- | Solving size constraints under hypotheses.
+--
+-- The size solver proceeds as follows:
+--
+-- 1. Get size constraints, cluster into connected components.
+--
+--    All size constraints that mention the same metas go into the same
+--    cluster.  Each cluster can be solved by itself.
+--
+--    Constraints that do not fit our format are ignored.
+--    We check whether our computed solution fulfills them as well
+--    in the last step.
+--
+-- 2. Find a joint context for each cluster.
+--
+--    Each constraint comes with its own typing context, which
+--    contains size hypotheses @j : Size< i@.  We need to find a
+--    common super context in which all constraints of a cluster live,
+--    and raise all constraints to this context.
+--
+--    There might not be a common super context.  Then we are screwed,
+--    since our solver is not ready to deal with such a situation.  We
+--    will blatantly refuse to solve this cluster and blame it on the
+--    user.
+--
+-- 3. Convert the joint context into a hypothesis graph.
+--
+--    This is straightforward.  Each de Bruijn index becomes a
+--    rigid variable, each typing assumption @j : Size< i@ becomes an
+--    arc.
+--
+-- 4. Convert the constraints into a constraint graph.
+--
+--    Here we need to convert @MetaV@s into flexible variables.
+--
+-- 5. Run the solver
+--
+-- 6. Convert the solution into meta instantiations.
+--
+-- 7. Double-check whether the constraints are solved.
+
+-- Opportunities for optimization:
+--
+-- - NamedRigids has some cost to retrieve variable names
+--   just for the sake of debug printing.
+
+module Agda.TypeChecking.SizedTypes.Solve where
+
+import Prelude hiding (null)
+
+import Control.Monad hiding (forM, forM_)
+import Control.Monad.Except
+import Control.Monad.Trans.Maybe
+
+import Data.Either
+import Data.Foldable (forM_)
+import qualified Data.Foldable as Fold
+import Data.Function (on)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Monoid
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Traversable (forM)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.MetaVars
+
+import Agda.TypeChecking.Monad as TCM hiding (Offset)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.MetaVars
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Constraints as C
+
+import qualified Agda.TypeChecking.SizedTypes as S
+import Agda.TypeChecking.SizedTypes.Syntax as Size
+import Agda.TypeChecking.SizedTypes.Utils
+import Agda.TypeChecking.SizedTypes.WarshallSolver as Size
+
+import Agda.Utils.Cluster
+import Agda.Utils.Function
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+import Agda.Utils.List1 (List1, pattern (:|), nonEmpty, (<|))
+import qualified Agda.Utils.List as List
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty (Pretty, prettyShow)
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import qualified Agda.Utils.VarSet as VarSet
+
+import Agda.Utils.Impossible
+
+type CC = ProblemConstraint
+
+-- | Flag to control the behavior of size solver.
+data DefaultToInfty
+  = DefaultToInfty      -- ^ Instantiate all unconstrained size variables to ∞.
+  | DontDefaultToInfty  -- ^ Leave unconstrained size variables unsolved.
+  deriving (Eq, Ord, Show)
+
+-- | Solve size constraints involving hypotheses.
+
+solveSizeConstraints :: DefaultToInfty -> TCM ()
+solveSizeConstraints flag =  do
+
+  -- 1. Take out the size constraints normalised.
+
+  let norm c = mapClosure normalise (theConstraint c) <&> \ cl -> c { theConstraint = cl }
+  cs0 <- mapM norm =<< S.takeSizeConstraints (== CmpLeq)
+    -- NOTE: this deletes the size constraints from the constraint set!
+  unless (null cs0) $
+    reportSDoc "tc.size.solve" 40 $ vcat $
+      text ( "Solving constraints (" ++ show flag ++ ")" ) : map prettyTCM cs0
+  let -- Error for giving up
+      cannotSolve :: TCM a -- Defined, but not currently used
+      cannotSolve = typeError . GenericDocError =<<
+        vcat ("Cannot solve size constraints" : map prettyTCM cs0)
+
+  -- 2. Cluster the constraints by common size metas.
+
+  -- Get all size metas.
+  sizeMetaSet <- Set.fromList . map (\ (x, _t, _tel) -> x) <$> S.getSizeMetas True
+
+  -- Pair each constraint with its list of size metas occurring in it.
+  cms <- forM cs0 $ \ cl -> enterClosure (theConstraint cl) $ \ c -> do
+
+    -- @allMetas@ does not reduce or instantiate;
+    -- this is why we require the size constraints to be normalised.
+    return (cl, Set.toList $
+      sizeMetaSet `Set.intersection` allMetas singleton c)
+
+  -- Now, some constraints may have no metas (clcs), the others have at least one (othercs).
+  let classify :: (a, [b]) -> Either a (a, List1 b)
+      classify (cl, [])     = Left  cl
+      classify (cl, (x:xs)) = Right (cl, x :| xs)
+  let (clcs, othercs) = partitionEithers $ map classify cms
+
+  -- We cluster the constraints by their metas.
+  let ccs = cluster' othercs
+
+  -- 3. Solve each cluster
+
+  -- Solve the closed constraints, one by one.
+
+  forM_ clcs $ \ c -> () <$ solveSizeConstraints_ flag [c]
+
+  -- Solve the clusters.
+
+  constrainedMetas <- Set.unions <$> do
+    forM  (ccs) $ \ (cs :: List1 CC) -> do
+
+      reportSDoc "tc.size.solve" 60 $ vcat $
+        "size constraint cluster:" <| fmap (text . show) cs
+
+      -- Convert each constraint in the cluster to the largest context.
+      -- (Keep fingers crossed).
+
+      enterClosure (Fold.maximumBy (compare `on` (length . envContext . clEnv)) $ fmap theConstraint cs) $ \ _ -> do
+        -- Get all constraints that can be cast to the longest context.
+        cs' :: [ProblemConstraint] <- List1.catMaybes <$> do
+          mapM (runMaybeT . castConstraintToCurrentContext) cs
+
+        reportSDoc "tc.size.solve" 20 $ vcat $
+          ( "converted size constraints to context: " <+> do
+              tel <- getContextTelescope
+              inTopContext $ prettyTCM tel
+          ) : map (nest 2 . prettyTCM) cs'
+
+        -- Solve the converted constraints.
+        solveSizeConstraints_ flag cs'
+
+  -- 4. Possibly set remaining metas to infinity.
+
+  -- Andreas, issue 1862: do not default to ∞ always, could be too early.
+  when (flag == DefaultToInfty) $ do
+
+    -- let constrainedMetas = Set.fromList $ concat $
+    --       for cs0 $ \ Closure{ clValue = ValueCmp _ _ u v } ->
+    --         allMetas u ++ allMetas v
+
+    -- Set the unconstrained, open size metas to ∞.
+    ms <- S.getSizeMetas False -- do not get interaction metas
+    unless (null ms) $ do
+      inf <- primSizeInf
+      forM_ ms $ \ (m, t, tel) -> do
+        unless (m `Set.member` constrainedMetas) $ do
+        unlessM (isFrozen m) $ do
+        reportSDoc "tc.size.solve" 20 $
+          "solution " <+> prettyTCM (MetaV m []) <+>
+          " := "      <+> prettyTCM inf
+        assignMeta 0 m t (List.downFrom $ size tel) inf
+
+  -- -- Double check.
+  -- unless (null cs0 && null ms) $ do
+  --   flip catchError (const cannotSolve) $
+  --     noConstraints $
+  --       forM_ cs0 $ \ cl -> enterClosure cl solveConstraint
+
+  -- 5. Make sure we did not lose any constraints.
+
+  -- This is necessary since we have removed the size constraints.
+  forM_ cs0 $ withConstraint solveConstraint
+
+
+-- | TODO: this does not actually work!
+--
+--   We would like to use a constraint @c@ created in context @Δ@ from module @N@
+--   in the current context @Γ@ and current module @M@.
+--
+--   @Δ@ is module tel @Δ₁@ of @N@ extended by some local bindings @Δ₂@.
+--   @Γ@ is the current context.
+--   The module parameter substitution from current @M@ to @N@ be
+--   @Γ ⊢ σ : Δ₁@.
+--
+--   If @M == N@, we do not need the parameter substitution.  We try raising.
+--
+--   We first strengthen @Δ ⊢ c@ to live in @Δ₁@ and obtain @c₁ = strengthen Δ₂ c@.
+--   We then transport @c₁@ to @Γ@ and obtain @c₂ = applySubst σ c₁@.
+--
+--   This works for different modules, but if @M == N@ we should not strengthen
+--   and then weaken, because strengthening is a partial operation.
+--   We should rather lift the substitution @σ@ by @Δ₂@ and then
+--   raise by @Γ₂ - Δ₂@.
+--   This "raising" might be a strengthening if @Γ₂@ is shorter than @Δ₂@.
+--
+--   (TODO: If the module substitution does not exist, because @N@ is not
+--   a parent of @M@, we cannot use the constraint, as it has been created
+--   in an unrelated context.)
+
+castConstraintToCurrentContext' :: Closure TCM.Constraint -> MaybeT TCM TCM.Constraint
+castConstraintToCurrentContext' cl = do
+  let modN  = envCurrentModule $ clEnv cl
+      delta = envContext $ clEnv cl
+  -- The module telescope of the constraint.
+  -- The constraint could come from the module telescope of the top level module.
+  -- In this case, it does not live in any module!
+  -- Thus, getSection can return Nothing.
+  delta1 <- liftTCM $ maybe empty (^. secTelescope) <$> getSection modN
+  -- The number of locals of the constraint.
+  let delta2 = size delta - size delta1
+  unless (delta2 >= 0) __IMPOSSIBLE__
+
+  -- The current module M and context Γ.
+  modM  <- currentModule
+  gamma <- liftTCM $ getContextSize
+  -- The current module telescope.
+  -- Could also be empty, if we are in the front matter or telescope of the top-level module.
+  gamma1 <-liftTCM $ maybe empty (^. secTelescope) <$> getSection modM
+  -- The current locals.
+  let gamma2 = gamma - size gamma1
+
+  -- Γ ⊢ σ : Δ₁
+  sigma <- liftTCM $ fromMaybe idS <$> getModuleParameterSub modN
+
+  -- Debug printing.
+  reportSDoc "tc.constr.cast" 40 $ "casting constraint" $$ do
+    tel <- getContextTelescope
+    inTopContext $ nest 2 $ vcat $
+      [ "current module                = " <+> prettyTCM modM
+      , "current module telescope      = " <+> prettyTCM gamma1
+      , "current context               = " <+> prettyTCM tel
+      , "constraint module             = " <+> prettyTCM modN
+      , "constraint module telescope   = " <+> prettyTCM delta1
+      , "constraint context            = " <+> (prettyTCM =<< enterClosure cl (const $ getContextTelescope))
+      , "constraint                    = " <+> enterClosure cl prettyTCM
+      , "module parameter substitution = " <+> prettyTCM sigma
+      ]
+
+  -- If gamma2 < 0, we must be in the wrong context.
+  -- E.g. we could have switched to the empty context even though
+  -- we are still inside a module with parameters.
+  -- In this case, we cannot safely convert the constraint,
+  -- since the module parameter substitution may be wrong.
+  guard (gamma2 >= 0)
+
+  -- Shortcut for modN == modM:
+  -- Raise constraint from Δ to Γ, if possible.
+  -- This might save us some strengthening.
+  if modN == modM then raiseMaybe (gamma - size delta) $ clValue cl else do
+
+  -- Strengthen constraint to Δ₁ ⊢ c
+  c <- raiseMaybe (-delta2) $ clValue cl
+
+  -- Ulf, 2016-11-09: I don't understand what this function does when M and N
+  -- are not related. Certainly things can go terribly wrong (see
+  -- test/Succeed/Issue2223b.agda)
+  fv <- liftTCM $ getModuleFreeVars modN
+  guard $ fv == size delta1
+
+  -- Γ ⊢ c[σ]
+  return $ applySubst sigma c
+  where
+    raiseMaybe n c = do
+      -- Fine if we have to weaken or strengthening is safe.
+      guard $
+        n >= 0 ||
+        -- Are all free variables at least -n?
+        IntSet.null (fst $ IntSet.split (-n) $ allFreeVars c)
+      return $ raise n c
+
+
+-- | A hazardous hack, may the Gods have mercy on us.
+--
+--   To cast to the current context, we match the context of the
+--   given constraint by 'CtxId', and as fallback, by variable name (douh!).
+--
+--   This hack lets issue 2046 go through.
+
+castConstraintToCurrentContext :: ProblemConstraint -> MaybeT TCM ProblemConstraint
+castConstraintToCurrentContext c = do
+  -- The checkpoint of the contraint
+  let cl = theConstraint c
+      cp = envCurrentCheckpoint $ clEnv cl
+  sigma <- caseMaybeM (viewTC $ eCheckpoints . key cp)
+          (do
+            -- We are not in a descendant of the constraint checkpoint.
+            -- Here be dragons!!
+            gamma <- asksTC envContext -- The target context
+            let findInGamma (Dom {unDom = (x, t)}) =
+                  -- match by name (hazardous)
+                  -- This is one of the seven deadly sins (not respecting alpha).
+                  List.findIndex ((x ==) . fst . unDom) gamma
+            let delta = envContext $ clEnv cl
+                cand  = map findInGamma delta
+            -- The domain of our substitution
+            let coveredVars = VarSet.fromList $ catMaybes $ zipWith ($>) cand [0..]
+            -- Check that all the free variables of the constraint are contained in
+            -- coveredVars.
+            -- We ignore the free variables occurring in sorts.
+            guard $ getAll $ runFree (All . (`VarSet.member` coveredVars)) IgnoreAll (clValue cl)
+            -- Turn cand into a substitution.
+            -- Since we ignored the free variables in sorts, we better patch up
+            -- the substitution with some dummy term rather than __IMPOSSIBLE__.
+            return $ parallelS $ map (maybe __DUMMY_TERM__ var) cand
+          ) return -- Phew, we've got the checkpoint! All is well.
+  -- Apply substitution to constraint and pray that the Gods are merciful on us.
+  cl' <- buildClosure $ applySubst sigma (clValue cl)
+  return $ c { theConstraint = cl' }
+  -- Note: the resulting constraint may not well-typed.
+  -- Even if it is, it may map variables to their wrong counterpart.
+
+-- | Return the size metas occurring in the simplified constraints.
+--   A constraint like @↑ _j =< ∞ : Size@ simplifies to nothing,
+--   so @_j@ would not be in this set.
+solveSizeConstraints_ :: DefaultToInfty -> [CC] -> TCM (Set MetaId)
+solveSizeConstraints_ flag cs0 = do
+  -- Pair constraints with their representation as size constraints.
+  -- Discard constraints that do not have such a representation.
+  ccs :: [(CC,HypSizeConstraint)] <- catMaybes <$> do
+    forM cs0 $ \ c0 -> fmap (c0,) <$> computeSizeConstraint c0
+
+  -- Simplify constraints and check for obvious inconsistencies.
+  ccs' <- concat <$> do
+    forM ccs $ \ (c0, HypSizeConstraint cxt hids hs sc) -> do
+      case simplify1 (\ sc -> return [sc]) sc of
+        Left _ -> typeError . GenericDocError =<< do
+          "Contradictory size constraint" <+> prettyTCM c0
+        Right cs -> return $ (c0,) . HypSizeConstraint cxt hids hs <$> cs
+
+  -- Cluster constraints according to the meta variables they mention.
+  -- @csNoM@ are the constraints that do not mention any meta.
+  let (csNoM, csMs) = (`List.partitionMaybe` ccs') $ \ p@(c0, c) ->
+        fmap (p,) $ nonEmpty $ map sizeMetaId $ Set.toList $ flexs c
+  -- @css@ are the clusters of constraints.
+      css :: [List1 (CC,HypSizeConstraint)]
+      css = cluster' csMs
+
+  -- Check that the closed constraints are valid.
+  whenJust (nonEmpty csNoM) $ solveCluster flag
+
+  -- Now, process the clusters.
+  forM_ css $ solveCluster flag
+
+  return $ Set.mapMonotonic sizeMetaId $ flexs $ map (snd . fst) csMs
+
+-- | Solve a cluster of constraints sharing some metas.
+--
+solveCluster :: DefaultToInfty -> List1 (CC, HypSizeConstraint) -> TCM ()
+solveCluster flag ccs = do
+  let cs = fmap snd ccs
+  let prettyCs   = map prettyTCM $ List1.toList cs
+  let err reason = typeError . GenericDocError =<< do
+        vcat $
+          [ text $ "Cannot solve size constraints" ] ++ prettyCs ++
+          [ "Reason:" <+> reason ]
+  reportSDoc "tc.size.solve" 20 $ vcat $
+    "Solving constraint cluster" : prettyCs
+  -- Find the super context of all contexts.
+{-
+  -- We use the @'ctxId'@s.
+  let cis@(ci:cis') = for cs $ \ c -> (c, reverse $ map ctxId $ sizeContext c)
+--  let cis@(ci:cis') = for cs $ \ c -> (c, reverse $ sizeHypIds c)
+      max a@Left{}            _            = a
+      max a@(Right ci@(c,is)) ci'@(c',is') =
+        case preOrSuffix is is' of
+          -- No common context:
+          IsNofix    -> Left (ci, ci')
+          IsPrefix{} -> Right ci'
+          _          -> a
+      res = foldl' max (Right ci) cis'
+      noContext ((c,is),(c',is')) = typeError . GenericDocError =<< vcat
+        [ "Cannot solve size constraints; the following constraints have no common typing context:"
+        , prettyTCM c
+        , prettyTCM c'
+        ]
+  flip (either noContext) res $ \ (HypSizeConstraint gamma hids hs _, _) -> do
+-}
+  -- We rely on the fact that contexts are only extended...
+  -- Just take the longest context.
+  let HypSizeConstraint gamma hids hs _ = Fold.maximumBy (compare `on` (length . sizeContext)) cs
+  -- Length of longest context.
+  let n = size gamma
+
+  -- Now convert all size constraints to the largest context.
+      csL = for cs $ \ (HypSizeConstraint cxt _ _ c) -> raise (n - size cxt) c
+  -- Canonicalize the constraints.
+  -- This is unsound in the presence of hypotheses.
+      csC :: [SizeConstraint]
+      csC = applyWhen (null hs) (mapMaybe canonicalizeSizeConstraint) $ List1.toList csL
+  reportSDoc "tc.size.solve" 30 $ vcat $
+    [ "Size hypotheses" ] ++
+    map (prettyTCM . HypSizeConstraint gamma hids hs) hs ++
+    [ "Canonicalized constraints" ] ++
+    map (prettyTCM . HypSizeConstraint gamma hids hs) csC
+
+  -- -- ALT:
+  -- -- Now convert all size constraints to de Bruijn levels.
+
+  -- -- To get from indices in a context of length m <= n
+  -- -- to levels into the target context of length n,
+  -- -- we apply the following substitution:
+  -- -- Index m-1 needs to be mapped to level 0,
+  -- -- index m-2 needs to be mapped to level 1,
+  -- -- index 0 needs to be mapped to level m-1,
+  -- -- so the desired substitution is @downFrom m@.
+  -- let sub m = applySubst $ parallelS $ map var $ downFrom m
+
+  -- -- We simply reverse the context to get to de Bruijn levels.
+  -- -- Of course, all types in the context are broken, but
+  -- -- only need it for pretty printing constraints.
+  -- gamma <- return $ reverse gamma
+
+  -- -- We convert the hypotheses to de Bruijn levels.
+  -- hs <- return $ sub n hs
+
+  -- -- We get a form for pretty-printing
+  -- let prettyC = prettyTCM . HypSizeConstraint gamma hids hs
+
+  -- -- We convert the constraints to de Bruijn level format.
+  -- let csC :: [SizeConstraint]
+  --     csC = for cs $ \ (HypSizeConstraint cxt _ _ c) -> sub (size cxt) c
+
+  -- reportSDoc "tc.size.solve" 30 $ vcat $
+  --   [ "Size hypotheses" ]           ++ map prettyC hs ++
+  --   [ "Canonicalized constraints" ] ++ map prettyC csC
+
+  -- Convert size metas to flexible vars.
+  let metas :: [SizeMeta]
+      metas = concatMap (foldMap (:[])) csC
+      csF   :: [Size.Constraint' NamedRigid MetaId]
+      csF   = map (fmap sizeMetaId) csC
+
+  -- Construct the hypotheses graph.
+  let hyps = map (fmap sizeMetaId) hs
+  -- There cannot be negative cycles in hypotheses graph due to scoping.
+  let hg = either __IMPOSSIBLE__ id $ hypGraph (rigids csF) hyps
+
+  -- -- Construct the constraint graph.
+  -- --    g :: Size.Graph NamedRigid Int Label
+  -- g <- either err return $ constraintGraph csF hg
+  -- reportSDoc "tc.size.solve" 40 $ vcat $
+  --   [ "Constraint graph"
+  --   , text (show g)
+  --   ]
+
+  -- sol :: Solution NamedRigid Int <- either err return $ solveGraph Map.empty hg g
+  -- either err return $ verifySolution hg csF sol
+
+  -- Andreas, 2016-07-13, issue 2096.
+  -- Running the solver once might result in unsolvable left-over constraints.
+  -- We need to iterate the solver to detect this.
+  sol :: Solution NamedRigid MetaId <- either err return $
+    iterateSolver Map.empty hg csF emptySolution
+
+  -- Convert solution to meta instantiation.
+  solved <- fmap Set.unions $ forM (Map.assocs $ theSolution sol) $ \ (m, a) -> do
+    unless (validOffset a) __IMPOSSIBLE__
+    -- Solution does not contain metas
+    u <- unSizeExpr $ fmap __IMPOSSIBLE__ a
+    let SizeMeta _ xs = fromMaybe __IMPOSSIBLE__ $
+          List.find ((m ==) . sizeMetaId) metas
+    -- Check that solution is well-scoped
+    let ys = rigidIndex <$> Set.toList (rigids a)
+        ok = all (`elem` xs) ys -- TODO: more efficient
+    -- unless ok $ err "ill-scoped solution for size meta variable"
+    u <- if ok then return u else primSizeInf
+    t <- getMetaType m
+    reportSDoc "tc.size.solve" 20 $ unsafeModifyContext (const gamma) $ do
+      let args = map (Apply . defaultArg . var) xs
+      "solution " <+> prettyTCM (MetaV m args) <+> " := " <+> prettyTCM u
+    reportSDoc "tc.size.solve" 60 $ vcat
+      [ text $ "  xs = " ++ show xs
+      , text $ "  u  = " ++ show u
+      ]
+    ifM (isFrozen m `or2M` (not <$> asksTC envAssignMetas)) (return Set.empty) $ do
+      assignMeta n m t xs u
+      return $ Set.singleton m
+    -- WRONG:
+    -- let partialSubst = List.sort $ zip xs $ map var $ downFrom n
+    -- assignMeta' n m t (length xs) partialSubst u
+    -- WRONG: assign DirEq m (map (defaultArg . var) xs) u
+
+  -- Possibly set remaining size metas to ∞ (issue 1862)
+  -- unless we have an interaction meta in the cluster (issue 2095).
+
+  ims <- Set.fromList <$> getInteractionMetas
+
+  --  ms = unsolved size metas from cluster
+  let ms = Set.fromList (map sizeMetaId metas) Set.\\ solved
+  --  Make sure they do not contain an interaction point
+  let noIP = Set.disjoint ims ms
+
+  unless (null ms) $ reportSDoc "tc.size.solve" 30 $ fsep $
+    "cluster did not solve these size metas: " : map prettyTCM (Set.toList ms)
+
+  solvedAll <- do
+    -- If no metas are left, we have solved this cluster completely.
+    if Set.null ms                then return True  else do
+    -- Otherwise, we can solve it completely if we are allowed to set to ∞.
+    if flag == DontDefaultToInfty then return False else do
+    -- Which is only the case when we have no interaction points in the cluster.
+    if not noIP                   then return False else do
+    -- Try to set all unconstrained size metas to ∞.
+    inf <- primSizeInf
+    and <$> do
+      forM (Set.toList ms) $ \ m -> do
+        -- If one variable is frozen, we cannot set it (and hence not all) to ∞
+        let no = do
+              reportSDoc "tc.size.solve" 30 $
+                prettyTCM (MetaV m []) <+> "is frozen, cannot set it to ∞"
+              return False
+        ifM (isFrozen m `or2M` do not <$> asksTC envAssignMetas) no $ {-else-} do
+          reportSDoc "tc.size.solve" 20 $
+            "solution " <+> prettyTCM (MetaV m []) <+>
+            " := "      <+> prettyTCM inf
+          t <- metaType m
+          TelV tel core <- telView t
+          unlessM (isJust <$> isSizeType core) __IMPOSSIBLE__
+          assignMeta 0 m t (List.downFrom $ size tel) inf
+          return True
+
+  -- Double check.
+  when solvedAll $ do
+    let cs0 = fmap fst ccs
+        -- Error for giving up
+        cannotSolve = typeError . GenericDocError =<<
+          vcat ("Cannot solve size constraints" <| fmap prettyTCM cs0)
+    flip catchError (const cannotSolve) $
+      noConstraints $
+        forM_ cs0 $ withConstraint solveConstraint
+
+-- | Collect constraints from a typing context, looking for SIZELT hypotheses.
+getSizeHypotheses :: Context -> TCM [(Nat, SizeConstraint)]
+getSizeHypotheses gamma = unsafeModifyContext (const gamma) $ do
+  (_, msizelt) <- getBuiltinSize
+  caseMaybe msizelt (return []) $ \ sizelt -> do
+    -- Traverse the context from newest to oldest de Bruijn Index
+    catMaybes <$> do
+      forM (zip [0..] gamma) $ \ (i, ce) -> do
+        -- Get name and type of variable i.
+        let (x, t) = unDom ce
+            s      = prettyShow x
+        t <- reduce . raise (1 + i) . unEl $ t
+        case t of
+          Def d [Apply u] | d == sizelt -> do
+            caseMaybeM (sizeExpr $ unArg u) (return Nothing) $ \ a ->
+              return $ Just $ (i, Constraint (Rigid (NamedRigid s i) 0) Lt a)
+          _ -> return Nothing
+
+-- | Convert size constraint into form where each meta is applied
+--   to indices @n-1,...,1,0@ where @n@ is the arity of that meta.
+--
+--   @X[σ] <= t@ becomes @X[id] <= t[σ^-1]@
+--
+--   @X[σ] ≤ Y[τ]@ becomes @X[id] ≤ Y[τ[σ^-1]]@ or @X[σ[τ^1]] ≤ Y[id]@
+--   whichever is defined.  If none is defined, we give up.
+--
+--   Cf. @SizedTypes.oldCanonicalizeSizeConstraint@.
+--
+--   Fixes (the rather artificial) issue 300.
+--   But it is unsound when pruned metas occur and triggers issue 1914.
+--   Thus we deactivate it.
+--   This needs to be properly implemented, possibly using the
+--   metaPermuatation of each meta variable.
+
+canonicalizeSizeConstraint :: SizeConstraint -> Maybe (SizeConstraint)
+canonicalizeSizeConstraint c@(Constraint a cmp b) = Just c
+{-
+  case (a,b) of
+
+    -- Case flex-flex
+    (Flex (SizeMeta m xs) n, Flex (SizeMeta l ys) n')
+         -- try to invert xs on ys
+       | let len = size xs
+       , Just ys' <- mapM (\ y -> (len-1 -) <$> findIndex (==y) xs) ys ->
+           return $ Constraint (Flex (SizeMeta m $ downFrom len) n)
+                           cmp (Flex (SizeMeta l ys') n')
+         -- try to invert ys on xs
+       | let len = size ys
+       , Just xs' <- mapM (\ x -> (len-1 -) <$> findIndex (==x) ys) xs ->
+           return $ Constraint (Flex (SizeMeta m xs') n)
+                           cmp (Flex (SizeMeta l $ downFrom len) n')
+         -- give up
+       | otherwise -> Nothing
+
+    -- Case flex-rigid
+    (Flex (SizeMeta m xs) n, Rigid (NamedRigid x i) n') -> do
+      let len = size xs
+      j <- (len-1 -) <$> findIndex (==i) xs
+      return $ Constraint (Flex (SizeMeta m $ downFrom len) n)
+                      cmp (Rigid (NamedRigid x j) n')
+
+    -- Case rigid-flex
+    (Rigid (NamedRigid x i) n, Flex (SizeMeta m xs) n') -> do
+      let len = size xs
+      j <- (len-1 -) <$> findIndex (==i) xs
+      return $ Constraint (Rigid (NamedRigid x j) n)
+                      cmp (Flex (SizeMeta m $ downFrom len) n')
+
+    -- Case flex-const
+    (Flex (SizeMeta m xs) n, _)      ->
+      return $ Constraint (Flex (SizeMeta m $ downFrom $ size xs) n) cmp b
+
+    -- Case const-flex
+    (_, Flex (SizeMeta m xs) n') -> do
+      return $ Constraint a cmp (Flex (SizeMeta m $ downFrom $ size xs) n')
+
+    -- Case no flex
+    _ -> return c
+-}
+
+-- | Identifiers for rigid variables.
+data NamedRigid = NamedRigid
+  { rigidName  :: String   -- ^ Name for printing in debug messages.
+  , rigidIndex :: Int      -- ^ De Bruijn index.
+  } deriving (Show)
+
+instance Eq NamedRigid where (==) = (==) `on` rigidIndex
+instance Ord NamedRigid where compare = compare `on` rigidIndex
+instance Pretty NamedRigid where pretty = P.text . rigidName
+instance Plus NamedRigid Int NamedRigid where
+  plus (NamedRigid x i) j = NamedRigid x (i + j)
+
+-- | Size metas in size expressions.
+data SizeMeta = SizeMeta
+  { sizeMetaId   :: MetaId
+  -- TODO to fix issue 300?
+  -- , sizeMetaPerm :: Permutation -- ^ Permutation from the current context
+  --                               --   to the context of the meta.
+  , sizeMetaArgs :: [Int]       -- ^ De Bruijn indices.
+  } deriving (Show)
+
+-- | An equality which ignores the meta arguments.
+instance Eq  SizeMeta where (==)    = (==)    `on` sizeMetaId
+-- | An order which ignores the meta arguments.
+instance Ord SizeMeta where compare = compare `on` sizeMetaId
+
+instance Pretty SizeMeta where pretty = P.pretty . sizeMetaId
+
+instance PrettyTCM SizeMeta where
+  prettyTCM (SizeMeta x es) = prettyTCM (MetaV x $ map (Apply . defaultArg . var) es)
+
+instance Subst SizeMeta where
+  type SubstArg SizeMeta = Term
+  applySubst sigma (SizeMeta x es) = SizeMeta x (map raise es)
+    where
+      raise i =
+        case lookupS sigma i of
+          Var j [] -> j
+          _        -> __IMPOSSIBLE__
+
+-- | Size expression with de Bruijn indices.
+type DBSizeExpr = SizeExpr' NamedRigid SizeMeta
+
+-- deriving instance Functor     (SizeExpr' Int)
+-- deriving instance Foldable    (SizeExpr' Int)
+-- deriving instance Traversable (SizeExpr' Int)
+
+-- | Only for 'raise'.
+instance Subst (SizeExpr' NamedRigid SizeMeta) where
+  type SubstArg (SizeExpr' NamedRigid SizeMeta) = Term
+  applySubst sigma a =
+    case a of
+      Infty   -> a
+      Const{} -> a
+      Flex  x n -> Flex (applySubst sigma x) n
+      Rigid r n ->
+        case lookupS sigma $ rigidIndex r of
+          Var j [] -> Rigid r{ rigidIndex = j } n
+          _        -> __IMPOSSIBLE__
+
+type SizeConstraint = Constraint' NamedRigid SizeMeta
+
+instance Subst SizeConstraint where
+  type SubstArg SizeConstraint = Term
+  applySubst sigma (Constraint a cmp b) =
+    Constraint (applySubst sigma a) cmp (applySubst sigma b)
+
+-- | Assumes we are in the right context.
+instance PrettyTCM (SizeConstraint) where
+  prettyTCM (Constraint a cmp b) = do
+    u <- unSizeExpr a
+    v <- unSizeExpr b
+    prettyTCM u <+> pretty cmp <+> prettyTCM v
+
+-- | Size constraint with de Bruijn indices.
+data HypSizeConstraint = HypSizeConstraint
+  { sizeContext    :: Context
+  , sizeHypIds     :: [Nat] -- ^ DeBruijn indices
+  , sizeHypotheses :: [SizeConstraint]  -- ^ Living in @Context@.
+  , sizeConstraint :: SizeConstraint    -- ^ Living in @Context@.
+  }
+
+instance Flexs HypSizeConstraint where
+  type FlexOf HypSizeConstraint = SizeMeta
+  flexs (HypSizeConstraint _ _ hs c) = flexs hs `mappend` flexs c
+
+instance PrettyTCM HypSizeConstraint where
+  prettyTCM (HypSizeConstraint cxt _ hs c) =
+    unsafeModifyContext (const cxt) $ do
+      let cxtNames = reverse $ map (fst . unDom) cxt
+      -- text ("[#cxt=" ++ show (size cxt) ++ "]") <+> do
+      prettyList (map prettyTCM cxtNames) <+> do
+      applyUnless (null hs)
+       ((hcat (punctuate ", " $ map prettyTCM hs) <+> "|-") <+>)
+       (prettyTCM c)
+
+-- | Turn a constraint over de Bruijn indices into a size constraint.
+computeSizeConstraint :: ProblemConstraint -> TCM (Maybe HypSizeConstraint)
+computeSizeConstraint c = do
+  let cxt = envContext $ clEnv $ theConstraint c
+  unsafeModifyContext (const cxt) $ do
+    case clValue $ theConstraint c of
+      ValueCmp CmpLeq _ u v -> do
+        reportSDoc "tc.size.solve" 50 $ sep $
+          [ "converting size constraint"
+          , prettyTCM c
+          ]
+        ma <- sizeExpr u
+        mb <- sizeExpr v
+        (hids, hs) <- unzip <$> getSizeHypotheses cxt
+        let mk a b = HypSizeConstraint cxt hids hs $ Size.Constraint a Le b
+        -- We only create a size constraint if both terms can be
+        -- parsed to our format of size expressions.
+        return $ mk <$> ma <*> mb
+      _ -> __IMPOSSIBLE__
+
+-- | Turn a term into a size expression.
+--
+--   Returns 'Nothing' if the term isn't a proper size expression.
+
+sizeExpr :: Term -> TCM (Maybe DBSizeExpr)
+sizeExpr u = do
+  u <- reduce u -- Andreas, 2009-02-09.
+                -- This is necessary to surface the solutions of metavariables.
+  reportSDoc "tc.conv.size" 60 $ "sizeExpr:" <+> prettyTCM u
+  s <- sizeView u
+  case s of
+    SizeInf     -> return $ Just Infty
+    SizeSuc u   -> fmap (`plus` (1 :: Offset)) <$> sizeExpr u
+    OtherSize u -> case u of
+      Var i []    -> (\ x -> Just $ Rigid (NamedRigid x i) 0) . prettyShow <$> nameOfBV i
+--      MetaV m es  -> return $ Just $ Flex (SizeMeta m es) 0
+      MetaV m es | Just xs <- mapM isVar es, List.fastDistinct xs
+                  -> return $ Just $ Flex (SizeMeta m xs) 0
+      _           -> return Nothing
+  where
+    isVar (Proj{})  = Nothing
+    isVar (IApply _ _ v) = isVar (Apply (defaultArg v))
+    isVar (Apply v) = case unArg v of
+      Var i [] -> Just i
+      _        -> Nothing
+
+-- | Turn a de size expression into a term.
+unSizeExpr :: HasBuiltins m => DBSizeExpr -> m Term
+unSizeExpr a =
+  case a of
+    Infty         -> fromMaybe __IMPOSSIBLE__ <$> getBuiltin' builtinSizeInf
+    Rigid r (O n) -> do
+      unless (n >= 0) __IMPOSSIBLE__
+      sizeSuc n $ var $ rigidIndex r
+    Flex (SizeMeta x es) (O n) -> do
+      unless (n >= 0) __IMPOSSIBLE__
+      sizeSuc n $ MetaV x $ map (Apply . defaultArg . var) es
+    Const{} -> __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/SizedTypes/Syntax.hs b/src/full/Agda/TypeChecking/SizedTypes/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SizedTypes/Syntax.hs
@@ -0,0 +1,342 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Syntax of size expressions and constraints.
+
+module Agda.TypeChecking.SizedTypes.Syntax where
+
+import Prelude hiding ( null )
+
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.TypeChecking.Monad.Base (TCM)
+import qualified Agda.TypeChecking.Pretty as P
+import Agda.TypeChecking.SizedTypes.Utils
+
+import Agda.Utils.Functor
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+-- * Syntax
+
+-- | Constant finite sizes @n >= 0@.
+newtype Offset = O Int
+  deriving (Eq, Ord, Num, Enum)
+
+-- This Show instance is ok because of the Num constraint.
+instance Show Offset where
+  show (O n) = show n
+
+instance Pretty Offset where
+  pretty (O n) = pretty n
+
+instance MeetSemiLattice Offset where
+  meet = min
+
+instance Plus Offset Offset Offset where
+  plus (O x) (O y) = O (plus x y)
+
+-- | Fixed size variables @i@.
+newtype Rigid  = RigidId { rigidId :: String }
+  deriving (Eq, Ord)
+
+instance Show Rigid where
+  show (RigidId s) = "RigidId " ++ show s
+
+instance Pretty Rigid where
+  pretty = text . rigidId
+
+-- | Size meta variables @X@ to solve for.
+newtype Flex   = FlexId { flexId :: String }
+  deriving (Eq, Ord)
+
+instance Show Flex where
+  show (FlexId s) = "FlexId " ++ show s
+
+instance Pretty Flex where
+  pretty = text . flexId
+
+instance P.PrettyTCM Flex where
+  prettyTCM = return . pretty
+
+-- | Size expressions appearing in constraints.
+data SizeExpr' rigid flex
+  = Const { offset :: Offset }                   -- ^ Constant number @n@.
+  | Rigid { rigid  :: rigid, offset :: Offset }  -- ^ Variable plus offset @i + n@.
+  | Infty                                        -- ^ Infinity @∞@.
+  | Flex  { flex   :: flex, offset :: Offset }   -- ^ Meta variable @X + n@.
+    deriving (Show, Eq, Ord, Functor, Foldable, Traversable)
+
+type SizeExpr = SizeExpr' Rigid Flex
+
+-- | Comparison operator, e.g. for size expression.
+data Cmp
+  = Lt  -- ^ @<@.
+  | Le  -- ^ @≤@.
+  deriving (Show, Eq, Bounded, Enum)
+
+instance Dioid Cmp where
+  compose     = min
+  unitCompose = Le
+
+-- | Comparison operator is ordered @'Lt' < 'Le'@.
+instance Ord Cmp where
+  Lt <= x  = True
+  Le <= Lt = False
+  Le <= Le = True
+
+instance MeetSemiLattice Cmp where
+  meet = min
+
+instance Top Cmp where
+  top = Le
+
+-- | Constraint: an inequation between size expressions,
+--   e.g. @X < ∞@ or @i + 3 ≤ j@.
+data Constraint' rigid flex = Constraint
+  { leftExpr  :: SizeExpr' rigid flex
+  , cmp       :: Cmp
+  , rightExpr :: SizeExpr' rigid flex
+  }
+  deriving (Show, Functor, Foldable, Traversable)
+
+type Constraint = Constraint' Rigid Flex
+
+-- * Polarities to specify solutions.
+------------------------------------------------------------------------
+
+-- | What type of solution are we looking for?
+data Polarity = Least | Greatest
+  deriving (Eq, Ord)
+
+-- | Assigning a polarity to a flexible variable.
+data PolarityAssignment flex = PolarityAssignment Polarity flex
+
+-- | Type of solution wanted for each flexible.
+type Polarities flex = Map flex Polarity
+
+emptyPolarities :: Polarities flex
+emptyPolarities = Map.empty
+
+-- Used in size-solver (Andreas, 2021-08-20)
+polaritiesFromAssignments :: Ord flex => [PolarityAssignment flex] -> Polarities flex
+polaritiesFromAssignments = Map.fromListWith __IMPOSSIBLE__ . map (\ (PolarityAssignment p x) -> (x,p))
+
+-- | Default polarity is 'Least'.
+getPolarity :: Ord flex => Polarities flex -> flex -> Polarity
+getPolarity pols x = Map.findWithDefault Least x pols
+
+-- * Solutions.
+------------------------------------------------------------------------
+
+-- | Partial substitution from flexible variables to size expression.
+newtype Solution rigid flex = Solution { theSolution :: Map flex (SizeExpr' rigid flex) }
+  deriving (Show, Null)
+
+instance (Pretty r, Pretty f) => Pretty (Solution r f) where
+  pretty (Solution sol) = prettyList $ for (Map.toList sol) $ \ (x, e) ->
+    pretty x <+> ":=" <+> pretty e
+
+emptySolution :: Solution r f
+emptySolution = Solution Map.empty
+
+-- | Executing a substitution.
+class Substitute r f a where
+  subst :: Solution r f -> a -> a
+
+instance Ord f => Substitute r f (SizeExpr' r f) where
+  subst (Solution sol) e =
+    case e of
+      Flex x n -> maybe e (`plus` n) $ Map.lookup x sol
+      _        -> e
+
+instance Ord f => Substitute r f (Constraint' r f) where
+  subst sol (Constraint e cmp e') = Constraint (subst sol e) cmp (subst sol e')
+
+instance Substitute r f a => Substitute r f [a] where
+  subst = map . subst
+
+instance Substitute r f a => Substitute r f (Map k a) where
+  subst = fmap . subst
+
+instance Ord f => Substitute r f (Solution r f) where
+  subst s = Solution . subst s . theSolution
+
+-- | Add offset to size expression.
+instance Plus (SizeExpr' r f) Offset (SizeExpr' r f) where
+  plus e m =
+    case e of
+      Const   n -> Const   $ n + m
+      Rigid i n -> Rigid i $ n + m
+      Flex x  n -> Flex x  $ n + m
+      Infty     -> Infty
+
+-- | Error messages produced by the constraint simplification monad.
+
+type Error = TCM Doc
+
+-- * Constraint simplification
+
+type CTrans r f = Constraint' r f -> Either Error [Constraint' r f]
+
+-- | Returns an error message if we have a contradictory constraint.
+simplify1 :: (Pretty f, Pretty r, Eq r) => CTrans r f -> CTrans r f
+simplify1 test c = do
+  let err = Left $ "size constraint" P.<+> P.pretty c P.<+>
+                   "is inconsistent"
+  case c of
+    -- rhs is Infty
+    Constraint a           Le  Infty -> return []
+    Constraint Const{}     Lt  Infty -> return []
+    Constraint Infty       Lt  Infty -> err
+    Constraint (Rigid i n) Lt  Infty -> test $ Constraint (Rigid i 0) Lt Infty
+    Constraint a@Flex{}    Lt  Infty -> return [c { leftExpr = a { offset = 0 }}]
+
+    -- rhs is Const
+    Constraint (Const n)   cmp (Const m) -> if compareOffset n cmp m then return [] else err
+    Constraint Infty       cmp  Const{}  -> err
+    Constraint (Rigid i n) cmp (Const m) ->
+      if compareOffset n cmp m then
+        test (Constraint (Rigid i 0) Le (Const (m - n - ifLe cmp 0 1)))
+       else err
+    Constraint (Flex x n)  cmp (Const m) ->
+      if compareOffset n cmp m
+       then return [Constraint (Flex x 0) Le (Const (m - n - ifLe cmp 0 1))]
+       else err
+
+    -- rhs is Rigid
+    Constraint Infty cmp Rigid{} -> err
+    Constraint (Const m) cmp (Rigid i n) ->
+      if compareOffset m cmp n then return []
+      else test (Constraint (Const $ m - n) cmp (Rigid i 0))
+    Constraint (Rigid j m) cmp (Rigid i n) | i == j ->
+      if compareOffset m cmp n then return [] else err
+    Constraint (Rigid j m) cmp (Rigid i n) -> test c
+    Constraint (Flex x m)  cmp (Rigid i n) ->
+      if compareOffset m cmp n
+       then return [Constraint (Flex x 0) Le (Rigid i (n - m - ifLe cmp 0 1))]
+       else return [Constraint (Flex x $ m - n + ifLe cmp 0 1) Le (Rigid i 0)]
+
+    -- rhs is Flex
+    Constraint Infty Le (Flex x n) -> return [Constraint Infty Le (Flex x 0)]
+    Constraint Infty Lt (Flex x n) -> err
+    Constraint (Const m) cmp (Flex x n) ->
+      if compareOffset m cmp n then return []
+      else return [Constraint (Const $ m - n + ifLe cmp 0 1) Le (Flex x 0)]
+    Constraint (Rigid i m) cmp (Flex x n) ->
+      if compareOffset m cmp n
+      then return [Constraint (Rigid i 0) cmp (Flex x $ n - m)]
+      else return [Constraint (Rigid i $ m - n) cmp (Flex x 0)]
+    Constraint (Flex y m) cmp (Flex x n) ->
+      if compareOffset m cmp n
+      then return [Constraint (Flex y 0) cmp (Flex x $ n - m)]
+      else return [Constraint (Flex y $ m - n) cmp (Flex x 0)]
+
+-- | 'Le' acts as 'True', 'Lt' as 'False'.
+ifLe :: Cmp -> a -> a -> a
+ifLe Le a b = a
+ifLe Lt a b = b
+
+-- | Interpret 'Cmp' as relation on 'Offset'.
+compareOffset :: Offset -> Cmp -> Offset -> Bool
+compareOffset n Le m = n <= m
+compareOffset n Lt m = n <  m
+
+-- * Printing
+
+instance (Pretty r, Pretty f) => Pretty (SizeExpr' r f) where
+  pretty (Const n)   = pretty n
+  pretty (Infty)     = "∞"
+  pretty (Rigid i 0) = pretty i
+  pretty (Rigid i n) = pretty i <> text ("+" ++ show n)
+  pretty (Flex  x 0) = pretty x
+  pretty (Flex  x n) = pretty x <> text ("+" ++ show n)
+
+instance Pretty Polarity where
+  pretty Least    = "-"
+  pretty Greatest = "+"
+
+instance Pretty flex => Pretty (PolarityAssignment flex) where
+  pretty (PolarityAssignment pol flex) = pretty pol <> pretty flex
+
+instance Pretty Cmp where
+  pretty Le = "≤"
+  pretty Lt = "<"
+
+instance (Pretty r, Pretty f) => Pretty (Constraint' r f) where
+  pretty (Constraint a cmp b) = pretty a <+> pretty cmp <+> pretty b
+
+-- * Wellformedness
+
+-- | Offsets @+ n@ must be non-negative
+class ValidOffset a where
+  validOffset :: a -> Bool
+
+instance ValidOffset Offset where
+  validOffset = (>= 0)
+
+instance ValidOffset (SizeExpr' r f) where
+  validOffset e =
+    case e of
+      Infty -> True
+      _     -> validOffset (offset e)
+
+-- | Make offsets non-negative by rounding up.
+class TruncateOffset a where
+  truncateOffset :: a -> a
+
+instance TruncateOffset Offset where
+  truncateOffset n | n >= 0    = n
+                   | otherwise = 0
+
+instance TruncateOffset (SizeExpr' r f) where
+  truncateOffset e =
+    case e of
+      Infty     -> e
+      Const n   -> Const   $ truncateOffset n
+      Rigid i n -> Rigid i $ truncateOffset n
+      Flex  x n -> Flex  x $ truncateOffset n
+
+-- * Computing variable sets
+
+-- | The rigid variables contained in a pice of syntax.
+class Ord (RigidOf a) => Rigids a where
+  type RigidOf a
+  rigids :: a -> Set (RigidOf a)
+
+instance Rigids a => Rigids [a] where
+  type RigidOf [a] = RigidOf a
+  rigids as = Set.unions (map rigids as)
+
+instance Ord r => Rigids (SizeExpr' r f) where
+  type RigidOf (SizeExpr' r f) = r
+  rigids (Rigid x _) = Set.singleton x
+
+  rigids _           = Set.empty
+
+instance Ord r => Rigids (Constraint' r f) where
+  type RigidOf (Constraint' r f) = r
+  rigids (Constraint l _ r) = Set.union (rigids l) (rigids r)
+
+-- | The flexibe variables contained in a pice of syntax.
+class Ord (FlexOf a) => Flexs a where
+  type FlexOf a
+  flexs :: a -> Set (FlexOf a)
+
+instance Flexs a => Flexs [a] where
+  type FlexOf [a] = FlexOf a
+  flexs as = Set.unions (map flexs as)
+
+instance Ord flex => Flexs (SizeExpr' rigid flex) where
+  type FlexOf (SizeExpr' rigid flex) = flex
+  flexs (Flex x _) = Set.singleton x
+  flexs _          = Set.empty
+
+instance Ord flex => Flexs (Constraint' rigid flex) where
+  type FlexOf (Constraint' rigid flex) = flex
+  flexs (Constraint l _ r) = Set.union (flexs l) (flexs r)
diff --git a/src/full/Agda/TypeChecking/SizedTypes/Utils.hs b/src/full/Agda/TypeChecking/SizedTypes/Utils.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SizedTypes/Utils.hs
@@ -0,0 +1,41 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.SizedTypes.Utils where
+
+import Data.IORef
+import qualified Debug.Trace as Debug
+import System.IO.Unsafe
+
+import Agda.Utils.Function
+
+{-# NOINLINE debug #-}
+debug :: IORef Bool
+debug = unsafePerformIO $ newIORef False
+
+setDebugging :: Bool -> IO ()
+setDebugging = writeIORef debug
+
+trace :: String -> a -> a
+trace s = applyWhen (unsafePerformIO $ readIORef debug) $ Debug.trace s
+
+traceM :: Applicative f => String -> f ()
+traceM s = trace s $ pure ()
+
+class Eq a => Top a where
+  top   :: a
+  isTop :: a -> Bool
+  isTop = (== top)
+
+class Plus a b c where
+  plus :: a -> b -> c
+
+instance Plus Int Int Int where
+  plus = (+)
+
+class MeetSemiLattice a where
+  meet :: a -> a -> a
+
+-- | Semiring with idempotent '+' == dioid
+class (MeetSemiLattice a, Top a) => Dioid a where
+  compose     :: a -> a -> a  -- ^ E.g. +
+  unitCompose :: a            -- ^ neutral element of @compose@, e.g. zero
diff --git a/src/full/Agda/TypeChecking/SizedTypes/WarshallSolver.hs b/src/full/Agda/TypeChecking/SizedTypes/WarshallSolver.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SizedTypes/WarshallSolver.hs
@@ -0,0 +1,1022 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.SizedTypes.WarshallSolver where
+
+import Prelude hiding ( null, truncate )
+
+
+import Control.Monad
+
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.TypeChecking.Pretty (PrettyTCM)
+import qualified Agda.TypeChecking.Pretty as P
+import Agda.TypeChecking.SizedTypes.Syntax
+import Agda.TypeChecking.SizedTypes.Utils
+
+import Agda.Utils.Graph.AdjacencyMap.Unidirectional
+  (Edge(..), Nodes(..), nodes, computeNodes)
+-- (Edge'(..), allNodes, emptyGraph, insertEdge, graphToList, graphFromList, nodes, lookupEdge, outgoing, incoming, diagonal, transClos)
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as Graph
+
+import Agda.Utils.Functor
+import Agda.Utils.Null
+import Agda.Syntax.Common.Pretty
+
+import Agda.Utils.Impossible
+
+type Graph r f a = Graph.Graph (Node r f) a
+type Edge' r f a = Graph.Edge  (Node r f) a
+type Key r f = Edge' r f ()
+type Nodes r f = Graph.Nodes (Node r f)
+type LabelledEdge r f = Edge' r f Label
+
+src :: Edge n e -> n
+src = Graph.source
+
+dest :: Edge n e -> n
+dest = Graph.target
+
+lookupEdge :: Ord n => Graph.Graph n e -> n -> n -> Maybe e
+lookupEdge g s t = Graph.lookup s t g
+
+graphToList :: Graph.Graph n e -> [Edge n e]
+graphToList = Graph.edges
+
+graphFromList :: Ord n => [Edge n e] -> Graph.Graph n e
+graphFromList = Graph.fromEdges
+
+insertEdge :: (Ord n, MeetSemiLattice e, Top e) =>
+              Edge n e -> Graph.Graph n e -> Graph.Graph n e
+insertEdge e g
+  | isTop (label e) = g
+  | otherwise       = Graph.insertEdgeWith meet e g
+
+-- | Compute list of edges that start in a given node.
+outgoing :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a]
+outgoing g s = Graph.edgesFrom g [s]
+
+-- | Compute list of edges that target a given node.
+--
+--   Note: expensive for unidirectional graph representations.
+incoming :: (Ord r, Ord f) => Graph r f a -> Node r f -> [Edge' r f a]
+incoming g t = Graph.edgesTo g [t]
+
+-- | @Set.foldl@ does not exist in legacy versions of the @containers@ package.
+setFoldl :: (b -> a -> b) -> b -> Set a -> b
+setFoldl step start = List.foldl' step start . Set.toAscList
+-- setFoldl = Set.foldl'
+
+-- | Floyd-Warshall algorithm.
+transClos :: forall n a . (Ord n, Dioid a) => Graph.Graph n a -> Graph.Graph n a
+transClos g = setFoldl step g $ allNodes ns
+  where
+    ns       = computeNodes g
+    srcs     = Set.toAscList $ srcNodes ns
+    dests    = Set.toAscList $ tgtNodes ns
+    -- @step g v@ adds all intermediate edges @u --> w@ via @v@ to @g@
+    -- step :: (Ord n, Dioid a) => Graph.Graph n n a -> n -> Graph.Graph n n a
+    step g v = foldl (flip insertEdge) g $
+      [ Edge u w $ l1 `compose` l2
+        | u <- srcs
+        , w <- dests
+        , l1 <- maybeToList $ lookupEdge g u v
+        , l2 <- maybeToList $ lookupEdge g v w
+      ]
+
+-- * Edge weights
+
+data Weight
+  = Offset Offset
+  | Infinity
+  deriving (Eq, Show)
+
+instance Pretty Weight where
+  pretty (Offset x) = pretty x
+  pretty Infinity   = "∞"
+
+instance Ord Weight where
+  x        <= Infinity = True
+  Infinity <= y        = False
+  Offset x <= Offset y = x <= y
+
+instance MeetSemiLattice Weight where
+  meet = min
+
+instance Top Weight where
+  top  = Infinity
+
+instance Enum Weight where
+  succ (Offset x) = Offset (succ x)
+  succ (Infinity) = Infinity
+  pred (Offset x) = Offset (pred x)
+  pred (Infinity) = Infinity
+  toEnum = Offset . toEnum
+  fromEnum (Offset x) = fromEnum x
+  fromEnum (Infinity) = __IMPOSSIBLE__
+
+-- | Partial implementation of @Num@.
+instance Num Weight where
+  Infinity + y        = Infinity
+  x + Infinity        = Infinity
+  Offset x + Offset y = Offset $ x + y
+  Infinity - Offset y = Infinity
+  Offset x - Offset y = Offset $ x - y
+  x        - Infinity = __IMPOSSIBLE__
+  abs (Offset x)      = Offset $ abs x
+  abs Infinity        = Infinity
+  signum (Offset x)   = Offset $ signum x
+  signum Infinity     = Offset $ 1
+  fromInteger x       = Offset (fromInteger x)
+  x * y = __IMPOSSIBLE__
+
+instance Plus Weight Offset Weight where
+  plus w k = w + (Offset k)
+
+-- | Test for negativity, used to detect negative cycles.
+class Negative a where
+  negative :: a -> Bool
+
+{- leads to Undecidable/OverlappingInstances:
+instance (Ord a, Num a) => Negative a where
+  negative = (< 0)
+-}
+
+instance Negative Int where
+  negative = (< 0)
+
+instance Negative Offset where
+  negative (O x) = negative x
+
+instance Negative Weight where
+  negative Infinity = False
+  negative (Offset x) = negative x
+
+-- * Edge labels
+
+-- | Going from @Lt@ to @Le@ is @pred@, going from @Le@ to @Lt@ is @succ@.
+--
+--   @X --(R,n)--> Y@
+--   means  @X (R) Y + n@.
+--   [                      ... if @n@ positive
+--     and    @X + (-n) (R) Y@  if @n@ negative. ]
+data Label
+  = Label { lcmp :: Cmp, loffset :: Offset }
+  | LInf  -- ^ Nodes not connected.
+  deriving (Show)
+
+
+-- | Convert a label to a weight, decrementing in case of 'Lt'.
+toWeight :: Label -> Weight
+toWeight (Label Le w) = Offset w
+toWeight (Label Lt w) = Offset $ pred w
+toWeight LInf         = Infinity
+
+instance Negative Label where
+  negative = negative . toWeight
+
+instance Eq Label where
+  Label cmp w == Label cmp' w' = cmp == cmp' && w == w'
+  LInf        == LInf          = True
+  _           == _             = False
+
+instance Ord Label where
+  Label Lt  w <= Label Lt w' = w <= w'
+  Label Le  w <= Label Le w' = w <= w'
+  Label Lt  w <= Label Le w' = pred w <= w'
+  Label Le  w <= Label Lt w' = succ w <= w'
+  _           <= LInf        = True
+  LInf{}      <= Label{}     = False
+
+instance Pretty Label where
+  pretty (Label cmp w) = pretty cmp <> pretty w
+  pretty LInf          = "∞"
+
+instance MeetSemiLattice Label where
+  -- one label is neutral
+  LInf       `meet` l           = l
+  l          `meet` LInf        = l
+  -- other cases
+  Label Lt w `meet` Label Lt w' = Label Lt $ w      `meet` w'
+  Label Le w `meet` Label Le w' = Label Le $ w      `meet` w'
+  Label Lt w `meet` Label Le w' = Label Lt $      w `meet` succ w'
+  Label Le w `meet` Label Lt w' = Label Lt $ succ w `meet` w'
+
+instance Top Label where
+  top                 = LInf
+  isTop Label{}       = False
+  isTop LInf          = True
+
+-- * Semiring with idempotent '+' == dioid
+
+instance Dioid Weight where
+  compose     = (+)
+  unitCompose = 0
+
+instance Dioid Label where
+  compose (Label Lt w) (Label Lt w')    = Label Lt $ pred $ w + w'
+  compose (Label cmp w) (Label cmp' w') = Label (compose cmp cmp') $ w + w'
+  compose _             LInf            = LInf
+  compose LInf          _               = LInf
+  unitCompose = Label Le 0
+
+-- * Graphs
+
+-- ** Nodes
+
+data Node rigid flex
+  = NodeZero
+  | NodeInfty
+  | NodeRigid rigid
+  | NodeFlex  flex
+  deriving (Show, Eq, Ord)
+
+instance (Pretty rigid, Pretty flex) => Pretty (Node rigid flex) where
+  pretty NodeZero      = "0"
+  pretty NodeInfty     = "∞"
+  pretty (NodeRigid x) = pretty x
+  pretty (NodeFlex  x) = pretty x
+
+isFlexNode :: Node rigid flex -> Maybe flex
+isFlexNode (NodeFlex x) = Just x
+isFlexNode _            = Nothing
+
+isZeroNode :: Node rigid flex -> Bool
+isZeroNode NodeZero{} = True
+isZeroNode _          = False
+
+isInftyNode :: Node rigid flex -> Bool
+isInftyNode NodeInfty{} = True
+isInftyNode _           = False
+
+nodeToSizeExpr :: Node rigid flex -> SizeExpr' rigid flex
+nodeToSizeExpr n =
+  case n of
+    NodeZero    -> Const 0
+    NodeInfty   -> Infty
+    NodeRigid i -> Rigid i 0
+    NodeFlex x  -> Flex x 0
+
+-- ** Edges
+
+-- | An edge is negative if its label is.
+instance Negative a => Negative (Edge' r f a) where
+  negative = negative . label
+
+instance (Ord r, Ord f, MeetSemiLattice a) => MeetSemiLattice (Edge' r f a) where
+  e@(Edge u v l) `meet` e'@(Edge u' v' l')
+    | u == u' && v == v' = Edge u v $ l `meet` l'
+    | otherwise          = __IMPOSSIBLE__
+       -- error $ show e ++ " `meet` " ++ show e'
+
+instance (Ord r, Ord f, Top a) => Top (Edge' r f a) where
+  top = __IMPOSSIBLE__
+  isTop e = isTop (label e)
+
+instance (Ord r, Ord f, Dioid a) => Dioid (Edge' r f a) where
+  e@(Edge u v l) `compose` e'@(Edge v' w l')
+   | v == v'    = Edge u w $ l `compose` l'
+   | otherwise = __IMPOSSIBLE__
+      -- error $ show e ++ " `compose` " ++ show e'
+  unitCompose  = __IMPOSSIBLE__
+
+-- ** Graphs
+
+-- | A graph forest.
+type Graphs r f a = [Graph r f a]
+
+emptyGraphs :: Graphs r f a
+emptyGraphs = []
+
+-- | Split a list of graphs @gs@ into those that mention node @n@ and those that do not.
+--   If @n@ is zero or infinity, we regard it as "not mentioned".
+mentions :: (Ord r, Ord f) => Node r f -> Graphs r f a -> (Graphs r f a, Graphs r f a)
+mentions NodeZero    gs = ([], gs)
+mentions NodeInfty   gs = ([], gs)
+mentions NodeRigid{} gs = ([], gs)
+mentions n           gs = List.partition (Set.member n . nodes) gs
+
+-- | Add an edge to a graph forest.
+--   Graphs that share a node with the edge are joined.
+addEdge :: (Ord r, Ord f, MeetSemiLattice a, Top a) => Edge' r f a -> Graphs r f a -> Graphs r f a
+addEdge e@(Edge src dest l) gs =
+  -- Note: If we started from an empty forest
+  -- and only added edges via @addEdge@, then
+  -- @gsSrc@ and @gsDest@ contain each at most one graph.
+  let (gsSrc , gsNotSrc)  = mentions src  gs
+      (gsDest, gsNotDest) = mentions dest gsNotSrc
+  in insertEdge e (Graph.unionsWith meet $ gsSrc ++ gsDest) : gsNotDest
+
+-- | Reflexive closure.  Add edges @0 -> n -> n -> oo@ for all nodes @n@.
+reflClos :: (Ord r, Ord f, Dioid a) => Set (Node r f) -> Graph r f a -> Graph r f a
+reflClos ns g = setFoldl step g ns' where
+    -- have at least the nodes in @ns@
+    ns'      = nodes g `Set.union` ns
+    -- add the trivial edges for all nodes ns'
+    step g n = foldl (flip insertEdge) g es where
+      es = [ Edge NodeZero n  unitCompose
+           , Edge n        n  unitCompose
+           , Edge n NodeInfty unitCompose
+           ]
+
+-- UNUSED
+-- -- | Reflexive-transitive closure.
+-- complete :: (Pretty a, Dioid a) => Graph r f a -> Graph r f a
+-- complete = transClos . reflClos
+
+-- | A graph is 'negative' if it contains a negative loop (diagonal edge).
+--   Makes sense on transitive graphs.
+instance (Ord r, Ord f, Negative a) => Negative (Graph r f a) where
+  negative = any negative . Graph.diagonal
+
+instance (Ord r, Ord f, Negative a) => Negative (Graphs r f a) where
+  negative = any negative
+
+-- | @h `implies` g@ if any edge in @g@ between rigids and constants
+--   is implied by a corresponding edge in @h@, which means that
+--   the edge in @g@ carries at most the information of the one in @h@.
+--
+--   Application: Constraint implication: Constraints are compatible
+--   with hypotheses.
+implies :: (Ord r, Ord f, Pretty r, Pretty f, Pretty a, Top a, Ord a, Negative a)
+  => Graph r f a -> Graph r f a -> Bool
+-- iterate 'test' over all edges in g
+implies h g = all test (graphToList g)
+  where
+    -- NB: doing the @test k l@ before the recursive @b@ gives
+    -- opportunity to short-cut the conjunction @&&@.
+    -- test :: Key -> a -> Bool
+    test k@(Edge src dest l)
+      | isZeroNode src, not (negative l) = True
+      | isInftyNode dest                 = True
+      | isJust $ isFlexNode src          = True
+      | isJust $ isFlexNode dest         = True
+      | isTop l                          = True
+      | otherwise = case lookupEdge h src dest of
+        Nothing -> False
+        Just l' ->
+          (l' <= l) || ( trace
+                           ( "edge " ++ prettyShow (l <$ k)
+                               ++ " not implied by "
+                               ++ prettyShow (l' <$ k)
+                           )
+                           $ False
+                       )
+
+-- implies h g = Map.foldlWithKey (\ b k l -> test k l && b) True g
+--   -- NB: doing the @test k l@ before the recursive @b@ gives
+--   -- opportunity to short-cut the conjunction @&&@.
+--   where
+--     -- test :: Key -> a -> Bool
+--     test k@(Edge src dest ()) l
+--       | isZeroNode src, not (negative l) = True
+--       | isInftyNode dest                 = True
+--       | isJust $ isFlexNode src          = True
+--       | isJust $ isFlexNode dest         = True
+--       | isTop l                          = True
+--       | otherwise = case lookupEdge h src dest of
+--         Nothing -> False
+--         Just l' -> if l' <= l then True else
+--           trace ("edge " ++ show (l <$ k) ++ " not implied by " ++ show (l' <$ k)) $
+--             False
+
+nodeFromSizeExpr :: SizeExpr' rigid flex -> (Node rigid flex, Offset)
+nodeFromSizeExpr = \case
+  Const   n -> (NodeZero   , n)
+  Rigid i n -> (NodeRigid i, n)
+  Flex  x n -> (NodeFlex x , n)
+  Infty     -> (NodeInfty  , 0)
+
+edgeFromConstraint :: Constraint' rigid flex -> LabelledEdge rigid flex
+edgeFromConstraint (Constraint lexp cmp rexp) =
+  let (leftNode , n) = nodeFromSizeExpr lexp
+      (rightNode, m) = nodeFromSizeExpr rexp
+  in Edge leftNode rightNode (Label cmp $ m - n)
+
+-- | Build a graph from list of simplified constraints.
+graphFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graph rigid flex Label
+graphFromConstraints cs =
+  let -- convert to edges
+      edges = map edgeFromConstraint cs
+      -- build a graph from the edges
+      g     = foldl (flip insertEdge) Graph.empty edges
+  in  g
+
+-- | Build a graph from list of simplified constraints.
+graphsFromConstraints :: (Ord rigid, Ord flex) => [Constraint' rigid flex] -> Graphs rigid flex Label
+graphsFromConstraints cs =
+  let -- convert to edges
+      edges = map edgeFromConstraint cs
+      -- get all the flexibles mentioned in constraints
+      xs    = Set.toList $ flexs cs
+      -- for each flexible X, add edges 0 <= X and X <= oo
+      fedges = concat $ forM xs $ \ x ->
+        [ Edge NodeZero (NodeFlex x) (Label Le 0)
+        , Edge (NodeFlex x) NodeInfty (Label Le 0)
+        ]
+      -- build a graph from the edges
+      gs    = foldl (flip addEdge) emptyGraphs (fedges ++ edges)
+  in  gs
+
+-- Build hypotheses graph, complete it, check for negative loops.
+
+type Hyp = Constraint
+type Hyp' = Constraint'
+type HypGraph r f = Graph r f Label
+
+hypGraph :: (Ord rigid, Ord flex, Pretty rigid, Pretty flex) =>
+  Set rigid -> [Hyp' rigid flex] -> Either Error (HypGraph rigid flex)
+hypGraph is hyps0 = do
+  -- get a list of hypothesis from a list of constraints
+  hyps <- concat <$> mapM (simplify1 $ \ c -> return [c]) hyps0
+  let g = transClos $
+            reflClos (Set.mapMonotonic NodeRigid is) $
+              graphFromConstraints hyps
+  when (negative g) $ Left "size hypotheses graph has negative loop"
+  return g
+
+hypConn :: (Ord r, Ord f) => HypGraph r f -> Node r f -> Node r f -> Label
+-- hypConn hg NodeZero n2  = Label Le 0  -- WRONG: not the best information
+-- hypConn hg n1 NodeInfty = Label Le 0
+hypConn hg n1 n2
+  | n1 == n2                                = Label Le 0
+  | Just l <- lookupEdge hg n1 n2 = l
+  | otherwise                               = top
+
+simplifyWithHypotheses ::
+  (Ord rigid, Ord flex, Pretty rigid, Pretty flex) =>
+  HypGraph rigid flex -> [Constraint' rigid flex] ->
+  Either Error [Constraint' rigid flex]
+simplifyWithHypotheses hg cons = concat <$> mapM (simplify1 test) cons
+  where
+    -- Test whether a constraint is compatible with the hypotheses:
+    -- Succeeds, if constraint is implied by hypotheses,
+    -- fails otherwise.
+    test c = do
+      let Edge n1 n2 l = edgeFromConstraint c
+          l' = hypConn hg n1 n2
+      -- l' <- lookupEdge hg n1 n2
+      unless (l' <= l) $ Left $
+        "size constraint" P.<+> P.pretty c P.<+>
+        "not consistent with size hypotheses"
+      return [c]
+      -- if (l' <= l) then Just [c] else Nothing
+
+-- Build constraint graph, complete it, check for negative loops.
+-- Check that hypotheses graph implies constraint graphs (rigids).
+
+type ConGraph r f = Graph r f Label
+
+constraintGraph ::
+  (Ord r, Ord f, Pretty r, Pretty f) =>
+  [Constraint' r f] -> HypGraph r f -> Either Error (ConGraph r f)
+constraintGraph cons0 hg = do
+  traceM $ "original constraints cons0 = " ++ prettyShow cons0
+  -- Simplify constraints, ensure they are locally consistent with
+  -- hypotheses.
+  cons <- simplifyWithHypotheses hg cons0
+  traceM $ "simplified constraints cons = " ++ prettyShow cons
+  -- Build a transitive graph from constraints.
+  let g = transClos $ graphFromConstraints cons
+  traceM $ "transitive graph g = " ++ prettyShow (graphToList g)
+  -- Ensure it has no negative loops.
+  when (negative g) $ Left $
+    "size constraint graph has negative loops"
+  -- Ensure it does not constrain the hypotheses.
+  unless (hg `implies` g) $ Left $
+    "size constraint graph constrains size hypotheses"
+  return g
+
+type ConGraphs r f = Graphs r f Label
+
+constraintGraphs ::
+  (Ord r, Ord f, Pretty r, Pretty f) =>
+  [Constraint' r f] -> HypGraph r f -> Either Error ([f], ConGraphs r f)
+constraintGraphs cons0 hg = do
+  traceM $ "original constraints cons0 = " ++ prettyShow cons0
+  -- Simplify constraints, ensure they are locally consistent with
+  -- hypotheses.
+  cons <- simplifyWithHypotheses hg cons0
+  traceM $ "simplified constraints cons = " ++ prettyShow cons
+  -- Build a transitive graph forest from constraints.
+  let gs0 = graphsFromConstraints cons
+  traceM $ "constraint forest gs0 = " ++ prettyShow (map graphToList gs0)
+  let gs1 = map transClos gs0
+  traceM $ "transitive forest gs1 = " ++ prettyShow (map graphToList gs1)
+  -- Check for flexibles to be set to infinity
+  let (xss,gs) = unzip $ map infinityFlexs gs1
+      xs       = concat xss
+  unless (null xs) $ do
+    traceM $ "flexibles to set to oo = " ++ prettyShow xs
+    traceM $ "forest after oo-subst  = " ++ prettyShow (map graphToList gs)
+  -- Ensure none has negative loops.
+  when (negative gs) $ Left $ "size constraint graph has negative loop"
+  traceM $ "we are free of negative loops"
+  -- Ensure it does not constrain the hypotheses.
+  forM_ gs $ \ g -> unless (hg `implies` g) $ Left $
+    "size constraint graph constrains size hypotheses"
+  traceM $ "any constraint between rigids is implied by the hypotheses"
+  return (xs, gs)
+
+-- | If we have an edge @X + n <= X@ (with n >= 0), we must set @X = oo@.
+infinityFlexs :: (Ord r, Ord f) => ConGraph r f -> ([f], ConGraph r f)
+infinityFlexs g = (infFlexs, setToInfty infFlexs g)
+  where
+    -- get the flexibles that need to be set to infinity
+    infFlexs = mapMaybe flexNeg $ Graph.diagonal g
+    flexNeg e = do
+      guard $ negative e
+      isFlexNode (src e)
+
+class SetToInfty f a where
+  setToInfty :: [f] -> a -> a
+
+instance (Eq f) => SetToInfty f (Node r f) where
+  setToInfty xs (NodeFlex x) | x `elem` xs = NodeInfty
+  setToInfty xs n = n
+
+instance (Eq f) => SetToInfty f (Edge' r f a) where
+  setToInfty xs (Edge n1 n2 l) = Edge (setToInfty xs n1) (setToInfty xs n2) l
+
+instance (Ord r, Ord f) => SetToInfty f (ConGraph r f) where
+  setToInfty xs = graphFromList . filter h . map (setToInfty xs) . graphToList
+    where
+      -- filter out edges @oo + k <= oo@
+      h (Edge NodeInfty NodeInfty (Label Le _)) = False
+      h _ = True
+
+
+-- * Compute solution from constraint graph.
+
+instance Plus Offset Weight Weight where
+  plus e Infinity   = Infinity
+  plus e (Offset x) = Offset $ plus e x
+
+instance Plus (SizeExpr' r f) Weight (SizeExpr' r f) where
+  plus e Infinity   = Infty
+  plus e (Offset x) = plus e x
+
+instance Plus (SizeExpr' r f) Label (SizeExpr' r f) where
+  plus e l = plus e (toWeight l)
+
+-- | Lower or upper bound for a flexible variable
+type Bound r f = Map f (Set (SizeExpr' r f))
+
+emptyBound :: Bound r f
+emptyBound = Map.empty
+
+data Bounds r f = Bounds
+  { lowerBounds :: Bound r f
+  , upperBounds :: Bound r f
+  , mustBeFinite :: Set f
+    -- ^ These metas are < ∞.
+  }
+
+-- | Compute a lower bound for a flexible from an edge.
+edgeToLowerBound :: LabelledEdge r f -> Maybe (f, SizeExpr' r f)
+edgeToLowerBound e =
+  case e of
+    (Edge n1 n2 LInf) -> __IMPOSSIBLE__
+    (Edge NodeZero (NodeFlex x) (Label Le o)) | o >= 0 -> Just (x, Const 0)
+    (Edge NodeZero (NodeFlex x) (Label Lt o)) | o >= 1 -> Just (x, Const 0)
+    (Edge n1 (NodeFlex x) l) -> Just (x, nodeToSizeExpr n1 `plus` (- (toWeight l)))
+    _ -> Nothing
+
+-- | Compute an upper bound for a flexible from an edge.
+edgeToUpperBound :: LabelledEdge r f -> Maybe (f, Cmp, SizeExpr' r f)
+edgeToUpperBound e =
+  case e of
+    (Edge n1 n2 LInf) -> __IMPOSSIBLE__
+    (Edge n1           NodeInfty (Label Le _)) -> Nothing
+    (Edge (NodeFlex x) NodeInfty (Label Lt _)) -> Just (x, Lt, Infty)
+    (Edge (NodeFlex x) n2        l           ) -> Just (x, Le, nodeToSizeExpr n2 `plus` (toWeight l))
+    _ -> Nothing
+
+-- | Compute the lower bounds for all flexibles in a graph.
+graphToLowerBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> Bound r f
+graphToLowerBounds = flip foldl emptyBound $ \ bs e ->
+  case edgeToLowerBound e of
+    Nothing          -> bs
+    Just (x, Flex{}) -> bs  -- ignore flexible bounds
+    Just (x, a)      -> Map.insertWith Set.union x (Set.singleton a) bs
+
+-- | Compute the upper bounds for all flexibles in a graph.
+graphToUpperBounds :: (Ord r, Ord f) => [LabelledEdge r f] -> (Bound r f, Set f)
+graphToUpperBounds = flip foldl (emptyBound, Set.empty) $ \ (bs, fs) e ->
+  case edgeToUpperBound e of
+    Nothing             -> (bs, fs)
+    Just (x, _, Flex{}) -> (bs, fs)  -- ignore flexible bounds
+    Just (x, Lt, Infty) -> (bs, Set.insert x fs)
+    Just (x, Le, a)     -> (Map.insertWith Set.union x (Set.singleton a) bs, fs)
+    _                   -> __IMPOSSIBLE__
+
+-- | Compute the bounds for all flexibles in a graph.
+bounds :: (Ord r, Ord f) => ConGraph r f -> Bounds r f
+bounds g = Bounds lbs ubs fs
+  where edges     = graphToList g
+        lbs       = graphToLowerBounds edges
+        (ubs, fs) = graphToUpperBounds edges
+
+
+-- | Compute the relative minima in a set of nodes (those that do not have
+--   a predecessor in the set).
+smallest ::(Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f]
+smallest hg ns
+  | NodeZero `elem` ns = [NodeZero]
+  | otherwise          = filter hasNoPred ns where
+      hasNoPred NodeInfty = False
+      hasNoPred n = null $ mapMaybe strictEdge ns where
+        -- is there an edge n -l-> n' with l <= 0
+        strictEdge n' = do
+          guard (n /= n')  -- exclude loops
+          l <- lookupEdge hg n' n
+          guard (toWeight l <= 0)
+          return ()
+
+-- | Compute the relative maxima in a set of nodes (those that do not have
+--   a successor in the set).
+largest ::(Ord r, Ord f) => HypGraph r f -> [Node r f] -> [Node r f]
+largest hg ns
+  | NodeInfty `elem` ns = [NodeInfty]
+  | otherwise          = filter hasNoSucc ns where
+      hasNoSucc NodeZero = False
+      hasNoSucc n = null $ mapMaybe strictEdge ns where
+        -- is there an edge n -l-> n' with l <= 0
+        strictEdge n' = do
+          guard (n /= n')  -- exclude loops
+          l <- lookupEdge hg n n'
+          guard (toWeight l <= 0)
+          return ()
+
+{-|  Given source nodes n1,n2,... find all target nodes m1,m2, such
+     that for all j, there are edges  n_i --l_ij--> m_j  for all i.
+     Return these edges as a map from target notes to a list of edges.
+     We assume the graph is reflexive-transitive.
+ -}
+commonSuccs :: (Ord r, Ord f) =>
+               Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a]
+commonSuccs hg srcs = intersectAll $ map (buildmap . outgoing hg) srcs
+  where
+   buildmap            = Map.fromListWith __IMPOSSIBLE__ . map (\ e -> (dest e, [e]))
+     -- __IMPOSSIBLE__ because it is not a multi-graph; there is at most one egde per (src,dest)
+   intersectAll []     = Map.empty
+   intersectAll (m:ms) = foldl (Map.intersectionWith (++)) m ms
+
+{-|  Given target nodes m1,m2,... find all source nodes n1,n2, such
+     that for all j, there are edges  n_i --l_ij--> m_j  for all i.
+     Return these edges as a map from target notes to a list of edges.
+     We assume the graph is reflexive-transitive.
+ -}
+commonPreds :: (Ord r, Ord f) => Graph r f a -> [Node r f] -> Map (Node r f) [Edge' r f a]
+commonPreds hg tgts = intersectAll $  map (buildmap . incoming hg) tgts
+  where
+   buildmap = Map.fromListWith __IMPOSSIBLE__ . map (\ e -> (src e, [e]))
+   intersectAll []     = Map.empty
+   intersectAll (m:ms) = foldl (Map.intersectionWith (++)) m ms
+
+-- | Compute the sup of two different rigids or a rigid and a constant.
+lub'
+  :: forall r f . (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f)
+  => HypGraph r f
+  -> (Node r f, Offset)
+  -> (Node r f, Offset)
+  -> Maybe (SizeExpr' r f)
+lub' hg (node1, n) (node2, m) = do
+  let sucs     = commonSuccs hg [node1, node2]
+      sucNodes = smallest hg $ Map.keys sucs
+  traceM ("lub': sucs = " ++ show sucs) -- FIXME: prettyShow
+  case sucNodes of
+    -- there is a unique smallest common successor n0 of node1 and node2
+    [n0] -> do
+      -- then there are exactly two edges node1 --l1--> n0 and node2 --l2--> n0
+      -- Andreas, 2017-04-28, issue #2558: The following invariant does not hold always
+      -- -- with non-positive weights l1, l2
+      let es = fromMaybe __IMPOSSIBLE__ $ Map.lookup n0 sucs
+      case es of
+        [ Edge node1x n1 l1 ,
+          Edge node2x n2 l2 ] -> do
+          unless (n0 == n1)         __IMPOSSIBLE__
+          unless (n0 == n2)         __IMPOSSIBLE__
+          unless (node1 == node1x)  __IMPOSSIBLE__
+          unless (node2 == node2x)  __IMPOSSIBLE__
+          -- Andreas, 2017-04-28, issue #2558: The following invariant does not hold always
+          -- unless (toWeight l1 <= 0) __IMPOSSIBLE__
+          -- unless (toWeight l2 <= 0) __IMPOSSIBLE__
+          let o :: Weight
+              o = max (n `plus` toWeight l1) (m `plus` toWeight l2)
+          return $ nodeToSizeExpr n0 `plus` o
+        _ -> __IMPOSSIBLE__
+    -- otherwise, we cannot compute the sup
+    _ -> do
+      let a1 :: SizeExpr' r f = nodeToSizeExpr node1 `plus` n
+      let a2 :: SizeExpr' r f = nodeToSizeExpr node2 `plus` m
+      traceM ("cannot compute lub of " ++ prettyShow a1 ++ " and " ++ prettyShow a2 ++ " because sucNodes = " ++ prettyShow sucNodes)
+      Nothing
+
+-- | Compute the inf of two different rigids or a rigid and a constant.
+glb'
+  :: forall r f . (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f)
+  => HypGraph r f
+  -> (Node r f, Offset)
+  -> (Node r f, Offset)
+  -> Maybe (SizeExpr' r f)
+glb' hg (node1, n) (node2, m) = do
+  let preds     = commonPreds hg [node1, node2]
+      predNodes = largest hg $ Map.keys preds
+  traceM ("glb': preds = " ++ show preds) -- FIXME: prettyShow
+  case predNodes of
+    -- there is a unique greatest common predecessor n0 of node1 and node2
+    [n0] -> do
+      -- then there are exactly two edges n0 --l1--> node1 and n0 --l2--> node2
+      -- Andreas, 2017-04-28, issue #2558: The following invariant may not hold always
+      -- -- with non-positive weigths l1, l2
+      let es = fromMaybe __IMPOSSIBLE__ $ Map.lookup n0 preds
+      case es of
+        [ Edge n1 node1x l1 ,
+          Edge n2 node2x l2] -> do
+          unless (n0 == n1)         __IMPOSSIBLE__
+          unless (n0 == n2)         __IMPOSSIBLE__
+          unless (node1 == node1x)  __IMPOSSIBLE__
+          unless (node2 == node2x)  __IMPOSSIBLE__
+          -- Andreas, 2017-04-28, issue #2558: The following invariant may not hold always
+          -- unless (toWeight l1 <= 0) __IMPOSSIBLE__
+          -- unless (toWeight l2 <= 0) __IMPOSSIBLE__
+          let o :: Weight
+              o = max (n `plus` toWeight l1) (m `plus` toWeight l2)
+          return $ nodeToSizeExpr n0 `plus` o
+        _ -> __IMPOSSIBLE__
+    -- otherwise, we cannot compute the sup
+    _ -> do
+      let a1 :: SizeExpr' r f = nodeToSizeExpr node1 `plus` n
+      let a2 :: SizeExpr' r f = nodeToSizeExpr node2 `plus` m
+      traceM ("cannot compute glb of " ++ prettyShow a1 ++ " and " ++ prettyShow a2 ++ " because predNodes = " ++ prettyShow predNodes)
+      Nothing
+
+-- | Compute the least upper bound (sup).
+lub
+  :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f)
+  => HypGraph r f
+  -> SizeExpr' r f
+  -> SizeExpr' r f
+  -> Maybe (SizeExpr' r f)
+lub hg a1 a2 =
+  case (a1, a2) of
+    (Flex{}, _)   -> __IMPOSSIBLE__
+    (_, Flex{})   -> __IMPOSSIBLE__
+    (Infty, a2)   -> Just Infty
+    (a1, Infty)   -> Just Infty
+    (Const n  , Const m  )
+                  -> Just $ Const $ max n m
+    (Const n  , Rigid j m)
+      | m >= n    -> Just a2
+      | otherwise -> lub' hg (NodeZero, n) (NodeRigid j, m)
+    (Rigid i n, Const m  )
+      | n >= m    -> Just a1
+      | otherwise -> lub' hg (NodeRigid i, n) (NodeZero, m)
+    (Rigid i n, Rigid j m)
+      | i == j    -> Just $ Rigid i $ max n m
+      | otherwise -> lub' hg (NodeRigid i, n) (NodeRigid j, m)
+
+{- Finding the glb of two rigid size expressions in hypotheses graph
+
+  a1 = Rigid i n
+  a2 = Rigid j m
+
+  Find the topological predecessors of (NodeRigid i)
+  Find the topological predecessors of (NodeRigid j)
+
+-}
+
+-- | Compute the greatest lower bound (inf) of size expressions relative
+--   to a hypotheses graph.
+glb
+  :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f)
+  => HypGraph r f
+  -> SizeExpr' r f
+  -> SizeExpr' r f
+  -> Maybe (SizeExpr' r f)
+glb hg a1 a2 =
+  case (a1, a2) of
+    (Flex{}, _) -> __IMPOSSIBLE__
+    (_, Flex{}) -> __IMPOSSIBLE__
+    (Infty, a2) -> Just a2
+    (a1, Infty) -> Just a1
+    (Const n  , Const m  )          -> Just $ Const $ min n m
+    (Const n  , Rigid i m)
+      | n <= m    -> Just a1
+      | otherwise -> glb' hg (NodeZero, n) (NodeRigid i, m)
+    (Rigid i n, Const m  )
+      | m <= n    -> Just a2
+      | otherwise -> glb' hg (NodeRigid i, n) (NodeZero, m)
+    (Rigid i n, Rigid j m)
+      | i == j    -> Just $ Rigid i $ min n m
+      | otherwise -> glb' hg (NodeRigid i, n) (NodeRigid j, m)
+{-
+    (Rigid i n, Rigid j m) -> do
+      let iLeqj = Map.lookup (Edge (NodeRigid i) (NodeRigid j) ()) hg
+          jLeqi = Map.lookup (Edge (NodeRigid j) (NodeRigid i) ()) hg
+      case (iLeqj, jLeqi) of
+        (Nothing, Nothing) -> Nothing -- maximum as size expression
+        (Just l, Nothing) | Offset k <- toWeight l ->
+          if k + n <= m then Just a1
+          else Nothing -- no guaranteed infimum
+        (Nothing, Just l) | Offset k <- toWeight l ->
+          if k + m <= n then Just a2
+          else Nothing
+        (Just{}, Just{}) -> Nothing
+{-
+      let lbi = incoming hg (NodeRigid i)
+          lbj = incoming hg (NodeRigid j)
+          srci = Set.fromList $ map src lbi
+          srcj = Set.fromList $ map src lbj
+          srcs =  Set.intersection srci srcj
+-}
+    _ -> trace ("cannot compute glb of " ++ prettyShow a1 ++ " and " ++ prettyShow a2) $
+      Nothing -- TODO!
+-}
+
+findRigidBelow :: (Ord r, Ord f) => HypGraph r f -> (SizeExpr' r f) -> Maybe (SizeExpr' r f)
+findRigidBelow hg (Rigid i m) | m < 0 = do
+  let v     = NodeRigid i
+      preds = incoming hg v
+      filt e@(Edge n n' l)
+        | n' == v   =
+          case toWeight l of
+            Infinity -> Nothing
+            Offset o -> if o <= m then Just (n, o) else Nothing
+        | otherwise = __IMPOSSIBLE__
+            -- error $ "findRigidBelow: impossible: " ++ prettyShow e
+      cands = mapMaybe filt preds
+  (n, o) <- do
+    case cands of
+      []  -> Nothing
+      [c] -> return c
+      _   -> return $
+               List.maximumBy (compare `on` snd) $
+                 filter ((NodeZero /=) . fst) cands
+  let offset = m - o
+  unless (offset >= 0) __IMPOSSIBLE__
+  return $ nodeToSizeExpr n `plus` offset
+findRigidBelow hg e = __IMPOSSIBLE__
+  -- error $ "findRigidBelow: impossible: " ++ prettyShow e
+
+
+solveGraph
+  :: (Ord r, Ord f, Pretty r, Pretty f, PrettyTCM f, Show r, Show f)
+  => Polarities f
+  -> HypGraph r f
+  -> ConGraph r f
+  -> Either Error (Solution r f)
+solveGraph pols hg g = do
+  let (Bounds lbs ubs fs) = bounds g
+      -- flexibles to solve for
+      xs = Set.toAscList $ Set.unions [ Map.keysSet lbs, Map.keysSet ubs, fs ]
+  -- iterate over all flexible variables
+  xas <- catMaybes <$> do
+    forM xs $ \ x -> fmap (x,) <$> do
+      -- get lower and upper bounds for flexible x
+      let lx = Set.toList $ Map.findWithDefault Set.empty x lbs
+          ux = Set.toList $ Map.findWithDefault Set.empty x ubs
+      traceM ("lower bounds for " ++ prettyShow x ++ ": " ++ prettyShow lx)
+      traceM ("upper bounds for " ++ prettyShow x ++ ": " ++ prettyShow ux)
+      -- compute maximum of lower bounds
+      lb <- do
+        case lx of
+          []     -> return $ Nothing
+          (a:as) -> do
+            case foldM (lub hg) a as of
+              Just l  -> return $ Just $ truncateOffset l
+              Nothing -> Left $
+                "inconsistent lower bound for" P.<+> P.prettyTCM x
+      -- compute minimum of upper bounds
+      ub <- do
+        case ux of
+          []     -> return $ Nothing
+          (a:as) -> do
+            case foldM (glb hg) a as of
+              Just l | validOffset l                  -> return $ Just l
+                     | Just l' <- findRigidBelow hg l -> return $ Just l'
+              _ -> Left $
+                "inconsistent upper bound for" P.<+> P.prettyTCM x
+      case (lb, ub) of
+        (Just l, Nothing) -> return $ Just l  -- solve x = lower bound
+        (Nothing, Just u) -> return $ Just u  -- solve x = upper bound
+        (Just l,  Just u) -> do
+          traceM ("lower bound for " ++ prettyShow x ++ ": " ++ prettyShow l)
+          traceM ("upper bound for " ++ prettyShow x ++ ": " ++ prettyShow u)
+          case getPolarity pols x of
+            Least    -> return $ Just l
+            Greatest -> return $ Just u
+        _ -> return Nothing
+  return $ Solution $ Map.fromDistinctAscList xas
+
+-- | Solve a forest of constraint graphs relative to a hypotheses graph.
+--   Concatenate individual solutions.
+solveGraphs
+  :: (Ord r, Ord f, Pretty r, Pretty f, PrettyTCM f, Show r, Show f)
+  => Polarities f
+  -> HypGraph r f
+  -> ConGraphs r f
+  -> Either Error (Solution r f)
+solveGraphs pols hg gs =
+  Solution . Map.unions <$> mapM (theSolution <.> solveGraph pols hg) gs
+
+-- * Verify solution
+
+-- | Check that after substitution of the solution,
+--   constraints are implied by hypotheses.
+verifySolution
+  :: (Ord r, Ord f, Pretty r, Pretty f, Show r, Show f)
+  => HypGraph r f
+  -> [Constraint' r f]
+  -> Solution r f
+  -> Either Error ()
+verifySolution hg cs sol = do
+  cs <- return $ subst sol cs
+  traceM $ "substituted constraints " ++ prettyShow cs
+  cs <- -- maybe (Left "solution produces inconsistency") Right $
+          concat <$> mapM (simplify1 $ \ c -> return [c]) cs
+  traceM $ "simplified substituted constraints " ++ prettyShow cs
+  -- cs <- maybe (Left "solution produces inconsistency") Right $
+  --         simplifyWithHypotheses hg cs
+  let g = graphFromConstraints cs
+  unless (hg `implies` g) $
+    Left "solution not implied by hypotheses"
+{-
+  case simplifyWithHypotheses hg $ subst sol cs of
+    Nothing -> Left "solution produces inconsistency"
+    Just [] -> Right ()
+    Just cs -> Left $ "solution leaves constraints " ++ prettyShow cs
+-}
+
+-- | Iterate solver until no more metas can be solved.
+--
+--   This might trigger a (wanted) error on the second iteration (see Issue 2096)
+--   which would otherwise go unnoticed.
+
+iterateSolver
+  :: (Ord r, Ord f, Pretty r, Pretty f, PrettyTCM f, Show r, Show f)
+  => Polarities f
+     -- ^ Meta variable polarities (prefer lower or upper solution?).
+  -> HypGraph r f
+     -- ^ Hypotheses (assumed to have no metas, so, fixed during iteration).
+  -> [Constraint' r f]
+     -- ^ Constraints to solve.
+  -> Solution r f
+     -- ^ Previous substitution (already applied to constraints).
+  -> Either Error (Solution r f)
+     -- ^ Accumulated substition.
+
+iterateSolver pols hg cs sol0 = do
+  g <- constraintGraph cs hg
+  sol <- solveGraph pols hg g
+  traceM $ "(partial) solution " ++ prettyShow sol
+  if null sol then return sol0 else
+    iterateSolver pols hg (subst sol cs) $ Solution $
+      Map.unionWith __IMPOSSIBLE__ (theSolution sol) $
+        theSolution $ subst sol sol0
+
+-- * Tests
+
+testSuccs :: Ord f => Map (Node [Char] f) [Edge' [Char] f Label]
+testSuccs = commonSuccs hg [n1,n2]
+  where
+    n1 = NodeRigid "i"
+    n2 = NodeRigid "j"
+    n3 = NodeRigid "k"
+    n4 = NodeRigid "l"
+    n5 = NodeRigid "m"
+    hg = Graph.fromEdges
+         [ Graph.Edge n1 n3 $ Label Le 1
+         , Graph.Edge n1 n4 $ Label Le 2
+         , Graph.Edge n1 n5 $ Label Le 3
+         , Graph.Edge n2 n3 $ Label Le 4
+         , Graph.Edge n2 n4 $ Label Le 5
+         , Graph.Edge n2 n5 $ Label Le 6
+         ]
+
+-- testLub = smallest hg $ Map.keys $ commonSuccs hg [n1,n2] --
+testLub :: (Pretty f, Ord f, Show f) => Maybe (SizeExpr' [Char] f)
+testLub = lub hg (Rigid "i" 0) (Rigid "j" 2)
+  where
+    n1 = NodeRigid "i"
+    n2 = NodeRigid "j"
+    n3 = NodeRigid "k"
+    n4 = NodeRigid "l"
+    n5 = NodeRigid "m"
+    hg = Graph.fromEdges
+         [ Graph.Edge n1 n3 $ Label Le 0
+         , Graph.Edge n1 n4 $ Label Le 2
+         , Graph.Edge n1 n5 $ Label Le 4
+         , Graph.Edge n2 n3 $ Label Le 1
+         , Graph.Edge n2 n4 $ Label Le 3
+         , Graph.Edge n2 n5 $ Label Le 5
+         , Graph.Edge n3 n4 $ Label Le 0
+         , Graph.Edge n3 n5 $ Label Lt 0
+         ]
diff --git a/src/full/Agda/TypeChecking/Sort.hs b/src/full/Agda/TypeChecking/Sort.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Sort.hs
@@ -0,0 +1,280 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ScopedTypeVariables #-}
+
+-- | This module contains the rules for Agda's sort system viewed as a pure
+--   type system (pts). The specification of a pts consists of a set
+--   of axioms of the form @s1 : s2@ specifying when a sort fits in
+--   another sort, and a set of rules of the form @(s1,s2,s3)@
+--   specifying that a pi type with domain in @s1@ and codomain in
+--   @s2@ itself fits into sort @s3@.
+--
+--   To ensure unique principal types, the axioms and rules of Agda's
+--   pts are given by two partial functions @univSort'@ and @piSort'@
+--   (see @Agda.TypeChecking.Substitute@). If these functions return
+--   @Nothing@, a constraint is added to ensure that the sort will be
+--   computed eventually.
+--
+--   One 'upgrade' over the standard definition of a pts is that in a
+--   rule @(s1,s2,s3)@, in Agda the sort @s2@ can depend on a variable
+--   of some type in @s1@. This is needed to support Agda's universe
+--   polymorphism where we can have e.g. a function of type @∀ {ℓ} →
+--   Set ℓ@.
+
+module Agda.TypeChecking.Sort where
+
+import Control.Monad
+import Control.Monad.Except
+
+import Data.Functor
+import Data.Maybe
+
+import Agda.Interaction.Options (optCumulativity, optRewriting)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import {-# SOURCE #-} Agda.TypeChecking.Constraints () -- instance only
+import {-# SOURCE #-} Agda.TypeChecking.Conversion
+import {-# SOURCE #-} Agda.TypeChecking.MetaVars () -- instance only
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Constraints (addConstraint, MonadConstraint)
+import Agda.TypeChecking.Monad.Context
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.MetaVars (metaType)
+import Agda.TypeChecking.Monad.Pure
+import Agda.TypeChecking.Monad.Signature (HasConstInfo(..), applyDef)
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Records (getDefType)
+import Agda.TypeChecking.ProjectionLike
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible
+
+{-# SPECIALIZE inferUnivSort :: Sort -> TCM Sort #-}
+-- | Infer the sort of another sort. If we can compute the bigger sort
+--   straight away, return that. Otherwise, return @UnivSort s@ and add a
+--   constraint to ensure we can compute the sort eventually.
+inferUnivSort
+  :: (PureTCM m, MonadConstraint m)
+  => Sort -> m Sort
+inferUnivSort s = do
+  s <- reduce s
+  case univSort' s of
+    Right s' -> return s'
+    Left _ -> do
+      -- Jesper, 2020-04-19: With the addition of Setωᵢ and the PTS
+      -- rule SizeUniv : Setω, every sort (with no metas) now has a
+      -- bigger sort, so we do not need to add a constraint.
+      -- addConstraint $ HasBiggerSort s
+      return $ UnivSort s
+
+{-# SPECIALIZE sortFitsIn :: Sort -> Sort -> TCM () #-}
+sortFitsIn :: MonadConversion m => Sort -> Sort -> m ()
+sortFitsIn a b = do
+  b' <- inferUnivSort a
+  ifM (optCumulativity <$> pragmaOptions)
+    (leqSort b' b)
+    (equalSort b' b)
+
+hasBiggerSort :: Sort -> TCM ()
+hasBiggerSort = void . inferUnivSort
+
+{-# SPECIALIZE inferPiSort :: Dom Type -> Abs Sort -> TCM Sort #-}
+-- | Infer the sort of a Pi type.
+--   If we can compute the sort straight away, return that.
+--   Otherwise, return a 'PiSort' and add a constraint to ensure we can compute the sort eventually.
+--
+inferPiSort :: (PureTCM m, MonadConstraint m)
+  => Dom Type  -- ^ Domain of the Pi type.
+  -> Abs Sort  -- ^ (Dependent) sort of the codomain of the Pi type.
+  -> m Sort    -- ^ Sort of the Pi type.
+inferPiSort a s = do
+  s1' <- reduceB $ getSort a
+  s2' <- mapAbstraction a reduceB s
+  let s1 = ignoreBlocking s1'
+  let s2 = ignoreBlocking <$> s2'
+  --Jesper, 2018-04-23: disabled PTS constraints for now,
+  --this assumes that piSort can only be blocked by unsolved metas.
+  --Arthur Adjedj, 2023-02-27, Turned PTS back on,
+  --piSort can now be blocked by Leveluniv
+  case piSort' (unEl <$> a) s1 s2 of
+    Right s -> return s
+    Left b -> do
+      let b' = unblockOnEither (getBlocker s1') (getBlocker $ unAbs s2')
+      addConstraint (unblockOnEither b b') $ HasPTSRule a s2
+      return $ PiSort (unEl <$> a) s1 s2
+
+{-# SPECIALIZE inferFunSort :: Dom Type -> Sort -> TCM Sort #-}
+-- | As @inferPiSort@, but for a nondependent function type.
+--
+inferFunSort :: (PureTCM m, MonadConstraint m)
+  => Dom Type  -- ^ Domain of the function type.
+  -> Sort      -- ^ Sort of the codomain of the function type.
+  -> m Sort    -- ^ Sort of the function type.
+inferFunSort a s = do
+  s1' <- reduceB $ getSort a
+  s2' <- reduceB s
+  let s1 = ignoreBlocking s1'
+  let s2 = ignoreBlocking s2'
+  case funSort' s1 s2 of
+    Right s -> return s
+    Left b -> do
+      let b' = unblockOnEither (getBlocker s1') (getBlocker s2')
+      addConstraint (unblockOnEither b b') $ HasPTSRule a (NoAbs "_" s2)
+      return $ FunSort s1 s2
+  -- Andreas, 2023-05-20:  I made inferFunSort step-by-step analogous to inferPiSort.
+  -- Unifying them seems unfeasible, though; too much parametrization...
+
+-- | @hasPTSRule a x.s@ checks that we can form a Pi-type @(x : a) -> b@ where @b : s@.
+--
+hasPTSRule :: Dom Type -> Abs Sort -> TCM ()
+hasPTSRule a s = do
+  reportSDoc "tc.conv.sort" 35 $ vcat
+    [ "hasPTSRule"
+    , "a =" <+> prettyTCM a
+    , "s =" <+> prettyTCM (unAbs s)
+    ]
+  if alwaysValidCodomain $ unAbs s
+  then yes
+  else do
+    sb <- reduceB =<< inferPiSort a s
+    case sb of
+      Blocked b t | neverUnblock == b -> no sb t
+      NotBlocked _ t@FunSort{}        -> no sb t
+      NotBlocked _ t@PiSort{}         -> no sb t
+      _ -> yes
+  where
+    -- Do we end in a standard sort (Prop, Type, SSet)?
+    alwaysValidCodomain = \case
+      Inf{} -> True
+      Univ{} -> True
+      FunSort _ s -> alwaysValidCodomain s
+      PiSort _ _ s -> alwaysValidCodomain $ unAbs s
+      _ -> False
+
+    yes = do
+      reportSLn "tc.conv.sort" 35 "hasPTSRule succeeded"
+    no sb t = do
+      reportSDoc "tc.conv.sort" 35 $ "hasPTSRule fails on" <+> prettyTCM sb
+      typeError $ InvalidTypeSort t
+
+-- | Recursively check that an iterated function type constructed by @telePi@
+--   is well-sorted.
+checkTelePiSort :: Type -> TCM ()
+-- Jesper, 2019-07-27: This is currently doing nothing (see comment in inferPiSort)
+checkTelePiSort (El s (Pi a b)) = do
+  -- Since the function type is assumed to be constructed by @telePi@,
+  -- we already know that @s == piSort (getSort a) (getSort <$> b)@,
+  -- so we just check that this sort is well-formed.
+  hasPTSRule a (getSort <$> b)
+  underAbstraction a b checkTelePiSort
+checkTelePiSort _ = return ()
+
+ifIsSort :: (MonadReduce m, MonadBlock m) => Type -> (Sort -> m a) -> m a -> m a
+ifIsSort t yes no = do
+  -- Jesper, 2020-09-06, subtle: do not use @abortIfBlocked@ here
+  -- since we want to take the yes branch whenever the type is a sort,
+  -- even if it is blocked.
+  bt <- reduceB t
+  case unEl (ignoreBlocking bt) of
+    Sort s                     -> yes s
+    _      | Blocked m _ <- bt -> patternViolation m
+           | otherwise         -> no
+
+{-# SPECIALIZE ifNotSort :: Type -> TCM a -> (Sort -> TCM a) -> TCM a #-}
+ifNotSort :: (MonadReduce m, MonadBlock m) => Type -> m a -> (Sort -> m a) -> m a
+ifNotSort t = flip $ ifIsSort t
+
+{-# SPECIALIZE shouldBeSort :: Type -> TCM Sort #-}
+-- | Result is in reduced form.
+shouldBeSort
+  :: (PureTCM m, MonadBlock m, MonadError TCErr m)
+  => Type -> m Sort
+shouldBeSort t = ifIsSort t return (typeError $ ShouldBeASort t)
+
+{-# SPECIALIZE sortOf :: Term -> TCM Sort #-}
+-- | Reconstruct the sort of a term.
+--
+--   Precondition: given term is a well-sorted type.
+sortOf
+  :: forall m. (PureTCM m, MonadBlock m, MonadConstraint m)
+  => Term -> m Sort
+sortOf t = do
+  reportSDoc "tc.sort" 60 $ "sortOf" <+> prettyTCM t
+  sortOfT =<< elimView EvenLone t
+
+  where
+    sortOfT :: Term -> m Sort
+    sortOfT = \case
+      Pi adom b -> do
+        let a = unEl $ unDom adom
+        sa <- sortOf a
+        sb <- mapAbstraction adom (sortOf . unEl) b
+        inferPiSort (adom $> El sa a) sb
+      Sort s     -> return $ univSort s
+      Var i es   -> do
+        a <- typeOfBV i
+        sortOfE a (Var i) es
+      Def f es   -> do
+        a <- defType <$> getConstInfo f
+        sortOfE a (Def f) es
+      MetaV x es -> do
+        a <- metaType x
+        sortOfE a (MetaV x) es
+      Lam{}      -> __IMPOSSIBLE__
+      Con{}      -> __IMPOSSIBLE__
+      Lit{}      -> __IMPOSSIBLE__
+      Level{}    -> __IMPOSSIBLE__
+      DontCare{} -> __IMPOSSIBLE__
+      Dummy s _  -> __IMPOSSIBLE_VERBOSE__ s
+
+    sortOfE :: Type -> (Elims -> Term) -> Elims -> m Sort
+    sortOfE a hd []     = ifIsSort a return __IMPOSSIBLE__
+    sortOfE a hd (e:es) = do
+      reportSDoc "tc.sort" 50 $ vcat
+        [ "sortOfE"
+        , "  a  = " <+> prettyTCM a
+        , "  hd = " <+> prettyTCM (hd [])
+        , "  e  = " <+> prettyTCM e
+        ]
+
+      ba <- reduceB a
+
+      let
+        a' = ignoreBlocking ba
+        fallback = case ba of
+          Blocked m _ -> patternViolation m
+
+          -- Not IMPOSSIBLE because of possible non-confluent rewriting (see #5531)
+          _ -> ifM (optRewriting <$> pragmaOptions)
+            {-then-} (patternViolation neverUnblock)
+            {-else-} __IMPOSSIBLE__
+
+      case e of
+        Apply (Arg ai v) -> case unEl a' of
+          Pi b c -> sortOfE (c `absApp` v) (hd . (e:)) es
+          _ -> fallback
+
+        Proj o f -> case unEl a' of
+          Def{} -> do
+            ~(El _ (Pi b c)) <- fromMaybe __IMPOSSIBLE__ <$> getDefType f a'
+            hd' <- applyE <$> applyDef o f (argFromDom b $> hd [])
+            sortOfE (c `absApp` (hd [])) hd' es
+          _ -> fallback
+
+        IApply x y r -> do
+          (b , c) <- fromMaybe __IMPOSSIBLE__ <$> isPath a'
+          sortOfE (c `absApp` r) (hd . (e:)) es
+
+{-# INLINE sortOfType #-}
+-- | Reconstruct the minimal sort of a type (ignoring the sort annotation).
+sortOfType
+  :: forall m. (PureTCM m, MonadBlock m,MonadConstraint m)
+  => Type -> m Sort
+sortOfType = sortOf . unEl
diff --git a/src/full/Agda/TypeChecking/Substitute.hs b/src/full/Agda/TypeChecking/Substitute.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Substitute.hs
@@ -0,0 +1,1777 @@
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE ViewPatterns        #-}
+{-# LANGUAGE TypeApplications    #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+{-# OPTIONS_GHC -ddump-simpl -dsuppress-all -ddump-to-file #-}
+
+-- | This module contains the definition of hereditary substitution
+-- and application operating on internal syntax which is in β-normal
+-- form (β including projection reductions).
+--
+-- Further, it contains auxiliary functions which rely on substitution
+-- but not on reduction.
+
+module Agda.TypeChecking.Substitute
+  ( module Agda.TypeChecking.Substitute
+  , module Agda.TypeChecking.Substitute.Class
+  , module Agda.TypeChecking.Substitute.DeBruijn
+  , Substitution'(..), Substitution
+  ) where
+
+import Control.Arrow (first, second)
+import Control.Monad (guard)
+
+import Data.Coerce
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map.Strict as MapS
+import Data.Maybe
+import Data.HashMap.Strict (HashMap)
+
+import Debug.Trace (trace)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Position
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+import qualified Agda.Syntax.Abstract as A
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Free as Free
+import Agda.TypeChecking.CompiledClause
+import Agda.TypeChecking.Positivity.Occurrence as Occ
+
+import Agda.TypeChecking.Substitute.Class
+import Agda.TypeChecking.Substitute.DeBruijn
+
+import Agda.Utils.Either
+import Agda.Utils.Empty
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+
+-- | Apply @Elims@ while using the given function to report ill-typed
+--   redexes.
+--   Recursive calls for @applyE@ and @applySubst@ happen at type @t@ to
+--   propagate the same strategy to subtrees.
+{-# SPECIALIZE applyTermE :: (Empty -> Term -> Elims -> Term) -> Term -> Elims -> Term #-}
+{-# SPECIALIZE applyTermE :: (Empty -> Term -> Elims -> Term) -> BraveTerm -> Elims -> BraveTerm #-}
+applyTermE :: forall t. (Coercible Term t, Apply t, EndoSubst t)
+           => (Empty -> Term -> Elims -> Term) -> t -> Elims -> t
+applyTermE err' m [] = m
+applyTermE err' m es = coerce $
+    case coerce m of
+      Var i es'   -> Var i (es' ++ es)
+      Def f es'   -> defApp f es' es  -- remove projection redexes
+      Con c ci args -> conApp @t err' c ci args es
+      Lam _ b     ->
+        case es of
+          Apply a : es0      -> lazyAbsApp (coerce b :: Abs t) (coerce $ unArg a) `app` es0
+          IApply _ _ a : es0 -> lazyAbsApp (coerce b :: Abs t) (coerce a)         `app` es0
+          _                  -> err __IMPOSSIBLE__
+      MetaV x es' -> MetaV x (es' ++ es)
+      Lit{}       -> err __IMPOSSIBLE__
+      Level{}     -> err __IMPOSSIBLE__
+      Pi _ _      -> err __IMPOSSIBLE__
+      Sort s      -> Sort $ s `applyE` es
+      Dummy s es' -> Dummy s (es' ++ es)
+      DontCare mv -> dontCare $ mv `app` es  -- Andreas, 2011-10-02
+        -- need to go under DontCare, since "with" might resurrect irrelevant term
+   where
+     app :: Coercible t a => a -> Elims -> Term
+     app u es = coerce $ (coerce u :: t) `applyE` es
+     err e = err' e (coerce m) es
+
+instance Apply Term where
+  applyE = applyTermE absurd
+
+instance Apply BraveTerm where
+  applyE = applyTermE (\ _ t es ->  Dummy "applyE" (Apply (defaultArg t) : es))
+
+-- | If @v@ is a record or constructed value, @canProject f v@
+--   returns its field @f@.
+canProject :: QName -> Term -> Maybe (Arg Term)
+canProject f v =
+  case v of
+    -- Andreas, 2022-06-10, issue #5922: also unfold data projections
+    -- (not just record projections).
+    (Con (ConHead _ _ _ fs) _ vs) -> do
+      (fld, i) <- findWithIndex ((f ==) . unArg) fs
+      -- Jesper, 2019-10-17: dont unfold irrelevant projections
+      guard $ not $ isIrrelevant fld
+      -- Andreas, 2018-06-12, issue #2170
+      -- The ArgInfo from the ConHead is more accurate (relevance subtyping!).
+      setArgInfo (getArgInfo fld) <.> isApplyElim =<< listToMaybe (drop i vs)
+    _ -> Nothing
+
+-- | Eliminate a constructed term.
+conApp :: forall t. (Coercible t Term, Apply t) => (Empty -> Term -> Elims -> Term) -> ConHead -> ConInfo -> Elims -> Elims -> Term
+conApp fallback ch                    ci args []                  = Con ch ci args
+conApp fallback ch                    ci args    (a@Apply{} : es) = conApp @t fallback ch ci (args ++ [a]) es
+conApp fallback ch                    ci args   (a@IApply{} : es) = conApp @t fallback ch ci (args ++ [a]) es
+conApp fallback ch@(ConHead c _ _ fs) ci args ees@(Proj o f : es) =
+  let failure :: forall a. a -> a
+      failure err = flip trace err $ concat
+        [ "conApp: constructor ", prettyShow c
+        , unlines $ " with fields" : map (("  " ++) . prettyShow) fs
+        , unlines $ " and args"    : map (("  " ++) . prettyShow) args
+        , " projected by ", prettyShow f
+        ]
+      isApply e = fromMaybe (failure __IMPOSSIBLE__) $ isApplyElim e
+      stuck err = fallback err (Con ch ci args) [Proj o f]
+      -- Recurse using the instance for 't', see @applyTermE@
+      app :: Term -> Elims -> Term
+      app v es = coerce $ applyE (coerce v :: t) es
+  in
+   case findWithIndex ((f ==) . unArg) fs of
+     Nothing -> failure $ stuck __IMPOSSIBLE__ `app` es
+     Just (fld, i) -> let
+      -- Andreas, 2018-06-12, issue #2170
+      -- We safe-guard the projected value by DontCare using the ArgInfo stored at the record constructor,
+      -- since the ArgInfo in the constructor application might be inaccurate because of subtyping.
+      v = maybe (failure $ stuck __IMPOSSIBLE__) (relToDontCare fld . argToDontCare . isApply) $ listToMaybe $ drop i args
+      in v `app` es
+
+  -- -- Andreas, 2016-07-20 futile attempt to magically fix ProjOrigin
+  --     fallback = v
+  -- in  if not $ null es then applyE v es else
+  --     -- If we have no more eliminations, we can return v
+  --     if o == ProjSystem then fallback else
+  --       -- If the result is a projected term with ProjSystem,
+  --       -- we can can restore it to ProjOrigin o.
+  --       -- Otherwise, we get unpleasant printing with eta-expanded record metas.
+  --     caseMaybe (hasElims v) fallback $ \ (hd, es0) ->
+  --       caseMaybe (initLast es0) fallback $ \ (es1, e2) ->
+  --         case e2 of
+  --           -- We want to replace this ProjSystem by o.
+  --           Proj ProjSystem q -> hd (es1 ++ [Proj o q])
+  --             -- Andreas, 2016-07-21 for the whole testsuite
+  --             -- this case was never triggered!
+  --           _ -> fallback
+
+{-
+      i = maybe failure id    $ elemIndex f $ map unArg fs
+      v = maybe failure unArg $ listToMaybe $ drop i args
+      -- Andreas, 2013-10-20 see Issue543a:
+      -- protect result of irrelevant projection.
+      r = maybe __IMPOSSIBLE__ getRelevance $ listToMaybe $ drop i fs
+      u | Irrelevant <- r = DontCare v
+        | otherwise       = v
+  in  applyE v es
+-}
+
+-- | @defApp f us vs@ applies @Def f us@ to further arguments @vs@,
+--   eliminating top projection redexes.
+--   If @us@ is not empty, we cannot have a projection redex, since
+--   the record argument is the first one.
+defApp :: QName -> Elims -> Elims -> Term
+defApp f [] (Apply a : es) | Just v <- canProject f (unArg a)
+  = argToDontCare v `applyE` es
+defApp f es0 es = Def f $ es0 ++ es
+
+-- protect irrelevant fields (see issue 610)
+argToDontCare :: Arg Term -> Term
+argToDontCare (Arg ai v) = relToDontCare ai v
+
+relToDontCare :: LensRelevance a => a -> Term -> Term
+relToDontCare ai v
+  | Irrelevant <- getRelevance ai = dontCare v
+  | otherwise                     = v
+
+-- Andreas, 2016-01-19: In connection with debugging issue #1783,
+-- I consider the Apply instance for Type harmful, as piApply is not
+-- safe if the type is not sufficiently reduced.
+-- (piApply is not in the monad and hence cannot unfold type synonyms).
+--
+-- Without apply for types, one has to at least use piApply and be
+-- aware of doing something which has a precondition
+-- (type sufficiently reduced).
+--
+-- By grepping for piApply, one can quickly get an overview over
+-- potentially harmful uses.
+--
+-- In general, piApplyM is preferable over piApply since it is more robust
+-- and fails earlier than piApply, which may only fail at serialization time,
+-- when all thunks are forced.
+
+-- REMOVED:
+-- instance Apply Type where
+--   apply = piApply
+--   -- Maybe an @applyE@ instance would be useful here as well.
+--   -- A record type could be applied to a projection name
+--   -- to yield the field type.
+--   -- However, this works only in the monad where we can
+--   -- look up the fields of a record type.
+
+instance Apply Sort where
+  applyE s [] = s
+  applyE s es = case s of
+    MetaS x es' -> MetaS x $ es' ++ es
+    DefS  d es' -> DefS  d $ es' ++ es
+    _ -> __IMPOSSIBLE__
+
+-- @applyE@ does not make sense for telecopes, definitions, clauses etc.
+
+instance TermSubst a => Apply (Tele a) where
+  apply tel               []       = tel
+  apply EmptyTel          _        = __IMPOSSIBLE__
+  apply (ExtendTel _ tel) (t : ts) = lazyAbsApp tel (unArg t) `apply` ts
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply Definition where
+  apply (Defn info x t pol occ gens gpars df m c inst copy ma nc inj copat blk lang d) args =
+    Defn info x (piApply t args) (apply pol args) (apply occ args) (apply gens args) (drop (length args) gpars) df m c inst copy ma nc inj copat blk lang (apply d args)
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply RewriteRule where
+  apply r args =
+    let newContext = apply (rewContext r) args
+        sub        = liftS (size newContext) $ parallelS $
+                       reverse $ map (PTerm . unArg) args
+    in RewriteRule
+       { rewName    = rewName r
+       , rewContext = newContext
+       , rewHead    = rewHead r
+       , rewPats    = applySubst sub (rewPats r)
+       , rewRHS     = applyNLPatSubst sub (rewRHS r)
+       , rewType    = applyNLPatSubst sub (rewType r)
+       , rewFromClause = rewFromClause r
+       }
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance {-# OVERLAPPING #-} Apply [Occ.Occurrence] where
+  apply occ args = List.drop (length args) occ
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance {-# OVERLAPPING #-} Apply [Polarity] where
+  apply pol args = List.drop (length args) pol
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply NumGeneralizableArgs where
+  apply NoGeneralizableArgs       args = NoGeneralizableArgs
+  apply (SomeGeneralizableArgs n) args = SomeGeneralizableArgs (n - length args)
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+-- | Make sure we only drop variable patterns.
+instance {-# OVERLAPPING #-} Apply [NamedArg (Pattern' a)] where
+  apply ps args = loop (length args) ps
+    where
+    loop 0 ps = ps
+    loop n [] = __IMPOSSIBLE__
+    loop n (p : ps) =
+      let recurse = loop (n - 1) ps
+      in  case namedArg p of
+            VarP{}  -> recurse
+            DotP{}  -> __IMPOSSIBLE__
+            LitP{}  -> __IMPOSSIBLE__
+            ConP{}  -> __IMPOSSIBLE__
+            DefP{}  -> __IMPOSSIBLE__
+            ProjP{} -> __IMPOSSIBLE__
+            IApplyP{} -> recurse
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply Projection where
+  apply p args = p
+    { projIndex = projIndex p - size args
+    , projLams  = projLams p `apply` args
+    }
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply ProjLams where
+  apply (ProjLams lams) args = ProjLams $ List.drop (length args) lams
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply Defn where
+  apply d [] = d
+  apply d args@(arg1:args1) = case d of
+    Axiom{} -> d
+    DataOrRecSig n -> DataOrRecSig (n - length args)
+    GeneralizableVar{} -> d
+    AbstractDefn d -> AbstractDefn $ apply d args
+    Function{ funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv
+            , funExtLam = extLam
+            , funProjection = Left _ } ->
+      d { funClauses    = apply cs args
+        , funCompiled   = apply cc args
+        , funCovering   = apply cov args
+        , funInv        = apply inv args
+        , funExtLam     = modifySystem (`apply` args) <$> extLam
+        }
+
+    Function{ funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv
+            , funExtLam = extLam
+            , funProjection = Right p0 } ->
+      case p0 `apply` args of
+        p@Projection{ projIndex = n }
+          | n < 0     -> d { funProjection = __IMPOSSIBLE__ } -- TODO (#3123): we actually get here!
+          -- case: applied only to parameters
+          | n > 0     -> d { funProjection = Right p }
+          -- case: applied also to record value (n == 0)
+          | otherwise ->
+              d { funClauses        = apply cs args'
+                , funCompiled       = apply cc args'
+                , funCovering       = apply cov args'
+                , funInv            = apply inv args'
+                , funProjection     = if isVar0 then Right p{ projIndex = 0 } else Left MaybeProjection
+                , funExtLam         = modifySystem (\ _ -> __IMPOSSIBLE__) <$> extLam
+                }
+              where
+                larg  = last1 arg1 args1 -- the record value
+                args' = [larg]
+                isVar0 = case unArg larg of Var 0 [] -> True; _ -> False
+
+    Datatype{ dataPars = np, dataClause = cl } ->
+      d { dataPars = np - size args
+        , dataClause     = apply cl args
+        }
+    Record{ recPars = np, recClause = cl, recTel = tel
+          {-, recArgOccurrences = occ-} } ->
+      d { recPars = np - size args
+        , recClause = apply cl args, recTel = apply tel args
+--        , recArgOccurrences = List.drop (length args) occ
+        }
+    Constructor{ conPars = np } ->
+      d { conPars = np - size args }
+    Primitive{ primClauses = cs } ->
+      d { primClauses = apply cs args }
+    PrimitiveSort{} -> d
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply PrimFun where
+  apply (PrimFun x ar occs def) args =
+    PrimFun x (ar - n) (drop n occs) $ \ vs -> def (args ++ vs)
+    where
+    n = size args
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply Clause where
+    -- This one is a little bit tricksy after the parameter refinement change.
+    -- It is assumed that we only apply a clause to "parameters", i.e.
+    -- arguments introduced by lambda lifting. The problem is that these aren't
+    -- necessarily the first elements of the clause telescope.
+    apply cls@(Clause rl rf tel ps b t catchall exact recursive unreachable ell wm) args
+      | length args > length ps = __IMPOSSIBLE__
+      | otherwise =
+      Clause rl rf
+             tel'
+             (applySubst rhoP $ drop (length args) ps)
+             (applySubst rho b)
+             (applySubst rho t)
+             catchall
+             exact
+             recursive
+             unreachable
+             ell
+             wm
+      where
+        -- We have
+        --  Γ ⊢ args, for some outer context Γ
+        --  Δ ⊢ ps,   where Δ is the clause telescope (tel)
+        rargs = map unArg $ reverse args
+        rps   = reverse $ take (length args) ps
+        n     = size tel
+
+        -- This is the new telescope. Created by substituting the args into the
+        -- appropriate places in the old telescope. We know where those are by
+        -- looking at the deBruijn indices of the patterns.
+        tel' = newTel n tel rps rargs
+
+        -- We then have to create a substitution from the old telescope to the
+        -- new telescope that we can apply to dot patterns and the clause body.
+        rhoP :: PatternSubstitution
+        rhoP = mkSub dotP n rps rargs
+        rho  = mkSub id   n rps rargs
+
+        substP :: Nat -> Term -> [NamedArg DeBruijnPattern] -> [NamedArg DeBruijnPattern]
+        substP i v = subst i (dotP v)
+
+        -- Building the substitution from the old telescope to the new. The
+        -- interesting case is when we have a variable pattern:
+        --  We need Δ′ ⊢ ρ : Δ
+        --  where Δ′ = newTel Δ (xⁱ : ps) (v : vs)
+        --           = newTel Δ[xⁱ:=v] ps[xⁱ:=v'] vs
+        --  Note that we need v' = raise (|Δ| - 1) v, to make Γ ⊢ v valid in
+        --  ΓΔ[xⁱ:=v].
+        --  A recursive call ρ′ = mkSub (substP i v' ps) vs gets us
+        --    Δ′ ⊢ ρ′ : Δ[xⁱ:=v]
+        --  so we just need Δ[xⁱ:=v] ⊢ σ : Δ and then ρ = ρ′ ∘ σ.
+        --  That's achieved by σ = singletonS i v'.
+        mkSub :: EndoSubst a => (Term -> a) -> Nat -> [NamedArg DeBruijnPattern] -> [Term] -> Substitution' a
+        mkSub _ _ [] [] = idS
+        mkSub tm n (p : ps) (v : vs) =
+          case namedArg p of
+            VarP _ (DBPatVar _ i) -> mkSub tm (n - 1) (substP i v' ps) vs `composeS` singletonS i (tm v')
+              where v' = raise (n - 1) v
+            DotP{}  -> mkSub tm n ps vs
+            ConP c _ ps' -> mkSub tm n (ps' ++ ps) (projections c v ++ vs)
+            DefP{}  -> __IMPOSSIBLE__
+            LitP{}  -> __IMPOSSIBLE__
+            ProjP{} -> __IMPOSSIBLE__
+            IApplyP _ _ _ (DBPatVar _ i) -> mkSub tm (n - 1) (substP i v' ps) vs `composeS` singletonS i (tm v')
+              where v' = raise (n - 1) v
+        mkSub _ _ _ _ = __IMPOSSIBLE__
+
+        -- The parameter patterns 'ps' are all variables or dot patterns, or eta
+        -- expanded record patterns (issue #2550). If they are variables they
+        -- can appear anywhere in the clause telescope. This function
+        -- constructs the new telescope with 'vs' substituted for 'ps'.
+        -- Example:
+        --    tel = (x : A) (y : B) (z : C) (w : D)
+        --    ps  = y@3 w@0
+        --    vs  = u v
+        --    newTel tel ps vs = (x : A) (z : C[u/y])
+        newTel :: Nat -> Telescope -> [NamedArg DeBruijnPattern] -> [Term] -> Telescope
+        newTel n tel [] [] = tel
+        newTel n tel (p : ps) (v : vs) =
+          case namedArg p of
+            VarP _ (DBPatVar _ i) -> newTel (n - 1) (subTel (size tel - 1 - i) v tel) (substP i (raise (n - 1) v) ps) vs
+            DotP{}              -> newTel n tel ps vs
+            ConP c _ ps'        -> newTel n tel (ps' ++ ps) (projections c v ++ vs)
+            DefP{}  -> __IMPOSSIBLE__
+            LitP{}  -> __IMPOSSIBLE__
+            ProjP{} -> __IMPOSSIBLE__
+            IApplyP _ _ _ (DBPatVar _ i) -> newTel (n - 1) (subTel (size tel - 1 - i) v tel) (substP i (raise (n - 1) v) ps) vs
+        newTel _ tel _ _ = __IMPOSSIBLE__
+
+        projections :: ConHead -> Term -> [Term]
+        projections c v = [ relToDontCare ai $
+                            -- #4528: We might have bogus terms here when printing a clause that
+                            --        cannot be taken. To mitigate the problem we use a Def instead
+                            --        a Proj elim for data constructors, which at least stops conApp
+                            --        from crashing. See #4989 for not printing bogus terms at all.
+                            case conDataRecord c of
+                              IsData     -> defApp f [] [Apply (Arg ai v)]
+                                              -- Andreas, 2022-06-10, issue #5922.
+                                              -- This was @Def f [Apply (Arg ai v)]@, but are we sure
+                                              -- that @v@ isn't a matching @Con@?  The testcase for
+                                              -- #5922 does not require this precaution,
+                                              -- but I sleep better this way...
+                              IsRecord{} -> applyE v [Proj ProjSystem f]
+                          | Arg ai f <- conFields c ]
+
+        -- subTel i v (Δ₁ (xᵢ : A) Δ₂) = Δ₁ Δ₂[xᵢ = v]
+        subTel i v EmptyTel = __IMPOSSIBLE__
+        subTel 0 v (ExtendTel _ tel) = absApp tel v
+        subTel i v (ExtendTel a tel) = ExtendTel a $ subTel (i - 1) (raise 1 v) <$> tel
+
+    applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply CompiledClauses where
+  apply cc args = case cc of
+    Fail hs -> Fail (drop len hs)
+    Done hs t
+      | length hs >= len ->
+         let sub = parallelS $ map var [0..length hs - len - 1] ++ map unArg args
+         in  Done (List.drop len hs) $ applySubst sub t
+      | otherwise -> __IMPOSSIBLE__
+    Case n bs
+      | unArg n >= len -> Case (n <&> \ m -> m - len) (apply bs args)
+      | otherwise -> __IMPOSSIBLE__
+    where
+      len = length args
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply ExtLamInfo where
+  apply (ExtLamInfo m b sys) args = ExtLamInfo m b (apply sys args)
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply System where
+  -- We assume we apply a system only to arguments introduced by
+  -- lambda lifting.
+  apply (System tel sys) args
+      = if nargs > ntel then __IMPOSSIBLE__
+        else System newTel (map (map (f -*- id) -*- f) sys)
+
+    where
+      f = applySubst sigma
+      nargs = length args
+      ntel = size tel
+      newTel = apply tel args
+      -- newTel ⊢ σ : tel
+      sigma = liftS (ntel - nargs) (parallelS (reverse $ map unArg args))
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply a => Apply (WithArity a) where
+  apply  (WithArity n a) args = WithArity n $ apply  a args
+  applyE (WithArity n a) es   = WithArity n $ applyE a es
+
+instance Apply a => Apply (Case a) where
+  apply (Branches cop cs eta ls m b lz) args =
+    Branches cop (apply cs args) (second (`apply` args) <$> eta) (apply ls args) (apply m args) b lz
+  applyE (Branches cop cs eta ls m b lz) es =
+    Branches cop (applyE cs es) (second (`applyE` es) <$> eta)(applyE ls es) (applyE m es) b lz
+
+instance Apply FunctionInverse where
+  apply NotInjective  args = NotInjective
+  apply (Inverse inv) args = Inverse $ apply inv args
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Apply DisplayTerm where
+  apply (DTerm' v es)      args = DTerm' v       $ es ++ map Apply args
+  apply (DDot' v es)       args = DDot' v        $ es ++ map Apply args
+  apply (DCon c ci vs)     args = DCon c ci     $ vs ++ map (fmap DTerm) args
+  apply (DDef c es)        args = DDef c        $ es ++ map (Apply . fmap DTerm) args
+  apply (DWithApp v ws es) args = DWithApp v ws $ es ++ map Apply args
+
+  applyE (DTerm' v es')      es = DTerm' v $ es' ++ es
+  applyE (DDot' v es')       es = DDot' v $ es' ++ es
+  applyE (DCon c ci vs)      es = DCon c ci $ vs ++ map (fmap DTerm) ws
+    where ws = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+  applyE (DDef c es')        es = DDef c $ es' ++ map (fmap DTerm) es
+  applyE (DWithApp v ws es') es = DWithApp v ws $ es' ++ es
+
+instance {-# OVERLAPPABLE #-} Apply t => Apply [t] where
+  apply  ts args = map (`apply` args) ts
+  applyE ts es   = map (`applyE` es) ts
+
+instance Apply t => Apply (Blocked t) where
+  apply  b args = fmap (`apply` args) b
+  applyE b es   = fmap (`applyE` es) b
+
+instance Apply t => Apply (Maybe t) where
+  apply  x args = fmap (`apply` args) x
+  applyE x es   = fmap (`applyE` es) x
+
+instance Apply t => Apply (Strict.Maybe t) where
+  apply  x args = fmap (`apply` args) x
+  applyE x es   = fmap (`applyE` es) x
+
+instance Apply v => Apply (Map k v) where
+  apply  x args = fmap (`apply` args) x
+  applyE x es   = fmap (`applyE` es) x
+
+instance Apply v => Apply (HashMap k v) where
+  apply  x args = fmap (`apply` args) x
+  applyE x es   = fmap (`applyE` es) x
+
+instance (Apply a, Apply b) => Apply (a,b) where
+  apply  (x,y) args = (apply  x args, apply  y args)
+  applyE (x,y) es   = (applyE x es  , applyE y es  )
+
+instance (Apply a, Apply b, Apply c) => Apply (a,b,c) where
+  apply  (x,y,z) args = (apply  x args, apply  y args, apply  z args)
+  applyE (x,y,z) es   = (applyE x es  , applyE y es  , applyE z es  )
+
+instance DoDrop a => Apply (Drop a) where
+  apply x args = dropMore (size args) x
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance DoDrop a => Abstract (Drop a) where
+  abstract tel x = unDrop (size tel) x
+
+instance Apply Permutation where
+  -- The permutation must start with [0..m - 1]
+  -- NB: section (- m) not possible (unary minus), hence (flip (-) m)
+  apply (Perm n xs) args = Perm (n - m) $ map (flip (-) m) $ drop m xs
+    where
+      m = size args
+
+  applyE t es = apply t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+
+instance Abstract Permutation where
+  abstract tel (Perm n xs) = Perm (n + m) $ [0..m - 1] ++ map (+ m) xs
+    where
+      m = size tel
+
+-- | @(x:A)->B(x) `piApply` [u] = B(u)@
+--
+--   Precondition: The type must contain the right number of pis without
+--   having to perform any reduction.
+--
+--   @piApply@ is potentially unsafe, the monadic 'piApplyM' is preferable.
+piApply :: Type -> Args -> Type
+piApply t []                      = t
+piApply (El _ (Pi  _ b)) (a:args) = lazyAbsApp b (unArg a) `piApply` args
+piApply t args                    =
+  trace ("piApply t = " ++ prettyShow t ++ "\n  args = " ++ prettyShow args) __IMPOSSIBLE__
+
+---------------------------------------------------------------------------
+-- * Abstraction
+---------------------------------------------------------------------------
+
+instance Abstract Term where
+  abstract = teleLam
+
+instance Abstract Type where
+  abstract = telePi_
+
+instance Abstract Sort where
+  abstract EmptyTel s = s
+  abstract _        s = __IMPOSSIBLE__
+
+instance Abstract Telescope where
+  EmptyTel           `abstract` tel = tel
+  ExtendTel arg xtel `abstract` tel = ExtendTel arg $ xtel <&> (`abstract` tel)
+
+instance Abstract Definition where
+  abstract tel (Defn info x t pol occ gens gpars df m c inst copy ma nc inj copat blk lang d) =
+    Defn info x (abstract tel t) (abstract tel pol) (abstract tel occ) (abstract tel gens)
+      (replicate (size tel) Nothing ++ gpars)
+      df m c inst copy ma nc inj copat blk lang (abstract tel d)
+
+-- | @tel ⊢ (Γ ⊢ lhs ↦ rhs : t)@ becomes @tel, Γ ⊢ lhs ↦ rhs : t)@
+--   we do not need to change lhs, rhs, and t since they live in Γ.
+--   See 'Abstract Clause'.
+instance Abstract RewriteRule where
+  abstract tel (RewriteRule q gamma f ps rhs t c) =
+    RewriteRule q (abstract tel gamma) f ps rhs t c
+
+instance {-# OVERLAPPING #-} Abstract [Occ.Occurrence] where
+  abstract tel []  = []
+  abstract tel occ = replicate (size tel) Mixed ++ occ -- TODO: check occurrence
+
+instance {-# OVERLAPPING #-} Abstract [Polarity] where
+  abstract tel []  = []
+  abstract tel pol = replicate (size tel) Invariant ++ pol -- TODO: check polarity
+
+instance Abstract NumGeneralizableArgs where
+  abstract tel NoGeneralizableArgs       = NoGeneralizableArgs
+  abstract tel (SomeGeneralizableArgs n) = SomeGeneralizableArgs (size tel + n)
+
+instance Abstract Projection where
+  abstract tel p = p
+    { projIndex = size tel + projIndex p
+    , projLams  = abstract tel $ projLams p
+    }
+
+instance Abstract ProjLams where
+  abstract tel (ProjLams lams) = ProjLams $
+    map (\ !dom -> argFromDom (fst <$> dom)) (telToList tel) ++ lams
+
+instance Abstract System where
+  abstract tel (System tel1 sys) = System (abstract tel tel1) sys
+
+instance Abstract Defn where
+  abstract tel d = case d of
+    Axiom{} -> d
+    DataOrRecSig n -> DataOrRecSig (size tel + n)
+    GeneralizableVar{} -> d
+    AbstractDefn d -> AbstractDefn $ abstract tel d
+    Function{ funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv
+            , funExtLam = extLam
+            , funProjection = Left _  } ->
+      d { funClauses  = abstract tel cs
+        , funCompiled = abstract tel cc
+        , funCovering = abstract tel cov
+        , funInv      = abstract tel inv
+        , funExtLam   = modifySystem (abstract tel) <$> extLam
+        }
+    Function{ funClauses = cs, funCompiled = cc, funCovering = cov, funInv = inv
+            , funExtLam = extLam
+            , funProjection = Right p } ->
+      -- Andreas, 2015-05-11 if projection was applied to Var 0
+      -- then abstract over last element of tel (the others are params).
+      if projIndex p > 0 then
+        d { funProjection = Right $ abstract tel p
+          , funClauses    = map (abstractClause EmptyTel) cs
+          }
+      else
+        d { funProjection = Right $ abstract tel p
+          , funClauses    = map (abstractClause tel1) cs
+          , funCompiled   = abstract tel1 cc
+          , funCovering   = abstract tel1 cov
+          , funInv        = abstract tel1 inv
+          , funExtLam     = modifySystem (\ _ -> __IMPOSSIBLE__) <$> extLam
+          }
+        where
+          tel1 = telFromList $ drop (size tel - 1) $ telToList tel
+          -- #5128: clause telescopes should be abstracted over the full telescope, regardless of
+          --        projection shenanigans.
+          abstractClause tel1 c = (abstract tel1 c) { clauseTel = abstract tel $ clauseTel c }
+
+    Datatype{ dataPars = np, dataClause = cl } ->
+      d { dataPars       = np + size tel
+        , dataClause     = abstract tel cl
+        }
+    Record{ recPars = np, recClause = cl, recTel = tel' } ->
+      d { recPars    = np + size tel
+        , recClause  = abstract tel cl
+        , recTel     = abstract tel tel'
+        }
+    Constructor{ conPars = np } ->
+      d { conPars = np + size tel }
+    Primitive{ primClauses = cs } ->
+      d { primClauses = abstract tel cs }
+    PrimitiveSort{} -> d
+
+instance Abstract PrimFun where
+    abstract tel (PrimFun x ar occs def) =
+      PrimFun x (ar + n) (replicate n Mixed ++ occs) $ \ts ->
+        def $ drop n ts
+        where n = size tel
+
+instance Abstract Clause where
+  abstract tel (Clause rl rf tel' ps b t catchall exact recursive unreachable ell wm) =
+    Clause rl rf (abstract tel tel')
+           (namedTelVars m tel ++ ps)
+           b
+           t -- nothing to do for t, since it lives under the telescope
+           catchall
+           exact
+           recursive
+           unreachable
+           ell
+           wm
+      where m = size tel + size tel'
+
+instance Abstract CompiledClauses where
+  abstract tel cc = case cc of
+      Fail xs   -> Fail (hs ++ xs)
+      Done xs t -> Done (hs ++ xs) t
+      Case n bs -> Case (n <&> \ i -> i + size tel) (abstract tel bs)
+    where
+      hs = map (argFromDom . fmap fst) $ telToList tel
+
+instance Abstract a => Abstract (WithArity a) where
+  abstract tel (WithArity n a) = WithArity n $ abstract tel a
+
+instance Abstract a => Abstract (Case a) where
+  abstract tel (Branches cop cs eta ls m b lz) =
+    Branches cop (abstract tel cs) (second (abstract tel) <$> eta)
+                 (abstract tel ls) (abstract tel m) b lz
+
+telVars :: Int -> Telescope -> [Arg DeBruijnPattern]
+telVars m = map (fmap namedThing) . (namedTelVars m)
+
+namedTelVars :: Int -> Telescope -> [NamedArg DeBruijnPattern]
+namedTelVars m EmptyTel                     = []
+namedTelVars m (ExtendTel !dom tel) =
+  Arg (domInfo dom) (namedDBVarP (m-1) $ absName tel) :
+  namedTelVars (m-1) (unAbs tel)
+
+instance Abstract FunctionInverse where
+  abstract tel NotInjective  = NotInjective
+  abstract tel (Inverse inv) = Inverse $ abstract tel inv
+
+instance {-# OVERLAPPABLE #-} Abstract t => Abstract [t] where
+  abstract tel = map (abstract tel)
+
+instance Abstract t => Abstract (Maybe t) where
+  abstract tel x = fmap (abstract tel) x
+
+instance Abstract v => Abstract (Map k v) where
+  abstract tel m = fmap (abstract tel) m
+
+instance Abstract v => Abstract (HashMap k v) where
+  abstract tel m = fmap (abstract tel) m
+
+abstractArgs :: Abstract a => Args -> a -> a
+abstractArgs args x = abstract tel x
+    where
+        tel   = foldr (\arg@(Arg info x) -> ExtendTel (__DUMMY_TYPE__ <$ domFromArg arg) . Abs x)
+                      EmptyTel
+              $ zipWith (<$) names args
+        names = cycle $ map (stringToArgName . (:[])) ['a'..'z']
+
+---------------------------------------------------------------------------
+-- * Substitution and shifting\/weakening\/strengthening
+---------------------------------------------------------------------------
+
+-- | If @permute π : [a]Γ -> [a]Δ@, then @applySubst (renaming _ π) : Term Γ -> Term Δ@
+renaming :: forall a. DeBruijn a => Impossible -> Permutation -> Substitution' a
+renaming err p = prependS err gamma $ raiseS $ size p
+  where
+    gamma :: [Maybe a]
+    gamma = inversePermute p (deBruijnVar :: Int -> a)
+    -- gamma = safePermute (invertP (-1) p) $ map deBruijnVar [0..]
+
+-- | If @permute π : [a]Γ -> [a]Δ@, then @applySubst (renamingR π) : Term Δ -> Term Γ@
+renamingR :: DeBruijn a => Permutation -> Substitution' a
+renamingR p@(Perm n is) = xs ++# raiseS n
+  where
+  xs = map (\i -> deBruijnVar (n - 1 - i)) (reverse is)
+
+  -- The list xs used to be defined in the following way:
+  --
+  --   permute (reverseP p) (map deBruijnVar [0..])
+  --
+  -- We have that
+  --
+  --     permute (reverseP p) (map deBruijnVar [0..])
+  --   = permute (Perm n $ map ((n - 1) -) $ reverse is)
+  --       (map deBruijnVar [0..])
+  --   = map (map deBruijnVar [0..] !!)
+  --       (map ((n - 1) -) $ reverse is)
+  --   = map deBruijnVar (map ((n - 1) -) $ reverse is)
+  --   = map (\i -> deBruijnVar (n - 1 - i)) (reverse is).
+  --
+  -- The latter code is linear in the length of is (if deBruijnVar
+  -- takes constant time), while the time complexity of the former
+  -- code depends on the value of the largest index in is.
+
+-- | The permutation should permute the corresponding context. (right-to-left list)
+renameP :: Subst a => Impossible -> Permutation -> a -> a
+renameP err p = applySubst (renaming err p)
+
+instance EndoSubst a => Subst (Substitution' a) where
+  type SubstArg (Substitution' a) = a
+  applySubst rho sgm = composeS rho sgm
+
+{-# SPECIALIZE applySubstTerm :: Substitution -> Term -> Term #-}
+{-# SPECIALIZE applySubstTerm :: Substitution' BraveTerm -> BraveTerm -> BraveTerm #-}
+applySubstTerm :: forall t. (Coercible t Term, EndoSubst t, Apply t) => Substitution' t -> t -> t
+applySubstTerm IdS t = t
+applySubstTerm rho t    = coerce $ case coerce t of
+    Var i es    -> coerce $ lookupS rho i  `applyE` subE es
+    Lam h m     -> Lam h $ sub @(Abs t) m
+    Def f es    -> defApp f [] $ subE es
+    Con c ci vs -> Con c ci $ subE vs
+    MetaV x es  -> MetaV x $ subE es
+    Lit l       -> Lit l
+    Level l     -> levelTm $ sub @(Level' t) l
+    Pi a b      -> uncurry Pi $ subPi (a,b)
+    Sort s      -> Sort $ sub @(Sort' t) s
+    DontCare mv -> dontCare $ sub @t mv
+    Dummy s es  -> Dummy s $ subE es
+ where
+   sub :: forall a b. (Coercible b a, SubstWith t a) => b -> b
+   sub t = coerce $ applySubst rho (coerce t :: a)
+   subE :: Elims -> Elims
+   subE  = sub @[Elim' t]
+   subPi :: (Dom Type, Abs Type) -> (Dom Type, Abs Type)
+   subPi = sub @(Dom' t (Type'' t t), Abs (Type'' t t))
+
+instance Subst Term where
+  type SubstArg Term = Term
+  applySubst = applySubstTerm
+
+-- András 2023-09-25: we can only put this here, because at the original definition site there's no Subst Term instance.
+{-# SPECIALIZE lookupS :: Substitution' Term -> Nat -> Term #-}
+
+instance Subst BraveTerm where
+  type SubstArg BraveTerm = BraveTerm
+  applySubst = applySubstTerm
+
+instance (Coercible a Term, Subst a, Subst b, SubstArg a ~ SubstArg b) => Subst (Type'' a b) where
+  type SubstArg (Type'' a b) = SubstArg a
+  applySubst rho (El s t) = applySubst rho s `El` applySubst rho t
+
+instance (Coercible a Term, Subst a) => Subst (Sort' a) where
+  type SubstArg (Sort' a) = SubstArg a
+  applySubst rho = \case
+    Univ u n   -> Univ u $ sub n
+    Inf u n    -> Inf u n
+    SizeUniv   -> SizeUniv
+    LockUniv   -> LockUniv
+    LevelUniv  -> LevelUniv
+    IntervalUniv -> IntervalUniv
+    PiSort a s1 s2 -> coerce $ piSort (coerce $ sub a) (coerce $ sub s1) (coerce $ sub s2)
+    FunSort s1 s2 -> coerce $ funSort (coerce $ sub s1) (coerce $ sub s2)
+    UnivSort s -> coerce $ univSort $ coerce $ sub s
+    MetaS x es -> MetaS x $ sub es
+    DefS d es  -> DefS d $ sub es
+    s@DummyS{} -> s
+    where
+      sub :: forall b. (Subst b, SubstArg a ~ SubstArg b) => b -> b
+      sub x = applySubst rho x
+
+instance Subst a => Subst (Level' a) where
+  type SubstArg (Level' a) = SubstArg a
+  applySubst rho (Max n as) = Max n $ applySubst rho as
+
+instance Subst a => Subst (PlusLevel' a) where
+  type SubstArg (PlusLevel' a) = SubstArg a
+  applySubst rho (Plus n l) = Plus n $ applySubst rho l
+
+instance Subst Name where
+  type SubstArg Name = Term
+  applySubst rho = id
+
+instance Subst ConPatternInfo where
+  type SubstArg ConPatternInfo = Term
+  applySubst rho i = i{ conPType = applySubst rho $ conPType i }
+
+instance Subst Pattern where
+  type SubstArg Pattern = Term
+  applySubst rho = \case
+    ConP c mt ps    -> ConP c (applySubst rho mt) $ applySubst rho ps
+    DefP o q ps     -> DefP o q $ applySubst rho ps
+    DotP o t        -> DotP o $ applySubst rho t
+    p@(VarP _o _x)  -> p
+    p@(LitP _o _l)  -> p
+    p@(ProjP _o _x) -> p
+    IApplyP o t u x -> IApplyP o (applySubst rho t) (applySubst rho u) x
+
+instance Subst A.ProblemEq where
+  type SubstArg A.ProblemEq = Term
+  applySubst rho (A.ProblemEq p v a) =
+    uncurry (A.ProblemEq p) $ applySubst rho (v,a)
+
+instance DeBruijn BraveTerm where
+  deBruijnVar = BraveTerm . deBruijnVar
+  deBruijnView = deBruijnView . unBrave
+
+instance DeBruijn NLPat where
+  deBruijnVar i = PVar i []
+  deBruijnView = \case
+    PVar i []   -> Just i
+    PVar{}      -> Nothing
+    PDef{}      -> Nothing
+    PLam{}      -> Nothing
+    PPi{}       -> Nothing
+    PSort{}     -> Nothing
+    PBoundVar{} -> Nothing -- or... ?
+    PTerm{}     -> Nothing -- or... ?
+
+applyNLPatSubst :: TermSubst a => Substitution' NLPat -> a -> a
+applyNLPatSubst = applySubst . fmap nlPatToTerm
+  where
+    nlPatToTerm :: NLPat -> Term
+    nlPatToTerm = \case
+      PVar i xs      -> Var i $ map (Apply . fmap var) xs
+      PTerm u        -> u
+      PDef f es      -> __IMPOSSIBLE__
+      PLam i u       -> __IMPOSSIBLE__
+      PPi a b        -> __IMPOSSIBLE__
+      PSort s        -> __IMPOSSIBLE__
+      PBoundVar i es -> __IMPOSSIBLE__
+
+applyNLSubstToDom :: SubstWith NLPat a => Substitution' NLPat -> Dom a -> Dom a
+applyNLSubstToDom rho dom = applySubst rho <$> dom{ domTactic = applyNLPatSubst rho $ domTactic dom }
+
+instance Subst NLPat where
+  type SubstArg NLPat = NLPat
+  applySubst rho = \case
+    PVar i bvs     -> lookupS rho i `applyBV` bvs
+    PDef f es      -> PDef f $ applySubst rho es
+    PLam i u       -> PLam i $ applySubst rho u
+    PPi a b        -> PPi (applyNLSubstToDom rho a) (applySubst rho b)
+    PSort s        -> PSort $ applySubst rho s
+    PBoundVar i es -> PBoundVar i $ applySubst rho es
+    PTerm u        -> PTerm $ applyNLPatSubst rho u
+
+    where
+      applyBV :: NLPat -> [Arg Int] -> NLPat
+      applyBV p ys = case p of
+        PVar i xs      -> PVar i (xs ++ ys)
+        PTerm u        -> PTerm $ u `apply` map (fmap var) ys
+        PDef f es      -> __IMPOSSIBLE__
+        PLam i u       -> __IMPOSSIBLE__
+        PPi a b        -> __IMPOSSIBLE__
+        PSort s        -> __IMPOSSIBLE__
+        PBoundVar i es -> __IMPOSSIBLE__
+
+instance Subst NLPType where
+  type SubstArg NLPType = NLPat
+  applySubst rho (NLPType s a) = NLPType (applySubst rho s) (applySubst rho a)
+
+instance Subst NLPSort where
+  type SubstArg NLPSort = NLPat
+  applySubst rho = \case
+    PUniv u l -> PUniv u $ applySubst rho l
+    PInf f n  -> PInf f n
+    PSizeUniv -> PSizeUniv
+    PLockUniv -> PLockUniv
+    PLevelUniv -> PLevelUniv
+    PIntervalUniv -> PIntervalUniv
+
+instance Subst RewriteRule where
+  type SubstArg RewriteRule = NLPat
+  applySubst rho (RewriteRule q gamma f ps rhs t c) =
+    RewriteRule q (applyNLPatSubst rho gamma)
+                f (applySubst (liftS n rho) ps)
+                  (applyNLPatSubst (liftS n rho) rhs)
+                  (applyNLPatSubst (liftS n rho) t)
+                  c
+    where n = size gamma
+
+instance Subst a => Subst (Blocked a) where
+  type SubstArg (Blocked a) = SubstArg a
+  applySubst rho b = fmap (applySubst rho) b
+
+instance Subst DisplayForm where
+  type SubstArg DisplayForm = Term
+  applySubst rho (Display n ps v) =
+    Display n (applySubst (liftS n rho) ps)
+              (applySubst (liftS n rho) v)
+
+instance Subst DisplayTerm where
+  type SubstArg DisplayTerm = Term
+  applySubst rho (DTerm' v es)      = DTerm' (applySubst rho v) $ applySubst rho es
+  applySubst rho (DDot' v es)       = DDot'  (applySubst rho v) $ applySubst rho es
+  applySubst rho (DCon c ci vs)     = DCon c ci $ applySubst rho vs
+  applySubst rho (DDef c es)        = DDef c $ applySubst rho es
+  applySubst rho (DWithApp v vs es) = uncurry3 DWithApp $ applySubst rho (v, vs, es)
+
+instance Subst a => Subst (Tele a) where
+  type SubstArg (Tele a) = SubstArg a
+  applySubst rho  EmptyTel         = EmptyTel
+  applySubst rho (ExtendTel t tel) = uncurry ExtendTel $ applySubst rho (t, tel)
+
+instance Subst Constraint where
+  type SubstArg Constraint = Term
+
+  applySubst rho = \case
+    ValueCmp cmp a u v       -> ValueCmp cmp (rf a) (rf u) (rf v)
+    ValueCmpOnFace cmp p t u v -> ValueCmpOnFace cmp (rf p) (rf t) (rf u) (rf v)
+    ElimCmp ps fs a v e1 e2  -> ElimCmp ps fs (rf a) (rf v) (rf e1) (rf e2)
+    SortCmp cmp s1 s2        -> SortCmp cmp (rf s1) (rf s2)
+    LevelCmp cmp l1 l2       -> LevelCmp cmp (rf l1) (rf l2)
+    IsEmpty r a              -> IsEmpty r (rf a)
+    CheckSizeLtSat t         -> CheckSizeLtSat (rf t)
+    FindInstance m cands     -> FindInstance m (rf cands)
+    c@UnBlock{}              -> c
+    c@CheckFunDef{}          -> c
+    HasBiggerSort s          -> HasBiggerSort (rf s)
+    HasPTSRule a s           -> HasPTSRule (rf a) (rf s)
+    CheckLockedVars a b c d  -> CheckLockedVars (rf a) (rf b) (rf c) (rf d)
+    UnquoteTactic t h g      -> UnquoteTactic (rf t) (rf h) (rf g)
+    CheckDataSort q s        -> CheckDataSort q (rf s)
+    CheckMetaInst m          -> CheckMetaInst m
+    CheckType t              -> CheckType (rf t)
+    UsableAtModality cc ms mod m -> UsableAtModality cc (rf ms) mod (rf m)
+    where
+      rf :: forall a. TermSubst a => a -> a
+      rf x = applySubst rho x
+
+instance Subst CompareAs where
+  type SubstArg CompareAs = Term
+  applySubst rho (AsTermsOf a) = AsTermsOf $ applySubst rho a
+  applySubst rho AsSizes       = AsSizes
+  applySubst rho AsTypes       = AsTypes
+
+instance Subst a => Subst (Elim' a) where
+  type SubstArg (Elim' a) = SubstArg a
+  applySubst rho = \case
+    Apply v      -> Apply $ applySubst rho v
+    IApply x y r -> IApply (applySubst rho x) (applySubst rho y) (applySubst rho r)
+    e@Proj{}     -> e
+
+instance Subst a => Subst (Abs a) where
+  type SubstArg (Abs a) = SubstArg a
+  applySubst rho (Abs x a)   = Abs x $ applySubst (liftS 1 rho) a
+  applySubst rho (NoAbs x a) = NoAbs x $ applySubst rho a
+
+instance Subst a => Subst (Arg a) where
+  type SubstArg (Arg a) = SubstArg a
+  applySubst IdS arg = arg
+  applySubst rho arg = setFreeVariables unknownFreeVariables $ fmap (applySubst rho) arg
+
+instance Subst a => Subst (Named name a) where
+  type SubstArg (Named name a) = SubstArg a
+  applySubst rho = fmap (applySubst rho)
+
+instance (Subst a, Subst b, SubstArg a ~ SubstArg b) => Subst (Dom' a b) where
+  type SubstArg (Dom' a b) = SubstArg a
+
+  applySubst IdS dom = dom
+  applySubst rho dom = setFreeVariables unknownFreeVariables $
+    fmap (applySubst rho) dom{ domTactic = applySubst rho (domTactic dom) }
+  {-# INLINABLE applySubst #-}
+
+instance Subst LetBinding where
+  type SubstArg LetBinding = Term
+  applySubst rho (LetBinding o v t) = LetBinding o (applySubst rho v) (applySubst rho t)
+
+instance Subst a => Subst (Maybe a) where
+  type SubstArg (Maybe a) = SubstArg a
+
+instance Subst a => Subst [a] where
+  type SubstArg [a] = SubstArg a
+
+instance (Ord k, Subst a) => Subst (Map k a) where
+  type SubstArg (Map k a) = SubstArg a
+
+instance Subst a => Subst (WithHiding a) where
+  type SubstArg (WithHiding a) = SubstArg a
+
+instance Subst () where
+  type SubstArg () = Term
+  applySubst _ _ = ()
+
+instance (Subst a, Subst b, SubstArg a ~ SubstArg b) => Subst (a, b) where
+  type SubstArg (a, b) = SubstArg a
+  applySubst rho (x,y) = (applySubst rho x, applySubst rho y)
+
+instance (Subst a, Subst b, Subst c, SubstArg a ~ SubstArg b, SubstArg b ~ SubstArg c) => Subst (a, b, c) where
+  type SubstArg (a, b, c) = SubstArg a
+  applySubst rho (x,y,z) = (applySubst rho x, applySubst rho y, applySubst rho z)
+
+instance
+  ( Subst a, Subst b, Subst c, Subst d
+  , SubstArg a ~ SubstArg b
+  , SubstArg b ~ SubstArg c
+  , SubstArg c ~ SubstArg d
+  ) => Subst (a, b, c, d) where
+  type SubstArg (a, b, c, d) = SubstArg a
+  applySubst rho (x,y,z,u) = (applySubst rho x, applySubst rho y, applySubst rho z, applySubst rho u)
+
+instance Subst Candidate where
+  type SubstArg Candidate = Term
+  applySubst rho (Candidate q u t ov) = Candidate q (applySubst rho u) (applySubst rho t) ov
+
+instance Subst EqualityView where
+  type SubstArg EqualityView = Term
+  applySubst rho = \case
+    OtherType t          -> OtherType $ applySubst rho t
+    IdiomType t          -> IdiomType $ applySubst rho t
+    EqualityViewType eqt -> EqualityViewType $ applySubst rho eqt
+
+instance Subst EqualityTypeData where
+  type SubstArg EqualityTypeData = Term
+  applySubst rho (EqualityTypeData s eq l t a b) = EqualityTypeData
+    (applySubst rho s)
+    eq
+    (map (applySubst rho) l)
+    (applySubst rho t)
+    (applySubst rho a)
+    (applySubst rho b)
+
+instance DeBruijn a => DeBruijn (Pattern' a) where
+  debruijnNamedVar n i             = varP $ debruijnNamedVar n i
+  -- deBruijnView returns Nothing, to prevent consS and the like
+  -- from dropping the names and origins when building a substitution.
+  deBruijnView _                   = Nothing
+
+fromPatternSubstitution :: PatternSubstitution -> Substitution
+fromPatternSubstitution = fmap patternToTerm
+
+applyPatSubst :: TermSubst a => PatternSubstitution -> a -> a
+applyPatSubst = applySubst . fromPatternSubstitution
+
+
+usePatOrigin :: PatOrigin -> Pattern' a -> Pattern' a
+usePatOrigin o p = case patternInfo p of
+  Nothing -> p
+  Just i  -> usePatternInfo (i { patOrigin = o }) p
+
+usePatternInfo :: PatternInfo -> Pattern' a -> Pattern' a
+usePatternInfo i p = case patternOrigin p of
+  Nothing         -> p
+  Just PatOSplit  -> p
+  Just PatOAbsurd -> p
+  Just _          -> case p of
+    (VarP _ x) -> VarP i x
+    (DotP _ u) -> DotP i u
+    (ConP c (ConPatternInfo _ r ft b l) ps)
+      -> ConP c (ConPatternInfo i r ft b l) ps
+    DefP _ q ps -> DefP i q ps
+    (LitP _ l) -> LitP i l
+    ProjP{} -> __IMPOSSIBLE__
+    (IApplyP _ t u x) -> IApplyP i t u x
+
+instance Subst DeBruijnPattern where
+  type SubstArg DeBruijnPattern = DeBruijnPattern
+  applySubst IdS = id
+  applySubst rho = \case
+    VarP i x     ->
+      usePatternInfo i $
+      useName (dbPatVarName x) $
+      lookupS rho $ dbPatVarIndex x
+    DotP i u     -> DotP i $ applyPatSubst rho u
+    ConP c ci ps -> ConP c ci {conPType = applyPatSubst rho (conPType ci)} $ applySubst rho ps
+    DefP i q ps  -> DefP i q $ applySubst rho ps
+    p@(LitP _ _) -> p
+    p@ProjP{}    -> p
+    IApplyP i t u x ->
+      case useName (dbPatVarName x) $ lookupS rho $ dbPatVarIndex x of
+        IApplyP _ _ _ y -> IApplyP i (applyPatSubst rho t) (applyPatSubst rho u) y
+        VarP  _ y       -> IApplyP i (applyPatSubst rho t) (applyPatSubst rho u) y
+        _ -> __IMPOSSIBLE__
+    where
+      useName :: PatVarName -> DeBruijnPattern -> DeBruijnPattern
+      useName n (VarP o x)
+        | isUnderscore (dbPatVarName x)
+        = VarP o $ x { dbPatVarName = n }
+      useName _ x = x
+
+instance Subst Range where
+  type SubstArg Range = Term
+  applySubst _ = id
+
+---------------------------------------------------------------------------
+-- * Projections
+---------------------------------------------------------------------------
+
+-- | @projDropParsApply proj o args = 'projDropPars' proj o `'apply'` args@
+--
+--   This function is an optimization, saving us from construction lambdas we
+--   immediately remove through application.
+projDropParsApply :: Projection -> ProjOrigin -> Relevance -> Args -> Term
+projDropParsApply (Projection prop d r _ lams) o rel args =
+  case initLast $ getProjLams lams of
+    -- If we have no more abstractions, we must be a record field
+    -- (projection applied already to record value).
+    Nothing -> if proper then Def d $ map Apply args else __IMPOSSIBLE__
+    Just (pars, Arg i y) ->
+      let irr = isIrrelevant rel
+          core
+            | proper && not irr = Lam i $ Abs y $ Var 0 [Proj o d]
+            | otherwise         = Lam i $ Abs y $ Def d [Apply $ Var 0 [] <$ r]
+            -- Issue2226: get ArgInfo for principal argument from projFromType
+      -- Now drop pars many args
+          (pars', args') = dropCommon pars args
+      -- We only have to abstract over the parameters that exceed the arguments.
+      -- We only have to apply to the arguments that exceed the parameters.
+      in List.foldr (\ (Arg ai x) -> Lam ai . NoAbs x) (core `apply` args') pars'
+  where proper = isJust prop
+
+---------------------------------------------------------------------------
+-- * Telescopes
+---------------------------------------------------------------------------
+
+-- ** Telescope view of a type
+
+type TelView = TelV Type
+data TelV a  = TelV { theTel :: Tele (Dom a), theCore :: a }
+  deriving (Show, Functor)
+
+deriving instance (TermSubst a, Eq  a) => Eq  (TelV a)
+deriving instance (TermSubst a, Ord a) => Ord (TelV a)
+
+-- | Takes off all exposed function domains from the given type.
+--   This means that it does not reduce to expose @Pi@-types.
+telView' :: Type -> TelView
+telView' = telView'UpTo (-1)
+
+-- | @telView'UpTo n t@ takes off the first @n@ exposed function types of @t@.
+-- Takes off all (exposed ones) if @n < 0@.
+telView'UpTo :: Int -> Type -> TelView
+telView'UpTo 0 t = TelV EmptyTel t
+telView'UpTo n t = case unEl t of
+  Pi a b  -> absV a (absName b) $ telView'UpTo (n - 1) (absBody b)
+  _       -> TelV EmptyTel t
+
+-- | Add given binding to the front of the telescope.
+absV :: Dom a -> ArgName -> TelV a -> TelV a
+absV a x (TelV tel t) = TelV (ExtendTel a (Abs x tel)) t
+
+
+-- ** Creating telescopes from lists of types
+
+-- | Turn a typed binding @(x1 .. xn : A)@ into a telescope.
+bindsToTel' :: (Name -> a) -> [Name] -> Dom Type -> ListTel' a
+bindsToTel' f []     t = []
+bindsToTel' f (x:xs) t = fmap (f x,) t : bindsToTel' f xs (raise 1 t)
+
+bindsToTel :: [Name] -> Dom Type -> ListTel
+bindsToTel = bindsToTel' nameToArgName
+
+bindsToTel'1 :: (Name -> a) -> List1 Name -> Dom Type -> ListTel' a
+bindsToTel'1 f = bindsToTel' f . List1.toList
+
+bindsToTel1 :: List1 Name -> Dom Type -> ListTel
+bindsToTel1 = bindsToTel . List1.toList
+
+-- | Turn a typed binding @(x1 .. xn : A)@ into a telescope.
+namedBindsToTel :: [NamedArg Name] -> Type -> Telescope
+namedBindsToTel []       t = EmptyTel
+namedBindsToTel (x : xs) t =
+  ExtendTel (t <$ domFromNamedArgName x) $ Abs (nameToArgName $ namedArg x) $ namedBindsToTel xs (raise 1 t)
+
+namedBindsToTel1 :: List1 (NamedArg Name) -> Type -> Telescope
+namedBindsToTel1 = namedBindsToTel . List1.toList
+
+domFromNamedArgName :: NamedArg Name -> Dom ()
+domFromNamedArgName x = () <$ domFromNamedArg (fmap forceName x)
+  where
+    -- If no explicit name is given we use the bound name for the label.
+    forceName (Named Nothing x) = Named (Just $ WithOrigin Inserted $ Ranged (getRange x) $ nameToArgName x) x
+    forceName x = x
+
+-- ** Abstracting in terms and types
+
+mkPiSort :: Dom Type -> Abs Type -> Sort
+mkPiSort a b = piSort (unEl <$> a) (getSort $ unDom a) (getSort <$> b)
+
+-- | @mkPi dom t = telePi (telFromList [dom]) t@
+mkPi :: Dom (ArgName, Type) -> Type -> Type
+mkPi !dom b = el $ Pi a (mkAbs x b)
+  where
+    x = fst $ unDom dom
+    a = snd <$> dom
+    el = El $ mkPiSort a (Abs x b)
+
+mkLam :: Arg ArgName -> Term -> Term
+mkLam a v = Lam (argInfo a) (Abs (unArg a) v)
+
+lamView :: Term -> ([Arg ArgName], Term)
+lamView (Lam h (Abs   x b)) = first (Arg h x :) $ lamView b
+lamView (Lam h (NoAbs x b)) = first (Arg h x :) $ lamView (raise 1 b)
+lamView t                   = ([], t)
+
+unlamView :: [Arg ArgName] -> Term -> Term
+unlamView xs b = foldr mkLam b xs
+
+telePi' :: (Abs Type -> Abs Type) -> Telescope -> Type -> Type
+telePi' reAbs = telePi where
+  telePi EmptyTel          t = t
+  telePi (ExtendTel u tel) t = el $ Pi u $ reAbs b
+    where
+      b  = (`telePi` t) <$> tel
+      el = El $ mkPiSort u b
+
+-- | Uses free variable analysis to introduce 'NoAbs' bindings.
+telePi :: Telescope -> Type -> Type
+telePi = telePi' reAbs
+
+-- | Everything will be an 'Abs'.
+telePi_ :: Telescope -> Type -> Type
+telePi_ = telePi' id
+
+-- | Only abstract the visible components of the telescope,
+--   and all that bind variables.  Everything will be an 'Abs'!
+-- Caution: quadratic time!
+
+telePiVisible :: Telescope -> Type -> Type
+telePiVisible EmptyTel t = t
+telePiVisible (ExtendTel u tel) t
+    -- If u is not declared visible and b can be strengthened, skip quantification of u.
+    | notVisible u, NoAbs x t' <- b' = t'
+    -- Otherwise, include quantification over u.
+    | otherwise = El (mkPiSort u b) $ Pi u b
+  where
+    b  = tel <&> (`telePiVisible` t)
+    b' = reAbs b
+
+-- | Abstract over a telescope in a term, producing lambdas.
+--   Dumb abstraction: Always produces 'Abs', never 'NoAbs'.
+--
+--   The implementation is sound because 'Telescope' does not use 'NoAbs'.
+teleLam :: Telescope -> Term -> Term
+teleLam  EmptyTel         t = t
+teleLam (ExtendTel u tel) t = Lam (domInfo u) $ flip teleLam t <$> tel
+
+-- | Performs void ('noAbs') abstraction over telescope.
+class TeleNoAbs a where
+  teleNoAbs :: a -> Term -> Term
+
+instance TeleNoAbs ListTel where
+  teleNoAbs tel t = foldr (\ Dom{domInfo = ai, unDom = (x, _)} -> Lam ai . NoAbs x) t tel
+
+instance TeleNoAbs Telescope where
+  teleNoAbs tel = teleNoAbs $ telToList tel
+
+
+-- ** Telescope typing
+
+-- | Given arguments @vs : tel@ (vector typing), extract their individual types.
+--   Returns @Nothing@ is @tel@ is not long enough.
+
+typeArgsWithTel :: Telescope -> [Term] -> Maybe [Dom Type]
+typeArgsWithTel _ []                         = return []
+typeArgsWithTel (ExtendTel dom tel) (v : vs) = (dom :) <$> typeArgsWithTel (absApp tel v) vs
+typeArgsWithTel EmptyTel{} (_:_)             = Nothing
+
+---------------------------------------------------------------------------
+-- * Clauses
+---------------------------------------------------------------------------
+
+-- | In compiled clauses, the variables in the clause body are relative to the
+--   pattern variables (including dot patterns) instead of the clause telescope.
+compiledClauseBody :: Clause -> Maybe Term
+compiledClauseBody cl = applySubst (renamingR perm) $ clauseBody cl
+  where perm = fromMaybe __IMPOSSIBLE__ $ clausePerm cl
+
+---------------------------------------------------------------------------
+-- * Syntactic equality and order
+--
+-- Needs weakening.
+---------------------------------------------------------------------------
+
+deriving instance Eq Substitution
+deriving instance Ord Substitution
+
+deriving instance Eq Sort
+deriving instance Ord Sort
+deriving instance Eq Level
+deriving instance Ord Level
+deriving instance Eq PlusLevel
+deriving instance Eq NotBlocked
+deriving instance Eq t => Eq (Blocked t)
+deriving instance Eq CandidateKind
+deriving instance Eq Candidate
+
+deriving instance (Subst a, Eq a)  => Eq  (Tele a)
+deriving instance (Subst a, Ord a) => Ord (Tele a)
+
+-- Andreas, 2019-11-16, issue #4201: to avoid potential unintended
+-- performance loss, the Eq instance for Constraint is disabled:
+--
+-- -- deriving instance Eq Constraint
+--
+-- I am tempted to write
+--
+--   instance Eq Constraint where (==) = undefined
+--
+-- but this does not give a compilation error anymore when trying
+-- to use equality on constraints.
+-- Therefore, I hope this comment is sufficient to prevent a resurrection
+-- of the Eq instance for Constraint.
+
+deriving instance Eq Section
+
+instance Ord PlusLevel where
+  -- Compare on the atom first. Makes most sense for levelMax.
+  compare (Plus n a) (Plus m b) = compare (a,n) (b,m)
+
+-- | Syntactic 'Type' equality, ignores sort annotations.
+instance Eq a => Eq (Type' a) where
+  (==) = (==) `on` unEl
+
+instance Ord a => Ord (Type' a) where
+  compare = compare `on` unEl
+
+-- | Syntactic 'Term' equality, ignores stuff below @DontCare@ and sharing.
+instance Eq Term where
+  Var x vs   == Var x' vs'   = x == x' && vs == vs'
+  Lam h v    == Lam h' v'    = h == h' && v  == v'
+  Lit l      == Lit l'       = l == l'
+  Def x vs   == Def x' vs'   = x == x' && vs == vs'
+  Con x _ vs == Con x' _ vs' = x == x' && vs == vs'
+  Pi a b     == Pi a' b'     = a == a' && b == b'
+  Sort s     == Sort s'      = s == s'
+  Level l    == Level l'     = l == l'
+  MetaV m vs == MetaV m' vs' = m == m' && vs == vs'
+  DontCare _ == DontCare _   = True
+  Dummy{}    == Dummy{}      = True
+  _          == _            = False
+
+instance Eq a => Eq (Pattern' a) where
+  VarP _ x        == VarP _ y          = x == y
+  DotP _ u        == DotP _ v          = u == v
+  ConP c _ ps     == ConP c' _ qs      = c == c && ps == qs
+  LitP _ l        == LitP _ l'         = l == l'
+  ProjP _ f       == ProjP _ g         = f == g
+  IApplyP _ u v x == IApplyP _ u' v' y = u == u' && v == v' && x == y
+  DefP _ f ps     == DefP _ g qs       = f == g && ps == qs
+  _               == _                 = False
+
+instance Ord Term where
+  Var a b    `compare` Var x y    = compare (x, b) (a, y)
+                                    -- sort de Bruijn indices down (#2765)
+  Var{}      `compare` _          = LT
+  _          `compare` Var{}      = GT
+  Def a b    `compare` Def x y    = compare (a, b) (x, y)
+  Def{}      `compare` _          = LT
+  _          `compare` Def{}      = GT
+  Con a _ b  `compare` Con x _ y  = compare (a, b) (x, y)
+  Con{}      `compare` _          = LT
+  _          `compare` Con{}      = GT
+  Lit a      `compare` Lit x      = compare a x
+  Lit{}      `compare` _          = LT
+  _          `compare` Lit{}      = GT
+  Lam a b    `compare` Lam x y    = compare (a, b) (x, y)
+  Lam{}      `compare` _          = LT
+  _          `compare` Lam{}      = GT
+  Pi a b     `compare` Pi x y     = compare (a, b) (x, y)
+  Pi{}       `compare` _          = LT
+  _          `compare` Pi{}       = GT
+  Sort a     `compare` Sort x     = compare a x
+  Sort{}     `compare` _          = LT
+  _          `compare` Sort{}     = GT
+  Level a    `compare` Level x    = compare a x
+  Level{}    `compare` _          = LT
+  _          `compare` Level{}    = GT
+  MetaV a b  `compare` MetaV x y  = compare (a, b) (x, y)
+  MetaV{}    `compare` _          = LT
+  _          `compare` MetaV{}    = GT
+  DontCare{} `compare` DontCare{} = EQ
+  DontCare{} `compare` _          = LT
+  _          `compare` DontCare{} = GT
+  Dummy{}    `compare` Dummy{}    = EQ
+
+-- Andreas, 2017-10-04, issue #2775, ignore irrelevant arguments during with-abstraction.
+--
+-- For reasons beyond my comprehension, the following Eq instances are not employed
+-- by with-abstraction in TypeChecking.Abstract.isPrefixOf.
+-- Instead, I modified the general Eq instance for Arg to ignore the argument
+-- if irrelevant.
+
+-- -- | Ignore irrelevant arguments in equality check.
+-- --   Also ignore origin.
+-- instance {-# OVERLAPPING #-} Eq (Arg Term) where
+--   a@(Arg (ArgInfo h r _o) t) == a'@(Arg (ArgInfo h' r' _o') t') = trace ("Eq (Arg Term) on " ++ show a ++ " and " ++ show a') $
+--     h == h' && ((r == Irrelevant) || (r' == Irrelevant) || (t == t'))
+--     -- Andreas, 2017-10-04: According to Syntax.Common, equality on Arg ignores Relevance and Origin.
+
+-- instance {-# OVERLAPPING #-} Eq Args where
+--   us == vs = length us == length vs && and (zipWith (==) us vs)
+
+-- instance {-# OVERLAPPING #-} Eq Elims where
+--   us == vs = length us == length vs && and (zipWith (==) us vs)
+
+-- | Equality of binders relies on weakening
+--   which is a special case of renaming
+--   which is a special case of substitution.
+instance (Subst a, Eq a) => Eq (Abs a) where
+  NoAbs _ a == NoAbs _ b = a == b  -- no need to raise if both are NoAbs
+  a         == b         = absBody a == absBody b
+
+instance (Subst a, Ord a) => Ord (Abs a) where
+  NoAbs _ a `compare` NoAbs _ b = a `compare` b  -- no need to raise if both are NoAbs
+  a         `compare` b         = absBody a `compare` absBody b
+
+deriving instance Ord a => Ord (Dom a)
+
+instance (Subst a, Eq a)  => Eq  (Elim' a) where
+  Apply  a == Apply  b = a == b
+  Proj _ x == Proj _ y = x == y
+  IApply x y r == IApply x' y' r' = x == x' && y == y' && r == r'
+  _ == _ = False
+
+instance (Subst a, Ord a) => Ord (Elim' a) where
+  Apply  a `compare` Apply  b = a `compare` b
+  Proj _ x `compare` Proj _ y = x `compare` y
+  IApply x y r `compare` IApply x' y' r' = compare x x' `mappend` compare y y' `mappend` compare r r'
+  Apply{}  `compare` _        = LT
+  _        `compare` Apply{}  = GT
+  Proj{}   `compare` _        = LT
+  _        `compare` Proj{}   = GT
+
+
+---------------------------------------------------------------------------
+-- * Sort stuff
+---------------------------------------------------------------------------
+
+-- | @univSort' univInf s@ gets the next higher sort of @s@, if it is
+--   known (i.e. it is not just @UnivSort s@).
+--
+--   Precondition: @s@ is reduced
+univSort' :: Sort -> Either Blocker Sort
+univSort' (Univ u l)   = Right $ Univ (univUniv u) $ levelSuc l
+univSort' (Inf u n)    = Right $ Inf (univUniv u) $ 1 + n
+univSort' SizeUniv     = Right $ Inf UType 0
+univSort' LockUniv     = Right $ Type $ ClosedLevel 1
+univSort' LevelUniv    = Right $ Type $ ClosedLevel 1
+univSort' IntervalUniv = Right $ SSet $ ClosedLevel 1
+univSort' (MetaS m _)  = Left neverUnblock
+univSort' FunSort{}    = Left neverUnblock
+univSort' PiSort{}     = Left neverUnblock
+univSort' UnivSort{}   = Left neverUnblock
+univSort' DefS{}       = Left neverUnblock
+univSort' DummyS{}     = Left neverUnblock
+
+univSort :: Sort -> Sort
+univSort s = fromRight (const $ UnivSort s) $ univSort' s
+
+sort :: Sort -> Type
+sort s = El (univSort s) $ Sort s
+
+ssort :: Level -> Type
+ssort l = sort (SSet l)
+
+-- | A sort can either be small (Set l, Prop l, Size, ...)  or large
+--   (Setω n).
+data SizeOfSort = SizeOfSort
+  { szSortUniv :: Univ
+  , szSortSize :: Integer
+  }
+
+pattern SmallSort :: Univ -> SizeOfSort
+pattern SmallSort u = SizeOfSort u (-1)
+
+pattern LargeSort :: Univ -> Integer -> SizeOfSort
+-- What I want to write here is:
+-- @
+--   pattern LargeSort u n = SizeOfSort u n | n >= 0
+-- @
+-- But I have to write:
+pattern LargeSort u n <- ((\ x@(SizeOfSort u n) -> guard (n >= 0) $> x) -> Just (SizeOfSort u n))
+-- DON'T WORK:
+-- pattern LargeSort u n <- (n >= 0 -> True)
+-- pattern LargeSort u n <- (n >= 0 -> SizeOfSort u n)
+-- pattern LargeSort u n <- ((>= 0) . szSortSize -> SizeOfSort u n)
+  where LargeSort u n = SizeOfSort u n
+
+{-# COMPLETE SmallSort, LargeSort #-}
+
+-- | Returns @Left blocker@ for unknown (blocked) sorts, and otherwise
+--   returns @Right s@ where @s@ indicates the size and fibrancy.
+sizeOfSort :: Sort -> Either Blocker SizeOfSort
+sizeOfSort = \case
+  Univ u _     -> Right $ SmallSort u
+  SizeUniv     -> Right $ SmallSort UType
+  LockUniv     -> Right $ SmallSort UType
+  LevelUniv    -> Right $ SmallSort UType
+  IntervalUniv -> Right $ SmallSort USSet
+  Inf u n      -> Right $ LargeSort u n
+  MetaS m _    -> Left $ unblockOnMeta m
+  FunSort{}    -> Left neverUnblock
+  PiSort{}     -> Left neverUnblock
+  UnivSort{}   -> Left neverUnblock
+  DefS{}       -> Left neverUnblock
+  DummyS{}     -> Left neverUnblock
+
+isSmallSort :: Sort -> Bool
+isSmallSort s = case sizeOfSort s of
+  Right SmallSort{} -> True
+  _                 -> False
+
+-- | Compute the sort of a function type from the sorts of its domain and codomain.
+--
+--   This function should only be called on reduced sorts,
+--   since the @LevelUniv@ rules should only apply when the sort does not reduce to @Set@.
+funSort' :: Sort -> Sort -> Either Blocker Sort
+-- Andreas, 2023-05-12, AIM XXXVI, pri #6623:
+-- On GHC 8.6 and 8.8 this pattern matching triggers warning
+-- "Pattern match checker exceeded (2000000) iterations in a case alternative."
+-- No clue how to turn off this warning, so we have to turn off -Werror for GHC < 8.10.
+funSort' = curry \case
+  (Univ u a      , Univ u' b    ) -> Right $ Univ (funUniv u u') $ levelLub a b
+  (Inf ua m      , b            ) -> sizeOfSort b <&> \ (SizeOfSort ub n) -> Inf (funUniv ua ub) (max m n)
+  (a             , Inf ub n     ) -> sizeOfSort a <&> \ (SizeOfSort ua m) -> Inf (funUniv ua ub) (max m n)
+  (LockUniv      , LevelUniv    ) -> Left neverUnblock
+  (LockUniv      , b            ) -> Right b
+  -- No functions into lock types
+  (a             , LockUniv     ) -> Left neverUnblock
+  -- @IntervalUniv@ behaves like @SSet@, but functions into @Type@ land in @Type@
+  (IntervalUniv  , IntervalUniv ) -> Right $ SSet $ ClosedLevel 0
+  (IntervalUniv  , Univ u b     ) -> Right $ Univ u b
+  (IntervalUniv  , _            ) -> Left neverUnblock
+  (Univ u a      , IntervalUniv ) -> Right $ SSet $ a
+  (_             , IntervalUniv ) -> Left neverUnblock
+  (SizeUniv      , b            ) -> Right b
+  (a             , SizeUniv     ) -> sizeOfSort a >>= \case
+    SmallSort{} -> Right SizeUniv
+    LargeSort{} -> Left neverUnblock
+  -- No need to handle @LevelUniv@ in a special way here when --level-universe isn't on,
+  -- since this function is currently always called after reduction.
+  -- It would be safer to take it into account here, but would imply passing the option along as an argument.
+  (LevelUniv     , LevelUniv    ) -> Right LevelUniv
+  (_             , LevelUniv    ) -> Left neverUnblock
+  (LevelUniv     , b            ) -> sizeOfSort b <&> \case
+    SmallSort ub -> Inf ub 0
+    LargeSort{}  -> b
+  (MetaS m _     , _            ) -> Left $ unblockOnMeta m
+  (_             , MetaS m _    ) -> Left $ unblockOnMeta m
+  (FunSort{}     , _            ) -> Left neverUnblock
+  (_             , FunSort{}    ) -> Left neverUnblock
+  (PiSort{}      , _            ) -> Left neverUnblock
+  (_             , PiSort{}     ) -> Left neverUnblock
+  (UnivSort{}    , _            ) -> Left neverUnblock
+  (_             , UnivSort{}   ) -> Left neverUnblock
+  (DefS{}        , _            ) -> Left neverUnblock
+  (_             , DefS{}       ) -> Left neverUnblock
+  (DummyS{}      , _            ) -> Left neverUnblock
+  (_             , DummyS{}     ) -> Left neverUnblock
+
+funSort :: Sort -> Sort -> Sort
+funSort a b = fromRight (const $ FunSort a b) $ funSort' a b
+
+-- | Compute the sort of a pi type from the sorts of its domain
+--   and codomain.
+-- This function should only be called on reduced sorts, since the @LevelUniv@ rules should only apply when the sort doesn't reduce to @Set@
+piSort' :: Dom Term -> Sort -> Abs Sort -> Either Blocker Sort
+piSort' a s1       (NoAbs _ s2) = Right $ FunSort s1 s2
+piSort' a s1 s2Abs@(Abs   _ s2) = case flexRigOccurrenceIn 0 s2 of
+  Nothing -> Right $ FunSort s1 $ noabsApp __IMPOSSIBLE__ s2Abs
+  Just o  -> case (sizeOfSort s1 , sizeOfSort s2) of
+    (Right (SmallSort u1) , Right (SmallSort u2)) -> case o of
+      StronglyRigid -> Right $ Inf (funUniv u1 u2) 0
+      Unguarded     -> Right $ Inf (funUniv u1 u2) 0
+      WeaklyRigid   -> Right $ Inf (funUniv u1 u2) 0
+      Flexible ms   -> Left $ metaSetToBlocker ms
+    (Right (LargeSort u1 n) , Right (SmallSort u2)) -> Right $ Inf (funUniv u1 u2) n
+    (_                     , Right LargeSort{}    ) ->
+       -- large sorts cannot depend on variables
+       __IMPOSSIBLE__
+       -- (`trace` __IMPOSSIBLE__) $ unlines
+       --   [ "piSort': unexpected dependency in large codomain s2"
+       --   , "- a  = " ++ prettyShow a
+       --   , "- s1 = " ++ prettyShow s1
+       --   , "- s2 = " ++ prettyShow s2
+       --   , "- s2 (raw) = " ++ show s2
+       --   ]
+    (Left blocker          , Right _              ) -> Left blocker
+    (Right _               , Left blocker         ) -> Left blocker
+    (Left blocker1         , Left blocker2        ) -> Left $ unblockOnBoth blocker1 blocker2
+
+-- Andreas, 2019-06-20
+-- KEEP the following commented out code for the sake of the discussion on irrelevance.
+-- piSort' a bAbs@(Abs   _ b) = case occurrence 0 b of
+--     -- Andreas, Jesper, AIM XXIX, 2019-03-18, issue #3631
+--     -- Remember the NoAbs here!
+--     NoOccurrence  -> Just $ funSort a $ noabsApp __IMPOSSIBLE__ bAbs
+--     -- Andreas, 2017-01-18, issue #2408:
+--     -- The sort of @.(a : A) → Set (f a)@ in context @f : .A → Level@
+--     -- is @dLub Set λ a → Set (lsuc (f a))@, but @DLub@s are not serialized.
+--     -- Alternatives:
+--     -- 1. -- Irrelevantly -> sLub s1 (absApp b $ DontCare $ Sort Prop)
+--     --    We cheat here by simplifying the sort to @Set (lsuc (f *))@
+--     --    where * is a dummy value.  The rationale is that @f * = f a@ (irrelevance!)
+--     --    and that if we already have a neutral level @f a@
+--     --    it should not hurt to have @f *@ even if type @A@ is empty.
+--     --    However: sorts are printed in error messages when sorts do not match.
+--     --    Also, sorts with a dummy like Prop would be ill-typed.
+--     -- 2. We keep the DLub, and serialize it.
+--     --    That's clean and principled, even though DLubs make level solving harder.
+--     -- Jesper, 2018-04-20: another alternative:
+--     -- 3. Return @Inf@ as in the relevant case. This is conservative and might result
+--     --    in more occurrences of @Setω@ than desired, but at least it doesn't pollute
+--     --    the sort system with new 'exotic' sorts.
+--     Irrelevantly  -> Just Inf
+--     StronglyRigid -> Just Inf
+--     Unguarded     -> Just Inf
+--     WeaklyRigid   -> Just Inf
+--     Flexible _    -> Nothing
+
+piSort :: Dom Term -> Sort -> Abs Sort -> Sort
+piSort a s1 s2 = fromRight (const $ PiSort a s1 s2) $ piSort' a s1 s2
+
+---------------------------------------------------------------------------
+-- * Level stuff
+---------------------------------------------------------------------------
+
+-- ^ Computes @n0 ⊔ a₁ ⊔ a₂ ⊔ ... ⊔ aₙ@ and return its canonical form.
+levelMax :: Integer -> [PlusLevel] -> Level
+levelMax !n0 as0 = Max n as
+  where
+    -- step 1: flatten nested @Level@ expressions in @PlusLevel@s
+    Max n1 as1 = expandLevel $ Max n0 as0
+    -- step 2: remove subsumed @PlusLevel@s and sort what remains
+    as        = removeSubsumed as1
+    -- step 3: set constant to 0 if it is subsumed by one of the @PlusLevel@s
+    greatestB = Prelude.maximum $ 0 : [ n | Plus n _ <- as ]
+    n | n1 > greatestB = n1
+      | otherwise      = 0
+
+    lmax :: Integer -> [PlusLevel] -> [Level] -> Level
+    lmax m as []              = Max m as
+    lmax m as (Max n bs : ls) = lmax (max m n) (bs ++ as) ls
+
+    expandLevel :: Level -> Level
+    expandLevel (Max m as) = lmax m [] $ map expandPlus as
+
+    expandPlus :: PlusLevel -> Level
+    expandPlus (Plus m l) = levelPlus m (expandTm l)
+
+    expandTm (Level l)       = expandLevel l
+    expandTm l               = atomicLevel l
+
+    removeSubsumed =
+      map (\(a, n) -> Plus n a) .
+      MapS.toAscList .
+      MapS.fromListWith max .
+      map (\(Plus n a) -> (a, n))
+
+-- | Given two levels @a@ and @b@, compute @a ⊔ b@ and return its
+--   canonical form.
+levelLub :: Level -> Level -> Level
+levelLub (Max m as) (Max n bs) = levelMax (max m n) $ as ++ bs
+
+levelTm :: Level -> Term
+levelTm l =
+  case l of
+    Max 0 [Plus 0 l] -> l
+    _                -> Level l
diff --git a/src/full/Agda/TypeChecking/Substitute/Class.hs b/src/full/Agda/TypeChecking/Substitute/Class.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Substitute/Class.hs
@@ -0,0 +1,350 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Substitute.Class where
+
+import Control.Arrow ((***), second)
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Substitute.DeBruijn
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Application
+---------------------------------------------------------------------------
+
+-- | Apply something to a bunch of arguments.
+--   Preserves blocking tags (application can never resolve blocking).
+class Apply t where
+  apply  :: t -> Args -> t
+  applyE :: t -> Elims -> t
+
+  apply t args = applyE t $ map Apply args
+  -- Andreas, 2018-06-18, issue #3136
+  -- This default instance should be removed to get more precise
+  -- crash locations (raise the IMPOSSIBLE in a more specific place).
+  -- applyE t es  = apply  t $ fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+    -- precondition: all @es@ are @Apply@s
+
+-- | Apply to some default arguments.
+applys :: Apply t => t -> [Term] -> t
+applys t vs = apply t $ map defaultArg vs
+
+-- | Apply to a single default argument.
+apply1 :: Apply t => t -> Term -> t
+apply1 t u = applys t [ u ]
+
+---------------------------------------------------------------------------
+-- * Abstraction
+---------------------------------------------------------------------------
+
+-- | @(abstract args v) `apply` args --> v[args]@.
+class Abstract t where
+  abstract :: Telescope -> t -> t
+
+---------------------------------------------------------------------------
+-- * Substitution and shifting\/weakening\/strengthening
+---------------------------------------------------------------------------
+
+-- | Apply a substitution.
+
+-- For terms:
+--
+--  Γ ⊢ ρ : Δ
+--  Δ ⊢ t : A
+-- -----------
+-- Γ ⊢ tρ : Aρ
+
+class DeBruijn (SubstArg a) => Subst a where
+  type SubstArg a
+  applySubst :: Substitution' (SubstArg a) -> a -> a
+
+  default applySubst :: (a ~ f b, Functor f, Subst b, SubstArg a ~ SubstArg b) => Substitution' (SubstArg a) -> a -> a
+  applySubst rho = fmap (applySubst rho)
+
+-- | Simple constraint alias for a `Subst` instance `a` with arg type `t`.
+type SubstWith t a = (Subst a, SubstArg a ~ t)
+
+-- | `Subst` instance whose agument type is itself
+type EndoSubst a = SubstWith a a
+
+-- | `Subst` instance whose argument type is `Term`
+type TermSubst a = SubstWith Term a
+
+-- | Raise de Bruijn index, i.e. weakening
+raise :: Subst a => Nat -> a -> a
+raise = raiseFrom 0
+
+raiseFrom :: Subst a => Nat -> Nat -> a -> a
+raiseFrom n k = applySubst (raiseFromS n k)
+
+-- | Replace de Bruijn index i by a 'Term' in something.
+subst :: Subst a => Int -> SubstArg a -> a -> a
+subst i u = applySubst $ singletonS i u
+
+strengthen :: Subst a => Impossible -> a -> a
+strengthen err = applySubst (strengthenS err 1)
+
+-- | Replace what is now de Bruijn index 0, but go under n binders.
+--   @substUnder n u == subst n (raise n u)@.
+substUnder :: Subst a => Nat -> SubstArg a -> a -> a
+substUnder n u = applySubst (liftS n (singletonS 0 u))
+
+-- ** Identity instances
+
+instance Subst QName where
+  type SubstArg QName = Term
+  applySubst _ q = q
+
+---------------------------------------------------------------------------
+-- * Explicit substitutions
+---------------------------------------------------------------------------
+
+-- See Syntax.Internal for the definition.
+
+idS :: Substitution' a
+idS = IdS
+
+wkS :: Int -> Substitution' a -> Substitution' a
+wkS 0 rho        = rho
+wkS n (Wk m rho) = Wk (n + m) rho
+wkS n (EmptyS err) = EmptyS err
+wkS n rho        = Wk n rho
+
+raiseS :: Int -> Substitution' a
+raiseS n = wkS n idS
+
+{-# INLINABLE consS #-}
+consS :: DeBruijn a => a -> Substitution' a -> Substitution' a
+consS t (Wk m rho)
+  | Just n <- deBruijnView t,
+    n + 1 == m = wkS (m - 1) (liftS 1 rho)
+consS u rho = seq u (u :# rho)
+{-# SPECIALIZE consS :: Term  -> Substitution' Term  -> Substitution' Term #-}
+{-# SPECIALIZE consS :: Level -> Substitution' Level -> Substitution' Level #-}
+
+{-# INLINABLE singletonS #-}
+-- | To replace index @n@ by term @u@, do @applySubst (singletonS n u)@.
+--   @
+--               Γ, Δ ⊢ u : A
+--    ---------------------------------
+--    Γ, Δ ⊢ singletonS |Δ| u : Γ, A, Δ
+--   @
+singletonS :: DeBruijn a => Int -> a -> Substitution' a
+singletonS n u = map deBruijnVar [0..n-1] ++# consS u (raiseS n)
+  -- ALT: foldl (\ s i -> deBruijnVar i `consS` s) (consS u $ raiseS n) $ downFrom n
+{-# SPECIALIZE singletonS :: Int -> Term -> Substitution' Term #-}
+{-# SPECIALIZE singletonS :: Int -> Level -> Substitution' Level #-}
+
+-- | Single substitution without disturbing any deBruijn indices.
+--   @
+--             Γ, A, Δ ⊢ u : A
+--    ---------------------------------
+--    Γ, A, Δ ⊢ inplace |Δ| u : Γ, A, Δ
+--   @
+inplaceS :: EndoSubst a => Int -> a -> Substitution' a
+inplaceS k u = singletonS k u `composeS` liftS (k + 1) (raiseS 1)
+
+-- | Lift a substitution under k binders.
+liftS :: Int -> Substitution' a -> Substitution' a
+liftS 0 rho          = rho
+liftS k IdS          = IdS
+liftS k (Lift n rho) = Lift (n + k) rho
+liftS k rho          = Lift k rho
+
+-- | @
+--         Γ ⊢ ρ : Δ, Ψ
+--      -------------------
+--      Γ ⊢ dropS |Ψ| ρ : Δ
+--   @
+dropS :: Int -> Substitution' a -> Substitution' a
+dropS 0 rho                = rho
+dropS n IdS                = raiseS n
+dropS n (Wk m rho)         = wkS m (dropS n rho)
+dropS n (u :# rho)         = dropS (n - 1) rho
+dropS n (EmptyS err)       = throwImpossible err
+dropS n (Lift m rho)
+  -- dropS n (Lift m rho) =
+  --   wkS 1 $ dropS (n - 1) $ liftS (m - 1) rho
+  | n > m     = wkS m $ dropS (n - m) rho
+  | otherwise = wkS n $ liftS (m - n) rho
+dropS n (Strengthen err m rho)
+  | n < m     = Strengthen err (m - n) rho
+  | otherwise = dropS (n - m) rho
+
+{-# INLINABLE composeS #-}
+-- | @applySubst (ρ `composeS` σ) v == applySubst ρ (applySubst σ v)@
+composeS :: EndoSubst a => Substitution' a -> Substitution' a -> Substitution' a
+composeS rho IdS = rho
+composeS IdS sgm = sgm
+composeS rho (EmptyS err) = EmptyS err
+composeS rho (Wk n sgm) = composeS (dropS n rho) sgm
+composeS rho (u :# sgm) = applySubst rho u :# composeS rho sgm
+composeS rho (Strengthen err n sgm) = Strengthen err n (composeS rho sgm)
+composeS rho (Lift 0 sgm) = __IMPOSSIBLE__
+composeS (u :# rho) (Lift n sgm) = u :# composeS rho (liftS (n - 1) sgm)
+composeS rho (Lift n sgm) = lookupS rho 0 :# composeS rho (wkS 1 (liftS (n - 1) sgm))
+
+-- If Γ ⊢ ρ : Δ, Θ then splitS |Θ| ρ = (σ, δ), with
+--   Γ ⊢ σ : Δ
+--   Γ ⊢ δ : Θσ
+splitS :: Int -> Substitution' a -> (Substitution' a, Substitution' a)
+splitS 0 rho                    = (rho, EmptyS impossible)
+splitS n (u :# rho)             = second (u :#) $ splitS (n - 1) rho
+splitS n (Lift 0 _)             = __IMPOSSIBLE__
+splitS n (Wk m rho)             = wkS m *** wkS m $ splitS n rho
+splitS n IdS                    = ( raiseS n
+                                  , liftS n $ EmptyS impossible
+                                  )
+splitS n (Lift m rho)           = wkS 1 *** liftS 1 $
+                                  splitS (n - 1) (liftS (m - 1) rho)
+splitS n (EmptyS err)           = __IMPOSSIBLE__
+splitS n (Strengthen err m rho)
+  -- splitS n (Strengthen err 1 rho) =
+  --   second (Strengthen err) $ splitS (n - 1) rho
+  | n > m     = second (Strengthen err m) $
+                splitS (n - m) rho
+  | otherwise = second (Strengthen err n) $
+                splitS 0 (Strengthen err (m - n) rho)
+
+infixr 4 ++#
+
+(++#) :: DeBruijn a => [a] -> Substitution' a -> Substitution' a
+us ++# rho = foldr consS rho us
+
+-- | @
+--      Γ ⊢ ρ : Δ  Γ ⊢ reverse vs : Θ
+--      ----------------------------- (treating Nothing as having any type)
+--        Γ ⊢ prependS vs ρ : Δ, Θ
+--   @
+prependS :: DeBruijn a => Impossible -> [Maybe a] -> Substitution' a -> Substitution' a
+prependS err us rho = go 0 us
+  where
+  -- The function strengthenS' is not used here, to avoid replacing
+  -- the "error message" of a potential outermost Strengthen
+  -- constructor in rho.
+  str 0 = id
+  str n = Strengthen err n
+
+  go !n (Just u  : us) = str n (consS u (go 0 us))
+  go  n (Nothing : us) = go (1 + n) us
+  go  n []             = str n rho
+
+-- | @
+--        Γ ⊢ reverse vs : Δ
+--      -----------------------------
+--        Γ ⊢ parallelS vs ρ : Γ, Δ
+--   @
+--
+--   Note the @Γ@ in @Γ, Δ@.
+parallelS :: DeBruijn a => [a] -> Substitution' a
+parallelS us = us ++# idS
+
+-- | Γ ⊢ (strengthenS ⊥ |Δ|) : Γ,Δ
+strengthenS :: Impossible -> Int -> Substitution' a
+strengthenS err n = case compare n 0 of
+  LT -> __IMPOSSIBLE__
+  EQ -> idS
+  GT -> Strengthen err n idS
+
+-- | A \"smart\" variant of 'Strengthen'. If 'strengthenS' is applied
+-- to a substitution with an outermost 'Strengthen' constructor, then
+-- the \"error message\" of that constructor is discarded in favour of
+-- the 'Impossible' argument of this function.
+strengthenS' :: Impossible -> Int -> Substitution' a -> Substitution' a
+strengthenS' err m rho = case compare m 0 of
+  LT -> __IMPOSSIBLE__
+  EQ -> rho
+  GT -> case rho of
+    Strengthen _ n rho -> Strengthen err (m + n) rho
+    _                  -> Strengthen err m       rho
+
+{-# INLINABLE lookupS #-}
+lookupS :: EndoSubst a => Substitution' a -> Nat -> a
+lookupS rho i = case rho of
+  IdS                    -> deBruijnVar i
+  Wk n IdS               -> let j = i + n in
+                            if  j < 0 then __IMPOSSIBLE__ else deBruijnVar j
+  Wk n rho               -> applySubst (raiseS n) (lookupS rho i)
+  u :# rho   | i == 0    -> u
+             | i < 0     -> __IMPOSSIBLE__
+             | otherwise -> lookupS rho (i - 1)
+  Strengthen err n rho
+             | i < 0     -> __IMPOSSIBLE__
+             | i < n     -> throwImpossible err
+             | otherwise -> lookupS rho (i - n)
+  Lift n rho | i < n     -> deBruijnVar i
+             | otherwise -> raise n $ lookupS rho (i - n)
+  EmptyS err             -> throwImpossible err
+
+
+-- | lookupS (listS [(x0,t0)..(xn,tn)]) xi = ti, assuming x0 < .. < xn.
+
+
+listS :: EndoSubst a => [(Int,a)] -> Substitution' a
+listS ((i,t):ts) = singletonS i t `composeS` listS ts
+listS []         = IdS
+
+-- | @Γ, Ξ, Δ ⊢ raiseFromS |Δ| |Ξ| : Γ, Δ@
+raiseFromS :: Nat -> Nat -> Substitution' a
+raiseFromS n k = liftS n $ raiseS k
+
+
+---------------------------------------------------------------------------
+-- * Functions on abstractions
+--   and things we couldn't do before we could define 'absBody'
+---------------------------------------------------------------------------
+
+-- | Instantiate an abstraction. Strict in the term.
+absApp :: Subst a => Abs a -> SubstArg a -> a
+absApp (Abs   _ v) u = subst 0 u v
+absApp (NoAbs _ v) _ = v
+
+-- | Instantiate an abstraction. Lazy in the term, which allow it to be
+--   __IMPOSSIBLE__ in the case where the variable shouldn't be used but we
+--   cannot use 'noabsApp'. Used in Apply.
+lazyAbsApp :: Subst a => Abs a -> SubstArg a -> a
+lazyAbsApp (Abs   _ v) u = applySubst (u :# IdS) v  -- Note: do not use consS here!
+lazyAbsApp (NoAbs _ v) _ = v
+
+-- | Instantiate an abstraction that doesn't use its argument.
+noabsApp :: Subst a => Impossible -> Abs a -> a
+noabsApp err (Abs   _ v) = strengthen err v
+noabsApp _   (NoAbs _ v) = v
+
+absBody :: Subst a => Abs a -> a
+absBody (Abs   _ v) = v
+absBody (NoAbs _ v) = raise 1 v
+
+mkAbs :: (Subst a, Free a) => ArgName -> a -> Abs a
+mkAbs x v | 0 `freeIn` v = Abs x v
+          | otherwise    = NoAbs x (raise (-1) v)
+
+reAbs :: (Subst a, Free a) => Abs a -> Abs a
+reAbs (NoAbs x v) = NoAbs x v
+reAbs (Abs x v)   = mkAbs x v
+
+-- | @underAbs k a b@ applies @k@ to @a@ and the content of
+--   abstraction @b@ and puts the abstraction back.
+--   @a@ is raised if abstraction was proper such that
+--   at point of application of @k@ and the content of @b@
+--   are at the same context.
+--   Precondition: @a@ and @b@ are at the same context at call time.
+underAbs :: Subst a => (a -> b -> b) -> a -> Abs b -> Abs b
+underAbs cont a = \case
+  Abs   x t -> Abs   x $ cont (raise 1 a) t
+  NoAbs x t -> NoAbs x $ cont a t
+
+-- | @underLambdas n k a b@ drops @n@ initial 'Lam's from @b@,
+--   performs operation @k@ on @a@ and the body of @b@,
+--   and puts the 'Lam's back.  @a@ is raised correctly
+--   according to the number of abstractions.
+underLambdas :: TermSubst a => Int -> (a -> Term -> Term) -> a -> Term -> Term
+underLambdas n cont = loop n where
+  loop 0 a = cont a
+  loop n a = \case
+    Lam h b -> Lam h $ underAbs (loop $ n-1) a b
+    _       -> __IMPOSSIBLE__
diff --git a/src/full/Agda/TypeChecking/Substitute/DeBruijn.hs b/src/full/Agda/TypeChecking/Substitute/DeBruijn.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Substitute/DeBruijn.hs
@@ -0,0 +1,54 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Substitute.DeBruijn where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+-- | Things we can substitute for a variable.
+--   Needs to be able to represent variables, e.g. for substituting under binders.
+class DeBruijn a where
+
+  -- | Produce a variable without name suggestion.
+  deBruijnVar  :: Int -> a
+  deBruijnVar = debruijnNamedVar underscore
+
+  -- | Produce a variable with name suggestion.
+  debruijnNamedVar :: String -> Int -> a
+  debruijnNamedVar _ = deBruijnVar
+
+  -- | Are we dealing with a variable?
+  --   If yes, what is its index?
+  deBruijnView :: a -> Maybe Int
+
+-- | We can substitute @Term@s for variables.
+instance DeBruijn Term where
+  deBruijnVar = var
+  deBruijnView u =
+    case u of
+      Var i [] -> Just i
+      Level l -> deBruijnView l
+      _ -> Nothing
+
+instance DeBruijn PlusLevel where
+  deBruijnVar = Plus 0 . deBruijnVar
+  deBruijnView l =
+    case l of
+      Plus 0 a -> deBruijnView a
+      _ -> Nothing
+
+instance DeBruijn Level where
+  deBruijnVar i = Max 0 [deBruijnVar i]
+  deBruijnView l =
+    case l of
+      Max 0 [p] -> deBruijnView p
+      _ -> Nothing
+
+instance DeBruijn DBPatVar where
+  debruijnNamedVar = DBPatVar
+  deBruijnView = Just . dbPatVarIndex
+
+
+instance DeBruijn a => DeBruijn (Named_ a) where
+  debruijnNamedVar nm i = unnamed $ debruijnNamedVar nm i
+  deBruijnView = deBruijnView . namedThing
diff --git a/src/full/Agda/TypeChecking/SyntacticEquality.hs b/src/full/Agda/TypeChecking/SyntacticEquality.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/SyntacticEquality.hs
@@ -0,0 +1,242 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | A syntactic equality check that takes meta instantiations into account,
+--   but does not reduce.  It replaces
+--   @
+--      (v, v') <- instantiateFull (v, v')
+--      v == v'
+--   @
+--   by a more efficient routine which only traverses and instantiates the terms
+--   as long as they are equal.
+
+module Agda.TypeChecking.SyntacticEquality
+  ( SynEq
+  , checkSyntacticEquality
+  , checkSyntacticEquality'
+  , syntacticEqualityFuelRemains
+  )
+  where
+
+import Control.Arrow            ( (***) )
+import Control.Monad            ( zipWithM )
+import Control.Monad.State      ( MonadState(..), StateT, runStateT )
+import Control.Monad.Trans      ( lift )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Monad  ( ReduceM, MonadReduce(..), TCEnv(..), MonadTCEnv(..) )
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Monad (ifM)
+import Agda.Utils.Unsafe (unsafeComparePointers)
+
+-- | Syntactic equality check for terms. If syntactic equality
+-- checking has fuel left, then 'checkSyntacticEquality' behaves as if
+-- it were implemented in the following way (which does not match the
+-- given type signature), only that @v@ and @v'@ are only fully
+-- instantiated to the depth where they are equal (and the amount of
+-- fuel is reduced by one unit in the failure branch):
+--   @
+--      checkSyntacticEquality v v' s f = do
+--        (v, v') <- instantiateFull (v, v')
+--        if v == v' then s v v' else f v v'
+--   @
+-- If syntactic equality checking does not have fuel left, then
+-- 'checkSyntacticEquality' instantiates the two terms and takes the
+-- failure branch.
+--
+-- Note that in either case the returned values @v@ and @v'@ cannot be
+-- @MetaV@s that are instantiated.
+
+{-# SPECIALIZE checkSyntacticEquality ::
+      Term -> Term ->
+      (Term -> Term -> ReduceM a) ->
+      (Term -> Term -> ReduceM a) ->
+      ReduceM a #-}
+{-# SPECIALIZE checkSyntacticEquality ::
+      Type -> Type ->
+      (Type -> Type -> ReduceM a) ->
+      (Type -> Type -> ReduceM a) ->
+      ReduceM a #-}
+checkSyntacticEquality
+  :: (Instantiate a, SynEq a, MonadReduce m)
+  => a
+  -> a
+  -> (a -> a -> m b)  -- ^ Continuation used upon success.
+  -> (a -> a -> m b)  -- ^ Continuation used upon failure, or if
+                      --   syntactic equality checking has been turned
+                      --   off.
+  -> m b
+checkSyntacticEquality u v s f =
+  ifM syntacticEqualityFuelRemains
+  {-then-} (checkSyntacticEquality' u v s (\u v -> localTC decreaseFuel (f u v)))
+  {-else-} (uncurry f =<< instantiate (u, v))
+  where
+  decreaseFuel env =
+    case envSyntacticEqualityFuel env of
+      Strict.Nothing -> env
+      Strict.Just n  ->
+        env { envSyntacticEqualityFuel = Strict.Just (pred n) }
+
+-- | Syntactic equality check for terms without checking remaining fuel.
+
+{-# SPECIALIZE checkSyntacticEquality' ::
+      Term -> Term ->
+      (Term -> Term -> ReduceM a) ->
+      (Term -> Term -> ReduceM a) ->
+      ReduceM a #-}
+{-# SPECIALIZE checkSyntacticEquality' ::
+      Type -> Type ->
+      (Type -> Type -> ReduceM a) ->
+      (Type -> Type -> ReduceM a) ->
+      ReduceM a #-}
+checkSyntacticEquality'
+  :: (Instantiate a, SynEq a, MonadReduce m)
+  => a
+  -> a
+  -> (a -> a -> m b)  -- ^ Continuation used upon success.
+  -> (a -> a -> m b)  -- ^ Continuation used upon failure.
+  -> m b
+checkSyntacticEquality' u v s f = do
+  ((u, v), equal) <- liftReduce $ synEq u v `runStateT` True
+  if equal then s u v else f u v
+
+-- | Does the syntactic equality check have any remaining fuel?
+
+syntacticEqualityFuelRemains :: MonadReduce m => m Bool
+syntacticEqualityFuelRemains = do
+  fuel <- envSyntacticEqualityFuel <$> askTC
+  return $ case fuel of
+    Strict.Nothing -> True
+    Strict.Just n  -> n > 0
+
+-- | Monad for checking syntactic equality
+type SynEqM = StateT Bool ReduceM
+
+-- | Return, flagging inequalty.
+inequal :: a -> SynEqM a
+inequal a = put False >> return a
+
+-- | If inequality is flagged, return, else continue.
+ifEqual :: (a -> SynEqM a) -> (a -> SynEqM a)
+ifEqual cont a = ifM get (cont a) (return a)
+
+-- Since List2 is only Applicative, not a monad, I cannot
+-- define a List2T monad transformer, so we do it manually:
+
+(<$$>) :: Functor f => (a -> b) -> f (a, a) -> f (b, b)
+f <$$> xx = (f *** f) <$> xx
+
+pure2 :: Applicative f => a -> f (a, a)
+pure2 a = pure (a, a)
+
+(<**>) :: Applicative f => f (a -> b, a -> b) -> f (a, a) -> f (b, b)
+ff <**> xx = (uncurry (***)) <$> ff <*> xx
+
+-- | Instantiate full as long as things are equal
+class SynEq a where
+  synEq  :: a -> a -> SynEqM (a, a)
+  synEq' :: a -> a -> SynEqM (a, a)
+  synEq' a a' = ifEqual (uncurry synEq) (a, a')
+
+instance SynEq Bool where
+  synEq x y | x == y    = return (x, y)
+  synEq x y | otherwise = inequal (x, y)
+
+-- | Syntactic term equality ignores 'DontCare' stuff.
+instance SynEq Term where
+  synEq v v' = if unsafeComparePointers v v' then return (v, v') else do
+    (v, v') <- lift $ instantiate' (v, v')
+    case (v, v') of
+      (Var   i vs, Var   i' vs') | i == i' -> Var i   <$$> synEq vs vs'
+      (Con c i vs, Con c' i' vs') | c == c' -> Con c (bestConInfo i i') <$$> synEq vs vs'
+      (Def   f vs, Def   f' vs') | f == f' -> Def f   <$$> synEq vs vs'
+      (MetaV x vs, MetaV x' vs') | x == x' -> MetaV x <$$> synEq vs vs'
+      (Lit   l   , Lit   l'    ) | l == l' -> pure2 $ v
+      (Lam   h b , Lam   h' b' )           -> Lam <$$> synEq h h' <**> synEq b b'
+      (Level l   , Level l'    )           -> levelTm <$$> synEq l l'
+      (Sort  s   , Sort  s'    )           -> Sort    <$$> synEq s s'
+      (Pi    a b , Pi    a' b' )           -> Pi      <$$> synEq a a' <**> synEq' b b'
+      (DontCare u, DontCare u' )           -> DontCare <$$> synEq u u'
+         -- Irrelevant things are not syntactically equal. ALT:
+         -- pure (u, u')
+         -- Jesper, 2019-10-21: considering irrelevant things to be
+         -- syntactically equal causes implicit arguments to go
+         -- unsolved, so it is better to go under the DontCare.
+      (Dummy{}   , Dummy{}     )           -> pure (v, v')
+      _                                    -> inequal (v, v')
+
+instance SynEq Level where
+  synEq l@(Max n vs) l'@(Max n' vs')
+    | n == n'   = levelMax n <$$> synEq vs vs'
+    | otherwise = inequal (l, l')
+
+instance SynEq PlusLevel where
+  synEq l@(Plus n v) l'@(Plus n' v')
+    | n == n'   = Plus n <$$> synEq v v'
+    | otherwise = inequal (l, l')
+
+instance SynEq Sort where
+  synEq s s' = if unsafeComparePointers s s' then return (s, s') else do
+    (s, s') <- lift $ instantiate' (s, s')
+    case (s, s') of
+      (Univ u l, Univ u' l') | u == u' -> Univ u <$$> synEq l l'
+      (PiSort a b c, PiSort a' b' c') -> piSort <$$> synEq a a' <**> synEq' b b' <**> synEq' c c'
+      (FunSort a b, FunSort a' b') -> funSort <$$> synEq a a' <**> synEq' b b'
+      (UnivSort a, UnivSort a') -> UnivSort <$$> synEq a a'
+      (SizeUniv, SizeUniv  ) -> pure2 s
+      (LockUniv, LockUniv  ) -> pure2 s
+      (LevelUniv, LevelUniv  ) -> pure2 s
+      (IntervalUniv, IntervalUniv) -> pure2 s
+      (Inf u m , Inf u' n) | u == u', m == n -> pure2 s
+      (MetaS x es , MetaS x' es') | x == x' -> MetaS x <$$> synEq es es'
+      (DefS  d es , DefS  d' es') | d == d' -> DefS d  <$$> synEq es es'
+      (DummyS{}, DummyS{}) -> pure (s, s')
+      _ -> inequal (s, s')
+
+-- | Syntactic equality ignores sorts.
+instance SynEq Type where
+  synEq (El s t) (El s' t') = (El s *** El s') <$> synEq t t'
+
+instance SynEq a => SynEq [a] where
+  synEq as as'
+    | length as == length as' = unzip <$> zipWithM synEq' as as'
+    | otherwise               = inequal (as, as')
+
+instance (SynEq a, SynEq b) => SynEq (a,b) where
+  synEq (a,b) (a',b') = (,) <$$> synEq a a' <**> synEq b b'
+
+instance SynEq a => SynEq (Elim' a) where
+  synEq e e' =
+    case (e, e') of
+      (Proj _ f, Proj _ f') | f == f' -> pure2 e
+      (Apply a, Apply a') -> Apply <$$> synEq a a'
+      (IApply u v r, IApply u' v' r')
+                          -> (IApply u v *** IApply u' v') <$> synEq r r'
+      _                   -> inequal (e, e')
+
+instance (Subst a, SynEq a) => SynEq (Abs a) where
+  synEq a a' =
+    case (a, a') of
+      (NoAbs x b, NoAbs x' b') -> (NoAbs x *** NoAbs x') <$>  synEq b b'
+      (Abs   x b, Abs   x' b') -> (Abs x *** Abs x') <$> synEq b b'
+      (Abs   x b, NoAbs x' b') -> Abs x  <$$> synEq b (raise 1 b')  -- TODO: mkAbs?
+      (NoAbs x b, Abs   x' b') -> Abs x' <$$> synEq (raise 1 b) b'
+
+-- NOTE: Do not ignore 'ArgInfo', or test/fail/UnequalHiding will pass.
+instance SynEq a => SynEq (Arg a) where
+  synEq (Arg ai a) (Arg ai' a') = Arg <$$> synEq ai ai' <**> synEq a a'
+
+-- Ignore the tactic.
+instance SynEq a => SynEq (Dom a) where
+  synEq d@(Dom ai x f t a) d'@(Dom ai' x' f' _ a')
+    | x == x'   = Dom <$$> synEq ai ai' <**> pure2 x <**> synEq f f' <**> pure2 t <**> synEq a a'
+    | otherwise = inequal (d, d')
+
+instance SynEq ArgInfo where
+  synEq ai@(ArgInfo h r o _ a) ai'@(ArgInfo h' r' o' _ a')
+    | h == h', sameModality r r', a == a' = pure2 ai
+    | otherwise        = inequal (ai, ai')
diff --git a/src/full/Agda/TypeChecking/Telescope.hs b/src/full/Agda/TypeChecking/Telescope.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Telescope.hs
@@ -0,0 +1,771 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE ViewPatterns #-}
+
+module Agda.TypeChecking.Telescope where
+
+import Prelude hiding (null)
+
+import Control.Monad
+
+import Data.Bifunctor (first)
+import Data.Foldable (find)
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Maybe
+import Data.Monoid
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.Syntax.Internal.Pattern
+
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Warnings
+
+import Agda.Utils.CallStack ( withCallerCallStack )
+import Agda.Utils.Either
+import Agda.Utils.Empty
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Null
+import Agda.Utils.Permutation
+import Agda.Utils.Singleton
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+import Agda.Utils.VarSet (VarSet)
+import qualified Agda.Utils.VarSet as VarSet
+
+import Agda.Utils.Impossible
+
+-- | Flatten telescope: (Γ : Tel) -> [Type Γ]
+flattenTel :: TermSubst a => Tele (Dom a) -> [Dom a]
+flattenTel EmptyTel          = []
+flattenTel (ExtendTel a tel) = raise (size tel + 1) a : flattenTel (absBody tel)
+
+{-# SPECIALIZE flattenTel :: Telescope -> [Dom Type] #-}
+
+-- | Order a flattened telescope in the correct dependeny order: Γ ->
+--   Permutation (Γ -> Γ~)
+--
+--   Since @reorderTel tel@ uses free variable analysis of type in @tel@,
+--   the telescope should be 'normalise'd.
+reorderTel :: [Dom Type] -> Maybe Permutation
+reorderTel tel = topoSort comesBefore tel'
+  where
+    tel' = zip (downFrom $ size tel) tel
+    (i, _) `comesBefore` (_, a) = i `freeIn` unEl (unDom a) -- a tiny bit unsafe
+
+reorderTel_ :: [Dom Type] -> Permutation
+reorderTel_ tel = fromMaybe __IMPOSSIBLE__ (reorderTel tel)
+
+-- | Unflatten: turns a flattened telescope into a proper telescope. Must be
+--   properly ordered.
+unflattenTel :: [ArgName] -> [Dom Type] -> Telescope
+unflattenTel xs tel = unflattenTel' (size tel) xs tel
+
+-- | A variant of 'unflattenTel' which takes the size of the last
+-- argument as an argument.
+unflattenTel' :: Int -> [ArgName] -> [Dom Type] -> Telescope
+unflattenTel' !n xs tel = case (xs, tel) of
+  ([],     [])      -> EmptyTel
+  (x : xs, a : tel) -> ExtendTel a' (Abs x tel')
+    where
+    tel' = unflattenTel' (n - 1) xs tel
+    a'   = applySubst rho a
+    rho  = parallelS $
+           replicate n (withCallerCallStack impossibleTerm)
+  ([],    _ : _) -> __IMPOSSIBLE__
+  (_ : _, [])    -> __IMPOSSIBLE__
+
+-- | Rename the variables in the telescope to the given names
+--   Precondition: @size xs == size tel@.
+renameTel :: [Maybe ArgName] -> Telescope -> Telescope
+renameTel []           EmptyTel           = EmptyTel
+renameTel (Nothing:xs) (ExtendTel a tel') = ExtendTel a $ renameTel xs <$> tel'
+renameTel (Just x :xs) (ExtendTel a tel') = ExtendTel a $ renameTel xs <$> (tel' { absName = x })
+renameTel []           (ExtendTel _ _   ) = __IMPOSSIBLE__
+renameTel (_      :_ ) EmptyTel           = __IMPOSSIBLE__
+
+-- | Get the suggested names from a telescope
+teleNames :: Telescope -> [ArgName]
+teleNames = map (fst . unDom) . telToList
+
+teleArgNames :: Telescope -> [Arg ArgName]
+teleArgNames = map (argFromDom . fmap fst) . telToList
+
+teleArgs :: (DeBruijn a) => Tele (Dom t) -> [Arg a]
+teleArgs = map argFromDom . teleDoms
+
+teleDoms :: (DeBruijn a) => Tele (Dom t) -> [Dom a]
+teleDoms tel = zipWith (\ i dom -> deBruijnVar i <$ dom) (downFrom $ size l) l
+  where l = telToList tel
+
+-- UNUSED
+-- withNamedArgsFromTel :: [a] -> Telescope -> [NamedArg a]
+-- xs `withNamedArgsFromTel` tel =
+--   [ Arg info (Named (Just $ Ranged empty $ argNameToString name) x)
+--   | (x, Dom {domInfo = info, unDom = (name,_)}) <- zip xs l ]
+--   where l = telToList tel
+
+teleNamedArgs :: (DeBruijn a) => Tele (Dom t) -> [NamedArg a]
+teleNamedArgs = map namedArgFromDom . teleDoms
+
+{-# INLINABLE tele2NamedArgs #-}
+-- | A variant of `teleNamedArgs` which takes the argument names (and the argument info)
+--   from the first telescope and the variable names from the second telescope.
+--
+--   Precondition: the two telescopes have the same length.
+tele2NamedArgs :: (DeBruijn a) => Telescope -> Telescope -> [NamedArg a]
+tele2NamedArgs tel0 tel =
+  [ Arg info (Named (Just $ WithOrigin Inserted $ unranged $ argNameToString argName) (debruijnNamedVar varName i))
+  | (i, Dom{domInfo = info, unDom = (argName,_)}, Dom{unDom = (varName,_)}) <- zip3 (downFrom $ size l) l0 l ]
+  where
+  l  = telToList tel
+  l0 = telToList tel0
+
+-- | Split the telescope at the specified position.
+splitTelescopeAt :: Int -> Telescope -> (Telescope,Telescope)
+splitTelescopeAt n tel
+  | n <= 0    = (EmptyTel, tel)
+  | otherwise = splitTelescopeAt' n tel
+    where
+      splitTelescopeAt' _ EmptyTel          = (EmptyTel,EmptyTel)
+      splitTelescopeAt' 1 (ExtendTel a tel) = (ExtendTel a (tel $> EmptyTel), absBody tel)
+      splitTelescopeAt' m (ExtendTel a tel) = (ExtendTel a (tel $> tel'), tel'')
+        where
+          (tel', tel'') = splitTelescopeAt (m - 1) $ absBody tel
+
+-- | Permute telescope: permutes or drops the types in the telescope according
+--   to the given permutation. Assumes that the permutation preserves the
+--   dependencies in the telescope.
+--
+--   For example (Andreas, 2016-12-18, issue #2344):
+--   @
+--     tel                     = (A : Set) (X : _18 A) (i : Fin (_m_23 A X))
+--     tel (de Bruijn)         = 2:Set, 1:_18 @0, 0:Fin(_m_23 @1 @0)
+--     flattenTel tel          = 2:Set, 1:_18 @0, 0:Fin(_m_23 @1 @0) |- [ Set, _18 @2, Fin (_m_23 @2 @1) ]
+--     perm                    = 0,1,2 -> 0,1  (picks the first two)
+--     renaming _ perm         = [var 0, var 1, error]  -- THE WRONG RENAMING!
+--     renaming _ (flipP perm) = [error, var 1, var 0]  -- The correct renaming!
+--     apply to flattened tel  = ... |- [ Set, _18 @1, Fin (_m_23 @1 @0) ]
+--     permute perm it         = ... |- [ Set, _18 @1 ]
+--     unflatten (de Bruijn)   = 1:Set, 0: _18 @0
+--     unflatten               = (A : Set) (X : _18 A)
+--  @
+permuteTel :: Permutation -> Telescope -> Telescope
+permuteTel perm tel =
+  let names = permute perm $ teleNames tel
+      types = permute perm $ renameP impossible (flipP perm) $ flattenTel tel
+  in  unflattenTel names types
+
+-- | Recursively computes dependencies of a set of variables in a given
+--   telescope. Any dependencies outside of the telescope are ignored.
+varDependencies :: Telescope -> IntSet -> IntSet
+varDependencies tel = addLocks . allDependencies IntSet.empty
+  where
+    addLocks s | IntSet.null s = s
+               | otherwise = IntSet.union s $ IntSet.fromList $ filter (>= m) locks
+      where
+        locks = catMaybes [ deBruijnView (unArg a) | (a :: Arg Term) <- teleArgs tel, IsLock{} <- pure (getLock a)]
+        m = IntSet.findMin s
+    n  = size tel
+    ts = flattenTel tel
+
+    directDependencies :: Int -> IntSet
+    directDependencies i = allFreeVars $ indexWithDefault __IMPOSSIBLE__ ts (n-1-i)
+
+    allDependencies :: IntSet -> IntSet -> IntSet
+    allDependencies =
+      IntSet.foldr $ \j soFar ->
+        if j >= n || j `IntSet.member` soFar
+        then soFar
+        else IntSet.insert j $ allDependencies soFar $ directDependencies j
+
+-- | Computes the set of variables in a telescope whose type depend on
+--   one of the variables in the given set (including recursive
+--   dependencies). Any dependencies outside of the telescope are
+--   ignored.
+varDependents :: Telescope -> IntSet -> IntSet
+varDependents tel = allDependents
+  where
+    n  = size tel
+    ts = flattenTel tel
+
+    directDependents :: IntSet -> IntSet
+    directDependents is = IntSet.fromList
+      [ j | j <- downFrom n
+          , let tj = indexWithDefault __IMPOSSIBLE__ ts (n-1-j)
+          , getAny $ runFree (Any . (`IntSet.member` is)) IgnoreNot tj
+          ]
+
+    allDependents :: IntSet -> IntSet
+    allDependents is
+     | null new  = empty
+     | otherwise = new `IntSet.union` allDependents new
+      where new = directDependents is
+
+-- | A telescope split in two.
+data SplitTel = SplitTel
+  { firstPart  :: Telescope
+  , secondPart :: Telescope
+  , splitPerm  :: Permutation
+    -- ^ The permutation takes us from the original telescope to
+    --   @firstPart ++ secondPart@.
+  }
+
+-- | Split a telescope into the part that defines the given variables and the
+--   part that doesn't.
+--
+--   See 'Agda.TypeChecking.Tests.prop_splitTelescope'.
+splitTelescope
+  :: VarSet     -- ^ A set of de Bruijn indices.
+  -> Telescope  -- ^ Original telescope.
+  -> SplitTel   -- ^ @firstPart@ mentions the given variables, @secondPart@ not.
+splitTelescope fv tel = SplitTel tel1 tel2 perm
+  where
+    names = teleNames tel
+    ts0   = flattenTel tel
+    n     = size tel
+
+    is    = varDependencies tel fv
+    isC   = IntSet.fromList [0..(n-1)] `IntSet.difference` is
+
+    perm  = Perm n $ map (n-1-) $ VarSet.toDescList is ++ VarSet.toDescList isC
+
+    ts1   = renameP impossible (reverseP perm) (permute perm ts0)
+
+    tel'  = unflattenTel (permute perm names) ts1
+
+    m     = size is
+    (tel1, tel2) = telFromList -*- telFromList $ splitAt m $ telToList tel'
+
+-- | As splitTelescope, but fails if any additional variables or reordering
+--   would be needed to make the first part well-typed.
+splitTelescopeExact
+  :: [Int]          -- ^ A list of de Bruijn indices
+  -> Telescope      -- ^ The telescope to split
+  -> Maybe SplitTel -- ^ @firstPart@ mentions the given variables in the given order,
+                    --   @secondPart@ contains all other variables
+splitTelescopeExact is tel = guard ok $> SplitTel tel1 tel2 perm
+  where
+    names = teleNames tel
+    ts0   = flattenTel tel
+    n     = size tel
+
+    checkDependencies :: IntSet -> [Int] -> Bool
+    checkDependencies soFar []     = True
+    checkDependencies soFar (j:js) = ok && checkDependencies (IntSet.insert j soFar) js
+      where
+        t   = indexWithDefault __IMPOSSIBLE__ ts0 (n-1-j)  -- ts0[n-1-j]
+        -- Skip the construction of intermediate @IntSet@s in the check @ok@.
+        -- ok  = (allFreeVars t `IntSet.intersection` IntSet.fromAscList [ 0 .. n-1 ])
+        --       `IntSet.isSubsetOf` soFar
+        good i = All $ (i < n) `implies` (i `IntSet.member` soFar) where implies = (<=)
+        ok = getAll $ runFree good IgnoreNot t
+
+    ok    = all (< n) is && checkDependencies IntSet.empty is
+
+    isC   = downFrom n List.\\ is
+
+    perm  = Perm n $ map (n-1-) $ is ++ isC
+
+    ts1   = renameP impossible (reverseP perm) (permute perm ts0)
+
+    tel'  = unflattenTel (permute perm names) ts1
+
+    m     = size is
+    (tel1, tel2) = telFromList -*- telFromList $ splitAt m $ telToList tel'
+
+-- | Try to instantiate one variable in the telescope (given by its de Bruijn
+--   level) with the given value, returning the new telescope and a
+--   substitution to the old one. Returns Nothing if the given value depends
+--   (directly or indirectly) on the variable.
+instantiateTelescope
+  :: Telescope -- ^ ⊢ Γ
+  -> Int       -- ^ Γ ⊢ var k : A   de Bruijn _level_
+  -> DeBruijnPattern -- ^ Γ ⊢ u : A
+  -> Maybe (Telescope,           -- ⊢ Γ'
+            PatternSubstitution, -- Γ' ⊢ σ : Γ
+            Permutation)         -- Γ  ⊢ flipP ρ : Γ'
+instantiateTelescope tel k p = guard ok $> (tel', sigma, rho)
+  where
+    names = teleNames tel
+    ts0   = flattenTel tel
+    n     = size tel
+    j     = n-1-k
+    u     = patternToTerm p
+
+    -- Jesper, 2019-12-31: Previous implementation that does some
+    -- unneccessary reordering but is otherwise correct (keep!)
+    -- -- is0 is the part of Γ that is needed to type u
+    -- is0   = varDependencies tel $ allFreeVars u
+    -- -- is1 is the rest of Γ (minus the variable we are instantiating)
+    -- is1   = IntSet.delete j $
+    --           IntSet.fromAscList [ 0 .. n-1 ] `IntSet.difference` is0
+    -- -- we work on de Bruijn indices, so later parts come first
+    -- is    = IntSet.toAscList is1 ++ IntSet.toAscList is0
+
+    -- -- if u depends on var j, we cannot instantiate
+    -- ok    = not $ j `IntSet.member` is0
+
+    -- is0 is the part of Γ that is needed to type u
+    is0   = varDependencies tel $ allFreeVars u
+    -- is1 is the part of Γ that depends on variable j
+    is1   = varDependents tel $ singleton j
+    -- lasti is the last (rightmost) variable of is0
+    lasti = if null is0 then n else IntSet.findMin is0
+    -- we move each variable in is1 to the right until it comes after
+    -- all variables in is0 (i.e. after lasti)
+    (as,bs) = List.partition (`IntSet.member` is1) [ n-1 , n-2 .. lasti ]
+    is    = reverse $ List.delete j $ bs ++ as ++ downFrom lasti
+
+    -- if u depends on var j, we cannot instantiate
+    ok    = not $ j `IntSet.member` is0
+
+    perm  = Perm n $ is    -- works on de Bruijn indices
+    rho   = reverseP perm  -- works on de Bruijn levels
+
+    p1    = renameP impossible perm p -- Γ' ⊢ p1 : A'
+    us    = map (\i -> maybe p1 deBruijnVar (List.elemIndex i is)) [ 0 .. n-1 ]
+    sigma = us ++# raiseS (n-1)
+
+    ts1   = permute rho $ applyPatSubst sigma ts0
+    tel'  = unflattenTel (permute rho names) ts1
+
+-- | Try to eta-expand one variable in the telescope (given by its de Bruijn
+--   level)
+expandTelescopeVar
+  :: Telescope  -- Γ = Γ₁(x : D pars)Γ₂
+  -> Int        -- k = size Γ₁
+  -> Telescope  -- Γ₁ ⊢ Δ
+  -> ConHead    -- Γ₁ ⊢ c : Δ → D pars
+  -> ( Telescope            -- Γ' = Γ₁ΔΓ₂[x ↦ c Δ]
+     , PatternSubstitution) -- Γ' ⊢ ρ : Γ
+expandTelescopeVar gamma k delta c = (tel', rho)
+  where
+    (ts1,xa:ts2) = fromMaybe __IMPOSSIBLE__ $
+                    splitExactlyAt k $ telToList gamma
+    a = raise (size delta) (snd <$> xa) -- Γ₁Δ ⊢ D pars
+
+    cpi         = ConPatternInfo
+      { conPInfo   = defaultPatternInfo
+      , conPRecord = True
+      , conPFallThrough
+                   = False
+      , conPType   = Just $ argFromDom a
+      , conPLazy   = True
+      }
+    cargs       = map (setOrigin Inserted) $ teleNamedArgs delta
+    cdelta      = ConP c cpi cargs                    -- Γ₁Δ ⊢ c Δ : D pars
+    rho0        = consS cdelta $ raiseS (size delta)  -- Γ₁Δ ⊢ ρ₀ : Γ₁(x : D pars)
+    rho         = liftS (size ts2) rho0               -- Γ₁ΔΓ₂ρ₀ ⊢ ρ : Γ₁(x : D pars)Γ₂
+
+    gamma1      = telFromList ts1
+    gamma2'     = applyPatSubst rho0 $ telFromList ts2
+
+    tel'        = gamma1 `abstract` (delta `abstract` gamma2')
+
+
+{-# INLINE telView #-}
+-- | Gather leading Πs of a type in a telescope.
+telView :: (MonadReduce m, MonadAddContext m) => Type -> m TelView
+telView = telViewUpTo (-1)
+
+{-# INLINE telViewUpTo #-}
+-- | @telViewUpTo n t@ takes off the first @n@ function types of @t@.
+-- Takes off all if @n < 0@.
+telViewUpTo :: (MonadReduce m, MonadAddContext m) => Int -> Type -> m TelView
+telViewUpTo n t = telViewUpTo' n (const True) t
+
+{-# SPECIALIZE telViewUpTo' :: Int -> (Dom Type -> Bool) -> Type -> TCM TelView #-}
+-- | @telViewUpTo' n p t@ takes off $t$
+--   the first @n@ (or arbitrary many if @n < 0@) function domains
+--   as long as they satify @p@.
+telViewUpTo' :: (MonadReduce m, MonadAddContext m) => Int -> (Dom Type -> Bool) -> Type -> m TelView
+telViewUpTo' 0 p t = return $ TelV EmptyTel t
+telViewUpTo' n p t = do
+  t <- reduce t
+  case unEl t of
+    Pi a b | p a ->
+          -- Force the name to avoid retaining the rest of b.
+      let !bn = absName b in
+      absV a bn <$> do
+        underAbstractionAbs a b $ \b -> telViewUpTo' (n - 1) p b
+    _ -> return $ TelV EmptyTel t
+
+{-# INLINE telViewPath #-}
+telViewPath :: PureTCM m => Type -> m TelView
+telViewPath = telViewUpToPath (-1)
+
+{-# SPECIALIZE telViewUpToPath :: Int -> Type -> TCM TelView #-}
+-- | @telViewUpToPath n t@ takes off $t$
+--   the first @n@ (or arbitrary many if @n < 0@) function domains or Path types.
+--
+-- @telViewUpToPath n t = fst <$> telViewUpToPathBoundary'n t@
+telViewUpToPath :: PureTCM m => Int -> Type -> m TelView
+telViewUpToPath n t = if n == 0 then done t else do
+  pathViewAsPi t >>= \case
+    Left  (a, b)          -> recurse a b
+    Right (El _ (Pi a b)) -> recurse a b
+    Right t               -> done t
+  where
+    done t      = return $ TelV EmptyTel t
+    recurse a b = absV a (absName b) <$> telViewUpToPath (n - 1) (absBody b)
+
+-- | [[ (i,(x,y)) ]] = [(i=0) -> x, (i=1) -> y]
+type Boundary = Boundary' (Term,Term)
+type Boundary' a = [(Term,a)]
+
+
+{-# SPECIALIZE telViewUpToPathBoundary' :: Int -> Type -> TCM (TelView, Boundary) #-}
+-- | Like @telViewUpToPath@ but also returns the @Boundary@ expected
+-- by the Path types encountered. The boundary terms live in the
+-- telescope given by the @TelView@.
+-- Each point of the boundary has the type of the codomain of the Path type it got taken from, see @fullBoundary@.
+telViewUpToPathBoundary' :: PureTCM m => Int -> Type -> m (TelView, Boundary)
+telViewUpToPathBoundary' n t = if n == 0 then done t else do
+  pathViewAsPi' t >>= \case
+    Left ((a, b), xy)     -> addEndPoints xy <$> recurse a b
+    Right (El _ (Pi a b)) -> recurse a b
+    Right t               -> done t
+  where
+    done t      = return (TelV EmptyTel t, [])
+    recurse a b = first (absV a (absName b)) <$> do
+      underAbstractionAbs a b $ \b -> telViewUpToPathBoundary' (n - 1) b
+    addEndPoints xy (telv@(TelV tel _), cs) =
+      (telv, (var $ size tel - 1, raise (size tel) xy) : cs)
+
+
+fullBoundary :: Telescope -> Boundary -> Boundary
+fullBoundary tel bs =
+      -- tel = Γ
+      -- ΔΓ ⊢ b
+      -- Δ ⊢ a = PiPath Γ bs b
+      -- Δ.Γ ⊢ T is the codomain of the PathP at variable i
+      -- Δ.Γ ⊢ i : I
+      -- Δ.Γ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : T
+      -- Δ.Γ | PiPath Γ bs A ⊢ teleElims tel bs : b
+   let es = teleElims tel bs
+       l  = size tel
+   in map (\ (t@(Var i []), xy) -> (t, xy `applyE` (drop (l - i) es))) bs
+
+{-# SPECIALIZE telViewUpToPathBoundary :: Int -> Type -> TCM (TelView, Boundary) #-}
+-- | @(TelV Γ b, [(i,t_i,u_i)]) <- telViewUpToPathBoundary n a@
+--  Input:  Δ ⊢ a
+--  Output: ΔΓ ⊢ b
+--          ΔΓ ⊢ i : I
+--          ΔΓ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : b
+telViewUpToPathBoundary :: PureTCM m => Int -> Type -> m (TelView,Boundary)
+telViewUpToPathBoundary i a = do
+   (telv@(TelV tel b), bs) <- telViewUpToPathBoundary' i a
+   return $ (telv, fullBoundary tel bs)
+
+{-# INLINE telViewUpToPathBoundaryP #-}
+-- | @(TelV Γ b, [(i,t_i,u_i)]) <- telViewUpToPathBoundaryP n a@
+--  Input:  Δ ⊢ a
+--  Output: Δ.Γ ⊢ b
+--          Δ.Γ ⊢ T is the codomain of the PathP at variable i
+--          Δ.Γ ⊢ i : I
+--          Δ.Γ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : T
+-- Useful to reconstruct IApplyP patterns after teleNamedArgs Γ.
+telViewUpToPathBoundaryP :: PureTCM m => Int -> Type -> m (TelView,Boundary)
+telViewUpToPathBoundaryP = telViewUpToPathBoundary'
+
+{-# INLINE telViewPathBoundaryP #-}
+telViewPathBoundaryP :: PureTCM m => Type -> m (TelView,Boundary)
+telViewPathBoundaryP = telViewUpToPathBoundaryP (-1)
+
+
+-- | @teleElimsB args bs = es@
+--  Input:  Δ.Γ ⊢ args : Γ
+--          Δ.Γ ⊢ T is the codomain of the PathP at variable i
+--          Δ.Γ ⊢ i : I
+--          Δ.Γ ⊢ bs = [ (i=0) -> t_i; (i=1) -> u_i ] : T
+--  Output: Δ.Γ | PiPath Γ bs A ⊢ es : A
+teleElims :: DeBruijn a => Telescope -> Boundary' (a,a) -> [Elim' a]
+teleElims tel [] = map Apply $ teleArgs tel
+teleElims tel boundary = recurse (teleArgs tel)
+  where
+    recurse = fmap updateArg
+    matchVar x =
+      snd <$> find (\case
+        (Var i [],_) -> i == x
+        _            -> __IMPOSSIBLE__) boundary
+    updateArg a@(Arg info p) =
+      case deBruijnView p of
+        Just i | Just (t,u) <- matchVar i -> IApply t u p
+        _                                 -> Apply a
+
+{-# SPECIALIZE pathViewAsPi :: Type -> TCM (Either (Dom Type, Abs Type) Type) #-}
+-- | Reduces 'Type'.
+pathViewAsPi
+  :: PureTCM m => Type -> m (Either (Dom Type, Abs Type) Type)
+pathViewAsPi t = either (Left . fst) Right <$> pathViewAsPi' t
+
+{-# SPECIALIZE pathViewAsPi' :: Type -> TCM (Either ((Dom Type, Abs Type), (Term,Term)) Type) #-}
+-- | Reduces 'Type'.
+pathViewAsPi'
+  :: PureTCM m => Type -> m (Either ((Dom Type, Abs Type), (Term,Term)) Type)
+pathViewAsPi' t = do
+  pathViewAsPi'whnf <*> reduce t
+
+{-# SPECIALIZE pathViewAsPi'whnf :: TCM (Type -> Either ((Dom Type, Abs Type), (Term,Term)) Type) #-}
+pathViewAsPi'whnf
+  :: (HasBuiltins m)
+  => m (Type -> Either ((Dom Type, Abs Type), (Term,Term)) Type)
+pathViewAsPi'whnf = do
+  view <- pathView'
+  minterval  <- getTerm' builtinInterval
+  return $ \case
+    (view -> PathType s l p a x y) | Just interval <- minterval ->
+      let name | Lam _ (Abs n _) <- unArg a = n
+               | otherwise = "i"
+      in
+        Left ( ( defaultDom $ El intervalSort interval
+               , Abs name $ El (raise 1 s) $ raise 1 (unArg a) `apply` [defaultArg $ var 0]
+               )
+             , (unArg x, unArg y)
+             )
+
+    t    -> Right t
+
+-- | Returns @Left (a,b)@ in case the type is @Pi a b@ or @PathP b _ _@.
+--   Assumes the 'Type' is in whnf.
+piOrPath :: HasBuiltins m => Type -> m (Either (Dom Type, Abs Type) Type)
+piOrPath t = do
+  (pathViewAsPi'whnf <*> pure t) <&> \case
+    Left (p, _)           -> Left p
+    Right (El _ (Pi a b)) -> Left (a,b)
+    Right _               -> Right t
+
+-- | Assumes 'Type' is in whnf.
+telView'UpToPath :: Int -> Type -> TCM TelView
+telView'UpToPath n t = if n == 0 then done else do
+  piOrPath t >>= \case
+    Left (a, b) -> absV a (absName b) <$> telViewUpToPath (n - 1) (absBody b)
+    Right _     -> done
+  where
+    done = return $ TelV EmptyTel t
+
+telView'Path :: Type -> TCM TelView
+telView'Path = telView'UpToPath (-1)
+
+isPath :: PureTCM m => Type -> m (Maybe (Dom Type, Abs Type))
+isPath t = ifPath t (\a b -> return $ Just (a,b)) (const $ return Nothing)
+
+ifPath :: PureTCM m => Type -> (Dom Type -> Abs Type -> m a) -> (Type -> m a) -> m a
+ifPath t yes no = ifPathB t yes $ no . ignoreBlocking
+
+{-# SPECIALIZE ifPathB :: Type -> (Dom Type -> Abs Type -> TCM a) -> (Blocked Type -> TCM a) -> TCM a #-}
+ifPathB :: PureTCM m => Type -> (Dom Type -> Abs Type -> m a) -> (Blocked Type -> m a) -> m a
+ifPathB t yes no = ifBlocked t
+  (\b t -> no $ Blocked b t)
+  (\nb t -> caseEitherM (pathViewAsPi'whnf <*> pure t)
+    (uncurry yes . fst)
+    (no . NotBlocked nb))
+
+ifNotPathB :: PureTCM m => Type -> (Blocked Type -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
+ifNotPathB = flip . ifPathB
+
+ifPiOrPathB :: PureTCM m => Type -> (Dom Type -> Abs Type -> m a) -> (Blocked Type -> m a) -> m a
+ifPiOrPathB t yes no = ifPiTypeB t
+  (\a b -> yes a b)
+  (\bt -> caseEitherM (pathViewAsPi'whnf <*> pure (ignoreBlocking bt))
+    (uncurry yes . fst)
+    (no . (bt $>)))
+
+ifNotPiOrPathB :: PureTCM m => Type -> (Blocked Type -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
+ifNotPiOrPathB = flip . ifPiOrPathB
+
+telePatterns :: DeBruijn a => Telescope -> Boundary -> [NamedArg (Pattern' a)]
+telePatterns = telePatterns' teleNamedArgs
+
+telePatterns' :: DeBruijn a =>
+                (forall a. (DeBruijn a) => Telescope -> [NamedArg a]) -> Telescope -> Boundary -> [NamedArg (Pattern' a)]
+telePatterns' f tel [] = f tel
+telePatterns' f tel boundary = recurse $ f tel
+  where
+    recurse = (fmap . fmap . fmap) updateVar
+    matchVar x =
+      snd <$> find (\case
+        (Var i [],_) -> i == x
+        _            -> __IMPOSSIBLE__) boundary
+    updateVar x =
+      case deBruijnView x of
+        Just i | Just (t,u) <- matchVar i -> IApplyP defaultPatternInfo t u x
+        _                                 -> VarP defaultPatternInfo x
+
+-- | Decomposing a function type.
+
+mustBePi :: MonadReduce m => Type -> m (Dom Type, Abs Type)
+mustBePi t = ifNotPiType t __IMPOSSIBLE__ $ curry return
+
+-- | If the given type is a @Pi@, pass its parts to the first continuation.
+--   If not (or blocked), pass the reduced type to the second continuation.
+ifPi :: MonadReduce m => Term -> (Dom Type -> Abs Type -> m a) -> (Term -> m a) -> m a
+ifPi t yes no = ifPiB t yes (no . ignoreBlocking)
+
+ifPiB :: (MonadReduce m) => Term -> (Dom Type -> Abs Type -> m a) -> (Blocked Term -> m a) -> m a
+ifPiB t yes no = ifBlocked t
+  (\b t -> no $ Blocked b t) -- Pi type is never blocked
+  (\nb t -> case t of
+    Pi a b -> yes a b
+    _      -> no $ NotBlocked nb t)
+
+ifPiTypeB :: (MonadReduce m) => Type -> (Dom Type -> Abs Type -> m a) -> (Blocked Type -> m a) -> m a
+ifPiTypeB (El s t) yes no = ifPiB t yes (\bt -> no $ El s <$> bt)
+
+-- | If the given type is a @Pi@, pass its parts to the first continuation.
+--   If not (or blocked), pass the reduced type to the second continuation.
+ifPiType :: MonadReduce m => Type -> (Dom Type -> Abs Type -> m a) -> (Type -> m a) -> m a
+ifPiType (El s t) yes no = ifPi t yes (no . El s)
+
+-- | If the given type is blocked or not a @Pi@, pass it reduced to the first continuation.
+--   If it is a @Pi@, pass its parts to the second continuation.
+ifNotPi :: MonadReduce m => Term -> (Term -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
+ifNotPi = flip . ifPi
+
+-- | If the given type is blocked or not a @Pi@, pass it reduced to the first continuation.
+--   If it is a @Pi@, pass its parts to the second continuation.
+ifNotPiType :: MonadReduce m => Type -> (Type -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
+ifNotPiType = flip . ifPiType
+
+ifNotPiOrPathType :: (MonadReduce tcm, HasBuiltins tcm) => Type -> (Type -> tcm a) -> (Dom Type -> Abs Type -> tcm a) -> tcm a
+ifNotPiOrPathType t no yes = do
+  ifPiType t yes (\ t -> either (uncurry yes . fst) (const $ no t) =<< (pathViewAsPi'whnf <*> pure t))
+
+shouldBePath :: (PureTCM m, MonadBlock m, MonadTCError m) => Type -> m (Dom Type, Abs Type)
+shouldBePath t = ifPathB t
+  (curry return)
+  (fromBlocked >=> \case
+    El _ Dummy{} -> return (__DUMMY_DOM__, Abs "x" __DUMMY_TYPE__)
+    t -> typeError $ ShouldBePath t)
+
+shouldBePi :: (PureTCM m, MonadBlock m, MonadTCError m) => Type -> m (Dom Type, Abs Type)
+shouldBePi t = ifPiTypeB t
+  (curry return)
+  (fromBlocked >=> \case
+    El _ Dummy{} -> return (__DUMMY_DOM__, Abs "x" __DUMMY_TYPE__)
+    t -> typeError $ ShouldBePi t)
+
+shouldBePiOrPath :: (PureTCM m, MonadBlock m, MonadTCError m) => Type -> m (Dom Type, Abs Type)
+shouldBePiOrPath t = ifPiOrPathB t
+  (curry return)
+  (fromBlocked >=> \case
+    El _ Dummy{} -> return (__DUMMY_DOM__, Abs "x" __DUMMY_TYPE__)
+    t -> typeError $ ShouldBePi t) -- TODO: separate error
+
+-- | A safe variant of 'piApply'.
+
+class PiApplyM a where
+  piApplyM' :: (MonadReduce m, HasBuiltins m) => m Empty -> Type -> a -> m Type
+
+  piApplyM :: (MonadReduce m, HasBuiltins m) => Type -> a -> m Type
+  piApplyM = piApplyM' __IMPOSSIBLE__
+  {-# INLINE piApplyM #-}
+
+instance PiApplyM Term where
+  piApplyM' err t v = ifNotPiOrPathType t (\_ -> absurd <$> err) {-else-} $ \ _ b -> return $ absApp b v
+  {-# INLINABLE piApplyM' #-}
+
+{-# SPECIALIZE piApplyM' :: TCM Empty -> Type -> Term -> TCM Type #-}
+
+instance PiApplyM a => PiApplyM (Arg a) where
+  piApplyM' err t = piApplyM' err t . unArg
+
+instance PiApplyM a => PiApplyM (Named n a) where
+  piApplyM' err t = piApplyM' err t . namedThing
+
+instance PiApplyM a => PiApplyM [a] where
+  piApplyM' err t = foldl (\ mt v -> mt >>= \t -> (piApplyM' err t v)) (return t)
+
+
+-- | Compute type arity
+
+typeArity :: Type -> TCM Nat
+typeArity t = do
+  TelV tel _ <- telView t
+  return (size tel)
+
+---------------------------------------------------------------------------
+-- * Instance definitions
+---------------------------------------------------------------------------
+
+data OutputTypeName
+  = OutputTypeName QName
+  | OutputTypeVar
+  | OutputTypeVisiblePi
+  | OutputTypeNameNotYetKnown Blocker
+  | NoOutputTypeName
+
+-- | Strips all hidden and instance Pi's and return the argument
+--   telescope and head definition name, if possible.
+getOutputTypeName :: Type -> TCM (Telescope, OutputTypeName)
+-- 2023-10-26, Jesper, issue #6941: To make instance search work correctly for
+-- abstract or opaque instances, we need to ignore abstract mode when computing
+-- the output type name.
+getOutputTypeName t = ignoreAbstractMode $ do
+  TelV tel t' <- telViewUpTo' (-1) notVisible t
+  ifBlocked (unEl t') (\ b _ -> return (tel , OutputTypeNameNotYetKnown b)) $ \ _ v ->
+    case v of
+      -- Possible base types:
+      Def n _  -> return (tel , OutputTypeName n)
+      Sort{}   -> return (tel , NoOutputTypeName)
+      Var n _  -> return (tel , OutputTypeVar)
+      Pi{}     -> return (tel , OutputTypeVisiblePi)
+      -- Not base types:
+      Con{}    -> __IMPOSSIBLE__
+      Lam{}    -> __IMPOSSIBLE__
+      Lit{}    -> __IMPOSSIBLE__
+      Level{}  -> __IMPOSSIBLE__
+      MetaV{}  -> __IMPOSSIBLE__
+      DontCare{} -> __IMPOSSIBLE__
+      Dummy s _ -> __IMPOSSIBLE_VERBOSE__ s
+
+
+-- | Register the definition with the given type as an instance.
+--   Issue warnings if instance is unusable.
+addTypedInstance ::
+     QName  -- ^ Name of instance.
+  -> Type   -- ^ Type of instance.
+  -> TCM ()
+addTypedInstance = addTypedInstance' True
+
+-- | Register the definition with the given type as an instance.
+addTypedInstance' ::
+     Bool   -- ^ Should we print warnings for unusable instance declarations?
+  -> QName  -- ^ Name of instance.
+  -> Type   -- ^ Type of instance.
+  -> TCM ()
+addTypedInstance' w x t = do
+  (tel , n) <- getOutputTypeName t
+  case n of
+    OutputTypeName n            -> addNamedInstance x n
+    OutputTypeNameNotYetKnown{} -> addUnknownInstance x
+    NoOutputTypeName            -> when w $ warning $ WrongInstanceDeclaration
+    OutputTypeVar               -> when w $ warning $ WrongInstanceDeclaration
+    OutputTypeVisiblePi         -> when w $ warning $ InstanceWithExplicitArg x
+
+resolveUnknownInstanceDefs :: TCM ()
+resolveUnknownInstanceDefs = do
+  anonInstanceDefs <- getAnonInstanceDefs
+  clearAnonInstanceDefs
+  forM_ anonInstanceDefs $ \ n -> do
+    -- Andreas, 2022-12-04, issue #6380:
+    -- Do not warn about unusable instances here.
+    addTypedInstance' False n =<< typeOfConst n
+
+-- | Try to solve the instance definitions whose type is not yet known, report
+--   an error if it doesn't work and return the instance table otherwise.
+getInstanceDefs :: TCM InstanceTable
+getInstanceDefs = do
+  resolveUnknownInstanceDefs
+  insts <- getAllInstanceDefs
+  unless (null $ snd insts) $
+    typeError $ GenericError $ "There are instances whose type is still unsolved"
+  return $ fst insts
diff --git a/src/full/Agda/TypeChecking/Telescope.hs-boot b/src/full/Agda/TypeChecking/Telescope.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Telescope.hs-boot
@@ -0,0 +1,23 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.TypeChecking.Telescope where
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Context (MonadAddContext)
+import {-# SOURCE #-} Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Substitute
+import Agda.Utils.Empty (Empty)
+
+class PiApplyM a where
+  piApplyM' :: (MonadReduce m, HasBuiltins m) => m Empty -> Type -> a -> m Type
+
+  piApplyM :: (MonadReduce m, HasBuiltins m) => Type -> a -> m Type
+  piApplyM = piApplyM' __IMPOSSIBLE__
+
+instance PiApplyM Term where
+instance PiApplyM a => PiApplyM (Arg a) where
+instance PiApplyM a => PiApplyM [a] where
+
+telView :: (MonadReduce m, MonadAddContext m) => Type -> m TelView
diff --git a/src/full/Agda/TypeChecking/Telescope/Path.hs b/src/full/Agda/TypeChecking/Telescope/Path.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Telescope/Path.hs
@@ -0,0 +1,128 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+module Agda.TypeChecking.Telescope.Path where
+
+import Prelude hiding (null)
+
+import qualified Data.List as List
+import Data.Maybe
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal
+
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Monad.Builtin
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.Maybe
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+
+-- | In an ambient context Γ, @telePiPath f lams Δ t bs@ builds a type that
+-- can be @telViewPathBoundaryP'ed@ into (TelV Δ t, bs').
+--   Γ.Δ ⊢ t
+--   bs = [(i,u_i)]
+--   Δ = Δ0,(i : I),Δ1
+--   ∀ b ∈ {0,1}.  Γ.Δ0 | lams Δ1 (u_i .b) : (telePiPath f Δ1 t bs)(i = b) -- kinda: see lams
+--   Γ ⊢ telePiPath f Δ t bs
+telePiPath :: (Abs Type -> Abs Type) -> ([Arg ArgName] -> Term -> Term) -> Telescope -> Type -> Boundary -> TCM Type
+telePiPath reAbs lams tel t bs = do
+  mpp <- getTerm' builtinPathP
+  io <- primIOne
+  let
+    argN = Arg defaultArgInfo
+    argH = Arg $ setHiding Hidden defaultArgInfo
+    getLevel :: Abs Type -> TCM Level
+    getLevel b = do
+      s <- reduce $ getSort <$> b
+      case s of
+        NoAbs _ (Type l) -> return l
+        Abs n (Type l) | not (freeIn 0 s) -> return $ noabsApp __IMPOSSIBLE__ (Abs n l)
+        _ -> typeError . GenericError . show =<<
+             (text "The type is non-fibrant or its sort depends on an interval variable" <+> prettyTCM (unAbs b))
+             -- TODO better Type Error
+    telePiPath :: [Int] -> Telescope -> TCM Type
+    telePiPath []     EmptyTel          = pure $ t
+    telePiPath (x:xs) (ExtendTel a tel)
+      = case List.find (\ (t,_) -> t == var x) bs of
+          Just (_,u) -> do
+            let pp = fromMaybe __IMPOSSIBLE__ mpp
+            let names = teleArgNames $ unAbs tel
+            -- assume a = 𝕀
+            b <- b
+            l <- getLevel b
+            return $ El (Type l) $
+              pp `apply` [ argH (Level l)
+                         , argN (Lam defaultArgInfo (unEl <$> b))
+                         , argN $ lams names (fst u)
+                         , argN $ lams names (snd u)
+                         ]
+          Nothing    -> do
+            b <- b
+            return $ El (mkPiSort a b) (Pi a (reAbs b))
+      where
+        b  = traverse (telePiPath xs) tel
+    telePiPath _     EmptyTel = __IMPOSSIBLE__
+    telePiPath []    _        = __IMPOSSIBLE__
+  telePiPath (downFrom (size tel)) tel
+
+-- | @telePiPath_ Δ t [(i,u)]@
+--   Δ ⊢ t
+--   i ∈ Δ
+--   Δ ⊢ u_b : t  for  b ∈ {0,1}
+telePiPath_ :: Telescope -> Type -> [(Int,(Term,Term))] -> TCM Type
+telePiPath_ tel t bndry = do
+  reportSDoc "tc.tel.path" 40                  $ text "tel  " <+> prettyTCM tel
+  reportSDoc "tc.tel.path" 40 $ addContext tel $ text "type " <+> prettyTCM t
+  reportSDoc "tc.tel.path" 40 $ addContext tel $ text "bndry" <+> pretty bndry
+
+  telePiPath id argsLam tel t [(var i, u) | (i , u) <- bndry]
+ where
+   argsLam args tm = strengthenS impossible 1 `applySubst`
+     foldr (\ Arg{argInfo = ai, unArg = x} -> Lam ai . Abs x) tm args
+
+-- | arity of the type, including both Pi and Path.
+--   Does not reduce the type.
+arityPiPath :: Type -> TCM Int
+arityPiPath t = do
+  piOrPath t >>= \case
+    Left (_, u) -> (+ 1) <$> arityPiPath (unAbs u)
+    Right _     -> return 0
+
+-- | Collect the interval copattern variables as list of de Bruijn indices.
+class IApplyVars p where
+  iApplyVars :: p -> [Int]
+
+instance DeBruijn a => IApplyVars (Pattern' a) where
+  iApplyVars = \case
+    IApplyP _ t u x -> [ fromMaybe __IMPOSSIBLE__ $ deBruijnView x ]
+    VarP{}          -> []
+    ProjP{}         -> []
+    LitP{}          -> []
+    DotP{}          -> []
+    DefP _ _ ps     -> iApplyVars ps
+    ConP _ _ ps     -> iApplyVars ps
+
+instance IApplyVars p => IApplyVars (NamedArg p) where
+  iApplyVars = iApplyVars . namedArg
+
+instance IApplyVars p => IApplyVars [p] where
+  iApplyVars = concatMap iApplyVars
+
+{-# SPECIALIZE isInterval :: Type -> TCM Bool #-}
+-- | Check whether a type is the built-in interval type.
+isInterval :: (MonadTCM m, MonadReduce m) => Type -> m Bool
+isInterval t = liftTCM $ do
+  caseMaybeM (getName' builtinInterval) (return False) $ \ i -> do
+  reduce (unEl t) <&> \case
+    Def q [] -> q == i
+    _        -> False
diff --git a/src/full/Agda/TypeChecking/Unquote.hs b/src/full/Agda/TypeChecking/Unquote.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Unquote.hs
@@ -0,0 +1,1165 @@
+module Agda.TypeChecking.Unquote where
+
+import Control.Arrow          ( first, second, (&&&) )
+import Control.Monad          ( (<=<) )
+import Control.Monad.Except   ( MonadError(..), ExceptT(..), runExceptT )
+import Control.Monad.IO.Class ( MonadIO(..) )
+import Control.Monad.Reader   ( ReaderT(..), runReaderT )
+import Control.Monad.State    ( gets, modify, StateT(..), runStateT )
+import Control.Monad.Writer   ( MonadWriter(..), WriterT(..), runWriterT )
+import Control.Monad.Trans    ( lift )
+
+import Data.Char
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Maybe (fromMaybe)
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Text (Text)
+import qualified Data.Text as T
+import Data.Word
+
+import System.Directory (doesFileExist, getPermissions, executable)
+import System.Process ( readProcessWithExitCode )
+import System.Exit ( ExitCode(..) )
+
+import Agda.Syntax.Common hiding ( Nat )
+import Agda.Syntax.Internal as I
+import qualified Agda.Syntax.Reflected as R
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Views
+import Agda.Syntax.Translation.InternalToAbstract
+import Agda.Syntax.Literal
+import Agda.Syntax.Position
+import Agda.Syntax.Info as Info
+import Agda.Syntax.Translation.ReflectedToAbstract
+import Agda.Syntax.Scope.Base (KindOfName(ConName, DataName))
+
+import Agda.Interaction.Library ( ExeName )
+import Agda.Interaction.Options ( optTrustedExecutables, optAllowExec )
+
+import Agda.TypeChecking.Constraints
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Quote
+import Agda.TypeChecking.Conversion
+import Agda.TypeChecking.EtaContract
+import Agda.TypeChecking.Primitive
+import Agda.TypeChecking.ReconstructParameters
+import Agda.TypeChecking.CheckInternal
+import Agda.TypeChecking.InstanceArguments ( getInstanceCandidates )
+
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Term
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Def
+import {-# SOURCE #-} Agda.TypeChecking.Rules.Decl
+import Agda.TypeChecking.Rules.Data
+
+import Agda.Utils.Either
+import Agda.Utils.Lens
+import Agda.Utils.List1 (List1, pattern (:|))
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Monad
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Interaction.Options.Lenses as Lens
+
+import Agda.Utils.Impossible
+import Agda.Syntax.Abstract (TypedBindingInfo(tbTacticAttr))
+
+agdaTermType :: TCM Type
+agdaTermType = El (mkType 0) <$> primAgdaTerm
+
+agdaTypeType :: TCM Type
+agdaTypeType = agdaTermType
+
+qNameType :: TCM Type
+qNameType = El (mkType 0) <$> primQName
+
+data Dirty = Dirty | Clean
+  deriving (Eq)
+
+-- Keep track of the original context. We need to use that when adding new
+-- definitions. Also state snapshot from last commit and whether the state is
+-- dirty (definitions have been added).
+type UnquoteState = (Dirty, TCState)
+type UnquoteM = ReaderT Context (StateT UnquoteState (WriterT [QName] (ExceptT UnquoteError TCM)))
+
+type UnquoteRes a = Either UnquoteError ((a, UnquoteState), [QName])
+
+unpackUnquoteM :: UnquoteM a -> Context -> UnquoteState -> TCM (UnquoteRes a)
+unpackUnquoteM m cxt s = runExceptT $ runWriterT $ runStateT (runReaderT m cxt) s
+
+packUnquoteM :: (Context -> UnquoteState -> TCM (UnquoteRes a)) -> UnquoteM a
+packUnquoteM f = ReaderT $ \ cxt -> StateT $ \ s -> WriterT $ ExceptT $ f cxt s
+
+runUnquoteM :: UnquoteM a -> TCM (Either UnquoteError (a, [QName]))
+runUnquoteM m = do
+  cxt <- asksTC envContext
+  s   <- getTC
+  z   <- unpackUnquoteM m cxt (Clean, s)
+  case z of
+    Left err              -> return $ Left err
+    Right ((x, _), decls) -> Right (x, decls) <$ mapM_ isDefined decls
+  where
+    isDefined x = do
+      def <- theDef <$> getConstInfo x
+      case def of
+        Function{funClauses = []} -> genericError $ "Missing definition for " ++ prettyShow x
+        _       -> return ()
+
+liftU1 :: (TCM (UnquoteRes a) -> TCM (UnquoteRes b)) -> UnquoteM a -> UnquoteM b
+liftU1 f m = packUnquoteM $ \ cxt s -> f (unpackUnquoteM m cxt s)
+
+liftU2 :: (TCM (UnquoteRes a) -> TCM (UnquoteRes b) -> TCM (UnquoteRes c)) -> UnquoteM a -> UnquoteM b -> UnquoteM c
+liftU2 f m1 m2 = packUnquoteM $ \ cxt s -> f (unpackUnquoteM m1 cxt s) (unpackUnquoteM m2 cxt s)
+
+inOriginalContext :: UnquoteM a -> UnquoteM a
+inOriginalContext m =
+  packUnquoteM $ \ cxt s -> do
+    n <- getContextSize
+    escapeContext __IMPOSSIBLE__ (n - length cxt) $ unpackUnquoteM m cxt s
+
+isCon :: ConHead -> TCM Term -> UnquoteM Bool
+isCon con tm = do t <- liftTCM tm
+                  case t of
+                    Con con' _ _ -> return (con == con')
+                    _ -> return False
+
+isDef :: QName -> TCM Term -> UnquoteM Bool
+isDef f tm = loop <$> liftTCM tm
+  where
+    loop (Def g _) = f == g
+    loop (Lam _ b) = loop $ unAbs b
+    loop _         = False
+
+reduceQuotedTerm :: Term -> UnquoteM Term
+reduceQuotedTerm t = locallyReduceAllDefs $ do
+  ifBlocked t {-then-} (\ m _ -> do s <- gets snd; throwError $ BlockedOnMeta s m)
+              {-else-} (\ _ t -> return t)
+
+class Unquote a where
+  unquote :: I.Term -> UnquoteM a
+
+unquoteN :: Unquote a => Arg Term -> UnquoteM a
+unquoteN a | visible a && isRelevant a =
+    unquote $ unArg a
+unquoteN a = throwError $ BadVisibility "visible" a
+
+choice :: Monad m => [(m Bool, m a)] -> m a -> m a
+choice [] dflt = dflt
+choice ((mb, mx) : mxs) dflt = ifM mb mx $ choice mxs dflt
+
+ensureDef :: QName -> UnquoteM QName
+ensureDef x = do
+  i <- either (const defaultAxiom) theDef <$> getConstInfo' x  -- for recursive unquoteDecl
+  case i of
+    Constructor{} -> do
+      def <- liftTCM $ prettyTCM =<< primAgdaTermDef
+      con <- liftTCM $ prettyTCM =<< primAgdaTermCon
+      throwError $ ConInsteadOfDef x (show def) (show con)
+    _ -> return x
+
+ensureCon :: QName -> UnquoteM QName
+ensureCon x = do
+  i <- either (const defaultAxiom) theDef <$> getConstInfo' x  -- for recursive unquoteDecl
+  case i of
+    Constructor{} -> return x
+    _ -> do
+      def <- liftTCM $ prettyTCM =<< primAgdaTermDef
+      con <- liftTCM $ prettyTCM =<< primAgdaTermCon
+      throwError $ DefInsteadOfCon x (show def) (show con)
+
+pickName :: R.Type -> String
+pickName a =
+  case a of
+    R.Pi{}   -> "f"
+    R.Sort{} -> "A"
+    R.Def d _
+      | c : cs  <- prettyShow (qnameName d),
+        Just lc <- reallyToLower c,
+        not (null cs) || isUpper c -> [lc]
+    _        -> "_"
+  where
+    -- Heuristic (see #5048 for some discussion):
+    -- If first character can be `toLower`ed use that, unless the name has only one character and is
+    -- already lower case. (to avoid using the same name for the type and the bound variable).
+    reallyToLower c
+      | toUpper lc /= lc = Just lc
+      | otherwise        = Nothing
+      where lc = toLower c
+
+-- TODO: reflect Cohesion
+instance Unquote Modality where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [r,q] <- allApplyElims es ->
+        choice
+          [(c `isCon` primModalityConstructor,
+              Modality <$> unquoteN r
+                       <*> unquoteN q
+                       <*> pure defaultCohesion)]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "modality" t
+
+instance Unquote ArgInfo where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [h,m] <- allApplyElims es ->
+        choice
+          [(c `isCon` primArgArgInfo,
+              ArgInfo <$> unquoteN h
+                      <*> unquoteN m
+                      <*> pure Reflected
+                      <*> pure unknownFreeVariables
+                      <*> pure defaultAnnotation)]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "arg info" t
+
+instance Unquote a => Unquote (Arg a) where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [info,x] <- allApplyElims es ->
+        choice
+          [(c `isCon` primArgArg, Arg <$> unquoteN info <*> unquoteN x)]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "arg" t
+
+-- Andreas, 2013-10-20: currently, post-fix projections are not part of the
+-- quoted syntax.
+instance Unquote R.Elim where
+  unquote t = R.Apply <$> unquote t
+
+instance Unquote Bool where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice [ (c `isCon` primTrue,  pure True)
+               , (c `isCon` primFalse, pure False) ]
+               __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "boolean" t
+
+instance Unquote Integer where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitNat n) -> return n
+      _ -> throwError $ NonCanonical "integer" t
+
+instance Unquote Word64 where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitWord64 n) -> return n
+      _ -> throwError $ NonCanonical "word64" t
+
+instance Unquote Double where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitFloat x) -> return x
+      _ -> throwError $ NonCanonical "float" t
+
+instance Unquote Char where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitChar x) -> return x
+      _ -> throwError $ NonCanonical "char" t
+
+instance Unquote Text where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitString x) -> return x
+      _ -> throwError $ NonCanonical "string" t
+
+unquoteString :: Term -> UnquoteM String
+unquoteString x = T.unpack <$> unquote x
+
+unquoteNString :: Arg Term -> UnquoteM Text
+unquoteNString = unquoteN
+
+data ErrorPart = StrPart String | TermPart A.Expr | PattPart A.Pattern | NamePart QName
+
+instance PrettyTCM ErrorPart where
+  prettyTCM (StrPart s)  = text s
+  prettyTCM (TermPart t) = prettyTCM t
+  prettyTCM (PattPart p) = prettyTCM p
+  prettyTCM (NamePart x) = prettyTCM x
+
+-- | We do a little bit of work here to make it possible to generate nice
+--   layout for multi-line error messages. Specifically we split the parts
+--   into lines (indicated by \n in a string part) and vcat all the lines.
+renderErrorParts :: [ErrorPart] -> TCM Doc
+renderErrorParts = vcat . map (hcat . map prettyTCM) . splitLines
+  where
+    splitLines [] = []
+    splitLines (StrPart s : ss) =
+      case break (== '\n') s of
+        (s0, '\n' : s1) -> [StrPart s0] : splitLines (StrPart s1 : ss)
+        (s0, "")        -> consLine (StrPart s0) (splitLines ss)
+        _               -> __IMPOSSIBLE__
+    splitLines (p@TermPart{} : ss) = consLine p (splitLines ss)
+    splitLines (p@PattPart{} : ss) = consLine p (splitLines ss)
+    splitLines (p@NamePart{} : ss) = consLine p (splitLines ss)
+
+    consLine l []        = [[l]]
+    consLine l (l' : ls) = (l : l') : ls
+
+
+instance Unquote ErrorPart where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x] <- allApplyElims es ->
+        choice [ (c `isCon` primAgdaErrorPartString, StrPart . T.unpack <$> unquoteNString x)
+               , (c `isCon` primAgdaErrorPartTerm,   TermPart <$> ((liftTCM . toAbstractWithoutImplicit) =<< (unquoteN x :: UnquoteM R.Term)))
+               , (c `isCon` primAgdaErrorPartPatt,   PattPart <$> ((liftTCM . toAbstractWithoutImplicit) =<< (unquoteN x :: UnquoteM R.Pattern)))
+               , (c `isCon` primAgdaErrorPartName,   NamePart <$> unquoteN x) ]
+               __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "error part" t
+
+instance Unquote a => Unquote [a] where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x,xs] <- allApplyElims es ->
+        choice
+          [(c `isCon` primCons, (:) <$> unquoteN x <*> unquoteN xs)]
+          __IMPOSSIBLE__
+      Con c _ [] ->
+        choice
+          [(c `isCon` primNil, return [])]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "list" t
+
+instance (Unquote a, Unquote b) => Unquote (a, b) where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    SigmaKit{..} <- fromMaybe __IMPOSSIBLE__ <$> getSigmaKit
+    case t of
+      Con c _ es | Just [x,y] <- allApplyElims es ->
+        choice
+          [(pure (c == sigmaCon), (,) <$> unquoteN x <*> unquoteN y)]
+          __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "pair" t
+
+instance Unquote Hiding where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice
+          [(c `isCon` primHidden,  return Hidden)
+          ,(c `isCon` primInstance, return (Instance NoOverlap))
+          ,(c `isCon` primVisible, return NotHidden)]
+          __IMPOSSIBLE__
+      Con c _ vs -> __IMPOSSIBLE__
+      _        -> throwError $ NonCanonical "visibility" t
+
+instance Unquote Relevance where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice
+          [(c `isCon` primRelevant,   return Relevant)
+          ,(c `isCon` primIrrelevant, return Irrelevant)]
+          __IMPOSSIBLE__
+      Con c _ vs -> __IMPOSSIBLE__
+      _        -> throwError $ NonCanonical "relevance" t
+
+instance Unquote Quantity where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice
+          [(c `isCon` primQuantityω, return $ Quantityω QωInferred)
+          ,(c `isCon` primQuantity0, return $ Quantity0 Q0Inferred)]
+          __IMPOSSIBLE__
+      Con c _ vs -> __IMPOSSIBLE__
+      _        -> throwError $ NonCanonical "quantity" t
+
+instance Unquote QName where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitQName x) -> return x
+      _ -> throwError $ NonCanonical "name" t
+
+instance Unquote a => Unquote (R.Abs a) where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x,y] <- allApplyElims es ->
+        choice
+          [(c `isCon` primAbsAbs, R.Abs <$> (hint . T.unpack <$> unquoteNString x) <*> unquoteN y)]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "abstraction" t
+
+    where hint x | not (null x) = x
+                 | otherwise    = "_"
+
+instance Unquote Blocker where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaBlockerAny, UnblockOnAny . Set.fromList <$> unquoteN x)
+          , (c `isCon` primAgdaBlockerAll, UnblockOnAll . Set.fromList <$> unquoteN x)
+          , (c `isCon` primAgdaBlockerMeta, UnblockOnMeta <$> unquoteN x)]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "blocker" t
+
+instance Unquote MetaId where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Lit (LitMeta m x) -> liftTCM $ do
+        live <- (Just m ==) <$> currentTopLevelModule
+        unless live $
+            typeError . GenericDocError =<<
+              sep [ "Can't unquote stale metavariable"
+                  , pretty m <> "._" <> pretty (metaId x) ]
+        return x
+      _ -> throwError $ NonCanonical "meta variable" t
+
+instance Unquote a => Unquote (Dom a) where
+  unquote t = domFromArg <$> unquote t
+
+instance Unquote R.Sort where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice
+          [(c `isCon` primAgdaSortUnsupported, return R.UnknownS)]
+          __IMPOSSIBLE__
+      Con c _ es | Just [u] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaSortSet, R.SetS <$> unquoteN u)
+          , (c `isCon` primAgdaSortLit, R.LitS <$> unquoteN u)
+          , (c `isCon` primAgdaSortProp, R.PropS <$> unquoteN u)
+          , (c `isCon` primAgdaSortPropLit, R.PropLitS <$> unquoteN u)
+          , (c `isCon` primAgdaSortInf, R.InfS <$> unquoteN u)
+          ]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "sort" t
+
+instance Unquote Literal where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaLitNat,    LitNat    <$> unquoteN x)
+          , (c `isCon` primAgdaLitFloat,  LitFloat  <$> unquoteN x)
+          , (c `isCon` primAgdaLitChar,   LitChar   <$> unquoteN x)
+          , (c `isCon` primAgdaLitString, LitString <$> unquoteNString x)
+          , (c `isCon` primAgdaLitQName,  LitQName  <$> unquoteN x)
+          , (c `isCon` primAgdaLitMeta,
+             LitMeta
+               <$> (fromMaybe __IMPOSSIBLE__ <$> currentTopLevelModule)
+               <*> unquoteN x)
+          ]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "literal" t
+
+instance Unquote R.Term where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ [] ->
+        choice
+          [ (c `isCon` primAgdaTermUnsupported, return R.Unknown) ]
+          __IMPOSSIBLE__
+
+      Con c _ es | Just [x] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaTermSort,      R.Sort      <$> unquoteN x)
+          , (c `isCon` primAgdaTermLit,       R.Lit       <$> unquoteN x)
+          ]
+          __IMPOSSIBLE__
+
+      Con c _ es | Just [x, y] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaTermVar,     R.Var     <$> (fromInteger <$> unquoteN x) <*> unquoteN y)
+          , (c `isCon` primAgdaTermCon,     R.Con     <$> (ensureCon =<< unquoteN x) <*> unquoteN y)
+          , (c `isCon` primAgdaTermDef,     R.Def     <$> (ensureDef =<< unquoteN x) <*> unquoteN y)
+          , (c `isCon` primAgdaTermMeta,    R.Meta    <$> unquoteN x <*> unquoteN y)
+          , (c `isCon` primAgdaTermLam,     R.Lam     <$> unquoteN x <*> unquoteN y)
+          , (c `isCon` primAgdaTermPi,      mkPi      <$> unquoteN x <*> unquoteN y)
+          , (c `isCon` primAgdaTermExtLam,  R.ExtLam  <$> (List1.fromListSafe __IMPOSSIBLE__ <$> unquoteN x) <*> unquoteN y)
+          ]
+          __IMPOSSIBLE__
+        where
+          mkPi :: Dom R.Type -> R.Abs R.Type -> R.Term
+          -- TODO: implement Free for reflected syntax so this works again
+          --mkPi a (R.Abs "_" b) = R.Pi a (R.Abs x b)
+          --  where x | 0 `freeIn` b = pickName (unDom a)
+          --          | otherwise    = "_"
+          mkPi a (R.Abs "_" b) = R.Pi a (R.Abs (pickName (unDom a)) b)
+          mkPi a b = R.Pi a b
+
+      Con{} -> __IMPOSSIBLE__
+      Lit{} -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "term" t
+
+instance Unquote R.Pattern where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaPatVar,    R.VarP    . fromInteger <$> unquoteN x)
+          , (c `isCon` primAgdaPatAbsurd, R.AbsurdP . fromInteger <$> unquoteN x)
+          , (c `isCon` primAgdaPatDot,    R.DotP  <$> unquoteN x)
+          , (c `isCon` primAgdaPatProj,   R.ProjP <$> unquoteN x)
+          , (c `isCon` primAgdaPatLit,    R.LitP  <$> unquoteN x) ]
+          __IMPOSSIBLE__
+      Con c _ es | Just [x, y] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaPatCon, R.ConP <$> unquoteN x <*> unquoteN y) ]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "pattern" t
+
+instance Unquote R.Clause where
+  unquote t = do
+    t <- reduceQuotedTerm t
+    case t of
+      Con c _ es | Just [x, y] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaClauseAbsurd, R.AbsurdClause <$> unquoteN x <*> unquoteN y) ]
+          __IMPOSSIBLE__
+      Con c _ es | Just [x, y, z] <- allApplyElims es ->
+        choice
+          [ (c `isCon` primAgdaClauseClause, R.Clause <$> unquoteN x <*> unquoteN y <*> unquoteN z) ]
+          __IMPOSSIBLE__
+      Con c _ _ -> __IMPOSSIBLE__
+      _ -> throwError $ NonCanonical "clause" t
+
+-- Unquoting TCM computations ---------------------------------------------
+
+-- | Argument should be a term of type @Term → TCM A@ for some A. Returns the
+--   resulting term of type @A@. The second argument is the term for the hole,
+--   which will typically be a metavariable. This is passed to the computation
+--   (quoted).
+unquoteTCM :: I.Term -> I.Term -> UnquoteM I.Term
+unquoteTCM m hole = do
+  qhole <- liftTCM $ quoteTerm hole
+  evalTCM (m `apply` [defaultArg qhole])
+
+evalTCM :: I.Term -> UnquoteM I.Term
+evalTCM v = do
+  v <- reduceQuotedTerm v
+  liftTCM $ reportSDoc "tc.unquote.eval" 90 $ "evalTCM" <+> prettyTCM v
+  let failEval = throwError $ NonCanonical "type checking computation" v
+
+  case v of
+    I.Def f [] ->
+      choice [ (f `isDef` primAgdaTCMGetContext,       tcGetContext)
+             , (f `isDef` primAgdaTCMCommit,           tcCommit)
+             , (f `isDef` primAgdaTCMAskNormalisation, tcAskNormalisation)
+             , (f `isDef` primAgdaTCMAskReconstructed, tcAskReconstructed)
+             , (f `isDef` primAgdaTCMAskExpandLast,    tcAskExpandLast)
+             , (f `isDef` primAgdaTCMAskReduceDefs,    tcAskReduceDefs)
+             ]
+             failEval
+    I.Def f [u] ->
+      choice [ (f `isDef` primAgdaTCMInferType,                  tcFun1 tcInferType                  u)
+             , (f `isDef` primAgdaTCMNormalise,                  tcFun1 tcNormalise                  u)
+             , (f `isDef` primAgdaTCMReduce,                     tcFun1 tcReduce                     u)
+             , (f `isDef` primAgdaTCMGetType,                    tcFun1 tcGetType                    u)
+             , (f `isDef` primAgdaTCMGetDefinition,              tcFun1 tcGetDefinition              u)
+             , (f `isDef` primAgdaTCMFormatErrorParts,           tcFun1 tcFormatErrorParts           u)
+             , (f `isDef` primAgdaTCMIsMacro,                    tcFun1 tcIsMacro                    u)
+             , (f `isDef` primAgdaTCMFreshName,                  tcFun1 tcFreshName                  u)
+             , (f `isDef` primAgdaTCMGetInstances,               uqFun1 tcGetInstances               u)
+             ]
+             failEval
+    I.Def f [u, v] ->
+      choice [ (f `isDef` primAgdaTCMUnify,      tcFun2 tcUnify      u v)
+             , (f `isDef` primAgdaTCMCheckType,  tcFun2 tcCheckType  u v)
+             , (f `isDef` primAgdaTCMDeclareDef, uqFun2 tcDeclareDef u v)
+             , (f `isDef` primAgdaTCMDeclarePostulate, uqFun2 tcDeclarePostulate u v)
+             , (f `isDef` primAgdaTCMDefineData, uqFun2 tcDefineData u v)
+             , (f `isDef` primAgdaTCMDefineFun,  uqFun2 tcDefineFun  u v)
+             , (f `isDef` primAgdaTCMQuoteOmegaTerm, tcQuoteTerm (sort $ Inf UType 0) (unElim v))
+             , (f `isDef` primAgdaTCMPragmaForeign, tcFun2 tcPragmaForeign u v)
+             ]
+             failEval
+    I.Def f [l, a, u] ->
+      choice [ (f `isDef` primAgdaTCMReturn,             return (unElim u))
+             , (f `isDef` primAgdaTCMTypeError,          tcFun1 tcTypeError   u)
+             , (f `isDef` primAgdaTCMQuoteTerm,          tcQuoteTerm (mkT (unElim l) (unElim a)) (unElim u))
+             , (f `isDef` primAgdaTCMUnquoteTerm,        tcFun1 (tcUnquoteTerm (mkT (unElim l) (unElim a))) u)
+             , (f `isDef` primAgdaTCMBlock,              uqFun1 tcBlock u)
+             , (f `isDef` primAgdaTCMDebugPrint,         tcFun3 tcDebugPrint l a u)
+             , (f `isDef` primAgdaTCMNoConstraints,      tcNoConstraints (unElim u))
+             , (f `isDef` primAgdaTCMDeclareData, uqFun3 tcDeclareData l a u)
+             , (f `isDef` primAgdaTCMRunSpeculative,     tcRunSpeculative (unElim u))
+             , (f `isDef` primAgdaTCMExec, tcFun3 tcExec l a u)
+             , (f `isDef` primAgdaTCMPragmaCompile, tcFun3 tcPragmaCompile l a u)
+             ]
+             failEval
+    I.Def f [_, _, u, v] ->
+      choice [ (f `isDef` primAgdaTCMCatchError,        tcCatchError    (unElim u) (unElim v))
+             , (f `isDef` primAgdaTCMWithNormalisation, tcWithNormalisation (unElim u) (unElim v))
+             , (f `isDef` primAgdaTCMWithReconstructed, tcWithReconstructed (unElim u) (unElim v))
+             , (f `isDef` primAgdaTCMWithExpandLast,    tcWithExpandLast (unElim u) (unElim v))
+             , (f `isDef` primAgdaTCMWithReduceDefs,    tcWithReduceDefs (unElim u) (unElim v))
+             , (f `isDef` primAgdaTCMInContext,         tcInContext     (unElim u) (unElim v))
+             ]
+             failEval
+    I.Def f [_, _, u, v, w] ->
+      choice [ (f `isDef` primAgdaTCMExtendContext, tcExtendContext (unElim u) (unElim v) (unElim w))
+             ]
+             failEval
+    I.Def f [_, _, _, _, m, k] ->
+      choice [ (f `isDef` primAgdaTCMBind, tcBind (unElim m) (unElim k)) ]
+             failEval
+    _ -> failEval
+  where
+    unElim = unArg . fromMaybe __IMPOSSIBLE__ . isApplyElim
+    tcBind m k = do v <- evalTCM m
+                    evalTCM (k `apply` [defaultArg v])
+
+    process :: (InstantiateFull a, Normalise a) => a -> TCM a
+    process v = do
+      norm <- viewTC eUnquoteNormalise
+      if norm then normalise v else instantiateFull v
+
+    mkT l a = El s a
+      where s = Type $ atomicLevel l
+
+    -- Don't catch Unquote errors!
+    tcCatchError :: Term -> Term -> UnquoteM Term
+    tcCatchError m h =
+      liftU2 (\ m1 m2 -> m1 `catchError` \ _ -> m2) (evalTCM m) (evalTCM h)
+
+    tcAskLens :: ToTerm a => Lens' TCEnv a -> UnquoteM Term
+    tcAskLens l = liftTCM (toTerm <*> asksTC (\ e -> e ^. l))
+
+    tcWithLens :: Unquote a => Lens' TCEnv a -> Term -> Term -> UnquoteM Term
+    tcWithLens l b m = do
+      v <- unquote b
+      liftU1 (locallyTC l $ const v) (evalTCM m)
+
+    tcWithNormalisation, tcWithReconstructed, tcWithExpandLast, tcWithReduceDefs :: Term -> Term -> UnquoteM Term
+    tcWithNormalisation = tcWithLens eUnquoteNormalise
+    tcWithReconstructed = tcWithLens eReconstructed
+    tcWithExpandLast    = tcWithLens eExpandLastBool
+    tcWithReduceDefs    = tcWithLens eReduceDefsPair
+
+    tcAskNormalisation, tcAskReconstructed, tcAskExpandLast, tcAskReduceDefs :: UnquoteM Term
+    tcAskNormalisation = tcAskLens eUnquoteNormalise
+    tcAskReconstructed = tcAskLens eReconstructed
+    tcAskExpandLast    = tcAskLens eExpandLastBool
+    tcAskReduceDefs    = tcAskLens eReduceDefsPair
+
+    uqFun1 :: Unquote a => (a -> UnquoteM b) -> Elim -> UnquoteM b
+    uqFun1 fun a = do
+      a <- unquote (unElim a)
+      fun a
+
+    tcFun1 :: Unquote a => (a -> TCM b) -> Elim -> UnquoteM b
+    tcFun1 fun = uqFun1 (liftTCM . fun)
+
+    uqFun2 :: (Unquote a, Unquote b) => (a -> b -> UnquoteM c) -> Elim -> Elim -> UnquoteM c
+    uqFun2 fun a b = do
+      a <- unquote (unElim a)
+      b <- unquote (unElim b)
+      fun a b
+
+    uqFun3 :: (Unquote a, Unquote b, Unquote c) => (a -> b -> c -> UnquoteM d) -> Elim -> Elim -> Elim -> UnquoteM d
+    uqFun3 fun a b c = do
+      a <- unquote (unElim a)
+      b <- unquote (unElim b)
+      c <- unquote (unElim c)
+      fun a b c
+
+    tcFun2 :: (Unquote a, Unquote b) => (a -> b -> TCM c) -> Elim -> Elim -> UnquoteM c
+    tcFun2 fun = uqFun2 (\ x y -> liftTCM (fun x y))
+
+    tcFun3 :: (Unquote a, Unquote b, Unquote c) => (a -> b -> c -> TCM d) -> Elim -> Elim -> Elim -> UnquoteM d
+    tcFun3 fun = uqFun3 (\ x y z -> liftTCM (fun x y z))
+
+    tcFreshName :: Text -> TCM Term
+    tcFreshName s = do
+      whenM (viewTC eCurrentlyElaborating) $
+        typeError $ GenericError "Not supported: declaring new names from an edit-time macro"
+      m <- currentModule
+      quoteName . qualify m <$> freshName_ (T.unpack s)
+
+    tcUnify :: R.Term -> R.Term -> TCM Term
+    tcUnify u v = do
+      (u, a) <- locallyReduceAllDefs $ inferExpr        =<< toAbstract_ u
+      v      <- locallyReduceAllDefs $ flip checkExpr a =<< toAbstract_ v
+      equalTerm a u v
+      primUnitUnit
+
+    tcBlock :: Blocker -> UnquoteM Term
+    tcBlock x = do
+      s <- gets snd
+      liftTCM $ reportSDoc "tc.unquote.block" 10 $ pretty (show x)
+      throwError (BlockedOnMeta s x)
+
+    tcCommit :: UnquoteM Term
+    tcCommit = do
+      dirty <- gets fst
+      when (dirty == Dirty) $
+        liftTCM $ typeError $ GenericError "Cannot use commitTC after declaring new definitions."
+      s <- getTC
+      modify (second $ const s)
+      liftTCM primUnitUnit
+
+    tcFormatErrorParts :: [ErrorPart] -> TCM Term
+    tcFormatErrorParts msg = quoteString . prettyShow <$> renderErrorParts msg
+
+    tcTypeError :: [ErrorPart] -> TCM a
+    tcTypeError err = typeError . GenericDocError =<< renderErrorParts err
+
+    tcDebugPrint :: Text -> Integer -> [ErrorPart] -> TCM Term
+    tcDebugPrint s n msg = do
+      alwaysReportSDoc (T.unpack s) (fromIntegral n) $ renderErrorParts msg
+      primUnitUnit
+
+    tcNoConstraints :: Term -> UnquoteM Term
+    tcNoConstraints m = liftU1 noConstraints (evalTCM m)
+
+    tcInferType :: R.Term -> TCM Term
+    tcInferType v = do
+      r <- isReconstructed
+      (_, a) <- inferExpr =<< toAbstract_ v
+      if r then do
+        a <- process a
+        a <- locallyReduceAllDefs $ reconstructParametersInType a
+        reportSDoc "tc.reconstruct" 50 $ "Infer after reconstruct:"
+          <+> pretty a
+        locallyReconstructed (quoteType a)
+      else
+        quoteType =<< process a
+
+    tcCheckType :: R.Term -> R.Type -> TCM Term
+    tcCheckType v a = do
+      r <- isReconstructed
+      a <- workOnTypes $ locallyReduceAllDefs $ isType_ =<< toAbstract_ a
+      e <- toAbstract_ v
+      v <- checkExpr e a
+      if r then do
+        v <- process v
+        v <- locallyReduceAllDefs $ reconstructParameters a v
+        locallyReconstructed (quoteTerm v)
+      else
+        quoteTerm =<< process v
+
+    tcQuoteTerm :: Type -> Term -> UnquoteM Term
+    tcQuoteTerm a v = liftTCM $ do
+      r <- isReconstructed
+      if r then do
+        v <- process v
+        v <- locallyReduceAllDefs $ reconstructParameters a v
+        locallyReconstructed (quoteTerm v)
+      else
+        quoteTerm =<< process v
+
+    tcUnquoteTerm :: Type -> R.Term -> TCM Term
+    tcUnquoteTerm a v = do
+      e <- toAbstract_ v
+      checkExpr e a
+
+    tcNormalise :: R.Term -> TCM Term
+    tcNormalise v = do
+      r <- isReconstructed
+      (v, t) <- locallyReduceAllDefs $ inferExpr  =<< toAbstract_ v
+      if r then do
+        v <- normalise v
+        t <- normalise t
+        v <- locallyReduceAllDefs $ reconstructParameters' defaultAction t v
+        reportSDoc "tc.reconstruct" 50 $ "Normalise reconstruct:" <+> pretty v
+        locallyReconstructed $ quoteTerm v
+      else
+       quoteTerm =<< normalise v
+
+    tcReduce :: R.Term -> TCM Term
+    tcReduce v = do
+      r <- isReconstructed
+      (v, t) <- locallyReduceAllDefs $ inferExpr =<< toAbstract_ v
+      if r then do
+        v <- reduce =<< instantiateFull v
+        t <- reduce =<< instantiateFull t
+        v <- locallyReduceAllDefs $ reconstructParameters' defaultAction t v
+        reportSDoc "tc.reconstruct" 50 $ "Reduce reconstruct:" <+> pretty v
+        locallyReconstructed $ quoteTerm v
+      else
+        quoteTerm =<< reduce =<< instantiateFull v
+
+    tcGetContext :: UnquoteM Term
+    tcGetContext = liftTCM $ do
+      r <- isReconstructed
+      as <- map (nameToArgName . fst . unDom &&& fmap snd) <$> getContext
+      as <- etaContract =<< process as
+      if r then do
+        as <- recons (reverse as)
+        let as' = reverse as
+        locallyReconstructed $ buildList <*> mapM quoteDomWithName as'
+      else
+        buildList <*> mapM quoteDomWithName as
+      where
+        recons :: [(ArgName, Dom Type)] -> TCM [(ArgName, Dom Type)]
+        recons []                        = return []
+        recons ((s, d@Dom {unDom=t}):ds) = do
+          t <- locallyReduceAllDefs $ reconstructParametersInType t
+          let d' = d{unDom=t}
+          ds' <- addContext (s, d') $ recons ds
+          return $ (s, d'):ds'
+
+        quoteDomWithName :: (ArgName, Dom Type) -> TCM Term
+        quoteDomWithName (x, t) = toTerm <*> pure (T.pack x, t)
+
+    extendCxt :: Text -> Arg R.Type -> UnquoteM a -> UnquoteM a
+    extendCxt s a m = do
+      a <- workOnTypes $ locallyReduceAllDefs $ liftTCM $ traverse (isType_ <=< toAbstract_) a
+      liftU1 (addContext (s, domFromArg a :: Dom Type)) m
+
+    tcExtendContext :: Term -> Term -> Term -> UnquoteM Term
+    tcExtendContext s a m = do
+      s <- unquote s
+      a <- unquote a
+      fmap (strengthen impossible) $ extendCxt s a $ do
+        v <- evalTCM $ raise 1 m
+        when (freeIn 0 v) $ liftTCM $ genericDocError =<<
+          hcat ["Local variable '", prettyTCM (var 0), "' escaping in result of extendContext:"]
+            <?> prettyTCM v
+        return v
+
+    tcInContext :: Term -> Term -> UnquoteM Term
+    tcInContext c m = do
+      c <- unquote c
+      inOriginalContext $ go c (evalTCM m)
+      where
+        go :: [(Text , Arg R.Type)] -> UnquoteM Term -> UnquoteM Term
+        go []             m = m
+        go ((s , a) : as) m = go as (extendCxt s a m)
+
+    constInfo :: QName -> TCM Definition
+    constInfo x = either err return =<< getConstInfo' x
+      where err _ = genericError $ "Unbound name: " ++ prettyShow x
+
+    tcGetType :: QName -> TCM Term
+    tcGetType x = do
+      r  <- isReconstructed
+      ci <- constInfo x >>= instantiateDef
+      let t = defType ci
+      if r then do
+        t <- locallyReduceAllDefs $ reconstructParametersInType t
+        quoteType t
+      else
+        quoteType t
+
+
+    tcIsMacro :: QName -> TCM Term
+    tcIsMacro x = do
+      true  <- primTrue
+      false <- primFalse
+      let qBool True  = true
+          qBool False = false
+      qBool . isMacro . theDef <$> constInfo x
+
+    tcGetDefinition :: QName -> TCM Term
+    tcGetDefinition x = do
+      r <- isReconstructed
+      if r then
+        tcGetDefinitionRecons x
+      else
+        quoteDefn =<< instantiateDef =<< constInfo x
+
+    tcGetDefinitionRecons :: QName -> TCM Term
+    tcGetDefinitionRecons x = do
+      ci@(Defn {theDef=d}) <- constInfo x >>= instantiateDef
+      case d of
+        f@(Function {funClauses=cs}) -> do
+          cs' <- mapM reconsClause cs
+          locallyReconstructed $ quoteDefn ci{theDef=f{funClauses=cs'}}
+
+        _ -> quoteDefn ci
+
+      where
+        reconsClause :: Clause -> TCM Clause
+        reconsClause c = do
+          tel' <- reconsTel $ clauseTel c
+          b' <- case (clauseType c, clauseBody c) of
+                (Just t, Just b) ->
+                  addContext (clauseTel c) $ do
+                     bb <- locallyReduceAllDefs
+                           $ reconstructParameters' defaultAction (unArg t) b
+                     return $ Just bb
+                _ -> return $ clauseBody c
+          let c' = c{clauseBody=b', clauseTel=tel'}
+          reportSDoc "tc.reconstruct" 50
+                   $ "getDefinition reconstructed clause:" <+> pretty c'
+          return c'
+
+        reconsTel :: Telescope -> TCM Telescope
+        reconsTel EmptyTel = return EmptyTel
+        reconsTel (ExtendTel _ NoAbs{}) = __IMPOSSIBLE__
+        reconsTel (ExtendTel (d@Dom{unDom=t}) ds@Abs{unAbs=ts}) = do
+           t <- locallyReduceAllDefs $ reconstructParametersInType t
+           let d' = d{unDom=t}
+           ts' <- addContext d' $ reconsTel ts
+           return $ ExtendTel d' ds{unAbs=ts'}
+
+
+    setDirty :: UnquoteM ()
+    setDirty = modify (first $ const Dirty)
+
+    tcDeclareDef :: Arg QName -> R.Type -> UnquoteM Term
+    tcDeclareDef (Arg i x) a = inOriginalContext $ do
+      setDirty
+      when (hidden i) $ liftTCM $ typeError . GenericDocError =<<
+        "Cannot declare hidden function" <+> prettyTCM x
+      tell [x]
+      liftTCM $ do
+        alwaysReportSDoc "tc.unquote.decl" 10 $ sep
+          [ "declare" <+> prettyTCM x <+> ":"
+          , nest 2 $ prettyR a
+          ]
+        a <- locallyReduceAllDefs $ isType_ =<< toAbstract_ a
+        alreadyDefined <- isRight <$> getConstInfo' x
+        when alreadyDefined $ genericError $ "Multiple declarations of " ++ prettyShow x
+        addConstant' x i x a =<< emptyFunction
+        when (isInstance i) $ addTypedInstance x a
+        primUnitUnit
+
+    tcDeclarePostulate :: Arg QName -> R.Type -> UnquoteM Term
+    tcDeclarePostulate (Arg i x) a = inOriginalContext $ do
+      clo <- commandLineOptions
+      when (Lens.getSafeMode clo) $ liftTCM $ typeError . GenericDocError =<<
+        "Cannot postulate '" <+> prettyTCM x <+> ":" <+> prettyR a <+> "' with safe flag"
+      setDirty
+      when (hidden i) $ liftTCM $ typeError . GenericDocError =<<
+        "Cannot declare hidden function" <+> prettyTCM x
+      tell [x]
+      liftTCM $ do
+        alwaysReportSDoc "tc.unquote.decl" 10 $ sep
+          [ "declare Postulate" <+> prettyTCM x <+> ":"
+          , nest 2 $ prettyR a
+          ]
+        a <- locallyReduceAllDefs $ isType_ =<< toAbstract_ a
+        alreadyDefined <- isRight <$> getConstInfo' x
+        when alreadyDefined $ genericError $ "Multiple declarations of " ++ prettyShow x
+        addConstant' x i x a defaultAxiom
+        when (isInstance i) $ addTypedInstance x a
+        primUnitUnit
+
+    -- A datatype is expected to be declared with a function type.
+    -- The second argument indicates how many preceding types are parameters.
+    tcDeclareData :: QName -> Integer -> R.Type -> UnquoteM Term
+    tcDeclareData x npars t = inOriginalContext $ do
+      setDirty
+      tell [x]
+      liftTCM $ do
+        alwaysReportSDoc "tc.unquote.decl" 10 $ sep
+          [ "declare Data" <+> prettyTCM x <+> ":"
+          , nest 2 $ prettyR t
+          ]
+        alreadyDefined <- isRight <$> getConstInfo' x
+        when alreadyDefined $ genericError $ "Multiple declarations of " ++ prettyShow x
+        e <- toAbstract_ t
+        -- The type to be checked with @checkSig@ is without parameters.
+        let (tel, e') = splitPars (fromInteger npars) e
+        ac <- asksTC (^. lensIsAbstract)
+        let defIn = mkDefInfo (nameConcrete $ qnameName x) noFixity' PublicAccess ac noRange
+        checkSig DataName defIn defaultErased x
+          (A.GeneralizeTel Map.empty tel) e'
+        primUnitUnit
+
+    tcDefineData :: QName -> [(QName, R.Type)] -> UnquoteM Term
+    tcDefineData x cs = inOriginalContext $ (setDirty >>) $ liftTCM $ do
+      caseEitherM (getConstInfo' x)
+        (const $ genericError $ "Missing declaration for " ++ prettyShow x) $ \def -> do
+        npars <- case theDef def of
+                   DataOrRecSig n -> return n
+                   _              -> genericError $ prettyShow x ++
+                     " is not declared as a datatype or record, or it already has a definition."
+
+        -- For some reasons, reifying parameters and adding them to the context via
+        -- `addContext` before `toAbstract_` is different from substituting the type after
+        -- `toAbstract_, so some dummy parameters are added and removed later.
+        es <- mapM (toAbstract_ . addDummy npars . snd) cs
+        alwaysReportSDoc "tc.unquote.def" 10 $ vcat $
+          [ "declaring constructors of" <+> prettyTCM x <+> ":" ] ++ map prettyA es
+
+        -- Translate parameters from internal definitions back to abstract syntax.
+        t   <- instantiateFull . defType =<< instantiateDef def
+        tel <- reify =<< theTel <$> telViewUpTo npars t
+
+        es' <- case mapM (uncurry (substNames' tel) . splitPars npars) es of
+                 Nothing -> genericError $ "Number of parameters doesn't match!"
+                 Just es -> return es
+
+        ac <- asksTC (^. lensIsAbstract)
+        let i = mkDefInfo (nameConcrete $ qnameName x) noFixity' PublicAccess ac noRange
+            conNames = map fst cs
+            toAxiom c e = A.Axiom ConName i defaultArgInfo Nothing c e
+            as = zipWith toAxiom conNames es'
+            lams = map (\case {A.TBind _ tac (b :| []) _ -> A.DomainFree (tbTacticAttr tac) b
+                              ;_ -> __IMPOSSIBLE__ }) tel
+        alwaysReportSDoc "tc.unquote.def" 10 $ vcat $
+          [ "checking datatype: " <+> prettyTCM x <+> " with constructors:"
+          , nest 2 (vcat (map prettyTCM conNames))
+          ]
+        checkDataDef i x YesUniverseCheck (A.DataDefParams Set.empty lams) as
+        primUnitUnit
+      where
+        addDummy :: Int -> R.Type -> R.Type
+        addDummy 0 t = t
+        addDummy n t = R.Pi (defaultDom (R.Sort $ R.LitS 0)) (R.Abs "dummy" $ addDummy (n - 1) t)
+
+        substNames' :: [A.TypedBinding] -> [A.TypedBinding] -> A.Expr -> Maybe A.Expr
+        substNames' (a : as) (b : bs) e = do
+          let (A.TBind _ _ (na :| _) expra) = a
+              (A.TBind _ _ (nb :| _) exprb) = b
+              getName n = A.unBind . A.binderName $ namedArg n
+          e' <- substNames' as bs e
+          return $ mapExpr (substName (getName na) (getName nb)) e'
+          where
+            -- Substitute @Var x@ for @Var y@ in an @Expr@.
+            substName :: Name -> Name -> (A.Expr -> A.Expr)
+            substName x y e@(A.Var n)
+                    | y == n    = A.Var x
+                    | otherwise = e
+            substName _ _ e = e
+        substNames' [] [] e = return e
+        substNames' _ _ _ = Nothing
+
+    tcDefineFun :: QName -> [R.Clause] -> UnquoteM Term
+    tcDefineFun x cs = inOriginalContext $ (setDirty >>) $ liftTCM $ do
+      whenM (isLeft <$> getConstInfo' x) $
+        genericError $ "Missing declaration for " ++ prettyShow x
+      cs <- mapM (toAbstract_ . QNamed x) cs
+      alwaysReportSDoc "tc.unquote.def" 10 $ vcat $ map prettyA cs
+      let accessDontCare = __IMPOSSIBLE__  -- or ConcreteDef, value not looked at
+      ac <- asksTC (^. lensIsAbstract)     -- Issue #4012, respect AbstractMode
+      oc <- asksTC (^. lensIsOpaque)       -- Issue #6959, respect current opaque block
+      let
+        i' = mkDefInfo (nameConcrete $ qnameName x) noFixity' accessDontCare ac noRange
+        i = i' { Info.defOpaque = oc }
+      locallyReduceAllDefs $ checkFunDef i x cs
+      primUnitUnit
+
+    tcPragmaForeign :: Text -> Text -> TCM Term
+    tcPragmaForeign backend code = do
+      addForeignCode (T.unpack backend) (T.unpack code)
+      primUnitUnit
+
+    tcPragmaCompile :: Text -> QName -> Text -> TCM Term
+    tcPragmaCompile backend name code = do
+      modifySignature $ updateDefinition name $
+        addCompilerPragma (T.unpack backend) $ CompilerPragma noRange (T.unpack code)
+      primUnitUnit
+
+    tcRunSpeculative :: Term -> UnquoteM Term
+    tcRunSpeculative mu = do
+      oldState <- getTC
+      u <- reduce =<< evalTCM mu
+      case u of
+        Con _ _ [Apply (Arg { unArg = x }), Apply (Arg { unArg = b })] -> do
+          unlessM (unquote b) $ putTC oldState
+          return x
+        _ -> liftTCM $ typeError . GenericDocError =<<
+          "Should be a pair: " <+> prettyTCM u
+
+    tcGetInstances :: MetaId -> UnquoteM Term
+    tcGetInstances m = liftTCM (getInstanceCandidates m) >>= \case
+      Left unblock -> do
+        s <- gets snd
+        throwError (BlockedOnMeta s unblock)
+      Right cands -> liftTCM $
+        buildList <*> mapM (quoteTerm . candidateTerm) cands
+
+    splitPars :: Int -> A.Expr -> ([A.TypedBinding], A.Expr)
+    splitPars 0 e = ([] , e)
+    splitPars npars (A.Pi _ (n :| _) e) = first (n :) (splitPars (npars - 1) e)
+    splitPars npars e = __IMPOSSIBLE__
+------------------------------------------------------------------------
+-- * Trusted executables
+------------------------------------------------------------------------
+
+type ExeArg  = Text
+type StdIn   = Text
+type StdOut  = Text
+type StdErr  = Text
+
+-- | Raise an error if the @--allow-exec@ option was not specified.
+--
+requireAllowExec :: TCM ()
+requireAllowExec = do
+  allowExec <- optAllowExec <$> pragmaOptions
+  unless allowExec $
+    typeError $ GenericError "Missing option --allow-exec"
+
+-- | Convert an @ExitCode@ to an Agda natural number.
+--
+exitCodeToNat :: ExitCode -> Nat
+exitCodeToNat  ExitSuccess    = Nat 0
+exitCodeToNat (ExitFailure n) = Nat (toInteger n)
+
+-- | Call a trusted executable with the given arguments and input.
+--
+--   Returns the exit code, stdout, and stderr.
+--
+tcExec :: ExeName -> [ExeArg] -> StdIn -> TCM Term
+tcExec exe args stdIn = do
+  requireAllowExec
+  exes <- optTrustedExecutables <$> commandLineOptions
+  case Map.lookup exe exes of
+    Nothing -> raiseExeNotTrusted exe exes
+    Just fp -> do
+      -- Check that the executable exists.
+      unlessM (liftIO $ doesFileExist fp) $ raiseExeNotFound exe fp
+      -- Check that the executable is executable.
+      unlessM (liftIO $ executable <$> getPermissions fp) $ raiseExeNotExecutable exe fp
+
+      let strArgs    = T.unpack <$> args
+      let strStdIn   = T.unpack stdIn
+      (datExitCode, strStdOut, strStdErr) <- lift $ readProcessWithExitCode fp strArgs strStdIn
+      let natExitCode = exitCodeToNat datExitCode
+      let txtStdOut   = T.pack strStdOut
+      let txtStdErr   = T.pack strStdErr
+      toR <- toTerm
+      return $ toR (natExitCode, (txtStdOut, txtStdErr))
+
+-- | Raise an error if the trusted executable cannot be found.
+--
+raiseExeNotTrusted :: ExeName -> Map ExeName FilePath -> TCM a
+raiseExeNotTrusted exe exes = genericDocError =<< do
+  vcat . map pretty $
+    ("Could not find '" ++ T.unpack exe ++ "' in list of trusted executables:") :
+    [ "  - " ++ T.unpack exe | exe <- Map.keys exes ]
+
+raiseExeNotFound :: ExeName -> FilePath -> TCM a
+raiseExeNotFound exe fp = genericDocError =<< do
+  text $ "Could not find file '" ++ fp ++ "' for trusted executable " ++ T.unpack exe
+
+raiseExeNotExecutable :: ExeName -> FilePath -> TCM a
+raiseExeNotExecutable exe fp = genericDocError =<< do
+  text $ "File '" ++ fp ++ "' for trusted executable" ++ T.unpack exe ++ " does not have permission to execute"
diff --git a/src/full/Agda/TypeChecking/Warnings.hs b/src/full/Agda/TypeChecking/Warnings.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/Warnings.hs
@@ -0,0 +1,222 @@
+
+module Agda.TypeChecking.Warnings
+  ( MonadWarning(..)
+  , genericWarning
+  , warning'_, warning_, warning', warning, warnings
+  , raiseWarningsOnUsage
+  , isUnsolvedWarning
+  , isMetaWarning
+  , isMetaTCWarning
+  , onlyShowIfUnsolved
+  , WhichWarnings(..), classifyWarning
+  -- not exporting constructor of WarningsAndNonFatalErrors
+  , WarningsAndNonFatalErrors, tcWarnings, nonFatalErrors
+  , emptyWarningsAndNonFatalErrors, classifyWarnings
+  , runPM
+  ) where
+
+import Control.Monad ( forM, unless )
+import Control.Monad.Except ( MonadError(..) )
+import Control.Monad.Reader ( ReaderT )
+import Control.Monad.State ( StateT )
+import Control.Monad.Trans ( MonadTrans, lift )
+
+import qualified Data.List as List
+import qualified Data.Map  as Map
+import qualified Data.Set  as Set
+import Data.Maybe     ( catMaybes )
+import Data.Semigroup ( Semigroup, (<>) )
+
+import Agda.TypeChecking.Monad.Base
+import Agda.TypeChecking.Monad.Debug
+import Agda.TypeChecking.Monad.Caching
+import {-# SOURCE #-} Agda.TypeChecking.Pretty (MonadPretty, prettyTCM, ($$))
+import {-# SOURCE #-} Agda.TypeChecking.Pretty.Call
+import {-# SOURCE #-} Agda.TypeChecking.Pretty.Warning ( prettyWarning, prettyWarningName )
+
+import Agda.Syntax.Abstract.Name ( QName )
+import Agda.Syntax.Position
+import Agda.Syntax.Parser
+
+import Agda.Interaction.Options
+import Agda.Interaction.Options.Warnings
+import {-# SOURCE #-} Agda.Interaction.Highlighting.Generate (highlightWarning)
+
+import Agda.Utils.CallStack ( CallStack, HasCallStack, withCallerCallStack )
+import Agda.Utils.Function  ( applyUnless )
+import Agda.Utils.Lens
+import qualified Agda.Syntax.Common.Pretty as P
+
+import Agda.Utils.Impossible
+
+
+-- * The warning monad
+---------------------------------------------------------------------------
+
+class (MonadPretty m, MonadError TCErr m) => MonadWarning m where
+  -- | Store a warning and generate highlighting from it.
+  addWarning :: TCWarning -> m ()
+
+  default addWarning
+    :: (MonadWarning n, MonadTrans t, t n ~ m)
+    => TCWarning -> m ()
+  addWarning = lift . addWarning
+
+instance MonadWarning m => MonadWarning (ReaderT r m)
+instance MonadWarning m => MonadWarning (StateT s m)
+
+instance MonadWarning TCM where
+  addWarning tcwarn = do
+    stTCWarnings `modifyTCLens` add w' tcwarn
+    highlightWarning tcwarn
+    where
+      w' = tcWarning tcwarn
+
+      add w tcwarn tcwarns
+        | onlyOnce w && elem tcwarn tcwarns = tcwarns -- Eq on TCWarning only checks head constructor
+        | otherwise                         = tcwarn : tcwarns
+
+-- * Raising warnings
+---------------------------------------------------------------------------
+
+{-# SPECIALIZE genericWarning :: P.Doc -> TCM () #-}
+genericWarning :: MonadWarning m => P.Doc -> m ()
+genericWarning = warning . GenericWarning
+
+{-# SPECIALIZE warning'_ :: CallStack -> Warning -> TCM TCWarning #-}
+warning'_ :: (MonadWarning m) => CallStack -> Warning -> m TCWarning
+warning'_ loc w = do
+  r <- viewTC eRange
+  c <- viewTC eCall
+  b <- areWeCaching
+  -- NicifierIssues come with their own error locations.
+  let r' = case w of { NicifierIssue w0 -> getRange w0 ; _ -> r }
+  let wn = warningName w
+  p <- sayWhen r' c $
+    -- Only benign warnings can be deactivated with -WnoXXX, so don't
+    -- display hint for error warnings.
+    applyUnless (wn `elem` errorWarnings) (prettyWarningName wn $$) $
+      prettyWarning w
+  return $ TCWarning loc r w p b
+
+{-# SPECIALIZE warning_ :: Warning -> TCM TCWarning #-}
+warning_ :: (HasCallStack, MonadWarning m) => Warning -> m TCWarning
+warning_ = withCallerCallStack . flip warning'_
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+---- | @applyWarningMode@ filters out the warnings the user has not requested
+---- Users are not allowed to ignore non-fatal errors.
+--
+--applyWarningMode :: WarningMode -> Warning -> Maybe Warning
+--applyWarningMode wm w = case classifyWarning w of
+--  ErrorWarnings -> Just w
+--  AllWarnings   -> w <$ guard (Set.member (warningName w) $ wm ^. warningSet)
+
+{-# SPECIALIZE warnings' :: CallStack -> [Warning] -> TCM () #-}
+warnings' :: MonadWarning m => CallStack -> [Warning] -> m ()
+warnings' loc ws = do
+
+  wmode <- optWarningMode <$> pragmaOptions
+
+  -- We collect *all* of the warnings no matter whether they are in the @warningSet@
+  -- or not. If we find one which should be turned into an error, we keep processing
+  -- the rest of the warnings and *then* report all of the errors at once.
+  merrs <- forM ws $ \ w' -> do
+    tcwarn <- warning'_ loc w'
+    if wmode ^. warn2Error && warningName w' `elem` wmode ^. warningSet
+    then pure (Just tcwarn)
+    else Nothing <$ addWarning tcwarn
+
+  let errs = catMaybes merrs
+  unless (null errs) $ typeError' loc $ NonFatalErrors errs
+
+{-# SPECIALIZE warnings :: HasCallStack => [Warning] -> TCM () #-}
+warnings :: (HasCallStack, MonadWarning m) => [Warning] -> m ()
+warnings = withCallerCallStack . flip warnings'
+
+{-# SPECIALIZE warning' :: CallStack -> Warning -> TCM () #-}
+warning' :: MonadWarning m => CallStack -> Warning -> m ()
+warning' loc = warnings' loc . pure
+
+{-# SPECIALIZE warning :: HasCallStack => Warning -> TCM () #-}
+warning :: (HasCallStack, MonadWarning m) => Warning -> m ()
+warning = withCallerCallStack . flip warning'
+
+-- | Raise every 'WARNING_ON_USAGE' connected to a name.
+{-# SPECIALIZE raiseWarningsOnUsage :: QName -> TCM () #-}
+raiseWarningsOnUsage :: (MonadWarning m, ReadTCState m) => QName -> m ()
+raiseWarningsOnUsage d = do
+  -- In case we find a defined name, we start by checking whether there's
+  -- a warning attached to it
+  reportSLn "scope.warning.usage" 50 $ "Checking usage of " ++ P.prettyShow d
+  mapM_ (warning . UserWarning) =<< Map.lookup d <$> getUserWarnings
+
+
+-- * Classifying warnings
+---------------------------------------------------------------------------
+
+isUnsolvedWarning :: Warning -> Bool
+isUnsolvedWarning w = warningName w `Set.member` unsolvedWarnings
+
+isMetaWarning :: Warning -> Bool
+isMetaWarning = \case
+   UnsolvedInteractionMetas{} -> True
+   UnsolvedMetaVariables{}    -> True
+   _                          -> False
+
+isMetaTCWarning :: TCWarning -> Bool
+isMetaTCWarning = isMetaWarning . tcWarning
+
+-- | Should we only emit a single warning with this constructor.
+onlyOnce :: Warning -> Bool
+onlyOnce InversionDepthReached{} = True
+onlyOnce _ = False
+
+onlyShowIfUnsolved :: Warning -> Bool
+onlyShowIfUnsolved InversionDepthReached{} = True
+onlyShowIfUnsolved _ = False
+
+-- | Classifying warnings: some are benign, others are (non-fatal) errors
+
+data WhichWarnings =
+    ErrorWarnings -- ^ warnings that will be turned into errors
+  | AllWarnings   -- ^ all warnings, including errors and benign ones
+  -- Note: order of constructors is important for the derived Ord instance
+  deriving (Eq, Ord)
+
+classifyWarning :: Warning -> WhichWarnings
+classifyWarning w =
+  if warningName w `Set.member` errorWarnings
+  then ErrorWarnings
+  else AllWarnings
+
+-- | Assorted warnings and errors to be displayed to the user
+data WarningsAndNonFatalErrors = WarningsAndNonFatalErrors
+  { tcWarnings     :: [TCWarning]
+  , nonFatalErrors :: [TCWarning]
+  }
+
+-- | The only way to construct a empty WarningsAndNonFatalErrors
+
+emptyWarningsAndNonFatalErrors :: WarningsAndNonFatalErrors
+emptyWarningsAndNonFatalErrors = WarningsAndNonFatalErrors [] []
+
+classifyWarnings :: [TCWarning] -> WarningsAndNonFatalErrors
+classifyWarnings ws = WarningsAndNonFatalErrors warnings errors
+  where
+    partite = (< AllWarnings) . classifyWarning . tcWarning
+    (errors, warnings) = List.partition partite ws
+
+
+-- * Warnings in the parser
+---------------------------------------------------------------------------
+
+-- | running the Parse monad
+
+runPM :: PM a -> TCM a
+runPM m = do
+  (res, ws) <- runPMIO m
+  mapM_ (warning . ParseWarning) ws
+  case res of
+    Left  e -> throwError (Exception (getRange e) (P.pretty e))
+    Right a -> return a
diff --git a/src/full/Agda/TypeChecking/With.hs b/src/full/Agda/TypeChecking/With.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/TypeChecking/With.hs
@@ -0,0 +1,769 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE NondecreasingIndentation #-}
+
+module Agda.TypeChecking.With where
+
+import Prelude hiding ((!!))
+
+import Control.Monad
+import Control.Monad.Writer (WriterT, runWriterT, tell)
+
+import qualified Data.List as List
+import Data.Maybe
+import Data.Foldable ( foldrM )
+
+import Agda.Syntax.Common
+import Agda.Syntax.Internal as I
+import Agda.Syntax.Internal.Pattern
+import qualified Agda.Syntax.Abstract as A
+import Agda.Syntax.Abstract.Pattern as A
+import Agda.Syntax.Abstract.Views
+import Agda.Syntax.Info
+import Agda.Syntax.Position
+
+import Agda.TypeChecking.Monad
+import Agda.TypeChecking.Reduce
+import Agda.TypeChecking.Datatypes
+import Agda.TypeChecking.EtaContract
+import Agda.TypeChecking.Free
+import Agda.TypeChecking.Patterns.Abstract
+import Agda.TypeChecking.Pretty
+import Agda.TypeChecking.Primitive ( getRefl )
+import Agda.TypeChecking.Records
+import Agda.TypeChecking.Substitute
+import Agda.TypeChecking.Telescope
+import Agda.TypeChecking.Telescope.Path
+
+import Agda.TypeChecking.Abstract
+import Agda.TypeChecking.Rules.LHS.Implicit
+import Agda.TypeChecking.Rules.LHS.Problem (ProblemEq(..))
+
+import Agda.Utils.Functor
+import Agda.Utils.List
+import Agda.Utils.List1 (List1)
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+import Agda.Utils.Null (empty)
+import Agda.Utils.Permutation
+import Agda.Syntax.Common.Pretty (prettyShow)
+import qualified Agda.Syntax.Common.Pretty as P
+import Agda.Utils.Size
+
+import Agda.Utils.Impossible
+
+-- | Split pattern variables according to with-expressions.
+
+--   Input:
+--
+--   [@Δ@]         context of types and with-arguments.
+--
+--   [@Δ ⊢ t@]     type of rhs.
+--
+--   [@Δ ⊢ vs : as@]    with arguments and their types
+--
+--   Output:
+--
+--   [@Δ₁@]              part of context needed for with arguments and their types.
+--
+--   [@Δ₂@]              part of context not needed for with arguments and their types.
+--
+--   [@π@]               permutation from Δ to Δ₁Δ₂ as returned by 'splitTelescope'.
+--
+--   [@Δ₁Δ₂ ⊢ t'@]       type of rhs under @π@
+--
+--   [@Δ₁ ⊢ vs' : as'@]  with-arguments and their types depending only on @Δ₁@.
+
+splitTelForWith
+  -- Input:
+  :: Telescope                         -- ^ __@Δ@__             context of types and with-arguments.
+  -> Type                              -- ^ __@Δ ⊢ t@__         type of rhs.
+  -> [Arg (Term, EqualityView)]        -- ^ __@Δ ⊢ vs : as@__   with arguments and their types.
+  -- Output:
+  -> ( Telescope                         -- @Δ₁@             part of context needed for with arguments and their types.
+     , Telescope                         -- @Δ₂@             part of context not needed for with arguments and their types.
+     , Permutation                       -- @π@              permutation from Δ to Δ₁Δ₂ as returned by 'splitTelescope'.
+     , Type                              -- @Δ₁Δ₂ ⊢ t'@      type of rhs under @π@
+     , [Arg (Term, EqualityView)]        -- @Δ₁ ⊢ vs' : as'@ with- and rewrite-arguments and types under @π@.
+     )              -- ^ (__@Δ₁@__,__@Δ₂@__,__@π@__,__@t'@__,__@vtys'@__) where
+--
+--   [@Δ₁@]        part of context needed for with arguments and their types.
+--
+--   [@Δ₂@]        part of context not needed for with arguments and their types.
+--
+--   [@π@]         permutation from Δ to Δ₁Δ₂ as returned by 'splitTelescope'.
+--
+--   [@Δ₁Δ₂ ⊢ t'@] type of rhs under @π@
+--
+--   [@Δ₁ ⊢ vtys'@]  with-arguments and their types under @π@.
+
+splitTelForWith delta t vtys = let
+    -- Split the telescope into the part needed to type the with arguments
+    -- and all the other stuff.
+    fv = allFreeVars vtys
+    SplitTel delta1 delta2 perm = splitTelescope fv delta
+
+    -- Δ₁Δ₂ ⊢ π : Δ
+    pi = renaming impossible (reverseP perm)
+    -- Δ₁ ⊢ ρ : Δ₁Δ₂  (We know that as does not depend on Δ₂.)
+    rho = strengthenS impossible $ size delta2
+    -- Δ₁ ⊢ ρ ∘ π : Δ
+    rhopi = composeS rho pi
+
+    -- We need Δ₁Δ₂ ⊢ t'
+    t' = applySubst pi t
+    -- and Δ₁ ⊢ vtys'
+    vtys' = applySubst rhopi vtys
+
+  in (delta1, delta2, perm, t', vtys')
+
+
+-- | Abstract with-expressions @vs@ to generate type for with-helper function.
+--
+-- Each @EqualityType@, coming from a @rewrite@, will turn into 2 abstractions.
+
+withFunctionType
+  :: Telescope                          -- ^ @Δ₁@                        context for types of with types.
+  -> [Arg (Term, EqualityView)]         -- ^ @Δ₁,Δ₂ ⊢ vs : raise Δ₂ as@  with and rewrite-expressions and their type.
+  -> Telescope                          -- ^ @Δ₁ ⊢ Δ₂@                   context extension to type with-expressions.
+  -> Type                               -- ^ @Δ₁,Δ₂ ⊢ b@                 type of rhs.
+  -> [(Int,(Term,Term))]                -- ^ @Δ₁,Δ₂ ⊢ [(i,(u0,u1))] : b  boundary.
+  -> TCM (Type, Nat)
+    -- ^ @Δ₁ → wtel → Δ₂′ → b′@ such that
+    --     @[vs/wtel]wtel = as@ and
+    --     @[vs/wtel]Δ₂′ = Δ₂@ and
+    --     @[vs/wtel]b′ = b@.
+    -- Plus the final number of with-arguments.
+withFunctionType delta1 vtys delta2 b bndry = addContext delta1 $ do
+
+  reportSLn "tc.with.abstract" 20 $ "preparing for with-abstraction"
+
+  -- Normalize and η-contract the type @b@ of the rhs and the types @delta2@
+  -- of the pattern variables not mentioned in @vs : as@.
+  let dbg n s x = reportSDoc "tc.with.abstract" n $ nest 2 $ text (s ++ " =") <+> prettyTCM x
+
+  d2b <- telePiPath_ delta2 b bndry
+  dbg 30 "Δ₂ → B" d2b
+  d2b  <- normalise d2b
+  dbg 30 "normal Δ₂ → B" d2b
+  d2b  <- etaContract d2b
+  dbg 30 "eta-contracted Δ₂ → B" d2b
+
+  vtys <- etaContract =<< normalise vtys
+
+  -- wd2db = wtel → [vs : as] (Δ₂ → B)
+  wd2b <- foldrM piAbstract d2b vtys
+  dbg 30 "wΓ → Δ₂ → B" wd2b
+
+  let nwithargs = countWithArgs (map (snd . unArg) vtys)
+
+  TelV wtel _ <- telViewUpTo nwithargs wd2b
+
+  -- select the boundary for "Δ₁" abstracting over "wΓ.Δ₂"
+  let bndry' = [(i - sd2,(lams u0, lams u1)) | (i,(u0,u1)) <- bndry, i >= sd2]
+        where sd2 = size delta2
+              lams u = teleNoAbs wtel (abstract delta2 u)
+
+  d1wd2b <- telePiPath_ delta1 wd2b bndry'
+
+  dbg 30 "Δ₁ → wΓ → Δ₂ → B" d1wd2b
+
+  return (d1wd2b, nwithargs)
+
+countWithArgs :: [EqualityView] -> Nat
+countWithArgs = sum . map countArgs
+  where
+    countArgs OtherType{}    = 1
+    countArgs IdiomType{}    = 2
+    countArgs EqualityType{} = 2
+
+-- | From a list of @with@ and @rewrite@ expressions and their types,
+--   compute the list of final @with@ expressions (after expanding the @rewrite@s).
+withArguments :: [Arg (Term, EqualityView)] ->
+                 TCM [Arg Term]
+withArguments vtys = do
+  tss <- forM vtys $ \ (Arg info ts) -> fmap (map (Arg info)) $ case ts of
+    (v, OtherType a) -> pure [v]
+    (prf, eqt@(EqualityType s _eq _pars _t v _v')) -> pure [unArg v, prf]
+    (v, IdiomType t) -> do
+       mkRefl <- getRefl
+       pure [v, mkRefl (defaultArg v)]
+  pure (concat tss)
+
+-- | Compute the clauses for the with-function given the original patterns.
+buildWithFunction
+  :: [Name]               -- ^ Names of the module parameters of the parent function.
+  -> QName                -- ^ Name of the parent function.
+  -> QName                -- ^ Name of the with-function.
+  -> Type                 -- ^ Types of the parent function.
+  -> Telescope            -- ^ Context of parent patterns.
+  -> [NamedArg DeBruijnPattern] -- ^ Parent patterns.
+  -> Nat                  -- ^ Number of module parameters in parent patterns
+  -> Substitution         -- ^ Substitution from parent lhs to with function lhs
+  -> Permutation          -- ^ Final permutation.
+  -> Nat                  -- ^ Number of needed vars.
+  -> Nat                  -- ^ Number of with expressions.
+  -> List1 A.SpineClause  -- ^ With-clauses.
+  -> TCM (List1 A.SpineClause) -- ^ With-clauses flattened wrt. parent patterns.
+buildWithFunction cxtNames f aux t delta qs npars withSub perm n1 n cs = mapM buildWithClause cs
+  where
+    -- Nested with-functions will iterate this function once for each parent clause.
+    buildWithClause (A.Clause (A.SpineLHS i _ allPs) inheritedPats rhs wh catchall) = do
+      let (ps, wps)    = splitOffTrailingWithPatterns allPs
+          (wps0, wps1) = splitAt n wps
+          ps0          = map (updateNamedArg fromWithP) wps0
+            where
+            fromWithP (A.WithP _ p) = p
+            fromWithP _ = __IMPOSSIBLE__
+      reportSDoc "tc.with" 50 $ "inheritedPats:" <+> vcat
+        [ prettyA p <+> "=" <+> prettyTCM v <+> ":" <+> prettyTCM a
+        | A.ProblemEq p v a <- inheritedPats
+        ]
+      (strippedPats, ps') <- stripWithClausePatterns cxtNames f aux t delta qs npars perm ps
+      reportSDoc "tc.with" 50 $ hang "strippedPats:" 2 $
+                                  vcat [ prettyA p <+> "==" <+> prettyTCM v <+> (":" <+> prettyTCM t)
+                                       | A.ProblemEq p v t <- strippedPats ]
+      rhs <- buildRHS strippedPats rhs
+      let (ps1, ps2) = splitAt n1 ps'
+      let result = A.Clause (A.SpineLHS i aux $ ps1 ++ ps0 ++ ps2 ++ wps1)
+                     (inheritedPats ++ strippedPats)
+                     rhs wh catchall
+      reportSDoc "tc.with" 20 $ vcat
+        [ "buildWithClause returns" <+> prettyA result
+        ]
+      return result
+
+    buildRHS _ rhs@A.RHS{}                 = return rhs
+    buildRHS _ rhs@A.AbsurdRHS             = return rhs
+    buildRHS _ (A.WithRHS q es cs)         = A.WithRHS q es <$>
+      mapM ((A.spineToLhs . permuteNamedDots) <.> buildWithClause . A.lhsToSpine) cs
+    buildRHS strippedPats1 (A.RewriteRHS qes strippedPats2 rhs wh) =
+      flip (A.RewriteRHS qes (applySubst withSub $ strippedPats1 ++ strippedPats2)) wh <$> buildRHS [] rhs
+
+    -- The stripped patterns computed by buildWithClause lives in the context
+    -- of the top with-clause (of the current call to buildWithFunction). When
+    -- we recurse we expect inherited patterns to live in the context
+    -- of the innermost parent clause. Note that this makes them live in the
+    -- context of the with-function arguments before any pattern matching. We
+    -- need to update again once the with-clause patterns have been checked.
+    -- This happens in Rules.Def.checkClause before calling checkRHS.
+    permuteNamedDots :: A.SpineClause -> A.SpineClause
+    permuteNamedDots (A.Clause lhs strippedPats rhs wh catchall) =
+      A.Clause lhs (applySubst withSub strippedPats) rhs wh catchall
+
+
+-- The arguments of @stripWithClausePatterns@ are documented
+-- at its type signature.
+-- The following is duplicate information, but may help reading the examples below.
+--
+-- [@Δ@]   context bound by lhs of original function.
+-- [@f@]   name of @with@-function.
+-- [@t@]   type of the original function.
+-- [@qs@]  internal patterns for original function.
+-- [@np@]  number of module parameters in @qs@
+-- [@π@]   permutation taking @vars(qs)@ to @support(Δ)@.
+-- [@ps@]  patterns in with clause (eliminating type @t@).
+-- [@ps'@] patterns for with function (presumably of type @Δ@).
+
+{-| @stripWithClausePatterns cxtNames parent f t Δ qs np π ps = ps'@
+
+Example:
+
+@
+  record Stream (A : Set) : Set where
+    coinductive
+    constructor delay
+    field       force : A × Stream A
+
+  record SEq (s t : Stream A) : Set where
+    coinductive
+    field
+      ~force : let a , as = force s
+                   b , bs = force t
+               in  a ≡ b × SEq as bs
+
+  test : (s : Nat × Stream Nat) (t : Stream Nat) → SEq (delay s) t → SEq t (delay s)
+  ~force (test (a     , as) t p) with force t
+  ~force (test (suc n , as) t p) | b , bs = ?
+@
+
+With function:
+
+@
+  f : (t : Stream Nat) (w : Nat × Stream Nat) (a : Nat) (as : Stream Nat)
+      (p : SEq (delay (a , as)) t) → (fst w ≡ a) × SEq (snd w) as
+
+  Δ  = t a as p   -- reorder to bring with-relevant (= needed) vars first
+  π  = a as t p → Δ
+  qs = (a     , as) t p ~force
+  ps = (suc n , as) t p ~force
+  ps' = (suc n) as t p
+@
+
+Resulting with-function clause is:
+
+@
+  f t (b , bs) (suc n) as t p
+@
+
+Note: stripWithClausePatterns factors __@ps@__ through __@qs@__, thus
+
+@
+  ps = qs[ps']
+@
+
+where @[..]@ is to be understood as substitution.
+The projection patterns have vanished from __@ps'@__ (as they are already in __@qs@__).
+-}
+
+stripWithClausePatterns
+  :: [Name]                   -- ^ __@cxtNames@__ names of the module parameters of the parent function
+  -> QName                    -- ^ __@parent@__ name of the parent function.
+  -> QName                    -- ^ __@f@__   name of with-function.
+  -> Type                     -- ^ __@t@__   top-level type of the original function.
+  -> Telescope                -- ^ __@Δ@__   context of patterns of parent function.
+  -> [NamedArg DeBruijnPattern] -- ^ __@qs@__  internal patterns for original function.
+  -> Nat                      -- ^ __@npars@__ number of module parameters in @qs@.
+  -> Permutation              -- ^ __@π@__   permutation taking @vars(qs)@ to @support(Δ)@.
+  -> [NamedArg A.Pattern]     -- ^ __@ps@__  patterns in with clause (eliminating type @t@).
+  -> TCM ([A.ProblemEq], [NamedArg A.Pattern]) -- ^ __@ps'@__ patterns for with function (presumably of type @Δ@).
+stripWithClausePatterns cxtNames parent f t delta qs npars perm ps = do
+  -- Andreas, 2014-03-05 expand away pattern synoyms (issue 1074)
+  ps <- expandPatternSynonyms ps
+  -- Ulf, 2016-11-16 Issue 2303: We need the module parameter
+  -- instantiations from qs, so we make sure
+  -- that t is the top-level type of the parent function and add patterns for
+  -- the module parameters to ps before stripping.
+  let paramPat i _ = A.VarP $ A.mkBindName $ indexWithDefault __IMPOSSIBLE__ cxtNames i
+      ps' = zipWith (fmap . fmap . paramPat) [0..] (take npars qs) ++ ps
+  psi <- insertImplicitPatternsT ExpandLast ps' t
+  reportSDoc "tc.with.strip" 10 $ vcat
+    [ "stripping patterns"
+    , nest 2 $ "t   = " <+> prettyTCM t
+    , nest 2 $ "ps  = " <+> fsep (punctuate comma $ map prettyA ps)
+    , nest 2 $ "ps' = " <+> fsep (punctuate comma $ map prettyA ps')
+    , nest 2 $ "psi = " <+> fsep (punctuate comma $ map prettyA psi)
+    , nest 2 $ "qs  = " <+> fsep (punctuate comma $ map (prettyTCM . namedArg) qs)
+    , nest 2 $ "perm= " <+> text (show perm)
+    ]
+
+  -- Andreas, 2015-11-09 Issue 1710: self starts with parent-function, not with-function!
+  (ps', strippedPats) <- runWriterT $ strip (Def parent []) t psi qs
+  reportSDoc "tc.with.strip" 50 $ nest 2 $
+    "strippedPats:" <+> vcat [ prettyA p <+> "=" <+> prettyTCM v <+> ":" <+> prettyTCM a | A.ProblemEq p v a <- strippedPats ]
+  let psp = permute perm ps'
+  reportSDoc "tc.with.strip" 10 $ vcat
+    [ nest 2 $ "ps' = " <+> fsep (punctuate comma $ map prettyA ps')
+    , nest 2 $ "psp = " <+> fsep (punctuate comma $ map prettyA $ psp)
+    ]
+  return (strippedPats, psp)
+  where
+
+    -- We need to get the correct hiding from the lhs context. The unifier may have moved bindings
+    -- sites around so we can't trust the hiding of the parent pattern variables. We should preserve
+    -- the origin though.
+    varArgInfo = \ x -> let n = dbPatVarIndex x in
+                        if n < length infos then infos !! n else __IMPOSSIBLE__
+      where infos = reverse $ map getArgInfo $ telToList delta
+
+    setVarArgInfo x p = setOrigin (getOrigin p) $ setArgInfo (varArgInfo x) p
+
+    strip
+      :: Term                         -- Self.
+      -> Type                         -- The type to be eliminated.
+      -> [NamedArg A.Pattern]         -- With-clause patterns.
+      -> [NamedArg DeBruijnPattern]   -- Parent-clause patterns with de Bruijn indices relative to Δ.
+      -> WriterT [ProblemEq] TCM [NamedArg A.Pattern]
+            -- With-clause patterns decomposed by parent-clause patterns.
+            -- Also outputs named dot patterns from the parent clause that
+            -- we need to add let-bindings for.
+
+    -- Case: out of with-clause patterns.
+    strip self t [] qs@(_ : _) = do
+      reportSDoc "tc.with.strip" 15 $ vcat
+        [ "strip (out of A.Patterns)"
+        , nest 2 $ "qs  =" <+> fsep (punctuate comma $ map (prettyTCM . namedArg) qs)
+        , nest 2 $ "self=" <+> prettyTCM self
+        , nest 2 $ "t   =" <+> prettyTCM t
+        ]
+      -- Andreas, 2015-06-11, issue 1551:
+      -- As the type t develops, we need to insert more implicit patterns,
+      -- due to copatterns / flexible arity.
+      ps <- liftTCM $ insertImplicitPatternsT ExpandLast [] t
+      if null ps then
+        typeError $ GenericError $ "Too few arguments given in with-clause"
+       else strip self t ps qs
+
+    -- Case: out of parent-clause patterns.
+    -- This is only ok if all remaining with-clause patterns
+    -- are implicit patterns (we inserted too many).
+    strip _ _ ps      []      = do
+      let implicit (A.WildP{})     = True
+          implicit (A.ConP ci _ _) = conPatOrigin ci == ConOSystem
+          implicit _               = False
+      unless (all (implicit . namedArg) ps) $
+        typeError $ GenericError $ "Too many arguments given in with-clause"
+      return []
+
+    -- Case: both parent-clause pattern and with-clause pattern present.
+    -- Make sure they match, and decompose into subpatterns.
+    strip self t (p0 : ps) qs@(q : _)
+      | A.AsP _ x p <- namedArg p0 = do
+        (a, _) <- mustBePi t
+        let v = patternToTerm (namedArg q)
+        tell [ProblemEq (A.VarP x) v a]
+        strip self t (fmap (p <$) p0 : ps) qs
+    strip self t ps0@(p0 : ps) qs0@(q : qs) = do
+      p <- liftTCM $ (traverse . traverse) expandLitPattern p0
+      reportSDoc "tc.with.strip" 15 $ vcat
+        [ "strip"
+        , nest 2 $ "ps0 =" <+> fsep (punctuate comma $ map prettyA ps0)
+        , nest 2 $ "exp =" <+> prettyA p
+        , nest 2 $ "qs0 =" <+> fsep (punctuate comma $ map (prettyTCM . namedArg) qs0)
+        , nest 2 $ "self=" <+> prettyTCM self
+        , nest 2 $ "t   =" <+> prettyTCM t
+        ]
+      case namedArg q of
+        ProjP o d -> case A.isProjP p of
+          Just (o', AmbQ ds) -> do
+            -- We assume here that neither @o@ nor @o'@ can be @ProjSystem@.
+            if o /= o' then liftTCM $ mismatchOrigin o o' else do
+            -- Andreas, 2016-12-28, issue #2360:
+            -- We disambiguate the projection in the with clause
+            -- to the projection in the parent clause.
+            d  <- liftTCM $ getOriginalProjection d
+            found <- anyM ds $ \ d' -> liftTCM $ (Just d ==) . fmap projOrig <$> isProjection d'
+            if not found then mismatch else do
+              (self1, t1, ps) <- liftTCM $ do
+                t <- reduce t
+                (_, self1, t1) <- fromMaybe __IMPOSSIBLE__ <$> projectTyped self t o d
+                -- Andreas, 2016-01-21, issue #1791
+                -- The type of a field might start with hidden quantifiers.
+                -- So we may have to insert more implicit patterns here.
+                ps <- insertImplicitPatternsT ExpandLast ps t1
+                return (self1, t1, ps)
+              strip self1 t1 ps qs
+          Nothing -> mismatch
+
+        -- We can safely strip dots from variables. The unifier will put them back when required.
+        VarP _ x | A.DotP _ u <- namedArg p
+                 , A.Var y <- unScope u -> do
+          (setVarArgInfo x (setNamedArg p $ A.VarP $ A.mkBindName y) :) <$>
+            recurse (var (dbPatVarIndex x))
+
+        VarP _ x  ->
+          (setVarArgInfo x p :) <$> recurse (var (dbPatVarIndex x))
+
+        IApplyP _ _ _ x  ->
+          (setVarArgInfo x p :) <$> recurse (var (dbPatVarIndex x))
+
+        DefP{}  -> typeError $ GenericError $ "with clauses not supported in the presence of hcomp patterns" -- TODO this should actually be impossible
+
+        DotP i v  -> do
+          (a, _) <- mustBePi t
+          tell [ProblemEq (namedArg p) v a]
+          case v of
+            Var x [] | PatOVar{} <- patOrigin i
+               -> (p :) <$> recurse (var x)
+            _  -> (makeWildP p :) <$> recurse v
+
+        q'@(ConP c ci qs') -> do
+         reportSDoc "tc.with.strip" 60 $
+           "parent pattern is constructor " <+> prettyTCM c
+         (a, b) <- mustBePi t
+         -- The type of the current pattern is a datatype.
+         Def d es <- liftTCM $ reduce (unEl $ unDom a)
+         let us = fromMaybe __IMPOSSIBLE__ $ allApplyElims es
+         -- Get the original constructor and field names.
+         c <- either __IMPOSSIBLE__ (`withRangeOf` c) <$> do liftTCM $ getConForm $ conName c
+
+         case namedArg p of
+
+          -- Andreas, 2015-07-07 Issue 1606.
+          -- Agda sometimes changes a record of dot patterns into a dot pattern,
+          -- so the user should be allowed to do likewise.
+          -- Jesper, 2017-11-16. This is now also allowed for data constructors.
+          A.DotP r e -> do
+            tell [ProblemEq (A.DotP r e) (patternToTerm q') a]
+            ps' <-
+              case appView e of
+                -- If dot-pattern is an application of the constructor, try to preserve the
+                -- arguments.
+                Application (A.Con (A.AmbQ cs')) es -> do
+                  cs' <- liftTCM $ List1.rights <$> mapM getConForm cs'
+                  unless (c `elem` cs') mismatch
+                  return $ (map . fmap . fmap) (A.DotP r) es
+                _  -> return $ map (unnamed (A.WildP empty) <$) qs'
+            stripConP d us b c ConOCon qs' ps'
+
+          -- Andreas, 2016-12-29, issue #2363.
+          -- Allow _ to stand for the corresponding parent pattern.
+          A.WildP{} -> do
+            -- Andreas, 2017-10-13, issue #2803:
+            -- Delete the name, since it can confuse insertImplicitPattern.
+            let ps' = map (unnamed (A.WildP empty) <$) qs'
+            stripConP d us b c ConOCon qs' ps'
+
+          -- Jesper, 2018-05-13, issue #2998.
+          -- We also allow turning a constructor pattern into a variable.
+          -- In general this is not type-safe since the types of some variables
+          -- in the constructor pattern may have changed, so we have to
+          -- re-check these solutions when checking the with clause (see LHS.hs)
+          A.VarP x -> do
+            tell [ProblemEq (A.VarP x) (patternToTerm q') a]
+            let ps' = map (unnamed (A.WildP empty) <$) qs'
+            stripConP d us b c ConOCon qs' ps'
+
+          A.ConP _ (A.AmbQ cs') ps' -> do
+            -- Check whether the with-clause constructor can be (possibly trivially)
+            -- disambiguated to be equal to the parent-clause constructor.
+            -- Andreas, 2017-08-13, herein, ignore abstract constructors.
+            cs' <- liftTCM $ List1.rights <$> mapM getConForm cs'
+            unless (c `elem` cs') mismatch
+            -- Strip the subpatterns ps' and then continue.
+            stripConP d us b c ConOCon qs' ps'
+
+          A.RecP _ fs -> caseMaybeM (liftTCM $ isRecord d) mismatch $ \ def -> do
+            ps' <- liftTCM $ insertMissingFieldsFail d (const $ A.WildP empty) fs
+                                                 (map argFromDom $ recordFieldNames def)
+            stripConP d us b c ConORec qs' ps'
+
+          p@(A.PatternSynP pi' c' ps') -> do
+             reportSDoc "impossible" 10 $
+               "stripWithClausePatterns: encountered pattern synonym " <+> prettyA p
+             __IMPOSSIBLE__
+
+          p -> do
+           reportSDoc "tc.with.strip" 60 $
+             text $ "with clause pattern is  " ++ show p
+           mismatch
+
+        LitP _ lit -> case namedArg p of
+          A.LitP _ lit' | lit == lit' -> recurse $ Lit lit
+          A.WildP{}                   -> recurse $ Lit lit
+
+          p@(A.PatternSynP pi' c' [ps']) -> do
+             reportSDoc "impossible" 10 $
+               "stripWithClausePatterns: encountered pattern synonym " <+> prettyA p
+             __IMPOSSIBLE__
+
+          _ -> mismatch
+      where
+        recurse v = do
+          -- caseMaybeM (liftTCM $ isPath t) (return ()) $ \ _ ->
+          --   typeError $ GenericError $
+          --     "With-clauses currently not supported under Path abstraction."
+
+          let piOrPathApplyM t v = do
+                (TelV tel t', bs) <- telViewUpToPathBoundaryP 1 t
+                unless (size tel == 1) $ __IMPOSSIBLE__
+                return (teleElims tel bs, subst 0 v t')
+          (e, t') <- piOrPathApplyM t v
+          strip (self `applyE` e) t' ps qs
+
+        mismatch :: forall m a. (MonadAddContext m, MonadTCError m) => m a
+        mismatch = addContext delta $ typeError $
+          WithClausePatternMismatch (namedArg p0) q
+        mismatchOrigin o o' = addContext delta . typeError . GenericDocError =<< fsep
+          [ "With clause pattern"
+          , prettyA p0
+          , "is not an instance of its parent pattern"
+          , P.fsep <$> prettyTCMPatterns [q]
+          , text $ "since the parent pattern is " ++ prettyProjOrigin o ++
+                   " and the with clause pattern is " ++ prettyProjOrigin o'
+          ]
+        prettyProjOrigin ProjPrefix  = "a prefix projection"
+        prettyProjOrigin ProjPostfix = "a postfix projection"
+        prettyProjOrigin ProjSystem  = __IMPOSSIBLE__
+
+        -- Make a WildP, keeping arg. info.
+        makeWildP :: NamedArg A.Pattern -> NamedArg A.Pattern
+        makeWildP = updateNamedArg $ const $ A.WildP patNoRange
+
+        -- case I.ConP / A.ConP
+        stripConP
+          :: QName       -- Data type name of this constructor pattern.
+          -> [Arg Term]  -- Data type arguments of this constructor pattern.
+          -> Abs Type    -- Type the remaining patterns eliminate.
+          -> ConHead     -- Constructor of this pattern.
+          -> ConInfo     -- Constructor info of this pattern (constructor/record).
+          -> [NamedArg DeBruijnPattern]  -- Argument patterns (parent clause).
+          -> [NamedArg A.Pattern]        -- Argument patterns (with clause).
+          -> WriterT [ProblemEq] TCM [NamedArg A.Pattern]  -- Stripped patterns.
+        stripConP d us b c ci qs' ps' = do
+
+          -- Get the type and number of parameters of the constructor.
+          Defn {defType = ct, theDef = Constructor{conPars = np}}  <- getConInfo c
+          -- Compute the argument telescope for the constructor
+          let ct' = ct `piApply` take np us
+          TelV tel' _ <- liftTCM $ telViewPath ct'
+          -- (TelV tel' _, _boundary) <- liftTCM $ telViewPathBoundaryP ct'
+
+          reportSDoc "tc.with.strip" 20 $
+            vcat [ "ct  = " <+> prettyTCM ct
+                 , "ct' = " <+> prettyTCM ct'
+                 , "np  = " <+> text (show np)
+                 , "us  = " <+> prettyList (map prettyTCM us)
+                 , "us' = " <+> prettyList (map prettyTCM $ take np us)
+                 ]
+
+          -- TODO Andrea: preserve IApplyP patterns in v, see _boundary?
+          -- Compute the new type
+          let v  = Con c ci [ Apply $ Arg info (var i) | (i, Arg info _) <- zip (downFrom $ size qs') qs' ]
+              t' = tel' `abstract` absApp (raise (size tel') b) v
+              self' = tel' `abstract` apply1 (raise (size tel') self) v  -- Issue 1546
+
+          reportSDoc "tc.with.strip" 15 $ sep
+            [ "inserting implicit"
+            , nest 2 $ prettyList $ map prettyA (ps' ++ ps)
+            , nest 2 $ ":" <+> prettyTCM t'
+            ]
+
+          -- Insert implicit patterns (just for the constructor arguments)
+          psi' <- liftTCM $ insertImplicitPatterns ExpandLast ps' tel'
+          unless (size psi' == size tel') $ typeError $
+            WrongNumberOfConstructorArguments (conName c) (size tel') (size psi')
+
+          -- Andreas, Ulf, 2016-06-01, Ulf's variant at issue #679
+          -- Since instantiating the type with a constructor pattern
+          -- can reveal more hidden arguments, we need to insert them here.
+          psi <- liftTCM $ insertImplicitPatternsT ExpandLast (psi' ++ ps) t'
+
+          -- Keep going
+          strip self' t' psi (qs' ++ qs)
+
+-- | Construct the display form for a with function. It will display
+--   applications of the with function as applications to the original function.
+--   For instance,
+--
+--   @
+--     aux a b c
+--   @
+--
+--   as
+--
+--   @
+--     f (suc a) (suc b) | c
+--   @
+withDisplayForm
+  :: QName
+       -- ^ The name of parent function.
+  -> QName
+       -- ^ The name of the @with@-function.
+  -> Telescope
+       -- ^ __@Δ₁@__     The arguments of the @with@ function before the @with@ expressions.
+  -> Telescope
+       -- ^ __@Δ₂@__     The arguments of the @with@ function after the @with@ expressions.
+  -> Nat
+       -- ^ __@n@__      The number of @with@ expressions.
+  -> [NamedArg DeBruijnPattern]
+      -- ^ __@qs@__      The parent patterns.
+  -> Permutation
+      -- ^ __@perm@__    Permutation to split into needed and unneeded vars.
+  -> Permutation
+      -- ^ __@lhsPerm@__ Permutation reordering the variables in parent patterns.
+  -> TCM DisplayForm
+withDisplayForm f aux delta1 delta2 n qs perm@(Perm m _) lhsPerm = do
+
+  -- Compute the arity of the display form.
+  let arity0 = n + size delta1 + size delta2
+  -- The currently free variables have to be added to the front.
+  topArgs <- raise arity0 <$> getContextArgs
+  let top    = length topArgs
+      arity  = arity0 + top
+
+  -- Build the rhs of the display form.
+  wild <- freshNoName_ <&> \ x -> Def (qualify_ x) []
+  let -- Convert the parent patterns to terms.
+      tqs0       = patsToElims qs
+      -- Build a substitution to replace the parent pattern vars
+      -- by the pattern vars of the with-function.
+      (ys0, ys1) = splitAt (size delta1) $ permute perm $ downFrom m
+      ys         = reverse (map Just ys0 ++ replicate n Nothing ++ map Just ys1)
+                   ++ map (Just . (m +)) [0..top-1]
+      rho        = sub top ys wild
+      tqs        = applySubst rho tqs0
+      -- Build the arguments to the with function.
+      es         = map (Apply . fmap DTerm) topArgs ++ tqs
+      withArgs   = map var $ take n $ downFrom $ size delta2 + n
+      dt         = DWithApp (DDef f es) (map DTerm withArgs) []
+
+  -- Build the lhs of the display form and finish.
+  -- @var 0@ is the pattern variable (hole).
+  let display = Display arity [Apply $ defaultArg $ var i | i <- downFrom arity] dt
+
+  -- Debug printing.
+  let addFullCtx = addContext delta1
+                 . flip (foldr addContext) (for [1..n] $ \ i -> "w" ++ show i)
+                 . addContext delta2
+  reportSDoc "tc.with.display" 20 $ vcat
+    [ "withDisplayForm"
+    , nest 2 $ vcat
+      [ "f      =" <+> text (prettyShow f)
+      , "aux    =" <+> text (prettyShow aux)
+      , "delta1 =" <+> prettyTCM delta1
+      , "delta2 =" <+> do addContext delta1 $ prettyTCM delta2
+      , "n      =" <+> text (show n)
+      , "perm   =" <+> text (show perm)
+      , "top    =" <+> do addFullCtx $ prettyTCM topArgs
+      , "qs     =" <+> prettyList (map pretty qs)
+      , "qsToTm =" <+> prettyTCM tqs0 -- ctx would be permuted form of delta1 ++ delta2
+      , "ys     =" <+> text (show ys)
+      , "rho    =" <+> text (prettyShow rho)
+      , "qs[rho]=" <+> do addFullCtx $ prettyTCM tqs
+      , "dt     =" <+> do addFullCtx $ prettyTCM dt
+      ]
+    ]
+  reportSDoc "tc.with.display" 70 $ nest 2 $ vcat
+      [ "raw    =" <+> text (show display)
+      ]
+
+  return display
+  where
+    -- Ulf, 2014-02-19: We need to rename the module parameters as well! (issue1035)
+    -- sub top ys wild = map term [0 .. m - 1] ++# raiseS (length qs)
+    -- Andreas, 2015-10-28: Yes, but properly! (Issue 1407)
+    sub top ys wild = parallelS $ map term [0 .. m + top - 1]
+      where
+        term i = maybe wild var $ List.elemIndex (Just i) ys
+
+-- Andreas, 2014-12-05 refactored using numberPatVars
+-- Andreas, 2013-02-28 modeled after Coverage/Match/buildMPatterns
+patsToElims :: [NamedArg DeBruijnPattern] -> [I.Elim' DisplayTerm]
+patsToElims = map $ toElim . fmap namedThing
+  where
+    toElim :: Arg DeBruijnPattern -> I.Elim' DisplayTerm
+    toElim (Arg ai p) = case p of
+      ProjP o d -> I.Proj o d
+      p         -> I.Apply $ Arg ai $ toTerm p
+
+    toTerms :: [NamedArg DeBruijnPattern] -> [Arg DisplayTerm]
+    toTerms = map $ fmap $ toTerm . namedThing
+
+    toTerm :: DeBruijnPattern -> DisplayTerm
+    toTerm p = case patOrigin $ fromMaybe __IMPOSSIBLE__ $ patternInfo p of
+      PatOSystem -> toDisplayPattern p
+      PatOSplit  -> toDisplayPattern p
+      PatOVar{}  -> toVarOrDot p
+      PatODot    -> DDot $ patternToTerm p
+      PatOWild   -> toVarOrDot p
+      PatOCon    -> toDisplayPattern p
+      PatORec    -> toDisplayPattern p
+      PatOLit    -> toDisplayPattern p
+      PatOAbsurd -> toDisplayPattern p -- see test/Succeed/Issue2849.agda
+
+    toDisplayPattern :: DeBruijnPattern -> DisplayTerm
+    toDisplayPattern = \case
+      IApplyP _ _ _ x -> DTerm $ var $ dbPatVarIndex x -- TODO, should be an Elim' DisplayTerm ?
+      ProjP _ d  -> __IMPOSSIBLE__
+      VarP i x -> DTerm  $ var $ dbPatVarIndex x
+      DotP i t -> DDot   $ t
+      p@(ConP c cpi ps) -> DCon c (fromConPatternInfo cpi) $ toTerms ps
+      LitP i l -> DTerm  $ Lit l
+      DefP _ q ps -> DDef q $ map Apply $ toTerms ps
+
+    toVarOrDot :: DeBruijnPattern -> DisplayTerm
+    toVarOrDot p = case patternToTerm p of
+      Var i [] -> DTerm $ var i
+      t        -> DDot t
diff --git a/src/full/Agda/Utils/AffineHole.hs b/src/full/Agda/Utils/AffineHole.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/AffineHole.hs
@@ -0,0 +1,30 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Contexts with at most one hole.
+
+module Agda.Utils.AffineHole where
+
+
+
+data AffineHole r a
+  = ZeroHoles a
+      -- ^ A constant term.
+  | OneHole (r -> a) r
+      -- ^ A term with one hole and the (old) contents.
+  | ManyHoles
+      -- ^ A term with many holes (error value).
+  deriving (Functor)
+
+instance Applicative (AffineHole r) where
+  pure = ZeroHoles
+
+  ZeroHoles f <*> ZeroHoles a = ZeroHoles $ f a
+  ZeroHoles f <*> OneHole g y = OneHole (f . g) y
+  OneHole h x <*> ZeroHoles a = OneHole (`h` a) x
+  _ <*> _ = ManyHoles
+
+-- NB: @AffineHole r@ is not a monad.
+-- @
+--   OneHole (h :: r -> a) >>= (k :: a -> AffineHole r b) = _ :: AffineHole r b
+-- @
+-- We are lacking an @r@ to make use of @h@.
diff --git a/src/full/Agda/Utils/Applicative.hs b/src/full/Agda/Utils/Applicative.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Applicative.hs
@@ -0,0 +1,35 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Applicative
+       ( (?*>)
+       , (?$>)
+       , foldA
+       , foldMapA
+       , forA
+       )
+       where
+
+import Control.Applicative
+import Data.Monoid ( Alt(..) )
+import Data.Traversable ( for )
+
+-- | Better name for 'for'.
+forA :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
+forA = for
+
+-- | Guard: return the action @f@ only if the boolean is @True@
+(?*>) :: Alternative f => Bool -> f a -> f a
+b ?*> f = if b then f else empty
+
+-- | Guard: return the value @a@ only if the boolean is @True@
+(?$>) :: Alternative f => Bool -> a -> f a
+b ?$> a = b ?*> pure a
+
+-- | Branch over a 'Foldable' collection of values.
+foldA :: (Alternative f, Foldable t) => t a -> f a
+foldA = foldMapA pure
+
+-- | Branch over a 'Foldable' collection of values using the supplied
+--   action.
+foldMapA :: (Alternative f, Foldable t) => (a -> f b) -> t a -> f b
+foldMapA f = getAlt . foldMap (Alt . f)
diff --git a/src/full/Agda/Utils/AssocList.hs b/src/full/Agda/Utils/AssocList.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/AssocList.hs
@@ -0,0 +1,97 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Additional functions for association lists.
+
+module Agda.Utils.AssocList
+  ( module Agda.Utils.AssocList
+  , lookup
+  ) where
+
+import Prelude hiding (lookup)
+
+import Data.Function (on)
+import Data.List (lookup)
+import qualified Data.List as List
+import qualified Data.Map  as Map
+
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+-- | A finite map, represented as a set of pairs.
+--
+--   Invariant: at most one value per key.
+type AssocList k v = [(k,v)]
+
+-- Lookup, reexported from Data.List.
+-- O(n).
+-- lookup :: Eq k => k -> AssocList k v -> Maybe v
+
+-- | Lookup keys in the same association list often.
+--   Use partially applied to create partial function
+--   @apply m :: k -> Maybe v@.
+--
+--   * First time: @O(n log n)@ in the worst case.
+--   * Subsequently: @O(log n)@.
+--
+--   Specification: @apply m == (`lookup` m)@.
+apply :: Ord k => AssocList k v -> k -> Maybe v
+apply m = (`Map.lookup` Map.fromListWith (\ _new old -> old) m)
+
+-- | O(n).
+--   Get the domain (list of keys) of the finite map.
+keys :: AssocList k v -> [k]
+keys = map fst
+
+-- | O(1).
+--   Add a new binding.
+--   Assumes the binding is not yet in the list.
+insert :: k -> v -> AssocList k v -> AssocList k v
+insert k v = ((k,v) :)
+
+-- | O(n).
+--   Update the value at a key.
+--   The key must be in the domain of the finite map.
+--   Otherwise, an internal error is raised.
+update :: Eq k => k -> v -> AssocList k v -> AssocList k v
+update k v = updateAt k $ const v
+
+-- | O(n).
+--   Delete a binding.
+--   The key must be in the domain of the finite map.
+--   Otherwise, an internal error is raised.
+delete :: Eq k => k -> AssocList k v -> AssocList k v
+delete k = List.deleteBy ((==) `on` fst) (k, __IMPOSSIBLE__)
+
+-- | O(n).
+--   Update the value at a key with a certain function.
+--   The key must be in the domain of the finite map.
+--   Otherwise, an internal error is raised.
+updateAt :: Eq k => k -> (v -> v) -> AssocList k v -> AssocList k v
+updateAt k f = loop where
+  loop []       = __IMPOSSIBLE__
+  loop (p@(k',v) : ps)
+    | k == k'   = (k, f v) : ps
+    | otherwise = p : loop ps
+
+-- | O(n).
+--   Map over an association list, preserving the order.
+mapWithKey :: (k -> v -> v) -> AssocList k v -> AssocList k v
+mapWithKey f = map $ \ (k,v) -> (k, f k v)
+
+-- | O(n).
+--   If called with a effect-producing function, violation of the invariant
+--   could matter here (duplicating effects).
+mapWithKeyM :: Applicative m => (k -> v -> m v) -> AssocList k v -> m (AssocList k v)
+mapWithKeyM f = mapM $ \ (k,v) -> (k,) <$> f k v
+  where
+    -- mapM is applicative!
+    mapM g [] = pure []
+    mapM g (x : xs) = (:) <$> g x <*> mapM g xs
+
+-- | O(n).
+--   Named in analogy to 'Data.Map.mapKeysMonotonic'.
+--   To preserve the invariant, it is sufficient that the key
+--   transformation is injective (rather than monotonic).
+mapKeysMonotonic :: (k -> k') -> AssocList k v -> AssocList k' v
+mapKeysMonotonic f = map $ mapFst f
diff --git a/src/full/Agda/Utils/Bag.hs b/src/full/Agda/Utils/Bag.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Bag.hs
@@ -0,0 +1,160 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | A simple overlay over Data.Map to manage unordered sets with duplicates.
+
+module Agda.Utils.Bag where
+
+import Prelude hiding (null, map)
+
+import Text.Show.Functions () -- instance only
+
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Semigroup
+
+import Agda.Utils.Functor
+
+import Agda.Utils.Impossible
+
+-- | A set with duplicates.
+--   Faithfully stores elements which are equal with regard to (==).
+newtype Bag a = Bag
+  { bag :: Map a [a]
+      -- ^ The list contains all occurrences of @a@ (not just the duplicates!).
+      --   Hence, the invariant: the list is never empty.
+  }
+  deriving (Eq, Ord)
+  -- The list contains all occurrences of @a@ (not just the duplicates!).
+  -- Hence the invariant: the list is never empty.
+  --
+  -- This is slightly wasteful, but much easier to implement
+  -- in terms of @Map@ as the alternative, which is to store
+  -- only the duplicates in the list.
+  -- See, e.g., implementation of 'union' which would be impossible
+  -- to do in the other representation.  We would need a
+  -- 'Map.unionWithKey' that passes us *both* keys.
+  -- But Map works under the assumption that Eq for keys is identity,
+  -- it does not honor information in keys that goes beyond Ord.
+
+------------------------------------------------------------------------
+-- * Query
+------------------------------------------------------------------------
+
+-- | Is the bag empty?
+null :: Bag a -> Bool
+null = Map.null . bag
+
+-- | Number of elements in the bag.  Duplicates count. O(n).
+size :: Bag a -> Int
+size = getSum . foldMap (Sum . length) . bag
+
+-- | @(bag ! a)@ finds all elements equal to @a@.  O(log n).
+--   Total function, returns @[]@ if none are.
+(!) :: Ord a => Bag a -> a -> [a]
+(!) (Bag b) a = Map.findWithDefault [] a b
+  -- Note: not defined infix because of BangPatterns.
+
+-- | O(log n).
+member :: Ord a => a -> Bag a -> Bool
+member a = not . notMember a
+
+-- | O(log n).
+notMember :: Ord a => a -> Bag a -> Bool
+notMember a b = List.null (b ! a)
+
+-- | Return the multiplicity of the given element. O(log n + count _ _).
+count :: Ord a => a -> Bag a -> Int
+count a b = length (b ! a)
+
+------------------------------------------------------------------------
+-- * Construction
+------------------------------------------------------------------------
+
+-- | O(1)
+empty :: Bag a
+empty = Bag $ Map.empty
+
+-- | O(1)
+singleton :: a -> Bag a
+singleton a = Bag $ Map.singleton a [a]
+
+union :: Ord a => Bag a -> Bag a -> Bag a
+union (Bag b) (Bag c) = Bag $ Map.unionWith (++) b c
+
+unions :: Ord a => [Bag a] -> Bag a
+unions = Bag . Map.unionsWith (++)  . List.map bag
+
+-- | @insert a b = union b (singleton a)@
+insert :: Ord a => a -> Bag a -> Bag a
+insert a = Bag . Map.insertWith (++) a [a] . bag
+
+-- | @fromList = unions . map singleton@
+fromList :: Ord a => [a] -> Bag a
+fromList = Bag . Map.fromListWith (++) . List.map (\ a -> (a,[a]))
+
+------------------------------------------------------------------------
+-- * Destruction
+------------------------------------------------------------------------
+
+-- | Returns the elements of the bag, grouped by equality (==).
+groups :: Bag a -> [[a]]
+groups = Map.elems . bag
+
+-- | Returns the bag, with duplicates.
+toList :: Bag a -> [a]
+toList = concat . groups
+
+-- | Returns the bag without duplicates.
+keys :: Bag a -> [a]
+keys = Map.keys . bag
+-- Works because of the invariant!
+-- keys = catMaybes . map listToMaybe . Map.elems . bag
+--   -- Map.keys does not work, as zero copies @(a,[])@
+--   -- should count as not present in the bag.
+
+-- | Returns the bag, with duplicates.
+elems :: Bag a -> [a]
+elems = toList
+
+toAscList :: Bag a -> [a]
+toAscList = toList
+
+------------------------------------------------------------------------
+-- * Traversal
+------------------------------------------------------------------------
+
+map :: Ord b => (a -> b) -> Bag a -> Bag b
+map f = Bag . Map.fromListWith (++) . List.map ff . Map.elems . bag
+  where
+    ff (a : as) = (b, b : List.map f as) where b = f a
+    ff []       = __IMPOSSIBLE__
+
+traverse' :: forall a b m . (Applicative m, Ord b) =>
+             (a -> m b) -> Bag a -> m (Bag b)
+traverse' f = (Bag . Map.fromListWith (++)) <.> traverse trav . Map.elems . bag
+  where
+    trav :: [a] -> m (b, [b])
+    trav (a : as) = (\ b bs -> (b, b:bs)) <$> f a <*> traverse f as
+    trav []       = __IMPOSSIBLE__
+
+------------------------------------------------------------------------
+-- Instances
+------------------------------------------------------------------------
+
+instance Show a => Show (Bag a) where
+  showsPrec _ (Bag b) = ("Agda.Utils.Bag.Bag (" ++) . shows b . (')':)
+
+instance Ord a => Semigroup (Bag a) where
+  (<>) = union
+
+instance Ord a => Monoid (Bag a) where
+  mempty  = empty
+  mappend = (<>)
+  mconcat = unions
+
+instance Foldable Bag where
+  foldMap f = foldMap f . toList
+
+-- not a Functor (only works for 'Ord'ered types)
+-- not Traversable (only works for 'Ord'ered types)
diff --git a/src/full/Agda/Utils/Benchmark.hs b/src/full/Agda/Utils/Benchmark.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Benchmark.hs
@@ -0,0 +1,246 @@
+
+-- | Tools for benchmarking and accumulating results.
+--   Nothing Agda-specific in here.
+
+module Agda.Utils.Benchmark where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+import qualified Control.Exception as E (evaluate)
+import Control.Monad.Except
+import Control.Monad.Reader
+import Control.Monad.Writer
+import Control.Monad.State
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Monoid
+import Data.Maybe
+
+import GHC.Generics (Generic)
+
+import qualified Text.PrettyPrint.Boxes as Boxes
+
+import Agda.Utils.ListT
+import Agda.Utils.Null
+import Agda.Utils.Monad hiding (finally)
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.Time
+import Agda.Utils.Trie (Trie)
+import qualified Agda.Utils.Trie as Trie
+
+
+-- * Benchmark trie
+
+-- | Account we can bill computation time to.
+type Account a = [a]
+
+-- | Record when we started billing the current account.
+type CurrentAccount a = Strict.Maybe (Account a, CPUTime)
+
+type Timings        a = Trie a CPUTime
+
+data BenchmarkOn a = BenchmarkOff | BenchmarkOn | BenchmarkSome (Account a -> Bool)
+  deriving Generic
+
+isBenchmarkOn :: Account a -> BenchmarkOn a -> Bool
+isBenchmarkOn _ BenchmarkOff      = False
+isBenchmarkOn _ BenchmarkOn       = True
+isBenchmarkOn a (BenchmarkSome p) = p a
+
+-- | Benchmark structure is a trie, mapping accounts (phases and subphases)
+--   to CPU time spent on their performance.
+data Benchmark a = Benchmark
+  { benchmarkOn    :: !(BenchmarkOn a)
+    -- ^ Are we benchmarking at all?
+  , currentAccount :: !(CurrentAccount a)
+    -- ^ What are we billing to currently?
+  , timings        :: !(Timings a)
+    -- ^ The accounts and their accumulated timing bill.
+  }
+  deriving Generic
+
+-- | Initial benchmark structure (empty).
+instance Null (Benchmark a) where
+  empty = Benchmark
+    { benchmarkOn = BenchmarkOff
+    , currentAccount = Strict.Nothing
+    , timings = empty
+    }
+  null = null . timings
+
+-- | Semantic editor combinator.
+mapBenchmarkOn :: (BenchmarkOn a -> BenchmarkOn a) -> Benchmark a -> Benchmark a
+mapBenchmarkOn f b = b { benchmarkOn = f $ benchmarkOn b }
+
+-- | Semantic editor combinator.
+mapCurrentAccount ::
+  (CurrentAccount a -> CurrentAccount a) -> Benchmark a -> Benchmark a
+mapCurrentAccount f b = b { currentAccount = f (currentAccount b) }
+
+-- | Semantic editor combinator.
+mapTimings :: (Timings a -> Timings a) -> Benchmark a -> Benchmark a
+mapTimings f b = b { timings = f (timings b) }
+
+-- | Add to specified CPU time account.
+addCPUTime :: Ord a => Account a -> CPUTime -> Benchmark a -> Benchmark a
+addCPUTime acc t = mapTimings (Trie.insertWith (+) acc t)
+
+-- | Print benchmark as three-column table with totals.
+instance (Ord a, Pretty a) => Pretty (Benchmark a) where
+  pretty b = text $ Boxes.render table
+    where
+    trie = timings b
+    (accounts, times0) = unzip $ Trie.toListOrderedBy (flip compare `on` snd)
+                               $ Trie.filter ((> fromMilliseconds 10) . snd)
+                               $ Trie.mapSubTries (Just . aggr) trie
+    times = map fst times0
+    aggr t = (fromMaybe 0 $ Trie.lookup [] t, getSum $ foldMap Sum t)
+    aggrTimes = do
+      (a, (t, aggrT)) <- zip accounts times0
+      return $ if t == aggrT || null a
+               then ""
+               else Boxes.text $ "(" ++ prettyShow aggrT ++ ")"
+
+    -- Generate a table.
+    table = Boxes.hsep 1 Boxes.left [col1, col2, col3]
+
+    -- First column: Accounts.
+    col1 = Boxes.vcat Boxes.left $
+           map Boxes.text $
+           "Total" : map showAccount accounts
+    -- Second column: Times.
+    col2 = Boxes.vcat Boxes.right $
+           map (Boxes.text . prettyShow) $
+           sum times : times
+    -- Thid column: Aggregate times.
+    col3 = Boxes.vcat Boxes.right $
+           "" : aggrTimes
+
+    showAccount [] = "Miscellaneous"
+    showAccount ks = List.intercalate "." $ map prettyShow ks
+
+
+-- * Benchmarking monad.
+
+-- | Monad with access to benchmarking data.
+
+class (Ord (BenchPhase m), Functor m, MonadIO m) => MonadBench m where
+  type BenchPhase m
+  getBenchmark :: m (Benchmark (BenchPhase m))
+
+  putBenchmark :: Benchmark (BenchPhase m) -> m ()
+  putBenchmark b = modifyBenchmark $ const b
+
+  modifyBenchmark :: (Benchmark (BenchPhase m) -> Benchmark (BenchPhase m)) -> m ()
+  modifyBenchmark f = do
+    b <- getBenchmark
+    putBenchmark $! f b
+
+  -- | We need to be able to terminate benchmarking in case of an exception.
+  finally :: m b -> m c -> m b
+
+getsBenchmark :: MonadBench m => (Benchmark (BenchPhase m) -> c) -> m c
+getsBenchmark f = f <$> getBenchmark
+
+instance MonadBench m => MonadBench (ReaderT r m) where
+  type BenchPhase (ReaderT r m) = BenchPhase m
+  getBenchmark    = lift $ getBenchmark
+  putBenchmark    = lift . putBenchmark
+  modifyBenchmark = lift . modifyBenchmark
+  finally m f = ReaderT $ \ r ->
+    finally (m `runReaderT` r) (f `runReaderT` r)
+
+instance (MonadBench m, Monoid w) => MonadBench (WriterT w m) where
+  type BenchPhase (WriterT w m) = BenchPhase m
+  getBenchmark    = lift $ getBenchmark
+  putBenchmark    = lift . putBenchmark
+  modifyBenchmark = lift . modifyBenchmark
+  finally m f = WriterT $ finally (runWriterT m) (runWriterT f)
+
+instance MonadBench m => MonadBench (StateT r m) where
+  type BenchPhase (StateT r m) = BenchPhase m
+
+  getBenchmark    = lift $ getBenchmark
+  putBenchmark    = lift . putBenchmark
+  modifyBenchmark = lift . modifyBenchmark
+  finally m f = StateT $ \s ->
+    finally (m `runStateT` s) (f `runStateT` s)
+
+instance MonadBench m => MonadBench (ExceptT e m) where
+  type BenchPhase (ExceptT e m) = BenchPhase m
+
+  getBenchmark    = lift $ getBenchmark
+  putBenchmark    = lift . putBenchmark
+  modifyBenchmark = lift . modifyBenchmark
+  finally m f = ExceptT $ finally (runExceptT m) (runExceptT f)
+
+instance MonadBench m => MonadBench (ListT m) where
+  type BenchPhase (ListT m) = BenchPhase m
+
+  getBenchmark    = lift getBenchmark
+  putBenchmark    = lift . putBenchmark
+  modifyBenchmark = lift . modifyBenchmark
+  finally m f = ListT $ finally (runListT m) (runListT f)
+
+-- | Turn benchmarking on/off.
+
+setBenchmarking :: MonadBench m => BenchmarkOn (BenchPhase m) -> m ()
+setBenchmarking b = modifyBenchmark $ mapBenchmarkOn $ const b
+
+-- | Bill current account with time up to now.
+--   Switch to new account.
+--   Return old account (if any).
+
+switchBenchmarking :: MonadBench m
+  => Strict.Maybe (Account (BenchPhase m))      -- ^ Maybe new account.
+  -> m (Strict.Maybe (Account (BenchPhase m)))  -- ^ Maybe old account.
+switchBenchmarking newAccount = do
+  now <- liftIO $ getCPUTime
+  -- Stop and bill current benchmarking.
+  oldAccount <- getsBenchmark currentAccount
+  Strict.whenJust oldAccount $ \ (acc, start) ->
+    modifyBenchmark $ addCPUTime acc $ now - start
+  -- Switch to new account.
+  modifyBenchmark $ mapCurrentAccount $ const $ (, now) <$> newAccount
+  return $ fst <$> oldAccount
+
+-- | Resets the account and the timing information.
+
+reset :: MonadBench m => m ()
+reset = modifyBenchmark $
+  mapCurrentAccount (const Strict.Nothing) .
+  mapTimings (const Trie.empty)
+
+{-# INLINABLE billTo #-}
+-- | Bill a computation to a specific account.
+--   Works even if the computation is aborted by an exception.
+
+billTo :: MonadBench m => Account (BenchPhase m) -> m c -> m c
+billTo account m = ifNotM (isBenchmarkOn account <$> getsBenchmark benchmarkOn) m $ do
+  -- Switch to new account.
+  old <- switchBenchmarking $ Strict.Just account
+  -- Compute and switch back to old account.
+  (liftIO . E.evaluate =<< m) `finally` switchBenchmarking old
+
+-- | Bill a CPS function to an account. Can't handle exceptions.
+billToCPS :: MonadBench m => Account (BenchPhase m) -> ((b -> m c) -> m c) -> (b -> m c) -> m c
+billToCPS account f k = ifNotM (isBenchmarkOn account <$> getsBenchmark benchmarkOn) (f k) $ do
+  -- Switch to new account.
+  old <- switchBenchmarking $ Strict.Just account
+  f $ \ x -> x `seq` do
+    _ <- switchBenchmarking old
+    k x
+
+-- | Bill a pure computation to a specific account.
+billPureTo :: MonadBench m  => Account (BenchPhase m) -> c -> m c
+billPureTo account = billTo account . return
+
+-- NFData instances.
+
+instance NFData a => NFData (BenchmarkOn a)
+instance NFData a => NFData (Benchmark a)
diff --git a/src/full/Agda/Utils/BiMap.hs b/src/full/Agda/Utils/BiMap.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/BiMap.hs
@@ -0,0 +1,451 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Partly invertible finite maps.
+--
+-- Time complexities are given under the assumption that all relevant
+-- instance functions, as well as arguments of function type, take
+-- constant time, and "n" is the number of keys involved in the
+-- operation.
+
+module Agda.Utils.BiMap where
+
+import Prelude hiding (null, lookup)
+
+import Control.Monad.Identity
+import Control.Monad.State
+
+import Data.Function (on)
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Maybe
+import Data.Ord
+import Data.Tuple
+
+import GHC.Generics (Generic)
+
+import Agda.Utils.List
+import Agda.Utils.Null
+
+-- | Partial injections from a type to some tag type.
+--
+-- The idea is that 'tag' should be injective on its domain: if
+-- @'tag' x = 'tag' y = 'Just' i@, then @x = y@. However, this
+-- property does not need to hold globally. The preconditions of the
+-- 'BiMap' operations below specify for which sets of values 'tag'
+-- must be injective.
+
+class HasTag a where
+  type Tag a
+  tag :: a -> Maybe (Tag a)
+
+-- | Checks if the function 'tag' is injective for the values in the
+-- given list for which the function is defined.
+
+tagInjectiveFor ::
+  (Eq v, Eq (Tag v), HasTag v) =>
+  [v] -> Bool
+tagInjectiveFor vs = and
+  [ v1 == v2
+  | v1 <- vs
+  , v2 <- vs
+  , isJust (tag v1)
+  , tag v1 == tag v2
+  ]
+
+-- | Finite maps from @k@ to @v@, with a way to quickly get from @v@
+-- to @k@ for certain values of type @v@ (those for which 'tag' is
+-- defined).
+--
+-- Every value of this type must satisfy 'biMapInvariant'.
+
+data BiMap k v = BiMap
+  { biMapThere :: !(Map k v)
+  , biMapBack  :: !(Map (Tag v) k)
+  }
+  deriving Generic
+
+-- | The invariant for 'BiMap'.
+
+biMapInvariant ::
+  (Eq k, Eq v, Ord (Tag v), HasTag v) =>
+  BiMap k v -> Bool
+biMapInvariant m@(BiMap t u) =
+  u ==
+  Map.fromList
+    [ (k', k)
+    | (k, v) <- Map.toList t
+    , Just k' <- [tag v]
+    ]
+    &&
+  tagInjectiveFor (map snd $ toList m)
+
+instance Null (BiMap k v) where
+  empty = BiMap Map.empty Map.empty
+  null  = null . biMapThere
+
+-- | Is the value a source key? O(log n).
+
+source :: Ord k => k -> BiMap k v -> Bool
+source k = Map.member k . biMapThere
+
+-- | Is the value a target key? O(log n).
+
+target :: Ord (Tag v) => Tag v -> BiMap k v -> Bool
+target k = Map.member k . biMapBack
+
+-- | Lookup. O(log n).
+
+lookup :: Ord k => k -> BiMap k v -> Maybe v
+lookup a = Map.lookup a . biMapThere
+
+-- | Inverse lookup. O(log n).
+
+invLookup :: Ord (Tag v) => Tag v -> BiMap k v -> Maybe k
+invLookup k = Map.lookup k . biMapBack
+
+-- | Singleton map. O(1).
+
+singleton :: HasTag v => k -> v -> BiMap k v
+singleton k v =
+  BiMap
+    (Map.singleton k v)
+    (case tag v of
+       Nothing -> Map.empty
+       Just k' -> Map.singleton k' k)
+
+-- | Insertion. Overwrites existing values. O(log n).
+--
+-- Precondition: See 'insertPrecondition'.
+
+insert ::
+  (Ord k, HasTag v, Ord (Tag v)) =>
+  k -> v -> BiMap k v -> BiMap k v
+insert k v (BiMap t b) =
+  BiMap
+    (Map.insert k v t)
+    (case tag v of
+       Nothing -> b'
+       Just k' -> Map.insert k' k b')
+  where
+  b' = case tag =<< Map.lookup k t of
+    Nothing -> b
+    Just k' -> Map.delete k' b
+
+-- | The precondition for @'insert' k v m@: If @v@ has a 'tag' (@'tag'
+-- v ≠ 'Nothing'@), then @m@ must not contain any mapping @k' ↦ v'@
+-- for which @k ≠ k'@ and @'tag' v = 'tag' v'@.
+
+insertPrecondition ::
+  (Eq k, Eq v, Eq (Tag v), HasTag v) =>
+  k -> v -> BiMap k v -> Bool
+insertPrecondition k v m =
+  case tag v of
+    Nothing -> True
+    Just _  ->
+      not $ any (\(k', v') -> k' /= k && tag v == tag v') $ toList m
+
+-- | Modifies the value at the given position, if any. If the function
+-- returns 'Nothing', then the value is removed. O(log n).
+--
+-- The precondition for @'alterM' f k m@ is that, if the value @v@ is
+-- inserted into @m@, and @'tag' v@ is defined, then no key other than
+-- @k@ may map to a value @v'@ for which @'tag' v' = 'tag' v@.
+
+alterM ::
+  forall k v m. (Ord k, Ord (Tag v), HasTag v, Monad m) =>
+  (Maybe v -> m (Maybe v)) -> k -> BiMap k v -> m (BiMap k v)
+alterM f k m@(BiMap t b) = do
+  (t', r) <- runStateT (Map.alterF f' k t) Nothing
+  return $ case r of
+    Nothing -> m
+    Just r  -> BiMap t' (updateBack r b)
+  where
+  f' ::
+    Maybe v ->
+    StateT (Maybe (Maybe (Tag v), Maybe (Tag v))) m (Maybe v)
+  f' v = do
+    r <- lift (f v)
+    put $ Just (tag =<< v, tag =<< r)
+    return r
+
+  updateBack (k'1, k'2) =
+    if k'1 == k'2
+    then id
+    else maybe id (flip Map.insert k) k'2 .
+         maybe id Map.delete k'1
+
+-- | Modifies the value at the given position, if any. If the function
+-- returns 'Nothing', then the value is removed. O(log n).
+--
+-- Precondition: See 'alterPrecondition'.
+
+alter ::
+  forall k v. (Ord k, Ord (Tag v), HasTag v) =>
+  (Maybe v -> Maybe v) -> k -> BiMap k v -> BiMap k v
+alter f k m = runIdentity $ alterM (Identity . f) k m
+
+-- | The precondition for @'alter' f k m@ is that, if the value @v@ is
+-- inserted into @m@, and @'tag' v@ is defined, then no key other than
+-- @k@ may map to a value @v'@ for which @'tag' v' = 'tag' v@.
+
+alterPrecondition ::
+  (Ord k, Eq v, Eq (Tag v), HasTag v) =>
+  (Maybe v -> Maybe v) -> k -> BiMap k v -> Bool
+alterPrecondition f k m =
+  case tag =<< f (lookup k m) of
+    Nothing -> True
+    Just k' -> and
+      [ Just k' /= tag v
+      | (k'', v) <- toList m
+      , k'' /= k
+      ]
+
+-- | Modifies the value at the given position, if any. If the function
+-- returns 'Nothing', then the value is removed. O(log n).
+--
+-- Precondition: See 'updatePrecondition'.
+
+update ::
+  (Ord k, Ord (Tag v), HasTag v) =>
+  (v -> Maybe v) -> k -> BiMap k v -> BiMap k v
+update f = alter (f =<<)
+
+-- | The precondition for @'update' f k m@ is that, if the value @v@
+-- is inserted into @m@, and @'tag' v@ is defined, then no key other
+-- than @k@ may map to a value @v'@ for which @'tag' v' = 'tag' v@.
+
+updatePrecondition ::
+  (Ord k, Eq v, Eq (Tag v), HasTag v) =>
+  (v -> Maybe v) -> k -> BiMap k v -> Bool
+updatePrecondition f = alterPrecondition (f =<<)
+
+-- | Modifies the value at the given position, if any. O(log n).
+--
+-- Precondition: See 'adjustPrecondition'.
+
+adjust ::
+  (Ord k, Ord (Tag v), HasTag v) =>
+  (v -> v) -> k -> BiMap k v -> BiMap k v
+adjust f = update (Just . f)
+
+-- | The precondition for @'adjust' f k m@ is that, if the value @v@
+-- is inserted into @m@, and @'tag' v@ is defined, then no key other
+-- than @k@ may map to a value @v'@ for which @'tag' v' = 'tag' v@.
+
+adjustPrecondition ::
+  (Ord k, Eq v, Eq (Tag v), HasTag v) =>
+  (v -> v) -> k -> BiMap k v -> Bool
+adjustPrecondition f = updatePrecondition (Just . f)
+
+-- | Inserts a binding into the map. If a binding for the key already
+-- exists, then the value obtained by applying the function to the
+-- key, the new value and the old value is inserted, and the old value
+-- is returned.
+--
+-- Precondition: See 'insertLookupWithKeyPrecondition'.
+
+insertLookupWithKey ::
+  forall k v. (Ord k, Ord (Tag v), HasTag v) =>
+  (k -> v -> v -> v) -> k -> v -> BiMap k v -> (Maybe v, BiMap k v)
+insertLookupWithKey f k v m = swap $ runState (alterM f' k m) Nothing
+  where
+  f' :: Maybe v -> State (Maybe v) (Maybe v)
+  f' Nothing     = return $ Just v
+  f' r@(Just v') = do
+    put r
+    return $ Just (f k v v')
+
+-- | The precondition for @'insertLookupWithKey' f k v m@ is that, if
+-- the value @v'@ is inserted into @m@, and @'tag' v'@ is defined,
+-- then no key other than @k@ may map to a value @v''@ for which
+-- @'tag' v'' = 'tag' v'@.
+
+insertLookupWithKeyPrecondition ::
+  (Ord k, Eq v, Eq (Tag v), HasTag v) =>
+  (k -> v -> v -> v) -> k -> v -> BiMap k v -> Bool
+insertLookupWithKeyPrecondition f k v =
+  alterPrecondition (Just . maybe v (f k v)) k
+
+-- | Changes all the values using the given function, which is also
+-- given access to keys. O(n log n).
+--
+-- Precondition: See 'mapWithKeyPrecondition'.
+
+mapWithKey ::
+  (Ord k, Ord (Tag v), HasTag v) =>
+  (k -> v -> v) -> BiMap k v -> BiMap k v
+mapWithKey f = fromList . map (\(k, v) -> (k, f k v)) . toList
+
+-- | The precondition for @'mapWithKey' f m@: For any two distinct
+-- mappings @k₁ ↦ v₁@, @k₂ ↦ v₂@ in @m@ for which the tags of
+-- @f k₁ v₁@ and @f k₂ v₂@ are defined the values of @f@ must be
+-- distinct (@f k₁ v₁ ≠ f k₂ v₂@). Furthermore 'tag' must be injective
+-- for @{ f k v | (k, v) ∈ m }@.
+
+mapWithKeyPrecondition ::
+  (Eq k, Eq v, Eq (Tag v), HasTag v) =>
+  (k -> v -> v) -> BiMap k v -> Bool
+mapWithKeyPrecondition f =
+  fromListPrecondition . map (\(k, v) -> (k, f k v)) . toList
+
+-- | Changes all the values using the given function, which is also
+-- given access to keys. O(n).
+--
+-- Precondition: See 'mapWithKeyFixedTagsPrecondition'. Note that tags
+-- must not change.
+
+mapWithKeyFixedTags :: (k -> v -> v) -> BiMap k v -> BiMap k v
+mapWithKeyFixedTags f (BiMap t b) = BiMap (Map.mapWithKey f t) b
+
+-- | The precondition for @'mapWithKeyFixedTags' f m@ is that, if @m@
+-- maps @k@ to @v@, then @'tag' (f k v) == 'tag' v@.
+
+mapWithKeyFixedTagsPrecondition ::
+  (Eq v, Eq (Tag v), HasTag v) =>
+  (k -> v -> v) -> BiMap k v -> Bool
+mapWithKeyFixedTagsPrecondition f m = and
+  [ tag (f k v) == tag v
+  | (k, v) <- toList m
+  ]
+
+-- | Left-biased union. For the time complexity, see 'Map.union'.
+--
+-- Precondition: See 'unionPrecondition'.
+
+union :: (Ord k, Ord (Tag v)) => BiMap k v -> BiMap k v -> BiMap k v
+union (BiMap t1 b1) (BiMap t2 b2) =
+  BiMap (Map.union t1 t2) (Map.union b1 b2)
+
+-- The precondition for @'union' m₁ m₂@: If @k@ is mapped to @v₁@ in
+-- @m₁@ and @v₂@ in @m₂@, then @'tag' v₂ = 'Nothing'@ or @'tag' v₁ =
+-- 'tag' v₂@. Furthermore, if @k₁@ is mapped to @v₁@ in @m₁@ and @k₂@
+-- is mapped to @v₂@ in @m₂@, where @'tag' v₁ = 'tag' v₂ = 'Just' k@,
+-- then @k₁ = k₂@. Finally 'tag' must be injective for
+-- @{v₁ | (k₁, v₁) ∈ m₁} ∪ {v₂ | (k₂, v₂) ∈ m₂, k₂ ∉ m₁}@.
+
+unionPrecondition ::
+  (Ord k, Eq v, Eq (Tag v), HasTag v) =>
+  BiMap k v -> BiMap k v -> Bool
+unionPrecondition m1@(BiMap t1 _) m2@(BiMap t2 _) =
+  and
+    [ tag v2 == Nothing || tag v1 == tag v2
+    | (v1, v2) <- Map.elems $ Map.intersectionWith (,) t1 t2
+    ] &&
+  and
+    [ k1 == k2
+    | (k1, v1) <- toList m1
+    , (k2, v2) <- toList m2
+    , tag v1 == tag v2
+    , isJust (tag v1)
+    ]
+    &&
+  tagInjectiveFor
+    ([ v1
+     | (_, v1) <- toList m1
+     ] ++
+     [ v2
+     | (k2, v2) <- toList m2
+     , not (k2 `elem` ks1)
+     ])
+  where
+  ks1 = map fst (toList m1)
+
+-- | Conversion from lists of pairs. Later entries take precedence
+-- over earlier ones. O(n log n).
+--
+-- Precondition: See 'fromListPrecondition'.
+
+fromList ::
+  (Ord k, Ord (Tag v), HasTag v) =>
+  [(k, v)] -> BiMap k v
+fromList = List.foldr (uncurry insert) empty
+
+-- The precondition for @'fromList' kvs@: For all pairs @(k₁, v₁)@,
+-- @(k₂, v₂)@ in @kvs@ for which the tags of @v₁@ and @v₂@ are
+-- defined, if @v₁ = v₂@ then @k₁ = k₂@. Furthermore 'tag' must be
+-- injective for the values in the list.
+
+fromListPrecondition ::
+  (Eq k, Eq v, Eq (Tag v), HasTag v) =>
+  [(k, v)] -> Bool
+fromListPrecondition kvs =
+  and
+    [ k1 == k2
+    | (k1, v1) <- kvs
+    , (k2, v2) <- kvs
+    , isJust (tag v1)
+    , isJust (tag v2)
+    , v1 == v2
+    ]
+    &&
+  tagInjectiveFor (map snd kvs)
+
+-- | Conversion to lists of pairs, with the keys in ascending order.
+-- O(n).
+
+toList :: BiMap k v -> [(k, v)]
+toList = Map.toAscList . biMapThere
+
+-- | The keys, in ascending order. O(n).
+
+keys :: BiMap k v -> [k]
+keys = Map.keys . biMapThere
+
+-- | The values, ordered according to the corresponding keys. O(n).
+
+elems :: BiMap k v -> [v]
+elems = Map.elems . biMapThere
+
+-- | Conversion from two lists that contain distinct keys/tags, with
+-- the keys/tags in ascending order. O(n).
+--
+-- Precondition: See 'fromDistinctAscendingListsPrecondition'.
+
+fromDistinctAscendingLists ::
+  ([(k, v)], [(Tag v, k)]) -> BiMap k v
+fromDistinctAscendingLists (t, b) =
+  BiMap (Map.fromDistinctAscList t) (Map.fromDistinctAscList b)
+
+-- The precondition for @'fromDistinctAscendingLists' (kvs, kks)@: The
+-- lists must contain distinct keys/tags, and must be sorted according
+-- to the keys/tags. Furthermore, for every pair @(k, v)@ in the first
+-- list for which @'tag' v = 'Just' k'@ there must be a pair @(k', k)@
+-- in the second list, and there must not be any other pairs in that
+-- list. Finally 'tag' must be injective for @{v | (_, v) ∈ kvs }@.
+
+fromDistinctAscendingListsPrecondition ::
+  (Ord k, Eq v, Ord (Tag v), HasTag v) =>
+  ([(k, v)], [(Tag v, k)]) -> Bool
+fromDistinctAscendingListsPrecondition (kvs, kks) =
+  fastDistinct (map fst kvs) && sorted (map fst kvs)
+    &&
+  fastDistinct (map fst kks) && sorted (map fst kks)
+    &&
+  kks ==
+  List.sortBy (comparing fst)
+    [ (k', k)
+    | (k, v) <- kvs
+    , Just k' <- [tag v]
+    ]
+    &&
+  tagInjectiveFor [ v | (_, v) <- kvs ]
+
+-- | Generates input suitable for 'fromDistinctAscendingLists'. O(n).
+
+toDistinctAscendingLists :: BiMap k v -> ([(k, v)], [(Tag v, k)])
+toDistinctAscendingLists (BiMap t b) =
+  (Map.toAscList t, Map.toAscList b)
+
+------------------------------------------------------------------------
+-- Instances
+------------------------------------------------------------------------
+
+instance (Eq k, Eq v) => Eq (BiMap k v) where
+  (==) = (==) `on` biMapThere
+
+instance (Ord k, Ord v) => Ord (BiMap k v) where
+  compare = compare `on` biMapThere
+
+instance (Show k, Show v) => Show (BiMap k v) where
+  show bimap = "Agda.Utils.BiMap.fromList " ++ show (toList bimap)
diff --git a/src/full/Agda/Utils/BoolSet.hs b/src/full/Agda/Utils/BoolSet.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/BoolSet.hs
@@ -0,0 +1,184 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Representation of @'Set' 'Bool'@ as a 4-element enum type.
+--
+-- All operations in constant time and space.
+--
+-- Mimics the interface of 'Data.Set'.
+--
+-- Import as:
+-- @
+--    import qualified Agda.Utils.BoolSet as BoolSet
+--    import Agda.Utils.BoolSet (BoolSet)
+-- @
+
+module Agda.Utils.BoolSet
+  ( BoolSet
+  , (\\)
+  , complement
+  , delete
+  , difference
+  , elems
+  , empty
+  , fromList, fromAscList, fromDistinctAscList
+  , insert
+  , intersection
+  , isSubsetOf
+  , lookupMin
+  , member
+  , notMember
+  , null
+  , singleton
+  , size
+  , toList, toAscList
+  , toSingleton
+  , total
+  , union
+  ) where
+
+import Prelude hiding (null)
+
+import Agda.Utils.Impossible
+
+-- | Isomorphic to @'Set' 'Bool'@.
+data BoolSet = SetEmpty | SetTrue | SetFalse | SetBoth
+  deriving (Eq, Ord, Show, Enum, Bounded)
+
+-- * Query
+
+null :: BoolSet -> Bool
+null = (SetEmpty ==)
+
+size :: BoolSet -> Int
+size = \case
+  SetEmpty -> 0
+  SetTrue  -> 1
+  SetFalse -> 1
+  SetBoth  -> 2
+
+member :: Bool -> BoolSet -> Bool
+member b = \case
+  SetEmpty -> False
+  SetBoth  -> True
+  SetTrue  -> b
+  SetFalse -> not b
+
+-- | @not . member b@.
+notMember :: Bool -> BoolSet -> Bool
+notMember b = not . member b
+
+isSubsetOf ::  BoolSet -> BoolSet -> Bool
+isSubsetOf = curry $ \case
+  (SetEmpty , _        ) -> True
+  (_        , SetBoth  ) -> True
+  (SetTrue  , SetTrue  ) -> True
+  (SetFalse , SetFalse ) -> True
+  _                      -> False
+
+lookupMin :: BoolSet -> Maybe Bool
+lookupMin = \case
+  SetEmpty -> Nothing
+  SetTrue  -> Just True
+  _        -> Just False
+
+-- | @toSingleton s == Just b@ iff @s == singleton b@.
+toSingleton :: BoolSet -> Maybe Bool
+toSingleton  = \case
+  SetTrue  -> Just True
+  SetFalse -> Just False
+  _        -> Nothing
+
+-- * Construction
+
+-- | The empty set.
+empty :: BoolSet
+empty = SetEmpty
+
+-- | The full set.
+total :: BoolSet
+total = SetBoth
+
+-- | A singleton set.
+singleton :: Bool -> BoolSet
+singleton = \case
+  True  -> SetTrue
+  False -> SetFalse
+
+insert :: Bool -> BoolSet -> BoolSet
+insert b = \case
+  SetBoth  -> SetBoth
+  SetEmpty -> singleton b
+  SetTrue  -> if b then SetTrue else SetBoth
+  SetFalse -> if b then SetBoth else SetFalse
+
+delete :: Bool -> BoolSet -> BoolSet
+delete b = \case
+  SetEmpty -> SetEmpty
+  SetTrue  -> if b then SetEmpty else SetTrue
+  SetFalse -> if b then SetFalse else SetEmpty
+  SetBoth  -> if b then SetFalse else SetTrue
+
+-- * Combine
+
+complement :: BoolSet -> BoolSet
+complement = \case
+  SetEmpty -> SetBoth
+  SetBoth  -> SetEmpty
+  SetTrue  -> SetFalse
+  SetFalse -> SetTrue
+
+difference, (\\) :: BoolSet -> BoolSet -> BoolSet
+difference = curry $ \case
+  (SetEmpty , _        ) -> SetEmpty
+  (_        , SetBoth  ) -> SetEmpty
+  (s        , SetEmpty ) -> s
+  (SetBoth  , SetTrue  ) -> SetFalse
+  (SetBoth  , SetFalse ) -> SetTrue
+  (SetTrue  , SetTrue  ) -> SetEmpty
+  (SetTrue  , SetFalse ) -> SetTrue
+  (SetFalse , SetTrue  ) -> SetFalse
+  (SetFalse , SetFalse ) -> SetEmpty
+(\\)       = difference
+
+intersection ::  BoolSet -> BoolSet -> BoolSet
+intersection = curry $ \case
+  (SetEmpty , _        ) -> SetEmpty
+  (_        , SetEmpty ) -> SetEmpty
+  (SetBoth  , s        ) -> s
+  (s        , SetBoth  ) -> s
+  (SetTrue  , SetTrue  ) -> SetTrue
+  (SetFalse , SetTrue  ) -> SetEmpty
+  (SetTrue  , SetFalse ) -> SetEmpty
+  (SetFalse , SetFalse ) -> SetFalse
+
+union ::  BoolSet -> BoolSet -> BoolSet
+union = curry $ \case
+  (SetBoth  , _        ) -> SetBoth
+  (_        , SetBoth  ) -> SetBoth
+  (SetEmpty , s        ) -> s
+  (s        , SetEmpty ) -> s
+  (SetTrue  , SetTrue  ) -> SetTrue
+  (SetFalse , SetTrue  ) -> SetBoth
+  (SetTrue  , SetFalse ) -> SetBoth
+  (SetFalse , SetFalse ) -> SetFalse
+
+-- * Conversion
+
+elems, toList, toAscList :: BoolSet -> [Bool]
+elems     = \case
+  SetEmpty -> []
+  SetTrue  -> [True]
+  SetFalse -> [False]
+  SetBoth  -> [False, True]
+toList    = elems
+toAscList = elems
+
+fromList, fromAscList, fromDistinctAscList :: [Bool] -> BoolSet
+fromList            = foldr insert SetEmpty
+fromAscList         = fromList
+fromDistinctAscList = \case
+  []            -> SetEmpty
+  [False]       -> SetFalse
+  [True]        -> SetTrue
+  [False, True] -> SetBoth
+  _             -> __IMPOSSIBLE__
diff --git a/src/full/Agda/Utils/Boolean.hs b/src/full/Agda/Utils/Boolean.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Boolean.hs
@@ -0,0 +1,89 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Boolean algebras and types isomorphic to 'Bool'.
+--
+-- There are already solutions for 'Boolean' algebras in the Haskell ecosystem,
+-- but they do not offer easy instantiations for types isomorphic to 'Bool'.
+-- In particular, if type @a@ is isomorphic to 'Bool', so it satisfies `IsBool a`,
+-- we would like to instantiate 'Boolean a' by just giving 'true' and 'false'.
+-- To facilitate this within the limits of the Haskell class system,
+-- we define the class 'Boolean' mutually with class 'IsBool',
+-- so that operations 'not', '(&&)', and '(||)' can get default implementations.
+--
+-- Usage:
+-- @
+--    import Prelude hiding ( not, (&&), (||) )
+--    import Agda.Utils.Boolean
+-- @
+
+module Agda.Utils.Boolean where
+
+import Prelude ( Bool(True,False), Eq, ($), (.), const, id )
+import qualified Prelude as P
+
+infixr 3 &&
+infixr 2 ||
+
+-- | Boolean algebras.
+--
+class Boolean a where
+  fromBool :: Bool -> a
+
+  true :: a
+  true = fromBool True
+
+  false :: a
+  false = fromBool False
+
+  not :: a -> a
+
+  (&&) :: a -> a -> a
+
+  (||) :: a -> a -> a
+
+  implies :: a -> a -> a
+  implies a b = b || not a
+
+  -- | Set difference, dual to 'implies'.
+  butNot :: a -> a -> a
+  butNot a b = a && not b
+
+  default not :: IsBool a => a -> a
+  not = fromBool1 P.not
+
+  default (&&) :: IsBool a => a -> a -> a
+  (&&) = fromBool2 (P.&&)
+
+  default (||) :: IsBool a => a -> a -> a
+  (||) = fromBool2 (P.||)
+
+-- | Types isomorphic to 'Bool'.
+--
+class (Boolean a, Eq a) => IsBool a where
+  toBool :: a -> Bool
+
+  ifThenElse :: a -> b -> b -> b
+  ifThenElse c t e = if toBool c then t else e
+
+  fromBool1 :: (Bool -> Bool) -> (a -> a)
+  fromBool1 f = fromBool . f . toBool
+
+  fromBool2 :: (Bool -> Bool -> Bool) -> (a -> a -> a)
+  fromBool2 f a b = fromBool $ f (toBool a) (toBool b)
+
+  {-# MINIMAL toBool #-}
+
+instance Boolean Bool where
+  fromBool = id
+
+instance IsBool Bool where
+  toBool = id
+  -- optional
+  fromBool1 = id
+  fromBool2 = id
+
+instance Boolean b => Boolean (a -> b) where
+  fromBool   = const . fromBool
+  not f      = not . f
+  (f && g) a = f a && g a
+  (f || g) a = f a || g a
diff --git a/src/full/Agda/Utils/CallStack.hs b/src/full/Agda/Utils/CallStack.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/CallStack.hs
@@ -0,0 +1,5 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.CallStack (module Exports) where
+import Agda.Utils.CallStack.Base as Exports
+import Agda.Utils.CallStack.Pretty as Exports ()
diff --git a/src/full/Agda/Utils/CallStack/Base.hs b/src/full/Agda/Utils/CallStack/Base.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/CallStack/Base.hs
@@ -0,0 +1,141 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.CallStack.Base (
+  -- * Simple type aliases
+    SrcLocPackage
+  , SrcLocModule
+  , SrcFun
+  , SrcLocFile
+  , SrcLocLine
+  , SrcLocCol
+  , CallSite
+  , CallSiteFilter
+
+  -- * String-based "pretty" representations
+  , prettySrcLoc
+  , prettyCallSite
+  , prettyCallStack
+
+  -- * Generic utilities over CallStack and CallSite
+  , filterCallStack
+  , headCallSite
+  , overCallSites
+  , popnCallStack
+  , truncatedCallStack
+  , withCallerCallStack
+  , withCurrentCallStack
+  , withNBackCallStack
+
+  -- * Re-exported stuff
+  , CallStack
+  , callStack
+  , fromCallSiteList
+  , getCallStack
+  , HasCallStack
+  , SrcLoc(..)
+  )
+  where
+
+import Data.List ( intercalate )
+import Data.Maybe ( listToMaybe )
+import GHC.Stack
+  ( callStack
+  , CallStack
+  , emptyCallStack
+  , fromCallSiteList
+  , getCallStack
+  , HasCallStack
+  , popCallStack
+  , prettySrcLoc
+  , SrcLoc(..)
+  )
+
+-- * Type aliases
+
+-- | Type of the package name of a @SrcLoc@
+-- | e.g. `Agda-2.…`
+type SrcLocPackage = String
+
+-- | Type of the module name of a @SrcLoc@
+-- | e.g. `Agda.Utils.Foo`
+type SrcLocModule = String
+
+-- | Type of the name of a function in a @CallSite@
+-- | e.g. `proveEverything`
+type SrcFun = String
+
+-- | Type of a filename of a @SrcLoc@
+-- | e.g. `src/full/Agda/Utils/Foo.hs`
+type SrcLocFile = String
+
+-- | Type of a line number of a @SrcLoc@
+type SrcLocLine = Int
+
+-- | Type of a column of a @SrcLoc@
+type SrcLocCol = Int
+
+-- | Type of an entry in  a @CallStack@
+type CallSite = (SrcFun, SrcLoc)
+
+-- | Type of a filter for @CallSite@
+type CallSiteFilter = CallSite -> Bool
+
+-- * Simple String representations
+-- Note that there are @Agda.Syntax.Common.Pretty@ instances defined in @Agda.Utils.CallStack.Pretty@
+
+-- | The same as the un-exported internal function in @GHC.Exceptions (prettyCallStackLines)@
+--  Prints like: @doFoo, called at foo.hs:190:24 in main:Main@
+prettyCallSite :: CallSite -> String
+prettyCallSite (fun, loc) = fun ++ ", called at " ++ prettySrcLoc loc
+
+-- | Pretty-print a @CallStack@. This has a few differences from @GHC.Stack.prettyCallStackLines@.
+-- We omit the "CallStack (from GetCallStack)" header line for brevity.
+-- If there is only one entry (which is common, due to the manual nature of the @HasCallStack@ constraint),
+-- shows the entry on one line. If there are multiple, then the following lines are indented.
+prettyCallStack :: CallStack -> String
+prettyCallStack cs = case map prettyCallSite (getCallStack cs) of
+  []                  -> "(empty CallStack)"
+  firstLoc : restLocs -> intercalate "\n" (firstLoc : (map ("  " ++) restLocs))
+
+-- * Generic utilities over CallStack and CallSite
+
+-- | Get the most recent @CallSite@ in a @CallStack@, if there is one.
+headCallSite :: CallStack -> Maybe CallSite
+headCallSite = listToMaybe . getCallStack
+
+-- | @CallStack@ comprising only the most recent @CallSite@
+truncatedCallStack :: CallStack -> CallStack
+truncatedCallStack cs = maybe emptyCallStack (fromCallSiteList . pure) (headCallSite cs)
+
+-- | Transform a @CallStack@ by transforming its list of @CallSite@
+overCallSites :: ([CallSite] -> [CallSite]) -> CallStack -> CallStack
+overCallSites f = fromCallSiteList . f . getCallStack
+
+-- | Transform a @CallStack@ by filtering each @CallSite@
+filterCallStack :: CallSiteFilter -> CallStack -> CallStack
+filterCallStack = overCallSites . filter
+
+-- | Pops n entries off a @CallStack@ using @popCallStack@.
+-- Note that frozen callstacks are unaffected.
+popnCallStack :: Word -> CallStack -> CallStack
+popnCallStack 0 = id
+popnCallStack n = (popnCallStack (n - 1)) . popCallStack
+
+withNBackCallStack :: HasCallStack => Word -> (CallStack -> b) -> b
+withNBackCallStack n f = f (popnCallStack n from)
+  where
+    -- This very line (always dropped):
+    here = callStack
+    -- The invoker (n = 0):
+    from = popCallStack here
+
+withCurrentCallStack :: HasCallStack => (CallStack -> b) -> b
+withCurrentCallStack = withNBackCallStack 0
+  -- 0 => this line in this utility function.
+  -- 1 => the invocation of this utility function.
+
+withCallerCallStack :: HasCallStack => (CallStack -> b) -> b
+withCallerCallStack = withNBackCallStack 1
+  -- 0 => this line in this utility function.
+  -- 1 => our caller.
+  -- 2 => their caller.
diff --git a/src/full/Agda/Utils/CallStack/Pretty.hs b/src/full/Agda/Utils/CallStack/Pretty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/CallStack/Pretty.hs
@@ -0,0 +1,32 @@
+module Agda.Utils.CallStack.Pretty
+  ( -- This module only exports instances.
+  ) where
+
+import Agda.Utils.CallStack.Base
+  ( CallSite
+  , CallStack
+  , SrcLoc(..)
+  , getCallStack
+  )
+import Agda.Syntax.Common.Pretty
+  ( (<+>), ($+$), (<>)
+  , pshow, text
+  , colon, comma
+  , nest, parens
+  , hcat, hsep, vcat
+  , Pretty(pretty)
+  )
+
+instance Pretty SrcLoc where
+  pretty SrcLoc {..} = hsep [physicalLoc, "in", logicalLoc]
+      where
+        physicalLoc = hcat [text srcLocFile, colon, pshow srcLocStartLine, colon, pshow srcLocStartCol]
+        logicalLoc = hcat [text srcLocPackage, colon, text srcLocModule]
+
+instance Pretty CallSite where
+  pretty (fun, loc) = hsep [text fun <> comma, "called at", pretty loc]
+
+instance Pretty CallStack where
+  pretty cs = case fmap pretty (getCallStack cs) of
+    []                  -> parens "empty CallStack"
+    firstLoc : restLocs -> firstLoc $+$ nest 2 (vcat restLocs)
diff --git a/src/full/Agda/Utils/Char.hs b/src/full/Agda/Utils/Char.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Char.hs
@@ -0,0 +1,37 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- |
+-- Agda strings uses Data.Text [1], which can only represent unicode scalar values [2], excluding
+-- the surrogate code points [3] (@U+D800..U+DFFF@). To allow @primStringFromList@ to be injective
+-- we make sure character values also exclude surrogate code points, mapping them to the replacement
+-- character @U+FFFD@.
+--
+-- See #4999 for more information.
+--
+-- [1] https://hackage.haskell.org/package/text-1.2.4.0/docs/Data-Text.html#g:2
+-- [2] https://www.unicode.org/glossary/#unicode_scalar_value
+-- [3] https://www.unicode.org/glossary/#surrogate_code_point
+
+module Agda.Utils.Char where
+
+import Data.Char
+
+-- | The unicode replacement character � .
+replacementChar :: Char
+replacementChar = '\xFFFD'
+
+-- | Is a character a surrogate code point.
+isSurrogateCodePoint :: Char -> Bool
+isSurrogateCodePoint c = generalCategory c == Surrogate
+
+-- | Map surrogate code points to the unicode replacement character.
+replaceSurrogateCodePoint :: Char -> Char
+replaceSurrogateCodePoint c
+  | isSurrogateCodePoint c = replacementChar
+  | otherwise              = c
+
+-- | Total function to convert an integer to a character. Maps surrogate code points
+--   to the replacement character @U+FFFD@.
+integerToChar :: Integer -> Char
+integerToChar = replaceSurrogateCodePoint . toEnum . fromIntegral . (`mod` 0x110000)
+
diff --git a/src/full/Agda/Utils/Cluster.hs b/src/full/Agda/Utils/Cluster.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Cluster.hs
@@ -0,0 +1,70 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Create clusters of non-overlapping things.
+
+module Agda.Utils.Cluster
+  ( cluster
+  , cluster'
+  , cluster1
+  , cluster1'
+  ) where
+
+import Control.Monad
+
+-- An imperative union-find library:
+import Data.Equivalence.Monad ( runEquivT, equateAll, classDesc )
+
+-- NB: We keep this module independent of Agda.Utils.List1
+import Data.List.NonEmpty     ( NonEmpty(..), nonEmpty, toList )
+import Data.Maybe             ( fromMaybe )
+
+import qualified Data.Map.Strict as MapS
+
+import Agda.Utils.Functor
+import Agda.Utils.Singleton
+import Agda.Utils.Fail
+
+-- | Given a function @f :: a -> NonEmpty c@ which returns a non-empty list of
+--   characteristics of @a@, partition a list of @a@s into groups such
+--   that each element in a group shares at least one characteristic
+--   with at least one other element of the group.
+cluster :: Ord c => (a -> NonEmpty c) -> [a] -> [NonEmpty a]
+cluster = liftList1 . cluster1
+
+-- | Partition a list of @a@s paired with a non-empty list of
+--   characteristics into groups such that each element in a group
+--   shares at least one characteristic with at least one other
+--   element of the group.
+cluster' :: Ord c => [(a, NonEmpty c)] -> [NonEmpty a]
+cluster' = liftList1 cluster1'
+
+-- | Lift a function on non-empty lists to a function on lists.
+--
+-- Duplicate of 'Agda.Utils.List1.liftList1'.
+liftList1 :: (NonEmpty a -> NonEmpty b) -> [a] -> [b]
+liftList1 f = \case
+  []     -> []
+  a : as -> toList $ f $ a :| as
+
+-- | Given a function @f :: a -> NonEmpty c@ which returns a non-empty list of
+--   characteristics of @a@, partition a non-empty list of @a@s into groups such
+--   that each element in a group shares at least one characteristic
+--   with at least one other element of the group.
+cluster1 :: Ord c => (a -> NonEmpty c) -> NonEmpty a -> NonEmpty (NonEmpty a)
+cluster1 f as = cluster1' $ fmap (\ a -> (a, f a)) as
+
+-- | Partition a non-empty list of @a@s paired with a non-empty list of
+--   characteristics into groups such that each element in a group
+--   shares at least one characteristic with at least one other
+--   element of the group.
+cluster1' :: Ord c => NonEmpty (a, NonEmpty c) -> NonEmpty (NonEmpty a)
+cluster1' acs = runFail_ $ runEquivT id const $ do
+  -- Construct the equivalence classes of characteristics.
+  forM_ acs $ \ (_, c :| cs) -> equateAll $ c:cs
+  -- Pair each element with its class.
+  cas <- forM acs $ \ (a, c :| _) -> classDesc c <&> \ k -> MapS.singleton k (singleton a)
+  -- Create a map from class to elements.
+  let m = MapS.unionsWith (<>) cas
+  -- Return the values of the map
+  return $ fromMaybe (error "impossibility at Agda.Utils.Cluster.cluster'") $ nonEmpty $
+    MapS.elems m
diff --git a/src/full/Agda/Utils/Either.hs b/src/full/Agda/Utils/Either.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Either.hs
@@ -0,0 +1,129 @@
+------------------------------------------------------------------------
+-- | Utilities for the 'Either' type.
+------------------------------------------------------------------------
+
+module Agda.Utils.Either
+  ( whileLeft
+  , caseEitherM
+  , mapLeft
+  , mapRight
+  , traverseEither
+  , isLeft
+  , isRight
+  , fromLeft
+  , fromRight
+  , fromLeftM
+  , fromRightM
+  , maybeLeft
+  , maybeRight
+  , allLeft
+  , allRight
+  , groupByEither
+  , maybeToEither
+  , swapEither
+  ) where
+
+import Data.Bifunctor
+import Data.Either (isLeft, isRight)
+import Data.List   (unfoldr)
+
+import Agda.Utils.List ( spanJust )
+import Agda.Utils.List1 ( List1, pattern (:|), (<|) )
+import qualified Agda.Utils.List1 as List1
+
+-- | Loop while we have an exception.
+
+whileLeft :: Monad m => (a -> Either b c) -> (a -> b -> m a) -> (a -> c -> m d) -> a -> m d
+whileLeft test left right = loop where
+  loop a =
+    case test a of
+      Left  b -> loop =<< left a b
+      Right c -> right a c
+
+-- | Monadic version of 'either' with a different argument ordering.
+
+caseEitherM :: Monad m => m (Either a b) -> (a -> m c) -> (b -> m c) -> m c
+caseEitherM mm f g = either f g =<< mm
+
+-- | 'Either _ b' is a functor.
+
+mapLeft :: (a -> c) -> Either a b -> Either c b
+mapLeft = first
+
+-- | 'Either a' is a functor.
+
+mapRight :: (b -> d) -> Either a b -> Either a d
+mapRight = second
+
+-- | 'Either' is bitraversable.
+-- Note: From @base >= 4.10.0.0@ already present in `Data.Bitraversable`.
+traverseEither :: Functor f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d)
+traverseEither f g = either (fmap Left . f) (fmap Right . g)
+
+-- | Analogue of 'Data.Maybe.fromMaybe'.
+fromLeft :: (b -> a) -> Either a b -> a
+fromLeft = (id `either`)
+
+-- | Analogue of 'Data.Maybe.fromMaybe'.
+fromRight :: (a -> b) -> Either a b -> b
+fromRight = (`either` id)
+
+-- | Analogue of 'Agda.Utils.Maybe.fromMaybeM'.
+fromLeftM :: Monad m => (b -> m a) -> m (Either a b) -> m a
+fromLeftM f m = either return f =<< m
+
+-- | Analogue of 'Agda.Utils.Maybe.fromMaybeM'.
+fromRightM :: Monad m => (a -> m b) -> m (Either a b) -> m b
+fromRightM f m = either f return =<< m
+
+-- | Safe projection from 'Left'.
+--
+--   > maybeLeft (Left a) = Just a
+--   > maybeLeft Right{}  = Nothing
+--
+maybeLeft :: Either a b -> Maybe a
+maybeLeft = either Just (const Nothing)
+
+-- | Safe projection from 'Right'.
+--
+--   > maybeRight (Right b) = Just b
+--   > maybeRight Left{}    = Nothing
+--
+maybeRight :: Either a b -> Maybe b
+maybeRight = either (const Nothing) Just
+
+-- | Returns @'Just' input_with_tags_stripped@ if all elements are
+-- to the 'Left', and otherwise 'Nothing'.
+allLeft :: [Either a b] -> Maybe [a]
+allLeft = mapM maybeLeft
+
+-- | Returns @'Just' input_with_tags_stripped@ if all elements are
+-- to the right, and otherwise 'Nothing'.
+--
+-- @
+--  allRight xs ==
+--    if all isRight xs then
+--      Just (map (\(Right x) -> x) xs)
+--     else
+--      Nothing
+-- @
+
+allRight :: [Either a b] -> Maybe [b]
+allRight = mapM maybeRight
+
+-- | Groups a list into alternating chunks of 'Left' and 'Right' values
+groupByEither :: forall a b. [Either a b] -> [Either (List1 a) (List1 b)]
+groupByEither = unfoldr c
+  where
+  c :: [Either a b] -> Maybe (Either (List1 a) (List1 b), [Either a b])
+  c []             = Nothing
+  c (Left  a : xs) = Just $ first (Left  . (a :|)) $ spanJust maybeLeft  xs
+  c (Right b : xs) = Just $ first (Right . (b :|)) $ spanJust maybeRight xs
+
+-- | Convert 'Maybe' to @'Either' e@, given an error @e@ for the 'Nothing' case.
+maybeToEither :: e -> Maybe a -> Either e a
+maybeToEither e = maybe (Left e) Right
+
+-- | Swap tags 'Left' and 'Right'.
+swapEither :: Either a b -> Either b a
+swapEither = either Right Left
diff --git a/src/full/Agda/Utils/Empty.hs b/src/full/Agda/Utils/Empty.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Empty.hs
@@ -0,0 +1,45 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | An empty type with some useful instances.
+module Agda.Utils.Empty where
+
+import Control.DeepSeq
+import Control.Exception (evaluate)
+
+import Agda.Utils.Impossible
+
+
+data Empty
+
+-- | Values of type 'Empty' are not forced, because 'Empty' is used as
+-- a constructor argument in 'Agda.Syntax.Internal.Substitution''.
+
+instance NFData Empty where
+  rnf _ = ()
+
+instance Eq Empty where
+  _ == _ = True
+
+instance Ord Empty where
+  compare _ _ = EQ
+
+instance Show Empty where
+  showsPrec p _ = showParen (p > 9) $ showString "error \"Agda.Utils.Empty.Empty\""
+
+absurd :: Empty -> a
+absurd e = seq e __IMPOSSIBLE__
+
+
+-- | @toImpossible e@ extracts the @Impossible@ value raised via
+--   @__IMPOSSIBLE__@ to create the element @e@ of type @Empty@.
+--   It proceeds by evaluating @e@ to weak head normal form and
+--   catching the exception.
+--   We are forced to wrap things in a @Maybe@ because of
+--   @catchImpossible@'s type.
+
+toImpossible :: Empty -> IO Impossible
+toImpossible e = do
+  s <- catchImpossible (Nothing <$ evaluate e) (return . Just)
+  case s of
+    Just i  -> return i
+    Nothing -> absurd e -- this should never happen
diff --git a/src/full/Agda/Utils/Environment.hs b/src/full/Agda/Utils/Environment.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Environment.hs
@@ -0,0 +1,70 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Expand environment variables in strings
+module Agda.Utils.Environment
+  ( EnvVars
+  , expandEnvironmentVariables
+  , expandEnvVarTelescope
+  ) where
+
+import Data.Char
+import Data.Maybe
+import System.Environment
+import System.Directory ( getHomeDirectory )
+
+expandEnvironmentVariables :: String -> IO String
+expandEnvironmentVariables s = do
+  env  <- getEnvironment
+  home <- getHomeDirectory
+  return $ expandVars home env s
+
+expandVars
+  :: String              -- ^ Home directory.
+  -> EnvVars             -- ^ Environment variable substitution map.
+  -> String              -- ^ Input.
+  -> String              -- ^ Output with variables and @~@ (home) substituted.
+expandVars home env s = concatMap repl $ tokens s
+  where
+    repl Home    = home ++ "/"
+    repl (Var x) = fromMaybe "" $ lookup x env
+    repl (Str s) = s
+
+-- | List of environment variable bindings.
+type EnvVars = [(String, String)]
+
+-- | Expand a telescope of environment variables
+--   (each value may refer to variables earlier in the list).
+expandEnvVarTelescope :: String -> EnvVars -> EnvVars
+expandEnvVarTelescope home = reverse . foldl  -- foldl reverses, so re-reverse afterwards
+  (\ acc (var, val) -> (var, expandVars home acc val) : acc) []
+
+-- | Tokenization for environment variable substitution.
+data Token
+  = Home        -- ^ @~@.
+  | Var String  -- ^ @$VARIABLE@ or @${VARIABLE}$.
+  | Str String  -- ^ Ordinary characters.
+  deriving (Eq, Show)
+
+-- | Tokenize a string.
+--   The @~@ is recognized as @$HOME@ only at the beginning of the string.
+tokens :: String -> [Token]
+tokens = \case
+  '~'  : '/' : s -> Home : tokens' s
+  '\\' : '~' : s -> cons '~' $ tokens' s
+  s -> tokens' s
+  where
+    tokens' :: String -> [Token]
+    tokens' = \case
+        '$' : '$' : s -> cons '$' $ tokens' s
+        '$' : s@(c : _) | c == '_' || isAlpha c -> Var x : tokens' s'
+          where
+          (x, s') = span (\ c -> c == '_' || isAlphaNum c) s
+        '$' : '{' : s ->
+          case break (== '}') s of
+            (x, '}' : s) -> Var x : tokens' s
+            _            -> [Str $ "${" ++ s] -- abort on unterminated '{'
+        c : s -> cons c $ tokens' s
+        ""    -> []
+    cons :: Char -> [Token] -> [Token]
+    cons c (Str s : ts) = Str (c : s) : ts
+    cons c ts           = Str [c] : ts
diff --git a/src/full/Agda/Utils/Fail.hs b/src/full/Agda/Utils/Fail.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Fail.hs
@@ -0,0 +1,14 @@
+-- | A pure MonadFail.
+module Agda.Utils.Fail where
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail
+
+newtype Fail a = Fail { runFail :: Either String a }
+  deriving (Functor, Applicative, Monad)
+
+instance MonadFail Fail where
+  fail = Fail . Left
+
+runFail_ :: Fail a -> a
+runFail_ = either error id . runFail
diff --git a/src/full/Agda/Utils/Favorites.hs b/src/full/Agda/Utils/Favorites.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Favorites.hs
@@ -0,0 +1,114 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Maintaining a list of favorites of some partially ordered type.
+--   Only the best elements are kept.
+--
+--   To avoid name clashes, import this module qualified, as in
+--   @
+--      import Agda.Utils.Favorites (Favorites)
+--      import qualified Agda.Utils.Favorites as Fav
+--   @
+
+module Agda.Utils.Favorites where
+
+import Prelude hiding ( null )
+
+import qualified Data.List as List
+import qualified Data.Set as Set
+
+import Agda.Utils.Null
+import Agda.Utils.PartialOrd
+import Agda.Utils.Singleton
+import Agda.Utils.Tuple
+
+-- | A list of incomparable favorites.
+newtype Favorites a = Favorites { toList :: [a] }
+  deriving (Foldable, Show, Null, Singleton a)
+
+-- | Equality checking is a bit expensive, since we need to sort!
+--   Maybe use a 'Set' of favorites in the first place?
+instance Ord a => Eq (Favorites a) where
+  as == bs = Set.fromList (toList as) == Set.fromList (toList bs)
+
+-- | Result of comparing a candidate with the current favorites.
+data CompareResult a
+  = Dominates   { dominated :: [a], notDominated :: [a] }
+    -- ^ Great, you are dominating a possibly (empty list of favorites)
+    --   but there is also a rest that is not dominated.
+    --   If @null dominated@, then @notDominated@ is necessarily the
+    --   complete list of favorites.
+  | IsDominated { dominator :: a }
+    -- ^ Sorry, but you are dominated by that favorite.
+
+
+-- | Gosh, got some pretty @a@ here, compare with my current favorites!
+--   Discard it if there is already one that is better or equal.
+--   (Skewed conservatively: faithful to the old favorites.)
+--   If there is no match for it, add it, and
+--   dispose of all that are worse than @a@.
+--
+--   We require a partial ordering.  Less is better! (Maybe paradoxically.)
+compareWithFavorites :: PartialOrd a => a -> Favorites a -> CompareResult a
+compareWithFavorites a favs = loop $ toList favs where
+  loop []          = Dominates [] []
+  loop as@(b : bs) = case comparable a b of
+    POLT -> dominates b $ loop bs  -- @a@ is a new favorite, bye-bye, @b@
+    POLE -> dominates b $ loop bs  -- ditto
+    POEQ -> IsDominated b          -- @b@ is as least as good as @a@, bye-bye, @a@
+    POGE -> IsDominated b          -- ditto
+    POGT -> IsDominated b          -- ditto
+    POAny -> doesnotd b $ loop bs -- don't know, compare with my other favorites
+  -- add an outperformed favorite
+  dominates b (Dominates bs as) = Dominates (b : bs) as
+  dominates b r@IsDominated{}   = r
+  -- add an uncomparable favorite
+  doesnotd  b (Dominates as bs) = Dominates as (b : bs)
+  doesnotd  b r@IsDominated{}   = r
+
+-- | Compare a new set of favorites to an old one and discard
+--   the new favorites that are dominated by the old ones
+--   and vice verse.
+--   (Skewed conservatively: faithful to the old favorites.)
+--
+--   @compareFavorites new old = (new', old')@
+compareFavorites :: PartialOrd a => Favorites a -> Favorites a ->
+                    (Favorites a, Favorites a)
+compareFavorites new old = mapFst Favorites $ loop (toList new) old where
+  loop []        old = ([], old)
+  loop (a : new) old = case compareWithFavorites a old of
+    -- Better: Discard all @old@ ones that @a@ dominates and keep @a@
+    Dominates _ old -> mapFst (a:) $ loop new (Favorites old)
+    -- Not better:  Discard @a@
+    IsDominated{}   -> loop new old
+
+unionCompared :: (Favorites a, Favorites a) -> Favorites a
+unionCompared (Favorites new, Favorites old) = Favorites $ new ++ old
+
+-- | After comparing, do the actual insertion.
+insertCompared :: a -> Favorites a -> CompareResult a -> Favorites a
+insertCompared a _ (Dominates _ as) = Favorites (a : as)
+insertCompared _ l IsDominated{}    = l
+
+-- | Compare, then insert accordingly.
+--   @insert a l = insertCompared a l (compareWithFavorites a l)@
+insert :: PartialOrd a => a -> Favorites a -> Favorites a
+insert a l = insertCompared a l (compareWithFavorites a l)
+
+-- | Insert all the favorites from the first list into the second.
+union :: PartialOrd a => Favorites a -> Favorites a -> Favorites a
+union (Favorites as) bs = List.foldr insert bs as
+
+-- | Construct favorites from elements of a partial order.
+--   The result depends on the order of the list if it
+--   contains equal elements, since earlier seen elements
+--   are favored over later seen equals.
+--   The first element of the list is seen first.
+fromList :: PartialOrd a => [a] -> Favorites a
+fromList = List.foldl' (flip insert) empty
+
+-- | 'Favorites' forms a 'Monoid' under 'empty' and 'union.
+instance PartialOrd a => Semigroup (Favorites a) where
+  (<>) = union
+instance PartialOrd a => Monoid (Favorites a) where
+  mempty  = empty
+  mappend = (<>)
diff --git a/src/full/Agda/Utils/FileName.hs b/src/full/Agda/Utils/FileName.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/FileName.hs
@@ -0,0 +1,148 @@
+{-# LANGUAGE CPP                        #-}
+
+{-| Operations on file names. -}
+module Agda.Utils.FileName
+  ( AbsolutePath(AbsolutePath)
+  , filePath
+  , mkAbsolute
+  , absolute
+  , canonicalizeAbsolutePath
+  , sameFile
+  , doesFileExistCaseSensitive
+  , isNewerThan
+  , relativizeAbsolutePath
+  ) where
+
+import System.Directory
+import System.FilePath
+
+import Control.Applicative ( liftA2 )
+import Control.DeepSeq
+#ifdef mingw32_HOST_OS
+import Control.Exception   ( bracket )
+import System.Win32        ( findFirstFile, findClose, getFindDataFileName )
+#endif
+
+import Data.Function (on)
+import Data.Hashable       ( Hashable )
+import Data.Text           ( Text )
+import qualified Data.Text as Text
+
+import Agda.Utils.Monad
+
+import Agda.Utils.Impossible
+
+-- | Paths which are known to be absolute.
+--
+-- Note that the 'Eq' and 'Ord' instances do not check if different
+-- paths point to the same files or directories.
+
+newtype AbsolutePath = AbsolutePath { textPath :: Text }
+  deriving (Show, Eq, Ord, Hashable, NFData)
+
+-- | Extract the 'AbsolutePath' to be used as 'FilePath'.
+filePath :: AbsolutePath -> FilePath
+filePath = Text.unpack . textPath
+
+-- | Constructs 'AbsolutePath's.
+--
+-- Precondition: The path must be absolute and valid.
+
+mkAbsolute :: FilePath -> AbsolutePath
+mkAbsolute f
+  | isAbsolute f =
+      AbsolutePath $ Text.pack $ dropTrailingPathSeparator $ normalise f
+        -- normalize does not resolve symlinks
+  | otherwise    = __IMPOSSIBLE__
+
+-- UNUSED Liang-Ting Chen 2019-07-16
+---- | maps @/bla/bla/bla/foo.bar.xxx@ to @foo.bar@.
+--rootName :: AbsolutePath -> String
+--rootName = dropExtension . snd . splitFileName . filePath
+
+-- | Makes the path absolute.
+--
+-- This function may raise an @\_\_IMPOSSIBLE\_\_@ error if
+-- 'canonicalizePath' does not return an absolute path.
+
+absolute :: FilePath -> IO AbsolutePath
+absolute f = mkAbsolute <$> do
+  -- canonicalizePath sometimes truncates paths pointing to
+  -- non-existing files/directories.
+  ex <- doesFileExist f `or2M` doesDirectoryExist f
+  if ex then do
+    -- Andreas, 2020-08-11, issue #4828
+    -- Do not use @canonicalizePath@ on the full path as it resolves symlinks,
+    -- which leads to wrong placement of the .agdai file.
+    dir <- canonicalizePath (takeDirectory f)
+    return (dir </> takeFileName f)
+   else do
+    cwd <- getCurrentDirectory
+    return (cwd </> f)
+
+-- | Resolve symlinks etc.  Preserves 'sameFile'.
+
+canonicalizeAbsolutePath :: AbsolutePath -> IO AbsolutePath
+canonicalizeAbsolutePath (AbsolutePath f) =
+  AbsolutePath . Text.pack <$> canonicalizePath (Text.unpack f)
+
+-- | Tries to establish if the two file paths point to the same file
+-- (or directory). False negatives may be returned.
+
+sameFile :: AbsolutePath -> AbsolutePath -> IO Bool
+sameFile = liftA2 equalFilePath `on` (canonicalizePath . filePath)
+
+-- | Case-sensitive 'doesFileExist' for Windows.
+--
+-- This is case-sensitive only on the file name part, not on the directory part.
+-- (Ideally, path components coming from module name components should be
+--  checked case-sensitively and the other path components should be checked
+--  case insensitively.)
+
+doesFileExistCaseSensitive :: FilePath -> IO Bool
+#ifdef mingw32_HOST_OS
+doesFileExistCaseSensitive f = do
+  doesFileExist f `and2M` do
+    bracket (findFirstFile f) (findClose . fst) $
+      fmap (takeFileName f ==) . getFindDataFileName . snd
+#else
+doesFileExistCaseSensitive = doesFileExist
+#endif
+
+-- | True if the first file is newer than the second file. If a file doesn't
+-- exist it is considered to be infinitely old.
+isNewerThan :: FilePath -> FilePath -> IO Bool
+isNewerThan new old = do
+    newExist <- doesFileExist new
+    oldExist <- doesFileExist old
+    if not (newExist && oldExist)
+        then return newExist
+        else do
+            newT <- getModificationTime new
+            oldT <- getModificationTime old
+            return $ newT >= oldT
+
+-- | A partial version of 'System.FilePath.makeRelative' with flipped arguments,
+--   returning 'Nothing' if the given path cannot be relativized to the given @root@.
+relativizeAbsolutePath ::
+     AbsolutePath
+       -- ^ The absolute path we see to relativize.
+  -> AbsolutePath
+       -- ^ The root for relativization.
+  -> Maybe FilePath
+       -- ^ The relative path, if any.
+relativizeAbsolutePath apath aroot
+  | rest /= path = Just rest
+  | otherwise    = Nothing
+  where
+  path = filePath apath
+  root = filePath aroot
+  rest = makeRelative root path
+    -- Andreas, 2022-10-10
+    -- See https://gitlab.haskell.org/haskell/filepath/-/issues/130.
+    -- 'System.FilePath.makeRelative' is strangely enough a total function,
+    -- and it returns the original @path@ if it could not be relativized to
+    -- the @root@, or if the @root@ was ".".
+    -- In our case, the @root@ is absolute, so we should expect @rest@ to
+    -- always be different from @path@ if @path@ is relative to @root@.
+    -- In the extreme case, @root = "/"@ and @path == "/" ++ rest@.
diff --git a/src/full/Agda/Utils/Float.hs b/src/full/Agda/Utils/Float.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Float.hs
@@ -0,0 +1,311 @@
+
+-- | Logically consistent comparison of floating point numbers.
+
+module Agda.Utils.Float
+  ( asFinite
+  , isPosInf
+  , isNegInf
+  , isPosZero
+  , isNegZero
+  , isSafeInteger
+  , doubleEq
+  , doubleLe
+  , doubleLt
+  , intToDouble
+  , doublePlus
+  , doubleMinus
+  , doubleTimes
+  , doubleNegate
+  , doubleDiv
+  , doublePow
+  , doubleSqrt
+  , doubleExp
+  , doubleLog
+  , doubleSin
+  , doubleCos
+  , doubleTan
+  , doubleASin
+  , doubleACos
+  , doubleATan
+  , doubleATan2
+  , doubleSinh
+  , doubleCosh
+  , doubleTanh
+  , doubleASinh
+  , doubleACosh
+  , doubleATanh
+  , doubleRound
+  , doubleFloor
+  , doubleCeiling
+  , doubleDenotEq
+  , doubleDenotOrd
+  , doubleToWord64
+  , doubleToRatio
+  , ratioToDouble
+  , doubleDecode
+  , doubleEncode
+  , toStringWithoutDotZero
+  ) where
+
+import Data.Bifunctor   ( second )
+import Data.Function    ( on )
+import Data.Maybe       ( fromMaybe )
+import Data.Ratio       ( (%), numerator, denominator )
+import Data.Word        ( Word64 )
+
+import Agda.Utils.List  ( stripSuffix )
+
+import GHC.Float (castDoubleToWord64, castWord64ToDouble)
+
+
+{-# INLINE doubleEq #-}
+doubleEq :: Double -> Double -> Bool
+doubleEq = (==)
+
+{-# INLINE doubleLe #-}
+doubleLe :: Double -> Double -> Bool
+doubleLe = (<=)
+
+{-# INLINE doubleLt #-}
+doubleLt :: Double -> Double -> Bool
+doubleLt = (<)
+
+truncateDouble :: Double -> Double
+truncateDouble = castWord64ToDouble . castDoubleToWord64
+
+{-# INLINE intToDouble #-}
+intToDouble :: Integral a => a -> Double
+intToDouble = truncateDouble . fromIntegral
+
+{-# INLINE doublePlus #-}
+doublePlus :: Double -> Double -> Double
+doublePlus x y = truncateDouble (x + y)
+
+{-# INLINE doubleMinus #-}
+doubleMinus :: Double -> Double -> Double
+doubleMinus x y = truncateDouble (x - y)
+
+{-# INLINE doubleTimes #-}
+doubleTimes :: Double -> Double -> Double
+doubleTimes x y = truncateDouble (x * y)
+
+{-# INLINE doubleNegate #-}
+doubleNegate :: Double -> Double
+doubleNegate = negate -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleDiv #-}
+doubleDiv :: Double -> Double -> Double
+doubleDiv = (/) -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doublePow #-}
+doublePow :: Double -> Double -> Double
+doublePow x y = truncateDouble (x ** y)
+
+{-# INLINE doubleSqrt #-}
+doubleSqrt :: Double -> Double
+doubleSqrt = sqrt -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleExp #-}
+doubleExp :: Double -> Double
+doubleExp x = truncateDouble (exp x)
+
+{-# INLINE doubleLog #-}
+doubleLog :: Double -> Double
+doubleLog = log -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleSin #-}
+doubleSin :: Double -> Double
+doubleSin = sin -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleCos #-}
+doubleCos :: Double -> Double
+doubleCos = cos -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleTan #-}
+doubleTan :: Double -> Double
+doubleTan = tan -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleASin #-}
+doubleASin :: Double -> Double
+doubleASin = asin -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleACos #-}
+doubleACos :: Double -> Double
+doubleACos = acos -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATan #-}
+doubleATan :: Double -> Double
+doubleATan = atan -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATan2 #-}
+doubleATan2 :: Double -> Double -> Double
+doubleATan2 = atan2 -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleSinh #-}
+doubleSinh :: Double -> Double
+doubleSinh = sinh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleCosh #-}
+doubleCosh :: Double -> Double
+doubleCosh = cosh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleTanh #-}
+doubleTanh :: Double -> Double
+doubleTanh = tanh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleASinh #-}
+doubleASinh :: Double -> Double
+doubleASinh = asinh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleACosh #-}
+doubleACosh :: Double -> Double
+doubleACosh = acosh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE doubleATanh #-}
+doubleATanh :: Double -> Double
+doubleATanh = atanh -- NOTE: doesn't cause underflow/overflow
+
+{-# INLINE negativeZero #-}
+negativeZero :: Double
+negativeZero = -0.0
+
+positiveInfinity :: Double
+positiveInfinity = 1.0 / 0.0
+
+negativeInfinity :: Double
+negativeInfinity = -positiveInfinity
+
+nan :: Double
+nan = 0.0 / 0.0
+
+isPosInf :: Double -> Bool
+isPosInf x = x > 0.0 && isInfinite x
+
+isNegInf :: Double -> Bool
+isNegInf x = x < 0.0 && isInfinite x
+
+isPosZero :: Double -> Bool
+isPosZero x = doubleDenotEq x 0.0
+
+isNegZero :: Double -> Bool
+isNegZero x = doubleDenotEq x (-0.0)
+
+doubleRound :: Double -> Maybe Integer
+doubleRound = fmap round . asFinite
+
+doubleFloor :: Double -> Maybe Integer
+doubleFloor = fmap floor . asFinite
+
+doubleCeiling :: Double -> Maybe Integer
+doubleCeiling = fmap ceiling . asFinite
+
+normaliseNaN :: Double -> Double
+normaliseNaN x
+  | isNaN x   = nan
+  | otherwise = x
+
+doubleToWord64 :: Double -> Maybe Word64
+doubleToWord64 x
+  | isNaN x   = Nothing
+  | otherwise = Just (castDoubleToWord64 x)
+
+-- |Denotational equality for floating point numbers, checks bitwise equality.
+--
+--  NOTE: Denotational equality distinguishes NaNs, so its results may vary
+--        depending on the architecture and compilation flags. Unfortunately,
+--        this is a problem with floating-point numbers in general.
+--
+doubleDenotEq :: Double -> Double -> Bool
+doubleDenotEq = (==) `on` doubleToWord64
+
+-- |I guess "denotational orderings" are now a thing? The point is that we need
+--  an Ord instance which provides a total ordering, and is consistent with the
+--  denotational equality.
+--
+--  NOTE: The ordering induced via `doubleToWord64` is total, and is consistent
+--        with `doubleDenotEq`. However, it is *deeply* unintuitive. For one, it
+--        considers all negative numbers to be larger than positive numbers.
+--
+doubleDenotOrd :: Double -> Double -> Ordering
+doubleDenotOrd = compare `on` doubleToWord64
+
+-- |Return Just x if it's a finite number, otherwise return Nothing.
+asFinite :: Double -> Maybe Double
+asFinite x
+  | isNaN      x = Nothing
+  | isInfinite x = Nothing
+  | otherwise    = Just x
+
+-- |Remove suffix @.0@ from printed floating point number.
+toStringWithoutDotZero :: Double -> String
+toStringWithoutDotZero d = fromMaybe s $ stripSuffix ".0" s
+  where s = show d
+
+-- |Decode a Double to an integer ratio.
+doubleToRatio :: Double -> (Integer, Integer)
+doubleToRatio x
+  | isNaN      x = (0, 0)
+  | isInfinite x = (signum (floor x), 0)
+  | otherwise    = let r = toRational x in (numerator r, denominator r)
+
+-- |Encode an integer ratio as a double.
+ratioToDouble :: Integer -> Integer -> Double
+ratioToDouble n d
+  | d == 0 = case compare n 0 of
+      LT -> negativeInfinity
+      EQ -> nan
+      GT -> positiveInfinity
+  | otherwise = fromRational (n % d)
+
+-- |Decode a Double to its mantissa and its exponent, normalised such that the
+--  mantissa is the smallest possible number without loss of accuracy.
+doubleDecode :: Double -> Maybe (Integer, Integer)
+doubleDecode x
+  | isNaN      x = Nothing
+  | isInfinite x = Nothing
+  | otherwise    = Just (uncurry normalise (second toInteger (decodeFloat x)))
+  where
+    normalise :: Integer -> Integer -> (Integer, Integer)
+    normalise mantissa exponent
+      | even mantissa = normalise (mantissa `div` 2) (exponent + 1)
+      | otherwise = (mantissa, exponent)
+
+-- |Checks whether or not the Double is within a safe range of operation.
+isSafeInteger :: Double -> Bool
+isSafeInteger x = case properFraction x of
+  (n, f) -> f == 0.0 && minMantissa <= n && n <= maxMantissa
+
+doubleRadix :: Integer
+doubleRadix = floatRadix (undefined :: Double)
+
+doubleDigits :: Int
+doubleDigits = floatDigits (undefined :: Double)
+
+doubleRange :: (Int, Int)
+doubleRange = floatRange (undefined :: Double)
+
+-- |The smallest representable mantissa. Simultaneously, the smallest integer which can be
+--  represented as a Double without loss of precision.
+minMantissa :: Integer
+minMantissa = - maxMantissa
+
+-- |The largest representable mantissa. Simultaneously, the largest integer which can be
+--  represented as a Double without loss of precision.
+maxMantissa :: Integer
+maxMantissa = (doubleRadix ^ toInteger doubleDigits) - 1
+
+-- |The largest representable exponent.
+minExponent :: Integer
+minExponent = toInteger $ (fst doubleRange - doubleDigits) - 1
+
+-- |The smallest representable exponent.
+maxExponent :: Integer
+maxExponent = toInteger $ snd doubleRange - doubleDigits
+
+-- |Encode a mantissa and an exponent as a Double.
+doubleEncode :: Integer -> Integer -> Maybe Double
+doubleEncode mantissa exponent
+  = if minMantissa <= mantissa && mantissa <= maxMantissa &&
+       minExponent <= exponent && exponent <= maxExponent
+    then Just (encodeFloat mantissa (fromInteger exponent))
+    else Nothing
diff --git a/src/full/Agda/Utils/Function.hs b/src/full/Agda/Utils/Function.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Function.hs
@@ -0,0 +1,146 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE RebindableSyntax #-}
+
+module Agda.Utils.Function where
+
+import Prelude hiding ( not, (&&), (||) )
+import Data.String    ( fromString )       -- for RebindableSyntax, somehow not covered by Prelude
+
+import Agda.Utils.Boolean
+
+-- | Repeat a state transition @f :: a -> (b, a)@ with output @b@
+--   while condition @cond@ on the output is true.
+--   Return all intermediate results and the final result
+--   where @cond@ is @False@.
+--
+--   Postconditions (when it terminates):
+--   @fst (last (iterWhile cond f a)) == False@.
+--   @all fst (init (interWhile cond f a))@.
+
+iterWhile :: (b -> Bool) -> (a -> (b, a)) -> a -> [(b,a)]
+iterWhile cond f = loop where
+  loop a = r : if cond b then loop a' else []
+    where r@(b, a') = f a
+
+-- | Repeat something while a condition on some state is true.
+--   Return the last state (including the changes of the last
+--   transition, even if the condition became false then).
+
+repeatWhile :: (a -> (Bool, a)) -> a -> a
+repeatWhile f = loop where
+  loop a = if again then loop a' else a'
+    where (again, a') = f a
+
+-- | Monadic version of 'repeatWhile'.
+repeatWhileM :: (Monad m) => (a -> m (Bool, a)) -> a -> m a
+repeatWhileM f = loop where
+  loop a = do
+    (again, a') <- f a
+    if again then loop a' else return a'
+
+-- | A version of the trampoline function.
+--
+--   The usual function iterates @f :: a -> Maybe a@ as long
+--   as @Just{}@ is returned, and returns the last value of @a@
+--   upon @Nothing@.
+--
+--   @usualTrampoline f = trampolineWhile $ \ a -> maybe (False,a) (True,) (f a)@.
+--
+--   @trampolineWhile@ is very similar to @repeatWhile@, only that
+--   it discards the state on which the condition went @False@,
+--   and returns the last state on which the condition was @True@.
+trampolineWhile :: (a -> (Bool, a)) -> a -> a
+trampolineWhile f = repeatWhile $ \ a ->
+  let (again, a') = f a
+  in (again,) $ if again then a' else a
+
+-- | Monadic version of 'trampolineWhile'.
+trampolineWhileM :: (Monad m) => (a -> m (Bool, a)) -> a -> m a
+trampolineWhileM f = repeatWhileM $ \ a -> do
+  (again, a') <- f a
+  return $ (again,) $ if again then a' else a
+
+-- | More general trampoline, which allows some final computation
+--   from iteration state @a@ into result type @b@.
+trampoline :: (a -> Either b a) -> a -> b
+trampoline f = loop where
+  loop a = either id loop $ f a
+
+-- | Monadic version of 'trampoline'.
+trampolineM :: Monad m => (a -> m (Either b a)) -> a -> m b
+trampolineM f = loop where
+  loop a = either return loop =<< f a
+
+-- | Iteration to fixed-point.
+--
+--   @iterateUntil r f a0@ iterates endofunction @f@, starting with @a0@,
+--   until @r@ relates its result to its input, i.e., @f a `r` a@.
+--
+--   This is the generic pattern behind saturation algorithms.
+--
+--   If @f@ is monotone with regard to @r@,
+--   meaning @a `r` b@ implies @f a `r` f b@,
+--   and @f@-chains starting with @a0@ are finite
+--   then iteration is guaranteed to terminate.
+--
+--   A typical instance will work on sets, and @r@ could be set inclusion,
+--   and @a0@ the empty set, and @f@ the step function of a saturation algorithm.
+iterateUntil :: (a -> a -> Bool) -> (a -> a) -> a -> a
+iterateUntil r f = loop where
+  loop a = if r a' a then a' else loop a'
+    where a' = f a
+
+-- | Monadic version of 'iterateUntil'.
+iterateUntilM :: Monad m => (a -> a -> Bool) -> (a -> m a) -> a -> m a
+iterateUntilM r f = loop where
+  loop a = do
+    a' <- f a
+    if r a' a then return a' else loop a'
+
+-- | @'iterate'' n f x@ applies @f@ to @x@ @n@ times and returns the
+-- result.
+--
+-- The applications are calculated strictly.
+
+iterate' :: Integral i => i -> (a -> a) -> a -> a
+iterate' 0 _ x             = x
+iterate' n f x | n > 0     = iterate' (n - 1) f $! f x
+               | otherwise = error "iterate': Negative input."
+
+-- * Iteration over Booleans.
+
+-- | @applyWhen b f a@ applies @f@ to @a@ when @b@.
+{-# SPECIALIZE applyWhen :: Bool -> (a -> a) -> (a -> a) #-}
+{-# INLINE applyWhen #-}
+applyWhen :: IsBool b => b -> (a -> a) -> a -> a
+applyWhen b f = if b then f else id
+  -- Note: RebindableSyntax translates this if-then-else to ifThenElse of IsBool.
+
+-- | @applyUnless b f a@ applies @f@ to @a@ unless @b@.
+{-# SPECIALIZE applyUnless :: Bool -> (a -> a) -> (a -> a) #-}
+{-# INLINE applyUnless #-}
+applyUnless :: IsBool b => b -> (a -> a) -> a -> a
+applyUnless b f = if b then id else f
+
+-- | Monadic version of @applyWhen@
+{-# SPECIALIZE applyWhenM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a #-}
+{-# INLINE applyWhenM #-}
+applyWhenM :: (IsBool b, Monad m) => m b -> (m a -> m a) -> m a -> m a
+applyWhenM mb f x = mb >>= \ b -> applyWhen b f x
+
+-- | Monadic version of @applyUnless@
+{-# SPECIALIZE applyUnlessM :: Monad m => m Bool -> (m a -> m a) -> m a -> m a #-}
+{-# INLINE applyUnlessM #-}
+applyUnlessM :: (IsBool b, Monad m) => m b -> (m a -> m a) -> m a -> m a
+applyUnlessM mb f x = mb >>= \ b -> applyUnless b f x
+
+-- | 'Maybe' version of 'applyWhen'.
+{-# INLINE applyWhenJust #-}
+applyWhenJust :: Maybe b -> (b -> a -> a) -> a -> a
+applyWhenJust m f = maybe id f m
+
+-- | 'Maybe' version of 'applyUnless'.
+{-# INLINE applyWhenNothing #-}
+applyWhenNothing :: Maybe b -> (a -> a) -> a -> a
+applyWhenNothing m f = maybe f (const id) m
diff --git a/src/full/Agda/Utils/Functor.hs b/src/full/Agda/Utils/Functor.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Functor.hs
@@ -0,0 +1,82 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Utilities for functors.
+
+module Agda.Utils.Functor
+  ( (<.>)
+  , for
+  , Decoration(traverseF, distributeF)
+  , dmap
+  , dget
+  -- From Data.Functor:
+  , (<$>)
+  , ($>)
+  , (<&>)
+  )
+  where
+
+import Control.Applicative ( Const(Const), getConst )
+
+import Data.Functor (($>), (<&>))
+import Data.Functor.Identity
+import Data.Functor.Compose
+
+
+infixr 9 <.>
+
+-- | Composition: pure function after functorial (monadic) function.
+(<.>) :: Functor m => (b -> c) -> (a -> m b) -> a -> m c
+(f <.> g) a = f <$> g a
+
+-- | The true pure @for@ loop.
+--   'Data.Traversable.for' is a misnomer, it should be @forA@.
+for :: Functor m => m a -> (a -> b) -> m b
+for a b = fmap b a
+{-# INLINE for #-}
+
+-- | A decoration is a functor that is traversable into any functor.
+--
+--   The 'Functor' superclass is given because of the limitations
+--   of the Haskell class system.
+--   @traverseF@ actually implies functoriality.
+--
+--   Minimal complete definition: @traverseF@ or @distributeF@.
+class Functor t => Decoration t where
+
+  -- | @traverseF@ is the defining property.
+  traverseF :: Functor m => (a -> m b) -> t a -> m (t b)
+  traverseF f = distributeF . fmap f
+
+  -- | Decorations commute into any functor.
+  distributeF :: (Functor m) => t (m a) -> m (t a)
+  distributeF = traverseF id
+
+-- | Any decoration is traversable with @traverse = traverseF@.
+--   Just like any 'Traversable' is a functor, so is
+--   any decoration, given by just @traverseF@, a functor.
+dmap :: Decoration t => (a -> b) -> t a -> t b
+dmap f = runIdentity . traverseF (Identity . f)
+
+-- | Any decoration is a lens.  @set@ is a special case of @dmap@.
+dget :: Decoration t => t a -> a
+dget = getConst . traverseF Const
+
+-- | The identity functor is a decoration.
+instance Decoration Identity where
+  traverseF f (Identity x) = Identity <$> f x
+
+-- | Decorations compose.  (Thus, they form a category.)
+instance (Decoration d, Decoration t) => Decoration (Compose d t) where
+  -- traverseF . traverseF :: Functor m => (a -> m b) -> d (t a) -> m (d (t a))
+  traverseF f (Compose x) = Compose <$> traverseF (traverseF f) x
+
+-- Not a decoration are:
+--
+-- * The constant functor.
+-- * Maybe.  Can only be traversed into pointed functors.
+-- * Other disjoint sum types, like lists etc.
+--   (Can only be traversed into Applicative.)
+
+-- | A typical decoration is pairing with some stuff.
+instance Decoration ((,) a) where
+  traverseF f (a, x) = (a,) <$> f x
diff --git a/src/full/Agda/Utils/Graph/AdjacencyMap/Unidirectional.hs b/src/full/Agda/Utils/Graph/AdjacencyMap/Unidirectional.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Graph/AdjacencyMap/Unidirectional.hs
@@ -0,0 +1,1094 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Directed graphs (can of course simulate undirected graphs).
+--
+--   Represented as adjacency maps in direction from source to target.
+--
+--   Each source node maps to an adjacency map of outgoing edges,
+--   which is a map from target nodes to edges.
+--
+--   Listed time complexities are for the worst case (and possibly
+--   amortised), with /n/ standing for the number of nodes in the
+--   graph and /e/ standing for the number of edges. Comparisons,
+--   predicates etc. are assumed to take constant time (unless
+--   otherwise stated).
+
+module Agda.Utils.Graph.AdjacencyMap.Unidirectional
+  ( -- * Graphs and edges
+    Graph(..)
+  , invariant
+  , Edge(..)
+    -- * Queries
+  , lookup
+  , edges
+  , neighbours, neighboursMap
+  , edgesFrom
+  , edgesTo
+  , diagonal
+  , nodes, sourceNodes, targetNodes, isolatedNodes
+  , Nodes(..), computeNodes
+  , discrete
+  , acyclic
+    -- * Construction
+  , fromNodes, fromNodeSet
+  , fromEdges, fromEdgesWith
+  , empty
+  , singleton
+  , insert, insertWith
+  , insertEdge, insertEdgeWith
+  , union, unionWith
+  , unions, unionsWith
+    -- * Transformation
+  , mapWithEdge
+  , transposeEdge, transpose
+  , clean
+  , removeNode, removeNodes
+  , removeEdge
+  , filterNodes
+  , filterEdges
+  , filterNodesKeepingEdges
+  , renameNodes, renameNodesMonotonic
+  , WithUniqueInt(..), addUniqueInts
+  , unzip
+  , composeWith
+    -- * Strongly connected components
+  , sccs'
+  , sccs
+  , DAG(..)
+  , dagInvariant
+  , oppositeDAG
+  , reachable
+  , sccDAG'
+  , sccDAG
+    -- * Reachability
+  , reachableFrom, reachableFromSet
+  , walkSatisfying
+  , longestPaths
+    -- * Transitive closure
+  , gaussJordanFloydWarshallMcNaughtonYamada
+  , gaussJordanFloydWarshallMcNaughtonYamadaReference
+  , transitiveClosure
+  , transitiveReduction
+  , complete, completeIter
+  )
+  where
+
+import Prelude hiding ( lookup, null, unzip )
+
+
+
+
+import qualified Data.Array.IArray as Array
+import Data.Sequence (Seq)
+import qualified Data.Sequence as Seq
+import Data.Function (on)
+import qualified Data.Graph as Graph
+import Data.IntMap.Strict (IntMap)
+import qualified Data.IntMap.Strict as IntMap
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import qualified Data.Map.Strict as Map
+import Data.Map.Strict (Map)
+import Data.Foldable (toList)
+
+import Data.Maybe (maybeToList, fromMaybe)
+import qualified Data.Set as Set
+import Data.Set (Set)
+import qualified Data.Tree as Tree
+
+import Agda.Utils.Function
+
+import Agda.Utils.Null (Null(null))
+import qualified Agda.Utils.Null as Null
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.SemiRing
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+import Agda.Utils.Functor
+
+------------------------------------------------------------------------
+-- Graphs and edges
+
+-- | @Graph n e@ is a type of directed graphs with nodes in @n@ and
+--   edges in @e@.
+--
+--   At most one edge is allowed between any two nodes. Multigraphs
+--   can be simulated by letting the edge type @e@ be a collection
+--   type.
+--
+--   The graphs are represented as adjacency maps (adjacency lists,
+--   but using finite maps instead of arrays and lists). This makes it
+--   possible to compute a node's outgoing edges in logarithmic time
+--   (/O(log n)/). However, computing the incoming edges may be more
+--   expensive.
+--
+--   Note that neither the number of nodes nor the number of edges may
+--   exceed @'maxBound' :: 'Int'@.
+
+newtype Graph n e = Graph
+  { graph :: Map n (Map n e) -- ^ Forward edges.
+  }
+  deriving Eq
+
+-- The Functor instance for strict maps is the one for lazy maps, so a
+-- custom Functor instance using strict map functions is used here.
+
+instance Functor (Graph n) where
+  fmap f = Graph . Map.map (Map.map f) . graph
+
+-- | Internal invariant.
+
+invariant :: Ord n => Graph n e -> Bool
+invariant g =
+  -- Every target node must be present in the graph as a source node,
+  -- possibly without outgoing edges.
+  Set.isSubsetOf (targetNodes g) (nodes g)
+
+instance (Ord n, Pretty n, Pretty e) => Pretty (Graph n e) where
+  pretty g = vcat (concatMap pretty' (Set.toAscList (nodes g)))
+    where
+    pretty' n = case edgesFrom g [n] of
+      [] -> [pretty n]
+      es -> map pretty es
+
+instance (Ord n, Show n, Show e) => Show (Graph n e) where
+  showsPrec _ g =
+    showString "union (fromEdges " .
+    shows (edges g) .
+    showString ") (fromNodes " .
+    shows (Set.toList (isolatedNodes g)) .
+    showString ")"
+
+-- | Edges.
+
+data Edge n e = Edge
+  { source :: n  -- ^ Outgoing node.
+  , target :: n  -- ^ Incoming node.
+  , label  :: e  -- ^ Edge label (weight).
+  } deriving (Eq, Ord, Functor, Show)
+
+instance (Pretty n, Pretty e) => Pretty (Edge n e) where
+  pretty (Edge s t e) =
+    pretty s <+> ("--(" <> pretty e <> ")-->") <+> pretty t
+
+------------------------------------------------------------------------
+-- Queries
+
+-- | If there is an edge from @s@ to @t@, then @lookup s t g@ is
+-- @'Just' e@, where @e@ is the edge's label. /O(log n)/.
+
+lookup :: Ord n => n -> n -> Graph n e -> Maybe e
+lookup s t (Graph g) = Map.lookup t =<< Map.lookup s g
+
+-- | The graph's edges. /O(n + e)/.
+
+edges :: Graph n e -> [Edge n e]
+edges (Graph g) =
+  [ Edge s t e
+  | (s, tes) <- Map.assocs g
+  , (t, e)   <- Map.assocs tes
+  ]
+
+-- | @neighbours u g@ consists of all nodes @v@ for which there is an
+-- edge from @u@ to @v@ in @g@, along with the corresponding edge
+-- labels. /O(log n + |@neighbours u g@|)/.
+
+neighbours :: Ord n => n -> Graph n e -> [(n, e)]
+neighbours s = Map.toList . neighboursMap s
+
+-- | @neighboursMap u g@ consists of all nodes @v@ for which there is
+-- an edge from @u@ to @v@ in @g@, along with the corresponding edge
+-- labels. /O(log n)/.
+
+neighboursMap :: Ord n => n -> Graph n e -> Map n e
+neighboursMap s (Graph g) = fromMaybe Map.empty $ Map.lookup s g
+
+-- | @edgesFrom g ns@ is a list containing all edges originating in
+-- the given nodes (i.e., all outgoing edges for the given nodes). If
+-- @ns@ does not contain duplicates, then the resulting list does not
+-- contain duplicates. /O(|@ns@| log |@n@| + |@edgesFrom g ns@|)/.
+
+edgesFrom :: Ord n => Graph n e -> [n] -> [Edge n e]
+edgesFrom (Graph g) ss =
+  [ Edge s t e
+  | s <- ss
+  , m <- maybeToList $ Map.lookup s g
+  , (t, e) <- Map.assocs m
+  ]
+
+-- | @edgesTo g ns@ is a list containing all edges ending in the given
+-- nodes (i.e., all incoming edges for the given nodes). If @ns@ does
+-- not contain duplicates, then the resulting list does not contain
+-- duplicates. /O(|@ns@| n log n)/.
+
+edgesTo :: Ord n => Graph n e -> [n] -> [Edge n e]
+edgesTo (Graph g) ts =
+  [ Edge s t e
+  | (s, m) <- Map.assocs g
+  , t <- ts
+  , e <- maybeToList $ Map.lookup t m
+  ]
+
+-- | All self-loops. /O(n log n)/.
+
+diagonal :: Ord n => Graph n e -> [Edge n e]
+diagonal (Graph g) =
+  [ Edge s s e
+  | (s, m) <- Map.assocs g
+  , e      <- maybeToList $ Map.lookup s m
+  ]
+
+-- | All nodes. /O(n)/.
+
+nodes :: Graph n e -> Set n
+nodes = Map.keysSet . graph
+
+-- | Nodes with outgoing edges. /O(n)/.
+
+sourceNodes :: Graph n e -> Set n
+sourceNodes = Map.keysSet . Map.filter (not . Map.null) . graph
+
+-- | Nodes with incoming edges. /O(n + e log n)/.
+
+targetNodes :: Ord n => Graph n e -> Set n
+targetNodes = Set.fromList . map target . edges
+
+-- | Various kinds of nodes.
+
+data Nodes n = Nodes
+  { srcNodes :: Set n
+    -- ^ Nodes with outgoing edges.
+  , tgtNodes :: Set n
+    -- ^ Nodes with incoming edges.
+  , allNodes :: Set n
+    -- ^ All nodes, with or without edges.
+  }
+
+-- | Constructs a 'Nodes' structure. /O(n + e log n)/.
+
+computeNodes :: Ord n => Graph n e -> Nodes n
+computeNodes g =
+  Nodes { srcNodes = Set.filter (not . null . flip neighbours g) ns
+        , tgtNodes = targetNodes g
+        , allNodes = ns
+        }
+  where
+  ns = nodes g
+
+-- | Nodes without incoming or outgoing edges. /O(n + e log n)/.
+
+isolatedNodes :: Ord n => Graph n e -> Set n
+isolatedNodes g =
+  Set.difference (allNodes ns) (Set.union (srcNodes ns) (tgtNodes ns))
+  where
+  ns = computeNodes g
+
+-- | Checks whether the graph is discrete (containing no edges other
+-- than 'null' edges). /O(n + e)/.
+
+discrete :: Null e => Graph n e -> Bool
+discrete = all' (all' null) . graph
+  where all' p = List.all p . Map.elems
+
+-- | Returns @True@ iff the graph is acyclic.
+
+acyclic :: Ord n => Graph n e -> Bool
+acyclic = all isAcyclic . sccs'
+  where
+  isAcyclic Graph.AcyclicSCC{} = True
+  isAcyclic Graph.CyclicSCC{}  = False
+
+------------------------------------------------------------------------
+-- Construction
+
+-- | Constructs a completely disconnected graph containing the given
+--   nodes. /O(n log n)/.
+
+fromNodes :: Ord n => [n] -> Graph n e
+fromNodes ns = Graph $ Map.fromList $ map (, Map.empty) ns
+
+-- | Constructs a completely disconnected graph containing the given
+--   nodes. /O(n)/.
+
+fromNodeSet :: Ord n => Set n -> Graph n e
+fromNodeSet ns = Graph $ Map.fromSet (\_ -> Map.empty) ns
+
+-- | @fromEdges es@ is a graph containing the edges in @es@, with the
+-- caveat that later edges overwrite earlier edges. /O(|@es@| log n)/.
+
+fromEdges :: Ord n => [Edge n e] -> Graph n e
+fromEdges = fromEdgesWith $ \ new old -> new
+
+-- | @fromEdgesWith f es@ is a graph containing the edges in @es@.
+-- Later edges are combined with earlier edges using the supplied
+-- function. /O(|@es@| log n)/.
+
+fromEdgesWith :: Ord n => (e -> e -> e) -> [Edge n e] -> Graph n e
+fromEdgesWith f = List.foldl' (flip (insertEdgeWith f)) empty
+
+-- | Empty graph (no nodes, no edges). /O(1)/.
+
+empty :: Graph n e
+empty = Graph Map.empty
+
+-- | A graph with two nodes and a single connecting edge. /O(1)/.
+
+singleton :: Ord n => n -> n -> e -> Graph n e
+singleton s t e = insert s t e empty
+
+-- | Inserts an edge into the graph. /O(log n)/.
+
+insert :: Ord n => n -> n -> e -> Graph n e -> Graph n e
+insert = insertWith $ \ new old -> new
+
+-- | Inserts an edge into the graph. /O(log n)/.
+
+insertEdge :: Ord n => Edge n e -> Graph n e -> Graph n e
+insertEdge (Edge s t e) = insert s t e
+
+-- | @insertWith f s t new@ inserts an edge from @s@ to @t@ into the
+-- graph. If there is already an edge from @s@ to @t@ with label @old@,
+-- then this edge gets replaced by an edge with label @f new old@, and
+-- otherwise the edge's label is @new@. /O(log n)/.
+
+insertWith ::
+  Ord n => (e -> e -> e) -> n -> n -> e -> Graph n e -> Graph n e
+insertWith f s t e (Graph g) =
+  Graph (Map.alter (Just . insNode) t $ Map.alter (Just . insEdge) s g)
+  where
+  insEdge Nothing  = Map.singleton t e
+  insEdge (Just m) = Map.insertWith f t e m
+
+  insNode Nothing  = Map.empty
+  insNode (Just m) = m
+
+-- | A variant of 'insertWith'. /O(log n)/.
+
+insertEdgeWith ::
+  Ord n => (e -> e -> e) -> Edge n e -> Graph n e -> Graph n e
+insertEdgeWith f (Edge s t e) = insertWith f s t e
+
+-- | Left-biased union.
+--
+-- Time complexity: See 'unionWith'.
+
+union :: Ord n => Graph n e -> Graph n e -> Graph n e
+union = unionWith $ \ left right -> left
+
+-- | Union. The function is used to combine edge labels for edges that
+-- occur in both graphs (labels from the first graph are given as the
+-- first argument to the function).
+--
+-- Time complexity: /O(n₁ log (n₂/n₁ + 1) + e₁ log e₂)/, where /n₁/ is
+-- the number of nodes in the graph with the smallest number of nodes
+-- and /n₂/ is the number of nodes in the other graph, and /e₁/ is the
+-- number of edges in the graph with the smallest number of edges and
+-- /e₂/ is the number of edges in the other graph.
+--
+-- Less complicated time complexity: /O((n + e) log n/ (where /n/ and
+-- /e/ refer to the resulting graph).
+
+unionWith ::
+  Ord n => (e -> e -> e) -> Graph n e -> Graph n e -> Graph n e
+unionWith f (Graph g) (Graph g') =
+  Graph $ Map.unionWith (Map.unionWith f) g g'
+
+-- | Union. /O((n + e) log n/ (where /n/ and /e/ refer to the
+-- resulting graph).
+
+unions :: Ord n => [Graph n e] -> Graph n e
+unions = unionsWith $ \ left right -> left
+
+-- | Union. The function is used to combine edge labels for edges that
+-- occur in several graphs. /O((n + e) log n/ (where /n/ and /e/ refer
+-- to the resulting graph).
+
+unionsWith :: Ord n => (e -> e -> e) -> [Graph n e] -> Graph n e
+unionsWith f = List.foldl' (unionWith f) empty
+
+------------------------------------------------------------------------
+-- Transformation
+
+-- | A variant of 'fmap' that provides extra information to the
+-- function argument. /O(n + e)/.
+
+mapWithEdge :: (Edge n e -> e') -> Graph n e -> Graph n e'
+mapWithEdge f (Graph g) = Graph $ flip Map.mapWithKey g $ \ s m ->
+  flip Map.mapWithKey m $ \ t e -> f (Edge s t e)
+
+-- | Reverses an edge. /O(1)/.
+
+transposeEdge :: Edge n e -> Edge n e
+transposeEdge (Edge s t e) = Edge t s e
+
+-- | The opposite graph (with all edges reversed). /O((n + e) log n)/.
+
+transpose :: Ord n => Graph n e -> Graph n e
+transpose g =
+  fromEdges (map transposeEdge (edges g))
+    `union`
+  fromNodeSet (isolatedNodes g)
+
+-- | Removes 'null' edges. /O(n + e)/.
+
+clean :: Null e => Graph n e -> Graph n e
+clean = Graph . Map.map (Map.filter (not . null)) . graph
+
+-- | The graph @filterNodes p g@ contains exactly those nodes from @g@
+-- that satisfy the predicate @p@. Edges to or from nodes that are
+-- removed are also removed. /O(n + e)/.
+
+filterNodes :: Ord n => (n -> Bool) -> Graph n e -> Graph n e
+filterNodes p (Graph g) = Graph (Map.mapMaybeWithKey remSrc g)
+  where
+  remSrc s m
+    | p s       = Just (Map.filterWithKey (\t _ -> p t) m)
+    | otherwise = Nothing
+
+-- | @removeNodes ns g@ removes the nodes in @ns@ (and all
+-- corresponding edges) from @g@. /O((n + e) log |@ns@|)/.
+
+removeNodes :: Ord n => Set n -> Graph n e -> Graph n e
+removeNodes ns = filterNodes (\n -> not (Set.member n ns))
+
+-- | @removeNode n g@ removes the node @n@ (and all corresponding
+-- edges) from @g@. /O(n + e)/.
+
+removeNode :: Ord n => n -> Graph n e -> Graph n e
+removeNode = removeNodes . Set.singleton
+
+-- | @removeEdge s t g@ removes the edge going from @s@ to @t@, if any.
+--   /O(log n)/.
+
+removeEdge :: Ord n => n -> n -> Graph n e -> Graph n e
+removeEdge s t (Graph g) = Graph $ Map.adjust (Map.delete t) s g
+
+-- | Keep only the edges that satisfy the predicate. /O(n + e)/.
+
+filterEdges :: (Edge n e -> Bool) -> Graph n e -> Graph n e
+filterEdges f =
+  Graph .
+  Map.mapWithKey (\s ->
+    Map.filterWithKey (\t l ->
+      f (Edge { source = s, target = t, label = l }))) .
+  graph
+
+-- | Removes the nodes that do not satisfy the predicate from the
+-- graph, but keeps the edges: if there is a path in the original
+-- graph between two nodes that are retained, then there is a path
+-- between these two nodes also in the resulting graph.
+--
+-- Precondition: The graph must be acyclic.
+--
+-- Worst-case time complexity: /O(e n log n)/ (this has not been
+-- verified carefully).
+
+filterNodesKeepingEdges ::
+  forall n e. (Ord n, SemiRing e) =>
+  (n -> Bool) -> Graph n e -> Graph n e
+filterNodesKeepingEdges p g =
+  foldr (insertEdgeWith oplus) (filterNodes p g)
+    (fst edgesToAddAndRemove)
+  where
+  -- The new edges that should be added, and a map from nodes that
+  -- should be removed to edges that should potentially be added
+  -- (after being combined with paths into the nodes that should be
+  -- removed).
+  edgesToAddAndRemove :: ([Edge n e], Map n (Map n e))
+  edgesToAddAndRemove =
+    List.foldl' edgesToAddAndRemoveForSCC ([], Map.empty) (sccs' g)
+
+  edgesToAddAndRemoveForSCC (add, !remove) (Graph.AcyclicSCC n)
+    | p n =
+      ( (do (n', e) <- neighbours n g
+            case Map.lookup n' remove of
+              Nothing -> []
+              Just es ->
+                for (Map.toList es) $ \(n', e') -> Edge
+                  { source = n
+                  , target = n'
+                  , label  = e `otimes` e'
+                  })
+          ++
+        add
+      , remove
+      )
+    | otherwise =
+      ( add
+      , Map.insert
+          n
+          (Map.unionsWith oplus $
+           for (neighbours n g) $ \(n', e) ->
+             case Map.lookup n' remove of
+               Nothing -> Map.singleton n' e
+               Just es -> fmap (e `otimes`) es)
+          remove
+      )
+  edgesToAddAndRemoveForSCC _ (Graph.CyclicSCC{}) = __IMPOSSIBLE__
+
+-- | Renames the nodes.
+--
+-- Precondition: The renaming function must be injective.
+--
+-- Time complexity: /O((n + e) log n)/.
+
+renameNodes :: Ord n2 => (n1 -> n2) -> Graph n1 e -> Graph n2 e
+renameNodes ren =
+  Graph .
+  fmap (Map.mapKeys ren) .
+  Map.mapKeys ren .
+  graph
+
+-- | Renames the nodes.
+--
+-- Precondition: The renaming function @ren@ must be strictly
+-- increasing (if @x '<' y@ then @ren x '<' ren y@).
+--
+-- Time complexity: /O(n + e)/.
+
+renameNodesMonotonic ::
+  (Ord n1, Ord n2) => (n1 -> n2) -> Graph n1 e -> Graph n2 e
+renameNodesMonotonic ren =
+  Graph .
+  fmap (Map.mapKeysMonotonic ren) .
+  Map.mapKeysMonotonic ren .
+  graph
+
+-- | @WithUniqueInt n@ consists of pairs of (unique) 'Int's and values
+-- of type @n@.
+--
+-- Values of this type are compared by comparing the 'Int's.
+
+data WithUniqueInt n = WithUniqueInt
+  { uniqueInt  :: !Int
+  , otherValue :: !n
+  }
+  deriving (Show, Functor)
+
+instance Eq (WithUniqueInt n) where
+  WithUniqueInt i1 _ == WithUniqueInt i2 _ = i1 == i2
+
+instance Ord (WithUniqueInt n) where
+  compare (WithUniqueInt i1 _) (WithUniqueInt i2 _) = compare i1 i2
+
+instance Pretty n => Pretty (WithUniqueInt n) where
+  pretty (WithUniqueInt i n) =
+    parens ((pretty i <> comma) <+> pretty n)
+
+-- | Combines each node label with a unique 'Int'.
+--
+-- Precondition: The number of nodes in the graph must not be larger
+-- than @'maxBound' :: 'Int'@.
+--
+-- Time complexity: /O(n + e log n)/.
+
+addUniqueInts ::
+  forall n e. Ord n => Graph n e -> Graph (WithUniqueInt n) e
+addUniqueInts g =
+  Graph $
+  Map.fromDistinctAscList $
+  map (\(i, (n, m)) ->
+        (WithUniqueInt i n, Map.mapKeysMonotonic ren m)) $
+  zip [0..] $
+  Map.toAscList $
+  graph g
+  where
+  renaming :: Map n Int
+  renaming = snd $ Map.mapAccum (\i _ -> (succ i, i)) 0 (graph g)
+
+  ren :: n -> WithUniqueInt n
+  ren n = case Map.lookup n renaming of
+    Just i  -> WithUniqueInt i n
+    Nothing -> __IMPOSSIBLE__
+
+-- | Unzips the graph. /O(n + e)/.
+
+-- This is a naive implementation that uses fmap.
+
+unzip :: Graph n (e, e') -> (Graph n e, Graph n e')
+unzip g = (fst <$> g, snd <$> g)
+
+-- | @composeWith times plus g g'@ finds all edges
+--   @s --c_i--> t_i --d_i--> u@ and constructs the
+--   result graph from @edge(s,u) = sum_i (c_i times d_i)@.
+--
+--   Complexity:  For each edge @s --> t@ in @g@ we look up
+--   all edges starting with @t@ in @g'@.
+--
+--   Precondition: The two graphs must have exactly the same nodes.
+
+composeWith ::
+  Ord n =>
+  (c -> d -> e) -> (e -> e -> e) ->
+  Graph n c -> Graph n d -> Graph n e
+composeWith times plus (Graph g) (Graph g') = Graph (Map.map comp g)
+  where
+  comp m = Map.fromListWith plus
+    [ (u, c `times` d)
+    | (t, c) <- Map.assocs m
+    , m'     <- maybeToList (Map.lookup t g')
+    , (u, d) <- Map.assocs m'
+    ]
+
+------------------------------------------------------------------------
+-- Strongly connected components
+
+-- | The graph's strongly connected components, in reverse topological
+-- order.
+--
+-- The time complexity is likely /O(n + e log n)/ (but this depends on
+-- the, at the time of writing undocumented, time complexity of
+-- 'Graph.stronglyConnComp').
+
+sccs' :: Ord n => Graph n e -> [Graph.SCC n]
+sccs' g =
+  Graph.stronglyConnComp
+    [ (n, n, Map.keys es)
+    | (n, es) <- Map.toAscList (graph g)
+    ]
+    -- Graph.stronglyConnComp sorts this list, and the sorting
+    -- algorithm that is used is adaptive, so it may make sense to
+    -- generate a sorted list. (These comments apply to one specific
+    -- version of the code in Graph, compiled in a specific way.)
+
+-- | The graph's strongly connected components, in reverse topological
+-- order.
+--
+-- The time complexity is likely /O(n + e log n)/ (but this depends on
+-- the, at the time of writing undocumented, time complexity of
+-- 'Graph.stronglyConnComp').
+
+sccs :: Ord n => Graph n e -> [[n]]
+sccs = map Graph.flattenSCC . sccs'
+
+-- | SCC DAGs.
+--
+-- The maps map SCC indices to and from SCCs/nodes.
+
+data DAG n = DAG
+  { dagGraph        :: Graph.Graph
+  , dagComponentMap :: IntMap (Graph.SCC n)
+  , dagNodeMap      :: Map n Int
+  }
+
+-- | 'DAG' invariant.
+
+dagInvariant :: Ord n => DAG n -> Bool
+dagInvariant g =
+  Set.fromList (concatMap Graph.flattenSCC
+                          (IntMap.elems (dagComponentMap g)))
+    ==
+  Map.keysSet (dagNodeMap g)
+    &&
+  IntSet.fromList (Map.elems (dagNodeMap g))
+    ==
+  IntMap.keysSet (dagComponentMap g)
+    &&
+  and [ n `elem` Graph.flattenSCC
+                   (dagComponentMap g IntMap.! (dagNodeMap g Map.! n))
+      | n <- Map.keys (dagNodeMap g)
+      ]
+    &&
+  and [ dagNodeMap g Map.! n == i
+      | i <- Graph.vertices (dagGraph g)
+      , n <- Graph.flattenSCC (dagComponentMap g IntMap.! i)
+      ]
+    &&
+  IntSet.fromList (Graph.vertices (dagGraph g))
+    ==
+  IntMap.keysSet (dagComponentMap g)
+    &&
+  all isAcyclic (Graph.scc (dagGraph g))
+  where
+  isAcyclic (Tree.Node r []) = r `notElem` (dagGraph g Array.! r)
+  isAcyclic _                = False
+
+-- | The opposite DAG.
+
+oppositeDAG :: DAG n -> DAG n
+oppositeDAG g = g { dagGraph = Graph.transposeG (dagGraph g) }
+
+-- | The nodes reachable from the given SCC.
+
+reachable :: Ord n => DAG n -> Graph.SCC n -> [n]
+reachable g scc = case scc of
+  Graph.AcyclicSCC n      -> List.delete n (reachable' n)
+  Graph.CyclicSCC (n : _) -> reachable' n
+  Graph.CyclicSCC []      -> __IMPOSSIBLE__
+  where
+  lookup' g k = fromMaybe __IMPOSSIBLE__ (IntMap.lookup k g)
+
+  lookup'' g k = fromMaybe __IMPOSSIBLE__ (Map.lookup k g)
+
+  reachable' n =
+    concatMap (Graph.flattenSCC . lookup' (dagComponentMap g)) $
+    Graph.reachable (dagGraph g) (lookup'' (dagNodeMap g) n)
+
+-- | Constructs a DAG containing the graph's strongly connected
+-- components.
+
+sccDAG' ::
+  forall n e. Ord n
+  => Graph n e
+  -> [Graph.SCC n]
+     -- ^ The graph's strongly connected components.
+  -> DAG n
+sccDAG' g sccs = DAG theDAG componentMap secondNodeMap
+  where
+  components :: [(Int, Graph.SCC n)]
+  components = zip [1..] sccs
+
+  firstNodeMap :: Map n Int
+  firstNodeMap = Map.fromList
+    [ (n, i)
+    | (i, c) <- components
+    , n      <- Graph.flattenSCC c
+    ]
+
+  targets :: Int -> [n] -> [Int]
+  targets i ns =
+    IntSet.toList $ IntSet.fromList
+      [ j
+      | e <- edgesFrom g ns
+      , let j = fromMaybe __IMPOSSIBLE__ (Map.lookup (target e) firstNodeMap)
+      , j /= i
+      ]
+
+  (theDAG, _, toVertex) =
+    Graph.graphFromEdges
+      [ (i, i, targets i (Graph.flattenSCC c))
+      | (i, c) <- components
+      ]
+
+  convertInt :: Int -> Graph.Vertex
+  convertInt i = fromMaybe __IMPOSSIBLE__ (toVertex i)
+
+  componentMap :: IntMap (Graph.SCC n)
+  componentMap = IntMap.fromList (map (mapFst convertInt) components)
+
+  secondNodeMap :: Map n Int
+  secondNodeMap = Map.map convertInt firstNodeMap
+
+-- | Constructs a DAG containing the graph's strongly connected
+-- components.
+
+sccDAG :: Ord n => Graph n e -> DAG n
+sccDAG g = sccDAG' g (sccs' g)
+
+------------------------------------------------------------------------
+-- Reachability
+
+-- | @reachableFrom g n@ is a map containing all nodes reachable from
+-- @n@ in @g@. For each node a simple path to the node is given, along
+-- with its length (the number of edges). The paths are as short as
+-- possible (in terms of the number of edges).
+--
+-- Precondition: @n@ must be a node in @g@. The number of nodes in the
+-- graph must not be larger than @'maxBound' :: 'Int'@.
+--
+-- Amortised time complexity (assuming that comparisons take constant
+-- time): /O(e log n)/, if the lists are not inspected. Inspection of
+-- a prefix of a list is linear in the length of the prefix.
+
+reachableFrom :: Ord n => Graph n e -> n -> Map n (Int, [Edge n e])
+reachableFrom g n = reachableFromInternal g (Set.singleton n)
+
+-- | @reachableFromSet g ns@ is a set containing all nodes reachable
+-- from @ns@ in @g@.
+--
+-- Precondition: Every node in @ns@ must be a node in @g@. The number
+-- of nodes in the graph must not be larger than @'maxBound' ::
+-- 'Int'@.
+--
+-- Amortised time complexity (assuming that comparisons take constant
+-- time): /O((|@ns@| + e) log n)/.
+
+reachableFromSet :: Ord n => Graph n e -> Set n -> Set n
+reachableFromSet g ns = Map.keysSet (reachableFromInternal g ns)
+
+-- | Used to implement 'reachableFrom' and 'reachableFromSet'.
+
+reachableFromInternal ::
+  Ord n => Graph n e -> Set n -> Map n (Int, [Edge n e])
+reachableFromInternal g ns =
+  bfs (Seq.fromList (map (, Seq.empty) (toList ns))) Map.empty
+  where
+  bfs !q !map = case Seq.viewl q of
+    Seq.EmptyL -> map
+    (u, p) Seq.:< q ->
+      if u `Map.member` map
+      then bfs q map
+      else bfs (foldr (flip (Seq.|>)) q
+                      [ (v, p Seq.|> Edge u v e)
+                      | (v, e) <- neighbours u g
+                      ])
+               (let n = Seq.length p in
+                n `seq` Map.insert u (n, toList p) map)
+
+-- | @walkSatisfying every some g from to@ determines if there is a
+-- walk from @from@ to @to@ in @g@, in which every edge satisfies the
+-- predicate @every@, and some edge satisfies the predicate @some@. If
+-- there are several such walks, then a shortest one (in terms of the
+-- number of edges) is returned.
+--
+-- Precondition: @from@ and @to@ must be nodes in @g@. The number of
+-- nodes in the graph must not be larger than @'maxBound' :: 'Int'@.
+--
+-- Amortised time complexity (assuming that comparisons and the
+-- predicates take constant time to compute): /O(n + e log n)/.
+
+walkSatisfying ::
+  Ord n =>
+  (Edge n e -> Bool) -> (Edge n e -> Bool) ->
+  Graph n e -> n -> n -> Maybe [Edge n e]
+walkSatisfying every some g from to =
+  case
+    [ (l1 + l2, p1 ++ [e] ++ map transposeEdge (reverse p2))
+    | e <- everyEdges
+    , some e
+    , (l1, p1) <- maybeToList (Map.lookup (source e) fromReaches)
+    , (l2, p2) <- maybeToList (Map.lookup (target e) reachesTo)
+    ] of
+    []  -> Nothing
+    ess -> Just $ snd $ List.minimumBy (compare `on` fst) ess
+  where
+  everyEdges = [ e | e <- edges g, every e ]
+
+  fromReaches = reachableFrom (fromEdges everyEdges) from
+
+  reachesTo =
+    reachableFrom (fromEdges (map transposeEdge everyEdges)) to
+
+-- | Constructs a graph @g'@ with the same nodes as the original graph
+-- @g@. In @g'@ there is an edge from @n1@ to @n2@ if and only if
+-- there is a (possibly empty) simple path from @n1@ to @n2@ in @g@.
+-- In that case the edge is labelled with all of the longest (in terms
+-- of numbers of edges) simple paths from @n1@ to @n2@ in @g@, as well
+-- as the lengths of these paths.
+--
+-- Precondition: The graph must be acyclic. The number of nodes in the
+-- graph must not be larger than @'maxBound' :: 'Int'@.
+--
+-- Worst-case time complexity (if the paths are not inspected):
+-- /O(e n log n)/ (this has not been verified carefully).
+--
+-- The algorithm is based on one found on Wikipedia.
+
+longestPaths ::
+  forall n e. Ord n => Graph n e -> Graph n (Int, [[Edge n e]])
+longestPaths g =
+  Graph $
+  fmap (fmap (mapSnd toList)) $
+  List.foldl' (flip addLongestFrom) Map.empty $
+  sccs' g
+  where
+  addLongestFrom ::
+    Graph.SCC n ->
+    Map n (Map n (Int, Seq [Edge n e])) ->
+    Map n (Map n (Int, Seq [Edge n e]))
+  addLongestFrom Graph.CyclicSCC{}    !_  = __IMPOSSIBLE__
+  addLongestFrom (Graph.AcyclicSCC n) pss =
+    Map.insert n
+      (Map.insert n (0, Seq.singleton []) $
+       Map.unionsWith longest candidates)
+      pss
+    where
+    longest p1@(n1, ps1) p2@(n2, ps2) = case compare n1 n2 of
+      GT -> p1
+      LT -> p2
+      EQ -> (n1, ps1 Seq.>< ps2)
+
+    candidates :: [Map n (Int, Seq [Edge n e])]
+    candidates =
+      for (neighbours n g) $ \(n', e) ->
+      let edge = Edge
+            { source = n
+            , target = n'
+            , label  = e
+            }
+      in case Map.lookup n' pss of
+        Nothing -> Map.empty
+        Just ps -> fmap (succ -*- fmap (edge :)) ps
+
+------------------------------------------------------------------------
+-- Transitive closure
+
+-- | Transitive closure ported from "Agda.Termination.CallGraph".
+--
+--   Relatively efficient, see Issue 1560.
+
+complete :: (Eq e, Null e, SemiRing e, Ord n) => Graph n e -> Graph n e
+complete g = repeatWhile (mapFst (not . discrete) . combineNewOld' g) g
+  where
+    combineNewOld' new old = unzip $ unionWith comb new' old'
+      where
+      -- The following procedure allows us to check if anything new happened:
+      -- Pair the composed graphs with an empty graph.
+      -- The empty graph will remain empty.  We only need it due to the typing
+      -- of Map.unionWith.
+      new' = (,Null.empty) <$> composeWith otimes oplus new old
+      -- Pair an empty graph with the old graph.
+      old' = (Null.empty,) <$> old
+      -- Combine the pairs.
+      -- Update 'old' with 'new'.  This will be the new 'old'. No new 'new' if no change.
+      comb (new, _) (_, old) = (if x == old then Null.empty else x, x)
+        where x = old `oplus` new
+
+-- | Version of 'complete' that produces a list of intermediate results
+--   paired to the left with a difference that lead to the new intermediat result.
+--
+--   The last element in the list is the transitive closure, paired with the empty graph.
+--
+--   @complete g = snd $ last $ completeIter g@
+
+completeIter :: (Eq e, Null e, SemiRing e, Ord n) => Graph n e -> [(Graph n e, Graph n e)]
+completeIter g = iterWhile (not . discrete) (combineNewOld' g) g
+  where
+    combineNewOld' new old = unzip $ unionWith comb new' old'
+      where
+      -- The following procedure allows us to check if anything new happened:
+      -- Pair the composed graphs with an empty graph.
+      -- The empty graph will remain empty.  We only need it due to the typing
+      -- of Map.unionWith.
+      new' = (,Null.empty) <$> composeWith otimes oplus new old
+      -- Pair an empty graph with the old graph.
+      old' = (Null.empty,) <$> old
+      -- Combine the pairs.
+      -- Update 'old' with 'new'.  This will be the new 'old'. No new 'new' if no change.
+      comb (new, _) (_, old) = (if x == old then Null.empty else x, x)
+        where x = old `oplus` new
+
+-- | Computes the transitive closure of the graph.
+--
+-- Uses the Gauss-Jordan-Floyd-Warshall-McNaughton-Yamada algorithm
+-- (as described by Russell O'Connor in \"A Very General Method of
+-- Computing Shortest Paths\"
+-- <http://r6.ca/blog/20110808T035622Z.html>), implemented using
+-- matrices.
+--
+-- The resulting graph does not contain any zero edges.
+--
+-- This algorithm should be seen as a reference implementation. In
+-- practice 'gaussJordanFloydWarshallMcNaughtonYamada' is likely to be
+-- more efficient.
+
+gaussJordanFloydWarshallMcNaughtonYamadaReference ::
+  forall n e. (Ord n, Eq e, StarSemiRing e) =>
+  Graph n e -> Graph n e
+gaussJordanFloydWarshallMcNaughtonYamadaReference g =
+  toGraph (foldr step initialMatrix nodeIndices)
+  where
+  indicesAndNodes = zip [1..] $ Set.toList $ nodes g
+  nodeMap         = Map.fromList $ map swap indicesAndNodes
+  indexMap        = Map.fromList            indicesAndNodes
+
+  noNodes      = Map.size nodeMap
+  nodeIndices  = [1 .. noNodes]
+  matrixBounds = ((1, 1), (noNodes, noNodes))
+
+  initialMatrix :: Array.Array (Int, Int) e
+  initialMatrix =
+    Array.accumArray
+      oplus ozero
+      matrixBounds
+      [ ((nodeMap Map.! source e, nodeMap Map.! target e), label e)
+      | e <- edges g
+      ]
+
+  rightStrictPair i !e = (i , e)
+
+  step k !m =
+    Array.array
+      matrixBounds
+      [ rightStrictPair
+          (i, j)
+          (oplus (m Array.! (i, j))
+                 (otimes (m Array.! (i, k))
+                         (otimes (ostar (m Array.! (k, k)))
+                                 (m Array.! (k, j)))))
+      | i <- nodeIndices, j <- nodeIndices
+      ]
+
+  toGraph m =
+    fromEdges [ Edge (indexMap Map.! i) (indexMap Map.! j) e
+              | ((i, j), e) <- Array.assocs m
+              , e /= ozero
+              ]
+      `union`
+    fromNodeSet (nodes g)
+
+-- | Computes the transitive closure of the graph.
+--
+-- Uses the Gauss-Jordan-Floyd-Warshall-McNaughton-Yamada algorithm
+-- (as described by Russell O'Connor in \"A Very General Method of
+-- Computing Shortest Paths\"
+-- <http://r6.ca/blog/20110808T035622Z.html>), implemented using
+-- 'Graph', and with some shortcuts:
+--
+-- * Zero edge differences are not added to the graph, thus avoiding
+--   some zero edges.
+--
+-- * Strongly connected components are used to avoid computing some
+--   zero edges.
+--
+-- The graph's strongly connected components (in reverse topological
+-- order) are returned along with the transitive closure.
+
+gaussJordanFloydWarshallMcNaughtonYamada ::
+  forall n e. (Ord n, Eq e, StarSemiRing e) =>
+  Graph n e -> (Graph n e, [Graph.SCC n])
+gaussJordanFloydWarshallMcNaughtonYamada g =
+  (loop components g, components)
+  where
+  components = sccs' g
+  forwardDAG = sccDAG' g components
+  reverseDAG = oppositeDAG forwardDAG
+
+  loop :: [Graph.SCC n] -> Graph n e -> Graph n e
+  loop []           !g = g
+  loop (scc : sccs)  g =
+    loop sccs (foldr step g (Graph.flattenSCC scc))
+    where
+    -- All nodes that are reachable from the SCC.
+    canBeReached = reachable forwardDAG scc
+    -- All nodes that can reach the SCC.
+    canReach     = reachable reverseDAG scc
+
+    step :: n -> Graph n e -> Graph n e
+    step k !g =
+      foldr (insertEdgeWith oplus) g
+        [ Edge i j e
+        | i <- canReach
+        , j <- canBeReached
+        , let e = otimes (lookup' i k) (starTimes (lookup' k j))
+        , e /= ozero
+        ]
+      where
+      starTimes = otimes (ostar (lookup' k k))
+
+      lookup' s t = fromMaybe ozero (lookup s t g)
+
+-- | The transitive closure. Using 'gaussJordanFloydWarshallMcNaughtonYamada'.
+--   NOTE: DO NOT USE () AS EDGE LABEL SINCE THIS MEANS EVERY EDGE IS CONSIDERED A ZERO EDGE AND NO
+--         NEW EDGES WILL BE ADDED! Use 'Maybe ()' instead.
+transitiveClosure :: (Ord n, Eq e, StarSemiRing e) => Graph n e -> Graph n e
+transitiveClosure = fst . gaussJordanFloydWarshallMcNaughtonYamada
+
+-- | The transitive reduction of the graph: a graph with the same
+-- reachability relation as the graph, but with as few edges as
+-- possible.
+--
+-- Precondition: The graph must be acyclic. The number of nodes in the
+-- graph must not be larger than @'maxBound' :: 'Int'@.
+--
+-- Worst-case time complexity: /O(e n log n)/ (this has not been
+-- verified carefully).
+--
+-- The algorithm is based on one found on Wikipedia.
+
+transitiveReduction :: Ord n => Graph n e -> Graph n ()
+transitiveReduction g =
+  fmap (const ()) $
+  filterEdges ((== 1) . fst . label) $
+  longestPaths g
diff --git a/src/full/Agda/Utils/Graph/TopSort.hs b/src/full/Agda/Utils/Graph/TopSort.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Graph/TopSort.hs
@@ -0,0 +1,51 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Graph.TopSort
+    ( topSort
+    ) where
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Map as Map
+import qualified Agda.Utils.Graph.AdjacencyMap.Unidirectional as G
+
+-- NB:: Defined but not used
+mergeBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
+mergeBy _ [] xs = xs
+mergeBy _ xs [] = xs
+mergeBy f (x:xs) (y:ys)
+    | f x y = x: mergeBy f xs (y:ys)
+    | otherwise = y: mergeBy f (x:xs) ys
+
+-- | topoligical sort with smallest-numbered available vertex first
+-- | input: nodes, edges
+-- | output is Nothing if the graph is not a DAG
+--   Note: should be stable to preserve order of generalizable variables. Algorithm due to Richard
+--   Eisenberg, and works by walking over the list left-to-right and moving each node the minimum
+--   distance left to guarantee topological ordering.
+topSort :: Ord n => Set n -> [(n, n)] -> Maybe [n]
+topSort nodes edges = go [] (Set.toList nodes)
+  where
+    -- #4253: The input edges do not necessarily include transitive dependencies, so take transitive
+    --        closure before sorting.
+    w      = Just () -- () is not a good edge label since it counts as a "zero" edge and will be ignored
+    g      = G.transitiveClosure $
+               G.fromNodeSet nodes `G.union`
+               G.fromEdges [G.Edge a b w | (a, b) <- edges]
+    -- Only the keys of these maps are used.
+    deps a = G.graph g Map.! a
+
+    -- acc: Already sorted nodes in reverse order paired with accumulated set of nodes that must
+    -- come before it
+    go acc [] = Just $ reverse $ map fst acc
+    go acc (n : ns) = (`go` ns) =<< insert n acc
+
+    insert a [] = Just [(a, deps a)]
+    insert a bs0@((b, before_b) : bs)
+      | before && after = Nothing
+      | before          = ((b, Map.union before_a before_b) :) <$> insert a bs  -- a must come before b
+      | otherwise       = Just $ (a, Map.union before_a before_b) : bs0
+      where
+        before_a = deps a
+        before = Map.member a before_b
+        after  = Map.member b before_a
diff --git a/src/full/Agda/Utils/Hash.hs b/src/full/Agda/Utils/Hash.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Hash.hs
@@ -0,0 +1,38 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-| Instead of checking time-stamps we compute a hash of the module source and
+    store it in the interface file. This module contains the functions to do
+    that. -}
+module Agda.Utils.Hash where
+
+import Data.ByteString as B
+import Data.Word
+import qualified Data.Hash as H
+import qualified Data.List as L
+import Data.Digest.Murmur64
+import qualified Data.Text.Encoding as T
+import Data.Text.Lazy (Text)
+import qualified Data.Text.Lazy as T
+
+import Agda.Utils.FileName
+import Agda.Utils.IO.UTF8 (readTextFile)
+
+type Hash = Word64
+
+hashByteString :: ByteString -> Hash
+hashByteString = H.asWord64 . B.foldl' (\h b -> H.combine h (H.hashWord8 b)) (H.hashWord8 0)
+
+hashTextFile :: AbsolutePath -> IO Hash
+hashTextFile file = hashText <$> readTextFile (filePath file)
+
+-- | Hashes a piece of 'Text'.
+
+hashText :: Text -> Hash
+hashText = hashByteString . T.encodeUtf8 . T.toStrict
+
+combineHashes :: [Hash] -> Hash
+combineHashes hs = H.asWord64 $ L.foldl' H.combine (H.hashWord8 0) $ L.map H.hash hs
+
+-- | Hashing a module name for unique identifiers.
+hashString :: String -> Word64
+hashString = asWord64 . hash64
diff --git a/src/full/Agda/Utils/HashTable.hs b/src/full/Agda/Utils/HashTable.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/HashTable.hs
@@ -0,0 +1,72 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | Hash tables.
+------------------------------------------------------------------------
+
+module Agda.Utils.HashTable
+  ( HashTable
+  , empty
+  , insert
+  , lookup
+  , toList
+  , keySet
+  ) where
+
+import Prelude hiding (lookup)
+
+import Data.Hashable
+import qualified Data.Vector.Hashtables as H
+import qualified Data.Vector.Mutable as VM
+import qualified Data.Vector as V
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+-- | Hash tables.
+
+-- A very limited amount of (possibly outdated) testing indicates
+-- that, for the use in Agda's serialiser/deserialiser,
+-- Data.HashTable.IO.CuckooHashTable is somewhat slower than
+-- Data.HashTable.IO.BasicHashTable, and that
+-- Data.HashTable.IO.LinearHashTable and the hashtables from
+-- Data.Hashtable are much slower. However, other (also possibly
+-- outdated) testing suggests that Data.HashTable.IO.CuckooHashTable
+-- is quite a bit faster than Data.HashTable.IO.BasicHashTable for
+-- 64-bit Windows. Some more recent, also limited, testing suggests
+-- that the following hash table implementation from
+-- Data.Vector.Hashtables is quite a bit faster than
+-- Data.HashTable.IO.BasicHashTable (see issue #5966).
+
+newtype HashTable k v =
+  HashTable (H.Dictionary (H.PrimState IO) VM.MVector k VM.MVector v)
+
+-- | An empty hash table.
+
+empty :: IO (HashTable k v)
+empty = HashTable <$> H.initialize 0
+
+-- | Inserts the key and the corresponding value into the hash table.
+
+insert :: (Eq k, Hashable k) => HashTable k v -> k -> v -> IO ()
+insert (HashTable h) = H.insert h
+{-# INLINABLE insert #-}
+
+-- | Tries to find a value corresponding to the key in the hash table.
+
+lookup :: (Eq k, Hashable k) => HashTable k v -> k -> IO (Maybe v)
+lookup (HashTable h) = H.lookup h
+{-# INLINABLE lookup #-}
+
+-- | Converts the hash table to a list.
+--
+-- The order of the elements in the list is unspecified.
+
+toList :: (Eq k, Hashable k) => HashTable k v -> IO [(k, v)]
+toList (HashTable h) = H.toList h
+{-# INLINABLE toList #-}
+
+keySet :: forall k v. Ord k => HashTable k v -> IO (Set k)
+keySet (HashTable h) = do
+  (ks :: V.Vector k) <- H.keys h
+  pure $! V.foldl' (flip Set.insert) mempty ks
+{-# INLINABLE keySet #-}
diff --git a/src/full/Agda/Utils/Haskell/Syntax.hs b/src/full/Agda/Utils/Haskell/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Haskell/Syntax.hs
@@ -0,0 +1,127 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | ASTs for subset of GHC Haskell syntax.
+
+module Agda.Utils.Haskell.Syntax where
+
+import Data.Text (Text)
+
+-- * Modules
+
+data Module = Module ModuleName [ModulePragma] [ImportDecl] [Decl]
+
+data ModulePragma
+  = LanguagePragma [Name]
+  | OtherPragma String  -- ^ Unstructured pragma (Andreas, 2017-08-23, issue #2712).
+
+data ImportDecl = ImportDecl
+  { importModule    :: ModuleName
+  , importQualified :: Bool
+  , importSpecs     :: Maybe (Bool, [ImportSpec])
+  }
+
+data ImportSpec = IVar Name
+
+-- * Declarations
+
+data Decl = TypeDecl Name [TyVarBind] Type
+          | DataDecl DataOrNew Name [TyVarBind] [ConDecl] [Deriving]
+          | TypeSig [Name] Type
+          | FunBind [Match]
+            -- ^ Should not be used when 'LocalBind' could be used.
+          | LocalBind Strictness Name Rhs
+            -- ^ Should only be used in @let@ or @where@.
+          | PatSyn Pat Pat
+          | FakeDecl String
+          | Comment String
+  deriving (Eq)
+
+data DataOrNew = DataType | NewType
+  deriving (Eq)
+
+data ConDecl = ConDecl Name [(Maybe Strictness, Type)]
+  deriving (Eq)
+
+data Strictness = Lazy | Strict
+  deriving (Eq)
+
+type Deriving = (QName, [Type])
+
+data Binds = BDecls [Decl]
+  deriving (Eq)
+
+data Rhs = UnGuardedRhs Exp
+         | GuardedRhss [GuardedRhs]
+  deriving (Eq)
+
+data GuardedRhs = GuardedRhs [Stmt] Exp
+  deriving (Eq)
+
+data Match = Match Name [Pat] Rhs (Maybe Binds)
+  deriving (Eq)
+
+-- * Expressions
+
+data Type = TyForall [TyVarBind] Type
+          | TyFun Type Type
+          | TyCon QName
+          | TyVar Name
+          | TyApp Type Type
+          | FakeType String
+  deriving (Eq)
+
+data Pat = PVar Name
+         | PLit Literal
+         | PAsPat Name Pat
+         | PWildCard
+         | PBangPat Pat
+         | PApp QName [Pat]
+         | PatTypeSig Pat Type
+         | PIrrPat Pat
+  deriving (Eq)
+
+
+data Stmt = Qualifier Exp
+          | Generator Pat Exp
+  deriving (Eq)
+
+data Exp = Var QName
+         | Con QName
+         | Lit Literal
+         | InfixApp Exp QOp Exp
+         | Ann Exp Type
+         | App Exp Exp
+         | Lambda [Pat] Exp
+         | Let Binds Exp
+         | If Exp Exp Exp
+         | Case Exp [Alt]
+         | ExpTypeSig Exp Type
+         | NegApp Exp
+         | FakeExp String
+  deriving (Eq)
+
+data Alt = Alt Pat Rhs (Maybe Binds)
+  deriving (Eq)
+
+data Literal = Int Integer | Frac Rational | Char Char | String Text
+  deriving (Eq)
+
+-- * Names
+
+data ModuleName = ModuleName String
+  deriving (Eq, Ord)
+
+data QName = Qual ModuleName Name | UnQual Name
+  deriving (Eq)
+
+data Name = Ident String | Symbol String
+  deriving (Eq)
+
+data QOp = QVarOp QName
+  deriving (Eq)
+
+data TyVarBind = UnkindedVar Name
+  deriving (Eq)
+
+unit_con :: Exp
+unit_con = Con (UnQual (Ident "()"))
diff --git a/src/full/Agda/Utils/IO.hs b/src/full/Agda/Utils/IO.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IO.hs
@@ -0,0 +1,29 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Auxiliary functions for the IO monad.
+
+module Agda.Utils.IO where
+
+import Control.Exception
+import Control.Monad.State
+import Control.Monad.Writer
+
+-- | Catch 'IOException's.
+--
+class CatchIO m where
+  catchIO :: m a -> (IOException -> m a) -> m a
+
+-- | Alias of 'catch' for the IO monad.
+--
+instance CatchIO IO where
+  catchIO = catch
+
+-- | Upon exception, the written output is lost.
+--
+instance CatchIO m => CatchIO (WriterT w m) where
+  catchIO m h = WriterT $ runWriterT m `catchIO` \ e -> runWriterT (h e)
+
+-- | Upon exception, the state is reset.
+--
+instance CatchIO m => CatchIO (StateT s m) where
+  catchIO m h = StateT $ \s -> runStateT m s `catchIO` \ e -> runStateT (h e) s
diff --git a/src/full/Agda/Utils/IO/Binary.hs b/src/full/Agda/Utils/IO/Binary.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IO/Binary.hs
@@ -0,0 +1,18 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Binary IO.
+
+module Agda.Utils.IO.Binary
+  ( readBinaryFile'
+  ) where
+
+import System.IO
+import Data.ByteString.Lazy as BS
+
+-- | Returns a close function for the file together with the contents.
+
+readBinaryFile' :: FilePath -> IO (ByteString, IO ())
+readBinaryFile' file = do
+    h <- openBinaryFile file ReadMode
+    s <- BS.hGetContents h
+    return (s, hClose h)
diff --git a/src/full/Agda/Utils/IO/Directory.hs b/src/full/Agda/Utils/IO/Directory.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IO/Directory.hs
@@ -0,0 +1,74 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.IO.Directory
+  ( copyDirContent
+  , copyIfChanged
+  )
+where
+
+import Control.Monad
+import Control.Monad.Writer ( WriterT, execWriterT, tell )
+import Control.Monad.Trans  ( lift )
+
+import Data.Monoid          ( Endo(Endo, appEndo) )
+
+import System.Directory
+import System.FilePath
+import Data.ByteString as BS
+
+
+
+
+
+-- | @copyDirContent src dest@ recursively copies directory @src@ onto @dest@.
+--
+--   First, a to-do list of copy actions is created.
+--   Then, the to-do list is carried out.
+--
+--   This avoids copying files we have just created again, which can happen
+--   if @src@ and @dest@ are not disjoint.
+--   (See issue #2705.)
+--
+copyDirContent :: FilePath -> FilePath -> IO ()
+copyDirContent src dest = mapM_ performAction =<< do
+  (`appEndo` []) <$> execWriterT (copyDirContentDryRun src dest)
+
+-- | Action to be carried out for copying a directory recursively.
+--
+data CopyDirAction
+  = MkDir    FilePath
+      -- ^ Create directory if missing.
+  | CopyFile FilePath FilePath
+      -- ^ Copy file if changed.
+
+-- | Perform scheduled 'CopyDirAction'.
+--
+performAction :: CopyDirAction -> IO ()
+performAction = \case
+  MkDir d           -> createDirectoryIfMissing True d
+  CopyFile src dest -> copyIfChanged src dest
+
+-- | @copyDirContentDryRun src dest@ creates a to-do list
+--   for recursively copying directory @src@ onto @dest@.
+--
+copyDirContentDryRun :: FilePath -> FilePath -> WriterT (Endo [CopyDirAction]) IO ()
+copyDirContentDryRun src dest = do
+  tell $ Endo (MkDir dest :)
+  chlds <- lift $ getDirectoryContents src
+  forM_ chlds $ \ x -> do
+    isDir <- lift $ doesDirectoryExist (src </> x)
+    case isDir of
+      _ | x == "." || x == ".." -> return ()
+      True  -> copyDirContentDryRun (src </> x) (dest </> x)
+      False -> tell $ Endo (CopyFile (src </> x) (dest </> x) :)
+
+-- | @copyIfChanged src dst@ makes sure that @dst@ exists
+--   and has the same content as @dst@.
+--
+copyIfChanged :: FilePath -> FilePath -> IO ()
+copyIfChanged src dst = do
+  exist <- doesFileExist dst
+  if not exist then copyFile src dst else do
+    new <- BS.readFile src
+    old <- BS.readFile dst
+    unless (old == new) $ copyFile src dst
diff --git a/src/full/Agda/Utils/IO/TempFile.hs b/src/full/Agda/Utils/IO/TempFile.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IO/TempFile.hs
@@ -0,0 +1,20 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Common syntax highlighting functions for Emacs and JSON
+
+module Agda.Utils.IO.TempFile
+  ( writeToTempFile
+  ) where
+
+import qualified Control.Exception as E
+import qualified System.Directory as D
+import qualified System.IO as IO
+
+-- | Creates a temporary file, writes some stuff, and returns the filepath
+writeToTempFile :: String -> IO FilePath
+writeToTempFile content = do
+  dir      <- D.getTemporaryDirectory
+  E.bracket (IO.openTempFile dir "agda2-mode") (IO.hClose . snd) $ \ (filepath, handle) -> do
+    IO.hSetEncoding handle IO.utf8
+    IO.hPutStr handle content
+    return filepath
diff --git a/src/full/Agda/Utils/IO/UTF8.hs b/src/full/Agda/Utils/IO/UTF8.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IO/UTF8.hs
@@ -0,0 +1,97 @@
+-- | Text IO using the UTF8 character encoding.
+
+module Agda.Utils.IO.UTF8
+  ( ReadException
+  , readTextFile
+  , Agda.Utils.IO.UTF8.readFile
+  , Agda.Utils.IO.UTF8.writeFile
+  , writeTextToFile
+  ) where
+
+import Control.Exception
+import Data.Maybe (fromMaybe)
+import Data.Text.Lazy (Text)
+import qualified Data.Text.Lazy as T
+import qualified Data.Text.Lazy.Encoding as T
+import qualified Data.Text.Lazy.IO as T
+import qualified Data.ByteString.Lazy as BS
+import qualified System.IO as IO
+
+-- | Converts many character sequences which may be interpreted as
+-- line or paragraph separators into '\n'.
+
+convertLineEndings :: Text -> Text
+convertLineEndings = T.map convert . convertCRLF
+  where
+  -- Replaces CR LF with LF.
+  convertCRLF = T.replace "\x000D\n" "\n"
+
+  -- ASCII:
+  convert '\x000D' = '\n'  -- CR  (Carriage return)
+  convert '\x000C' = '\n'  -- FF  (Form feed)
+  -- Unicode:
+  convert '\x0085' = '\n'  -- NEXT LINE
+  convert '\x2028' = '\n'  -- LINE SEPARATOR
+  convert '\x2029' = '\n'  -- PARAGRAPH SEPARATOR
+  -- Not a line ending (or '\x000A'):
+  convert c        = c
+
+-- | Strip the byte order mark (BOM) from a Text.
+--
+-- - https://github.com/agda/agda/issues/6524
+-- - https://github.com/haskell-hvr/cassava/issues/106#issuecomment-373986176
+--
+stripUtf8Bom :: BS.ByteString -> BS.ByteString
+stripUtf8Bom bs = fromMaybe bs (BS.stripPrefix "\239\187\191" bs)
+
+-- | A kind of exception that can be thrown by 'readTextFile' and
+-- 'readFile'.
+newtype ReadException
+  = DecodingError FilePath
+    -- ^ Decoding failed for the given file.
+  deriving Show
+
+instance Exception ReadException where
+  displayException (DecodingError file) =
+    "Failed to read " ++ file ++ ".\n" ++
+    "Please ensure that this file uses the UTF-8 character encoding."
+
+-- | Reads a UTF8-encoded text file and converts many character
+-- sequences which may be interpreted as line or paragraph separators
+-- into '\n'.
+--
+-- If the file cannot be decoded, then a 'ReadException' is raised.
+
+readTextFile :: FilePath -> IO Text
+readTextFile file = do
+  s <- T.decodeUtf8' . stripUtf8Bom <$> BS.readFile file
+  case s of
+    Right s -> return $ convertLineEndings s
+    Left _  -> throw $ DecodingError file
+
+-- | Reads a UTF8-encoded text file and converts many character
+-- sequences which may be interpreted as line or paragraph separators
+-- into '\n'.
+--
+-- If the file cannot be decoded, then a 'ReadException' is raised.
+
+readFile :: FilePath -> IO String
+readFile f = do
+  s <- readTextFile f
+  return $ T.unpack s
+
+-- | Writes a UTF8-encoded text file. The native convention for line
+-- endings is used.
+
+writeFile :: FilePath -> String -> IO ()
+writeFile file s = IO.withFile file IO.WriteMode $ \h -> do
+  IO.hSetEncoding h IO.utf8
+  IO.hPutStr h s
+
+-- | Writes a UTF8-encoded text file. The native convention for line
+-- endings is used.
+
+writeTextToFile :: FilePath -> Text -> IO ()
+writeTextToFile file s = IO.withFile file IO.WriteMode $ \h -> do
+  IO.hSetEncoding h IO.utf8
+  T.hPutStr h s
diff --git a/src/full/Agda/Utils/IORef.hs b/src/full/Agda/Utils/IORef.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IORef.hs
@@ -0,0 +1,17 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Utilities for Data.IORef.
+
+module Agda.Utils.IORef
+  ( module Data.IORef
+  , module Agda.Utils.IORef
+  ) where
+
+import Data.IORef
+
+-- | Read 'IORef', modify it strictly, and return old value.
+readModifyIORef' :: IORef a -> (a -> a) -> IO a
+readModifyIORef' ref f = do
+    x <- readIORef ref
+    writeIORef ref $! f x
+    return x
diff --git a/src/full/Agda/Utils/Impossible.hs b/src/full/Agda/Utils/Impossible.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Impossible.hs
@@ -0,0 +1,108 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | An interface for reporting \"impossible\" errors
+------------------------------------------------------------------------
+
+
+module Agda.Utils.Impossible where
+
+import Control.Exception (Exception(..), throw, catchJust)
+import Control.DeepSeq
+import Agda.Utils.CallStack.Base
+    ( CallStack
+    , HasCallStack
+    , prettyCallStack
+    , withCallerCallStack
+    )
+
+-- | \"Impossible\" errors, annotated with a file name and a line
+-- number corresponding to the source code location of the error.
+
+data Impossible
+
+  = Impossible CallStack
+    -- ^ We reached a program point which should be unreachable.
+
+  | Unreachable CallStack
+    -- ^ @Impossible@ with a different error message.
+    --   Used when we reach a program point which can in principle
+    --   be reached, but not for a certain run.
+
+  | ImpMissingDefinitions [String] String
+    -- ^ We reached a program point without all the required
+    -- primitives or BUILTIN to proceed forward.
+    -- @ImpMissingDefinitions neededDefs forThis@
+
+-- Identify all values of Impossible. We use Impossible as a stand-in for the empty type, so all
+-- values are morally equal.
+instance Eq Impossible where
+  _ == _ = True
+
+instance Ord Impossible where
+  compare _ _ = EQ
+
+instance NFData Impossible where
+  rnf _ = ()
+
+instance Show Impossible where
+  show (Impossible loc) = unlines
+    [ "An internal error has occurred. Please report this as a bug."
+    , "Location of the error: " ++ prettyCallStack loc
+    ]
+  show (Unreachable loc) = unlines
+    [ "We reached a program point we did not want to reach."
+    , "Location of the error: " ++ prettyCallStack loc
+    ]
+  show (ImpMissingDefinitions needed forthis) = unlines
+    [ "The following builtins or primitives need to be bound to use " ++ forthis ++ ":"
+    , unwords needed
+    ]
+
+instance Exception Impossible
+
+-- | Abort by throwing an \"impossible\" error. You should not use
+-- this function directly. Instead use __IMPOSSIBLE__
+
+throwImpossible :: Impossible -> a
+throwImpossible = throw
+
+-- | Monads in which we can catch an \"impossible\" error, if possible.
+
+class CatchImpossible m where
+
+  -- | Catch any 'Impossible' exception.
+  catchImpossible :: m a -> (Impossible -> m a) -> m a
+  catchImpossible = catchImpossibleJust Just
+
+  -- | Catch only 'Impossible' exceptions selected by the filter.
+  catchImpossibleJust :: (Impossible -> Maybe b) -> m a -> (b -> m a) -> m a
+  catchImpossibleJust = flip . handleImpossibleJust
+
+  -- | Version of 'catchImpossible' with argument order suiting short handlers.
+  handleImpossible :: (Impossible -> m a) -> m a -> m a
+  handleImpossible = flip catchImpossible
+
+  -- | Version of 'catchImpossibleJust' with argument order suiting short handlers.
+  handleImpossibleJust :: (Impossible -> Maybe b) -> (b -> m a) -> m a -> m a
+  handleImpossibleJust = flip . catchImpossibleJust
+
+  {-# MINIMAL catchImpossibleJust | handleImpossibleJust #-}
+
+instance CatchImpossible IO where
+  catchImpossibleJust = catchJust
+
+-- | Throw an "Impossible" error reporting the *caller's* call site.
+
+__IMPOSSIBLE__ :: HasCallStack => a
+__IMPOSSIBLE__ = withCallerCallStack $ throwImpossible . Impossible
+
+impossible :: HasCallStack => Impossible
+impossible = withCallerCallStack Impossible
+
+-- | Throw an "Unreachable" error reporting the *caller's* call site.
+-- Note that this call to "withFileAndLine" will be filtered out
+-- due its filter on the srcLocModule.
+
+__UNREACHABLE__ :: HasCallStack => a
+__UNREACHABLE__ = withCallerCallStack $ throwImpossible . Unreachable
diff --git a/src/full/Agda/Utils/IndexedList.hs b/src/full/Agda/Utils/IndexedList.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IndexedList.hs
@@ -0,0 +1,70 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE DataKinds #-}
+
+module Agda.Utils.IndexedList where
+
+import Data.Kind ( Type )
+import Agda.Utils.Lens
+
+-- | Existential wrapper for indexed types.
+data Some :: (k -> Type) -> Type where
+  Some :: f i -> Some f
+
+-- | Unpacking a wrapped value.
+withSome :: Some b -> (forall i. b i -> a) -> a
+withSome (Some x) f = f x
+
+-- | Lists indexed by a type-level list. A value of type @All p [x₁..xₙ]@ is a
+--   sequence of values of types @p x₁@, .., @p xₙ@.
+data All :: (x -> Type) -> [x] -> Type where
+  Nil  :: All p '[]
+  Cons :: p x -> All p xs -> All p (x ': xs)
+
+-- | Constructing an indexed list from a plain list.
+makeAll :: (a -> Some b) -> [a] -> Some (All b)
+makeAll f [] = Some Nil
+makeAll f (x : xs) =
+  case (f x, makeAll f xs) of
+    (Some y, Some ys) -> Some (Cons y ys)
+
+-- | Turning an indexed list back into a plain list.
+forgetAll :: (forall x. b x -> a) -> All b xs -> [a]
+forgetAll f Nil         = []
+forgetAll f (Cons x xs) = f x : forgetAll f xs
+
+-- | An index into a type-level list.
+data Index :: [x] -> x -> Type where
+  Zero :: Index (x ': xs) x
+  Suc  :: Index xs x -> Index (y ': xs) x
+
+-- | Indices are just natural numbers.
+forgetIndex :: Index xs x -> Int
+forgetIndex Zero    = 0
+forgetIndex (Suc i) = 1 + forgetIndex i
+
+-- | Mapping over an indexed list.
+mapWithIndex :: (forall x. Index xs x -> p x -> q x) -> All p xs -> All q xs
+mapWithIndex f Nil = Nil
+mapWithIndex f (Cons p ps) = Cons (f Zero p) $ mapWithIndex (f . Suc) ps
+
+-- | If you have an index you can get a lens for the given element.
+lIndex :: Index xs x -> Lens' (All p xs) (p x)
+lIndex Zero    f (Cons x xs) = f x           <&> \ x  -> Cons x xs
+lIndex (Suc i) f (Cons x xs) = lIndex i f xs <&> \ xs -> Cons x xs
+
+-- | Looking up an element in an indexed list.
+lookupIndex :: All p xs -> Index xs x -> p x
+lookupIndex = flip ix
+  where
+    -- -Wincomplete-patterns fails for the other argument order!
+    ix :: Index xs x -> All p xs -> p x
+    ix Zero    (Cons x xs) = x
+    ix (Suc i) (Cons x xs) = ix i xs
+
+-- | All indices into an indexed list.
+allIndices :: All p xs -> All (Index xs) xs
+allIndices = mapWithIndex const
diff --git a/src/full/Agda/Utils/IntSet/Infinite.hs b/src/full/Agda/Utils/IntSet/Infinite.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/IntSet/Infinite.hs
@@ -0,0 +1,169 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- |  Possibly infinite sets of integers (but with finitely many consecutive
+--    segments). Used for checking guard coverage in int/nat cases in the
+--    treeless compiler.
+
+module Agda.Utils.IntSet.Infinite
+  ( IntSet
+  , empty, full, below, above, singleton
+  , difference, member, toFiniteList
+  , invariant )
+  where
+
+
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+-- | Represents a set of integers.
+--   Invariants:
+--     - All cannot be the argument to `Below` or `Above`
+--     - at most one 'IntsBelow'
+--     - at most one 'IntsAbove'
+--     - if `Below lo` and `Below hi`, then `lo < hi`
+--     - if `Below lo .. (Some xs)` then `all (> lo) xs`
+--     - if `Above hi .. (Some xs)` then `all (< hi - 1) xs`
+data IntSet = All
+              | Some (Set Integer)
+              | Below Integer IntSet  -- exclusive
+              | Above Integer IntSet  -- inclusive
+  deriving (Show)
+
+instance Eq IntSet where
+  r == r' = norm r == norm r'
+    where
+      norm All          = Nothing
+      norm (Some xs)    = Just (Nothing, Nothing, xs)
+      norm (Below lo r) = do (_, hi, xs) <- norm r; return (Just lo, hi, xs)
+      norm (Above hi r) = do (lo, _, xs) <- norm r; return (lo, Just hi, xs)
+
+below' :: Integer -> IntSet -> IntSet
+below' _  All = All
+below' lo r@(Some xs)
+  | lo `Set.member` xs = below' (lo + 1) r
+  | otherwise  = Below lo $ Some $ Set.filter (>= lo) xs
+below' lo r0@(Below lo' r)
+  | lo' >= lo = r0
+  | otherwise = below' lo r
+below' lo (Above hi r)
+  | hi <= lo  = All
+  | otherwise = Above hi $ below' lo r
+
+above' :: Integer -> IntSet -> IntSet
+above' _  All = All
+above' hi r@(Some xs)
+  | (hi - 1) `Set.member` xs = above' (hi - 1) r
+  | otherwise        = Above hi $ Some $ Set.filter (< hi) xs
+above' hi r0@(Above hi' r)
+  | hi' <= hi = r0
+  | otherwise = above' hi r
+above' hi (Below lo r)
+  | hi <= lo  = All
+  | otherwise = Below lo $ above' hi r
+
+some' :: Set Integer -> IntSet -> IntSet
+some' xs r | null xs = r
+some' xs (Some ys) = Some (Set.union xs ys)
+some' _  All = All
+some' xs (Below lo r)
+  | lo `Set.member` xs = some' xs (Below (lo + 1) r)
+  | otherwise  = below' lo $ some' (Set.filter (>= lo) xs) r
+some' xs (Above hi r)
+  | (hi - 1) `Set.member` xs = some' xs (Above (hi - 1) r)
+  | otherwise        = above' hi $ some' (Set.filter (< hi) xs) r
+
+difference :: IntSet -> IntSet -> IntSet
+difference r All           = empty
+difference r (Some xs)     = subtractSome r xs
+difference r (Below lo r') = difference (subtractBelow r lo) r'
+difference r (Above hi r') = difference (subtractAbove r hi) r'
+
+subtractSome :: IntSet -> Set Integer -> IntSet
+subtractSome r xs | null xs = r
+subtractSome All xs = below lo <> above hi <> Some (Set.fromList [lo..hi - 1] `Set.difference` xs)
+  where lo = minimum xs
+        hi = maximum xs + 1
+subtractSome (Some ys) xs = Some (Set.difference ys xs)
+subtractSome (Below lo r) xs = Below (min lo lo') $ subtractSome (Some (Set.fromList [lo'..lo - 1]) <> r) xs
+  where lo' = minimum xs
+subtractSome (Above hi r) xs = Above (max hi hi') $ subtractSome (Some (Set.fromList [hi..hi' - 1]) <> r) xs
+  where hi' = maximum xs + 1
+
+subtractBelow :: IntSet -> Integer -> IntSet
+subtractBelow All           lo = above lo
+subtractBelow (Below lo' r) lo = some' (Set.fromList [lo..lo' - 1]) (subtractBelow r lo)
+subtractBelow (Above hi r)  lo = Above (max hi lo) (subtractBelow r lo)
+subtractBelow (Some xs)     lo = Some $ Set.filter (>= lo) xs
+
+subtractAbove :: IntSet -> Integer -> IntSet
+subtractAbove All           hi = below hi
+subtractAbove (Above hi' r) hi = some' (Set.fromList [hi'..hi - 1]) (subtractAbove r hi)
+subtractAbove (Below lo r)  hi = Below (min lo hi) (subtractAbove r hi)
+subtractAbove (Some xs)     hi = Some $ Set.filter (< hi) xs
+
+instance Semigroup IntSet where
+  Below lo r <> r' = below' lo (r <> r')
+  Above hi r <> r' = above' hi (r <> r')
+  Some xs    <> r' = some' xs r'
+  All        <> _  = All
+
+instance Monoid IntSet where
+  mempty  = empty
+  mappend = (<>)
+
+-- | Membership
+member :: Integer -> IntSet -> Bool
+member _ All          = True
+member x (Some xs)    = Set.member x xs
+member x (Below lo s) = x < lo  || member x s
+member x (Above hi s) = x >= hi || member x s
+
+-- | All integers `< n`
+below :: Integer -> IntSet
+below lo = Below lo empty
+
+-- | All integers `>= n`
+above :: Integer -> IntSet
+above hi = Above hi empty
+
+-- | A single integer.
+singleton :: Integer -> IntSet
+singleton x = fromList [x]
+
+-- | From a list of integers.
+fromList :: [Integer] -> IntSet
+fromList xs = Some (Set.fromList xs)
+
+-- | No integers.
+empty :: IntSet
+empty = Some Set.empty
+
+-- | All integers.
+full :: IntSet
+full = All
+
+-- | If finite, return the list of elements.
+toFiniteList :: IntSet -> Maybe [Integer]
+toFiniteList (Some xs) = Just $ Set.toList xs
+toFiniteList All       = Nothing
+toFiniteList Above{}   = Nothing
+toFiniteList Below{}   = Nothing
+
+-- | Invariant.
+invariant :: IntSet -> Bool
+invariant xs =
+  case xs of
+    All         -> True
+    Some{}      -> True
+    Below lo ys -> invariant ys && invBelow lo ys
+    Above hi ys -> invariant ys && invAbove hi ys
+  where
+    invBelow lo All          = False
+    invBelow lo (Some xs)    = all (> lo) xs
+    invBelow lo Below{}      = False
+    invBelow lo (Above hi r) = lo < hi && invBelow lo r
+
+    invAbove hi All          = False
+    invAbove hi (Some xs)    = all (< hi - 1) xs
+    invAbove hi Above{}      = False
+    invAbove hi (Below lo r) = lo < hi && invAbove hi r
diff --git a/src/full/Agda/Utils/Lens.hs b/src/full/Agda/Utils/Lens.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Lens.hs
@@ -0,0 +1,130 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | A cut-down implementation of lenses, with names taken from
+--   Edward Kmett's lens package.
+
+module Agda.Utils.Lens
+  ( module Agda.Utils.Lens
+  , (<&>) -- reexported from Agda.Utils.Functor
+  ) where
+
+import Control.Applicative ( Const(Const), getConst )
+import Control.Monad.State
+import Control.Monad.Reader
+import Control.Monad.Writer
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Data.Functor.Identity
+
+import Agda.Utils.Functor ((<&>))
+
+-- * Type-preserving lenses.
+
+-- | Van Laarhoven style homogeneous lenses.
+--   Mnemoic: "Lens outer inner", same type argument order as 'get :: o -> i'.
+type Lens' o i = forall f. Functor f => (i -> f i) -> o -> f o
+
+type LensGet o i = o -> i
+type LensSet o i = i -> o -> o
+type LensMap o i = (i -> i) -> o -> o
+
+-- * Some simple lenses.
+
+lFst :: Lens' (a, b) a
+lFst f (x, y) = (, y) <$> f x
+
+lSnd :: Lens' (a, b) b
+lSnd f (x, y) = (x,) <$> f y
+
+-- * Elementary lens operations.
+
+infixl 8 ^.
+-- | Get inner part @i@ of structure @o@ as designated by @Lens' o i@.
+(^.) :: o -> Lens' o i -> i
+o ^. l = getConst $ l Const o
+
+-- | Set inner part @i@ of structure @o@ as designated by @Lens' o i@.
+set :: Lens' o i -> LensSet o i
+set l = over l . const
+
+-- | Modify inner part @i@ of structure @o@ using a function @i -> i@.
+over :: Lens' o i -> LensMap o i
+over l f o = runIdentity $ l (Identity . f) o
+
+
+-- * State accessors and modifiers using 'StateT'.
+
+-- | Focus on a part of the state for a stateful computation.
+focus :: Monad m => Lens' o i -> StateT i m a -> StateT o m a
+focus l m = StateT $ \ o -> do
+  (a, i) <- runStateT m (o ^. l)
+  return (a, set l i o)
+
+-- * State accessors and modifiers using 'MonadState'.
+
+-- | Read a part of the state.
+use :: MonadState o m => Lens' o i -> m i
+use l = do !x <- gets (^. l)
+           return x
+
+infix 4 .=
+-- | Write a part of the state.
+(.=) :: MonadState o m => Lens' o i -> i -> m ()
+l .= i = modify $ set l i
+
+infix 4 %=
+-- | Modify a part of the state.
+(%=) :: MonadState o m => Lens' o i -> (i -> i) -> m ()
+l %= f = modify $ over l f
+
+infix 4 %==
+-- | Modify a part of the state monadically.
+(%==) :: MonadState o m => Lens' o i -> (i -> m i) -> m ()
+l %== f = put =<< l f =<< get
+
+infix 4 %%=
+-- | Modify a part of the state monadically, and return some result.
+(%%=) :: MonadState o m => Lens' o i -> (i -> m (i, r)) -> m r
+l %%= f = do
+  o <- get
+  (o', r) <- runWriterT $ l (WriterT . f) o
+  put o'
+  return r
+
+-- | Modify a part of the state locally.
+locallyState :: MonadState o m => Lens' o i -> (i -> i) -> m r -> m r
+locallyState l f k = do
+  old <- use l
+  l %= f
+  x <- k
+  l .= old
+  return x
+
+-- * Read-only state accessors and modifiers.
+
+-- | Ask for part of read-only state.
+view :: MonadReader o m => Lens' o i -> m i
+view l = asks (^. l)
+
+-- | Modify a part of the state in a subcomputation.
+locally :: MonadReader o m => Lens' o i -> (i -> i) -> m a -> m a
+locally l = local . over l
+
+locally' :: ((o -> o) -> m a -> m a) -> Lens' o i -> (i -> i) -> m a -> m a
+locally' local l = local . over l
+
+-- * Lenses for collections
+
+-- | Access a map value at a given key.
+key :: Ord k => k -> Lens' (Map k v) (Maybe v)
+key k f m = f (Map.lookup k m) <&> \ v -> Map.alter (const v) k m
+
+-- | Focus on given element in a set.
+contains :: Ord k => k -> Lens' (Set k) Bool
+contains k f s = f (Set.member k s) <&> \case
+  True  -> Set.insert k s
+  False -> Set.delete k s
diff --git a/src/full/Agda/Utils/Lens/Examples.hs b/src/full/Agda/Utils/Lens/Examples.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Lens/Examples.hs
@@ -0,0 +1,20 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Examples how to use "Agda.Utils.Lens".
+
+module Agda.Utils.Lens.Examples where
+
+import Agda.Utils.Functor
+import Agda.Utils.Lens
+
+data Record a b = Record
+  { field1 :: a
+  , field2 :: b
+  }
+
+-- | (View source:) This is how you implement a lens for a record field.
+lensField1 :: Lens' (Record a b) a
+lensField1 f r = f (field1 r) <&> \ a -> r { field1 = a }
+
+lensField2 :: Lens' (Record a b) b
+lensField2 f r = f (field2 r) <&> \ b -> r { field2 = b }
diff --git a/src/full/Agda/Utils/List.hs b/src/full/Agda/Utils/List.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/List.hs
@@ -0,0 +1,801 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Utility functions for lists.
+
+module Agda.Utils.List where
+
+import Control.Monad (filterM)
+
+import Data.Array (Array, array, listArray)
+import qualified Data.Array as Array
+import Data.Bifunctor
+import Data.Function (on)
+import Data.Hashable
+import qualified Data.List as List
+import qualified Data.List.NonEmpty as List1
+import Data.List.NonEmpty (pattern (:|), (<|))
+import Data.Maybe
+import qualified Data.Map as Map
+import qualified Data.HashMap.Strict as HMap
+import qualified Data.Set as Set
+
+import qualified Agda.Utils.Bag as Bag
+import Agda.Utils.CallStack.Base
+import Agda.Utils.Function (applyWhen)
+import Agda.Utils.Functor  ((<.>))
+import Agda.Utils.Tuple
+
+import {-# SOURCE #-} Agda.Utils.List1 (List1)
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+-- * Variants of list case, cons, head, tail, init, last
+---------------------------------------------------------------------------
+
+-- | Append a single element at the end.
+--   Time: O(length); use only on small lists.
+snoc :: [a] -> a -> [a]
+snoc xs x = xs ++ [x]
+
+-- | Case distinction for lists, with list first.
+--   O(1).
+--
+--   Cf. 'Agda.Utils.Null.ifNull'.
+caseList :: [a] -> b -> (a -> [a] -> b) -> b
+caseList xs n c = listCase n c xs
+
+-- | Case distinction for lists, with list first.
+--   O(1).
+--
+--   Cf. 'Agda.Utils.Null.ifNull'.
+caseListM :: Monad m => m [a] -> m b -> (a -> [a] -> m b) -> m b
+caseListM mxs n c = listCase n c =<< mxs
+
+-- | Case distinction for lists, with list last.
+--   O(1).
+--
+listCase :: b -> (a -> [a] -> b) -> [a] -> b
+listCase n c []     = n
+listCase n c (x:xs) = c x xs
+
+-- | Head function (safe). Returns a default value on empty lists.
+--   O(1).
+--
+-- > headWithDefault 42 []      = 42
+-- > headWithDefault 42 [1,2,3] = 1
+headWithDefault :: a -> [a] -> a
+headWithDefault def = fromMaybe def . listToMaybe
+
+-- | Tail function (safe).
+--   O(1).
+tailMaybe :: [a] -> Maybe [a]
+tailMaybe = fmap snd . uncons
+
+-- | Tail function (safe).  Returns a default list on empty lists.
+--   O(1).
+tailWithDefault :: [a] -> [a] -> [a]
+tailWithDefault def = fromMaybe def . tailMaybe
+
+-- | Last element (safe).
+--   O(n).
+lastMaybe :: [a] -> Maybe a
+lastMaybe [] = Nothing
+lastMaybe xs = Just $ last xs
+
+-- | Last element (safe).  Returns a default list on empty lists.
+--   O(n).
+lastWithDefault :: a -> [a] -> a
+lastWithDefault = last1
+
+-- | Last element of non-empty list (safe).
+--   O(n).
+--   @last1 a as = last (a : as)@
+last1 :: a -> [a] -> a
+last1 a = \case
+  [] -> a
+  b:bs -> last1 b bs
+
+-- | Last two elements (safe).
+--   O(n).
+--
+last2 :: [a] -> Maybe (a, a)
+last2 (x : y : xs) = Just $ last2' x y xs
+last2 _ = Nothing
+
+-- | @last2' x y zs@ computes the last two elements of @x:y:zs@.
+--   O(n).
+--
+last2' :: a -> a -> [a] -> (a, a)
+last2' x y = \case
+  []  -> (x, y)
+  z:zs -> last2' y z zs
+
+-- | Opposite of cons @(:)@, safe.
+--   O(1).
+uncons :: [a] -> Maybe (a, [a])
+uncons []     = Nothing
+uncons (x:xs) = Just (x,xs)
+
+-- | Maybe cons.
+--   O(1).
+--   @mcons ma as = maybeToList ma ++ as@
+mcons :: Maybe a -> [a] -> [a]
+mcons ma as = maybe as (:as) ma
+
+-- | 'init' and 'last' in one go, safe.
+--   O(n).
+initLast :: [a] -> Maybe ([a],a)
+initLast []     = Nothing
+initLast (a:as) = Just $ initLast1 a as
+
+-- | 'init' and 'last' of non-empty list, safe.
+--   O(n).
+--   @initLast1 a as = (init (a:as), last (a:as)@
+initLast1 :: a -> [a] -> ([a], a)
+initLast1 a = \case
+  []   -> ([], a)
+  b:bs -> first (a:) $ initLast1 b bs
+
+-- | 'init' of non-empty list, safe.
+--   O(n).
+--   @init1 a as = init (a:as)@
+init1 :: a -> [a] -> [a]
+init1 a = \case
+  []   -> []
+  b:bs -> a : init1 b bs
+
+-- | @init@, safe.
+--   O(n).
+initMaybe :: [a] -> Maybe [a]
+initMaybe = \case
+  []   -> Nothing
+  a:as -> Just $ init1 a as
+
+-- | @init@, safe.
+--   O(n).
+initWithDefault :: [a] -> [a] -> [a]
+initWithDefault as []     = as
+initWithDefault _  (a:as) = init1 a as
+
+---------------------------------------------------------------------------
+-- * Lookup and indexing
+---------------------------------------------------------------------------
+
+-- | Lookup function (safe).
+--   O(min n index).
+(!!!) :: [a] -> Int -> Maybe a
+xs !!! (!i)
+  | i < 0     = Nothing
+  | otherwise = index xs i
+  where
+  index []       !i = Nothing
+  index (x : xs) 0  = Just x
+  index (x : xs) i  = index xs (i - 1)
+
+-- | A variant of 'Prelude.!!' that might provide more informative
+-- error messages if the index is out of bounds.
+--
+-- Precondition: The index should not be out of bounds.
+
+(!!) :: HasCallStack => [a] -> Int -> a
+xs !! i = case xs !!! i of
+  Just x  -> x
+  Nothing -> __IMPOSSIBLE__
+
+-- | Lookup function with default value for index out of range.
+--   O(min n index).
+--
+--   The name is chosen akin to 'Data.List.genericIndex'.
+indexWithDefault :: a -> [a] -> Int -> a
+indexWithDefault a []       _ = a
+indexWithDefault a (x : _)  0 = x
+indexWithDefault a (_ : xs) n = indexWithDefault a xs (n - 1)
+
+-- | Find an element satisfying a predicate and return it with its index.
+--   O(n) in the worst case, e.g. @findWithIndex f xs = Nothing@.
+--
+--   TODO: more efficient implementation!?
+findWithIndex :: (a -> Bool) -> [a] -> Maybe (a, Int)
+findWithIndex p as = List.find (p . fst) (zip as [0..])
+
+-- | A generalised variant of 'elemIndex'.
+-- O(n).
+genericElemIndex :: (Eq a, Integral i) => a -> [a] -> Maybe i
+genericElemIndex x xs =
+  listToMaybe $
+  map fst $
+  filter snd $
+  zip [0..] $
+  map (== x) xs
+
+-- | @downFrom n = [n-1,..1,0]@.
+--   O(n).
+downFrom :: Integral a => a -> [a]
+downFrom n | n <= 0     = []
+           | otherwise = let n' = n-1 in n' : downFrom n'
+
+---------------------------------------------------------------------------
+-- * Update
+---------------------------------------------------------------------------
+
+-- | Update the first element of a list, if it exists.
+--   O(1).
+updateHead :: (a -> a) -> [a] -> [a]
+updateHead _ []       = []
+updateHead f (a : as) = f a : as
+
+-- | Update the last element of a list, if it exists.
+--   O(n).
+updateLast :: (a -> a) -> [a] -> [a]
+updateLast _ [] = []
+updateLast f (a : as) = loop a as
+  -- Using a helper function to minimize the pattern matching.
+  where
+  loop a []       = [f a]
+  loop a (b : bs) = a : loop b bs
+
+-- | Update nth element of a list, if it exists.
+--   @O(min index n)@.
+--
+--   Precondition: the index is >= 0.
+updateAt :: Int -> (a -> a) -> [a] -> [a]
+updateAt _ _ [] = []
+updateAt 0 f (a : as) = f a : as
+updateAt n f (a : as) = a : updateAt (n-1) f as
+
+---------------------------------------------------------------------------
+-- * Sublist extraction and partitioning
+---------------------------------------------------------------------------
+
+type Prefix a = [a]  -- ^ The list before the split point.
+type Suffix a = [a]  -- ^ The list after the split point.
+
+-- | @splitExactlyAt n xs = Just (ys, zs)@ iff @xs = ys ++ zs@
+--   and @genericLength ys = n@.
+splitExactlyAt :: Integral n => n -> [a] -> Maybe (Prefix a, Suffix a)
+splitExactlyAt 0 xs       = return ([], xs)
+splitExactlyAt n []       = Nothing
+splitExactlyAt n (x : xs) = mapFst (x :) <$> splitExactlyAt (n-1) xs
+
+-- | Drop from the end of a list.
+--   O(length).
+--
+--   @dropEnd n = reverse . drop n . reverse@
+--
+--   Forces the whole list even for @n==0@.
+dropEnd :: forall a. Int -> [a] -> Prefix a
+dropEnd n = snd . foldr f (n, [])
+  where
+  f :: a -> (Int, [a]) -> (Int, [a])
+  f x (n, xs) = (n-1, applyWhen (n <= 0) (x:) xs)
+
+-- | Split off the largest suffix whose elements satisfy a predicate.
+--   O(n).
+--
+--   @spanEnd p xs = (ys, zs)@
+--   where @xs = ys ++ zs@
+--   and @all p zs@
+--   and @maybe True (not . p) (lastMaybe yz)@.
+spanEnd :: forall a. (a -> Bool) -> [a] -> (Prefix a, Suffix a)
+spanEnd p = snd . foldr f (True, ([], []))
+  where
+  f :: a -> (Bool, ([a], [a])) -> (Bool, ([a], [a]))
+  f x (b', (xs, ys)) = (b, if b then (xs, x:ys) else (x:xs, ys))
+    where b = b' && p x
+
+-- | Breaks a list just /after/ an element satisfying the predicate is
+--   found.
+--
+--   >>> breakAfter1 even 1 [3,5,2,4,7,8]
+--   (1 :| [3,5,2],[4,7,8])
+
+breakAfter1 :: (a -> Bool) -> a -> [a] -> (List1 a, [a])
+breakAfter1 p = loop
+  where
+  loop x = \case
+    xs@[]         -> (x :| [], xs)
+    xs@(y : ys)
+      | p x       -> (x :| [], xs)
+      | otherwise -> let (vs, ws) = loop y ys in (x <| vs, ws)
+
+-- | Breaks a list just /after/ an element satisfying the predicate is
+--   found.
+--
+--   >>> breakAfter even [1,3,5,2,4,7,8]
+--   ([1,3,5,2],[4,7,8])
+
+breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
+breakAfter p = \case
+  []   -> ([], [])
+  x:xs -> first List1.toList $ breakAfter1 p x xs
+
+-- | A generalized version of @takeWhile@.
+--   (Cf. @mapMaybe@ vs. @filter@).
+--   @O(length . takeWhileJust f).
+--
+--   @takeWhileJust f = fst . spanJust f@.
+takeWhileJust :: (a -> Maybe b) -> [a] -> Prefix b
+takeWhileJust p = loop
+  where
+    loop (a : as) | Just b <- p a = b : loop as
+    loop _ = []
+
+-- | A generalized version of @span@.
+--   @O(length . fst . spanJust f)@.
+spanJust :: (a -> Maybe b) -> [a] -> (Prefix b, Suffix a)
+spanJust p = loop
+  where
+    loop (a : as) | Just b <- p a = mapFst (b :) $ loop as
+    loop as                       = ([], as)
+
+-- | Partition a list into 'Nothing's and 'Just's.
+--   O(n).
+--
+--   @partitionMaybe f = partitionEithers . map (\ a -> maybe (Left a) Right (f a))@
+--
+--   Note: @'mapMaybe' f = snd . partitionMaybe f@.
+partitionMaybe :: (a -> Maybe b) -> [a] -> ([a], [b])
+partitionMaybe f = loop
+  where
+    loop []       = ([], [])
+    loop (a : as) = case f a of
+      Nothing -> mapFst (a :) $ loop as
+      Just b  -> mapSnd (b :) $ loop as
+
+-- | Like 'filter', but additionally return the last partition
+--   of the list where the predicate is @False@ everywhere.
+--   O(n).
+filterAndRest :: (a -> Bool) -> [a] -> ([a], Suffix a)
+filterAndRest p = mapMaybeAndRest $ \ a -> if p a then Just a else Nothing
+
+-- | Like 'mapMaybe', but additionally return the last partition
+--   of the list where the function always returns @Nothing@.
+--   O(n).
+mapMaybeAndRest :: (a -> Maybe b) -> [a] -> ([b], Suffix a)
+mapMaybeAndRest f = loop [] where
+  loop acc = \case
+    []                   -> ([], reverse acc)
+    x:xs | Just y <- f x -> first (y:) $ loop [] xs
+         | otherwise     -> loop (x:acc) xs
+
+-- | Sublist relation.
+isSublistOf :: Eq a => [a] -> [a] -> Bool
+isSublistOf = List.isSubsequenceOf
+
+-- | All ways of removing one element from a list.
+--   O(n²).
+holes :: [a] -> [(a, [a])]
+holes []     = []
+holes (x:xs) = (x, xs) : map (second (x:)) (holes xs)
+
+---------------------------------------------------------------------------
+-- * Prefix and suffix
+---------------------------------------------------------------------------
+
+-- ** Prefix
+
+-- | Compute the common prefix of two lists.
+--   O(min n m).
+commonPrefix :: Eq a => [a] -> [a] -> Prefix a
+commonPrefix [] _ = []
+commonPrefix _ [] = []
+commonPrefix (x:xs) (y:ys)
+  | x == y    = x : commonPrefix xs ys
+  | otherwise = []
+
+-- | Drops from both lists simultaneously until one list is empty.
+--   O(min n m).
+dropCommon :: [a] -> [b] -> (Suffix a, Suffix b)
+dropCommon (x : xs) (y : ys) = dropCommon xs ys
+dropCommon xs ys = (xs, ys)
+
+-- | Check if a list has a given prefix. If so, return the list
+--   minus the prefix.
+--   O(length prefix).
+stripPrefixBy :: (a -> a -> Bool) -> Prefix a -> [a] -> Maybe (Suffix a)
+stripPrefixBy eq = loop
+  where
+  loop []    rest = Just rest
+  loop (_:_) []   = Nothing
+  loop (p:pat) (r:rest)
+    | eq p r    = loop pat rest
+    | otherwise = Nothing
+
+-- ** Suffix
+
+-- | Compute the common suffix of two lists.
+--   O(n + m).
+commonSuffix :: Eq a => [a] -> [a] -> Suffix a
+commonSuffix xs ys = reverse $ (commonPrefix `on` reverse) xs ys
+
+-- | @stripSuffix suf xs = Just pre@ iff @xs = pre ++ suf@.
+-- O(n).
+stripSuffix :: Eq a => Suffix a -> [a] -> Maybe (Prefix a)
+stripSuffix [] = Just
+stripSuffix s  = stripReversedSuffix (reverse s)
+
+type ReversedSuffix a = [a]
+
+-- | @stripReversedSuffix rsuf xs = Just pre@ iff @xs = pre ++ reverse suf@.
+--   O(n).
+stripReversedSuffix :: forall a. Eq a => ReversedSuffix a -> [a] -> Maybe (Prefix a)
+stripReversedSuffix rs = final . foldr step (SSSStrip rs)
+  where
+  -- Step of the automaton (reading input from right to left).
+  step :: a -> StrSufSt a -> StrSufSt a
+  step x = \case
+    SSSMismatch   -> SSSMismatch
+    SSSResult xs  -> SSSResult (x:xs)
+    SSSStrip []   -> SSSResult [x]
+    SSSStrip (y:ys)
+      | x == y    -> SSSStrip ys
+      | otherwise -> SSSMismatch
+
+  -- Output of the automaton.
+  final :: StrSufSt a -> Maybe (Prefix a)
+  final = \case
+    SSSResult xs -> Just xs
+    SSSStrip []  -> Just []
+    _            -> Nothing  -- We have not stripped the whole suffix or encountered a mismatch.
+
+-- | Internal state for stripping suffix.
+data StrSufSt a
+  = SSSMismatch                 -- ^ Error.
+  | SSSStrip (ReversedSuffix a) -- ^ "Negative string" to remove from end. List may be empty.
+  | SSSResult [a]               -- ^ "Positive string" (result). Non-empty list.
+
+-- | Returns a list with one boolean for each non-empty suffix of the
+-- list, starting with the longest suffix (the entire list). Each
+-- boolean is 'True' exactly when every element in the corresponding
+-- suffix satisfies the predicate.
+--
+-- An example:
+-- @
+--  'suffixesSatisfying' 'Data.Char.isLower' "AbCde" =
+--  [False, False, False, True, True]
+-- @
+--
+-- For total predicates @p@ and finite and total lists @xs@ the
+-- following holds:
+-- @
+--  'suffixesSatisfying' p xs = 'map' ('all' p) ('List.init' ('List.tails' xs))
+-- @
+suffixesSatisfying :: (a -> Bool) -> [a] -> [Bool]
+suffixesSatisfying p =
+  snd .
+  foldr (\x (b, bs) -> let !b' = p x && b in (b', b' : bs))
+        (True, [])
+
+-- ** Finding overlap
+
+-- | Find the longest suffix of the first string @xs@
+--   that is a prefix of the second string @ys@.
+--   So, basically, find the overlap where the strings can be glued together.
+--   Returns the index where the overlap starts and the length of the overlap.
+--   The length of the overlap plus the index is the length of the first string.
+--   Note that in the worst case, the empty overlap @(length xs,0)@ is returned.
+--
+--   Worst-case time complexity is quadratic: @O(min(n,m)²)@
+--   where @n = length xs@ and @m = length ys@.
+--
+--   There might be asymptotically better implementations following
+--   Knuth-Morris-Pratt (KMP), but for rather short lists this is good enough.
+--
+findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
+findOverlap xs ys =
+  headWithDefault __IMPOSSIBLE__ $ mapMaybe maybePrefix $ zip [0..] (List.tails xs)
+  where
+  maybePrefix :: (Int, [a]) -> Maybe (Int, Int)
+  maybePrefix (k, xs')
+    | xs' `List.isPrefixOf` ys = Just (k, length xs')
+    | otherwise                = Nothing
+
+---------------------------------------------------------------------------
+-- * Chunks
+---------------------------------------------------------------------------
+
+-- | Chop up a list in chunks of a given length.
+-- O(n).
+chop :: Int -> [a] -> [[a]]
+chop _ [] = []
+chop n xs = ys : chop n zs
+    where (ys,zs) = splitAt n xs
+
+-- | Chop a list at the positions when the predicate holds. Contrary to
+--   'wordsBy', consecutive separator elements will result in an empty segment
+--   in the result.
+--   O(n).
+--
+--    > intercalate [x] (chopWhen (== x) xs) == xs
+chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
+chopWhen p []     = []
+chopWhen p (x:xs) = loop (x :| xs)
+  where
+  -- Local function to avoid unnecessary pattern matching.
+  loop :: List1 a -> [[a]]
+  loop xs = case List1.break p xs of
+    (w, []        ) -> [w]
+    (w, _ : []    ) -> [w, []]
+    (w, _ : y : ys) -> w : loop (y :| ys)
+
+---------------------------------------------------------------------------
+-- * List as sets
+---------------------------------------------------------------------------
+
+-- | Check membership for the same list often.
+--   Use partially applied to create membership predicate
+--   @hasElem xs :: a -> Bool@.
+--
+--   * First time: @O(n log n)@ in the worst case.
+--   * Subsequently: @O(log n)@.
+--
+--   Specification: @hasElem xs == (`elem` xs)@.
+hasElem :: Ord a => [a] -> a -> Bool
+hasElem xs = (`Set.member` Set.fromList xs)
+
+-- | Check whether a list is sorted.
+-- O(n).
+--
+-- Assumes that the 'Ord' instance implements a partial order.
+
+sorted :: Ord a => [a] -> Bool
+sorted = allConsecutive (<=)
+
+-- | Check whether all consecutive elements of a list satisfy the given relation.
+-- O(n).
+--
+allConsecutive :: (a -> a -> Bool) -> [a] -> Bool
+allConsecutive cmp xs = and $ zipWith cmp xs $ drop 1 xs
+
+-- | Check whether all elements in a list are distinct from each other.
+--   Assumes that the 'Eq' instance stands for an equivalence relation.
+--
+--   O(n²) in the worst case @distinct xs == True@.
+distinct :: Eq a => [a] -> Bool
+distinct []     = True
+distinct (x:xs) = x `notElem` xs && distinct xs
+
+-- | An optimised version of 'distinct'.
+--   O(n log n).
+--
+--   Precondition: The list's length must fit in an 'Int'.
+
+fastDistinct :: Ord a => [a] -> Bool
+fastDistinct xs = Set.size (Set.fromList xs) == length xs
+
+-- | Returns an (arbitrary) representative for each list element
+--   that occurs more than once.
+--   O(n log n).
+duplicates :: Ord a => [a] -> [a]
+duplicates = mapMaybe dup . Bag.groups . Bag.fromList
+  where
+    dup (a : _ : _) = Just a
+    dup _           = Nothing
+
+-- | Remove the first representative for each list element.
+--   Thus, returns all duplicate copies.
+--   O(n log n).
+--
+--   @allDuplicates xs == sort $ xs \\ nub xs@.
+allDuplicates :: Ord a => [a] -> [a]
+allDuplicates = concatMap (drop 1 . reverse) . Bag.groups . Bag.fromList
+  -- The reverse is necessary to actually remove the *first* occurrence
+  -- of each element.
+
+-- | Partition a list into first and later occurrences of elements
+--   (modulo some quotient given by a representation function).
+--
+--  Time: O(n log n).
+--
+--  Specification:
+--
+--  > nubAndDuplicatesOn f xs = (ys, xs List.\\ ys)
+--  >   where ys = nubOn f xs
+
+nubAndDuplicatesOn :: Ord b => (a -> b) -> [a] -> ([a], [a])
+nubAndDuplicatesOn f = loop Set.empty
+  where
+  loop s [] = ([], [])
+  loop s (a:as)
+    | b `Set.member` s = second (a:) $ loop s as
+    | otherwise        = first  (a:) $ loop (Set.insert b s) as
+    where b = f a
+
+-- | Efficient variant of 'nubBy' for lists, using a set to store already seen elements.
+-- O(n log n)
+--
+-- Specification:
+--
+-- > nubOn f xs == 'nubBy' ((==) `'on'` f) xs.
+
+nubOn :: Ord b => (a -> b) -> [a] -> [a]
+nubOn f = loop Set.empty
+  where
+  loop s [] = []
+  loop s (a:as)
+    | b `Set.member` s = loop s as
+    | otherwise        = a : loop (Set.insert b s) as
+    where b = f a
+
+-- | A variant of 'nubOn' that is parametrised by a function that is
+-- used to select which element from a group of equal elements that is
+-- returned. The returned elements keep the order that they had in the
+-- input list.
+--
+-- Precondition: The length of the input list must be at most
+-- @'maxBound' :: 'Int'@.
+
+nubFavouriteOn
+  :: forall a b c. (Ord b, Eq c, Hashable c)
+  => (a -> b)
+     -- ^ The values returned by this function are used to determine
+     -- which element from a group of equal elements that is returned:
+     -- the smallest one is chosen (and if two elements are equally
+     -- small, then the first one is chosen).
+  -> (a -> c)
+     -- ^ Two elements are treated as equal if this function returns
+     -- the same value for both elements.
+  -> [a] -> [a]
+nubFavouriteOn fav f = go 0 HMap.empty
+  where
+  go :: Int -> HMap.HashMap c ((b, Int), a) -> [a] -> [a]
+  go !pos !acc (x : xs) =
+    go (1 + pos)
+       (HMap.insertWith
+          (\new old -> if fst new < fst old then new else old)
+          (f x) ((fav x, pos), x) acc)
+       xs
+  go _ acc [] =
+    map snd $ List.sortBy (compare `on` snd . fst) $
+    HMap.elems acc
+
+-- -- | Efficient variant of 'nubBy' for finite lists (using sorting).
+-- -- O(n log n)
+-- --
+-- -- Specification:
+-- --
+-- -- > nubOn2 f xs == 'nubBy' ((==) `'on'` f) xs.
+--
+-- nubOn2 :: Ord b => (a -> b) -> [a] -> [a]
+-- nubOn2 tag =
+--     -- Throw away numbering
+--   map snd
+--     -- Restore original order
+--   . List.sortBy (compare `on` fst)
+--     -- Retain first entry of each @tag@ group
+--   . map (snd . head)
+--   . List.groupBy ((==) `on` fst)
+--     -- Sort by tag (stable)
+--   . List.sortBy (compare `on` fst)
+--     -- Tag with @tag@ and sequential numbering
+--   . map (\p@(_, x) -> (tag x, p))
+--   . zip [1..]
+
+-- | Efficient variant of 'nubBy' for finite lists.
+-- O(n log n).
+--
+-- > uniqOn f == 'List.sortBy' (compare `'on'` f) . 'nubBy' ((==) `'on'` f)
+--
+-- If there are several elements with the same @f@-representative,
+-- the first of these is kept.
+--
+uniqOn :: Ord b => (a -> b) -> [a] -> [a]
+uniqOn key = Map.elems . Map.fromListWith (\ _ -> id) . map (\ a -> (key a, a))
+
+-- | Checks if all the elements in the list are equal. Assumes that
+--   the 'Eq' instance stands for an equivalence relation.
+--   O(n).
+allEqual :: Eq a => [a] -> Bool
+allEqual []       = True
+allEqual (x : xs) = all (== x) xs
+
+-- | Non-efficient, monadic 'nub'.
+-- O(n²).
+nubM :: Monad m => (a -> a -> m Bool) -> [a] -> m [a]
+nubM eq = loop where
+  loop []     = return []
+  loop (a:as) = (a :) <$> do loop =<< filterM (not <.> eq a) as
+
+---------------------------------------------------------------------------
+-- * Zipping
+---------------------------------------------------------------------------
+
+-- | Requires both lists to have the same length.
+--   O(n).
+--
+--   Otherwise, @Nothing@ is returned.
+
+zipWith' :: (a -> b -> c) -> [a] -> [b] -> Maybe [c]
+zipWith' f = loop
+  where
+  loop []        []      = Just []
+  loop (x : xs) (y : ys) = (f x y :) <$> loop xs ys
+  loop []       (_ : _)  = Nothing
+  loop (_ : _)  []       = Nothing
+
+-- | Like 'zipWith' but keep the rest of the second list as-is
+--   (in case the second list is longer).
+-- O(n).
+--
+-- @
+--   zipWithKeepRest f as bs == zipWith f as bs ++ drop (length as) bs
+-- @
+zipWithKeepRest :: (a -> b -> b) -> [a] -> [b] -> [b]
+zipWithKeepRest f = loop
+  where
+  loop []       bs       = bs
+  loop as       []       = []
+  loop (a : as) (b : bs) = f a b : loop as bs
+
+-- -- UNUSED; a better type would be
+-- -- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], Either [a] [b])
+
+-- -- | Like zipWith, but returns the leftover elements of the input lists.
+-- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], [a] , [b])
+-- zipWithTails f xs       []       = ([], xs, [])
+-- zipWithTails f []       ys       = ([], [] , ys)
+-- zipWithTails f (x : xs) (y : ys) = (f x y : zs , as , bs)
+--   where (zs , as , bs) = zipWithTails f xs ys
+
+
+---------------------------------------------------------------------------
+-- * Unzipping
+---------------------------------------------------------------------------
+
+unzipWith :: (a -> (b, c)) -> [a] -> ([b], [c])
+unzipWith f = unzip . map f
+
+---------------------------------------------------------------------------
+-- * Edit distance
+---------------------------------------------------------------------------
+
+-- | Implemented using tree recursion, don't run me at home!
+--   O(3^(min n m)).
+editDistanceSpec :: Eq a => [a] -> [a] -> Int
+editDistanceSpec [] ys = length ys
+editDistanceSpec xs [] = length xs
+editDistanceSpec (x : xs) (y : ys)
+  | x == y    = editDistanceSpec xs ys
+  | otherwise = 1 + minimum [ editDistanceSpec (x : xs) ys
+                            , editDistanceSpec xs (y : ys)
+                            , editDistanceSpec xs ys ]
+
+-- | Implemented using dynamic programming and @Data.Array@.
+--   O(n*m).
+editDistance :: forall a. Eq a => [a] -> [a] -> Int
+editDistance xs ys = editD 0 0
+  where
+  editD i j = tbl Array.! (i, j)
+  -- Tabulate editD' in immutable boxed array (content computed lazily).
+  tbl :: Array (Int,Int) Int
+  tbl = array ((0,0), (n,m)) [ ((i, j), editD' i j) | i <- [0..n], j <- [0..m] ]
+  editD' i j =
+    case (compare i n, compare j m) of
+      -- Interior
+      (LT, LT)
+        | xsA Array.! i == ysA Array.! j
+                    -> editD i' j'
+        | otherwise -> 1 + minimum [ editD i' j, editD i j', editD i' j' ]
+      -- Border: one list is empty
+      (EQ, LT)      ->  m - j
+      (LT, EQ)      ->  n - i
+      -- Corner (EQ, EQ): both lists are empty
+      _             -> 0
+      -- GT cases are impossible.
+    where (i', j') = (i + 1, j + 1)
+  n   = length xs
+  m   = length ys
+  xsA, ysA :: Array Int a
+  xsA = listArray (0, n - 1) xs
+  ysA = listArray (0, m - 1) ys
+
+
+mergeStrictlyOrderedBy :: (a -> a -> Bool) -> [a] -> [a] -> Maybe [a]
+mergeStrictlyOrderedBy (<) = loop where
+  loop [] ys = Just ys
+  loop xs [] = Just xs
+  loop (x:xs) (y:ys)
+    | x < y = (x:) <$> loop xs (y:ys)
+    | y < x = (y:) <$> loop (x:xs) ys
+    | otherwise = Nothing
diff --git a/src/full/Agda/Utils/List1.hs b/src/full/Agda/Utils/List1.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/List1.hs
@@ -0,0 +1,292 @@
+{-# LANGUAGE CPP #-}
+
+-- | Non-empty lists.
+--
+--   Better name @List1@ for non-empty lists, plus missing functionality.
+--
+--   Import:
+--   @
+--
+--     {-# LANGUAGE PatternSynonyms #-}
+--
+--     import           Agda.Utils.List1 (List1, pattern (:|))
+--     import qualified Agda.Utils.List1 as List1
+--
+--   @
+
+{-# OPTIONS_GHC -Wno-incomplete-patterns #-}
+  -- because of https://gitlab.haskell.org/ghc/ghc/issues/10339
+
+module Agda.Utils.List1
+  ( module Agda.Utils.List1
+  , module List1
+  , module IsList
+  ) where
+
+import Prelude hiding (filter)
+
+import Control.Arrow ((&&&))
+import Control.Monad (filterM)
+import qualified Control.Monad as List (zipWithM, zipWithM_)
+
+import qualified Data.Either as Either
+import Data.Function ( on )
+import qualified Data.List as List
+import qualified Data.Maybe as Maybe
+
+import Data.List.NonEmpty as List1 hiding (fromList, toList)
+import qualified Data.List.NonEmpty as List1 (toList)
+
+import GHC.Exts as IsList ( IsList(..) )
+
+import Agda.Utils.Functor ((<.>), (<&>))
+import Agda.Utils.Null (Null(..))
+import qualified Agda.Utils.List as List
+
+-- Set up doctest.
+-- $setup
+-- >>> :seti -XOverloadedLists
+
+type List1 = NonEmpty
+type String1 = List1 Char
+
+-- | Lossless 'toList', opposite of 'nonEmpty'.
+--
+toList' :: Maybe (List1 a) -> [a]
+toList' = maybe [] toList
+
+-- | Lift a function on non-empty lists to a function on lists.
+--
+-- This is in essence 'fmap' for 'Maybe', if we take @[a] = Maybe (List1 a)@.
+--
+liftList1 :: (List1 a -> List1 b) -> [a] -> [b]
+liftList1 f = toList' . fmap f . nonEmpty
+
+-- | Safe version of 'Data.List.NonEmpty.fromList'.
+
+fromListSafe
+  :: List1 a  -- ^ Default value if convertee is empty.
+  -> [a]      -- ^ List to convert, supposedly non-empty.
+  -> List1 a  -- ^ Converted list.
+fromListSafe err   [] = err
+fromListSafe _ (x:xs) = x :| xs
+
+-- | Return the last element and the rest.
+
+initLast :: List1 a -> ([a], a)
+initLast = List1.init &&& List1.last
+  -- traverses twice, but does not create intermediate pairs
+
+-- | Last two elements (safe).
+--   O(n).
+last2 :: List1 a -> Maybe (a, a)
+last2 (x :| y : xs) = Just $ List.last2' x y xs
+last2 _ = Nothing
+
+-- | Build a list with one element.
+
+#if !(MIN_VERSION_base(4,15,0))
+singleton :: a -> List1 a
+singleton = (:| [])
+#endif
+
+#if !MIN_VERSION_base(4,16,0)
+-- | Append a list to a non-empty list.
+
+appendList :: List1 a -> [a] -> List1 a
+appendList (x :| xs) ys = x :| mappend xs ys
+
+-- | Prepend a list to a non-empty list.
+
+prependList :: [a] -> List1 a -> List1 a
+prependList as bs = Prelude.foldr (<|) bs as
+#endif
+
+-- | More precise type for @snoc@.
+
+snoc :: [a] -> a -> List1 a
+snoc as a = prependList as $ a :| []
+
+-- | @'groupOn' f = 'groupBy' (('==') \`on\` f) '.' 'List.sortBy' ('compare' \`on\` f)@.
+-- O(n log n).
+groupOn :: Ord b => (a -> b) -> [a] -> [List1 a]
+groupOn f = List1.groupBy ((==) `on` f) . List.sortBy (compare `on` f)
+
+groupOn1 :: Ord b => (a -> b) -> List1 a -> List1 (List1 a)
+groupOn1 f = List1.groupBy1 ((==) `on` f) . List1.sortBy (compare `on` f)
+
+-- | More precise type for 'Agda.Utils.List.groupBy''.
+--
+-- A variant of 'List.groupBy' which applies the predicate to consecutive
+-- pairs.
+-- O(n).
+groupBy' :: forall a. (a -> a -> Bool) -> [a] -> [List1 a]
+groupBy' _ []           = []
+groupBy' p xxs@(x : xs) = grp x $ List.zipWith (\ x y -> (p x y, y)) xxs xs
+  where
+  grp :: a -> [(Bool,a)] -> [List1 a]
+  grp x ys
+    | let (xs, rest) = List.span fst ys
+    = (x :| List.map snd xs) : case rest of
+      []                 -> []
+      ((_false, z) : zs) -> grp z zs
+
+-- | Group consecutive items that share the same first component.
+--
+groupByFst :: forall a b. Eq a => [(a,b)] -> [(a, List1 b)]
+groupByFst =
+    List.map (\ ((tag, b) :| xs) -> (tag, b :| List.map snd xs))
+      -- Float the grouping to the top level
+  . List1.groupBy ((==) `on` fst)
+      -- Group together characters in the same role.
+
+-- | Group consecutive items that share the same first component.
+--
+groupByFst1 :: forall a b. Eq a => List1 (a, b) -> List1 (a, List1 b)
+groupByFst1 =
+    fmap (\ ((tag, b) :| xs) -> (tag, b :| List.map snd xs))
+      -- Float the grouping to the top level
+  . List1.groupBy1 ((==) `on` fst)
+      -- Group together characters in the same role.
+
+-- | Split a list into sublists. Generalisation of the prelude function
+--   @words@.
+--   Same as 'Data.List.Split.wordsBy' and 'Data.List.Extra.wordsBy',
+--   but with the non-emptyness guarantee on the chunks.
+--   O(n).
+--
+--   > words xs == wordsBy isSpace xs
+wordsBy :: (a -> Bool) -> [a] -> [List1 a]
+wordsBy p = loop
+  where
+  loop as = case List.dropWhile p as of
+    []   -> []
+    x:xs -> (x :| ys) : loop zs where (ys, zs) = List.break p xs
+
+-- | Breaks a list just /after/ an element satisfying the predicate is
+--   found.
+--
+--   >>> breakAfter even [1,3,5,2,4,7,8]
+--   (1 :| [3,5,2],[4,7,8])
+
+breakAfter :: (a -> Bool) -> List1 a -> (List1 a, [a])
+breakAfter p (x :| xs) = List.breakAfter1 p x xs
+
+-- | Concatenate one or more non-empty lists.
+
+concat :: [List1 a] -> [a]
+concat = concatMap toList
+
+concatMap1 :: (a -> List1 b) -> List1 a -> List1 b
+concatMap1 = (=<<)
+
+-- | Like 'Data.List.union'.  Duplicates in the first list are not removed.
+-- O(nm).
+union :: Eq a => List1 a -> List1 a -> List1 a
+union (a :| as) bs = a :| List.union as (filter (/= a) bs)
+
+-- * Recovering non-emptyness.
+
+ifNull :: [a] -> b -> (List1 a -> b) -> b
+ifNull []       b _ = b
+ifNull (a : as) _ f = f $ a :| as
+
+ifNotNull :: [a] -> (List1 a -> b) -> b -> b
+ifNotNull []       _ b = b
+ifNotNull (a : as) f _ = f $ a :| as
+
+unlessNull :: Null m => [a] -> (List1 a -> m) -> m
+unlessNull []       _ = empty
+unlessNull (x : xs) f = f $ x :| xs
+
+-- * List functions with no special behavior for non-empty lists.
+
+-- | Checks if all the elements in the list are equal. Assumes that
+--   the 'Eq' instance stands for an equivalence relation.
+--   O(n).
+allEqual :: Eq a => List1 a -> Bool
+allEqual (x :| xs) = all (== x) xs
+
+-- | Like 'Maybe.catMaybes'.
+
+catMaybes :: List1 (Maybe a) -> [a]
+catMaybes =  Maybe.catMaybes . List1.toList
+
+-- | Like 'Maybe.mapMaybe'.
+
+mapMaybe :: (a -> Maybe b) -> List1 a -> [b]
+mapMaybe f = Maybe.mapMaybe f . List1.toList
+
+-- | Like 'List.find'.
+
+find :: (a -> Bool) -> List1 a -> Maybe a
+find f = List.find f . List1.toList
+
+-- | Like 'Data.Either.partitionEithers'.
+
+partitionEithers :: List1 (Either a b) -> ([a], [b])
+partitionEithers = Either.partitionEithers . List1.toList
+
+-- | Like 'Data.Either.lefts'.
+
+lefts :: List1 (Either a b) -> [a]
+lefts = Either.lefts  . List1.toList
+
+-- | Like 'Data.Either.rights'.
+
+rights :: List1 (Either a b) -> [b]
+rights = Either.rights  . List1.toList
+
+-- | Like 'Data.List.unwords'.
+
+unwords :: List1 String -> String
+unwords = List.unwords . List1.toList
+
+-- | Non-efficient, monadic 'nub'.
+-- O(n²).
+nubM :: Monad m => (a -> a -> m Bool) -> List1 a -> m (List1 a)
+nubM eq (a :| as) = (a :|) <$> do List.nubM eq =<< filterM (not <.> eq a) as
+
+-- | Like 'Control.Monad.zipWithM'.
+
+zipWithM :: Applicative m => (a -> b -> m c) -> List1 a -> List1 b -> m (List1 c)
+zipWithM f (a :| as) (b :| bs) = (:|) <$> f a b <*> List.zipWithM f as bs
+
+-- | Like 'Control.Monad.zipWithM'.
+
+zipWithM_ :: Applicative m => (a -> b -> m c) -> List1 a -> List1 b -> m ()
+zipWithM_ f (a :| as) (b :| bs) = f a b *> List.zipWithM_ f as bs
+
+-- | List 'Data.List.foldr' but with a base case for the singleton list.
+
+foldr :: (a -> b -> b) -> (a -> b) -> List1 a -> b
+foldr f g (x :| xs) = loop x xs
+  where
+  loop x []       = g x
+  loop x (y : ys) = f x $ loop y ys
+
+-- | Update the first element of a non-empty list.
+--   O(1).
+updateHead :: (a -> a) -> List1 a -> List1 a
+updateHead f (a :| as) = f a :| as
+
+-- | Update the last element of a non-empty list.
+--   O(n).
+updateLast :: (a -> a) -> List1 a -> List1 a
+updateLast f (a :| as) = loop a as
+  where
+  loop a []       = singleton $ f a
+  loop a (b : bs) = cons a $ loop b bs
+
+-- | Focus on the first element of a non-empty list.
+--   O(1).
+lensHead :: Functor f => (a -> f a) -> List1 a -> f (List1 a)
+lensHead f (a :| as) = f a <&> (:| as)
+
+-- | Focus on the last element of a non-empty list.
+--   O(n).
+lensLast :: Functor f => (a -> f a) -> List1 a -> f (List1 a)
+lensLast f (a :| as) = loop a as
+  where
+  loop a []       = singleton <$> f a
+  loop a (b : bs) = cons a <$> loop b bs
diff --git a/src/full/Agda/Utils/List1.hs-boot b/src/full/Agda/Utils/List1.hs-boot
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/List1.hs-boot
@@ -0,0 +1,5 @@
+module Agda.Utils.List1 where
+
+import qualified Data.List.NonEmpty (NonEmpty)
+
+type List1 = Data.List.NonEmpty.NonEmpty
diff --git a/src/full/Agda/Utils/List2.hs b/src/full/Agda/Utils/List2.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/List2.hs
@@ -0,0 +1,112 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Lists of length at least 2.
+--
+--   Import as:
+--   @
+--      import Agda.Utils.List2 (List2(List2))
+--      import qualified Agda.Utils.List2 as List2
+--   @
+
+module Agda.Utils.List2
+  ( module Agda.Utils.List2
+  , module Reexport
+  ) where
+
+import Control.DeepSeq
+import Control.Monad                   ( (<=<) )
+
+import qualified Data.List as List
+
+import GHC.Exts                        ( IsList(..) )
+import qualified GHC.Exts  as Reexport ( toList )
+
+import Agda.Utils.List1                ( List1, pattern (:|) )
+import qualified Agda.Utils.List1 as List1
+
+import Agda.Utils.Impossible
+
+-- | Lists of length ≥2.
+data List2 a = List2 a a [a]
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+-- * Conversion from and to other list types.
+
+-- | 'fromList' is unsafe.
+instance IsList (List2 a) where
+  type Item (List2 a) = a
+
+  -- Unsafe! O(1).
+  fromList :: [a] -> List2 a
+  fromList (a : b : cs) = List2 a b cs
+  fromList _            = __IMPOSSIBLE__
+
+  toList :: List2 a -> [a]
+  toList (List2 a b cs) = a : b : cs
+
+-- | Unsafe! O(1).
+fromList1 :: List1 a -> List2 a
+fromList1 (a :| b : cs) = List2 a b cs
+fromList1 _             = __IMPOSSIBLE__
+
+-- | Safe. O(1).
+toList1 :: List2 a -> List1 a
+toList1 (List2 a b cs) = a :| b : cs
+
+-- | Safe. O(1).
+fromListMaybe :: [a] -> Maybe (List2 a)
+fromListMaybe = fromList1Maybe <=< List1.nonEmpty
+
+-- | Safe. O(1).
+fromList1Maybe :: List1 a -> Maybe (List2 a)
+fromList1Maybe = \case
+  (a :| b : cs) -> Just (List2 a b cs)
+  _ -> Nothing
+
+-- | Any 'List1' is either a singleton or a 'List2'. O(1).
+fromList1Either :: List1 a -> Either a (List2 a)
+fromList1Either (a :| as) = case as of
+  []   -> Left a
+  b:bs -> Right (List2 a b bs)
+
+-- | Inverse of 'fromList1Either'. O(1).
+toList1Either :: Either a (List2 a) -> List1 a
+toList1Either = \case
+  Left  a              -> a :| []
+  Right (List2 a b bs) -> a :| b : bs
+
+-- * Construction
+
+-- | O(1).
+cons :: a -> List1 a -> List2 a
+cons x (y :| ys) = List2 x y ys
+
+-- | O(length first list).
+append :: List1 a -> List1 a -> List2 a
+append (x :| xs) ys = cons x $ List1.prependList xs ys
+
+-- | O(length first list).
+appendList :: List2 a -> [a] -> List2 a
+appendList (List2 x y ys) zs = List2 x y $ mappend ys zs
+
+-- * Destruction
+
+-- | Safe. O(1).
+head :: List2 a -> a
+head (List2 a _ _) = a
+
+-- | Safe. O(1).
+tail :: List2 a -> List1 a
+tail (List2 a b cs) = b :| cs
+
+-- | Safe. O(n).
+init :: List2 a -> List1 a
+init (List2 a b cs) = a :| List1.init (b :| cs)
+
+-- * Partition
+
+break :: (a -> Bool) -> List2 a -> ([a],[a])
+break p = List.break p . toList
+
+instance NFData a => NFData (List2 a) where
+  rnf (List2 a b cs) = rnf a `seq` rnf b `seq` rnf cs
diff --git a/src/full/Agda/Utils/ListT.hs b/src/full/Agda/Utils/ListT.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/ListT.hs
@@ -0,0 +1,160 @@
+{-# LANGUAGE UndecidableInstances  #-} -- Due MonadReader/MonadState fundep
+
+-- | @ListT@ done right,
+--   see https://www.haskell.org/haskellwiki/ListT_done_right_alternative
+--
+--   There is also the @list-t@ package on hackage (Nikita Volkov)
+--   but it again depends on other packages we do not use yet,
+--   so we rather implement the few bits we need afresh.
+
+module Agda.Utils.ListT where
+
+import Control.Applicative ( Alternative((<|>), empty) )
+import Control.Monad
+import Control.Monad.Fail as Fail
+import Control.Monad.Reader
+import Control.Monad.State
+import Control.Monad.IO.Class ( MonadIO(..) )
+
+import Agda.Utils.Maybe
+import Agda.Utils.Monad
+
+-- | Lazy monadic computation of a list of results.
+newtype ListT m a = ListT { runListT :: m (Maybe (a, ListT m a)) }
+  deriving (Functor)
+
+-- | Boilerplate function to lift 'MonadReader' through the 'ListT' transformer.
+mapListT :: (m (Maybe (a, ListT m a)) -> n (Maybe (b, ListT n b))) -> ListT m a -> ListT n b
+mapListT f = ListT . f . runListT
+
+-- | Inverse to 'mapListT'.
+unmapListT :: (ListT m a -> ListT n b) -> m (Maybe (a, ListT m a)) -> n (Maybe (b, ListT n b))
+unmapListT f = runListT . f . ListT
+
+-- * List operations
+
+-- | The empty lazy list.
+nilListT :: Monad m => ListT m a
+nilListT = ListT $ return Nothing
+
+-- | Consing a value to a lazy list.
+consListT :: Monad m => a -> ListT m a -> ListT m a
+consListT a l = ListT $ return $ Just (a, l)
+
+-- | Singleton lazy list.
+sgListT ::  Monad m => a -> ListT m a
+sgListT a = consListT a nilListT
+
+-- | Case distinction over lazy list.
+caseListT :: Monad m => ListT m a -> m b -> (a -> ListT m a -> m b) -> m b
+caseListT l nil cons = caseMaybeM (runListT l) nil $ uncurry cons
+
+-- | Folding a lazy list, effects left-to-right.
+foldListT :: Monad m => (a -> m b -> m b) -> m b -> ListT m a -> m b
+foldListT cons nil = loop where
+  loop l = caseListT l nil $ \ a l' -> cons a $ loop l'
+
+-- | Lazy monadic disjunction of lazy monadic list, effects left-to-right
+anyListT :: Monad m => ListT m a -> (a -> m Bool) -> m Bool
+anyListT xs f = foldListT (or2M . f) (return False) xs
+
+-- | Lazy monadic conjunction of lazy monadic list, effects left-to-right
+allListT :: Monad m => ListT m a -> (a -> m Bool) -> m Bool
+allListT xs f = foldListT (and2M . f) (return True) xs
+
+-- | Force all values in the lazy list, effects left-to-right
+sequenceListT :: Monad m => ListT m a -> m [a]
+sequenceListT = foldListT ((<$>) . (:)) $ pure []
+
+-- | The join operation of the @ListT m@ monad.
+concatListT :: Monad m => ListT m (ListT m a) -> ListT m a
+concatListT = ListT . foldListT (unmapListT . mappend) (return Nothing)
+
+-- * Monadic list operations.
+
+-- | We can ``run'' a computation of a 'ListT' as it is monadic itself.
+runMListT :: Monad m => m (ListT m a) -> ListT m a
+runMListT ml = ListT $ runListT =<< ml
+
+-- | Monadic cons.
+consMListT :: Monad m => m a -> ListT m a -> ListT m a
+consMListT ma l = ListT $ (Just . (,l)) <$> ma
+-- consMListT ma l = runMListT $ liftM (`consListT` l) ma
+
+-- simplification:
+-- consMListT ma l = ListT $ runListT =<< liftM (`consListT` l) ma
+-- consMListT ma l = ListT $ runListT =<< (`consListT` l) <$> ma
+-- consMListT ma l = ListT $ runListT =<< do a <- ma; return $ a `consListT` l
+-- consMListT ma l = ListT $ do a <- ma; runListT =<< do return $ a `consListT` l
+-- consMListT ma l = ListT $ do a <- ma; runListT $ a `consListT` l
+-- consMListT ma l = ListT $ do a <- ma; runListT $ ListT $ return $ Just (a, l)
+-- consMListT ma l = ListT $ do a <- ma; return $ Just (a, l)
+-- consMListT ma l = ListT $ Just . (,l) <$> ma
+
+-- | Monadic singleton.
+sgMListT ::  Monad m => m a -> ListT m a
+sgMListT ma = consMListT ma nilListT
+
+-- | Extending a monadic function to 'ListT'.
+mapMListT :: Monad m => (a -> m b) -> ListT m a -> ListT m b
+mapMListT f (ListT ml) = ListT $ do
+  caseMaybeM ml (return Nothing) $ \ (a, as) -> do
+    b  <- f a
+    return $ Just (b , mapMListT f as)
+
+-- | Alternative implementation using 'foldListT'.
+mapMListT_alt :: Monad m => (a -> m b) -> ListT m a -> ListT m b
+mapMListT_alt f = runMListT . foldListT cons (return nilListT)
+  where cons a ml = consMListT (f a) <$> ml
+
+-- | Change from one monad to another
+liftListT :: (Monad m, Monad m') => (forall a. m a -> m' a) -> ListT m a -> ListT m' a
+liftListT lift xs = runMListT $ caseMaybeM (lift $ runListT xs) (return nilListT) $
+    \(x,xs) -> return $ consListT x $ liftListT lift xs
+
+-- Instances
+
+instance Monad m => Semigroup (ListT m a) where
+  l1 <> l2 = ListT $ foldListT (unmapListT . consListT) (runListT l2) l1
+
+instance Monad m => Monoid (ListT m a) where
+  mempty = nilListT
+
+instance (Functor m, Applicative m, Monad m) => Alternative (ListT m) where
+  empty = mempty
+  (<|>) = mappend
+
+instance (Functor m, Applicative m, Monad m) => MonadPlus (ListT m) where
+  mzero = mempty
+  mplus = mappend
+
+instance (Functor m, Applicative m, Monad m) => Applicative (ListT m) where
+  pure  = sgListT
+  (<*>) = ap
+
+  -- Another Applicative, but not the canonical one.
+  -- l1 <*> l2 = ListT $ loop <$> runListT l1 <*> runListT l2
+  --   where
+  --   loop (Just (f, l1')) (Just (a, l2')) = Just (f a, l1' <*> l2')
+  --   loop _ _ = Nothing
+
+instance (Functor m, Applicative m, Monad m) => Monad (ListT m) where
+  return  = pure
+  l >>= k = concatListT $ k <$> l
+
+instance MonadTrans ListT where
+  lift = sgMListT
+
+instance (Applicative m, MonadIO m) => MonadIO (ListT m) where
+  liftIO = lift . liftIO
+
+instance (Applicative m, MonadReader r m) => MonadReader r (ListT m) where
+  ask     = lift ask
+  local   = mapListT . local
+
+instance (Applicative m, MonadState s m) => MonadState s (ListT m) where
+  get = lift get
+  put = lift . put
+
+instance Monad m => MonadFail (ListT m) where
+  fail _ = empty
diff --git a/src/full/Agda/Utils/Map.hs b/src/full/Agda/Utils/Map.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Map.hs
@@ -0,0 +1,74 @@
+module Agda.Utils.Map where
+
+import Data.Functor.Compose
+import Data.Map (Map)
+import qualified Data.Map as Map
+-- import Data.Maybe (mapMaybe) -- UNUSED
+
+import Agda.Utils.Impossible
+
+-- * Monadic map operations
+---------------------------------------------------------------------------
+
+-- | Update monadically the value at one position (must exist!).
+adjustM :: (Functor f, Ord k) => (v -> f v) -> k -> Map k v -> f (Map k v)
+adjustM f = Map.alterF $ \case
+  Nothing -> __IMPOSSIBLE__
+  Just v  -> Just <$> f v
+
+-- | Wrapper for 'adjustM' for convenience.
+adjustM' :: (Functor f, Ord k) => (v -> f (a, v)) -> k -> Map k v -> f (a, Map k v)
+adjustM' f k = getCompose . adjustM (Compose . f) k
+
+-- UNUSED Liang-Ting Chen (05-07-2019)
+-- data EitherOrBoth a b = L a | B a b | R b
+--
+-- -- | Not very efficient (goes via a list), but it'll do.
+-- unionWithM :: (Ord k, Monad m) => (a -> a -> m a) -> Map k a -> Map k a -> m (Map k a)
+-- unionWithM f m1 m2 = fromList <$> mapM combine (toList m)
+--     where
+--         m = unionWith both (map L m1) (map R m2)
+--
+--         both (L a) (R b) = B a b
+--         both _     _     = __IMPOSSIBLE__
+--
+--         combine (k, B a b) = (,) k <$> f a b
+--         combine (k, L a)   = return (k, a)
+--         combine (k, R b)   = return (k, b)
+--
+-- UNUSED Liang-Ting Chen (05-07-2019)
+-- insertWithKeyM :: (Ord k, Monad m) => (k -> a -> a -> m a) -> k -> a -> Map k a -> m (Map k a)
+-- insertWithKeyM clash k x m =
+--     case lookup k m of
+--         Just y  -> do
+--             z <- clash k x y
+--             return $ insert k z m
+--         Nothing -> return $ insert k x m
+
+-- * Non-monadic map operations
+---------------------------------------------------------------------------
+
+-- UNUSED Liang-Ting Chen (05-07-2019)
+-- -- | Big conjunction over a map.
+-- allWithKey :: (k -> a -> Bool) -> Map k a -> Bool
+-- allWithKey f = Map.foldrWithKey (\ k a b -> f k a && b) True
+
+-- | Filter a map based on the keys.
+filterKeys :: (k -> Bool) -> Map k a -> Map k a
+filterKeys p = Map.filterWithKey (const . p)
+
+-- UNUSED Andreas (2021-08-19)
+-- -- | O(n log n).  Rebuilds the map from scratch.
+-- --   Not worse than 'Map.mapKeys'.
+-- mapMaybeKeys :: (Ord k1, Ord k2) => (k1 -> Maybe k2) -> Map k1 a -> Map k2 a
+-- mapMaybeKeys f = Map.fromList . mapMaybe (\ (k,a) -> (,a) <$> f k) . Map.toList
+
+-- UNUSED Liang-Ting Chen (05-07-2019)
+-- -- | Unzip a map.
+-- unzip :: Map k (a, b) -> (Map k a, Map k b)
+-- unzip m = (Map.map fst m, Map.map snd m)
+--
+-- UNUSED Liang-Ting Chen (05-07-2019)
+-- unzip3 :: Map k (a, b, c) -> (Map k a, Map k b, Map k c)
+-- unzip3 m = (Map.map fst3 m, Map.map snd3 m, Map.map thd3 m)
+--
diff --git a/src/full/Agda/Utils/Maybe.hs b/src/full/Agda/Utils/Maybe.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Maybe.hs
@@ -0,0 +1,129 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Extend 'Data.Maybe' by common operations for the 'Maybe' type.
+--
+--   Note: since this module is usually imported unqualified,
+--   we do not use short names, but all names contain 'Maybe',
+--   'Just', or 'Nothing.
+
+module Agda.Utils.Maybe
+    ( module Agda.Utils.Maybe
+    , module Data.Maybe
+    ) where
+
+import Control.Applicative
+import Control.Monad.Trans.Maybe
+
+import Data.Maybe
+
+-- * Conversion.
+
+-- | Retain object when tag is 'True'.
+boolToMaybe :: Bool -> a -> Maybe a
+boolToMaybe b x = if b then Just x else Nothing
+
+-- * Collection operations.
+
+-- | @unionWith@ for collections of size <= 1.
+unionMaybeWith :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a
+unionMaybeWith f Nothing mb      = mb
+unionMaybeWith f ma      Nothing = ma
+unionMaybeWith f (Just a) (Just b) = Just $ f a b
+
+-- | @unionsWith@ for collections of size <= 1.
+unionsMaybeWith :: (a -> a -> a) -> [Maybe a] -> Maybe a
+unionsMaybeWith f ms = case catMaybes ms of
+  [] -> Nothing
+  as -> Just $ foldl1 f as
+
+-- | Unzipping a list of length <= 1.
+
+unzipMaybe :: Maybe (a,b) -> (Maybe a, Maybe b)
+unzipMaybe Nothing      = (Nothing, Nothing)
+unzipMaybe (Just (a,b)) = (Just a, Just b)
+
+-- | Filtering a singleton list.
+--
+--   @filterMaybe p a = 'listToMaybe' ('filter' p [a])@
+
+filterMaybe :: (a -> Bool) -> a -> Maybe a
+filterMaybe p a
+  | p a       = Just a
+  | otherwise = Nothing
+
+-- * Conditionals and loops.
+
+-- | Version of 'mapMaybe' with different argument ordering.
+
+forMaybe :: [a] -> (a -> Maybe b) -> [b]
+forMaybe = flip mapMaybe
+
+-- | Version of 'maybe' with different argument ordering.
+--   Often, we want to case on a 'Maybe', do something interesting
+--   in the 'Just' case, but only a default action in the 'Nothing'
+--   case.  Then, the argument ordering of @caseMaybe@ is preferable.
+--
+--   @caseMaybe m d f = flip (maybe d) m f@
+caseMaybe :: Maybe a -> b -> (a -> b) -> b
+caseMaybe m d f = maybe d f m
+
+-- | 'caseMaybe' with flipped branches.
+ifJust :: Maybe a -> (a -> b) -> b -> b
+ifJust m f d = maybe d f m
+
+-- * Monads and Maybe.
+
+-- | Monadic version of 'maybe'.
+
+maybeM :: Monad m => m b -> (a -> m b) -> m (Maybe a) -> m b
+maybeM n j mm = maybe n j =<< mm
+
+-- | Monadic version of 'fromMaybe'.
+
+fromMaybeM :: Monad m => m a -> m (Maybe a) -> m a
+fromMaybeM m mm = maybeM m return mm
+
+-- | Monadic version of 'caseMaybe'.
+--   That is, 'maybeM' with a different argument ordering.
+caseMaybeM :: Monad m => m (Maybe a) -> m b -> (a -> m b) -> m b
+caseMaybeM mm d f = maybeM d f mm
+
+-- | 'caseMaybeM' with flipped branches.
+ifJustM :: Monad m => m (Maybe a) -> (a -> m b) -> m b -> m b
+ifJustM mm = flip (caseMaybeM mm)
+
+-- | A more telling name for 'Traversable.forM_' for the 'Maybe' collection type.
+--   Or: 'caseMaybe' without the 'Nothing' case.
+whenJust :: Monad m => Maybe a -> (a -> m ()) -> m ()
+whenJust m k = caseMaybe m (return ()) k
+
+-- | 'caseMaybe' without the 'Just' case.
+whenNothing :: Monoid m => Maybe a -> m -> m
+whenNothing m d = caseMaybe m d (\_ -> mempty)
+
+-- | 'caseMaybeM' without the 'Nothing' case.
+whenJustM :: Monad m => m (Maybe a) -> (a -> m ()) -> m ()
+whenJustM c m = c >>= (`whenJust` m)
+
+-- | 'caseMaybeM' without the 'Just' case.
+whenNothingM :: Monad m => m (Maybe a) -> m () -> m ()
+whenNothingM mm d = maybe d (\_ -> return ()) =<< mm
+
+-- | Lazy version of @allJust <.> sequence@.
+--   (@allJust = mapM@ for the @Maybe@ monad.)
+--   Only executes monadic effect while @isJust@.
+allJustM :: Monad m => [m (Maybe a)] -> m (Maybe [a])
+allJustM = runMaybeT . mapM MaybeT
+
+-- | Lift a maybe to an Alternative.
+liftMaybe :: Alternative f => Maybe a -> f a
+liftMaybe = maybe empty pure
+
+-- | Like 'span', takes the prefix of a list satisfying a predicate.
+-- Returns the run of 'Just's until the first 'Nothing', and the tail of
+-- the list.
+spanMaybe :: (a -> Maybe b) -> [a] -> ([b],[a])
+spanMaybe _ [] = ([], [])
+spanMaybe p xs@(x:xs') = case p x of
+    Just y  -> let (ys, zs) = spanMaybe p xs' in (y : ys, zs)
+    Nothing -> ([], xs)
diff --git a/src/full/Agda/Utils/Maybe/Strict.hs b/src/full/Agda/Utils/Maybe/Strict.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Maybe/Strict.hs
@@ -0,0 +1,105 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | A strict version of the 'Maybe' type.
+--
+--   Import qualified, as in
+--   @
+--     import qualified Agda.Utils.Maybe.Strict as Strict
+--   @
+
+module Agda.Utils.Maybe.Strict
+  ( module Data.Strict.Maybe
+  , module Data.Strict.Classes
+  , module Agda.Utils.Maybe.Strict
+  ) where
+
+import Prelude hiding (Maybe(..), maybe)
+
+import Data.Strict.Classes
+import Data.Strict.Maybe
+
+import Agda.Utils.Null
+
+-- | Note that strict Maybe is an 'Applicative' only modulo strictness.
+--   The laws only hold in the strict semantics.
+--   Eg. @pure f <*> pure _|_ = _|_@, but according to the laws for
+--   'Applicative' it should be @pure (f _|_)@.
+--   We ignore this issue here, it applies also to 'Foldable' and 'Traversable'.
+
+instance Applicative Maybe where
+  pure              = Just
+  Just f <*> Just x = Just $ f x
+  _      <*> _      = Nothing
+
+instance Null (Maybe a) where
+  empty = Nothing
+  null = isNothing
+
+-- * Collection operations.
+
+-- | @unionWith@ for collections of size <= 1.
+unionMaybeWith :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a
+unionMaybeWith f Nothing mb      = mb
+unionMaybeWith f ma      Nothing = ma
+unionMaybeWith f (Just a) (Just b) = Just $ f a b
+
+-- | Unzipping a list of length <= 1.
+
+unzipMaybe :: Maybe (a,b) -> (Maybe a, Maybe b)
+unzipMaybe Nothing      = (Nothing, Nothing)
+unzipMaybe (Just (a,b)) = (Just a, Just b)
+
+-- | Filtering a singleton list.
+--
+--   @filterMaybe p a = 'listToMaybe' ('filter' p [a])@
+
+filterMaybe :: (a -> Bool) -> a -> Maybe a
+filterMaybe p a
+  | p a       = Just a
+  | otherwise = Nothing
+
+-- * Conditionals and loops.
+
+-- | Version of 'mapMaybe' with different argument ordering.
+
+forMaybe :: [a] -> (a -> Maybe b) -> [b]
+forMaybe = flip mapMaybe
+
+-- | Version of 'maybe' with different argument ordering.
+--   Often, we want to case on a 'Maybe', do something interesting
+--   in the 'Just' case, but only a default action in the 'Nothing'
+--   case.  Then, the argument ordering of @caseMaybe@ is preferable.
+--
+--   @caseMaybe m err f = flip (maybe err) m f@
+caseMaybe :: Maybe a -> b -> (a -> b) -> b
+caseMaybe m err f = maybe err f m
+
+-- * Monads and Maybe.
+
+-- | Monadic version of 'maybe'.
+
+maybeM :: Monad m => m b -> (a -> m b) -> m (Maybe a) -> m b
+maybeM n j mm = maybe n j =<< mm
+
+-- | Monadic version of 'fromMaybe'.
+
+fromMaybeM :: Monad m => m a -> m (Maybe a) -> m a
+fromMaybeM m mm = maybeM m return mm
+
+-- | Monadic version of 'caseMaybe'.
+--   That is, 'maybeM' with a different argument ordering.
+caseMaybeM :: Monad m => m (Maybe a) -> m b -> (a -> m b) -> m b
+caseMaybeM mm err f = maybeM  err f mm
+
+-- | 'caseMaybeM' with flipped branches.
+ifJustM :: Monad m => m (Maybe a) -> (a -> m b) -> m b -> m b
+ifJustM mm = flip (caseMaybeM mm)
+
+-- | A more telling name for 'Traversable.forM' for the 'Maybe' collection type.
+--   Or: 'caseMaybe' without the 'Nothing' case.
+whenJust :: Monad m => Maybe a -> (a -> m ()) -> m ()
+whenJust m k = caseMaybe m (return ()) k
+
+-- | 'caseMaybeM' without the 'Nothing' case.
+whenJustM :: Monad m => m (Maybe a) -> (a -> m ()) -> m ()
+whenJustM c m = c >>= (`whenJust` m)
diff --git a/src/full/Agda/Utils/Memo.hs b/src/full/Agda/Utils/Memo.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Memo.hs
@@ -0,0 +1,66 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Memo where
+
+import Control.Monad.State
+import System.IO.Unsafe
+import Data.IORef
+import qualified Data.Map as Map
+import qualified Data.HashMap.Strict as HMap
+import Data.Hashable
+
+import Agda.Utils.Lens
+
+-- Simple memoisation in a state monad
+
+-- | Simple, non-reentrant memoisation.
+memo :: MonadState s m => Lens' s (Maybe a) -> m a -> m a
+memo tbl compute = do
+  mv <- use tbl
+  case mv of
+    Just x  -> return x
+    Nothing -> do
+      x <- compute
+      x <$ (tbl .= Just x)
+
+-- | Recursive memoisation, second argument is the value you get
+--   on recursive calls.
+memoRec :: MonadState s m => Lens' s (Maybe a) -> a -> m a -> m a
+memoRec tbl ih compute = do
+  mv <- use tbl
+  case mv of
+    Just x  -> return x
+    Nothing -> do
+      tbl .= Just ih
+      x <- compute
+      x <$ (tbl .= Just x)
+
+{-# NOINLINE memoUnsafe #-}
+memoUnsafe :: Ord a => (a -> b) -> (a -> b)
+memoUnsafe f = unsafePerformIO $ do
+  tbl <- newIORef Map.empty
+  return (unsafePerformIO . f' tbl)
+  where
+    f' tbl x = do
+      m <- readIORef tbl
+      case Map.lookup x m of
+        Just y  -> return y
+        Nothing -> do
+          let y = f x
+          writeIORef tbl (Map.insert x y m)
+          return y
+
+{-# NOINLINE memoUnsafeH #-}
+memoUnsafeH :: (Eq a, Hashable a) => (a -> b) -> (a -> b)
+memoUnsafeH f = unsafePerformIO $ do
+  tbl <- newIORef HMap.empty
+  return (unsafePerformIO . f' tbl)
+  where
+    f' tbl x = do
+      m <- readIORef tbl
+      case HMap.lookup x m of
+        Just y  -> return y
+        Nothing -> do
+          let y = f x
+          writeIORef tbl (HMap.insert x y m)
+          return y
diff --git a/src/full/Agda/Utils/Monad.hs b/src/full/Agda/Utils/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Monad.hs
@@ -0,0 +1,248 @@
+
+module Agda.Utils.Monad
+    ( module Agda.Utils.Monad
+    , when, unless, MonadPlus(..)
+    , (<$>), (<*>)
+    , (<$)
+    )
+    where
+
+import Control.Applicative    ( liftA2 )
+import Control.Monad          ( MonadPlus(..), guard, unless, when )
+import Control.Monad.Except   ( MonadError(catchError, throwError) )
+import Control.Monad.Identity ( runIdentity )
+import Control.Monad.State    ( MonadState(get, put) )
+import Control.Monad.Writer   ( MonadWriter(tell), Writer, WriterT, mapWriterT )
+
+import Data.Bifunctor         ( first, second )
+import Data.Bool              ( bool )
+import Data.Traversable as Trav hiding (for, sequence)
+import Data.Foldable as Fold
+import Data.Maybe
+import Data.Monoid
+
+import Agda.Utils.Applicative
+import Agda.Utils.Either
+import Agda.Utils.Null (empty, ifNotNullM)
+import Agda.Utils.Singleton
+
+import Agda.Utils.Impossible
+
+---------------------------------------------------------------------------
+
+-- | Binary bind.
+(==<<) :: Monad m => (a -> b -> m c) -> (m a, m b) -> m c
+k ==<< (ma, mb) = ma >>= \ a -> k a =<< mb
+
+-- Conditionals and monads ------------------------------------------------
+
+whenM :: Monad m => m Bool -> m () -> m ()
+whenM c m = c >>= (`when` m)
+
+unlessM :: Monad m => m Bool -> m () -> m ()
+unlessM c m = c >>= (`unless` m)
+
+-- | Monadic guard.
+guardM :: (Monad m, MonadPlus m) => m Bool -> m ()
+guardM c = guard =<< c
+
+-- | Monadic if-then-else.
+ifM :: Monad m => m Bool -> m a -> m a -> m a
+ifM c m m' = c >>= \b -> if b then m else m'
+
+-- | @ifNotM mc = ifM (not <$> mc)@
+ifNotM :: Monad m => m Bool -> m a -> m a -> m a
+ifNotM c = flip $ ifM c
+
+-- | Lazy monadic conjunction.
+and2M :: Monad m => m Bool -> m Bool -> m Bool
+and2M ma mb = ifM ma mb (return False)
+
+andM :: (Foldable f, Monad m) => f (m Bool) -> m Bool
+andM = Fold.foldl' and2M (return True)
+
+allM :: (Foldable f, Monad m) => f a -> (a -> m Bool) -> m Bool
+allM xs f = Fold.foldl' (\b -> and2M b . f) (return True) xs
+
+-- | Lazy monadic disjunction.
+or2M :: Monad m => m Bool -> m Bool -> m Bool
+or2M ma = ifM ma (return True)
+
+orM :: (Foldable f, Monad m) => f (m Bool) -> m Bool
+orM = Fold.foldl' or2M (return False)
+
+anyM :: (Foldable f, Monad m) => f a -> (a -> m Bool) -> m Bool
+anyM xs f = Fold.foldl' (\b -> or2M b . f) (return False) xs
+
+-- | Lazy monadic disjunction with @Either@  truth values.
+--   Returns the last error message if all fail.
+altM1 :: Monad m => (a -> m (Either err b)) -> [a] -> m (Either err b)
+altM1 f []       = __IMPOSSIBLE__
+altM1 f [a]      = f a
+altM1 f (a : as) = either (const $ altM1 f as) (return . Right) =<< f a
+
+-- | Lazy monadic disjunction with accumulation of errors in a monoid.
+--   Errors are discarded if we succeed.
+orEitherM :: (Monoid e, Monad m, Functor m) => [m (Either e b)] -> m (Either e b)
+orEitherM []       = return $ Left mempty
+orEitherM (m : ms) = caseEitherM m (\e -> mapLeft (e `mappend`) <$> orEitherM ms)
+                                   (return . Right)
+
+-- Loops gathering results in a Monoid ------------------------------------
+
+-- | Generalized version of @traverse_ :: Applicative m => (a -> m ()) -> [a] -> m ()@
+--   Executes effects and collects results in left-to-right order.
+--   Works best with left-associative monoids.
+--
+--   Note that there is an alternative
+--
+--     @mapM' f t = foldr mappend mempty <$> mapM f t@
+--
+--   that collects results in right-to-left order
+--   (effects still left-to-right).
+--   It might be preferable for right associative monoids.
+mapM' :: (Foldable t, Applicative m, Monoid b) => (a -> m b) -> t a -> m b
+mapM' f = Fold.foldl (\ mb a -> liftA2 mappend mb (f a)) (pure mempty)
+
+-- | Generalized version of @for_ :: Applicative m => [a] -> (a -> m ()) -> m ()@
+forM' :: (Foldable t, Applicative m, Monoid b) => t a -> (a -> m b) -> m b
+forM' = flip mapM'
+
+-- Variations of Traversable
+
+mapMM :: (Traversable t, Monad m) => (a -> m b) -> m (t a) -> m (t b)
+mapMM f mxs = Trav.mapM f =<< mxs
+
+forMM :: (Traversable t, Monad m) => m (t a) -> (a -> m b) -> m (t b)
+forMM = flip mapMM
+
+-- Variations of Foldable
+
+mapMM_ :: (Foldable t, Monad m) => (a -> m ()) -> m (t a) -> m ()
+mapMM_ f mxs = Fold.mapM_ f =<< mxs
+
+forMM_ :: (Foldable t, Monad m) => m (t a) -> (a -> m ()) -> m ()
+forMM_ = flip mapMM_
+
+-- Continuation monad -----------------------------------------------------
+
+-- Andreas, 2017-04-11, issue #2543
+-- The terribly useful thread function is now UNUSED.  [Sadistic laughter :)]
+--
+-- type Cont r a = (a -> r) -> r
+--
+-- -- | 'Control.Monad.mapM' for the continuation monad. Terribly useful.
+-- thread :: (a -> Cont r b) -> [a] -> Cont r [b]
+-- thread f [] ret = ret []
+-- thread f (x:xs) ret =
+--     f x $ \y -> thread f xs $ \ys -> ret (y:ys)
+
+-- Lists and monads -------------------------------------------------------
+
+concatMapM :: Monad m => (a -> m [b]) -> [a] -> m [b]
+concatMapM f xs = concat <$> Trav.mapM f xs
+
+-- | A monadic version of @'mapMaybe' :: (a -> Maybe b) -> [a] -> [b]@.
+mapMaybeM :: Monad m => (a -> m (Maybe b)) -> [a] -> m [b]
+mapMaybeM f xs = catMaybes <$> Trav.mapM f xs
+
+-- | A version of @'mapMaybeM'@ with a computation for the input list.
+mapMaybeMM :: Monad m => (a -> m (Maybe b)) -> m [a] -> m [b]
+mapMaybeMM f m = mapMaybeM f =<< m
+
+-- | The @for@ version of 'mapMaybeM'.
+forMaybeM :: Monad m => [a] -> (a -> m (Maybe b)) -> m [b]
+forMaybeM = flip mapMaybeM
+
+-- | The @for@ version of 'mapMaybeMM'.
+forMaybeMM :: Monad m => m [a] -> (a -> m (Maybe b)) -> m [b]
+forMaybeMM = flip mapMaybeMM
+
+-- | A monadic version of @'dropWhile' :: (a -> Bool) -> [a] -> [a]@.
+dropWhileM :: Monad m => (a -> m Bool) -> [a] -> m [a]
+dropWhileM p []       = return []
+dropWhileM p (x : xs) = ifM (p x) (dropWhileM p xs) (return (x : xs))
+
+-- | A monadic version of @'dropWhileEnd' :: (a -> Bool) -> [a] -> m [a]@.
+--   Effects happen starting at the end of the list until @p@ becomes false.
+dropWhileEndM :: Monad m => (a -> m Bool) -> [a] -> m [a]
+dropWhileEndM p []       = return []
+dropWhileEndM p (x : xs) = ifNotNullM (dropWhileEndM p xs) (return . (x:)) $ {-else-}
+  ifM (p x) (return []) (return [x])
+
+-- | A ``monadic'' version of @'partition' :: (a -> Bool) -> [a] -> ([a],[a])
+partitionM :: (Functor m, Applicative m) => (a -> m Bool) -> [a] -> m ([a], [a])
+partitionM f =
+  foldr (\ x mlr -> bool (first (x:)) (second (x:)) <$> f x <*> mlr)
+        (pure empty)
+
+-- MonadPlus -----------------------------------------------------------------
+
+-- | Translates 'Maybe' to 'MonadPlus'.
+fromMaybeMP :: MonadPlus m => Maybe a -> m a
+fromMaybeMP = foldA
+
+-- | Generalises the 'catMaybes' function from lists to an arbitrary
+-- 'MonadPlus'.
+catMaybesMP :: MonadPlus m => m (Maybe a) -> m a
+catMaybesMP = scatterMP
+
+-- | Branch over elements of a monadic 'Foldable' data structure.
+scatterMP :: (MonadPlus m, Foldable t) => m (t a) -> m a
+scatterMP = (>>= foldA)
+
+
+-- Error monad ------------------------------------------------------------
+
+-- | Finally for the 'Error' class. Errors in the finally part take
+-- precedence over prior errors.
+
+finally :: MonadError e m => m a -> m () -> m a
+first `finally` after = do
+  r <- catchError (fmap Right first) (return . Left)
+  after
+  case r of
+    Left e  -> throwError e
+    Right r -> return r
+
+-- | Try a computation, return 'Nothing' if an 'Error' occurs.
+
+tryMaybe :: (MonadError e m, Functor m) => m a -> m (Maybe a)
+tryMaybe m = (Just <$> m) `catchError` \ _ -> return Nothing
+
+-- | Run a command, catch the exception and return it.
+
+tryCatch :: (MonadError e m, Functor m) => m () -> m (Maybe e)
+tryCatch m = (Nothing <$ m) `catchError` \ err -> return $ Just err
+
+-- | Like 'guard', but raise given error when condition fails.
+
+guardWithError :: MonadError e m => e -> Bool -> m ()
+guardWithError e b = if b then return () else throwError e
+
+-- State monad ------------------------------------------------------------
+
+-- | Bracket without failure.  Typically used to preserve state.
+bracket_ :: Monad m
+         => m a         -- ^ Acquires resource. Run first.
+         -> (a -> m ())  -- ^ Releases resource. Run last.
+         -> m b         -- ^ Computes result. Run in-between.
+         -> m b
+bracket_ acquire release compute = do
+  resource <- acquire
+  result <- compute
+  release resource
+  return result
+
+-- | Restore state after computation.
+localState :: MonadState s m => m a -> m a
+localState = bracket_ get put
+
+-- Writer monad -----------------------------------------------------------
+
+embedWriter :: (Monoid w, Monad m) => Writer w a -> WriterT w m a
+embedWriter = mapWriterT (pure . runIdentity)
+
+-- | Output a single value.
+tell1 :: (Monoid ws, Singleton w ws, MonadWriter ws m) => w -> m ()
+tell1 = tell . singleton
diff --git a/src/full/Agda/Utils/Monoid.hs b/src/full/Agda/Utils/Monoid.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Monoid.hs
@@ -0,0 +1,18 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | More monoids.
+
+module Agda.Utils.Monoid where
+
+-- | Maximum of on-negative (small) natural numbers.
+
+newtype MaxNat = MaxNat { getMaxNat :: Int }
+  deriving (Num, Eq, Ord, Show, Enum)
+
+instance Semigroup MaxNat where
+  (<>) = max
+
+instance Monoid MaxNat where
+  mempty     = 0
+  mconcat [] = 0
+  mconcat ms = maximum ms
diff --git a/src/full/Agda/Utils/Null.hs b/src/full/Agda/Utils/Null.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Null.hs
@@ -0,0 +1,184 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-- | Overloaded @null@ and @empty@ for collections and sequences.
+
+module Agda.Utils.Null where
+
+import Prelude hiding (null)
+
+import Control.Monad          ( when, unless )
+import Control.Monad.Except   ( ExceptT )
+import Control.Monad.Identity ( Identity(..) )
+import Control.Monad.Reader   ( ReaderT )
+import Control.Monad.State    ( StateT  )
+import Control.Monad.Writer   ( WriterT )
+import Control.Monad.Trans    ( lift    )
+
+import Data.Maybe             ( isNothing )
+
+import qualified Data.ByteString.Char8 as ByteStringChar8
+import qualified Data.ByteString.Lazy as ByteStringLazy
+
+import Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as HashMap
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as HashSet
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Sequence (Seq)
+import qualified Data.Sequence as Seq
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Data.Text (Text)
+import qualified Data.Text as Text
+
+import Text.PrettyPrint.Annotated (Doc, isEmpty)
+
+import Agda.Utils.Bag (Bag)
+import qualified Agda.Utils.Bag as Bag
+
+import Agda.Utils.Impossible
+
+class Null a where
+  empty :: a
+  null  :: a -> Bool
+  -- ^ Satisfying @null empty == True@.
+
+  default null :: Eq a => a -> Bool
+  null = (== empty)
+
+instance Null () where
+  empty  = ()
+  null _ = True
+
+instance (Null a, Null b) => Null (a,b) where
+  empty      = (empty, empty)
+  null (a,b) = null a && null b
+
+instance (Null a, Null b, Null c) => Null (a,b,c) where
+  empty        = (empty, empty, empty)
+  null (a,b,c) = null a && null b && null c
+
+instance (Null a, Null b, Null c, Null d) => Null (a,b,c,d) where
+  empty          = (empty, empty, empty, empty)
+  null (a,b,c,d) = null a && null b && null c && null d
+
+instance Null ByteStringChar8.ByteString where
+  empty = ByteStringChar8.empty
+  null  = ByteStringChar8.null
+
+instance Null ByteStringLazy.ByteString where
+  empty = ByteStringLazy.empty
+  null  = ByteStringLazy.null
+
+instance Null Text where
+  empty = Text.empty
+  null  = Text.null
+
+instance Null [a] where
+  empty = []
+  null  = List.null
+
+instance Null (Bag a) where
+  empty = Bag.empty
+  null  = Bag.null
+
+instance Null (IntMap a) where
+  empty = IntMap.empty
+  null  = IntMap.null
+
+instance Null IntSet where
+  empty = IntSet.empty
+  null  = IntSet.null
+
+instance Null (Map k a) where
+  empty = Map.empty
+  null  = Map.null
+
+instance Null (HashMap k a) where
+  empty = HashMap.empty
+  null  = HashMap.null
+
+instance Null (HashSet a) where
+  empty = HashSet.empty
+  null  = HashSet.null
+
+instance Null (Seq a) where
+  empty = Seq.empty
+  null  = Seq.null
+
+instance Null (Set a) where
+  empty = Set.empty
+  null  = Set.null
+
+-- | A 'Maybe' is 'null' when it corresponds to the empty list.
+instance Null (Maybe a) where
+  empty = Nothing
+  null  = isNothing
+
+-- | Viewing 'Bool' as @'Maybe' ()@, a boolean is 'null' when it is false.
+instance Null Bool where
+  empty = False
+  null  = not
+
+instance Null (Doc a) where
+  empty = mempty
+  null  = isEmpty
+
+instance Null a => Null (Identity a) where
+  empty = return empty
+  null  = null . runIdentity
+
+instance Null a => Null (IO a) where
+  empty = return empty
+  null  = __IMPOSSIBLE__
+
+instance (Null (m a), Monad m) => Null (ExceptT e m a) where
+  empty = lift empty
+  null  = __IMPOSSIBLE__
+
+instance (Null (m a), Monad m) => Null (ReaderT r m a) where
+  empty = lift empty
+  null  = __IMPOSSIBLE__
+
+instance (Null (m a), Monad m) => Null (StateT s m a) where
+  empty = lift empty
+  null  = __IMPOSSIBLE__
+
+instance (Null (m a), Monad m, Monoid w) => Null (WriterT w m a) where
+  empty = lift empty
+  null  = __IMPOSSIBLE__
+
+-- * Testing for null.
+
+ifNull :: (Null a) => a -> b -> (a -> b) -> b
+ifNull a b k = if null a then b else k a
+
+ifNotNull :: (Null a) => a -> (a -> b) -> b -> b
+ifNotNull a k b = ifNull a b k
+
+ifNullM :: (Monad m, Null a) => m a -> m b -> (a -> m b) -> m b
+ifNullM ma mb k = ma >>= \ a -> ifNull a mb k
+
+ifNotNullM :: (Monad m, Null a) => m a -> (a -> m b) -> m b -> m b
+ifNotNullM ma k mb = ifNullM ma mb k
+
+whenNull :: (Monad m, Null a) => a -> m () -> m ()
+whenNull = when . null
+
+unlessNull :: (Monad m, Null a) => a -> (a -> m ()) -> m ()
+unlessNull a k = unless (null a) $ k a
+
+whenNullM :: (Monad m, Null a) => m a -> m () -> m ()
+whenNullM ma k = ma >>= (`whenNull` k)
+
+unlessNullM :: (Monad m, Null a) => m a -> (a -> m ()) -> m ()
+unlessNullM ma k = ma >>= (`unlessNull` k)
diff --git a/src/full/Agda/Utils/POMonoid.hs b/src/full/Agda/Utils/POMonoid.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/POMonoid.hs
@@ -0,0 +1,65 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Partially ordered monoids.
+
+module Agda.Utils.POMonoid where
+
+import Agda.Utils.PartialOrd
+
+-- | Partially ordered semigroup.
+--
+-- Law: composition must be monotone.
+--
+-- @
+--   related x POLE x' && related y POLE y' ==>
+--   related (x <> y) POLE (x' <> y')
+-- @
+
+class (PartialOrd a, Semigroup a) => POSemigroup a where
+
+-- | Partially ordered monoid.
+--
+-- Law: composition must be monotone.
+--
+-- @
+--   related x POLE x' && related y POLE y' ==>
+--   related (x <> y) POLE (x' <> y')
+-- @
+
+class (PartialOrd a, Semigroup a, Monoid a) => POMonoid a where
+
+-- | Completing POMonoids with inverses to form a Galois connection.
+--
+-- Law: composition and inverse composition form a Galois connection.
+--
+-- @
+--   related (inverseCompose p x) POLE y <==> related x POLE (p <> y)
+-- @
+
+class POMonoid a => LeftClosedPOMonoid a where
+  inverseCompose :: a -> a -> a
+
+
+-- | @hasLeftAdjoint x@ checks whether
+--   @x^-1 := x `inverseCompose` mempty@ is such that
+--   @x `inverseCompose` y == x^-1 <> y@ for any @y@.
+hasLeftAdjoint :: LeftClosedPOMonoid a => a -> Bool
+hasLeftAdjoint x = related (inverseCompose x mempty <> x) POLE mempty
+  -- It is enough to check the above, because of the following proof:
+  -- I will write _\_ for `inverseCompose`, id for mempty, and _._ for (<>).
+  -- Assume (*) x^-1 . x <= id, as checked.
+  -- Show x^-1 . y <=> x \ y
+  --
+  -- 1. (>=)
+     -- id     <= x . (x \ id)      (galois)
+     -- id . y <= x . (x \ id) . y
+     -- y      <= x . (x \ id) . y
+     -- x \ y  <= (x \ id) . y      (galois)
+     -- x^-1 . y >= x \ y           qed
+  --
+  -- 2. (<=)
+     --        y <=        x . (x \ y)   (galois)
+     -- x^-1 . y <= x^-1 . x . (x \ y)
+     --          <= id       . (x \ y)   (*)
+     --          <= x \ y
+     -- x^-1 . y <= x \ y                qed
diff --git a/src/full/Agda/Utils/Parser/MemoisedCPS.hs b/src/full/Agda/Utils/Parser/MemoisedCPS.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Parser/MemoisedCPS.hs
@@ -0,0 +1,355 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+------------------------------------------------------------------------
+-- | Parser combinators with support for left recursion, following
+-- Johnson\'s \"Memoization in Top-Down Parsing\".
+--
+-- This implementation is based on an implementation due to Atkey
+-- (attached to an edlambda-members mailing list message from
+-- 2011-02-15 titled \'Slides for \"Introduction to Parser
+-- Combinators\"\').
+--
+-- Note that non-memoised left recursion is not guaranteed to work.
+--
+-- The code contains an important deviation from Johnson\'s paper: the
+-- check for subsumed results is not included. This means that one can
+-- get the same result multiple times when parsing using ambiguous
+-- grammars. As an example, parsing the empty string using @S ∷= ε |
+-- ε@ succeeds twice. This change also means that parsing fails to
+-- terminate for some cyclic grammars that would otherwise be handled
+-- successfully, such as @S ∷= S | ε@. However, the library is not
+-- intended to handle infinitely ambiguous grammars. (It is unclear to
+-- the author of this module whether the change leads to more
+-- non-termination for grammars that are not cyclic.)
+
+
+module Agda.Utils.Parser.MemoisedCPS
+  ( ParserClass(..)
+  , sat, token, tok, doc
+  , DocP, bindP, choiceP, seqP, starP, atomP
+  , Parser
+  , ParserWithGrammar
+  ) where
+
+import Control.Applicative ( Alternative((<|>), empty, many, some) )
+import Control.Monad (liftM2, (<=<))
+import Control.Monad.State.Strict (State, evalState, runState, get, modify')
+
+import Data.Array
+import Data.Hashable
+import qualified Data.HashMap.Strict as Map
+import Data.HashMap.Strict (HashMap)
+
+
+import qualified Data.IntMap.Strict as IntMap
+import Data.IntMap.Strict (IntMap)
+import qualified Data.List as List
+import Data.Maybe
+
+import qualified Agda.Utils.Null as Null
+import Agda.Syntax.Common.Pretty hiding (annotate)
+
+import Agda.Utils.Impossible
+
+-- | Positions.
+
+type Pos = Int
+
+-- | State monad used by the parser.
+
+type M k r tok b = State (IntMap (HashMap k (Value k r tok b)))
+
+-- | Continuations.
+
+type Cont k r tok b a = Pos -> a -> M k r tok b [b]
+
+-- | Memoised values.
+
+data Value k r tok b = Value
+  { _results       :: !(IntMap [r])
+  , _continuations :: [Cont k r tok b r]
+  }
+
+-- | The parser type.
+--
+-- The parameters of the type @Parser k r tok a@ have the following
+-- meanings:
+--
+-- [@k@] Type used for memoisation keys.
+--
+-- [@r@] The type of memoised values. (Yes, all memoised values have
+-- to have the same type.)
+--
+-- [@tok@] The token type.
+--
+-- [@a@] The result type.
+
+newtype Parser k r tok a =
+  P { unP :: forall b.
+             Array Pos tok ->
+             Pos ->
+             Cont k r tok b a ->
+             M k r tok b [b]
+    }
+
+instance Monad (Parser k r tok) where
+  return    = pure
+  P p >>= f = P $ \input i k ->
+    p input i $ \j x -> unP (f x) input j k
+
+instance Functor (Parser k r tok) where
+  fmap f (P p) = P $ \input i k ->
+    p input i $ \i -> k i . f
+
+instance Applicative (Parser k r tok) where
+  pure x        = P $ \_ i k -> k i x
+  P p1 <*> P p2 = P $ \input i k ->
+    p1 input i $ \i f ->
+    p2 input i $ \i x ->
+    k i (f x)
+
+instance Alternative (Parser k r tok) where
+  empty         = P $ \_ _ _ -> return []
+  P p1 <|> P p2 = P $ \input i k ->
+    liftM2 (++) (p1 input i k) (p2 input i k)
+
+class (Functor p, Applicative p, Alternative p, Monad p) =>
+      ParserClass p k r tok | p -> k, p -> r, p -> tok where
+  -- | Runs the parser.
+  parse :: p a -> [tok] -> [a]
+
+  -- | Tries to print the parser, or returns 'PP.empty', depending on
+  -- the implementation. This function might not terminate.
+  grammar :: Show k => p a -> Doc
+
+  -- | Parses a token satisfying the given predicate. The computed
+  -- value is returned.
+  sat' :: (tok -> Maybe a) -> p a
+
+  -- | Uses the given function to modify the printed representation
+  -- (if any) of the given parser.
+  annotate :: (DocP -> DocP) -> p a -> p a
+
+  -- | Memoises the given parser.
+  --
+  -- Every memoised parser must be annotated with a /unique/ key.
+  -- (Parametrised parsers must use distinct keys for distinct
+  -- inputs.)
+  memoise :: (Eq k, Hashable k, Show k) => k -> p r -> p r
+
+  -- | Memoises the given parser, but only if printing, not if
+  -- parsing.
+  --
+  -- Every memoised parser must be annotated with a /unique/ key.
+  -- (Parametrised parsers must use distinct keys for distinct
+  -- inputs.)
+  memoiseIfPrinting :: (Eq k, Hashable k, Show k) => k -> p r -> p r
+
+-- | Uses the given document as the printed representation of the
+-- given parser. The document's precedence is taken to be 'atomP'.
+
+doc :: ParserClass p k r tok => Doc -> p a -> p a
+doc d = annotate (\_ -> (d, atomP))
+
+-- | Parses a token satisfying the given predicate.
+
+sat :: ParserClass p k r tok => (tok -> Bool) -> p tok
+sat p = sat' (\t -> if p t then Just t else Nothing)
+
+-- | Parses a single token.
+
+token :: ParserClass p k r tok => p tok
+token = doc "·" (sat' Just)
+
+-- | Parses a given token.
+
+tok :: (ParserClass p k r tok, Eq tok, Show tok) => tok -> p tok
+tok t = doc (text (show t)) (sat (t ==))
+
+instance ParserClass (Parser k r tok) k r tok where
+  parse p toks =
+    flip evalState IntMap.empty $
+    unP p (listArray (0, n - 1) toks) 0 $ \j x ->
+      if j == n then return [x] else return []
+    where n = List.genericLength toks
+
+  grammar _ = Null.empty
+
+  sat' p = P $ \input i k ->
+    if inRange (bounds input) i then
+      case p (input ! i) of
+        Nothing -> return []
+        Just x  -> (k $! (i + 1)) $! x
+    else
+      return []
+
+  annotate _ p = p
+
+  memoiseIfPrinting _ p = p
+
+  memoise key p = P $ \input i k -> do
+
+    let alter j zero f m =
+          IntMap.alter (Just . f . fromMaybe zero) j m
+
+        lookupTable   = fmap (Map.lookup key <=< IntMap.lookup i) get
+        insertTable v = modify' $ alter i Map.empty (Map.insert key v)
+
+    v <- lookupTable
+    case v of
+      Nothing -> do
+        insertTable (Value IntMap.empty [k])
+        unP p input i $ \j r -> do
+          ~(Just (Value rs ks)) <- lookupTable
+          insertTable (Value (alter j [] (r :) rs) ks)
+          concat <$> mapM (\k -> k j r) ks  -- See note [Reverse ks?].
+      Just (Value rs ks) -> do
+        insertTable (Value rs (k : ks))
+        concat . concat <$>
+          mapM (\(i, rs) -> mapM (k i) rs) (IntMap.toList rs)
+
+-- [Reverse ks?]
+--
+-- If ks were reversed, then the code would be productive for some
+-- infinitely ambiguous grammars, including S ∷= S | ε. However, in
+-- some cases the results would not be fair (some valid results would
+-- never be returned).
+
+-- | An extended parser type, with some support for printing parsers.
+
+data ParserWithGrammar k r tok a =
+  PG (Bool -> Either (Parser k r tok a) (Docs k))
+  -- ^ Invariant: If the boolean is 'True', then the result must be
+  -- @'Left' something@, and if the boolean is 'False', then the
+  -- result must be @'Right' something@.
+
+-- | Documents paired with precedence levels.
+
+type DocP = (Doc, Int)
+
+-- | Precedence of @>>=@.
+
+bindP :: Int
+bindP = 10
+
+-- | Precedence of @<|>@.
+
+choiceP :: Int
+choiceP = 20
+
+-- | Precedence of @<*>@.
+
+seqP :: Int
+seqP = 30
+
+-- | Precedence of @⋆@ and @+@.
+
+starP :: Int
+starP = 40
+
+-- | Precedence of atoms.
+
+atomP :: Int
+atomP = 50
+
+-- | The extended parser type computes one top-level document, plus
+-- one document per encountered memoisation key.
+--
+-- 'Nothing' is used to mark that a given memoisation key has been
+-- seen, but that no corresponding document has yet been stored.
+
+type Docs k = State (HashMap k (Maybe DocP)) DocP
+
+-- | A smart constructor.
+
+pg :: Parser k r tok a -> Docs k -> ParserWithGrammar k r tok a
+pg p d = PG $ \b -> if b then Left p else Right d
+
+-- | Extracts the parser.
+
+parser :: ParserWithGrammar k r tok a -> Parser k r tok a
+parser (PG p) = either id __IMPOSSIBLE__ (p True)
+
+-- | Extracts the documents.
+
+docs :: ParserWithGrammar k r tok a -> Docs k
+docs (PG p) = either __IMPOSSIBLE__ id (p False)
+
+instance Monad (ParserWithGrammar k r tok) where
+  return  = pure
+  p >>= f =
+    pg (parser p >>= parser . f)
+       ((\(d, p) -> (mparens (p < bindP) d <+> ">>= ?", bindP))
+          <$> docs p)
+
+instance Functor (ParserWithGrammar k r tok) where
+  fmap f p = pg (fmap f (parser p)) (docs p)
+
+instance Applicative (ParserWithGrammar k r tok) where
+  pure x    = pg (pure x) (return ("ε", atomP))
+  p1 <*> p2 =
+    pg (parser p1 <*> parser p2)
+       (liftM2 (\(d1, p1) (d2, p2) ->
+                   (sep [ mparens (p1 < seqP) d1
+                        , mparens (p2 < seqP) d2
+                        ], seqP))
+               (docs p1) (docs p2))
+
+-- | A helper function.
+
+starDocs :: String -> ParserWithGrammar k r tok a -> Docs k
+starDocs s p =
+  (\(d, p) -> (mparens (p < starP) d <+> text s, starP)) <$> docs p
+
+instance Alternative (ParserWithGrammar k r tok) where
+  empty     = pg empty (return ("∅", atomP))
+  p1 <|> p2 =
+    pg (parser p1 <|> parser p2)
+       (liftM2 (\(d1, p1) (d2, p2) ->
+                   (sep [ mparens (p1 < choiceP) d1
+                        , "|"
+                        , mparens (p2 < choiceP) d2
+                        ], choiceP))
+               (docs p1) (docs p2))
+
+  many p = pg (many (parser p)) (starDocs "⋆" p)
+  some p = pg (some (parser p)) (starDocs "+" p)
+
+-- | Pretty-prints a memoisation key.
+
+prettyKey :: Show k => k -> DocP
+prettyKey key = (text ("<" ++ show key ++ ">"), atomP)
+
+-- | A helper function.
+
+memoiseDocs ::
+  (Eq k, Hashable k, Show k) =>
+  k -> ParserWithGrammar k r tok r -> Docs k
+memoiseDocs key p = do
+  r <- Map.lookup key <$> get
+  case r of
+    Just _  -> return ()
+    Nothing -> do
+      modify' (Map.insert key Nothing)
+      d <- docs p
+      modify' (Map.insert key (Just d))
+  return (prettyKey key)
+
+instance ParserClass (ParserWithGrammar k r tok) k r tok where
+  parse p                 = parse (parser p)
+  sat' p                  = pg (sat' p) (return ("<sat ?>", atomP))
+  annotate f p            = pg (parser p) (f <$> docs p)
+  memoise key p           = pg (memoise key (parser p))
+                               (memoiseDocs key p)
+  memoiseIfPrinting key p = pg (parser p) (memoiseDocs key p)
+
+  grammar p =
+    d
+      $+$
+    nest 2 (foldr1 ($+$) $
+      "where" :
+      map (\(k, d) -> fst (prettyKey k) <+> "∷=" <+>
+                        maybe __IMPOSSIBLE__ fst d)
+          (Map.toList ds))
+    where
+    ((d, _), ds) = runState (docs p) Map.empty
diff --git a/src/full/Agda/Utils/PartialOrd.hs b/src/full/Agda/Utils/PartialOrd.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/PartialOrd.hs
@@ -0,0 +1,286 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.PartialOrd where
+
+import Data.Maybe
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+-- import Agda.Utils.List
+
+-- | The result of comparing two things (of the same type).
+data PartialOrdering
+  = POLT  -- ^ Less than.
+  | POLE  -- ^ Less or equal than.
+  | POEQ  -- ^ Equal
+  | POGE  -- ^ Greater or equal.
+  | POGT  -- ^ Greater than.
+  | POAny -- ^ No information (incomparable).
+  deriving (Eq, Show, Enum, Bounded)
+
+-- | Comparing the information content of two elements of
+--   'PartialOrdering'.  More precise information is smaller.
+--
+--   Includes equality: @x `leqPO` x == True@.
+
+leqPO :: PartialOrdering -> PartialOrdering -> Bool
+
+leqPO _   POAny = True
+
+leqPO POLT POLT = True
+leqPO POLT POLE = True
+
+leqPO POLE POLE = True
+
+leqPO POEQ POLE = True
+leqPO POEQ POEQ = True
+leqPO POEQ POGE = True
+
+leqPO POGE POGE = True
+
+leqPO POGT POGT = True
+leqPO POGT POGE = True
+
+leqPO _ _ = False
+
+-- | Opposites.
+--
+--   @related a po b@ iff @related b (oppPO po) a@.
+
+oppPO :: PartialOrdering -> PartialOrdering
+oppPO POLT  = POGT
+oppPO POLE  = POGE
+oppPO POEQ  = POEQ
+oppPO POGE  = POLE
+oppPO POGT  = POLT
+oppPO POAny = POAny
+
+-- | Combining two pieces of information (picking the least information).
+--   Used for the dominance ordering on tuples.
+--
+--   @orPO@ is associative, commutative, and idempotent.
+--   @orPO@ has dominant element @POAny@, but no neutral element.
+
+orPO :: PartialOrdering -> PartialOrdering -> PartialOrdering
+
+orPO POAny _   = POAny   -- Shortcut if no information on first.
+
+orPO POLT POLT = POLT   -- idempotent
+orPO POLT POLE = POLE
+orPO POLT POEQ = POLE
+
+orPO POLE POLT = POLE
+orPO POLE POLE = POLE   -- idempotent
+orPO POLE POEQ = POLE
+
+orPO POEQ POLT = POLE
+orPO POEQ POLE = POLE
+orPO POEQ POEQ = POEQ   -- idempotent
+orPO POEQ POGE = POGE
+orPO POEQ POGT = POGE
+
+orPO POGE POEQ = POGE
+orPO POGE POGE = POGE   -- idempotent
+orPO POGE POGT = POGE
+
+orPO POGT POEQ = POGE
+orPO POGT POGE = POGE
+orPO POGT POGT = POGT   -- idempotent
+
+orPO _    _    = POAny
+
+-- | Chains (transitivity) @x R y S z@.
+--
+--   @seqPO@ is associative, commutative, and idempotent.
+--   @seqPO@ has dominant element @POAny@ and neutral element (unit) @POEQ@.
+
+seqPO :: PartialOrdering -> PartialOrdering -> PartialOrdering
+
+seqPO POAny _   = POAny  -- Shortcut if no information on first.
+seqPO POEQ p    = p      -- No need to look at second if first is neutral.
+
+seqPO POLT POLT = POLT   -- idempotent
+seqPO POLT POLE = POLT
+seqPO POLT POEQ = POLT   -- unit
+
+seqPO POLE POLT = POLT
+seqPO POLE POLE = POLE   -- idempotent
+seqPO POLE POEQ = POLE   -- unit
+
+seqPO POGE POEQ = POGE   -- unit
+seqPO POGE POGE = POGE   -- idempotent
+seqPO POGE POGT = POGT
+
+seqPO POGT POEQ = POGT   -- unit
+seqPO POGT POGE = POGT
+seqPO POGT POGT = POGT   -- idempotent
+
+seqPO _    _    = POAny
+
+-- | Partial ordering forms a monoid under sequencing.
+instance Semigroup PartialOrdering where
+  (<>) = seqPO
+
+instance Monoid PartialOrdering where
+  mempty  = POEQ
+  mappend = (<>)
+
+-- | Embed 'Ordering'.
+fromOrdering :: Ordering -> PartialOrdering
+fromOrdering LT = POLT
+fromOrdering EQ = POEQ
+fromOrdering GT = POGT
+
+-- | Represent a non-empty disjunction of 'Ordering's as 'PartialOrdering'.
+fromOrderings :: [Ordering] -> PartialOrdering
+fromOrderings = foldr1 orPO . map fromOrdering
+
+-- | A 'PartialOrdering' information is a disjunction of 'Ordering' informations.
+toOrderings :: PartialOrdering -> [Ordering]
+toOrderings POLT  = [LT]
+toOrderings POLE  = [LT, EQ]
+toOrderings POEQ  = [EQ]
+toOrderings POGE  = [EQ, GT]
+toOrderings POGT  = [GT]
+toOrderings POAny = [LT, EQ, GT]
+
+-- * Comparison with partial result
+
+type Comparable a = a -> a -> PartialOrdering
+
+-- | Decidable partial orderings.
+class PartialOrd a where
+  comparable :: Comparable a
+
+-- | Any 'Ord' is a 'PartialOrd'.
+comparableOrd :: Ord a => Comparable a
+comparableOrd x y = fromOrdering $ compare x y
+
+-- | Are two elements related in a specific way?
+--
+--   @related a o b@ holds iff @comparable a b@ is contained in @o@.
+
+related :: PartialOrd a => a -> PartialOrdering -> a -> Bool
+related a o b = comparable a b `leqPO` o
+
+-- * Totally ordered types.
+
+instance PartialOrd Int where
+  comparable = comparableOrd
+
+instance PartialOrd Integer where
+  comparable = comparableOrd
+
+-- * Generic partially ordered types.
+
+instance PartialOrd () where
+  comparable _ _ = POEQ
+
+-- | 'Nothing' and @'Just' _@ are unrelated.
+--
+--   Partial ordering for @Maybe a@ is the same as for @Either () a@.
+
+instance PartialOrd a => PartialOrd (Maybe a) where
+  comparable mx my = case (mx, my) of
+    (Nothing, Nothing) -> POEQ
+    (Nothing, Just{} ) -> POAny
+    (Just{} , Nothing) -> POAny
+    (Just x , Just y ) -> comparable x y
+
+-- | Partial ordering for disjoint sums: @Left _@ and @Right _@ are unrelated.
+
+instance (PartialOrd a, PartialOrd b) => PartialOrd (Either a b) where
+  comparable mx my = case (mx, my) of
+    (Left  x, Left  y) -> comparable x y
+    (Left  _, Right _) -> POAny
+    (Right _, Left  _) -> POAny
+    (Right x, Right y) -> comparable x y
+
+-- | Pointwise partial ordering for tuples.
+--
+--   @related (x1,x2) o (y1,y2)@ iff @related x1 o x2@ and @related y1 o y2@.
+
+instance (PartialOrd a, PartialOrd b) => PartialOrd (a, b) where
+  comparable (x1, x2) (y1, y2) =
+    comparable x1 y1 `orPO`
+    comparable x2 y2
+
+-- | Pointwise comparison wrapper.
+
+newtype Pointwise a = Pointwise { pointwise :: a }
+  deriving (Eq, Show, Functor)
+
+-- | The pointwise ordering for lists of the same length.
+--
+--   There are other partial orderings for lists,
+--   e.g., prefix, sublist, subset, lexicographic, simultaneous order.
+
+instance PartialOrd a => PartialOrd (Pointwise [a]) where
+  comparable (Pointwise xs) (Pointwise ys) = loop Nothing xs ys
+    -- We need an accumulator since @orPO@ does not have a neutral element.
+    where
+      loop mo []     []     = fromMaybe POEQ mo
+      loop _  []     ys     = POAny
+      loop _  xs     []     = POAny
+      loop mo (x:xs) (y:ys) =
+        let o = comparable x y in
+        case maybe o (orPO o) mo of
+          POAny -> POAny
+          o     -> loop (Just o) xs ys
+
+-- | Inclusion comparison wrapper.
+
+newtype Inclusion a = Inclusion { inclusion :: a }
+  deriving (Eq, Ord, Show, Functor)
+
+-- | Sublist for ordered lists.
+
+instance (Ord a) => PartialOrd (Inclusion [a]) where
+  comparable (Inclusion xs) (Inclusion ys) = merge POEQ xs ys
+    where
+      -- We use an accumulator in order to short-cut computation
+      -- once we know the lists are incomparable.
+      merge' POAny xs ys = POAny
+      merge' o     xs ys = merge o xs ys
+      merge o [] [] = o
+      merge o [] ys = mappend o POLT
+      merge o xs [] = mappend o POGT
+      merge o xs@(x:xs') ys@(y:ys') =
+        case compare x y of
+          -- xs has an element that ys does not have => POGT
+          LT -> merge' (mappend o POGT) xs' ys
+          -- equal elements can be cancelled
+          EQ -> merge o xs' ys'
+          -- ys has an element that xs does not have => POLT
+          GT -> merge' (mappend o POLT) xs ys'
+
+-- | Sets are partially ordered by inclusion.
+
+instance Ord a => PartialOrd (Inclusion (Set a)) where
+  comparable s t = comparable (Set.toAscList <$> s) (Set.toAscList <$> t)
+
+-- * PartialOrdering is itself partially ordered!
+
+-- | Less is ``less general'' (i.e., more precise).
+instance PartialOrd PartialOrdering where
+  -- working our way down: POAny is top
+  comparable POAny POAny = POEQ
+  comparable POAny _     = POGT
+  comparable _     POAny = POLT
+  -- next are the fuzzy notions POLE and POGE
+  comparable POLE  POLE  = POEQ
+  comparable POLE  POLT  = POGT
+  comparable POLE  POEQ  = POGT
+  comparable POGE  POGE  = POEQ
+  comparable POGE  POGT  = POGT
+  comparable POGE  POEQ  = POGT
+  -- lowest are the precise notions POLT POEQ POGT
+  comparable POLT  POLT  = POEQ
+  comparable POLT  POLE  = POLT
+  comparable POEQ  POEQ  = POEQ
+  comparable POEQ  POLE  = POLT
+  comparable POEQ  POGE  = POLT
+  comparable POGT  POGT  = POEQ
+  comparable POGT  POGE  = POLT
+  -- anything horizontal is not comparable
+  comparable _     _     = POAny
diff --git a/src/full/Agda/Utils/Permutation.hs b/src/full/Agda/Utils/Permutation.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Permutation.hs
@@ -0,0 +1,291 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Permutation where
+
+import Prelude hiding (drop, null)
+
+import Control.DeepSeq
+import Control.Monad (filterM)
+
+import Data.Array.Unboxed
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import qualified Data.IntMap.Strict as IntMapS
+import qualified Data.IntSet as IntSet
+import Data.Functor.Identity
+import qualified Data.List as List
+import Data.Maybe
+
+import GHC.Generics (Generic)
+
+import Agda.Utils.Functor
+import Agda.Utils.Null
+import Agda.Utils.Size
+import Agda.Utils.Tuple
+
+import Agda.Utils.Impossible
+
+-- | Partial permutations. Examples:
+--
+--   @permute [1,2,0]   [x0,x1,x2] = [x1,x2,x0]@     (proper permutation).
+--
+--   @permute [1,0]     [x0,x1,x2] = [x1,x0]@        (partial permuation).
+--
+--   @permute [1,0,1,2] [x0,x1,x2] = [x1,x0,x1,x2]@  (not a permutation because not invertible).
+--
+--   Agda typing would be:
+--   @Perm : {m : Nat}(n : Nat) -> Vec (Fin n) m -> Permutation@
+--   @m@ is the 'size' of the permutation.
+data Permutation = Perm { permRange :: Int, permPicks :: [Int] }
+  deriving (Eq, Generic)
+
+instance Show Permutation where
+  show (Perm n xs) = showx [0..n - 1] ++ " -> " ++ showx xs
+    where showx = showList "," (\ i -> "x" ++ show i)
+          showList :: String -> (a -> String) -> [a] -> String
+          showList sep f [] = ""
+          showList sep f [e] = f e
+          showList sep f (e:es) = f e ++ sep ++ showList sep f es
+
+instance Sized Permutation where
+  size    (Perm _ xs) = size xs
+  natSize (Perm _ xs) = natSize xs
+
+instance Null Permutation where
+  empty = Perm 0 []
+  null (Perm _ picks) = null picks
+
+instance NFData Permutation
+
+-- | @permute [1,2,0] [x0,x1,x2] = [x1,x2,x0]@
+--   More precisely, @permute indices list = sublist@, generates @sublist@
+--   from @list@ by picking the elements of list as indicated by @indices@.
+--   @permute [1,3,0] [x0,x1,x2,x3] = [x1,x3,x0]@
+--
+--   Agda typing:
+--   @permute (Perm {m} n is) : Vec A m -> Vec A n@
+--
+-- Precondition for @'permute' ('Perm' _ is) xs@: Every index in @is@
+-- must be non-negative and, if @xs@ is finite, then every index must
+-- also be smaller than the length of @xs@.
+--
+-- The implementation is supposed to be extensionally equal to the
+-- following one (if different exceptions are identified), but in some
+-- cases more efficient:
+-- @
+--   permute ('Perm' _ is) xs = 'map' (xs 'Agda.Utils.List.!!') is
+-- @
+permute :: Permutation -> [a] -> [a]
+permute (Perm _ is) xs = go mempty 0 xs is
+  where
+  -- Computes the list of permuted elements.
+  go :: IntMap a  -- A map from positions to elements that have
+                  -- already been seen.
+     -> Int       -- The number of elements that have been seen (the
+                  -- size of the map).
+     -> [a]       -- Elements that have not yet been seen.
+     -> [Int]     -- Indices to process.
+     -> [a]
+  go seen !n xs []       = []
+  go seen  n xs (i : is)
+    | i < n     = fromMaybe __IMPOSSIBLE__
+                    (IntMap.lookup i seen) :
+                  go seen n xs is
+    | otherwise = scan seen n xs (i - n) is
+
+  -- Finds the element at the given position and continues.
+  scan :: IntMap a -> Int -> [a] -> Int -> [Int] -> [a]
+  scan seen !n (x : xs) !i is
+    | i == 0 = x : (go $! seen') n' xs is
+    | i > 0  = (scan $! seen') n' xs (i - 1) is
+    where
+    seen' = IntMap.insert n x seen
+    n'    = n + 1
+  scan seen n xs !_ is = __IMPOSSIBLE__ : go seen n xs is
+
+-- |  Invert a Permutation on a partial finite int map.
+-- @inversePermute perm f = f'@
+-- such that @permute perm f' = f@
+--
+-- Example, with map represented as @[Maybe a]@:
+-- @
+--   f    = [Nothing, Just a, Just b ]
+--   perm = Perm 4 [3,0,2]
+--   f'   = [ Just a , Nothing , Just b , Nothing ]
+-- @
+-- Zipping @perm@ with @f@ gives @[(0,a),(2,b)]@, after compression
+-- with @catMaybes@.  This is an @IntMap@ which can easily
+-- written out into a substitution again.
+
+class InversePermute a b where
+  inversePermute :: Permutation -> a -> b
+
+instance InversePermute [Maybe a] [(Int,a)] where
+  inversePermute (Perm n is) = catMaybes . zipWith (\ i ma -> (i,) <$> ma) is
+
+instance InversePermute [Maybe a] (IntMap a) where
+  inversePermute p = IntMap.fromList . inversePermute p
+
+instance InversePermute [Maybe a] [Maybe a] where
+  inversePermute p@(Perm n _) = tabulate . inversePermute p
+    where tabulate m = for [0..n-1] $ \ i -> IntMap.lookup i m
+
+instance InversePermute (Int -> a) [Maybe a] where
+  inversePermute (Perm n xs) f =
+    for [0..n-1] $ \i -> f <$> IntMap.lookup i m
+    where
+    m = IntMapS.fromListWith (flip const) $ zip xs [0..]
+
+-- | Identity permutation.
+idP :: Int -> Permutation
+idP n = Perm n [0..n - 1]
+
+-- | Restrict a permutation to work on @n@ elements, discarding picks @>=n@.
+takeP :: Int -> Permutation -> Permutation
+takeP n (Perm m xs) = Perm n $ filter (< n) xs
+
+-- | Pick the elements that are not picked by the permutation.
+droppedP :: Permutation -> Permutation
+droppedP (Perm n xs) = Perm n $ filter (notInXs !) [0 .. n - 1]
+  where
+  notInXs :: UArray Int Bool
+  notInXs =
+    accumArray (flip const) True (0, n - 1) (zip xs (repeat False))
+
+-- | @liftP k@ takes a @Perm {m} n@ to a @Perm {m+k} (n+k)@.
+--   Analogous to 'Agda.TypeChecking.Substitution.liftS',
+--   but Permutations operate on de Bruijn LEVELS, not indices.
+liftP :: Int -> Permutation -> Permutation
+liftP n (Perm m xs) = Perm (n + m) $ xs ++ [m .. m + n - 1]
+-- liftP n (Perm m xs) = Perm (n + m) $ [0..n-1] ++ map (n+) xs -- WRONG, works for indices, but not for levels
+
+-- | @permute (compose p1 p2) == permute p1 . permute p2@
+composeP :: Permutation -> Permutation -> Permutation
+composeP p1 (Perm n xs) = Perm n $ permute p1 xs
+  {- proof:
+      permute (compose (Perm xs) (Perm ys)) zs
+      == permute (Perm (permute (Perm xs) ys)) zs
+      == map (zs !!) (permute (Perm xs) ys)
+      == map (zs !!) (map (ys !!) xs)
+      == map (zs !! . ys !!) xs
+      == map (\x -> zs !! (ys !! x)) xs
+      == map (\x -> map (zs !!) ys !! x) xs  {- map f xs !! n == f (xs !! n) -}
+      == map (map (zs !!) ys !!) xs
+      == permute (Perm xs) (permute (Perm ys) zs)
+  -}
+
+-- | @invertP err p@ is the inverse of @p@ where defined,
+--   otherwise defaults to @err@.
+--   @composeP p (invertP err p) == p@
+invertP :: Int -> Permutation -> Permutation
+invertP err p@(Perm n xs) = Perm (size xs) $ elems tmpArray
+  where
+  -- This array cannot be unboxed, because it should be possible to
+  -- instantiate err with __IMPOSSIBLE__.
+  tmpArray :: Array Int Int
+  tmpArray = accumArray (const id) err (0, n-1) $ zip xs [0..]
+
+-- | Turn a possible non-surjective permutation into a surjective permutation.
+compactP :: Permutation -> Permutation
+compactP p@(Perm _ xs) = Perm (length xs) $ map adjust xs
+  where
+  missing      = IntSet.fromList $ permPicks $ droppedP p
+  holesBelow k = IntSet.size $ fst $ IntSet.split k missing
+  adjust k     = k - holesBelow k
+
+-- | @permute (reverseP p) xs ==
+--    reverse $ permute p $ reverse xs@
+--
+--   Example:
+--   @
+--        permute (reverseP (Perm 4 [1,3,0])) [x0,x1,x2,x3]
+--     == permute (Perm 4 $ map (3-) [0,3,1]) [x0,x1,x2,x3]
+--     == permute (Perm 4 [3,0,2]) [x0,x1,x2,x3]
+--     == [x3,x0,x2]
+--     == reverse [x2,x0,x3]
+--     == reverse $ permute (Perm 4 [1,3,0]) [x3,x2,x1,x0]
+--     == reverse $ permute (Perm 4 [1,3,0]) $ reverse [x0,x1,x2,x3]
+--   @
+--
+--   With @reverseP@, you can convert a permutation on de Bruijn indices
+--   to one on de Bruijn levels, and vice versa.
+reverseP :: Permutation -> Permutation
+reverseP (Perm n xs) = Perm n $ map ((n - 1) -) $ reverse xs
+                  -- = flipP $ Perm n $ reverse xs
+
+-- | @permPicks (flipP p) = permute p (downFrom (permRange p))@
+--   or
+--   @permute (flipP (Perm n xs)) [0..n-1] = permute (Perm n xs) (downFrom n)@
+--
+--   Can be use to turn a permutation from (de Bruijn) levels to levels
+--   to one from levels to indices.
+--
+--   See 'Agda.Syntax.Internal.Patterns.numberPatVars'.
+flipP :: Permutation -> Permutation
+flipP (Perm n xs) = Perm n $ map (n - 1 -) xs
+
+-- | @expandP i n π@ in the domain of @π@ replace the /i/th element by /n/ elements.
+expandP :: Int -> Int -> Permutation -> Permutation
+expandP i n (Perm m xs) = Perm (m + n - 1) $ concatMap expand xs
+  where
+    expand j
+      | j == i    = [i..i + n - 1]
+      | j < i     = [j]
+      | otherwise = [j + n - 1]
+
+-- | Stable topologic sort. The first argument decides whether its first
+--   argument is an immediate parent to its second argument.
+topoSort :: (a -> a -> Bool) -> [a] -> Maybe Permutation
+topoSort parent xs = runIdentity $ topoSortM (\x y -> Identity $ parent x y) xs
+
+topoSortM :: Monad m => (a -> a -> m Bool) -> [a] -> m (Maybe Permutation)
+topoSortM parent xs = do
+  let nodes     = zip [0..] xs
+      parents x = map fst <$> filterM (\(_, y) -> parent y x) nodes
+  g <- mapM (mapSndM parents) nodes
+  return $ Perm (size xs) <$> topo g
+  where
+
+    topo :: Eq node => [(node, [node])] -> Maybe [node]
+    topo [] = return []
+    topo g  = case xs of
+      []    -> fail "cycle detected"
+      x : _ -> do
+        ys <- topo $ remove x g
+        return $ x : ys
+      where
+        xs = [ x | (x, []) <- g ]
+        remove x g = [ (y, filter (/= x) ys) | (y, ys) <- g, x /= y ]
+
+------------------------------------------------------------------------
+-- * Drop (apply) and undrop (abstract)
+------------------------------------------------------------------------
+
+-- | Delayed dropping which allows undropping.
+data Drop a = Drop
+  { dropN    :: Int  -- ^ Non-negative number of things to drop.
+  , dropFrom :: a    -- ^ Where to drop from.
+  }
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+-- | Things that support delayed dropping.
+class DoDrop a where
+
+  doDrop :: Drop a -> a              -- ^ Perform the dropping.
+
+  dropMore :: Int -> Drop a -> Drop a  -- ^ Drop more.
+  dropMore n (Drop m xs) = Drop (m + n) xs
+
+  unDrop :: Int -> Drop a -> Drop a  -- ^ Pick up dropped stuff.
+  unDrop n (Drop m xs)
+    | n <= m    = Drop (m - n) xs
+    | otherwise = __IMPOSSIBLE__
+
+instance DoDrop [a] where
+  doDrop   (Drop m xs) = List.drop m xs
+
+instance DoDrop Permutation where
+  doDrop (Drop k (Perm n xs)) =
+    Perm (n + m) $ [0..m-1] ++ map (+ m) (List.drop k xs)
+    where m = -k
+  unDrop m = dropMore (-m) -- allow picking up more than dropped
diff --git a/src/full/Agda/Utils/Pointer.hs b/src/full/Agda/Utils/Pointer.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Pointer.hs
@@ -0,0 +1,72 @@
+
+module Agda.Utils.Pointer
+  ( Ptr, newPtr, derefPtr, setPtr
+  , updatePtr, updatePtrM
+  ) where
+
+import Control.DeepSeq
+import Control.Concurrent.MVar
+
+import Data.Function (on)
+import Data.Hashable
+import Data.IORef
+
+import System.IO.Unsafe
+
+data Ptr a = Ptr { ptrTag :: !Integer
+                 , ptrRef :: !(IORef a) }
+
+{-# NOINLINE freshVar #-}
+freshVar :: MVar Integer
+freshVar = unsafePerformIO $ newMVar 0
+
+fresh :: IO Integer
+fresh = do
+    x <- takeMVar freshVar
+    putMVar freshVar $! x + 1
+    return x
+
+{-# NOINLINE newPtr #-}
+newPtr :: a -> Ptr a
+newPtr x = unsafePerformIO $ do
+  i <- fresh
+  Ptr i <$> newIORef x
+
+derefPtr :: Ptr a -> a
+derefPtr p = unsafePerformIO $ readIORef $ ptrRef p
+
+{-# NOINLINE updatePtr #-}
+updatePtr :: (a -> a) -> Ptr a -> Ptr a
+updatePtr f p = unsafePerformIO $ p <$ modifyIORef (ptrRef p) f
+
+setPtr :: a -> Ptr a -> Ptr a
+setPtr !x = updatePtr (const x)
+
+-- | If @f a@ contains many copies of @a@ they will all be the same pointer in
+--   the result. If the function is well-behaved (i.e. preserves the implicit
+--   equivalence, this shouldn't matter).
+updatePtrM :: Functor f => (a -> f a) -> Ptr a -> f (Ptr a)
+updatePtrM f p = flip setPtr p <$> f (derefPtr p)
+
+instance Show a => Show (Ptr a) where
+  show p = "#" ++ show (ptrTag p) ++ "{" ++ show (derefPtr p) ++ "}"
+
+instance Functor Ptr where
+  fmap f = newPtr . f . derefPtr
+
+instance Foldable Ptr where
+  foldMap f = f . derefPtr
+
+instance Traversable Ptr where
+  traverse f p = newPtr <$> f (derefPtr p)
+
+instance Eq (Ptr a) where
+  (==) = (==) `on` ptrTag
+
+instance Ord (Ptr a) where
+  compare = compare `on` ptrTag
+
+instance Hashable (Ptr a) where
+  hashWithSalt salt = (hashWithSalt salt) . ptrTag
+
+instance NFData (Ptr a) where rnf x = seq x ()
diff --git a/src/full/Agda/Utils/ProfileOptions.hs b/src/full/Agda/Utils/ProfileOptions.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/ProfileOptions.hs
@@ -0,0 +1,112 @@
+
+module Agda.Utils.ProfileOptions
+  ( ProfileOption(..)
+  , ProfileOptions
+  , noProfileOptions
+  , addProfileOption
+  , containsProfileOption
+  , profileOptionsToList
+  , profileOptionsFromList
+  , validProfileOptionStrings
+  ) where
+
+import Control.DeepSeq
+import Control.Monad
+import Data.List (intercalate)
+import Data.Char (toLower)
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.Map (Map)
+import qualified Data.Map as Map
+import GHC.Generics (Generic)
+import Text.EditDistance (restrictedDamerauLevenshteinDistance, defaultEditCosts)
+
+import qualified Agda.Utils.List1 as List1
+import Agda.Utils.Null (Null, empty)
+
+-- | Various things that can be measured when checking an Agda development. Turned on with
+--   the `--profile` flag, for instance `--profile=sharing` to turn on the 'Sharing' option.
+--   'Internal', 'Modules', and 'Definitions' are mutually exclusive.
+--
+--   NOTE: Changing this data type requires bumping the interface version number in
+--   'Agda.TypeChecking.Serialise.currentInterfaceVersion'.
+data ProfileOption = Internal     -- ^ Measure time taken by various parts of the system (type checking, serialization, etc)
+                   | Modules      -- ^ Measure time spent on individual (Agda) modules
+                   | Definitions  -- ^ Measure time spent on individual (Agda) definitions
+                   | Sharing      -- ^ Measure things related to sharing
+                   | Serialize    -- ^ Collect detailed statistics about serialization
+                   | Constraints  -- ^ Collect statistics about constraint solving
+                   | Metas        -- ^ Count number of created metavariables
+                   | Interactive  -- ^ Measure time of interactive commands
+                   | Conversion   -- ^ Collect statistics about conversion checking
+  deriving (Show, Eq, Ord, Enum, Bounded, Generic)
+
+instance NFData ProfileOption
+
+-- | A set of 'ProfileOption's
+newtype ProfileOptions = ProfileOpts { unProfileOpts :: Set ProfileOption }
+  deriving (Show, Eq, NFData, Null)
+
+-- | The empty set of profiling options.
+noProfileOptions :: ProfileOptions
+noProfileOptions = empty
+
+addAllProfileOptions :: ProfileOptions -> ProfileOptions
+addAllProfileOptions (ProfileOpts opts) = ProfileOpts $ foldl ins opts [minBound..maxBound]
+  where
+    ins os o | any (incompatible o) os = os
+             | otherwise               = Set.insert o os
+
+-- | Strings accepted by 'addProfileOption'
+validProfileOptionStrings :: [String]
+validProfileOptionStrings = "all" : map optName [minBound .. maxBound :: ProfileOption]
+
+parseOpt :: String -> Either String ProfileOption
+parseOpt = \ s -> case Map.lookup s names of
+    Nothing -> Left $ err s
+    Just o  -> Right o
+  where
+    names = Map.fromList [ (optName o, o) | o <- [minBound .. maxBound] ]
+
+    close s t = restrictedDamerauLevenshteinDistance defaultEditCosts s t <= 3
+    err  s = concat ["Not a valid profiling option: '", s, "'. ", hint s]
+    hint s = case filter (close s) (Map.keys names) of
+               [] -> concat [ "Valid options are ", intercalate ", " $ Map.keys names, ", or all." ]
+               ss -> concat [ "Did you mean ", intercalate " or " ss, "?" ]
+
+optName :: ProfileOption -> String
+optName = map toLower . show
+
+incompatible :: ProfileOption -> ProfileOption -> Bool
+incompatible o1 o2
+  | o1 == o2  = False
+  | otherwise = any (\ set -> elem o1 set && elem o2 set) sets
+  where
+    sets = [[Internal, Modules, Definitions]]
+
+-- | Parse and add a profiling option to a set of profiling options. Returns `Left` with a helpful
+--   error message if the option doesn't parse or if it's incompatible with existing options.
+--   The special string "all" adds all options compatible with the given set and prefering the first
+--   of incompatible options. So `--profile=all` sets 'Internal' over 'Modules' and 'Definitions',
+--   but `--profile=modules --profile=all` sets 'Modules' and not 'Internal'.
+addProfileOption :: String -> ProfileOptions -> Either String ProfileOptions
+addProfileOption "all" opts = pure $ addAllProfileOptions opts
+addProfileOption s (ProfileOpts opts) = do
+  o <- parseOpt s
+  List1.ifNull (filter (incompatible o) $ Set.toList opts)
+    {-then-}
+    (return $ ProfileOpts $ Set.insert o opts)
+    {-else-} $ \ conflicts ->
+    Left $ concat ["Cannot use profiling option '", s, "' with '", optName $ List1.head $ conflicts, "'"]
+
+-- | Check if a given profiling option is present in a set of profiling options.
+containsProfileOption :: ProfileOption -> ProfileOptions -> Bool
+containsProfileOption o (ProfileOpts opts) = Set.member o opts
+
+-- | Use only for serialization.
+profileOptionsToList :: ProfileOptions -> [ProfileOption]
+profileOptionsToList (ProfileOpts opts) = Set.toList opts
+
+-- | Use only for serialization.
+profileOptionsFromList :: [ProfileOption] -> ProfileOptions
+profileOptionsFromList opts = ProfileOpts $ Set.fromList opts
diff --git a/src/full/Agda/Utils/RangeMap.hs b/src/full/Agda/Utils/RangeMap.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/RangeMap.hs
@@ -0,0 +1,370 @@
+-- | Maps containing non-overlapping intervals.
+
+module Agda.Utils.RangeMap
+  ( IsBasicRangeMap(..)
+  , several
+  , PairInt(..)
+  , RangeMap(..)
+  , rangeMapInvariant
+  , fromNonOverlappingNonEmptyAscendingList
+  , insert
+  , splitAt
+  , insideAndOutside
+  , restrictTo
+  )
+  where
+
+import Prelude hiding (null, splitAt)
+
+import Control.DeepSeq
+
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+
+import Data.Map.Strict (Map)
+import qualified Data.Map.Strict as Map
+
+import Data.Semigroup
+
+import Data.Strict.Tuple (Pair(..))
+
+import Agda.Interaction.Highlighting.Range
+import Agda.Utils.List
+import Agda.Utils.Null
+
+------------------------------------------------------------------------
+-- An abstraction
+
+-- | A class that is intended to make it easy to swap between
+-- different range map implementations.
+--
+-- Note that some 'RangeMap' operations are not included in this
+-- class.
+
+class IsBasicRangeMap a m | m -> a where
+
+  -- | The map @'singleton' rs x@ contains the ranges from @rs@, and
+  -- every position in those ranges is associated with @x@.
+
+  singleton :: Ranges -> a -> m
+
+  -- | Converts range maps to 'IntMap's from positions to values.
+
+  toMap :: m -> IntMap a
+
+  -- | Converts the map to a list. The ranges are non-overlapping and
+  -- non-empty, and earlier ranges precede later ones in the list.
+
+  toList :: m -> [(Range, a)]
+
+  -- | Returns the smallest range covering everything in the map (or
+  -- 'Nothing', if the range would be empty).
+  --
+  -- Note that the default implementation of this operation might be
+  -- inefficient.
+
+  coveringRange :: m -> Maybe Range
+  coveringRange f = do
+    min <- fst <$> IntMap.lookupMin m
+    max <- fst <$> IntMap.lookupMax m
+    return (Range { from = min, to = max + 1 })
+    where
+    m = toMap f
+
+-- | Like 'singleton', but with several 'Ranges' instead of only one.
+
+several ::
+  (IsBasicRangeMap a hl, Monoid hl) =>
+  [Ranges] -> a -> hl
+several rss m = mconcat $ map (flip singleton m) rss
+
+------------------------------------------------------------------------
+-- A strict pair type
+
+-- | A strict pair type where the first argument must be an 'Int'.
+--
+-- This type is included because there is no 'NFData' instance for
+-- 'Pair' in the package @strict@ before version 4.
+
+newtype PairInt a = PairInt (Pair Int a)
+  deriving Show
+
+instance NFData a => NFData (PairInt a) where
+  rnf (PairInt (_ :!: y)) = rnf y
+
+-- | Constructs a pair.
+
+pair :: Int -> a -> PairInt a
+pair x y = PairInt (x :!: y)
+
+------------------------------------------------------------------------
+-- The type
+
+-- | Maps containing non-overlapping intervals.
+--
+-- The implementation does not use IntMap, because IntMap does not
+-- come with a constant-time size function.
+--
+-- Note the invariant which 'RangeMap's should satisfy
+-- ('rangeMapInvariant').
+
+newtype RangeMap a = RangeMap
+  { rangeMap :: Map Int (PairInt a)
+    -- ^ The keys are starting points of ranges, and the pairs contain
+    -- endpoints and values.
+  }
+  deriving (Show, NFData)
+
+-- | Invariant for 'RangeMap'.
+--
+-- The ranges must not be empty, and they must not overlap.
+
+rangeMapInvariant :: RangeMap a -> Bool
+rangeMapInvariant f = and
+  [ all rangeInvariant rs
+  , all (not . null) rs
+  , caseList rs True $ \ r rs' ->
+      and $ zipWith (<=) (map to $ init1 r rs') (map from rs')
+  ]
+  where
+  rs = map fst $ toList f
+
+------------------------------------------------------------------------
+-- Construction, conversion and inspection
+
+instance Null (RangeMap a) where
+  empty = RangeMap { rangeMap = Map.empty }
+  null  = Map.null . rangeMap
+
+instance IsBasicRangeMap a (RangeMap a) where
+  singleton (Ranges rs) m =
+    RangeMap { rangeMap = Map.fromDistinctAscList rms }
+    where
+    rms =
+      [ (from r, pair (to r) m)
+      | r <- rs
+      , not (null r)
+      ]
+
+  toMap f =
+    IntMap.fromList
+      [ (p, m)
+      | (r, m) <- toList f
+      , p <- rangeToPositions r
+      ]
+
+  toList =
+    map (\(f, PairInt (t :!: a)) -> (Range { from = f, to = t } , a)) .
+    Map.toAscList .
+    rangeMap
+
+  coveringRange f = do
+    min <- fst <$> Map.lookupMin (rangeMap f)
+    max <- (\(_, PairInt (p :!: _)) -> p) <$> Map.lookupMax (rangeMap f)
+    return (Range { from = min, to = max })
+
+-- | Converts a list of pairs of ranges and values to a 'RangeMap'.
+-- The ranges have to be non-overlapping and non-empty, and earlier
+-- ranges have to precede later ones.
+
+fromNonOverlappingNonEmptyAscendingList :: [(Range, a)] -> RangeMap a
+fromNonOverlappingNonEmptyAscendingList =
+  RangeMap .
+  Map.fromDistinctAscList .
+  map (\(r, m) -> (from r, pair (to r) m))
+
+-- | The number of ranges in the map.
+--
+-- This function should not be exported.
+
+size :: RangeMap a -> Int
+size = Map.size . rangeMap
+
+------------------------------------------------------------------------
+-- Merging
+
+-- | Inserts a value, along with a corresponding 'Range', into a
+-- 'RangeMap'. No attempt is made to merge adjacent ranges with equal
+-- values.
+--
+-- The function argument is used to combine values. The inserted value
+-- is given as the first argument to the function.
+
+insert :: (a -> a -> a) -> Range -> a -> RangeMap a -> RangeMap a
+insert combine r m (RangeMap f)
+  | null r    = RangeMap f
+  | otherwise =
+    case equal of
+      Just (PairInt (p :!: m')) ->
+        case compare (to r) p of
+          EQ ->
+            -- The range r matches exactly.
+            RangeMap $
+            Map.insert (from r) (pair p (combine m m')) f
+          LT ->
+            -- The range r is strictly shorter.
+            RangeMap $
+            Map.insert (to r) (pair p m') $
+            Map.insert (from r) (pair (to r) (combine m m')) f
+          GT ->
+            -- The range r is strictly longer. Continue recursively.
+            insert combine (Range { from = p, to = to r }) m $
+            RangeMap $
+            Map.insert (from r) (pair p (combine m m')) f
+      Nothing ->
+        -- Find the part of r that does not overlap with anything in
+        -- smaller or larger, if any.
+        case (overlapLeft, overlapRight) of
+          (Nothing, Nothing) ->
+            -- No overlap.
+            RangeMap $
+            Map.insert (from r) (pair (to r) m) f
+          (Nothing, Just p) ->
+            -- Overlap on the right. Continue recursively.
+            insert combine (Range { from = p, to = to r }) m $
+            RangeMap $
+            Map.insert (from r) (pair p m) f
+          (Just (p1, PairInt (p2 :!: m')), Just p3) ->
+            -- Overlap on both sides. Continue recursively.
+            insert combine (Range { from = p3, to = to r }) m $
+            RangeMap $
+            (if p2 == p3 then
+               -- The left range ends exactly where the right range
+               -- starts.
+               id
+             else
+               -- There is something between the left and right
+               -- ranges.
+               Map.insert p2 (pair p3 m)) $
+            Map.insert (from r) (pair p2 (combine m m')) $
+            Map.insert p1 (pair (from r) m') f
+          (Just (p1, PairInt (p2 :!: m')), Nothing) ->
+            case compare p2 (to r) of
+              LT ->
+                -- Overlap on the left, the left range ends before r.
+                RangeMap $
+                Map.insert p2 (pair (to r) m) $
+                Map.insert (from r) (pair p2 (combine m m')) $
+                Map.insert p1 (pair (from r) m') f
+              EQ ->
+                -- Overlap on the left, the left range ends where r
+                -- ends.
+                RangeMap $
+                Map.insert (from r) (pair (to r) (combine m m')) $
+                Map.insert p1 (pair (from r) m') f
+              GT ->
+                -- Overlap on the left, the left range ends after r.
+                RangeMap $
+                Map.insert (to r) (pair p2 m') $
+                Map.insert (from r) (pair (to r) (combine m m')) $
+                Map.insert p1 (pair (from r) m') f
+    where
+    (smaller, equal, larger) = Map.splitLookup (from r) f
+
+    overlapRight = case Map.lookupMin larger of
+      Nothing -> Nothing
+      Just (from, _)
+        | from < to r -> Just from
+        | otherwise   -> Nothing
+
+    overlapLeft = case Map.lookupMax smaller of
+      Nothing -> Nothing
+      Just s@(_, PairInt (to :!: _))
+        | from r < to -> Just s
+        | otherwise   -> Nothing
+
+-- | Merges 'RangeMap's by inserting every \"piece\" of the smaller
+-- one into the larger one.
+
+instance Semigroup a => Semigroup (RangeMap a) where
+  f1 <> f2
+    | size f1 <= size f2 =
+      foldr (uncurry $ insert (<>)) f2 (toList f1)
+    | otherwise =
+      foldr (uncurry $ insert (flip (<>))) f1 (toList f2)
+
+-- | Merges 'RangeMap's by inserting every \"piece\" of the smaller
+-- one into the larger one.
+
+instance Semigroup a => Monoid (RangeMap a) where
+  mempty  = empty
+  mappend = (<>)
+
+------------------------------------------------------------------------
+-- Splitting
+
+-- | The value of @'splitAt' p f@ is a pair @(f1, f2)@ which contains
+-- everything from @f@. All the positions in @f1@ are less than @p@,
+-- and all the positions in @f2@ are greater than or equal to @p@.
+
+splitAt :: Int -> RangeMap a -> (RangeMap a, RangeMap a)
+splitAt p f = (before, after)
+  where
+  (before, _, after) = splitAt' p f
+
+-- | A variant of 'splitAt'. If a range in the middle was split into
+-- two pieces, then those two pieces are returned.
+
+splitAt' ::
+  Int -> RangeMap a ->
+  ( RangeMap a
+  , Maybe ((Int, PairInt a), (Int, PairInt a))
+  , RangeMap a
+  )
+splitAt' p (RangeMap f) =
+  case equal of
+    Just r  -> ( RangeMap maybeOverlapping
+               , Nothing
+               , RangeMap (Map.insert p r larger)
+               )
+    Nothing ->
+      -- Check if maybeOverlapping overlaps with p.
+      case Map.maxViewWithKey maybeOverlapping of
+        Nothing ->
+          (empty, Nothing, RangeMap larger)
+        Just ((from, PairInt (to :!: m)), smaller)
+          | to <= p ->
+            ( RangeMap maybeOverlapping
+            , Nothing
+            , RangeMap larger
+            )
+          | otherwise ->
+            -- Here from < p < to.
+            ( RangeMap (Map.insert from (pair p m) smaller)
+            , Just ((from, pair p m), (p, pair to m))
+            , RangeMap (Map.insert p (pair to m) larger)
+            )
+  where
+  (maybeOverlapping, equal, larger) = Map.splitLookup p f
+
+-- | Returns a 'RangeMap' overlapping the given range, as well as the
+-- rest of the map.
+
+insideAndOutside :: Range -> RangeMap a -> (RangeMap a, RangeMap a)
+insideAndOutside r f
+  | from r == to r = (empty, f)
+  | otherwise      =
+    ( middle
+    , -- Because it takes so long to recompile Agda with all
+      -- optimisations and run a benchmark no experimental
+      -- verification has been made that the code below is better than
+      -- reasonable variants. Perhaps it would make sense to benchmark
+      -- RangeMap independently of Agda.
+      if size before < size middle || size after < size middle then
+        RangeMap $ Map.union (rangeMap before) (rangeMap after)
+      else
+        -- If the number of pieces in the middle is "small", remove
+        -- the pieces from f instead of merging before and after.
+        RangeMap $
+        maybe id (uncurry Map.insert . snd) split1 $
+        maybe id (uncurry Map.insert . fst) split2 $
+        Map.difference (rangeMap f) (rangeMap middle)
+    )
+  where
+  (beforeMiddle, split1, after) = splitAt' (to r) f
+  (before, split2, middle)      = splitAt' (from r) beforeMiddle
+
+-- | Restricts the 'RangeMap' to the given range.
+
+restrictTo :: Range -> RangeMap a -> RangeMap a
+restrictTo r = fst . insideAndOutside r
diff --git a/src/full/Agda/Utils/SemiRing.hs b/src/full/Agda/Utils/SemiRing.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/SemiRing.hs
@@ -0,0 +1,42 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.SemiRing where
+
+-- | Semirings (<https://en.wikipedia.org/wiki/Semiring>).
+
+class SemiRing a where
+  ozero  :: a
+  oone   :: a
+  oplus  :: a -> a -> a
+  otimes :: a -> a -> a
+
+instance SemiRing () where
+  ozero      = ()
+  oone       = ()
+  oplus  _ _ = ()
+  otimes _ _ = ()
+
+instance SemiRing a => SemiRing (Maybe a) where
+  ozero = Nothing
+  oone  = Just oone
+
+  oplus Nothing y = y
+  oplus x Nothing = x
+  oplus (Just x) (Just y) = Just (oplus x y)
+
+  otimes Nothing _ = Nothing
+  otimes _ Nothing = Nothing
+  otimes (Just x) (Just y) = Just (otimes x y)
+
+-- | Star semirings
+-- (<https://en.wikipedia.org/wiki/Semiring#Star_semirings>).
+
+class SemiRing a => StarSemiRing a where
+  ostar :: a -> a
+
+instance StarSemiRing () where
+  ostar _ = ()
+
+instance StarSemiRing a => StarSemiRing (Maybe a) where
+  ostar Nothing  = oone
+  ostar (Just x) = Just (ostar x)
diff --git a/src/full/Agda/Utils/Semigroup.hs b/src/full/Agda/Utils/Semigroup.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Semigroup.hs
@@ -0,0 +1,20 @@
+-- | Some semigroup instances used in several places
+
+module Agda.Utils.Semigroup (
+  module Data.Semigroup)
+where
+
+import Data.Semigroup ( Semigroup, (<>) )
+
+import Control.Applicative (liftA2)
+
+import Control.Monad.Reader (ReaderT)
+import Control.Monad.State  (StateT)
+
+instance (Applicative m, Semigroup doc) => Semigroup (ReaderT s m doc) where
+  {-# INLINE (<>) #-}
+  (<>) = liftA2 (<>)
+
+instance (Monad m, Semigroup doc)       => Semigroup (StateT s m doc)  where
+  {-# INLINE (<>) #-}
+  (<>) = liftA2 (<>)
diff --git a/src/full/Agda/Utils/Singleton.hs b/src/full/Agda/Utils/Singleton.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Singleton.hs
@@ -0,0 +1,125 @@
+
+-- | Constructing singleton collections.
+
+module Agda.Utils.Singleton where
+
+import Data.Semigroup (Semigroup(..))
+import Data.Maybe
+import Data.Monoid (Endo(..))
+
+import Data.DList (DList)
+import qualified Data.DList as DL
+import Data.Hashable (Hashable)
+import Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as HashMap
+import Data.HashSet (HashSet)
+import qualified Data.HashSet as HashSet
+import Data.List.NonEmpty (NonEmpty(..))
+
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IntMap
+import Data.IntSet (IntSet)
+import qualified Data.IntSet as IntSet
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Sequence (Seq)
+import qualified Data.Sequence as Seq
+import Data.Set (Set)
+import qualified Data.Set as Set
+
+import Agda.Utils.Null     (Null, empty)
+import Agda.Utils.SmallSet (SmallSet, SmallSetElement)
+import qualified Agda.Utils.SmallSet as SmallSet
+
+-- | A create-only possibly empty collection is a monoid with the possibility
+--   to inject elements.
+
+class (Semigroup coll, Monoid coll, Singleton el coll) => Collection el coll
+    | coll -> el where
+  fromList :: [el] -> coll
+  fromList = mconcat . map singleton
+
+instance Collection a       [a]           where fromList = id
+instance Collection a       ([a] -> [a])  where fromList = (++)
+instance Collection a       (Endo [a])    where fromList = Endo . fromList
+instance Collection a       (DList a)     where fromList = DL.fromList
+instance Collection a       (Seq a)       where fromList = Seq.fromList
+instance Collection Int     IntSet        where fromList = IntSet.fromList
+instance Collection (Int,a) (IntMap a)    where fromList = IntMap.fromList
+
+instance Ord a =>
+         Collection a       (Set a)       where fromList = Set.fromList
+
+instance Ord k =>
+         Collection (k, a)  (Map k a)     where fromList = Map.fromList
+
+instance (Eq a, Hashable a) =>
+         Collection a       (HashSet a)   where fromList = HashSet.fromList
+
+instance (Eq k, Hashable k) =>
+         Collection (k, a)  (HashMap k a) where fromList = HashMap.fromList
+
+instance SmallSetElement a => Collection a (SmallSet a) where fromList = SmallSet.fromList
+
+-- | Create-only collection with at most one element.
+
+class (Null coll, Singleton el coll) => CMaybe el coll | coll -> el where
+  cMaybe :: Maybe el -> coll
+  cMaybe = maybe empty singleton
+
+instance CMaybe a (Maybe a) where cMaybe = id
+instance CMaybe a [a]       where cMaybe = maybeToList
+
+-- | Overloaded @singleton@ constructor for collections.
+
+class Singleton el coll | coll -> el where
+  singleton :: el -> coll
+
+instance Singleton a   (Maybe a)   where singleton = Just
+instance Singleton a   [a]         where singleton = (:[])
+instance Singleton a  ([a] -> [a]) where singleton = (:)
+instance Singleton a   (Endo [a])  where singleton = Endo . (:)
+instance Singleton a   (DList a)   where singleton = DL.singleton
+instance Singleton a   (NonEmpty a)
+                                   where singleton = (:| [])
+instance Singleton a   (Seq a)     where singleton = Seq.singleton
+instance Singleton a   (Set a)     where singleton = Set.singleton
+instance Singleton Int IntSet      where singleton = IntSet.singleton
+instance SmallSetElement a => Singleton a (SmallSet a) where singleton = SmallSet.singleton
+
+instance Singleton (k  ,a) (Map  k a) where singleton = uncurry Map.singleton
+instance Singleton (Int,a) (IntMap a) where singleton = uncurry IntMap.singleton
+
+instance Hashable a => Singleton a     (HashSet   a) where singleton = HashSet.singleton
+instance Hashable k => Singleton (k,a) (HashMap k a) where singleton = uncurry HashMap.singleton
+
+-- Testing newtype-deriving:
+
+-- newtype Wrap c = Wrap c
+--   deriving (Singleton k)  -- Succeeds
+
+-- Type family version:
+
+-- class Singleton c where
+--   type Elem c
+--   singleton :: Elem c -> c
+
+-- instance Singleton [a] where
+--   type Elem [a] = a
+--   singleton = (:[])
+
+-- instance Singleton (Maybe a) where
+--   type Elem (Maybe a) = a
+--   singleton = Just
+
+-- instance Singleton (Set a) where
+--   type Elem (Set a) = a
+--   singleton = Set.singleton
+
+-- instance Singleton (Map k a) where
+--   type Elem (Map k a) = (k,a)
+--   singleton = uncurry Map.singleton
+
+-- newtype Wrap a = Wrap a
+--   deriving (Singleton)  -- Fails
diff --git a/src/full/Agda/Utils/Size.hs b/src/full/Agda/Utils/Size.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Size.hs
@@ -0,0 +1,83 @@
+-- | Collection size.
+--
+--   For 'TermSize' see "Agda.Syntax.Internal".
+
+module Agda.Utils.Size
+  ( Sized(..)
+  , SizedThing(..)
+  , sizeThing
+  , module X
+  ) where
+
+import Prelude hiding (null, length)
+
+import Data.Peano as X     ( Peano(Zero,Succ) )
+import Data.Foldable       (Foldable, length)
+import Data.HashMap.Strict (HashMap)
+import Data.HashSet        (HashSet)
+import Data.IntMap         (IntMap)
+import Data.IntSet         (IntSet)
+import qualified Data.IntSet as IntSet
+import Data.Map            (Map)
+import Data.Set            (Set)
+import Data.Sequence       (Seq)
+
+import Agda.Utils.List1    (List1)
+import Agda.Utils.Null
+
+-- | The size of a collection (i.e., its length).
+
+class Sized a where
+  -- | Strict size computation.
+  --
+  -- Anti-patterns: @size xs == n@ where @n@ is @0@, @1@ or another number
+  -- that is likely smaller than @size xs@.
+  -- Similar for @size xs >= 1@ etc.
+  -- Use 'natSize' instead.
+  --
+  -- See https://wiki.haskell.org/Haskell_programming_tips#Don.27t_ask_for_the_length_of_a_list_when_you_don.27t_need_it .
+  size :: a -> Int
+
+  default size :: (Foldable t, t b ~ a) => a -> Int
+  size = length
+
+  -- | Lazily compute a (possibly infinite) size.
+  --
+  -- Use when comparing a size against a fixed number.
+  natSize :: a -> Peano
+
+  default natSize :: (Foldable t, t b ~ a) => a -> Peano
+  natSize = foldr (const Succ) Zero
+
+instance Sized [a]
+instance Sized (Set a)
+instance Sized (HashMap k a)
+instance Sized (HashSet a)
+instance Sized (IntMap a)
+instance Sized (List1 a)
+instance Sized (Map k a)
+instance Sized (Seq a)
+instance Sized IntSet where
+  size = IntSet.size
+  natSize = toEnum . size
+
+-- | Thing decorated with its size.
+--   The thing should fit into main memory, thus, the size is an @Int@.
+
+data SizedThing a = SizedThing
+  { theSize    :: !Int
+  , sizedThing :: a
+  }
+
+-- | Cache the size of an object.
+sizeThing :: Sized a => a -> SizedThing a
+sizeThing a = SizedThing (size a) a
+
+-- | Return the cached size.
+instance Sized (SizedThing a) where
+  size = theSize
+  natSize = toEnum . theSize
+
+instance Null a => Null (SizedThing a) where
+  empty = SizedThing 0 empty
+  null  = null . sizedThing
diff --git a/src/full/Agda/Utils/SmallSet.hs b/src/full/Agda/Utils/SmallSet.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/SmallSet.hs
@@ -0,0 +1,143 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Small sets represented as a bitmask for fast membership checking.
+--
+-- With the exception of converting to/from lists, all operations are O(1).
+--
+-- Mimics the interface of 'Data.Set'.
+--
+-- Import as:
+-- @
+--    import qualified Agda.Utils.SmallSet as SmallSet
+--    import Agda.Utils.SmallSet (SmallSet)
+-- @
+
+module Agda.Utils.SmallSet
+  ( SmallSet()
+  , SmallSetElement
+  , Ix
+  , (\\)
+  , complement
+  , delete
+  , difference
+  , elems
+  , empty
+  , fromList, fromAscList, fromDistinctAscList
+  , insert
+  , intersection
+  , member
+  , notMember
+  , null
+  , singleton
+  , toList, toAscList
+  , total
+  , union
+  ) where
+
+import Prelude hiding (null)
+
+import Control.DeepSeq
+
+import Data.Word (Word64)
+import Data.List (foldl')
+import Data.Bits hiding (complement)
+import qualified Data.Bits as Bits
+import Data.Ix
+
+import qualified Agda.Utils.Null as Null
+
+-- | An element in a small set.
+--
+-- This must implement 'Bounded' and 'Ix', and contain at most 64 values.
+class (Bounded a, Ix a) => SmallSetElement a where
+
+newtype SmallSet a = SmallSet { theSmallSet :: Word64 }
+  deriving (Eq, Ord, Show, NFData)
+
+
+instance SmallSetElement a => Null.Null (SmallSet a) where
+  empty = empty
+  null = null
+
+instance SmallSetElement a => Semigroup (SmallSet a) where
+  (<>) = union
+
+instance SmallSetElement a => Monoid (SmallSet a) where
+  mempty = empty
+
+-- * Query
+
+-- | Time O(1).
+null :: SmallSetElement a => SmallSet a -> Bool
+null s = theSmallSet s == 0
+
+-- | Time O(1).
+member :: SmallSetElement a => a -> SmallSet a -> Bool
+member a s = theSmallSet s `testBit` idx a
+
+-- | @not . member a@.  Time O(1).
+notMember :: SmallSetElement a => a -> SmallSet a -> Bool
+notMember a = not . member a
+
+-- * Construction
+
+-- | The empty set.  Time O(1).
+empty :: SmallSetElement a => SmallSet a
+empty = SmallSet 0
+
+-- | The full set.  Time O(1).
+total :: forall a. SmallSetElement a => SmallSet a
+total = SmallSet $ Bits.complement 0
+
+-- | A singleton set.  Time O(1).
+singleton :: SmallSetElement a => a -> SmallSet a
+singleton a = SmallSet $ bit (idx a)
+
+-- | Time O(1).
+insert :: SmallSetElement a => a -> SmallSet a -> SmallSet a
+insert a s = SmallSet $ theSmallSet s `setBit` idx a
+
+-- | Time O(1).
+delete :: SmallSetElement a => a -> SmallSet a -> SmallSet a
+delete a s = SmallSet $ theSmallSet s `clearBit` idx a
+
+-- * Combine
+
+-- | Time O(n).
+complement :: SmallSetElement a => SmallSet a -> SmallSet a
+complement = SmallSet . Bits.complement . theSmallSet
+
+-- | Time O(1).
+difference, (\\) :: SmallSetElement a => SmallSet a -> SmallSet a -> SmallSet a
+difference s t = SmallSet $ theSmallSet s .&. Bits.complement (theSmallSet t)
+(\\)       = difference
+
+-- | Time O(1).
+intersection ::  SmallSetElement a => SmallSet a -> SmallSet a -> SmallSet a
+intersection s t = SmallSet $ theSmallSet s .&. theSmallSet t
+
+-- | Time O(n).
+union ::  SmallSetElement a => SmallSet a -> SmallSet a -> SmallSet a
+union s t = SmallSet $ theSmallSet s .|. theSmallSet t
+
+-- * Conversion
+
+-- | Time O(n).
+elems, toList, toAscList :: SmallSetElement a => SmallSet a -> [a]
+elems s   = filter (\i -> theSmallSet s `testBit` idx i) (range bounds)
+toList    = elems
+toAscList = elems
+
+-- | Time O(n).
+fromList, fromAscList, fromDistinctAscList :: SmallSetElement a => [a] -> SmallSet a
+fromList            = foldl' (flip insert) empty
+fromAscList         = fromList
+fromDistinctAscList = fromList
+
+-- * Internals
+
+bounds :: SmallSetElement a => (a, a)
+bounds = (minBound, maxBound)
+
+idx :: SmallSetElement a => a -> Int
+idx a = index bounds a
diff --git a/src/full/Agda/Utils/String.hs b/src/full/Agda/Utils/String.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/String.hs
@@ -0,0 +1,106 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.String where
+
+import Control.Monad.Reader
+import Control.Monad.State
+
+import Data.Char
+import qualified Data.List as List
+import Data.String
+
+import Agda.Utils.List
+
+-- | 'quote' adds double quotes around the string, replaces newline
+-- characters with @\n@, and escapes double quotes and backslashes
+-- within the string. This is different from the behaviour of 'show':
+--
+-- @
+-- \> 'putStrLn' $ 'show' \"\\x2200\"
+-- \"\\8704\"
+-- \> 'putStrLn' $ 'quote' \"\\x2200\"
+-- \"∀\"
+-- @
+--
+-- (The code examples above have been tested using version 4.2.0.0 of
+-- the base library.)
+
+quote :: String -> String
+quote s = "\"" ++ concatMap escape s ++ "\""
+  where
+  escape c | c == '\n'            = "\\n"
+           | c `elem` escapeChars = ['\\', c]
+           | otherwise            = [c]
+
+  escapeChars :: String
+  escapeChars = "\"\\"
+
+-- | Turns the string into a Haskell string literal, avoiding escape
+-- codes.
+
+haskellStringLiteral :: String -> String
+haskellStringLiteral s = "\"" ++ concatMap escape s ++ "\""
+  where
+  escape c | c == '\n'         = "\\n"
+           | c == '"'          = "\\\""
+           | c == '\\'         = "\\\\"
+           | ok c              = [c]
+           | otherwise         = [c]
+
+  ok c = case generalCategory c of
+    UppercaseLetter -> True
+    LowercaseLetter -> True
+    TitlecaseLetter -> True
+    _               -> isSymbol c || isPunctuation c
+
+-- | Adds hyphens around the given string
+--
+-- >>> putStrLn $ delimiter "Title"
+-- ———— Title —————————————————————————————————————————————————
+
+delimiter :: String -> String
+delimiter s = concat [ replicate 4 '\x2014'
+                     , " ", s, " "
+                     , replicate (54 - length s) '\x2014'
+                     ]
+
+-- | Adds a final newline if there is not already one.
+
+addFinalNewLine :: String -> String
+addFinalNewLine "" = "\n"
+addFinalNewLine s@(c:cs)
+  | last1 c cs == '\n' = s
+  | otherwise          = s ++ "\n"
+
+-- | Indents every line the given number of steps.
+
+indent :: Integral i => i -> String -> String
+indent i = unlines . map (List.genericReplicate i ' ' ++) . lines
+
+-- | 'unwords', but remove empty words first.
+
+unwords1 :: [String] -> String
+unwords1 = unwords . filter (not . null)
+
+-- | Show a number using comma to separate powers of 1,000.
+
+showThousandSep :: Show a => a -> String
+showThousandSep = reverse . List.intercalate "," . chop 3 . reverse . show
+
+-- | Remove leading whitespace.
+ltrim :: String -> String
+ltrim = dropWhile isSpace
+
+-- | Remove trailing whitespace.
+rtrim :: String -> String
+rtrim = List.dropWhileEnd isSpace
+
+-- | Remove leading and trailing whitesapce.
+trim :: String -> String
+trim = rtrim . ltrim
+
+instance (IsString (m a), Monad m) => IsString (ReaderT r m a) where
+  fromString = lift . fromString
+
+instance (IsString (m a), Monad m) => IsString (StateT s m a) where
+  fromString = lift . fromString
diff --git a/src/full/Agda/Utils/Suffix.hs b/src/full/Agda/Utils/Suffix.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Suffix.hs
@@ -0,0 +1,82 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Suffix where
+
+import Data.Char
+import qualified Data.List as List
+
+import Agda.Utils.Impossible
+
+------------------------------------------------------------------------
+-- Subscript digits
+
+-- | Is the character one of the subscripts @'₀'@-@'₉'@?
+
+isSubscriptDigit :: Char -> Bool
+isSubscriptDigit c = '₀' <= c && c <= '₉'
+
+-- | Converts @'0'@-@'9'@ to @'₀'@-@'₉'@
+--
+-- Precondition: The digit needs to be in range.
+
+toSubscriptDigit :: Char -> Char
+toSubscriptDigit d
+  | isDigit d = toEnum (fromEnum '₀' + (fromEnum d - fromEnum '0'))
+  | otherwise = __IMPOSSIBLE__
+
+-- | Converts @'₀'@-@'₉'@ to @'0'@-@'9'@.
+--
+-- Precondition: The digit needs to be in range.
+
+fromSubscriptDigit :: Char -> Char
+fromSubscriptDigit d
+  | isSubscriptDigit d = toEnum (fromEnum '0' + (fromEnum d - fromEnum '₀'))
+  | otherwise          = __IMPOSSIBLE__
+
+------------------------------------------------------------------------
+-- Suffices
+
+-- | Classification of identifier variants.
+
+data Suffix
+  = Prime     Integer  -- ^ Identifier ends in @Integer@ many primes.
+  | Index     Integer  -- ^ Identifier ends in number @Integer@ (ordinary digits).
+  | Subscript Integer  -- ^ Identifier ends in number @Integer@ (subscript digits).
+
+-- | Increase the suffix by one.
+
+nextSuffix :: Suffix -> Suffix
+nextSuffix (Prime i)     = Prime $ i + 1
+nextSuffix (Index i)     = Index $ i + 1
+nextSuffix (Subscript i) = Subscript $ i + 1
+
+-- | Parse suffix.
+
+suffixView :: String -> (String, Maybe Suffix)
+suffixView s
+    | (ps@(_:_), s') <- span (== '\'') rs        = (reverse s', Just $ Prime $ List.genericLength ps)
+    | (ns@(_:_), s') <- span isDigit rs          = (reverse s', Just $ Index $ read $ reverse ns)
+    | (ns@(_:_), s') <- span isSubscriptDigit rs = (reverse s', Just $ Subscript $ read $
+                                                      map fromSubscriptDigit $ reverse ns)
+    | otherwise                                  = (s, Nothing)
+    where rs = reverse s
+
+-- Note: suffixView could be implemented using spanEnd, but the implementation using reverse
+-- looks more efficient, since the reversal is only done once.
+--
+-- suffixView :: String -> (String, Maybe Suffix)
+-- suffixView s
+--     | (s', ps@(_:_)) <- spanEnd (=='\'') s         = (s', Just $ Prime $ length ps)
+--     | (s', ns@(_:_)) <- spanEnd isDigit s          = (s', Just $ Index $ read ns)
+--     | (s', ns@(_:_)) <- spanEnd isSubscriptDigit s = (s', Just $ Subscript $ read $ map fromSubscriptDigit ns)
+--     | otherwise                                    = (s, Nothing)
+
+-- | Print suffix.
+
+renderSuffix :: Suffix -> String
+renderSuffix (Prime n)     = List.genericReplicate n '\''
+renderSuffix (Index i)     = show i
+renderSuffix (Subscript i) = map toSubscriptDigit (show i)
+
+addSuffix :: String -> Suffix -> String
+addSuffix str suffix = str ++ renderSuffix suffix
diff --git a/src/full/Agda/Utils/Three.hs b/src/full/Agda/Utils/Three.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Three.hs
@@ -0,0 +1,53 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Tools for 3-way partitioning.
+
+module Agda.Utils.Three where
+
+-- | Enum type with 3 elements.
+--
+data Three
+  = One
+  | Two
+  | Three
+  deriving (Eq, Ord, Show, Bounded, Enum)
+
+-- | Partition a list into 3 groups.
+--
+--   Preserves the relative order or elements.
+--
+partition3 :: (a -> Three) -> [a] -> ([a], [a], [a])
+partition3  f = loop where
+  loop []     = ([], [], [])
+  loop (x:xs) = case f x of
+      One   -> (x:as, bs, cs)
+      Two   -> (as, x:bs, cs)
+      Three -> (as, bs, x:cs)
+    where (as, bs, cs) = loop xs
+
+-- | Disjoint sum of three.
+--
+data Either3 a b c
+  = In1 a
+  | In2 b
+  | In3 c
+  deriving (Eq, Ord, Show)
+
+-- | Partition a list into 3 groups.
+--
+--   Preserves the relative order or elements.
+--
+partitionEithers3 :: [Either3 a b c] -> ([a], [b], [c])
+partitionEithers3 = \case
+  []     -> ([], [], [])
+  (x:xs) -> case x of
+      In1 a -> (a:as, bs, cs)
+      In2 b -> (as, b:bs, cs)
+      In3 c -> (as, bs, c:cs)
+    where (as, bs, cs) = partitionEithers3 xs
+
+mapEither3M :: Applicative m => (a -> m (Either3 b c d)) -> [a] -> m ([b], [c], [d])
+mapEither3M f xs = partitionEithers3 <$> traverse f xs
+
+forEither3M :: Applicative m => [a] -> (a -> m (Either3 b c d)) -> m ([b], [c], [d])
+forEither3M = flip mapEither3M
diff --git a/src/full/Agda/Utils/Time.hs b/src/full/Agda/Utils/Time.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Time.hs
@@ -0,0 +1,61 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- To avoid warning on derived Integral instance for CPUTime.
+{-# OPTIONS_GHC -fno-warn-identities #-}
+
+-- | Time-related utilities.
+
+module Agda.Utils.Time
+  ( ClockTime
+  , getClockTime
+  , getCPUTime
+  , measureTime
+  , CPUTime(..)
+  , fromMilliseconds
+  ) where
+
+import Control.DeepSeq
+import Control.Monad.Trans
+import qualified System.CPUTime as CPU
+
+
+import qualified Data.Time
+
+import Agda.Syntax.Common.Pretty
+import Agda.Utils.String
+
+-- | Timestamps.
+
+type ClockTime = Data.Time.UTCTime
+
+-- | The current time.
+
+getClockTime :: IO ClockTime
+getClockTime = Data.Time.getCurrentTime
+
+-- | CPU time in pico (10^-12) seconds.
+
+newtype CPUTime = CPUTime Integer
+  deriving (Eq, Show, Ord, Num, Real, Enum, Integral, NFData)
+
+fromMilliseconds :: Integer -> CPUTime
+fromMilliseconds n = CPUTime (n * 1000000000)
+
+-- | Print CPU time in milli (10^-3) seconds.
+
+instance Pretty CPUTime where
+  pretty (CPUTime ps) =
+    text $ showThousandSep (div ps 1000000000) ++ "ms"
+
+{-# SPECIALIZE getCPUTime :: IO CPUTime #-}
+getCPUTime :: MonadIO m => m CPUTime
+getCPUTime = liftIO $ CPUTime <$> CPU.getCPUTime
+
+-- | Measure the time of a computation.
+--   Of course, does not work with exceptions.
+measureTime :: MonadIO m => m a -> m (a, CPUTime)
+measureTime m = do
+  start <- liftIO $ getCPUTime
+  x     <- m
+  stop  <- liftIO $ getCPUTime
+  return (x, stop - start)
diff --git a/src/full/Agda/Utils/Trie.hs b/src/full/Agda/Utils/Trie.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Trie.hs
@@ -0,0 +1,170 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Strict tries (based on "Data.Map.Strict" and "Agda.Utils.Maybe.Strict").
+
+module Agda.Utils.Trie
+  ( Trie(..)
+  , empty, singleton, everyPrefix, insert, insertWith, union, unionWith
+  , adjust, delete
+  , toList, toAscList, toListOrderedBy
+  , lookup, member, lookupPath, lookupTrie
+  , mapSubTries, filter
+  , valueAt
+  ) where
+
+import Prelude hiding (null, lookup, filter)
+
+import Control.DeepSeq
+
+import Data.Function (on)
+import qualified Data.Maybe as Lazy
+import Data.Map.Strict (Map)
+import qualified Data.Map.Strict as Map
+
+import qualified Data.List as List
+
+import qualified Agda.Utils.Maybe.Strict as Strict
+import Agda.Utils.Null
+import Agda.Utils.Lens
+
+-- | Finite map from @[k]@ to @v@.
+--
+--   With the strict 'Maybe' type, 'Trie' is also strict in 'v'.
+data Trie k v = Trie !(Strict.Maybe v) !(Map k (Trie k v))
+  deriving ( Show
+           , Eq
+           , Functor
+           , Foldable
+           )
+
+instance (NFData k, NFData v) => NFData (Trie k v) where
+  rnf (Trie a b) = rnf a `seq` rnf b
+
+-- | Empty trie.
+instance Null (Trie k v) where
+  empty = Trie Strict.Nothing Map.empty
+  null (Trie v t) = null v && null t
+
+-- | Helper function used to implement 'singleton' and 'everyPrefix'.
+singletonOrEveryPrefix :: Bool -> [k] -> v -> Trie k v
+singletonOrEveryPrefix _           []       !v =
+  Trie (Strict.Just v) Map.empty
+singletonOrEveryPrefix everyPrefix (x : xs) !v =
+  Trie (if everyPrefix then Strict.Just v else Strict.Nothing)
+       (Map.singleton x (singletonOrEveryPrefix everyPrefix xs v))
+
+-- | Singleton trie.
+singleton :: [k] -> v -> Trie k v
+singleton = singletonOrEveryPrefix False
+
+-- | @everyPrefix k v@ is a trie where every prefix of @k@ (including
+-- @k@ itself) is mapped to @v@.
+everyPrefix :: [k] -> v -> Trie k v
+everyPrefix = singletonOrEveryPrefix True
+
+-- | Left biased union.
+--
+--   @union = unionWith (\ new old -> new)@.
+union :: (Ord k) => Trie k v -> Trie k v -> Trie k v
+union = unionWith const
+
+-- | Pointwise union with merge function for values.
+unionWith :: (Ord k) => (v -> v -> v) -> Trie k v -> Trie k v -> Trie k v
+unionWith f (Trie v ss) (Trie w ts) =
+  Trie (Strict.unionMaybeWith f v w) (Map.unionWith (unionWith f) ss ts)
+
+-- | Insert.  Overwrites existing value if present.
+--
+--   @insert = insertWith (\ new old -> new)@
+insert :: (Ord k) => [k] -> v -> Trie k v -> Trie k v
+insert k v t = (singleton k v) `union` t
+
+-- | Insert with function merging new value with old value.
+insertWith :: (Ord k) => (v -> v -> v) -> [k] -> v -> Trie k v -> Trie k v
+insertWith f k v t = unionWith f (singleton k v) t
+
+-- | Delete value at key, but leave subtree intact.
+delete :: Ord k => [k] -> Trie k v -> Trie k v
+delete path = adjust path (const Strict.Nothing)
+
+-- | Adjust value at key, leave subtree intact.
+adjust ::
+  Ord k =>
+  [k] -> (Strict.Maybe v -> Strict.Maybe v) -> Trie k v -> Trie k v
+adjust path f t@(Trie v ts) =
+  case path of
+    -- case: found the value we want to adjust: adjust it!
+    []                                 -> Trie (f v) ts
+    -- case: found the subtrie matching the first key: adjust recursively
+    k : ks | Just s <- Map.lookup k ts -> Trie v $ Map.insert k (adjust ks f s) ts
+    -- case: subtrie not found: leave trie untouched
+    _ -> t
+
+-- | Convert to ascending list.
+toList :: Ord k => Trie k v -> [([k],v)]
+toList = toAscList
+
+-- | Convert to ascending list.
+toAscList :: Ord k => Trie k v -> [([k],v)]
+toAscList (Trie mv ts) = Strict.maybeToList (([],) <$> mv) ++
+  [ (k:ks, v)
+  | (k,  t) <- Map.toAscList ts
+  , (ks, v) <- toAscList t
+  ]
+
+-- | Convert to list where nodes at the same level are ordered according to the
+--   given ordering.
+toListOrderedBy :: Ord k => (v -> v -> Ordering) -> Trie k v -> [([k], v)]
+toListOrderedBy cmp (Trie mv ts) =
+  Strict.maybeToList (([],) <$> mv) ++
+  [ (k : ks, v) | (k, t)  <- List.sortBy (cmp' `on` val . snd) $ Map.toAscList ts,
+                  (ks, v) <- toListOrderedBy cmp t ]
+  where
+    cmp' Strict.Nothing  Strict.Just{}   = LT
+    cmp' Strict.Just{}   Strict.Nothing  = GT
+    cmp' Strict.Nothing  Strict.Nothing  = EQ
+    cmp' (Strict.Just x) (Strict.Just y) = cmp x y
+    val (Trie mv _) = mv
+
+-- | Create new values based on the entire subtrie. Almost, but not quite
+--   comonad extend.
+mapSubTries :: Ord k => (Trie k u -> Maybe v) -> Trie k u -> Trie k v
+mapSubTries f t@(Trie mv ts) = Trie (Strict.toStrict (f t)) (fmap (mapSubTries f) ts)
+
+-- | Returns the value associated with the given key, if any.
+lookup :: Ord k => [k] -> Trie k v -> Maybe v
+lookup []       (Trie v _)  = Strict.toLazy v
+lookup (k : ks) (Trie _ ts) = case Map.lookup k ts of
+  Nothing -> Nothing
+  Just t  -> lookup ks t
+
+-- | Is the given key present in the trie?
+member :: Ord k => [k] -> Trie k v -> Bool
+member ks t = Lazy.isJust (lookup ks t)
+
+-- | Collect all values along a given path.
+lookupPath :: Ord k => [k] -> Trie k v -> [v]
+lookupPath xs (Trie v cs) = case xs of
+    []     -> Strict.maybeToList v
+    x : xs -> Strict.maybeToList v ++
+              maybe [] (lookupPath xs) (Map.lookup x cs)
+
+-- | Get the subtrie rooted at the given key.
+lookupTrie :: Ord k => [k] -> Trie k v -> Trie k v
+lookupTrie []       t           = t
+lookupTrie (k : ks) (Trie _ cs) = maybe empty (lookupTrie ks) (Map.lookup k cs)
+
+-- | Filter a trie.
+filter :: Ord k => (v -> Bool) -> Trie k v -> Trie k v
+filter p (Trie mv ts) = Trie mv' (Map.filter (not . null) $ filter p <$> ts)
+  where
+    mv' =
+      case mv of
+        Strict.Just v | p v -> mv
+        _                   -> Strict.Nothing
+
+-- | Key lens.
+valueAt :: Ord k => [k] -> Lens' (Trie k v) (Maybe v)
+valueAt path f t = f (lookup path t) <&> \ case
+  Nothing -> delete path t
+  Just v  -> insert path v t
diff --git a/src/full/Agda/Utils/Tuple.hs b/src/full/Agda/Utils/Tuple.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Tuple.hs
@@ -0,0 +1,82 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Tuple
+  ( (-*-)
+  , mapFst
+  , mapSnd
+  , (/\)
+  , fst3
+  , snd3
+  , thd3
+  , swap
+  , uncurry3
+  , uncurry4
+  , mapPairM
+  , mapFstM
+  , mapSndM
+  , Pair(..)
+  ) where
+
+import Control.Arrow  ((&&&))
+import Data.Bifunctor (bimap, first, second)
+import Data.Tuple (swap)
+
+infix 2 -*-
+infix 3 /\ -- backslashes at EOL interact badly with CPP...
+
+-- | Bifunctoriality for pairs.
+(-*-) :: (a -> c) -> (b -> d) -> (a,b) -> (c,d)
+(-*-) = bimap
+
+-- | @mapFst f = f -*- id@
+mapFst :: (a -> c) -> (a,b) -> (c,b)
+mapFst = first
+
+-- | @mapSnd g = id -*- g@
+mapSnd :: (b -> d) -> (a,b) -> (a,d)
+mapSnd = second
+
+-- | Lifted pairing.
+(/\) :: (a -> b) -> (a -> c) -> a -> (b,c)
+(/\) = (&&&)
+
+-- * Triple (stolen from Data.Tuple.HT)
+
+{-# INLINE fst3 #-}
+fst3 :: (a,b,c) -> a
+fst3 ~(x,_,_) = x
+
+{-# INLINE snd3 #-}
+snd3 :: (a,b,c) -> b
+snd3 ~(_,x,_) = x
+
+{-# INLINE thd3 #-}
+thd3 :: (a,b,c) -> c
+thd3 ~(_,_,x) = x
+
+{-# INLINE uncurry3 #-}
+uncurry3 :: (a -> b -> c -> d) -> (a,b,c) -> d
+uncurry3 f ~(x,y,z) = f x y z
+
+{-# INLINE uncurry4 #-}
+uncurry4 :: (a -> b -> c -> d -> e) -> (a,b,c,d) -> e
+uncurry4 f ~(w,x,y,z) = f w x y z
+
+-- | Monadic version of '-*-'.
+mapPairM :: (Applicative m) => (a -> m c) -> (b -> m d) -> (a,b) -> m (c,d)
+mapPairM f g ~(a,b) = (,) <$> f a <*> g b
+
+-- | Monadic 'mapFst'.
+mapFstM :: Functor m => (a -> m c) -> (a,b) -> m (c,b)
+mapFstM f ~(a,b) = (,b) <$> f a
+
+-- | Monadic 'mapSnd'.
+mapSndM :: Functor m => (b -> m d) -> (a,b) -> m (a,d)
+mapSndM f ~(a,b) = (a,) <$> f b
+
+data Pair a = Pair a a
+  deriving (Eq, Functor, Foldable, Traversable)
+
+instance Applicative Pair where
+  pure a                  = Pair a a
+  Pair f f' <*> Pair a a' = Pair (f a) (f' a')
diff --git a/src/full/Agda/Utils/TypeLevel.hs b/src/full/Agda/Utils/TypeLevel.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/TypeLevel.hs
@@ -0,0 +1,156 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE GADTs                #-}
+{-# LANGUAGE DataKinds            #-}
+{-# LANGUAGE PolyKinds            #-}
+{-# LANGUAGE TypeOperators        #-}
+
+-- We need undecidable instances for the definition of @Foldr@,
+-- and @Domains@ and @CoDomain@ using @If@ for instance.
+{-# LANGUAGE UndecidableInstances #-}
+
+module Agda.Utils.TypeLevel where
+
+import Data.Kind ( Type )
+import Data.Proxy
+import GHC.Exts (Constraint)
+
+------------------------------------------------------------------
+-- CONSTRAINTS
+------------------------------------------------------------------
+
+-- | @All p as@ ensures that the constraint @p@ is satisfied by
+--   all the 'types' in @as@.
+--   (Types is between scare-quotes here because the code is
+--   actually kind polymorphic)
+
+type family All (p :: k -> Constraint) (as :: [k]) :: Constraint where
+  All p '[]       = ()
+  All p (a ': as) = (p a, All p as)
+
+------------------------------------------------------------------
+-- FUNCTIONS
+-- Type-level and Kind polymorphic versions of usual value-level
+-- functions.
+------------------------------------------------------------------
+
+-- | On Booleans
+type family If (b :: Bool) (l :: k) (r :: k) :: k where
+  If 'True  l r = l
+  If 'False l r = r
+
+-- | On Lists
+type family Foldr (c :: k -> l -> l) (n :: l) (as :: [k]) :: l where
+  Foldr c n '[]       = n
+  Foldr c n (a ': as) = c a (Foldr c n as)
+
+-- | Version of @Foldr@ taking a defunctionalised argument so
+--   that we can use partially applied functions.
+type family Foldr' (c :: Function k (Function l l -> Type) -> Type)
+                   (n :: l) (as :: [k]) :: l where
+  Foldr' c n '[]       = n
+  Foldr' c n (a ': as) = Apply (Apply c a) (Foldr' c n as)
+
+type family Map (f :: Function k l -> Type) (as :: [k]) :: [l] where
+  Map f as = Foldr' (ConsMap0 f) '[] as
+
+data ConsMap0 :: (Function k l -> Type) -> Function k (Function [l] [l] -> Type) -> Type
+data ConsMap1 :: (Function k l -> Type) -> k -> Function [l] [l] -> Type
+type instance Apply (ConsMap0 f)    a = ConsMap1 f a
+type instance Apply (ConsMap1 f a) tl = Apply f a ': tl
+
+type family Constant (b :: l) (as :: [k]) :: [l] where
+  Constant b as = Map (Constant1 b) as
+
+------------------------------------------------------------------
+-- TYPE FORMERS
+------------------------------------------------------------------
+
+-- | @Arrows [a1,..,an] r@ corresponds to @a1 -> .. -> an -> r@
+-- | @Products [a1,..,an]@ corresponds to @(a1, (..,( an, ())..))@
+
+type Arrows   (as :: [Type]) (r :: Type) = Foldr (->) r as
+type Products (as :: [Type])             = Foldr (,) () as
+
+data StrictPair a b = Pair a b
+type StrictProducts (as :: [Type]) = Foldr StrictPair () as
+
+strictCurry :: (StrictPair a b -> c) -> (a -> b -> c)
+strictCurry f = \ !a !b -> f (Pair a b)
+{-# INLINE strictCurry #-}
+
+strictUncurry :: (a -> b -> c) -> (StrictPair a b -> c)
+strictUncurry f = \ !(Pair a b) -> f a b
+{-# INLINE strictUncurry #-}
+
+-- | @IsBase t@ is @'True@ whenever @t@ is *not* a function space.
+
+type family IsBase (t :: Type) :: Bool where
+  IsBase (a -> t) = 'False
+  IsBase a        = 'True
+
+-- | Using @IsBase@ we can define notions of @Domains@ and @CoDomains@
+--   which *reduce* under positive information @IsBase t ~ 'True@ even
+--   though the shape of @t@ is not formally exposed
+
+type family Domains (t :: Type) :: [Type] where
+  Domains t = If (IsBase t) '[] (Domains' t)
+type family Domains' (t :: Type) :: [Type] where
+  Domains' (a -> t) = a ': Domains t
+
+type family CoDomain (t :: Type) :: Type where
+  CoDomain t = If (IsBase t) t (CoDomain' t)
+type family CoDomain' (t :: Type) :: Type where
+  CoDomain' (a -> t) = CoDomain t
+
+------------------------------------------------------------------
+-- TYPECLASS MAGIC
+------------------------------------------------------------------
+
+-- | @Currying as b@ witnesses the isomorphism between @Arrows as b@
+--   and @Products as -> b@. It is defined as a type class rather
+--   than by recursion on a singleton for @as@ so all of that these
+--   conversions are inlined at compile time for concrete arguments.
+
+class Currying as b where
+  uncurrys :: Proxy as -> Proxy b -> Arrows as b -> Products as -> b
+  currys   :: Proxy as -> Proxy b -> (Products as -> b) -> Arrows as b
+
+instance Currying '[] b where
+  uncurrys _ _ f = \ () -> f
+  currys   _ _ f = f ()
+
+instance Currying as b => Currying (a ': as) b where
+  uncurrys _ p f = uncurry $ uncurrys (Proxy :: Proxy as) p . f
+  currys   _ p f = currys (Proxy :: Proxy as) p . curry f
+
+
+class StrictCurrying as b where
+  strictUncurrys :: Proxy as -> Proxy b -> Arrows as b -> StrictProducts as -> b
+  strictCurrys   :: Proxy as -> Proxy b -> (StrictProducts as -> b) -> Arrows as b
+
+instance StrictCurrying '[] b where
+  strictUncurrys _ _ f = \ () -> f; {-# INLINE strictUncurrys #-}
+  strictCurrys   _ _ f = f ();      {-# INLINE strictCurrys #-}
+
+instance StrictCurrying as b => StrictCurrying (a ': as) b where
+  strictUncurrys _ p f = strictUncurry $ strictUncurrys (Proxy :: Proxy as) p . f
+  {-# INLINE strictUncurrys #-}
+  strictCurrys   _ p f = strictCurrys (Proxy :: Proxy as) p . strictCurry f
+  {-# INLINE strictCurrys #-}
+
+------------------------------------------------------------------
+-- DEFUNCTIONALISATION
+-- Cf. Eisenberg and Stolarek's paper:
+-- Promoting Functions to Type Families in Haskell
+------------------------------------------------------------------
+
+data Function :: Type -> Type -> Type
+
+data Constant0 :: Function a (Function b a -> Type) -> Type
+data Constant1 :: Type -> Function b a -> Type
+
+type family Apply (t :: Function k l -> Type) (u :: k) :: l
+
+type instance Apply Constant0     a = Constant1 a
+type instance Apply (Constant1 a) b = a
diff --git a/src/full/Agda/Utils/TypeLits.hs b/src/full/Agda/Utils/TypeLits.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/TypeLits.hs
@@ -0,0 +1,35 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE DataKinds      #-}
+{-# LANGUAGE GADTs          #-}
+
+-- | Type level literals, inspired by GHC.TypeLits.
+
+module Agda.Utils.TypeLits where
+
+-- | Singleton for type level booleans.
+
+data SBool (b :: Bool) where
+  STrue  :: SBool 'True
+  SFalse :: SBool 'False
+
+eraseSBool :: SBool b -> Bool
+eraseSBool = \case
+  STrue  -> True
+  SFalse -> False
+
+-- | A known boolean is one we can obtain a singleton for.
+--   Concrete values are trivially known.
+
+class KnownBool (b :: Bool) where
+  boolSing :: SBool b
+
+instance KnownBool 'True where
+  boolSing = STrue
+
+instance KnownBool 'False where
+  boolSing = SFalse
+
+boolVal :: forall proxy b. KnownBool b => proxy b -> Bool
+boolVal _ = eraseSBool (boolSing :: SBool b)
diff --git a/src/full/Agda/Utils/Unsafe.hs b/src/full/Agda/Utils/Unsafe.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Unsafe.hs
@@ -0,0 +1,12 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE MagicHash #-}
+module Agda.Utils.Unsafe (unsafeComparePointers) where
+
+import GHC.Exts (reallyUnsafePtrEquality#, isTrue#)
+
+-- | Checks if two arguments are equal as pointers in memory.
+-- Please note, that this function is a hack, and it can worsen the behavior of compiler.
+-- See https://gitlab.haskell.org/ghc/ghc/-/blob/d151546e59a50158f25c3df6728b00d3c27bb4b9/compiler/GHC/Builtin/primops.txt.pp#L3455
+unsafeComparePointers :: a -> a -> Bool
+unsafeComparePointers x y = x `seq` y `seq` isTrue# (reallyUnsafePtrEquality# x y)
diff --git a/src/full/Agda/Utils/Update.hs b/src/full/Agda/Utils/Update.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Update.hs
@@ -0,0 +1,205 @@
+
+module Agda.Utils.Update
+  ( ChangeT
+  , runChangeT, mapChangeT
+  , UpdaterT
+  , runUpdaterT
+  , Change
+  , MonadChange(..)
+  , runChange
+  , Updater
+  , sharing
+  , runUpdater
+  , dirty
+  , ifDirty
+  , Updater1(..)
+  , Updater2(..)
+  ) where
+
+-- Control.Monad.Fail import is redundant since GHC 8.8.1
+import Control.Monad.Fail (MonadFail)
+
+import Control.Monad.Identity
+import Control.Monad.Trans
+import Control.Monad.Trans.Control
+import Control.Monad.Writer.Strict ( MonadWriter(..), Writer, WriterT, mapWriterT, runWriterT )
+
+import Data.Monoid ( Any(..) )
+
+import Agda.Utils.Tuple
+
+-- * Change monad.
+
+-- | The class of change monads.
+class Monad m => MonadChange m where
+  tellDirty   :: m () -- ^ Mark computation as having changed something.
+  listenDirty :: m a -> m (a, Bool)
+
+-- | The @ChangeT@ monad transformer.
+newtype ChangeT m a = ChangeT { fromChangeT :: WriterT Any m a }
+  deriving (Functor, Applicative, Monad, MonadTrans, MonadFail, MonadIO)
+
+-- This instance cannot be derived in older ghcs like 8.0
+-- because of the associated type synonym.
+-- 8.4 can derive it, but needs UndecidableInstances.
+instance MonadTransControl ChangeT where
+  type StT ChangeT a = (a, Any) -- StT (WriterT Any) a  would require UndecidableInstances
+  liftWith f = ChangeT $ liftWith $ \ runWriterT -> f $ runWriterT . fromChangeT
+  -- Andreas, 2020-04-17: these point-free variants do not seem to type check:
+  -- liftWith f = ChangeT $ liftWith $ f . (. fromChangeT)
+  -- liftWith = ChangeT . liftWith . (. (. fromChangeT))
+  restoreT = ChangeT . restoreT
+
+instance Monad m => MonadChange (ChangeT m) where
+  tellDirty     = ChangeT $ tell $ Any True
+  listenDirty m = ChangeT $ do
+    (a, Any dirty) <- listen (fromChangeT m)
+    return (a, dirty)
+
+-- | Run a 'ChangeT' computation, returning result plus change flag.
+runChangeT :: Functor m => ChangeT m a -> m (a, Bool)
+runChangeT = fmap (mapSnd getAny) . runWriterT . fromChangeT
+{-# INLINE runChangeT #-}
+
+-- | Run a 'ChangeT' computation, but ignore change flag.
+execChangeT :: Functor m => ChangeT m a -> m a -- A library function, so keep
+execChangeT = fmap fst . runChangeT
+{-# INLINE execChangeT #-}
+
+-- | Map a 'ChangeT' computation (monad transformer action).
+mapChangeT :: (m (a, Any) -> n (b, Any)) -> ChangeT m a -> ChangeT n b
+mapChangeT f (ChangeT m) = ChangeT (mapWriterT f m)
+{-# INLINE mapChangeT #-}
+
+-- Don't actually track changes with the identity monad:
+
+-- | A mock change monad.  Always assume change has happened.
+instance MonadChange Identity where
+  tellDirty   = return ()
+  listenDirty = fmap (,True)
+
+instance Monad m => MonadChange (IdentityT m) where
+  tellDirty   = IdentityT    $ return ()
+  listenDirty = mapIdentityT $ fmap (,True)
+
+-- * Pure endo function and updater
+
+type UpdaterT m a = a -> ChangeT m a
+
+-- | Blindly run an updater.
+runUpdaterT :: Functor m => UpdaterT m a -> a -> m (a, Bool)
+runUpdaterT f a = runChangeT $ f a
+
+type EndoFun a = a -> a
+type Change  a = ChangeT Identity a
+type Updater a = UpdaterT Identity a
+
+-- NB:: Defined but not used
+fromChange :: Change a -> Writer Any a
+fromChange = fromChangeT
+
+-- | Run a 'Change' computation, returning result plus change flag.
+{-# INLINE runChange #-}
+runChange :: Change a -> (a, Bool)
+runChange = runIdentity . runChangeT
+
+-- | Blindly run an updater.
+{-# INLINE runUpdater #-}
+runUpdater :: Updater a -> a -> (a, Bool)
+runUpdater f a = runChange $ f a
+
+-- | Mark a computation as dirty.
+dirty :: Monad m => UpdaterT m a
+dirty a = do
+  tellDirty
+  return a
+{-# INLINE dirty #-}
+
+{-# SPECIALIZE ifDirty :: Change a -> (a -> Change b) -> (a -> Change b) -> Change b #-}
+{-# SPECIALIZE ifDirty :: Identity a -> (a -> Identity b) -> (a -> Identity b) -> Identity b #-}
+ifDirty :: (Monad m, MonadChange m) => m a -> (a -> m b) -> (a -> m b) -> m b
+ifDirty m f g = do
+  (a, dirty) <- listenDirty m
+  if dirty then f a else g a
+
+-- * Proper updater (Q-combinators)
+
+-- | Replace result of updating with original input if nothing has changed.
+sharing :: Monad m => UpdaterT m a -> UpdaterT m a
+sharing f a = do
+  (a', changed) <- listenDirty $ f a
+  return $ if changed then a' else a
+{-# INLINE sharing #-}
+
+-- | Eval an updater (using 'sharing').
+evalUpdater :: Updater a -> EndoFun a
+evalUpdater f a = fst $ runChange $ sharing f a
+{-# INLINE evalUpdater #-}
+
+-- END REAL STUFF
+
+-- * Updater transformer classes
+
+-- ** Unary (functors)
+
+-- | Like 'Functor', but preserving sharing.
+class Traversable f => Updater1 f where
+  updater1 :: Updater a -> Updater (f a)
+  updates1 :: Updater a -> Updater (f a) -- ^ @= sharing . updater1@
+  update1  :: Updater a -> EndoFun (f a)
+
+  updater1   = traverse
+  updates1 f = sharing $ updater1 f
+  update1  f = evalUpdater $ updater1 f
+
+instance Updater1 Maybe where
+
+instance Updater1 [] where
+  updater1 f []       = return []
+  updater1 f (x : xs) = (:) <$> f x <*> updates1 f xs
+
+-- ** Binary (bifunctors)
+
+-- | Like 'Bifunctor', but preserving sharing.
+class Updater2 f where
+  updater2 :: Updater a -> Updater b -> Updater (f a b)
+  updates2 :: Updater a -> Updater b -> Updater (f a b)
+  update2  :: Updater a -> Updater b -> EndoFun (f a b)
+
+  updates2 f1 f2 = sharing $ updater2 f1 f2
+  update2  f1 f2 = evalUpdater $ updater2 f1 f2
+
+instance Updater2 (,) where
+  updater2 f1 f2 (a,b) = (,) <$> sharing f1 a <*> sharing f2 b
+
+instance Updater2 Either where
+  updater2 f1 f2 (Left a)  = Left <$> f1 a
+  updater2 f1 f2 (Right b) = Right <$> f2 b
+
+
+{-- BEGIN MOCK
+
+-- * Mock updater
+
+type Change = Identity
+
+-- | Replace result of updating with original input if nothing has changed.
+{-# INLINE sharing #-}
+sharing :: Updater a -> Updater a
+sharing f a = f a
+
+-- | Run an updater.
+{-# INLINE evalUpdater #-}
+evalUpdater :: Updater a -> EndoFun a
+evalUpdater f a = runIdentity (f a)
+
+-- | Mark a computation as dirty.
+{-# INLINE dirty #-}
+dirty :: Updater a
+dirty = Identity
+
+{-# INLINE ifDirty #-}
+ifDirty :: Identity a -> (a -> Identity b) -> (a -> Identity b) -> Identity b
+ifDirty m f g = m >>= f
+
+-- END MOCK -}
diff --git a/src/full/Agda/Utils/VarSet.hs b/src/full/Agda/Utils/VarSet.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/VarSet.hs
@@ -0,0 +1,59 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+-- | Var field implementation of sets of (small) natural numbers.
+
+module Agda.Utils.VarSet
+  ( VarSet
+  , union, unions, member, empty, delete, singleton
+  , fromList, toList, toDescList
+  , isSubsetOf, IntSet.null
+  , intersection, difference
+  , Agda.Utils.VarSet.subtract
+  )
+  where
+
+import Data.IntSet as IntSet
+
+type VarSet = IntSet
+
+subtract :: Int -> VarSet -> VarSet
+subtract n = IntSet.map (Prelude.subtract n)
+
+{-
+import Data.Bits
+
+type VarSet = Integer
+type Var    = Integer
+
+union :: VarSet -> VarSet -> VarSet
+union = (.|.)
+
+member :: Var -> VarSet -> Bool
+member b s = testVar s (fromIntegral b)
+
+empty :: VarSet
+empty = 0
+
+delete :: Var -> VarSet -> VarSet
+delete b s = clearVar s (fromIntegral b)
+
+singleton :: Var -> VarSet
+singleton = bit
+
+subtract :: Int -> VarSet -> VarSet
+subtract n s = shiftR s n
+
+fromList :: [Var] -> VarSet
+fromList = foldr (union . singleton . fromIntegral) empty
+
+isSubsetOf :: VarSet -> VarSet -> Bool
+isSubsetOf s1 s2 = 0 == (s1 .&. complement s2)
+
+toList :: VarSet -> [Var]
+toList s = loop 0 s
+  where
+    loop i 0 = []
+    loop i n
+      | testVar n 0 = fromIntegral i : (loop $! i + 1) (shiftR n 1)
+      | otherwise   = (loop $! i + 1) (shiftR n 1)
+-}
diff --git a/src/full/Agda/Utils/Warshall.hs b/src/full/Agda/Utils/Warshall.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Warshall.hs
@@ -0,0 +1,430 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{- | Construct a graph from constraints
+@
+   x + n <= y   becomes   x ---(-n)---> y
+   x <= n + y   becomes   x ---(+n)---> y
+@
+the default edge (= no edge) is labelled with infinity.
+
+Building the graph involves keeping track of the node names.
+We do this in a finite map, assigning consecutive numbers to nodes.
+-}
+module Agda.Utils.Warshall where
+
+import Prelude hiding ((!!))
+
+import Control.Monad.State
+
+import Data.Maybe
+import Data.Array
+import qualified Data.List as List
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Agda.Utils.SemiRing
+import Agda.Utils.List ((!!), nubOn)
+import Agda.Syntax.Common.Pretty as P
+
+import Agda.Utils.Impossible
+
+type Matrix a = Array (Int,Int) a
+
+-- assuming a square matrix
+warshall :: SemiRing a => Matrix a -> Matrix a
+warshall a0 = loop r a0 where
+  b@((r,c),(r',c')) = bounds a0 -- assuming r == c and r' == c'
+  loop k a
+    | k <= r' =
+        loop (k + 1) $ array b $
+          [ ((i, j), (a ! (i, j)) `oplus` ((a ! (i, k)) `otimes` (a ! (k, j))))
+          | i <- [r .. r']
+          , j <- [c .. c']
+          ]
+    | otherwise = a
+
+type AdjList node edge = Map node [(node, edge)]
+
+-- | Warshall's algorithm on a graph represented as an adjacency list.
+warshallG :: (SemiRing edge, Ord node) => AdjList node edge -> AdjList node edge
+warshallG g = fromMatrix $ warshall m
+  where
+    nodes = zip (nubOn id $ Map.keys g ++ map fst (concat $ Map.elems g))
+                [0..]
+    len   = length nodes
+    b     = ((0,0), (len - 1,len - 1))
+
+    edge i j = do
+      es <- Map.lookup i g
+      foldr oplus Nothing [ Just v | (j', v) <- es, j == j' ]
+
+    m = array b [ ((n, m), edge i j) | (i, n) <- nodes, (j, m) <- nodes ]
+
+    fromMatrix matrix = Map.fromListWith __IMPOSSIBLE__ $ do
+      (i, n) <- nodes
+      let es = [ (fst (nodes !! m), e)
+               | m <- [0..len - 1]
+               , Just e <- [matrix ! (n, m)]
+               ]
+      return (i, es)
+
+-- | Edge weight in the graph, forming a semi ring.
+data Weight
+  = Finite Int
+  | Infinite
+  deriving (Eq, Show)
+
+inc :: Weight -> Int -> Weight
+inc Infinite   n = Infinite
+inc (Finite k) n = Finite (k + n)
+
+instance Pretty Weight where
+  pretty (Finite i) = pretty i
+  pretty Infinite   = "."
+
+instance Ord Weight where
+  a <= Infinite = True
+  Infinite <= b = False
+  Finite a <= Finite b = a <= b
+
+instance SemiRing Weight where
+  ozero = Infinite
+  oone  = Finite 0
+
+  oplus = min
+
+  otimes Infinite _ = Infinite
+  otimes _ Infinite = Infinite
+  otimes (Finite a) (Finite b) = Finite (a + b)
+
+-- constraints ---------------------------------------------------
+
+-- | Nodes of the graph are either
+-- - flexible variables (with identifiers drawn from @Int@),
+-- - rigid variables (also identified by @Int@s), or
+-- - constants (like 0, infinity, or anything between).
+
+data Node = Rigid Rigid
+          | Flex  FlexId
+            deriving (Eq, Ord)
+
+data Rigid = RConst Weight
+           | RVar RigidId
+             deriving (Eq, Ord)
+
+type NodeId  = Int
+type RigidId = Int
+type FlexId  = Int
+type Scope   = RigidId -> Bool
+-- ^ Which rigid variables a flex may be instatiated to.
+
+instance Pretty Node where
+  pretty (Flex  i)                   = "?" P.<> pretty i
+  pretty (Rigid (RVar i))            = "v" P.<> pretty i
+  pretty (Rigid (RConst Infinite))   = "#"
+  pretty (Rigid (RConst (Finite n))) = pretty n
+
+infinite :: Rigid -> Bool
+infinite (RConst Infinite) = True
+infinite _                 = False
+
+-- | @isBelow r w r'@
+--   checks, if @r@ and @r'@ are connected by @w@ (meaning @w@ not infinite),
+--   whether @r + w <= r'@.
+--   Precondition: not the same rigid variable.
+isBelow :: Rigid -> Weight -> Rigid -> Bool
+isBelow _ Infinite _ = True
+isBelow _ n (RConst Infinite) = True
+isBelow (RConst (Finite i)) (Finite n) (RConst (Finite j)) = i + n <= j
+isBelow _ _ _ = False -- rigid variables are not related
+
+-- | A constraint is an edge in the graph.
+data Constraint
+  = NewFlex FlexId Scope
+  | Arc Node Int Node
+    -- ^ For @Arc v1 k v2@  at least one of @v1@ or @v2@ is a @MetaV@ (Flex),
+    --                      the other a @MetaV@ or a @Var@ (Rigid).
+    --   If @k <= 0@ this means  @suc^(-k) v1 <= v2@
+    --   otherwise               @v1 <= suc^k v3@.
+
+instance Pretty Constraint where
+  pretty (NewFlex i s) = hcat [ "SizeMeta(?", pretty i, ")" ]
+  pretty (Arc v1 k v2)
+    | k == 0    = hcat [ pretty v1, "<=", pretty v2 ]
+    | k < 0     = hcat [ pretty v1, "+", pretty (-k), "<=", pretty v2 ]
+    | otherwise = hcat [ pretty v1, "<=", pretty v2, "+", pretty k ]
+
+type Constraints = [Constraint]
+
+emptyConstraints :: Constraints
+emptyConstraints = []
+
+-- graph (matrix) ------------------------------------------------
+
+data Graph = Graph
+  { flexScope :: Map FlexId Scope           -- ^ Scope for each flexible var.
+  , nodeMap   :: Map Node NodeId            -- ^ Node labels to node numbers.
+  , intMap    :: Map NodeId Node            -- ^ Node numbers to node labels.
+  , nextNode  :: NodeId                     -- ^ Number of nodes @n@.
+  , graph     :: NodeId -> NodeId -> Weight -- ^ The edges (restrict to @[0..n[@).
+  }
+
+-- | The empty graph: no nodes, edges are all undefined (infinity weight).
+initGraph :: Graph
+initGraph = Graph Map.empty Map.empty Map.empty 0 (\ x y -> Infinite)
+
+-- | The Graph Monad, for constructing a graph iteratively.
+type GM = State Graph
+
+-- | Add a size meta node.
+addFlex :: FlexId -> Scope -> GM ()
+addFlex x scope = do
+  modify $ \ st -> st { flexScope = Map.insert x scope (flexScope st) }
+  _ <- addNode (Flex x)
+  return ()
+
+-- | Lookup identifier of a node.
+--   If not present, it is added first.
+addNode :: Node -> GM Int
+addNode n = do
+  st <- get
+  case Map.lookup n (nodeMap st) of
+    Just i -> return i
+    Nothing -> do
+      let i = nextNode st
+      put $ st { nodeMap  = Map.insert n i (nodeMap st)
+               , intMap   = Map.insert i n (intMap st)
+               , nextNode = i + 1
+               }
+      return i
+
+-- | @addEdge n1 k n2@
+--   improves the weight of egde @n1->n2@ to be at most @k@.
+--   Also adds nodes if not yet present.
+addEdge :: Node -> Int -> Node -> GM ()
+addEdge n1 k n2 = do
+  i1 <- addNode n1
+  i2 <- addNode n2
+  st <- get
+  let graph' x y = if (x,y) == (i1,i2) then Finite k `oplus` graph st x y
+                   else graph st x y
+  put $ st { graph = graph' }
+
+addConstraint :: Constraint -> GM ()
+addConstraint (NewFlex x scope) = addFlex x scope
+addConstraint (Arc n1 k n2)     = addEdge n1 k n2
+
+buildGraph :: Constraints -> Graph
+buildGraph cs = execState (mapM_ addConstraint cs) initGraph
+
+mkMatrix :: Int -> (Int -> Int -> Weight) -> Matrix Weight
+mkMatrix n g = array ((0,0),(n-1,n-1))
+                 [ ((i,j), g i j) | i <- [0..n-1], j <- [0..n-1]]
+
+-- displaying matrices with row and column labels --------------------
+
+-- | A matrix with row descriptions in @b@ and column descriptions in @c@.
+data LegendMatrix a b c = LegendMatrix
+  { matrix   :: Matrix a
+  , rowdescr :: Int -> b
+  , coldescr :: Int -> c
+  }
+
+instance (Pretty a, Pretty b, Pretty c) => Pretty (LegendMatrix a b c) where
+  pretty (LegendMatrix m rd cd) =
+    -- first show column description
+    let ((r, c), (r', c')) = bounds m
+    in foldr (\ j s -> "\t" P.<> pretty (cd j) P.<> s) "" [c .. c'] P.<>
+    -- then output rows
+       foldr (\ i s -> "\n" P.<> pretty (rd i) P.<>
+                foldr (\ j t -> "\t" P.<> pretty (m ! (i, j)) P.<> t)
+                      s
+                      [c .. c'])
+             "" [r .. r']
+
+-- solving the constraints -------------------------------------------
+
+-- | A solution assigns to each flexible variable a size expression
+--   which is either a constant or a @v + n@ for a rigid variable @v@.
+type Solution = Map Int SizeExpr
+
+emptySolution :: Solution
+emptySolution = Map.empty
+
+extendSolution :: Solution -> Int -> SizeExpr -> Solution
+extendSolution subst k v = Map.insert k v subst
+
+data SizeExpr = SizeVar RigidId Int   -- ^ e.g. x + 5
+              | SizeConst Weight      -- ^ a number or infinity
+
+instance Pretty SizeExpr where
+  pretty (SizeVar n 0) = pretty (Rigid (RVar n))
+  pretty (SizeVar n k) = pretty (Rigid (RVar n)) P.<> "+" P.<> pretty k
+  pretty (SizeConst w) = pretty w
+
+-- | @sizeRigid r n@ returns the size expression corresponding to @r + n@
+sizeRigid :: Rigid -> Int -> SizeExpr
+sizeRigid (RConst k) n = SizeConst (inc k n)
+sizeRigid (RVar i)   n = SizeVar i n
+
+{-
+apply :: SizeExpr -> Solution -> SizeExpr
+apply e@(SizeExpr (Rigid _) _) phi = e
+apply e@(SizeExpr (Flex  x) i) phi = case Map.lookup x phi of
+  Nothing -> e
+  Just (SizeExpr v j) -> SizeExpr v (i + j)
+
+after :: Solution -> Solution -> Solution
+after psi phi = Map.map (\ e -> e `apply` phi) psi
+-}
+
+{- compute solution
+
+a solution CANNOT exist if
+
+  v < v  for a rigid variable v
+
+  -- Andreas, 2012-09-19 OUTDATED are:
+
+  -- v <= v' for rigid variables v,v'
+
+  -- x < v   for a flexible variable x and a rigid variable v
+
+
+thus, for each flexible x, only one of the following cases is possible
+
+  r+n <= x+m <= infty  for a unique rigid r  (meaning r --(m-n)--> x)
+  x <= r+n             for a unique rigid r  (meaning x --(n)--> r)
+
+we are looking for the least values for flexible variables that solve
+the constraints.  Algorithm
+
+while flexible variables and rigid rows left
+  find a rigid variable row i
+    for all flexible columns j
+      if i --n--> j with n<=0 (meaning i+n <= j) then j = i + n
+
+while flexible variables j left
+  search the row j for entry i
+    if j --n--> i with n >= 0 (meaning j <= i + n) then j = i + n
+
+-}
+
+solve :: Constraints -> Maybe Solution
+solve cs = -- trace (prettyShow cs) $
+   -- trace (prettyShow lm0) $
+    -- trace (prettyShow lm) $ -- trace (prettyShow d) $
+     let solution = if solvable then loop1 flexs rigids emptySolution
+                    else Nothing
+     in -- trace (prettyShow solution) $
+         solution
+   where -- compute the graph and its transitive closure m
+         gr  = buildGraph cs
+         n   = nextNode gr            -- number of nodes
+         m0  = mkMatrix n (graph gr)
+         m   = warshall m0
+
+         -- tracing only: build output version of transitive graph
+         legend i = fromJust $ Map.lookup i (intMap gr) -- trace only
+         lm0 = LegendMatrix m0 legend legend            -- trace only
+         lm  = LegendMatrix m legend legend             -- trace only
+
+         -- compute the sets of flexible and rigid node numbers
+         ns  = Map.keys (nodeMap gr)
+         -- a set of flexible variables
+         flexs  = List.foldl' (\ l -> \case (Flex i ) -> i : l
+                                            (Rigid _) -> l)     [] ns
+         -- a set of rigid variables
+         rigids = List.foldl' (\ l -> \case (Flex _ ) -> l
+                                            (Rigid i) -> i : l) [] ns
+
+         -- rigid matrix indices
+         rInds = List.foldl' (\ l r -> let Just i = Map.lookup (Rigid r) (nodeMap gr)
+                                       in i : l) [] rigids
+
+         -- check whether there is a solution
+         -- d   = [ m!(i,i) | i <- [0 .. (n-1)] ]  -- diagonal
+-- a rigid variable might not be less than it self, so no -.. on the
+-- rigid part of the diagonal
+         solvable = all (>= Finite 0) [ m ! (i, i) | i <- rInds ]
+
+{-  Andreas, 2012-09-19
+    We now can have constraints between rigid variables, like i < j.
+    Thus we skip the following two test.  However, a solution must be
+    checked for consistency with the constraints on rigid vars.
+
+-- a rigid variable might not be bounded below by infinity or
+-- bounded above by a constant
+-- it might not be related to another rigid variable
+           all (\ (r,  r') -> r == r' ||
+                let Just row = (Map.lookup (Rigid r)  (nodeMap gr))
+                    Just col = (Map.lookup (Rigid r') (nodeMap gr))
+                    edge = m!(row,col)
+                in  isBelow r edge r' )
+             [ (r,r') | r <- rigids, r' <- rigids ]
+           &&
+-- a flexible variable might not be strictly below a rigid variable
+           all (\ (x, v) ->
+                let Just row = (Map.lookup (Flex x)  (nodeMap gr))
+                    Just col = (Map.lookup (Rigid (RVar v)) (nodeMap gr))
+                    edge = m!(row,col)
+                in  edge >= Finite 0)
+             [ (x,v) | x <- flexs, (RVar v) <- rigids ]
+-}
+
+         inScope :: FlexId -> Rigid -> Bool
+         inScope x (RConst _) = True
+         inScope x (RVar v)   = scope v
+             where Just scope = Map.lookup x (flexScope gr)
+
+{- loop1
+
+while flexible variables and rigid rows left
+  find a rigid variable row i
+    for all flexible columns j
+      if i --n--> j with n<=0 (meaning i + n <= j) then j = i + n
+
+-}
+         loop1 :: [FlexId] -> [Rigid] -> Solution -> Maybe Solution
+         loop1 [] rgds subst = Just subst
+         loop1 flxs [] subst = loop2 flxs subst
+         loop1 flxs (r:rgds) subst =
+            let row = fromJust $ Map.lookup (Rigid r) (nodeMap gr)
+                (flxs', subst') =
+                  List.foldl' (\ (flx, sub) f ->
+                          let col = fromJust $ Map.lookup (Flex f) (nodeMap gr)
+                          in  case (inScope f r, m ! (row, col)) of
+--                                Finite z | z <= 0 ->
+                                (True, Finite z) ->
+                                   let trunc z
+                                         | z >= 0    = 0
+                                         | otherwise = -z
+                                   in (flx, extendSolution sub f (sizeRigid r (trunc z)))
+                                _ -> (f : flx, sub)
+                     ) ([], subst) flxs
+            in loop1 flxs' rgds subst'
+
+{- loop2
+
+while flexible variables j left
+  search the row j for entry i
+    if j --n--> i with n >= 0 (meaning j <= i + n) then j = i
+
+-}
+         loop2 :: [FlexId] -> Solution -> Maybe Solution
+         loop2 [] subst = Just subst
+         loop2 (f:flxs) subst = loop3 0 subst
+           where row = fromJust $ Map.lookup (Flex f) (nodeMap gr)
+                 loop3 col subst | col >= n =
+                   -- default to infinity
+                    loop2 flxs (extendSolution subst f (SizeConst Infinite))
+                 loop3 col subst =
+                   case Map.lookup col (intMap gr) of
+                     Just (Rigid r) | not (infinite r) ->
+                       case (inScope f r, m ! (row,col)) of
+                        (True, Finite z) | z >= 0 ->
+                            loop2 flxs (extendSolution subst f (sizeRigid r z))
+                        (_, Infinite) -> loop3 (col + 1) subst
+                        _ -> -- trace ("unusable rigid: " ++ prettyShow r ++ " for flex " ++ prettyShow f)
+                              Nothing  -- NOT: loop3 (col+1) subst
+                     _ -> loop3 (col + 1) subst
diff --git a/src/full/Agda/Utils/WithDefault.hs b/src/full/Agda/Utils/WithDefault.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/WithDefault.hs
@@ -0,0 +1,83 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE DataKinds      #-}
+
+-- | Potentially uninitialised Booleans.
+--
+-- The motivation for this small library is to distinguish
+-- between a boolean option with a default value and an option which has been
+-- set to what happens to be the default value.  In one case the default can be
+-- overriden (e.g. @--cubical@ implies @--without-K@) while in the other case the
+-- user has made a mistake which they need to fix.
+
+module Agda.Utils.WithDefault where
+
+import Control.DeepSeq
+
+import Agda.Utils.Boolean
+import Agda.Utils.Lens
+import Agda.Utils.Null
+import Agda.Utils.TypeLits
+
+-- | We don't want to have to remember for each flag whether its default value
+-- is @True@ or @False@. So we bake it into the representation: the flag's type
+-- will mention its default value as a phantom parameter.
+--
+data WithDefault' a (b :: Bool) = Default | Value !a
+  deriving (Eq, Show)
+  -- Note: the argument @b@ must be last, because this is matched against @proxy b@
+  -- in 'Agda.Utils.TypeLits.boolVal'.
+  -- Thus, we cannot make it a 'Functor' in @a@.
+  -- Instead, we define 'mapValue'.
+
+type WithDefault b = WithDefault' Bool b
+
+instance NFData (WithDefault' a b) where
+  rnf Default   = ()
+  rnf (Value _) = ()
+
+-- | The null value of 'WithDefault b' is 'Default'.
+--
+instance Null (WithDefault' a b) where
+  empty = Default
+  null = \case
+    Default -> True
+    Value _ -> False
+
+-- | The main mode of operation of these flags, apart from setting them explicitly,
+-- is to toggle them one way or the other if they hadn't been set already.
+--
+setDefault :: Boolean a => a -> WithDefault' a b -> WithDefault' a b
+setDefault b = \case
+  Default -> Value b
+  t -> t
+
+-- | Only modify non-'Default' values.
+--
+mapValue :: Boolean a => (a -> a) -> WithDefault' a b -> WithDefault' a b
+mapValue f = \case
+  Default -> Default
+  Value b -> Value (f b)
+
+-- | Provided that the default value is a known boolean (in practice we only use
+-- @True@ or @False@), we can collapse a potentially uninitialised value to a boolean.
+--
+collapseDefault :: (Boolean a, KnownBool b) => WithDefault' a b -> a
+collapseDefault = \case
+  w@Default -> fromBool (boolVal w)
+  Value b -> b
+
+-- | Focus, overwriting 'Default'.
+--
+lensCollapseDefault :: (Boolean a, KnownBool b) => Lens' (WithDefault' a b) a
+lensCollapseDefault f w = Value <$> f (collapseDefault w)
+
+-- | Update, but keep 'Default' when new value is default value.
+--
+lensKeepDefault :: (Boolean a, Eq a, KnownBool b) => Lens' (WithDefault' a b) a
+lensKeepDefault f = \case
+  Value b   -> Value <$> f b
+  w@Default -> f b <&> \ b' -> if b == b' then Default else Value b'
+    where
+    b  = fromBool (boolVal w)
diff --git a/src/full/Agda/Utils/Zipper.hs b/src/full/Agda/Utils/Zipper.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Utils/Zipper.hs
@@ -0,0 +1,52 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Utils.Zipper where
+
+
+class Zipper z where
+  type Carrier z
+  type Element z
+  firstHole :: Carrier z -> Maybe (Element z, z)
+  plugHole  :: Element z -> z -> Carrier z
+  nextHole  :: Element z -> z -> Either (Carrier z) (Element z, z)
+
+data ListZipper a = ListZip [a] [a]
+  deriving (Eq, Ord, Show, Functor, Foldable, Traversable)
+
+instance Zipper (ListZipper a) where
+  type Carrier (ListZipper a) = [a]
+  type Element (ListZipper a) = a
+  firstHole (x : xs)               = Just (x, ListZip [] xs)
+  firstHole []                     = Nothing
+  plugHole x (ListZip ys zs)       = reverse ys ++ x : zs
+  nextHole x (ListZip ys [])       = Left (reverse (x : ys))
+  nextHole x (ListZip ys (z : zs)) = Right (z, ListZip (x : ys) zs)
+
+data ComposeZipper f g = ComposeZip f g
+
+instance (Zipper f, Zipper g, Element f ~ Carrier g) => Zipper (ComposeZipper f g) where
+  type Carrier (ComposeZipper f g) = Carrier f
+  type Element (ComposeZipper f g) = Element g
+  firstHole c1 = do
+    (c2, z1) <- firstHole c1
+    go c2 z1
+    where
+      go c2 z1 =
+        case firstHole c2 of
+          Nothing -> case nextHole c2 z1 of
+            Left{} -> Nothing
+            Right (c2', z1') -> go c2' z1'
+          Just (x, z2) -> Just (x, ComposeZip z1 z2)
+  plugHole x (ComposeZip z1 z2) = plugHole (plugHole x z2) z1
+  nextHole x (ComposeZip z1 z2) =
+    case nextHole x z2 of
+      Right (y, z2') -> Right (y, ComposeZip z1 z2')
+      Left c2        -> go c2 z1
+        where
+          go c2 z1 =
+            case nextHole c2 z1 of
+              Right (c2', z1') ->
+                case firstHole c2' of
+                  Nothing       -> go c2' z1'
+                  Just (x, z2') -> Right (x, ComposeZip z1' z2')
+              Left c1 -> Left c1
diff --git a/src/full/Agda/Version.hs b/src/full/Agda/Version.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/Version.hs
@@ -0,0 +1,33 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+module Agda.Version
+  ( version
+  , package
+  , docsUrl
+  ) where
+
+import GHC.Generics ( Generic, Rep, packageName )
+import Data.List ( intercalate )
+import Data.Version ( Version(versionBranch) )
+
+import qualified Paths_Agda as PA
+
+-- | The version of Agda.
+
+version :: String
+version = intercalate "." $ map show $
+            versionBranch PA.version
+
+-- | This package name.
+-- This is mainly intended for use in the test suites to filter ephemeral
+-- hash-fingerprinted package names like @Agda-2.6.2-5ceeWeguf1QFMaHLput4zw@.
+
+package :: String
+package = packageName (undefined :: Rep AnArbitrarySymbolInThisPackage p)
+
+-- | Returns a URL corresponding to the given section in the documentation for
+-- the current version.
+docsUrl :: String -> String
+docsUrl section = "https://agda.readthedocs.io/en/v" ++ version ++ "/" ++ section
+
+data AnArbitrarySymbolInThisPackage deriving Generic
diff --git a/src/full/Agda/VersionCommit.hs b/src/full/Agda/VersionCommit.hs
new file mode 100644
--- /dev/null
+++ b/src/full/Agda/VersionCommit.hs
@@ -0,0 +1,32 @@
+{-# OPTIONS_GHC -Wunused-imports #-}
+
+{-# LANGUAGE CPP             #-}
+{-# LANGUAGE TemplateHaskell #-}
+
+#if __GLASGOW_HASKELL__ >= 900
+{-# OPTIONS_GHC -Wno-overlapping-patterns #-}
+#endif
+
+module Agda.VersionCommit where
+
+import Development.GitRev
+
+import Agda.Version
+
+versionWithCommitInfo :: String
+versionWithCommitInfo = version ++ maybe "" ("-" ++) commitInfo
+
+-- | Information about current git commit, generated at compile time
+commitInfo :: Maybe String
+commitInfo
+  | hash == "UNKNOWN" = Nothing
+  | otherwise         = Just $ abbrev hash ++ dirty
+  where
+    hash = $(gitHash)
+
+    -- Check if any tracked files have uncommitted changes
+    dirty | $(gitDirtyTracked) = "-dirty"
+          | otherwise          = ""
+
+    -- Abbreviate a commit hash while keeping it unambiguous
+    abbrev = take 7
diff --git a/src/main/Main.hs b/src/main/Main.hs
new file mode 100644
--- /dev/null
+++ b/src/main/Main.hs
@@ -0,0 +1,12 @@
+-- | Wrapper for "Agda.Main".
+--
+-- Agda is installed as a library. This module is used to build the
+-- executable.
+
+module Main (main) where
+
+import Agda.Main ( runAgda )
+import Prelude ( IO )
+
+main :: IO ()
+main = runAgda []
diff --git a/stack-8.10.7.yaml b/stack-8.10.7.yaml
new file mode 100644
--- /dev/null
+++ b/stack-8.10.7.yaml
@@ -0,0 +1,7 @@
+resolver: lts-18.28
+compiler: ghc-8.10.7
+compiler-check: match-exact
+
+extra-deps:
+- text-icu-0.8.0.2
+- vector-hashtables-0.1.1.1
diff --git a/stack-8.6.5.yaml b/stack-8.6.5.yaml
new file mode 100644
--- /dev/null
+++ b/stack-8.6.5.yaml
@@ -0,0 +1,15 @@
+resolver: lts-14.27
+compiler: ghc-8.6.5
+compiler-check: match-exact
+
+extra-deps:
+- STMonadTrans-0.4.3
+- data-hash-0.2.0.1
+- equivalence-0.3.4
+- primitive-0.7.4.0
+- regex-base-0.94.0.0
+- regex-tdfa-1.3.1.0
+- strict-0.4.0.1
+- these-1.1.1.1
+- text-icu-0.8.0.2
+- vector-hashtables-0.1.1.1
diff --git a/stack-8.8.4.yaml b/stack-8.8.4.yaml
new file mode 100644
--- /dev/null
+++ b/stack-8.8.4.yaml
@@ -0,0 +1,9 @@
+resolver: lts-16.31
+compiler: ghc-8.8.4
+compiler-check: match-exact
+
+extra-deps:
+- primitive-0.7.4.0
+- strict-0.4.0.1
+- text-icu-0.8.0.2
+- vector-hashtables-0.1.1.1
diff --git a/stack-9.0.2.yaml b/stack-9.0.2.yaml
new file mode 100644
--- /dev/null
+++ b/stack-9.0.2.yaml
@@ -0,0 +1,7 @@
+resolver: lts-19.33
+compiler: ghc-9.0.2
+compiler-check: match-exact
+
+extra-deps:
+- text-icu-0.8.0.2
+- vector-hashtables-0.1.1.1
diff --git a/stack-9.2.8.yaml b/stack-9.2.8.yaml
new file mode 100644
--- /dev/null
+++ b/stack-9.2.8.yaml
@@ -0,0 +1,3 @@
+resolver: lts-20.26
+compiler: ghc-9.2.8
+compiler-check: match-exact
diff --git a/stack-9.4.8.yaml b/stack-9.4.8.yaml
new file mode 100644
--- /dev/null
+++ b/stack-9.4.8.yaml
@@ -0,0 +1,9 @@
+resolver: lts-21.25
+compiler: ghc-9.4.8
+compiler-check: match-exact
+
+flags:
+  mintty:
+    win32-2-13-1: false
+  ansi-terminal:
+    win32-2-13-1: false
diff --git a/stack-9.6.4.yaml b/stack-9.6.4.yaml
new file mode 100644
--- /dev/null
+++ b/stack-9.6.4.yaml
@@ -0,0 +1,3 @@
+resolver: lts-22.9
+compiler: ghc-9.6.4
+compiler-check: match-exact
diff --git a/stack-9.8.1.yaml b/stack-9.8.1.yaml
new file mode 100644
--- /dev/null
+++ b/stack-9.8.1.yaml
@@ -0,0 +1,3 @@
+resolver: nightly-2024-02-09
+compiler: ghc-9.8.1
+compiler-check: match-exact
